Subgroups — C₂₃×#34655 #19182281

Order 5888.

3910 conjugacy classes of subgroups.

The subgroup lattice has 1104 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₃×#525	C₂	1	2	yes	maximal, complemented
2	C₂²×C₄×D₄×C₂₃	C₂	1	2	yes	maximal, complemented
3	C₂₃×#2463	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₃×#2456	C₂	1	2	yes	maximal, complemented
5	C₂₃×#2455	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₃×#2449	C₂	1	2	yes	maximal, complemented
7	C₂₃×#2443	C₂	1	2	yes	maximal, complemented
8	C₂₃×#2437	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₃×#2424	C₂	1	2	yes	maximal, complemented
10	C₂₃×#2418	C₂	1	2	yes	maximal, complemented
11	C₂₃×#2410	C₂	1	2	yes	maximal, complemented
12	C₂₃×#2403	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₃×#2397	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₃×#2392	C₂	1	2	yes	maximal, complemented
15	C₂₃×#2388	C₂	1	1	yes	maximal, characteristic, complemented
16	C₄×C₂₃×#121	C₂	1	2	yes	maximal, complemented
17	C₄×C₂₃×#120	C₂	1	1	yes	maximal, characteristic, complemented
18	C₄×C₂₃×#120	C₂	1	2	yes	maximal, complemented
19	C₂₃×#2290	C₂	1	2	yes	maximal, complemented
20	C₂²×#41×C₂₃	C₂²	1	1	yes	characteristic, complemented
21	C₂³×D₄×C₂₃	C₂²	1	2	yes	—
22	C₂⁴×C₄×C₂₃	C₂²	1	1	yes	characteristic
23	C₂⁴×C₄×C₂₃	C₂²	1	2	yes	complemented
24	C₂₃×#525	—	2	16	no	—
25	C₂×C₂₃×#123	C₂²	1	2	yes	complemented
26	C₂×C₂₃×#123	C₂²	1	2	yes	complemented
27	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
28	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
29	C₂×C₂₃×#121	C₂²	1	2	yes	—
30	C₂×C₂₃×#121	C₂²	1	2	yes	—
31	C₂×C₂₃×#121	C₂²	1	2	yes	complemented
32	C₂×C₂₃×#120	C₂²	1	2	yes	—
33	C₂×C₂₃×#120	C₂²	1	2	yes	—
34	C₂×C₂₃×#120	C₂²	1	1	yes	characteristic
35	C₂×C₂₃×#120	C₂²	1	2	yes	complemented
36	C₂×C₄×D₄×C₂₃	—	2	16	no	—
37	C₂×C₄×D₄×C₂₃	C₂²	1	2	yes	—
38	C₂×C₄×D₄×C₂₃	C₂²	1	2	yes	—
39	C₂×C₄×D₄×C₂₃	C₂²	1	2	yes	—
40	C₂×C₄×D₄×C₂₃	C₂²	1	2	yes	—
41	C₂×C₄×D₄×C₂₃	C₂²	1	2	yes	complemented
42	C₂×C₄×D₄×C₂₃	C₂²	1	2	yes	complemented
43	C₂×C₄×D₄×C₂₃	C₂²	1	2	yes	complemented
44	C₂×C₄×D₄×C₂₃	C₂²	1	2	yes	complemented
45	C₂×C₄×D₄×C₂₃	C₂²	1	2	yes	complemented
46	C₂×C₄×D₄×C₂₃	C₂²	1	2	yes	complemented
47	C₂×C₄×D₄×C₂₃	C₂²	1	2	yes	complemented
48	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic, complemented
49	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic, complemented
50	C₂×C₂₃×#117	C₂²	1	2	yes	complemented
51	C₂²×C₄⋊C₄×C₂₃	C₂²	1	2	yes	complemented
52	C₂²×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	—
53	C₂²×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	complemented
54	C₂²×C₄²×C₂₃	C₂²	1	2	yes	complemented
55	C₂₃×#399	C₂²	1	2	yes	complemented
56	C₂₃×#399	C₂²	1	1	yes	characteristic, complemented
57	C₂₃×#399	C₂²	1	1	yes	characteristic, complemented
58	C₂₃×#398	C₂²	1	2	yes	complemented
59	C₂₃×#397	C₂²	1	2	yes	complemented
60	C₂₃×#396	C₂²	1	2	yes	complemented
61	C₂₃×#396	C₂²	1	2	yes	complemented
62	C₂₃×#395	C₂²	1	1	yes	characteristic, complemented
63	C₂₃×#394	C₂²	1	2	yes	complemented
64	C₂₃×#394	C₂²	1	2	yes	complemented
65	C₂₃×#394	C₂²	1	1	yes	characteristic, complemented
66	C₂₃×#394	C₂²	1	2	yes	complemented
67	C₂₃×#394	C₂²	1	2	yes	complemented
68	C₂₃×#393	C₂²	1	1	yes	characteristic, complemented
69	C₂₃×#392	C₂²	1	1	yes	characteristic
70	C₂₃×#392	C₂²	1	1	yes	characteristic
71	C₂₃×#392	C₂²	1	2	yes	—
72	C₂₃×#392	C₂²	1	2	yes	complemented
73	C₂₃×#392	C₂²	1	1	yes	characteristic, complemented
74	C₂₃×#392	C₂²	1	2	yes	complemented
75	C₂₃×#390	C₂²	1	2	yes	complemented
76	C₂₃×#389	C₂²	1	2	yes	complemented
77	C₂₃×#388	C₂²	1	2	yes	complemented
78	C₂₃×#388	C₂²	1	2	yes	complemented
79	C₂₃×#388	C₂²	1	2	yes	complemented
80	C₂₃×#388	C₂²	1	2	yes	complemented
81	C₂₃×#387	C₂²	1	2	yes	complemented
82	C₂₃×#387	C₂²	1	2	yes	complemented
83	C₂₃×#386	C₂²	1	2	yes	—
84	C₂₃×#386	C₂²	1	2	yes	—
85	C₂₃×#386	C₂²	1	2	yes	—
86	C₂₃×#386	C₂²	1	2	yes	—
87	C₂₃×#386	C₂²	1	2	yes	complemented
88	C₂₃×#386	C₂²	1	2	yes	complemented
89	C₂₃×#386	C₂²	1	2	yes	complemented
90	C₂₃×#386	C₂²	1	2	yes	complemented
91	C₂₃×#386	C₂²	1	1	yes	characteristic, complemented
92	C₂₃×#385	C₂²	1	2	yes	complemented
93	C₂₃×#385	C₂²	1	2	yes	complemented
94	C₂₃×#385	C₂²	1	2	yes	complemented
95	C₂₃×#385	C₂²	1	2	yes	complemented
96	C₂₃×#385	C₂²	1	2	yes	complemented
97	C₂₃×#385	C₂²	1	2	yes	complemented
98	C₂₃×#385	C₂²	1	1	yes	characteristic, complemented
99	C₂₃×#380	C₂²	1	2	yes	complemented
100	C₂₃×#379	C₂²	1	1	yes	characteristic
101	C₂₃×#379	C₂²	1	2	yes	complemented
102	C₄×C₄⋊C₄×C₂₃	C₂²	1	2	yes	complemented
103	C₄×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	complemented
104	C₄×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	complemented
105	C₄×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	complemented
106	C₄×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic, complemented
107	C₄×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic, complemented
108	C₂₃×#376	C₂²	1	1	yes	characteristic, complemented
109	C₂⁵×C₂₃	C₂³	1	2	yes	—
110	C₂⁵×C₂₃	C₂³	1	1	yes	characteristic
111	C₂×#41×C₂₃	—	2	8	no	—
112	C₂×#41×C₂₃	—	4	2	no	—
113	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
114	C₂²×D₄×C₂₃	—	2	8	no	—
115	C₂²×D₄×C₂₃	—	2	8	no	—
116	C₂²×D₄×C₂₃	—	2	8	no	—
117	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
118	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
