Subgroups — C₂₃×#34715 #19182341

Order 5888.

2840 conjugacy classes of subgroups.

The subgroup lattice has 1156 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₃×#532	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄×#41×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#2476	C₂	1	2	yes	maximal, complemented
4	C₂₃×#2474	C₂	1	2	yes	maximal, complemented
5	C₂₃×#2459	C₂	1	2	yes	maximal, complemented
6	C₂₃×#2456	C₂	1	2	yes	maximal, complemented
7	C₂₃×#2451	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₃×#2445	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₃×#2439	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₃×#2431	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₃×#2426	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₃×#2420	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₃×#2414	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₃×#2407	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₃×#2392	C₂	1	2	yes	maximal, complemented
16	C₂₃×#2388	C₂	1	2	yes	maximal, complemented
17	C₄×C₂₃×#124	C₂	1	1	yes	maximal, characteristic, complemented
18	C₄×C₂₃×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
19	C₄×C₂₃×#123	C₂	1	2	yes	maximal, complemented
20	C₄×C₂₃×#121	C₂	1	1	yes	maximal, characteristic, complemented
21	C₂₃×#2297	C₂	1	2	yes	maximal, complemented
22	C₂₃×#2293	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄²×D₄×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂²×#41×C₂₃	C₂²	1	1	yes	characteristic
25	C₂²×#41×C₂₃	C₂²	1	2	yes	—
26	C₂₃×#532	—	2	8	no	—
27	C₂×C₂₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
28	C₂×C₂₃×#127	C₂²	1	1	yes	characteristic
29	C₂×C₂₃×#124	C₂²	1	2	yes	—
30	C₂×C₂₃×#124	C₂²	1	1	yes	characteristic
31	C₂×C₂₃×#123	C₂²	1	2	yes	—
32	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
33	C₂×C₂₃×#121	C₂²	1	1	yes	characteristic
34	C₂×C₂₃×#121	C₂²	1	1	yes	characteristic
35	C₂×C₂₃×#121	C₂²	1	1	yes	characteristic
36	C₂×C₂₃×#121	C₂²	1	2	yes	—
37	C₄×#41×C₂₃	—	2	8	no	—
38	C₂×C₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic
39	C₂×C₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic
40	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
41	C₂×C₄×D₄×C₂₃	C₂²	1	2	yes	—
42	C₂×C₄×D₄×C₂₃	C₂²	1	2	yes	—
43	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
44	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
45	C₂×C₄×D₄×C₂₃	C₂²	1	2	yes	—
46	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
47	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
48	C₂×C₄×D₄×C₂₃	C₂²	1	2	yes	—
49	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
50	C₂×C₂₃×#117	C₂²	1	1	yes	characteristic
51	C₂×C₂₃×#117	C₂²	1	2	yes	—
52	C₂×C₂₃×#117	C₂²	1	2	yes	—
53	C₂²×C₄²×C₂₃	C₂²	1	1	yes	characteristic
54	C₂²×C₄²×C₂₃	C₂²	1	2	yes	—
55	C₂²×C₄²×C₂₃	C₂²	1	1	yes	characteristic
56	C₂₃×#398	C₂²	1	2	yes	—
57	C₂₃×#397	C₂²	1	2	yes	—
58	C₂₃×#396	C₂²	1	2	yes	—
59	C₂₃×#396	C₂²	1	2	yes	—
60	C₂₃×#395	C₂²	1	2	yes	—
61	C₂₃×#394	C₂²	1	2	yes	—
62	C₂₃×#394	C₂²	1	2	yes	—
63	C₂₃×#394	C₂²	1	2	yes	—
64	C₂₃×#394	C₂²	1	2	yes	—
65	C₂₃×#394	C₂²	1	2	yes	—
66	C₂₃×#394	C₂²	1	2	yes	—
67	C₂₃×#393	C₂²	1	2	yes	—
68	C₂₃×#392	C₂²	1	2	yes	—
69	C₂₃×#392	C₂²	1	2	yes	—
70	C₂₃×#392	C₂²	1	2	yes	—
71	C₂₃×#392	C₂²	1	2	yes	—
72	C₂₃×#391	C₂²	1	1	yes	characteristic
73	C₂₃×#391	C₂²	1	1	yes	characteristic
74	C₂₃×#391	C₂²	1	2	yes	—
75	C₂₃×#391	C₂²	1	2	yes	—
76	C₂₃×#390	C₂²	1	1	yes	characteristic
77	C₂₃×#390	C₂²	1	1	yes	characteristic
78	C₂₃×#390	C₂²	1	2	yes	—
79	C₂₃×#390	C₂²	1	1	yes	characteristic
80	C₂₃×#390	C₂²	1	1	yes	characteristic
81	C₂₃×#390	C₂²	1	2	yes	—
82	C₂₃×#389	C₂²	1	1	yes	characteristic
83	C₂₃×#389	C₂²	1	1	yes	characteristic
84	C₂₃×#389	C₂²	1	1	yes	characteristic
85	C₂₃×#389	C₂²	1	1	yes	characteristic
86	C₂₃×#388	C₂²	1	2	yes	—
87	C₂₃×#388	C₂²	1	2	yes	—
88	C₂₃×#388	C₂²	1	2	yes	—
89	C₂₃×#388	C₂²	1	2	yes	—
90	C₂₃×#388	C₂²	1	2	yes	—
91	C₂₃×#388	C₂²	1	2	yes	—
92	C₂₃×#388	C₂²	1	2	yes	—
93	C₂₃×#387	C₂²	1	2	yes	—
94	C₂₃×#387	C₂²	1	2	yes	—
95	C₂₃×#387	C₂²	1	2	yes	—
96	C₂₃×#386	C₂²	1	2	yes	—
97	C₂₃×#386	C₂²	1	2	yes	—
98	C₂₃×#386	C₂²	1	2	yes	—
99	C₂₃×#386	C₂²	1	2	yes	—
100	C₂₃×#386	C₂²	1	2	yes	—
101	C₂₃×#386	C₂²	1	2	yes	—
102	C₂₃×#385	C₂²	1	2	yes	—
103	C₂₃×#385	C₂²	1	2	yes	—
104	C₂₃×#382	C₂²	1	1	yes	characteristic
105	C₂₃×#381	C₂²	1	2	yes	—
106	C₂₃×#380	C₂²	1	1	yes	characteristic
107	C₂₃×#380	C₂²	1	1	yes	characteristic
108	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
109	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
110	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
111	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
112	C₄×C₄⋊C₄×C₂₃	C₂²	1	2	yes	—
113	C₄×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
114	C₄×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
115	C₄×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
116	C₄×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
117	C₄×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
118	C₄×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
119	C₄×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	—
120	C₄×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	—
121	C₄×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	—
122	C₄×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	—
123	C₄×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	—
124	C₄³×C₂₃	C₂²	1	1	yes	characteristic
