Subgroups — C₂₃×#36621 #19184247

Order 5888.

3202 conjugacy classes of subgroups.

The subgroup lattice has 814 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₃×#529	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂³×C₄²×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#2855	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₃×#2854	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₃×#2853	C₂	1	2	yes	maximal, complemented
6	C₂₃×#2852	C₂	1	4	yes	maximal, complemented
7	C₂₃×#2851	C₂	1	2	yes	maximal, complemented
8	C₂₃×#2850	C₂	1	2	yes	maximal, complemented
9	C₂₃×#2849	C₂	1	2	yes	maximal, complemented
10	C₂₃×#2848	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₃×#2847	C₂	1	1	yes	maximal, characteristic
12	C₄×C₂₃×C₂²⋊Q₈	C₂	1	2	yes	maximal, complemented
13	C₄×C₂₃×#123	C₂	1	2	yes	maximal, complemented
14	C₄×C₂₃×#121	C₂	1	2	yes	maximal, complemented
15	C₄×C₂₃×#120	C₂	1	2	yes	maximal, complemented
16	C₂₃×#2290	C₂	1	4	yes	maximal, complemented
17	C₂₃×#2283	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂⁴×C₄×C₂₃	C₂²	1	1	yes	characteristic
19	C₂⁴×C₄×C₂₃	C₂²	1	1	yes	characteristic
20	C₂⁴×C₄×C₂₃	C₂²	1	1	yes	characteristic
21	C₂₃×#529	—	2	8	no	—
22	C₂×C₂₃×#126	C₂²	1	2	yes	complemented
23	C₂×C₂₃×#125	C₂²	1	1	yes	characteristic, complemented
24	C₂×C₂₃×#124	C₂²	1	1	yes	characteristic, complemented
25	C₂×C₂₃×#123	C₂²	1	2	yes	—
26	C₂×C₂₃×#123	C₂²	1	2	yes	—
27	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
28	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	2	yes	—
29	C₂×C₂₃×#121	C₂²	1	1	yes	characteristic
30	C₂×C₂₃×#121	C₂²	1	2	yes	—
31	C₂×C₂₃×#120	C₂²	1	2	yes	—
32	C₂×C₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic, complemented
33	C₂×C₄×D₄×C₂₃	C₂²	1	2	yes	—
34	C₂×C₄×D₄×C₂₃	C₂²	1	4	yes	—
35	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic, complemented
36	C₂×C₂₃×#117	C₂²	1	2	yes	complemented
37	C₂²×C₄²×C₂₃	—	2	8	no	—
38	C₂²×C₄²×C₂₃	C₂²	1	2	yes	—
39	C₂²×C₄²×C₂₃	C₂²	1	2	yes	—
40	C₂²×C₄²×C₂₃	C₂²	1	1	yes	characteristic
41	C₂²×C₄²×C₂₃	C₂²	1	2	yes	—
42	C₂²×C₄²×C₂₃	C₂²	1	2	yes	—
43	C₂²×C₄²×C₂₃	C₂²	1	1	yes	characteristic
44	C₂²×C₄²×C₂₃	C₂²	1	1	yes	characteristic
45	C₂²×C₄²×C₂₃	C₂²	1	1	yes	characteristic
46	C₂₃×#391	C₂²	1	2	yes	complemented
47	C₂₃×#390	C₂²	1	2	yes	complemented
48	C₂₃×#389	C₂²	1	2	yes	complemented
49	C₂₃×#389	C₂²	1	2	yes	complemented
50	C₂₃×#388	C₂²	1	4	yes	complemented
51	C₂₃×#388	C₂²	1	4	yes	complemented
52	C₂₃×#388	C₂²	1	4	yes	complemented
53	C₂₃×#388	C₂²	1	4	yes	complemented
54	C₂₃×#387	C₂²	1	4	yes	complemented
55	C₂₃×#387	C₂²	1	4	yes	complemented
56	C₂₃×#387	C₂²	1	4	yes	complemented
57	C₂₃×#387	C₂²	1	4	yes	complemented
58	C₂₃×#386	C₂²	1	4	yes	—
59	C₂₃×#386	C₂²	1	4	yes	—
60	C₂₃×#386	C₂²	1	4	yes	—
61	C₂₃×#386	C₂²	1	2	yes	—
62	C₂₃×#386	C₂²	1	4	yes	—
63	C₂₃×#386	C₂²	1	2	yes	—
64	C₂₃×#385	C₂²	1	4	yes	—
65	C₂₃×#385	C₂²	1	4	yes	—
66	C₂₃×#385	C₂²	1	4	yes	—
67	C₂₃×#385	C₂²	1	2	yes	—
68	C₂₃×#385	C₂²	1	2	yes	—
69	C₂₃×#385	C₂²	1	4	yes	—
70	C₂₃×#383	C₂²	1	2	yes	complemented
71	C₂₃×#382	C₂²	1	2	yes	complemented
72	C₂₃×#381	C₂²	1	2	yes	—
73	C₂₃×#381	C₂²	1	2	yes	—
74	C₂₃×#380	C₂²	1	1	yes	characteristic
75	C₂₃×#380	C₂²	1	1	yes	characteristic
76	C₂₃×#380	C₂²	1	2	yes	—
77	C₂₃×#380	C₂²	1	2	yes	—
78	C₂₃×#379	C₂²	1	2	yes	—
79	C₄×C₄⋊C₄×C₂₃	C₂²	1	2	yes	complemented
80	C₄×C₄⋊C₄×C₂₃	C₂²	1	4	yes	complemented
81	C₄×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	—
82	C₄×C₂²⋊C₄×C₂₃	C₂²	1	4	yes	—
83	C₄×C₂²⋊C₄×C₂₃	C₂²	1	4	yes	complemented
84	C₂₃×#376	C₂²	1	2	yes	complemented
85	C₂⁵×C₂₃	C₂³	1	1	yes	characteristic
86	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
87	C₂²×D₄×C₂₃	C₂³	1	4	yes	—
88	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
89	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
90	C₂³×C₄×C₂₃	—	2	4	no	—
91	C₂³×C₄×C₂₃	—	2	4	no	—
