Subgroups — C₂₃×#61703 #19209329

Order 5888.

1780 conjugacy classes of subgroups.

The subgroup lattice has 1132 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3520	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂₃×#3475	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#3342	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₃×#3340	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₃×#3337	C₂	1	2	yes	maximal, complemented
6	C₂₃×#3336	C₂	1	2	yes	maximal, complemented
7	C₂₃×#3335	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₃×#3334	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₃×#3303	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₃×#3302	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₃×#3301	C₂	1	2	yes	maximal, complemented
12	C₂₃×#3300	C₂	1	2	yes	maximal, complemented
13	C₂₃×#3299	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₃×#3298	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₃×#3233	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂₃×#3231	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂₃×#3191	C₂	1	2	yes	maximal, complemented
18	C₂₃×#3190	C₂	1	2	yes	maximal, complemented
19	C₂₃×#3107	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂₃×#3102	C₂	1	1	yes	maximal, characteristic, complemented
21	C₂₃×#3091	C₂	1	2	yes	maximal, complemented
22	C₂×C₂₃×#485	C₂	1	2	yes	maximal, complemented
23	C₂₃×#2972	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂₃×#556	C₂²	1	1	yes	characteristic
25	C₂₃×#556	C₂²	1	1	yes	characteristic
26	C₂₃×#555	C₂²	1	1	yes	characteristic
27	C₂₃×#554	—	2	1	no	—
28	C₂₃×#554	C₂²	1	1	yes	characteristic
29	C₂₃×#553	C₂²	1	2	yes	—
30	C₂₃×#552	—	2	1	no	—
31	C₂₃×#552	C₂²	1	2	yes	—
32	C₂₃×#552	C₂²	1	2	yes	—
33	C₂₃×#551	—	2	2	no	—
34	C₂₃×#551	—	2	2	no	—
35	D₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic
36	C₂₃×#548	C₂²	1	2	yes	—
37	C₂₃×#547	C₂²	1	1	yes	characteristic
38	C₂₃×#547	C₂²	1	1	yes	characteristic
39	C₂₃×#547	C₂²	1	1	yes	characteristic
40	C₂₃×#546	—	2	1	no	—
41	C₂₃×#546	—	2	1	no	—
42	C₂₃×#542	—	2	1	no	—
43	C₂₃×#539	—	2	2	no	—
44	C₂₃×#533	C₂²	1	1	yes	characteristic
45	C₂₃×#533	C₂²	1	1	yes	characteristic
46	C₂₃×#529	—	2	2	no	—
47	C₂₃×#529	—	2	1	no	—
48	C₂₃×#529	C₂²	1	1	yes	characteristic
49	C₂₃×#525	C₂²	1	2	yes	—
50	C₂₃×#525	C₂²	1	2	yes	—
51	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	2	yes	—
52	C₂₃×#520	—	2	1	no	—
53	C₄×#41×C₂₃	—	2	1	no	—
54	C₄×#41×C₂₃	C₂²	1	1	yes	characteristic
55	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
56	C₂×C₂₃×#117	C₂²	1	2	yes	—
57	C₂₃×#500	C₂²	1	1	yes	characteristic, complemented
58	C₂₃×#499	C₂²	1	2	yes	complemented
59	C₂₃×#498	C₂²	1	1	yes	characteristic, complemented
60	C₂₃×#488	C₂²	1	2	yes	complemented
61	C₂₃×#487	C₂²	1	1	yes	characteristic, complemented
62	C₂₃×#487	C₂²	1	1	yes	characteristic, complemented
63	C₂₃×#485	C₂²	1	2	yes	—
64	C₂₃×#485	C₂²	1	2	yes	—
65	C₂₃×#485	C₂²	1	2	yes	—
66	C₂₃×#485	C₂²	1	1	yes	characteristic
67	C₂₃×#485	C₂²	1	2	yes	—
68	C₂₃×#485	C₂²	1	2	yes	complemented
69	C₂₃×#485	C₂²	1	2	yes	complemented
70	C₂₃×#485	C₂²	1	2	yes	complemented
71	C₂₃×#485	C₂²	1	2	yes	complemented
72	C₂₃×#485	C₂²	1	2	yes	complemented
73	C₂₃×#484	C₂²	1	2	yes	complemented
74	C₂₃×#483	C₂²	1	2	yes	complemented
75	C₂₃×#483	C₂²	1	2	yes	complemented
76	C₂₃×#482	C₂²	1	2	yes	—
77	C₂₃×#482	C₂²	1	1	yes	characteristic
78	C₂₃×#482	C₂²	1	2	yes	complemented
79	C₂₃×#481	C₂²	1	2	yes	complemented
80	C₂₃×#480	C₂²	1	2	yes	complemented
81	C₂₃×#480	C₂²	1	2	yes	complemented
82	C₂₃×#479	C₂²	1	2	yes	complemented
83	C₂₃×#479	C₂²	1	2	yes	complemented
84	C₂₃×#479	C₂²	1	1	yes	characteristic, complemented
85	C₂₃×#478	C₂²	1	1	yes	characteristic, complemented
86	C₂₃×#477	C₂²	1	1	yes	characteristic, complemented
87	C₂₃×#476	C₂²	1	1	yes	characteristic, complemented
88	C₂₃×#475	C₂²	1	1	yes	characteristic, complemented
89	C₂₃×#475	C₂²	1	1	yes	characteristic, complemented
90	C₂₃×#474	C₂²	1	1	yes	characteristic, complemented
91	C₂₃×#474	C₂²	1	1	yes	characteristic, complemented
92	C₂₃×#467	C₂²	1	2	yes	complemented
93	C₂₃×#467	C₂²	1	2	yes	complemented
94	C₂₃×#467	C₂²	1	2	yes	complemented
95	C₂₃×#466	C₂²	1	2	yes	complemented
96	C₂₃×#465	C₂²	1	2	yes	complemented
97	C₂₃×#465	C₂²	1	2	yes	complemented
98	C₂₃×#465	C₂²	1	2	yes	complemented
99	C₂₃×#465	C₂²	1	2	yes	complemented
100	C₂₃×#464	C₂²	1	1	yes	characteristic, complemented
101	C₂₃×#463	C₂²	1	1	yes	characteristic, complemented
102	C₂₃×#462	C₂²	1	1	yes	characteristic, complemented
103	C₂₃×#461	C₂²	1	1	yes	characteristic, complemented
104	C₂₃×#452	C₂²	1	1	yes	characteristic
105	C₂₃×#452	C₂²	1	2	yes	—
106	C₂₃×#452	C₂²	1	2	yes	complemented
107	C₂₃×#451	C₂²	1	2	yes	complemented
108	C₂₃×#449	C₂²	1	1	yes	characteristic
109	C₂₃×#449	C₂²	1	2	yes	complemented
110	C₂₃×#448	C₂²	1	2	yes	complemented
111	C₄×Q₁₆×C₂₃	C₂²	1	1	yes	characteristic, complemented
112	C₄×Q₁₆×C₂₃	C₂²	1	2	yes	complemented
113	C₄×SD₁₆×C₂₃	C₂²	1	1	yes	characteristic, complemented
114	C₄×SD₁₆×C₂₃	C₂²	1	2	yes	complemented
115	C₄×SD₁₆×C₂₃	C₂²	1	1	yes	characteristic, complemented
116	C₄×D₈×C₂₃	C₂²	1	1	yes	characteristic, complemented
117	C₈×D₄×C₂₃	C₂²	1	1	yes	characteristic
118	C₈×D₄×C₂₃	C₂²	1	1	yes	characteristic
119	C₈×D₄×C₂₃	C₂²	1	2	yes	—
120	C₈×D₄×C₂₃	C₂²	1	2	yes	—
121	C₈×D₄×C₂₃	C₂²	1	1	yes	characteristic
122	C₈×D₄×C₂₃	C₂²	1	1	yes	characteristic
123	C₂₃×#431	C₂²	1	1	yes	characteristic
124	C₂₃×#431	C₂²	1	1	yes	characteristic
125	C₂₃×#427	C₂²	1	2	yes	complemented
126	C₂₃×#427	C₂²	1	2	yes	complemented
127	C₂×C₂₃×#107	C₂²	1	2	yes	complemented
