Subgroups — C₂₃×#34754 #19182380

Order 5888.

2182 conjugacy classes of subgroups.

The subgroup lattice has 870 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#2523	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂₃×#2518	C₂	1	2	yes	maximal, complemented
3	C₂₃×#2517	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₃×#2510	C₂	1	2	yes	maximal, complemented
5	C₂₃×#2505	C₂	1	2	yes	maximal, complemented
6	C₂₃×#2493	C₂	1	2	yes	maximal, complemented
7	C₂₃×#2488	C₂	1	2	yes	maximal, complemented
8	C₂₃×#2483	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₃×#2437	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₃×#2412	C₂	1	2	yes	maximal
11	C₂₃×#2401	C₂	1	2	yes	maximal, complemented
12	C₂₃×#2398	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₃×#2395	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄×C₂₃×C₂²⋊Q₈	C₂	1	2	yes	maximal, complemented
15	C₄×C₂₃×#123	C₂	1	2	yes	maximal, complemented
16	C₄×C₂₃×#120	C₂	1	1	yes	maximal, characteristic
17	C₂₃×#2290	C₂	1	2	yes	maximal, complemented
18	C₂₃×#2283	C₂	1	2	yes	maximal, complemented
19	C₂×C₄×C₂²⋊C₄×C₂₃	C₂	1	2	yes	maximal, complemented
20	C₂⁴×C₄×C₂₃	C₂²	1	1	yes	characteristic
21	C₂×C₂₃×#123	C₂²	1	2	yes	—
22	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	2	yes	—
23	C₂×C₂₃×#120	C₂²	1	1	yes	characteristic
24	C₂×C₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic, complemented
25	C₂×C₄×D₄×C₂₃	C₂²	1	2	yes	—
26	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
27	C₂×C₂₃×#117	C₂²	1	1	yes	characteristic, complemented
28	C₂²×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	—
29	C₂²×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	—
30	C₂²×C₄²×C₂₃	C₂²	1	2	yes	—
31	C₂²×C₄²×C₂₃	C₂²	1	2	yes	—
32	C₂₃×#401	C₂²	1	2	yes	complemented
33	C₂₃×#400	C₂²	1	2	yes	complemented
34	C₂₃×#400	C₂²	1	2	yes	complemented
35	C₂₃×#400	C₂²	1	2	yes	complemented
36	C₂₃×#400	C₂²	1	2	yes	complemented
37	C₂₃×#400	C₂²	1	1	yes	characteristic, complemented
38	C₂₃×#399	C₂²	1	1	yes	characteristic
39	C₂₃×#398	C₂²	1	1	yes	characteristic, complemented
40	C₂₃×#397	C₂²	1	1	yes	characteristic
41	C₂₃×#397	C₂²	1	2	yes	—
42	C₂₃×#397	C₂²	1	2	yes	—
43	C₂₃×#397	C₂²	1	2	yes	—
44	C₂₃×#397	C₂²	1	1	yes	characteristic
45	C₂₃×#397	C₂²	1	1	yes	characteristic, complemented
46	C₂₃×#397	C₂²	1	2	yes	complemented
47	C₂₃×#396	C₂²	1	2	yes	—
48	C₂₃×#394	C₂²	1	2	yes	—
49	C₂₃×#394	C₂²	1	2	yes	—
50	C₂₃×#393	C₂²	1	1	yes	characteristic
51	C₂₃×#393	C₂²	1	1	yes	characteristic, complemented
52	C₂₃×#391	C₂²	1	2	yes	complemented
53	C₂₃×#389	C₂²	1	2	yes	complemented
54	C₂₃×#388	C₂²	1	2	yes	complemented
55	C₂₃×#388	C₂²	1	2	yes	complemented
56	C₂₃×#388	C₂²	1	2	yes	complemented
57	C₂₃×#388	C₂²	1	2	yes	complemented
58	C₂₃×#387	C₂²	1	2	yes	complemented
59	C₂₃×#387	C₂²	1	2	yes	complemented
60	C₂₃×#387	C₂²	1	2	yes	complemented
61	C₂₃×#387	C₂²	1	2	yes	complemented
62	C₂₃×#387	C₂²	1	2	yes	complemented
63	C₂₃×#387	C₂²	1	2	yes	complemented
64	C₂₃×#386	C₂²	1	2	yes	—
65	C₂₃×#386	C₂²	1	2	yes	—
66	C₂₃×#386	C₂²	1	2	yes	—
67	C₂₃×#386	C₂²	1	2	yes	—
68	C₂₃×#386	C₂²	1	1	yes	characteristic
69	C₂₃×#385	C₂²	1	2	yes	—
70	C₂₃×#385	C₂²	1	2	yes	—
71	C₂₃×#385	C₂²	1	2	yes	—
72	C₂₃×#385	C₂²	1	2	yes	—
73	C₂₃×#385	C₂²	1	2	yes	—
74	C₂₃×#385	C₂²	1	2	yes	—
75	C₂₃×#385	C₂²	1	1	yes	characteristic
76	C₂₃×#383	C₂²	1	2	yes	complemented
77	C₂₃×#383	C₂²	1	2	yes	complemented
78	C₂₃×#382	C₂²	1	2	yes	complemented
79	C₂₃×#382	C₂²	1	2	yes	complemented
80	C₂₃×#381	C₂²	1	2	yes	—
81	C₂₃×#381	C₂²	1	2	yes	—
82	C₂₃×#381	C₂²	1	2	yes	—
83	C₂₃×#380	C₂²	1	2	yes	—
84	C₂₃×#380	C₂²	1	2	yes	—
85	C₂₃×#380	C₂²	1	2	yes	—
86	C₂₃×#379	C₂²	1	1	yes	characteristic
87	C₄×C₄⋊C₄×C₂₃	C₂²	1	2	yes	complemented
88	C₄×C₄⋊C₄×C₂₃	C₂²	1	2	yes	complemented
89	C₄×C₄⋊C₄×C₂₃	C₂²	1	2	yes	complemented
90	C₄×C₄⋊C₄×C₂₃	C₂²	1	2	yes	complemented
91	C₄×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	—
92	C₄×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
93	C₄×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	—
94	C₄×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	—
95	C₄×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	—
96	C₄×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	—
