Subgroups — C₂₃×#60950 #19208576

Order 5888.

1812 conjugacy classes of subgroups.

The subgroup lattice has 832 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₃×#533	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₂₃×#529	C₂	1	1	yes	maximal, characteristic
3	C₂₃×#3252	C₂	1	4	yes	maximal, complemented
4	C₂₃×#3238	C₂	1	2	yes	maximal, complemented
5	C₂₃×#3236	C₂	1	2	yes	maximal, complemented
6	C₂₃×#3218	C₂	1	2	yes	maximal, complemented
7	C₂₃×#3215	C₂	1	2	yes	maximal, complemented
8	C₂₃×#3195	C₂	1	2	yes	maximal, complemented
9	C₂₃×#3193	C₂	1	2	yes	maximal
10	C₂₃×#3172	C₂	1	4	yes	maximal, complemented
11	C₂₃×#3108	C₂	1	4	yes	maximal, complemented
12	C₂₃×#3104	C₂	1	2	yes	maximal, complemented
13	C₂₃×#3101	C₂	1	2	yes	maximal, complemented
14	C₂₃×#2920	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₃×#533	—	2	1	no	—
16	C₂₃×#533	—	2	1	no	—
17	C₂₃×#533	—	2	1	no	—
18	C₂₃×#533	—	2	1	no	—
19	C₂₃×#533	C₂²	1	2	yes	—
20	C₂₃×#533	C₂²	1	2	yes	—
21	C₂₃×#533	C₂²	1	2	yes	complemented
22	C₂₃×#533	C₂²	1	2	yes	complemented
23	C₂×C₂₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
24	C₂×C₂₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
25	C₂₃×#529	—	2	1	no	—
26	C₂₃×#529	—	2	1	no	—
27	C₂₃×#529	—	2	1	no	—
28	C₂₃×#529	—	2	1	no	—
29	C₂₃×#529	C₂²	1	2	yes	—
30	C₂₃×#529	C₂²	1	2	yes	—
31	C₂₃×#529	C₂²	1	2	yes	—
32	C₂₃×#529	C₂²	1	2	yes	—
33	C₂×C₂₃×#126	—	2	1	no	—
34	C₂×C₂₃×#125	—	2	1	no	—
35	C₂×C₂₃×#125	C₂²	1	1	yes	characteristic
36	C₂×C₂₃×#124	C₂²	1	1	yes	characteristic
37	C₂×C₂₃×#123	—	2	1	no	—
38	C₂×C₂₃×C₂²⋊Q₈	—	2	1	no	—
39	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
40	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	2	yes	—
41	C₂×C₂₃×#121	C₂²	1	1	yes	characteristic
42	C₂×C₄×Q₈×C₂₃	—	2	1	no	—
43	C₂×C₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic
44	C₂×C₄×Q₈×C₂₃	C₂²	1	2	yes	complemented
45	C₂×C₄×D₄×C₂₃	—	2	1	no	—
46	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
47	C₂×C₂₃×#117	—	2	1	no	—
48	C₂×C₂₃×#117	—	2	1	no	—
49	C₂²×C₄²×C₂₃	C₂²	1	1	yes	characteristic
50	C₂₃×#501	C₂²	1	4	yes	complemented
51	C₂₃×#497	C₂²	1	4	yes	complemented
52	C₂₃×#491	C₂²	1	4	yes	complemented
53	C₂₃×#489	C₂²	1	4	yes	complemented
54	C₂₃×#484	C₂²	1	4	yes	—
55	C₂₃×#483	C₂²	1	4	yes	—
56	C₂₃×#483	C₂²	1	4	yes	complemented
57	C₂₃×#480	C₂²	1	4	yes	—
58	C₂₃×#479	C₂²	1	8	yes	complemented
59	C₂₃×#477	C₂²	1	4	yes	complemented
60	C₂₃×#476	C₂²	1	4	yes	complemented
61	C₂₃×#470	C₂²	1	8	yes	complemented
62	C₂₃×#468	C₂²	1	8	yes	—
63	C₂₃×#464	C₂²	1	8	yes	complemented
64	C₂₃×#462	C₂²	1	4	yes	complemented
65	C₂₃×#461	C₂²	1	4	yes	complemented
66	C₂₃×#451	C₂²	1	4	yes	—
67	C₂₃×#451	C₂²	1	4	yes	complemented
68	C₂₃×#450	C₂²	1	4	yes	—
69	C₂₃×#448	C₂²	1	4	yes	—
70	C₄×Q₁₆×C₂₃	C₂²	1	8	yes	complemented
71	C₄×SD₁₆×C₂₃	C₂²	1	8	yes	complemented
72	C₂₃×#432	C₂²	1	2	yes	—
73	C₂₃×#432	C₂²	1	2	yes	complemented
74	C₂₃×#431	C₂²	1	2	yes	—
75	C₂₃×#431	C₂²	1	2	yes	complemented
76	C₂₃×#423	C₂²	1	2	yes	complemented
77	C₂₃×#407	C₂²	1	2	yes	—
78	C₄×M₁₆×C₂₃	C₂²	1	2	yes	complemented
79	C₂²×Q₈×C₂₃	—	2	1	no	—
80	C₂²×Q₈×C₂₃	C₂³	1	2	yes	—
81	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
82	C₂²×D₄×C₂₃	—	2	1	no	—
83	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
84	C₂³×C₄×C₂₃	—	2	1	no	—
85	C₂³×C₄×C₂₃	D₄	1	1	yes	characteristic
86	C₂³×C₄×C₂₃	D₄	1	1	yes	characteristic
87	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
88	C₂×Q₁₆×C₂₃	C₂³	1	8	yes	—
89	C₂×SD₁₆×C₂₃	C₂³	1	8	yes	—
90	C₂×M₁₆×C₂₃	C₂³	1	4	yes	—
91	C₂₃×C₄⋊Q₈	—	2	1	no	—
92	C₂₃×C₄⋊Q₈	—	2	1	no	—
93	C₂₃×C₄⋊Q₈	—	2	1	no	—
94	C₂₃×C₄⋊Q₈	—	2	1	no	—
95	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
96	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
97	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
98	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
99	C₂₃×#126	—	2	2	no	—
