Subgroups — C₂₃×#34334 #19181960

Order 5888.

2500 conjugacy classes of subgroups.

The subgroup lattice has 706 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₄×Q₈×C₂₃	C₂	1	1	yes	maximal, characteristic
2	C₂₃×#2369	C₂	1	2	yes	maximal, complemented
3	C₂₃×#2368	C₂	1	4	yes	maximal, complemented
4	C₂₃×#2365	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₃×#2360	C₂	1	2	yes	maximal, complemented
6	C₂₃×#2355	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₃×#2349	C₂	1	2	yes	maximal
8	D₄×C₄⋊C₄×C₂₃	C₂	1	1	yes	maximal, characteristic
9	Q₈×C₂²⋊C₄×C₂₃	C₂	1	2	yes	maximal, complemented
10	C₂₃×#2331	C₂	1	2	yes	maximal, complemented
11	C₂₃×#2329	C₂	1	4	yes	maximal, complemented
12	C₄×C₂₃×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
13	C₄×C₂₃×C₂²⋊Q₈	C₂	1	2	yes	maximal, complemented
14	C₂₃×#2295	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₂₃×#391	C₂	1	2	yes	maximal, complemented
16	C₂₃×#2275	C₂	1	2	yes	maximal
17	C₄²×D₄×C₂₃	C₂	1	1	yes	maximal, characteristic
18	C₂³×Q₈×C₂₃	C₂²	1	2	yes	—
19	D₄×Q₈×C₂₃	C₄	1	16	yes	complemented
20	C₂×C₂₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
21	C₂×C₂₃×C₄⋊Q₈	C₂²	1	2	yes	—
22	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	2	yes	—
23	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	4	yes	—
24	C₂×C₄×Q₈×C₂₃	C₂²	1	2	yes	—
25	C₂×C₄×Q₈×C₂₃	C₂²	1	2	yes	—
26	C₂×C₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic
27	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
28	C₂×C₄×D₄×C₂₃	C₂²	1	2	yes	—
29	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
30	C₂×C₄×D₄×C₂₃	C₂²	1	2	yes	—
31	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
32	C₂²×C₄⋊C₄×C₂₃	C₂²	1	2	yes	—
33	C₂²×C₄²×C₂₃	C₂²	1	2	yes	—
34	C₂₃×#391	C₂²	1	1	yes	characteristic
35	C₂₃×#391	C₂²	1	2	yes	—
36	C₂₃×#391	C₂²	1	4	yes	—
37	C₂₃×#391	C₂²	1	2	yes	—
38	C₂₃×#391	C₂²	1	2	yes	—
39	C₂₃×#391	C₂²	1	4	yes	—
40	C₂₃×#391	C₂²	1	1	yes	characteristic
41	C₂₃×#391	C₂²	1	4	yes	—
42	C₂₃×#391	C₂²	1	4	yes	—
43	C₂₃×#389	C₂²	1	1	yes	characteristic
44	C₂₃×#389	C₂²	1	1	yes	characteristic
45	C₂₃×#389	C₂²	1	2	yes	—
46	C₂₃×#389	C₂²	1	2	yes	—
47	C₂₃×#389	C₂²	1	4	yes	—
48	C₂₃×#389	C₂²	1	2	yes	—
49	C₂₃×#389	C₂²	1	2	yes	—
50	C₂₃×#387	C₂²	1	2	yes	—
51	C₂₃×#387	C₂²	1	2	yes	—
52	C₂₃×#387	C₂²	1	4	yes	—
53	C₂₃×#387	C₂²	1	4	yes	—
54	C₂₃×#387	C₂²	1	4	yes	—
55	C₂₃×#387	C₂²	1	4	yes	—
56	C₂₃×#385	C₂²	1	4	yes	—
57	C₂₃×#385	C₂²	1	4	yes	—
58	C₂₃×#385	C₂²	1	4	yes	—
59	C₂₃×#384	C₂²	1	1	yes	characteristic
60	C₂₃×#382	C₂²	1	2	yes	—
61	C₂₃×#380	C₂²	1	2	yes	—
62	C₂₃×#380	C₂²	1	4	yes	—
63	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
64	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
65	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
66	C₄×C₄⋊C₄×C₂₃	C₂²	1	2	yes	—
67	C₄×C₄⋊C₄×C₂₃	C₂²	1	2	yes	—
68	C₄×C₄⋊C₄×C₂₃	C₂²	1	2	yes	—
69	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
