Subgroups — C₂₃×#61757 #19209383

Order 5888.

1674 conjugacy classes of subgroups.

The subgroup lattice has 1024 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3538	C₂	1	1	yes	maximal, characteristic
2	C₂₃×#3495	C₂	1	1	yes	maximal, characteristic
3	C₂₃×#3352	C₂	1	2	yes	maximal, complemented
4	C₂₃×#3349	C₂	1	2	yes	maximal, complemented
5	C₂₃×#3344	C₂	1	2	yes	maximal, complemented
6	C₂₃×#3336	C₂	1	2	yes	maximal, complemented
7	C₂₃×#3328	C₂	1	2	yes	maximal, complemented
8	C₂₃×#3312	C₂	1	2	yes	maximal, complemented
9	C₂₃×#3312	C₂	1	2	yes	maximal, complemented
10	C₂₃×#3299	C₂	1	2	yes	maximal, complemented
11	C₂₃×#3242	C₂	1	2	yes	maximal, complemented
12	C₂₃×#3202	C₂	1	2	yes	maximal, complemented
13	C₂₃×#3195	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₃×#3189	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₃×#3127	C₂	1	2	yes	maximal, complemented
16	C₂₃×#3097	C₂	1	2	yes	maximal, complemented
17	C₂₃×#3095	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₂₃×#485	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂₃×#2976	C₂	1	1	yes	maximal, characteristic
20	C₂₃×#563	—	2	2	no	—
21	C₂₃×#556	C₂²	1	2	yes	—
22	C₂₃×#554	C₂²	1	2	yes	—
23	C₂₃×#552	—	2	2	no	—
24	C₂₃×#552	C₂²	1	2	yes	—
25	C₂₃×#552	C₂²	1	2	yes	—
26	C₂₃×#552	C₂²	1	2	yes	—
27	C₂₃×#552	C₂²	1	2	yes	—
28	C₂₃×#551	—	2	2	no	—
29	C₂₃×#551	—	2	2	no	—
30	D₄×Q₈×C₂₃	C₂²	1	2	yes	—
31	D₄×Q₈×C₂₃	C₂²	1	2	yes	—
32	C₂₃×#544	—	2	1	no	—
33	C₂₃×#544	—	2	1	no	—
34	C₂₃×#544	C₂²	1	1	yes	characteristic
35	C₂₃×#542	—	2	1	no	—
36	C₂₃×#541	—	2	1	no	—
37	C₂₃×#541	C₂²	1	2	yes	—
38	C₂₃×#539	—	2	1	no	—
39	C₂₃×#539	—	2	1	no	—
40	C₂₃×#536	C₂²	1	1	yes	characteristic
41	C₂₃×#536	C₂²	1	2	yes	—
42	C₂₃×#533	—	2	1	no	—
43	C₂₃×#529	—	2	1	no	—
44	C₂₃×#525	C₂²	1	1	yes	characteristic
45	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
46	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
47	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
48	C₂₃×#520	C₂²	1	1	yes	characteristic
49	C₂₃×#519	C₂²	1	1	yes	characteristic
50	C₂×C₂₃×#117	C₂²	1	1	yes	characteristic
51	C₂₃×#501	C₂²	1	2	yes	complemented
52	C₂₃×#499	C₂²	1	2	yes	complemented
53	C₂₃×#491	C₂²	1	2	yes	complemented
54	C₂₃×#487	C₂²	1	2	yes	complemented
55	C₂₃×#485	C₂²	1	2	yes	—
56	C₂₃×#485	C₂²	1	2	yes	—
57	C₂₃×#485	C₂²	1	2	yes	—
58	C₂₃×#485	C₂²	1	2	yes	—
59	C₂₃×#485	C₂²	1	2	yes	—
60	C₂₃×#485	C₂²	1	2	yes	—
61	C₂₃×#485	C₂²	1	2	yes	complemented
62	C₂₃×#485	C₂²	1	2	yes	complemented
63	C₂₃×#485	C₂²	1	2	yes	complemented
64	C₂₃×#485	C₂²	1	2	yes	complemented
65	C₂₃×#484	C₂²	1	2	yes	—
66	C₂₃×#484	C₂²	1	2	yes	—
67	C₂₃×#484	C₂²	1	2	yes	—
68	C₂₃×#484	C₂²	1	2	yes	complemented
69	C₂₃×#483	C₂²	1	2	yes	—
70	C₂₃×#483	C₂²	1	2	yes	—
71	C₂₃×#483	C₂²	1	2	yes	—
72	C₂₃×#483	C₂²	1	2	yes	complemented
73	C₂₃×#479	C₂²	1	2	yes	complemented
74	C₂₃×#479	C₂²	1	2	yes	complemented
75	C₂₃×#479	C₂²	1	2	yes	complemented
76	C₂₃×#479	C₂²	1	2	yes	complemented
77	C₂₃×#477	C₂²	1	2	yes	complemented
78	C₂₃×#475	C₂²	1	2	yes	complemented
79	C₂₃×#470	C₂²	1	2	yes	—
80	C₂₃×#470	C₂²	1	2	yes	—
81	C₂₃×#470	C₂²	1	2	yes	complemented
82	C₂₃×#470	C₂²	1	2	yes	complemented
83	C₂₃×#467	C₂²	1	2	yes	—
84	C₂₃×#467	C₂²	1	2	yes	—
85	C₂₃×#467	C₂²	1	2	yes	complemented
86	C₂₃×#467	C₂²	1	2	yes	complemented
87	C₂₃×#462	C₂²	1	2	yes	complemented
88	C₂₃×#462	C₂²	1	2	yes	complemented
89	C₂₃×#451	C₂²	1	2	yes	—
90	C₂₃×#451	C₂²	1	2	yes	—
91	C₂₃×#451	C₂²	1	2	yes	—
92	C₂₃×#451	C₂²	1	2	yes	—
93	C₂₃×#451	C₂²	1	2	yes	complemented
94	C₂₃×#451	C₂²	1	2	yes	complemented
95	C₂₃×#441	C₂²	1	2	yes	complemented
96	C₂₃×#441	C₂²	1	2	yes	complemented
97	C₄×Q₁₆×C₂₃	C₂²	1	2	yes	complemented
98	C₄×Q₁₆×C₂₃	C₂²	1	2	yes	complemented
99	C₂₃×#436	C₂²	1	2	yes	—
100	C₂₃×#435	C₂²	1	2	yes	—
101	C₂₃×#435	C₂²	1	2	yes	—
102	C₈×D₄×C₂₃	C₂²	1	2	yes	—
103	C₂₃×#433	C₂²	1	2	yes	—
104	C₂₃×#428	C₂²	1	1	yes	characteristic
105	C₂₃×#428	C₂²	1	1	yes	characteristic
106	C₂₃×#428	C₂²	1	2	yes	complemented
107	C₂₃×#427	C₂²	1	2	yes	complemented
108	C₂×C₂₃×#107	C₂²	1	1	yes	characteristic
109	C₂×C₂₃×#106	C₂²	1	1	yes	characteristic
110	C₂₃×#419	C₂²	1	1	yes	characteristic
111	C₂₃×#419	C₂²	1	1	yes	characteristic
112	C₂₃×#419	C₂²	1	2	yes	complemented
113	C₂×C₂₃×#103	C₂²	1	1	yes	characteristic
114	C₂×C₂₃×#103	C₂²	1	1	yes	characteristic
115	C₂×C₂₃×#103	C₂²	1	2	yes	complemented
116	C₂₃×#408	C₂²	1	2	yes	—
117	C₂₃×#407	C₂²	1	1	yes	characteristic
118	C₂×C₂₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
119	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
120	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
121	C₂²×Q₈×C₂₃	C₂³	1	2	yes	—
122	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
123	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