128	C₂×C₂₃×#106	C₂²	1	2	yes	complemented
129	C₂₃×#416	C₂²	1	2	yes	complemented
130	C₂₃×#416	C₂²	1	2	yes	complemented
131	C₂×C₂₃×#103	C₂²	1	2	yes	complemented
132	C₂×C₂₃×#103	C₂²	1	2	yes	complemented
133	C₂×C₂₃×C₂²⋊C₈	C₂²	1	2	yes	—
134	C₂×C₂₃×C₂²⋊C₈	C₂²	1	2	yes	—
135	C₂×#41×C₂₃	—	2	1	no	—
136	C₂×#41×C₂₃	—	2	1	no	—
137	C₂×#41×C₂₃	C₂³	1	2	yes	—
138	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
139	C₂²×Q₈×C₂₃	C₂³	1	2	yes	—
140	C₂²×D₄×C₂₃	D₄	1	1	yes	characteristic
141	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
142	C₂×Q₁₆×C₂₃	C₂³	1	1	yes	characteristic
143	C₂×Q₁₆×C₂₃	C₂³	1	2	yes	—
144	C₂×SD₁₆×C₂₃	C₂³	1	1	yes	characteristic
145	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
146	C₂×SD₁₆×C₂₃	C₂³	1	1	yes	characteristic
147	C₂×D₈×C₂₃	C₂³	1	1	yes	characteristic
148	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
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	C₂₃×C₄⋊Q₈	—	2	1	no	—
153	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
154	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
155	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
156	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
157	C₂₃×#126	—	2	2	no	—
158	C₂₃×#126	—	2	2	no	—
159	C₂₃×#126	—	2	2	no	—
160	C₂₃×#126	—	2	2	no	—
161	C₂₃×#126	—	2	2	no	—
162	C₂₃×#126	—	2	1	no	—
163	C₂₃×#125	—	2	2	no	—
164	C₂₃×#125	—	2	1	no	—
165	C₂₃×#125	—	2	2	no	—
166	C₂₃×#125	—	2	1	no	—
167	C₂₃×#125	C₂³	1	1	yes	characteristic
168	C₂₃×#125	C₂³	1	2	yes	—
169	C₂₃×#124	—	2	1	no	—
170	C₂₃×#124	—	2	1	no	—
171	C₂₃×#124	—	2	2	no	—
172	C₂₃×#124	—	2	2	no	—
173	C₂₃×#124	C₂³	1	1	yes	characteristic
174	C₂₃×#123	—	2	2	no	—
175	C₂₃×#123	—	2	2	no	—
176	C₂₃×#123	—	2	1	no	—
177	C₂₃×#123	—	2	2	no	—
178	C₂₃×#123	—	2	2	no	—
179	C₂₃×#123	—	2	2	no	—
180	C₂₃×#123	—	2	2	no	—
181	C₂₃×#123	—	2	2	no	—
182	C₂₃×#123	—	2	2	no	—
183	C₂₃×C₂²⋊Q₈	—	2	1	no	—
184	C₂₃×C₂²⋊Q₈	—	2	2	no	—
185	C₂₃×C₂²⋊Q₈	—	2	1	no	—
186	C₂₃×C₂²⋊Q₈	—	2	1	no	—
187	C₂₃×C₂²⋊Q₈	—	2	2	no	—
188	C₂₃×C₂²⋊Q₈	—	2	1	no	—
189	C₂₃×C₂²⋊Q₈	—	2	1	no	—
190	C₂₃×C₂²⋊Q₈	—	2	2	no	—
191	C₂₃×C₂²⋊Q₈	—	2	2	no	—
192	C₂₃×C₂²⋊Q₈	—	2	2	no	—
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×C₂²⋊Q₈	C₂³	1	2	yes	—
197	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
198	C₂₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
199	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
200	C₂₃×#121	—	2	1	no	—
201	C₂₃×#121	—	2	2	no	—
202	C₂₃×#121	—	2	2	no	—
203	C₂₃×#121	—	2	1	no	—
204	C₂₃×#121	C₂³	1	2	yes	—
205	C₂₃×#121	C₂³	1	2	yes	—
206	C₂₃×#121	C₂³	1	2	yes	—
207	C₂₃×#121	C₂³	1	1	yes	characteristic
208	C₂₃×#120	—	2	2	no	—
209	C₂₃×#120	—	2	2	no	—
210	C₄×Q₈×C₂₃	—	2	1	no	—
211	C₄×Q₈×C₂₃	—	2	1	no	—
212	C₄×Q₈×C₂₃	—	2	1	no	—
213	C₄×Q₈×C₂₃	—	2	1	no	—
214	C₄×Q₈×C₂₃	—	2	1	no	—
215	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
216	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
217	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
218	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
219	C₄×D₄×C₂₃	—	2	1	no	—
220	C₄×D₄×C₂₃	—	2	1	no	—
221	C₄×D₄×C₂₃	—	2	1	no	—
222	C₄×D₄×C₂₃	—	2	2	no	—
223	C₄×D₄×C₂₃	—	2	1	no	—
224	C₄×D₄×C₂₃	—	2	1	no	—
225	C₄×D₄×C₂₃	—	2	2	no	—
226	C₄×D₄×C₂₃	—	2	2	no	—
227	C₄×D₄×C₂₃	—	2	2	no	—
228	C₄×D₄×C₂₃	—	2	2	no	—
229	C₄×D₄×C₂₃	—	2	2	no	—
230	C₄×D₄×C₂₃	D₄	1	1	yes	characteristic
231	C₄×D₄×C₂₃	D₄	1	2	yes	—
232	C₄×D₄×C₂₃	D₄	1	1	yes	characteristic
233	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
234	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
235	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
236	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
237	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
238	C₄×D₄×C₂₃	C₂³	1	2	yes	—
239	C₂₃×#117	—	2	1	no	—
240	C₂₃×#117	—	2	2	no	—
241	C₂₃×#117	—	2	2	no	—
242	C₂₃×#117	—	2	1	no	—
243	C₂₃×#117	—	2	2	no	—
244	C₂₃×#117	—	2	2	no	—
245	C₂₃×#117	—	2	1	no	—
246	C₂₃×#117	—	2	1	no	—
247	C₂₃×#117	C₂³	1	2	yes	—
248	C₂₃×#117	C₂³	1	2	yes	—
249	C₂₃×#117	C₂³	1	2	yes	—
250	C₂₃×#117	C₂³	1	1	yes	characteristic
251	C₂₃×#117	C₂³	1	2	yes	—
252	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
253	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
254	C₂×C₄⋊C₄×C₂₃	D₄	1	1	yes	characteristic
255	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
256	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
257	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
258	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
259	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
260	C₂×C₂²⋊C₄×C₂₃	D₄	1	2	yes	—
261	C₂×C₄²×C₂₃	—	2	2	no	—
262	C₂×C₄²×C₂₃	—	2	1	no	—
263	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
264	C₂₃×#107	C₂³	1	1	yes	characteristic
265	C₂₃×#107	C₂³	1	2	yes	—
266	C₂₃×#107	C₂³	1	2	yes	—
267	C₂₃×#107	C₂³	1	2	yes	—
268	C₂₃×#107	C₂³	1	1	yes	characteristic
269	C₂₃×#107	C₂³	1	2	yes	—
270	C₂₃×#107	C₂³	1	2	yes	—
271	C₂₃×#106	C₂³	1	1	yes	characteristic
272	C₂₃×#106	C₂³	1	2	yes	—
273	C₂₃×#106	C₂³	1	2	yes	—
274	C₂₃×#106	C₂³	1	2	yes	—
275	C₂₃×#106	C₂³	1	1	yes	characteristic
276	C₂₃×#106	C₂³	1	2	yes	—
277	C₂₃×#106	C₂³	1	2	yes	—
278	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
279	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
280	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
281	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
282	C₂₃×#103	C₂³	1	1	yes	characteristic
283	C₂₃×#103	C₂³	1	1	yes	characteristic
284	C₂₃×#103	C₂³	1	2	yes	—
285	C₂₃×#103	C₂³	1	2	yes	—
286	C₂₃×#103	C₂³	1	2	yes	—
287	C₂₃×#103	C₂³	1	2	yes	—
288	C₂₃×#103	C₂³	1	2	yes	—
289	C₂₃×#103	C₂³	1	2	yes	—