119	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
120	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
121	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
122	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
123	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
124	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
125	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
126	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
127	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
128	C₂³×C₄×C₂₃	—	2	8	no	—
129	C₂³×C₄×C₂₃	—	2	8	no	—
130	C₂³×C₄×C₂₃	—	2	8	no	—
131	C₂³×C₄×C₂₃	—	4	2	no	—
132	C₂³×C₄×C₂₃	—	4	4	no	—
133	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
134	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
135	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
136	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
137	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
138	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
139	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
140	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
141	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
142	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
143	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
144	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
145	C₂₃×#123	—	2	8	no	—
146	C₂₃×#123	—	2	8	no	—
147	C₂₃×C₂²⋊Q₈	—	2	8	no	—
148	C₂₃×C₂²⋊Q₈	—	2	8	no	—
149	C₂₃×#121	—	2	8	no	—
150	C₂₃×#121	—	2	8	no	—
151	C₂₃×#121	—	2	8	no	—
152	C₂₃×#120	—	2	4	no	—
153	C₂₃×#120	—	2	8	no	—
154	C₂₃×#120	—	2	8	no	—
155	C₂₃×#120	—	2	8	no	—
156	C₄×D₄×C₂₃	—	2	8	no	—
157	C₄×D₄×C₂₃	—	2	8	no	—
158	C₄×D₄×C₂₃	—	2	8	no	—
159	C₄×D₄×C₂₃	—	2	8	no	—
160	C₄×D₄×C₂₃	—	2	8	no	—
161	C₄×D₄×C₂₃	—	2	8	no	—
162	C₄×D₄×C₂₃	—	2	8	no	—
163	C₄×D₄×C₂₃	—	2	8	no	—
164	C₄×D₄×C₂₃	—	2	8	no	—
165	C₄×D₄×C₂₃	—	2	8	no	—
166	C₄×D₄×C₂₃	—	4	2	no	—
167	C₄×D₄×C₂₃	—	4	2	no	—
168	C₄×D₄×C₂₃	D₄	1	16	yes	complemented
169	C₂₃×#117	—	2	8	no	—
170	C₂×C₄⋊C₄×C₂₃	—	2	8	no	—
171	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
172	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
173	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
174	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
175	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
176	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
177	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
178	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
179	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
180	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
181	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
182	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
183	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
184	C₂×C₂²⋊C₄×C₂₃	—	2	8	no	—
185	C₂×C₂²⋊C₄×C₂₃	—	2	8	no	—
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×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
190	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
191	C₂×C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
192	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
193	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
194	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
195	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
196	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
197	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
198	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
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	1	yes	characteristic
208	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
209	C₂×C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
210	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
211	C₂×C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
212	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
213	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
214	C₂×C₄²×C₂₃	—	2	8	no	—
215	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
216	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
217	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
218	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
219	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
220	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
221	C₂₃×#95	C₂³	1	1	yes	characteristic
222	C₂₃×#95	C₂³	1	2	yes	—
223	C₂₃×#95	C₂³	1	1	yes	characteristic
224	C₂₃×#95	C₂³	1	1	yes	characteristic
225	C₂₃×#95	C₂³	1	2	yes	—
226	C₂₃×#95	C₂³	1	2	yes	—
227	C₂₃×#95	C₂³	1	2	yes	—
228	C₂₃×#95	C₂³	1	2	yes	—
229	C₂₃×#95	C₂³	1	2	yes	—
230	C₂₃×#95	C₂³	1	2	yes	—
231	C₂₃×#95	C₂³	1	2	yes	—
232	C₂₃×#95	C₂³	1	1	yes	characteristic
233	C₂₃×#95	C₂³	1	2	yes	—
234	C₂₃×#95	C₂³	1	2	yes	—
235	C₂⁴×C₂₃	—	2	4	no	—
236	C₂⁴×C₂₃	—	2	4	no	—
237	C₂⁴×C₂₃	—	2	4	no	—
238	C₂⁴×C₂₃	—	2	4	no	—
239	C₂⁴×C₂₃	—	2	4	no	—
240	C₂⁴×C₂₃	—	2	4	no	—
241	C₂⁴×C₂₃	—	2	4	no	—
242	C₂⁴×C₂₃	—	4	1	no	—
243	C₂⁴×C₂₃	—	4	2	no	—
244	C₂⁴×C₂₃	—	4	1	no	—
245	C₂⁴×C₂₃	—	4	2	no	—
246	C₂⁴×C₂₃	#41	1	4	yes	complemented
247	C₂⁴×C₂₃	C₂⁴	1	1	yes	characteristic
248	C₂⁴×C₂₃	C₂⁴	1	2	yes	—
249	C₂⁴×C₂₃	C₂⁴	1	2	yes	—
250	C₂⁴×C₂₃	C₂⁴	1	1	yes	characteristic
251	C₂⁴×C₂₃	C₂⁴	1	2	yes	—
252	#41×C₂₃	—	4	16	no	—
253	C₂×Q₈×C₂₃	—	2	4	no	—
254	C₂×Q₈×C₂₃	—	4	1	no	—
255	C₂×D₄×C₂₃	—	2	64	no	—
256	C₂×D₄×C₂₃	—	2	4	no	—