124	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
125	C₂×Q₁₆×C₂₃	C₂³	1	2	yes	—
126	C₂×Q₁₆×C₂₃	C₂³	1	2	yes	—
127	C₂×Q₁₆×C₂₃	C₂³	1	2	yes	—
128	C₂×Q₁₆×C₂₃	C₂³	1	2	yes	—
129	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
130	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
131	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
132	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
133	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
134	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
135	C₂₃×C₄⋊Q₈	—	2	1	no	—
136	C₂₃×C₄⋊Q₈	—	2	2	no	—
137	C₂₃×C₄⋊Q₈	—	2	2	no	—
138	C₂₃×C₄⋊Q₈	—	2	2	no	—
139	C₂₃×C₄⋊Q₈	—	2	1	no	—
140	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
141	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
142	C₂₃×#126	—	2	2	no	—
143	C₂₃×#126	—	2	2	no	—
144	C₂₃×#126	—	2	2	no	—
145	C₂₃×#126	—	2	2	no	—
146	C₂₃×#126	—	2	2	no	—
147	C₂₃×#126	—	2	2	no	—
148	C₂₃×#126	—	2	2	no	—
149	C₂₃×#126	—	2	2	no	—
150	C₂₃×#125	—	2	2	no	—
151	C₂₃×#125	—	2	2	no	—
152	C₂₃×#125	—	2	2	no	—
153	C₂₃×#125	—	2	2	no	—
154	C₂₃×#125	—	2	2	no	—
155	C₂₃×#125	—	2	1	no	—
156	C₂₃×#125	—	2	2	no	—
157	C₂₃×#125	—	2	2	no	—
158	C₂₃×#125	C₂³	1	2	yes	—
159	C₂₃×#125	C₂³	1	2	yes	—
160	C₂₃×#124	—	2	2	no	—
161	C₂₃×#124	—	2	2	no	—
162	C₂₃×#124	—	2	1	no	—
163	C₂₃×#123	—	2	2	no	—
164	C₂₃×#123	—	2	2	no	—
165	C₂₃×#123	—	2	2	no	—
166	C₂₃×#123	—	2	2	no	—
167	C₂₃×#123	—	2	2	no	—
168	C₂₃×#123	—	2	2	no	—
169	C₂₃×#123	—	2	2	no	—
170	C₂₃×#123	D₄	1	2	yes	—
171	C₂₃×C₂²⋊Q₈	—	2	1	no	—
172	C₂₃×C₂²⋊Q₈	—	2	1	no	—
173	C₂₃×C₂²⋊Q₈	—	2	1	no	—
174	C₂₃×C₂²⋊Q₈	—	2	1	no	—
175	C₂₃×C₂²⋊Q₈	—	2	1	no	—
176	C₂₃×C₂²⋊Q₈	—	2	1	no	—
177	C₂₃×C₂²⋊Q₈	—	2	2	no	—
178	C₂₃×C₂²⋊Q₈	—	2	2	no	—
179	C₂₃×C₂²⋊Q₈	—	2	2	no	—
180	C₂₃×C₂²⋊Q₈	—	2	2	no	—
181	C₂₃×C₂²⋊Q₈	—	2	2	no	—
182	C₂₃×C₂²⋊Q₈	—	2	2	no	—
183	C₂₃×C₂²⋊Q₈	—	2	2	no	—
184	C₂₃×C₂²⋊Q₈	D₄	1	1	yes	characteristic
185	C₂₃×C₂²⋊Q₈	D₄	1	1	yes	characteristic
186	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
187	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
188	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
189	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
190	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
191	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
192	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
193	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
194	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
195	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
196	C₂₃×#121	D₄	1	1	yes	characteristic
197	C₂₃×#121	D₄	1	1	yes	characteristic
198	C₂₃×#120	D₄	1	2	yes	—
199	C₄×Q₈×C₂₃	—	2	1	no	—
200	C₄×Q₈×C₂₃	—	2	2	no	—
201	C₄×Q₈×C₂₃	—	2	1	no	—
202	C₄×Q₈×C₂₃	—	2	1	no	—
203	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
204	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
205	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
206	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
207	C₄×D₄×C₂₃	—	2	2	no	—
208	C₄×D₄×C₂₃	—	2	2	no	—
209	C₄×D₄×C₂₃	—	2	2	no	—
210	C₄×D₄×C₂₃	—	2	2	no	—
211	C₄×D₄×C₂₃	—	2	1	no	—
212	C₄×D₄×C₂₃	C₂³	1	2	yes	—
213	C₄×D₄×C₂₃	C₂³	1	2	yes	—
214	C₂₃×#117	—	2	1	no	—
215	C₂₃×#117	—	2	1	no	—
216	C₂₃×#117	—	2	2	no	—
217	C₂₃×#117	—	2	2	no	—
218	C₂₃×#117	—	2	2	no	—
219	C₂₃×#117	—	2	2	no	—
220	C₂₃×#117	—	2	2	no	—
221	C₂₃×#117	C₂³	1	1	yes	characteristic
222	C₂₃×#117	C₂³	1	2	yes	—
223	C₂₃×#117	C₂³	1	2	yes	—
224	C₂₃×#117	C₂³	1	1	yes	characteristic
225	C₂₃×#117	C₂³	1	1	yes	characteristic
226	C₂₃×#117	C₂³	1	1	yes	characteristic
227	C₂₃×#117	C₂³	1	1	yes	characteristic
228	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
229	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
230	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
231	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
232	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
233	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
234	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
235	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
236	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
237	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
238	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
239	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
240	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
241	C₂×C₄²×C₂₃	—	2	1	no	—
242	C₂₃×#107	C₂³	1	2	yes	—
243	C₂₃×#107	C₂³	1	2	yes	—
244	C₂₃×#107	C₂³	1	2	yes	—
245	C₂₃×#107	C₂³	1	2	yes	—
246	C₂₃×#107	C₂³	1	2	yes	—
247	C₂₃×#107	C₂³	1	2	yes	—
248	C₂₃×#106	C₂³	1	2	yes	—
249	C₂₃×#106	C₂³	1	2	yes	—
250	C₂₃×#106	C₂³	1	2	yes	—
251	C₂₃×#106	C₂³	1	2	yes	—
252	C₂₃×#106	C₂³	1	2	yes	—