97	C₄×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	—
98	C₄×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	—
99	C₄×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	—
100	C₄×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	—
101	C₄×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	complemented
102	C₄×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic, complemented
103	C₂₃×#376	C₂²	1	1	yes	characteristic, complemented
104	C₂₃×#376	C₂²	1	2	yes	complemented
105	C₂×C₂₃×#95	C₂²	1	2	yes	—
106	C₂×C₂₃×#95	C₂²	1	2	yes	—
107	C₂⁵×C₂₃	C₂³	1	1	yes	characteristic
108	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
109	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
110	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
111	C₂³×C₄×C₂₃	—	2	8	no	—
112	C₂³×C₄×C₂₃	—	4	2	no	—
113	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
114	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
115	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
116	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
117	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
118	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
119	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
120	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
121	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
122	C₂₃×#123	—	2	8	no	—
123	C₂₃×C₂²⋊Q₈	—	2	8	no	—
124	C₂₃×#120	—	2	4	no	—
125	C₄×Q₈×C₂₃	—	4	2	no	—
126	C₄×D₄×C₂₃	—	2	8	no	—
127	C₄×D₄×C₂₃	—	4	2	no	—
128	C₂₃×#117	—	4	2	no	—
129	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
130	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
131	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	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×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
137	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
138	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
139	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
140	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
141	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
142	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
143	C₂×C₂²⋊C₄×C₂₃	—	2	8	no	—
144	C₂×C₂²⋊C₄×C₂₃	—	2	8	no	—
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×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
150	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
151	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
152	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
153	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
154	C₂×C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
155	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
156	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
157	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
158	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
159	C₂×C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
160	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
161	C₂×C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
162	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
163	C₂×C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
164	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
165	C₂×C₄²×C₂₃	—	2	8	no	—
166	C₂×C₄²×C₂₃	—	4	4	no	—
167	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
168	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
169	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
170	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
171	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
172	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
173	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
174	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
175	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
176	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
177	C₂₃×#95	C₂³	1	2	yes	—
178	C₂₃×#95	C₂³	1	2	yes	—
179	C₂₃×#95	C₂³	1	2	yes	—
180	C₂₃×#95	C₂³	1	2	yes	—
181	C₂₃×#95	C₂³	1	2	yes	—
182	C₂₃×#95	C₂³	1	2	yes	—
183	C₂₃×#95	C₂³	1	2	yes	—
184	C₂₃×#95	C₂³	1	2	yes	—
185	C₂₃×#95	C₂³	1	1	yes	characteristic
186	C₂₃×#95	C₂³	1	2	yes	—
187	C₂₃×#95	C₂³	1	2	yes	—