257	C₂×D₄×C₂₃	—	2	4	no	—
258	C₂×D₄×C₂₃	—	2	4	no	—
259	C₂×D₄×C₂₃	—	2	4	no	—
260	C₂×D₄×C₂₃	—	2	4	no	—
261	C₂×D₄×C₂₃	—	2	4	no	—
262	C₂×D₄×C₂₃	—	2	4	no	—
263	C₂×D₄×C₂₃	—	2	4	no	—
264	C₂×D₄×C₂₃	—	2	4	no	—
265	C₂×D₄×C₂₃	—	2	4	no	—
266	C₂×D₄×C₂₃	—	2	4	no	—
267	C₂×D₄×C₂₃	—	2	4	no	—
268	C₂×D₄×C₂₃	—	2	4	no	—
269	C₂×D₄×C₂₃	—	2	4	no	—
270	C₂×D₄×C₂₃	—	2	2	no	—
271	C₂×D₄×C₂₃	—	2	4	no	—
272	C₂×D₄×C₂₃	—	2	4	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	—	4	1	no	—
279	C₂×D₄×C₂₃	—	4	1	no	—
280	C₂×D₄×C₂₃	—	4	2	no	—
281	C₂×D₄×C₂₃	—	4	1	no	—
282	C₂×D₄×C₂₃	—	4	2	no	—
283	C₂×D₄×C₂₃	—	4	2	no	—
284	C₂×D₄×C₂₃	—	4	1	no	—
285	C₂×D₄×C₂₃	C₂×D₄	1	8	yes	—
286	C₂×D₄×C₂₃	#41	1	8	yes	complemented
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	—	2	4	no	—
293	C₂²×C₄×C₂₃	—	2	4	no	—
294	C₂²×C₄×C₂₃	—	2	4	no	—
295	C₂²×C₄×C₂₃	—	2	4	no	—
296	C₂²×C₄×C₂₃	—	2	4	no	—
297	C₂²×C₄×C₂₃	—	2	4	no	—
298	C₂²×C₄×C₂₃	—	2	4	no	—
299	C₂²×C₄×C₂₃	—	2	4	no	—
300	C₂²×C₄×C₂₃	—	2	4	no	—
301	C₂²×C₄×C₂₃	—	2	4	no	—
302	C₂²×C₄×C₂₃	—	2	4	no	—
303	C₂²×C₄×C₂₃	—	2	4	no	—
304	C₂²×C₄×C₂₃	—	2	4	no	—
305	C₂²×C₄×C₂₃	—	2	4	no	—
306	C₂²×C₄×C₂₃	—	2	4	no	—
307	C₂²×C₄×C₂₃	—	2	4	no	—
308	C₂²×C₄×C₂₃	—	2	4	no	—
309	C₂²×C₄×C₂₃	—	2	2	no	—
310	C₂²×C₄×C₂₃	—	2	4	no	—
311	C₂²×C₄×C₂₃	—	2	2	no	—
312	C₂²×C₄×C₂₃	—	4	1	no	—
313	C₂²×C₄×C₂₃	—	4	2	no	—
314	C₂²×C₄×C₂₃	—	4	2	no	—
315	C₂²×C₄×C₂₃	—	4	2	no	—
316	C₂²×C₄×C₂₃	—	4	2	no	—
317	C₂²×C₄×C₂₃	—	4	2	no	—
318	C₂²×C₄×C₂₃	—	4	16	no	—
319	C₂²×C₄×C₂₃	—	4	32	no	—
320	C₂²×C₄×C₂₃	C₂×D₄	1	8	yes	—
321	C₂²×C₄×C₂₃	C₂×D₄	1	8	yes	complemented
322	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
323	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
324	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
325	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
326	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
327	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
328	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
329	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
330	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
331	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
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	1	yes	characteristic
336	C₄⋊C₄×C₂₃	—	2	4	no	—
337	C₄⋊C₄×C₂₃	—	2	4	no	—
338	C₄⋊C₄×C₂₃	—	2	4	no	—
339	C₄⋊C₄×C₂₃	—	2	4	no	—
340	C₄⋊C₄×C₂₃	—	2	4	no	—
341	C₄⋊C₄×C₂₃	—	2	4	no	—
342	C₄⋊C₄×C₂₃	—	2	4	no	—
343	C₄⋊C₄×C₂₃	—	2	4	no	—
344	C₄⋊C₄×C₂₃	—	2	4	no	—
345	C₄⋊C₄×C₂₃	—	4	2	no	—
346	C₄⋊C₄×C₂₃	—	4	1	no	—
347	C₄⋊C₄×C₂₃	—	4	1	no	—
348	C₄⋊C₄×C₂₃	C₂×D₄	1	8	yes	complemented
349	C₂²⋊C₄×C₂₃	—	2	4	no	—
350	C₂²⋊C₄×C₂₃	—	2	4	no	—
351	C₂²⋊C₄×C₂₃	—	2	4	no	—
352	C₂²⋊C₄×C₂₃	—	2	4	no	—
353	C₂²⋊C₄×C₂₃	—	2	2	no	—
354	C₂²⋊C₄×C₂₃	—	2	4	no	—
355	C₂²⋊C₄×C₂₃	—	2	4	no	—
356	C₂²⋊C₄×C₂₃	—	2	4	no	—
357	C₂²⋊C₄×C₂₃	—	2	4	no	—
358	C₂²⋊C₄×C₂₃	—	2	4	no	—
359	C₂²⋊C₄×C₂₃	—	2	4	no	—
360	C₂²⋊C₄×C₂₃	—	2	4	no	—
361	C₂²⋊C₄×C₂₃	—	2	4	no	—
362	C₂²⋊C₄×C₂₃	—	2	4	no	—
363	C₂²⋊C₄×C₂₃	—	2	4	no	—
364	C₂²⋊C₄×C₂₃	—	2	4	no	—
365	C₂²⋊C₄×C₂₃	—	2	4	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	4	no	—
370	C₂²⋊C₄×C₂₃	—	4	2	no	—
371	C₂²⋊C₄×C₂₃	—	4	1	no	—
372	C₂²⋊C₄×C₂₃	—	4	2	no	—
373	C₂²⋊C₄×C₂₃	—	4	1	no	—
374	C₂²⋊C₄×C₂₃	—	4	1	no	—
375	C₂²⋊C₄×C₂₃	C₂×D₄	1	8	yes	—
376	C₂²⋊C₄×C₂₃	C₂×D₄	1	8	yes	complemented
377	C₄²×C₂₃	—	2	4	no	—
378	C₄²×C₂₃	—	2	4	no	—
379	C₄²×C₂₃	—	2	4	no	—
380	C₄²×C₂₃	—	2	4	no	—
381	C₄²×C₂₃	—	2	2	no	—
382	C₄²×C₂₃	C₂×D₄	1	8	yes	complemented
383	#34655	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
384	C₂³×C₂₃	—	2	2	no	—
385	C₂³×C₂₃	—	2	2	no	—
386	C₂³×C₂₃	—	2	2	no	—
387	C₂³×C₂₃	—	2	2	no	—
388	C₂³×C₂₃	—	2	16	no	—
389	C₂³×C₂₃	—	2	16	no	—
390	C₂³×C₂₃	—	2	2	no	—
391	C₂³×C₂₃	—	2	2	no	—
392	C₂³×C₂₃	—	2	2	no	—
393	C₂³×C₂₃	—	2	2	no	—
394	C₂³×C₂₃	—	2	2	no	—
395	C₂³×C₂₃	—	2	2	no	—
396	C₂³×C₂₃	—	2	2	no	—
397	C₂³×C₂₃	—	2	2	no	—
398	C₂³×C₂₃	—	2	2	no	—
399	C₂³×C₂₃	—	2	2	no	—
400	C₂³×C₂₃	—	2	1	no	—
401	C₂³×C₂₃	—	2	2	no	—
402	C₂³×C₂₃	—	2	2	no	—
403	C₂³×C₂₃	—	2	1	no	—
404	C₂³×C₂₃	—	2	2	no	—
405	C₂³×C₂₃	—	2	2	no	—
406	C₂³×C₂₃	—	2	2	no	—
407	C₂³×C₂₃	—	2	2	no	—
408	C₂³×C₂₃	—	2	1	no	—
409	C₂³×C₂₃	—	2	1	no	—
410	C₂³×C₂₃	—	2	1	no	—
411	C₂³×C₂₃	—	4	4	no	—
412	C₂³×C₂₃	—	4	4	no	—
413	C₂³×C₂₃	—	4	8	no	—
414	C₂³×C₂₃	—	4	8	no	—
415	C₂³×C₂₃	—	4	8	no	—
416	C₂³×C₂₃	—	4	8	no	—
417	C₂³×C₂₃	—	4	4	no	—
418	C₂³×C₂₃	—	4	8	no	—
419	C₂³×C₂₃	—	4	8	no	—
420	C₂³×C₂₃	—	4	8	no	—
421	C₂³×C₂₃	C₂²×D₄	1	4	yes	—
422	C₂³×C₂₃	C₂²×D₄	1	4	yes	—
423	C₂³×C₂₃	C₂×#41	1	2	yes	—
424	C₂³×C₂₃	C₂×#41	1	4	yes	—
425	C₂³×C₂₃	C₂×#41	1	4	yes	—
426	C₂³×C₂₃	C₂×#41	1	4	yes	—
427	C₂³×C₂₃	C₂⁵	1	1	yes	characteristic
428	Q₈×C₂₃	—	4	4	no	—
429	D₄×C₂₃	—	2	16	no	—
430	D₄×C₂₃	—	2	16	no	—
431	D₄×C₂₃	—	2	16	no	—
432	D₄×C₂₃	—	2	16	no	—
433	D₄×C₂₃	—	4	8	no	—
434	D₄×C₂₃	—	4	8	no	—
435	D₄×C₂₃	—	4	8	no	—
436	D₄×C₂₃	—	4	4	no	—
437	D₄×C₂₃	—	4	4	no	—
438	D₄×C₂₃	—	4	4	no	—
439	D₄×C₂₃	—	4	8	no	—
440	C₂×C₄×C₂₃	—	2	16	no	—
441	C₂×C₄×C₂₃	—	2	2	no	—
442	C₂×C₄×C₂₃	—	2	2	no	—
443	C₂×C₄×C₂₃	—	2	2	no	—
444	C₂×C₄×C₂₃	—	2	2	no	—
445	C₂×C₄×C₂₃	—	2	2	no	—
446	C₂×C₄×C₂₃	—	2	2	no	—
447	C₂×C₄×C₂₃	—	2	2	no	—
448	C₂×C₄×C₂₃	—	2	2	no	—
449	C₂×C₄×C₂₃	—	2	2	no	—
450	C₂×C₄×C₂₃	—	2	2	no	—
451	C₂×C₄×C₂₃	—	2	16	no	—
452	C₂×C₄×C₂₃	—	2	16	no	—
453	C₂×C₄×C₂₃	—	2	2	no	—
454	C₂×C₄×C₂₃	—	2	2	no	—
455	C₂×C₄×C₂₃	—	2	2	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	2	no	—
460	C₂×C₄×C₂₃	—	2	2	no	—