253	C₂₃×#106	C₂³	1	2	yes	—
254	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
255	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
256	C₂₃×#103	C₂³	1	2	yes	—
257	C₂₃×#103	C₂³	1	2	yes	—
258	C₂₃×#103	C₂³	1	2	yes	—
259	C₂₃×#103	C₂³	1	2	yes	—
260	C₂₃×#103	C₂³	1	2	yes	—
261	C₂₃×#103	C₂³	1	2	yes	—
262	C₂₃×#103	C₂³	1	2	yes	—
263	C₂₃×#103	C₂³	1	2	yes	—
264	C₂₃×#103	C₂³	1	2	yes	—
265	C₂₃×#103	C₂³	1	2	yes	—
266	C₂₃×#103	C₂³	1	2	yes	—
267	C₂₃×#103	C₂³	1	2	yes	—
268	C₂₃×#103	C₂³	1	2	yes	—
269	C₂₃×#103	C₂³	1	2	yes	—
270	C₂₃×#103	C₂³	1	2	yes	—
271	C₂₃×#103	C₂³	1	2	yes	—
272	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
273	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
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×#97	C₂³	1	2	yes	—
279	C₄×C₈×C₂₃	C₂³	1	2	yes	—
280	C₂⁴×C₂₃	C₂×D₄	1	1	yes	characteristic
281	#41×C₂₃	—	4	1	no	—
282	#41×C₂₃	—	4	1	no	—
283	C₂×Q₈×C₂₃	—	2	1	no	—
284	C₂×Q₈×C₂₃	—	2	2	no	—
285	C₂×Q₈×C₂₃	—	2	1	no	—
286	C₂×Q₈×C₂₃	—	2	1	no	—
287	C₂×Q₈×C₂₃	—	2	2	no	—
288	C₂×Q₈×C₂₃	—	4	1	no	—
289	C₂×Q₈×C₂₃	—	4	1	no	—
290	C₂×Q₈×C₂₃	—	4	1	no	—
291	C₂×Q₈×C₂₃	—	4	1	no	—
292	C₂×Q₈×C₂₃	—	4	2	no	—
293	C₂×Q₈×C₂₃	—	4	1	no	—
294	C₂×Q₈×C₂₃	—	4	1	no	—
295	C₂×Q₈×C₂₃	—	4	2	no	—
296	C₂×Q₈×C₂₃	C₂×D₄	1	1	yes	characteristic
297	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
298	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
299	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
300	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
301	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
302	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
303	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
304	C₂²×C₄×C₂₃	—	2	1	no	—
305	C₂²×C₄×C₂₃	—	2	1	no	—
306	C₂²×C₄×C₂₃	—	2	1	no	—
307	C₂²×C₄×C₂₃	—	2	1	no	—
308	C₂²×C₄×C₂₃	—	2	1	no	—
309	C₂²×C₄×C₂₃	—	2	1	no	—
310	C₂²×C₄×C₂₃	—	2	1	no	—
311	C₂²×C₄×C₂₃	—	2	1	no	—
312	C₂²×C₄×C₂₃	—	2	2	no	—
313	C₂²×C₄×C₂₃	—	2	2	no	—
314	C₂²×C₄×C₂₃	—	4	1	no	—
315	C₂²×C₄×C₂₃	—	4	1	no	—
316	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
317	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
318	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
319	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
320	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
321	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
322	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
323	Q₁₆×C₂₃	—	4	2	no	—
324	Q₁₆×C₂₃	—	4	2	no	—
325	Q₁₆×C₂₃	—	4	2	no	—
326	Q₁₆×C₂₃	—	4	2	no	—
327	M₁₆×C₂₃	—	4	1	no	—
328	M₁₆×C₂₃	—	4	2	no	—
329	M₁₆×C₂₃	—	4	1	no	—
330	C₂×C₈×C₂₃	—	4	1	no	—
331	C₂×C₈×C₂₃	—	4	2	no	—
332	C₂×C₈×C₂₃	—	4	1	no	—
333	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
334	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
335	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
336	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
337	C₄⋊C₄×C₂₃	—	2	2	no	—
338	C₄⋊C₄×C₂₃	—	2	2	no	—
339	C₄⋊C₄×C₂₃	—	2	2	no	—
340	C₄⋊C₄×C₂₃	—	2	2	no	—
341	C₄⋊C₄×C₂₃	—	2	2	no	—
342	C₄⋊C₄×C₂₃	—	2	2	no	—
343	C₄⋊C₄×C₂₃	—	2	1	no	—
344	C₄⋊C₄×C₂₃	—	2	1	no	—
345	C₄⋊C₄×C₂₃	—	2	1	no	—
346	C₄⋊C₄×C₂₃	—	2	2	no	—
347	C₄⋊C₄×C₂₃	—	2	1	no	—
348	C₄⋊C₄×C₂₃	—	2	1	no	—
349	C₄⋊C₄×C₂₃	—	2	2	no	—
350	C₄⋊C₄×C₂₃	—	2	2	no	—
351	C₄⋊C₄×C₂₃	—	2	2	no	—
352	C₄⋊C₄×C₂₃	—	2	2	no	—
353	C₄⋊C₄×C₂₃	—	2	2	no	—
354	C₄⋊C₄×C₂₃	—	2	2	no	—
355	C₄⋊C₄×C₂₃	—	2	2	no	—
356	C₄⋊C₄×C₂₃	—	2	2	no	—
357	C₄⋊C₄×C₂₃	—	2	2	no	—
358	C₄⋊C₄×C₂₃	—	2	2	no	—
359	C₄⋊C₄×C₂₃	—	2	2	no	—
360	C₄⋊C₄×C₂₃	—	2	2	no	—
361	C₄⋊C₄×C₂₃	—	2	2	no	—
362	C₄⋊C₄×C₂₃	—	2	2	no	—
363	C₄⋊C₄×C₂₃	—	2	2	no	—
364	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
365	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
366	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
367	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
368	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
369	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
370	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
371	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
372	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
373	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
374	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
375	C₂²⋊C₄×C₂₃	—	2	1	no	—
376	C₂²⋊C₄×C₂₃	—	2	1	no	—
377	C₂²⋊C₄×C₂₃	—	2	1	no	—
378	C₂²⋊C₄×C₂₃	—	2	1	no	—
379	C₂²⋊C₄×C₂₃	—	2	2	no	—
380	C₂²⋊C₄×C₂₃	—	2	2	no	—
381	C₂²⋊C₄×C₂₃	—	2	2	no	—
382	C₂²⋊C₄×C₂₃	—	2	2	no	—
383	C₂²⋊C₄×C₂₃	—	2	2	no	—
384	C₂²⋊C₄×C₂₃	—	2	2	no	—
385	C₂²⋊C₄×C₂₃	—	2	2	no	—
386	C₂²⋊C₄×C₂₃	—	2	2	no	—
387	C₂²⋊C₄×C₂₃	—	2	2	no	—
388	C₂²⋊C₄×C₂₃	—	2	2	no	—
389	C₂²⋊C₄×C₂₃	—	2	2	no	—
390	C₂²⋊C₄×C₂₃	—	2	2	no	—
391	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