290	C₂₃×#103	C₂³	1	2	yes	—
291	C₂₃×#103	C₂³	1	2	yes	—
292	C₂₃×#103	C₂³	1	1	yes	characteristic
293	C₂₃×#103	C₂³	1	1	yes	characteristic
294	C₂₃×#103	C₂³	1	2	yes	—
295	C₂₃×#102	C₂³	1	1	yes	characteristic
296	C₂₃×#102	C₂³	1	1	yes	characteristic
297	C₂₃×#102	C₂³	1	2	yes	—
298	C₂₃×#102	C₂³	1	2	yes	—
299	C₂₃×#102	C₂³	1	1	yes	characteristic
300	C₂₃×#102	C₂³	1	1	yes	characteristic
301	C₂₃×#102	C₂³	1	2	yes	—
302	C₂₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
303	C₂₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
304	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
305	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
306	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
307	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
308	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
309	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
310	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
311	C₄×C₈×C₂₃	C₂³	1	2	yes	—
312	C₂⁴×C₂₃	C₂×D₄	1	2	yes	—
313	#41×C₂₃	—	4	1	no	—
314	#41×C₂₃	—	4	1	no	—
315	#41×C₂₃	—	4	2	no	—
316	#41×C₂₃	—	4	2	no	—
317	#41×C₂₃	—	4	4	no	—
318	#41×C₂₃	—	4	4	no	—
319	C₂×Q₈×C₂₃	—	2	1	no	—
320	C₂×Q₈×C₂₃	—	2	1	no	—
321	C₂×Q₈×C₂₃	—	2	1	no	—
322	C₂×Q₈×C₂₃	—	2	2	no	—
323	C₂×Q₈×C₂₃	—	4	2	no	—
324	C₂×Q₈×C₂₃	—	4	2	no	—
325	C₂×Q₈×C₂₃	C₂⁴	1	1	yes	characteristic
326	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
327	C₂×Q₈×C₂₃	C₂⁴	1	1	yes	characteristic
328	C₂×D₄×C₂₃	—	2	4	no	—
329	C₂×D₄×C₂₃	—	2	1	no	—
330	C₂×D₄×C₂₃	—	2	1	no	—
331	C₂×D₄×C₂₃	—	2	2	no	—
332	C₂×D₄×C₂₃	—	2	2	no	—
333	C₂×D₄×C₂₃	—	2	2	no	—
334	C₂×D₄×C₂₃	—	2	2	no	—
335	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
336	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
337	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
338	C₂×D₄×C₂₃	C₂⁴	1	1	yes	characteristic
339	C₂×D₄×C₂₃	C₂⁴	1	1	yes	characteristic
340	C₂²×C₄×C₂₃	—	2	2	no	—
341	C₂²×C₄×C₂₃	—	2	2	no	—
342	C₂²×C₄×C₂₃	—	2	2	no	—
343	C₂²×C₄×C₂₃	—	2	2	no	—
344	C₂²×C₄×C₂₃	—	2	1	no	—
345	C₂²×C₄×C₂₃	—	2	1	no	—
346	C₂²×C₄×C₂₃	—	2	1	no	—
347	C₂²×C₄×C₂₃	—	2	1	no	—
348	C₂²×C₄×C₂₃	—	2	2	no	—
349	C₂²×C₄×C₂₃	—	4	2	no	—
350	C₂²×C₄×C₂₃	—	4	2	no	—
351	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
352	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
353	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
354	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
355	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
356	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
357	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
358	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
359	Q₁₆×C₂₃	—	4	1	no	—
360	Q₁₆×C₂₃	—	4	2	no	—
361	SD₁₆×C₂₃	—	4	1	no	—
362	SD₁₆×C₂₃	—	4	2	no	—
363	SD₁₆×C₂₃	—	4	1	no	—
364	D₈×C₂₃	—	4	1	no	—
365	C₂×C₈×C₂₃	—	4	2	no	—
366	C₂×C₈×C₂₃	—	4	2	no	—
367	C₂×C₈×C₂₃	—	4	2	no	—
368	C₂×C₈×C₂₃	—	4	2	no	—
369	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
370	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
371	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
372	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
373	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
374	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
375	C₄⋊C₄×C₂₃	—	2	1	no	—
376	C₄⋊C₄×C₂₃	—	2	2	no	—
377	C₄⋊C₄×C₂₃	—	2	1	no	—
378	C₄⋊C₄×C₂₃	—	2	2	no	—
379	C₄⋊C₄×C₂₃	—	2	2	no	—
380	C₄⋊C₄×C₂₃	—	2	2	no	—
381	C₄⋊C₄×C₂₃	—	2	2	no	—
382	C₄⋊C₄×C₂₃	—	2	2	no	—
383	C₄⋊C₄×C₂₃	—	2	1	no	—
384	C₄⋊C₄×C₂₃	—	2	1	no	—
385	C₄⋊C₄×C₂₃	—	2	2	no	—
386	C₄⋊C₄×C₂₃	—	2	2	no	—
387	C₄⋊C₄×C₂₃	—	2	1	no	—
388	C₄⋊C₄×C₂₃	—	2	1	no	—
389	C₄⋊C₄×C₂₃	—	2	1	no	—
390	C₄⋊C₄×C₂₃	—	2	1	no	—
391	C₄⋊C₄×C₂₃	—	2	2	no	—
392	C₄⋊C₄×C₂₃	—	2	2	no	—
393	C₄⋊C₄×C₂₃	—	2	1	no	—
394	C₄⋊C₄×C₂₃	—	2	2	no	—
395	C₄⋊C₄×C₂₃	—	2	1	no	—
396	C₄⋊C₄×C₂₃	—	2	2	no	—
397	C₄⋊C₄×C₂₃	—	2	1	no	—
398	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
399	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
400	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
401	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
402	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
403	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
404	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
405	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
406	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
407	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
408	C₂²⋊C₄×C₂₃	—	2	1	no	—
409	C₂²⋊C₄×C₂₃	—	2	1	no	—
410	C₂²⋊C₄×C₂₃	—	2	2	no	—
411	C₂²⋊C₄×C₂₃	—	2	2	no	—
412	C₂²⋊C₄×C₂₃	—	2	2	no	—
413	C₂²⋊C₄×C₂₃	—	2	2	no	—
414	C₂²⋊C₄×C₂₃	—	2	2	no	—
415	C₂²⋊C₄×C₂₃	—	2	2	no	—
416	C₂²⋊C₄×C₂₃	—	2	2	no	—
417	C₂²⋊C₄×C₂₃	—	2	2	no	—
418	C₂²⋊C₄×C₂₃	—	2	2	no	—
419	C₂²⋊C₄×C₂₃	—	2	2	no	—
420	C₂²⋊C₄×C₂₃	—	2	1	no	—
421	C₂²⋊C₄×C₂₃	—	2	2	no	—
422	C₂²⋊C₄×C₂₃	—	2	1	no	—
423	C₂²⋊C₄×C₂₃	—	2	1	no	—
424	C₂²⋊C₄×C₂₃	—	2	1	no	—
425	C₂²⋊C₄×C₂₃	—	2	1	no	—
426	C₂²⋊C₄×C₂₃	—	2	2	no	—
427	C₂²⋊C₄×C₂₃	—	2	2	no	—
428	C₂²⋊C₄×C₂₃	—	2	1	no	—
429	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
430	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
431	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
432	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
433	C₄²×C₂₃	—	2	1	no	—
434	C₄²×C₂₃	—	2	2	no	—
435	C₄²×C₂₃	—	2	1	no	—
436	C₄²×C₂₃	—	2	2	no	—
437	C₄²×C₂₃	—	2	2	no	—
438	C₄²×C₂₃	—	2	1	no	—
439	C₄²×C₂₃	—	2	2	no	—
440	C₄²×C₂₃	—	2	2	no	—
441	C₄²×C₂₃	—	2	1	no	—
442	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
443	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
