Subgroups — C₂₃×#61875 #19209501

Order 5888.

1598 conjugacy classes of subgroups.

The subgroup lattice has 942 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3555	C₂	1	1	yes	maximal, characteristic
2	C₂₃×#3502	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#3390	C₂	1	2	yes	maximal, complemented
4	C₂₃×#3388	C₂	1	2	yes	maximal, complemented
5	C₂₃×#3387	C₂	1	2	yes	maximal, complemented
6	C₂₃×#3387	C₂	1	2	yes	maximal, complemented
7	C₂₃×#3377	C₂	1	2	yes	maximal, complemented
8	C₂₃×#3377	C₂	1	2	yes	maximal, complemented
9	C₂₃×#3374	C₂	1	2	yes	maximal, complemented
10	C₂₃×#3369	C₂	1	2	yes	maximal, complemented
11	C₂₃×#3244	C₂	1	2	yes	maximal
12	C₂₃×#3242	C₂	1	2	yes	maximal, complemented
13	C₂₃×#3240	C₂	1	1	yes	maximal, characteristic
14	C₂₃×#3237	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₃×#3127	C₂	1	2	yes	maximal, complemented
16	C₂₃×#3121	C₂	1	2	yes	maximal
17	C₂₃×#3117	C₂	1	1	yes	maximal, characteristic
18	C₂₃×#3113	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂₃×#2987	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂₃×#563	—	2	2	no	—
21	Q₈²×C₂₃	—	2	1	no	—
22	Q₈²×C₂₃	C₂²	1	2	yes	—
23	Q₈²×C₂₃	C₂²	1	1	yes	characteristic
24	C₂₃×#557	—	2	1	no	—
25	C₂₃×#557	—	2	2	no	—
26	C₂₃×#557	C₂²	1	1	yes	characteristic
27	C₂₃×#557	C₂²	1	2	yes	—
28	C₂₃×#557	C₂²	1	2	yes	—
29	C₂₃×#557	C₂²	1	2	yes	—
30	C₂₃×#557	C₂²	1	2	yes	—
31	C₂₃×#556	—	2	1	no	—
32	C₂₃×#556	C₂²	1	2	yes	—
33	C₂₃×#556	C₂²	1	1	yes	characteristic
34	C₂₃×#554	C₂²	1	1	yes	characteristic
35	C₂₃×#552	—	2	1	no	—
36	C₂₃×#544	—	2	1	no	—
37	C₂₃×#544	—	2	1	no	—
38	C₂₃×#544	—	2	1	no	—
39	C₂₃×#544	C₂²	1	2	yes	—
40	C₂₃×#542	C₂²	1	2	yes	—
41	C₂₃×#541	—	2	1	no	—
42	C₂₃×#541	—	2	2	no	—
43	C₂₃×#541	C₂²	1	2	yes	—
44	C₂₃×#533	—	2	2	no	—
45	C₂₃×#533	C₂²	1	1	yes	characteristic
46	C₂₃×#533	C₂²	1	1	yes	characteristic
47	C₂₃×#533	C₂²	1	1	yes	characteristic
48	C₂₃×#529	C₂²	1	1	yes	characteristic
49	C₂₃×#519	C₂²	1	2	yes	—
50	C₂×C₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic
51	C₂₃×#501	C₂²	1	2	yes	—
52	C₂₃×#501	C₂²	1	1	yes	characteristic
53	C₂₃×#501	C₂²	1	1	yes	characteristic
54	C₂₃×#501	C₂²	1	2	yes	—
55	C₂₃×#501	C₂²	1	2	yes	—
56	C₂₃×#499	C₂²	1	2	yes	—
57	C₂₃×#498	C₂²	1	2	yes	—
58	C₂₃×#491	C₂²	1	2	yes	—
59	C₂₃×#491	C₂²	1	2	yes	—
60	C₂₃×#489	C₂²	1	1	yes	characteristic
61	C₂₃×#489	C₂²	1	1	yes	characteristic
62	C₂₃×#489	C₂²	1	2	yes	—
63	C₂₃×#488	C₂²	1	2	yes	—
64	C₂₃×#487	C₂²	1	2	yes	—
65	C₂₃×#485	C₂²	1	2	yes	—
66	C₂₃×#485	C₂²	1	2	yes	—
67	C₂₃×#485	C₂²	1	2	yes	—
68	C₂₃×#484	C₂²	1	1	yes	characteristic
69	C₂₃×#483	C₂²	1	2	yes	—
70	C₂₃×#482	C₂²	1	2	yes	—
71	C₂₃×#481	C₂²	1	1	yes	characteristic
72	C₂₃×#479	C₂²	1	2	yes	—
73	C₂₃×#479	C₂²	1	2	yes	—
74	C₂₃×#479	C₂²	1	2	yes	—
75	C₂₃×#479	C₂²	1	2	yes	—
76	C₂₃×#479	C₂²	1	2	yes	—
77	C₂₃×#479	C₂²	1	2	yes	—
78	C₂₃×#479	C₂²	1	2	yes	—
79	C₂₃×#478	C₂²	1	2	yes	—
80	C₂₃×#478	C₂²	1	2	yes	—
81	C₂₃×#477	C₂²	1	2	yes	—
82	C₂₃×#477	C₂²	1	2	yes	—
83	C₂₃×#477	C₂²	1	2	yes	—
84	C₂₃×#476	C₂²	1	2	yes	—
85	C₂₃×#475	C₂²	1	2	yes	—
86	C₂₃×#475	C₂²	1	2	yes	—
87	C₂₃×#475	C₂²	1	2	yes	—
88	C₂₃×#475	C₂²	1	2	yes	—
89	C₂₃×#475	C₂²	1	2	yes	—
90	C₂₃×#464	C₂²	1	2	yes	—
91	C₂₃×#464	C₂²	1	2	yes	—
92	C₂₃×#464	C₂²	1	2	yes	—
93	C₂₃×#462	C₂²	1	2	yes	—
94	C₂₃×#462	C₂²	1	2	yes	—
95	C₂₃×#462	C₂²	1	2	yes	—
96	C₂₃×#451	C₂²	1	2	yes	—
97	C₂₃×#451	C₂²	1	1	yes	characteristic
98	C₂₃×#448	C₂²	1	1	yes	characteristic
99	C₂₃×#446	C₂²	1	2	yes	—
100	C₂₃×#446	C₂²	1	2	yes	—
101	C₂₃×#446	C₂²	1	2	yes	—
102	C₂₃×#446	C₂²	1	2	yes	—
103	C₂₃×#441	C₂²	1	2	yes	—
104	C₂₃×#441	C₂²	1	2	yes	—
105	C₂₃×#441	C₂²	1	2	yes	—
106	C₂₃×#441	C₂²	1	2	yes	—
107	C₂₃×#441	C₂²	1	2	yes	—
108	C₂₃×#441	C₂²	1	2	yes	—
109	C₂₃×#440	C₂²	1	2	yes	—
110	C₂₃×#440	C₂²	1	2	yes	—
111	C₄×Q₁₆×C₂₃	C₂²	1	2	yes	—
112	C₄×Q₁₆×C₂₃	C₂²	1	2	yes	—
113	C₄×Q₁₆×C₂₃	C₂²	1	2	yes	—
114	C₄×SD₁₆×C₂₃	C₂²	1	2	yes	—
115	C₂₃×#433	C₂²	1	2	yes	—
116	C₂₃×#433	C₂²	1	2	yes	—
117	C₂₃×#432	C₂²	1	1	yes	characteristic