100	C₂₃×#126	—	2	2	no	—
101	C₂₃×#126	—	2	2	no	—
102	C₂₃×#126	—	2	2	no	—
103	C₂₃×#125	—	2	2	no	—
104	C₂₃×#125	—	2	2	no	—
105	C₂₃×#125	—	2	2	no	—
106	C₂₃×#125	—	2	2	no	—
107	C₂₃×#125	—	2	1	no	—
108	C₂₃×#125	—	2	1	no	—
109	C₂₃×#125	C₂³	1	2	yes	—
110	C₂₃×#125	C₂³	1	2	yes	—
111	C₂₃×#124	—	2	1	no	—
112	C₂₃×#124	—	2	1	no	—
113	C₂₃×#124	C₂³	1	2	yes	—
114	C₂₃×#124	C₂³	1	2	yes	—
115	C₂₃×#123	—	2	2	no	—
116	C₂₃×#123	—	2	2	no	—
117	C₂₃×#123	—	2	2	no	—
118	C₂₃×#123	—	2	2	no	—
119	C₂₃×C₂²⋊Q₈	—	2	2	no	—
120	C₂₃×C₂²⋊Q₈	—	2	2	no	—
121	C₂₃×C₂²⋊Q₈	—	2	2	no	—
122	C₂₃×C₂²⋊Q₈	—	2	2	no	—
123	C₂₃×C₂²⋊Q₈	—	2	1	no	—
124	C₂₃×C₂²⋊Q₈	—	2	1	no	—
125	C₂₃×C₂²⋊Q₈	—	2	2	no	—
126	C₂₃×C₂²⋊Q₈	—	2	2	no	—
127	C₂₃×C₂²⋊Q₈	C₂³	1	4	yes	—
128	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
129	C₂₃×C₂²⋊Q₈	C₂³	1	4	yes	—
130	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
131	C₂₃×#121	—	2	1	no	—
132	C₂₃×#121	—	2	1	no	—
133	C₂₃×#121	C₂³	1	2	yes	—
134	C₂₃×#121	C₂³	1	2	yes	—
135	C₄×Q₈×C₂₃	—	2	2	no	—
136	C₄×Q₈×C₂₃	—	2	2	no	—
137	C₄×Q₈×C₂₃	—	2	2	no	—
138	C₄×Q₈×C₂₃	—	2	2	no	—
139	C₄×Q₈×C₂₃	—	2	1	no	—
140	C₄×Q₈×C₂₃	—	2	1	no	—
141	C₄×Q₈×C₂₃	—	2	2	no	—
142	C₄×Q₈×C₂₃	—	2	2	no	—
143	C₄×Q₈×C₂₃	C₂³	1	4	yes	—
144	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
145	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
146	C₄×Q₈×C₂₃	C₂³	1	4	yes	—
147	C₄×D₄×C₂₃	—	2	2	no	—
148	C₄×D₄×C₂₃	—	2	2	no	—
149	C₄×D₄×C₂₃	—	2	2	no	—
150	C₄×D₄×C₂₃	—	2	2	no	—
151	C₄×D₄×C₂₃	—	2	1	no	—
152	C₄×D₄×C₂₃	—	2	1	no	—
153	C₄×D₄×C₂₃	C₂³	1	2	yes	—
154	C₄×D₄×C₂₃	C₂³	1	2	yes	—
155	C₂₃×#117	—	2	2	no	—
156	C₂₃×#117	—	2	2	no	—
157	C₂₃×#117	—	2	2	no	—
158	C₂₃×#117	—	2	2	no	—
159	C₂₃×#117	—	2	2	no	—
160	C₂₃×#117	—	2	2	no	—
161	C₂₃×#117	—	2	2	no	—
162	C₂₃×#117	—	2	2	no	—
163	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
164	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
165	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
166	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
167	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
168	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
169	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
170	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
171	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
172	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
173	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
174	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
175	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
176	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
177	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
178	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
179	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
180	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
181	C₂×C₄²×C₂₃	—	2	1	no	—
182	C₂×C₄²×C₂₃	—	2	2	no	—
183	C₂×C₄²×C₂₃	D₄	1	1	yes	characteristic
184	C₂×C₄²×C₂₃	D₄	1	1	yes	characteristic
185	C₂×C₄²×C₂₃	D₄	1	1	yes	characteristic
186	C₂×C₄²×C₂₃	D₄	1	1	yes	characteristic
187	C₂×C₄²×C₂₃	D₄	1	1	yes	characteristic
188	C₂×C₄²×C₂₃	D₄	1	1	yes	characteristic
189	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
190	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
191	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
192	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
193	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
194	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
195	C₂₃×#107	C₂³	1	8	yes	—
196	C₂₃×#106	C₂³	1	8	yes	—
197	C₂₃×C₄⋊C₈	C₂³	1	4	yes	—
198	C₂₃×C₄⋊C₈	C₂³	1	4	yes	—
199	C₂₃×#103	C₂³	1	8	yes	—
200	C₂₃×#103	C₂³	1	8	yes	—
201	C₂₃×#103	C₂³	1	8	yes	—
202	C₂₃×#102	C₂³	1	8	yes	—
203	C₂₃×C₂²⋊C₈	C₂³	1	4	yes	—
204	C₂₃×C₂²⋊C₈	C₂³	1	4	yes	—
205	C₂₃×#97	C₂³	1	4	yes	—
206	C₄×C₈×C₂₃	C₂³	1	4	yes	—
207	C₂⁴×C₂₃	—	2	1	no	—
208	C₂⁴×C₂₃	C₂×D₄	1	1	yes	characteristic
