Subgroups — C₂₃×#60298 #19207924

Order 5888.

1772 conjugacy classes of subgroups.

The subgroup lattice has 1124 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3475	C₂	1	1	yes	maximal, characteristic
2	C₂₃×#2994	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×#2992	C₂	1	2	yes	maximal, complemented
6	C₂₃×#2990	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₃×#2988	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₃×#2986	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₃×#2985	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₃×#2977	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×#2972	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₃×#2970	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₃×#2969	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂₃×#2968	C₂	1	2	yes	maximal, complemented
17	C₂₃×#2966	C₂	1	2	yes	maximal, complemented
18	C₂₃×#2966	C₂	1	1	yes	maximal, characteristic, complemented
19	C₈×#41×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂₃×#2925	C₂	1	1	yes	maximal, characteristic, complemented
21	C₂₃×#2924	C₂	1	2	yes	maximal, complemented
22	C₂₃×#2922	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂×C₂₃×#433	C₂	1	2	yes	maximal, complemented
24	C₂₃×#556	C₄	1	1	yes	characteristic
25	C₂₃×#555	C₄	1	1	yes	characteristic
26	C₂₃×#554	C₄	1	1	yes	characteristic
27	C₂₃×#553	C₄	1	2	yes	—
28	C₂₃×#552	C₄	1	2	yes	—
29	C₂₃×#552	C₄	1	1	yes	characteristic
30	C₂₃×#552	C₄	1	1	yes	characteristic
31	C₂₃×#551	C₄	1	2	yes	—
32	C₂₃×#551	C₄	1	2	yes	—
33	C₂₃×#547	C₄	1	1	yes	characteristic
34	C₂₃×#546	C₄	1	1	yes	characteristic
35	C₂₃×#546	C₄	1	1	yes	characteristic
36	C₂₃×#533	C₂²	1	1	yes	characteristic
37	C₂₃×#529	C₂²	1	2	yes	—
38	C₂₃×#529	C₂²	1	1	yes	characteristic
39	C₂₃×#529	C₂²	1	2	yes	—
40	C₂₃×#529	C₂²	1	1	yes	characteristic
41	C₂₃×#525	C₂²	1	2	yes	—
42	C₄×#41×C₂₃	C₂²	1	1	yes	characteristic
43	C₄×#41×C₂₃	C₂²	1	1	yes	characteristic
44	C₄×#41×C₂₃	C₂²	1	1	yes	characteristic
45	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
46	C₂×C₂₃×#117	C₂²	1	2	yes	—
47	C₂₃×#446	C₂²	1	2	yes	complemented
48	C₂₃×#446	C₂²	1	1	yes	characteristic, complemented
49	C₂₃×#446	C₂²	1	2	yes	complemented
50	C₂₃×#446	C₂²	1	2	yes	complemented
51	C₂₃×#446	C₂²	1	1	yes	characteristic, complemented
52	C₂₃×#446	C₂²	1	1	yes	characteristic, complemented
53	C₂₃×#446	C₂²	1	1	yes	characteristic, complemented
54	C₈×Q₈×C₂₃	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	C₈×Q₈×C₂₃	C₂²	1	2	yes	complemented
58	C₈×Q₈×C₂₃	C₂²	1	1	yes	characteristic, complemented
59	C₂₃×#436	C₂²	1	1	yes	characteristic
60	C₂₃×#436	C₂²	1	1	yes	characteristic
61	C₂₃×#436	C₂²	1	2	yes	complemented
62	C₂₃×#436	C₂²	1	2	yes	complemented
63	C₂₃×#435	C₂²	1	2	yes	—
64	C₂₃×#435	C₂²	1	2	yes	—
65	C₂₃×#435	C₂²	1	2	yes	complemented
66	C₂₃×#435	C₂²	1	2	yes	complemented
67	C₂₃×#435	C₂²	1	2	yes	complemented
68	C₂₃×#435	C₂²	1	2	yes	complemented
69	C₂₃×#435	C₂²	1	2	yes	complemented
70	C₂₃×#435	C₂²	1	2	yes	complemented
71	C₂₃×#435	C₂²	1	2	yes	complemented
72	C₂₃×#435	C₂²	1	2	yes	complemented
73	C₈×D₄×C₂₃	C₂²	1	1	yes	characteristic
74	C₈×D₄×C₂₃	C₂²	1	1	yes	characteristic
75	C₈×D₄×C₂₃	C₂²	1	2	yes	—
76	C₈×D₄×C₂₃	C₂²	1	1	yes	characteristic
77	C₈×D₄×C₂₃	C₂²	1	2	yes	—
78	C₈×D₄×C₂₃	C₂²	1	1	yes	characteristic
79	C₈×D₄×C₂₃	C₂²	1	1	yes	characteristic
80	C₈×D₄×C₂₃	C₂²	1	1	yes	characteristic
81	C₈×D₄×C₂₃	C₂²	1	2	yes	complemented
82	C₈×D₄×C₂₃	C₂²	1	2	yes	complemented
83	C₈×D₄×C₂₃	C₂²	1	2	yes	complemented
84	C₈×D₄×C₂₃	C₂²	1	2	yes	complemented
85	C₈×D₄×C₂₃	C₂²	1	2	yes	complemented
86	C₈×D₄×C₂₃	C₂²	1	2	yes	complemented
87	C₂₃×#433	C₂²	1	1	yes	characteristic
88	C₂₃×#433	C₂²	1	2	yes	—
89	C₂₃×#433	C₂²	1	2	yes	—
90	C₂₃×#433	C₂²	1	2	yes	—
91	C₂₃×#433	C₂²	1	1	yes	characteristic
92	C₂₃×#433	C₂²	1	2	yes	—
93	C₂₃×#433	C₂²	1	2	yes	—
94	C₂₃×#433	C₂²	1	2	yes	complemented
95	C₂₃×#433	C₂²	1	2	yes	complemented
96	C₂₃×#433	C₂²	1	2	yes	complemented
97	C₂₃×#433	C₂²	1	2	yes	complemented
98	C₂₃×#433	C₂²	1	1	yes	characteristic, complemented
99	C₂₃×#433	C₂²	1	1	yes	characteristic, complemented
100	C₂₃×#433	C₂²	1	2	yes	complemented
101	C₂₃×#432	C₂²	1	1	yes	characteristic
102	C₂₃×#432	C₂²	1	2	yes	complemented
103	C₂₃×#432	C₂²	1	2	yes	complemented
104	C₂₃×#432	C₂²	1	1	yes	characteristic, complemented
105	C₂₃×#431	C₂²	1	1	yes	characteristic
106	C₂₃×#431	C₂²	1	1	yes	characteristic
107	C₂₃×#431	C₂²	1	1	yes	characteristic
108	C₂₃×#431	C₂²	1	1	yes	characteristic, complemented
109	C₂₃×#431	C₂²	1	1	yes	characteristic, complemented
110	C₂₃×#431	C₂²	1	2	yes	complemented
111	C₂₃×#431	C₂²	1	2	yes	complemented
112	C₂₃×#431	C₂²	1	1	yes	characteristic, complemented
113	C₂₃×#424	C₂²	1	1	yes	characteristic, complemented
114	C₂₃×#424	C₂²	1	1	yes	characteristic, complemented
115	C₂₃×#424	C₂²	1	2	yes	complemented
116	C₂₃×#424	C₂²	1	2	yes	complemented
117	C₂₃×#423	C₂²	1	1	yes	characteristic, complemented
118	C₂×C₂₃×C₄⋊C₈	C₂²	1	2	yes	complemented
119	C₂×C₂₃×C₄⋊C₈	C₂²	1	2	yes	complemented
120	C₂×C₂₃×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
121	C₂₃×#408	C₂²	1	1	yes	characteristic
122	C₂₃×#408	C₂²	1	1	yes	characteristic
123	C₂₃×#408	C₂²	1	2	yes	—
124	C₂₃×#407	C₂²	1	2	yes	—
125	C₂×C₂₃×C₂²⋊C₈	C₂²	1	2	yes	—
126	C₂×C₂₃×C₂²⋊C₈	C₂²	1	2	yes	—
127	C₂×C₂₃×C₂²⋊C₈	C₂²	1	2	yes	—
128	C₂₃×#405	C₂²	1	2	yes	complemented
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, complemented
132	C₂×C₂₃×#97	C₂²	1	2	yes	complemented
133	C₂×C₄×C₈×C₂₃	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	1	yes	characteristic
138	C₂²×D₄×C₂₃	C₂×C₄	1	1	yes	characteristic
139	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
140	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
141	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
142	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
143	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
144	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
145	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
146	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
147	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
148	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
149	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
150	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
151	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
152	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
153	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
154	C₂₃×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