125	C₂×#41×C₂₃	—	2	4	no	—
126	C₂×#41×C₂₃	—	2	4	no	—
127	C₂×#41×C₂₃	—	2	8	no	—
128	C₂×#41×C₂₃	—	2	4	no	—
129	C₂×#41×C₂₃	—	2	8	no	—
130	C₂×#41×C₂₃	—	4	4	no	—
131	C₂²×Q₈×C₂₃	C₂³	1	2	yes	—
132	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
133	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
134	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
135	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
136	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
137	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
138	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
139	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
140	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
141	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
142	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
143	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
144	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
145	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
146	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
147	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
148	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
149	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
150	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
151	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
152	C₂₃×C₄⋊Q₈	—	2	4	no	—
153	C₂₃×#127	—	2	4	no	—
154	C₂₃×#124	—	2	4	no	—
155	C₂₃×#124	—	2	8	no	—
156	C₂₃×#123	—	2	8	no	—
157	C₂₃×C₂²⋊Q₈	—	2	4	no	—
158	C₂₃×#121	—	2	4	no	—
159	C₂₃×#121	—	2	4	no	—
160	C₂₃×#121	—	2	4	no	—
161	C₂₃×#121	—	2	8	no	—
162	C₄×Q₈×C₂₃	—	2	4	no	—
163	C₄×Q₈×C₂₃	—	2	4	no	—
164	C₄×D₄×C₂₃	—	2	4	no	—
165	C₄×D₄×C₂₃	—	2	8	no	—
166	C₄×D₄×C₂₃	—	2	8	no	—
167	C₄×D₄×C₂₃	—	2	4	no	—
168	C₄×D₄×C₂₃	—	2	4	no	—
169	C₄×D₄×C₂₃	—	2	4	no	—
170	C₄×D₄×C₂₃	—	2	8	no	—
171	C₄×D₄×C₂₃	—	2	4	no	—
172	C₄×D₄×C₂₃	—	4	4	no	—
173	C₄×D₄×C₂₃	D₄	1	8	yes	complemented
174	C₂₃×#117	—	2	4	no	—
175	C₂₃×#117	—	2	8	no	—
176	C₂₃×#117	—	4	4	no	—
177	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
178	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
179	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
180	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
181	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
182	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
183	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
184	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
185	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
186	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
187	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
188	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
189	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
190	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
191	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
192	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
193	C₂×C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
194	C₂×C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
195	C₂×C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
196	C₂×C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
197	C₂×C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
198	C₂×C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
199	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
200	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
201	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
202	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
203	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
204	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
205	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
206	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
207	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
208	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
209	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
210	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
211	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
212	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
213	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
214	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
215	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
216	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
217	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
218	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
219	C₂×C₄²×C₂₃	—	2	8	no	—
220	C₂×C₄²×C₂₃	—	2	4	no	—
221	C₂×C₄²×C₂₃	—	2	4	no	—
222	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
223	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
224	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
225	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
226	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
227	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
228	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
229	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
230	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
231	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
232	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
233	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
234	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
