Subgroups — C₂₃×#61742 #19209368

Order 5888.

1750 conjugacy classes of subgroups.

The subgroup lattice has 1122 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3501	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂₃×#3475	C₂	1	1	yes	maximal, characteristic
3	C₂₃×#3357	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₃×#3356	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₃×#3346	C₂	1	2	yes	maximal, complemented
6	C₂₃×#3344	C₂	1	2	yes	maximal, complemented
7	C₂₃×#3338	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₃×#3335	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₃×#3329	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₃×#3328	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₃×#3320	C₂	1	2	yes	maximal, complemented
12	C₂₃×#3312	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×#3237	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂₃×#3231	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂₃×#3196	C₂	1	2	yes	maximal, complemented
18	C₂₃×#3190	C₂	1	2	yes	maximal, complemented
19	C₂₃×#3116	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂₃×#3107	C₂	1	1	yes	maximal, characteristic, complemented
21	C₂₃×#3095	C₂	1	2	yes	maximal, complemented
22	C₂×C₂₃×#485	C₂	1	2	yes	maximal, complemented
23	C₂₃×#2974	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂₃×#556	C₂²	1	1	yes	characteristic
25	C₂₃×#555	C₂²	1	1	yes	characteristic
26	C₂₃×#554	—	2	1	no	—
27	C₂₃×#554	—	2	2	no	—
28	C₂₃×#554	—	2	1	no	—
29	C₂₃×#554	C₂²	1	1	yes	characteristic
30	C₂₃×#554	C₂²	1	1	yes	characteristic
31	C₂₃×#554	C₂²	1	2	yes	—
32	C₂₃×#554	C₂²	1	1	yes	characteristic
33	C₂₃×#553	C₂²	1	2	yes	—
34	C₂₃×#552	—	2	1	no	—
35	C₂₃×#552	C₂²	1	2	yes	—
36	C₂₃×#551	—	2	2	no	—
37	D₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic
38	D₄×Q₈×C₂₃	C₂²	1	2	yes	—
39	D₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic
40	C₂₃×#547	C₂²	1	1	yes	characteristic
41	C₂₃×#546	—	2	1	no	—
42	C₂₃×#544	—	2	1	no	—
43	C₂₃×#543	—	2	2	no	—
44	C₂₃×#533	C₂²	1	1	yes	characteristic
45	C₂₃×#533	C₂²	1	1	yes	characteristic
46	C₂₃×#533	C₂²	1	1	yes	characteristic
47	C₂₃×#529	—	2	2	no	—
48	C₂₃×#529	—	2	1	no	—
49	C₂₃×#525	C₂²	1	2	yes	—
50	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	2	yes	—
51	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	2	yes	—
52	C₂₃×#518	—	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×#501	C₂²	1	2	yes	complemented
58	C₂₃×#500	C₂²	1	1	yes	characteristic, complemented
59	C₂₃×#498	C₂²	1	1	yes	characteristic, complemented
60	C₂₃×#491	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	2	yes	—
67	C₂₃×#485	C₂²	1	1	yes	characteristic
68	C₂₃×#485	C₂²	1	2	yes	—
69	C₂₃×#485	C₂²	1	1	yes	characteristic
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×#485	C₂²	1	2	yes	complemented
74	C₂₃×#484	C₂²	1	2	yes	complemented
75	C₂₃×#484	C₂²	1	2	yes	complemented
76	C₂₃×#484	C₂²	1	2	yes	complemented
77	C₂₃×#483	C₂²	1	2	yes	complemented
78	C₂₃×#483	C₂²	1	2	yes	complemented
79	C₂₃×#483	C₂²	1	2	yes	complemented
80	C₂₃×#481	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×#477	C₂²	1	1	yes	characteristic, complemented
85	C₂₃×#477	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×#475	C₂²	1	1	yes	characteristic, complemented
91	C₂₃×#474	C₂²	1	1	yes	characteristic, complemented
92	C₂₃×#470	C₂²	1	2	yes	complemented
93	C₂₃×#470	C₂²	1	2	yes	complemented
94	C₂₃×#468	C₂²	1	2	yes	complemented
95	C₂₃×#468	C₂²	1	2	yes	complemented
96	C₂₃×#467	C₂²	1	2	yes	complemented
97	C₂₃×#467	C₂²	1	2	yes	complemented
98	C₂₃×#465	C₂²	1	2	yes	complemented
99	C₂₃×#465	C₂²	1	2	yes	complemented
100	C₂₃×#462	C₂²	1	1	yes	characteristic, complemented
101	C₂₃×#462	C₂²	1	1	yes	characteristic, complemented
102	C₂₃×#461	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	1	yes	characteristic
107	C₂₃×#451	C₂²	1	2	yes	complemented
108	C₂₃×#451	C₂²	1	2	yes	complemented
109	C₂₃×#448	C₂²	1	2	yes	complemented
110	C₂₃×#448	C₂²	1	2	yes	complemented
111	C₂₃×#441	C₂²	1	2	yes	complemented
112	C₂₃×#440	C₂²	1	2	yes	complemented
113	C₄×Q₁₆×C₂₃	C₂²	1	1	yes	characteristic, complemented
114	C₄×Q₁₆×C₂₃	C₂²	1	1	yes	characteristic, complemented
115	C₄×SD₁₆×C₂₃	C₂²	1	1	yes	characteristic, complemented
116	C₄×SD₁₆×C₂₃	C₂²	1	1	yes	characteristic, complemented
117	C₂₃×#436	C₂²	1	1	yes	characteristic
118	C₂₃×#436	C₂²	1	1	yes	characteristic
119	C₂₃×#435	C₂²	1	2	yes	—
120	C₂₃×#435	C₂²	1	2	yes	—
121	C₈×D₄×C₂₃	C₂²	1	1	yes	characteristic
122	C₈×D₄×C₂₃	C₂²	1	1	yes	characteristic
123	C₂₃×#432	C₂²	1	1	yes	characteristic
124	C₂₃×#431	C₂²	1	1	yes	characteristic
125	C₂₃×#428	C₂²	1	2	yes	complemented
126	C₂₃×#428	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×#419	C₂²	1	2	yes	complemented
130	C₂₃×#419	C₂²	1	2	yes	complemented
131	C₂×C₂₃×#103	C₂²	1	2	yes	complemented
132	C₂×C₂₃×#103	C₂²	1	2	yes	complemented
133	C₂₃×#407	C₂²	1	2	yes	—
134	C₂×C₂₃×C₂²⋊C₈	C₂²	1	2	yes	—
135	C₂×#41×C₂₃	—	2	1	no	—
136	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
137	C₂²×Q₈×C₂₃	C₂³	1	2	yes	—
