Subgroups — C₂₃×#60272 #19207898

Order 5888.

1832 conjugacy classes of subgroups.

The subgroup lattice has 1176 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×#2995	C₂	1	2	yes	maximal, complemented
3	C₂₃×#2995	C₂	1	2	yes	maximal, complemented
4	C₂₃×#2994	C₂	1	2	yes	maximal, complemented
5	C₂₃×#2993	C₂	1	2	yes	maximal, complemented
6	C₂₃×#2992	C₂	1	2	yes	maximal, complemented
7	C₂₃×#2992	C₂	1	2	yes	maximal, complemented
8	C₂₃×#2990	C₂	1	2	yes	maximal, complemented
9	C₂₃×#2989	C₂	1	2	yes	maximal, complemented
10	C₂₃×#2962	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₃×#2961	C₂	1	1	yes	maximal, characteristic, complemented
12	D₄×M₁₆×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₃×#2933	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₃×#2933	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₃×#2930	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂₃×#2929	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×C₂₃×#435	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂₃×#2924	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂₃×#2924	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂₃×#2923	C₂	1	1	yes	maximal, characteristic, complemented
21	C₂₃×#2906	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂₃×#2905	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂×C₂₃×#424	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₂₃×#131	C₂²	1	1	yes	characteristic
25	C₂×C₂₃×#131	C₂²	1	1	yes	characteristic
26	C₂²×M₁₆×C₂₃	C₂²	1	1	yes	characteristic
27	C₂²×M₁₆×C₂₃	C₂²	1	1	yes	characteristic
28	C₂²×M₁₆×C₂₃	C₂²	1	1	yes	characteristic
29	C₂³×C₈×C₂₃	C₂²	1	1	yes	characteristic
30	C₂₃×#556	C₄	1	1	yes	characteristic
31	C₂₃×#555	C₄	1	1	yes	characteristic
32	C₂₃×#554	C₄	1	1	yes	characteristic
33	C₂₃×#553	C₄	1	1	yes	characteristic
34	C₂₃×#553	C₄	1	1	yes	characteristic
35	C₂₃×#552	C₄	1	1	yes	characteristic
36	C₂₃×#552	C₄	1	1	yes	characteristic
37	C₂₃×#552	C₄	1	2	yes	—
38	C₂₃×#551	C₄	1	2	yes	—
39	C₂₃×#551	C₄	1	2	yes	—
40	C₂₃×#547	C₄	1	1	yes	characteristic
41	C₂₃×#546	C₄	1	2	yes	—
42	C₂₃×#533	C₂²	1	1	yes	characteristic
43	C₂₃×#529	C₂²	1	2	yes	—
44	C₂₃×#529	C₂²	1	2	yes	—
45	C₂₃×#529	C₂²	1	2	yes	—
46	C₂₃×#525	C₂²	1	1	yes	characteristic
47	C₂₃×#525	C₂²	1	1	yes	characteristic
48	C₄×#41×C₂₃	C₂²	1	2	yes	—
49	C₄×#41×C₂₃	C₂²	1	1	yes	characteristic
50	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
51	C₂×C₂₃×#117	C₂²	1	1	yes	characteristic
52	C₂×C₂₃×#117	C₂²	1	1	yes	characteristic
53	C₂₃×#446	C₂²	1	2	yes	complemented
54	C₂₃×#446	C₂²	1	2	yes	complemented
55	C₂₃×#446	C₂²	1	2	yes	complemented
56	C₂₃×#446	C₂²	1	2	yes	complemented
57	C₂₃×#446	C₂²	1	2	yes	complemented
58	C₂₃×#446	C₂²	1	2	yes	complemented
59	C₂₃×#446	C₂²	1	2	yes	complemented
60	C₈×Q₈×C₂₃	C₂²	1	2	yes	complemented
61	C₂₃×#436	C₂²	1	2	yes	—
62	C₂₃×#436	C₂²	1	2	yes	complemented
63	C₂₃×#436	C₂²	1	2	yes	complemented
64	C₂₃×#436	C₂²	1	2	yes	complemented
65	C₂₃×#436	C₂²	1	2	yes	complemented
66	C₂₃×#435	C₂²	1	1	yes	characteristic
67	C₂₃×#435	C₂²	1	1	yes	characteristic
68	C₂₃×#435	C₂²	1	1	yes	characteristic
69	C₂₃×#435	C₂²	1	1	yes	characteristic
70	C₂₃×#435	C₂²	1	1	yes	characteristic
71	C₂₃×#435	C₂²	1	1	yes	characteristic
72	C₂₃×#435	C₂²	1	1	yes	characteristic
73	C₂₃×#435	C₂²	1	1	yes	characteristic
74	C₂₃×#435	C₂²	1	2	yes	—
75	C₂₃×#435	C₂²	1	2	yes	—
76	C₂₃×#435	C₂²	1	2	yes	complemented
77	C₂₃×#435	C₂²	1	2	yes	complemented
78	C₂₃×#435	C₂²	1	2	yes	complemented
79	C₂₃×#435	C₂²	1	2	yes	complemented
80	C₂₃×#435	C₂²	1	2	yes	complemented
81	C₂₃×#435	C₂²	1	2	yes	complemented
82	C₂₃×#435	C₂²	1	2	yes	complemented
83	C₂₃×#435	C₂²	1	2	yes	complemented
84	C₈×D₄×C₂₃	C₂²	1	2	yes	—
85	C₈×D₄×C₂₃	C₂²	1	2	yes	complemented
86	C₈×D₄×C₂₃	C₂²	1	2	yes	complemented
87	C₈×D₄×C₂₃	C₂²	1	2	yes	complemented
88	C₈×D₄×C₂₃	C₂²	1	2	yes	complemented
89	C₂₃×#433	C₂²	1	2	yes	complemented
90	C₂₃×#433	C₂²	1	2	yes	complemented
91	C₂₃×#433	C₂²	1	2	yes	complemented
92	C₂₃×#433	C₂²	1	2	yes	complemented
93	C₂₃×#433	C₂²	1	2	yes	complemented
94	C₂₃×#433	C₂²	1	2	yes	complemented
95	C₂₃×#432	C₂²	1	2	yes	complemented
96	C₂₃×#432	C₂²	1	2	yes	complemented
97	C₂₃×#432	C₂²	1	2	yes	complemented
98	C₂₃×#432	C₂²	1	2	yes	complemented
99	C₂₃×#431	C₂²	1	2	yes	complemented
100	C₂₃×#431	C₂²	1	2	yes	complemented
101	C₂₃×#424	C₂²	1	1	yes	characteristic
102	C₂₃×#424	C₂²	1	1	yes	characteristic
103	C₂₃×#424	C₂²	1	1	yes	characteristic
104	C₂₃×#424	C₂²	1	1	yes	characteristic
105	C₂₃×#424	C₂²	1	1	yes	characteristic
106	C₂₃×#424	C₂²	1	1	yes	characteristic
107	C₂₃×#424	C₂²	1	1	yes	characteristic
108	C₂₃×#424	C₂²	1	1	yes	characteristic
109	C₂₃×#424	C₂²	1	2	yes	complemented
110	C₂₃×#424	C₂²	1	2	yes	complemented
111	C₂₃×#424	C₂²	1	2	yes	complemented
112	C₂₃×#424	C₂²	1	2	yes	complemented
113	C₂₃×#424	C₂²	1	2	yes	complemented
114	C₂₃×#424	C₂²	1	2	yes	complemented
115	C₂₃×#423	C₂²	1	1	yes	characteristic
116	C₂₃×#423	C₂²	1	2	yes	complemented
117	C₂₃×#423	C₂²	1	2	yes	complemented
118	C₂₃×#423	C₂²	1	2	yes	complemented
119	C₂×C₂₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
120	C₂×C₂₃×C₄⋊C₈	C₂²	1	2	yes	complemented
121	C₂×C₂₃×C₄⋊C₈	C₂²	1	2	yes	complemented
122	C₂×C₂₃×C₄⋊C₈	C₂²	1	2	yes	complemented
123	C₂₃×#408	C₂²	1	1	yes	characteristic
124	C₂₃×#408	C₂²	1	1	yes	characteristic
125	C₂₃×#407	C₂²	1	1	yes	characteristic
126	C₂₃×#407	C₂²	1	1	yes	characteristic
127	C₂×C₂₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
128	C₂×C₂₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
129	C₂₃×#405	C₂²	1	1	yes	characteristic
130	C₂₃×#405	C₂²	1	1	yes	characteristic
131	C₂₃×#405	C₂²	1	1	yes	characteristic
132	C₂₃×#405	C₂²	1	1	yes	characteristic
133	C₄×M₁₆×C₂₃	C₂²	1	1	yes	characteristic
134	C₂×C₂₃×#97	C₂²	1	1	yes	characteristic
135	C₂×#41×C₂₃	C₂×C₄	1	2	yes	—
136	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
137	C₂²×D₄×C₂₃	C₂×C₄	1	1	yes	characteristic
138	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
139	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