92	C₂³×C₄×C₂₃	—	2	4	no	—
93	C₂³×C₄×C₂₃	—	2	4	no	—
94	C₂³×C₄×C₂₃	—	2	8	no	—
95	C₂³×C₄×C₂₃	—	2	8	no	—
96	C₂³×C₄×C₂₃	—	2	4	no	—
97	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
98	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
99	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
100	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
101	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
102	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
103	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
104	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
105	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
106	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
107	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
108	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
109	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
110	C₂₃×#126	—	2	8	no	—
111	C₂₃×#125	—	2	4	no	—
112	C₂₃×#124	—	2	4	no	—
113	C₂₃×#123	—	2	8	no	—
114	C₂₃×#123	—	2	8	no	—
115	C₂₃×C₂²⋊Q₈	—	2	4	no	—
116	C₂₃×C₂²⋊Q₈	—	2	8	no	—
117	C₂₃×#121	—	2	4	no	—
118	C₂₃×#121	—	2	8	no	—
119	C₂₃×#120	—	2	8	no	—
120	C₄×Q₈×C₂₃	—	2	4	no	—
121	C₄×D₄×C₂₃	—	2	8	no	—
122	C₄×D₄×C₂₃	—	2	16	no	—
123	C₄×D₄×C₂₃	—	2	4	no	—
124	C₂₃×#117	—	2	8	no	—
125	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
126	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
127	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
128	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
129	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
130	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
131	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
132	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
133	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
134	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
135	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
136	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
137	C₂×C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
138	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
139	C₂×C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
140	C₂×C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
141	C₂×C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
142	C₂×C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
143	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
144	C₂×C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
145	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
146	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
147	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
148	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
149	C₂×C₄²×C₂₃	—	2	4	no	—
150	C₂×C₄²×C₂₃	—	2	4	no	—
151	C₂×C₄²×C₂₃	—	2	4	no	—
152	C₂×C₄²×C₂₃	—	2	8	no	—
153	C₂×C₄²×C₂₃	—	2	8	no	—
154	C₂×C₄²×C₂₃	—	2	8	no	—
155	C₂×C₄²×C₂₃	—	2	8	no	—
156	C₂×C₄²×C₂₃	D₄	1	8	yes	complemented
157	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
158	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
159	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
160	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
161	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
162	C₂×C₄²×C₂₃	C₂³	1	4	yes	—
163	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
164	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
165	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
166	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
167	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
168	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
169	C₂₃×#95	C₂³	1	2	yes	—
170	C₂₃×#95	C₂³	1	2	yes	—
171	C₂₃×#95	C₂³	1	4	yes	—
172	C₂₃×#95	C₂³	1	4	yes	—
173	C₂₃×#95	C₂³	1	4	yes	—
174	C₂₃×#95	C₂³	1	4	yes	—
175	C₂₃×#95	C₂³	1	4	yes	—
176	C₂₃×#95	C₂³	1	4	yes	—
177	C₂₃×#95	C₂³	1	4	yes	—