118	C₂₃×#432	C₂²	1	1	yes	characteristic
119	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
120	C₂×Q₁₆×C₂₃	C₂³	1	2	yes	—
121	C₂×Q₁₆×C₂₃	C₂³	1	2	yes	—
122	C₂×Q₁₆×C₂₃	C₂³	1	2	yes	—
123	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
124	C₂₃×C₄⋊Q₈	—	2	2	no	—
125	C₂₃×C₄⋊Q₈	—	2	2	no	—
126	C₂₃×C₄⋊Q₈	—	2	2	no	—
127	C₂₃×C₄⋊Q₈	—	2	2	no	—
128	C₂₃×C₄⋊Q₈	—	2	1	no	—
129	C₂₃×C₄⋊Q₈	—	2	2	no	—
130	C₂₃×C₄⋊Q₈	—	2	2	no	—
131	C₂₃×C₄⋊Q₈	—	2	2	no	—
132	C₂₃×C₄⋊Q₈	—	2	2	no	—
133	C₂₃×C₄⋊Q₈	—	2	2	no	—
134	C₂₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
135	C₂₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
136	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
137	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
138	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
139	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
140	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
141	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
142	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
143	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
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×#126	—	2	1	no	—
151	C₂₃×#125	—	2	2	no	—
152	C₂₃×#125	—	2	1	no	—
153	C₂₃×#125	—	2	2	no	—
154	C₂₃×#125	—	2	2	no	—
155	C₂₃×#125	—	2	2	no	—
156	C₂₃×#125	—	2	2	no	—
157	C₂₃×#125	—	2	2	no	—
158	C₂₃×#125	—	2	2	no	—
159	C₂₃×#125	—	2	2	no	—
160	C₂₃×#125	—	2	2	no	—
161	C₂₃×#125	—	2	2	no	—
162	C₂₃×#125	—	2	2	no	—
163	C₂₃×#125	—	2	2	no	—
164	C₂₃×#125	—	2	1	no	—
165	C₂₃×#125	D₄	1	2	yes	—
166	C₂₃×#125	C₂³	1	2	yes	—
167	C₂₃×#125	C₂³	1	2	yes	—
168	C₂₃×#125	C₂³	1	2	yes	—
169	C₂₃×#125	C₂³	1	2	yes	—
170	C₂₃×#125	C₂³	1	1	yes	characteristic
171	C₂₃×#124	—	2	2	no	—
172	C₂₃×#124	C₂³	1	2	yes	—
173	C₂₃×#124	C₂³	1	1	yes	characteristic
174	C₂₃×#123	—	2	1	no	—
175	C₂₃×#123	—	2	2	no	—
176	C₂₃×C₂²⋊Q₈	—	2	1	no	—
177	C₂₃×C₂²⋊Q₈	—	2	1	no	—
178	C₂₃×C₂²⋊Q₈	—	2	2	no	—
179	C₂₃×C₂²⋊Q₈	—	2	1	no	—
180	C₂₃×C₂²⋊Q₈	—	2	1	no	—
181	C₂₃×C₂²⋊Q₈	—	2	1	no	—
182	C₂₃×C₂²⋊Q₈	—	2	2	no	—
183	C₂₃×C₂²⋊Q₈	—	2	2	no	—
184	C₂₃×C₂²⋊Q₈	—	2	2	no	—
185	C₂₃×C₂²⋊Q₈	—	2	2	no	—
186	C₂₃×C₂²⋊Q₈	D₄	1	1	yes	characteristic
187	C₂₃×C₂²⋊Q₈	D₄	1	1	yes	characteristic
188	C₂₃×C₂²⋊Q₈	D₄	1	2	yes	—
189	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
190	C₂₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
191	C₂₃×#121	C₂³	1	1	yes	characteristic
192	C₄×Q₈×C₂₃	—	2	1	no	—
193	C₄×Q₈×C₂₃	—	2	1	no	—
194	C₄×Q₈×C₂₃	—	2	2	no	—
195	C₄×Q₈×C₂₃	—	2	2	no	—
196	C₄×Q₈×C₂₃	—	2	2	no	—
197	C₄×Q₈×C₂₃	—	2	2	no	—
198	C₄×Q₈×C₂₃	—	2	2	no	—
199	C₄×Q₈×C₂₃	—	2	2	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	—	2	1	no	—
204	C₄×Q₈×C₂₃	—	2	1	no	—
205	C₄×Q₈×C₂₃	—	2	1	no	—
206	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
207	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
208	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
209	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
210	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
211	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
212	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
213	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
214	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
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×Q₈×C₂₃	C₂³	1	2	yes	—
220	C₄×D₄×C₂₃	—	2	1	no	—
221	C₄×D₄×C₂₃	C₂³	1	2	yes	—
222	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
223	C₂₃×#117	—	2	1	no	—
224	C₂₃×#117	—	2	2	no	—
225	C₂₃×#117	—	2	1	no	—
226	C₂₃×#117	—	2	2	no	—
227	C₂₃×#117	—	2	2	no	—
228	C₂₃×#117	—	2	1	no	—
229	C₂₃×#117	C₂³	1	2	yes	—
230	C₂₃×#117	C₂³	1	2	yes	—
231	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
232	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
233	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
234	C₂×C₄²×C₂₃	—	2	1	no	—
235	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
236	C₂₃×#107	C₂³	1	2	yes	—