444	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
445	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
446	#61703	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
447	C₂³×C₂₃	—	2	4	no	—
448	C₂³×C₂₃	—	2	1	no	—
449	C₂³×C₂₃	—	2	1	no	—
450	C₂³×C₂₃	—	4	2	no	—
451	C₂³×C₂₃	—	4	2	no	—
452	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
453	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
454	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
455	Q₈×C₂₃	—	2	1	no	—
456	Q₈×C₂₃	—	2	1	no	—
457	Q₈×C₂₃	—	2	2	no	—
458	Q₈×C₂₃	—	2	1	no	—
459	Q₈×C₂₃	—	2	1	no	—
460	Q₈×C₂₃	—	2	2	no	—
461	Q₈×C₂₃	—	4	2	no	—
462	Q₈×C₂₃	—	4	2	no	—
463	Q₈×C₂₃	—	8	1	no	—
464	Q₈×C₂₃	—	8	2	no	—
465	D₄×C₂₃	—	2	4	no	—
466	D₄×C₂₃	—	2	2	no	—
467	D₄×C₂₃	—	2	1	no	—
468	D₄×C₂₃	—	2	1	no	—
469	D₄×C₂₃	—	2	1	no	—
470	D₄×C₂₃	—	2	1	no	—
471	D₄×C₂₃	—	4	2	no	—
472	D₄×C₂₃	—	4	2	no	—
473	D₄×C₂₃	—	4	4	no	—
474	D₄×C₂₃	—	4	4	no	—
475	D₄×C₂₃	—	8	2	no	—
476	D₄×C₂₃	—	8	2	no	—
477	D₄×C₂₃	#135	1	4	yes	—
478	C₂×C₄×C₂₃	—	2	2	no	—
479	C₂×C₄×C₂₃	—	2	2	no	—
480	C₂×C₄×C₂₃	—	2	2	no	—
481	C₂×C₄×C₂₃	—	2	2	no	—
482	C₂×C₄×C₂₃	—	2	2	no	—
483	C₂×C₄×C₂₃	—	2	1	no	—
484	C₂×C₄×C₂₃	—	2	1	no	—
485	C₂×C₄×C₂₃	—	2	1	no	—
486	C₂×C₄×C₂₃	—	2	1	no	—
487	C₂×C₄×C₂₃	—	2	1	no	—
488	C₂×C₄×C₂₃	—	2	1	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	2	no	—
494	C₂×C₄×C₂₃	—	2	1	no	—
495	C₂×C₄×C₂₃	—	4	2	no	—
496	C₂×C₄×C₂₃	—	4	2	no	—
497	C₂×C₄×C₂₃	—	4	2	no	—
498	C₂×C₄×C₂₃	—	4	1	no	—
499	C₂×C₄×C₂₃	—	4	2	no	—
500	C₂×C₄×C₂₃	—	4	4	no	—
501	C₂×C₄×C₂₃	—	4	4	no	—
502	C₂×C₄×C₂₃	—	4	2	no	—
503	C₂×C₄×C₂₃	—	4	2	no	—
504	C₂×C₄×C₂₃	—	8	1	no	—
505	C₂×C₄×C₂₃	—	8	2	no	—
506	C₂×C₄×C₂₃	—	8	2	no	—
507	C₂×C₄×C₂₃	—	8	2	no	—
508	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
509	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
510	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
511	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
512	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
513	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
514	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
515	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
516	C₈×C₂₃	—	2	1	no	—
517	C₈×C₂₃	—	2	1	no	—
518	C₈×C₂₃	—	2	1	no	—
519	C₈×C₂₃	—	2	2	no	—
520	C₈×C₂₃	—	2	2	no	—
521	C₈×C₂₃	—	2	1	no	—
522	#3520	C₂×C₂₃	1	1	yes	characteristic, complemented
523	#3475	C₂×C₂₃	1	1	yes	characteristic, complemented
524	#3342	C₂×C₂₃	1	1	yes	characteristic, complemented
525	#3340	C₂×C₂₃	1	1	yes	characteristic, complemented
526	#3337	C₂×C₂₃	1	2	yes	complemented
527	#3336	C₂×C₂₃	1	2	yes	complemented
528	#3335	C₂×C₂₃	1	1	yes	characteristic, complemented
529	#3334	C₂×C₂₃	1	1	yes	characteristic, complemented
530	#3303	C₂×C₂₃	1	1	yes	characteristic, complemented
531	#3302	C₂×C₂₃	1	1	yes	characteristic, complemented
532	#3301	C₂×C₂₃	1	2	yes	complemented
533	#3300	C₂×C₂₃	1	2	yes	complemented
534	#3299	C₂×C₂₃	1	1	yes	characteristic, complemented
535	#3298	C₂×C₂₃	1	1	yes	characteristic, complemented
536	#3233	C₂×C₂₃	1	1	yes	characteristic, complemented
537	#3231	C₂×C₂₃	1	1	yes	characteristic, complemented
538	#3191	C₂×C₂₃	1	2	yes	complemented
539	#3190	C₂×C₂₃	1	2	yes	complemented
540	#3107	C₂×C₂₃	1	1	yes	characteristic, complemented
541	#3102	C₂×C₂₃	1	1	yes	characteristic, complemented
542	#3091	C₂×C₂₃	1	2	yes	complemented
543	C₂×#485	C₂×C₂₃	1	2	yes	complemented
544	#2972	C₂×C₂₃	1	1	yes	characteristic, complemented
545	C₂²×C₂₃	—	2	2	no	—
546	C₂²×C₂₃	—	2	2	no	—
547	C₂²×C₂₃	—	2	1	no	—
548	C₂²×C₂₃	—	2	2	no	—
549	C₂²×C₂₃	—	2	1	no	—
550	C₂²×C₂₃	—	2	2	no	—
551	C₂²×C₂₃	—	2	1	no	—
552	C₂²×C₂₃	—	2	2	no	—
553	C₂²×C₂₃	—	4	1	no	—
554	C₂²×C₂₃	—	4	1	no	—
555	C₂²×C₂₃	—	4	1	no	—
556	C₂²×C₂₃	—	4	1	no	—
557	C₂²×C₂₃	—	4	1	no	—
558	C₂²×C₂₃	—	4	1	no	—
559	C₂²×C₂₃	—	8	4	no	—
560	C₂²×C₂₃	C₂×#135	1	4	yes	—
561	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
562	C₄×C₂₃	—	2	1	no	—
563	C₄×C₂₃	—	2	1	no	—
564	C₄×C₂₃	—	2	1	no	—
565	C₄×C₂₃	—	2	2	no	—
566	C₄×C₂₃	—	2	2	no	—
567	C₄×C₂₃	—	2	1	no	—
568	C₄×C₂₃	—	4	1	no	—
569	C₄×C₂₃	—	4	2	no	—
570	C₄×C₂₃	—	4	1	no	—
571	C₄×C₂₃	—	4	1	no	—
572	C₄×C₂₃	—	4	2	no	—
573	C₄×C₂₃	—	4	1	no	—
574	C₄×C₂₃	—	4	1	no	—
575	C₄×C₂₃	—	4	1	no	—
576	C₄×C₂₃	—	4	2	no	—
577	C₄×C₂₃	—	4	2	no	—
578	C₄×C₂₃	C₂×#135	1	2	yes	—
579	C₄×C₂₃	#585	1	1	yes	characteristic
580	C₄×C₂₃	#585	1	1	yes	characteristic
581	#556	C₂²×C₂₃	1	1	yes	characteristic
582	#556	C₂²×C₂₃	1	1	yes	characteristic
583	#555	C₂²×C₂₃	1	1	yes	characteristic
584	#554	—	2	1	no	—
585	#554	C₂²×C₂₃	1	1	yes	characteristic
586	#553	C₂²×C₂₃	1	2	yes	—
587	#552	—	2	1	no	—
588	#552	C₂²×C₂₃	1	2	yes	—
589	#552	C₂²×C₂₃	1	2	yes	—
590	#551	—	2	2	no	—
591	#551	—	2	2	no	—
592	D₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
593	#548	C₂²×C₂₃	1	2	yes	—
594	#547	C₂²×C₂₃	1	1	yes	characteristic
595	#547	C₂²×C₂₃	1	1	yes	characteristic
596	#547	C₂²×C₂₃	1	1	yes	characteristic
597	#546	—	2	1	no	—
598	#546	—	2	1	no	—
599	#542	—	2	1	no	—
600	#539	—	2	2	no	—
601	#533	C₂²×C₂₃	1	1	yes	characteristic
602	#533	C₂²×C₂₃	1	1	yes	characteristic
603	#529	—	2	2	no	—
604	#529	—	2	1	no	—
605	#529	C₂²×C₂₃	1	1	yes	characteristic
606	#525	C₂²×C₂₃	1	2	yes	—
607	#525	C₂²×C₂₃	1	2	yes	—
608	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	2	yes	—
609	#520	—	2	1	no	—
610	C₄×#41	—	2	1	no	—
611	C₄×#41	C₂²×C₂₃	1	1	yes	characteristic
612	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
613	C₂×#117	C₂²×C₂₃	1	2	yes	—
614	#500	C₂²×C₂₃	1	1	yes	characteristic, complemented
615	#499	C₂²×C₂₃	1	2	yes	complemented
616	#498	C₂²×C₂₃	1	1	yes	characteristic, complemented
