Subgroups — C₂₃×#36729 #19184355

Order 5888.

2034 conjugacy classes of subgroups.

The subgroup lattice has 1000 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#2848	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂₃×#2847	C₂	1	1	yes	maximal, characteristic
3	C₂₃×#2747	C₂	1	2	yes	maximal, complemented
4	C₂₃×#2742	C₂	1	2	yes	maximal, complemented
5	C₂₃×#2741	C₂	1	2	yes	maximal, complemented
6	C₂₃×#2717	C₂	1	2	yes	maximal, complemented
7	C₂₃×#2702	C₂	1	2	yes	maximal, complemented
8	C₂₃×#2692	C₂	1	2	yes	maximal, complemented
9	C₂₃×#2691	C₂	1	2	yes	maximal, complemented
10	C₂₃×#2672	C₂	1	2	yes	maximal, complemented
11	C₂₃×#2659	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₃×#2639	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₃×#2481	C₂	1	2	yes	maximal, complemented
14	C₂₃×#2472	C₂	1	2	yes	maximal, complemented
15	C₂₃×#2449	C₂	1	2	yes	maximal, complemented
16	C₂₃×#2418	C₂	1	2	yes	maximal, complemented
17	C₂₃×#2329	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂₃×#2325	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂×C₂₃×#380	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂⁴×C₄×C₂₃	C₂²	1	1	yes	characteristic
21	C₂×C₂₃×#126	C₂²	1	2	yes	complemented
22	C₂×C₂₃×#124	C₂²	1	2	yes	—
23	C₂×C₂₃×#123	C₂²	1	2	yes	—
24	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
25	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	2	yes	—
26	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
27	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
28	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
29	C₂×C₂₃×#121	C₂²	1	1	yes	characteristic
30	C₂×C₂₃×#121	C₂²	1	1	yes	characteristic
31	C₂×C₂₃×#121	C₂²	1	1	yes	characteristic
32	C₂×C₂₃×#120	C₂²	1	2	yes	—
33	C₂×C₄×D₄×C₂₃	C₂²	1	2	yes	—
34	C₂²×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
35	C₂²×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
36	C₂²×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
37	C₂²×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
38	C₂₃×#400	C₂²	1	2	yes	complemented
39	C₂₃×#400	C₂²	1	2	yes	complemented
40	C₂₃×#400	C₂²	1	2	yes	complemented
41	C₂₃×#399	C₂²	1	2	yes	—
42	C₂₃×#399	C₂²	1	2	yes	complemented
43	C₂₃×#398	C₂²	1	2	yes	complemented
44	C₂₃×#398	C₂²	1	2	yes	complemented
45	C₂₃×#398	C₂²	1	2	yes	complemented
46	C₂₃×#397	C₂²	1	2	yes	—
47	C₂₃×#397	C₂²	1	2	yes	—
48	C₂₃×#397	C₂²	1	2	yes	complemented
49	C₂₃×#397	C₂²	1	2	yes	complemented
50	C₂₃×#396	C₂²	1	2	yes	complemented
51	C₂₃×#396	C₂²	1	2	yes	complemented
52	C₂₃×#395	C₂²	1	2	yes	complemented
53	C₂₃×#395	C₂²	1	2	yes	complemented
54	C₂₃×#395	C₂²	1	2	yes	complemented
55	C₂₃×#394	C₂²	1	2	yes	—
56	C₂₃×#394	C₂²	1	2	yes	—
57	C₂₃×#394	C₂²	1	2	yes	—
58	C₂₃×#394	C₂²	1	2	yes	—
59	C₂₃×#394	C₂²	1	2	yes	complemented
60	C₂₃×#393	C₂²	1	2	yes	—
61	C₂₃×#393	C₂²	1	2	yes	complemented
62	C₂₃×#391	C₂²	1	2	yes	complemented
63	C₂₃×#390	C₂²	1	2	yes	—
64	C₂₃×#389	C₂²	1	2	yes	complemented
65	C₂₃×#389	C₂²	1	2	yes	complemented
66	C₂₃×#388	C₂²	1	2	yes	—
67	C₂₃×#388	C₂²	1	2	yes	—
68	C₂₃×#388	C₂²	1	2	yes	—
69	C₂₃×#388	C₂²	1	2	yes	—
70	C₂₃×#388	C₂²	1	2	yes	complemented
71	C₂₃×#388	C₂²	1	2	yes	complemented
72	C₂₃×#387	C₂²	1	2	yes	complemented
73	C₂₃×#387	C₂²	1	2	yes	complemented
74	C₂₃×#387	C₂²	1	2	yes	complemented
75	C₂₃×#387	C₂²	1	2	yes	complemented
76	C₂₃×#387	C₂²	1	2	yes	complemented
77	C₂₃×#387	C₂²	1	2	yes	complemented
78	C₂₃×#386	C₂²	1	2	yes	—
79	C₂₃×#386	C₂²	1	2	yes	—
80	C₂₃×#386	C₂²	1	2	yes	—
81	C₂₃×#386	C₂²	1	2	yes	—
82	C₂₃×#386	C₂²	1	2	yes	—
83	C₂₃×#386	C₂²	1	2	yes	—
84	C₂₃×#386	C₂²	1	2	yes	—
85	C₂₃×#386	C₂²	1	2	yes	complemented
86	C₂₃×#385	C₂²	1	2	yes	—
87	C₂₃×#385	C₂²	1	2	yes	—
88	C₂₃×#385	C₂²	1	2	yes	—
89	C₂₃×#385	C₂²	1	2	yes	—
90	C₂₃×#385	C₂²	1	2	yes	complemented
91	C₂₃×#385	C₂²	1	2	yes	complemented
92	C₂₃×#380	C₂²	1	2	yes	—
93	C₂₃×#380	C₂²	1	1	yes	characteristic
94	C₂₃×#380	C₂²	1	1	yes	characteristic
95	C₂₃×#380	C₂²	1	2	yes	—
96	C₂₃×#380	C₂²	1	2	yes	—
97	C₂₃×#380	C₂²	1	2	yes	—
98	C₂₃×#380	C₂²	1	2	yes	—
99	C₂₃×#380	C₂²	1	1	yes	characteristic
100	C₂₃×#380	C₂²	1	1	yes	characteristic
101	C₂₃×#380	C₂²	1	1	yes	characteristic
102	C₂₃×#380	C₂²	1	1	yes	characteristic
103	C₂₃×#379	C₂²	1	2	yes	—
104	C₄×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	—
105	C₂×C₂₃×#95	C₂²	1	1	yes	characteristic
106	C₂×C₂₃×#95	C₂²	1	1	yes	characteristic
107	C₂⁵×C₂₃	C₂³	1	1	yes	characteristic
108	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
109	C₂²×Q₈×C₂₃	C₂³	1	2	yes	—
110	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
111	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
112	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