461	C₂×C₄×C₂₃	—	2	2	no	—
462	C₂×C₄×C₂₃	—	2	1	no	—
463	C₂×C₄×C₂₃	—	2	2	no	—
464	C₂×C₄×C₂₃	—	2	2	no	—
465	C₂×C₄×C₂₃	—	2	2	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	1	no	—
470	C₂×C₄×C₂₃	—	2	1	no	—
471	C₂×C₄×C₂₃	—	2	1	no	—
472	C₂×C₄×C₂₃	—	2	2	no	—
473	C₂×C₄×C₂₃	—	2	2	no	—
474	C₂×C₄×C₂₃	—	4	4	no	—
475	C₂×C₄×C₂₃	—	4	8	no	—
476	C₂×C₄×C₂₃	—	4	8	no	—
477	C₂×C₄×C₂₃	—	4	8	no	—
478	C₂×C₄×C₂₃	—	4	8	no	—
479	C₂×C₄×C₂₃	—	4	8	no	—
480	C₂×C₄×C₂₃	—	4	8	no	—
481	C₂×C₄×C₂₃	—	4	4	no	—
482	C₂×C₄×C₂₃	—	4	4	no	—
483	C₂×C₄×C₂₃	C₂²×D₄	1	4	yes	—
484	C₂×C₄×C₂₃	C₂²×D₄	1	4	yes	—
485	C₂×C₄×C₂₃	C₂²×D₄	1	4	yes	—
486	C₂×C₄×C₂₃	C₂²×D₄	1	4	yes	—
487	C₂×C₄×C₂₃	C₂²×D₄	1	4	yes	—
488	C₂×C₄×C₂₃	C₂×#41	1	4	yes	—
489	C₂×C₄×C₂₃	H(5,𝔽₂)	1	2	yes	—
490	C₂×#525	C₂×C₂₃	1	2	yes	complemented
491	C₂²×C₄×D₄	C₂×C₂₃	1	2	yes	complemented
492	#2463	C₂×C₂₃	1	1	yes	characteristic, complemented
493	#2456	C₂×C₂₃	1	2	yes	complemented
494	#2455	C₂×C₂₃	1	1	yes	characteristic, complemented
495	#2449	C₂×C₂₃	1	2	yes	complemented
496	#2443	C₂×C₂₃	1	2	yes	complemented
497	#2437	C₂×C₂₃	1	1	yes	characteristic, complemented
498	#2424	C₂×C₂₃	1	2	yes	complemented
499	#2418	C₂×C₂₃	1	2	yes	complemented
500	#2410	C₂×C₂₃	1	2	yes	complemented
501	#2403	C₂×C₂₃	1	1	yes	characteristic, complemented
502	#2397	C₂×C₂₃	1	1	yes	characteristic, complemented
503	#2392	C₂×C₂₃	1	2	yes	complemented
504	#2388	C₂×C₂₃	1	1	yes	characteristic, complemented
505	C₄×#121	C₂×C₂₃	1	2	yes	complemented
506	C₄×#120	C₂×C₂₃	1	2	yes	complemented
507	C₄×#120	C₂×C₂₃	1	1	yes	characteristic, complemented
508	#2290	C₂×C₂₃	1	2	yes	complemented
509	C₂²×C₂₃	—	2	4	no	—
510	C₂²×C₂₃	—	2	4	no	—
511	C₂²×C₂₃	—	2	4	no	—
512	C₂²×C₂₃	—	2	4	no	—
513	C₂²×C₂₃	—	2	4	no	—
514	C₂²×C₂₃	—	2	4	no	—
515	C₂²×C₂₃	—	2	4	no	—
516	C₂²×C₂₃	—	2	4	no	—
517	C₂²×C₂₃	—	2	4	no	—
518	C₂²×C₂₃	—	2	2	no	—
519	C₂²×C₂₃	—	2	4	no	—
520	C₂²×C₂₃	—	2	4	no	—
521	C₂²×C₂₃	—	2	4	no	—
522	C₂²×C₂₃	—	2	4	no	—
523	C₂²×C₂₃	—	4	16	no	—
524	C₂²×C₂₃	—	4	32	no	—
525	C₂²×C₂₃	—	4	2	no	—
526	C₂²×C₂₃	—	4	2	no	—
527	C₂²×C₂₃	—	4	2	no	—
528	C₂²×C₂₃	—	4	2	no	—
529	C₂²×C₂₃	—	4	1	no	—
530	C₂²×C₂₃	—	4	2	no	—
531	C₂²×C₂₃	—	4	2	no	—
532	C₂²×C₂₃	—	4	2	no	—
533	C₂²×C₂₃	—	4	2	no	—
534	C₂²×C₂₃	—	4	2	no	—
535	C₂²×C₂₃	—	4	1	no	—
536	C₂²×C₂₃	—	4	2	no	—
537	C₂²×C₂₃	—	4	1	no	—
538	C₂²×C₂₃	—	4	1	no	—
539	C₂²×C₂₃	—	4	2	no	—
540	C₂²×C₂₃	—	4	1	no	—
541	C₂²×C₂₃	#525	1	8	yes	complemented
542	C₂²×C₂₃	C₂³×D₄	1	2	yes	—
543	C₂²×C₂₃	C₂²×#41	1	1	yes	characteristic
544	C₂²×C₂₃	C₂²×#41	1	2	yes	—
545	C₂²×C₂₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
546	C₂²×C₂₃	#585	1	1	yes	characteristic
547	C₄×C₂₃	—	2	4	no	—
548	C₄×C₂₃	—	2	4	no	—
549	C₄×C₂₃	—	2	4	no	—
550	C₄×C₂₃	—	2	4	no	—
551	C₄×C₂₃	—	2	4	no	—
552	C₄×C₂₃	—	4	2	no	—
553	C₄×C₂₃	—	4	1	no	—
554	C₄×C₂₃	—	4	1	no	—
555	C₄×C₂₃	—	4	2	no	—
556	C₄×C₂₃	—	4	1	no	—
557	C₄×C₂₃	—	4	2	no	—
558	C₄×C₂₃	—	4	2	no	—
559	C₄×C₂₃	—	4	1	no	—
560	C₄×C₂₃	D₄²	1	4	yes	—
561	C₂²×#41	C₂²×C₂₃	1	1	yes	characteristic, complemented
562	C₂³×D₄	C₂²×C₂₃	1	2	yes	—
563	C₂⁴×C₄	C₂²×C₂₃	1	1	yes	characteristic
564	C₂⁴×C₄	C₂²×C₂₃	1	2	yes	complemented
565	#525	—	2	16	no	—
566	C₂×#123	C₂²×C₂₃	1	2	yes	complemented
567	C₂×#123	C₂²×C₂₃	1	2	yes	complemented
568	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	2	yes	complemented
569	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	2	yes	complemented
570	C₂×#121	C₂²×C₂₃	1	2	yes	—
571	C₂×#121	C₂²×C₂₃	1	2	yes	—
572	C₂×#121	C₂²×C₂₃	1	2	yes	complemented
573	C₂×#120	C₂²×C₂₃	1	2	yes	—
574	C₂×#120	C₂²×C₂₃	1	2	yes	—
575	C₂×#120	C₂²×C₂₃	1	1	yes	characteristic
576	C₂×#120	C₂²×C₂₃	1	2	yes	complemented
577	C₂×C₄×D₄	—	2	16	no	—
578	C₂×C₄×D₄	C₂²×C₂₃	1	2	yes	—
579	C₂×C₄×D₄	C₂²×C₂₃	1	2	yes	—
580	C₂×C₄×D₄	C₂²×C₂₃	1	2	yes	—
581	C₂×C₄×D₄	C₂²×C₂₃	1	2	yes	—
582	C₂×C₄×D₄	C₂²×C₂₃	1	2	yes	complemented
583	C₂×C₄×D₄	C₂²×C₂₃	1	2	yes	complemented
584	C₂×C₄×D₄	C₂²×C₂₃	1	2	yes	complemented
585	C₂×C₄×D₄	C₂²×C₂₃	1	2	yes	complemented
586	C₂×C₄×D₄	C₂²×C₂₃	1	2	yes	complemented
587	C₂×C₄×D₄	C₂²×C₂₃	1	2	yes	complemented
588	C₂×C₄×D₄	C₂²×C₂₃	1	2	yes	complemented
589	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic, complemented
590	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic, complemented
591	C₂×#117	C₂²×C₂₃	1	2	yes	complemented
592	C₂²×C₄⋊C₄	C₂²×C₂₃	1	2	yes	complemented
593	C₂²×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
594	C₂²×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	complemented
595	C₂²×C₄²	C₂²×C₂₃	1	2	yes	complemented
596	#399	C₂²×C₂₃	1	2	yes	complemented
597	#399	C₂²×C₂₃	1	1	yes	characteristic, complemented
598	#399	C₂²×C₂₃	1	1	yes	characteristic, complemented
599	#398	C₂²×C₂₃	1	2	yes	complemented
600	#397	C₂²×C₂₃	1	2	yes	complemented
601	#396	C₂²×C₂₃	1	2	yes	complemented
602	#396	C₂²×C₂₃	1	2	yes	complemented
603	#395	C₂²×C₂₃	1	1	yes	characteristic, complemented
604	#394	C₂²×C₂₃	1	1	yes	characteristic, complemented
605	#394	C₂²×C₂₃	1	2	yes	complemented
606	#394	C₂²×C₂₃	1	2	yes	complemented
607	#394	C₂²×C₂₃	1	2	yes	complemented
608	#394	C₂²×C₂₃	1	2	yes	complemented
609	#393	C₂²×C₂₃	1	1	yes	characteristic, complemented
610	#392	C₂²×C₂₃	1	1	yes	characteristic
611	#392	C₂²×C₂₃	1	2	yes	—
612	#392	C₂²×C₂₃	1	1	yes	characteristic
613	#392	C₂²×C₂₃	1	2	yes	complemented
614	#392	C₂²×C₂₃	1	2	yes	complemented
615	#392	C₂²×C₂₃	1	1	yes	characteristic, complemented