209	C₂×Q₈×C₂₃	—	2	1	no	—
210	C₂×Q₈×C₂₃	—	2	2	no	—
211	C₂×Q₈×C₂₃	—	2	2	no	—
212	C₂×Q₈×C₂₃	—	2	2	no	—
213	C₂×Q₈×C₂₃	—	4	2	no	—
214	C₂×Q₈×C₂₃	—	4	4	no	—
215	C₂×Q₈×C₂₃	—	4	4	no	—
216	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
217	C₂×Q₈×C₂₃	C₂⁴	1	4	yes	—
218	C₂×D₄×C₂₃	—	2	2	no	—
219	C₂×D₄×C₂₃	—	2	2	no	—
220	C₂×D₄×C₂₃	—	2	1	no	—
221	C₂×D₄×C₂₃	—	4	2	no	—
222	C₂×D₄×C₂₃	—	4	4	no	—
223	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
224	C₂²×C₄×C₂₃	—	2	4	no	—
225	C₂²×C₄×C₂₃	—	2	1	no	—
226	C₂²×C₄×C₂₃	—	2	2	no	—
227	C₂²×C₄×C₂₃	—	2	1	no	—
228	C₂²×C₄×C₂₃	—	2	2	no	—
229	C₂²×C₄×C₂₃	—	2	1	no	—
230	C₂²×C₄×C₂₃	—	2	2	no	—
231	C₂²×C₄×C₂₃	—	2	2	no	—
232	C₂²×C₄×C₂₃	—	4	2	no	—
233	C₂²×C₄×C₂₃	—	4	2	no	—
234	C₂²×C₄×C₂₃	—	4	4	no	—
235	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
236	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
237	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
238	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
239	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
240	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
241	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
242	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
243	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
244	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
245	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
246	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
247	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
248	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
249	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
250	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
251	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
252	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
253	Q₁₆×C₂₃	—	4	8	no	—
254	SD₁₆×C₂₃	—	4	8	no	—
255	M₁₆×C₂₃	—	4	4	no	—
256	C₂×C₈×C₂₃	C₂⁴	1	8	yes	—
257	C₄⋊C₄×C₂₃	—	2	2	no	—
258	C₄⋊C₄×C₂₃	—	2	2	no	—
259	C₄⋊C₄×C₂₃	—	2	2	no	—
260	C₄⋊C₄×C₂₃	—	2	2	no	—
261	C₄⋊C₄×C₂₃	—	2	2	no	—
262	C₄⋊C₄×C₂₃	—	2	2	no	—
263	C₄⋊C₄×C₂₃	—	2	2	no	—
264	C₄⋊C₄×C₂₃	—	2	2	no	—
265	C₄⋊C₄×C₂₃	—	2	2	no	—
266	C₄⋊C₄×C₂₃	—	2	2	no	—
267	C₄⋊C₄×C₂₃	—	2	2	no	—
268	C₄⋊C₄×C₂₃	—	2	2	no	—
269	C₄⋊C₄×C₂₃	—	2	4	no	—
270	C₄⋊C₄×C₂₃	—	2	4	no	—
271	C₄⋊C₄×C₂₃	—	2	4	no	—
272	C₄⋊C₄×C₂₃	—	2	4	no	—
273	C₄⋊C₄×C₂₃	—	2	2	no	—
274	C₄⋊C₄×C₂₃	—	2	2	no	—
275	C₄⋊C₄×C₂₃	—	2	1	no	—
276	C₄⋊C₄×C₂₃	—	2	1	no	—
277	C₄⋊C₄×C₂₃	—	2	2	no	—
278	C₄⋊C₄×C₂₃	C₂⁴	1	4	yes	—
279	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
280	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
281	C₂²⋊C₄×C₂₃	—	2	4	no	—
282	C₂²⋊C₄×C₂₃	—	2	4	no	—
283	C₂²⋊C₄×C₂₃	—	2	2	no	—
284	C₂²⋊C₄×C₂₃	—	2	2	no	—
285	C₂²⋊C₄×C₂₃	—	2	2	no	—
286	C₂²⋊C₄×C₂₃	—	2	2	no	—
287	C₂²⋊C₄×C₂₃	—	2	2	no	—
288	C₂²⋊C₄×C₂₃	—	2	2	no	—
289	C₂²⋊C₄×C₂₃	—	2	2	no	—
290	C₂²⋊C₄×C₂₃	—	2	2	no	—
291	C₂²⋊C₄×C₂₃	—	2	2	no	—
292	C₂²⋊C₄×C₂₃	—	2	2	no	—
293	C₄²×C₂₃	—	2	2	no	—
294	C₄²×C₂₃	—	2	4	no	—
295	C₄²×C₂₃	—	2	2	no	—
296	C₄²×C₂₃	—	2	4	no	—
297	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
298	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
299	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
300	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
301	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
302	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
303	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
304	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
305	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
306	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
307	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
308	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
309	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
310	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