140	C₂₃×#131	—	4	2	no	—
141	C₂₃×#131	—	4	2	no	—
142	C₂×M₁₆×C₂₃	—	4	2	no	—
143	C₂×M₁₆×C₂₃	—	4	2	no	—
144	C₂×M₁₆×C₂₃	—	4	2	no	—
145	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
146	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
147	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
148	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
149	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
150	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
151	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
152	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
153	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
154	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
155	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
156	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
157	C₂²×C₈×C₂₃	—	4	2	no	—
158	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
159	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
160	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
161	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
162	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
163	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
164	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
165	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
166	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
167	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
168	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
169	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
170	C₂₃×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
171	C₂₃×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
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×#126	C₂×C₄	1	2	yes	—
176	C₂₃×#126	C₂×C₄	1	2	yes	—
177	C₂₃×#126	C₂×C₄	1	2	yes	—
178	C₂₃×#125	C₂×C₄	1	2	yes	—
179	C₂₃×#125	C₂×C₄	1	2	yes	—
180	C₂₃×#125	C₂×C₄	1	1	yes	characteristic
181	C₂₃×#125	C₂×C₄	1	1	yes	characteristic
182	C₂₃×#125	C₂×C₄	1	2	yes	—
183	C₂₃×#124	C₂×C₄	1	2	yes	—
184	C₂₃×#124	C₂×C₄	1	2	yes	—
185	C₂₃×#124	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×#123	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	2	yes	—
198	C₂₃×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
199	C₂₃×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
200	C₂₃×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
201	C₂₃×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
202	C₂₃×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
203	C₂₃×#121	C₂×C₄	1	1	yes	characteristic
204	C₂₃×#121	C₂×C₄	1	1	yes	characteristic
205	C₂₃×#121	C₂×C₄	1	1	yes	characteristic
206	C₂₃×#121	C₂×C₄	1	1	yes	characteristic
207	C₂₃×#121	C₂×C₄	1	2	yes	—
208	C₂₃×#121	C₂×C₄	1	2	yes	—
209	C₂₃×#121	C₂×C₄	1	2	yes	—
210	C₂₃×#120	C₂×C₄	1	2	yes	—
211	C₂₃×#120	C₂×C₄	1	2	yes	—
212	C₄×Q₈×C₂₃	C₂×C₄	1	1	yes	characteristic
213	C₄×Q₈×C₂₃	C₂×C₄	1	2	yes	—
214	C₄×Q₈×C₂₃	C₂×C₄	1	1	yes	characteristic
215	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
216	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
217	C₄×D₄×C₂₃	C₂×C₄	1	1	yes	characteristic
218	C₄×D₄×C₂₃	C₂×C₄	1	1	yes	characteristic
219	C₄×D₄×C₂₃	C₂×C₄	1	2	yes	—
220	C₄×D₄×C₂₃	C₂×C₄	1	2	yes	—
221	C₄×D₄×C₂₃	C₂×C₄	1	2	yes	—
222	C₄×D₄×C₂₃	C₂×C₄	1	1	yes	characteristic
223	C₄×D₄×C₂₃	C₂×C₄	1	1	yes	characteristic
224	C₄×D₄×C₂₃	C₂×C₄	1	2	yes	—
225	C₄×D₄×C₂₃	C₂×C₄	1	1	yes	characteristic
226	C₄×D₄×C₂₃	C₂×C₄	1	2	yes	—
227	C₄×D₄×C₂₃	C₂×C₄	1	1	yes	characteristic
228	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
229	C₄×D₄×C₂₃	C₂³	1	2	yes	—
230	C₄×D₄×C₂₃	C₂³	1	2	yes	—
231	C₄×D₄×C₂₃	C₂³	1	2	yes	—
232	C₄×D₄×C₂₃	C₂³	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	2	yes	—
236	C₂₃×#117	C₂×C₄	1	2	yes	—
237	C₂₃×#117	C₂×C₄	1	2	yes	—
238	C₂₃×#117	C₂×C₄	1	2	yes	—
239	C₂₃×#117	C₂×C₄	1	2	yes	—
240	C₂₃×#117	C₂×C₄	1	1	yes	characteristic
241	C₂₃×#117	C₂×C₄	1	1	yes	characteristic
242	C₂₃×#117	C₂×C₄	1	2	yes	—
243	C₂₃×#117	C₂×C₄	1	1	yes	characteristic
244	C₂₃×#117	C₂×C₄	1	1	yes	characteristic
245	C₂₃×#117	C₂³	1	1	yes	characteristic
246	C₂₃×#117	C₂³	1	1	yes	characteristic
247	C₂₃×#117	C₂³	1	1	yes	characteristic
248	C₂₃×#117	C₂³	1	2	yes	—
249	C₂₃×#117	C₂³	1	2	yes	—
250	C₂₃×#117	C₂³	1	2	yes	—
251	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
252	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
253	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
254	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
255	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
256	C₂×C₂²⋊C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
257	C₂×C₂²⋊C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
258	C₂×C₂²⋊C₄×C₂₃	C₂×C₄	1	2	yes	—
259	C₂×C₂²⋊C₄×C₂₃	C₂×C₄	1	2	yes	—
260	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
261	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
262	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
263	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
264	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
265	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
266	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
267	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
268	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
269	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
270	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
271	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
272	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
273	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
274	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
275	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
276	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
277	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
278	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
279	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