235	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
236	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
237	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
238	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
239	C₂₃×#95	C₂³	1	1	yes	characteristic
240	C₂₃×#95	C₂³	1	1	yes	characteristic
241	C₂₃×#95	C₂³	1	1	yes	characteristic
242	C₂₃×#95	C₂³	1	1	yes	characteristic
243	C₂₃×#95	C₂³	1	1	yes	characteristic
244	C₂₃×#95	C₂³	1	1	yes	characteristic
245	C₂₃×#95	C₂³	1	2	yes	—
246	C₂₃×#95	C₂³	1	2	yes	—
247	C₂₃×#95	C₂³	1	2	yes	—
248	C₂₃×#95	C₂³	1	2	yes	—
249	C₂₃×#95	C₂³	1	2	yes	—
250	C₂₃×#95	C₂³	1	2	yes	—
251	C₂₃×#95	C₂³	1	2	yes	—
252	C₂₃×#95	C₂³	1	2	yes	—
253	C₂₃×#95	C₂³	1	2	yes	—
254	C₂₃×#95	C₂³	1	2	yes	—
255	C₂₃×#95	C₂³	1	2	yes	—
256	C₂₃×#95	C₂³	1	2	yes	—
257	C₂₃×#95	C₂³	1	2	yes	—
258	C₂⁴×C₂₃	C₂⁴	1	2	yes	—
259	C₂⁴×C₂₃	C₂⁴	1	2	yes	—
260	C₂⁴×C₂₃	C₂⁴	1	1	yes	characteristic
261	C₂⁴×C₂₃	C₂⁴	1	1	yes	characteristic
262	#41×C₂₃	—	2	32	no	—
263	#41×C₂₃	—	4	32	no	—
264	C₂×Q₈×C₂₃	—	2	2	no	—
265	C₂×Q₈×C₂₃	—	2	4	no	—
266	C₂×Q₈×C₂₃	—	2	2	no	—
267	C₂×Q₈×C₂₃	—	2	4	no	—
268	C₂×Q₈×C₂₃	—	4	2	no	—
269	C₂×Q₈×C₂₃	#41	1	4	yes	complemented
270	C₂×D₄×C₂₃	—	2	4	no	—
271	C₂×D₄×C₂₃	—	2	2	no	—
272	C₂×D₄×C₂₃	—	2	2	no	—
273	C₂×D₄×C₂₃	—	2	4	no	—
274	C₂×D₄×C₂₃	—	2	4	no	—
275	C₂×D₄×C₂₃	—	2	4	no	—
276	C₂×D₄×C₂₃	—	2	4	no	—
277	C₂×D₄×C₂₃	—	2	4	no	—
278	C₂×D₄×C₂₃	—	2	4	no	—
279	C₂×D₄×C₂₃	—	2	4	no	—
280	C₂×D₄×C₂₃	—	2	2	no	—
281	C₂×D₄×C₂₃	—	2	4	no	—
282	C₂×D₄×C₂₃	—	2	2	no	—
283	C₂×D₄×C₂₃	—	2	4	no	—
284	C₂×D₄×C₂₃	—	2	2	no	—
285	C₂×D₄×C₂₃	—	2	2	no	—
286	C₂×D₄×C₂₃	—	2	2	no	—
287	C₂×D₄×C₂₃	—	2	4	no	—
288	C₂×D₄×C₂₃	—	2	2	no	—
289	C₂×D₄×C₂₃	—	2	4	no	—
290	C₂×D₄×C₂₃	—	4	2	no	—
291	C₂×D₄×C₂₃	—	4	2	no	—
292	C₂×D₄×C₂₃	—	4	2	no	—
293	C₂×D₄×C₂₃	—	4	2	no	—
294	C₂×D₄×C₂₃	—	4	2	no	—
295	C₂×D₄×C₂₃	—	4	2	no	—
296	C₂×D₄×C₂₃	C₂×D₄	1	4	yes	—
297	C₂²×C₄×C₂₃	—	2	4	no	—
298	C₂²×C₄×C₂₃	—	2	2	no	—
299	C₂²×C₄×C₂₃	—	2	2	no	—
300	C₂²×C₄×C₂₃	—	2	4	no	—
301	C₂²×C₄×C₂₃	—	2	4	no	—
302	C₂²×C₄×C₂₃	—	2	2	no	—
303	C₂²×C₄×C₂₃	—	2	4	no	—
304	C₂²×C₄×C₂₃	—	2	4	no	—
305	C₂²×C₄×C₂₃	—	2	2	no	—
306	C₂²×C₄×C₂₃	—	2	4	no	—
307	C₂²×C₄×C₂₃	—	2	2	no	—
308	C₂²×C₄×C₂₃	—	2	2	no	—
309	C₂²×C₄×C₂₃	—	2	2	no	—
310	C₂²×C₄×C₂₃	—	2	2	no	—
311	C₂²×C₄×C₂₃	—	2	4	no	—
312	C₂²×C₄×C₂₃	—	2	2	no	—
313	C₂²×C₄×C₂₃	—	2	2	no	—
314	C₂²×C₄×C₂₃	—	2	2	no	—
315	C₂²×C₄×C₂₃	—	2	2	no	—
316	C₂²×C₄×C₂₃	—	2	2	no	—
317	C₂²×C₄×C₂₃	—	2	4	no	—
318	C₂²×C₄×C₂₃	—	2	4	no	—
319	C₂²×C₄×C₂₃	—	2	2	no	—
320	C₂²×C₄×C₂₃	—	2	4	no	—
321	C₂²×C₄×C₂₃	—	4	1	no	—
322	C₂²×C₄×C₂₃	—	4	1	no	—
323	C₂²×C₄×C₂₃	—	4	2	no	—
324	C₂²×C₄×C₂₃	C₂×D₄	1	8	yes	—
325	C₂²×C₄×C₂₃	#41	1	4	yes	complemented
326	C₂²×C₄×C₂₃	#41	1	4	yes	complemented
327	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
328	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
329	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
330	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
331	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
332	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
333	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
334	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
335	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
336	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
337	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
338	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
339	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
340	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
341	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
342	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
343	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
344	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
345	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
346	C₄⋊C₄×C₂₃	—	2	4	no	—
347	C₄⋊C₄×C₂₃	—	2	4	no	—
348	C₄⋊C₄×C₂₃	—	2	2	no	—
349	C₄⋊C₄×C₂₃	—	2	4	no	—
350	C₄⋊C₄×C₂₃	—	2	2	no	—
351	C₄⋊C₄×C₂₃	—	2	2	no	—
352	C₄⋊C₄×C₂₃	—	2	2	no	—
353	C₄⋊C₄×C₂₃	—	2	2	no	—
354	C₄⋊C₄×C₂₃	—	2	2	no	—
355	C₄⋊C₄×C₂₃	—	2	4	no	—
356	C₄⋊C₄×C₂₃	—	2	4	no	—
357	C₄⋊C₄×C₂₃	—	4	2	no	—
358	C₄⋊C₄×C₂₃	—	4	2	no	—
359	C₄⋊C₄×C₂₃	—	4	2	no	—
360	C₄⋊C₄×C₂₃	C₂×D₄	1	4	yes	—
361	C₄⋊C₄×C₂₃	#41	1	4	yes	complemented
362	C₂²⋊C₄×C₂₃	—	2	4	no	—
363	C₂²⋊C₄×C₂₃	—	2	4	no	—
364	C₂²⋊C₄×C₂₃	—	2	2	no	—
365	C₂²⋊C₄×C₂₃	—	2	2	no	—
366	C₂²⋊C₄×C₂₃	—	2	4	no	—
367	C₂²⋊C₄×C₂₃	—	2	4	no	—
368	C₂²⋊C₄×C₂₃	—	2	4	no	—
369	C₂²⋊C₄×C₂₃	—	2	2	no	—
370	C₂²⋊C₄×C₂₃	—	2	2	no	—
371	C₂²⋊C₄×C₂₃	—	2	2	no	—
372	C₂²⋊C₄×C₂₃	—	2	2	no	—
373	C₂²⋊C₄×C₂₃	—	2	4	no	—
374	C₂²⋊C₄×C₂₃	—	2	4	no	—
375	C₂²⋊C₄×C₂₃	—	2	4	no	—
376	C₂²⋊C₄×C₂₃	—	2	4	no	—
377	C₂²⋊C₄×C₂₃	—	2	4	no	—
378	C₂²⋊C₄×C₂₃	—	2	4	no	—
379	C₂²⋊C₄×C₂₃	—	2	4	no	—
380	C₂²⋊C₄×C₂₃	—	4	2	no	—
381	C₂²⋊C₄×C₂₃	—	4	2	no	—
382	C₂²⋊C₄×C₂₃	—	4	2	no	—
383	C₂²⋊C₄×C₂₃	—	4	2	no	—
384	C₂²⋊C₄×C₂₃	—	4	2	no	—
385	C₂²⋊C₄×C₂₃	—	4	2	no	—
386	C₂²⋊C₄×C₂₃	—	4	2	no	—
387	C₂²⋊C₄×C₂₃	C₂×D₄	1	8	yes	—
388	C₄²×C₂₃	—	2	2	no	—
389	C₄²×C₂₃	—	2	2	no	—
390	C₄²×C₂₃	—	2	4	no	—
391	C₄²×C₂₃	—	2	2	no	—
392	C₄²×C₂₃	—	2	4	no	—
393	C₄²×C₂₃	—	2	2	no	—
394	C₄²×C₂₃	—	2	4	no	—
395	C₄²×C₂₃	—	2	2	no	—
396	C₄²×C₂₃	—	2	2	no	—
397	C₄²×C₂₃	—	2	2	no	—
398	C₄²×C₂₃	—	2	2	no	—
399	C₄²×C₂₃	—	2	2	no	—
400	C₄²×C₂₃	—	2	2	no	—
401	C₄²×C₂₃	—	2	2	no	—
402	C₄²×C₂₃	—	2	4	no	—
403	C₄²×C₂₃	—	4	1	no	—
404	C₄²×C₂₃	C₂×D₄	1	4	yes	—
405	#34715	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