113	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
114	C₂³×C₄×C₂₃	—	2	4	no	—
115	C₂³×C₄×C₂₃	—	4	2	no	—
116	C₂³×C₄×C₂₃	—	4	2	no	—
117	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
118	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
119	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
120	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
121	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
122	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
123	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
124	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
125	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
126	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
127	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
128	C₂₃×#126	—	4	4	no	—
129	C₂₃×#124	—	4	4	no	—
130	C₂₃×#123	—	4	4	no	—
131	C₂₃×C₂²⋊Q₈	—	2	4	no	—
132	C₂₃×C₂²⋊Q₈	—	4	4	no	—
133	C₂₃×C₂²⋊Q₈	—	4	4	no	—
134	C₂₃×C₂²⋊Q₈	—	4	2	no	—
135	C₂₃×C₂²⋊Q₈	—	4	2	no	—
136	C₂₃×#121	—	2	4	no	—
137	C₂₃×#121	—	4	2	no	—
138	C₂₃×#121	—	4	2	no	—
139	C₂₃×#120	—	4	4	no	—
140	C₄×D₄×C₂₃	—	4	4	no	—
141	C₂×C₄⋊C₄×C₂₃	—	4	2	no	—
142	C₂×C₄⋊C₄×C₂₃	—	4	2	no	—
143	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
144	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
145	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
146	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
147	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
148	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
149	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
150	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
151	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
152	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
153	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
154	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
155	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
156	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
157	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
158	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
159	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
160	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
161	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
162	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
163	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
164	C₂×C₂²⋊C₄×C₂₃	—	4	2	no	—
165	C₂×C₂²⋊C₄×C₂₃	—	4	2	no	—
166	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
167	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
168	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
169	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
170	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
171	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
172	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
173	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
174	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
175	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
176	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
177	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
178	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
179	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
180	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
181	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
182	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
183	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
184	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
185	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
186	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
187	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
188	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
189	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
190	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
191	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
192	C₂₃×#95	C₂³	1	2	yes	—
193	C₂₃×#95	C₂³	1	2	yes	—
194	C₂₃×#95	C₂³	1	2	yes	—
195	C₂₃×#95	C₂³	1	2	yes	—
196	C₂₃×#95	C₂³	1	2	yes	—
197	C₂₃×#95	C₂³	1	2	yes	—
198	C₂₃×#95	C₂³	1	2	yes	—
199	C₂₃×#95	C₂³	1	2	yes	—
200	C₂₃×#95	C₂³	1	2	yes	—
201	C₂₃×#95	C₂³	1	2	yes	—
202	C₂₃×#95	C₂³	1	2	yes	—
203	C₂₃×#95	C₂³	1	2	yes	—
204	C₂₃×#95	C₂³	1	2	yes	—
205	C₂₃×#95	C₂³	1	2	yes	—
206	C₂₃×#95	C₂³	1	2	yes	—
207	C₂₃×#95	C₂³	1	2	yes	—
208	C₂₃×#95	C₂³	1	2	yes	—
209	C₂₃×#95	C₂³	1	2	yes	—
210	C₂₃×#95	C₂³	1	2	yes	—
211	C₂₃×#95	C₂³	1	2	yes	—
212	C₂₃×#95	C₂³	1	2	yes	—
213	C₂₃×#95	C₂³	1	2	yes	—