280	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
281	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
282	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
283	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
284	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
285	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
286	C₂₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
287	C₂₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
288	C₂₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
289	C₂₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
290	C₂₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
291	C₂₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
292	C₂₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
293	C₂₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
294	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
295	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
296	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
297	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
298	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
299	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
300	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
301	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
302	C₂₃×#97	C₂³	1	1	yes	characteristic
303	C₂₃×#97	C₂³	1	1	yes	characteristic
304	C₂₃×#97	C₂³	1	1	yes	characteristic
305	C₂₃×#97	C₂³	1	1	yes	characteristic
306	C₂₃×#97	C₂³	1	2	yes	—
307	C₂₃×#97	C₂³	1	2	yes	—
308	C₂₃×#97	C₂³	1	2	yes	—
309	C₂₃×#97	C₂³	1	2	yes	—
310	C₂₃×#97	C₂³	1	2	yes	—
311	C₄×C₈×C₂₃	C₂³	1	2	yes	—
312	C₄×C₈×C₂₃	C₂³	1	2	yes	—
313	C₄×C₈×C₂₃	C₂³	1	2	yes	—
314	C₄×C₈×C₂₃	C₂³	1	2	yes	—
315	C₄×C₈×C₂₃	C₂³	1	2	yes	—
316	C₂⁴×C₂₃	C₂²×C₄	1	1	yes	characteristic
317	C₂⁴×C₂₃	C₂²×C₄	1	1	yes	characteristic
318	#41×C₂₃	—	2	2	no	—
319	#41×C₂₃	—	2	2	no	—
320	#41×C₂₃	—	4	4	no	—
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	2	yes	—
327	C₂×D₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
328	C₂×D₄×C₂₃	C₂²×C₄	1	2	yes	—
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	1	yes	characteristic
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	C₂²×C₄×C₂₃	—	2	2	no	—
336	C₂²×C₄×C₂₃	—	2	2	no	—
337	C₂²×C₄×C₂₃	—	2	2	no	—
338	C₂²×C₄×C₂₃	—	2	2	no	—
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	1	yes	characteristic
343	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
344	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
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	2	yes	—
348	C₂²×C₄×C₂₃	C₂²×C₄	1	2	yes	—
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	2	yes	—
353	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
354	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
355	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
356	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
357	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
358	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
359	M₁₆×C₂₃	—	2	2	no	—
360	M₁₆×C₂₃	—	2	2	no	—
361	M₁₆×C₂₃	—	2	2	no	—
362	M₁₆×C₂₃	—	2	2	no	—
363	M₁₆×C₂₃	—	4	1	no	—
364	M₁₆×C₂₃	—	4	1	no	—
365	M₁₆×C₂₃	—	4	1	no	—
366	M₁₆×C₂₃	—	4	1	no	—
367	M₁₆×C₂₃	—	4	2	no	—
368	M₁₆×C₂₃	—	4	2	no	—
369	M₁₆×C₂₃	—	4	2	no	—
370	M₁₆×C₂₃	—	4	2	no	—
371	C₂×C₈×C₂₃	—	2	2	no	—
372	C₂×C₈×C₂₃	—	2	2	no	—
373	C₂×C₈×C₂₃	—	2	2	no	—
374	C₂×C₈×C₂₃	—	2	2	no	—
375	C₂×C₈×C₂₃	—	4	1	no	—
376	C₂×C₈×C₂₃	—	4	1	no	—
377	C₂×C₈×C₂₃	—	4	1	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	1	yes	characteristic
384	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
385	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
386	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
387	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
388	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
389	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
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	2	yes	—
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	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	1	yes	characteristic
401	C₄⋊C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
402	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
403	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
404	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
405	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
406	C₄⋊C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
407	C₄⋊C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
408	C₄⋊C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
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	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
417	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
418	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
419	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
420	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
421	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
422	C₂²⋊C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
423	C₂²⋊C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
424	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
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	2	yes	—
428	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
429	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
430	C₂²⋊C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
431	C₂²⋊C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
432	C₂²⋊C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
433	C₂²⋊C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
434	C₂²⋊C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
435	C₂²⋊C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
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	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
442	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
443	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