188	C₂₃×#95	C₂³	1	2	yes	—
189	C₂₃×#95	C₂³	1	1	yes	characteristic
190	C₂₃×#95	C₂³	1	2	yes	—
191	C₂₃×#95	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	1	yes	characteristic
196	C₂₃×#95	C₂³	1	2	yes	—
197	C₂₃×#95	C₂³	1	2	yes	—
198	C₂₃×#95	C₂³	1	1	yes	characteristic
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	C₂⁴×C₂₃	—	2	4	no	—
208	C₂⁴×C₂₃	—	2	4	no	—
209	C₂⁴×C₂₃	—	4	1	no	—
210	C₂⁴×C₂₃	—	4	1	no	—
211	C₂⁴×C₂₃	#41	1	4	yes	—
212	C₂⁴×C₂₃	C₂⁴	1	1	yes	characteristic
213	C₂⁴×C₂₃	C₂⁴	1	1	yes	characteristic
214	C₂⁴×C₂₃	C₂⁴	1	2	yes	—
215	C₂×Q₈×C₂₃	—	2	4	no	—
216	C₂×Q₈×C₂₃	—	4	1	no	—
217	C₂×D₄×C₂₃	—	2	4	no	—
218	C₂×D₄×C₂₃	—	2	2	no	—
219	C₂×D₄×C₂₃	—	2	4	no	—
220	C₂×D₄×C₂₃	—	2	4	no	—
221	C₂×D₄×C₂₃	—	4	1	no	—
222	C₂×D₄×C₂₃	—	4	1	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	4	no	—
229	C₂²×C₄×C₂₃	—	2	4	no	—
230	C₂²×C₄×C₂₃	—	2	4	no	—
231	C₂²×C₄×C₂₃	—	2	4	no	—
232	C₂²×C₄×C₂₃	—	2	4	no	—
233	C₂²×C₄×C₂₃	—	2	4	no	—
234	C₂²×C₄×C₂₃	—	2	4	no	—
235	C₂²×C₄×C₂₃	—	2	4	no	—
236	C₂²×C₄×C₂₃	—	2	4	no	—
237	C₂²×C₄×C₂₃	—	2	4	no	—
238	C₂²×C₄×C₂₃	—	2	2	no	—
239	C₂²×C₄×C₂₃	—	2	2	no	—
240	C₂²×C₄×C₂₃	—	4	2	no	—
241	C₂²×C₄×C₂₃	—	4	2	no	—
242	C₂²×C₄×C₂₃	—	4	1	no	—
243	C₂²×C₄×C₂₃	—	4	2	no	—
244	C₂²×C₄×C₂₃	—	4	2	no	—
245	C₂²×C₄×C₂₃	—	4	2	no	—
246	C₂²×C₄×C₂₃	—	4	16	no	—
247	C₂²×C₄×C₂₃	#41	1	8	yes	—
248	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
249	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
250	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
251	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
252	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
253	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
254	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
255	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
256	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
257	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
258	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
259	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
260	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
261	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
262	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
263	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
264	C₄⋊C₄×C₂₃	—	2	4	no	—
265	C₄⋊C₄×C₂₃	—	2	4	no	—
266	C₄⋊C₄×C₂₃	—	2	4	no	—
267	C₄⋊C₄×C₂₃	—	2	4	no	—
268	C₄⋊C₄×C₂₃	—	2	4	no	—
269	C₄⋊C₄×C₂₃	—	2	4	no	—
270	C₄⋊C₄×C₂₃	—	4	2	no	—
271	C₄⋊C₄×C₂₃	—	4	2	no	—
272	C₄⋊C₄×C₂₃	—	4	2	no	—
273	C₄⋊C₄×C₂₃	—	4	1	no	—
274	C₄⋊C₄×C₂₃	—	4	1	no	—
275	C₄⋊C₄×C₂₃	—	4	1	no	—
276	C₄⋊C₄×C₂₃	—	4	2	no	—
277	C₄⋊C₄×C₂₃	—	4	1	no	—
278	C₂²⋊C₄×C₂₃	—	2	4	no	—
279	C₂²⋊C₄×C₂₃	—	2	4	no	—
280	C₂²⋊C₄×C₂₃	—	2	4	no	—
281	C₂²⋊C₄×C₂₃	—	2	4	no	—
282	C₂²⋊C₄×C₂₃	—	2	4	no	—
283	C₂²⋊C₄×C₂₃	—	2	4	no	—
284	C₂²⋊C₄×C₂₃	—	2	2	no	—
285	C₂²⋊C₄×C₂₃	—	2	4	no	—
286	C₂²⋊C₄×C₂₃	—	2	4	no	—
287	C₂²⋊C₄×C₂₃	—	2	4	no	—
288	C₂²⋊C₄×C₂₃	—	2	4	no	—
289	C₂²⋊C₄×C₂₃	—	2	4	no	—
290	C₂²⋊C₄×C₂₃	—	2	4	no	—
291	C₂²⋊C₄×C₂₃	—	2	4	no	—
292	C₂²⋊C₄×C₂₃	—	4	1	no	—
293	C₂²⋊C₄×C₂₃	—	4	2	no	—
294	C₂²⋊C₄×C₂₃	—	4	2	no	—
295	C₂²⋊C₄×C₂₃	—	4	1	no	—
296	C₂²⋊C₄×C₂₃	—	4	1	no	—
297	C₂²⋊C₄×C₂₃	#41	1	8	yes	—
298	C₄²×C₂₃	—	2	4	no	—
299	C₄²×C₂₃	—	2	4	no	—
300	C₄²×C₂₃	—	2	4	no	—
301	C₄²×C₂₃	—	2	4	no	—
302	C₄²×C₂₃	—	2	4	no	—
303	C₄²×C₂₃	—	2	4	no	—
304	C₄²×C₂₃	—	2	4	no	—
305	C₄²×C₂₃	—	2	2	no	—
306	C₄²×C₂₃	—	4	2	no	—
307	C₄²×C₂₃	—	4	2	no	—
308	#34754	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
309	C₂³×C₂₃	—	2	2	no	—
310	C₂³×C₂₃	—	2	2	no	—
311	C₂³×C₂₃	—	2	2	no	—
312	C₂³×C₂₃	—	2	2	no	—
313	C₂³×C₂₃	—	2	16	no	—
314	C₂³×C₂₃	—	2	2	no	—
315	C₂³×C₂₃	—	2	2	no	—
316	C₂³×C₂₃	—	2	1	no	—
317	C₂³×C₂₃	—	2	1	no	—
318	C₂³×C₂₃	—	2	2	no	—
319	C₂³×C₂₃	—	2	2	no	—
320	C₂³×C₂₃	—	2	1	no	—
321	C₂³×C₂₃	—	2	1	no	—
322	C₂³×C₂₃	—	2	1	no	—
323	C₂³×C₂₃	—	4	4	no	—
324	C₂³×C₂₃	—	4	4	no	—
325	C₂³×C₂₃	—	4	8	no	—
326	C₂³×C₂₃	—	4	4	no	—
327	C₂³×C₂₃	C₂×#41	1	2	yes	—
328	C₂³×C₂₃	C₂×#41	1	4	yes	—
329	C₂³×C₂₃	C₂×#41	1	4	yes	—
330	C₂³×C₂₃	C₂×#41	1	4	yes	—
331	C₂³×C₂₃	C₂⁵	1	1	yes	characteristic
332	Q₈×C₂₃	—	4	4	no	—
333	D₄×C₂₃	—	4	4	no	—
334	D₄×C₂₃	—	4	8	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	16	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	2	no	—