237	C₂₃×#107	C₂³	1	2	yes	—
238	C₂₃×#107	C₂³	1	2	yes	—
239	C₂₃×#107	C₂³	1	2	yes	—
240	C₂₃×#107	C₂³	1	2	yes	—
241	C₂₃×#106	C₂³	1	2	yes	—
242	C₂₃×#106	C₂³	1	2	yes	—
243	C₂₃×#106	C₂³	1	2	yes	—
244	C₂₃×#106	C₂³	1	2	yes	—
245	C₂₃×#106	C₂³	1	2	yes	—
246	C₂₃×#106	C₂³	1	2	yes	—
247	C₂₃×#106	C₂³	1	2	yes	—
248	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
249	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
250	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
251	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
252	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
253	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
254	C₂₃×#103	C₂³	1	2	yes	—
255	C₂₃×#103	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×#102	C₂³	1	2	yes	—
268	C₂₃×#102	C₂³	1	2	yes	—
269	C₂₃×#102	C₂³	1	2	yes	—
270	C₂₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
271	C₂₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
272	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
273	C₂₃×#97	C₂³	1	2	yes	—
274	C₂₃×#97	C₂³	1	1	yes	characteristic
275	C₂₃×#97	C₂³	1	1	yes	characteristic
276	C₂₃×#97	C₂³	1	2	yes	—
277	C₂₃×#97	C₂³	1	2	yes	—
278	C₄×C₈×C₂₃	C₂³	1	2	yes	—
279	C₄×C₈×C₂₃	C₂³	1	2	yes	—
280	C₂×Q₈×C₂₃	—	2	4	no	—
281	C₂×Q₈×C₂₃	—	2	1	no	—
282	C₂×Q₈×C₂₃	—	2	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	2	no	—
287	C₂×Q₈×C₂₃	—	2	2	no	—
288	C₂×Q₈×C₂₃	C₂×D₄	1	2	yes	—
289	C₂×Q₈×C₂₃	C₂×D₄	1	1	yes	characteristic
290	C₂×Q₈×C₂₃	C₂×D₄	1	1	yes	characteristic
291	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
292	C₂×Q₈×C₂₃	C₂⁴	1	1	yes	characteristic
293	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
294	C₂×D₄×C₂₃	—	2	1	no	—
295	C₂×D₄×C₂₃	C₂⁴	1	1	yes	characteristic
296	C₂²×C₄×C₂₃	—	2	1	no	—
297	C₂²×C₄×C₂₃	—	2	1	no	—
298	C₂²×C₄×C₂₃	—	2	1	no	—
299	C₂²×C₄×C₂₃	—	2	2	no	—
300	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
301	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
302	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
303	Q₁₆×C₂₃	—	2	4	no	—
304	Q₁₆×C₂₃	—	2	4	no	—
305	Q₁₆×C₂₃	—	2	4	no	—
306	SD₁₆×C₂₃	—	2	4	no	—
307	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
308	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
309	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
310	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
311	C₄⋊C₄×C₂₃	—	2	1	no	—
312	C₄⋊C₄×C₂₃	—	2	2	no	—
313	C₄⋊C₄×C₂₃	—	2	2	no	—
314	C₄⋊C₄×C₂₃	—	2	2	no	—
315	C₄⋊C₄×C₂₃	—	2	1	no	—
316	C₄⋊C₄×C₂₃	—	2	1	no	—
317	C₄⋊C₄×C₂₃	—	2	2	no	—
318	C₄⋊C₄×C₂₃	—	2	2	no	—
319	C₄⋊C₄×C₂₃	—	2	2	no	—
320	C₄⋊C₄×C₂₃	—	2	2	no	—
321	C₄⋊C₄×C₂₃	—	2	2	no	—
322	C₄⋊C₄×C₂₃	—	2	1	no	—
323	C₄⋊C₄×C₂₃	—	2	1	no	—
324	C₄⋊C₄×C₂₃	—	2	1	no	—
325	C₄⋊C₄×C₂₃	—	2	2	no	—
326	C₄⋊C₄×C₂₃	—	2	1	no	—
327	C₄⋊C₄×C₂₃	—	2	2	no	—
328	C₄⋊C₄×C₂₃	—	2	2	no	—
329	C₄⋊C₄×C₂₃	—	2	1	no	—
330	C₄⋊C₄×C₂₃	—	2	2	no	—
331	C₄⋊C₄×C₂₃	—	2	2	no	—
332	C₄⋊C₄×C₂₃	—	2	2	no	—
333	C₄⋊C₄×C₂₃	—	2	2	no	—
334	C₄⋊C₄×C₂₃	—	2	2	no	—
335	C₄⋊C₄×C₂₃	—	2	2	no	—
336	C₄⋊C₄×C₂₃	—	2	2	no	—
337	C₄⋊C₄×C₂₃	—	2	1	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	2	no	—
344	C₄⋊C₄×C₂₃	—	2	1	no	—
345	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
346	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
347	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
348	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
349	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
350	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
351	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
352	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
353	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
354	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
355	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
356	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
357	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
358	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