311	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
312	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
313	#60950	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
314	C₂³×C₂₃	—	2	2	no	—
315	C₂³×C₂₃	—	2	2	no	—
316	C₂³×C₂₃	—	2	2	no	—
317	C₂³×C₂₃	—	4	1	no	—
318	C₂³×C₂₃	—	4	2	no	—
319	C₂³×C₂₃	—	4	2	no	—
320	C₂³×C₂₃	—	4	2	no	—
321	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
322	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
323	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
324	Q₈×C₂₃	—	2	8	no	—
325	Q₈×C₂₃	—	2	4	no	—
326	Q₈×C₂₃	—	4	2	no	—
327	Q₈×C₂₃	—	4	4	no	—
328	Q₈×C₂₃	—	4	4	no	—
329	Q₈×C₂₃	—	4	4	no	—
330	D₄×C₂₃	—	2	4	no	—
331	D₄×C₂₃	—	4	2	no	—
332	D₄×C₂₃	—	4	4	no	—
333	D₄×C₂₃	—	4	4	no	—
334	C₂×C₄×C₂₃	—	2	2	no	—
335	C₂×C₄×C₂₃	—	2	2	no	—
336	C₂×C₄×C₂₃	—	2	2	no	—
337	C₂×C₄×C₂₃	—	2	2	no	—
338	C₂×C₄×C₂₃	—	2	2	no	—
339	C₂×C₄×C₂₃	—	2	2	no	—
340	C₂×C₄×C₂₃	—	2	2	no	—
341	C₂×C₄×C₂₃	—	2	2	no	—
342	C₂×C₄×C₂₃	—	2	2	no	—
343	C₂×C₄×C₂₃	—	2	2	no	—
344	C₂×C₄×C₂₃	—	2	2	no	—
345	C₂×C₄×C₂₃	—	2	4	no	—
346	C₂×C₄×C₂₃	—	2	2	no	—
347	C₂×C₄×C₂₃	—	2	4	no	—
348	C₂×C₄×C₂₃	—	2	2	no	—
349	C₂×C₄×C₂₃	—	4	1	no	—
350	C₂×C₄×C₂₃	—	4	1	no	—
351	C₂×C₄×C₂₃	—	4	1	no	—
352	C₂×C₄×C₂₃	—	4	1	no	—
353	C₂×C₄×C₂₃	—	4	1	no	—
354	C₂×C₄×C₂₃	—	4	1	no	—
355	C₂×C₄×C₂₃	—	4	1	no	—
356	C₂×C₄×C₂₃	—	4	2	no	—
357	C₂×C₄×C₂₃	—	4	4	no	—
358	C₂×C₄×C₂₃	—	4	2	no	—
359	C₂×C₄×C₂₃	—	4	2	no	—
360	C₂×C₄×C₂₃	—	4	4	no	—
361	C₂×C₄×C₂₃	—	4	4	no	—
362	C₂×C₄×C₂₃	—	4	4	no	—
363	C₂×C₄×C₂₃	#137	1	4	yes	—
364	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
365	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
366	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
367	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
368	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
369	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
370	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
371	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
372	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
373	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
374	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
375	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
376	C₈×C₂₃	—	2	8	no	—
377	C₂×#533	C₂×C₂₃	1	1	yes	characteristic, complemented
378	C₂×#529	C₂×C₂₃	1	1	yes	characteristic
379	#3252	C₂×C₂₃	1	4	yes	complemented
380	#3238	C₂×C₂₃	1	2	yes	complemented
381	#3236	C₂×C₂₃	1	2	yes	complemented
382	#3218	C₂×C₂₃	1	2	yes	complemented
383	#3215	C₂×C₂₃	1	2	yes	complemented
384	#3195	C₂×C₂₃	1	2	yes	complemented
385	#3193	C₂×C₂₃	1	2	yes	—
386	#3172	C₂×C₂₃	1	4	yes	complemented
387	#3108	C₂×C₂₃	1	4	yes	complemented
388	#3104	C₂×C₂₃	1	2	yes	complemented
389	#3101	C₂×C₂₃	1	2	yes	complemented
390	#2920	C₂×C₂₃	1	1	yes	characteristic, complemented
391	C₂²×C₂₃	—	2	1	no	—
392	C₂²×C₂₃	—	2	1	no	—
393	C₂²×C₂₃	—	2	1	no	—
394	C₂²×C₂₃	—	2	1	no	—
395	C₂²×C₂₃	—	2	1	no	—
396	C₂²×C₂₃	—	2	1	no	—
397	C₂²×C₂₃	—	2	1	no	—
398	C₂²×C₂₃	—	4	4	no	—
399	C₂²×C₂₃	—	4	2	no	—
400	C₂²×C₂₃	—	4	2	no	—
401	C₂²×C₂₃	—	4	2	no	—
402	C₂²×C₂₃	—	8	4	no	—
403	C₂²×C₂₃	C₂×#137	1	2	yes	—
404	C₂²×C₂₃	#575	1	2	yes	—
405	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
406	C₄×C₂₃	—	2	1	no	—
407	C₄×C₂₃	—	2	1	no	—
408	C₄×C₂₃	—	2	1	no	—
409	C₄×C₂₃	—	2	1	no	—
410	C₄×C₂₃	—	2	1	no	—
411	C₄×C₂₃	—	2	1	no	—
412	C₄×C₂₃	—	2	1	no	—
413	C₄×C₂₃	—	2	1	no	—
414	C₄×C₂₃	—	2	1	no	—
415	C₄×C₂₃	—	4	2	no	—
416	C₄×C₂₃	—	4	4	no	—
417	C₄×C₂₃	—	4	2	no	—
418	C₄×C₂₃	—	4	2	no	—
419	C₄×C₂₃	—	4	4	no	—
420	C₄×C₂₃	C₂×#137	1	2	yes	—
421	C₄×C₂₃	C₂×#137	1	2	yes	—
422	C₄×C₂₃	#585	1	2	yes	—
423	#533	—	2	1	no	—
424	#533	—	2	1	no	—
425	#533	—	2	1	no	—
426	#533	—	2	1	no	—
427	#533	C₂²×C₂₃	1	2	yes	—
428	#533	C₂²×C₂₃	1	2	yes	—
429	#533	C₂²×C₂₃	1	2	yes	complemented
430	#533	C₂²×C₂₃	1	2	yes	complemented
431	C₂×C₄⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