392	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
393	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
394	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
395	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
396	C₄²×C₂₃	—	2	1	no	—
397	C₄²×C₂₃	—	2	1	no	—
398	C₄²×C₂₃	—	2	1	no	—
399	C₄²×C₂₃	—	2	1	no	—
400	C₄²×C₂₃	—	2	2	no	—
401	C₄²×C₂₃	—	2	2	no	—
402	C₄²×C₂₃	—	2	2	no	—
403	C₄²×C₂₃	—	2	2	no	—
404	C₄²×C₂₃	—	2	2	no	—
405	C₄²×C₂₃	—	2	2	no	—
406	C₄²×C₂₃	C₂⁴	1	2	yes	—
407	#61757	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
408	C₂³×C₂₃	—	2	2	no	—
409	C₂³×C₂₃	—	4	1	no	—
410	C₂³×C₂₃	—	4	1	no	—
411	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
412	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
413	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
414	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
415	Q₈×C₂₃	—	2	2	no	—
416	Q₈×C₂₃	—	2	2	no	—
417	Q₈×C₂₃	—	2	2	no	—
418	Q₈×C₂₃	—	2	2	no	—
419	Q₈×C₂₃	—	2	2	no	—
420	Q₈×C₂₃	—	2	2	no	—
421	Q₈×C₂₃	—	4	1	no	—
422	Q₈×C₂₃	—	4	2	no	—
423	Q₈×C₂₃	—	8	2	no	—
424	Q₈×C₂₃	—	8	1	no	—
425	Q₈×C₂₃	—	8	1	no	—
426	Q₈×C₂₃	—	8	2	no	—
427	D₄×C₂₃	—	2	4	no	—
428	D₄×C₂₃	—	4	2	no	—
429	D₄×C₂₃	—	4	1	no	—
430	D₄×C₂₃	—	4	2	no	—
431	C₂×C₄×C₂₃	—	2	1	no	—
432	C₂×C₄×C₂₃	—	2	1	no	—
433	C₂×C₄×C₂₃	—	2	2	no	—
434	C₂×C₄×C₂₃	—	2	1	no	—
435	C₂×C₄×C₂₃	—	2	1	no	—
436	C₂×C₄×C₂₃	—	2	2	no	—
437	C₂×C₄×C₂₃	—	2	1	no	—
438	C₂×C₄×C₂₃	—	2	1	no	—
439	C₂×C₄×C₂₃	—	2	1	no	—
440	C₂×C₄×C₂₃	—	2	1	no	—
441	C₂×C₄×C₂₃	—	2	2	no	—
442	C₂×C₄×C₂₃	—	2	1	no	—
443	C₂×C₄×C₂₃	—	2	2	no	—
444	C₂×C₄×C₂₃	—	2	2	no	—
445	C₂×C₄×C₂₃	—	2	1	no	—
446	C₂×C₄×C₂₃	—	2	2	no	—
447	C₂×C₄×C₂₃	—	2	2	no	—
448	C₂×C₄×C₂₃	—	2	2	no	—
449	C₂×C₄×C₂₃	—	4	1	no	—
450	C₂×C₄×C₂₃	—	4	1	no	—
451	C₂×C₄×C₂₃	—	4	1	no	—
452	C₂×C₄×C₂₃	—	4	2	no	—
453	C₂×C₄×C₂₃	—	4	2	no	—
454	C₂×C₄×C₂₃	—	4	2	no	—
455	C₂×C₄×C₂₃	—	4	2	no	—
456	C₂×C₄×C₂₃	—	8	2	no	—
457	C₂×C₄×C₂₃	—	8	1	no	—
458	C₂×C₄×C₂₃	—	8	1	no	—
459	C₂×C₄×C₂₃	—	8	1	no	—
460	C₂×C₄×C₂₃	—	8	1	no	—
461	C₂×C₄×C₂₃	—	8	2	no	—
462	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
463	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
464	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
465	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
466	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
467	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
468	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
469	C₈×C₂₃	—	2	2	no	—
470	C₈×C₂₃	—	2	2	no	—
471	C₈×C₂₃	—	2	2	no	—
472	C₈×C₂₃	—	2	2	no	—
473	#3538	C₂×C₂₃	1	1	yes	characteristic
474	#3495	C₂×C₂₃	1	1	yes	characteristic
475	#3352	C₂×C₂₃	1	2	yes	complemented
476	#3349	C₂×C₂₃	1	2	yes	complemented
477	#3344	C₂×C₂₃	1	2	yes	complemented
478	#3336	C₂×C₂₃	1	2	yes	complemented
479	#3328	C₂×C₂₃	1	2	yes	complemented
480	#3312	C₂×C₂₃	1	2	yes	complemented
481	#3312	C₂×C₂₃	1	2	yes	complemented
482	#3299	C₂×C₂₃	1	2	yes	complemented
483	#3242	C₂×C₂₃	1	2	yes	complemented
484	#3202	C₂×C₂₃	1	2	yes	complemented
485	#3195	C₂×C₂₃	1	1	yes	characteristic, complemented
486	#3189	C₂×C₂₃	1	1	yes	characteristic, complemented
487	#3127	C₂×C₂₃	1	2	yes	complemented
488	#3097	C₂×C₂₃	1	2	yes	complemented
489	#3095	C₂×C₂₃	1	1	yes	characteristic, complemented
490	C₂×#485	C₂×C₂₃	1	1	yes	characteristic, complemented
491	#2976	C₂×C₂₃	1	1	yes	characteristic
492	C₂²×C₂₃	—	2	1	no	—
493	C₂²×C₂₃	—	2	1	no	—
494	C₂²×C₂₃	—	2	1	no	—
495	C₂²×C₂₃	—	2	2	no	—
496	C₂²×C₂₃	—	2	1	no	—
497	C₂²×C₂₃	—	2	1	no	—
498	C₂²×C₂₃	—	2	1	no	—
499	C₂²×C₂₃	—	2	2	no	—
500	C₂²×C₂₃	—	2	2	no	—
501	C₂²×C₂₃	—	2	1	no	—
502	C₂²×C₂₃	—	2	1	no	—
503	C₂²×C₂₃	—	8	2	no	—
504	C₂²×C₂₃	#578	1	2	yes	—
505	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
506	C₄×C₂₃	—	2	2	no	—
507	C₄×C₂₃	—	2	1	no	—
508	C₄×C₂₃	—	2	1	no	—
509	C₄×C₂₃	—	2	1	no	—
510	C₄×C₂₃	—	2	2	no	—
511	C₄×C₂₃	—	2	2	no	—
512	C₄×C₂₃	—	4	2	no	—
513	C₄×C₂₃	—	4	1	no	—
514	C₄×C₂₃	—	4	2	no	—
515	C₄×C₂₃	—	4	1	no	—
516	C₄×C₂₃	—	4	2	no	—
517	C₄×C₂₃	—	4	2	no	—
518	C₄×C₂₃	—	4	2	no	—
519	C₄×C₂₃	—	4	1	no	—
520	C₄×C₂₃	—	4	1	no	—
521	C₄×C₂₃	—	4	2	no	—
522	C₄×C₂₃	#585	1	1	yes	characteristic
523	C₄×C₂₃	#585	1	1	yes	characteristic
524	#563	—	2	2	no	—
525	#556	C₂²×C₂₃	1	2	yes	—
526	#554	C₂²×C₂₃	1	2	yes	—
527	#552	—	2	2	no	—
528	#552	C₂²×C₂₃	1	2	yes	—
529	#552	C₂²×C₂₃	1	2	yes	—
530	#552	C₂²×C₂₃	1	2	yes	—
531	#552	C₂²×C₂₃	1	2	yes	—
532	#551	—	2	2	no	—
533	#551	—	2	2	no	—
534	D₄×Q₈	C₂²×C₂₃	1	2	yes	—
535	D₄×Q₈	C₂²×C₂₃	1	2	yes	—
536	#544	—	2	1	no	—
537	#544	—	2	1	no	—
538	#544	C₂²×C₂₃	1	1	yes	characteristic
539	#542	—	2	1	no	—
540	#541	—	2	1	no	—
541	#541	C₂²×C₂₃	1	2	yes	—
542	#539	—	2	1	no	—
543	#539	—	2	1	no	—
544	#536	C₂²×C₂₃	1	2	yes	—