359	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
360	C₂²⋊C₄×C₂₃	—	2	2	no	—
361	C₂²⋊C₄×C₂₃	—	2	2	no	—
362	C₂²⋊C₄×C₂₃	—	2	1	no	—
363	C₂²⋊C₄×C₂₃	—	2	1	no	—
364	C₂²⋊C₄×C₂₃	—	2	1	no	—
365	C₂²⋊C₄×C₂₃	—	2	1	no	—
366	C₂²⋊C₄×C₂₃	—	2	2	no	—
367	C₂²⋊C₄×C₂₃	—	2	2	no	—
368	C₂²⋊C₄×C₂₃	—	2	1	no	—
369	C₂²⋊C₄×C₂₃	—	2	2	no	—
370	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
371	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
372	C₄²×C₂₃	—	2	2	no	—
373	C₄²×C₂₃	—	2	2	no	—
374	C₄²×C₂₃	—	2	2	no	—
375	C₄²×C₂₃	—	2	1	no	—
376	C₄²×C₂₃	—	2	2	no	—
377	C₄²×C₂₃	—	2	2	no	—
378	C₄²×C₂₃	—	2	2	no	—
379	C₄²×C₂₃	—	2	2	no	—
380	C₄²×C₂₃	—	2	2	no	—
381	C₄²×C₂₃	—	2	2	no	—
382	C₄²×C₂₃	—	2	2	no	—
383	C₄²×C₂₃	—	2	2	no	—
384	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
385	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
386	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
387	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
388	C₄²×C₂₃	C₂⁴	1	2	yes	—
389	C₄²×C₂₃	C₂⁴	1	2	yes	—
390	#61875	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
391	C₂³×C₂₃	—	2	1	no	—
392	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
393	Q₈×C₂₃	—	2	4	no	—
394	Q₈×C₂₃	—	2	2	no	—
395	Q₈×C₂₃	—	2	2	no	—
396	Q₈×C₂₃	—	2	2	no	—
397	Q₈×C₂₃	—	2	2	no	—
398	Q₈×C₂₃	—	4	1	no	—
399	Q₈×C₂₃	—	4	1	no	—
400	Q₈×C₂₃	—	4	2	no	—
401	Q₈×C₂₃	—	4	2	no	—
402	Q₈×C₂₃	—	8	1	no	—
403	Q₈×C₂₃	—	8	1	no	—
404	Q₈×C₂₃	—	8	2	no	—
405	Q₈×C₂₃	—	8	2	no	—
406	Q₈×C₂₃	—	8	2	no	—
407	Q₈×C₂₃	2₋¹⁺⁴	1	4	yes	—
408	D₄×C₂₃	—	2	2	no	—
409	D₄×C₂₃	—	8	1	no	—
410	C₂×C₄×C₂₃	—	2	4	no	—
411	C₂×C₄×C₂₃	—	2	2	no	—
412	C₂×C₄×C₂₃	—	2	2	no	—
413	C₂×C₄×C₂₃	—	2	2	no	—
414	C₂×C₄×C₂₃	—	2	1	no	—
415	C₂×C₄×C₂₃	—	2	2	no	—
416	C₂×C₄×C₂₃	—	2	1	no	—
417	C₂×C₄×C₂₃	—	2	2	no	—
418	C₂×C₄×C₂₃	—	2	1	no	—
419	C₂×C₄×C₂₃	—	2	2	no	—
420	C₂×C₄×C₂₃	—	2	2	no	—
421	C₂×C₄×C₂₃	—	4	1	no	—
422	C₂×C₄×C₂₃	—	4	1	no	—
423	C₂×C₄×C₂₃	—	4	2	no	—
424	C₂×C₄×C₂₃	—	8	2	no	—
425	C₂×C₄×C₂₃	—	8	1	no	—
426	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
427	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
428	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
429	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
430	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
431	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
432	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
433	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
434	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
435	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
436	C₈×C₂₃	—	2	2	no	—
437	C₈×C₂₃	—	2	2	no	—
438	C₈×C₂₃	—	2	2	no	—
439	C₈×C₂₃	—	2	2	no	—
440	#3555	C₂×C₂₃	1	1	yes	characteristic
441	#3502	C₂×C₂₃	1	1	yes	characteristic, complemented
442	#3390	C₂×C₂₃	1	2	yes	complemented
443	#3388	C₂×C₂₃	1	2	yes	complemented
444	#3387	C₂×C₂₃	1	2	yes	complemented
445	#3387	C₂×C₂₃	1	2	yes	complemented
446	#3377	C₂×C₂₃	1	2	yes	complemented
447	#3377	C₂×C₂₃	1	2	yes	complemented
448	#3374	C₂×C₂₃	1	2	yes	complemented
449	#3369	C₂×C₂₃	1	2	yes	complemented
450	#3244	C₂×C₂₃	1	2	yes	—
451	#3242	C₂×C₂₃	1	2	yes	complemented
452	#3240	C₂×C₂₃	1	1	yes	characteristic
453	#3237	C₂×C₂₃	1	1	yes	characteristic, complemented
454	#3127	C₂×C₂₃	1	2	yes	complemented
455	#3121	C₂×C₂₃	1	2	yes	—
456	#3117	C₂×C₂₃	1	1	yes	characteristic
457	#3113	C₂×C₂₃	1	1	yes	characteristic, complemented
458	#2987	C₂×C₂₃	1	1	yes	characteristic, complemented
459	C₂²×C₂₃	—	2	1	no	—
460	C₂²×C₂₃	—	2	1	no	—
461	C₂²×C₂₃	—	2	1	no	—
462	C₂²×C₂₃	—	4	1	no	—
463	C₂²×C₂₃	—	4	1	no	—
464	C₂²×C₂₃	—	4	1	no	—
465	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
466	C₄×C₂₃	—	2	1	no	—
467	C₄×C₂₃	—	2	1	no	—
468	C₄×C₂₃	—	2	1	no	—
469	C₄×C₂₃	—	2	1	no	—
470	C₄×C₂₃	—	2	2	no	—
471	C₄×C₂₃	—	2	2	no	—
472	C₄×C₂₃	—	2	2	no	—
473	C₄×C₂₃	—	2	2	no	—
474	C₄×C₂₃	—	2	4	no	—
475	C₄×C₂₃	—	2	1	no	—
476	C₄×C₂₃	—	4	1	no	—
477	C₄×C₂₃	—	4	2	no	—
478	C₄×C₂₃	—	4	2	no	—