406	C₂³×C₂₃	—	2	1	no	—
407	C₂³×C₂₃	—	2	1	no	—
408	C₂³×C₂₃	—	2	1	no	—
409	C₂³×C₂₃	—	2	1	no	—
410	C₂³×C₂₃	—	2	1	no	—
411	C₂³×C₂₃	—	2	1	no	—
412	C₂³×C₂₃	—	2	1	no	—
413	C₂³×C₂₃	—	2	2	no	—
414	C₂³×C₂₃	—	2	2	no	—
415	C₂³×C₂₃	—	2	2	no	—
416	C₂³×C₂₃	—	2	1	no	—
417	C₂³×C₂₃	—	2	2	no	—
418	C₂³×C₂₃	—	2	1	no	—
419	C₂³×C₂₃	—	2	2	no	—
420	C₂³×C₂₃	—	2	1	no	—
421	C₂³×C₂₃	—	2	1	no	—
422	C₂³×C₂₃	—	2	2	no	—
423	C₂³×C₂₃	—	2	1	no	—
424	C₂³×C₂₃	—	2	2	no	—
425	C₂³×C₂₃	—	2	2	no	—
426	C₂³×C₂₃	—	2	2	no	—
427	C₂³×C₂₃	—	2	2	no	—
428	C₂³×C₂₃	—	2	2	no	—
429	C₂³×C₂₃	—	2	2	no	—
430	C₂³×C₂₃	—	2	2	no	—
431	C₂³×C₂₃	C₂²×D₄	1	4	yes	—
432	C₂³×C₂₃	C₂×#41	1	2	yes	—
433	C₂³×C₂₃	C₂×#41	1	2	yes	—
434	C₂³×C₂₃	C₂⁵	1	1	yes	characteristic
435	Q₈×C₂₃	—	2	8	no	—
436	Q₈×C₂₃	—	4	8	no	—
437	D₄×C₂₃	—	2	8	no	—
438	D₄×C₂₃	—	2	16	no	—
439	D₄×C₂₃	—	2	8	no	—
440	D₄×C₂₃	—	4	8	no	—
441	D₄×C₂₃	—	4	8	no	—
442	D₄×C₂₃	—	4	8	no	—
443	D₄×C₂₃	—	4	8	no	—
444	D₄×C₂₃	—	4	8	no	—
445	D₄×C₂₃	—	4	4	no	—
446	C₂×C₄×C₂₃	—	2	16	no	—
447	C₂×C₄×C₂₃	—	2	1	no	—
448	C₂×C₄×C₂₃	—	2	1	no	—
449	C₂×C₄×C₂₃	—	2	1	no	—
450	C₂×C₄×C₂₃	—	2	2	no	—
451	C₂×C₄×C₂₃	—	2	1	no	—
452	C₂×C₄×C₂₃	—	2	1	no	—
453	C₂×C₄×C₂₃	—	2	1	no	—
454	C₂×C₄×C₂₃	—	2	1	no	—
455	C₂×C₄×C₂₃	—	2	1	no	—
456	C₂×C₄×C₂₃	—	2	2	no	—
457	C₂×C₄×C₂₃	—	2	2	no	—
458	C₂×C₄×C₂₃	—	2	2	no	—
459	C₂×C₄×C₂₃	—	2	1	no	—
460	C₂×C₄×C₂₃	—	2	1	no	—
461	C₂×C₄×C₂₃	—	2	1	no	—
462	C₂×C₄×C₂₃	—	2	1	no	—
463	C₂×C₄×C₂₃	—	2	8	no	—
464	C₂×C₄×C₂₃	—	2	16	no	—
465	C₂×C₄×C₂₃	—	2	8	no	—
466	C₂×C₄×C₂₃	—	2	1	no	—
467	C₂×C₄×C₂₃	—	2	1	no	—
468	C₂×C₄×C₂₃	—	2	2	no	—
469	C₂×C₄×C₂₃	—	2	2	no	—
470	C₂×C₄×C₂₃	—	2	1	no	—
471	C₂×C₄×C₂₃	—	2	1	no	—
472	C₂×C₄×C₂₃	—	2	1	no	—
473	C₂×C₄×C₂₃	—	2	1	no	—
474	C₂×C₄×C₂₃	—	2	1	no	—
475	C₂×C₄×C₂₃	—	2	2	no	—
476	C₂×C₄×C₂₃	—	2	2	no	—
477	C₂×C₄×C₂₃	—	2	1	no	—
478	C₂×C₄×C₂₃	—	2	1	no	—
479	C₂×C₄×C₂₃	—	2	2	no	—
480	C₂×C₄×C₂₃	—	2	2	no	—
481	C₂×C₄×C₂₃	—	2	1	no	—
482	C₂×C₄×C₂₃	—	2	2	no	—
483	C₂×C₄×C₂₃	—	2	2	no	—
484	C₂×C₄×C₂₃	—	2	1	no	—
485	C₂×C₄×C₂₃	—	2	1	no	—
486	C₂×C₄×C₂₃	—	2	2	no	—
487	C₂×C₄×C₂₃	—	2	1	no	—
488	C₂×C₄×C₂₃	—	2	2	no	—
489	C₂×C₄×C₂₃	—	2	1	no	—
490	C₂×C₄×C₂₃	—	2	1	no	—
491	C₂×C₄×C₂₃	—	2	2	no	—
492	C₂×C₄×C₂₃	—	2	2	no	—
493	C₂×C₄×C₂₃	—	4	4	no	—
494	C₂×C₄×C₂₃	—	4	4	no	—
495	C₂×C₄×C₂₃	—	4	8	no	—
496	C₂×C₄×C₂₃	—	4	4	no	—
497	C₂×C₄×C₂₃	—	4	4	no	—
498	C₂×C₄×C₂₃	—	4	8	no	—
499	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
500	C₂×C₄×C₂₃	C₂²×D₄	1	4	yes	—
501	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
502	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
503	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
504	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
505	C₂×C₄×C₂₃	C₂×#41	1	4	yes	—
506	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
507	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
508	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
509	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
510	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
511	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
512	C₂×C₄×C₂₃	H(5,𝔽₂)	1	2	yes	—
513	C₂×#532	C₂×C₂₃	1	1	yes	characteristic, complemented
514	C₂×C₄×#41	C₂×C₂₃	1	1	yes	characteristic, complemented
515	#2476	C₂×C₂₃	1	2	yes	complemented
516	#2474	C₂×C₂₃	1	2	yes	complemented
517	#2459	C₂×C₂₃	1	2	yes	complemented
518	#2456	C₂×C₂₃	1	2	yes	complemented
519	#2451	C₂×C₂₃	1	1	yes	characteristic, complemented
520	#2445	C₂×C₂₃	1	1	yes	characteristic, complemented
521	#2439	C₂×C₂₃	1	1	yes	characteristic, complemented
522	#2431	C₂×C₂₃	1	1	yes	characteristic, complemented
523	#2426	C₂×C₂₃	1	1	yes	characteristic, complemented
524	#2420	C₂×C₂₃	1	1	yes	characteristic, complemented
525	#2414	C₂×C₂₃	1	1	yes	characteristic, complemented
526	#2407	C₂×C₂₃	1	1	yes	characteristic, complemented
527	#2392	C₂×C₂₃	1	2	yes	complemented
528	#2388	C₂×C₂₃	1	2	yes	complemented
529	C₄×#124	C₂×C₂₃	1	1	yes	characteristic, complemented
530	C₄×C₂²⋊Q₈	C₂×C₂₃	1	1	yes	characteristic, complemented
531	C₄×#123	C₂×C₂₃	1	2	yes	complemented
532	C₄×#121	C₂×C₂₃	1	1	yes	characteristic, complemented
533	#2297	C₂×C₂₃	1	2	yes	complemented
534	#2293	C₂×C₂₃	1	1	yes	characteristic, complemented
535	C₄²×D₄	C₂×C₂₃	1	1	yes	characteristic, complemented
536	C₂²×C₂₃	—	2	4	no	—
537	C₂²×C₂₃	—	2	2	no	—
538	C₂²×C₂₃	—	2	2	no	—
539	C₂²×C₂₃	—	2	2	no	—
540	C₂²×C₂₃	—	2	2	no	—
541	C₂²×C₂₃	—	2	2	no	—
542	C₂²×C₂₃	—	2	4	no	—
543	C₂²×C₂₃	—	2	4	no	—
544	C₂²×C₂₃	—	2	2	no	—
545	C₂²×C₂₃	—	4	1	no	—
546	C₂²×C₂₃	—	4	2	no	—
547	C₂²×C₂₃	—	4	1	no	—
548	C₂²×C₂₃	—	4	2	no	—
549	C₂²×C₂₃	—	4	1	no	—
550	C₂²×C₂₃	—	4	1	no	—
551	C₂²×C₂₃	—	4	1	no	—
552	C₂²×C₂₃	—	4	1	no	—
553	C₂²×C₂₃	—	4	2	no	—
554	C₂²×C₂₃	—	4	1	no	—
555	C₂²×C₂₃	—	4	2	no	—
556	C₂²×C₂₃	—	4	1	no	—
557	C₂²×C₂₃	—	4	2	no	—
558	C₂²×C₂₃	—	4	2	no	—
559	C₂²×C₂₃	—	4	2	no	—
560	C₂²×C₂₃	—	4	2	no	—
561	C₂²×C₂₃	—	4	2	no	—
562	C₂²×C₂₃	—	4	2	no	—
563	C₂²×C₂₃	—	4	2	no	—
564	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
565	C₂²×C₂₃	C₂²×#41	1	1	yes	characteristic
566	C₂²×C₂₃	C₂²×#41	1	1	yes	characteristic
567	C₂²×C₂₃	C₂²×#41	1	1	yes	characteristic
568	C₂²×C₂₃	C₂²×#41	1	1	yes	characteristic
569	C₂²×C₂₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
570	C₂²×C₂₃	#585	1	1	yes	characteristic
571	C₄×C₂₃	—	2	2	no	—
572	C₄×C₂₃	—	2	4	no	—
573	C₄×C₂₃	—	2	2	no	—
574	C₄×C₂₃	—	2	4	no	—
575	C₄×C₂₃	—	2	2	no	—
576	C₄×C₂₃	—	2	2	no	—
577	C₄×C₂₃	—	2	2	no	—
578	C₄×C₂₃	—	2	2	no	—