178	C₂₃×#95	C₂³	1	4	yes	—
179	C₂₃×#95	C₂³	1	4	yes	—
180	C₂⁴×C₂₃	—	2	2	no	—
181	C₂⁴×C₂₃	—	2	4	no	—
182	C₂⁴×C₂₃	—	2	4	no	—
183	C₂⁴×C₂₃	—	2	2	no	—
184	C₂⁴×C₂₃	#41	1	4	yes	—
185	C₂⁴×C₂₃	C₂⁴	1	2	yes	—
186	C₂⁴×C₂₃	C₂⁴	1	1	yes	characteristic
187	C₂⁴×C₂₃	C₂⁴	1	2	yes	—
188	C₂×Q₈×C₂₃	—	2	2	no	—
189	C₂×Q₈×C₂₃	—	2	4	no	—
190	C₂×D₄×C₂₃	—	2	4	no	—
191	C₂×D₄×C₂₃	—	2	8	no	—
192	C₂×D₄×C₂₃	—	2	4	no	—
193	C₂×D₄×C₂₃	—	2	8	no	—
194	C₂×D₄×C₂₃	—	2	8	no	—
195	C₂×D₄×C₂₃	—	2	4	no	—
196	C₂×D₄×C₂₃	—	2	2	no	—
197	C₂×D₄×C₂₃	—	2	4	no	—
198	C₂²×C₄×C₂₃	—	2	32	no	—
199	C₂²×C₄×C₂₃	—	2	32	no	—
200	C₂²×C₄×C₂₃	—	2	32	no	—
201	C₂²×C₄×C₂₃	—	2	2	no	—
202	C₂²×C₄×C₂₃	—	2	2	no	—
203	C₂²×C₄×C₂₃	—	2	2	no	—
204	C₂²×C₄×C₂₃	—	2	4	no	—
205	C₂²×C₄×C₂₃	—	2	4	no	—
206	C₂²×C₄×C₂₃	—	2	4	no	—
207	C₂²×C₄×C₂₃	—	2	4	no	—
208	C₂²×C₄×C₂₃	—	2	2	no	—
209	C₂²×C₄×C₂₃	—	2	2	no	—
210	C₂²×C₄×C₂₃	—	2	2	no	—
211	C₂²×C₄×C₂₃	—	2	4	no	—
212	C₂²×C₄×C₂₃	—	2	4	no	—
213	C₂²×C₄×C₂₃	—	2	4	no	—
214	C₂²×C₄×C₂₃	—	2	4	no	—
215	C₂²×C₄×C₂₃	—	2	4	no	—
216	C₂²×C₄×C₂₃	—	2	4	no	—
217	C₂²×C₄×C₂₃	—	2	4	no	—
218	C₂²×C₄×C₂₃	—	2	4	no	—
219	C₂²×C₄×C₂₃	—	2	4	no	—
220	C₂²×C₄×C₂₃	—	2	4	no	—
221	C₂²×C₄×C₂₃	—	2	4	no	—
222	C₂²×C₄×C₂₃	—	2	4	no	—
223	C₂²×C₄×C₂₃	—	2	4	no	—
224	C₂²×C₄×C₂₃	—	2	4	no	—
225	C₂²×C₄×C₂₃	—	2	4	no	—
226	C₂²×C₄×C₂₃	—	2	4	no	—
227	C₂²×C₄×C₂₃	—	2	4	no	—
228	C₂²×C₄×C₂₃	—	2	8	no	—
229	C₂²×C₄×C₂₃	C₂×D₄	1	4	yes	—
230	C₂²×C₄×C₂₃	C₂×D₄	1	4	yes	—
231	C₂²×C₄×C₂₃	C₂×D₄	1	4	yes	—
232	C₂²×C₄×C₂₃	#41	1	8	yes	—
233	C₂²×C₄×C₂₃	#41	1	8	yes	—
234	C₂²×C₄×C₂₃	#41	1	4	yes	—
235	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
236	C₂²×C₄×C₂₃	C₂⁴	1	4	yes	—
237	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
238	C₂²×C₄×C₂₃	C₂⁴	1	4	yes	—
239	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
240	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
241	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
242	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
243	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
244	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
245	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
246	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
247	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
248	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
249	C₄⋊C₄×C₂₃	—	2	4	no	—
250	C₄⋊C₄×C₂₃	—	2	4	no	—
251	C₄⋊C₄×C₂₃	—	2	2	no	—
252	C₄⋊C₄×C₂₃	—	2	4	no	—
253	C₄⋊C₄×C₂₃	—	2	2	no	—
254	C₄⋊C₄×C₂₃	—	2	4	no	—
255	C₄⋊C₄×C₂₃	—	2	8	no	—
256	C₄⋊C₄×C₂₃	—	2	4	no	—
257	C₄⋊C₄×C₂₃	—	2	4	no	—
258	C₄⋊C₄×C₂₃	—	2	8	no	—
259	C₄⋊C₄×C₂₃	—	2	8	no	—
260	C₂²⋊C₄×C₂₃	—	2	4	no	—
261	C₂²⋊C₄×C₂₃	—	2	8	no	—
262	C₂²⋊C₄×C₂₃	—	2	4	no	—
263	C₂²⋊C₄×C₂₃	—	2	8	no	—
264	C₂²⋊C₄×C₂₃	—	2	8	no	—
265	C₂²⋊C₄×C₂₃	—	2	4	no	—
266	C₂²⋊C₄×C₂₃	—	2	4	no	—
267	C₂²⋊C₄×C₂₃	—	2	4	no	—
268	C₂²⋊C₄×C₂₃	—	2	4	no	—
269	C₂²⋊C₄×C₂₃	—	2	4	no	—
270	C₂²⋊C₄×C₂₃	—	2	8	no	—
271	C₂²⋊C₄×C₂₃	—	2	8	no	—
272	C₂²⋊C₄×C₂₃	—	2	8	no	—
273	C₄²×C₂₃	—	2	4	no	—
274	C₄²×C₂₃	—	2	4	no	—
275	C₄²×C₂₃	—	2	4	no	—
276	C₄²×C₂₃	—	2	4	no	—
277	C₄²×C₂₃	—	2	4	no	—
278	C₄²×C₂₃	—	2	4	no	—
279	C₄²×C₂₃	—	2	4	no	—
280	C₄²×C₂₃	—	2	8	no	—
281	C₄²×C₂₃	C₂×D₄	1	4	yes	—
282	C₄²×C₂₃	C₂×D₄	1	4	yes	—
283	C₄²×C₂₃	C₂×D₄	1	4	yes	—
284	C₄²×C₂₃	C₂×D₄	1	4	yes	—
285	#36621	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
286	C₂³×C₂₃	—	2	8	no	—
287	C₂³×C₂₃	—	2	8	no	—
288	C₂³×C₂₃	—	2	16	no	—
289	C₂³×C₂₃	—	2	8	no	—
290	C₂³×C₂₃	—	2	16	no	—
291	C₂³×C₂₃	—	2	2	no	—
292	C₂³×C₂₃	—	2	2	no	—
293	C₂³×C₂₃	—	2	2	no	—
294	C₂³×C₂₃	—	2	2	no	—
295	C₂³×C₂₃	—	2	2	no	—
296	C₂³×C₂₃	—	2	2	no	—
297	C₂³×C₂₃	—	2	2	no	—
298	C₂³×C₂₃	—	2	2	no	—
299	C₂³×C₂₃	—	2	4	no	—
300	C₂³×C₂₃	—	2	4	no	—
301	C₂³×C₂₃	—	2	2	no	—
302	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
303	C₂³×C₂₃	C₂×#41	1	2	yes	—
304	C₂³×C₂₃	C₂×#41	1	2	yes	—
305	C₂³×C₂₃	C₂×#41	1	4	yes	—
306	C₂³×C₂₃	C₂×#41	1	4	yes	—