70	C₄×C₄⋊C₄×C₂₃	C₂²	1	2	yes	—
71	C₄×C₄⋊C₄×C₂₃	C₂²	1	2	yes	—
72	C₄×C₄⋊C₄×C₂₃	C₂²	1	4	yes	—
73	C₄×C₄⋊C₄×C₂₃	C₂²	1	2	yes	—
74	C₄×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	—
75	C₄×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	—
76	C₄×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	—
77	C₄×C₂²⋊C₄×C₂₃	C₂²	1	4	yes	—
78	C₄×C₂²⋊C₄×C₂₃	C₂²	1	4	yes	—
79	C₄×C₂²⋊C₄×C₂₃	C₂²	1	4	yes	—
80	C₂₃×#376	C₂²	1	2	yes	—
81	C₂×C₂₃×#95	C₂²	1	4	yes	—
82	C₂×C₂₃×#95	C₂²	1	4	yes	—
83	C₄³×C₂₃	C₂²	1	1	yes	characteristic
84	C₂²×Q₈×C₂₃	—	4	4	no	—
85	C₂²×Q₈×C₂₃	—	4	4	no	—
86	C₂²×Q₈×C₂₃	C₂×C₄	1	16	yes	complemented
87	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
88	C₂²×Q₈×C₂₃	C₂³	1	2	yes	—
89	C₂²×Q₈×C₂₃	C₂³	1	4	yes	—
90	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
91	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
92	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
93	C₂³×C₄×C₂₃	C₂³	1	4	yes	—
94	C₂³×C₄×C₂₃	C₂³	1	4	yes	—
95	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
96	C₂₃×C₄⋊Q₈	C₂×C₄	1	8	yes	complemented
97	C₂₃×C₄⋊Q₈	C₂×C₄	1	16	yes	complemented
98	C₂₃×C₂²⋊Q₈	C₂×C₄	1	16	yes	complemented
99	C₂₃×C₂²⋊Q₈	C₂×C₄	1	32	yes	complemented
100	C₄×Q₈×C₂₃	—	4	4	no	—
101	C₄×Q₈×C₂₃	—	4	4	no	—
102	C₄×Q₈×C₂₃	C₂×C₄	1	8	yes	complemented
103	C₄×D₄×C₂₃	—	2	4	no	—
104	C₄×D₄×C₂₃	—	2	8	no	—
105	C₄×D₄×C₂₃	C₂×C₄	1	8	yes	—
106	C₄×D₄×C₂₃	C₂×C₄	1	16	yes	—
107	C₄×D₄×C₂₃	Q₈	1	8	yes	complemented
108	C₂×C₄⋊C₄×C₂₃	—	4	4	no	—
109	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
110	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
111	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
112	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
113	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
114	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
115	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
116	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
117	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
118	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
119	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
120	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
121	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
122	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
123	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
124	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
125	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
126	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
127	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
128	C₂×C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
129	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
130	C₂×C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
131	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
132	C₂×C₄²×C₂₃	—	4	4	no	—