579	C₄×C₂₃	—	4	1	no	—
580	C₄×C₂₃	—	4	1	no	—
581	C₄×C₂₃	—	4	2	no	—
582	C₄×C₂₃	—	4	1	no	—
583	C₄×C₂₃	—	4	2	no	—
584	C₄×C₂₃	—	4	2	no	—
585	C₄×C₂₃	—	4	1	no	—
586	C₄×C₂₃	—	4	1	no	—
587	C₄×C₂₃	—	4	2	no	—
588	C₄×C₂₃	#525	1	4	yes	—
589	C₄×C₂₃	#546	1	4	yes	—
590	C₂²×#41	C₂²×C₂₃	1	1	yes	characteristic
591	C₂²×#41	C₂²×C₂₃	1	2	yes	—
592	#532	—	2	8	no	—
593	C₂×C₄⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
594	C₂×#127	C₂²×C₂₃	1	1	yes	characteristic
595	C₂×#124	C₂²×C₂₃	1	2	yes	—
596	C₂×#124	C₂²×C₂₃	1	1	yes	characteristic
597	C₂×#123	C₂²×C₂₃	1	2	yes	—
598	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
599	C₂×#121	C₂²×C₂₃	1	1	yes	characteristic
600	C₂×#121	C₂²×C₂₃	1	1	yes	characteristic
601	C₂×#121	C₂²×C₂₃	1	1	yes	characteristic
602	C₂×#121	C₂²×C₂₃	1	2	yes	—
603	C₄×#41	—	2	8	no	—
604	C₂×C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
605	C₂×C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
606	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
607	C₂×C₄×D₄	C₂²×C₂₃	1	2	yes	—
608	C₂×C₄×D₄	C₂²×C₂₃	1	2	yes	—
609	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
610	C₂×C₄×D₄	C₂²×C₂₃	1	2	yes	—
611	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
612	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
613	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
614	C₂×C₄×D₄	C₂²×C₂₃	1	2	yes	—
615	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
616	C₂×#117	C₂²×C₂₃	1	1	yes	characteristic
617	C₂×#117	C₂²×C₂₃	1	2	yes	—
618	C₂×#117	C₂²×C₂₃	1	2	yes	—
619	C₂²×C₄²	C₂²×C₂₃	1	1	yes	characteristic
620	C₂²×C₄²	C₂²×C₂₃	1	2	yes	—
621	C₂²×C₄²	C₂²×C₂₃	1	1	yes	characteristic
622	#398	C₂²×C₂₃	1	2	yes	—
623	#397	C₂²×C₂₃	1	2	yes	—
624	#396	C₂²×C₂₃	1	2	yes	—
625	#396	C₂²×C₂₃	1	2	yes	—
626	#395	C₂²×C₂₃	1	2	yes	—
627	#394	C₂²×C₂₃	1	2	yes	—
628	#394	C₂²×C₂₃	1	2	yes	—
629	#394	C₂²×C₂₃	1	2	yes	—
630	#394	C₂²×C₂₃	1	2	yes	—
631	#394	C₂²×C₂₃	1	2	yes	—
632	#394	C₂²×C₂₃	1	2	yes	—
633	#393	C₂²×C₂₃	1	2	yes	—
634	#392	C₂²×C₂₃	1	2	yes	—
635	#392	C₂²×C₂₃	1	2	yes	—
636	#392	C₂²×C₂₃	1	2	yes	—
637	#392	C₂²×C₂₃	1	2	yes	—
638	#391	C₂²×C₂₃	1	1	yes	characteristic
639	#391	C₂²×C₂₃	1	1	yes	characteristic
640	#391	C₂²×C₂₃	1	2	yes	—
641	#391	C₂²×C₂₃	1	2	yes	—
642	#390	C₂²×C₂₃	1	1	yes	characteristic
643	#390	C₂²×C₂₃	1	1	yes	characteristic
644	#390	C₂²×C₂₃	1	2	yes	—
645	#390	C₂²×C₂₃	1	1	yes	characteristic
646	#390	C₂²×C₂₃	1	1	yes	characteristic
647	#390	C₂²×C₂₃	1	2	yes	—
648	#389	C₂²×C₂₃	1	1	yes	characteristic
649	#389	C₂²×C₂₃	1	1	yes	characteristic
650	#389	C₂²×C₂₃	1	1	yes	characteristic
651	#389	C₂²×C₂₃	1	1	yes	characteristic
652	#388	C₂²×C₂₃	1	2	yes	—
653	#388	C₂²×C₂₃	1	2	yes	—
654	#388	C₂²×C₂₃	1	2	yes	—
655	#388	C₂²×C₂₃	1	2	yes	—
656	#388	C₂²×C₂₃	1	2	yes	—
657	#388	C₂²×C₂₃	1	2	yes	—
658	#388	C₂²×C₂₃	1	2	yes	—
659	#387	C₂²×C₂₃	1	2	yes	—
660	#387	C₂²×C₂₃	1	2	yes	—
661	#387	C₂²×C₂₃	1	2	yes	—
662	#386	C₂²×C₂₃	1	2	yes	—
663	#386	C₂²×C₂₃	1	2	yes	—
664	#386	C₂²×C₂₃	1	2	yes	—
665	#386	C₂²×C₂₃	1	2	yes	—
666	#386	C₂²×C₂₃	1	2	yes	—
667	#386	C₂²×C₂₃	1	2	yes	—
668	#385	C₂²×C₂₃	1	2	yes	—
669	#385	C₂²×C₂₃	1	2	yes	—
670	#382	C₂²×C₂₃	1	1	yes	characteristic
671	#381	C₂²×C₂₃	1	2	yes	—
672	#380	C₂²×C₂₃	1	1	yes	characteristic
673	#380	C₂²×C₂₃	1	1	yes	characteristic
674	C₄×C₄⋊C₄	C₂²×C₂₃	1	2	yes	—
675	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
676	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
677	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
678	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
679	C₄×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
680	C₄×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
681	C₄×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
682	C₄×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
683	C₄×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
684	C₄×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
685	C₄×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
686	C₄×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
687	C₄×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
688	C₄×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
689	C₄×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
690	C₄³	C₂²×C₂₃	1	1	yes	characteristic
691	C₂×C₂₃	—	4	4	no	—
692	C₂×C₂₃	—	4	2	no	—
693	C₂×C₂₃	—	4	2	no	—
694	C₂×C₂₃	—	8	2	no	—
695	C₂×C₂₃	C₂×#525	1	1	yes	characteristic
696	C₂×C₂₃	#3444	1	1	yes	characteristic
697	C₂×C₂₃	#3460	1	1	yes	characteristic
698	C₂×C₂₃	C₂×#546	1	1	yes	characteristic
699	C₂×C₂₃	D₄×#41	1	1	yes	characteristic
700	C₂×C₂₃	#3480	1	1	yes	characteristic
701	C₂×C₂₃	#3483	1	1	yes	characteristic
702	C₂×#41	—	2	4	no	—
703	C₂×#41	—	2	4	no	—
704	C₂×#41	—	2	8	no	—
705	C₂×#41	—	2	4	no	—
706	C₂×#41	—	2	8	no	—
707	C₂×#41	—	4	4	no	—
708	C₂²×Q₈	C₂³×C₂₃	1	2	yes	—
709	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
710	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
711	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
712	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
713	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
714	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
715	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
716	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
717	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
718	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