479	C₄×C₂₃	—	4	1	no	—
480	C₄×C₂₃	—	4	2	no	—
481	C₄×C₂₃	—	4	2	no	—
482	C₄×C₂₃	—	4	2	no	—
483	C₄×C₂₃	—	4	1	no	—
484	C₄×C₂₃	C₂×2₋¹⁺⁴	1	2	yes	—
485	#563	—	2	2	no	—
486	Q₈²	—	2	1	no	—
487	Q₈²	C₂²×C₂₃	1	2	yes	—
488	Q₈²	C₂²×C₂₃	1	1	yes	characteristic
489	#557	—	2	1	no	—
490	#557	—	2	2	no	—
491	#557	C₂²×C₂₃	1	1	yes	characteristic
492	#557	C₂²×C₂₃	1	2	yes	—
493	#557	C₂²×C₂₃	1	2	yes	—
494	#557	C₂²×C₂₃	1	2	yes	—
495	#557	C₂²×C₂₃	1	2	yes	—
496	#556	—	2	1	no	—
497	#556	C₂²×C₂₃	1	2	yes	—
498	#556	C₂²×C₂₃	1	1	yes	characteristic
499	#554	C₂²×C₂₃	1	1	yes	characteristic
500	#552	—	2	1	no	—
501	#544	—	2	1	no	—
502	#544	—	2	1	no	—
503	#544	—	2	1	no	—
504	#544	C₂²×C₂₃	1	2	yes	—
505	#542	C₂²×C₂₃	1	2	yes	—
506	#541	—	2	1	no	—
507	#541	—	2	2	no	—
508	#541	C₂²×C₂₃	1	2	yes	—
509	#533	—	2	2	no	—
510	#533	C₂²×C₂₃	1	1	yes	characteristic
511	#533	C₂²×C₂₃	1	1	yes	characteristic
512	#533	C₂²×C₂₃	1	1	yes	characteristic
513	#529	C₂²×C₂₃	1	1	yes	characteristic
514	#519	C₂²×C₂₃	1	2	yes	—
515	C₂×C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
516	#501	C₂²×C₂₃	1	1	yes	characteristic
517	#501	C₂²×C₂₃	1	2	yes	—
518	#501	C₂²×C₂₃	1	2	yes	—
519	#501	C₂²×C₂₃	1	2	yes	—
520	#501	C₂²×C₂₃	1	1	yes	characteristic
521	#499	C₂²×C₂₃	1	2	yes	—
522	#498	C₂²×C₂₃	1	2	yes	—
523	#491	C₂²×C₂₃	1	2	yes	—
524	#491	C₂²×C₂₃	1	2	yes	—
525	#489	C₂²×C₂₃	1	1	yes	characteristic
526	#489	C₂²×C₂₃	1	2	yes	—
527	#489	C₂²×C₂₃	1	1	yes	characteristic
528	#488	C₂²×C₂₃	1	2	yes	—
529	#487	C₂²×C₂₃	1	2	yes	—
530	#485	C₂²×C₂₃	1	2	yes	—
531	#485	C₂²×C₂₃	1	2	yes	—
532	#485	C₂²×C₂₃	1	2	yes	—
533	#484	C₂²×C₂₃	1	1	yes	characteristic
534	#483	C₂²×C₂₃	1	2	yes	—
535	#482	C₂²×C₂₃	1	2	yes	—
536	#481	C₂²×C₂₃	1	1	yes	characteristic
537	#479	C₂²×C₂₃	1	2	yes	—
538	#479	C₂²×C₂₃	1	2	yes	—
539	#479	C₂²×C₂₃	1	2	yes	—
540	#479	C₂²×C₂₃	1	2	yes	—
541	#479	C₂²×C₂₃	1	2	yes	—
542	#479	C₂²×C₂₃	1	2	yes	—
543	#479	C₂²×C₂₃	1	2	yes	—
544	#478	C₂²×C₂₃	1	2	yes	—
545	#478	C₂²×C₂₃	1	2	yes	—
546	#477	C₂²×C₂₃	1	2	yes	—
547	#477	C₂²×C₂₃	1	2	yes	—
548	#477	C₂²×C₂₃	1	2	yes	—
549	#476	C₂²×C₂₃	1	2	yes	—
550	#475	C₂²×C₂₃	1	2	yes	—
551	#475	C₂²×C₂₃	1	2	yes	—
552	#475	C₂²×C₂₃	1	2	yes	—
553	#475	C₂²×C₂₃	1	2	yes	—
554	#475	C₂²×C₂₃	1	2	yes	—
555	#464	C₂²×C₂₃	1	2	yes	—
556	#464	C₂²×C₂₃	1	2	yes	—
557	#464	C₂²×C₂₃	1	2	yes	—
558	#462	C₂²×C₂₃	1	2	yes	—
559	#462	C₂²×C₂₃	1	2	yes	—
560	#462	C₂²×C₂₃	1	2	yes	—
561	#451	C₂²×C₂₃	1	2	yes	—
562	#451	C₂²×C₂₃	1	1	yes	characteristic
563	#448	C₂²×C₂₃	1	1	yes	characteristic
564	#446	C₂²×C₂₃	1	2	yes	—
565	#446	C₂²×C₂₃	1	2	yes	—
566	#446	C₂²×C₂₃	1	2	yes	—
567	#446	C₂²×C₂₃	1	2	yes	—
568	#441	C₂²×C₂₃	1	2	yes	—
569	#441	C₂²×C₂₃	1	2	yes	—
570	#441	C₂²×C₂₃	1	2	yes	—
571	#441	C₂²×C₂₃	1	2	yes	—
572	#441	C₂²×C₂₃	1	2	yes	—
573	#441	C₂²×C₂₃	1	2	yes	—
574	#440	C₂²×C₂₃	1	2	yes	—
575	#440	C₂²×C₂₃	1	2	yes	—
576	C₄×Q₁₆	C₂²×C₂₃	1	2	yes	—
577	C₄×Q₁₆	C₂²×C₂₃	1	2	yes	—
578	C₄×Q₁₆	C₂²×C₂₃	1	2	yes	—
579	C₄×SD₁₆	C₂²×C₂₃	1	2	yes	—
580	#433	C₂²×C₂₃	1	2	yes	—
581	#433	C₂²×C₂₃	1	2	yes	—
582	#432	C₂²×C₂₃	1	1	yes	characteristic
583	#432	C₂²×C₂₃	1	1	yes	characteristic
584	C₂×C₂₃	—	4	1	no	—
585	C₂×C₂₃	—	8	1	no	—
586	C₂×C₂₃	#3486	1	1	yes	characteristic
587	C₂×C₂₃	#3586	1	1	yes	characteristic
588	C₂×C₂₃	#3586	1	1	yes	characteristic
589	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
590	C₂×Q₁₆	C₂³×C₂₃	1	2	yes	—
591	C₂×Q₁₆	C₂³×C₂₃	1	2	yes	—
592	C₂×Q₁₆	C₂³×C₂₃	1	2	yes	—
593	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
594	C₄⋊Q₈	—	2	2	no	—
595	C₄⋊Q₈	—	2	2	no	—
596	C₄⋊Q₈	—	2	2	no	—
597	C₄⋊Q₈	—	2	2	no	—
598	C₄⋊Q₈	—	2	2	no	—
599	C₄⋊Q₈	—	2	2	no	—
600	C₄⋊Q₈	—	2	1	no	—
601	C₄⋊Q₈	—	2	2	no	—
602	C₄⋊Q₈	—	2	2	no	—
603	C₄⋊Q₈	—	2	2	no	—
604	C₄⋊Q₈	D₄×C₂₃	1	1	yes	characteristic
605	C₄⋊Q₈	D₄×C₂₃	1	1	yes	characteristic
606	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
607	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
608	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