545	#536	C₂²×C₂₃	1	1	yes	characteristic
546	#533	—	2	1	no	—
547	#529	—	2	1	no	—
548	#525	C₂²×C₂₃	1	1	yes	characteristic
549	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
550	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
551	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
552	#520	C₂²×C₂₃	1	1	yes	characteristic
553	#519	C₂²×C₂₃	1	1	yes	characteristic
554	C₂×#117	C₂²×C₂₃	1	1	yes	characteristic
555	#501	C₂²×C₂₃	1	2	yes	complemented
556	#499	C₂²×C₂₃	1	2	yes	complemented
557	#491	C₂²×C₂₃	1	2	yes	complemented
558	#487	C₂²×C₂₃	1	2	yes	complemented
559	#485	C₂²×C₂₃	1	2	yes	—
560	#485	C₂²×C₂₃	1	2	yes	—
561	#485	C₂²×C₂₃	1	2	yes	—
562	#485	C₂²×C₂₃	1	2	yes	—
563	#485	C₂²×C₂₃	1	2	yes	—
564	#485	C₂²×C₂₃	1	2	yes	—
565	#485	C₂²×C₂₃	1	2	yes	complemented
566	#485	C₂²×C₂₃	1	2	yes	complemented
567	#485	C₂²×C₂₃	1	2	yes	complemented
568	#485	C₂²×C₂₃	1	2	yes	complemented
569	#484	C₂²×C₂₃	1	2	yes	—
570	#484	C₂²×C₂₃	1	2	yes	—
571	#484	C₂²×C₂₃	1	2	yes	—
572	#484	C₂²×C₂₃	1	2	yes	complemented
573	#483	C₂²×C₂₃	1	2	yes	—
574	#483	C₂²×C₂₃	1	2	yes	—
575	#483	C₂²×C₂₃	1	2	yes	—
576	#483	C₂²×C₂₃	1	2	yes	complemented
577	#479	C₂²×C₂₃	1	2	yes	complemented
578	#479	C₂²×C₂₃	1	2	yes	complemented
579	#479	C₂²×C₂₃	1	2	yes	complemented
580	#479	C₂²×C₂₃	1	2	yes	complemented
581	#477	C₂²×C₂₃	1	2	yes	complemented
582	#475	C₂²×C₂₃	1	2	yes	complemented
583	#470	C₂²×C₂₃	1	2	yes	—
584	#470	C₂²×C₂₃	1	2	yes	—
585	#470	C₂²×C₂₃	1	2	yes	complemented
586	#470	C₂²×C₂₃	1	2	yes	complemented
587	#467	C₂²×C₂₃	1	2	yes	—
588	#467	C₂²×C₂₃	1	2	yes	—
589	#467	C₂²×C₂₃	1	2	yes	complemented
590	#467	C₂²×C₂₃	1	2	yes	complemented
591	#462	C₂²×C₂₃	1	2	yes	complemented
592	#462	C₂²×C₂₃	1	2	yes	complemented
593	#451	C₂²×C₂₃	1	2	yes	—
594	#451	C₂²×C₂₃	1	2	yes	—
595	#451	C₂²×C₂₃	1	2	yes	—
596	#451	C₂²×C₂₃	1	2	yes	—
597	#451	C₂²×C₂₃	1	2	yes	complemented
598	#451	C₂²×C₂₃	1	2	yes	complemented
599	#441	C₂²×C₂₃	1	2	yes	complemented
600	#441	C₂²×C₂₃	1	2	yes	complemented
601	C₄×Q₁₆	C₂²×C₂₃	1	2	yes	complemented
602	C₄×Q₁₆	C₂²×C₂₃	1	2	yes	complemented
603	#436	C₂²×C₂₃	1	2	yes	—
604	#435	C₂²×C₂₃	1	2	yes	—
605	#435	C₂²×C₂₃	1	2	yes	—
606	C₈×D₄	C₂²×C₂₃	1	2	yes	—
607	#433	C₂²×C₂₃	1	2	yes	—
608	#428	C₂²×C₂₃	1	1	yes	characteristic
609	#428	C₂²×C₂₃	1	1	yes	characteristic
610	#428	C₂²×C₂₃	1	2	yes	complemented
611	#427	C₂²×C₂₃	1	2	yes	complemented
612	C₂×#107	C₂²×C₂₃	1	1	yes	characteristic
613	C₂×#106	C₂²×C₂₃	1	1	yes	characteristic
614	#419	C₂²×C₂₃	1	1	yes	characteristic
615	#419	C₂²×C₂₃	1	1	yes	characteristic
616	#419	C₂²×C₂₃	1	2	yes	complemented
617	C₂×#103	C₂²×C₂₃	1	1	yes	characteristic
618	C₂×#103	C₂²×C₂₃	1	1	yes	characteristic
619	C₂×#103	C₂²×C₂₃	1	2	yes	complemented
620	#408	C₂²×C₂₃	1	2	yes	—
621	#407	C₂²×C₂₃	1	1	yes	characteristic
622	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
623	C₂×C₂₃	—	2	2	no	—
624	C₂×C₂₃	—	4	2	no	—
625	C₂×C₂₃	—	4	1	no	—
626	C₂×C₂₃	—	4	1	no	—
627	C₂×C₂₃	#3485	1	1	yes	characteristic
628	C₂×C₂₃	C₂×#578	1	1	yes	characteristic
629	C₂×C₂₃	#3586	1	1	yes	characteristic
630	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
631	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
632	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
633	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
634	C₂²×Q₈	C₂³×C₂₃	1	2	yes	—
635	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
636	C₂×Q₁₆	C₂³×C₂₃	1	2	yes	—
637	C₂×Q₁₆	C₂³×C₂₃	1	2	yes	—
638	C₂×Q₁₆	C₂³×C₂₃	1	2	yes	—
639	C₂×Q₁₆	C₂³×C₂₃	1	2	yes	—
640	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
641	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
642	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
643	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
644	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
645	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
646	C₄⋊Q₈	—	2	1	no	—
647	C₄⋊Q₈	—	2	2	no	—
648	C₄⋊Q₈	—	2	1	no	—
649	C₄⋊Q₈	—	2	2	no	—
650	C₄⋊Q₈	—	2	2	no	—
651	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
652	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
653	#126	—	2	2	no	—
654	#126	—	2	2	no	—
655	#126	—	2	2	no	—
656	#126	—	2	2	no	—
657	#126	—	2	2	no	—
658	#126	—	2	2	no	—
659	#126	—	2	2	no	—
660	#126	—	2	2	no	—
661	#125	—	2	1	no	—
662	#125	—	2	2	no	—
663	#125	—	2	2	no	—
664	#125	—	2	2	no	—
665	#125	—	2	2	no	—
666	#125	—	2	2	no	—
667	#125	—	2	2	no	—
668	#125	—	2	2	no	—
669	#125	C₂³×C₂₃	1	2	yes	—
670	#125	C₂³×C₂₃	1	2	yes	—
671	#124	—	2	1	no	—
672	#124	—	2	2	no	—
673	#124	—	2	2	no	—
674	#123	—	2	2	no	—
675	#123	—	2	2	no	—
676	#123	—	2	2	no	—
677	#123	—	2	2	no	—
678	#123	—	2	2	no	—
679	#123	—	2	2	no	—
680	#123	—	2	2	no	—
681	#123	D₄×C₂₃	1	2	yes	—
682	C₂²⋊Q₈	—	2	1	no	—