214	C₂⁴×C₂₃	—	2	2	no	—
215	C₂⁴×C₂₃	—	2	2	no	—
216	C₂⁴×C₂₃	—	2	2	no	—
217	C₂⁴×C₂₃	—	2	2	no	—
218	C₂⁴×C₂₃	—	2	2	no	—
219	C₂⁴×C₂₃	—	4	1	no	—
220	C₂⁴×C₂₃	—	4	1	no	—
221	C₂⁴×C₂₃	C₂⁴	1	2	yes	—
222	C₂⁴×C₂₃	C₂⁴	1	1	yes	characteristic
223	C₂⁴×C₂₃	C₂⁴	1	1	yes	characteristic
224	C₂⁴×C₂₃	C₂⁴	1	1	yes	characteristic
225	C₂×Q₈×C₂₃	—	2	2	no	—
226	C₂×Q₈×C₂₃	—	4	1	no	—
227	C₂×Q₈×C₂₃	—	4	1	no	—
228	C₂×Q₈×C₂₃	—	4	2	no	—
229	C₂×Q₈×C₂₃	—	4	2	no	—
230	C₂×Q₈×C₂₃	—	4	2	no	—
231	C₂×D₄×C₂₃	—	2	4	no	—
232	C₂×D₄×C₂₃	—	2	4	no	—
233	C₂×D₄×C₂₃	—	2	4	no	—
234	C₂×D₄×C₂₃	—	2	4	no	—
235	C₂×D₄×C₂₃	—	2	4	no	—
236	C₂×D₄×C₂₃	—	2	2	no	—
237	C₂×D₄×C₂₃	—	4	2	no	—
238	C₂×D₄×C₂₃	—	4	2	no	—
239	C₂×D₄×C₂₃	—	4	1	no	—
240	C₂×D₄×C₂₃	—	4	1	no	—
241	C₂×D₄×C₂₃	—	4	2	no	—
242	C₂×D₄×C₂₃	—	4	2	no	—
243	C₂²×C₄×C₂₃	—	2	2	no	—
244	C₂²×C₄×C₂₃	—	2	2	no	—
245	C₂²×C₄×C₂₃	—	2	2	no	—
246	C₂²×C₄×C₂₃	—	2	2	no	—
247	C₂²×C₄×C₂₃	—	2	2	no	—
248	C₂²×C₄×C₂₃	—	2	2	no	—
249	C₂²×C₄×C₂₃	—	2	2	no	—
250	C₂²×C₄×C₂₃	—	2	2	no	—
251	C₂²×C₄×C₂₃	—	2	2	no	—
252	C₂²×C₄×C₂₃	—	2	2	no	—
253	C₂²×C₄×C₂₃	—	2	2	no	—
254	C₂²×C₄×C₂₃	—	2	2	no	—
255	C₂²×C₄×C₂₃	—	2	2	no	—
256	C₂²×C₄×C₂₃	—	2	2	no	—
257	C₂²×C₄×C₂₃	—	2	2	no	—
258	C₂²×C₄×C₂₃	—	4	1	no	—
259	C₂²×C₄×C₂₃	—	4	1	no	—
260	C₂²×C₄×C₂₃	—	4	1	no	—
261	C₂²×C₄×C₂₃	—	4	1	no	—
262	C₂²×C₄×C₂₃	—	4	1	no	—
263	C₂²×C₄×C₂₃	—	4	1	no	—
264	C₂²×C₄×C₂₃	—	4	1	no	—
265	C₂²×C₄×C₂₃	—	4	1	no	—
266	C₂²×C₄×C₂₃	—	4	1	no	—
267	C₂²×C₄×C₂₃	—	4	1	no	—
268	C₂²×C₄×C₂₃	—	4	1	no	—
269	C₂²×C₄×C₂₃	—	4	1	no	—
270	C₂²×C₄×C₂₃	—	4	1	no	—
271	C₂²×C₄×C₂₃	—	4	1	no	—
272	C₂²×C₄×C₂₃	—	4	2	no	—
273	C₂²×C₄×C₂₃	—	4	2	no	—
274	C₂²×C₄×C₂₃	—	4	2	no	—
275	C₂²×C₄×C₂₃	—	4	16	no	—
276	C₂²×C₄×C₂₃	#41	1	4	yes	—
277	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
278	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
279	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
280	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
281	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
282	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
283	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
284	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
285	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
286	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
287	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
288	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
289	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
290	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
291	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
292	C₄⋊C₄×C₂₃	—	2	2	no	—
293	C₄⋊C₄×C₂₃	—	2	2	no	—
294	C₄⋊C₄×C₂₃	—	2	4	no	—
295	C₄⋊C₄×C₂₃	—	2	4	no	—
296	C₄⋊C₄×C₂₃	—	2	4	no	—
297	C₄⋊C₄×C₂₃	—	2	4	no	—
298	C₄⋊C₄×C₂₃	—	2	4	no	—
299	C₄⋊C₄×C₂₃	—	4	2	no	—
300	C₄⋊C₄×C₂₃	—	4	2	no	—
301	C₄⋊C₄×C₂₃	—	4	2	no	—
302	C₄⋊C₄×C₂₃	—	4	1	no	—
303	C₄⋊C₄×C₂₃	—	4	1	no	—
304	C₄⋊C₄×C₂₃	—	4	1	no	—
305	C₄⋊C₄×C₂₃	—	4	1	no	—
306	C₄⋊C₄×C₂₃	—	4	2	no	—
307	C₄⋊C₄×C₂₃	—	4	2	no	—
308	C₄⋊C₄×C₂₃	—	4	2	no	—
309	C₄⋊C₄×C₂₃	—	4	2	no	—
310	C₄⋊C₄×C₂₃	—	4	2	no	—
311	C₄⋊C₄×C₂₃	—	4	2	no	—
312	C₄⋊C₄×C₂₃	—	4	2	no	—
313	C₂²⋊C₄×C₂₃	—	2	4	no	—
314	C₂²⋊C₄×C₂₃	—	2	4	no	—
315	C₂²⋊C₄×C₂₃	—	2	4	no	—
316	C₂²⋊C₄×C₂₃	—	2	4	no	—
317	C₂²⋊C₄×C₂₃	—	2	4	no	—
318	C₂²⋊C₄×C₂₃	—	2	4	no	—
319	C₂²⋊C₄×C₂₃	—	2	4	no	—
320	C₂²⋊C₄×C₂₃	—	2	4	no	—
321	C₂²⋊C₄×C₂₃	—	2	4	no	—
322	C₂²⋊C₄×C₂₃	—	2	4	no	—
323	C₂²⋊C₄×C₂₃	—	4	2	no	—
324	C₂²⋊C₄×C₂₃	—	4	2	no	—
325	C₂²⋊C₄×C₂₃	—	4	2	no	—
326	C₂²⋊C₄×C₂₃	—	4	2	no	—
327	C₂²⋊C₄×C₂₃	—	4	2	no	—
328	C₂²⋊C₄×C₂₃	—	4	2	no	—
329	C₂²⋊C₄×C₂₃	—	4	2	no	—
330	C₂²⋊C₄×C₂₃	—	4	2	no	—
331	C₂²⋊C₄×C₂₃	—	4	2	no	—
332	C₂²⋊C₄×C₂₃	—	4	2	no	—
333	C₂²⋊C₄×C₂₃	—	4	2	no	—
334	C₂²⋊C₄×C₂₃	—	4	2	no	—
335	C₂²⋊C₄×C₂₃	—	4	2	no	—
336	C₄²×C₂₃	—	4	2	no	—
337	C₄²×C₂₃	—	4	2	no	—
338	C₄²×C₂₃	—	4	2	no	—
339	#36729	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
340	C₂³×C₂₃	—	2	1	no	—
341	C₂³×C₂₃	—	2	1	no	—
342	C₂³×C₂₃	—	2	1	no	—
343	C₂³×C₂₃	—	2	1	no	—
344	C₂³×C₂₃	—	2	8	no	—
345	C₂³×C₂₃	—	2	1	no	—
346	C₂³×C₂₃	—	2	1	no	—
347	C₂³×C₂₃	—	2	1	no	—
348	C₂³×C₂₃	—	2	1	no	—
349	C₂³×C₂₃	—	2	1	no	—
350	C₂³×C₂₃	—	2	1	no	—
351	C₂³×C₂₃	—	2	1	no	—
352	C₂³×C₂₃	—	2	1	no	—
353	C₂³×C₂₃	—	2	1	no	—
354	C₂³×C₂₃	—	2	1	no	—
355	C₂³×C₂₃	—	2	1	no	—
356	C₂³×C₂₃	—	2	1	no	—
357	C₂³×C₂₃	—	2	2	no	—
358	C₂³×C₂₃	—	2	2	no	—
359	C₂³×C₂₃	—	2	2	no	—
360	C₂³×C₂₃	—	2	2	no	—
361	C₂³×C₂₃	—	2	2	no	—
362	C₂³×C₂₃	—	2	2	no	—
363	C₂³×C₂₃	—	2	2	no	—
364	C₂³×C₂₃	—	4	4	no	—
365	C₂³×C₂₃	—	4	4	no	—
366	C₂³×C₂₃	—	4	4	no	—
367	C₂³×C₂₃	—	4	4	no	—
368	C₂³×C₂₃	—	4	4	no	—
369	C₂³×C₂₃	—	4	4	no	—
370	C₂³×C₂₃	C₂×#41	1	2	yes	—
371	C₂³×C₂₃	H(5,𝔽₂)	1	2	yes	—
