Subgroups — C₂₃×#60319 #19207945

Order 5888.

1848 conjugacy classes of subgroups.

The subgroup lattice has 1170 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3460	C₂	1	1	yes	maximal, characteristic
2	C₂₃×#2995	C₂	1	2	yes	maximal, complemented
3	C₂₃×#2994	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₃×#2993	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₃×#2991	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₃×#2989	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₃×#2981	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₃×#2981	C₂	1	2	yes	maximal, complemented
9	C₂₃×#2979	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₃×#2978	C₂	1	2	yes	maximal, complemented
11	C₂₃×#2976	C₂	1	2	yes	maximal, complemented
12	C₂₃×#2974	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₃×#2970	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₃×#2969	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₃×#2968	C₂	1	2	yes	maximal, complemented
16	C₂₃×#2966	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂₃×#2965	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂₃×#2935	C₂	1	1	yes	maximal, characteristic, complemented
19	D₄×M₁₆×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂₃×#2933	C₂	1	2	yes	maximal, complemented
21	C₂₃×#2932	C₂	1	2	yes	maximal, complemented
22	C₂₃×#2931	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂₃×#2930	C₂	1	2	yes	maximal, complemented
24	C₂×C₂₃×#131	C₂²	1	2	yes	complemented
25	C₂×C₂₃×#131	C₂²	1	2	yes	complemented
26	C₂²×M₁₆×C₂₃	C₂²	1	2	yes	—
27	C₂₃×#544	C₄	1	1	yes	characteristic
28	C₂₃×#542	C₄	1	1	yes	characteristic
29	C₂₃×#542	C₄	1	1	yes	characteristic
30	C₂₃×#542	C₄	1	2	yes	—
31	C₂₃×#540	C₄	1	1	yes	characteristic
32	C₂₃×#540	C₄	1	1	yes	characteristic
33	C₂₃×#540	C₄	1	2	yes	—
34	C₂₃×#538	C₄	1	2	yes	—
35	C₂₃×#538	C₄	1	2	yes	—
36	C₂₃×#537	C₄	1	1	yes	characteristic
37	C₂₃×#535	C₄	1	1	yes	characteristic
38	C₂₃×#535	C₄	1	1	yes	characteristic
39	C₂₃×#532	C₂²	1	1	yes	characteristic
40	C₂₃×#532	C₂²	1	2	yes	—
41	C₂₃×#532	C₂²	1	1	yes	characteristic
42	C₂₃×#529	C₂²	1	1	yes	characteristic
43	C₂₃×#529	C₂²	1	2	yes	—
44	C₂₃×#529	C₂²	1	1	yes	characteristic
45	C₂₃×#525	C₂²	1	2	yes	—
46	C₂₃×#525	C₂²	1	2	yes	—
47	C₄×#41×C₂₃	C₂²	1	1	yes	characteristic
48	C₄×#41×C₂₃	C₂²	1	1	yes	characteristic
49	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
50	C₂₃×#446	C₂²	1	1	yes	characteristic, complemented
51	C₂₃×#446	C₂²	1	1	yes	characteristic, complemented
52	C₂₃×#446	C₂²	1	1	yes	characteristic, complemented
53	C₂₃×#446	C₂²	1	2	yes	complemented
54	C₂₃×#446	C₂²	1	1	yes	characteristic, complemented
55	C₈×Q₈×C₂₃	C₂²	1	1	yes	characteristic, complemented
56	C₈×Q₈×C₂₃	C₂²	1	1	yes	characteristic, complemented
57	C₂₃×#436	C₂²	1	2	yes	—
58	C₂₃×#436	C₂²	1	2	yes	—
59	C₂₃×#436	C₂²	1	1	yes	characteristic
60	C₂₃×#436	C₂²	1	1	yes	characteristic
61	C₂₃×#436	C₂²	1	2	yes	—
62	C₂₃×#436	C₂²	1	1	yes	characteristic
63	C₂₃×#436	C₂²	1	1	yes	characteristic
64	C₂₃×#436	C₂²	1	1	yes	characteristic
65	C₂₃×#436	C₂²	1	1	yes	characteristic
66	C₂₃×#436	C₂²	1	2	yes	complemented
67	C₂₃×#436	C₂²	1	2	yes	complemented
68	C₂₃×#436	C₂²	1	2	yes	complemented
69	C₂₃×#436	C₂²	1	1	yes	characteristic, complemented
70	C₂₃×#436	C₂²	1	1	yes	characteristic, complemented
71	C₂₃×#436	C₂²	1	2	yes	complemented
72	C₂₃×#435	C₂²	1	1	yes	characteristic
73	C₂₃×#435	C₂²	1	2	yes	—
74	C₂₃×#435	C₂²	1	2	yes	—
75	C₂₃×#435	C₂²	1	2	yes	—
76	C₂₃×#435	C₂²	1	2	yes	—
77	C₂₃×#435	C₂²	1	2	yes	—
78	C₂₃×#435	C₂²	1	1	yes	characteristic
79	C₂₃×#435	C₂²	1	2	yes	—
80	C₂₃×#435	C₂²	1	2	yes	—
81	C₂₃×#435	C₂²	1	2	yes	complemented
82	C₂₃×#435	C₂²	1	2	yes	complemented
83	C₂₃×#435	C₂²	1	1	yes	characteristic, complemented
84	C₂₃×#435	C₂²	1	2	yes	complemented
85	C₂₃×#435	C₂²	1	2	yes	complemented
86	C₂₃×#435	C₂²	1	2	yes	complemented
87	C₂₃×#435	C₂²	1	2	yes	complemented
88	C₂₃×#435	C₂²	1	2	yes	complemented
89	C₂₃×#435	C₂²	1	2	yes	complemented
90	C₂₃×#435	C₂²	1	1	yes	characteristic, complemented
91	C₂₃×#435	C₂²	1	2	yes	complemented
92	C₈×D₄×C₂₃	C₂²	1	1	yes	characteristic
93	C₈×D₄×C₂₃	C₂²	1	1	yes	characteristic
94	C₈×D₄×C₂₃	C₂²	1	1	yes	characteristic
95	C₈×D₄×C₂₃	C₂²	1	1	yes	characteristic
96	C₈×D₄×C₂₃	C₂²	1	2	yes	complemented
97	C₈×D₄×C₂₃	C₂²	1	1	yes	characteristic, complemented
98	C₈×D₄×C₂₃	C₂²	1	2	yes	complemented
99	C₈×D₄×C₂₃	C₂²	1	2	yes	complemented
100	C₈×D₄×C₂₃	C₂²	1	2	yes	complemented
101	C₈×D₄×C₂₃	C₂²	1	1	yes	characteristic, complemented
102	C₂₃×#433	C₂²	1	2	yes	complemented
103	C₂₃×#433	C₂²	1	2	yes	complemented
104	C₂₃×#433	C₂²	1	2	yes	complemented
105	C₂₃×#433	C₂²	1	2	yes	complemented
106	C₂₃×#432	C₂²	1	1	yes	characteristic
107	C₂₃×#432	C₂²	1	1	yes	characteristic, complemented
108	C₂₃×#432	C₂²	1	2	yes	complemented
109	C₂₃×#431	C₂²	1	1	yes	characteristic
110	C₂₃×#431	C₂²	1	1	yes	characteristic, complemented
111	C₂₃×#431	C₂²	1	1	yes	characteristic, complemented
112	C₂₃×#431	C₂²	1	2	yes	complemented
113	C₂₃×#431	C₂²	1	1	yes	characteristic, complemented
114	C₂₃×#424	C₂²	1	2	yes	complemented
115	C₂₃×#424	C₂²	1	2	yes	complemented
116	C₂₃×#423	C₂²	1	1	yes	characteristic
117	C₂₃×#423	C₂²	1	1	yes	characteristic, complemented
118	C₂₃×#423	C₂²	1	2	yes	complemented
119	C₂×C₂₃×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
120	C₂₃×#408	C₂²	1	2	yes	complemented
121	C₂₃×#408	C₂²	1	2	yes	complemented
122	C₂₃×#408	C₂²	1	2	yes	complemented
123	C₂₃×#408	C₂²	1	2	yes	complemented
124	C₂₃×#408	C₂²	1	2	yes	complemented
125	C₂₃×#408	C₂²	1	2	yes	complemented
126	C₂₃×#407	C₂²	1	2	yes	—
127	C₂₃×#407	C₂²	1	2	yes	—
128	C₂×C₂₃×C₂²⋊C₈	C₂²	1	2	yes	—
129	C₂₃×#405	C₂²	1	2	yes	complemented
130	C₂₃×#405	C₂²	1	2	yes	complemented
131	C₄×M₁₆×C₂₃	C₂²	1	1	yes	characteristic
132	C₄×M₁₆×C₂₃	C₂²	1	1	yes	characteristic, complemented
133	C₂×C₂₃×#97	C₂²	1	2	yes	complemented
134	C₂×C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic, complemented
135	C₂×#41×C₂₃	C₂×C₄	1	1	yes	characteristic
136	C₂×#41×C₂₃	C₂×C₄	1	1	yes	characteristic
137	C₂×#41×C₂₃	C₂³	1	2	yes	—
138	C₂×#41×C₂₃	C₂³	1	2	yes	—
139	C₂²×D₄×C₂₃	C₂×C₄	1	1	yes	characteristic
140	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
141	C₂₃×#131	—	4	4	no	—
142	C₂₃×#131	—	4	4	no	—
143	C₂×M₁₆×C₂₃	—	4	4	no	—
144	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
145	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
146	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
147	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
148	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
149	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
150	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
151	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
152	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