609	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
610	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
611	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
612	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
613	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
614	#126	—	2	2	no	—
615	#126	—	2	2	no	—
616	#126	—	2	2	no	—
617	#126	—	2	2	no	—
618	#126	—	2	2	no	—
619	#126	—	2	2	no	—
620	#126	—	2	1	no	—
621	#125	—	2	2	no	—
622	#125	—	2	2	no	—
623	#125	—	2	2	no	—
624	#125	—	2	2	no	—
625	#125	—	2	2	no	—
626	#125	—	2	2	no	—
627	#125	—	2	2	no	—
628	#125	—	2	1	no	—
629	#125	—	2	2	no	—
630	#125	—	2	2	no	—
631	#125	—	2	2	no	—
632	#125	—	2	2	no	—
633	#125	—	2	2	no	—
634	#125	—	2	1	no	—
635	#125	D₄×C₂₃	1	2	yes	—
636	#125	C₂³×C₂₃	1	1	yes	characteristic
637	#125	C₂³×C₂₃	1	2	yes	—
638	#125	C₂³×C₂₃	1	2	yes	—
639	#125	C₂³×C₂₃	1	2	yes	—
640	#125	C₂³×C₂₃	1	2	yes	—
641	#124	—	2	2	no	—
642	#124	C₂³×C₂₃	1	1	yes	characteristic
643	#124	C₂³×C₂₃	1	2	yes	—
644	#123	—	2	1	no	—
645	#123	—	2	2	no	—
646	C₂²⋊Q₈	—	2	1	no	—
647	C₂²⋊Q₈	—	2	1	no	—
648	C₂²⋊Q₈	—	2	2	no	—
649	C₂²⋊Q₈	—	2	1	no	—
650	C₂²⋊Q₈	—	2	1	no	—
651	C₂²⋊Q₈	—	2	1	no	—
652	C₂²⋊Q₈	—	2	2	no	—
653	C₂²⋊Q₈	—	2	2	no	—
654	C₂²⋊Q₈	—	2	2	no	—
655	C₂²⋊Q₈	—	2	2	no	—
656	C₂²⋊Q₈	D₄×C₂₃	1	2	yes	—
657	C₂²⋊Q₈	D₄×C₂₃	1	1	yes	characteristic
658	C₂²⋊Q₈	D₄×C₂₃	1	1	yes	characteristic
659	C₂²⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
660	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
661	#121	C₂³×C₂₃	1	1	yes	characteristic
662	C₄×Q₈	—	2	2	no	—
663	C₄×Q₈	—	2	1	no	—
664	C₄×Q₈	—	2	1	no	—
665	C₄×Q₈	—	2	2	no	—
666	C₄×Q₈	—	2	2	no	—
667	C₄×Q₈	—	2	2	no	—
668	C₄×Q₈	—	2	2	no	—
669	C₄×Q₈	—	2	2	no	—
670	C₄×Q₈	—	2	2	no	—
671	C₄×Q₈	—	2	1	no	—
672	C₄×Q₈	—	2	1	no	—
673	C₄×Q₈	—	2	1	no	—
674	C₄×Q₈	—	2	1	no	—
675	C₄×Q₈	—	2	1	no	—
676	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
677	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
678	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
679	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
680	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
681	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
682	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
683	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
684	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
685	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
686	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
687	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
688	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
689	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
690	C₄×D₄	—	2	1	no	—
691	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
692	C₄×D₄	C₂³×C₂₃	1	2	yes	—
693	#117	—	2	1	no	—
694	#117	—	2	2	no	—
695	#117	—	2	1	no	—
696	#117	—	2	2	no	—
697	#117	—	2	2	no	—
698	#117	—	2	1	no	—
699	#117	C₂³×C₂₃	1	2	yes	—
700	#117	C₂³×C₂₃	1	2	yes	—
701	C₂×C₄⋊C₄	—	2	1	no	—
702	C₂×C₄⋊C₄	—	2	1	no	—
703	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
704	C₂×C₄²	—	2	1	no	—
705	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
706	#107	C₂³×C₂₃	1	2	yes	—
707	#107	C₂³×C₂₃	1	2	yes	—
708	#107	C₂³×C₂₃	1	2	yes	—
709	#107	C₂³×C₂₃	1	2	yes	—
710	#107	C₂³×C₂₃	1	2	yes	—
711	#106	C₂³×C₂₃	1	2	yes	—
712	#106	C₂³×C₂₃	1	2	yes	—
713	#106	C₂³×C₂₃	1	2	yes	—
714	#106	C₂³×C₂₃	1	2	yes	—
715	#106	C₂³×C₂₃	1	2	yes	—
716	#106	C₂³×C₂₃	1	2	yes	—
717	#106	C₂³×C₂₃	1	2	yes	—
718	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
719	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
720	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
721	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
722	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
723	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
724	#103	C₂³×C₂₃	1	2	yes	—
725	#103	C₂³×C₂₃	1	2	yes	—
726	#103	C₂³×C₂₃	1	2	yes	—
727	#103	C₂³×C₂₃	1	2	yes	—