372	C₂³×C₂₃	H(5,𝔽₂)	1	2	yes	—
373	C₂³×C₂₃	2₋¹⁺⁴	1	2	yes	—
374	C₂³×C₂₃	2₋¹⁺⁴	1	2	yes	—
375	C₂³×C₂₃	C₂⁵	1	1	yes	characteristic
376	Q₈×C₂₃	—	8	2	no	—
377	Q₈×C₂₃	—	8	4	no	—
378	D₄×C₂₃	—	4	8	no	—
379	D₄×C₂₃	—	8	2	no	—
380	D₄×C₂₃	—	8	4	no	—
381	D₄×C₂₃	—	8	4	no	—
382	C₂×C₄×C₂₃	—	2	8	no	—
383	C₂×C₄×C₂₃	—	2	1	no	—
384	C₂×C₄×C₂₃	—	2	1	no	—
385	C₂×C₄×C₂₃	—	2	1	no	—
386	C₂×C₄×C₂₃	—	2	1	no	—
387	C₂×C₄×C₂₃	—	2	1	no	—
388	C₂×C₄×C₂₃	—	2	1	no	—
389	C₂×C₄×C₂₃	—	2	1	no	—
390	C₂×C₄×C₂₃	—	2	1	no	—
391	C₂×C₄×C₂₃	—	2	2	no	—
392	C₂×C₄×C₂₃	—	2	2	no	—
393	C₂×C₄×C₂₃	—	2	2	no	—
394	C₂×C₄×C₂₃	—	2	2	no	—
395	C₂×C₄×C₂₃	—	2	2	no	—
396	C₂×C₄×C₂₃	—	2	2	no	—
397	C₂×C₄×C₂₃	—	2	2	no	—
398	C₂×C₄×C₂₃	—	2	2	no	—
399	C₂×C₄×C₂₃	—	2	2	no	—
400	C₂×C₄×C₂₃	—	2	2	no	—
401	C₂×C₄×C₂₃	—	2	2	no	—
402	C₂×C₄×C₂₃	—	2	2	no	—
403	C₂×C₄×C₂₃	—	2	2	no	—
404	C₂×C₄×C₂₃	—	2	2	no	—
405	C₂×C₄×C₂₃	—	2	2	no	—
406	C₂×C₄×C₂₃	—	2	2	no	—
407	C₂×C₄×C₂₃	—	2	2	no	—
408	C₂×C₄×C₂₃	—	2	2	no	—
409	C₂×C₄×C₂₃	—	2	2	no	—
410	C₂×C₄×C₂₃	—	2	2	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	2	no	—
415	C₂×C₄×C₂₃	—	2	2	no	—
416	C₂×C₄×C₂₃	—	2	2	no	—
417	C₂×C₄×C₂₃	—	2	2	no	—
418	C₂×C₄×C₂₃	—	2	2	no	—
419	C₂×C₄×C₂₃	—	2	2	no	—
420	C₂×C₄×C₂₃	—	2	2	no	—
421	C₂×C₄×C₂₃	—	2	2	no	—
422	C₂×C₄×C₂₃	—	2	2	no	—
423	C₂×C₄×C₂₃	—	2	2	no	—
424	C₂×C₄×C₂₃	—	4	4	no	—
425	C₂×C₄×C₂₃	—	4	4	no	—
426	C₂×C₄×C₂₃	—	4	4	no	—
427	C₂×C₄×C₂₃	—	4	4	no	—
428	C₂×C₄×C₂₃	—	4	4	no	—
429	C₂×C₄×C₂₃	—	8	2	no	—
430	C₂×C₄×C₂₃	—	8	2	no	—
431	C₂×C₄×C₂₃	—	8	2	no	—
432	C₂×C₄×C₂₃	—	8	2	no	—
433	C₂×C₄×C₂₃	—	8	4	no	—
434	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
435	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
436	C₂×C₄×C₂₃	H(5,𝔽₂)	1	2	yes	—
437	C₂×C₄×C₂₃	H(5,𝔽₂)	1	2	yes	—
438	#2848	C₂×C₂₃	1	1	yes	characteristic, complemented
439	#2847	C₂×C₂₃	1	1	yes	characteristic
440	#2747	C₂×C₂₃	1	2	yes	complemented
441	#2742	C₂×C₂₃	1	2	yes	complemented
442	#2741	C₂×C₂₃	1	2	yes	complemented
443	#2717	C₂×C₂₃	1	2	yes	complemented
444	#2702	C₂×C₂₃	1	2	yes	complemented
445	#2692	C₂×C₂₃	1	2	yes	complemented
446	#2691	C₂×C₂₃	1	2	yes	complemented
447	#2672	C₂×C₂₃	1	2	yes	complemented
448	#2659	C₂×C₂₃	1	1	yes	characteristic, complemented
449	#2639	C₂×C₂₃	1	1	yes	characteristic, complemented
450	#2481	C₂×C₂₃	1	2	yes	complemented
451	#2472	C₂×C₂₃	1	2	yes	complemented
452	#2449	C₂×C₂₃	1	2	yes	complemented
453	#2418	C₂×C₂₃	1	2	yes	complemented
454	#2329	C₂×C₂₃	1	1	yes	characteristic, complemented
455	#2325	C₂×C₂₃	1	1	yes	characteristic, complemented
456	C₂×#380	C₂×C₂₃	1	1	yes	characteristic, complemented
457	C₂²×C₂₃	—	2	2	no	—
458	C₂²×C₂₃	—	2	2	no	—
459	C₂²×C₂₃	—	2	2	no	—
460	C₂²×C₂₃	—	2	2	no	—
461	C₂²×C₂₃	—	2	2	no	—
462	C₂²×C₂₃	—	2	2	no	—
463	C₂²×C₂₃	—	2	2	no	—
464	C₂²×C₂₃	—	2	2	no	—
465	C₂²×C₂₃	—	2	2	no	—
466	C₂²×C₂₃	—	2	2	no	—
467	C₂²×C₂₃	—	2	2	no	—
468	C₂²×C₂₃	—	2	2	no	—
469	C₂²×C₂₃	—	4	16	no	—
470	C₂²×C₂₃	—	4	1	no	—
471	C₂²×C₂₃	—	4	1	no	—
472	C₂²×C₂₃	—	4	1	no	—
473	C₂²×C₂₃	—	4	1	no	—
474	C₂²×C₂₃	—	4	1	no	—
475	C₂²×C₂₃	—	4	1	no	—
476	C₂²×C₂₃	—	4	1	no	—
477	C₂²×C₂₃	—	4	1	no	—
478	C₂²×C₂₃	—	4	2	no	—
479	C₂²×C₂₃	—	4	2	no	—
480	C₂²×C₂₃	—	4	2	no	—
481	C₂²×C₂₃	—	4	2	no	—
482	C₂²×C₂₃	—	4	2	no	—
483	C₂²×C₂₃	—	4	2	no	—
484	C₂²×C₂₃	—	4	2	no	—
485	C₂²×C₂₃	#542	1	4	yes	—
486	C₂²×C₂₃	C₂²×#41	1	1	yes	characteristic
487	C₂²×C₂₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
488	C₂²×C₂₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
489	C₂²×C₂₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
490	C₂²×C₂₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
491	C₂²×C₂₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
492	C₂²×C₂₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
493	C₄×C₂₃	—	2	2	no	—
494	C₄×C₂₃	—	2	2	no	—
495	C₄×C₂₃	—	2	2	no	—
496	C₄×C₂₃	—	2	2	no	—
497	C₄×C₂₃	—	4	2	no	—
498	C₄×C₂₃	—	4	2	no	—
499	C₄×C₂₃	—	4	2	no	—
500	C₄×C₂₃	—	4	2	no	—
501	C₄×C₂₃	—	4	2	no	—
502	C₄×C₂₃	—	4	2	no	—
503	C₄×C₂₃	—	4	2	no	—
504	C₄×C₂₃	—	4	2	no	—
505	C₄×C₂₃	—	4	2	no	—
506	C₄×C₂₃	—	4	2	no	—
507	C₄×C₂₃	—	4	2	no	—
508	C₂⁴×C₄	C₂²×C₂₃	1	1	yes	characteristic
509	C₂×#126	C₂²×C₂₃	1	2	yes	complemented
510	C₂×#124	C₂²×C₂₃	1	2	yes	—
511	C₂×#123	C₂²×C₂₃	1	2	yes	—
512	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
513	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
514	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
515	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	2	yes	—
516	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	2	yes	complemented
517	C₂×#121	C₂²×C₂₃	1	1	yes	characteristic
518	C₂×#121	C₂²×C₂₃	1	1	yes	characteristic
519	C₂×#121	C₂²×C₂₃	1	1	yes	characteristic