153	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
154	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
155	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
156	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
157	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
158	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
159	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
160	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
161	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
162	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
163	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
164	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
165	C₂₃×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
166	C₂₃×C₄⋊Q₈	C₂×C₄	1	2	yes	—
167	C₂₃×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
168	C₂₃×#127	C₂×C₄	1	1	yes	characteristic
169	C₂₃×#127	C₂×C₄	1	1	yes	characteristic
170	C₂₃×#127	C₂×C₄	1	2	yes	—
171	C₂₃×#126	C₂×C₄	1	2	yes	—
172	C₂₃×#126	C₂×C₄	1	2	yes	—
173	C₂₃×#126	C₂×C₄	1	2	yes	—
174	C₂₃×#126	C₂×C₄	1	2	yes	—
175	C₂₃×#125	C₂×C₄	1	1	yes	characteristic
176	C₂₃×#125	C₂×C₄	1	2	yes	—
177	C₂₃×#125	C₂×C₄	1	1	yes	characteristic
178	C₂₃×#124	C₂×C₄	1	1	yes	characteristic
179	C₂₃×#124	C₂×C₄	1	1	yes	characteristic
180	C₂₃×#124	C₂×C₄	1	2	yes	—
181	C₂₃×#124	C₂×C₄	1	2	yes	—
182	C₂₃×#124	C₂×C₄	1	2	yes	—
183	C₂₃×#124	C₂×C₄	1	2	yes	—
184	C₂₃×#124	C₂×C₄	1	2	yes	—
185	C₂₃×#123	C₂×C₄	1	2	yes	—
186	C₂₃×#123	C₂×C₄	1	2	yes	—
187	C₂₃×#123	C₂×C₄	1	2	yes	—
188	C₂₃×#123	C₂×C₄	1	2	yes	—
189	C₂₃×#123	C₂×C₄	1	2	yes	—
190	C₂₃×#123	C₂×C₄	1	2	yes	—
191	C₂₃×#123	C₂×C₄	1	2	yes	—
192	C₂₃×#123	C₂×C₄	1	2	yes	—
193	C₂₃×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
194	C₂₃×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
195	C₂₃×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
196	C₂₃×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
197	C₂₃×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
198	C₂₃×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
199	C₂₃×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
200	C₂₃×#121	C₂×C₄	1	2	yes	—
201	C₂₃×#121	C₂×C₄	1	2	yes	—
202	C₂₃×#121	C₂×C₄	1	2	yes	—
203	C₂₃×#121	C₂×C₄	1	2	yes	—
204	C₂₃×#121	C₂×C₄	1	1	yes	characteristic
205	C₂₃×#121	C₂×C₄	1	1	yes	characteristic
206	C₂₃×#121	C₂×C₄	1	2	yes	—
207	C₂₃×#121	C₂×C₄	1	1	yes	characteristic
208	C₂₃×#121	C₂×C₄	1	1	yes	characteristic
209	C₂₃×#121	C₂×C₄	1	2	yes	—
210	C₂₃×#121	C₂×C₄	1	1	yes	characteristic
211	C₂₃×#121	C₂×C₄	1	1	yes	characteristic
212	C₂₃×#121	C₂×C₄	1	2	yes	—
213	C₂₃×#121	C₂×C₄	1	2	yes	—
214	C₂₃×#121	C₂×C₄	1	2	yes	—
215	C₂₃×#121	C₂×C₄	1	2	yes	—
216	C₂₃×#121	C₂×C₄	1	2	yes	—
217	C₂₃×#120	C₂×C₄	1	2	yes	—
218	C₂₃×#120	C₂×C₄	1	2	yes	—
219	C₂₃×#120	C₂×C₄	1	2	yes	—
220	C₂₃×#120	C₂×C₄	1	2	yes	—
221	C₄×Q₈×C₂₃	C₂×C₄	1	1	yes	characteristic
222	C₄×Q₈×C₂₃	C₂×C₄	1	1	yes	characteristic
223	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
224	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
225	C₄×D₄×C₂₃	C₂×C₄	1	1	yes	characteristic
226	C₄×D₄×C₂₃	C₂×C₄	1	1	yes	characteristic
227	C₄×D₄×C₂₃	C₂×C₄	1	2	yes	—
228	C₄×D₄×C₂₃	C₂×C₄	1	1	yes	characteristic
229	C₄×D₄×C₂₃	C₂×C₄	1	1	yes	characteristic
230	C₄×D₄×C₂₃	C₂×C₄	1	2	yes	—
231	C₄×D₄×C₂₃	C₂×C₄	1	1	yes	characteristic
232	C₄×D₄×C₂₃	C₂×C₄	1	1	yes	characteristic
233	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
234	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
235	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
236	C₄×D₄×C₂₃	C₂³	1	2	yes	—
237	C₄×D₄×C₂₃	C₂³	1	2	yes	—
238	C₄×D₄×C₂₃	C₂³	1	2	yes	—
239	C₄×D₄×C₂₃	C₂³	1	2	yes	—
240	C₄×D₄×C₂₃	C₂³	1	2	yes	—
241	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
242	C₄×D₄×C₂₃	C₂³	1	2	yes	—
243	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
244	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
245	C₂₃×#117	C₂×C₄	1	1	yes	characteristic
246	C₂₃×#117	C₂×C₄	1	1	yes	characteristic
247	C₂₃×#117	C₂×C₄	1	1	yes	characteristic
248	C₂₃×#117	C₂×C₄	1	1	yes	characteristic
249	C₂₃×#117	C₂×C₄	1	2	yes	—
250	C₂₃×#117	C₂³	1	2	yes	—
251	C₂₃×#117	C₂³	1	2	yes	—
252	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
253	C₂×C₂²⋊C₄×C₂₃	C₂×C₄	1	2	yes	—
254	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
255	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
256	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
257	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
258	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
259	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
260	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
261	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
262	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
263	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
264	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
265	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
266	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
267	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
268	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
269	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
270	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
271	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
272	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
273	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
274	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
275	C₂₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
276	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
277	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
278	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
279	C₂₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
280	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
281	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
282	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
283	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
284	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
285	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
286	C₂₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
287	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
288	C₂₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
289	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
290	C₂₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
291	C₂₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
292	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
293	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
294	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
295	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
296	C₂₃×#97	C₂³	1	1	yes	characteristic
297	C₂₃×#97	C₂³	1	2	yes	—