432	C₂×C₄⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
433	#529	—	2	1	no	—
434	#529	—	2	1	no	—
435	#529	—	2	1	no	—
436	#529	—	2	1	no	—
437	#529	C₂²×C₂₃	1	2	yes	—
438	#529	C₂²×C₂₃	1	2	yes	—
439	#529	C₂²×C₂₃	1	2	yes	—
440	#529	C₂²×C₂₃	1	2	yes	—
441	C₂×#126	—	2	1	no	—
442	C₂×#125	—	2	1	no	—
443	C₂×#125	C₂²×C₂₃	1	1	yes	characteristic
444	C₂×#124	C₂²×C₂₃	1	1	yes	characteristic
445	C₂×#123	—	2	1	no	—
446	C₂×C₂²⋊Q₈	—	2	1	no	—
447	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
448	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	2	yes	—
449	C₂×#121	C₂²×C₂₃	1	1	yes	characteristic
450	C₂×C₄×Q₈	—	2	1	no	—
451	C₂×C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
452	C₂×C₄×Q₈	C₂²×C₂₃	1	2	yes	complemented
453	C₂×C₄×D₄	—	2	1	no	—
454	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
455	C₂×#117	—	2	1	no	—
456	C₂×#117	—	2	1	no	—
457	C₂²×C₄²	C₂²×C₂₃	1	1	yes	characteristic
458	#501	C₂²×C₂₃	1	4	yes	complemented
459	#497	C₂²×C₂₃	1	4	yes	complemented
460	#491	C₂²×C₂₃	1	4	yes	complemented
461	#489	C₂²×C₂₃	1	4	yes	complemented
462	#484	C₂²×C₂₃	1	4	yes	—
463	#483	C₂²×C₂₃	1	4	yes	—
464	#483	C₂²×C₂₃	1	4	yes	complemented
465	#480	C₂²×C₂₃	1	4	yes	—
466	#479	C₂²×C₂₃	1	8	yes	complemented
467	#477	C₂²×C₂₃	1	4	yes	complemented
468	#476	C₂²×C₂₃	1	4	yes	complemented
469	#470	C₂²×C₂₃	1	8	yes	complemented
470	#468	C₂²×C₂₃	1	8	yes	—
471	#464	C₂²×C₂₃	1	8	yes	complemented
472	#462	C₂²×C₂₃	1	4	yes	complemented
473	#461	C₂²×C₂₃	1	4	yes	complemented
474	#451	C₂²×C₂₃	1	4	yes	—
475	#451	C₂²×C₂₃	1	4	yes	complemented
476	#450	C₂²×C₂₃	1	4	yes	—
477	#448	C₂²×C₂₃	1	4	yes	—
478	C₄×Q₁₆	C₂²×C₂₃	1	8	yes	complemented
479	C₄×SD₁₆	C₂²×C₂₃	1	8	yes	complemented
480	#432	C₂²×C₂₃	1	2	yes	—
481	#432	C₂²×C₂₃	1	2	yes	complemented
482	#431	C₂²×C₂₃	1	2	yes	—
483	#431	C₂²×C₂₃	1	2	yes	complemented
484	#423	C₂²×C₂₃	1	2	yes	complemented
485	#407	C₂²×C₂₃	1	2	yes	—
486	C₄×M₁₆	C₂²×C₂₃	1	2	yes	complemented
487	C₂×C₂₃	—	2	2	no	—
488	C₂×C₂₃	—	2	2	no	—
489	C₂×C₂₃	—	4	1	no	—
490	C₂×C₂₃	—	8	2	no	—
491	C₂×C₂₃	#3449	1	1	yes	characteristic
492	C₂×C₂₃	C₂²×#137	1	1	yes	characteristic
493	C₂×C₂₃	C₂×#575	1	1	yes	characteristic
494	C₂²×Q₈	—	2	1	no	—
495	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
496	C₂²×Q₈	C₂³×C₂₃	1	2	yes	—
497	C₂²×D₄	—	2	1	no	—
498	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
499	C₂³×C₄	—	2	1	no	—
500	C₂³×C₄	D₄×C₂₃	1	1	yes	characteristic
501	C₂³×C₄	D₄×C₂₃	1	1	yes	characteristic
502	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
503	C₂×Q₁₆	C₂³×C₂₃	1	8	yes	—
504	C₂×SD₁₆	C₂³×C₂₃	1	8	yes	—
505	C₂×M₁₆	C₂³×C₂₃	1	4	yes	—
506	C₄⋊Q₈	—	2	1	no	—
507	C₄⋊Q₈	—	2	1	no	—
508	C₄⋊Q₈	—	2	1	no	—
509	C₄⋊Q₈	—	2	1	no	—
510	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
511	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
512	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
513	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
514	#126	—	2	2	no	—
515	#126	—	2	2	no	—
516	#126	—	2	2	no	—
517	#126	—	2	2	no	—
518	#125	—	2	2	no	—
519	#125	—	2	2	no	—
520	#125	—	2	2	no	—
521	#125	—	2	2	no	—
522	#125	—	2	1	no	—
523	#125	—	2	1	no	—
524	#125	C₂³×C₂₃	1	2	yes	—
525	#125	C₂³×C₂₃	1	2	yes	—
526	#124	—	2	1	no	—
527	#124	—	2	1	no	—
528	#124	C₂³×C₂₃	1	2	yes	—
529	#124	C₂³×C₂₃	1	2	yes	—
530	#123	—	2	2	no	—
531	#123	—	2	2	no	—
532	#123	—	2	2	no	—
533	#123	—	2	2	no	—
534	C₂²⋊Q₈	—	2	2	no	—
535	C₂²⋊Q₈	—	2	2	no	—
536	C₂²⋊Q₈	—	2	2	no	—
537	C₂²⋊Q₈	—	2	2	no	—
538	C₂²⋊Q₈	—	2	1	no	—
539	C₂²⋊Q₈	—	2	1	no	—
540	C₂²⋊Q₈	—	2	2	no	—
541	C₂²⋊Q₈	—	2	2	no	—
542	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
543	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
544	C₂²⋊Q₈	C₂³×C₂₃	1	4	yes	—
545	C₂²⋊Q₈	C₂³×C₂₃	1	4	yes	—
546	#121	—	2	1	no	—
547	#121	—	2	1	no	—
548	#121	C₂³×C₂₃	1	2	yes	—
549	#121	C₂³×C₂₃	1	2	yes	—
550	C₄×Q₈	—	2	2	no	—