520	C₂×#120	C₂²×C₂₃	1	2	yes	—
521	C₂×C₄×D₄	C₂²×C₂₃	1	2	yes	—
522	C₂²×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
523	C₂²×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
524	C₂²×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
525	C₂²×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
526	#400	C₂²×C₂₃	1	2	yes	complemented
527	#400	C₂²×C₂₃	1	2	yes	complemented
528	#400	C₂²×C₂₃	1	2	yes	complemented
529	#399	C₂²×C₂₃	1	2	yes	—
530	#399	C₂²×C₂₃	1	2	yes	complemented
531	#398	C₂²×C₂₃	1	2	yes	complemented
532	#398	C₂²×C₂₃	1	2	yes	complemented
533	#398	C₂²×C₂₃	1	2	yes	complemented
534	#397	C₂²×C₂₃	1	2	yes	—
535	#397	C₂²×C₂₃	1	2	yes	—
536	#397	C₂²×C₂₃	1	2	yes	complemented
537	#397	C₂²×C₂₃	1	2	yes	complemented
538	#396	C₂²×C₂₃	1	2	yes	complemented
539	#396	C₂²×C₂₃	1	2	yes	complemented
540	#395	C₂²×C₂₃	1	2	yes	complemented
541	#395	C₂²×C₂₃	1	2	yes	complemented
542	#395	C₂²×C₂₃	1	2	yes	complemented
543	#394	C₂²×C₂₃	1	2	yes	—
544	#394	C₂²×C₂₃	1	2	yes	—
545	#394	C₂²×C₂₃	1	2	yes	—
546	#394	C₂²×C₂₃	1	2	yes	—
547	#394	C₂²×C₂₃	1	2	yes	complemented
548	#393	C₂²×C₂₃	1	2	yes	—
549	#393	C₂²×C₂₃	1	2	yes	complemented
550	#391	C₂²×C₂₃	1	2	yes	complemented
551	#390	C₂²×C₂₃	1	2	yes	—
552	#389	C₂²×C₂₃	1	2	yes	complemented
553	#389	C₂²×C₂₃	1	2	yes	complemented
554	#388	C₂²×C₂₃	1	2	yes	—
555	#388	C₂²×C₂₃	1	2	yes	—
556	#388	C₂²×C₂₃	1	2	yes	—
557	#388	C₂²×C₂₃	1	2	yes	—
558	#388	C₂²×C₂₃	1	2	yes	complemented
559	#388	C₂²×C₂₃	1	2	yes	complemented
560	#387	C₂²×C₂₃	1	2	yes	complemented
561	#387	C₂²×C₂₃	1	2	yes	complemented
562	#387	C₂²×C₂₃	1	2	yes	complemented
563	#387	C₂²×C₂₃	1	2	yes	complemented
564	#387	C₂²×C₂₃	1	2	yes	complemented
565	#387	C₂²×C₂₃	1	2	yes	complemented
566	#386	C₂²×C₂₃	1	2	yes	—
567	#386	C₂²×C₂₃	1	2	yes	—
568	#386	C₂²×C₂₃	1	2	yes	—
569	#386	C₂²×C₂₃	1	2	yes	—
570	#386	C₂²×C₂₃	1	2	yes	—
571	#386	C₂²×C₂₃	1	2	yes	—
572	#386	C₂²×C₂₃	1	2	yes	—
573	#386	C₂²×C₂₃	1	2	yes	complemented
574	#385	C₂²×C₂₃	1	2	yes	—
575	#385	C₂²×C₂₃	1	2	yes	—
576	#385	C₂²×C₂₃	1	2	yes	—
577	#385	C₂²×C₂₃	1	2	yes	—
578	#385	C₂²×C₂₃	1	2	yes	complemented
579	#385	C₂²×C₂₃	1	2	yes	complemented
580	#380	C₂²×C₂₃	1	1	yes	characteristic
581	#380	C₂²×C₂₃	1	1	yes	characteristic
582	#380	C₂²×C₂₃	1	1	yes	characteristic
583	#380	C₂²×C₂₃	1	1	yes	characteristic
584	#380	C₂²×C₂₃	1	1	yes	characteristic
585	#380	C₂²×C₂₃	1	1	yes	characteristic
586	#380	C₂²×C₂₃	1	2	yes	—
587	#380	C₂²×C₂₃	1	2	yes	—
588	#380	C₂²×C₂₃	1	2	yes	—
589	#380	C₂²×C₂₃	1	2	yes	—
590	#380	C₂²×C₂₃	1	2	yes	—
591	#379	C₂²×C₂₃	1	2	yes	—
592	C₄×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
593	C₂×#95	C₂²×C₂₃	1	1	yes	characteristic
594	C₂×#95	C₂²×C₂₃	1	1	yes	characteristic
595	C₂×C₂₃	—	2	4	no	—
596	C₂×C₂₃	—	4	2	no	—
597	C₂×C₂₃	—	4	2	no	—
598	C₂×C₂₃	—	8	2	no	—
599	C₂×C₂₃	C₂×#542	1	1	yes	characteristic
600	C₂×C₂₃	#3490	1	1	yes	characteristic
601	C₂×C₂₃	#3492	1	1	yes	characteristic
602	C₂×C₂₃	#3536	1	1	yes	characteristic
603	C₂×C₂₃	#3536	1	1	yes	characteristic
604	C₂×C₂₃	#3537	1	1	yes	characteristic
605	C₂×C₂₃	#3538	1	1	yes	characteristic
606	C₂⁵	C₂³×C₂₃	1	1	yes	characteristic
607	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
608	C₂²×Q₈	C₂³×C₂₃	1	2	yes	—
609	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
610	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
611	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
612	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
613	C₂³×C₄	—	2	4	no	—
614	C₂³×C₄	—	4	2	no	—
615	C₂³×C₄	—	4	2	no	—
616	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
617	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
618	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
619	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
620	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
621	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
622	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
623	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
624	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
625	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
626	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
627	#126	—	4	4	no	—
628	#124	—	4	4	no	—
629	#123	—	4	4	no	—
630	C₂²⋊Q₈	—	2	4	no	—
631	C₂²⋊Q₈	—	4	4	no	—
632	C₂²⋊Q₈	—	4	4	no	—
633	C₂²⋊Q₈	—	4	2	no	—
634	C₂²⋊Q₈	—	4	2	no	—
635	#121	—	2	4	no	—
636	#121	—	4	2	no	—
637	#121	—	4	2	no	—
638	#120	—	4	4	no	—
639	C₄×D₄	—	4	4	no	—
640	C₂×C₄⋊C₄	—	4	2	no	—
641	C₂×C₄⋊C₄	—	4	2	no	—
642	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
643	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