155	C₂₃×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
156	C₂₃×#126	C₂×C₄	1	2	yes	—
157	C₂₃×#126	C₂×C₄	1	2	yes	—
158	C₂₃×#126	C₂×C₄	1	2	yes	—
159	C₂₃×#126	C₂×C₄	1	2	yes	—
160	C₂₃×#126	C₂×C₄	1	2	yes	—
161	C₂₃×#126	C₂×C₄	1	2	yes	—
162	C₂₃×#125	C₂×C₄	1	2	yes	—
163	C₂₃×#125	C₂×C₄	1	2	yes	—
164	C₂₃×#125	C₂×C₄	1	2	yes	—
165	C₂₃×#125	C₂×C₄	1	1	yes	characteristic
166	C₂₃×#125	C₂×C₄	1	1	yes	characteristic
167	C₂₃×#124	C₂×C₄	1	2	yes	—
168	C₂₃×#124	C₂×C₄	1	2	yes	—
169	C₂₃×#124	C₂×C₄	1	1	yes	characteristic
170	C₂₃×#124	C₂×C₄	1	1	yes	characteristic
171	C₂₃×#123	C₂×C₄	1	2	yes	—
172	C₂₃×#123	C₂×C₄	1	2	yes	—
173	C₂₃×#123	C₂×C₄	1	2	yes	—
174	C₂₃×#123	C₂×C₄	1	2	yes	—
175	C₂₃×#123	C₂×C₄	1	2	yes	—
176	C₂₃×#123	C₂×C₄	1	2	yes	—
177	C₂₃×#123	C₂×C₄	1	2	yes	—
178	C₂₃×#123	C₂×C₄	1	2	yes	—
179	C₂₃×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
180	C₂₃×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
181	C₂₃×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
182	C₂₃×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
183	C₂₃×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
184	C₂₃×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
185	C₂₃×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
186	C₂₃×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
187	C₂₃×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
188	C₂₃×#121	C₂×C₄	1	2	yes	—
189	C₂₃×#121	C₂×C₄	1	2	yes	—
190	C₂₃×#121	C₂×C₄	1	2	yes	—
191	C₂₃×#121	C₂×C₄	1	2	yes	—
192	C₂₃×#121	C₂×C₄	1	1	yes	characteristic
193	C₂₃×#121	C₂×C₄	1	1	yes	characteristic
194	C₂₃×#120	C₂×C₄	1	2	yes	—
195	C₂₃×#120	C₂×C₄	1	2	yes	—
196	C₄×Q₈×C₂₃	C₂×C₄	1	1	yes	characteristic
197	C₄×Q₈×C₂₃	C₂×C₄	1	1	yes	characteristic
198	C₄×Q₈×C₂₃	C₂×C₄	1	1	yes	characteristic
199	C₄×Q₈×C₂₃	C₂×C₄	1	1	yes	characteristic
200	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
201	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
202	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
203	C₄×D₄×C₂₃	C₂×C₄	1	1	yes	characteristic
204	C₄×D₄×C₂₃	C₂×C₄	1	1	yes	characteristic
205	C₄×D₄×C₂₃	C₂×C₄	1	1	yes	characteristic
206	C₄×D₄×C₂₃	C₂×C₄	1	1	yes	characteristic
207	C₄×D₄×C₂₃	C₂×C₄	1	2	yes	—
208	C₄×D₄×C₂₃	C₂×C₄	1	2	yes	—
209	C₄×D₄×C₂₃	C₂×C₄	1	2	yes	—
210	C₄×D₄×C₂₃	C₂×C₄	1	1	yes	characteristic
211	C₄×D₄×C₂₃	C₂×C₄	1	1	yes	characteristic
212	C₄×D₄×C₂₃	C₂×C₄	1	1	yes	characteristic
213	C₄×D₄×C₂₃	C₂×C₄	1	1	yes	characteristic
214	C₄×D₄×C₂₃	C₂×C₄	1	1	yes	characteristic
215	C₄×D₄×C₂₃	C₂×C₄	1	1	yes	characteristic
216	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
217	C₄×D₄×C₂₃	C₂³	1	2	yes	—
218	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
219	C₄×D₄×C₂₃	C₂³	1	2	yes	—
220	C₄×D₄×C₂₃	C₂³	1	2	yes	—
221	C₄×D₄×C₂₃	C₂³	1	2	yes	—
222	C₄×D₄×C₂₃	C₂³	1	2	yes	—
223	C₂₃×#117	C₂×C₄	1	2	yes	—
224	C₂₃×#117	C₂×C₄	1	2	yes	—
225	C₂₃×#117	C₂×C₄	1	2	yes	—
226	C₂₃×#117	C₂×C₄	1	2	yes	—
227	C₂₃×#117	C₂×C₄	1	2	yes	—
228	C₂₃×#117	C₂×C₄	1	1	yes	characteristic
229	C₂₃×#117	C₂×C₄	1	1	yes	characteristic
230	C₂₃×#117	C₂×C₄	1	2	yes	—
231	C₂₃×#117	C₂³	1	2	yes	—
232	C₂₃×#117	C₂³	1	1	yes	characteristic
233	C₂₃×#117	C₂³	1	2	yes	—
234	C₂₃×#117	C₂³	1	1	yes	characteristic
235	C₂₃×#117	C₂³	1	1	yes	characteristic
236	C₂₃×#117	C₂³	1	2	yes	—
237	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	2	yes	—
238	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
239	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	2	yes	—
240	C₂×C₂²⋊C₄×C₂₃	C₂×C₄	1	2	yes	—
241	C₂×C₂²⋊C₄×C₂₃	C₂×C₄	1	2	yes	—
242	C₂×C₂²⋊C₄×C₂₃	C₂×C₄	1	2	yes	—
243	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
244	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
245	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
246	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
247	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
248	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
249	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
250	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
251	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
252	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
253	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
254	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
255	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
256	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
257	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
258	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
259	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
260	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
261	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
262	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
263	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
264	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
265	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
266	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
267	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
268	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
269	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
270	C₂₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
271	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
272	C₂₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
273	C₂₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
274	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
275	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
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	2	yes	—
280	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
281	C₂₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
282	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
283	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
284	C₂₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
285	C₂₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
286	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
287	C₂₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
288	C₂₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
289	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
290	C₂₃×#97	C₂³	1	1	yes	characteristic
291	C₂₃×#97	C₂³	1	2	yes	—
292	C₂₃×#97	C₂³	1	2	yes	—
293	C₂₃×#97	C₂³	1	2	yes	—
294	C₂₃×#97	C₂³	1	1	yes	characteristic
295	C₂₃×#97	C₂³	1	2	yes	—
296	C₂₃×#97	C₂³	1	2	yes	—
297	C₂₃×#97	C₂³	1	2	yes	—
298	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