719	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
720	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
721	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
722	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
723	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
724	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
725	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
726	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
727	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
728	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
729	C₄⋊Q₈	—	2	4	no	—
730	#127	—	2	4	no	—
731	#124	—	2	4	no	—
732	#124	—	2	8	no	—
733	#123	—	2	8	no	—
734	C₂²⋊Q₈	—	2	4	no	—
735	#121	—	2	4	no	—
736	#121	—	2	4	no	—
737	#121	—	2	4	no	—
738	#121	—	2	8	no	—
739	C₄×Q₈	—	2	4	no	—
740	C₄×Q₈	—	2	4	no	—
741	C₄×D₄	—	2	4	no	—
742	C₄×D₄	—	2	8	no	—
743	C₄×D₄	—	2	8	no	—
744	C₄×D₄	—	2	4	no	—
745	C₄×D₄	—	2	4	no	—
746	C₄×D₄	—	2	4	no	—
747	C₄×D₄	—	2	8	no	—
748	C₄×D₄	—	2	4	no	—
749	C₄×D₄	—	4	4	no	—
750	C₄×D₄	D₄×C₂₃	1	8	yes	complemented
751	#117	—	2	4	no	—
752	#117	—	2	8	no	—
753	#117	—	4	4	no	—
754	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
755	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
756	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
757	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
758	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
759	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
760	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
761	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
762	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
763	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
764	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
765	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
766	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
767	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
768	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
769	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
770	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
771	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
772	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
773	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
774	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
775	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
776	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
777	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
778	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
779	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
780	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
781	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
782	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
783	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
784	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
785	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
786	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
787	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
788	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
789	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
790	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
791	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
792	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
793	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
794	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
795	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
796	C₂×C₄²	—	2	8	no	—
797	C₂×C₄²	—	2	4	no	—
798	C₂×C₄²	—	2	4	no	—
799	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
800	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
801	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
802	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
803	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
804	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
805	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
806	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
807	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
808	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
809	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
810	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
811	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
812	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
813	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
814	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
815	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
816	#95	C₂³×C₂₃	1	1	yes	characteristic
817	#95	C₂³×C₂₃	1	1	yes	characteristic
818	#95	C₂³×C₂₃	1	1	yes	characteristic
819	#95	C₂³×C₂₃	1	1	yes	characteristic
820	#95	C₂³×C₂₃	1	1	yes	characteristic
821	#95	C₂³×C₂₃	1	1	yes	characteristic
822	#95	C₂³×C₂₃	1	2	yes	—
823	#95	C₂³×C₂₃	1	2	yes	—
824	#95	C₂³×C₂₃	1	2	yes	—
825	#95	C₂³×C₂₃	1	2	yes	—
826	#95	C₂³×C₂₃	1	2	yes	—
827	#95	C₂³×C₂₃	1	2	yes	—
828	#95	C₂³×C₂₃	1	2	yes	—
829	#95	C₂³×C₂₃	1	2	yes	—
830	#95	C₂³×C₂₃	1	2	yes	—
831	#95	C₂³×C₂₃	1	2	yes	—
832	#95	C₂³×C₂₃	1	2	yes	—
833	#95	C₂³×C₂₃	1	2	yes	—
834	#95	C₂³×C₂₃	1	2	yes	—
835	C₂₃	#34715	1	1	yes	characteristic, direct product factor, Sylow
836	C₂⁴	C₂⁴×C₂₃	1	2	yes	—
837	C₂⁴	C₂⁴×C₂₃	1	2	yes	—
838	C₂⁴	C₂⁴×C₂₃	1	1	yes	characteristic