133	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
134	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
135	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
136	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
137	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
138	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
139	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
140	C₂×C₄²×C₂₃	C₂³	1	4	yes	—
141	C₂×C₄²×C₂₃	C₂³	1	4	yes	—
142	C₂×C₄²×C₂₃	C₂³	1	4	yes	—
143	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
144	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
145	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
146	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
147	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
148	C₂₃×#95	C₂³	1	2	yes	—
149	C₂₃×#95	C₂³	1	2	yes	—
150	C₂₃×#95	C₂³	1	4	yes	—
151	C₂₃×#95	C₂³	1	4	yes	—
152	C₂₃×#95	C₂³	1	4	yes	—
153	C₂₃×#95	C₂³	1	4	yes	—
154	C₂₃×#95	C₂³	1	4	yes	—
155	C₂₃×#95	C₂³	1	4	yes	—
156	C₂₃×#95	C₂³	1	2	yes	—
157	C₂₃×#95	C₂³	1	2	yes	—
158	C₂₃×#95	C₂³	1	2	yes	—
159	C₂₃×#95	C₂³	1	2	yes	—
160	C₂₃×#95	C₂³	1	2	yes	—
161	C₂₃×#95	C₂³	1	2	yes	—
162	C₂₃×#95	C₂³	1	2	yes	—
163	C₂₃×#95	C₂³	1	4	yes	—
164	C₂₃×#95	C₂³	1	4	yes	—
165	C₂₃×#95	C₂³	1	2	yes	—
166	C₂⁴×C₂₃	C₂⁴	1	2	yes	—
167	C₂×Q₈×C₂₃	—	2	4	no	—
168	C₂×Q₈×C₂₃	—	2	4	no	—
169	C₂×Q₈×C₂₃	—	2	2	no	—
170	C₂×Q₈×C₂₃	—	2	2	no	—
171	C₂×Q₈×C₂₃	—	4	4	no	—
172	C₂×Q₈×C₂₃	—	4	4	no	—
173	C₂×Q₈×C₂₃	—	4	32	no	—
174	C₂×Q₈×C₂₃	C₂²×C₄	1	4	yes	—
175	C₂×Q₈×C₂₃	C₂²×C₄	1	8	yes	—
176	C₂×Q₈×C₂₃	C₂²×C₄	1	16	yes	—
177	C₂×D₄×C₂₃	C₂²×C₄	1	4	yes	—
178	C₂×D₄×C₂₃	C₂×Q₈	1	4	yes	—
179	C₂×D₄×C₂₃	#41	1	4	yes	—
180	C₂²×C₄×C₂₃	—	2	4	no	—
181	C₂²×C₄×C₂₃	—	2	4	no	—
182	C₂²×C₄×C₂₃	—	2	4	no	—
183	C₂²×C₄×C₂₃	—	2	8	no	—
184	C₂²×C₄×C₂₃	—	2	4	no	—
185	C₂²×C₄×C₂₃	—	4	2	no	—
186	C₂²×C₄×C₂₃	—	4	2	no	—
187	C₂²×C₄×C₂₃	—	4	2	no	—
188	C₂²×C₄×C₂₃	—	4	4	no	—
189	C₂²×C₄×C₂₃	—	4	4	no	—
190	C₂²×C₄×C₂₃	—	4	4	no	—
191	C₂²×C₄×C₂₃	—	4	4	no	—
192	C₂²×C₄×C₂₃	C₂²×C₄	1	8	yes	—
193	C₂²×C₄×C₂₃	C₂²×C₄	1	16	yes	—
194	C₂²×C₄×C₂₃	C₂×Q₈	1	8	yes	complemented
195	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
196	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
197	C₂²×C₄×C₂₃	C₂⁴	1	4	yes	—
198	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
199	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
200	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
201	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
202	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
203	C₂²×C₄×C₂₃	C₂⁴	1	4	yes	—
204	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
205	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
206	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
207	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
208	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