617	#488	C₂²×C₂₃	1	2	yes	complemented
618	#487	C₂²×C₂₃	1	1	yes	characteristic, complemented
619	#487	C₂²×C₂₃	1	1	yes	characteristic, complemented
620	#485	C₂²×C₂₃	1	1	yes	characteristic
621	#485	C₂²×C₂₃	1	2	yes	—
622	#485	C₂²×C₂₃	1	2	yes	—
623	#485	C₂²×C₂₃	1	2	yes	—
624	#485	C₂²×C₂₃	1	2	yes	—
625	#485	C₂²×C₂₃	1	2	yes	complemented
626	#485	C₂²×C₂₃	1	2	yes	complemented
627	#485	C₂²×C₂₃	1	2	yes	complemented
628	#485	C₂²×C₂₃	1	2	yes	complemented
629	#485	C₂²×C₂₃	1	2	yes	complemented
630	#484	C₂²×C₂₃	1	2	yes	complemented
631	#483	C₂²×C₂₃	1	2	yes	complemented
632	#483	C₂²×C₂₃	1	2	yes	complemented
633	#482	C₂²×C₂₃	1	1	yes	characteristic
634	#482	C₂²×C₂₃	1	2	yes	—
635	#482	C₂²×C₂₃	1	2	yes	complemented
636	#481	C₂²×C₂₃	1	2	yes	complemented
637	#480	C₂²×C₂₃	1	2	yes	complemented
638	#480	C₂²×C₂₃	1	2	yes	complemented
639	#479	C₂²×C₂₃	1	1	yes	characteristic, complemented
640	#479	C₂²×C₂₃	1	2	yes	complemented
641	#479	C₂²×C₂₃	1	2	yes	complemented
642	#478	C₂²×C₂₃	1	1	yes	characteristic, complemented
643	#477	C₂²×C₂₃	1	1	yes	characteristic, complemented
644	#476	C₂²×C₂₃	1	1	yes	characteristic, complemented
645	#475	C₂²×C₂₃	1	1	yes	characteristic, complemented
646	#475	C₂²×C₂₃	1	1	yes	characteristic, complemented
647	#474	C₂²×C₂₃	1	1	yes	characteristic, complemented
648	#474	C₂²×C₂₃	1	1	yes	characteristic, complemented
649	#467	C₂²×C₂₃	1	2	yes	complemented
650	#467	C₂²×C₂₃	1	2	yes	complemented
651	#467	C₂²×C₂₃	1	2	yes	complemented
652	#466	C₂²×C₂₃	1	2	yes	complemented
653	#465	C₂²×C₂₃	1	2	yes	complemented
654	#465	C₂²×C₂₃	1	2	yes	complemented
655	#465	C₂²×C₂₃	1	2	yes	complemented
656	#465	C₂²×C₂₃	1	2	yes	complemented
657	#464	C₂²×C₂₃	1	1	yes	characteristic, complemented
658	#463	C₂²×C₂₃	1	1	yes	characteristic, complemented
659	#462	C₂²×C₂₃	1	1	yes	characteristic, complemented
660	#461	C₂²×C₂₃	1	1	yes	characteristic, complemented
661	#452	C₂²×C₂₃	1	1	yes	characteristic
662	#452	C₂²×C₂₃	1	2	yes	—
663	#452	C₂²×C₂₃	1	2	yes	complemented
664	#451	C₂²×C₂₃	1	2	yes	complemented
665	#449	C₂²×C₂₃	1	1	yes	characteristic
666	#449	C₂²×C₂₃	1	2	yes	complemented
667	#448	C₂²×C₂₃	1	2	yes	complemented
668	C₄×Q₁₆	C₂²×C₂₃	1	2	yes	complemented
669	C₄×Q₁₆	C₂²×C₂₃	1	1	yes	characteristic, complemented
670	C₄×SD₁₆	C₂²×C₂₃	1	1	yes	characteristic, complemented
671	C₄×SD₁₆	C₂²×C₂₃	1	2	yes	complemented
672	C₄×SD₁₆	C₂²×C₂₃	1	1	yes	characteristic, complemented
673	C₄×D₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
674	C₈×D₄	C₂²×C₂₃	1	1	yes	characteristic
675	C₈×D₄	C₂²×C₂₃	1	1	yes	characteristic
676	C₈×D₄	C₂²×C₂₃	1	2	yes	—
677	C₈×D₄	C₂²×C₂₃	1	2	yes	—
678	C₈×D₄	C₂²×C₂₃	1	1	yes	characteristic
679	C₈×D₄	C₂²×C₂₃	1	1	yes	characteristic
680	#431	C₂²×C₂₃	1	1	yes	characteristic
681	#431	C₂²×C₂₃	1	1	yes	characteristic
682	#427	C₂²×C₂₃	1	2	yes	complemented
683	#427	C₂²×C₂₃	1	2	yes	complemented
684	C₂×#107	C₂²×C₂₃	1	2	yes	complemented
685	C₂×#106	C₂²×C₂₃	1	2	yes	complemented
686	#416	C₂²×C₂₃	1	2	yes	complemented
687	#416	C₂²×C₂₃	1	2	yes	complemented
688	C₂×#103	C₂²×C₂₃	1	2	yes	complemented
689	C₂×#103	C₂²×C₂₃	1	2	yes	complemented
690	C₂×C₂²⋊C₈	C₂²×C₂₃	1	2	yes	—
691	C₂×C₂²⋊C₈	C₂²×C₂₃	1	2	yes	—
692	C₂×C₂₃	—	2	4	no	—
693	C₂×C₂₃	—	4	2	no	—
694	C₂×C₂₃	—	4	1	no	—
695	C₂×C₂₃	—	8	1	no	—
696	C₂×C₂₃	—	8	1	no	—
697	C₂×C₂₃	#3485	1	1	yes	characteristic
698	C₂×C₂₃	C₂²×#135	1	1	yes	characteristic
699	C₂×C₂₃	#3586	1	1	yes	characteristic
700	C₂×#41	—	2	1	no	—
701	C₂×#41	—	2	1	no	—
702	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
703	C₂×#41	C₂³×C₂₃	1	2	yes	—
704	C₂²×Q₈	C₂³×C₂₃	1	2	yes	—
705	C₂²×D₄	D₄×C₂₃	1	1	yes	characteristic
706	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
707	C₂×Q₁₆	C₂³×C₂₃	1	1	yes	characteristic
708	C₂×Q₁₆	C₂³×C₂₃	1	2	yes	—
709	C₂×SD₁₆	C₂³×C₂₃	1	1	yes	characteristic
710	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
711	C₂×SD₁₆	C₂³×C₂₃	1	1	yes	characteristic
712	C₂×D₈	C₂³×C₂₃	1	1	yes	characteristic
713	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
714	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
715	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
716	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
717	C₄⋊Q₈	—	2	1	no	—
718	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
719	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
720	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
721	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
722	#126	—	2	2	no	—
723	#126	—	2	2	no	—
724	#126	—	2	2	no	—
725	#126	—	2	2	no	—
726	#126	—	2	2	no	—
727	#126	—	2	1	no	—
728	#125	—	2	2	no	—
729	#125	—	2	1	no	—
730	#125	—	2	2	no	—
731	#125	—	2	1	no	—
732	#125	C₂³×C₂₃	1	1	yes	characteristic
733	#125	C₂³×C₂₃	1	2	yes	—
734	#124	—	2	1	no	—
735	#124	—	2	1	no	—
736	#124	—	2	2	no	—
737	#124	—	2	2	no	—
738	#124	C₂³×C₂₃	1	1	yes	characteristic
739	#123	—	2	2	no	—
740	#123	—	2	2	no	—
741	#123	—	2	2	no	—
742	#123	—	2	2	no	—
743	#123	—	2	1	no	—
744	#123	—	2	2	no	—
745	#123	—	2	2	no	—
746	#123	—	2	2	no	—
747	#123	—	2	2	no	—
748	C₂²⋊Q₈	—	2	2	no	—
749	C₂²⋊Q₈	—	2	2	no	—
750	C₂²⋊Q₈	—	2	1	no	—
751	C₂²⋊Q₈	—	2	1	no	—
752	C₂²⋊Q₈	—	2	1	no	—
753	C₂²⋊Q₈	—	2	1	no	—
754	C₂²⋊Q₈	—	2	2	no	—
755	C₂²⋊Q₈	—	2	1	no	—
756	C₂²⋊Q₈	—	2	2	no	—
757	C₂²⋊Q₈	—	2	2	no	—
758	C₂²⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
759	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
760	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
761	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
762	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
763	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