444	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
445	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
446	C₄²×C₂₃	C₂²×C₄	1	2	yes	—
447	C₄²×C₂₃	C₂²×C₄	1	2	yes	—
448	C₄²×C₂₃	C₂²×C₄	1	2	yes	—
449	C₄²×C₂₃	C₂²×C₄	1	2	yes	—
450	C₄²×C₂₃	C₂²×C₄	1	2	yes	—
451	C₄²×C₂₃	C₂²×C₄	1	1	yes	characteristic
452	C₄²×C₂₃	C₂²×C₄	1	1	yes	characteristic
453	C₄²×C₂₃	C₂²×C₄	1	2	yes	—
454	C₄²×C₂₃	C₂⁴	1	2	yes	—
455	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
456	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
457	C₄²×C₂₃	C₂⁴	1	2	yes	—
458	C₄²×C₂₃	C₂⁴	1	2	yes	—
459	#60272	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
460	C₂³×C₂₃	—	2	2	no	—
461	C₂³×C₂₃	—	2	2	no	—
462	C₂³×C₂₃	—	2	2	no	—
463	C₂³×C₂₃	—	4	1	no	—
464	C₂³×C₂₃	—	4	1	no	—
465	C₂³×C₂₃	—	4	1	no	—
466	C₂³×C₂₃	C₂³×C₄	1	1	yes	characteristic
467	C₂³×C₂₃	C₂³×C₄	1	1	yes	characteristic
468	C₂³×C₂₃	C₂³×C₄	1	2	yes	—
469	C₂³×C₂₃	C₂³×C₄	1	1	yes	characteristic
470	C₂³×C₂₃	C₂³×C₄	1	1	yes	characteristic
471	C₂³×C₂₃	C₂³×C₄	1	1	yes	characteristic
472	Q₈×C₂₃	—	2	2	no	—
473	Q₈×C₂₃	—	4	2	no	—
474	Q₈×C₂₃	—	4	2	no	—
475	D₄×C₂₃	—	2	4	no	—
476	D₄×C₂₃	—	2	2	no	—
477	D₄×C₂₃	—	2	2	no	—
478	D₄×C₂₃	—	2	4	no	—
479	D₄×C₂₃	—	2	2	no	—
480	D₄×C₂₃	—	4	1	no	—
481	D₄×C₂₃	—	4	1	no	—
482	D₄×C₂₃	—	4	2	no	—
483	D₄×C₂₃	—	4	2	no	—
484	D₄×C₂₃	—	4	2	no	—
485	C₂×C₄×C₂₃	—	2	2	no	—
486	C₂×C₄×C₂₃	—	2	2	no	—
487	C₂×C₄×C₂₃	—	2	4	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	2	no	—
492	C₂×C₄×C₂₃	—	2	1	no	—
493	C₂×C₄×C₂₃	—	2	1	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	1	no	—
498	C₂×C₄×C₂₃	—	2	1	no	—
499	C₂×C₄×C₂₃	—	2	1	no	—
500	C₂×C₄×C₂₃	—	2	1	no	—
501	C₂×C₄×C₂₃	—	2	2	no	—
502	C₂×C₄×C₂₃	—	4	2	no	—
503	C₂×C₄×C₂₃	—	4	2	no	—
504	C₂×C₄×C₂₃	—	4	2	no	—
505	C₂×C₄×C₂₃	—	4	1	no	—
506	C₂×C₄×C₂₃	—	4	1	no	—
507	C₂×C₄×C₂₃	—	4	2	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	2	yes	—
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	2	yes	—
516	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
517	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
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	2	yes	—
521	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
522	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
523	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
524	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
525	C₂×C₄×C₂₃	H(5,𝔽₂)	1	2	yes	—
526	C₂×C₄×C₂₃	2₋¹⁺⁴	1	2	yes	—
527	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
528	C₈×C₂₃	—	2	1	no	—
529	C₈×C₂₃	—	2	1	no	—
530	C₈×C₂₃	—	2	1	no	—
531	C₈×C₂₃	—	2	1	no	—
532	C₈×C₂₃	—	2	1	no	—
533	C₈×C₂₃	—	2	1	no	—
534	C₈×C₂₃	—	2	2	no	—
535	C₈×C₂₃	—	2	2	no	—
536	C₈×C₂₃	—	2	2	no	—
537	C₈×C₂₃	—	2	1	no	—
538	C₈×C₂₃	—	2	1	no	—
539	C₈×C₂₃	—	2	2	no	—
540	#3475	C₂×C₂₃	1	1	yes	characteristic
541	#2995	C₂×C₂₃	1	2	yes	complemented
542	#2995	C₂×C₂₃	1	2	yes	complemented
543	#2994	C₂×C₂₃	1	2	yes	complemented
544	#2993	C₂×C₂₃	1	2	yes	complemented
545	#2992	C₂×C₂₃	1	2	yes	complemented
546	#2992	C₂×C₂₃	1	2	yes	complemented
547	#2990	C₂×C₂₃	1	2	yes	complemented
548	#2989	C₂×C₂₃	1	2	yes	complemented
549	#2962	C₂×C₂₃	1	1	yes	characteristic, complemented
550	#2961	C₂×C₂₃	1	1	yes	characteristic, complemented
551	D₄×M₁₆	C₂×C₂₃	1	1	yes	characteristic, complemented
552	#2933	C₂×C₂₃	1	1	yes	characteristic, complemented
553	#2933	C₂×C₂₃	1	1	yes	characteristic, complemented
554	#2930	C₂×C₂₃	1	1	yes	characteristic, complemented
555	#2929	C₂×C₂₃	1	1	yes	characteristic, complemented
556	C₂×#435	C₂×C₂₃	1	1	yes	characteristic, complemented
557	#2924	C₂×C₂₃	1	1	yes	characteristic, complemented
558	#2924	C₂×C₂₃	1	1	yes	characteristic, complemented
559	#2923	C₂×C₂₃	1	1	yes	characteristic, complemented
560	#2906	C₂×C₂₃	1	1	yes	characteristic, complemented
561	#2905	C₂×C₂₃	1	1	yes	characteristic, complemented
562	C₂×#424	C₂×C₂₃	1	1	yes	characteristic, complemented
563	C₂²×C₂₃	—	2	1	no	—
564	C₂²×C₂₃	—	2	1	no	—
565	C₂²×C₂₃	—	2	1	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	1	no	—
572	C₂²×C₂₃	—	2	2	no	—
573	C₂²×C₂₃	—	2	1	no	—
574	C₂²×C₂₃	—	2	1	no	—
575	C₂²×C₂₃	—	2	1	no	—
576	C₂²×C₂₃	—	2	2	no	—
577	C₂²×C₂₃	—	2	1	no	—
578	C₂²×C₂₃	—	2	1	no	—
579	C₂²×C₂₃	—	4	4	no	—
580	C₂²×C₂₃	—	8	2	no	—
581	C₂²×C₂₃	#520	1	2	yes	—
582	C₂²×C₂₃	#568	1	2	yes	—
583	C₂²×C₂₃	C₂⁴×C₄	1	1	yes	characteristic
584	C₄×C₂₃	—	2	1	no	—
585	C₄×C₂₃	—	2	1	no	—
586	C₄×C₂₃	—	2	1	no	—
587	C₄×C₂₃	—	2	1	no	—
588	C₄×C₂₃	—	2	2	no	—
589	C₄×C₂₃	—	2	2	no	—
590	C₄×C₂₃	—	2	2	no	—
591	C₄×C₂₃	—	2	1	no	—
592	C₄×C₂₃	—	2	1	no	—
593	C₄×C₂₃	—	2	2	no	—
594	C₄×C₂₃	—	2	1	no	—
595	C₄×C₂₃	—	2	2	no	—
596	C₄×C₂₃	—	2	2	no	—
597	C₄×C₂₃	—	2	2	no	—
598	C₄×C₂₃	—	2	1	no	—
599	C₄×C₂₃	#520	1	2	yes	—
600	C₄×C₂₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
601	C₄×C₂₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
602	C₂×#131	C₂²×C₂₃	1	1	yes	characteristic
603	C₂×#131	C₂²×C₂₃	1	1	yes	characteristic
604	C₂²×M₁₆	C₂²×C₂₃	1	1	yes	characteristic
605	C₂²×M₁₆	C₂²×C₂₃	1	1	yes	characteristic
606	C₂²×M₁₆	C₂²×C₂₃	1	1	yes	characteristic
607	C₂³×C₈	C₂²×C₂₃	1	1	yes	characteristic
608	#556	C₄×C₂₃	1	1	yes	characteristic
609	#555	C₄×C₂₃	1	1	yes	characteristic
610	#554	C₄×C₂₃	1	1	yes	characteristic
611	#553	C₄×C₂₃	1	1	yes	characteristic
612	#553	C₄×C₂₃	1	1	yes	characteristic
613	#552	C₄×C₂₃	1	1	yes	characteristic
614	#552	C₄×C₂₃	1	1	yes	characteristic
615	#552	C₄×C₂₃	1	2	yes	—
616	#551	C₄×C₂₃	1	2	yes	—
617	#551	C₄×C₂₃	1	2	yes	—
618	#547	C₄×C₂₃	1	1	yes	characteristic
619	#546	C₄×C₂₃	1	2	yes	—
620	#533	C₂²×C₂₃	1	1	yes	characteristic
621	#529	C₂²×C₂₃	1	2	yes	—
622	#529	C₂²×C₂₃	1	2	yes	—
623	#529	C₂²×C₂₃	1	2	yes	—
624	#525	C₂²×C₂₃	1	1	yes	characteristic
625	#525	C₂²×C₂₃	1	1	yes	characteristic
626	C₄×#41	C₂²×C₂₃	1	2	yes	—
627	C₄×#41	C₂²×C₂₃	1	1	yes	characteristic
628	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
629	C₂×#117	C₂²×C₂₃	1	1	yes	characteristic
630	C₂×#117	C₂²×C₂₃	1	1	yes	characteristic
631	#446	C₂²×C₂₃	1	2	yes	complemented