299	C₄×C₈×C₂₃	C₂³	1	2	yes	—
300	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
301	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
302	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
303	C₄×C₈×C₂₃	C₂³	1	2	yes	—
304	C₄×C₈×C₂₃	C₂³	1	2	yes	—
305	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
306	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
307	C₄×C₈×C₂₃	C₂³	1	2	yes	—
308	C₄×C₈×C₂₃	C₂³	1	2	yes	—
309	C₄×C₈×C₂₃	C₂³	1	2	yes	—
310	C₂⁴×C₂₃	C₂²×C₄	1	2	yes	—
311	#41×C₂₃	—	2	4	no	—
312	#41×C₂₃	—	2	4	no	—
313	#41×C₂₃	—	4	1	no	—
314	#41×C₂₃	—	4	1	no	—
315	C₂×Q₈×C₂₃	C₂²×C₄	1	1	yes	characteristic
316	C₂×Q₈×C₂₃	C₂²×C₄	1	1	yes	characteristic
317	C₂×Q₈×C₂₃	C₂²×C₄	1	1	yes	characteristic
318	C₂×Q₈×C₂₃	C₂²×C₄	1	2	yes	—
319	C₂×D₄×C₂₃	—	2	4	no	—
320	C₂×D₄×C₂₃	C₂²×C₄	1	2	yes	—
321	C₂×D₄×C₂₃	C₂²×C₄	1	2	yes	—
322	C₂×D₄×C₂₃	C₂²×C₄	1	2	yes	—
323	C₂×D₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
324	C₂×D₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
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	2	yes	—
328	C₂×D₄×C₂₃	C₂²×C₄	1	2	yes	—
329	C₂×D₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
330	C₂²×C₄×C₂₃	—	4	2	no	—
331	C₂²×C₄×C₂₃	—	4	2	no	—
332	C₂²×C₄×C₂₃	C₂²×C₄	1	2	yes	—
333	C₂²×C₄×C₂₃	C₂²×C₄	1	2	yes	—
334	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
335	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
336	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
337	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
338	C₂²×C₄×C₂₃	C₂²×C₄	1	2	yes	—
339	C₂²×C₄×C₂₃	C₂²×C₄	1	2	yes	—
340	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
341	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
342	C₂²×C₄×C₂₃	C₂²×C₄	1	2	yes	—
343	C₂²×C₄×C₂₃	C₂²×C₄	1	2	yes	—
344	C₂²×C₄×C₂₃	C₂²×C₄	1	2	yes	—
345	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
346	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
347	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
348	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
349	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
350	M₁₆×C₂₃	—	4	1	no	—
351	M₁₆×C₂₃	—	4	2	no	—
352	M₁₆×C₂₃	—	4	2	no	—
353	M₁₆×C₂₃	—	4	1	no	—
354	M₁₆×C₂₃	—	4	2	no	—
355	C₂×C₈×C₂₃	—	4	2	no	—
356	C₂×C₈×C₂₃	—	4	1	no	—
357	C₂×C₈×C₂₃	—	4	2	no	—
358	C₂×C₈×C₂₃	—	4	2	no	—
359	C₂×C₈×C₂₃	—	4	2	no	—
360	C₂×C₈×C₂₃	—	4	2	no	—
361	C₂×C₈×C₂₃	—	4	1	no	—
362	C₂×C₈×C₂₃	—	4	2	no	—
363	C₂×C₈×C₂₃	—	4	2	no	—
364	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
365	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
366	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
367	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
368	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
369	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
370	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
371	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
372	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
373	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
374	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
375	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
376	C₄⋊C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
377	C₄⋊C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
378	C₄⋊C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
379	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
380	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
381	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
382	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
383	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
384	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
385	C₄⋊C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
386	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
387	C₄⋊C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
388	C₄⋊C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
389	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
390	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
391	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
392	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
393	C₄⋊C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
394	C₄⋊C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
395	C₄⋊C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
396	C₄⋊C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
397	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
398	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
399	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
400	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
401	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
402	C₂²⋊C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
403	C₂²⋊C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
404	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
405	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
406	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
407	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
408	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
409	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
410	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
411	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
412	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
413	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
414	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
415	C₂²⋊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	1	yes	characteristic
419	C₂²⋊C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
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	2	yes	—
424	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
425	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
426	C₄²×C₂₃	C₂²×C₄	1	2	yes	—
427	C₄²×C₂₃	C₂²×C₄	1	2	yes	—
428	C₄²×C₂₃	C₂²×C₄	1	2	yes	—
429	C₄²×C₂₃	C₂²×C₄	1	2	yes	—
430	C₄²×C₂₃	C₂²×C₄	1	1	yes	characteristic
431	C₄²×C₂₃	C₂²×C₄	1	1	yes	characteristic
432	C₄²×C₂₃	C₂²×C₄	1	1	yes	characteristic
433	C₄²×C₂₃	C₂²×C₄	1	1	yes	characteristic
434	C₄²×C₂₃	C₂²×C₄	1	1	yes	characteristic
435	C₄²×C₂₃	C₂²×C₄	1	1	yes	characteristic
436	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
437	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
438	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
439	C₄²×C₂₃	C₂⁴	1	2	yes	—
440	C₄²×C₂₃	C₂⁴	1	2	yes	—
441	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