138	C₂²×Q₈×C₂₃	C₂³	1	2	yes	—
139	C₂²×D₄×C₂₃	D₄	1	1	yes	characteristic
140	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
141	C₂×Q₁₆×C₂₃	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
146	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
147	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
148	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
149	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
150	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
151	C₂₃×C₄⋊Q₈	—	2	1	no	—
152	C₂₃×C₄⋊Q₈	—	2	1	no	—
153	C₂₃×C₄⋊Q₈	—	2	2	no	—
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×C₄⋊Q₈	C₂³	1	1	yes	characteristic
158	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
159	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
160	C₂₃×#126	—	2	2	no	—
161	C₂₃×#126	—	2	2	no	—
162	C₂₃×#126	—	2	2	no	—
163	C₂₃×#125	—	2	2	no	—
164	C₂₃×#125	—	2	1	no	—
165	C₂₃×#125	—	2	1	no	—
166	C₂₃×#125	—	2	1	no	—
167	C₂₃×#125	—	2	2	no	—
168	C₂₃×#125	—	2	1	no	—
169	C₂₃×#125	—	2	1	no	—
170	C₂₃×#125	C₂³	1	2	yes	—
171	C₂₃×#124	—	2	1	no	—
172	C₂₃×#124	—	2	2	no	—
173	C₂₃×#123	—	2	2	no	—
174	C₂₃×#123	—	2	2	no	—
175	C₂₃×#123	—	2	2	no	—
176	C₂₃×#123	—	2	2	no	—
177	C₂₃×C₂²⋊Q₈	—	2	1	no	—
178	C₂₃×C₂²⋊Q₈	—	2	1	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	1	no	—
184	C₂₃×C₂²⋊Q₈	—	2	1	no	—
185	C₂₃×C₂²⋊Q₈	—	2	1	no	—
186	C₂₃×C₂²⋊Q₈	—	2	2	no	—
187	C₂₃×C₂²⋊Q₈	—	2	2	no	—
188	C₂₃×C₂²⋊Q₈	—	2	2	no	—
189	C₂₃×C₂²⋊Q₈	—	2	2	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	—	2	2	no	—
194	C₂₃×C₂²⋊Q₈	—	2	2	no	—
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	2	yes	—
199	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
200	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
201	C₂₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
202	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
203	C₂₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
204	C₂₃×#121	—	2	2	no	—
205	C₂₃×#121	—	2	1	no	—
206	C₂₃×#121	C₂³	1	2	yes	—
207	C₂₃×#121	C₂³	1	2	yes	—
208	C₂₃×#120	—	2	2	no	—
209	C₄×Q₈×C₂₃	—	2	1	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	C₂³	1	1	yes	characteristic
215	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
216	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
217	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
218	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
219	C₄×D₄×C₂₃	—	2	2	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	1	no	—
226	C₄×D₄×C₂₃	—	2	1	no	—
227	C₄×D₄×C₂₃	—	2	1	no	—
228	C₄×D₄×C₂₃	—	2	2	no	—
229	C₄×D₄×C₂₃	—	2	2	no	—
230	C₄×D₄×C₂₃	—	2	2	no	—
231	C₄×D₄×C₂₃	D₄	1	1	yes	characteristic
232	C₄×D₄×C₂₃	D₄	1	1	yes	characteristic
233	C₄×D₄×C₂₃	D₄	1	2	yes	—
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	2	yes	—
238	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
239	C₂₃×#117	—	2	2	no	—
240	C₂₃×#117	—	2	2	no	—
241	C₂₃×#117	—	2	1	no	—
242	C₂₃×#117	—	2	1	no	—
243	C₂₃×#117	—	2	1	no	—
244	C₂₃×#117	—	2	2	no	—
245	C₂₃×#117	—	2	1	no	—
246	C₂₃×#117	C₂³	1	2	yes	—
247	C₂₃×#117	C₂³	1	2	yes	—
248	C₂₃×#117	C₂³	1	1	yes	characteristic
249	C₂₃×#117	C₂³	1	2	yes	—
250	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
251	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
252	C₂×C₄⋊C₄×C₂₃	D₄	1	1	yes	characteristic
253	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
254	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
255	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
256	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
257	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
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	1	yes	characteristic
291	C₂₃×#103	C₂³	1	1	yes	characteristic
292	C₂₃×#103	C₂³	1	2	yes	—
293	C₂₃×#103	C₂³	1	2	yes	—
294	C₂₃×#103	C₂³	1	2	yes	—
295	C₂₃×#103	C₂³	1	2	yes	—
296	C₂₃×#103	C₂³	1	1	yes	characteristic
297	C₂₃×#103	C₂³	1	1	yes	characteristic
298	C₂₃×#103	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	2	yes	—
304	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
305	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
306	C₂₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
307	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
308	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
309	C₂₃×#97	C₂³	1	2	yes	—
310	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
311	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
312	C₂⁴×C₂₃	C₂×D₄	1	2	yes	—
313	#41×C₂₃	—	4	1	no	—
314	#41×C₂₃	—	4	1	no	—
315	#41×C₂₃	—	4	4	no	—
316	C₂×Q₈×C₂₃	—	2	1	no	—
317	C₂×Q₈×C₂₃	—	2	1	no	—
318	C₂×Q₈×C₂₃	—	2	1	no	—
319	C₂×Q₈×C₂₃	—	2	1	no	—
320	C₂×Q₈×C₂₃	—	2	2	no	—
321	C₂×Q₈×C₂₃	—	2	2	no	—
322	C₂×Q₈×C₂₃	—	4	2	no	—
323	C₂×Q₈×C₂₃	—	4	2	no	—
324	C₂×Q₈×C₂₃	—	4	2	no	—
325	C₂×Q₈×C₂₃	—	4	2	no	—
326	C₂×Q₈×C₂₃	C₂⁴	1	1	yes	characteristic
327	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
328	C₂×Q₈×C₂₃	C₂⁴	1	1	yes	characteristic
329	C₂×Q₈×C₂₃	C₂⁴	1	1	yes	characteristic
330	C₂×D₄×C₂₃	—	2	4	no	—
331	C₂×D₄×C₂₃	—	2	1	no	—
332	C₂×D₄×C₂₃	—	2	2	no	—
333	C₂×D₄×C₂₃	—	2	2	no	—