644	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
645	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
646	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
647	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
648	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
649	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
650	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
651	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
652	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
653	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
654	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
655	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
656	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
657	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
658	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
659	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
660	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
661	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
662	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
663	C₂×C₂²⋊C₄	—	4	2	no	—
664	C₂×C₂²⋊C₄	—	4	2	no	—
665	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
666	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
667	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
668	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
669	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
670	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
671	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
672	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
673	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
674	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
675	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
676	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
677	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
678	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
679	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
680	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
681	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
682	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
683	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
684	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
685	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
686	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
687	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
688	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
689	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
690	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
691	#95	C₂³×C₂₃	1	2	yes	—
692	#95	C₂³×C₂₃	1	2	yes	—
693	#95	C₂³×C₂₃	1	2	yes	—
694	#95	C₂³×C₂₃	1	2	yes	—
695	#95	C₂³×C₂₃	1	2	yes	—
696	#95	C₂³×C₂₃	1	2	yes	—
697	#95	C₂³×C₂₃	1	2	yes	—
698	#95	C₂³×C₂₃	1	2	yes	—
699	#95	C₂³×C₂₃	1	2	yes	—
700	#95	C₂³×C₂₃	1	2	yes	—
701	#95	C₂³×C₂₃	1	2	yes	—
702	#95	C₂³×C₂₃	1	2	yes	—
703	#95	C₂³×C₂₃	1	2	yes	—
704	#95	C₂³×C₂₃	1	2	yes	—
705	#95	C₂³×C₂₃	1	2	yes	—
706	#95	C₂³×C₂₃	1	2	yes	—
707	#95	C₂³×C₂₃	1	2	yes	—
708	#95	C₂³×C₂₃	1	2	yes	—
709	#95	C₂³×C₂₃	1	2	yes	—
710	#95	C₂³×C₂₃	1	2	yes	—
711	#95	C₂³×C₂₃	1	2	yes	—
712	#95	C₂³×C₂₃	1	2	yes	—
713	C₂₃	#36729	1	1	yes	characteristic, direct product factor, Sylow
714	C₂⁴	—	2	2	no	—
715	C₂⁴	—	2	2	no	—
716	C₂⁴	—	2	2	no	—
717	C₂⁴	—	2	2	no	—
718	C₂⁴	—	2	2	no	—
719	C₂⁴	—	4	1	no	—
720	C₂⁴	—	4	1	no	—
721	C₂⁴	C₂⁴×C₂₃	1	2	yes	—
722	C₂⁴	C₂⁴×C₂₃	1	1	yes	characteristic
723	C₂⁴	C₂⁴×C₂₃	1	1	yes	characteristic
724	C₂⁴	C₂⁴×C₂₃	1	1	yes	characteristic
725	C₂×Q₈	—	2	2	no	—
726	C₂×Q₈	—	4	1	no	—
727	C₂×Q₈	—	4	1	no	—
728	C₂×Q₈	—	4	2	no	—
729	C₂×Q₈	—	4	2	no	—
730	C₂×Q₈	—	4	2	no	—
731	C₂×D₄	—	2	4	no	—
732	C₂×D₄	—	2	4	no	—
733	C₂×D₄	—	2	4	no	—
734	C₂×D₄	—	2	4	no	—
735	C₂×D₄	—	2	4	no	—
736	C₂×D₄	—	2	2	no	—
737	C₂×D₄	—	4	2	no	—
738	C₂×D₄	—	4	2	no	—
739	C₂×D₄	—	4	1	no	—
740	C₂×D₄	—	4	1	no	—
741	C₂×D₄	—	4	2	no	—
742	C₂×D₄	—	4	2	no	—
743	C₂²×C₄	—	2	2	no	—
744	C₂²×C₄	—	2	2	no	—
745	C₂²×C₄	—	2	2	no	—
746	C₂²×C₄	—	2	2	no	—
747	C₂²×C₄	—	2	2	no	—
748	C₂²×C₄	—	2	2	no	—
749	C₂²×C₄	—	2	2	no	—
750	C₂²×C₄	—	2	2	no	—
751	C₂²×C₄	—	2	2	no	—
752	C₂²×C₄	—	2	2	no	—
753	C₂²×C₄	—	2	2	no	—
754	C₂²×C₄	—	2	2	no	—
755	C₂²×C₄	—	2	2	no	—
756	C₂²×C₄	—	2	2	no	—
757	C₂²×C₄	—	2	2	no	—
758	C₂²×C₄	—	4	1	no	—
759	C₂²×C₄	—	4	1	no	—
760	C₂²×C₄	—	4	1	no	—
761	C₂²×C₄	—	4	1	no	—
762	C₂²×C₄	—	4	1	no	—
763	C₂²×C₄	—	4	1	no	—
764	C₂²×C₄	—	4	1	no	—
765	C₂²×C₄	—	4	1	no	—
766	C₂²×C₄	—	4	1	no	—
767	C₂²×C₄	—	4	1	no	—
768	C₂²×C₄	—	4	1	no	—
769	C₂²×C₄	—	4	1	no	—
770	C₂²×C₄	—	4	1	no	—