209	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
210	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
211	C₄⋊C₄×C₂₃	—	2	2	no	—
212	C₄⋊C₄×C₂₃	—	2	4	no	—
213	C₄⋊C₄×C₂₃	—	2	2	no	—
214	C₄⋊C₄×C₂₃	—	2	4	no	—
215	C₄⋊C₄×C₂₃	—	2	2	no	—
216	C₄⋊C₄×C₂₃	—	2	4	no	—
217	C₄⋊C₄×C₂₃	—	4	4	no	—
218	C₄⋊C₄×C₂₃	—	4	2	no	—
219	C₄⋊C₄×C₂₃	—	4	2	no	—
220	C₄⋊C₄×C₂₃	—	4	4	no	—
221	C₄⋊C₄×C₂₃	—	4	4	no	—
222	C₄⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
223	C₄⋊C₄×C₂₃	C₂²×C₄	1	8	yes	—
224	C₄⋊C₄×C₂₃	C₂²×C₄	1	8	yes	—
225	C₄⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
226	C₄⋊C₄×C₂₃	C₂²×C₄	1	16	yes	—
227	C₄⋊C₄×C₂₃	C₂²×C₄	1	8	yes	—
228	C₄⋊C₄×C₂₃	C₂×Q₈	1	4	yes	complemented
229	C₂²⋊C₄×C₂₃	—	2	4	no	—
230	C₂²⋊C₄×C₂₃	—	2	8	no	—
231	C₂²⋊C₄×C₂₃	C₂²×C₄	1	8	yes	—
232	C₂²⋊C₄×C₂₃	C₂²×C₄	1	16	yes	—
233	C₂²⋊C₄×C₂₃	C₂×Q₈	1	8	yes	complemented
234	C₄²×C₂₃	—	2	2	no	—
235	C₄²×C₂₃	—	2	4	no	—
236	C₄²×C₂₃	—	2	2	no	—
237	C₄²×C₂₃	—	2	4	no	—
238	C₄²×C₂₃	—	2	2	no	—
239	C₄²×C₂₃	—	2	2	no	—
240	C₄²×C₂₃	—	4	2	no	—
241	C₄²×C₂₃	—	4	2	no	—
242	C₄²×C₂₃	—	4	4	no	—
243	C₄²×C₂₃	—	4	1	no	—
244	C₄²×C₂₃	—	4	4	no	—
245	C₄²×C₂₃	—	4	4	no	—
246	C₄²×C₂₃	C₂²×C₄	1	8	yes	—
247	C₄²×C₂₃	C₂²×C₄	1	4	yes	—
248	C₄²×C₂₃	C₂×Q₈	1	4	yes	complemented
249	#34334	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
250	C₂³×C₂₃	—	2	2	no	—
251	C₂³×C₂₃	—	2	2	no	—
252	C₂³×C₂₃	—	2	2	no	—
253	C₂³×C₂₃	—	2	2	no	—
254	C₂³×C₂₃	C₂³×C₄	1	4	yes	—
255	C₂³×C₂₃	C₂²×Q₈	1	4	yes	—
256	C₂³×C₂₃	C₂×#41	1	4	yes	—
257	C₂³×C₂₃	C₂⁵	1	1	yes	characteristic
258	Q₈×C₂₃	—	2	8	no	—
259	Q₈×C₂₃	—	2	16	no	—
260	Q₈×C₂₃	—	4	16	no	—
261	D₄×C₂₃	C₄×Q₈	1	16	yes	complemented
262	C₂×C₄×C₂₃	—	2	1	no	—
263	C₂×C₄×C₂₃	—	2	1	no	—
264	C₂×C₄×C₂₃	—	2	2	no	—
265	C₂×C₄×C₂₃	—	2	1	no	—
266	C₂×C₄×C₂₃	—	2	1	no	—
267	C₂×C₄×C₂₃	—	2	2	no	—
268	C₂×C₄×C₂₃	—	2	4	no	—
269	C₂×C₄×C₂₃	—	2	4	no	—
270	C₂×C₄×C₂₃	—	2	2	no	—
271	C₂×C₄×C₂₃	—	2	2	no	—
272	C₂×C₄×C₂₃	—	2	2	no	—
273	C₂×C₄×C₂₃	—	2	1	no	—
274	C₂×C₄×C₂₃	—	2	1	no	—
275	C₂×C₄×C₂₃	—	2	2	no	—
276	C₂×C₄×C₂₃	—	2	2	no	—
277	C₂×C₄×C₂₃	—	2	2	no	—
278	C₂×C₄×C₂₃	—	2	1	no	—
279	C₂×C₄×C₂₃	—	2	1	no	—
280	C₂×C₄×C₂₃	—	2	16	no	—
281	C₂×C₄×C₂₃	—	2	1	no	—
282	C₂×C₄×C₂₃	—	2	2	no	—
283	C₂×C₄×C₂₃	—	2	2	no	—
284	C₂×C₄×C₂₃	—	2	4	no	—
285	C₂×C₄×C₂₃	—	2	2	no	—
286	C₂×C₄×C₂₃	—	2	2	no	—
287	C₂×C₄×C₂₃	—	2	1	no	—
288	C₂×C₄×C₂₃	—	2	2	no	—
289	C₂×C₄×C₂₃	—	2	4	no	—
290	C₂×C₄×C₂₃	—	2	2	no	—
291	C₂×C₄×C₂₃	—	2	2	no	—
292	C₂×C₄×C₂₃	—	2	2	no	—
293	C₂×C₄×C₂₃	—	2	1	no	—
294	C₂×C₄×C₂₃	—	2	4	no	—
295	C₂×C₄×C₂₃	—	2	2	no	—
296	C₂×C₄×C₂₃	—	4	16	no	—
297	C₂×C₄×C₂₃	—	4	8	no	—
298	C₂×C₄×C₂₃	—	4	8	no	—
299	C₂×C₄×C₂₃	—	8	8	no	—
300	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
301	C₂×C₄×C₂₃	C₂³×C₄	1	4	yes	—
302	C₂×C₄×C₂₃	C₂³×C₄	1	4	yes	—
303	C₂×C₄×C₂₃	C₂³×C₄	1	4	yes	—
304	C₂×C₄×C₂₃	C₂³×C₄	1	8	yes	—
305	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