307	C₂³×C₂₃	C₂×#41	1	4	yes	—
308	C₂³×C₂₃	C₂⁵	1	1	yes	characteristic
309	Q₈×C₂₃	—	4	4	no	—
310	D₄×C₂₃	—	4	8	no	—
311	D₄×C₂₃	—	4	16	no	—
312	D₄×C₂₃	—	4	4	no	—
313	C₂×C₄×C₂₃	—	2	16	no	—
314	C₂×C₄×C₂₃	—	2	16	no	—
315	C₂×C₄×C₂₃	—	2	16	no	—
316	C₂×C₄×C₂₃	—	2	16	no	—
317	C₂×C₄×C₂₃	—	2	8	no	—
318	C₂×C₄×C₂₃	—	2	8	no	—
319	C₂×C₄×C₂₃	—	2	8	no	—
320	C₂×C₄×C₂₃	—	2	8	no	—
321	C₂×C₄×C₂₃	—	2	2	no	—
322	C₂×C₄×C₂₃	—	2	2	no	—
323	C₂×C₄×C₂₃	—	2	2	no	—
324	C₂×C₄×C₂₃	—	2	1	no	—
325	C₂×C₄×C₂₃	—	2	1	no	—
326	C₂×C₄×C₂₃	—	2	2	no	—
327	C₂×C₄×C₂₃	—	2	2	no	—
328	C₂×C₄×C₂₃	—	2	1	no	—
329	C₂×C₄×C₂₃	—	2	1	no	—
330	C₂×C₄×C₂₃	—	2	2	no	—
331	C₂×C₄×C₂₃	—	2	2	no	—
332	C₂×C₄×C₂₃	—	2	2	no	—
333	C₂×C₄×C₂₃	—	2	8	no	—
334	C₂×C₄×C₂₃	—	2	8	no	—
335	C₂×C₄×C₂₃	—	2	16	no	—
336	C₂×C₄×C₂₃	—	2	16	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	4	no	—
341	C₂×C₄×C₂₃	—	2	4	no	—
342	C₂×C₄×C₂₃	—	2	4	no	—
343	C₂×C₄×C₂₃	—	2	2	no	—
344	C₂×C₄×C₂₃	—	2	4	no	—
345	C₂×C₄×C₂₃	—	2	4	no	—
346	C₂×C₄×C₂₃	—	2	4	no	—
347	C₂×C₄×C₂₃	—	2	4	no	—
348	C₂×C₄×C₂₃	—	2	4	no	—
349	C₂×C₄×C₂₃	—	2	2	no	—
350	C₂×C₄×C₂₃	—	4	8	no	—
351	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
352	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
353	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
354	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
355	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
356	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
357	C₂×C₄×C₂₃	C₂×#41	1	4	yes	—
358	C₂×C₄×C₂₃	C₂×#41	1	4	yes	—
359	C₂×C₄×C₂₃	C₂×#41	1	4	yes	—
360	C₂×C₄×C₂₃	C₂×#41	1	4	yes	—
361	C₂×C₄×C₂₃	C₂×#41	1	4	yes	—
362	C₂×#529	C₂×C₂₃	1	1	yes	characteristic, complemented
363	C₂³×C₄²	C₂×C₂₃	1	1	yes	characteristic, complemented
364	#2855	C₂×C₂₃	1	1	yes	characteristic, complemented
365	#2854	C₂×C₂₃	1	1	yes	characteristic, complemented
366	#2853	C₂×C₂₃	1	2	yes	complemented
367	#2852	C₂×C₂₃	1	4	yes	complemented
368	#2851	C₂×C₂₃	1	2	yes	complemented
369	#2850	C₂×C₂₃	1	2	yes	complemented
370	#2849	C₂×C₂₃	1	2	yes	complemented
371	#2848	C₂×C₂₃	1	1	yes	characteristic, complemented
372	#2847	C₂×C₂₃	1	1	yes	characteristic
373	C₄×C₂²⋊Q₈	C₂×C₂₃	1	2	yes	complemented
374	C₄×#123	C₂×C₂₃	1	2	yes	complemented
375	C₄×#121	C₂×C₂₃	1	2	yes	complemented
376	C₄×#120	C₂×C₂₃	1	2	yes	complemented
377	#2290	C₂×C₂₃	1	4	yes	complemented
378	#2283	C₂×C₂₃	1	1	yes	characteristic, complemented
379	C₂²×C₂₃	—	2	32	no	—
380	C₂²×C₂₃	—	2	2	no	—
381	C₂²×C₂₃	—	2	2	no	—
382	C₂²×C₂₃	—	2	4	no	—
383	C₂²×C₂₃	—	2	4	no	—
384	C₂²×C₂₃	—	2	4	no	—
385	C₂²×C₂₃	—	2	4	no	—
386	C₂²×C₂₃	—	2	4	no	—
387	C₂²×C₂₃	—	2	4	no	—
388	C₂²×C₂₃	—	2	4	no	—
389	C₂²×C₂₃	—	2	4	no	—
390	C₂²×C₂₃	—	4	2	no	—
391	C₂²×C₂₃	—	4	2	no	—
392	C₂²×C₂₃	—	4	2	no	—
393	C₂²×C₂₃	—	4	4	no	—
394	C₂²×C₂₃	—	4	4	no	—
395	C₂²×C₂₃	#525	1	4	yes	—
396	C₂²×C₂₃	#529	1	8	yes	complemented
397	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
398	C₂²×C₂₃	C₂²×#41	1	1	yes	characteristic
399	C₂²×C₂₃	C₂²×#41	1	2	yes	—
400	C₂²×C₂₃	C₂²×#41	1	2	yes	—
401	C₂²×C₂₃	C₂²×#41	1	1	yes	characteristic
402	C₄×C₂₃	—	2	2	no	—
403	C₄×C₂₃	—	2	2	no	—
404	C₄×C₂₃	—	2	2	no	—
405	C₄×C₂₃	—	2	2	no	—
406	C₄×C₂₃	—	2	4	no	—
407	C₄×C₂₃	—	2	4	no	—
408	C₄×C₂₃	—	2	4	no	—
409	C₄×C₂₃	—	4	2	no	—
410	C₄×C₂₃	—	4	2	no	—
411	C₄×C₂₃	—	4	2	no	—
412	C₄×C₂₃	—	4	4	no	—
413	C₄×C₂₃	—	4	4	no	—
414	C₄×C₂₃	#525	1	4	yes	—
415	C₄×C₂₃	#525	1	4	yes	—
416	C₂⁴×C₄	C₂²×C₂₃	1	1	yes	characteristic
417	C₂⁴×C₄	C₂²×C₂₃	1	1	yes	characteristic
418	C₂⁴×C₄	C₂²×C₂₃	1	1	yes	characteristic
419	#529	—	2	8	no	—
420	C₂×#126	C₂²×C₂₃	1	2	yes	complemented
421	C₂×#125	C₂²×C₂₃	1	1	yes	characteristic, complemented
422	C₂×#124	C₂²×C₂₃	1	1	yes	characteristic, complemented
423	C₂×#123	C₂²×C₂₃	1	2	yes	—
424	C₂×#123	C₂²×C₂₃	1	2	yes	—
425	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	2	yes	—
426	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