632	#446	C₂²×C₂₃	1	2	yes	complemented
633	#446	C₂²×C₂₃	1	2	yes	complemented
634	#446	C₂²×C₂₃	1	2	yes	complemented
635	#446	C₂²×C₂₃	1	2	yes	complemented
636	#446	C₂²×C₂₃	1	2	yes	complemented
637	#446	C₂²×C₂₃	1	2	yes	complemented
638	C₈×Q₈	C₂²×C₂₃	1	2	yes	complemented
639	#436	C₂²×C₂₃	1	2	yes	—
640	#436	C₂²×C₂₃	1	2	yes	complemented
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	#435	C₂²×C₂₃	1	1	yes	characteristic
645	#435	C₂²×C₂₃	1	1	yes	characteristic
646	#435	C₂²×C₂₃	1	1	yes	characteristic
647	#435	C₂²×C₂₃	1	1	yes	characteristic
648	#435	C₂²×C₂₃	1	1	yes	characteristic
649	#435	C₂²×C₂₃	1	1	yes	characteristic
650	#435	C₂²×C₂₃	1	1	yes	characteristic
651	#435	C₂²×C₂₃	1	1	yes	characteristic
652	#435	C₂²×C₂₃	1	2	yes	—
653	#435	C₂²×C₂₃	1	2	yes	—
654	#435	C₂²×C₂₃	1	2	yes	complemented
655	#435	C₂²×C₂₃	1	2	yes	complemented
656	#435	C₂²×C₂₃	1	2	yes	complemented
657	#435	C₂²×C₂₃	1	2	yes	complemented
658	#435	C₂²×C₂₃	1	2	yes	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	C₈×D₄	C₂²×C₂₃	1	2	yes	—
663	C₈×D₄	C₂²×C₂₃	1	2	yes	complemented
664	C₈×D₄	C₂²×C₂₃	1	2	yes	complemented
665	C₈×D₄	C₂²×C₂₃	1	2	yes	complemented
666	C₈×D₄	C₂²×C₂₃	1	2	yes	complemented
667	#433	C₂²×C₂₃	1	2	yes	complemented
668	#433	C₂²×C₂₃	1	2	yes	complemented
669	#433	C₂²×C₂₃	1	2	yes	complemented
670	#433	C₂²×C₂₃	1	2	yes	complemented
671	#433	C₂²×C₂₃	1	2	yes	complemented
672	#433	C₂²×C₂₃	1	2	yes	complemented
673	#432	C₂²×C₂₃	1	2	yes	complemented
674	#432	C₂²×C₂₃	1	2	yes	complemented
675	#432	C₂²×C₂₃	1	2	yes	complemented
676	#432	C₂²×C₂₃	1	2	yes	complemented
677	#431	C₂²×C₂₃	1	2	yes	complemented
678	#431	C₂²×C₂₃	1	2	yes	complemented
679	#424	C₂²×C₂₃	1	1	yes	characteristic
680	#424	C₂²×C₂₃	1	1	yes	characteristic
681	#424	C₂²×C₂₃	1	1	yes	characteristic
682	#424	C₂²×C₂₃	1	1	yes	characteristic
683	#424	C₂²×C₂₃	1	1	yes	characteristic
684	#424	C₂²×C₂₃	1	1	yes	characteristic
685	#424	C₂²×C₂₃	1	1	yes	characteristic
686	#424	C₂²×C₂₃	1	1	yes	characteristic
687	#424	C₂²×C₂₃	1	2	yes	complemented
688	#424	C₂²×C₂₃	1	2	yes	complemented
689	#424	C₂²×C₂₃	1	2	yes	complemented
690	#424	C₂²×C₂₃	1	2	yes	complemented
691	#424	C₂²×C₂₃	1	2	yes	complemented
692	#424	C₂²×C₂₃	1	2	yes	complemented
693	#423	C₂²×C₂₃	1	1	yes	characteristic
694	#423	C₂²×C₂₃	1	2	yes	complemented
695	#423	C₂²×C₂₃	1	2	yes	complemented
696	#423	C₂²×C₂₃	1	2	yes	complemented
697	C₂×C₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
698	C₂×C₄⋊C₈	C₂²×C₂₃	1	2	yes	complemented
699	C₂×C₄⋊C₈	C₂²×C₂₃	1	2	yes	complemented
700	C₂×C₄⋊C₈	C₂²×C₂₃	1	2	yes	complemented
701	#408	C₂²×C₂₃	1	1	yes	characteristic
702	#408	C₂²×C₂₃	1	1	yes	characteristic
703	#407	C₂²×C₂₃	1	1	yes	characteristic
704	#407	C₂²×C₂₃	1	1	yes	characteristic
705	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
706	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
707	#405	C₂²×C₂₃	1	1	yes	characteristic
708	#405	C₂²×C₂₃	1	1	yes	characteristic
709	#405	C₂²×C₂₃	1	1	yes	characteristic
710	#405	C₂²×C₂₃	1	1	yes	characteristic
711	C₄×M₁₆	C₂²×C₂₃	1	1	yes	characteristic
712	C₂×#97	C₂²×C₂₃	1	1	yes	characteristic
713	C₂×C₂₃	—	2	2	no	—
714	C₂×C₂₃	—	2	2	no	—
715	C₂×C₂₃	—	4	2	no	—
716	C₂×C₂₃	—	4	1	no	—
717	C₂×C₂₃	—	4	1	no	—
718	C₂×C₂₃	—	4	1	no	—
719	C₂×C₂₃	C₂×#520	1	1	yes	characteristic
720	C₂×C₂₃	C₂×#568	1	1	yes	characteristic
721	C₂×C₂₃	#3573	1	1	yes	characteristic
722	C₂×#41	C₂×C₄×C₂₃	1	2	yes	—
723	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
724	C₂²×D₄	C₂×C₄×C₂₃	1	1	yes	characteristic
725	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
726	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
727	#131	—	4	2	no	—
728	#131	—	4	2	no	—
729	C₂×M₁₆	—	4	2	no	—
730	C₂×M₁₆	—	4	2	no	—
731	C₂×M₁₆	—	4	2	no	—
732	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
733	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
734	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
735	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
736	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
737	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
738	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
739	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
740	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
741	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
742	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
743	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
744	C₂²×C₈	—	4	2	no	—
745	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
746	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
747	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
748	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
749	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
750	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
751	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
752	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
753	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
754	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
755	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
756	C₂²×C₈	C₂³×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	#126	C₂×C₄×C₂₃	1	2	yes	—
760	#126	C₂×C₄×C₂₃	1	2	yes	—
761	#126	C₂×C₄×C₂₃	1	2	yes	—
762	#126	C₂×C₄×C₂₃	1	2	yes	—
763	#126	C₂×C₄×C₂₃	1	2	yes	—
764	#126	C₂×C₄×C₂₃	1	2	yes	—
765	#125	C₂×C₄×C₂₃	1	2	yes	—
766	#125	C₂×C₄×C₂₃	1	2	yes	—
767	#125	C₂×C₄×C₂₃	1	2	yes	—
768	#125	C₂×C₄×C₂₃	1	1	yes	characteristic
769	#125	C₂×C₄×C₂₃	1	1	yes	characteristic
770	#124	C₂×C₄×C₂₃	1	2	yes	—
771	#124	C₂×C₄×C₂₃	1	2	yes	—
772	#124	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	#123	C₂×C₄×C₂₃	1	2	yes	—
778	#123	C₂×C₄×C₂₃	1	2	yes	—
779	#123	C₂×C₄×C₂₃	1	2	yes	—
780	#123	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	1	yes	characteristic
784	C₂²⋊Q₈	C₂×C₄×C₂₃	1	1	yes	characteristic
785	C₂²⋊Q₈	C₂×C₄×C₂₃	1	2	yes	—
786	C₂²⋊Q₈	C₂×C₄×C₂₃	1	2	yes	—
787	C₂²⋊Q₈	C₂×C₄×C₂₃	1	2	yes	—
788	C₂²⋊Q₈	C₂×C₄×C₂₃	1	2	yes	—