298	C₂₃×#97	C₂³	1	2	yes	—
299	C₂₃×#97	C₂³	1	2	yes	—
300	C₂₃×#97	C₂³	1	1	yes	characteristic
301	C₂₃×#97	C₂³	1	1	yes	characteristic
302	C₂₃×#97	C₂³	1	1	yes	characteristic
303	C₂₃×#97	C₂³	1	2	yes	—
304	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
305	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
306	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
307	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
308	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
309	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
310	C₄×C₈×C₂₃	C₂³	1	2	yes	—
311	C₄×C₈×C₂₃	C₂³	1	2	yes	—
312	C₄×C₈×C₂₃	C₂³	1	2	yes	—
313	C₂⁴×C₂₃	C₂²×C₄	1	2	yes	—
314	#41×C₂₃	—	4	2	no	—
315	#41×C₂₃	—	4	2	no	—
316	#41×C₂₃	—	4	2	no	—
317	#41×C₂₃	—	4	2	no	—
318	#41×C₂₃	—	4	2	no	—
319	#41×C₂₃	—	4	2	no	—
320	C₂×Q₈×C₂₃	C₂²×C₄	1	1	yes	characteristic
321	C₂×Q₈×C₂₃	C₂²×C₄	1	1	yes	characteristic
322	C₂×Q₈×C₂₃	C₂²×C₄	1	2	yes	—
323	C₂×Q₈×C₂₃	C₂²×C₄	1	2	yes	—
324	C₂×D₄×C₂₃	—	4	2	no	—
325	C₂×D₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
326	C₂×D₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
327	C₂×D₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
328	C₂×D₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
329	C₂×D₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
330	C₂×D₄×C₂₃	C₂²×C₄	1	2	yes	—
331	C₂×D₄×C₂₃	C₂²×C₄	1	2	yes	—
332	C₂×D₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
333	C₂×D₄×C₂₃	C₂²×C₄	1	2	yes	—
334	C₂×D₄×C₂₃	C₂²×C₄	1	2	yes	—
335	C₂×D₄×C₂₃	C₂²×C₄	1	2	yes	—
336	C₂×D₄×C₂₃	C₂²×C₄	1	2	yes	—
337	C₂×D₄×C₂₃	C₂²×C₄	1	2	yes	—
338	C₂×D₄×C₂₃	C₂²×C₄	1	2	yes	—
339	C₂×D₄×C₂₃	C₂²×C₄	1	2	yes	—
340	C₂×D₄×C₂₃	C₂²×C₄	1	2	yes	—
341	C₂×D₄×C₂₃	C₂²×C₄	1	2	yes	—
342	C₂×D₄×C₂₃	C₂²×C₄	1	2	yes	—
343	C₂²×C₄×C₂₃	—	4	2	no	—
344	C₂²×C₄×C₂₃	—	4	2	no	—
345	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
346	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
347	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
348	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
349	C₂²×C₄×C₂₃	C₂²×C₄	1	2	yes	—
350	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
351	C₂²×C₄×C₂₃	C₂²×C₄	1	2	yes	—
352	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
353	C₂²×C₄×C₂₃	C₂²×C₄	1	2	yes	—
354	C₂²×C₄×C₂₃	C₂²×C₄	1	2	yes	—
355	C₂²×C₄×C₂₃	C₂²×C₄	1	2	yes	—
356	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
357	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
358	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
359	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
360	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
361	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
362	M₁₆×C₂₃	—	2	2	no	—
363	M₁₆×C₂₃	—	2	4	no	—
364	M₁₆×C₂₃	—	2	2	no	—
365	M₁₆×C₂₃	—	4	2	no	—
366	M₁₆×C₂₃	—	4	2	no	—
367	M₁₆×C₂₃	—	4	1	no	—
368	M₁₆×C₂₃	—	4	2	no	—
369	M₁₆×C₂₃	—	4	1	no	—
370	M₁₆×C₂₃	—	4	2	no	—
371	M₁₆×C₂₃	—	4	2	no	—
372	M₁₆×C₂₃	—	4	2	no	—
373	M₁₆×C₂₃	—	4	2	no	—
374	C₂×C₈×C₂₃	—	2	4	no	—
375	C₂×C₈×C₂₃	—	2	4	no	—
376	C₂×C₈×C₂₃	—	2	2	no	—
377	C₂×C₈×C₂₃	—	4	2	no	—
378	C₂×C₈×C₂₃	—	4	1	no	—
379	C₂×C₈×C₂₃	—	4	2	no	—
380	C₂×C₈×C₂₃	—	4	2	no	—
381	C₂×C₈×C₂₃	—	4	2	no	—
382	C₂×C₈×C₂₃	—	4	2	no	—
383	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
384	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
385	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
386	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
387	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
388	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
389	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
390	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
391	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
392	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
393	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
394	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
395	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
396	C₄⋊C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
397	C₄⋊C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
398	C₄⋊C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
399	C₄⋊C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
400	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
401	C₄⋊C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
402	C₄⋊C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
403	C₄⋊C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
404	C₄⋊C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
405	C₄⋊C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
406	C₄⋊C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
407	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
408	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
409	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
410	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
411	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
412	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
413	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
414	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
415	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
416	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
417	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
418	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
419	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
420	C₂²⋊C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
421	C₂²⋊C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
422	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
423	C₂²⋊C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
424	C₂²⋊C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
425	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
426	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
427	C₂²⋊C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
428	C₂²⋊C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
429	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
430	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
431	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
432	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
433	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
434	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
435	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
436	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
437	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
438	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
439	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
440	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
441	C₄²×C₂₃	C₂²×C₄	1	1	yes	characteristic
442	C₄²×C₂₃	C₂²×C₄	1	1	yes	characteristic