442	#60298	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
443	C₂³×C₂₃	—	2	4	no	—
444	C₂³×C₂₃	—	4	2	no	—
445	C₂³×C₂₃	—	4	2	no	—
446	C₂³×C₂₃	C₂³×C₄	1	2	yes	—
447	C₂³×C₂₃	C₂³×C₄	1	1	yes	characteristic
448	C₂³×C₂₃	C₂³×C₄	1	1	yes	characteristic
449	C₂³×C₂₃	C₂³×C₄	1	1	yes	characteristic
450	C₂³×C₂₃	C₂³×C₄	1	2	yes	—
451	Q₈×C₂₃	—	2	2	no	—
452	Q₈×C₂₃	—	2	2	no	—
453	Q₈×C₂₃	—	4	2	no	—
454	Q₈×C₂₃	—	4	1	no	—
455	D₄×C₂₃	—	2	4	no	—
456	D₄×C₂₃	—	2	4	no	—
457	D₄×C₂₃	—	2	4	no	—
458	D₄×C₂₃	—	2	2	no	—
459	D₄×C₂₃	—	4	2	no	—
460	D₄×C₂₃	—	4	2	no	—
461	D₄×C₂₃	—	4	1	no	—
462	D₄×C₂₃	—	4	1	no	—
463	D₄×C₂₃	—	4	1	no	—
464	D₄×C₂₃	#131	1	4	yes	—
465	C₂×C₄×C₂₃	—	2	4	no	—
466	C₂×C₄×C₂₃	—	2	4	no	—
467	C₂×C₄×C₂₃	—	2	2	no	—
468	C₂×C₄×C₂₃	—	2	2	no	—
469	C₂×C₄×C₂₃	—	2	2	no	—
470	C₂×C₄×C₂₃	—	2	2	no	—
471	C₂×C₄×C₂₃	—	2	2	no	—
472	C₂×C₄×C₂₃	—	2	1	no	—
473	C₂×C₄×C₂₃	—	2	2	no	—
474	C₂×C₄×C₂₃	—	2	2	no	—
475	C₂×C₄×C₂₃	—	2	1	no	—
476	C₂×C₄×C₂₃	—	2	1	no	—
477	C₂×C₄×C₂₃	—	2	1	no	—
478	C₂×C₄×C₂₃	—	2	1	no	—
479	C₂×C₄×C₂₃	—	2	1	no	—
480	C₂×C₄×C₂₃	—	4	2	no	—
481	C₂×C₄×C₂₃	—	4	2	no	—
482	C₂×C₄×C₂₃	—	4	2	no	—
483	C₂×C₄×C₂₃	—	4	1	no	—
484	C₂×C₄×C₂₃	—	4	1	no	—
485	C₂×C₄×C₂₃	—	4	2	no	—
486	C₂×C₄×C₂₃	—	4	2	no	—
487	C₂×C₄×C₂₃	—	4	1	no	—
488	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
489	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
490	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
491	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
492	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
493	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
494	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
495	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
496	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
497	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
498	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
499	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
500	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
501	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
502	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
503	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
504	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
505	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
506	C₈×C₂₃	—	2	1	no	—
507	C₈×C₂₃	—	2	2	no	—
508	C₈×C₂₃	—	2	1	no	—
509	C₈×C₂₃	—	2	1	no	—
510	C₈×C₂₃	—	2	2	no	—
511	C₈×C₂₃	—	2	1	no	—
512	C₈×C₂₃	—	2	1	no	—
513	C₈×C₂₃	—	2	2	no	—
514	C₈×C₂₃	—	2	1	no	—
515	C₈×C₂₃	—	2	1	no	—
516	C₈×C₂₃	—	2	2	no	—
517	C₈×C₂₃	—	2	1	no	—
518	#3475	C₂×C₂₃	1	1	yes	characteristic
519	#2994	C₂×C₂₃	1	2	yes	complemented
520	#2994	C₂×C₂₃	1	1	yes	characteristic, complemented
521	#2993	C₂×C₂₃	1	1	yes	characteristic, complemented
522	#2992	C₂×C₂₃	1	2	yes	complemented
523	#2990	C₂×C₂₃	1	1	yes	characteristic, complemented
524	#2988	C₂×C₂₃	1	1	yes	characteristic, complemented
525	#2986	C₂×C₂₃	1	1	yes	characteristic, complemented
526	#2985	C₂×C₂₃	1	1	yes	characteristic, complemented
527	#2977	C₂×C₂₃	1	2	yes	complemented
528	#2976	C₂×C₂₃	1	2	yes	complemented
529	#2974	C₂×C₂₃	1	1	yes	characteristic, complemented
530	#2972	C₂×C₂₃	1	1	yes	characteristic, complemented
531	#2970	C₂×C₂₃	1	1	yes	characteristic, complemented
532	#2969	C₂×C₂₃	1	1	yes	characteristic, complemented
533	#2968	C₂×C₂₃	1	2	yes	complemented
534	#2966	C₂×C₂₃	1	2	yes	complemented
535	#2966	C₂×C₂₃	1	1	yes	characteristic, complemented
536	C₈×#41	C₂×C₂₃	1	1	yes	characteristic, complemented
537	#2925	C₂×C₂₃	1	1	yes	characteristic, complemented
538	#2924	C₂×C₂₃	1	2	yes	complemented
539	#2922	C₂×C₂₃	1	1	yes	characteristic, complemented
540	C₂×#433	C₂×C₂₃	1	2	yes	complemented
541	C₂²×C₂₃	—	2	2	no	—
542	C₂²×C₂₃	—	2	2	no	—
543	C₂²×C₂₃	—	2	1	no	—
544	C₂²×C₂₃	—	2	2	no	—
545	C₂²×C₂₃	—	2	1	no	—
546	C₂²×C₂₃	—	2	1	no	—
547	C₂²×C₂₃	—	2	1	no	—
548	C₂²×C₂₃	—	2	1	no	—
549	C₂²×C₂₃	—	2	1	no	—
550	C₂²×C₂₃	—	2	2	no	—
551	C₂²×C₂₃	—	2	1	no	—
552	C₂²×C₂₃	—	2	1	no	—
553	C₂²×C₂₃	—	2	1	no	—
554	C₂²×C₂₃	—	2	2	no	—
555	C₂²×C₂₃	—	8	4	no	—
556	C₂²×C₂₃	C₂×#131	1	4	yes	—
557	C₂²×C₂₃	C₂⁴×C₄	1	1	yes	characteristic
558	C₄×C₂₃	—	2	1	no	—
559	C₄×C₂₃	—	2	2	no	—
560	C₄×C₂₃	—	2	2	no	—
561	C₄×C₂₃	—	2	1	no	—
562	C₄×C₂₃	—	2	1	no	—
563	C₄×C₂₃	—	2	1	no	—
564	C₄×C₂₃	—	2	1	no	—
565	C₄×C₂₃	—	2	1	no	—
566	C₄×C₂₃	—	2	2	no	—
567	C₄×C₂₃	—	2	2	no	—
568	C₄×C₂₃	—	2	1	no	—
569	C₄×C₂₃	—	2	1	no	—
570	C₄×C₂₃	—	2	1	no	—
571	C₄×C₂₃	—	2	2	no	—
572	C₄×C₂₃	—	2	2	no	—
573	C₄×C₂₃	—	2	1	no	—
574	C₄×C₂₃	C₂×#131	1	2	yes	—
575	C₄×C₂₃	#585	1	1	yes	characteristic
576	C₄×C₂₃	#585	1	1	yes	characteristic
577	#556	C₄×C₂₃	1	1	yes	characteristic
578	#555	C₄×C₂₃	1	1	yes	characteristic
579	#554	C₄×C₂₃	1	1	yes	characteristic
580	#553	C₄×C₂₃	1	2	yes	—
581	#552	C₄×C₂₃	1	2	yes	—
582	#552	C₄×C₂₃	1	1	yes	characteristic
583	#552	C₄×C₂₃	1	1	yes	characteristic
584	#551	C₄×C₂₃	1	2	yes	—
585	#551	C₄×C₂₃	1	2	yes	—
586	#547	C₄×C₂₃	1	1	yes	characteristic
587	#546	C₄×C₂₃	1	1	yes	characteristic
588	#546	C₄×C₂₃	1	1	yes	characteristic
589	#533	C₂²×C₂₃	1	1	yes	characteristic
590	#529	C₂²×C₂₃	1	2	yes	—
591	#529	C₂²×C₂₃	1	1	yes	characteristic
592	#529	C₂²×C₂₃	1	2	yes	—
593	#529	C₂²×C₂₃	1	1	yes	characteristic
594	#525	C₂²×C₂₃	1	2	yes	—
595	C₄×#41	C₂²×C₂₃	1	1	yes	characteristic
596	C₄×#41	C₂²×C₂₃	1	1	yes	characteristic
597	C₄×#41	C₂²×C₂₃	1	1	yes	characteristic
598	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
599	C₂×#117	C₂²×C₂₃	1	2	yes	—
600	#446	C₂²×C₂₃	1	2	yes	complemented
601	#446	C₂²×C₂₃	1	1	yes	characteristic, complemented
602	#446	C₂²×C₂₃	1	2	yes	complemented
603	#446	C₂²×C₂₃	1	2	yes	complemented
604	#446	C₂²×C₂₃	1	1	yes	characteristic, complemented
605	#446	C₂²×C₂₃	1	1	yes	characteristic, complemented
606	#446	C₂²×C₂₃	1	1	yes	characteristic, complemented
607	C₈×Q₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
608	C₈×Q₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
609	C₈×Q₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
610	C₈×Q₈	C₂²×C₂₃	1	2	yes	complemented
611	C₈×Q₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
612	#436	C₂²×C₂₃	1	1	yes	characteristic
613	#436	C₂²×C₂₃	1	1	yes	characteristic
614	#436	C₂²×C₂₃	1	2	yes	complemented
615	#436	C₂²×C₂₃	1	2	yes	complemented
616	#435	C₂²×C₂₃	1	2	yes	—
617	#435	C₂²×C₂₃	1	2	yes	—
618	#435	C₂²×C₂₃	1	2	yes	complemented
619	#435	C₂²×C₂₃	1	2	yes	complemented
620	#435	C₂²×C₂₃	1	2	yes	complemented
621	#435	C₂²×C₂₃	1	2	yes	complemented
622	#435	C₂²×C₂₃	1	2	yes	complemented
623	#435	C₂²×C₂₃	1	2	yes	complemented