789	C₂²⋊Q₈	C₂×C₄×C₂₃	1	2	yes	—
790	#121	C₂×C₄×C₂₃	1	1	yes	characteristic
791	#121	C₂×C₄×C₂₃	1	1	yes	characteristic
792	#121	C₂×C₄×C₂₃	1	1	yes	characteristic
793	#121	C₂×C₄×C₂₃	1	1	yes	characteristic
794	#121	C₂×C₄×C₂₃	1	2	yes	—
795	#121	C₂×C₄×C₂₃	1	2	yes	—
796	#121	C₂×C₄×C₂₃	1	2	yes	—
797	#120	C₂×C₄×C₂₃	1	2	yes	—
798	#120	C₂×C₄×C₂₃	1	2	yes	—
799	C₄×Q₈	C₂×C₄×C₂₃	1	1	yes	characteristic
800	C₄×Q₈	C₂×C₄×C₂₃	1	2	yes	—
801	C₄×Q₈	C₂×C₄×C₂₃	1	1	yes	characteristic
802	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
803	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
804	C₄×D₄	C₂×C₄×C₂₃	1	1	yes	characteristic
805	C₄×D₄	C₂×C₄×C₂₃	1	1	yes	characteristic
806	C₄×D₄	C₂×C₄×C₂₃	1	1	yes	characteristic
807	C₄×D₄	C₂×C₄×C₂₃	1	1	yes	characteristic
808	C₄×D₄	C₂×C₄×C₂₃	1	2	yes	—
809	C₄×D₄	C₂×C₄×C₂₃	1	2	yes	—
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	2	yes	—
813	C₄×D₄	C₂×C₄×C₂₃	1	2	yes	—
814	C₄×D₄	C₂×C₄×C₂₃	1	1	yes	characteristic
815	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
816	C₄×D₄	C₂³×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	2	yes	—
821	C₄×D₄	C₂³×C₂₃	1	2	yes	—
822	C₄×D₄	C₂³×C₂₃	1	2	yes	—
823	#117	C₂×C₄×C₂₃	1	2	yes	—
824	#117	C₂×C₄×C₂₃	1	2	yes	—
825	#117	C₂×C₄×C₂₃	1	1	yes	characteristic
826	#117	C₂×C₄×C₂₃	1	1	yes	characteristic
827	#117	C₂×C₄×C₂₃	1	1	yes	characteristic
828	#117	C₂×C₄×C₂₃	1	1	yes	characteristic
829	#117	C₂×C₄×C₂₃	1	2	yes	—
830	#117	C₂×C₄×C₂₃	1	2	yes	—
831	#117	C₂×C₄×C₂₃	1	2	yes	—
832	#117	C₂³×C₂₃	1	1	yes	characteristic
833	#117	C₂³×C₂₃	1	1	yes	characteristic
834	#117	C₂³×C₂₃	1	1	yes	characteristic
835	#117	C₂³×C₂₃	1	2	yes	—
836	#117	C₂³×C₂₃	1	2	yes	—
837	#117	C₂³×C₂₃	1	2	yes	—
838	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
839	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
840	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
841	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
842	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
843	C₂×C₂²⋊C₄	C₂×C₄×C₂₃	1	2	yes	—
844	C₂×C₂²⋊C₄	C₂×C₄×C₂₃	1	2	yes	—
845	C₂×C₂²⋊C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
846	C₂×C₂²⋊C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
847	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
848	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
849	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
850	C₂×C₄²	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	1	yes	characteristic
854	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
855	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
856	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
857	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
858	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
859	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
860	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
861	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
862	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
863	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
864	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
865	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
866	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
867	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
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	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
872	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
873	C₂²⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
874	C₂²⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
875	C₂²⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
876	C₂²⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
877	C₂²⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
878	C₂²⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
879	C₂²⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
880	C₂²⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
881	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
882	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
883	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
884	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
885	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
886	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
887	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
888	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
889	#97	C₂³×C₂₃	1	1	yes	characteristic
890	#97	C₂³×C₂₃	1	1	yes	characteristic
891	#97	C₂³×C₂₃	1	1	yes	characteristic
892	#97	C₂³×C₂₃	1	1	yes	characteristic
893	#97	C₂³×C₂₃	1	2	yes	—
894	#97	C₂³×C₂₃	1	2	yes	—
895	#97	C₂³×C₂₃	1	2	yes	—
896	#97	C₂³×C₂₃	1	2	yes	—
897	#97	C₂³×C₂₃	1	2	yes	—
898	C₄×C₈	C₂³×C₂₃	1	2	yes	—
899	C₄×C₈	C₂³×C₂₃	1	2	yes	—
900	C₄×C₈	C₂³×C₂₃	1	2	yes	—
901	C₄×C₈	C₂³×C₂₃	1	2	yes	—
902	C₄×C₈	C₂³×C₂₃	1	2	yes	—
903	C₂₃	#60272	1	1	yes	characteristic, direct product factor, Sylow
904	C₂⁴	C₂²×C₄×C₂₃	1	1	yes	characteristic
905	C₂⁴	C₂²×C₄×C₂₃	1	1	yes	characteristic
906	#41	—	2	2	no	—
907	#41	—	2	2	no	—
908	#41	—	4	4	no	—
909	C₂×Q₈	C₂²×C₄×C₂₃	1	1	yes	characteristic
910	C₂×Q₈	C₂²×C₄×C₂₃	1	2	yes	—
911	C₂×Q₈	C₂²×C₄×C₂₃	1	2	yes	—
912	C₂×D₄	—	4	2	no	—
913	C₂×D₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
914	C₂×D₄	C₂²×C₄×C₂₃	1	2	yes	—
915	C₂×D₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
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	1	yes	characteristic
920	C₂×D₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
921	C₂×D₄	C₂²×C₄×C₂₃	1	2	yes	—
922	C₂×D₄	C₂²×C₄×C₂₃	1	2	yes	—
923	C₂²×C₄	—	2	2	no	—
924	C₂²×C₄	—	2	2	no	—
925	C₂²×C₄	—	2	2	no	—
926	C₂²×C₄	—	2	2	no	—
927	C₂²×C₄	C₂²×C₄×C₂₃	1	2	yes	—
928	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
929	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
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	1	yes	characteristic
935	C₂²×C₄	C₂²×C₄×C₂₃	1	2	yes	—
936	C₂²×C₄	C₂²×C₄×C₂₃	1	2	yes	—
937	C₂²×C₄	C₂²×C₄×C₂₃	1	2	yes	—