764	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
765	#121	—	2	2	no	—
766	#121	—	2	1	no	—
767	#121	—	2	2	no	—
768	#121	—	2	1	no	—
769	#121	C₂³×C₂₃	1	1	yes	characteristic
770	#121	C₂³×C₂₃	1	2	yes	—
771	#121	C₂³×C₂₃	1	2	yes	—
772	#121	C₂³×C₂₃	1	2	yes	—
773	#120	—	2	2	no	—
774	#120	—	2	2	no	—
775	C₄×Q₈	—	2	1	no	—
776	C₄×Q₈	—	2	1	no	—
777	C₄×Q₈	—	2	1	no	—
778	C₄×Q₈	—	2	1	no	—
779	C₄×Q₈	—	2	1	no	—
780	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
781	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
782	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
783	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
784	C₄×D₄	—	2	1	no	—
785	C₄×D₄	—	2	1	no	—
786	C₄×D₄	—	2	2	no	—
787	C₄×D₄	—	2	1	no	—
788	C₄×D₄	—	2	1	no	—
789	C₄×D₄	—	2	2	no	—
790	C₄×D₄	—	2	2	no	—
791	C₄×D₄	—	2	2	no	—
792	C₄×D₄	—	2	1	no	—
793	C₄×D₄	—	2	2	no	—
794	C₄×D₄	—	2	2	no	—
795	C₄×D₄	D₄×C₂₃	1	1	yes	characteristic
796	C₄×D₄	D₄×C₂₃	1	2	yes	—
797	C₄×D₄	D₄×C₂₃	1	1	yes	characteristic
798	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
799	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
800	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
801	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
802	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
803	C₄×D₄	C₂³×C₂₃	1	2	yes	—
804	#117	—	2	2	no	—
805	#117	—	2	2	no	—
806	#117	—	2	1	no	—
807	#117	—	2	1	no	—
808	#117	—	2	2	no	—
809	#117	—	2	2	no	—
810	#117	—	2	1	no	—
811	#117	—	2	1	no	—
812	#117	C₂³×C₂₃	1	1	yes	characteristic
813	#117	C₂³×C₂₃	1	2	yes	—
814	#117	C₂³×C₂₃	1	2	yes	—
815	#117	C₂³×C₂₃	1	2	yes	—
816	#117	C₂³×C₂₃	1	2	yes	—
817	C₂×C₄⋊C₄	—	2	2	no	—
818	C₂×C₄⋊C₄	—	2	1	no	—
819	C₂×C₄⋊C₄	D₄×C₂₃	1	1	yes	characteristic
820	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
821	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
822	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
823	C₂×C₂²⋊C₄	—	2	2	no	—
824	C₂×C₂²⋊C₄	—	2	2	no	—
825	C₂×C₂²⋊C₄	D₄×C₂₃	1	2	yes	—
826	C₂×C₄²	—	2	2	no	—
827	C₂×C₄²	—	2	1	no	—
828	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
829	#107	C₂³×C₂₃	1	1	yes	characteristic
830	#107	C₂³×C₂₃	1	2	yes	—
831	#107	C₂³×C₂₃	1	2	yes	—
832	#107	C₂³×C₂₃	1	2	yes	—
833	#107	C₂³×C₂₃	1	1	yes	characteristic
834	#107	C₂³×C₂₃	1	2	yes	—
835	#107	C₂³×C₂₃	1	2	yes	—
836	#106	C₂³×C₂₃	1	1	yes	characteristic
837	#106	C₂³×C₂₃	1	2	yes	—
838	#106	C₂³×C₂₃	1	2	yes	—
839	#106	C₂³×C₂₃	1	2	yes	—
840	#106	C₂³×C₂₃	1	1	yes	characteristic
841	#106	C₂³×C₂₃	1	2	yes	—
842	#106	C₂³×C₂₃	1	2	yes	—
843	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
844	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
845	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
846	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
847	#103	C₂³×C₂₃	1	1	yes	characteristic
848	#103	C₂³×C₂₃	1	1	yes	characteristic
849	#103	C₂³×C₂₃	1	2	yes	—
850	#103	C₂³×C₂₃	1	2	yes	—
851	#103	C₂³×C₂₃	1	2	yes	—
852	#103	C₂³×C₂₃	1	2	yes	—
853	#103	C₂³×C₂₃	1	2	yes	—
854	#103	C₂³×C₂₃	1	2	yes	—
855	#103	C₂³×C₂₃	1	2	yes	—
856	#103	C₂³×C₂₃	1	2	yes	—
857	#103	C₂³×C₂₃	1	1	yes	characteristic
858	#103	C₂³×C₂₃	1	1	yes	characteristic
859	#103	C₂³×C₂₃	1	2	yes	—
860	#102	C₂³×C₂₃	1	1	yes	characteristic
861	#102	C₂³×C₂₃	1	1	yes	characteristic
862	#102	C₂³×C₂₃	1	2	yes	—
863	#102	C₂³×C₂₃	1	2	yes	—
864	#102	C₂³×C₂₃	1	1	yes	characteristic
865	#102	C₂³×C₂₃	1	1	yes	characteristic
866	#102	C₂³×C₂₃	1	2	yes	—
867	C₂²⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
868	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
869	C₂²⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
870	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
871	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
872	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
873	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
874	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
875	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
876	C₄×C₈	C₂³×C₂₃	1	2	yes	—
877	C₂₃	#61703	1	1	yes	characteristic, direct product factor, Sylow
878	C₂⁴	C₂×D₄×C₂₃	1	2	yes	—
879	#41	—	4	1	no	—
880	#41	—	4	1	no	—
881	#41	—	4	2	no	—
882	#41	—	4	2	no	—
883	#41	—	4	4	no	—
884	#41	—	4	4	no	—
885	C₂×Q₈	—	2	1	no	—
886	C₂×Q₈	—	2	1	no	—
887	C₂×Q₈	—	2	1	no	—
888	C₂×Q₈	—	2	2	no	—
889	C₂×Q₈	—	4	2	no	—
890	C₂×Q₈	—	4	2	no	—
891	C₂×Q₈	C₂⁴×C₂₃	1	1	yes	characteristic
892	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
893	C₂×Q₈	C₂⁴×C₂₃	1	1	yes	characteristic
894	C₂×D₄	—	2	4	no	—
895	C₂×D₄	—	2	1	no	—
896	C₂×D₄	—	2	1	no	—
897	C₂×D₄	—	2	2	no	—
898	C₂×D₄	—	2	2	no	—
899	C₂×D₄	—	2	2	no	—
900	C₂×D₄	—	2	2	no	—
901	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
902	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
903	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
904	C₂×D₄	C₂⁴×C₂₃	1	1	yes	characteristic
905	C₂×D₄	C₂⁴×C₂₃	1	1	yes	characteristic
906	C₂²×C₄	—	2	2	no	—
907	C₂²×C₄	—	2	2	no	—
908	C₂²×C₄	—	2	2	no	—
909	C₂²×C₄	—	2	2	no	—
910	C₂²×C₄	—	2	1	no	—
911	C₂²×C₄	—	2	1	no	—
912	C₂²×C₄	—	2	1	no	—
913	C₂²×C₄	—	2	1	no	—
914	C₂²×C₄	—	2	2	no	—
915	C₂²×C₄	—	4	2	no	—
916	C₂²×C₄	—	4	2	no	—
917	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
918	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
919	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
920	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
921	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
922	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
923	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
924	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