728	#103	C₂³×C₂₃	1	2	yes	—
729	#103	C₂³×C₂₃	1	2	yes	—
730	#103	C₂³×C₂₃	1	2	yes	—
731	#103	C₂³×C₂₃	1	2	yes	—
732	#103	C₂³×C₂₃	1	2	yes	—
733	#103	C₂³×C₂₃	1	2	yes	—
734	#103	C₂³×C₂₃	1	2	yes	—
735	#103	C₂³×C₂₃	1	2	yes	—
736	#103	C₂³×C₂₃	1	2	yes	—
737	#102	C₂³×C₂₃	1	2	yes	—
738	#102	C₂³×C₂₃	1	2	yes	—
739	#102	C₂³×C₂₃	1	2	yes	—
740	C₂²⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
741	C₂²⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
742	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
743	#97	C₂³×C₂₃	1	2	yes	—
744	#97	C₂³×C₂₃	1	1	yes	characteristic
745	#97	C₂³×C₂₃	1	1	yes	characteristic
746	#97	C₂³×C₂₃	1	2	yes	—
747	#97	C₂³×C₂₃	1	2	yes	—
748	C₄×C₈	C₂³×C₂₃	1	2	yes	—
749	C₄×C₈	C₂³×C₂₃	1	2	yes	—
750	C₂₃	#61875	1	1	yes	characteristic, direct product factor, Sylow
751	C₂×Q₈	—	2	4	no	—
752	C₂×Q₈	—	2	1	no	—
753	C₂×Q₈	—	2	1	no	—
754	C₂×Q₈	—	2	1	no	—
755	C₂×Q₈	—	2	2	no	—
756	C₂×Q₈	—	2	1	no	—
757	C₂×Q₈	—	2	2	no	—
758	C₂×Q₈	—	2	2	no	—
759	C₂×Q₈	C₂×D₄×C₂₃	1	2	yes	—
760	C₂×Q₈	C₂×D₄×C₂₃	1	1	yes	characteristic
761	C₂×Q₈	C₂×D₄×C₂₃	1	1	yes	characteristic
762	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
763	C₂×Q₈	C₂⁴×C₂₃	1	1	yes	characteristic
764	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
765	C₂×D₄	—	2	1	no	—
766	C₂×D₄	C₂⁴×C₂₃	1	1	yes	characteristic
767	C₂²×C₄	—	2	1	no	—
768	C₂²×C₄	—	2	1	no	—
769	C₂²×C₄	—	2	1	no	—
770	C₂²×C₄	—	2	2	no	—
771	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
772	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
773	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
774	Q₁₆	—	2	4	no	—
775	Q₁₆	—	2	4	no	—
776	Q₁₆	—	2	4	no	—
777	SD₁₆	—	2	4	no	—
778	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
779	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
780	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
781	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
782	C₄⋊C₄	—	2	1	no	—
783	C₄⋊C₄	—	2	2	no	—
784	C₄⋊C₄	—	2	2	no	—
785	C₄⋊C₄	—	2	2	no	—
786	C₄⋊C₄	—	2	1	no	—
787	C₄⋊C₄	—	2	1	no	—
788	C₄⋊C₄	—	2	2	no	—
789	C₄⋊C₄	—	2	2	no	—
790	C₄⋊C₄	—	2	2	no	—
791	C₄⋊C₄	—	2	2	no	—
792	C₄⋊C₄	—	2	2	no	—
793	C₄⋊C₄	—	2	1	no	—
794	C₄⋊C₄	—	2	1	no	—
795	C₄⋊C₄	—	2	1	no	—
796	C₄⋊C₄	—	2	2	no	—
797	C₄⋊C₄	—	2	1	no	—
798	C₄⋊C₄	—	2	2	no	—
799	C₄⋊C₄	—	2	2	no	—
800	C₄⋊C₄	—	2	1	no	—
801	C₄⋊C₄	—	2	2	no	—
802	C₄⋊C₄	—	2	2	no	—
803	C₄⋊C₄	—	2	2	no	—
804	C₄⋊C₄	—	2	2	no	—
805	C₄⋊C₄	—	2	2	no	—
806	C₄⋊C₄	—	2	2	no	—
807	C₄⋊C₄	—	2	2	no	—
808	C₄⋊C₄	—	2	1	no	—
809	C₄⋊C₄	—	2	2	no	—
810	C₄⋊C₄	—	2	2	no	—
811	C₄⋊C₄	—	2	2	no	—
812	C₄⋊C₄	—	2	2	no	—
813	C₄⋊C₄	—	2	2	no	—
814	C₄⋊C₄	—	2	2	no	—
815	C₄⋊C₄	—	2	1	no	—
816	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
817	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
818	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
819	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
820	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
821	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
822	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
823	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
824	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
825	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
826	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
827	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
828	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
829	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
830	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
831	C₂²⋊C₄	—	2	2	no	—
832	C₂²⋊C₄	—	2	2	no	—
833	C₂²⋊C₄	—	2	1	no	—
834	C₂²⋊C₄	—	2	1	no	—
835	C₂²⋊C₄	—	2	1	no	—
836	C₂²⋊C₄	—	2	1	no	—
837	C₂²⋊C₄	—	2	2	no	—
838	C₂²⋊C₄	—	2	2	no	—
839	C₂²⋊C₄	—	2	1	no	—
840	C₂²⋊C₄	—	2	2	no	—
841	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
842	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
843	C₄²	—	2	2	no	—
844	C₄²	—	2	2	no	—
845	C₄²	—	2	2	no	—
846	C₄²	—	2	1	no	—