683	C₂²⋊Q₈	—	2	1	no	—
684	C₂²⋊Q₈	—	2	1	no	—
685	C₂²⋊Q₈	—	2	1	no	—
686	C₂²⋊Q₈	—	2	1	no	—
687	C₂²⋊Q₈	—	2	1	no	—
688	C₂²⋊Q₈	—	2	2	no	—
689	C₂²⋊Q₈	—	2	2	no	—
690	C₂²⋊Q₈	—	2	2	no	—
691	C₂²⋊Q₈	—	2	2	no	—
692	C₂²⋊Q₈	—	2	2	no	—
693	C₂²⋊Q₈	—	2	2	no	—
694	C₂²⋊Q₈	—	2	2	no	—
695	C₂²⋊Q₈	D₄×C₂₃	1	1	yes	characteristic
696	C₂²⋊Q₈	D₄×C₂₃	1	1	yes	characteristic
697	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
698	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
699	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
700	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
701	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
702	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
703	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
704	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
705	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
706	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
707	#121	D₄×C₂₃	1	1	yes	characteristic
708	#121	D₄×C₂₃	1	1	yes	characteristic
709	#120	D₄×C₂₃	1	2	yes	—
710	C₄×Q₈	—	2	1	no	—
711	C₄×Q₈	—	2	1	no	—
712	C₄×Q₈	—	2	1	no	—
713	C₄×Q₈	—	2	2	no	—
714	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
715	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
716	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
717	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
718	C₄×D₄	—	2	1	no	—
719	C₄×D₄	—	2	2	no	—
720	C₄×D₄	—	2	2	no	—
721	C₄×D₄	—	2	2	no	—
722	C₄×D₄	—	2	2	no	—
723	C₄×D₄	C₂³×C₂₃	1	2	yes	—
724	C₄×D₄	C₂³×C₂₃	1	2	yes	—
725	#117	—	2	1	no	—
726	#117	—	2	1	no	—
727	#117	—	2	2	no	—
728	#117	—	2	2	no	—
729	#117	—	2	2	no	—
730	#117	—	2	2	no	—
731	#117	—	2	2	no	—
732	#117	C₂³×C₂₃	1	1	yes	characteristic
733	#117	C₂³×C₂₃	1	1	yes	characteristic
734	#117	C₂³×C₂₃	1	1	yes	characteristic
735	#117	C₂³×C₂₃	1	1	yes	characteristic
736	#117	C₂³×C₂₃	1	2	yes	—
737	#117	C₂³×C₂₃	1	2	yes	—
738	#117	C₂³×C₂₃	1	1	yes	characteristic
739	C₂×C₄⋊C₄	—	2	1	no	—
740	C₂×C₄⋊C₄	—	2	1	no	—
741	C₂×C₄⋊C₄	—	2	1	no	—
742	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
743	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
744	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
745	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
746	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
747	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
748	C₂×C₂²⋊C₄	—	2	1	no	—
749	C₂×C₂²⋊C₄	—	2	1	no	—
750	C₂×C₂²⋊C₄	—	2	1	no	—
751	C₂×C₂²⋊C₄	—	2	1	no	—
752	C₂×C₄²	—	2	1	no	—
753	#107	C₂³×C₂₃	1	2	yes	—
754	#107	C₂³×C₂₃	1	2	yes	—
755	#107	C₂³×C₂₃	1	2	yes	—
756	#107	C₂³×C₂₃	1	2	yes	—
757	#107	C₂³×C₂₃	1	2	yes	—
758	#107	C₂³×C₂₃	1	2	yes	—
759	#106	C₂³×C₂₃	1	2	yes	—
760	#106	C₂³×C₂₃	1	2	yes	—
761	#106	C₂³×C₂₃	1	2	yes	—
762	#106	C₂³×C₂₃	1	2	yes	—
763	#106	C₂³×C₂₃	1	2	yes	—
764	#106	C₂³×C₂₃	1	2	yes	—
765	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
766	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
767	#103	C₂³×C₂₃	1	2	yes	—
768	#103	C₂³×C₂₃	1	2	yes	—
769	#103	C₂³×C₂₃	1	2	yes	—
770	#103	C₂³×C₂₃	1	2	yes	—
771	#103	C₂³×C₂₃	1	2	yes	—
772	#103	C₂³×C₂₃	1	2	yes	—
773	#103	C₂³×C₂₃	1	2	yes	—
774	#103	C₂³×C₂₃	1	2	yes	—
775	#103	C₂³×C₂₃	1	2	yes	—
776	#103	C₂³×C₂₃	1	2	yes	—
777	#103	C₂³×C₂₃	1	2	yes	—
778	#103	C₂³×C₂₃	1	2	yes	—
779	#103	C₂³×C₂₃	1	2	yes	—
780	#103	C₂³×C₂₃	1	2	yes	—
781	#103	C₂³×C₂₃	1	2	yes	—
782	#103	C₂³×C₂₃	1	2	yes	—
783	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
784	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
785	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
786	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
787	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
788	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
789	#97	C₂³×C₂₃	1	2	yes	—
790	C₄×C₈	C₂³×C₂₃	1	2	yes	—
791	C₂₃	#61757	1	1	yes	characteristic, direct product factor, Sylow
792	C₂⁴	C₂×D₄×C₂₃	1	1	yes	characteristic
793	#41	—	4	1	no	—
794	#41	—	4	1	no	—
795	C₂×Q₈	—	2	1	no	—
796	C₂×Q₈	—	2	2	no	—
797	C₂×Q₈	—	2	1	no	—
798	C₂×Q₈	—	2	1	no	—
799	C₂×Q₈	—	2	2	no	—
800	C₂×Q₈	—	4	1	no	—
801	C₂×Q₈	—	4	1	no	—
802	C₂×Q₈	—	4	1	no	—
803	C₂×Q₈	—	4	1	no	—
804	C₂×Q₈	—	4	2	no	—
805	C₂×Q₈	—	4	1	no	—
806	C₂×Q₈	—	4	1	no	—
807	C₂×Q₈	—	4	2	no	—
808	C₂×Q₈	C₂×D₄×C₂₃	1	1	yes	characteristic
809	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
810	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
811	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
812	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
813	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
814	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
815	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