925	Q₁₆	—	4	1	no	—
926	Q₁₆	—	4	2	no	—
927	SD₁₆	—	4	1	no	—
928	SD₁₆	—	4	2	no	—
929	SD₁₆	—	4	1	no	—
930	D₈	—	4	1	no	—
931	C₂×C₈	—	4	2	no	—
932	C₂×C₈	—	4	2	no	—
933	C₂×C₈	—	4	2	no	—
934	C₂×C₈	—	4	2	no	—
935	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
936	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
937	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
938	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
939	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
940	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
941	C₄⋊C₄	—	2	1	no	—
942	C₄⋊C₄	—	2	2	no	—
943	C₄⋊C₄	—	2	1	no	—
944	C₄⋊C₄	—	2	2	no	—
945	C₄⋊C₄	—	2	2	no	—
946	C₄⋊C₄	—	2	2	no	—
947	C₄⋊C₄	—	2	2	no	—
948	C₄⋊C₄	—	2	2	no	—
949	C₄⋊C₄	—	2	1	no	—
950	C₄⋊C₄	—	2	1	no	—
951	C₄⋊C₄	—	2	2	no	—
952	C₄⋊C₄	—	2	2	no	—
953	C₄⋊C₄	—	2	1	no	—
954	C₄⋊C₄	—	2	1	no	—
955	C₄⋊C₄	—	2	1	no	—
956	C₄⋊C₄	—	2	1	no	—
957	C₄⋊C₄	—	2	2	no	—
958	C₄⋊C₄	—	2	2	no	—
959	C₄⋊C₄	—	2	1	no	—
960	C₄⋊C₄	—	2	2	no	—
961	C₄⋊C₄	—	2	1	no	—
962	C₄⋊C₄	—	2	2	no	—
963	C₄⋊C₄	—	2	1	no	—
964	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
965	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
966	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
967	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
968	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
969	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
970	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
971	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
972	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
973	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
974	C₂²⋊C₄	—	2	1	no	—
975	C₂²⋊C₄	—	2	1	no	—
976	C₂²⋊C₄	—	2	2	no	—
977	C₂²⋊C₄	—	2	2	no	—
978	C₂²⋊C₄	—	2	2	no	—
979	C₂²⋊C₄	—	2	2	no	—
980	C₂²⋊C₄	—	2	2	no	—
981	C₂²⋊C₄	—	2	2	no	—
982	C₂²⋊C₄	—	2	2	no	—
983	C₂²⋊C₄	—	2	2	no	—
984	C₂²⋊C₄	—	2	2	no	—
985	C₂²⋊C₄	—	2	2	no	—
986	C₂²⋊C₄	—	2	1	no	—
987	C₂²⋊C₄	—	2	2	no	—
988	C₂²⋊C₄	—	2	1	no	—
989	C₂²⋊C₄	—	2	1	no	—
990	C₂²⋊C₄	—	2	1	no	—
991	C₂²⋊C₄	—	2	1	no	—
992	C₂²⋊C₄	—	2	2	no	—
993	C₂²⋊C₄	—	2	2	no	—
994	C₂²⋊C₄	—	2	1	no	—
995	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
996	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
997	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
998	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
999	C₄²	—	2	1	no	—
1000	C₄²	—	2	2	no	—
1001	C₄²	—	2	1	no	—
1002	C₄²	—	2	2	no	—
1003	C₄²	—	2	2	no	—
1004	C₄²	—	2	1	no	—
1005	C₄²	—	2	2	no	—
1006	C₄²	—	2	2	no	—
1007	C₄²	—	2	1	no	—
1008	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
1009	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
1010	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
1011	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
1012	C₂³	—	2	4	no	—
1013	C₂³	—	2	1	no	—
1014	C₂³	—	2	1	no	—
1015	C₂³	—	4	2	no	—
1016	C₂³	—	4	2	no	—
1017	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
1018	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
1019	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
1020	Q₈	—	2	1	no	—
1021	Q₈	—	2	1	no	—
1022	Q₈	—	2	2	no	—
1023	Q₈	—	2	1	no	—
1024	Q₈	—	2	1	no	—
1025	Q₈	—	2	2	no	—
1026	Q₈	—	4	2	no	—
1027	Q₈	—	4	2	no	—
1028	Q₈	—	8	2	no	—
1029	Q₈	—	8	1	no	—
1030	D₄	—	2	4	no	—
1031	D₄	—	2	2	no	—
1032	D₄	—	2	1	no	—
1033	D₄	—	2	1	no	—
1034	D₄	—	2	1	no	—
1035	D₄	—	2	1	no	—
1036	D₄	—	4	2	no	—
1037	D₄	—	4	2	no	—
1038	D₄	—	4	4	no	—
1039	D₄	—	4	4	no	—
1040	D₄	—	8	2	no	—
1041	D₄	—	8	2	no	—
1042	D₄	C₂₃×#135	1	4	yes	—
1043	C₂×C₄	—	2	2	no	—
1044	C₂×C₄	—	2	2	no	—
1045	C₂×C₄	—	2	2	no	—
1046	C₂×C₄	—	2	2	no	—
1047	C₂×C₄	—	2	2	no	—
1048	C₂×C₄	—	2	1	no	—
1049	C₂×C₄	—	2	1	no	—
1050	C₂×C₄	—	2	1	no	—
1051	C₂×C₄	—	2	1	no	—
1052	C₂×C₄	—	2	1	no	—
1053	C₂×C₄	—	2	1	no	—
1054	C₂×C₄	—	2	2	no	—
1055	C₂×C₄	—	2	2	no	—
1056	C₂×C₄	—	2	2	no	—
1057	C₂×C₄	—	2	1	no	—
1058	C₂×C₄	—	2	2	no	—
1059	C₂×C₄	—	2	1	no	—
1060	C₂×C₄	—	4	2	no	—
1061	C₂×C₄	—	4	2	no	—
1062	C₂×C₄	—	4	2	no	—
1063	C₂×C₄	—	4	1	no	—
1064	C₂×C₄	—	4	2	no	—
1065	C₂×C₄	—	4	4	no	—
1066	C₂×C₄	—	4	4	no	—
1067	C₂×C₄	—	4	2	no	—
1068	C₂×C₄	—	4	2	no	—
1069	C₂×C₄	—	8	2	no	—
1070	C₂×C₄	—	8	1	no	—
1071	C₂×C₄	—	8	2	no	—
1072	C₂×C₄	—	8	2	no	—
1073	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1074	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1075	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
1076	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1077	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1078	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
1079	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1080	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
1081	C₈	—	2	1	no	—
1082	C₈	—	2	1	no	—
1083	C₈	—	2	1	no	—
1084	C₈	—	2	2	no	—
1085	C₈	—	2	2	no	—
1086	C₈	—	2	1	no	—
1087	C₂²	—	2	2	no	—
1088	C₂²	—	2	2	no	—
1089	C₂²	—	2	1	no	—
1090	C₂²	—	2	2	no	—
1091	C₂²	—	2	1	no	—
1092	C₂²	—	2	2	no	—
1093	C₂²	—	2	1	no	—
1094	C₂²	—	2	2	no	—
1095	C₂²	—	4	1	no	—
1096	C₂²	—	4	1	no	—
1097	C₂²	—	4	1	no	—
1098	C₂²	—	4	1	no	—
1099	C₂²	—	4	1	no	—
1100	C₂²	—	4	1	no	—
1101	C₂²	—	8	4	no	—
1102	C₂²	C₂×C₂₃×#135	1	4	yes	—
1103	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
1104	C₄	—	2	1	no	—
1105	C₄	—	2	2	no	—
1106	C₄	—	2	2	no	—
1107	C₄	—	2	1	no	—
1108	C₄	—	2	1	no	—
1109	C₄	—	2	1	no	—
1110	C₄	—	4	1	no	—
1111	C₄	—	4	2	no	—
1112	C₄	—	4	1	no	—
1113	C₄	—	4	1	no	—
1114	C₄	—	4	1	no	—
1115	C₄	—	4	2	no	—
1116	C₄	—	4	2	no	—
1117	C₄	—	4	1	no	—
1118	C₄	—	4	2	no	—
1119	C₄	—	4	1	no	—
1120	C₄	C₂×C₂₃×#135	1	2	yes	—
1121	C₄	C₂₃×#585	1	1	yes	characteristic