551	C₄×Q₈	—	2	2	no	—
552	C₄×Q₈	—	2	2	no	—
553	C₄×Q₈	—	2	2	no	—
554	C₄×Q₈	—	2	1	no	—
555	C₄×Q₈	—	2	1	no	—
556	C₄×Q₈	—	2	2	no	—
557	C₄×Q₈	—	2	2	no	—
558	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
559	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
560	C₄×Q₈	C₂³×C₂₃	1	4	yes	—
561	C₄×Q₈	C₂³×C₂₃	1	4	yes	—
562	C₄×D₄	—	2	2	no	—
563	C₄×D₄	—	2	2	no	—
564	C₄×D₄	—	2	2	no	—
565	C₄×D₄	—	2	2	no	—
566	C₄×D₄	—	2	1	no	—
567	C₄×D₄	—	2	1	no	—
568	C₄×D₄	C₂³×C₂₃	1	2	yes	—
569	C₄×D₄	C₂³×C₂₃	1	2	yes	—
570	#117	—	2	2	no	—
571	#117	—	2	2	no	—
572	#117	—	2	2	no	—
573	#117	—	2	2	no	—
574	#117	—	2	2	no	—
575	#117	—	2	2	no	—
576	#117	—	2	2	no	—
577	#117	—	2	2	no	—
578	C₂×C₄⋊C₄	—	2	1	no	—
579	C₂×C₄⋊C₄	—	2	1	no	—
580	C₂×C₄⋊C₄	—	2	1	no	—
581	C₂×C₄⋊C₄	—	2	1	no	—
582	C₂×C₄⋊C₄	—	2	1	no	—
583	C₂×C₄⋊C₄	—	2	1	no	—
584	C₂×C₄⋊C₄	—	2	2	no	—
585	C₂×C₄⋊C₄	—	2	1	no	—
586	C₂×C₄⋊C₄	—	2	2	no	—
587	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
588	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
589	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
590	C₂×C₂²⋊C₄	—	2	2	no	—
591	C₂×C₂²⋊C₄	—	2	1	no	—
592	C₂×C₂²⋊C₄	—	2	1	no	—
593	C₂×C₂²⋊C₄	—	2	1	no	—
594	C₂×C₂²⋊C₄	—	2	1	no	—
595	C₂×C₂²⋊C₄	—	2	1	no	—
596	C₂×C₄²	—	2	1	no	—
597	C₂×C₄²	—	2	2	no	—
598	C₂×C₄²	D₄×C₂₃	1	1	yes	characteristic
599	C₂×C₄²	D₄×C₂₃	1	1	yes	characteristic
600	C₂×C₄²	D₄×C₂₃	1	1	yes	characteristic
601	C₂×C₄²	D₄×C₂₃	1	1	yes	characteristic
602	C₂×C₄²	D₄×C₂₃	1	1	yes	characteristic
603	C₂×C₄²	D₄×C₂₃	1	1	yes	characteristic
604	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
605	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
606	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
607	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
608	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
609	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
610	#107	C₂³×C₂₃	1	8	yes	—
611	#106	C₂³×C₂₃	1	8	yes	—
612	C₄⋊C₈	C₂³×C₂₃	1	4	yes	—
613	C₄⋊C₈	C₂³×C₂₃	1	4	yes	—
614	#103	C₂³×C₂₃	1	8	yes	—
615	#103	C₂³×C₂₃	1	8	yes	—
616	#103	C₂³×C₂₃	1	8	yes	—
617	#102	C₂³×C₂₃	1	8	yes	—
618	C₂²⋊C₈	C₂³×C₂₃	1	4	yes	—
619	C₂²⋊C₈	C₂³×C₂₃	1	4	yes	—
620	#97	C₂³×C₂₃	1	4	yes	—
621	C₄×C₈	C₂³×C₂₃	1	4	yes	—
622	C₂₃	#60950	1	1	yes	characteristic, direct product factor, Sylow
623	C₂⁴	—	2	1	no	—
624	C₂⁴	C₂×D₄×C₂₃	1	1	yes	characteristic
625	C₂×Q₈	—	2	1	no	—
626	C₂×Q₈	—	2	2	no	—
627	C₂×Q₈	—	2	2	no	—
628	C₂×Q₈	—	2	2	no	—
629	C₂×Q₈	—	4	2	no	—
630	C₂×Q₈	—	4	4	no	—
631	C₂×Q₈	—	4	4	no	—
632	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
633	C₂×Q₈	C₂⁴×C₂₃	1	4	yes	—
634	C₂×D₄	—	2	2	no	—
635	C₂×D₄	—	2	2	no	—
636	C₂×D₄	—	2	1	no	—
637	C₂×D₄	—	4	2	no	—
638	C₂×D₄	—	4	4	no	—
639	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
640	C₂²×C₄	—	2	4	no	—
641	C₂²×C₄	—	2	1	no	—
642	C₂²×C₄	—	2	2	no	—
643	C₂²×C₄	—	2	1	no	—
644	C₂²×C₄	—	2	2	no	—
645	C₂²×C₄	—	2	1	no	—
646	C₂²×C₄	—	2	2	no	—
647	C₂²×C₄	—	2	2	no	—
648	C₂²×C₄	—	4	2	no	—
649	C₂²×C₄	—	4	2	no	—
650	C₂²×C₄	—	4	4	no	—
651	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
652	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
653	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
654	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
655	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
656	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
657	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
658	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
659	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
660	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
661	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
662	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
663	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
664	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
665	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