616	#390	C₂²×C₂₃	1	2	yes	complemented
617	#389	C₂²×C₂₃	1	2	yes	complemented
618	#388	C₂²×C₂₃	1	2	yes	complemented
619	#388	C₂²×C₂₃	1	2	yes	complemented
620	#388	C₂²×C₂₃	1	2	yes	complemented
621	#388	C₂²×C₂₃	1	2	yes	complemented
622	#387	C₂²×C₂₃	1	2	yes	complemented
623	#387	C₂²×C₂₃	1	2	yes	complemented
624	#386	C₂²×C₂₃	1	2	yes	—
625	#386	C₂²×C₂₃	1	2	yes	—
626	#386	C₂²×C₂₃	1	2	yes	—
627	#386	C₂²×C₂₃	1	2	yes	—
628	#386	C₂²×C₂₃	1	2	yes	complemented
629	#386	C₂²×C₂₃	1	2	yes	complemented
630	#386	C₂²×C₂₃	1	2	yes	complemented
631	#386	C₂²×C₂₃	1	2	yes	complemented
632	#386	C₂²×C₂₃	1	1	yes	characteristic, complemented
633	#385	C₂²×C₂₃	1	2	yes	complemented
634	#385	C₂²×C₂₃	1	2	yes	complemented
635	#385	C₂²×C₂₃	1	2	yes	complemented
636	#385	C₂²×C₂₃	1	2	yes	complemented
637	#385	C₂²×C₂₃	1	2	yes	complemented
638	#385	C₂²×C₂₃	1	2	yes	complemented
639	#385	C₂²×C₂₃	1	1	yes	characteristic, complemented
640	#380	C₂²×C₂₃	1	2	yes	complemented
641	#379	C₂²×C₂₃	1	1	yes	characteristic
642	#379	C₂²×C₂₃	1	2	yes	complemented
643	C₄×C₄⋊C₄	C₂²×C₂₃	1	2	yes	complemented
644	C₄×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	complemented
645	C₄×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic, complemented
646	C₄×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic, complemented
647	C₄×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	complemented
648	C₄×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	complemented
649	#376	C₂²×C₂₃	1	1	yes	characteristic, complemented
650	C₂×C₂₃	—	2	8	no	—
651	C₂×C₂₃	—	4	4	no	—
652	C₂×C₂₃	—	4	2	no	—
653	C₂×C₂₃	—	4	4	no	—
654	C₂×C₂₃	—	8	1	no	—
655	C₂×C₂₃	C₂×#525	1	2	yes	—
656	C₂×C₂₃	#3459	1	1	yes	characteristic
657	C₂×C₂₃	C₂×D₄²	1	1	yes	characteristic
658	C₂×C₂₃	D₄×#41	1	2	yes	—
659	C₂×C₂₃	#3481	1	1	yes	characteristic
660	C₂⁵	C₂³×C₂₃	1	2	yes	—
661	C₂⁵	C₂³×C₂₃	1	1	yes	characteristic
662	C₂×#41	—	2	8	no	—
663	C₂×#41	—	4	2	no	—
664	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
665	C₂²×D₄	—	2	8	no	—
666	C₂²×D₄	—	2	8	no	—
667	C₂²×D₄	—	2	8	no	—
668	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
669	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
670	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
671	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
672	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
673	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
674	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
675	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
676	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
677	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
678	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
679	C₂³×C₄	—	2	8	no	—
680	C₂³×C₄	—	2	8	no	—
681	C₂³×C₄	—	2	8	no	—
682	C₂³×C₄	—	4	2	no	—
683	C₂³×C₄	—	4	4	no	—
684	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
685	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
686	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
687	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
688	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
689	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
690	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
691	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
692	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
693	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
694	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
695	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
696	#123	—	2	8	no	—
697	#123	—	2	8	no	—
698	C₂²⋊Q₈	—	2	8	no	—
699	C₂²⋊Q₈	—	2	8	no	—
700	#121	—	2	8	no	—
701	#121	—	2	8	no	—
702	#121	—	2	8	no	—
703	#120	—	2	4	no	—
704	#120	—	2	8	no	—
705	#120	—	2	8	no	—
706	#120	—	2	8	no	—
707	C₄×D₄	—	2	8	no	—
708	C₄×D₄	—	2	8	no	—
709	C₄×D₄	—	2	8	no	—
710	C₄×D₄	—	2	8	no	—
711	C₄×D₄	—	2	8	no	—
712	C₄×D₄	—	2	8	no	—
713	C₄×D₄	—	2	8	no	—
714	C₄×D₄	—	2	8	no	—
715	C₄×D₄	—	2	8	no	—
716	C₄×D₄	—	2	8	no	—
717	C₄×D₄	—	4	2	no	—
718	C₄×D₄	—	4	2	no	—
719	C₄×D₄	D₄×C₂₃	1	16	yes	complemented
720	#117	—	2	8	no	—
721	C₂×C₄⋊C₄	—	2	8	no	—
722	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
723	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
724	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
725	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
726	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
727	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
728	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
729	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
730	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
731	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
732	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
733	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
734	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
735	C₂×C₂²⋊C₄	—	2	8	no	—
736	C₂×C₂²⋊C₄	—	2	8	no	—
737	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
738	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
739	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
740	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
741	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
742	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
743	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
744	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