346	C₂×C₄×C₂₃	—	2	2	no	—
347	C₂×C₄×C₂₃	—	2	2	no	—
348	C₂×C₄×C₂₃	—	2	2	no	—
349	C₂×C₄×C₂₃	—	2	2	no	—
350	C₂×C₄×C₂₃	—	2	2	no	—
351	C₂×C₄×C₂₃	—	2	2	no	—
352	C₂×C₄×C₂₃	—	2	2	no	—
353	C₂×C₄×C₂₃	—	2	2	no	—
354	C₂×C₄×C₂₃	—	2	1	no	—
355	C₂×C₄×C₂₃	—	2	2	no	—
356	C₂×C₄×C₂₃	—	2	2	no	—
357	C₂×C₄×C₂₃	—	2	2	no	—
358	C₂×C₄×C₂₃	—	2	2	no	—
359	C₂×C₄×C₂₃	—	2	2	no	—
360	C₂×C₄×C₂₃	—	2	2	no	—
361	C₂×C₄×C₂₃	—	2	2	no	—
362	C₂×C₄×C₂₃	—	2	2	no	—
363	C₂×C₄×C₂₃	—	2	2	no	—
364	C₂×C₄×C₂₃	—	2	2	no	—
365	C₂×C₄×C₂₃	—	2	2	no	—
366	C₂×C₄×C₂₃	—	2	1	no	—
367	C₂×C₄×C₂₃	—	2	1	no	—
368	C₂×C₄×C₂₃	—	2	1	no	—
369	C₂×C₄×C₂₃	—	2	1	no	—
370	C₂×C₄×C₂₃	—	2	2	no	—
371	C₂×C₄×C₂₃	—	2	2	no	—
372	C₂×C₄×C₂₃	—	2	2	no	—
373	C₂×C₄×C₂₃	—	2	2	no	—
374	C₂×C₄×C₂₃	—	2	1	no	—
375	C₂×C₄×C₂₃	—	4	4	no	—
376	C₂×C₄×C₂₃	—	4	8	no	—
377	C₂×C₄×C₂₃	—	4	8	no	—
378	C₂×C₄×C₂₃	—	4	8	no	—
379	C₂×C₄×C₂₃	—	4	8	no	—
380	C₂×C₄×C₂₃	—	4	8	no	—
381	C₂×C₄×C₂₃	—	4	4	no	—
382	C₂×C₄×C₂₃	—	4	4	no	—
383	C₂×C₄×C₂₃	C₂×#41	1	4	yes	—
384	C₂×C₄×C₂₃	C₂×#41	1	4	yes	—
385	C₂×C₄×C₂₃	C₂×#41	1	4	yes	—
386	C₂×C₄×C₂₃	C₂×#41	1	4	yes	—
387	C₂×C₄×C₂₃	H(5,𝔽₂)	1	2	yes	—
388	#2523	C₂×C₂₃	1	1	yes	characteristic, complemented
389	#2518	C₂×C₂₃	1	2	yes	complemented
390	#2517	C₂×C₂₃	1	1	yes	characteristic, complemented
391	#2510	C₂×C₂₃	1	2	yes	complemented
392	#2505	C₂×C₂₃	1	2	yes	complemented
393	#2493	C₂×C₂₃	1	2	yes	complemented
394	#2488	C₂×C₂₃	1	2	yes	complemented
395	#2483	C₂×C₂₃	1	1	yes	characteristic, complemented
396	#2437	C₂×C₂₃	1	1	yes	characteristic, complemented
397	#2412	C₂×C₂₃	1	2	yes	—
398	#2401	C₂×C₂₃	1	2	yes	complemented
399	#2398	C₂×C₂₃	1	1	yes	characteristic, complemented
400	#2395	C₂×C₂₃	1	1	yes	characteristic, complemented
401	C₄×C₂²⋊Q₈	C₂×C₂₃	1	2	yes	complemented
402	C₄×#123	C₂×C₂₃	1	2	yes	complemented
403	C₄×#120	C₂×C₂₃	1	1	yes	characteristic
404	#2290	C₂×C₂₃	1	2	yes	complemented
405	#2283	C₂×C₂₃	1	2	yes	complemented
406	C₂×C₄×C₂²⋊C₄	C₂×C₂₃	1	2	yes	complemented
407	C₂²×C₂₃	—	2	4	no	—
408	C₂²×C₂₃	—	2	4	no	—
409	C₂²×C₂₃	—	2	4	no	—
410	C₂²×C₂₃	—	2	4	no	—
411	C₂²×C₂₃	—	2	4	no	—
412	C₂²×C₂₃	—	2	4	no	—
413	C₂²×C₂₃	—	2	4	no	—
414	C₂²×C₂₃	—	2	2	no	—
415	C₂²×C₂₃	—	4	16	no	—
416	C₂²×C₂₃	—	4	1	no	—
417	C₂²×C₂₃	—	4	2	no	—
418	C₂²×C₂₃	—	4	1	no	—
419	C₂²×C₂₃	—	4	2	no	—
420	C₂²×C₂₃	—	4	1	no	—
421	C₂²×C₂₃	—	4	1	no	—
422	C₂²×C₂₃	—	4	2	no	—
423	C₂²×C₂₃	—	4	1	no	—
424	C₂²×C₂₃	#529	1	8	yes	—
425	C₂²×C₂₃	C₂²×#41	1	1	yes	characteristic
426	C₂²×C₂₃	C₂²×#41	1	2	yes	—
427	C₂²×C₂₃	C₂²×#41	1	2	yes	—
428	C₂²×C₂₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
429	C₂²×C₂₃	#585	1	1	yes	characteristic
430	C₄×C₂₃	—	2	4	no	—
431	C₄×C₂₃	—	2	4	no	—
432	C₄×C₂₃	—	2	4	no	—
433	C₄×C₂₃	—	4	2	no	—
434	C₄×C₂₃	—	4	2	no	—
435	C₄×C₂₃	—	4	2	no	—
436	C₄×C₂₃	—	4	2	no	—
437	C₄×C₂₃	—	4	2	no	—
438	C₄×C₂₃	—	4	1	no	—
439	C₄×C₂₃	—	4	1	no	—
440	C₄×C₂₃	—	4	1	no	—
441	C₄×C₂₃	—	4	2	no	—
442	C₄×C₂₃	—	4	2	no	—
443	C₄×C₂₃	—	4	2	no	—
444	C₄×C₂₃	—	4	1	no	—
445	C₄×C₂₃	#551	1	4	yes	—
446	C₂⁴×C₄	C₂²×C₂₃	1	1	yes	characteristic
447	C₂×#123	C₂²×C₂₃	1	2	yes	—
448	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	2	yes	—
449	C₂×#120	C₂²×C₂₃	1	1	yes	characteristic
450	C₂×C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
451	C₂×C₄×D₄	C₂²×C₂₃	1	2	yes	—
452	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
453	C₂×#117	C₂²×C₂₃	1	1	yes	characteristic, complemented
454	C₂²×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
455	C₂²×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
456	C₂²×C₄²	C₂²×C₂₃	1	2	yes	—
457	C₂²×C₄²	C₂²×C₂₃	1	2	yes	—
458	#401	C₂²×C₂₃	1	2	yes	complemented
459	#400	C₂²×C₂₃	1	1	yes	characteristic, complemented
460	#400	C₂²×C₂₃	1	2	yes	complemented
461	#400	C₂²×C₂₃	1	2	yes	complemented
462	#400	C₂²×C₂₃	1	2	yes	complemented
463	#400	C₂²×C₂₃	1	2	yes	complemented
464	#399	C₂²×C₂₃	1	1	yes	characteristic
465	#398	C₂²×C₂₃	1	1	yes	characteristic, complemented
466	#397	C₂²×C₂₃	1	1	yes	characteristic
467	#397	C₂²×C₂₃	1	1	yes	characteristic
468	#397	C₂²×C₂₃	1	2	yes	—
469	#397	C₂²×C₂₃	1	2	yes	—
470	#397	C₂²×C₂₃	1	2	yes	—
471	#397	C₂²×C₂₃	1	2	yes	complemented
472	#397	C₂²×C₂₃	1	1	yes	characteristic, complemented
473	#396	C₂²×C₂₃	1	2	yes	—