427	C₂×#121	C₂²×C₂₃	1	2	yes	—
428	C₂×#121	C₂²×C₂₃	1	1	yes	characteristic
429	C₂×#120	C₂²×C₂₃	1	2	yes	—
430	C₂×C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
431	C₂×C₄×D₄	C₂²×C₂₃	1	2	yes	—
432	C₂×C₄×D₄	C₂²×C₂₃	1	4	yes	—
433	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic, complemented
434	C₂×#117	C₂²×C₂₃	1	2	yes	complemented
435	C₂²×C₄²	—	2	8	no	—
436	C₂²×C₄²	C₂²×C₂₃	1	2	yes	—
437	C₂²×C₄²	C₂²×C₂₃	1	2	yes	—
438	C₂²×C₄²	C₂²×C₂₃	1	1	yes	characteristic
439	C₂²×C₄²	C₂²×C₂₃	1	1	yes	characteristic
440	C₂²×C₄²	C₂²×C₂₃	1	2	yes	—
441	C₂²×C₄²	C₂²×C₂₃	1	2	yes	—
442	C₂²×C₄²	C₂²×C₂₃	1	1	yes	characteristic
443	C₂²×C₄²	C₂²×C₂₃	1	1	yes	characteristic
444	#391	C₂²×C₂₃	1	2	yes	complemented
445	#390	C₂²×C₂₃	1	2	yes	complemented
446	#389	C₂²×C₂₃	1	2	yes	complemented
447	#389	C₂²×C₂₃	1	2	yes	complemented
448	#388	C₂²×C₂₃	1	4	yes	complemented
449	#388	C₂²×C₂₃	1	4	yes	complemented
450	#388	C₂²×C₂₃	1	4	yes	complemented
451	#388	C₂²×C₂₃	1	4	yes	complemented
452	#387	C₂²×C₂₃	1	4	yes	complemented
453	#387	C₂²×C₂₃	1	4	yes	complemented
454	#387	C₂²×C₂₃	1	4	yes	complemented
455	#387	C₂²×C₂₃	1	4	yes	complemented
456	#386	C₂²×C₂₃	1	4	yes	—
457	#386	C₂²×C₂₃	1	2	yes	—
458	#386	C₂²×C₂₃	1	4	yes	—
459	#386	C₂²×C₂₃	1	4	yes	—
460	#386	C₂²×C₂₃	1	4	yes	—
461	#386	C₂²×C₂₃	1	2	yes	—
462	#385	C₂²×C₂₃	1	4	yes	—
463	#385	C₂²×C₂₃	1	2	yes	—
464	#385	C₂²×C₂₃	1	4	yes	—
465	#385	C₂²×C₂₃	1	4	yes	—
466	#385	C₂²×C₂₃	1	4	yes	—
467	#385	C₂²×C₂₃	1	2	yes	—
468	#383	C₂²×C₂₃	1	2	yes	complemented
469	#382	C₂²×C₂₃	1	2	yes	complemented
470	#381	C₂²×C₂₃	1	2	yes	—
471	#381	C₂²×C₂₃	1	2	yes	—
472	#380	C₂²×C₂₃	1	2	yes	—
473	#380	C₂²×C₂₃	1	1	yes	characteristic
474	#380	C₂²×C₂₃	1	2	yes	—
475	#380	C₂²×C₂₃	1	1	yes	characteristic
476	#379	C₂²×C₂₃	1	2	yes	—
477	C₄×C₄⋊C₄	C₂²×C₂₃	1	2	yes	complemented
478	C₄×C₄⋊C₄	C₂²×C₂₃	1	4	yes	complemented
479	C₄×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
480	C₄×C₂²⋊C₄	C₂²×C₂₃	1	4	yes	—
481	C₄×C₂²⋊C₄	C₂²×C₂₃	1	4	yes	complemented
482	#376	C₂²×C₂₃	1	2	yes	complemented
483	C₂×C₂₃	—	2	4	no	—
484	C₂×C₂₃	—	2	8	no	—
485	C₂×C₂₃	—	8	2	no	—
486	C₂×C₂₃	C₂×#525	1	1	yes	characteristic
487	C₂×C₂₃	C₂×#525	1	1	yes	characteristic
488	C₂×C₂₃	C₂×#525	1	1	yes	characteristic
489	C₂×C₂₃	C₂×#529	1	2	yes	—
490	C₂×C₂₃	#3444	1	2	yes	—
491	C₂⁵	C₂³×C₂₃	1	1	yes	characteristic
492	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
493	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
494	C₂²×D₄	C₂³×C₂₃	1	4	yes	—
495	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
496	C₂³×C₄	—	2	4	no	—
497	C₂³×C₄	—	2	4	no	—
498	C₂³×C₄	—	2	4	no	—
499	C₂³×C₄	—	2	4	no	—
500	C₂³×C₄	—	2	8	no	—
501	C₂³×C₄	—	2	8	no	—
502	C₂³×C₄	—	2	4	no	—
503	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
504	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
505	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
506	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
507	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
508	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
509	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
510	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
511	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
512	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
513	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
514	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
515	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
516	#126	—	2	8	no	—
517	#125	—	2	4	no	—
518	#124	—	2	4	no	—
519	#123	—	2	8	no	—
520	#123	—	2	8	no	—
521	C₂²⋊Q₈	—	2	4	no	—
522	C₂²⋊Q₈	—	2	8	no	—
523	#121	—	2	4	no	—
524	#121	—	2	8	no	—
525	#120	—	2	8	no	—
526	C₄×Q₈	—	2	4	no	—
527	C₄×D₄	—	2	8	no	—
528	C₄×D₄	—	2	16	no	—
529	C₄×D₄	—	2	4	no	—
530	#117	—	2	8	no	—
531	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