745	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
746	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
747	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
748	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
749	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
750	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
751	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
752	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
753	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
754	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
755	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
756	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
757	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
758	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
759	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
760	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
761	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
762	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
763	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
764	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
765	C₂×C₄²	—	2	8	no	—
766	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
767	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
768	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
769	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
770	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
771	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
772	#95	C₂³×C₂₃	1	1	yes	characteristic
773	#95	C₂³×C₂₃	1	2	yes	—
774	#95	C₂³×C₂₃	1	1	yes	characteristic
775	#95	C₂³×C₂₃	1	1	yes	characteristic
776	#95	C₂³×C₂₃	1	2	yes	—
777	#95	C₂³×C₂₃	1	2	yes	—
778	#95	C₂³×C₂₃	1	2	yes	—
779	#95	C₂³×C₂₃	1	2	yes	—
780	#95	C₂³×C₂₃	1	2	yes	—
781	#95	C₂³×C₂₃	1	2	yes	—
782	#95	C₂³×C₂₃	1	2	yes	—
783	#95	C₂³×C₂₃	1	1	yes	characteristic
784	#95	C₂³×C₂₃	1	2	yes	—
785	#95	C₂³×C₂₃	1	2	yes	—
786	C₂₃	#34655	1	1	yes	characteristic, direct product factor, Sylow
787	C₂⁴	—	2	4	no	—
788	C₂⁴	—	2	4	no	—
789	C₂⁴	—	2	4	no	—
790	C₂⁴	—	2	4	no	—
791	C₂⁴	—	2	4	no	—
792	C₂⁴	—	2	4	no	—
793	C₂⁴	—	2	4	no	—
794	C₂⁴	—	4	1	no	—
795	C₂⁴	—	4	2	no	—
796	C₂⁴	—	4	1	no	—
797	C₂⁴	—	4	2	no	—
798	C₂⁴	#41×C₂₃	1	4	yes	complemented
799	C₂⁴	C₂⁴×C₂₃	1	1	yes	characteristic
800	C₂⁴	C₂⁴×C₂₃	1	2	yes	—
801	C₂⁴	C₂⁴×C₂₃	1	2	yes	—
802	C₂⁴	C₂⁴×C₂₃	1	1	yes	characteristic
803	C₂⁴	C₂⁴×C₂₃	1	2	yes	—
804	#41	—	4	16	no	—
805	C₂×Q₈	—	2	4	no	—
806	C₂×Q₈	—	4	1	no	—
807	C₂×D₄	—	2	64	no	—
808	C₂×D₄	—	2	4	no	—
809	C₂×D₄	—	2	4	no	—
810	C₂×D₄	—	2	4	no	—
811	C₂×D₄	—	2	4	no	—
812	C₂×D₄	—	2	4	no	—
813	C₂×D₄	—	2	4	no	—
814	C₂×D₄	—	2	4	no	—
815	C₂×D₄	—	2	4	no	—
816	C₂×D₄	—	2	4	no	—
817	C₂×D₄	—	2	4	no	—
818	C₂×D₄	—	2	4	no	—
819	C₂×D₄	—	2	4	no	—
820	C₂×D₄	—	2	4	no	—
821	C₂×D₄	—	2	4	no	—
822	C₂×D₄	—	2	2	no	—
823	C₂×D₄	—	2	4	no	—
824	C₂×D₄	—	2	4	no	—
825	C₂×D₄	—	2	4	no	—
826	C₂×D₄	—	2	4	no	—
827	C₂×D₄	—	2	4	no	—
828	C₂×D₄	—	2	4	no	—
829	C₂×D₄	—	2	4	no	—
830	C₂×D₄	—	4	1	no	—
831	C₂×D₄	—	4	1	no	—
832	C₂×D₄	—	4	2	no	—
833	C₂×D₄	—	4	1	no	—
834	C₂×D₄	—	4	2	no	—
835	C₂×D₄	—	4	1	no	—
836	C₂×D₄	—	4	2	no	—
837	C₂×D₄	C₂×D₄×C₂₃	1	8	yes	—
838	C₂×D₄	#41×C₂₃	1	8	yes	complemented
839	C₂²×C₄	—	2	4	no	—
840	C₂²×C₄	—	2	4	no	—
841	C₂²×C₄	—	2	4	no	—
842	C₂²×C₄	—	2	4	no	—
843	C₂²×C₄	—	2	4	no	—
844	C₂²×C₄	—	2	4	no	—
845	C₂²×C₄	—	2	4	no	—
846	C₂²×C₄	—	2	4	no	—
847	C₂²×C₄	—	2	4	no	—
848	C₂²×C₄	—	2	4	no	—
849	C₂²×C₄	—	2	4	no	—
850	C₂²×C₄	—	2	4	no	—
851	C₂²×C₄	—	2	4	no	—
852	C₂²×C₄	—	2	4	no	—
853	C₂²×C₄	—	2	4	no	—
854	C₂²×C₄	—	2	4	no	—
855	C₂²×C₄	—	2	4	no	—
856	C₂²×C₄	—	2	4	no	—
857	C₂²×C₄	—	2	4	no	—
858	C₂²×C₄	—	2	4	no	—
859	C₂²×C₄	—	2	4	no	—
860	C₂²×C₄	—	2	4	no	—
861	C₂²×C₄	—	2	2	no	—
862	C₂²×C₄	—	2	4	no	—
863	C₂²×C₄	—	2	2	no	—
864	C₂²×C₄	—	4	1	no	—
865	C₂²×C₄	—	4	2	no	—
866	C₂²×C₄	—	4	2	no	—
867	C₂²×C₄	—	4	2	no	—
868	C₂²×C₄	—	4	2	no	—
869	C₂²×C₄	—	4	2	no	—
870	C₂²×C₄	—	4	16	no	—
871	C₂²×C₄	—	4	32	no	—
872	C₂²×C₄	C₂×D₄×C₂₃	1	8	yes	—
873	C₂²×C₄	C₂×D₄×C₂₃	1	8	yes	complemented
874	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
875	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
876	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
877	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
878	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
879	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
880	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
881	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
882	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
883	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
884	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
885	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
886	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
887	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
888	C₄⋊C₄	—	2	4	no	—
889	C₄⋊C₄	—	2	4	no	—
890	C₄⋊C₄	—	2	4	no	—
891	C₄⋊C₄	—	2	4	no	—
892	C₄⋊C₄	—	2	4	no	—
893	C₄⋊C₄	—	2	4	no	—
894	C₄⋊C₄	—	2	4	no	—
895	C₄⋊C₄	—	2	4	no	—
896	C₄⋊C₄	—	2	4	no	—
897	C₄⋊C₄	—	4	1	no	—
898	C₄⋊C₄	—	4	1	no	—
899	C₄⋊C₄	—	4	2	no	—
900	C₄⋊C₄	C₂×D₄×C₂₃	1	8	yes	complemented
901	C₂²⋊C₄	—	2	4	no	—
902	C₂²⋊C₄	—	2	4	no	—
903	C₂²⋊C₄	—	2	4	no	—
904	C₂²⋊C₄	—	2	4	no	—
905	C₂²⋊C₄	—	2	2	no	—
906	C₂²⋊C₄	—	2	4	no	—
907	C₂²⋊C₄	—	2	4	no	—