474	#394	C₂²×C₂₃	1	2	yes	—
475	#394	C₂²×C₂₃	1	2	yes	—
476	#393	C₂²×C₂₃	1	1	yes	characteristic
477	#393	C₂²×C₂₃	1	1	yes	characteristic, complemented
478	#391	C₂²×C₂₃	1	2	yes	complemented
479	#389	C₂²×C₂₃	1	2	yes	complemented
480	#388	C₂²×C₂₃	1	2	yes	complemented
481	#388	C₂²×C₂₃	1	2	yes	complemented
482	#388	C₂²×C₂₃	1	2	yes	complemented
483	#388	C₂²×C₂₃	1	2	yes	complemented
484	#387	C₂²×C₂₃	1	2	yes	complemented
485	#387	C₂²×C₂₃	1	2	yes	complemented
486	#387	C₂²×C₂₃	1	2	yes	complemented
487	#387	C₂²×C₂₃	1	2	yes	complemented
488	#387	C₂²×C₂₃	1	2	yes	complemented
489	#387	C₂²×C₂₃	1	2	yes	complemented
490	#386	C₂²×C₂₃	1	2	yes	—
491	#386	C₂²×C₂₃	1	2	yes	—
492	#386	C₂²×C₂₃	1	2	yes	—
493	#386	C₂²×C₂₃	1	2	yes	—
494	#386	C₂²×C₂₃	1	1	yes	characteristic
495	#385	C₂²×C₂₃	1	2	yes	—
496	#385	C₂²×C₂₃	1	2	yes	—
497	#385	C₂²×C₂₃	1	2	yes	—
498	#385	C₂²×C₂₃	1	2	yes	—
499	#385	C₂²×C₂₃	1	2	yes	—
500	#385	C₂²×C₂₃	1	2	yes	—
501	#385	C₂²×C₂₃	1	1	yes	characteristic
502	#383	C₂²×C₂₃	1	2	yes	complemented
503	#383	C₂²×C₂₃	1	2	yes	complemented
504	#382	C₂²×C₂₃	1	2	yes	complemented
505	#382	C₂²×C₂₃	1	2	yes	complemented
506	#381	C₂²×C₂₃	1	2	yes	—
507	#381	C₂²×C₂₃	1	2	yes	—
508	#381	C₂²×C₂₃	1	2	yes	—
509	#380	C₂²×C₂₃	1	2	yes	—
510	#380	C₂²×C₂₃	1	2	yes	—
511	#380	C₂²×C₂₃	1	2	yes	—
512	#379	C₂²×C₂₃	1	1	yes	characteristic
513	C₄×C₄⋊C₄	C₂²×C₂₃	1	2	yes	complemented
514	C₄×C₄⋊C₄	C₂²×C₂₃	1	2	yes	complemented
515	C₄×C₄⋊C₄	C₂²×C₂₃	1	2	yes	complemented
516	C₄×C₄⋊C₄	C₂²×C₂₃	1	2	yes	complemented
517	C₄×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
518	C₄×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
519	C₄×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
520	C₄×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
521	C₄×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
522	C₄×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
523	C₄×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
524	C₄×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
525	C₄×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
526	C₄×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
527	C₄×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic, complemented
528	C₄×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	complemented
529	#376	C₂²×C₂₃	1	1	yes	characteristic, complemented
530	#376	C₂²×C₂₃	1	2	yes	complemented
531	C₂×#95	C₂²×C₂₃	1	2	yes	—
532	C₂×#95	C₂²×C₂₃	1	2	yes	—
533	C₂×C₂₃	—	2	8	no	—
534	C₂×C₂₃	—	4	2	no	—
535	C₂×C₂₃	—	8	1	no	—
536	C₂×C₂₃	C₂×#529	1	2	yes	—
537	C₂×C₂₃	#3459	1	1	yes	characteristic
538	C₂×C₂₃	C₂×#551	1	1	yes	characteristic
539	C₂×C₂₃	#3475	1	2	yes	—
540	C₂×C₂₃	#3481	1	1	yes	characteristic
541	C₂⁵	C₂³×C₂₃	1	1	yes	characteristic
542	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
543	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
544	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
545	C₂³×C₄	—	2	8	no	—
546	C₂³×C₄	—	4	2	no	—
547	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
548	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
549	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
550	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
551	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
552	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
553	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
554	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
555	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
556	#123	—	2	8	no	—
557	C₂²⋊Q₈	—	2	8	no	—
558	#120	—	2	4	no	—
559	C₄×Q₈	—	4	2	no	—
560	C₄×D₄	—	2	8	no	—
561	C₄×D₄	—	4	2	no	—
562	#117	—	4	2	no	—
563	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
564	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
565	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
566	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
567	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
568	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
569	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
570	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
571	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
572	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