334	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
335	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
336	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
337	C₂×D₄×C₂₃	C₂⁴	1	1	yes	characteristic
338	C₂²×C₄×C₂₃	—	2	2	no	—
339	C₂²×C₄×C₂₃	—	2	2	no	—
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	—	4	2	no	—
348	C₂²×C₄×C₂₃	—	4	2	no	—
349	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
350	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
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	2	yes	—
354	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
355	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
356	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
357	Q₁₆×C₂₃	—	4	1	no	—
358	Q₁₆×C₂₃	—	4	2	no	—
359	Q₁₆×C₂₃	—	4	1	no	—
360	SD₁₆×C₂₃	—	4	1	no	—
361	SD₁₆×C₂₃	—	4	2	no	—
362	SD₁₆×C₂₃	—	4	1	no	—
363	M₁₆×C₂₃	—	4	2	no	—
364	M₁₆×C₂₃	—	4	2	no	—
365	C₂×C₈×C₂₃	—	4	2	no	—
366	C₂×C₈×C₂₃	—	4	2	no	—
367	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
368	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
369	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
370	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
371	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
372	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
373	C₄⋊C₄×C₂₃	—	2	1	no	—
374	C₄⋊C₄×C₂₃	—	2	2	no	—
375	C₄⋊C₄×C₂₃	—	2	1	no	—
376	C₄⋊C₄×C₂₃	—	2	2	no	—
377	C₄⋊C₄×C₂₃	—	2	2	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	2	no	—
384	C₄⋊C₄×C₂₃	—	2	1	no	—
385	C₄⋊C₄×C₂₃	—	2	1	no	—
386	C₄⋊C₄×C₂₃	—	2	1	no	—
387	C₄⋊C₄×C₂₃	—	2	1	no	—
388	C₄⋊C₄×C₂₃	—	2	1	no	—
389	C₄⋊C₄×C₂₃	—	2	2	no	—
390	C₄⋊C₄×C₂₃	—	2	2	no	—
391	C₄⋊C₄×C₂₃	—	2	1	no	—
392	C₄⋊C₄×C₂₃	—	2	1	no	—
393	C₄⋊C₄×C₂₃	—	2	2	no	—
394	C₄⋊C₄×C₂₃	—	2	2	no	—
395	C₄⋊C₄×C₂₃	—	2	1	no	—
396	C₄⋊C₄×C₂₃	—	2	1	no	—
397	C₄⋊C₄×C₂₃	—	2	1	no	—
398	C₄⋊C₄×C₂₃	—	2	2	no	—
399	C₄⋊C₄×C₂₃	—	2	1	no	—
400	C₄⋊C₄×C₂₃	—	2	1	no	—
401	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
402	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
403	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
404	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
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	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
409	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
410	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
411	C₂²⋊C₄×C₂₃	—	2	1	no	—
412	C₂²⋊C₄×C₂₃	—	2	1	no	—
413	C₂²⋊C₄×C₂₃	—	2	2	no	—
414	C₂²⋊C₄×C₂₃	—	2	1	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	2	no	—
421	C₂²⋊C₄×C₂₃	—	2	2	no	—
422	C₂²⋊C₄×C₂₃	—	2	2	no	—
423	C₂²⋊C₄×C₂₃	—	2	2	no	—
424	C₂²⋊C₄×C₂₃	—	2	2	no	—
425	C₂²⋊C₄×C₂₃	—	2	1	no	—
426	C₂²⋊C₄×C₂₃	—	2	1	no	—
427	C₂²⋊C₄×C₂₃	—	2	2	no	—
428	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
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	C₄²×C₂₃	—	2	1	no	—
433	C₄²×C₂₃	—	2	2	no	—
434	C₄²×C₂₃	—	2	1	no	—
435	C₄²×C₂₃	—	2	2	no	—
436	C₄²×C₂₃	—	2	2	no	—
437	C₄²×C₂₃	—	2	1	no	—
438	C₄²×C₂₃	—	2	2	no	—
439	C₄²×C₂₃	—	2	1	no	—
440	C₄²×C₂₃	—	2	1	no	—
441	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
442	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
443	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
444	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
445	#61742	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
446	C₂³×C₂₃	—	2	4	no	—
447	C₂³×C₂₃	—	2	1	no	—
448	C₂³×C₂₃	—	4	2	no	—
449	C₂³×C₂₃	—	4	2	no	—
450	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
451	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
452	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
453	Q₈×C₂₃	—	2	1	no	—
454	Q₈×C₂₃	—	2	1	no	—
455	Q₈×C₂₃	—	2	2	no	—
456	Q₈×C₂₃	—	2	1	no	—
457	Q₈×C₂₃	—	2	1	no	—
458	Q₈×C₂₃	—	2	2	no	—
459	Q₈×C₂₃	—	2	1	no	—
460	Q₈×C₂₃	—	2	1	no	—
461	Q₈×C₂₃	—	4	2	no	—
462	Q₈×C₂₃	—	8	1	no	—
463	Q₈×C₂₃	—	8	1	no	—
464	Q₈×C₂₃	—	8	1	no	—
465	Q₈×C₂₃	—	8	2	no	—
466	Q₈×C₂₃	—	8	2	no	—
467	D₄×C₂₃	—	2	4	no	—
468	D₄×C₂₃	—	2	2	no	—
469	D₄×C₂₃	—	2	1	no	—
470	D₄×C₂₃	—	2	1	no	—
471	D₄×C₂₃	—	4	2	no	—
472	D₄×C₂₃	—	4	4	no	—
473	D₄×C₂₃	—	8	2	no	—
474	D₄×C₂₃	#137	1	4	yes	—
475	C₂×C₄×C₂₃	—	2	2	no	—
476	C₂×C₄×C₂₃	—	2	2	no	—
477	C₂×C₄×C₂₃	—	2	2	no	—
478	C₂×C₄×C₂₃	—	2	2	no	—
479	C₂×C₄×C₂₃	—	2	2	no	—
480	C₂×C₄×C₂₃	—	2	1	no	—
481	C₂×C₄×C₂₃	—	2	1	no	—
482	C₂×C₄×C₂₃	—	2	1	no	—
483	C₂×C₄×C₂₃	—	2	1	no	—
484	C₂×C₄×C₂₃	—	2	1	no	—
485	C₂×C₄×C₂₃	—	2	2	no	—
486	C₂×C₄×C₂₃	—	2	2	no	—
487	C₂×C₄×C₂₃	—	2	2	no	—
488	C₂×C₄×C₂₃	—	2	1	no	—
489	C₂×C₄×C₂₃	—	2	1	no	—
490	C₂×C₄×C₂₃	—	2	2	no	—
491	C₂×C₄×C₂₃	—	2	1	no	—
492	C₂×C₄×C₂₃	—	2	1	no	—
493	C₂×C₄×C₂₃	—	4	2	no	—
494	C₂×C₄×C₂₃	—	4	2	no	—
495	C₂×C₄×C₂₃	—	4	2	no	—
496	C₂×C₄×C₂₃	—	4	1	no	—
497	C₂×C₄×C₂₃	—	4	2	no	—
498	C₂×C₄×C₂₃	—	4	4	no	—
499	C₂×C₄×C₂₃	—	4	2	no	—
500	C₂×C₄×C₂₃	—	8	1	no	—
501	C₂×C₄×C₂₃	—	8	2	no	—
502	C₂×C₄×C₂₃	—	8	2	no	—
503	C₂×C₄×C₂₃	—	8	2	no	—
504	C₂×C₄×C₂₃	—	8	2	no	—
505	C₂×C₄×C₂₃	—	8	2	no	—
506	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
507	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