938	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
939	C₂²×C₄	C₂²×C₄×C₂₃	1	2	yes	—
940	C₂²×C₄	C₂²×C₄×C₂₃	1	2	yes	—
941	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
942	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
943	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
944	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
945	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
946	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
947	M₁₆	—	2	2	no	—
948	M₁₆	—	2	2	no	—
949	M₁₆	—	2	2	no	—
950	M₁₆	—	2	2	no	—
951	M₁₆	—	4	1	no	—
952	M₁₆	—	4	1	no	—
953	M₁₆	—	4	1	no	—
954	M₁₆	—	4	1	no	—
955	M₁₆	—	4	2	no	—
956	M₁₆	—	4	2	no	—
957	M₁₆	—	4	2	no	—
958	M₁₆	—	4	2	no	—
959	C₂×C₈	—	2	2	no	—
960	C₂×C₈	—	2	2	no	—
961	C₂×C₈	—	2	2	no	—
962	C₂×C₈	—	2	2	no	—
963	C₂×C₈	—	4	1	no	—
964	C₂×C₈	—	4	1	no	—
965	C₂×C₈	—	4	1	no	—
966	C₂×C₈	—	4	1	no	—
967	C₂×C₈	—	4	2	no	—
968	C₂×C₈	—	4	2	no	—
969	C₂×C₈	—	4	2	no	—
970	C₂×C₈	—	4	2	no	—
971	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
972	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
973	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
974	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
975	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
976	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
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	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
981	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
982	C₂×C₈	C₂⁴×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	1	yes	characteristic
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	2	yes	—
991	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
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	1	yes	characteristic
995	C₄⋊C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
996	C₄⋊C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
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	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
1002	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
1003	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
1004	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
1005	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
1006	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
1007	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
1008	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
1009	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
1010	C₂²⋊C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
1011	C₂²⋊C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
1012	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
1013	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
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	1	yes	characteristic
1019	C₂²⋊C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
1020	C₂²⋊C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
1021	C₂²⋊C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
1022	C₂²⋊C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
1023	C₂²⋊C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
1024	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
1025	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
1026	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
1027	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
1028	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
1029	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
1030	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
1031	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
1032	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
1033	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
1034	C₄²	C₂²×C₄×C₂₃	1	2	yes	—
1035	C₄²	C₂²×C₄×C₂₃	1	2	yes	—
1036	C₄²	C₂²×C₄×C₂₃	1	2	yes	—
1037	C₄²	C₂²×C₄×C₂₃	1	2	yes	—
1038	C₄²	C₂²×C₄×C₂₃	1	2	yes	—
1039	C₄²	C₂²×C₄×C₂₃	1	1	yes	characteristic
1040	C₄²	C₂²×C₄×C₂₃	1	1	yes	characteristic
1041	C₄²	C₂²×C₄×C₂₃	1	2	yes	—
1042	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
1043	C₄²	C₂⁴×C₂₃	1	2	yes	—
1044	C₄²	C₂⁴×C₂₃	1	2	yes	—
1045	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
1046	C₄²	C₂⁴×C₂₃	1	2	yes	—
1047	C₂³	—	2	2	no	—
1048	C₂³	—	2	2	no	—
1049	C₂³	—	2	2	no	—
1050	C₂³	—	4	1	no	—
1051	C₂³	—	4	1	no	—
1052	C₂³	—	4	1	no	—
1053	C₂³	C₂³×C₄×C₂₃	1	1	yes	characteristic
1054	C₂³	C₂³×C₄×C₂₃	1	1	yes	characteristic
1055	C₂³	C₂³×C₄×C₂₃	1	2	yes	—
1056	C₂³	C₂³×C₄×C₂₃	1	1	yes	characteristic
1057	C₂³	C₂³×C₄×C₂₃	1	1	yes	characteristic
1058	C₂³	C₂³×C₄×C₂₃	1	1	yes	characteristic
1059	Q₈	—	2	2	no	—
1060	Q₈	—	4	2	no	—
1061	Q₈	—	4	2	no	—
1062	D₄	—	2	2	no	—
1063	D₄	—	2	2	no	—
1064	D₄	—	2	4	no	—
1065	D₄	—	2	4	no	—
1066	D₄	—	2	2	no	—
1067	D₄	—	4	1	no	—
1068	D₄	—	4	1	no	—
1069	D₄	—	4	2	no	—
1070	D₄	—	4	2	no	—
1071	D₄	—	4	2	no	—
1072	C₂×C₄	—	2	4	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	1	no	—
1078	C₂×C₄	—	2	2	no	—
1079	C₂×C₄	—	2	1	no	—
1080	C₂×C₄	—	2	1	no	—
1081	C₂×C₄	—	2	1	no	—
1082	C₂×C₄	—	2	1	no	—
1083	C₂×C₄	—	2	1	no	—
1084	C₂×C₄	—	2	2	no	—
1085	C₂×C₄	—	2	2	no	—
1086	C₂×C₄	—	2	2	no	—
1087	C₂×C₄	—	2	2	no	—
1088	C₂×C₄	—	2	2	no	—
1089	C₂×C₄	—	4	1	no	—
1090	C₂×C₄	—	4	2	no	—
1091	C₂×C₄	—	4	2	no	—
1092	C₂×C₄	—	4	2	no	—
1093	C₂×C₄	—	4	2	no	—
1094	C₂×C₄	—	4	2	no	—
1095	C₂×C₄	—	4	1	no	—
1096	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
1097	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
1098	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
1099	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
1100	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
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	1	yes	characteristic
1104	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
1105	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
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	C₂³×C₄×C₂₃	1	1	yes	characteristic
1110	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