771	C₂²×C₄	—	4	1	no	—
772	C₂²×C₄	—	4	2	no	—
773	C₂²×C₄	—	4	2	no	—
774	C₂²×C₄	—	4	2	no	—
775	C₂²×C₄	—	4	16	no	—
776	C₂²×C₄	#41×C₂₃	1	4	yes	—
777	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
778	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
779	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
780	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
781	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
782	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
783	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
784	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
785	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
786	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
787	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
788	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
789	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
790	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
791	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
792	C₄⋊C₄	—	2	2	no	—
793	C₄⋊C₄	—	2	2	no	—
794	C₄⋊C₄	—	2	4	no	—
795	C₄⋊C₄	—	2	4	no	—
796	C₄⋊C₄	—	2	4	no	—
797	C₄⋊C₄	—	2	4	no	—
798	C₄⋊C₄	—	2	4	no	—
799	C₄⋊C₄	—	4	2	no	—
800	C₄⋊C₄	—	4	2	no	—
801	C₄⋊C₄	—	4	2	no	—
802	C₄⋊C₄	—	4	1	no	—
803	C₄⋊C₄	—	4	1	no	—
804	C₄⋊C₄	—	4	1	no	—
805	C₄⋊C₄	—	4	1	no	—
806	C₄⋊C₄	—	4	2	no	—
807	C₄⋊C₄	—	4	2	no	—
808	C₄⋊C₄	—	4	2	no	—
809	C₄⋊C₄	—	4	2	no	—
810	C₄⋊C₄	—	4	2	no	—
811	C₄⋊C₄	—	4	2	no	—
812	C₄⋊C₄	—	4	2	no	—
813	C₂²⋊C₄	—	2	4	no	—
814	C₂²⋊C₄	—	2	4	no	—
815	C₂²⋊C₄	—	2	4	no	—
816	C₂²⋊C₄	—	2	4	no	—
817	C₂²⋊C₄	—	2	4	no	—
818	C₂²⋊C₄	—	2	4	no	—
819	C₂²⋊C₄	—	2	4	no	—
820	C₂²⋊C₄	—	2	4	no	—
821	C₂²⋊C₄	—	2	4	no	—
822	C₂²⋊C₄	—	2	4	no	—
823	C₂²⋊C₄	—	4	2	no	—
824	C₂²⋊C₄	—	4	2	no	—
825	C₂²⋊C₄	—	4	2	no	—
826	C₂²⋊C₄	—	4	2	no	—
827	C₂²⋊C₄	—	4	2	no	—
828	C₂²⋊C₄	—	4	2	no	—
829	C₂²⋊C₄	—	4	2	no	—
830	C₂²⋊C₄	—	4	2	no	—
831	C₂²⋊C₄	—	4	2	no	—
832	C₂²⋊C₄	—	4	2	no	—
833	C₂²⋊C₄	—	4	2	no	—
834	C₂²⋊C₄	—	4	2	no	—
835	C₂²⋊C₄	—	4	2	no	—
836	C₄²	—	4	2	no	—
837	C₄²	—	4	2	no	—
838	C₄²	—	4	2	no	—
839	C₂³	—	2	1	no	—
840	C₂³	—	2	1	no	—
841	C₂³	—	2	1	no	—
842	C₂³	—	2	1	no	—
843	C₂³	—	2	8	no	—
844	C₂³	—	2	1	no	—
845	C₂³	—	2	1	no	—
846	C₂³	—	2	1	no	—
847	C₂³	—	2	1	no	—
848	C₂³	—	2	1	no	—
849	C₂³	—	2	1	no	—
850	C₂³	—	2	1	no	—
851	C₂³	—	2	1	no	—
852	C₂³	—	2	1	no	—
853	C₂³	—	2	1	no	—
854	C₂³	—	2	1	no	—
855	C₂³	—	2	1	no	—
856	C₂³	—	2	2	no	—
857	C₂³	—	2	2	no	—
858	C₂³	—	2	2	no	—
859	C₂³	—	2	2	no	—
860	C₂³	—	2	2	no	—
861	C₂³	—	2	2	no	—
862	C₂³	—	2	2	no	—
863	C₂³	—	4	4	no	—
864	C₂³	—	4	4	no	—
865	C₂³	—	4	4	no	—
866	C₂³	—	4	4	no	—
867	C₂³	—	4	4	no	—
868	C₂³	—	4	4	no	—
869	C₂³	C₂×#41×C₂₃	1	2	yes	—
870	C₂³	C₂₃×H(5,𝔽₂)	1	2	yes	—
871	C₂³	C₂₃×H(5,𝔽₂)	1	2	yes	—
872	C₂³	C₂₃×2₋¹⁺⁴	1	2	yes	—
873	C₂³	C₂₃×2₋¹⁺⁴	1	2	yes	—
874	C₂³	C₂⁵×C₂₃	1	1	yes	characteristic
875	Q₈	—	8	2	no	—
876	Q₈	—	8	4	no	—
877	D₄	—	4	8	no	—
878	D₄	—	8	2	no	—
879	D₄	—	8	4	no	—
880	D₄	—	8	4	no	—
881	C₂×C₄	—	2	8	no	—
882	C₂×C₄	—	2	1	no	—
883	C₂×C₄	—	2	1	no	—
884	C₂×C₄	—	2	1	no	—
885	C₂×C₄	—	2	1	no	—
886	C₂×C₄	—	2	1	no	—
887	C₂×C₄	—	2	1	no	—
888	C₂×C₄	—	2	1	no	—
889	C₂×C₄	—	2	1	no	—
890	C₂×C₄	—	2	2	no	—
891	C₂×C₄	—	2	2	no	—
892	C₂×C₄	—	2	2	no	—
893	C₂×C₄	—	2	2	no	—
894	C₂×C₄	—	2	2	no	—
895	C₂×C₄	—	2	2	no	—
896	C₂×C₄	—	2	2	no	—
897	C₂×C₄	—	2	2	no	—
898	C₂×C₄	—	2	2	no	—
899	C₂×C₄	—	2	2	no	—
900	C₂×C₄	—	2	2	no	—
901	C₂×C₄	—	2	2	no	—
902	C₂×C₄	—	2	2	no	—
903	C₂×C₄	—	2	2	no	—
904	C₂×C₄	—	2	2	no	—
905	C₂×C₄	—	2	2	no	—
906	C₂×C₄	—	2	2	no	—
907	C₂×C₄	—	2	2	no	—
908	C₂×C₄	—	2	2	no	—
909	C₂×C₄	—	2	2	no	—
910	C₂×C₄	—	2	2	no	—
911	C₂×C₄	—	2	2	no	—
912	C₂×C₄	—	2	2	no	—
913	C₂×C₄	—	2	2	no	—
914	C₂×C₄	—	2	2	no	—
915	C₂×C₄	—	2	2	no	—
916	C₂×C₄	—	2	2	no	—
917	C₂×C₄	—	2	2	no	—
918	C₂×C₄	—	2	2	no	—
919	C₂×C₄	—	2	2	no	—
920	C₂×C₄	—	2	2	no	—
921	C₂×C₄	—	2	2	no	—
922	C₂×C₄	—	2	2	no	—
923	C₂×C₄	—	4	4	no	—
924	C₂×C₄	—	4	4	no	—
925	C₂×C₄	—	4	4	no	—
926	C₂×C₄	—	4	4	no	—
927	C₂×C₄	—	4	4	no	—
928	C₂×C₄	—	8	2	no	—
929	C₂×C₄	—	8	2	no	—
930	C₂×C₄	—	8	2	no	—
931	C₂×C₄	—	8	2	no	—
932	C₂×C₄	—	8	4	no	—
933	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
934	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
935	C₂×C₄	C₂₃×H(5,𝔽₂)	1	2	yes	—
936	C₂×C₄	C₂₃×H(5,𝔽₂)	1	2	yes	—
937	C₂²	—	2	2	no	—
938	C₂²	—	2	2	no	—
939	C₂²	—	2	2	no	—
940	C₂²	—	2	2	no	—
941	C₂²	—	2	2	no	—
942	C₂²	—	2	2	no	—
943	C₂²	—	2	2	no	—
944	C₂²	—	2	2	no	—
945	C₂²	—	2	2	no	—
946	C₂²	—	2	2	no	—
947	C₂²	—	2	2	no	—
948	C₂²	—	2	2	no	—
949	C₂²	—	4	16	no	—
950	C₂²	—	4	1	no	—
951	C₂²	—	4	1	no	—
952	C₂²	—	4	1	no	—
953	C₂²	—	4	1	no	—
954	C₂²	—	4	1	no	—
955	C₂²	—	4	1	no	—
956	C₂²	—	4	1	no	—