443	C₄²×C₂₃	C₂²×C₄	1	2	yes	—
444	C₄²×C₂₃	C₂²×C₄	1	1	yes	characteristic
445	C₄²×C₂₃	C₂²×C₄	1	1	yes	characteristic
446	C₄²×C₂₃	C₂²×C₄	1	1	yes	characteristic
447	C₄²×C₂₃	C₂²×C₄	1	2	yes	—
448	C₄²×C₂₃	C₂²×C₄	1	1	yes	characteristic
449	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
450	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
451	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
452	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
453	C₄²×C₂₃	C₂⁴	1	2	yes	—
454	#60319	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
455	C₂³×C₂₃	—	4	2	no	—
456	C₂³×C₂₃	—	4	2	no	—
457	C₂³×C₂₃	—	4	2	no	—
458	C₂³×C₂₃	C₂³×C₄	1	2	yes	—
459	C₂³×C₂₃	C₂³×C₄	1	2	yes	—
460	C₂³×C₂₃	C₂³×C₄	1	1	yes	characteristic
461	C₂³×C₂₃	C₂³×C₄	1	1	yes	characteristic
462	C₂³×C₂₃	C₂³×C₄	1	1	yes	characteristic
463	C₂³×C₂₃	C₂³×C₄	1	2	yes	—
464	Q₈×C₂₃	—	2	2	no	—
465	Q₈×C₂₃	—	4	2	no	—
466	Q₈×C₂₃	—	4	2	no	—
467	Q₈×C₂₃	—	4	1	no	—
468	D₄×C₂₃	—	2	2	no	—
469	D₄×C₂₃	—	2	2	no	—
470	D₄×C₂₃	—	2	2	no	—
471	D₄×C₂₃	—	4	2	no	—
472	D₄×C₂₃	—	4	2	no	—
473	D₄×C₂₃	—	4	2	no	—
474	D₄×C₂₃	—	4	2	no	—
475	D₄×C₂₃	—	4	2	no	—
476	D₄×C₂₃	—	4	2	no	—
477	D₄×C₂₃	—	4	2	no	—
478	D₄×C₂₃	—	4	2	no	—
479	D₄×C₂₃	—	4	2	no	—
480	D₄×C₂₃	—	4	2	no	—
481	D₄×C₂₃	—	4	2	no	—
482	D₄×C₂₃	—	4	1	no	—
483	D₄×C₂₃	—	4	1	no	—
484	D₄×C₂₃	—	4	1	no	—
485	D₄×C₂₃	—	4	2	no	—
486	C₂×C₄×C₂₃	—	2	2	no	—
487	C₂×C₄×C₂₃	—	2	2	no	—
488	C₂×C₄×C₂₃	—	2	2	no	—
489	C₂×C₄×C₂₃	—	2	2	no	—
490	C₂×C₄×C₂₃	—	2	2	no	—
491	C₂×C₄×C₂₃	—	2	1	no	—
492	C₂×C₄×C₂₃	—	2	1	no	—
493	C₂×C₄×C₂₃	—	2	2	no	—
494	C₂×C₄×C₂₃	—	2	1	no	—
495	C₂×C₄×C₂₃	—	2	2	no	—
496	C₂×C₄×C₂₃	—	2	1	no	—
497	C₂×C₄×C₂₃	—	2	2	no	—
498	C₂×C₄×C₂₃	—	2	1	no	—
499	C₂×C₄×C₂₃	—	2	2	no	—
500	C₂×C₄×C₂₃	—	2	1	no	—
501	C₂×C₄×C₂₃	—	4	2	no	—
502	C₂×C₄×C₂₃	—	4	2	no	—
503	C₂×C₄×C₂₃	—	4	2	no	—
504	C₂×C₄×C₂₃	—	4	1	no	—
505	C₂×C₄×C₂₃	—	4	1	no	—
506	C₂×C₄×C₂₃	—	4	2	no	—
507	C₂×C₄×C₂₃	—	4	1	no	—
508	C₂×C₄×C₂₃	—	4	2	no	—
509	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
510	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
511	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
512	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
513	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
514	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
515	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
516	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
517	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
518	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
519	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
520	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
521	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
522	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
523	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
524	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
525	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
526	C₈×C₂₃	—	2	2	no	—
527	C₈×C₂₃	—	2	2	no	—
528	C₈×C₂₃	—	2	1	no	—
529	C₈×C₂₃	—	2	1	no	—
530	C₈×C₂₃	—	2	2	no	—
531	C₈×C₂₃	—	2	1	no	—
532	C₈×C₂₃	—	2	1	no	—
533	C₈×C₂₃	—	2	2	no	—
534	C₈×C₂₃	—	2	1	no	—
535	C₈×C₂₃	—	2	1	no	—
536	C₈×C₂₃	—	2	1	no	—
537	C₈×C₂₃	H(5,𝔽₂)	1	2	yes	—
538	#3460	C₂×C₂₃	1	1	yes	characteristic
539	#2995	C₂×C₂₃	1	2	yes	complemented
540	#2994	C₂×C₂₃	1	1	yes	characteristic, complemented
541	#2993	C₂×C₂₃	1	1	yes	characteristic, complemented
542	#2991	C₂×C₂₃	1	1	yes	characteristic, complemented
543	#2989	C₂×C₂₃	1	1	yes	characteristic, complemented
544	#2981	C₂×C₂₃	1	1	yes	characteristic, complemented
545	#2981	C₂×C₂₃	1	2	yes	complemented
546	#2979	C₂×C₂₃	1	1	yes	characteristic, complemented
547	#2978	C₂×C₂₃	1	2	yes	complemented
548	#2976	C₂×C₂₃	1	2	yes	complemented
549	#2974	C₂×C₂₃	1	1	yes	characteristic, complemented
550	#2970	C₂×C₂₃	1	1	yes	characteristic, complemented
551	#2969	C₂×C₂₃	1	1	yes	characteristic, complemented
552	#2968	C₂×C₂₃	1	2	yes	complemented
553	#2966	C₂×C₂₃	1	1	yes	characteristic, complemented
554	#2965	C₂×C₂₃	1	1	yes	characteristic, complemented
555	#2935	C₂×C₂₃	1	1	yes	characteristic, complemented
556	D₄×M₁₆	C₂×C₂₃	1	1	yes	characteristic, complemented
557	#2933	C₂×C₂₃	1	2	yes	complemented
558	#2932	C₂×C₂₃	1	2	yes	complemented
559	#2931	C₂×C₂₃	1	1	yes	characteristic, complemented
560	#2930	C₂×C₂₃	1	2	yes	complemented
561	C₂²×C₂₃	—	2	1	no	—
562	C₂²×C₂₃	—	2	2	no	—
563	C₂²×C₂₃	—	2	2	no	—
564	C₂²×C₂₃	—	2	1	no	—
565	C₂²×C₂₃	—	2	2	no	—
566	C₂²×C₂₃	—	2	1	no	—
567	C₂²×C₂₃	—	2	1	no	—
568	C₂²×C₂₃	—	2	1	no	—
569	C₂²×C₂₃	—	2	1	no	—
570	C₂²×C₂₃	—	2	2	no	—
571	C₂²×C₂₃	—	2	2	no	—
572	C₂²×C₂₃	—	2	2	no	—
573	C₂²×C₂₃	—	2	1	no	—
574	C₂²×C₂₃	—	2	1	no	—
575	C₂²×C₂₃	—	2	2	no	—
576	C₂²×C₂₃	—	2	1	no	—
577	C₂²×C₂₃	—	2	2	no	—
578	C₂²×C₂₃	—	2	2	no	—
579	C₂²×C₂₃	—	8	4	no	—
580	C₂²×C₂₃	C₂⁴×C₄	1	1	yes	characteristic
581	C₄×C₂₃	—	2	1	no	—
582	C₄×C₂₃	—	2	2	no	—
583	C₄×C₂₃	—	2	2	no	—
584	C₄×C₂₃	—	2	2	no	—
585	C₄×C₂₃	—	2	1	no	—
586	C₄×C₂₃	—	2	1	no	—
587	C₄×C₂₃	—	2	1	no	—
588	C₄×C₂₃	—	2	1	no	—
589	C₄×C₂₃	—	2	1	no	—
590	C₄×C₂₃	—	2	2	no	—
591	C₄×C₂₃	—	2	1	no	—
592	C₄×C₂₃	—	2	1	no	—
593	C₄×C₂₃	—	2	1	no	—
594	C₄×C₂₃	—	2	2	no	—
595	C₄×C₂₃	—	2	1	no	—
596	C₄×C₂₃	#568	1	2	yes	—
597	C₄×C₂₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
598	C₄×C₂₃	#585	1	1	yes	characteristic
599	C₂×#131	C₂²×C₂₃	1	2	yes	complemented
600	C₂×#131	C₂²×C₂₃	1	2	yes	complemented
601	C₂²×M₁₆	C₂²×C₂₃	1	2	yes	—
602	#544	C₄×C₂₃	1	1	yes	characteristic
603	#542	C₄×C₂₃	1	1	yes	characteristic
604	#542	C₄×C₂₃	1	1	yes	characteristic
605	#542	C₄×C₂₃	1	2	yes	—
606	#540	C₄×C₂₃	1	1	yes	characteristic
607	#540	C₄×C₂₃	1	1	yes	characteristic
608	#540	C₄×C₂₃	1	2	yes	—
609	#538	C₄×C₂₃	1	2	yes	—
610	#538	C₄×C₂₃	1	2	yes	—
611	#537	C₄×C₂₃	1	1	yes	characteristic
612	#535	C₄×C₂₃	1	1	yes	characteristic
613	#535	C₄×C₂₃	1	1	yes	characteristic
614	#532	C₂²×C₂₃	1	1	yes	characteristic
615	#532	C₂²×C₂₃	1	2	yes	—
616	#532	C₂²×C₂₃	1	1	yes	characteristic
617	#529	C₂²×C₂₃	1	1	yes	characteristic
618	#529	C₂²×C₂₃	1	2	yes	—
619	#529	C₂²×C₂₃	1	1	yes	characteristic
620	#525	C₂²×C₂₃	1	2	yes	—
621	#525	C₂²×C₂₃	1	2	yes	—
622	C₄×#41	C₂²×C₂₃	1	1	yes	characteristic
623	C₄×#41	C₂²×C₂₃	1	1	yes	characteristic
624	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
625	#446	C₂²×C₂₃	1	1	yes	characteristic, complemented
626	#446	C₂²×C₂₃	1	1	yes	characteristic, complemented
627	#446	C₂²×C₂₃	1	1	yes	characteristic, complemented
628	#446	C₂²×C₂₃	1	2	yes	complemented
629	#446	C₂²×C₂₃	1	1	yes	characteristic, complemented
630	C₈×Q₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
631	C₈×Q₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
632	#436	C₂²×C₂₃	1	2	yes	—
633	#436	C₂²×C₂₃	1	2	yes	—
634	#436	C₂²×C₂₃	1	1	yes	characteristic
635	#436	C₂²×C₂₃	1	1	yes	characteristic