1111	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
1112	C₂×C₄	C₂₃×H(5,𝔽₂)	1	2	yes	—
1113	C₂×C₄	C₂₃×2₋¹⁺⁴	1	2	yes	—
1114	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
1115	C₈	—	2	1	no	—
1116	C₈	—	2	1	no	—
1117	C₈	—	2	1	no	—
1118	C₈	—	2	1	no	—
1119	C₈	—	2	1	no	—
1120	C₈	—	2	1	no	—
1121	C₈	—	2	2	no	—
1122	C₈	—	2	2	no	—
1123	C₈	—	2	2	no	—
1124	C₈	—	2	1	no	—
1125	C₈	—	2	1	no	—
1126	C₈	—	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	1	no	—
1132	C₂²	—	2	1	no	—
1133	C₂²	—	2	1	no	—
1134	C₂²	—	2	2	no	—
1135	C₂²	—	2	1	no	—
1136	C₂²	—	2	2	no	—
1137	C₂²	—	2	1	no	—
1138	C₂²	—	2	1	no	—
1139	C₂²	—	2	1	no	—
1140	C₂²	—	2	2	no	—
1141	C₂²	—	2	1	no	—
1142	C₂²	—	2	1	no	—
1143	C₂²	—	4	4	no	—
1144	C₂²	—	8	2	no	—
1145	C₂²	C₂₃×#520	1	2	yes	—
1146	C₂²	C₂₃×#568	1	2	yes	—
1147	C₂²	C₂⁴×C₄×C₂₃	1	1	yes	characteristic
1148	C₄	—	2	1	no	—
1149	C₄	—	2	1	no	—
1150	C₄	—	2	1	no	—
1151	C₄	—	2	1	no	—
1152	C₄	—	2	2	no	—
1153	C₄	—	2	2	no	—
1154	C₄	—	2	2	no	—
1155	C₄	—	2	1	no	—
1156	C₄	—	2	1	no	—
1157	C₄	—	2	2	no	—
1158	C₄	—	2	1	no	—
1159	C₄	—	2	2	no	—
1160	C₄	—	2	2	no	—
1161	C₄	—	2	2	no	—
1162	C₄	—	2	1	no	—
1163	C₄	C₂₃×#520	1	2	yes	—
1164	C₄	C₂×C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
1165	C₄	C₂×C₂₃×2₋¹⁺⁴	1	1	yes	characteristic
1166	C₂	—	2	2	no	—
1167	C₂	—	2	2	no	—
1168	C₂	—	4	1	no	—
1169	C₂	—	4	1	no	—
1170	C₂	—	4	1	no	—
1171	C₂	—	4	2	no	—
1172	C₂	C₂×C₂₃×#520	1	1	yes	characteristic
1173	C₂	C₂×C₂₃×#568	1	1	yes	characteristic
1174	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×#2995	C₂	semidirect
3. C₂₃×#2995	C₂	semidirect
4. C₂₃×#2994	C₂	semidirect
5. C₂₃×#2993	C₂	semidirect
6. C₂₃×#2992	C₂	semidirect
7. C₂₃×#2992	C₂	semidirect
8. C₂₃×#2990	C₂	semidirect
9. C₂₃×#2989	C₂	semidirect
10. C₂₃×#2962	C₂	semidirect
11. C₂₃×#2961	C₂	semidirect
12. D₄×M₁₆×C₂₃	C₂	semidirect
13. C₂₃×#2933	C₂	semidirect
14. C₂₃×#2933	C₂	semidirect
15. C₂₃×#2930	C₂	semidirect
16. C₂₃×#2929	C₂	semidirect
17. C₂×C₂₃×#435	C₂	semidirect
18. C₂₃×#2924	C₂	semidirect
19. C₂₃×#2924	C₂	semidirect
20. C₂₃×#2923	C₂	semidirect
21. C₂₃×#2906	C₂	semidirect
22. C₂₃×#2905	C₂	semidirect
23. C₂×C₂₃×#424	C₂	semidirect
53. C₂₃×#446	C₂²	semidirect
54. C₂₃×#446	C₂²	semidirect
55. C₂₃×#446	C₂²	semidirect
56. C₂₃×#446	C₂²	semidirect
57. C₂₃×#446	C₂²	semidirect
58. C₂₃×#446	C₂²	semidirect
59. C₂₃×#446	C₂²	semidirect
60. C₈×Q₈×C₂₃	C₂²	semidirect
62. C₂₃×#436	C₂²	semidirect
63. C₂₃×#436	C₂²	semidirect
64. C₂₃×#436	C₂²	semidirect
65. C₂₃×#436	C₂²	semidirect
76. C₂₃×#435	C₂²	semidirect
77. C₂₃×#435	C₂²	semidirect
78. C₂₃×#435	C₂²	semidirect
79. C₂₃×#435	C₂²	semidirect
80. C₂₃×#435	C₂²	semidirect
81. C₂₃×#435	C₂²	semidirect
82. C₂₃×#435	C₂²	semidirect
83. C₂₃×#435	C₂²	semidirect
85. C₈×D₄×C₂₃	C₂²	semidirect
86. C₈×D₄×C₂₃	C₂²	semidirect
87. C₈×D₄×C₂₃	C₂²	semidirect
88. C₈×D₄×C₂₃	C₂²	semidirect
89. C₂₃×#433	C₂²	semidirect
90. C₂₃×#433	C₂²	semidirect
91. C₂₃×#433	C₂²	semidirect
92. C₂₃×#433	C₂²	semidirect
93. C₂₃×#433	C₂²	semidirect
94. C₂₃×#433	C₂²	semidirect
95. C₂₃×#432	C₂²	semidirect
96. C₂₃×#432	C₂²	semidirect
97. C₂₃×#432	C₂²	semidirect
98. C₂₃×#432	C₂²	semidirect
99. C₂₃×#431	C₂²	semidirect
100. C₂₃×#431	C₂²	semidirect
109. C₂₃×#424	C₂²	semidirect
110. C₂₃×#424	C₂²	semidirect
111. C₂₃×#424	C₂²	semidirect
112. C₂₃×#424	C₂²	semidirect
113. C₂₃×#424	C₂²	semidirect
114. C₂₃×#424	C₂²	semidirect
116. C₂₃×#423	C₂²	semidirect
117. C₂₃×#423	C₂²	semidirect
118. C₂₃×#423	C₂²	semidirect
120. C₂×C₂₃×C₄⋊C₈	C₂²	semidirect
121. C₂×C₂₃×C₄⋊C₈	C₂²	semidirect
122. C₂×C₂₃×C₄⋊C₈	C₂²	semidirect
459. #60272	C₂₃	direct (N × H)
541. #2995	C₂×C₂₃	semidirect
542. #2995	C₂×C₂₃	semidirect
543. #2994	C₂×C₂₃	semidirect
544. #2993	C₂×C₂₃	semidirect
545. #2992	C₂×C₂₃	semidirect
546. #2992	C₂×C₂₃	semidirect
547. #2990	C₂×C₂₃	semidirect
548. #2989	C₂×C₂₃	semidirect
549. #2962	C₂×C₂₃	semidirect
550. #2961	C₂×C₂₃	semidirect
551. D₄×M₁₆	C₂×C₂₃	semidirect
552. #2933	C₂×C₂₃	semidirect
553. #2933	C₂×C₂₃	semidirect
554. #2930	C₂×C₂₃	semidirect
555. #2929	C₂×C₂₃	semidirect
556. C₂×#435	C₂×C₂₃	semidirect
557. #2924	C₂×C₂₃	semidirect
558. #2924	C₂×C₂₃	semidirect
559. #2923	C₂×C₂₃	semidirect
560. #2906	C₂×C₂₃	semidirect
561. #2905	C₂×C₂₃	semidirect
562. C₂×#424	C₂×C₂₃	semidirect
631. #446	C₂²×C₂₃	semidirect
632. #446	C₂²×C₂₃	semidirect
633. #446	C₂²×C₂₃	semidirect
634. #446	C₂²×C₂₃	semidirect
635. #446	C₂²×C₂₃	semidirect
636. #446	C₂²×C₂₃	semidirect
637. #446	C₂²×C₂₃	semidirect
638. C₈×Q₈	C₂²×C₂₃	semidirect
640. #436	C₂²×C₂₃	semidirect
641. #436	C₂²×C₂₃	semidirect
642. #436	C₂²×C₂₃	semidirect
643. #436	C₂²×C₂₃	semidirect
654. #435	C₂²×C₂₃	semidirect
655. #435	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
663. C₈×D₄	C₂²×C₂₃	semidirect
664. C₈×D₄	C₂²×C₂₃	semidirect
665. C₈×D₄	C₂²×C₂₃	semidirect
666. C₈×D₄	C₂²×C₂₃	semidirect
667. #433	C₂²×C₂₃	semidirect
668. #433	C₂²×C₂₃	semidirect
669. #433	C₂²×C₂₃	semidirect
670. #433	C₂²×C₂₃	semidirect
671. #433	C₂²×C₂₃	semidirect
672. #433	C₂²×C₂₃	semidirect
673. #432	C₂²×C₂₃	semidirect
674. #432	C₂²×C₂₃	semidirect
675. #432	C₂²×C₂₃	semidirect
676. #432	C₂²×C₂₃	semidirect
677. #431	C₂²×C₂₃	semidirect
678. #431	C₂²×C₂₃	semidirect
687. #424	C₂²×C₂₃	semidirect
688. #424	C₂²×C₂₃	semidirect
689. #424	C₂²×C₂₃	semidirect
690. #424	C₂²×C₂₃	semidirect
691. #424	C₂²×C₂₃	semidirect
692. #424	C₂²×C₂₃	semidirect
694. #423	C₂²×C₂₃	semidirect
695. #423	C₂²×C₂₃	semidirect
696. #423	C₂²×C₂₃	semidirect
698. C₂×C₄⋊C₈	C₂²×C₂₃	semidirect
699. C₂×C₄⋊C₈	C₂²×C₂₃	semidirect
700. C₂×C₄⋊C₈	C₂²×C₂₃	semidirect
903. C₂₃	#60272	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×#2995	2
C₂₃×#2994	2
C₂₃×#2993	2
C₂₃×#2992	2
C₂₃×#2990	2
C₂₃×#2989	2
C₂₃×#2962	2
C₂₃×#2961	2
D₄×M₁₆×C₂₃	2
C₂₃×#2933	2
C₂₃×#2930	2
C₂₃×#2929	2
C₂×C₂₃×#435	2
C₂₃×#2924	2
C₂₃×#2923	2
C₂₃×#2906	2
C₂₃×#2905	2
C₂×C₂₃×#424	2
#60272	23

Subgroups — C23×#60272 #19207898

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#60272 #19207898