816	C₂²×C₄	—	2	1	no	—
817	C₂²×C₄	—	2	1	no	—
818	C₂²×C₄	—	2	1	no	—
819	C₂²×C₄	—	2	1	no	—
820	C₂²×C₄	—	2	1	no	—
821	C₂²×C₄	—	2	1	no	—
822	C₂²×C₄	—	2	1	no	—
823	C₂²×C₄	—	2	1	no	—
824	C₂²×C₄	—	2	2	no	—
825	C₂²×C₄	—	2	2	no	—
826	C₂²×C₄	—	4	1	no	—
827	C₂²×C₄	—	4	1	no	—
828	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
829	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
830	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
831	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
832	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
833	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
834	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
835	Q₁₆	—	4	2	no	—
836	Q₁₆	—	4	2	no	—
837	Q₁₆	—	4	2	no	—
838	Q₁₆	—	4	2	no	—
839	M₁₆	—	4	1	no	—
840	M₁₆	—	4	2	no	—
841	M₁₆	—	4	1	no	—
842	C₂×C₈	—	4	1	no	—
843	C₂×C₈	—	4	2	no	—
844	C₂×C₈	—	4	1	no	—
845	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
846	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
847	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
848	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
849	C₄⋊C₄	—	2	2	no	—
850	C₄⋊C₄	—	2	2	no	—
851	C₄⋊C₄	—	2	2	no	—
852	C₄⋊C₄	—	2	2	no	—
853	C₄⋊C₄	—	2	2	no	—
854	C₄⋊C₄	—	2	2	no	—
855	C₄⋊C₄	—	2	1	no	—
856	C₄⋊C₄	—	2	1	no	—
857	C₄⋊C₄	—	2	1	no	—
858	C₄⋊C₄	—	2	2	no	—
859	C₄⋊C₄	—	2	1	no	—
860	C₄⋊C₄	—	2	1	no	—
861	C₄⋊C₄	—	2	2	no	—
862	C₄⋊C₄	—	2	2	no	—
863	C₄⋊C₄	—	2	2	no	—
864	C₄⋊C₄	—	2	2	no	—
865	C₄⋊C₄	—	2	2	no	—
866	C₄⋊C₄	—	2	2	no	—
867	C₄⋊C₄	—	2	2	no	—
868	C₄⋊C₄	—	2	2	no	—
869	C₄⋊C₄	—	2	2	no	—
870	C₄⋊C₄	—	2	2	no	—
871	C₄⋊C₄	—	2	2	no	—
872	C₄⋊C₄	—	2	2	no	—
873	C₄⋊C₄	—	2	2	no	—
874	C₄⋊C₄	—	2	2	no	—
875	C₄⋊C₄	—	2	2	no	—
876	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
877	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
878	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
879	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
880	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
881	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
882	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
883	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
884	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
885	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
886	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
887	C₂²⋊C₄	—	2	1	no	—
888	C₂²⋊C₄	—	2	1	no	—
889	C₂²⋊C₄	—	2	1	no	—
890	C₂²⋊C₄	—	2	1	no	—
891	C₂²⋊C₄	—	2	2	no	—
892	C₂²⋊C₄	—	2	2	no	—
893	C₂²⋊C₄	—	2	2	no	—
894	C₂²⋊C₄	—	2	2	no	—
895	C₂²⋊C₄	—	2	2	no	—
896	C₂²⋊C₄	—	2	2	no	—
897	C₂²⋊C₄	—	2	2	no	—
898	C₂²⋊C₄	—	2	2	no	—
899	C₂²⋊C₄	—	2	2	no	—
900	C₂²⋊C₄	—	2	2	no	—
901	C₂²⋊C₄	—	2	2	no	—
902	C₂²⋊C₄	—	2	2	no	—
903	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
904	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
905	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
906	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
907	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
908	C₄²	—	2	1	no	—
909	C₄²	—	2	1	no	—
910	C₄²	—	2	1	no	—
911	C₄²	—	2	1	no	—
912	C₄²	—	2	2	no	—
913	C₄²	—	2	2	no	—
914	C₄²	—	2	2	no	—
915	C₄²	—	2	2	no	—
916	C₄²	—	2	2	no	—
917	C₄²	—	2	2	no	—
918	C₄²	C₂⁴×C₂₃	1	2	yes	—
919	C₂³	—	2	2	no	—
920	C₂³	—	4	1	no	—
921	C₂³	—	4	1	no	—
922	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
923	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
924	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
925	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
926	Q₈	—	2	2	no	—
927	Q₈	—	2	2	no	—
928	Q₈	—	2	2	no	—
929	Q₈	—	2	2	no	—
930	Q₈	—	2	2	no	—
931	Q₈	—	2	2	no	—
932	Q₈	—	4	1	no	—
933	Q₈	—	4	2	no	—
934	Q₈	—	8	1	no	—
935	Q₈	—	8	1	no	—
936	Q₈	—	8	2	no	—
937	Q₈	—	8	2	no	—
938	D₄	—	2	4	no	—
939	D₄	—	4	1	no	—
940	D₄	—	4	2	no	—
941	D₄	—	4	2	no	—
942	C₂×C₄	—	2	1	no	—
943	C₂×C₄	—	2	1	no	—
944	C₂×C₄	—	2	2	no	—
945	C₂×C₄	—	2	1	no	—
946	C₂×C₄	—	2	1	no	—
947	C₂×C₄	—	2	2	no	—
948	C₂×C₄	—	2	1	no	—
949	C₂×C₄	—	2	1	no	—
950	C₂×C₄	—	2	1	no	—
951	C₂×C₄	—	2	1	no	—
952	C₂×C₄	—	2	1	no	—
953	C₂×C₄	—	2	2	no	—
954	C₂×C₄	—	2	2	no	—
955	C₂×C₄	—	2	2	no	—
956	C₂×C₄	—	2	1	no	—
957	C₂×C₄	—	2	2	no	—
958	C₂×C₄	—	2	2	no	—
959	C₂×C₄	—	2	2	no	—
960	C₂×C₄	—	4	1	no	—
961	C₂×C₄	—	4	1	no	—
962	C₂×C₄	—	4	1	no	—
963	C₂×C₄	—	4	2	no	—
964	C₂×C₄	—	4	2	no	—
965	C₂×C₄	—	4	2	no	—
966	C₂×C₄	—	4	2	no	—
967	C₂×C₄	—	8	1	no	—
968	C₂×C₄	—	8	1	no	—
969	C₂×C₄	—	8	2	no	—
970	C₂×C₄	—	8	2	no	—
971	C₂×C₄	—	8	1	no	—
972	C₂×C₄	—	8	1	no	—
973	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
974	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
975	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
976	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