666	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
667	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
668	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
669	Q₁₆	—	4	8	no	—
670	SD₁₆	—	4	8	no	—
671	M₁₆	—	4	4	no	—
672	C₂×C₈	C₂⁴×C₂₃	1	8	yes	—
673	C₄⋊C₄	—	2	2	no	—
674	C₄⋊C₄	—	2	2	no	—
675	C₄⋊C₄	—	2	2	no	—
676	C₄⋊C₄	—	2	2	no	—
677	C₄⋊C₄	—	2	2	no	—
678	C₄⋊C₄	—	2	2	no	—
679	C₄⋊C₄	—	2	2	no	—
680	C₄⋊C₄	—	2	2	no	—
681	C₄⋊C₄	—	2	2	no	—
682	C₄⋊C₄	—	2	2	no	—
683	C₄⋊C₄	—	2	2	no	—
684	C₄⋊C₄	—	2	2	no	—
685	C₄⋊C₄	—	2	4	no	—
686	C₄⋊C₄	—	2	4	no	—
687	C₄⋊C₄	—	2	4	no	—
688	C₄⋊C₄	—	2	4	no	—
689	C₄⋊C₄	—	2	2	no	—
690	C₄⋊C₄	—	2	2	no	—
691	C₄⋊C₄	—	2	1	no	—
692	C₄⋊C₄	—	2	1	no	—
693	C₄⋊C₄	—	2	2	no	—
694	C₄⋊C₄	C₂⁴×C₂₃	1	4	yes	—
695	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
696	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
697	C₂²⋊C₄	—	2	4	no	—
698	C₂²⋊C₄	—	2	4	no	—
699	C₂²⋊C₄	—	2	2	no	—
700	C₂²⋊C₄	—	2	2	no	—
701	C₂²⋊C₄	—	2	2	no	—
702	C₂²⋊C₄	—	2	2	no	—
703	C₂²⋊C₄	—	2	2	no	—
704	C₂²⋊C₄	—	2	2	no	—
705	C₂²⋊C₄	—	2	2	no	—
706	C₂²⋊C₄	—	2	2	no	—
707	C₂²⋊C₄	—	2	2	no	—
708	C₂²⋊C₄	—	2	2	no	—
709	C₄²	—	2	2	no	—
710	C₄²	—	2	2	no	—
711	C₄²	—	2	4	no	—
712	C₄²	—	2	4	no	—
713	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
714	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
715	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
716	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
717	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
718	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
719	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
720	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
721	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
722	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
723	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
724	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
725	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
726	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
727	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
728	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
729	C₂³	—	2	2	no	—
730	C₂³	—	2	2	no	—
731	C₂³	—	2	2	no	—
732	C₂³	—	4	1	no	—
733	C₂³	—	4	2	no	—
734	C₂³	—	4	2	no	—
735	C₂³	—	4	2	no	—
736	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
737	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
738	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
739	Q₈	—	2	8	no	—
740	Q₈	—	2	4	no	—
741	Q₈	—	4	2	no	—
742	Q₈	—	4	4	no	—
743	Q₈	—	4	4	no	—
744	Q₈	—	4	4	no	—
745	D₄	—	2	4	no	—
746	D₄	—	4	2	no	—
747	D₄	—	4	4	no	—
748	D₄	—	4	4	no	—
749	C₂×C₄	—	2	2	no	—
750	C₂×C₄	—	2	2	no	—
751	C₂×C₄	—	2	2	no	—
752	C₂×C₄	—	2	2	no	—
753	C₂×C₄	—	2	2	no	—
754	C₂×C₄	—	2	2	no	—
755	C₂×C₄	—	2	2	no	—
756	C₂×C₄	—	2	2	no	—
757	C₂×C₄	—	2	2	no	—
758	C₂×C₄	—	2	2	no	—
759	C₂×C₄	—	2	2	no	—
760	C₂×C₄	—	2	4	no	—
761	C₂×C₄	—	2	2	no	—
762	C₂×C₄	—	2	4	no	—
763	C₂×C₄	—	2	2	no	—
764	C₂×C₄	—	4	1	no	—
765	C₂×C₄	—	4	1	no	—
766	C₂×C₄	—	4	1	no	—
767	C₂×C₄	—	4	1	no	—
768	C₂×C₄	—	4	1	no	—
769	C₂×C₄	—	4	1	no	—
770	C₂×C₄	—	4	1	no	—
771	C₂×C₄	—	4	2	no	—
772	C₂×C₄	—	4	4	no	—
773	C₂×C₄	—	4	2	no	—
774	C₂×C₄	—	4	2	no	—
775	C₂×C₄	—	4	4	no	—
776	C₂×C₄	—	4	4	no	—
777	C₂×C₄	—	4	4	no	—
778	C₂×C₄	C₂₃×#137	1	4	yes	—
779	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
780	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
781	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
782	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
783	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
784	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
785	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
786	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
787	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