847	C₄²	—	2	2	no	—
848	C₄²	—	2	2	no	—
849	C₄²	—	2	2	no	—
850	C₄²	—	2	2	no	—
851	C₄²	—	2	2	no	—
852	C₄²	—	2	2	no	—
853	C₄²	—	2	2	no	—
854	C₄²	—	2	2	no	—
855	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
856	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
857	C₄²	C₂⁴×C₂₃	1	2	yes	—
858	C₄²	C₂⁴×C₂₃	1	2	yes	—
859	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
860	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
861	C₂³	—	2	1	no	—
862	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
863	Q₈	—	2	4	no	—
864	Q₈	—	2	2	no	—
865	Q₈	—	2	2	no	—
866	Q₈	—	2	2	no	—
867	Q₈	—	2	2	no	—
868	Q₈	—	4	1	no	—
869	Q₈	—	4	1	no	—
870	Q₈	—	4	2	no	—
871	Q₈	—	4	2	no	—
872	Q₈	—	8	1	no	—
873	Q₈	—	8	1	no	—
874	Q₈	—	8	2	no	—
875	Q₈	—	8	2	no	—
876	Q₈	—	8	2	no	—
877	Q₈	C₂₃×2₋¹⁺⁴	1	4	yes	—
878	D₄	—	2	2	no	—
879	D₄	—	8	1	no	—
880	C₂×C₄	—	2	4	no	—
881	C₂×C₄	—	2	2	no	—
882	C₂×C₄	—	2	2	no	—
883	C₂×C₄	—	2	2	no	—
884	C₂×C₄	—	2	1	no	—
885	C₂×C₄	—	2	2	no	—
886	C₂×C₄	—	2	1	no	—
887	C₂×C₄	—	2	2	no	—
888	C₂×C₄	—	2	1	no	—
889	C₂×C₄	—	2	2	no	—
890	C₂×C₄	—	2	2	no	—
891	C₂×C₄	—	4	1	no	—
892	C₂×C₄	—	4	1	no	—
893	C₂×C₄	—	4	2	no	—
894	C₂×C₄	—	8	2	no	—
895	C₂×C₄	—	8	1	no	—
896	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
897	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
898	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
899	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
900	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
901	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
902	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
903	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
904	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
905	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
906	C₈	—	2	2	no	—
907	C₈	—	2	2	no	—
908	C₈	—	2	2	no	—
909	C₈	—	2	2	no	—
910	C₂²	—	2	1	no	—
911	C₂²	—	2	1	no	—
912	C₂²	—	2	1	no	—
913	C₂²	—	4	1	no	—
914	C₂²	—	4	1	no	—
915	C₂²	—	4	1	no	—
916	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
917	C₄	—	2	4	no	—
918	C₄	—	2	1	no	—
919	C₄	—	2	1	no	—
920	C₄	—	2	1	no	—
921	C₄	—	2	1	no	—
922	C₄	—	2	1	no	—
923	C₄	—	2	2	no	—
924	C₄	—	2	2	no	—
925	C₄	—	2	2	no	—
926	C₄	—	2	2	no	—
927	C₄	—	4	2	no	—
928	C₄	—	4	1	no	—
929	C₄	—	4	1	no	—
930	C₄	—	4	2	no	—
931	C₄	—	4	2	no	—
932	C₄	—	4	1	no	—
933	C₄	—	4	2	no	—
934	C₄	—	4	2	no	—
935	C₄	C₂×C₂₃×2₋¹⁺⁴	1	2	yes	—
936	C₂	—	4	1	no	—
937	C₂	—	8	1	no	—
938	C₂	C₂₃×#3486	1	1	yes	characteristic
939	C₂	C₂₃×#3586	1	1	yes	characteristic
940	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×#121	C₂³
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₃ ◁ C₂₃×#533 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂₃×#3502	C₂	semidirect
3. C₂₃×#3390	C₂	semidirect
4. C₂₃×#3388	C₂	semidirect
5. C₂₃×#3387	C₂	semidirect
6. C₂₃×#3387	C₂	semidirect
7. C₂₃×#3377	C₂	semidirect
8. C₂₃×#3377	C₂	semidirect
9. C₂₃×#3374	C₂	semidirect
10. C₂₃×#3369	C₂	semidirect
12. C₂₃×#3242	C₂	semidirect
14. C₂₃×#3237	C₂	semidirect
15. C₂₃×#3127	C₂	semidirect
18. C₂₃×#3113	C₂	semidirect
19. C₂₃×#2987	C₂	semidirect
390. #61875	C₂₃	direct (N × H)
441. #3502	C₂×C₂₃	semidirect
442. #3390	C₂×C₂₃	semidirect
443. #3388	C₂×C₂₃	semidirect
444. #3387	C₂×C₂₃	semidirect
445. #3387	C₂×C₂₃	semidirect
446. #3377	C₂×C₂₃	semidirect
447. #3377	C₂×C₂₃	semidirect
448. #3374	C₂×C₂₃	semidirect
449. #3369	C₂×C₂₃	semidirect
451. #3242	C₂×C₂₃	semidirect
453. #3237	C₂×C₂₃	semidirect
454. #3127	C₂×C₂₃	semidirect
457. #3113	C₂×C₂₃	semidirect
458. #2987	C₂×C₂₃	semidirect
750. C₂₃	#61875	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×#3555	2
C₂₃×#3502	2
C₂₃×#3390	2
C₂₃×#3388	2
C₂₃×#3387	2
C₂₃×#3377	2
C₂₃×#3374	2
C₂₃×#3369	2
C₂₃×#3244	2
C₂₃×#3242	2
C₂₃×#3240	2
C₂₃×#3237	2
C₂₃×#3127	2
C₂₃×#3121	2
C₂₃×#3117	2
C₂₃×#3113	2
C₂₃×#2987	2
#61875	23

Subgroups — C23×#61875 #19209501

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#61875 #19209501