908	C₂²⋊C₄	—	2	4	no	—
909	C₂²⋊C₄	—	2	4	no	—
910	C₂²⋊C₄	—	2	4	no	—
911	C₂²⋊C₄	—	2	4	no	—
912	C₂²⋊C₄	—	2	4	no	—
913	C₂²⋊C₄	—	2	4	no	—
914	C₂²⋊C₄	—	2	4	no	—
915	C₂²⋊C₄	—	2	4	no	—
916	C₂²⋊C₄	—	2	4	no	—
917	C₂²⋊C₄	—	2	4	no	—
918	C₂²⋊C₄	—	2	4	no	—
919	C₂²⋊C₄	—	2	4	no	—
920	C₂²⋊C₄	—	2	4	no	—
921	C₂²⋊C₄	—	2	4	no	—
922	C₂²⋊C₄	—	4	2	no	—
923	C₂²⋊C₄	—	4	1	no	—
924	C₂²⋊C₄	—	4	1	no	—
925	C₂²⋊C₄	—	4	2	no	—
926	C₂²⋊C₄	—	4	1	no	—
927	C₂²⋊C₄	C₂×D₄×C₂₃	1	8	yes	—
928	C₂²⋊C₄	C₂×D₄×C₂₃	1	8	yes	complemented
929	C₄²	—	2	4	no	—
930	C₄²	—	2	4	no	—
931	C₄²	—	2	4	no	—
932	C₄²	—	2	4	no	—
933	C₄²	—	2	2	no	—
934	C₄²	C₂×D₄×C₂₃	1	8	yes	complemented
935	C₂³	—	2	2	no	—
936	C₂³	—	2	2	no	—
937	C₂³	—	2	2	no	—
938	C₂³	—	2	2	no	—
939	C₂³	—	2	16	no	—
940	C₂³	—	2	2	no	—
941	C₂³	—	2	2	no	—
942	C₂³	—	2	2	no	—
943	C₂³	—	2	2	no	—
944	C₂³	—	2	2	no	—
945	C₂³	—	2	2	no	—
946	C₂³	—	2	2	no	—
947	C₂³	—	2	2	no	—
948	C₂³	—	2	2	no	—
949	C₂³	—	2	2	no	—
950	C₂³	—	2	1	no	—
951	C₂³	—	2	2	no	—
952	C₂³	—	2	2	no	—
953	C₂³	—	2	1	no	—
954	C₂³	—	2	2	no	—
955	C₂³	—	2	2	no	—
956	C₂³	—	2	16	no	—
957	C₂³	—	2	2	no	—
958	C₂³	—	2	2	no	—
959	C₂³	—	2	1	no	—
960	C₂³	—	2	1	no	—
961	C₂³	—	2	1	no	—
962	C₂³	—	4	4	no	—
963	C₂³	—	4	4	no	—
964	C₂³	—	4	8	no	—
965	C₂³	—	4	8	no	—
966	C₂³	—	4	8	no	—
967	C₂³	—	4	8	no	—
968	C₂³	—	4	4	no	—
969	C₂³	—	4	8	no	—
970	C₂³	—	4	8	no	—
971	C₂³	—	4	8	no	—
972	C₂³	C₂²×D₄×C₂₃	1	4	yes	—
973	C₂³	C₂²×D₄×C₂₃	1	4	yes	—
974	C₂³	C₂×#41×C₂₃	1	2	yes	—
975	C₂³	C₂×#41×C₂₃	1	4	yes	—
976	C₂³	C₂×#41×C₂₃	1	4	yes	—
977	C₂³	C₂×#41×C₂₃	1	4	yes	—
978	C₂³	C₂⁵×C₂₃	1	1	yes	characteristic
979	Q₈	—	4	4	no	—
980	D₄	—	2	16	no	—
981	D₄	—	2	16	no	—
982	D₄	—	2	16	no	—
983	D₄	—	2	16	no	—
984	D₄	—	4	8	no	—
985	D₄	—	4	8	no	—
986	D₄	—	4	4	no	—
987	D₄	—	4	8	no	—
988	D₄	—	4	4	no	—
989	D₄	—	4	4	no	—
990	D₄	—	4	8	no	—
991	C₂×C₄	—	2	16	no	—
992	C₂×C₄	—	2	2	no	—
993	C₂×C₄	—	2	2	no	—
994	C₂×C₄	—	2	2	no	—
995	C₂×C₄	—	2	2	no	—
996	C₂×C₄	—	2	2	no	—
997	C₂×C₄	—	2	2	no	—
998	C₂×C₄	—	2	2	no	—
999	C₂×C₄	—	2	2	no	—
1000	C₂×C₄	—	2	2	no	—
1001	C₂×C₄	—	2	2	no	—
1002	C₂×C₄	—	2	16	no	—
1003	C₂×C₄	—	2	16	no	—
1004	C₂×C₄	—	2	2	no	—
1005	C₂×C₄	—	2	2	no	—
1006	C₂×C₄	—	2	2	no	—
1007	C₂×C₄	—	2	2	no	—
1008	C₂×C₄	—	2	2	no	—
1009	C₂×C₄	—	2	2	no	—
1010	C₂×C₄	—	2	2	no	—
1011	C₂×C₄	—	2	2	no	—
1012	C₂×C₄	—	2	2	no	—
1013	C₂×C₄	—	2	1	no	—
1014	C₂×C₄	—	2	2	no	—
1015	C₂×C₄	—	2	2	no	—
1016	C₂×C₄	—	2	2	no	—
1017	C₂×C₄	—	2	1	no	—
1018	C₂×C₄	—	2	1	no	—
1019	C₂×C₄	—	2	2	no	—
1020	C₂×C₄	—	2	1	no	—
1021	C₂×C₄	—	2	1	no	—
1022	C₂×C₄	—	2	1	no	—
1023	C₂×C₄	—	2	2	no	—
1024	C₂×C₄	—	2	2	no	—
1025	C₂×C₄	—	4	4	no	—
1026	C₂×C₄	—	4	8	no	—
1027	C₂×C₄	—	4	8	no	—
1028	C₂×C₄	—	4	8	no	—
1029	C₂×C₄	—	4	8	no	—
1030	C₂×C₄	—	4	8	no	—
1031	C₂×C₄	—	4	8	no	—
1032	C₂×C₄	—	4	4	no	—
1033	C₂×C₄	—	4	4	no	—
1034	C₂×C₄	C₂²×D₄×C₂₃	1	4	yes	—
1035	C₂×C₄	C₂²×D₄×C₂₃	1	4	yes	—
1036	C₂×C₄	C₂²×D₄×C₂₃	1	4	yes	—
1037	C₂×C₄	C₂²×D₄×C₂₃	1	4	yes	—
1038	C₂×C₄	C₂²×D₄×C₂₃	1	4	yes	—
1039	C₂×C₄	C₂×#41×C₂₃	1	4	yes	—
1040	C₂×C₄	C₂₃×H(5,𝔽₂)	1	2	yes	—
1041	C₂²	—	2	4	no	—
1042	C₂²	—	2	4	no	—
1043	C₂²	—	2	4	no	—
1044	C₂²	—	2	4	no	—
1045	C₂²	—	2	4	no	—
1046	C₂²	—	2	4	no	—
1047	C₂²	—	2	4	no	—
1048	C₂²	—	2	4	no	—
1049	C₂²	—	2	4	no	—
1050	C₂²	—	2	2	no	—
1051	C₂²	—	2	4	no	—
1052	C₂²	—	2	4	no	—
1053	C₂²	—	2	4	no	—
1054	C₂²	—	2	4	no	—
1055	C₂²	—	4	16	no	—
1056	C₂²	—	4	32	no	—
1057	C₂²	—	4	2	no	—
1058	C₂²	—	4	2	no	—
1059	C₂²	—	4	2	no	—
1060	C₂²	—	4	2	no	—
1061	C₂²	—	4	1	no	—
1062	C₂²	—	4	2	no	—
1063	C₂²	—	4	2	no	—
1064	C₂²	—	4	2	no	—
1065	C₂²	—	4	2	no	—
1066	C₂²	—	4	2	no	—
1067	C₂²	—	4	1	no	—
1068	C₂²	—	4	2	no	—
1069	C₂²	—	4	1	no	—
1070	C₂²	—	4	1	no	—
1071	C₂²	—	4	2	no	—
1072	C₂²	—	4	1	no	—
1073	C₂²	C₂₃×#525	1	8	yes	complemented
1074	C₂²	C₂³×D₄×C₂₃	1	2	yes	—
1075	C₂²	C₂²×#41×C₂₃	1	1	yes	characteristic
1076	C₂²	C₂²×#41×C₂₃	1	2	yes	—
1077	C₂²	C₂×C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
1078	C₂²	C₂₃×#585	1	1	yes	characteristic
1079	C₄	—	2	4	no	—
1080	C₄	—	2	4	no	—
1081	C₄	—	2	4	no	—
1082	C₄	—	2	4	no	—
1083	C₄	—	2	4	no	—
1084	C₄	—	4	2	no	—
1085	C₄	—	4	1	no	—
1086	C₄	—	4	1	no	—
1087	C₄	—	4	2	no	—
1088	C₄	—	4	1	no	—
1089	C₄	—	4	2	no	—
1090	C₄	—	4	2	no	—
1091	C₄	—	4	1	no	—
1092	C₄	D₄²×C₂₃	1	4	yes	—
1093	C₂	—	2	8	no	—
1094	C₂	—	4	4	no	—
1095	C₂	—	4	2	no	—
1096	C₂	—	4	4	no	—
1097	C₂	—	8	1	no	—
1098	C₂	C₂×C₂₃×#525	1	2	yes	—
1099	C₂	C₂₃×#3459	1	1	yes	characteristic
1100	C₂	C₂×D₄²×C₂₃	1	1	yes	characteristic
1101	C₂	D₄×#41×C₂₃	1	2	yes	—
1102	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
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×#525	C₂	semidirect
2. C₂²×C₄×D₄×C₂₃	C₂	semidirect
3. C₂₃×#2463	C₂	semidirect
4. C₂₃×#2456	C₂	semidirect
5. C₂₃×#2455	C₂	semidirect
6. C₂₃×#2449	C₂	semidirect
7. C₂₃×#2443	C₂	semidirect
8. C₂₃×#2437	C₂	semidirect
9. C₂₃×#2424	C₂	semidirect
10. C₂₃×#2418	C₂	semidirect
11. C₂₃×#2410	C₂	semidirect
12. C₂₃×#2403	C₂	semidirect
13. C₂₃×#2397	C₂	semidirect
14. C₂₃×#2392	C₂	semidirect
15. C₂₃×#2388	C₂	semidirect
16. C₄×C₂₃×#121	C₂	semidirect
17. C₄×C₂₃×#120	C₂	semidirect
18. C₄×C₂₃×#120	C₂	semidirect
19. C₂₃×#2290	C₂	semidirect
20. C₂²×#41×C₂₃	C₂²	semidirect
23. C₂⁴×C₄×C₂₃	C₂²	semidirect
25. C₂×C₂₃×#123	C₂²	semidirect
26. C₂×C₂₃×#123	C₂²	semidirect
27. C₂×C₂₃×C₂²⋊Q₈	C₂²	semidirect
28. C₂×C₂₃×C₂²⋊Q₈	C₂²	semidirect
31. C₂×C₂₃×#121	C₂²	semidirect
35. C₂×C₂₃×#120	C₂²	semidirect
41. C₂×C₄×D₄×C₂₃	C₂²	semidirect