624	#435	C₂²×C₂₃	1	2	yes	complemented
625	#435	C₂²×C₂₃	1	2	yes	complemented
626	C₈×D₄	C₂²×C₂₃	1	1	yes	characteristic
627	C₈×D₄	C₂²×C₂₃	1	1	yes	characteristic
628	C₈×D₄	C₂²×C₂₃	1	2	yes	—
629	C₈×D₄	C₂²×C₂₃	1	1	yes	characteristic
630	C₈×D₄	C₂²×C₂₃	1	2	yes	—
631	C₈×D₄	C₂²×C₂₃	1	1	yes	characteristic
632	C₈×D₄	C₂²×C₂₃	1	1	yes	characteristic
633	C₈×D₄	C₂²×C₂₃	1	1	yes	characteristic
634	C₈×D₄	C₂²×C₂₃	1	2	yes	complemented
635	C₈×D₄	C₂²×C₂₃	1	2	yes	complemented
636	C₈×D₄	C₂²×C₂₃	1	2	yes	complemented
637	C₈×D₄	C₂²×C₂₃	1	2	yes	complemented
638	C₈×D₄	C₂²×C₂₃	1	2	yes	complemented
639	C₈×D₄	C₂²×C₂₃	1	2	yes	complemented
640	#433	C₂²×C₂₃	1	1	yes	characteristic
641	#433	C₂²×C₂₃	1	2	yes	—
642	#433	C₂²×C₂₃	1	2	yes	—
643	#433	C₂²×C₂₃	1	2	yes	—
644	#433	C₂²×C₂₃	1	1	yes	characteristic
645	#433	C₂²×C₂₃	1	2	yes	—
646	#433	C₂²×C₂₃	1	2	yes	—
647	#433	C₂²×C₂₃	1	2	yes	complemented
648	#433	C₂²×C₂₃	1	2	yes	complemented
649	#433	C₂²×C₂₃	1	2	yes	complemented
650	#433	C₂²×C₂₃	1	2	yes	complemented
651	#433	C₂²×C₂₃	1	1	yes	characteristic, complemented
652	#433	C₂²×C₂₃	1	1	yes	characteristic, complemented
653	#433	C₂²×C₂₃	1	2	yes	complemented
654	#432	C₂²×C₂₃	1	1	yes	characteristic
655	#432	C₂²×C₂₃	1	2	yes	complemented
656	#432	C₂²×C₂₃	1	2	yes	complemented
657	#432	C₂²×C₂₃	1	1	yes	characteristic, complemented
658	#431	C₂²×C₂₃	1	1	yes	characteristic
659	#431	C₂²×C₂₃	1	1	yes	characteristic
660	#431	C₂²×C₂₃	1	1	yes	characteristic
661	#431	C₂²×C₂₃	1	1	yes	characteristic, complemented
662	#431	C₂²×C₂₃	1	1	yes	characteristic, complemented
663	#431	C₂²×C₂₃	1	2	yes	complemented
664	#431	C₂²×C₂₃	1	2	yes	complemented
665	#431	C₂²×C₂₃	1	1	yes	characteristic, complemented
666	#424	C₂²×C₂₃	1	1	yes	characteristic, complemented
667	#424	C₂²×C₂₃	1	1	yes	characteristic, complemented
668	#424	C₂²×C₂₃	1	2	yes	complemented
669	#424	C₂²×C₂₃	1	2	yes	complemented
670	#423	C₂²×C₂₃	1	1	yes	characteristic, complemented
671	C₂×C₄⋊C₈	C₂²×C₂₃	1	2	yes	complemented
672	C₂×C₄⋊C₈	C₂²×C₂₃	1	2	yes	complemented
673	C₂×C₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
674	#408	C₂²×C₂₃	1	1	yes	characteristic
675	#408	C₂²×C₂₃	1	1	yes	characteristic
676	#408	C₂²×C₂₃	1	2	yes	—
677	#407	C₂²×C₂₃	1	2	yes	—
678	C₂×C₂²⋊C₈	C₂²×C₂₃	1	2	yes	—
679	C₂×C₂²⋊C₈	C₂²×C₂₃	1	2	yes	—
680	C₂×C₂²⋊C₈	C₂²×C₂₃	1	2	yes	—
681	#405	C₂²×C₂₃	1	2	yes	complemented
682	#405	C₂²×C₂₃	1	2	yes	complemented
683	#405	C₂²×C₂₃	1	2	yes	complemented
684	C₄×M₁₆	C₂²×C₂₃	1	1	yes	characteristic, complemented
685	C₂×#97	C₂²×C₂₃	1	2	yes	complemented
686	C₂×C₄×C₈	C₂²×C₂₃	1	2	yes	complemented
687	C₂×C₄×C₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
688	C₂×C₂₃	—	2	4	no	—
689	C₂×C₂₃	—	4	1	no	—
690	C₂×C₂₃	—	4	1	no	—
691	C₂×C₂₃	—	4	2	no	—
692	C₂×C₂₃	—	4	1	no	—
693	C₂×C₂₃	#3428	1	1	yes	characteristic
694	C₂×C₂₃	C₂²×#131	1	1	yes	characteristic
695	C₂×C₂₃	#3573	1	1	yes	characteristic
696	C₂×#41	C₂×C₄×C₂₃	1	1	yes	characteristic
697	C₂×#41	C₂×C₄×C₂₃	1	1	yes	characteristic
698	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
699	C₂²×D₄	C₂×C₄×C₂₃	1	1	yes	characteristic
700	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
701	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
702	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
703	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
704	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
705	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
706	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
707	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
708	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
709	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
710	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
711	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
712	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
713	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
714	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
715	C₄⋊Q₈	C₂×C₄×C₂₃	1	1	yes	characteristic
716	C₄⋊Q₈	C₂×C₄×C₂₃	1	1	yes	characteristic
717	#126	C₂×C₄×C₂₃	1	2	yes	—
718	#126	C₂×C₄×C₂₃	1	2	yes	—
719	#126	C₂×C₄×C₂₃	1	2	yes	—
720	#126	C₂×C₄×C₂₃	1	2	yes	—
721	#126	C₂×C₄×C₂₃	1	2	yes	—
722	#126	C₂×C₄×C₂₃	1	2	yes	—
723	#125	C₂×C₄×C₂₃	1	2	yes	—
724	#125	C₂×C₄×C₂₃	1	2	yes	—
725	#125	C₂×C₄×C₂₃	1	1	yes	characteristic
726	#125	C₂×C₄×C₂₃	1	1	yes	characteristic
727	#125	C₂×C₄×C₂₃	1	2	yes	—
728	#124	C₂×C₄×C₂₃	1	1	yes	characteristic
729	#124	C₂×C₄×C₂₃	1	1	yes	characteristic
730	#124	C₂×C₄×C₂₃	1	2	yes	—
731	#124	C₂×C₄×C₂₃	1	2	yes	—
732	#123	C₂×C₄×C₂₃	1	2	yes	—
733	#123	C₂×C₄×C₂₃	1	2	yes	—
734	#123	C₂×C₄×C₂₃	1	2	yes	—
735	#123	C₂×C₄×C₂₃	1	2	yes	—
736	#123	C₂×C₄×C₂₃	1	2	yes	—
737	#123	C₂×C₄×C₂₃	1	2	yes	—
738	#123	C₂×C₄×C₂₃	1	2	yes	—
739	#123	C₂×C₄×C₂₃	1	2	yes	—
740	C₂²⋊Q₈	C₂×C₄×C₂₃	1	2	yes	—
741	C₂²⋊Q₈	C₂×C₄×C₂₃	1	2	yes	—
742	C₂²⋊Q₈	C₂×C₄×C₂₃	1	1	yes	characteristic
743	C₂²⋊Q₈	C₂×C₄×C₂₃	1	1	yes	characteristic
744	C₂²⋊Q₈	C₂×C₄×C₂₃	1	2	yes	—
745	C₂²⋊Q₈	C₂×C₄×C₂₃	1	2	yes	—
746	C₂²⋊Q₈	C₂×C₄×C₂₃	1	1	yes	characteristic
747	C₂²⋊Q₈	C₂×C₄×C₂₃	1	1	yes	characteristic
748	C₂²⋊Q₈	C₂×C₄×C₂₃	1	2	yes	—
749	#121	C₂×C₄×C₂₃	1	2	yes	—
750	#121	C₂×C₄×C₂₃	1	2	yes	—
751	#121	C₂×C₄×C₂₃	1	2	yes	—
752	#121	C₂×C₄×C₂₃	1	2	yes	—
753	#121	C₂×C₄×C₂₃	1	1	yes	characteristic
754	#121	C₂×C₄×C₂₃	1	1	yes	characteristic
755	#120	C₂×C₄×C₂₃	1	2	yes	—
756	#120	C₂×C₄×C₂₃	1	2	yes	—
757	C₄×Q₈	C₂×C₄×C₂₃	1	1	yes	characteristic
758	C₄×Q₈	C₂×C₄×C₂₃	1	1	yes	characteristic
759	C₄×Q₈	C₂×C₄×C₂₃	1	1	yes	characteristic
760	C₄×Q₈	C₂×C₄×C₂₃	1	1	yes	characteristic
761	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
762	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
763	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
764	C₄×D₄	C₂×C₄×C₂₃	1	1	yes	characteristic
765	C₄×D₄	C₂×C₄×C₂₃	1	2	yes	—
766	C₄×D₄	C₂×C₄×C₂₃	1	1	yes	characteristic
767	C₄×D₄	C₂×C₄×C₂₃	1	1	yes	characteristic
768	C₄×D₄	C₂×C₄×C₂₃	1	1	yes	characteristic
769	C₄×D₄	C₂×C₄×C₂₃	1	1	yes	characteristic
770	C₄×D₄	C₂×C₄×C₂₃	1	1	yes	characteristic
771	C₄×D₄	C₂×C₄×C₂₃	1	1	yes	characteristic
772	C₄×D₄	C₂×C₄×C₂₃	1	1	yes	characteristic
773	C₄×D₄	C₂×C₄×C₂₃	1	1	yes	characteristic
774	C₄×D₄	C₂×C₄×C₂₃	1	2	yes	—
775	C₄×D₄	C₂×C₄×C₂₃	1	2	yes	—
776	C₄×D₄	C₂×C₄×C₂₃	1	1	yes	characteristic
777	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
778	C₄×D₄	C₂³×C₂₃	1	2	yes	—
779	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
780	C₄×D₄	C₂³×C₂₃	1	2	yes	—
781	C₄×D₄	C₂³×C₂₃	1	2	yes	—
782	C₄×D₄	C₂³×C₂₃	1	2	yes	—