508	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
509	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
510	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
511	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
512	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
513	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
514	C₈×C₂₃	—	2	1	no	—
515	C₈×C₂₃	—	2	1	no	—
516	C₈×C₂₃	—	2	2	no	—
517	C₈×C₂₃	—	2	2	no	—
518	C₈×C₂₃	—	2	1	no	—
519	C₈×C₂₃	—	2	1	no	—
520	#3501	C₂×C₂₃	1	1	yes	characteristic, complemented
521	#3475	C₂×C₂₃	1	1	yes	characteristic
522	#3357	C₂×C₂₃	1	1	yes	characteristic, complemented
523	#3356	C₂×C₂₃	1	1	yes	characteristic, complemented
524	#3346	C₂×C₂₃	1	2	yes	complemented
525	#3344	C₂×C₂₃	1	2	yes	complemented
526	#3338	C₂×C₂₃	1	1	yes	characteristic, complemented
527	#3335	C₂×C₂₃	1	1	yes	characteristic, complemented
528	#3329	C₂×C₂₃	1	1	yes	characteristic, complemented
529	#3328	C₂×C₂₃	1	1	yes	characteristic, complemented
530	#3320	C₂×C₂₃	1	2	yes	complemented
531	#3312	C₂×C₂₃	1	2	yes	complemented
532	#3299	C₂×C₂₃	1	1	yes	characteristic, complemented
533	#3298	C₂×C₂₃	1	1	yes	characteristic, complemented
534	#3237	C₂×C₂₃	1	1	yes	characteristic, complemented
535	#3231	C₂×C₂₃	1	1	yes	characteristic, complemented
536	#3196	C₂×C₂₃	1	2	yes	complemented
537	#3190	C₂×C₂₃	1	2	yes	complemented
538	#3116	C₂×C₂₃	1	1	yes	characteristic, complemented
539	#3107	C₂×C₂₃	1	1	yes	characteristic, complemented
540	#3095	C₂×C₂₃	1	2	yes	complemented
541	C₂×#485	C₂×C₂₃	1	2	yes	complemented
542	#2974	C₂×C₂₃	1	1	yes	characteristic, complemented
543	C₂²×C₂₃	—	2	2	no	—
544	C₂²×C₂₃	—	2	2	no	—
545	C₂²×C₂₃	—	2	1	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	—	4	1	no	—
552	C₂²×C₂₃	—	4	1	no	—
553	C₂²×C₂₃	—	4	1	no	—
554	C₂²×C₂₃	—	8	4	no	—
555	C₂²×C₂₃	C₂×#137	1	4	yes	—
556	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
557	C₄×C₂₃	—	2	1	no	—
558	C₄×C₂₃	—	2	1	no	—
559	C₄×C₂₃	—	2	1	no	—
560	C₄×C₂₃	—	2	2	no	—
561	C₄×C₂₃	—	2	2	no	—
562	C₄×C₂₃	—	2	1	no	—
563	C₄×C₂₃	—	4	1	no	—
564	C₄×C₂₃	—	4	1	no	—
565	C₄×C₂₃	—	4	2	no	—
566	C₄×C₂₃	—	4	1	no	—
567	C₄×C₂₃	—	4	2	no	—
568	C₄×C₂₃	—	4	1	no	—
569	C₄×C₂₃	—	4	1	no	—
570	C₄×C₂₃	—	4	2	no	—
571	C₄×C₂₃	—	4	1	no	—
572	C₄×C₂₃	—	4	1	no	—
573	C₄×C₂₃	—	4	2	no	—
574	C₄×C₂₃	C₂×#137	1	2	yes	—
575	C₄×C₂₃	#585	1	1	yes	characteristic
576	C₄×C₂₃	#585	1	1	yes	characteristic
577	#556	C₂²×C₂₃	1	1	yes	characteristic
578	#555	C₂²×C₂₃	1	1	yes	characteristic
579	#554	—	2	1	no	—
580	#554	—	2	2	no	—
581	#554	—	2	1	no	—
582	#554	C₂²×C₂₃	1	1	yes	characteristic
583	#554	C₂²×C₂₃	1	1	yes	characteristic
584	#554	C₂²×C₂₃	1	2	yes	—
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	#551	—	2	2	no	—
590	D₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
591	D₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
592	D₄×Q₈	C₂²×C₂₃	1	2	yes	—
593	#547	C₂²×C₂₃	1	1	yes	characteristic
594	#546	—	2	1	no	—
595	#544	—	2	1	no	—
596	#543	—	2	2	no	—
597	#533	C₂²×C₂₃	1	1	yes	characteristic
598	#533	C₂²×C₂₃	1	1	yes	characteristic
599	#533	C₂²×C₂₃	1	1	yes	characteristic
600	#529	—	2	2	no	—
601	#529	—	2	1	no	—
602	#525	C₂²×C₂₃	1	2	yes	—
603	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	2	yes	—
604	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	2	yes	—
605	#518	—	2	1	no	—
606	C₄×#41	—	2	1	no	—
607	C₄×#41	C₂²×C₂₃	1	1	yes	characteristic
608	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
609	C₂×#117	C₂²×C₂₃	1	2	yes	—
610	#501	C₂²×C₂₃	1	2	yes	complemented
611	#500	C₂²×C₂₃	1	1	yes	characteristic, complemented
612	#498	C₂²×C₂₃	1	1	yes	characteristic, complemented
613	#491	C₂²×C₂₃	1	2	yes	complemented
614	#487	C₂²×C₂₃	1	1	yes	characteristic, complemented
615	#487	C₂²×C₂₃	1	1	yes	characteristic, complemented
616	#485	C₂²×C₂₃	1	1	yes	characteristic
617	#485	C₂²×C₂₃	1	2	yes	—
618	#485	C₂²×C₂₃	1	2	yes	—
619	#485	C₂²×C₂₃	1	2	yes	—
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	complemented
624	#485	C₂²×C₂₃	1	2	yes	complemented
625	#485	C₂²×C₂₃	1	2	yes	complemented
626	#485	C₂²×C₂₃	1	2	yes	complemented
627	#484	C₂²×C₂₃	1	2	yes	complemented
628	#484	C₂²×C₂₃	1	2	yes	complemented
629	#484	C₂²×C₂₃	1	2	yes	complemented
630	#483	C₂²×C₂₃	1	2	yes	complemented
631	#483	C₂²×C₂₃	1	2	yes	complemented
632	#483	C₂²×C₂₃	1	2	yes	complemented
633	#481	C₂²×C₂₃	1	2	yes	complemented
634	#480	C₂²×C₂₃	1	2	yes	complemented
635	#479	C₂²×C₂₃	1	2	yes	complemented
636	#479	C₂²×C₂₃	1	2	yes	complemented
637	#477	C₂²×C₂₃	1	1	yes	characteristic, complemented
638	#477	C₂²×C₂₃	1	1	yes	characteristic, complemented
639	#477	C₂²×C₂₃	1	1	yes	characteristic, complemented
640	#476	C₂²×C₂₃	1	1	yes	characteristic, complemented
641	#475	C₂²×C₂₃	1	1	yes	characteristic, complemented
642	#475	C₂²×C₂₃	1	1	yes	characteristic, complemented
643	#475	C₂²×C₂₃	1	1	yes	characteristic, complemented
644	#474	C₂²×C₂₃	1	1	yes	characteristic, complemented
645	#470	C₂²×C₂₃	1	2	yes	complemented
646	#470	C₂²×C₂₃	1	2	yes	complemented
647	#468	C₂²×C₂₃	1	2	yes	complemented