839	C₂⁴	C₂⁴×C₂₃	1	1	yes	characteristic
840	#41	—	2	32	no	—
841	#41	—	4	32	no	—
842	C₂×Q₈	—	2	2	no	—
843	C₂×Q₈	—	2	4	no	—
844	C₂×Q₈	—	2	2	no	—
845	C₂×Q₈	—	2	4	no	—
846	C₂×Q₈	—	4	2	no	—
847	C₂×Q₈	#41×C₂₃	1	4	yes	complemented
848	C₂×D₄	—	2	4	no	—
849	C₂×D₄	—	2	2	no	—
850	C₂×D₄	—	2	2	no	—
851	C₂×D₄	—	2	4	no	—
852	C₂×D₄	—	2	4	no	—
853	C₂×D₄	—	2	4	no	—
854	C₂×D₄	—	2	4	no	—
855	C₂×D₄	—	2	4	no	—
856	C₂×D₄	—	2	4	no	—
857	C₂×D₄	—	2	4	no	—
858	C₂×D₄	—	2	2	no	—
859	C₂×D₄	—	2	4	no	—
860	C₂×D₄	—	2	2	no	—
861	C₂×D₄	—	2	4	no	—
862	C₂×D₄	—	2	2	no	—
863	C₂×D₄	—	2	2	no	—
864	C₂×D₄	—	2	2	no	—
865	C₂×D₄	—	2	4	no	—
866	C₂×D₄	—	2	2	no	—
867	C₂×D₄	—	2	4	no	—
868	C₂×D₄	—	4	2	no	—
869	C₂×D₄	—	4	2	no	—
870	C₂×D₄	—	4	2	no	—
871	C₂×D₄	—	4	2	no	—
872	C₂×D₄	—	4	2	no	—
873	C₂×D₄	—	4	2	no	—
874	C₂×D₄	C₂×D₄×C₂₃	1	4	yes	—
875	C₂²×C₄	—	2	4	no	—
876	C₂²×C₄	—	2	2	no	—
877	C₂²×C₄	—	2	2	no	—
878	C₂²×C₄	—	2	4	no	—
879	C₂²×C₄	—	2	4	no	—
880	C₂²×C₄	—	2	2	no	—
881	C₂²×C₄	—	2	4	no	—
882	C₂²×C₄	—	2	4	no	—
883	C₂²×C₄	—	2	2	no	—
884	C₂²×C₄	—	2	4	no	—
885	C₂²×C₄	—	2	2	no	—
886	C₂²×C₄	—	2	2	no	—
887	C₂²×C₄	—	2	2	no	—
888	C₂²×C₄	—	2	2	no	—
889	C₂²×C₄	—	2	4	no	—
890	C₂²×C₄	—	2	2	no	—
891	C₂²×C₄	—	2	2	no	—
892	C₂²×C₄	—	2	2	no	—
893	C₂²×C₄	—	2	2	no	—
894	C₂²×C₄	—	2	2	no	—
895	C₂²×C₄	—	2	4	no	—
896	C₂²×C₄	—	2	4	no	—
897	C₂²×C₄	—	2	2	no	—
898	C₂²×C₄	—	2	4	no	—
899	C₂²×C₄	—	4	1	no	—
900	C₂²×C₄	—	4	1	no	—
901	C₂²×C₄	—	4	2	no	—
902	C₂²×C₄	C₂×D₄×C₂₃	1	8	yes	—
903	C₂²×C₄	#41×C₂₃	1	4	yes	complemented
904	C₂²×C₄	#41×C₂₃	1	4	yes	complemented
905	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
906	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
907	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
908	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
909	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
910	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
911	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
912	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
913	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
914	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
915	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
916	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
917	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
918	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
919	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
920	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
921	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
922	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
923	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
924	C₄⋊C₄	—	2	4	no	—
925	C₄⋊C₄	—	2	4	no	—
926	C₄⋊C₄	—	2	2	no	—
927	C₄⋊C₄	—	2	4	no	—
928	C₄⋊C₄	—	2	2	no	—
929	C₄⋊C₄	—	2	2	no	—
930	C₄⋊C₄	—	2	2	no	—
931	C₄⋊C₄	—	2	2	no	—
932	C₄⋊C₄	—	2	2	no	—
933	C₄⋊C₄	—	2	4	no	—
934	C₄⋊C₄	—	2	4	no	—
935	C₄⋊C₄	—	4	2	no	—
936	C₄⋊C₄	—	4	2	no	—
937	C₄⋊C₄	—	4	2	no	—
938	C₄⋊C₄	C₂×D₄×C₂₃	1	4	yes	—
939	C₄⋊C₄	#41×C₂₃	1	4	yes	complemented
940	C₂²⋊C₄	—	2	4	no	—
941	C₂²⋊C₄	—	2	4	no	—
942	C₂²⋊C₄	—	2	2	no	—
943	C₂²⋊C₄	—	2	2	no	—
944	C₂²⋊C₄	—	2	4	no	—
945	C₂²⋊C₄	—	2	4	no	—
946	C₂²⋊C₄	—	2	4	no	—
947	C₂²⋊C₄	—	2	2	no	—
948	C₂²⋊C₄	—	2	2	no	—
949	C₂²⋊C₄	—	2	2	no	—
950	C₂²⋊C₄	—	2	2	no	—
951	C₂²⋊C₄	—	2	4	no	—
952	C₂²⋊C₄	—	2	4	no	—
953	C₂²⋊C₄	—	2	4	no	—
954	C₂²⋊C₄	—	2	4	no	—
955	C₂²⋊C₄	—	2	4	no	—
956	C₂²⋊C₄	—	2	4	no	—
957	C₂²⋊C₄	—	2	4	no	—
958	C₂²⋊C₄	—	4	2	no	—
959	C₂²⋊C₄	—	4	2	no	—
960	C₂²⋊C₄	—	4	2	no	—
961	C₂²⋊C₄	—	4	2	no	—
962	C₂²⋊C₄	—	4	2	no	—
963	C₂²⋊C₄	—	4	2	no	—
964	C₂²⋊C₄	—	4	2	no	—
965	C₂²⋊C₄	C₂×D₄×C₂₃	1	8	yes	—
966	C₄²	—	2	2	no	—
967	C₄²	—	2	2	no	—
968	C₄²	—	2	4	no	—
969	C₄²	—	2	2	no	—
970	C₄²	—	2	4	no	—
971	C₄²	—	2	2	no	—
972	C₄²	—	2	4	no	—
973	C₄²	—	2	2	no	—
974	C₄²	—	2	2	no	—
975	C₄²	—	2	2	no	—
976	C₄²	—	2	2	no	—
977	C₄²	—	2	2	no	—
978	C₄²	—	2	2	no	—
979	C₄²	—	2	2	no	—
980	C₄²	—	2	4	no	—
981	C₄²	—	4	1	no	—
982	C₄²	C₂×D₄×C₂₃	1	4	yes	—
983	C₂³	—	2	1	no	—
984	C₂³	—	2	1	no	—
985	C₂³	—	2	1	no	—
986	C₂³	—	2	1	no	—
987	C₂³	—	2	1	no	—
988	C₂³	—	2	1	no	—
989	C₂³	—	2	1	no	—
990	C₂³	—	2	2	no	—
991	C₂³	—	2	2	no	—
992	C₂³	—	2	2	no	—
993	C₂³	—	2	1	no	—
994	C₂³	—	2	2	no	—
995	C₂³	—	2	1	no	—
996	C₂³	—	2	2	no	—
997	C₂³	—	2	1	no	—
998	C₂³	—	2	1	no	—
999	C₂³	—	2	2	no	—
1000	C₂³	—	2	1	no	—
1001	C₂³	—	2	2	no	—
1002	C₂³	—	2	2	no	—
1003	C₂³	—	2	2	no	—
1004	C₂³	—	2	2	no	—
1005	C₂³	—	2	2	no	—
1006	C₂³	—	2	2	no	—
1007	C₂³	—	2	2	no	—
1008	C₂³	C₂²×D₄×C₂₃	1	4	yes	—
1009	C₂³	C₂×#41×C₂₃	1	2	yes	—
1010	C₂³	C₂×#41×C₂₃	1	2	yes	—
1011	C₂³	C₂⁵×C₂₃	1	1	yes	characteristic
1012	Q₈	—	2	8	no	—
1013	Q₈	—	4	8	no	—
1014	D₄	—	2	16	no	—
1015	D₄	—	2	8	no	—
1016	D₄	—	2	8	no	—
1017	D₄	—	4	8	no	—
1018	D₄	—	4	8	no	—
1019	D₄	—	4	8	no	—
1020	D₄	—	4	8	no	—
1021	D₄	—	4	8	no	—
1022	D₄	—	4	4	no	—
1023	C₂×C₄	—	2	16	no	—
1024	C₂×C₄	—	2	1	no	—
1025	C₂×C₄	—	2	1	no	—
1026	C₂×C₄	—	2	1	no	—
1027	C₂×C₄	—	2	2	no	—
1028	C₂×C₄	—	2	1	no	—
1029	C₂×C₄	—	2	1	no	—
1030	C₂×C₄	—	2	1	no	—
1031	C₂×C₄	—	2	1	no	—
1032	C₂×C₄	—	2	1	no	—
1033	C₂×C₄	—	2	2	no	—
1034	C₂×C₄	—	2	2	no	—
1035	C₂×C₄	—	2	2	no	—
1036	C₂×C₄	—	2	1	no	—
1037	C₂×C₄	—	2	1	no	—
1038	C₂×C₄	—	2	1	no	—
1039	C₂×C₄	—	2	1	no	—
1040	C₂×C₄	—	2	8	no	—
1041	C₂×C₄	—	2	16	no	—
1042	C₂×C₄	—	2	8	no	—
1043	C₂×C₄	—	2	1	no	—
1044	C₂×C₄	—	2	1	no	—
1045	C₂×C₄	—	2	2	no	—
1046	C₂×C₄	—	2	2	no	—
1047	C₂×C₄	—	2	1	no	—
1048	C₂×C₄	—	2	1	no	—