636	#436	C₂²×C₂₃	1	2	yes	—
637	#436	C₂²×C₂₃	1	1	yes	characteristic
638	#436	C₂²×C₂₃	1	1	yes	characteristic
639	#436	C₂²×C₂₃	1	1	yes	characteristic
640	#436	C₂²×C₂₃	1	1	yes	characteristic
641	#436	C₂²×C₂₃	1	2	yes	complemented
642	#436	C₂²×C₂₃	1	2	yes	complemented
643	#436	C₂²×C₂₃	1	2	yes	complemented
644	#436	C₂²×C₂₃	1	1	yes	characteristic, complemented
645	#436	C₂²×C₂₃	1	1	yes	characteristic, complemented
646	#436	C₂²×C₂₃	1	2	yes	complemented
647	#435	C₂²×C₂₃	1	1	yes	characteristic
648	#435	C₂²×C₂₃	1	2	yes	—
649	#435	C₂²×C₂₃	1	2	yes	—
650	#435	C₂²×C₂₃	1	2	yes	—
651	#435	C₂²×C₂₃	1	2	yes	—
652	#435	C₂²×C₂₃	1	2	yes	—
653	#435	C₂²×C₂₃	1	1	yes	characteristic
654	#435	C₂²×C₂₃	1	2	yes	—
655	#435	C₂²×C₂₃	1	2	yes	—
656	#435	C₂²×C₂₃	1	2	yes	complemented
657	#435	C₂²×C₂₃	1	2	yes	complemented
658	#435	C₂²×C₂₃	1	1	yes	characteristic, complemented
659	#435	C₂²×C₂₃	1	2	yes	complemented
660	#435	C₂²×C₂₃	1	2	yes	complemented
661	#435	C₂²×C₂₃	1	2	yes	complemented
662	#435	C₂²×C₂₃	1	2	yes	complemented
663	#435	C₂²×C₂₃	1	2	yes	complemented
664	#435	C₂²×C₂₃	1	2	yes	complemented
665	#435	C₂²×C₂₃	1	1	yes	characteristic, complemented
666	#435	C₂²×C₂₃	1	2	yes	complemented
667	C₈×D₄	C₂²×C₂₃	1	1	yes	characteristic
668	C₈×D₄	C₂²×C₂₃	1	1	yes	characteristic
669	C₈×D₄	C₂²×C₂₃	1	1	yes	characteristic
670	C₈×D₄	C₂²×C₂₃	1	1	yes	characteristic
671	C₈×D₄	C₂²×C₂₃	1	2	yes	complemented
672	C₈×D₄	C₂²×C₂₃	1	1	yes	characteristic, complemented
673	C₈×D₄	C₂²×C₂₃	1	2	yes	complemented
674	C₈×D₄	C₂²×C₂₃	1	2	yes	complemented
675	C₈×D₄	C₂²×C₂₃	1	2	yes	complemented
676	C₈×D₄	C₂²×C₂₃	1	1	yes	characteristic, complemented
677	#433	C₂²×C₂₃	1	2	yes	complemented
678	#433	C₂²×C₂₃	1	2	yes	complemented
679	#433	C₂²×C₂₃	1	2	yes	complemented
680	#433	C₂²×C₂₃	1	2	yes	complemented
681	#432	C₂²×C₂₃	1	1	yes	characteristic
682	#432	C₂²×C₂₃	1	1	yes	characteristic, complemented
683	#432	C₂²×C₂₃	1	2	yes	complemented
684	#431	C₂²×C₂₃	1	1	yes	characteristic
685	#431	C₂²×C₂₃	1	1	yes	characteristic, complemented
686	#431	C₂²×C₂₃	1	1	yes	characteristic, complemented
687	#431	C₂²×C₂₃	1	2	yes	complemented
688	#431	C₂²×C₂₃	1	1	yes	characteristic, complemented
689	#424	C₂²×C₂₃	1	2	yes	complemented
690	#424	C₂²×C₂₃	1	2	yes	complemented
691	#423	C₂²×C₂₃	1	1	yes	characteristic
692	#423	C₂²×C₂₃	1	1	yes	characteristic, complemented
693	#423	C₂²×C₂₃	1	2	yes	complemented
694	C₂×C₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
695	#408	C₂²×C₂₃	1	2	yes	complemented
696	#408	C₂²×C₂₃	1	2	yes	complemented
697	#408	C₂²×C₂₃	1	2	yes	complemented
698	#408	C₂²×C₂₃	1	2	yes	complemented
699	#408	C₂²×C₂₃	1	2	yes	complemented
700	#408	C₂²×C₂₃	1	2	yes	complemented
701	#407	C₂²×C₂₃	1	2	yes	—
702	#407	C₂²×C₂₃	1	2	yes	—
703	C₂×C₂²⋊C₈	C₂²×C₂₃	1	2	yes	—
704	#405	C₂²×C₂₃	1	2	yes	complemented
705	#405	C₂²×C₂₃	1	2	yes	complemented
706	C₄×M₁₆	C₂²×C₂₃	1	1	yes	characteristic
707	C₄×M₁₆	C₂²×C₂₃	1	1	yes	characteristic, complemented
708	C₂×#97	C₂²×C₂₃	1	2	yes	complemented
709	C₂×C₄×C₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
710	C₂×C₂₃	—	4	1	no	—
711	C₂×C₂₃	—	4	1	no	—
712	C₂×C₂₃	—	4	2	no	—
713	C₂×C₂₃	—	4	2	no	—
714	C₂×C₂₃	—	4	2	no	—
715	C₂×C₂₃	—	4	1	no	—
716	C₂×C₂₃	C₄×H(5,𝔽₂)	1	1	yes	characteristic
717	C₂×C₂₃	C₂×#568	1	1	yes	characteristic
718	C₂×C₂₃	#3573	1	1	yes	characteristic
719	C₂×#41	C₂×C₄×C₂₃	1	1	yes	characteristic
720	C₂×#41	C₂×C₄×C₂₃	1	1	yes	characteristic
721	C₂×#41	C₂³×C₂₃	1	2	yes	—
722	C₂×#41	C₂³×C₂₃	1	2	yes	—
723	C₂²×D₄	C₂×C₄×C₂₃	1	1	yes	characteristic
724	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
725	#131	—	4	4	no	—
726	#131	—	4	4	no	—
727	C₂×M₁₆	—	4	4	no	—
728	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
729	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
730	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
731	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
732	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
733	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
734	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
735	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
736	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
737	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
738	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
739	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
740	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
741	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
742	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
743	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
744	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
745	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
746	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
747	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
748	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
749	C₄⋊Q₈	C₂×C₄×C₂₃	1	1	yes	characteristic
750	C₄⋊Q₈	C₂×C₄×C₂₃	1	2	yes	—
751	C₄⋊Q₈	C₂×C₄×C₂₃	1	1	yes	characteristic
752	#127	C₂×C₄×C₂₃	1	1	yes	characteristic
753	#127	C₂×C₄×C₂₃	1	1	yes	characteristic
754	#127	C₂×C₄×C₂₃	1	2	yes	—
755	#126	C₂×C₄×C₂₃	1	2	yes	—
756	#126	C₂×C₄×C₂₃	1	2	yes	—
757	#126	C₂×C₄×C₂₃	1	2	yes	—
758	#126	C₂×C₄×C₂₃	1	2	yes	—
759	#125	C₂×C₄×C₂₃	1	1	yes	characteristic
760	#125	C₂×C₄×C₂₃	1	2	yes	—
761	#125	C₂×C₄×C₂₃	1	1	yes	characteristic
762	#124	C₂×C₄×C₂₃	1	1	yes	characteristic
763	#124	C₂×C₄×C₂₃	1	1	yes	characteristic
764	#124	C₂×C₄×C₂₃	1	2	yes	—
765	#124	C₂×C₄×C₂₃	1	2	yes	—
766	#124	C₂×C₄×C₂₃	1	2	yes	—
767	#124	C₂×C₄×C₂₃	1	2	yes	—
768	#124	C₂×C₄×C₂₃	1	2	yes	—
769	#123	C₂×C₄×C₂₃	1	2	yes	—
770	#123	C₂×C₄×C₂₃	1	2	yes	—
771	#123	C₂×C₄×C₂₃	1	2	yes	—
772	#123	C₂×C₄×C₂₃	1	2	yes	—
773	#123	C₂×C₄×C₂₃	1	2	yes	—
774	#123	C₂×C₄×C₂₃	1	2	yes	—
775	#123	C₂×C₄×C₂₃	1	2	yes	—
776	#123	C₂×C₄×C₂₃	1	2	yes	—
777	C₂²⋊Q₈	C₂×C₄×C₂₃	1	2	yes	—
778	C₂²⋊Q₈	C₂×C₄×C₂₃	1	2	yes	—
779	C₂²⋊Q₈	C₂×C₄×C₂₃	1	2	yes	—
780	C₂²⋊Q₈	C₂×C₄×C₂₃	1	2	yes	—
781	C₂²⋊Q₈	C₂×C₄×C₂₃	1	1	yes	characteristic
782	C₂²⋊Q₈	C₂×C₄×C₂₃	1	1	yes	characteristic
783	C₂²⋊Q₈	C₂×C₄×C₂₃	1	2	yes	—
784	#121	C₂×C₄×C₂₃	1	2	yes	—
785	#121	C₂×C₄×C₂₃	1	2	yes	—
786	#121	C₂×C₄×C₂₃	1	2	yes	—
787	#121	C₂×C₄×C₂₃	1	2	yes	—
788	#121	C₂×C₄×C₂₃	1	1	yes	characteristic
789	#121	C₂×C₄×C₂₃	1	1	yes	characteristic
790	#121	C₂×C₄×C₂₃	1	2	yes	—
791	#121	C₂×C₄×C₂₃	1	1	yes	characteristic
792	#121	C₂×C₄×C₂₃	1	1	yes	characteristic
793	#121	C₂×C₄×C₂₃	1	2	yes	—
794	#121	C₂×C₄×C₂₃	1	1	yes	characteristic
795	#121	C₂×C₄×C₂₃	1	1	yes	characteristic
796	#121	C₂×C₄×C₂₃	1	2	yes	—
797	#121	C₂×C₄×C₂₃	1	2	yes	—
798	#121	C₂×C₄×C₂₃	1	2	yes	—
799	#121	C₂×C₄×C₂₃	1	2	yes	—
800	#121	C₂×C₄×C₂₃	1	2	yes	—
801	#120	C₂×C₄×C₂₃	1	2	yes	—
802	#120	C₂×C₄×C₂₃	1	2	yes	—
803	#120	C₂×C₄×C₂₃	1	2	yes	—
804	#120	C₂×C₄×C₂₃	1	2	yes	—