1122	C₄	C₂₃×#585	1	1	yes	characteristic
1123	C₂	—	2	4	no	—
1124	C₂	—	4	1	no	—
1125	C₂	—	4	2	no	—
1126	C₂	—	8	1	no	—
1127	C₂	—	8	1	no	—
1128	C₂	C₂₃×#3485	1	1	yes	characteristic
1129	C₂	C₂²×C₂₃×#135	1	1	yes	characteristic
1130	C₂	C₂₃×#3586	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₂₃×#3520	C₂	semidirect
2. C₂₃×#3475	C₂	semidirect
3. C₂₃×#3342	C₂	semidirect
4. C₂₃×#3340	C₂	semidirect
5. C₂₃×#3337	C₂	semidirect
6. C₂₃×#3336	C₂	semidirect
7. C₂₃×#3335	C₂	semidirect
8. C₂₃×#3334	C₂	semidirect
9. C₂₃×#3303	C₂	semidirect
10. C₂₃×#3302	C₂	semidirect
11. C₂₃×#3301	C₂	semidirect
12. C₂₃×#3300	C₂	semidirect
13. C₂₃×#3299	C₂	semidirect
14. C₂₃×#3298	C₂	semidirect
15. C₂₃×#3233	C₂	semidirect
16. C₂₃×#3231	C₂	semidirect
17. C₂₃×#3191	C₂	semidirect
18. C₂₃×#3190	C₂	semidirect
19. C₂₃×#3107	C₂	semidirect
20. C₂₃×#3102	C₂	semidirect
21. C₂₃×#3091	C₂	semidirect
22. C₂×C₂₃×#485	C₂	semidirect
23. C₂₃×#2972	C₂	semidirect
57. C₂₃×#500	C₂²	semidirect
58. C₂₃×#499	C₂²	semidirect
59. C₂₃×#498	C₂²	semidirect
60. C₂₃×#488	C₂²	semidirect
61. C₂₃×#487	C₂²	semidirect
62. C₂₃×#487	C₂²	semidirect
68. C₂₃×#485	C₂²	semidirect
69. C₂₃×#485	C₂²	semidirect
70. C₂₃×#485	C₂²	semidirect
71. C₂₃×#485	C₂²	semidirect
72. C₂₃×#485	C₂²	semidirect
73. C₂₃×#484	C₂²	semidirect
74. C₂₃×#483	C₂²	semidirect
75. C₂₃×#483	C₂²	semidirect
78. C₂₃×#482	C₂²	semidirect
79. C₂₃×#481	C₂²	semidirect
80. C₂₃×#480	C₂²	semidirect
81. C₂₃×#480	C₂²	semidirect
82. C₂₃×#479	C₂²	semidirect
83. C₂₃×#479	C₂²	semidirect
84. C₂₃×#479	C₂²	semidirect
85. C₂₃×#478	C₂²	semidirect
86. C₂₃×#477	C₂²	semidirect
87. C₂₃×#476	C₂²	semidirect
88. C₂₃×#475	C₂²	semidirect
89. C₂₃×#475	C₂²	semidirect
90. C₂₃×#474	C₂²	semidirect
91. C₂₃×#474	C₂²	semidirect
92. C₂₃×#467	C₂²	semidirect
93. C₂₃×#467	C₂²	semidirect
94. C₂₃×#467	C₂²	semidirect
95. C₂₃×#466	C₂²	semidirect
96. C₂₃×#465	C₂²	semidirect
97. C₂₃×#465	C₂²	semidirect
98. C₂₃×#465	C₂²	semidirect
99. C₂₃×#465	C₂²	semidirect
100. C₂₃×#464	C₂²	semidirect
101. C₂₃×#463	C₂²	semidirect
102. C₂₃×#462	C₂²	semidirect
103. C₂₃×#461	C₂²	semidirect
106. C₂₃×#452	C₂²	semidirect
107. C₂₃×#451	C₂²	semidirect
109. C₂₃×#449	C₂²	semidirect
110. C₂₃×#448	C₂²	semidirect
111. C₄×Q₁₆×C₂₃	C₂²	semidirect
112. C₄×Q₁₆×C₂₃	C₂²	semidirect
113. C₄×SD₁₆×C₂₃	C₂²	semidirect
114. C₄×SD₁₆×C₂₃	C₂²	semidirect
115. C₄×SD₁₆×C₂₃	C₂²	semidirect
116. C₄×D₈×C₂₃	C₂²	semidirect
125. C₂₃×#427	C₂²	semidirect
126. C₂₃×#427	C₂²	semidirect
127. C₂×C₂₃×#107	C₂²	semidirect
128. C₂×C₂₃×#106	C₂²	semidirect
129. C₂₃×#416	C₂²	semidirect
130. C₂₃×#416	C₂²	semidirect
131. C₂×C₂₃×#103	C₂²	semidirect
132. C₂×C₂₃×#103	C₂²	semidirect
446. #61703	C₂₃	direct (N × H)
522. #3520	C₂×C₂₃	semidirect
523. #3475	C₂×C₂₃	semidirect
524. #3342	C₂×C₂₃	semidirect
525. #3340	C₂×C₂₃	semidirect
526. #3337	C₂×C₂₃	semidirect
527. #3336	C₂×C₂₃	semidirect
528. #3335	C₂×C₂₃	semidirect
529. #3334	C₂×C₂₃	semidirect
530. #3303	C₂×C₂₃	semidirect
531. #3302	C₂×C₂₃	semidirect
532. #3301	C₂×C₂₃	semidirect
533. #3300	C₂×C₂₃	semidirect
534. #3299	C₂×C₂₃	semidirect
535. #3298	C₂×C₂₃	semidirect
536. #3233	C₂×C₂₃	semidirect
537. #3231	C₂×C₂₃	semidirect
538. #3191	C₂×C₂₃	semidirect
539. #3190	C₂×C₂₃	semidirect
540. #3107	C₂×C₂₃	semidirect
541. #3102	C₂×C₂₃	semidirect
542. #3091	C₂×C₂₃	semidirect
543. C₂×#485	C₂×C₂₃	semidirect
544. #2972	C₂×C₂₃	semidirect
614. #500	C₂²×C₂₃	semidirect
615. #499	C₂²×C₂₃	semidirect
616. #498	C₂²×C₂₃	semidirect
617. #488	C₂²×C₂₃	semidirect
618. #487	C₂²×C₂₃	semidirect
619. #487	C₂²×C₂₃	semidirect
625. #485	C₂²×C₂₃	semidirect
626. #485	C₂²×C₂₃	semidirect
627. #485	C₂²×C₂₃	semidirect
628. #485	C₂²×C₂₃	semidirect
629. #485	C₂²×C₂₃	semidirect
630. #484	C₂²×C₂₃	semidirect
631. #483	C₂²×C₂₃	semidirect
632. #483	C₂²×C₂₃	semidirect
635. #482	C₂²×C₂₃	semidirect
636. #481	C₂²×C₂₃	semidirect
637. #480	C₂²×C₂₃	semidirect
638. #480	C₂²×C₂₃	semidirect
639. #479	C₂²×C₂₃	semidirect
640. #479	C₂²×C₂₃	semidirect
641. #479	C₂²×C₂₃	semidirect
642. #478	C₂²×C₂₃	semidirect
643. #477	C₂²×C₂₃	semidirect
644. #476	C₂²×C₂₃	semidirect
645. #475	C₂²×C₂₃	semidirect
646. #475	C₂²×C₂₃	semidirect
647. #474	C₂²×C₂₃	semidirect
648. #474	C₂²×C₂₃	semidirect
649. #467	C₂²×C₂₃	semidirect
650. #467	C₂²×C₂₃	semidirect
651. #467	C₂²×C₂₃	semidirect
652. #466	C₂²×C₂₃	semidirect
653. #465	C₂²×C₂₃	semidirect
654. #465	C₂²×C₂₃	semidirect
655. #465	C₂²×C₂₃	semidirect
656. #465	C₂²×C₂₃	semidirect
657. #464	C₂²×C₂₃	semidirect
658. #463	C₂²×C₂₃	semidirect
659. #462	C₂²×C₂₃	semidirect
660. #461	C₂²×C₂₃	semidirect
663. #452	C₂²×C₂₃	semidirect
664. #451	C₂²×C₂₃	semidirect
666. #449	C₂²×C₂₃	semidirect
667. #448	C₂²×C₂₃	semidirect
668. C₄×Q₁₆	C₂²×C₂₃	semidirect
669. C₄×Q₁₆	C₂²×C₂₃	semidirect
670. C₄×SD₁₆	C₂²×C₂₃	semidirect
671. C₄×SD₁₆	C₂²×C₂₃	semidirect
672. C₄×SD₁₆	C₂²×C₂₃	semidirect
673. C₄×D₈	C₂²×C₂₃	semidirect
682. #427	C₂²×C₂₃	semidirect
683. #427	C₂²×C₂₃	semidirect
684. C₂×#107	C₂²×C₂₃	semidirect
685. C₂×#106	C₂²×C₂₃	semidirect
686. #416	C₂²×C₂₃	semidirect
687. #416	C₂²×C₂₃	semidirect
688. C₂×#103	C₂²×C₂₃	semidirect
689. C₂×#103	C₂²×C₂₃	semidirect
877. C₂₃	#61703	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×#3520	2
C₂₃×#3475	2
C₂₃×#3342	2
C₂₃×#3340	2
C₂₃×#3337	2
C₂₃×#3336	2
C₂₃×#3335	2
C₂₃×#3334	2
C₂₃×#3303	2
C₂₃×#3302	2
C₂₃×#3301	2
C₂₃×#3300	2
C₂₃×#3299	2
C₂₃×#3298	2
C₂₃×#3233	2
C₂₃×#3231	2
C₂₃×#3191	2
C₂₃×#3190	2
C₂₃×#3107	2
C₂₃×#3102	2
C₂₃×#3091	2
C₂×C₂₃×#485	2
C₂₃×#2972	2
#61703	23

Subgroups — C23×#61703 #19209329

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#61703 #19209329