648	#468	C₂²×C₂₃	1	2	yes	complemented
649	#467	C₂²×C₂₃	1	2	yes	complemented
650	#467	C₂²×C₂₃	1	2	yes	complemented
651	#465	C₂²×C₂₃	1	2	yes	complemented
652	#465	C₂²×C₂₃	1	2	yes	complemented
653	#462	C₂²×C₂₃	1	1	yes	characteristic, complemented
654	#462	C₂²×C₂₃	1	1	yes	characteristic, complemented
655	#461	C₂²×C₂₃	1	1	yes	characteristic, complemented
656	#461	C₂²×C₂₃	1	1	yes	characteristic, complemented
657	#452	C₂²×C₂₃	1	1	yes	characteristic
658	#452	C₂²×C₂₃	1	1	yes	characteristic
659	#452	C₂²×C₂₃	1	2	yes	—
660	#451	C₂²×C₂₃	1	2	yes	complemented
661	#451	C₂²×C₂₃	1	2	yes	complemented
662	#448	C₂²×C₂₃	1	2	yes	complemented
663	#448	C₂²×C₂₃	1	2	yes	complemented
664	#441	C₂²×C₂₃	1	2	yes	complemented
665	#440	C₂²×C₂₃	1	2	yes	complemented
666	C₄×Q₁₆	C₂²×C₂₃	1	1	yes	characteristic, complemented
667	C₄×Q₁₆	C₂²×C₂₃	1	1	yes	characteristic, complemented
668	C₄×SD₁₆	C₂²×C₂₃	1	1	yes	characteristic, complemented
669	C₄×SD₁₆	C₂²×C₂₃	1	1	yes	characteristic, complemented
670	#436	C₂²×C₂₃	1	1	yes	characteristic
671	#436	C₂²×C₂₃	1	1	yes	characteristic
672	#435	C₂²×C₂₃	1	2	yes	—
673	#435	C₂²×C₂₃	1	2	yes	—
674	C₈×D₄	C₂²×C₂₃	1	1	yes	characteristic
675	C₈×D₄	C₂²×C₂₃	1	1	yes	characteristic
676	#432	C₂²×C₂₃	1	1	yes	characteristic
677	#431	C₂²×C₂₃	1	1	yes	characteristic
678	#428	C₂²×C₂₃	1	2	yes	complemented
679	#428	C₂²×C₂₃	1	2	yes	complemented
680	C₂×#107	C₂²×C₂₃	1	2	yes	complemented
681	C₂×#106	C₂²×C₂₃	1	2	yes	complemented
682	#419	C₂²×C₂₃	1	2	yes	complemented
683	#419	C₂²×C₂₃	1	2	yes	complemented
684	C₂×#103	C₂²×C₂₃	1	2	yes	complemented
685	C₂×#103	C₂²×C₂₃	1	2	yes	complemented
686	#407	C₂²×C₂₃	1	2	yes	—
687	C₂×C₂²⋊C₈	C₂²×C₂₃	1	2	yes	—
688	C₂×C₂₃	—	2	4	no	—
689	C₂×C₂₃	—	4	2	no	—
690	C₂×C₂₃	—	4	1	no	—
691	C₂×C₂₃	—	8	1	no	—
692	C₂×C₂₃	#3485	1	1	yes	characteristic
693	C₂×C₂₃	C₂²×#137	1	1	yes	characteristic
694	C₂×C₂₃	#3584	1	1	yes	characteristic
695	C₂×#41	—	2	1	no	—
696	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
697	C₂²×Q₈	C₂³×C₂₃	1	2	yes	—
698	C₂²×Q₈	C₂³×C₂₃	1	2	yes	—
699	C₂²×D₄	D₄×C₂₃	1	1	yes	characteristic
700	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
701	C₂×Q₁₆	C₂³×C₂₃	1	1	yes	characteristic
702	C₂×Q₁₆	C₂³×C₂₃	1	1	yes	characteristic
703	C₂×Q₁₆	C₂³×C₂₃	1	2	yes	—
704	C₂×SD₁₆	C₂³×C₂₃	1	1	yes	characteristic
705	C₂×SD₁₆	C₂³×C₂₃	1	1	yes	characteristic
706	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
707	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
708	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
709	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
710	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
711	C₄⋊Q₈	—	2	1	no	—
712	C₄⋊Q₈	—	2	1	no	—
713	C₄⋊Q₈	—	2	2	no	—
714	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
715	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
716	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
717	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
718	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
719	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
720	#126	—	2	2	no	—
721	#126	—	2	2	no	—
722	#126	—	2	2	no	—
723	#125	—	2	2	no	—
724	#125	—	2	1	no	—
725	#125	—	2	1	no	—
726	#125	—	2	1	no	—
727	#125	—	2	2	no	—
728	#125	—	2	1	no	—
729	#125	—	2	1	no	—
730	#125	C₂³×C₂₃	1	2	yes	—
731	#124	—	2	1	no	—
732	#124	—	2	2	no	—
733	#123	—	2	2	no	—
734	#123	—	2	2	no	—
735	#123	—	2	2	no	—
736	#123	—	2	2	no	—
737	C₂²⋊Q₈	—	2	2	no	—
738	C₂²⋊Q₈	—	2	2	no	—
739	C₂²⋊Q₈	—	2	2	no	—
740	C₂²⋊Q₈	—	2	2	no	—
741	C₂²⋊Q₈	—	2	1	no	—
742	C₂²⋊Q₈	—	2	1	no	—
743	C₂²⋊Q₈	—	2	1	no	—
744	C₂²⋊Q₈	—	2	1	no	—
745	C₂²⋊Q₈	—	2	1	no	—
746	C₂²⋊Q₈	—	2	2	no	—
747	C₂²⋊Q₈	—	2	2	no	—
748	C₂²⋊Q₈	—	2	2	no	—
749	C₂²⋊Q₈	—	2	2	no	—
750	C₂²⋊Q₈	—	2	2	no	—
751	C₂²⋊Q₈	—	2	2	no	—
752	C₂²⋊Q₈	—	2	2	no	—
753	C₂²⋊Q₈	—	2	2	no	—
754	C₂²⋊Q₈	—	2	2	no	—
755	C₂²⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
756	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
757	C₂²⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
758	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
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	#121	—	2	2	no	—
765	#121	—	2	1	no	—
766	#121	C₂³×C₂₃	1	2	yes	—
767	#121	C₂³×C₂₃	1	2	yes	—
768	#120	—	2	2	no	—
769	C₄×Q₈	—	2	1	no	—
770	C₄×Q₈	—	2	1	no	—
771	C₄×Q₈	—	2	1	no	—
772	C₄×Q₈	—	2	1	no	—
773	C₄×Q₈	—	2	1	no	—
774	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
775	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
776	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
777	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
778	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
779	C₄×D₄	—	2	1	no	—
780	C₄×D₄	—	2	2	no	—
781	C₄×D₄	—	2	1	no	—
782	C₄×D₄	—	2	1	no	—
783	C₄×D₄	—	2	2	no	—
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	D₄×C₂₃	1	1	yes	characteristic
792	C₄×D₄	D₄×C₂₃	1	1	yes	characteristic
793	C₄×D₄	D₄×C₂₃	1	2	yes	—
794	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
795	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