805	C₄×Q₈	C₂×C₄×C₂₃	1	1	yes	characteristic
806	C₄×Q₈	C₂×C₄×C₂₃	1	1	yes	characteristic
807	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
808	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
809	C₄×D₄	C₂×C₄×C₂₃	1	1	yes	characteristic
810	C₄×D₄	C₂×C₄×C₂₃	1	1	yes	characteristic
811	C₄×D₄	C₂×C₄×C₂₃	1	2	yes	—
812	C₄×D₄	C₂×C₄×C₂₃	1	1	yes	characteristic
813	C₄×D₄	C₂×C₄×C₂₃	1	1	yes	characteristic
814	C₄×D₄	C₂×C₄×C₂₃	1	2	yes	—
815	C₄×D₄	C₂×C₄×C₂₃	1	1	yes	characteristic
816	C₄×D₄	C₂×C₄×C₂₃	1	1	yes	characteristic
817	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
818	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
819	C₄×D₄	C₂³×C₂₃	1	2	yes	—
820	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
821	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
822	C₄×D₄	C₂³×C₂₃	1	2	yes	—
823	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
824	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
825	C₄×D₄	C₂³×C₂₃	1	2	yes	—
826	C₄×D₄	C₂³×C₂₃	1	2	yes	—
827	C₄×D₄	C₂³×C₂₃	1	2	yes	—
828	C₄×D₄	C₂³×C₂₃	1	2	yes	—
829	#117	C₂×C₄×C₂₃	1	1	yes	characteristic
830	#117	C₂×C₄×C₂₃	1	1	yes	characteristic
831	#117	C₂×C₄×C₂₃	1	1	yes	characteristic
832	#117	C₂×C₄×C₂₃	1	1	yes	characteristic
833	#117	C₂×C₄×C₂₃	1	2	yes	—
834	#117	C₂³×C₂₃	1	2	yes	—
835	#117	C₂³×C₂₃	1	2	yes	—
836	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
837	C₂×C₂²⋊C₄	C₂×C₄×C₂₃	1	2	yes	—
838	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
839	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
840	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
841	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
842	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
843	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
844	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
845	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
846	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
847	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
848	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
849	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
850	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
851	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
852	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
853	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
854	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
855	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
856	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
857	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
858	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
859	C₂²⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
860	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
861	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
862	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
863	C₂²⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
864	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
865	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
866	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
867	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
868	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
869	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
870	C₂²⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
871	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
872	C₂²⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
873	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
874	C₂²⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
875	C₂²⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
876	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
877	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
878	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
879	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
880	#97	C₂³×C₂₃	1	1	yes	characteristic
881	#97	C₂³×C₂₃	1	2	yes	—
882	#97	C₂³×C₂₃	1	2	yes	—
883	#97	C₂³×C₂₃	1	2	yes	—
884	#97	C₂³×C₂₃	1	1	yes	characteristic
885	#97	C₂³×C₂₃	1	1	yes	characteristic
886	#97	C₂³×C₂₃	1	1	yes	characteristic
887	#97	C₂³×C₂₃	1	2	yes	—
888	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
889	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
890	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
891	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
892	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
893	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
894	C₄×C₈	C₂³×C₂₃	1	2	yes	—
895	C₄×C₈	C₂³×C₂₃	1	2	yes	—
896	C₄×C₈	C₂³×C₂₃	1	2	yes	—
897	C₂₃	#60319	1	1	yes	characteristic, direct product factor, Sylow
898	C₂⁴	C₂²×C₄×C₂₃	1	2	yes	—
899	#41	—	4	2	no	—
900	#41	—	4	2	no	—
901	#41	—	4	2	no	—
902	#41	—	4	2	no	—
903	#41	—	4	2	no	—
904	#41	—	4	2	no	—
905	C₂×Q₈	C₂²×C₄×C₂₃	1	1	yes	characteristic
906	C₂×Q₈	C₂²×C₄×C₂₃	1	1	yes	characteristic
907	C₂×Q₈	C₂²×C₄×C₂₃	1	2	yes	—
908	C₂×Q₈	C₂²×C₄×C₂₃	1	2	yes	—
909	C₂×D₄	—	4	2	no	—
910	C₂×D₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
911	C₂×D₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
912	C₂×D₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
913	C₂×D₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
914	C₂×D₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
915	C₂×D₄	C₂²×C₄×C₂₃	1	2	yes	—
916	C₂×D₄	C₂²×C₄×C₂₃	1	2	yes	—
917	C₂×D₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
918	C₂×D₄	C₂²×C₄×C₂₃	1	2	yes	—
919	C₂×D₄	C₂²×C₄×C₂₃	1	2	yes	—
920	C₂×D₄	C₂²×C₄×C₂₃	1	2	yes	—
921	C₂×D₄	C₂²×C₄×C₂₃	1	2	yes	—
922	C₂×D₄	C₂²×C₄×C₂₃	1	2	yes	—
923	C₂×D₄	C₂²×C₄×C₂₃	1	2	yes	—
924	C₂×D₄	C₂²×C₄×C₂₃	1	2	yes	—
925	C₂×D₄	C₂²×C₄×C₂₃	1	2	yes	—
926	C₂×D₄	C₂²×C₄×C₂₃	1	2	yes	—
927	C₂×D₄	C₂²×C₄×C₂₃	1	2	yes	—
928	C₂²×C₄	—	4	2	no	—
929	C₂²×C₄	—	4	2	no	—
930	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
931	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
932	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
933	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
934	C₂²×C₄	C₂²×C₄×C₂₃	1	2	yes	—
935	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
936	C₂²×C₄	C₂²×C₄×C₂₃	1	2	yes	—
937	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
938	C₂²×C₄	C₂²×C₄×C₂₃	1	2	yes	—
939	C₂²×C₄	C₂²×C₄×C₂₃	1	2	yes	—
940	C₂²×C₄	C₂²×C₄×C₂₃	1	2	yes	—
941	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
942	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
943	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
944	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
945	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
946	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
947	M₁₆	—	2	2	no	—
948	M₁₆	—	2	4	no	—
949	M₁₆	—	2	2	no	—
950	M₁₆	—	4	2	no	—
951	M₁₆	—	4	2	no	—