783	C₄×D₄	C₂³×C₂₃	1	2	yes	—
784	#117	C₂×C₄×C₂₃	1	2	yes	—
785	#117	C₂×C₄×C₂₃	1	2	yes	—
786	#117	C₂×C₄×C₂₃	1	2	yes	—
787	#117	C₂×C₄×C₂₃	1	2	yes	—
788	#117	C₂×C₄×C₂₃	1	2	yes	—
789	#117	C₂×C₄×C₂₃	1	2	yes	—
790	#117	C₂×C₄×C₂₃	1	1	yes	characteristic
791	#117	C₂×C₄×C₂₃	1	1	yes	characteristic
792	#117	C₂³×C₂₃	1	1	yes	characteristic
793	#117	C₂³×C₂₃	1	2	yes	—
794	#117	C₂³×C₂₃	1	2	yes	—
795	#117	C₂³×C₂₃	1	2	yes	—
796	#117	C₂³×C₂₃	1	1	yes	characteristic
797	#117	C₂³×C₂₃	1	1	yes	characteristic
798	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	2	yes	—
799	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	2	yes	—
800	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
801	C₂×C₂²⋊C₄	C₂×C₄×C₂₃	1	2	yes	—
802	C₂×C₂²⋊C₄	C₂×C₄×C₂₃	1	2	yes	—
803	C₂×C₂²⋊C₄	C₂×C₄×C₂₃	1	2	yes	—
804	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
805	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
806	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
807	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
808	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
809	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
810	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
811	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
812	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
813	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
814	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
815	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
816	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
817	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
818	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
819	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
820	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
821	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
822	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
823	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
824	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
825	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
826	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
827	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
828	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
829	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
830	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
831	C₂²⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
832	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
833	C₂²⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
834	C₂²⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
835	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
836	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
837	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
838	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
839	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
840	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
841	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
842	C₂²⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
843	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
844	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
845	C₂²⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
846	C₂²⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
847	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
848	C₂²⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
849	C₂²⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
850	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
851	#97	C₂³×C₂₃	1	1	yes	characteristic
852	#97	C₂³×C₂₃	1	2	yes	—
853	#97	C₂³×C₂₃	1	2	yes	—
854	#97	C₂³×C₂₃	1	2	yes	—
855	#97	C₂³×C₂₃	1	1	yes	characteristic
856	#97	C₂³×C₂₃	1	2	yes	—
857	#97	C₂³×C₂₃	1	2	yes	—
858	#97	C₂³×C₂₃	1	2	yes	—
859	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
860	C₄×C₈	C₂³×C₂₃	1	2	yes	—
861	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
862	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
863	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
864	C₄×C₈	C₂³×C₂₃	1	2	yes	—
865	C₄×C₈	C₂³×C₂₃	1	2	yes	—
866	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
867	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
868	C₄×C₈	C₂³×C₂₃	1	2	yes	—
869	C₄×C₈	C₂³×C₂₃	1	2	yes	—
870	C₄×C₈	C₂³×C₂₃	1	2	yes	—
871	C₂₃	#60298	1	1	yes	characteristic, direct product factor, Sylow
872	C₂⁴	C₂²×C₄×C₂₃	1	2	yes	—
873	#41	—	2	4	no	—
874	#41	—	2	4	no	—
875	#41	—	4	1	no	—
876	#41	—	4	1	no	—
877	C₂×Q₈	C₂²×C₄×C₂₃	1	1	yes	characteristic
878	C₂×Q₈	C₂²×C₄×C₂₃	1	1	yes	characteristic
879	C₂×Q₈	C₂²×C₄×C₂₃	1	1	yes	characteristic
880	C₂×Q₈	C₂²×C₄×C₂₃	1	2	yes	—
881	C₂×D₄	—	2	4	no	—
882	C₂×D₄	C₂²×C₄×C₂₃	1	2	yes	—
883	C₂×D₄	C₂²×C₄×C₂₃	1	2	yes	—
884	C₂×D₄	C₂²×C₄×C₂₃	1	2	yes	—
885	C₂×D₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
886	C₂×D₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
887	C₂×D₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
888	C₂×D₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
889	C₂×D₄	C₂²×C₄×C₂₃	1	2	yes	—
890	C₂×D₄	C₂²×C₄×C₂₃	1	2	yes	—
891	C₂×D₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
892	C₂²×C₄	—	4	2	no	—
893	C₂²×C₄	—	4	2	no	—
894	C₂²×C₄	C₂²×C₄×C₂₃	1	2	yes	—
895	C₂²×C₄	C₂²×C₄×C₂₃	1	2	yes	—
896	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
897	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
898	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
899	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
900	C₂²×C₄	C₂²×C₄×C₂₃	1	2	yes	—
901	C₂²×C₄	C₂²×C₄×C₂₃	1	2	yes	—
902	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
903	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
904	C₂²×C₄	C₂²×C₄×C₂₃	1	2	yes	—
905	C₂²×C₄	C₂²×C₄×C₂₃	1	2	yes	—
906	C₂²×C₄	C₂²×C₄×C₂₃	1	2	yes	—
907	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
908	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
909	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
910	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
911	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
912	M₁₆	—	4	1	no	—
913	M₁₆	—	4	2	no	—
914	M₁₆	—	4	2	no	—
915	M₁₆	—	4	1	no	—
916	M₁₆	—	4	2	no	—
917	C₂×C₈	—	4	2	no	—
918	C₂×C₈	—	4	1	no	—
919	C₂×C₈	—	4	2	no	—
920	C₂×C₈	—	4	2	no	—
921	C₂×C₈	—	4	2	no	—
922	C₂×C₈	—	4	2	no	—
923	C₂×C₈	—	4	1	no	—
924	C₂×C₈	—	4	2	no	—
925	C₂×C₈	—	4	2	no	—
926	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