957	C₂²	—	4	1	no	—
958	C₂²	—	4	2	no	—
959	C₂²	—	4	2	no	—
960	C₂²	—	4	2	no	—
961	C₂²	—	4	2	no	—
962	C₂²	—	4	2	no	—
963	C₂²	—	4	2	no	—
964	C₂²	—	4	2	no	—
965	C₂²	C₂₃×#542	1	4	yes	—
966	C₂²	C₂²×#41×C₂₃	1	1	yes	characteristic
967	C₂²	C₂×C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
968	C₂²	C₂×C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
969	C₂²	C₂×C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
970	C₂²	C₂×C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
971	C₂²	C₂×C₂₃×2₋¹⁺⁴	1	1	yes	characteristic
972	C₂²	C₂×C₂₃×2₋¹⁺⁴	1	1	yes	characteristic
973	C₄	—	2	2	no	—
974	C₄	—	2	2	no	—
975	C₄	—	2	2	no	—
976	C₄	—	2	2	no	—
977	C₄	—	4	2	no	—
978	C₄	—	4	2	no	—
979	C₄	—	4	2	no	—
980	C₄	—	4	2	no	—
981	C₄	—	4	2	no	—
982	C₄	—	4	2	no	—
983	C₄	—	4	2	no	—
984	C₄	—	4	2	no	—
985	C₄	—	4	2	no	—
986	C₄	—	4	2	no	—
987	C₄	—	4	2	no	—
988	C₂	—	2	4	no	—
989	C₂	—	4	2	no	—
990	C₂	—	4	2	no	—
991	C₂	—	8	2	no	—
992	C₂	C₂×C₂₃×#542	1	1	yes	characteristic
993	C₂	C₂₃×#3490	1	1	yes	characteristic
994	C₂	C₂₃×#3492	1	1	yes	characteristic
995	C₂	C₂₃×#3536	1	1	yes	characteristic
996	C₂	C₂₃×#3536	1	1	yes	characteristic
997	C₂	C₂₃×#3537	1	1	yes	characteristic
998	C₂	C₂₃×#3538	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₂₃×#2848	C₂	semidirect
3. C₂₃×#2747	C₂	semidirect
4. C₂₃×#2742	C₂	semidirect
5. C₂₃×#2741	C₂	semidirect
6. C₂₃×#2717	C₂	semidirect
7. C₂₃×#2702	C₂	semidirect
8. C₂₃×#2692	C₂	semidirect
9. C₂₃×#2691	C₂	semidirect
10. C₂₃×#2672	C₂	semidirect
11. C₂₃×#2659	C₂	semidirect
12. C₂₃×#2639	C₂	semidirect
13. C₂₃×#2481	C₂	semidirect
14. C₂₃×#2472	C₂	semidirect
15. C₂₃×#2449	C₂	semidirect
16. C₂₃×#2418	C₂	semidirect
17. C₂₃×#2329	C₂	semidirect
18. C₂₃×#2325	C₂	semidirect
19. C₂×C₂₃×#380	C₂	semidirect
21. C₂×C₂₃×#126	C₂²	semidirect
28. C₂×C₂₃×C₂²⋊Q₈	C₂²	semidirect
38. C₂₃×#400	C₂²	semidirect
39. C₂₃×#400	C₂²	semidirect
40. C₂₃×#400	C₂²	semidirect
42. C₂₃×#399	C₂²	semidirect
43. C₂₃×#398	C₂²	semidirect
44. C₂₃×#398	C₂²	semidirect
45. C₂₃×#398	C₂²	semidirect
48. C₂₃×#397	C₂²	semidirect
49. C₂₃×#397	C₂²	semidirect
50. C₂₃×#396	C₂²	semidirect
51. C₂₃×#396	C₂²	semidirect
52. C₂₃×#395	C₂²	semidirect
53. C₂₃×#395	C₂²	semidirect
54. C₂₃×#395	C₂²	semidirect
59. C₂₃×#394	C₂²	semidirect
61. C₂₃×#393	C₂²	semidirect
62. C₂₃×#391	C₂²	semidirect
64. C₂₃×#389	C₂²	semidirect
65. C₂₃×#389	C₂²	semidirect
70. C₂₃×#388	C₂²	semidirect
71. C₂₃×#388	C₂²	semidirect
72. C₂₃×#387	C₂²	semidirect
73. C₂₃×#387	C₂²	semidirect
74. C₂₃×#387	C₂²	semidirect
75. C₂₃×#387	C₂²	semidirect
76. C₂₃×#387	C₂²	semidirect
77. C₂₃×#387	C₂²	semidirect
85. C₂₃×#386	C₂²	semidirect
90. C₂₃×#385	C₂²	semidirect
91. C₂₃×#385	C₂²	semidirect
339. #36729	C₂₃	direct (N × H)
438. #2848	C₂×C₂₃	semidirect
440. #2747	C₂×C₂₃	semidirect
441. #2742	C₂×C₂₃	semidirect
442. #2741	C₂×C₂₃	semidirect
443. #2717	C₂×C₂₃	semidirect
444. #2702	C₂×C₂₃	semidirect
445. #2692	C₂×C₂₃	semidirect
446. #2691	C₂×C₂₃	semidirect
447. #2672	C₂×C₂₃	semidirect
448. #2659	C₂×C₂₃	semidirect
449. #2639	C₂×C₂₃	semidirect
450. #2481	C₂×C₂₃	semidirect
451. #2472	C₂×C₂₃	semidirect
452. #2449	C₂×C₂₃	semidirect
453. #2418	C₂×C₂₃	semidirect
454. #2329	C₂×C₂₃	semidirect
455. #2325	C₂×C₂₃	semidirect
456. C₂×#380	C₂×C₂₃	semidirect
509. C₂×#126	C₂²×C₂₃	semidirect
516. C₂×C₂²⋊Q₈	C₂²×C₂₃	semidirect
526. #400	C₂²×C₂₃	semidirect
527. #400	C₂²×C₂₃	semidirect
528. #400	C₂²×C₂₃	semidirect
530. #399	C₂²×C₂₃	semidirect
531. #398	C₂²×C₂₃	semidirect
532. #398	C₂²×C₂₃	semidirect
533. #398	C₂²×C₂₃	semidirect
536. #397	C₂²×C₂₃	semidirect
537. #397	C₂²×C₂₃	semidirect
538. #396	C₂²×C₂₃	semidirect
539. #396	C₂²×C₂₃	semidirect
540. #395	C₂²×C₂₃	semidirect
541. #395	C₂²×C₂₃	semidirect
542. #395	C₂²×C₂₃	semidirect
547. #394	C₂²×C₂₃	semidirect
549. #393	C₂²×C₂₃	semidirect
550. #391	C₂²×C₂₃	semidirect
552. #389	C₂²×C₂₃	semidirect
553. #389	C₂²×C₂₃	semidirect
558. #388	C₂²×C₂₃	semidirect
559. #388	C₂²×C₂₃	semidirect
560. #387	C₂²×C₂₃	semidirect
561. #387	C₂²×C₂₃	semidirect
562. #387	C₂²×C₂₃	semidirect
563. #387	C₂²×C₂₃	semidirect
564. #387	C₂²×C₂₃	semidirect
565. #387	C₂²×C₂₃	semidirect
573. #386	C₂²×C₂₃	semidirect
578. #385	C₂²×C₂₃	semidirect
579. #385	C₂²×C₂₃	semidirect
713. C₂₃	#36729	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×#2848	2
C₂₃×#2847	2
C₂₃×#2747	2
C₂₃×#2742	2
C₂₃×#2741	2
C₂₃×#2717	2
C₂₃×#2702	2
C₂₃×#2692	2
C₂₃×#2691	2
C₂₃×#2672	2
C₂₃×#2659	2
C₂₃×#2639	2
C₂₃×#2481	2
C₂₃×#2472	2
C₂₃×#2449	2
C₂₃×#2418	2
C₂₃×#2329	2
C₂₃×#2325	2
C₂×C₂₃×#380	2
#36729	23

Subgroups — C23×#36729 #19184355

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#36729 #19184355