952	M₁₆	—	4	2	no	—
953	M₁₆	—	4	2	no	—
954	M₁₆	—	4	2	no	—
955	M₁₆	—	4	2	no	—
956	M₁₆	—	4	1	no	—
957	M₁₆	—	4	2	no	—
958	M₁₆	—	4	1	no	—
959	C₂×C₈	—	2	4	no	—
960	C₂×C₈	—	2	4	no	—
961	C₂×C₈	—	2	2	no	—
962	C₂×C₈	—	4	2	no	—
963	C₂×C₈	—	4	2	no	—
964	C₂×C₈	—	4	2	no	—
965	C₂×C₈	—	4	2	no	—
966	C₂×C₈	—	4	1	no	—
967	C₂×C₈	—	4	2	no	—
968	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
969	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
970	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
971	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
972	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
973	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
974	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
975	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
976	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
977	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
978	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
979	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
980	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
981	C₄⋊C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
982	C₄⋊C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
983	C₄⋊C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
984	C₄⋊C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
985	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
986	C₄⋊C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
987	C₄⋊C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
988	C₄⋊C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
989	C₄⋊C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
990	C₄⋊C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
991	C₄⋊C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
992	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
993	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
994	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
995	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
996	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
997	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
998	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
999	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
1000	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
1001	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
1002	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
1003	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
1004	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
1005	C₂²⋊C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
1006	C₂²⋊C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
1007	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
1008	C₂²⋊C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
1009	C₂²⋊C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
1010	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
1011	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
1012	C₂²⋊C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
1013	C₂²⋊C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
1014	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
1015	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
1016	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
1017	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
1018	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
1019	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
1020	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
1021	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
1022	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
1023	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
1024	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
1025	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
1026	C₄²	C₂²×C₄×C₂₃	1	1	yes	characteristic
1027	C₄²	C₂²×C₄×C₂₃	1	1	yes	characteristic
1028	C₄²	C₂²×C₄×C₂₃	1	2	yes	—
1029	C₄²	C₂²×C₄×C₂₃	1	1	yes	characteristic
1030	C₄²	C₂²×C₄×C₂₃	1	1	yes	characteristic
1031	C₄²	C₂²×C₄×C₂₃	1	1	yes	characteristic
1032	C₄²	C₂²×C₄×C₂₃	1	2	yes	—
1033	C₄²	C₂²×C₄×C₂₃	1	1	yes	characteristic
1034	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
1035	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
1036	C₄²	C₂⁴×C₂₃	1	2	yes	—
1037	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
1038	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
1039	C₂³	—	4	2	no	—
1040	C₂³	—	4	2	no	—
1041	C₂³	—	4	2	no	—
1042	C₂³	C₂³×C₄×C₂₃	1	2	yes	—
1043	C₂³	C₂³×C₄×C₂₃	1	2	yes	—
1044	C₂³	C₂³×C₄×C₂₃	1	1	yes	characteristic
1045	C₂³	C₂³×C₄×C₂₃	1	1	yes	characteristic
1046	C₂³	C₂³×C₄×C₂₃	1	1	yes	characteristic
1047	C₂³	C₂³×C₄×C₂₃	1	2	yes	—
1048	Q₈	—	2	2	no	—
1049	Q₈	—	4	2	no	—
1050	Q₈	—	4	2	no	—
1051	Q₈	—	4	1	no	—
1052	D₄	—	2	2	no	—
1053	D₄	—	2	2	no	—
1054	D₄	—	2	2	no	—
1055	D₄	—	4	2	no	—
1056	D₄	—	4	2	no	—
1057	D₄	—	4	2	no	—
1058	D₄	—	4	2	no	—
1059	D₄	—	4	2	no	—
1060	D₄	—	4	2	no	—
1061	D₄	—	4	2	no	—
1062	D₄	—	4	1	no	—
1063	D₄	—	4	1	no	—
1064	D₄	—	4	1	no	—
1065	D₄	—	4	2	no	—
1066	D₄	—	4	2	no	—
1067	D₄	—	4	2	no	—
1068	D₄	—	4	2	no	—
1069	D₄	—	4	2	no	—
1070	C₂×C₄	—	2	2	no	—
1071	C₂×C₄	—	2	2	no	—
1072	C₂×C₄	—	2	2	no	—
1073	C₂×C₄	—	2	2	no	—
1074	C₂×C₄	—	2	2	no	—
1075	C₂×C₄	—	2	1	no	—
1076	C₂×C₄	—	2	1	no	—
1077	C₂×C₄	—	2	2	no	—
1078	C₂×C₄	—	2	1	no	—
1079	C₂×C₄	—	2	2	no	—
1080	C₂×C₄	—	2	1	no	—
1081	C₂×C₄	—	2	2	no	—
1082	C₂×C₄	—	2	1	no	—
1083	C₂×C₄	—	2	2	no	—
1084	C₂×C₄	—	2	1	no	—
1085	C₂×C₄	—	4	2	no	—
1086	C₂×C₄	—	4	2	no	—
1087	C₂×C₄	—	4	2	no	—
1088	C₂×C₄	—	4	2	no	—
1089	C₂×C₄	—	4	1	no	—
1090	C₂×C₄	—	4	1	no	—
1091	C₂×C₄	—	4	2	no	—
1092	C₂×C₄	—	4	1	no	—
1093	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
1094	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
1095	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
1096	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
1097	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
1098	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
1099	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
1100	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
1101	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
1102	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
1103	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
1104	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
1105	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
1106	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
1107	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
1108	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
1109	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
1110	C₈	—	2	2	no	—
1111	C₈	—	2	2	no	—
1112	C₈	—	2	1	no	—
1113	C₈	—	2	1	no	—