42. C₂×C₄×D₄×C₂₃	C₂²	semidirect
43. C₂×C₄×D₄×C₂₃	C₂²	semidirect
44. C₂×C₄×D₄×C₂₃	C₂²	semidirect
45. C₂×C₄×D₄×C₂₃	C₂²	semidirect
46. C₂×C₄×D₄×C₂₃	C₂²	semidirect
47. C₂×C₄×D₄×C₂₃	C₂²	semidirect
48. C₂×C₄×D₄×C₂₃	C₂²	semidirect
49. C₂×C₄×D₄×C₂₃	C₂²	semidirect
50. C₂×C₂₃×#117	C₂²	semidirect
51. C₂²×C₄⋊C₄×C₂₃	C₂²	semidirect
53. C₂²×C₂²⋊C₄×C₂₃	C₂²	semidirect
54. C₂²×C₄²×C₂₃	C₂²	semidirect
55. C₂₃×#399	C₂²	semidirect
56. C₂₃×#399	C₂²	semidirect
57. C₂₃×#399	C₂²	semidirect
58. C₂₃×#398	C₂²	semidirect
59. C₂₃×#397	C₂²	semidirect
60. C₂₃×#396	C₂²	semidirect
61. C₂₃×#396	C₂²	semidirect
62. C₂₃×#395	C₂²	semidirect
63. C₂₃×#394	C₂²	semidirect
64. C₂₃×#394	C₂²	semidirect
65. C₂₃×#394	C₂²	semidirect
66. C₂₃×#394	C₂²	semidirect
67. C₂₃×#394	C₂²	semidirect
68. C₂₃×#393	C₂²	semidirect
72. C₂₃×#392	C₂²	semidirect
73. C₂₃×#392	C₂²	semidirect
74. C₂₃×#392	C₂²	semidirect
75. C₂₃×#390	C₂²	semidirect
76. C₂₃×#389	C₂²	semidirect
77. C₂₃×#388	C₂²	semidirect
78. C₂₃×#388	C₂²	semidirect
79. C₂₃×#388	C₂²	semidirect
80. C₂₃×#388	C₂²	semidirect
81. C₂₃×#387	C₂²	semidirect
82. C₂₃×#387	C₂²	semidirect
87. C₂₃×#386	C₂²	semidirect
88. C₂₃×#386	C₂²	semidirect
89. C₂₃×#386	C₂²	semidirect
90. C₂₃×#386	C₂²	semidirect
91. C₂₃×#386	C₂²	semidirect
92. C₂₃×#385	C₂²	semidirect
93. C₂₃×#385	C₂²	semidirect
94. C₂₃×#385	C₂²	semidirect
95. C₂₃×#385	C₂²	semidirect
96. C₂₃×#385	C₂²	semidirect
97. C₂₃×#385	C₂²	semidirect
98. C₂₃×#385	C₂²	semidirect
99. C₂₃×#380	C₂²	semidirect
101. C₂₃×#379	C₂²	semidirect
102. C₄×C₄⋊C₄×C₂₃	C₂²	semidirect
103. C₄×C₂²⋊C₄×C₂₃	C₂²	semidirect
104. C₄×C₂²⋊C₄×C₂₃	C₂²	semidirect
105. C₄×C₂²⋊C₄×C₂₃	C₂²	semidirect
106. C₄×C₂²⋊C₄×C₂₃	C₂²	semidirect
107. C₄×C₂²⋊C₄×C₂₃	C₂²	semidirect
108. C₂₃×#376	C₂²	semidirect
168. C₄×D₄×C₂₃	D₄	semidirect
246. C₂⁴×C₂₃	#41	semidirect
286. C₂×D₄×C₂₃	#41	semidirect
321. C₂²×C₄×C₂₃	C₂×D₄	semidirect
348. C₄⋊C₄×C₂₃	C₂×D₄	semidirect
376. C₂²⋊C₄×C₂₃	C₂×D₄	semidirect
382. C₄²×C₂₃	C₂×D₄	semidirect
383. #34655	C₂₃	direct (N × H)
490. C₂×#525	C₂×C₂₃	semidirect
491. C₂²×C₄×D₄	C₂×C₂₃	semidirect
492. #2463	C₂×C₂₃	semidirect
493. #2456	C₂×C₂₃	semidirect
494. #2455	C₂×C₂₃	semidirect
495. #2449	C₂×C₂₃	semidirect
496. #2443	C₂×C₂₃	semidirect
497. #2437	C₂×C₂₃	semidirect
498. #2424	C₂×C₂₃	semidirect
499. #2418	C₂×C₂₃	semidirect
500. #2410	C₂×C₂₃	semidirect
501. #2403	C₂×C₂₃	semidirect
502. #2397	C₂×C₂₃	semidirect
503. #2392	C₂×C₂₃	semidirect
504. #2388	C₂×C₂₃	semidirect
505. C₄×#121	C₂×C₂₃	semidirect
506. C₄×#120	C₂×C₂₃	semidirect
507. C₄×#120	C₂×C₂₃	semidirect
508. #2290	C₂×C₂₃	semidirect
541. C₂²×C₂₃	#525	semidirect
561. C₂²×#41	C₂²×C₂₃	semidirect
564. C₂⁴×C₄	C₂²×C₂₃	semidirect
566. C₂×#123	C₂²×C₂₃	semidirect
567. C₂×#123	C₂²×C₂₃	semidirect
568. C₂×C₂²⋊Q₈	C₂²×C₂₃	semidirect
569. C₂×C₂²⋊Q₈	C₂²×C₂₃	semidirect
572. C₂×#121	C₂²×C₂₃	semidirect
576. C₂×#120	C₂²×C₂₃	semidirect
582. C₂×C₄×D₄	C₂²×C₂₃	semidirect
583. C₂×C₄×D₄	C₂²×C₂₃	semidirect
584. C₂×C₄×D₄	C₂²×C₂₃	semidirect
585. C₂×C₄×D₄	C₂²×C₂₃	semidirect
586. C₂×C₄×D₄	C₂²×C₂₃	semidirect
587. C₂×C₄×D₄	C₂²×C₂₃	semidirect
588. C₂×C₄×D₄	C₂²×C₂₃	semidirect
589. C₂×C₄×D₄	C₂²×C₂₃	semidirect
590. C₂×C₄×D₄	C₂²×C₂₃	semidirect
591. C₂×#117	C₂²×C₂₃	semidirect
592. C₂²×C₄⋊C₄	C₂²×C₂₃	semidirect
594. C₂²×C₂²⋊C₄	C₂²×C₂₃	semidirect
595. C₂²×C₄²	C₂²×C₂₃	semidirect
596. #399	C₂²×C₂₃	semidirect
597. #399	C₂²×C₂₃	semidirect
598. #399	C₂²×C₂₃	semidirect
599. #398	C₂²×C₂₃	semidirect
600. #397	C₂²×C₂₃	semidirect
601. #396	C₂²×C₂₃	semidirect
602. #396	C₂²×C₂₃	semidirect
603. #395	C₂²×C₂₃	semidirect
604. #394	C₂²×C₂₃	semidirect
605. #394	C₂²×C₂₃	semidirect
606. #394	C₂²×C₂₃	semidirect
607. #394	C₂²×C₂₃	semidirect
608. #394	C₂²×C₂₃	semidirect
609. #393	C₂²×C₂₃	semidirect
613. #392	C₂²×C₂₃	semidirect
614. #392	C₂²×C₂₃	semidirect
615. #392	C₂²×C₂₃	semidirect
616. #390	C₂²×C₂₃	semidirect
617. #389	C₂²×C₂₃	semidirect
618. #388	C₂²×C₂₃	semidirect
619. #388	C₂²×C₂₃	semidirect
620. #388	C₂²×C₂₃	semidirect
621. #388	C₂²×C₂₃	semidirect
622. #387	C₂²×C₂₃	semidirect
623. #387	C₂²×C₂₃	semidirect
628. #386	C₂²×C₂₃	semidirect
629. #386	C₂²×C₂₃	semidirect
630. #386	C₂²×C₂₃	semidirect
631. #386	C₂²×C₂₃	semidirect
632. #386	C₂²×C₂₃	semidirect
633. #385	C₂²×C₂₃	semidirect
634. #385	C₂²×C₂₃	semidirect
635. #385	C₂²×C₂₃	semidirect
636. #385	C₂²×C₂₃	semidirect
637. #385	C₂²×C₂₃	semidirect
638. #385	C₂²×C₂₃	semidirect
639. #385	C₂²×C₂₃	semidirect
640. #380	C₂²×C₂₃	semidirect
642. #379	C₂²×C₂₃	semidirect
643. C₄×C₄⋊C₄	C₂²×C₂₃	semidirect
644. C₄×C₂²⋊C₄	C₂²×C₂₃	semidirect
645. C₄×C₂²⋊C₄	C₂²×C₂₃	semidirect
646. C₄×C₂²⋊C₄	C₂²×C₂₃	semidirect
647. C₄×C₂²⋊C₄	C₂²×C₂₃	semidirect
648. C₄×C₂²⋊C₄	C₂²×C₂₃	semidirect
649. #376	C₂²×C₂₃	semidirect
719. C₄×D₄	D₄×C₂₃	semidirect
786. C₂₃	#34655	direct (N × H)
798. C₂⁴	#41×C₂₃	semidirect
838. C₂×D₄	#41×C₂₃	semidirect
873. C₂²×C₄	C₂×D₄×C₂₃	semidirect
900. C₄⋊C₄	C₂×D₄×C₂₃	semidirect
928. C₂²⋊C₄	C₂×D₄×C₂₃	semidirect
934. C₄²	C₂×D₄×C₂₃	semidirect
1073. C₂²	C₂₃×#525	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₂₃×#525	2
C₂²×C₄×D₄×C₂₃	2
C₂₃×#2463	2
C₂₃×#2456	2
C₂₃×#2455	2
C₂₃×#2449	2
C₂₃×#2443	2
C₂₃×#2437	2
C₂₃×#2424	2
C₂₃×#2418	2
C₂₃×#2410	2
C₂₃×#2403	2
C₂₃×#2397	2
C₂₃×#2392	2
C₂₃×#2388	2
C₄×C₂₃×#121	2
C₄×C₂₃×#120	2
C₂₃×#2290	2
#34655	23

Subgroups — C23×#34655 #19182281

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#34655 #19182281