927	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
928	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
929	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
930	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
931	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
932	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
933	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
934	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
935	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
936	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
937	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
938	C₄⋊C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
939	C₄⋊C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
940	C₄⋊C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
941	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
942	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
943	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
944	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
945	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
946	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
947	C₄⋊C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
948	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
949	C₄⋊C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
950	C₄⋊C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
951	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
952	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
953	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
954	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
955	C₄⋊C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
956	C₄⋊C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
957	C₄⋊C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
958	C₄⋊C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
959	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
960	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
961	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
962	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
963	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
964	C₂²⋊C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
965	C₂²⋊C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
966	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
967	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
968	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
969	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
970	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
971	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
972	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
973	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
974	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
975	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
976	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
977	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
978	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
979	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
980	C₂²⋊C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
981	C₂²⋊C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
982	C₂²⋊C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
983	C₂²⋊C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
984	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
985	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
986	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
987	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
988	C₄²	C₂²×C₄×C₂₃	1	2	yes	—
989	C₄²	C₂²×C₄×C₂₃	1	2	yes	—
990	C₄²	C₂²×C₄×C₂₃	1	2	yes	—
991	C₄²	C₂²×C₄×C₂₃	1	2	yes	—
992	C₄²	C₂²×C₄×C₂₃	1	1	yes	characteristic
993	C₄²	C₂²×C₄×C₂₃	1	1	yes	characteristic
994	C₄²	C₂²×C₄×C₂₃	1	1	yes	characteristic
995	C₄²	C₂²×C₄×C₂₃	1	1	yes	characteristic
996	C₄²	C₂²×C₄×C₂₃	1	1	yes	characteristic
997	C₄²	C₂²×C₄×C₂₃	1	1	yes	characteristic
998	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
999	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
1000	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
1001	C₄²	C₂⁴×C₂₃	1	2	yes	—
1002	C₄²	C₂⁴×C₂₃	1	2	yes	—
1003	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
1004	C₂³	—	2	4	no	—
1005	C₂³	—	4	2	no	—
1006	C₂³	—	4	2	no	—
1007	C₂³	C₂³×C₄×C₂₃	1	2	yes	—
1008	C₂³	C₂³×C₄×C₂₃	1	1	yes	characteristic
1009	C₂³	C₂³×C₄×C₂₃	1	1	yes	characteristic
1010	C₂³	C₂³×C₄×C₂₃	1	1	yes	characteristic
1011	C₂³	C₂³×C₄×C₂₃	1	2	yes	—
1012	Q₈	—	2	2	no	—
1013	Q₈	—	2	2	no	—
1014	Q₈	—	4	1	no	—
1015	Q₈	—	4	2	no	—
1016	D₄	—	2	4	no	—
1017	D₄	—	2	4	no	—
1018	D₄	—	2	4	no	—
1019	D₄	—	2	2	no	—
1020	D₄	—	4	1	no	—
1021	D₄	—	4	1	no	—
1022	D₄	—	4	1	no	—
1023	D₄	—	4	2	no	—
1024	D₄	—	4	2	no	—
1025	D₄	C₂₃×#131	1	4	yes	—
1026	C₂×C₄	—	2	4	no	—
1027	C₂×C₄	—	2	4	no	—
1028	C₂×C₄	—	2	2	no	—
1029	C₂×C₄	—	2	2	no	—
1030	C₂×C₄	—	2	2	no	—
1031	C₂×C₄	—	2	2	no	—
1032	C₂×C₄	—	2	2	no	—
1033	C₂×C₄	—	2	1	no	—
1034	C₂×C₄	—	2	2	no	—
1035	C₂×C₄	—	2	2	no	—
1036	C₂×C₄	—	2	1	no	—
1037	C₂×C₄	—	2	1	no	—
1038	C₂×C₄	—	2	1	no	—
1039	C₂×C₄	—	2	1	no	—
1040	C₂×C₄	—	2	1	no	—
1041	C₂×C₄	—	4	2	no	—
1042	C₂×C₄	—	4	2	no	—
1043	C₂×C₄	—	4	2	no	—
1044	C₂×C₄	—	4	1	no	—
1045	C₂×C₄	—	4	1	no	—
1046	C₂×C₄	—	4	2	no	—
1047	C₂×C₄	—	4	2	no	—
1048	C₂×C₄	—	4	1	no	—
1049	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
1050	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
1051	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
1052	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
1053	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
1054	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
1055	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
1056	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
1057	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
1058	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
1059	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
1060	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
1061	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
1062	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
1063	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
1064	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
1065	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
1066	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
1067	C₈	—	2	1	no	—
1068	C₈	—	2	2	no	—
1069	C₈	—	2	1	no	—