573	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
574	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
575	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
576	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
577	C₂×C₂²⋊C₄	—	2	8	no	—
578	C₂×C₂²⋊C₄	—	2	8	no	—
579	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
580	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
581	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
582	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
583	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
584	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
585	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
586	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
587	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
588	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
589	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
590	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
591	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
592	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
593	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
594	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
595	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
596	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
597	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
598	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
599	C₂×C₄²	—	2	8	no	—
600	C₂×C₄²	—	4	4	no	—
601	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
602	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
603	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
604	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
605	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
606	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
607	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
608	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
609	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
610	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
611	#95	C₂³×C₂₃	1	2	yes	—
612	#95	C₂³×C₂₃	1	2	yes	—
613	#95	C₂³×C₂₃	1	2	yes	—
614	#95	C₂³×C₂₃	1	2	yes	—
615	#95	C₂³×C₂₃	1	2	yes	—
616	#95	C₂³×C₂₃	1	2	yes	—
617	#95	C₂³×C₂₃	1	2	yes	—
618	#95	C₂³×C₂₃	1	2	yes	—
619	#95	C₂³×C₂₃	1	1	yes	characteristic
620	#95	C₂³×C₂₃	1	2	yes	—
621	#95	C₂³×C₂₃	1	2	yes	—
622	#95	C₂³×C₂₃	1	2	yes	—
623	#95	C₂³×C₂₃	1	1	yes	characteristic
624	#95	C₂³×C₂₃	1	2	yes	—
625	#95	C₂³×C₂₃	1	2	yes	—
626	#95	C₂³×C₂₃	1	2	yes	—
627	#95	C₂³×C₂₃	1	2	yes	—
628	#95	C₂³×C₂₃	1	2	yes	—
629	#95	C₂³×C₂₃	1	1	yes	characteristic
630	#95	C₂³×C₂₃	1	2	yes	—
631	#95	C₂³×C₂₃	1	2	yes	—
632	#95	C₂³×C₂₃	1	1	yes	characteristic
633	#95	C₂³×C₂₃	1	2	yes	—
634	#95	C₂³×C₂₃	1	2	yes	—
635	#95	C₂³×C₂₃	1	2	yes	—
636	#95	C₂³×C₂₃	1	2	yes	—
637	#95	C₂³×C₂₃	1	2	yes	—
638	#95	C₂³×C₂₃	1	2	yes	—
639	#95	C₂³×C₂₃	1	2	yes	—
640	#95	C₂³×C₂₃	1	2	yes	—
641	C₂₃	#34754	1	1	yes	characteristic, direct product factor, Sylow
642	C₂⁴	—	2	4	no	—
643	C₂⁴	—	2	4	no	—
644	C₂⁴	—	4	1	no	—
645	C₂⁴	—	4	1	no	—
646	C₂⁴	#41×C₂₃	1	4	yes	—
647	C₂⁴	C₂⁴×C₂₃	1	1	yes	characteristic
648	C₂⁴	C₂⁴×C₂₃	1	1	yes	characteristic
649	C₂⁴	C₂⁴×C₂₃	1	2	yes	—
650	C₂×Q₈	—	2	4	no	—
651	C₂×Q₈	—	4	1	no	—
652	C₂×D₄	—	2	4	no	—
653	C₂×D₄	—	2	2	no	—
654	C₂×D₄	—	2	4	no	—
655	C₂×D₄	—	2	4	no	—
656	C₂×D₄	—	4	1	no	—
657	C₂×D₄	—	4	1	no	—
658	C₂²×C₄	—	2	4	no	—
659	C₂²×C₄	—	2	4	no	—
660	C₂²×C₄	—	2	4	no	—
661	C₂²×C₄	—	2	4	no	—
662	C₂²×C₄	—	2	4	no	—
663	C₂²×C₄	—	2	4	no	—
664	C₂²×C₄	—	2	4	no	—
665	C₂²×C₄	—	2	4	no	—
666	C₂²×C₄	—	2	4	no	—
667	C₂²×C₄	—	2	4	no	—
668	C₂²×C₄	—	2	4	no	—
669	C₂²×C₄	—	2	4	no	—
670	C₂²×C₄	—	2	4	no	—
671	C₂²×C₄	—	2	4	no	—
672	C₂²×C₄	—	2	4	no	—
673	C₂²×C₄	—	2	2	no	—
674	C₂²×C₄	—	2	2	no	—
675	C₂²×C₄	—	4	2	no	—
676	C₂²×C₄	—	4	2	no	—
677	C₂²×C₄	—	4	1	no	—
678	C₂²×C₄	—	4	2	no	—
679	C₂²×C₄	—	4	2	no	—
680	C₂²×C₄	—	4	2	no	—
681	C₂²×C₄	—	4	16	no	—
682	C₂²×C₄	#41×C₂₃	1	8	yes	—
683	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
684	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
685	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