977	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
978	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
979	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
980	C₈	—	2	2	no	—
981	C₈	—	2	2	no	—
982	C₈	—	2	2	no	—
983	C₈	—	2	2	no	—
984	C₂²	—	2	1	no	—
985	C₂²	—	2	1	no	—
986	C₂²	—	2	1	no	—
987	C₂²	—	2	1	no	—
988	C₂²	—	2	2	no	—
989	C₂²	—	2	2	no	—
990	C₂²	—	2	1	no	—
991	C₂²	—	2	1	no	—
992	C₂²	—	2	1	no	—
993	C₂²	—	2	2	no	—
994	C₂²	—	2	1	no	—
995	C₂²	—	8	2	no	—
996	C₂²	C₂₃×#578	1	2	yes	—
997	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
998	C₄	—	2	1	no	—
999	C₄	—	2	1	no	—
1000	C₄	—	2	1	no	—
1001	C₄	—	2	2	no	—
1002	C₄	—	2	2	no	—
1003	C₄	—	2	2	no	—
1004	C₄	—	4	2	no	—
1005	C₄	—	4	2	no	—
1006	C₄	—	4	2	no	—
1007	C₄	—	4	1	no	—
1008	C₄	—	4	1	no	—
1009	C₄	—	4	2	no	—
1010	C₄	—	4	2	no	—
1011	C₄	—	4	1	no	—
1012	C₄	—	4	2	no	—
1013	C₄	—	4	1	no	—
1014	C₄	C₂₃×#585	1	1	yes	characteristic
1015	C₄	C₂₃×#585	1	1	yes	characteristic
1016	C₂	—	2	2	no	—
1017	C₂	—	4	1	no	—
1018	C₂	—	4	1	no	—
1019	C₂	—	4	2	no	—
1020	C₂	C₂₃×#3485	1	1	yes	characteristic
1021	C₂	C₂×C₂₃×#578	1	1	yes	characteristic
1022	C₂	C₂₃×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₂₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₂₃
prime radical	C₂₃×#525	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₃ ◁ C₂₃×#525 ◁ G

Complements

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

N	H ≅ G/N	type
3. C₂₃×#3352	C₂	semidirect
4. C₂₃×#3349	C₂	semidirect
5. C₂₃×#3344	C₂	semidirect
6. C₂₃×#3336	C₂	semidirect
7. C₂₃×#3328	C₂	semidirect
8. C₂₃×#3312	C₂	semidirect
9. C₂₃×#3312	C₂	semidirect
10. C₂₃×#3299	C₂	semidirect
11. C₂₃×#3242	C₂	semidirect
12. C₂₃×#3202	C₂	semidirect
13. C₂₃×#3195	C₂	semidirect
14. C₂₃×#3189	C₂	semidirect
15. C₂₃×#3127	C₂	semidirect
16. C₂₃×#3097	C₂	semidirect
17. C₂₃×#3095	C₂	semidirect
18. C₂×C₂₃×#485	C₂	semidirect
51. C₂₃×#501	C₂²	semidirect
52. C₂₃×#499	C₂²	semidirect
53. C₂₃×#491	C₂²	semidirect
54. C₂₃×#487	C₂²	semidirect
61. C₂₃×#485	C₂²	semidirect
62. C₂₃×#485	C₂²	semidirect
63. C₂₃×#485	C₂²	semidirect
64. C₂₃×#485	C₂²	semidirect
68. C₂₃×#484	C₂²	semidirect
72. C₂₃×#483	C₂²	semidirect
73. C₂₃×#479	C₂²	semidirect
74. C₂₃×#479	C₂²	semidirect
75. C₂₃×#479	C₂²	semidirect
76. C₂₃×#479	C₂²	semidirect
77. C₂₃×#477	C₂²	semidirect
78. C₂₃×#475	C₂²	semidirect
81. C₂₃×#470	C₂²	semidirect
82. C₂₃×#470	C₂²	semidirect
85. C₂₃×#467	C₂²	semidirect
86. C₂₃×#467	C₂²	semidirect
87. C₂₃×#462	C₂²	semidirect
88. C₂₃×#462	C₂²	semidirect
93. C₂₃×#451	C₂²	semidirect
94. C₂₃×#451	C₂²	semidirect
95. C₂₃×#441	C₂²	semidirect
96. C₂₃×#441	C₂²	semidirect
97. C₄×Q₁₆×C₂₃	C₂²	semidirect
98. C₄×Q₁₆×C₂₃	C₂²	semidirect
106. C₂₃×#428	C₂²	semidirect
107. C₂₃×#427	C₂²	semidirect
112. C₂₃×#419	C₂²	semidirect
115. C₂×C₂₃×#103	C₂²	semidirect
407. #61757	C₂₃	direct (N × H)
475. #3352	C₂×C₂₃	semidirect
476. #3349	C₂×C₂₃	semidirect
477. #3344	C₂×C₂₃	semidirect
478. #3336	C₂×C₂₃	semidirect
479. #3328	C₂×C₂₃	semidirect
480. #3312	C₂×C₂₃	semidirect
481. #3312	C₂×C₂₃	semidirect
482. #3299	C₂×C₂₃	semidirect
483. #3242	C₂×C₂₃	semidirect
484. #3202	C₂×C₂₃	semidirect
485. #3195	C₂×C₂₃	semidirect
486. #3189	C₂×C₂₃	semidirect
487. #3127	C₂×C₂₃	semidirect
488. #3097	C₂×C₂₃	semidirect
489. #3095	C₂×C₂₃	semidirect
490. C₂×#485	C₂×C₂₃	semidirect
555. #501	C₂²×C₂₃	semidirect
556. #499	C₂²×C₂₃	semidirect
557. #491	C₂²×C₂₃	semidirect
558. #487	C₂²×C₂₃	semidirect
565. #485	C₂²×C₂₃	semidirect
566. #485	C₂²×C₂₃	semidirect
567. #485	C₂²×C₂₃	semidirect
568. #485	C₂²×C₂₃	semidirect
572. #484	C₂²×C₂₃	semidirect
576. #483	C₂²×C₂₃	semidirect
577. #479	C₂²×C₂₃	semidirect
578. #479	C₂²×C₂₃	semidirect
579. #479	C₂²×C₂₃	semidirect
580. #479	C₂²×C₂₃	semidirect
581. #477	C₂²×C₂₃	semidirect
582. #475	C₂²×C₂₃	semidirect
585. #470	C₂²×C₂₃	semidirect
586. #470	C₂²×C₂₃	semidirect
589. #467	C₂²×C₂₃	semidirect
590. #467	C₂²×C₂₃	semidirect
591. #462	C₂²×C₂₃	semidirect
592. #462	C₂²×C₂₃	semidirect
597. #451	C₂²×C₂₃	semidirect
598. #451	C₂²×C₂₃	semidirect
599. #441	C₂²×C₂₃	semidirect
600. #441	C₂²×C₂₃	semidirect
601. C₄×Q₁₆	C₂²×C₂₃	semidirect
602. C₄×Q₁₆	C₂²×C₂₃	semidirect
610. #428	C₂²×C₂₃	semidirect
611. #427	C₂²×C₂₃	semidirect
616. #419	C₂²×C₂₃	semidirect
619. C₂×#103	C₂²×C₂₃	semidirect
791. C₂₃	#61757	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×#3538	2
C₂₃×#3495	2
C₂₃×#3352	2
C₂₃×#3349	2
C₂₃×#3344	2
C₂₃×#3336	2
C₂₃×#3328	2
C₂₃×#3312	2
C₂₃×#3299	2
C₂₃×#3242	2
C₂₃×#3202	2
C₂₃×#3195	2
C₂₃×#3189	2
C₂₃×#3127	2
C₂₃×#3097	2
C₂₃×#3095	2
C₂×C₂₃×#485	2
C₂₃×#2976	2
#61757	23

Subgroups — C23×#61757 #19209383

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#61757 #19209383