532	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
533	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
534	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
535	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
536	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
537	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
538	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
539	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
540	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
541	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
542	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
543	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
544	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
545	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
546	C₂×C₂²⋊C₄	C₂³×C₂₃	1	4	yes	—
547	C₂×C₂²⋊C₄	C₂³×C₂₃	1	4	yes	—
548	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
549	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
550	C₂×C₂²⋊C₄	C₂³×C₂₃	1	4	yes	—
551	C₂×C₂²⋊C₄	C₂³×C₂₃	1	4	yes	—
552	C₂×C₂²⋊C₄	C₂³×C₂₃	1	4	yes	—
553	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
554	C₂×C₂²⋊C₄	C₂³×C₂₃	1	4	yes	—
555	C₂×C₄²	—	2	4	no	—
556	C₂×C₄²	—	2	4	no	—
557	C₂×C₄²	—	2	4	no	—
558	C₂×C₄²	—	2	8	no	—
559	C₂×C₄²	—	2	8	no	—
560	C₂×C₄²	—	2	8	no	—
561	C₂×C₄²	—	2	8	no	—
562	C₂×C₄²	D₄×C₂₃	1	8	yes	complemented
563	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
564	C₂×C₄²	C₂³×C₂₃	1	4	yes	—
565	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
566	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
567	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
568	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
569	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
570	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
571	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
572	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
573	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
574	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
575	#95	C₂³×C₂₃	1	2	yes	—
576	#95	C₂³×C₂₃	1	2	yes	—
577	#95	C₂³×C₂₃	1	4	yes	—
578	#95	C₂³×C₂₃	1	4	yes	—
579	#95	C₂³×C₂₃	1	4	yes	—
580	#95	C₂³×C₂₃	1	4	yes	—
581	#95	C₂³×C₂₃	1	4	yes	—
582	#95	C₂³×C₂₃	1	4	yes	—
583	#95	C₂³×C₂₃	1	4	yes	—
584	#95	C₂³×C₂₃	1	4	yes	—
585	#95	C₂³×C₂₃	1	4	yes	—
586	C₂₃	#36621	1	1	yes	characteristic, direct product factor, Sylow
587	C₂⁴	—	2	2	no	—
588	C₂⁴	—	2	4	no	—
589	C₂⁴	—	2	4	no	—
590	C₂⁴	—	2	2	no	—
591	C₂⁴	#41×C₂₃	1	4	yes	—
592	C₂⁴	C₂⁴×C₂₃	1	2	yes	—
593	C₂⁴	C₂⁴×C₂₃	1	1	yes	characteristic
594	C₂⁴	C₂⁴×C₂₃	1	2	yes	—
595	C₂×Q₈	—	2	2	no	—
596	C₂×Q₈	—	2	4	no	—
597	C₂×D₄	—	2	4	no	—
598	C₂×D₄	—	2	8	no	—
599	C₂×D₄	—	2	4	no	—
600	C₂×D₄	—	2	8	no	—
601	C₂×D₄	—	2	8	no	—
602	C₂×D₄	—	2	4	no	—
603	C₂×D₄	—	2	2	no	—
604	C₂×D₄	—	2	4	no	—
605	C₂²×C₄	—	2	32	no	—
606	C₂²×C₄	—	2	32	no	—
607	C₂²×C₄	—	2	32	no	—
608	C₂²×C₄	—	2	2	no	—
609	C₂²×C₄	—	2	2	no	—
610	C₂²×C₄	—	2	2	no	—
611	C₂²×C₄	—	2	4	no	—
612	C₂²×C₄	—	2	4	no	—
613	C₂²×C₄	—	2	4	no	—
614	C₂²×C₄	—	2	4	no	—
615	C₂²×C₄	—	2	2	no	—
616	C₂²×C₄	—	2	2	no	—
617	C₂²×C₄	—	2	2	no	—
618	C₂²×C₄	—	2	4	no	—
619	C₂²×C₄	—	2	4	no	—
620	C₂²×C₄	—	2	4	no	—
621	C₂²×C₄	—	2	4	no	—
622	C₂²×C₄	—	2	4	no	—
623	C₂²×C₄	—	2	4	no	—
624	C₂²×C₄	—	2	4	no	—
625	C₂²×C₄	—	2	4	no	—
626	C₂²×C₄	—	2	4	no	—
627	C₂²×C₄	—	2	4	no	—
628	C₂²×C₄	—	2	4	no	—
629	C₂²×C₄	—	2	4	no	—
630	C₂²×C₄	—	2	4	no	—
631	C₂²×C₄	—	2	4	no	—
632	C₂²×C₄	—	2	4	no	—
633	C₂²×C₄	—	2	4	no	—
634	C₂²×C₄	—	2	4	no	—
635	C₂²×C₄	—	2	8	no	—
636	C₂²×C₄	C₂×D₄×C₂₃	1	4	yes	—
637	C₂²×C₄	C₂×D₄×C₂₃	1	4	yes	—
638	C₂²×C₄	C₂×D₄×C₂₃	1	4	yes	—
639	C₂²×C₄	#41×C₂₃	1	8	yes	—
640	C₂²×C₄	#41×C₂₃	1	8	yes	—
641	C₂²×C₄	#41×C₂₃	1	4	yes	—
642	C₂²×C₄	C₂⁴×C₂₃	1	4	yes	—
643	C₂²×C₄	C₂⁴×C₂₃	1	4	yes	—
644	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