686	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
687	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
688	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
689	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
690	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
691	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
692	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
693	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
694	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
695	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
696	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
697	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
698	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
699	C₄⋊C₄	—	2	4	no	—
700	C₄⋊C₄	—	2	4	no	—
701	C₄⋊C₄	—	2	4	no	—
702	C₄⋊C₄	—	2	4	no	—
703	C₄⋊C₄	—	2	4	no	—
704	C₄⋊C₄	—	2	4	no	—
705	C₄⋊C₄	—	4	1	no	—
706	C₄⋊C₄	—	4	1	no	—
707	C₄⋊C₄	—	4	1	no	—
708	C₄⋊C₄	—	4	2	no	—
709	C₄⋊C₄	—	4	1	no	—
710	C₄⋊C₄	—	4	2	no	—
711	C₄⋊C₄	—	4	2	no	—
712	C₄⋊C₄	—	4	2	no	—
713	C₂²⋊C₄	—	2	4	no	—
714	C₂²⋊C₄	—	2	4	no	—
715	C₂²⋊C₄	—	2	4	no	—
716	C₂²⋊C₄	—	2	4	no	—
717	C₂²⋊C₄	—	2	4	no	—
718	C₂²⋊C₄	—	2	4	no	—
719	C₂²⋊C₄	—	2	2	no	—
720	C₂²⋊C₄	—	2	4	no	—
721	C₂²⋊C₄	—	2	4	no	—
722	C₂²⋊C₄	—	2	4	no	—
723	C₂²⋊C₄	—	2	4	no	—
724	C₂²⋊C₄	—	2	4	no	—
725	C₂²⋊C₄	—	2	4	no	—
726	C₂²⋊C₄	—	2	4	no	—
727	C₂²⋊C₄	—	4	2	no	—
728	C₂²⋊C₄	—	4	1	no	—
729	C₂²⋊C₄	—	4	1	no	—
730	C₂²⋊C₄	—	4	1	no	—
731	C₂²⋊C₄	—	4	2	no	—
732	C₂²⋊C₄	#41×C₂₃	1	8	yes	—
733	C₄²	—	2	4	no	—
734	C₄²	—	2	4	no	—
735	C₄²	—	2	4	no	—
736	C₄²	—	2	4	no	—
737	C₄²	—	2	4	no	—
738	C₄²	—	2	4	no	—
739	C₄²	—	2	4	no	—
740	C₄²	—	2	2	no	—
741	C₄²	—	4	2	no	—
742	C₄²	—	4	2	no	—
743	C₂³	—	2	2	no	—
744	C₂³	—	2	2	no	—
745	C₂³	—	2	2	no	—
746	C₂³	—	2	2	no	—
747	C₂³	—	2	2	no	—
748	C₂³	—	2	2	no	—
749	C₂³	—	2	1	no	—
750	C₂³	—	2	1	no	—
751	C₂³	—	2	16	no	—
752	C₂³	—	2	2	no	—
753	C₂³	—	2	2	no	—
754	C₂³	—	2	1	no	—
755	C₂³	—	2	1	no	—
756	C₂³	—	2	1	no	—
757	C₂³	—	4	4	no	—
758	C₂³	—	4	4	no	—
759	C₂³	—	4	8	no	—
760	C₂³	—	4	4	no	—
761	C₂³	C₂×#41×C₂₃	1	2	yes	—
762	C₂³	C₂×#41×C₂₃	1	4	yes	—
763	C₂³	C₂×#41×C₂₃	1	4	yes	—
764	C₂³	C₂×#41×C₂₃	1	4	yes	—
765	C₂³	C₂⁵×C₂₃	1	1	yes	characteristic
766	Q₈	—	4	4	no	—
767	D₄	—	4	4	no	—
768	D₄	—	4	8	no	—
769	C₂×C₄	—	2	2	no	—
770	C₂×C₄	—	2	2	no	—
771	C₂×C₄	—	2	2	no	—
772	C₂×C₄	—	2	2	no	—
773	C₂×C₄	—	2	2	no	—
774	C₂×C₄	—	2	2	no	—
775	C₂×C₄	—	2	16	no	—
776	C₂×C₄	—	2	2	no	—
777	C₂×C₄	—	2	2	no	—
778	C₂×C₄	—	2	2	no	—
779	C₂×C₄	—	2	2	no	—
780	C₂×C₄	—	2	2	no	—
781	C₂×C₄	—	2	2	no	—
782	C₂×C₄	—	2	2	no	—
783	C₂×C₄	—	2	2	no	—
784	C₂×C₄	—	2	2	no	—
785	C₂×C₄	—	2	2	no	—
786	C₂×C₄	—	2	2	no	—
787	C₂×C₄	—	2	2	no	—
788	C₂×C₄	—	2	1	no	—
789	C₂×C₄	—	2	2	no	—
790	C₂×C₄	—	2	2	no	—
791	C₂×C₄	—	2	2	no	—
792	C₂×C₄	—	2	2	no	—
793	C₂×C₄	—	2	2	no	—
794	C₂×C₄	—	2	2	no	—
795	C₂×C₄	—	2	2	no	—
796	C₂×C₄	—	2	2	no	—
797	C₂×C₄	—	2	2	no	—
798	C₂×C₄	—	2	2	no	—
799	C₂×C₄	—	2	2	no	—
800	C₂×C₄	—	2	1	no	—
801	C₂×C₄	—	2	1	no	—
802	C₂×C₄	—	2	1	no	—
803	C₂×C₄	—	2	1	no	—
804	C₂×C₄	—	2	2	no	—
805	C₂×C₄	—	2	2	no	—
806	C₂×C₄	—	2	2	no	—
807	C₂×C₄	—	2	2	no	—
808	C₂×C₄	—	2	1	no	—
809	C₂×C₄	—	4	4	no	—
810	C₂×C₄	—	4	8	no	—
811	C₂×C₄	—	4	8	no	—
812	C₂×C₄	—	4	8	no	—
813	C₂×C₄	—	4	8	no	—
814	C₂×C₄	—	4	8	no	—
815	C₂×C₄	—	4	4	no	—
816	C₂×C₄	—	4	4	no	—
817	C₂×C₄	C₂×#41×C₂₃	1	4	yes	—
818	C₂×C₄	C₂×#41×C₂₃	1	4	yes	—
819	C₂×C₄	C₂×#41×C₂₃	1	4	yes	—
820	C₂×C₄	C₂×#41×C₂₃	1	4	yes	—
821	C₂×C₄	C₂₃×H(5,𝔽₂)	1	2	yes	—
822	C₂²	—	2	4	no	—
823	C₂²	—	2	4	no	—
824	C₂²	—	2	4	no	—
825	C₂²	—	2	4	no	—
826	C₂²	—	2	4	no	—
827	C₂²	—	2	4	no	—
828	C₂²	—	2	4	no	—
829	C₂²	—	2	2	no	—
830	C₂²	—	4	16	no	—
831	C₂²	—	4	1	no	—
832	C₂²	—	4	2	no	—
833	C₂²	—	4	1	no	—
834	C₂²	—	4	2	no	—
835	C₂²	—	4	1	no	—
836	C₂²	—	4	1	no	—
837	C₂²	—	4	2	no	—
838	C₂²	—	4	1	no	—
839	C₂²	C₂₃×#529	1	8	yes	—
840	C₂²	C₂²×#41×C₂₃	1	1	yes	characteristic
841	C₂²	C₂²×#41×C₂₃	1	2	yes	—
842	C₂²	C₂²×#41×C₂₃	1	2	yes	—
843	C₂²	C₂×C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
844	C₂²	C₂₃×#585	1	1	yes	characteristic
845	C₄	—	2	4	no	—
846	C₄	—	2	4	no	—
847	C₄	—	2	4	no	—
848	C₄	—	4	2	no	—
849	C₄	—	4	2	no	—
850	C₄	—	4	2	no	—
851	C₄	—	4	2	no	—
852	C₄	—	4	2	no	—
853	C₄	—	4	1	no	—