796	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
797	C₄×D₄	C₂³×C₂₃	1	2	yes	—
798	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
799	#117	—	2	2	no	—
800	#117	—	2	2	no	—
801	#117	—	2	1	no	—
802	#117	—	2	1	no	—
803	#117	—	2	1	no	—
804	#117	—	2	2	no	—
805	#117	—	2	1	no	—
806	#117	C₂³×C₂₃	1	1	yes	characteristic
807	#117	C₂³×C₂₃	1	2	yes	—
808	#117	C₂³×C₂₃	1	2	yes	—
809	#117	C₂³×C₂₃	1	2	yes	—
810	C₂×C₄⋊C₄	—	2	2	no	—
811	C₂×C₄⋊C₄	—	2	2	no	—
812	C₂×C₄⋊C₄	D₄×C₂₃	1	1	yes	characteristic
813	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
814	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
815	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
816	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
817	C₂×C₂²⋊C₄	—	2	2	no	—
818	C₂×C₂²⋊C₄	—	2	2	no	—
819	C₂×C₂²⋊C₄	—	2	2	no	—
820	C₂×C₂²⋊C₄	D₄×C₂₃	1	2	yes	—
821	C₂×C₄²	—	2	2	no	—
822	C₂×C₄²	—	2	1	no	—
823	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
824	#107	C₂³×C₂₃	1	1	yes	characteristic
825	#107	C₂³×C₂₃	1	2	yes	—
826	#107	C₂³×C₂₃	1	2	yes	—
827	#107	C₂³×C₂₃	1	2	yes	—
828	#107	C₂³×C₂₃	1	1	yes	characteristic
829	#107	C₂³×C₂₃	1	2	yes	—
830	#107	C₂³×C₂₃	1	2	yes	—
831	#106	C₂³×C₂₃	1	1	yes	characteristic
832	#106	C₂³×C₂₃	1	2	yes	—
833	#106	C₂³×C₂₃	1	2	yes	—
834	#106	C₂³×C₂₃	1	2	yes	—
835	#106	C₂³×C₂₃	1	1	yes	characteristic
836	#106	C₂³×C₂₃	1	2	yes	—
837	#106	C₂³×C₂₃	1	2	yes	—
838	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
839	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
840	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
841	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
842	#103	C₂³×C₂₃	1	1	yes	characteristic
843	#103	C₂³×C₂₃	1	1	yes	characteristic
844	#103	C₂³×C₂₃	1	2	yes	—
845	#103	C₂³×C₂₃	1	2	yes	—
846	#103	C₂³×C₂₃	1	2	yes	—
847	#103	C₂³×C₂₃	1	2	yes	—
848	#103	C₂³×C₂₃	1	2	yes	—
849	#103	C₂³×C₂₃	1	2	yes	—
850	#103	C₂³×C₂₃	1	1	yes	characteristic
851	#103	C₂³×C₂₃	1	1	yes	characteristic
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	1	yes	characteristic
857	#103	C₂³×C₂₃	1	1	yes	characteristic
858	#103	C₂³×C₂₃	1	2	yes	—
859	#102	C₂³×C₂₃	1	1	yes	characteristic
860	#102	C₂³×C₂₃	1	1	yes	characteristic
861	#102	C₂³×C₂₃	1	2	yes	—
862	C₂²⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
863	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
864	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
865	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
866	C₂²⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
867	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
868	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
869	#97	C₂³×C₂₃	1	2	yes	—
870	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
871	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
872	C₂₃	#61742	1	1	yes	characteristic, direct product factor, Sylow
873	C₂⁴	C₂×D₄×C₂₃	1	2	yes	—
874	#41	—	4	1	no	—
875	#41	—	4	1	no	—
876	#41	—	4	4	no	—
877	C₂×Q₈	—	2	1	no	—
878	C₂×Q₈	—	2	1	no	—
879	C₂×Q₈	—	2	1	no	—
880	C₂×Q₈	—	2	1	no	—
881	C₂×Q₈	—	2	2	no	—
882	C₂×Q₈	—	2	2	no	—
883	C₂×Q₈	—	4	2	no	—
884	C₂×Q₈	—	4	2	no	—
885	C₂×Q₈	—	4	2	no	—
886	C₂×Q₈	—	4	2	no	—
887	C₂×Q₈	C₂⁴×C₂₃	1	1	yes	characteristic
888	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
889	C₂×Q₈	C₂⁴×C₂₃	1	1	yes	characteristic
890	C₂×Q₈	C₂⁴×C₂₃	1	1	yes	characteristic
891	C₂×D₄	—	2	4	no	—
892	C₂×D₄	—	2	1	no	—
893	C₂×D₄	—	2	2	no	—
894	C₂×D₄	—	2	2	no	—
895	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
896	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
897	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
898	C₂×D₄	C₂⁴×C₂₃	1	1	yes	characteristic
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	—	2	2	no	—
904	C₂²×C₄	—	2	2	no	—
905	C₂²×C₄	—	2	1	no	—
906	C₂²×C₄	—	2	1	no	—
907	C₂²×C₄	—	2	1	no	—
908	C₂²×C₄	—	4	2	no	—
909	C₂²×C₄	—	4	2	no	—
910	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
911	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
912	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
913	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
914	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
915	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
916	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
917	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
918	Q₁₆	—	4	1	no	—
919	Q₁₆	—	4	2	no	—
920	Q₁₆	—	4	1	no	—
921	SD₁₆	—	4	1	no	—
922	SD₁₆	—	4	2	no	—
923	SD₁₆	—	4	1	no	—
924	M₁₆	—	4	2	no	—
925	M₁₆	—	4	2	no	—
926	C₂×C₈	—	4	2	no	—
927	C₂×C₈	—	4	2	no	—
928	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
929	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
930	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
931	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
932	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
933	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
934	C₄⋊C₄	—	2	1	no	—
935	C₄⋊C₄	—	2	2	no	—
936	C₄⋊C₄	—	2	1	no	—
937	C₄⋊C₄	—	2	2	no	—
938	C₄⋊C₄	—	2	2	no	—
939	C₄⋊C₄	—	2	2	no	—
940	C₄⋊C₄	—	2	2	no	—
941	C₄⋊C₄	—	2	2	no	—
942	C₄⋊C₄	—	2	2	no	—