645	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
646	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
647	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
648	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
649	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
650	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
651	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
652	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
653	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
654	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
655	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
656	C₄⋊C₄	—	2	4	no	—
657	C₄⋊C₄	—	2	4	no	—
658	C₄⋊C₄	—	2	2	no	—
659	C₄⋊C₄	—	2	4	no	—
660	C₄⋊C₄	—	2	2	no	—
661	C₄⋊C₄	—	2	4	no	—
662	C₄⋊C₄	—	2	8	no	—
663	C₄⋊C₄	—	2	4	no	—
664	C₄⋊C₄	—	2	4	no	—
665	C₄⋊C₄	—	2	8	no	—
666	C₄⋊C₄	—	2	8	no	—
667	C₂²⋊C₄	—	2	4	no	—
668	C₂²⋊C₄	—	2	8	no	—
669	C₂²⋊C₄	—	2	4	no	—
670	C₂²⋊C₄	—	2	8	no	—
671	C₂²⋊C₄	—	2	8	no	—
672	C₂²⋊C₄	—	2	4	no	—
673	C₂²⋊C₄	—	2	4	no	—
674	C₂²⋊C₄	—	2	4	no	—
675	C₂²⋊C₄	—	2	4	no	—
676	C₂²⋊C₄	—	2	4	no	—
677	C₂²⋊C₄	—	2	8	no	—
678	C₂²⋊C₄	—	2	8	no	—
679	C₂²⋊C₄	—	2	8	no	—
680	C₄²	—	2	4	no	—
681	C₄²	—	2	4	no	—
682	C₄²	—	2	4	no	—
683	C₄²	—	2	4	no	—
684	C₄²	—	2	4	no	—
685	C₄²	—	2	4	no	—
686	C₄²	—	2	4	no	—
687	C₄²	—	2	8	no	—
688	C₄²	C₂×D₄×C₂₃	1	4	yes	—
689	C₄²	C₂×D₄×C₂₃	1	4	yes	—
690	C₄²	C₂×D₄×C₂₃	1	4	yes	—
691	C₄²	C₂×D₄×C₂₃	1	4	yes	—
692	C₂³	—	2	8	no	—
693	C₂³	—	2	8	no	—
694	C₂³	—	2	16	no	—
695	C₂³	—	2	2	no	—
696	C₂³	—	2	2	no	—
697	C₂³	—	2	2	no	—
698	C₂³	—	2	2	no	—
699	C₂³	—	2	2	no	—
700	C₂³	—	2	2	no	—
701	C₂³	—	2	8	no	—
702	C₂³	—	2	16	no	—
703	C₂³	—	2	2	no	—
704	C₂³	—	2	2	no	—
705	C₂³	—	2	4	no	—
706	C₂³	—	2	4	no	—
707	C₂³	—	2	2	no	—
708	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
709	C₂³	C₂×#41×C₂₃	1	2	yes	—
710	C₂³	C₂×#41×C₂₃	1	2	yes	—
711	C₂³	C₂×#41×C₂₃	1	4	yes	—
712	C₂³	C₂×#41×C₂₃	1	4	yes	—
713	C₂³	C₂×#41×C₂₃	1	4	yes	—
714	C₂³	C₂⁵×C₂₃	1	1	yes	characteristic
715	Q₈	—	4	4	no	—
716	D₄	—	4	8	no	—
717	D₄	—	4	16	no	—
718	D₄	—	4	4	no	—
719	C₂×C₄	—	2	16	no	—
720	C₂×C₄	—	2	16	no	—
721	C₂×C₄	—	2	16	no	—
722	C₂×C₄	—	2	16	no	—
723	C₂×C₄	—	2	8	no	—
724	C₂×C₄	—	2	8	no	—
725	C₂×C₄	—	2	2	no	—
726	C₂×C₄	—	2	2	no	—
727	C₂×C₄	—	2	2	no	—
728	C₂×C₄	—	2	1	no	—
729	C₂×C₄	—	2	1	no	—
730	C₂×C₄	—	2	2	no	—
731	C₂×C₄	—	2	2	no	—
732	C₂×C₄	—	2	1	no	—
733	C₂×C₄	—	2	1	no	—
734	C₂×C₄	—	2	2	no	—
735	C₂×C₄	—	2	2	no	—
736	C₂×C₄	—	2	2	no	—
737	C₂×C₄	—	2	8	no	—
738	C₂×C₄	—	2	8	no	—
739	C₂×C₄	—	2	8	no	—
740	C₂×C₄	—	2	8	no	—
741	C₂×C₄	—	2	16	no	—
742	C₂×C₄	—	2	16	no	—
743	C₂×C₄	—	2	2	no	—
744	C₂×C₄	—	2	2	no	—
745	C₂×C₄	—	2	2	no	—
746	C₂×C₄	—	2	4	no	—
747	C₂×C₄	—	2	4	no	—
748	C₂×C₄	—	2	4	no	—
749	C₂×C₄	—	2	2	no	—
750	C₂×C₄	—	2	4	no	—
751	C₂×C₄	—	2	4	no	—
752	C₂×C₄	—	2	4	no	—
753	C₂×C₄	—	2	4	no	—
754	C₂×C₄	—	2	4	no	—
755	C₂×C₄	—	2	2	no	—
756	C₂×C₄	—	4	8	no	—
757	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
758	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
759	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
760	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
761	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
762	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
763	C₂×C₄	C₂×#41×C₂₃	1	4	yes	—
764	C₂×C₄	C₂×#41×C₂₃	1	4	yes	—
765	C₂×C₄	C₂×#41×C₂₃	1	4	yes	—
766	C₂×C₄	C₂×#41×C₂₃	1	4	yes	—
767	C₂×C₄	C₂×#41×C₂₃	1	4	yes	—
768	C₂²	—	2	32	no	—
769	C₂²	—	2	2	no	—
770	C₂²	—	2	2	no	—
771	C₂²	—	2	4	no	—
772	C₂²	—	2	4	no	—
773	C₂²	—	2	4	no	—
774	C₂²	—	2	4	no	—
775	C₂²	—	2	4	no	—
776	C₂²	—	2	4	no	—
777	C₂²	—	2	4	no	—
778	C₂²	—	2	4	no	—
779	C₂²	—	4	2	no	—
780	C₂²	—	4	2	no	—
781	C₂²	—	4	2	no	—
782	C₂²	—	4	4	no	—
783	C₂²	—	4	4	no	—
784	C₂²	C₂₃×#525	1	4	yes	—
785	C₂²	C₂₃×#529	1	8	yes	complemented
786	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