854	C₄	—	4	1	no	—
855	C₄	—	4	1	no	—
856	C₄	—	4	2	no	—
857	C₄	—	4	2	no	—
858	C₄	—	4	2	no	—
859	C₄	—	4	1	no	—
860	C₄	C₂₃×#551	1	4	yes	—
861	C₂	—	2	8	no	—
862	C₂	—	4	2	no	—
863	C₂	—	8	1	no	—
864	C₂	C₂×C₂₃×#529	1	2	yes	—
865	C₂	C₂₃×#3459	1	1	yes	characteristic
866	C₂	C₂×C₂₃×#551	1	1	yes	characteristic
867	C₂	C₂₃×#3475	1	2	yes	—
868	C₂	C₂₃×#3481	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₂₃	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₂₃
socle	C₂³×C₂₃	C₂⁵
prime radical	C₂×C₂₃×#120	C₂²
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. C₂₃×#2523	C₂	semidirect
2. C₂₃×#2518	C₂	semidirect
3. C₂₃×#2517	C₂	semidirect
4. C₂₃×#2510	C₂	semidirect
5. C₂₃×#2505	C₂	semidirect
6. C₂₃×#2493	C₂	semidirect
7. C₂₃×#2488	C₂	semidirect
8. C₂₃×#2483	C₂	semidirect
9. C₂₃×#2437	C₂	semidirect
11. C₂₃×#2401	C₂	semidirect
12. C₂₃×#2398	C₂	semidirect
13. C₂₃×#2395	C₂	semidirect
14. C₄×C₂₃×C₂²⋊Q₈	C₂	semidirect
15. C₄×C₂₃×#123	C₂	semidirect
17. C₂₃×#2290	C₂	semidirect
18. C₂₃×#2283	C₂	semidirect
19. C₂×C₄×C₂²⋊C₄×C₂₃	C₂	semidirect
24. C₂×C₄×Q₈×C₂₃	C₂²	semidirect
27. C₂×C₂₃×#117	C₂²	semidirect
32. C₂₃×#401	C₂²	semidirect
33. C₂₃×#400	C₂²	semidirect
34. C₂₃×#400	C₂²	semidirect
35. C₂₃×#400	C₂²	semidirect
36. C₂₃×#400	C₂²	semidirect
37. C₂₃×#400	C₂²	semidirect
39. C₂₃×#398	C₂²	semidirect
45. C₂₃×#397	C₂²	semidirect
46. C₂₃×#397	C₂²	semidirect
51. C₂₃×#393	C₂²	semidirect
52. C₂₃×#391	C₂²	semidirect
53. C₂₃×#389	C₂²	semidirect
54. C₂₃×#388	C₂²	semidirect
55. C₂₃×#388	C₂²	semidirect
56. C₂₃×#388	C₂²	semidirect
57. C₂₃×#388	C₂²	semidirect
58. C₂₃×#387	C₂²	semidirect
59. C₂₃×#387	C₂²	semidirect
60. C₂₃×#387	C₂²	semidirect
61. C₂₃×#387	C₂²	semidirect
62. C₂₃×#387	C₂²	semidirect
63. C₂₃×#387	C₂²	semidirect
76. C₂₃×#383	C₂²	semidirect
77. C₂₃×#383	C₂²	semidirect
78. C₂₃×#382	C₂²	semidirect
79. C₂₃×#382	C₂²	semidirect
87. C₄×C₄⋊C₄×C₂₃	C₂²	semidirect
88. C₄×C₄⋊C₄×C₂₃	C₂²	semidirect
89. C₄×C₄⋊C₄×C₂₃	C₂²	semidirect
90. C₄×C₄⋊C₄×C₂₃	C₂²	semidirect
101. C₄×C₂²⋊C₄×C₂₃	C₂²	semidirect
102. C₄×C₂²⋊C₄×C₂₃	C₂²	semidirect
103. C₂₃×#376	C₂²	semidirect
104. C₂₃×#376	C₂²	semidirect
308. #34754	C₂₃	direct (N × H)
388. #2523	C₂×C₂₃	semidirect
389. #2518	C₂×C₂₃	semidirect
390. #2517	C₂×C₂₃	semidirect
391. #2510	C₂×C₂₃	semidirect
392. #2505	C₂×C₂₃	semidirect
393. #2493	C₂×C₂₃	semidirect
394. #2488	C₂×C₂₃	semidirect
395. #2483	C₂×C₂₃	semidirect
396. #2437	C₂×C₂₃	semidirect
398. #2401	C₂×C₂₃	semidirect
399. #2398	C₂×C₂₃	semidirect
400. #2395	C₂×C₂₃	semidirect
401. C₄×C₂²⋊Q₈	C₂×C₂₃	semidirect
402. C₄×#123	C₂×C₂₃	semidirect
404. #2290	C₂×C₂₃	semidirect
405. #2283	C₂×C₂₃	semidirect
406. C₂×C₄×C₂²⋊C₄	C₂×C₂₃	semidirect
450. C₂×C₄×Q₈	C₂²×C₂₃	semidirect
453. C₂×#117	C₂²×C₂₃	semidirect
458. #401	C₂²×C₂₃	semidirect
459. #400	C₂²×C₂₃	semidirect
460. #400	C₂²×C₂₃	semidirect
461. #400	C₂²×C₂₃	semidirect
462. #400	C₂²×C₂₃	semidirect
463. #400	C₂²×C₂₃	semidirect
465. #398	C₂²×C₂₃	semidirect
471. #397	C₂²×C₂₃	semidirect
472. #397	C₂²×C₂₃	semidirect
477. #393	C₂²×C₂₃	semidirect
478. #391	C₂²×C₂₃	semidirect
479. #389	C₂²×C₂₃	semidirect
480. #388	C₂²×C₂₃	semidirect
481. #388	C₂²×C₂₃	semidirect
482. #388	C₂²×C₂₃	semidirect
483. #388	C₂²×C₂₃	semidirect
484. #387	C₂²×C₂₃	semidirect
485. #387	C₂²×C₂₃	semidirect
486. #387	C₂²×C₂₃	semidirect
487. #387	C₂²×C₂₃	semidirect
488. #387	C₂²×C₂₃	semidirect
489. #387	C₂²×C₂₃	semidirect
502. #383	C₂²×C₂₃	semidirect
503. #383	C₂²×C₂₃	semidirect
504. #382	C₂²×C₂₃	semidirect
505. #382	C₂²×C₂₃	semidirect
513. C₄×C₄⋊C₄	C₂²×C₂₃	semidirect
514. C₄×C₄⋊C₄	C₂²×C₂₃	semidirect
515. C₄×C₄⋊C₄	C₂²×C₂₃	semidirect
516. C₄×C₄⋊C₄	C₂²×C₂₃	semidirect
527. C₄×C₂²⋊C₄	C₂²×C₂₃	semidirect
528. C₄×C₂²⋊C₄	C₂²×C₂₃	semidirect
529. #376	C₂²×C₂₃	semidirect
530. #376	C₂²×C₂₃	semidirect
641. C₂₃	#34754	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×#2523	2
C₂₃×#2518	2
C₂₃×#2517	2
C₂₃×#2510	2
C₂₃×#2505	2
C₂₃×#2493	2
C₂₃×#2488	2
C₂₃×#2483	2
C₂₃×#2437	2
C₂₃×#2412	2
C₂₃×#2401	2
C₂₃×#2398	2
C₂₃×#2395	2
C₄×C₂₃×C₂²⋊Q₈	2
C₄×C₂₃×#123	2
C₄×C₂₃×#120	2
C₂₃×#2290	2
C₂₃×#2283	2
C₂×C₄×C₂²⋊C₄×C₂₃	2
#34754	23

Subgroups — C23×#34754 #19182380

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#34754 #19182380