1070	C₈	—	2	1	no	—
1071	C₈	—	2	2	no	—
1072	C₈	—	2	1	no	—
1073	C₈	—	2	1	no	—
1074	C₈	—	2	2	no	—
1075	C₈	—	2	1	no	—
1076	C₈	—	2	1	no	—
1077	C₈	—	2	2	no	—
1078	C₈	—	2	1	no	—
1079	C₂²	—	2	2	no	—
1080	C₂²	—	2	2	no	—
1081	C₂²	—	2	1	no	—
1082	C₂²	—	2	2	no	—
1083	C₂²	—	2	1	no	—
1084	C₂²	—	2	1	no	—
1085	C₂²	—	2	1	no	—
1086	C₂²	—	2	1	no	—
1087	C₂²	—	2	1	no	—
1088	C₂²	—	2	2	no	—
1089	C₂²	—	2	1	no	—
1090	C₂²	—	2	1	no	—
1091	C₂²	—	2	1	no	—
1092	C₂²	—	2	2	no	—
1093	C₂²	—	8	4	no	—
1094	C₂²	C₂×C₂₃×#131	1	4	yes	—
1095	C₂²	C₂⁴×C₄×C₂₃	1	1	yes	characteristic
1096	C₄	—	2	1	no	—
1097	C₄	—	2	2	no	—
1098	C₄	—	2	2	no	—
1099	C₄	—	2	1	no	—
1100	C₄	—	2	1	no	—
1101	C₄	—	2	1	no	—
1102	C₄	—	2	1	no	—
1103	C₄	—	2	1	no	—
1104	C₄	—	2	2	no	—
1105	C₄	—	2	2	no	—
1106	C₄	—	2	1	no	—
1107	C₄	—	2	1	no	—
1108	C₄	—	2	1	no	—
1109	C₄	—	2	2	no	—
1110	C₄	—	2	2	no	—
1111	C₄	—	2	1	no	—
1112	C₄	C₂×C₂₃×#131	1	2	yes	—
1113	C₄	C₂₃×#585	1	1	yes	characteristic
1114	C₄	C₂₃×#585	1	1	yes	characteristic
1115	C₂	—	2	4	no	—
1116	C₂	—	4	1	no	—
1117	C₂	—	4	2	no	—
1118	C₂	—	4	1	no	—
1119	C₂	—	4	1	no	—
1120	C₂	C₂₃×#3428	1	1	yes	characteristic
1121	C₂	C₂²×C₂₃×#131	1	1	yes	characteristic
1122	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×#3475	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×#2994	C₂	semidirect
3. C₂₃×#2994	C₂	semidirect
4. C₂₃×#2993	C₂	semidirect
5. C₂₃×#2992	C₂	semidirect
6. C₂₃×#2990	C₂	semidirect
7. C₂₃×#2988	C₂	semidirect
8. C₂₃×#2986	C₂	semidirect
9. C₂₃×#2985	C₂	semidirect
10. C₂₃×#2977	C₂	semidirect
11. C₂₃×#2976	C₂	semidirect
12. C₂₃×#2974	C₂	semidirect
13. C₂₃×#2972	C₂	semidirect
14. C₂₃×#2970	C₂	semidirect
15. C₂₃×#2969	C₂	semidirect
16. C₂₃×#2968	C₂	semidirect
17. C₂₃×#2966	C₂	semidirect
18. C₂₃×#2966	C₂	semidirect
19. C₈×#41×C₂₃	C₂	semidirect
20. C₂₃×#2925	C₂	semidirect
21. C₂₃×#2924	C₂	semidirect
22. C₂₃×#2922	C₂	semidirect
23. C₂×C₂₃×#433	C₂	semidirect
47. C₂₃×#446	C₂²	semidirect
48. C₂₃×#446	C₂²	semidirect
49. C₂₃×#446	C₂²	semidirect
50. C₂₃×#446	C₂²	semidirect
51. C₂₃×#446	C₂²	semidirect
52. C₂₃×#446	C₂²	semidirect
53. C₂₃×#446	C₂²	semidirect
54. C₈×Q₈×C₂₃	C₂²	semidirect
55. C₈×Q₈×C₂₃	C₂²	semidirect
56. C₈×Q₈×C₂₃	C₂²	semidirect
57. C₈×Q₈×C₂₃	C₂²	semidirect
58. C₈×Q₈×C₂₃	C₂²	semidirect
61. C₂₃×#436	C₂²	semidirect
62. C₂₃×#436	C₂²	semidirect
65. C₂₃×#435	C₂²	semidirect
66. C₂₃×#435	C₂²	semidirect
67. C₂₃×#435	C₂²	semidirect
68. C₂₃×#435	C₂²	semidirect
69. C₂₃×#435	C₂²	semidirect
70. C₂₃×#435	C₂²	semidirect
71. C₂₃×#435	C₂²	semidirect
72. C₂₃×#435	C₂²	semidirect
81. C₈×D₄×C₂₃	C₂²	semidirect
82. C₈×D₄×C₂₃	C₂²	semidirect
83. C₈×D₄×C₂₃	C₂²	semidirect
84. C₈×D₄×C₂₃	C₂²	semidirect
85. C₈×D₄×C₂₃	C₂²	semidirect
86. C₈×D₄×C₂₃	C₂²	semidirect
94. C₂₃×#433	C₂²	semidirect
95. C₂₃×#433	C₂²	semidirect
96. C₂₃×#433	C₂²	semidirect
97. C₂₃×#433	C₂²	semidirect
98. C₂₃×#433	C₂²	semidirect
99. C₂₃×#433	C₂²	semidirect
100. C₂₃×#433	C₂²	semidirect
102. C₂₃×#432	C₂²	semidirect
103. C₂₃×#432	C₂²	semidirect
104. C₂₃×#432	C₂²	semidirect
108. C₂₃×#431	C₂²	semidirect
109. C₂₃×#431	C₂²	semidirect
110. C₂₃×#431	C₂²	semidirect
111. C₂₃×#431	C₂²	semidirect
112. C₂₃×#431	C₂²	semidirect
113. C₂₃×#424	C₂²	semidirect
114. C₂₃×#424	C₂²	semidirect
115. C₂₃×#424	C₂²	semidirect
116. C₂₃×#424	C₂²	semidirect
117. C₂₃×#423	C₂²	semidirect
118. C₂×C₂₃×C₄⋊C₈	C₂²	semidirect
119. C₂×C₂₃×C₄⋊C₈	C₂²	semidirect
120. C₂×C₂₃×C₄⋊C₈	C₂²	semidirect
128. C₂₃×#405	C₂²	semidirect
129. C₂₃×#405	C₂²	semidirect
130. C₂₃×#405	C₂²	semidirect
131. C₄×M₁₆×C₂₃	C₂²	semidirect
132. C₂×C₂₃×#97	C₂²	semidirect
133. C₂×C₄×C₈×C₂₃	C₂²	semidirect
134. C₂×C₄×C₈×C₂₃	C₂²	semidirect
442. #60298	C₂₃	direct (N × H)
519. #2994	C₂×C₂₃	semidirect
520. #2994	C₂×C₂₃	semidirect
521. #2993	C₂×C₂₃	semidirect
522. #2992	C₂×C₂₃	semidirect
523. #2990	C₂×C₂₃	semidirect
524. #2988	C₂×C₂₃	semidirect
525. #2986	C₂×C₂₃	semidirect
526. #2985	C₂×C₂₃	semidirect
527. #2977	C₂×C₂₃	semidirect
528. #2976	C₂×C₂₃	semidirect
529. #2974	C₂×C₂₃	semidirect
530. #2972	C₂×C₂₃	semidirect
531. #2970	C₂×C₂₃	semidirect
532. #2969	C₂×C₂₃	semidirect
533. #2968	C₂×C₂₃	semidirect
534. #2966	C₂×C₂₃	semidirect
535. #2966	C₂×C₂₃	semidirect
536. C₈×#41	C₂×C₂₃	semidirect
537. #2925	C₂×C₂₃	semidirect
538. #2924	C₂×C₂₃	semidirect
539. #2922	C₂×C₂₃	semidirect
540. C₂×#433	C₂×C₂₃	semidirect
600. #446	C₂²×C₂₃	semidirect
601. #446	C₂²×C₂₃	semidirect
602. #446	C₂²×C₂₃	semidirect
603. #446	C₂²×C₂₃	semidirect
604. #446	C₂²×C₂₃	semidirect
605. #446	C₂²×C₂₃	semidirect
606. #446	C₂²×C₂₃	semidirect
607. C₈×Q₈	C₂²×C₂₃	semidirect
608. C₈×Q₈	C₂²×C₂₃	semidirect
609. C₈×Q₈	C₂²×C₂₃	semidirect
610. C₈×Q₈	C₂²×C₂₃	semidirect
611. C₈×Q₈	C₂²×C₂₃	semidirect
614. #436	C₂²×C₂₃	semidirect
615. #436	C₂²×C₂₃	semidirect
618. #435	C₂²×C₂₃	semidirect
619. #435	C₂²×C₂₃	semidirect
620. #435	C₂²×C₂₃	semidirect
621. #435	C₂²×C₂₃	semidirect
622. #435	C₂²×C₂₃	semidirect
623. #435	C₂²×C₂₃	semidirect
624. #435	C₂²×C₂₃	semidirect
625. #435	C₂²×C₂₃	semidirect
634. C₈×D₄	C₂²×C₂₃	semidirect
635. C₈×D₄	C₂²×C₂₃	semidirect
636. C₈×D₄	C₂²×C₂₃	semidirect
637. C₈×D₄	C₂²×C₂₃	semidirect
638. C₈×D₄	C₂²×C₂₃	semidirect
639. C₈×D₄	C₂²×C₂₃	semidirect
647. #433	C₂²×C₂₃	semidirect
648. #433	C₂²×C₂₃	semidirect
649. #433	C₂²×C₂₃	semidirect
650. #433	C₂²×C₂₃	semidirect
651. #433	C₂²×C₂₃	semidirect
652. #433	C₂²×C₂₃	semidirect
653. #433	C₂²×C₂₃	semidirect
655. #432	C₂²×C₂₃	semidirect
656. #432	C₂²×C₂₃	semidirect
657. #432	C₂²×C₂₃	semidirect
661. #431	C₂²×C₂₃	semidirect
662. #431	C₂²×C₂₃	semidirect
663. #431	C₂²×C₂₃	semidirect
664. #431	C₂²×C₂₃	semidirect
665. #431	C₂²×C₂₃	semidirect
666. #424	C₂²×C₂₃	semidirect
667. #424	C₂²×C₂₃	semidirect
668. #424	C₂²×C₂₃	semidirect
669. #424	C₂²×C₂₃	semidirect
670. #423	C₂²×C₂₃	semidirect
671. C₂×C₄⋊C₈	C₂²×C₂₃	semidirect
672. C₂×C₄⋊C₈	C₂²×C₂₃	semidirect
673. C₂×C₄⋊C₈	C₂²×C₂₃	semidirect
681. #405	C₂²×C₂₃	semidirect
682. #405	C₂²×C₂₃	semidirect
683. #405	C₂²×C₂₃	semidirect
684. C₄×M₁₆	C₂²×C₂₃	semidirect
685. C₂×#97	C₂²×C₂₃	semidirect
686. C₂×C₄×C₈	C₂²×C₂₃	semidirect
687. C₂×C₄×C₈	C₂²×C₂₃	semidirect
871. C₂₃	#60298	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×#3475	2
C₂₃×#2994	2
C₂₃×#2993	2
C₂₃×#2992	2
C₂₃×#2990	2
C₂₃×#2988	2
C₂₃×#2986	2
C₂₃×#2985	2
C₂₃×#2977	2
C₂₃×#2976	2
C₂₃×#2974	2
C₂₃×#2972	2
C₂₃×#2970	2
C₂₃×#2969	2
C₂₃×#2968	2
C₂₃×#2966	2
C₈×#41×C₂₃	2
C₂₃×#2925	2
C₂₃×#2924	2
C₂₃×#2922	2
C₂×C₂₃×#433	2
#60298	23

Subgroups — C23×#60298 #19207924

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#60298 #19207924