943	C₄⋊C₄	—	2	2	no	—
944	C₄⋊C₄	—	2	2	no	—
945	C₄⋊C₄	—	2	1	no	—
946	C₄⋊C₄	—	2	1	no	—
947	C₄⋊C₄	—	2	1	no	—
948	C₄⋊C₄	—	2	1	no	—
949	C₄⋊C₄	—	2	1	no	—
950	C₄⋊C₄	—	2	2	no	—
951	C₄⋊C₄	—	2	2	no	—
952	C₄⋊C₄	—	2	1	no	—
953	C₄⋊C₄	—	2	1	no	—
954	C₄⋊C₄	—	2	2	no	—
955	C₄⋊C₄	—	2	2	no	—
956	C₄⋊C₄	—	2	1	no	—
957	C₄⋊C₄	—	2	1	no	—
958	C₄⋊C₄	—	2	1	no	—
959	C₄⋊C₄	—	2	2	no	—
960	C₄⋊C₄	—	2	1	no	—
961	C₄⋊C₄	—	2	1	no	—
962	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
963	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
964	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
965	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
966	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
967	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
968	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
969	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
970	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
971	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
972	C₂²⋊C₄	—	2	1	no	—
973	C₂²⋊C₄	—	2	1	no	—
974	C₂²⋊C₄	—	2	2	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	1	no	—
988	C₂²⋊C₄	—	2	2	no	—
989	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
990	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
991	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
992	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
993	C₄²	—	2	1	no	—
994	C₄²	—	2	2	no	—
995	C₄²	—	2	1	no	—
996	C₄²	—	2	2	no	—
997	C₄²	—	2	2	no	—
998	C₄²	—	2	1	no	—
999	C₄²	—	2	2	no	—
1000	C₄²	—	2	1	no	—
1001	C₄²	—	2	1	no	—
1002	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
1003	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
1004	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
1005	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
1006	C₂³	—	2	4	no	—
1007	C₂³	—	2	1	no	—
1008	C₂³	—	4	2	no	—
1009	C₂³	—	4	2	no	—
1010	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
1011	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
1012	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
1013	Q₈	—	2	1	no	—
1014	Q₈	—	2	1	no	—
1015	Q₈	—	2	2	no	—
1016	Q₈	—	2	1	no	—
1017	Q₈	—	2	1	no	—
1018	Q₈	—	2	2	no	—
1019	Q₈	—	2	1	no	—
1020	Q₈	—	2	1	no	—
1021	Q₈	—	4	2	no	—
1022	Q₈	—	8	2	no	—
1023	Q₈	—	8	2	no	—
1024	Q₈	—	8	1	no	—
1025	Q₈	—	8	1	no	—
1026	Q₈	—	8	1	no	—
1027	D₄	—	2	4	no	—
1028	D₄	—	2	2	no	—
1029	D₄	—	2	1	no	—
1030	D₄	—	2	1	no	—
1031	D₄	—	4	2	no	—
1032	D₄	—	4	4	no	—
1033	D₄	—	8	2	no	—
1034	D₄	C₂₃×#137	1	4	yes	—
1035	C₂×C₄	—	2	2	no	—
1036	C₂×C₄	—	2	2	no	—
1037	C₂×C₄	—	2	2	no	—
1038	C₂×C₄	—	2	2	no	—
1039	C₂×C₄	—	2	2	no	—
1040	C₂×C₄	—	2	1	no	—
1041	C₂×C₄	—	2	1	no	—
1042	C₂×C₄	—	2	1	no	—
1043	C₂×C₄	—	2	1	no	—
1044	C₂×C₄	—	2	1	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	2	no	—
1051	C₂×C₄	—	2	1	no	—
1052	C₂×C₄	—	2	1	no	—
1053	C₂×C₄	—	4	2	no	—
1054	C₂×C₄	—	4	2	no	—
1055	C₂×C₄	—	4	2	no	—
1056	C₂×C₄	—	4	1	no	—
1057	C₂×C₄	—	4	2	no	—
1058	C₂×C₄	—	4	4	no	—
1059	C₂×C₄	—	4	2	no	—
1060	C₂×C₄	—	8	1	no	—
1061	C₂×C₄	—	8	2	no	—
1062	C₂×C₄	—	8	2	no	—
1063	C₂×C₄	—	8	2	no	—
1064	C₂×C₄	—	8	2	no	—
1065	C₂×C₄	—	8	2	no	—
1066	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1067	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1068	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
1069	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1070	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1071	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
1072	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1073	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
1074	C₈	—	2	1	no	—
1075	C₈	—	2	1	no	—
1076	C₈	—	2	2	no	—
1077	C₈	—	2	2	no	—
1078	C₈	—	2	1	no	—
1079	C₈	—	2	1	no	—
1080	C₂²	—	2	2	no	—
1081	C₂²	—	2	2	no	—
1082	C₂²	—	2	1	no	—
1083	C₂²	—	2	2	no	—
1084	C₂²	—	2	1	no	—
1085	C₂²	—	2	2	no	—
1086	C₂²	—	2	1	no	—
1087	C₂²	—	2	2	no	—
1088	C₂²	—	4	1	no	—
1089	C₂²	—	4	1	no	—
1090	C₂²	—	4	1	no	—
1091	C₂²	—	8	4	no	—
1092	C₂²	C₂×C₂₃×#137	1	4	yes	—
1093	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
1094	C₄	—	2	1	no	—
1095	C₄	—	2	2	no	—
1096	C₄	—	2	2	no	—
1097	C₄	—	2	1	no	—
1098	C₄	—	2	1	no	—
1099	C₄	—	2	1	no	—
1100	C₄	—	4	1	no	—
1101	C₄	—	4	1	no	—
1102	C₄	—	4	2	no	—
1103	C₄	—	4	1	no	—
1104	C₄	—	4	1	no	—
1105	C₄	—	4	2	no	—
1106	C₄	—	4	1	no	—
1107	C₄	—	4	1	no	—
1108	C₄	—	4	2	no	—
1109	C₄	—	4	1	no	—
1110	C₄	—	4	2	no	—
1111	C₄	C₂×C₂₃×#137	1	2	yes	—
1112	C₄	C₂₃×#585	1	1	yes	characteristic
1113	C₄	C₂₃×#585	1	1	yes	characteristic
1114	C₂	—	2	4	no	—
1115	C₂	—	4	1	no	—
1116	C₂	—	4	2	no	—
1117	C₂	—	8	1	no	—
1118	C₂	C₂₃×#3485	1	1	yes	characteristic
1119	C₂	C₂²×C₂₃×#137	1	1	yes	characteristic
1120	C₂	C₂₃×#3584	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₂₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₂₃
prime radical	C₂₃×#3475	C₂
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×#3501	C₂	semidirect
3. C₂₃×#3357	C₂	semidirect
4. C₂₃×#3356	C₂	semidirect
5. C₂₃×#3346	C₂	semidirect
6. C₂₃×#3344	C₂	semidirect
7. C₂₃×#3338	C₂	semidirect