1049	C₂×C₄	—	2	1	no	—
1050	C₂×C₄	—	2	1	no	—
1051	C₂×C₄	—	2	1	no	—
1052	C₂×C₄	—	2	2	no	—
1053	C₂×C₄	—	2	2	no	—
1054	C₂×C₄	—	2	1	no	—
1055	C₂×C₄	—	2	1	no	—
1056	C₂×C₄	—	2	2	no	—
1057	C₂×C₄	—	2	2	no	—
1058	C₂×C₄	—	2	1	no	—
1059	C₂×C₄	—	2	2	no	—
1060	C₂×C₄	—	2	2	no	—
1061	C₂×C₄	—	2	1	no	—
1062	C₂×C₄	—	2	1	no	—
1063	C₂×C₄	—	2	2	no	—
1064	C₂×C₄	—	2	1	no	—
1065	C₂×C₄	—	2	2	no	—
1066	C₂×C₄	—	2	1	no	—
1067	C₂×C₄	—	2	1	no	—
1068	C₂×C₄	—	2	2	no	—
1069	C₂×C₄	—	2	2	no	—
1070	C₂×C₄	—	4	4	no	—
1071	C₂×C₄	—	4	4	no	—
1072	C₂×C₄	—	4	8	no	—
1073	C₂×C₄	—	4	4	no	—
1074	C₂×C₄	—	4	8	no	—
1075	C₂×C₄	—	4	4	no	—
1076	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
1077	C₂×C₄	C₂²×D₄×C₂₃	1	4	yes	—
1078	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
1079	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
1080	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
1081	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
1082	C₂×C₄	C₂×#41×C₂₃	1	4	yes	—
1083	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
1084	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
1085	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
1086	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
1087	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
1088	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
1089	C₂×C₄	C₂₃×H(5,𝔽₂)	1	2	yes	—
1090	C₂²	—	2	4	no	—
1091	C₂²	—	2	2	no	—
1092	C₂²	—	2	2	no	—
1093	C₂²	—	2	2	no	—
1094	C₂²	—	2	2	no	—
1095	C₂²	—	2	2	no	—
1096	C₂²	—	2	4	no	—
1097	C₂²	—	2	4	no	—
1098	C₂²	—	2	2	no	—
1099	C₂²	—	4	1	no	—
1100	C₂²	—	4	2	no	—
1101	C₂²	—	4	1	no	—
1102	C₂²	—	4	2	no	—
1103	C₂²	—	4	1	no	—
1104	C₂²	—	4	1	no	—
1105	C₂²	—	4	1	no	—
1106	C₂²	—	4	1	no	—
1107	C₂²	—	4	2	no	—
1108	C₂²	—	4	1	no	—
1109	C₂²	—	4	2	no	—
1110	C₂²	—	4	1	no	—
1111	C₂²	—	4	2	no	—
1112	C₂²	—	4	2	no	—
1113	C₂²	—	4	2	no	—
1114	C₂²	—	4	2	no	—
1115	C₂²	—	4	2	no	—
1116	C₂²	—	4	2	no	—
1117	C₂²	—	4	2	no	—
1118	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
1119	C₂²	C₂²×#41×C₂₃	1	1	yes	characteristic
1120	C₂²	C₂²×#41×C₂₃	1	1	yes	characteristic
1121	C₂²	C₂²×#41×C₂₃	1	1	yes	characteristic
1122	C₂²	C₂²×#41×C₂₃	1	1	yes	characteristic
1123	C₂²	C₂×C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
1124	C₂²	C₂₃×#585	1	1	yes	characteristic
1125	C₄	—	2	2	no	—
1126	C₄	—	2	4	no	—
1127	C₄	—	2	2	no	—
1128	C₄	—	2	4	no	—
1129	C₄	—	2	2	no	—
1130	C₄	—	2	2	no	—
1131	C₄	—	2	2	no	—
1132	C₄	—	2	2	no	—
1133	C₄	—	4	1	no	—
1134	C₄	—	4	2	no	—
1135	C₄	—	4	1	no	—
1136	C₄	—	4	2	no	—
1137	C₄	—	4	1	no	—
1138	C₄	—	4	2	no	—
1139	C₄	—	4	1	no	—
1140	C₄	—	4	1	no	—
1141	C₄	—	4	2	no	—
1142	C₄	C₂₃×#525	1	4	yes	—
1143	C₄	C₂₃×#546	1	4	yes	—
1144	C₂	—	4	4	no	—
1145	C₂	—	4	2	no	—
1146	C₂	—	4	2	no	—
1147	C₂	—	8	2	no	—
1148	C₂	C₂×C₂₃×#525	1	1	yes	characteristic
1149	C₂	C₂₃×#3444	1	1	yes	characteristic
1150	C₂	C₂₃×#3460	1	1	yes	characteristic
1151	C₂	C₂×C₂₃×#546	1	1	yes	characteristic
1152	C₂	D₄×#41×C₂₃	1	1	yes	characteristic
1153	C₂	C₂₃×#3480	1	1	yes	characteristic
1154	C₂	C₂₃×#3483	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₂₃	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₂₃
socle	C₂³×C₂₃	C₂⁵
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×#532	C₂	semidirect
2. C₂×C₄×#41×C₂₃	C₂	semidirect
3. C₂₃×#2476	C₂	semidirect
4. C₂₃×#2474	C₂	semidirect
5. C₂₃×#2459	C₂	semidirect
6. C₂₃×#2456	C₂	semidirect
7. C₂₃×#2451	C₂	semidirect
8. C₂₃×#2445	C₂	semidirect
9. C₂₃×#2439	C₂	semidirect
10. C₂₃×#2431	C₂	semidirect
11. C₂₃×#2426	C₂	semidirect
12. C₂₃×#2420	C₂	semidirect
13. C₂₃×#2414	C₂	semidirect
14. C₂₃×#2407	C₂	semidirect
15. C₂₃×#2392	C₂	semidirect
16. C₂₃×#2388	C₂	semidirect
17. C₄×C₂₃×#124	C₂	semidirect
18. C₄×C₂₃×C₂²⋊Q₈	C₂	semidirect
19. C₄×C₂₃×#123	C₂	semidirect
20. C₄×C₂₃×#121	C₂	semidirect
21. C₂₃×#2297	C₂	semidirect
22. C₂₃×#2293	C₂	semidirect
23. C₄²×D₄×C₂₃	C₂	semidirect
173. C₄×D₄×C₂₃	D₄	semidirect
269. C₂×Q₈×C₂₃	#41	semidirect
325. C₂²×C₄×C₂₃	#41	semidirect
326. C₂²×C₄×C₂₃	#41	semidirect
361. C₄⋊C₄×C₂₃	#41	semidirect
405. #34715	C₂₃	direct (N × H)
513. C₂×#532	C₂×C₂₃	semidirect
514. C₂×C₄×#41	C₂×C₂₃	semidirect
515. #2476	C₂×C₂₃	semidirect
516. #2474	C₂×C₂₃	semidirect
517. #2459	C₂×C₂₃	semidirect
518. #2456	C₂×C₂₃	semidirect
519. #2451	C₂×C₂₃	semidirect
520. #2445	C₂×C₂₃	semidirect
521. #2439	C₂×C₂₃	semidirect
522. #2431	C₂×C₂₃	semidirect
523. #2426	C₂×C₂₃	semidirect
524. #2420	C₂×C₂₃	semidirect
525. #2414	C₂×C₂₃	semidirect
526. #2407	C₂×C₂₃	semidirect
527. #2392	C₂×C₂₃	semidirect
528. #2388	C₂×C₂₃	semidirect
529. C₄×#124	C₂×C₂₃	semidirect
530. C₄×C₂²⋊Q₈	C₂×C₂₃	semidirect
531. C₄×#123	C₂×C₂₃	semidirect
532. C₄×#121	C₂×C₂₃	semidirect
533. #2297	C₂×C₂₃	semidirect
534. #2293	C₂×C₂₃	semidirect
535. C₄²×D₄	C₂×C₂₃	semidirect
750. C₄×D₄	D₄×C₂₃	semidirect
835. C₂₃	#34715	direct (N × H)
847. C₂×Q₈	#41×C₂₃	semidirect
903. C₂²×C₄	#41×C₂₃	semidirect
904. C₂²×C₄	#41×C₂₃	semidirect
939. C₄⋊C₄	#41×C₂₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₂₃×#532	2
C₂×C₄×#41×C₂₃	2
C₂₃×#2476	2
C₂₃×#2474	2
C₂₃×#2459	2
C₂₃×#2456	2
C₂₃×#2451	2
C₂₃×#2445	2
C₂₃×#2439	2
C₂₃×#2431	2
C₂₃×#2426	2
C₂₃×#2420	2
C₂₃×#2414	2
C₂₃×#2407	2
C₂₃×#2392	2
C₂₃×#2388	2
C₄×C₂₃×#124	2
C₄×C₂₃×C₂²⋊Q₈	2
C₄×C₂₃×#123	2
C₄×C₂₃×#121	2
C₂₃×#2297	2
C₂₃×#2293	2
C₄²×D₄×C₂₃	2
#34715	23

Subgroups — C23×#34715 #19182341

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#34715 #19182341