787	C₂²	C₂²×#41×C₂₃	1	1	yes	characteristic
788	C₂²	C₂²×#41×C₂₃	1	2	yes	—
789	C₂²	C₂²×#41×C₂₃	1	2	yes	—
790	C₂²	C₂²×#41×C₂₃	1	1	yes	characteristic
791	C₄	—	2	2	no	—
792	C₄	—	2	2	no	—
793	C₄	—	2	2	no	—
794	C₄	—	2	2	no	—
795	C₄	—	2	4	no	—
796	C₄	—	2	4	no	—
797	C₄	—	2	4	no	—
798	C₄	—	4	2	no	—
799	C₄	—	4	2	no	—
800	C₄	—	4	2	no	—
801	C₄	—	4	4	no	—
802	C₄	—	4	4	no	—
803	C₄	C₂₃×#525	1	4	yes	—
804	C₄	C₂₃×#525	1	4	yes	—
805	C₂	—	2	4	no	—
806	C₂	—	2	8	no	—
807	C₂	—	8	2	no	—
808	C₂	C₂×C₂₃×#525	1	1	yes	characteristic
809	C₂	C₂×C₂₃×#525	1	1	yes	characteristic
810	C₂	C₂×C₂₃×#525	1	1	yes	characteristic
811	C₂	C₂×C₂₃×#529	1	2	yes	—
812	C₂	C₂₃×#3444	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄×C₂₃	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₂₃
socle	C₂³×C₂₃	C₂⁵
prime radical	C₂₃×#2847	C₂
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₂₃×#529	C₂	semidirect
2. C₂³×C₄²×C₂₃	C₂	semidirect
3. C₂₃×#2855	C₂	semidirect
4. C₂₃×#2854	C₂	semidirect
5. C₂₃×#2853	C₂	semidirect
6. C₂₃×#2852	C₂	semidirect
7. C₂₃×#2851	C₂	semidirect
8. C₂₃×#2850	C₂	semidirect
9. C₂₃×#2849	C₂	semidirect
10. C₂₃×#2848	C₂	semidirect
12. C₄×C₂₃×C₂²⋊Q₈	C₂	semidirect
13. C₄×C₂₃×#123	C₂	semidirect
14. C₄×C₂₃×#121	C₂	semidirect
15. C₄×C₂₃×#120	C₂	semidirect
16. C₂₃×#2290	C₂	semidirect
17. C₂₃×#2283	C₂	semidirect
22. C₂×C₂₃×#126	C₂²	semidirect
23. C₂×C₂₃×#125	C₂²	semidirect
24. C₂×C₂₃×#124	C₂²	semidirect
32. C₂×C₄×Q₈×C₂₃	C₂²	semidirect
35. C₂×C₄×D₄×C₂₃	C₂²	semidirect
36. C₂×C₂₃×#117	C₂²	semidirect
46. C₂₃×#391	C₂²	semidirect
47. C₂₃×#390	C₂²	semidirect
48. C₂₃×#389	C₂²	semidirect
49. C₂₃×#389	C₂²	semidirect
50. C₂₃×#388	C₂²	semidirect
51. C₂₃×#388	C₂²	semidirect
52. C₂₃×#388	C₂²	semidirect
53. C₂₃×#388	C₂²	semidirect
54. C₂₃×#387	C₂²	semidirect
55. C₂₃×#387	C₂²	semidirect
56. C₂₃×#387	C₂²	semidirect
57. C₂₃×#387	C₂²	semidirect
70. C₂₃×#383	C₂²	semidirect
71. C₂₃×#382	C₂²	semidirect
79. C₄×C₄⋊C₄×C₂₃	C₂²	semidirect
80. C₄×C₄⋊C₄×C₂₃	C₂²	semidirect
83. C₄×C₂²⋊C₄×C₂₃	C₂²	semidirect
84. C₂₃×#376	C₂²	semidirect
156. C₂×C₄²×C₂₃	D₄	semidirect
285. #36621	C₂₃	direct (N × H)
362. C₂×#529	C₂×C₂₃	semidirect
363. C₂³×C₄²	C₂×C₂₃	semidirect
364. #2855	C₂×C₂₃	semidirect
365. #2854	C₂×C₂₃	semidirect
366. #2853	C₂×C₂₃	semidirect
367. #2852	C₂×C₂₃	semidirect
368. #2851	C₂×C₂₃	semidirect
369. #2850	C₂×C₂₃	semidirect
370. #2849	C₂×C₂₃	semidirect
371. #2848	C₂×C₂₃	semidirect
373. C₄×C₂²⋊Q₈	C₂×C₂₃	semidirect
374. C₄×#123	C₂×C₂₃	semidirect
375. C₄×#121	C₂×C₂₃	semidirect
376. C₄×#120	C₂×C₂₃	semidirect
377. #2290	C₂×C₂₃	semidirect
378. #2283	C₂×C₂₃	semidirect
396. C₂²×C₂₃	#529	semidirect
420. C₂×#126	C₂²×C₂₃	semidirect
421. C₂×#125	C₂²×C₂₃	semidirect
422. C₂×#124	C₂²×C₂₃	semidirect
430. C₂×C₄×Q₈	C₂²×C₂₃	semidirect
433. C₂×C₄×D₄	C₂²×C₂₃	semidirect
434. C₂×#117	C₂²×C₂₃	semidirect
444. #391	C₂²×C₂₃	semidirect
445. #390	C₂²×C₂₃	semidirect
446. #389	C₂²×C₂₃	semidirect
447. #389	C₂²×C₂₃	semidirect
448. #388	C₂²×C₂₃	semidirect
449. #388	C₂²×C₂₃	semidirect
450. #388	C₂²×C₂₃	semidirect
451. #388	C₂²×C₂₃	semidirect
452. #387	C₂²×C₂₃	semidirect
453. #387	C₂²×C₂₃	semidirect
454. #387	C₂²×C₂₃	semidirect
455. #387	C₂²×C₂₃	semidirect
468. #383	C₂²×C₂₃	semidirect
469. #382	C₂²×C₂₃	semidirect
477. C₄×C₄⋊C₄	C₂²×C₂₃	semidirect
478. C₄×C₄⋊C₄	C₂²×C₂₃	semidirect
481. C₄×C₂²⋊C₄	C₂²×C₂₃	semidirect
482. #376	C₂²×C₂₃	semidirect
562. C₂×C₄²	D₄×C₂₃	semidirect
586. C₂₃	#36621	direct (N × H)
785. C₂²	C₂₃×#529	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₂₃×#529	2
C₂³×C₄²×C₂₃	2
C₂₃×#2855	2
C₂₃×#2854	2
C₂₃×#2853	2
C₂₃×#2852	2
C₂₃×#2851	2
C₂₃×#2850	2
C₂₃×#2849	2
C₂₃×#2848	2
C₂₃×#2847	2
C₄×C₂₃×C₂²⋊Q₈	2
C₄×C₂₃×#123	2
C₄×C₂₃×#121	2
C₄×C₂₃×#120	2
C₂₃×#2290	2
C₂₃×#2283	2
#36621	23

Subgroups — C23×#36621 #19184247

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#36621 #19184247