8. C₂₃×#3335	C₂	semidirect
9. C₂₃×#3329	C₂	semidirect
10. C₂₃×#3328	C₂	semidirect
11. C₂₃×#3320	C₂	semidirect
12. C₂₃×#3312	C₂	semidirect
13. C₂₃×#3299	C₂	semidirect
14. C₂₃×#3298	C₂	semidirect
15. C₂₃×#3237	C₂	semidirect
16. C₂₃×#3231	C₂	semidirect
17. C₂₃×#3196	C₂	semidirect
18. C₂₃×#3190	C₂	semidirect
19. C₂₃×#3116	C₂	semidirect
20. C₂₃×#3107	C₂	semidirect
21. C₂₃×#3095	C₂	semidirect
22. C₂×C₂₃×#485	C₂	semidirect
23. C₂₃×#2974	C₂	semidirect
57. C₂₃×#501	C₂²	semidirect
58. C₂₃×#500	C₂²	semidirect
59. C₂₃×#498	C₂²	semidirect
60. C₂₃×#491	C₂²	semidirect
61. C₂₃×#487	C₂²	semidirect
62. C₂₃×#487	C₂²	semidirect
70. C₂₃×#485	C₂²	semidirect
71. C₂₃×#485	C₂²	semidirect
72. C₂₃×#485	C₂²	semidirect
73. C₂₃×#485	C₂²	semidirect
74. C₂₃×#484	C₂²	semidirect
75. C₂₃×#484	C₂²	semidirect
76. C₂₃×#484	C₂²	semidirect
77. C₂₃×#483	C₂²	semidirect
78. C₂₃×#483	C₂²	semidirect
79. C₂₃×#483	C₂²	semidirect
80. C₂₃×#481	C₂²	semidirect
81. C₂₃×#480	C₂²	semidirect
82. C₂₃×#479	C₂²	semidirect
83. C₂₃×#479	C₂²	semidirect
84. C₂₃×#477	C₂²	semidirect
85. C₂₃×#477	C₂²	semidirect
86. C₂₃×#477	C₂²	semidirect
87. C₂₃×#476	C₂²	semidirect
88. C₂₃×#475	C₂²	semidirect
89. C₂₃×#475	C₂²	semidirect
90. C₂₃×#475	C₂²	semidirect
91. C₂₃×#474	C₂²	semidirect
92. C₂₃×#470	C₂²	semidirect
93. C₂₃×#470	C₂²	semidirect
94. C₂₃×#468	C₂²	semidirect
95. C₂₃×#468	C₂²	semidirect
96. C₂₃×#467	C₂²	semidirect
97. C₂₃×#467	C₂²	semidirect
98. C₂₃×#465	C₂²	semidirect
99. C₂₃×#465	C₂²	semidirect
100. C₂₃×#462	C₂²	semidirect
101. C₂₃×#462	C₂²	semidirect
102. C₂₃×#461	C₂²	semidirect
103. C₂₃×#461	C₂²	semidirect
107. C₂₃×#451	C₂²	semidirect
108. C₂₃×#451	C₂²	semidirect
109. C₂₃×#448	C₂²	semidirect
110. C₂₃×#448	C₂²	semidirect
111. C₂₃×#441	C₂²	semidirect
112. C₂₃×#440	C₂²	semidirect
113. C₄×Q₁₆×C₂₃	C₂²	semidirect
114. C₄×Q₁₆×C₂₃	C₂²	semidirect
115. C₄×SD₁₆×C₂₃	C₂²	semidirect
116. C₄×SD₁₆×C₂₃	C₂²	semidirect
125. C₂₃×#428	C₂²	semidirect
126. C₂₃×#428	C₂²	semidirect
127. C₂×C₂₃×#107	C₂²	semidirect
128. C₂×C₂₃×#106	C₂²	semidirect
129. C₂₃×#419	C₂²	semidirect
130. C₂₃×#419	C₂²	semidirect
131. C₂×C₂₃×#103	C₂²	semidirect
132. C₂×C₂₃×#103	C₂²	semidirect
445. #61742	C₂₃	direct (N × H)
520. #3501	C₂×C₂₃	semidirect
522. #3357	C₂×C₂₃	semidirect
523. #3356	C₂×C₂₃	semidirect
524. #3346	C₂×C₂₃	semidirect
525. #3344	C₂×C₂₃	semidirect
526. #3338	C₂×C₂₃	semidirect
527. #3335	C₂×C₂₃	semidirect
528. #3329	C₂×C₂₃	semidirect
529. #3328	C₂×C₂₃	semidirect
530. #3320	C₂×C₂₃	semidirect
531. #3312	C₂×C₂₃	semidirect
532. #3299	C₂×C₂₃	semidirect
533. #3298	C₂×C₂₃	semidirect
534. #3237	C₂×C₂₃	semidirect
535. #3231	C₂×C₂₃	semidirect
536. #3196	C₂×C₂₃	semidirect
537. #3190	C₂×C₂₃	semidirect
538. #3116	C₂×C₂₃	semidirect
539. #3107	C₂×C₂₃	semidirect
540. #3095	C₂×C₂₃	semidirect
541. C₂×#485	C₂×C₂₃	semidirect
542. #2974	C₂×C₂₃	semidirect
610. #501	C₂²×C₂₃	semidirect
611. #500	C₂²×C₂₃	semidirect
612. #498	C₂²×C₂₃	semidirect
613. #491	C₂²×C₂₃	semidirect
614. #487	C₂²×C₂₃	semidirect
615. #487	C₂²×C₂₃	semidirect
623. #485	C₂²×C₂₃	semidirect
624. #485	C₂²×C₂₃	semidirect
625. #485	C₂²×C₂₃	semidirect
626. #485	C₂²×C₂₃	semidirect
627. #484	C₂²×C₂₃	semidirect
628. #484	C₂²×C₂₃	semidirect
629. #484	C₂²×C₂₃	semidirect
630. #483	C₂²×C₂₃	semidirect
631. #483	C₂²×C₂₃	semidirect
632. #483	C₂²×C₂₃	semidirect
633. #481	C₂²×C₂₃	semidirect
634. #480	C₂²×C₂₃	semidirect
635. #479	C₂²×C₂₃	semidirect
636. #479	C₂²×C₂₃	semidirect
637. #477	C₂²×C₂₃	semidirect
638. #477	C₂²×C₂₃	semidirect
639. #477	C₂²×C₂₃	semidirect
640. #476	C₂²×C₂₃	semidirect
641. #475	C₂²×C₂₃	semidirect
642. #475	C₂²×C₂₃	semidirect
643. #475	C₂²×C₂₃	semidirect
644. #474	C₂²×C₂₃	semidirect
645. #470	C₂²×C₂₃	semidirect
646. #470	C₂²×C₂₃	semidirect
647. #468	C₂²×C₂₃	semidirect
648. #468	C₂²×C₂₃	semidirect
649. #467	C₂²×C₂₃	semidirect
650. #467	C₂²×C₂₃	semidirect
651. #465	C₂²×C₂₃	semidirect
652. #465	C₂²×C₂₃	semidirect
653. #462	C₂²×C₂₃	semidirect
654. #462	C₂²×C₂₃	semidirect
655. #461	C₂²×C₂₃	semidirect
656. #461	C₂²×C₂₃	semidirect
660. #451	C₂²×C₂₃	semidirect
661. #451	C₂²×C₂₃	semidirect
662. #448	C₂²×C₂₃	semidirect
663. #448	C₂²×C₂₃	semidirect
664. #441	C₂²×C₂₃	semidirect
665. #440	C₂²×C₂₃	semidirect
666. C₄×Q₁₆	C₂²×C₂₃	semidirect
667. C₄×Q₁₆	C₂²×C₂₃	semidirect
668. C₄×SD₁₆	C₂²×C₂₃	semidirect
669. C₄×SD₁₆	C₂²×C₂₃	semidirect
678. #428	C₂²×C₂₃	semidirect
679. #428	C₂²×C₂₃	semidirect
680. C₂×#107	C₂²×C₂₃	semidirect
681. C₂×#106	C₂²×C₂₃	semidirect
682. #419	C₂²×C₂₃	semidirect
683. #419	C₂²×C₂₃	semidirect
684. C₂×#103	C₂²×C₂₃	semidirect
685. C₂×#103	C₂²×C₂₃	semidirect
872. C₂₃	#61742	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×#3501	2
C₂₃×#3475	2
C₂₃×#3357	2
C₂₃×#3356	2
C₂₃×#3346	2
C₂₃×#3344	2
C₂₃×#3338	2
C₂₃×#3335	2
C₂₃×#3329	2
C₂₃×#3328	2
C₂₃×#3320	2
C₂₃×#3312	2
C₂₃×#3299	2
C₂₃×#3298	2
C₂₃×#3237	2
C₂₃×#3231	2
C₂₃×#3196	2
C₂₃×#3190	2
C₂₃×#3116	2
C₂₃×#3107	2
C₂₃×#3095	2
C₂×C₂₃×#485	2
C₂₃×#2974	2
#61742	23

Subgroups — C23×#61742 #19209368

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#61742 #19209368