1114	C₈	—	2	2	no	—
1115	C₈	—	2	1	no	—
1116	C₈	—	2	1	no	—
1117	C₈	—	2	2	no	—
1118	C₈	—	2	1	no	—
1119	C₈	—	2	1	no	—
1120	C₈	—	2	1	no	—
1121	C₈	C₂₃×H(5,𝔽₂)	1	2	yes	—
1122	C₂²	—	2	1	no	—
1123	C₂²	—	2	2	no	—
1124	C₂²	—	2	2	no	—
1125	C₂²	—	2	1	no	—
1126	C₂²	—	2	2	no	—
1127	C₂²	—	2	1	no	—
1128	C₂²	—	2	1	no	—
1129	C₂²	—	2	1	no	—
1130	C₂²	—	2	1	no	—
1131	C₂²	—	2	2	no	—
1132	C₂²	—	2	2	no	—
1133	C₂²	—	2	2	no	—
1134	C₂²	—	2	1	no	—
1135	C₂²	—	2	1	no	—
1136	C₂²	—	2	2	no	—
1137	C₂²	—	2	1	no	—
1138	C₂²	—	2	2	no	—
1139	C₂²	—	2	2	no	—
1140	C₂²	—	8	4	no	—
1141	C₂²	C₂⁴×C₄×C₂₃	1	1	yes	characteristic
1142	C₄	—	2	1	no	—
1143	C₄	—	2	2	no	—
1144	C₄	—	2	2	no	—
1145	C₄	—	2	2	no	—
1146	C₄	—	2	1	no	—
1147	C₄	—	2	1	no	—
1148	C₄	—	2	1	no	—
1149	C₄	—	2	1	no	—
1150	C₄	—	2	1	no	—
1151	C₄	—	2	2	no	—
1152	C₄	—	2	1	no	—
1153	C₄	—	2	1	no	—
1154	C₄	—	2	1	no	—
1155	C₄	—	2	2	no	—
1156	C₄	—	2	1	no	—
1157	C₄	C₂₃×#568	1	2	yes	—
1158	C₄	C₂×C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
1159	C₄	C₂₃×#585	1	1	yes	characteristic
1160	C₂	—	4	1	no	—
1161	C₂	—	4	2	no	—
1162	C₂	—	4	2	no	—
1163	C₂	—	4	1	no	—
1164	C₂	—	4	1	no	—
1165	C₂	—	4	2	no	—
1166	C₂	C₄×C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
1167	C₂	C₂×C₂₃×#568	1	1	yes	characteristic
1168	C₂	C₂₃×#3573	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₂₃	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₂₃
Frattini, cosocle	C₂×C₄	C₂⁵×C₂₃
socle	C₂²×C₂₃	C₂⁴×C₄
prime radical	C₂₃×#3460	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₂₃ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
2. C₂₃×#2995	C₂	semidirect
3. C₂₃×#2994	C₂	semidirect
4. C₂₃×#2993	C₂	semidirect
5. C₂₃×#2991	C₂	semidirect
6. C₂₃×#2989	C₂	semidirect
7. C₂₃×#2981	C₂	semidirect
8. C₂₃×#2981	C₂	semidirect
9. C₂₃×#2979	C₂	semidirect
10. C₂₃×#2978	C₂	semidirect
11. C₂₃×#2976	C₂	semidirect
12. C₂₃×#2974	C₂	semidirect
13. C₂₃×#2970	C₂	semidirect
14. C₂₃×#2969	C₂	semidirect
15. C₂₃×#2968	C₂	semidirect
16. C₂₃×#2966	C₂	semidirect
17. C₂₃×#2965	C₂	semidirect
18. C₂₃×#2935	C₂	semidirect
19. D₄×M₁₆×C₂₃	C₂	semidirect
20. C₂₃×#2933	C₂	semidirect
21. C₂₃×#2932	C₂	semidirect
22. C₂₃×#2931	C₂	semidirect
23. C₂₃×#2930	C₂	semidirect
24. C₂×C₂₃×#131	C₂²	semidirect
25. C₂×C₂₃×#131	C₂²	semidirect
50. C₂₃×#446	C₂²	semidirect
51. C₂₃×#446	C₂²	semidirect
52. C₂₃×#446	C₂²	semidirect
53. C₂₃×#446	C₂²	semidirect
54. C₂₃×#446	C₂²	semidirect
55. C₈×Q₈×C₂₃	C₂²	semidirect
56. C₈×Q₈×C₂₃	C₂²	semidirect
66. C₂₃×#436	C₂²	semidirect
67. C₂₃×#436	C₂²	semidirect
68. C₂₃×#436	C₂²	semidirect
69. C₂₃×#436	C₂²	semidirect
70. C₂₃×#436	C₂²	semidirect
71. C₂₃×#436	C₂²	semidirect
81. C₂₃×#435	C₂²	semidirect
82. C₂₃×#435	C₂²	semidirect
83. C₂₃×#435	C₂²	semidirect
84. C₂₃×#435	C₂²	semidirect
85. C₂₃×#435	C₂²	semidirect
86. C₂₃×#435	C₂²	semidirect
87. C₂₃×#435	C₂²	semidirect
88. C₂₃×#435	C₂²	semidirect
89. C₂₃×#435	C₂²	semidirect
90. C₂₃×#435	C₂²	semidirect
91. C₂₃×#435	C₂²	semidirect
96. C₈×D₄×C₂₃	C₂²	semidirect
97. C₈×D₄×C₂₃	C₂²	semidirect
98. C₈×D₄×C₂₃	C₂²	semidirect
99. C₈×D₄×C₂₃	C₂²	semidirect
100. C₈×D₄×C₂₃	C₂²	semidirect
101. C₈×D₄×C₂₃	C₂²	semidirect
102. C₂₃×#433	C₂²	semidirect
103. C₂₃×#433	C₂²	semidirect
104. C₂₃×#433	C₂²	semidirect
105. C₂₃×#433	C₂²	semidirect
107. C₂₃×#432	C₂²	semidirect
108. C₂₃×#432	C₂²	semidirect
110. C₂₃×#431	C₂²	semidirect
111. C₂₃×#431	C₂²	semidirect
112. C₂₃×#431	C₂²	semidirect
113. C₂₃×#431	C₂²	semidirect
114. C₂₃×#424	C₂²	semidirect
115. C₂₃×#424	C₂²	semidirect
117. C₂₃×#423	C₂²	semidirect
118. C₂₃×#423	C₂²	semidirect
119. C₂×C₂₃×C₄⋊C₈	C₂²	semidirect
120. C₂₃×#408	C₂²	semidirect
121. C₂₃×#408	C₂²	semidirect
122. C₂₃×#408	C₂²	semidirect
123. C₂₃×#408	C₂²	semidirect
124. C₂₃×#408	C₂²	semidirect
125. C₂₃×#408	C₂²	semidirect
129. C₂₃×#405	C₂²	semidirect
130. C₂₃×#405	C₂²	semidirect
132. C₄×M₁₆×C₂₃	C₂²	semidirect
133. C₂×C₂₃×#97	C₂²	semidirect
134. C₂×C₄×C₈×C₂₃	C₂²	semidirect
454. #60319	C₂₃	direct (N × H)
539. #2995	C₂×C₂₃	semidirect
540. #2994	C₂×C₂₃	semidirect
541. #2993	C₂×C₂₃	semidirect
542. #2991	C₂×C₂₃	semidirect
543. #2989	C₂×C₂₃	semidirect
544. #2981	C₂×C₂₃	semidirect
545. #2981	C₂×C₂₃	semidirect
546. #2979	C₂×C₂₃	semidirect
547. #2978	C₂×C₂₃	semidirect
548. #2976	C₂×C₂₃	semidirect
549. #2974	C₂×C₂₃	semidirect
550. #2970	C₂×C₂₃	semidirect
551. #2969	C₂×C₂₃	semidirect
552. #2968	C₂×C₂₃	semidirect
553. #2966	C₂×C₂₃	semidirect
554. #2965	C₂×C₂₃	semidirect
555. #2935	C₂×C₂₃	semidirect
556. D₄×M₁₆	C₂×C₂₃	semidirect
557. #2933	C₂×C₂₃	semidirect
558. #2932	C₂×C₂₃	semidirect
559. #2931	C₂×C₂₃	semidirect
560. #2930	C₂×C₂₃	semidirect
599. C₂×#131	C₂²×C₂₃	semidirect
600. C₂×#131	C₂²×C₂₃	semidirect
625. #446	C₂²×C₂₃	semidirect
626. #446	C₂²×C₂₃	semidirect
627. #446	C₂²×C₂₃	semidirect
628. #446	C₂²×C₂₃	semidirect
629. #446	C₂²×C₂₃	semidirect
630. C₈×Q₈	C₂²×C₂₃	semidirect
631. C₈×Q₈	C₂²×C₂₃	semidirect
641. #436	C₂²×C₂₃	semidirect
642. #436	C₂²×C₂₃	semidirect
643. #436	C₂²×C₂₃	semidirect
644. #436	C₂²×C₂₃	semidirect
645. #436	C₂²×C₂₃	semidirect
646. #436	C₂²×C₂₃	semidirect
656. #435	C₂²×C₂₃	semidirect
657. #435	C₂²×C₂₃	semidirect
658. #435	C₂²×C₂₃	semidirect
659. #435	C₂²×C₂₃	semidirect
660. #435	C₂²×C₂₃	semidirect
661. #435	C₂²×C₂₃	semidirect
662. #435	C₂²×C₂₃	semidirect
663. #435	C₂²×C₂₃	semidirect
664. #435	C₂²×C₂₃	semidirect
665. #435	C₂²×C₂₃	semidirect
666. #435	C₂²×C₂₃	semidirect
671. C₈×D₄	C₂²×C₂₃	semidirect
672. C₈×D₄	C₂²×C₂₃	semidirect
673. C₈×D₄	C₂²×C₂₃	semidirect
674. C₈×D₄	C₂²×C₂₃	semidirect
675. C₈×D₄	C₂²×C₂₃	semidirect
676. C₈×D₄	C₂²×C₂₃	semidirect
677. #433	C₂²×C₂₃	semidirect
678. #433	C₂²×C₂₃	semidirect
679. #433	C₂²×C₂₃	semidirect
680. #433	C₂²×C₂₃	semidirect
682. #432	C₂²×C₂₃	semidirect
683. #432	C₂²×C₂₃	semidirect
685. #431	C₂²×C₂₃	semidirect
686. #431	C₂²×C₂₃	semidirect
687. #431	C₂²×C₂₃	semidirect
688. #431	C₂²×C₂₃	semidirect
689. #424	C₂²×C₂₃	semidirect
690. #424	C₂²×C₂₃	semidirect
692. #423	C₂²×C₂₃	semidirect
693. #423	C₂²×C₂₃	semidirect
694. C₂×C₄⋊C₈	C₂²×C₂₃	semidirect
695. #408	C₂²×C₂₃	semidirect
696. #408	C₂²×C₂₃	semidirect
697. #408	C₂²×C₂₃	semidirect
698. #408	C₂²×C₂₃	semidirect
699. #408	C₂²×C₂₃	semidirect
700. #408	C₂²×C₂₃	semidirect
704. #405	C₂²×C₂₃	semidirect
705. #405	C₂²×C₂₃	semidirect
707. C₄×M₁₆	C₂²×C₂₃	semidirect
708. C₂×#97	C₂²×C₂₃	semidirect
709. C₂×C₄×C₈	C₂²×C₂₃	semidirect
897. C₂₃	#60319	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂₃×#3460	2
C₂₃×#2995	2
C₂₃×#2994	2
C₂₃×#2993	2
C₂₃×#2991	2
C₂₃×#2989	2
C₂₃×#2981	2
C₂₃×#2979	2
C₂₃×#2978	2
C₂₃×#2976	2
C₂₃×#2974	2
C₂₃×#2970	2
C₂₃×#2969	2
C₂₃×#2968	2
C₂₃×#2966	2
C₂₃×#2965	2
C₂₃×#2935	2
D₄×M₁₆×C₂₃	2
C₂₃×#2933	2
C₂₃×#2932	2
C₂₃×#2931	2
C₂₃×#2930	2
#60319	23

Subgroups — C23×#60319 #19207945

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#60319 #19207945