788	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
789	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
790	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
791	C₈	—	2	8	no	—
792	C₂²	—	2	1	no	—
793	C₂²	—	2	1	no	—
794	C₂²	—	2	1	no	—
795	C₂²	—	2	1	no	—
796	C₂²	—	2	1	no	—
797	C₂²	—	2	1	no	—
798	C₂²	—	2	1	no	—
799	C₂²	—	4	4	no	—
800	C₂²	—	4	2	no	—
801	C₂²	—	4	2	no	—
802	C₂²	—	4	2	no	—
803	C₂²	—	8	4	no	—
804	C₂²	C₂×C₂₃×#137	1	2	yes	—
805	C₂²	C₂₃×#575	1	2	yes	—
806	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
807	C₄	—	2	1	no	—
808	C₄	—	2	1	no	—
809	C₄	—	2	1	no	—
810	C₄	—	2	1	no	—
811	C₄	—	2	1	no	—
812	C₄	—	2	1	no	—
813	C₄	—	2	1	no	—
814	C₄	—	2	1	no	—
815	C₄	—	2	1	no	—
816	C₄	—	4	2	no	—
817	C₄	—	4	4	no	—
818	C₄	—	4	2	no	—
819	C₄	—	4	2	no	—
820	C₄	—	4	4	no	—
821	C₄	C₂×C₂₃×#137	1	2	yes	—
822	C₄	C₂×C₂₃×#137	1	2	yes	—
823	C₄	C₂₃×#585	1	2	yes	—
824	C₂	—	2	2	no	—
825	C₂	—	2	2	no	—
826	C₂	—	4	1	no	—
827	C₂	—	8	2	no	—
828	C₂	C₂₃×#3449	1	1	yes	characteristic
829	C₂	C₂²×C₂₃×#137	1	1	yes	characteristic
830	C₂	C₂×C₂₃×#575	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₂₃	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₂₃
socle	C₂²×C₂₃	C₂³×D₄
prime radical	C₂×C₂₃×#121	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₂₃ ◁ C₂²×C₄²×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₂₃×#533	C₂	semidirect
3. C₂₃×#3252	C₂	semidirect
4. C₂₃×#3238	C₂	semidirect
5. C₂₃×#3236	C₂	semidirect
6. C₂₃×#3218	C₂	semidirect
7. C₂₃×#3215	C₂	semidirect
8. C₂₃×#3195	C₂	semidirect
10. C₂₃×#3172	C₂	semidirect
11. C₂₃×#3108	C₂	semidirect
12. C₂₃×#3104	C₂	semidirect
13. C₂₃×#3101	C₂	semidirect
14. C₂₃×#2920	C₂	semidirect
21. C₂₃×#533	C₂²	semidirect
22. C₂₃×#533	C₂²	semidirect
23. C₂×C₂₃×C₄⋊Q₈	C₂²	semidirect
24. C₂×C₂₃×C₄⋊Q₈	C₂²	semidirect
44. C₂×C₄×Q₈×C₂₃	C₂²	semidirect
50. C₂₃×#501	C₂²	semidirect
51. C₂₃×#497	C₂²	semidirect
52. C₂₃×#491	C₂²	semidirect
53. C₂₃×#489	C₂²	semidirect
56. C₂₃×#483	C₂²	semidirect
58. C₂₃×#479	C₂²	semidirect
59. C₂₃×#477	C₂²	semidirect
60. C₂₃×#476	C₂²	semidirect
61. C₂₃×#470	C₂²	semidirect
63. C₂₃×#464	C₂²	semidirect
64. C₂₃×#462	C₂²	semidirect
65. C₂₃×#461	C₂²	semidirect
67. C₂₃×#451	C₂²	semidirect
70. C₄×Q₁₆×C₂₃	C₂²	semidirect
71. C₄×SD₁₆×C₂₃	C₂²	semidirect
73. C₂₃×#432	C₂²	semidirect
75. C₂₃×#431	C₂²	semidirect
76. C₂₃×#423	C₂²	semidirect
78. C₄×M₁₆×C₂₃	C₂²	semidirect
313. #60950	C₂₃	direct (N × H)
377. C₂×#533	C₂×C₂₃	semidirect
379. #3252	C₂×C₂₃	semidirect
380. #3238	C₂×C₂₃	semidirect
381. #3236	C₂×C₂₃	semidirect
382. #3218	C₂×C₂₃	semidirect
383. #3215	C₂×C₂₃	semidirect
384. #3195	C₂×C₂₃	semidirect
386. #3172	C₂×C₂₃	semidirect
387. #3108	C₂×C₂₃	semidirect
388. #3104	C₂×C₂₃	semidirect
389. #3101	C₂×C₂₃	semidirect
390. #2920	C₂×C₂₃	semidirect
429. #533	C₂²×C₂₃	semidirect
430. #533	C₂²×C₂₃	semidirect
431. C₂×C₄⋊Q₈	C₂²×C₂₃	semidirect
432. C₂×C₄⋊Q₈	C₂²×C₂₃	semidirect
452. C₂×C₄×Q₈	C₂²×C₂₃	semidirect
458. #501	C₂²×C₂₃	semidirect
459. #497	C₂²×C₂₃	semidirect
460. #491	C₂²×C₂₃	semidirect
461. #489	C₂²×C₂₃	semidirect
464. #483	C₂²×C₂₃	semidirect
466. #479	C₂²×C₂₃	semidirect
467. #477	C₂²×C₂₃	semidirect
468. #476	C₂²×C₂₃	semidirect
469. #470	C₂²×C₂₃	semidirect
471. #464	C₂²×C₂₃	semidirect
472. #462	C₂²×C₂₃	semidirect
473. #461	C₂²×C₂₃	semidirect
475. #451	C₂²×C₂₃	semidirect
478. C₄×Q₁₆	C₂²×C₂₃	semidirect
479. C₄×SD₁₆	C₂²×C₂₃	semidirect
481. #432	C₂²×C₂₃	semidirect
483. #431	C₂²×C₂₃	semidirect
484. #423	C₂²×C₂₃	semidirect
486. C₄×M₁₆	C₂²×C₂₃	semidirect
622. C₂₃	#60950	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₂₃×#533	2
C₂×C₂₃×#529	2
C₂₃×#3252	2
C₂₃×#3238	2
C₂₃×#3236	2
C₂₃×#3218	2
C₂₃×#3215	2
C₂₃×#3195	2
C₂₃×#3193	2
C₂₃×#3172	2
C₂₃×#3108	2
C₂₃×#3104	2
C₂₃×#3101	2
C₂₃×#2920	2
#60950	23

Subgroups — C23×#60950 #19208576

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#60950 #19208576