306	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
307	C₂×C₄×C₂₃	C₂²×Q₈	1	2	yes	—
308	C₂×C₄×C₂₃	C₂²×Q₈	1	2	yes	—
309	C₂×C₄×C₂₃	C₂²×Q₈	1	4	yes	—
310	C₂×C₄×C₂₃	C₂²×Q₈	1	2	yes	—
311	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
312	C₂×C₄×C₂₃	H(5,𝔽₂)	1	2	yes	—
313	C₂×C₄×C₂₃	H(5,𝔽₂)	1	2	yes	—
314	C₂×C₄×C₂₃	2₋¹⁺⁴	1	2	yes	—
315	C₂×D₄×Q₈	C₂×C₂₃	1	1	yes	characteristic
316	#2369	C₂×C₂₃	1	2	yes	complemented
317	#2368	C₂×C₂₃	1	4	yes	complemented
318	#2365	C₂×C₂₃	1	1	yes	characteristic, complemented
319	#2360	C₂×C₂₃	1	2	yes	complemented
320	#2355	C₂×C₂₃	1	1	yes	characteristic, complemented
321	#2349	C₂×C₂₃	1	2	yes	—
322	D₄×C₄⋊C₄	C₂×C₂₃	1	1	yes	characteristic
323	Q₈×C₂²⋊C₄	C₂×C₂₃	1	2	yes	complemented
324	#2331	C₂×C₂₃	1	2	yes	complemented
325	#2329	C₂×C₂₃	1	4	yes	complemented
326	C₄×C₄⋊Q₈	C₂×C₂₃	1	1	yes	characteristic, complemented
327	C₄×C₂²⋊Q₈	C₂×C₂₃	1	2	yes	complemented
328	#2295	C₂×C₂₃	1	1	yes	characteristic, complemented
329	C₂×#391	C₂×C₂₃	1	2	yes	complemented
330	#2275	C₂×C₂₃	1	2	yes	—
331	C₄²×D₄	C₂×C₂₃	1	1	yes	characteristic
332	C₂²×C₂₃	—	2	4	no	—
333	C₂²×C₂₃	—	2	4	no	—
334	C₂²×C₂₃	—	2	4	no	—
335	C₂²×C₂₃	—	2	4	no	—
336	C₂²×C₂₃	—	2	4	no	—
337	C₂²×C₂₃	—	2	4	no	—
338	C₂²×C₂₃	C₂×C₄×Q₈	1	8	yes	—
339	C₂²×C₂₃	C₂⁴×C₄	1	1	yes	characteristic
340	C₂²×C₂₃	C₂³×Q₈	1	1	yes	characteristic
341	C₂²×C₂₃	C₂²×#41	1	1	yes	characteristic
342	C₂²×C₂₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
343	C₂²×C₂₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
344	C₂²×C₂₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
345	C₂²×C₂₃	#585	1	1	yes	characteristic
346	C₄×C₂₃	—	2	4	no	—
347	C₄×C₂₃	—	2	4	no	—
348	C₄×C₂₃	—	2	8	no	—
349	C₄×C₂₃	—	2	2	no	—
350	C₄×C₂₃	—	2	4	no	—
351	C₄×C₂₃	—	2	2	no	—
352	C₄×C₂₃	—	2	4	no	—
353	C₄×C₂₃	—	2	2	no	—
354	C₄×C₂₃	—	2	2	no	—
355	C₄×C₂₃	—	4	1	no	—
356	C₄×C₂₃	—	4	4	no	—
357	C₄×C₂₃	—	4	2	no	—
358	C₄×C₂₃	—	4	2	no	—
359	C₄×C₂₃	—	4	2	no	—
360	C₄×C₂₃	C₂×C₄×Q₈	1	4	yes	—
361	C₄×C₂₃	#518	1	4	yes	—
362	C₂³×Q₈	C₂²×C₂₃	1	2	yes	—
363	D₄×Q₈	C₄×C₂₃	1	16	yes	complemented
364	C₂×C₄⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
365	C₂×C₄⋊Q₈	C₂²×C₂₃	1	2	yes	—
366	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	4	yes	—
367	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	2	yes	—
368	C₂×C₄×Q₈	C₂²×C₂₃	1	2	yes	—
369	C₂×C₄×Q₈	C₂²×C₂₃	1	2	yes	—
370	C₂×C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
371	C₂×C₄×D₄	C₂²×C₂₃	1	2	yes	—
372	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
373	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
374	C₂×C₄×D₄	C₂²×C₂₃	1	2	yes	—
375	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
376	C₂²×C₄⋊C₄	C₂²×C₂₃	1	2	yes	—
377	C₂²×C₄²	C₂²×C₂₃	1	2	yes	—
378	#391	C₂²×C₂₃	1	2	yes	—
379	#391	C₂²×C₂₃	1	4	yes	—
380	#391	C₂²×C₂₃	1	4	yes	—
381	#391	C₂²×C₂₃	1	4	yes	—
382	#391	C₂²×C₂₃	1	1	yes	characteristic
383	#391	C₂²×C₂₃	1	2	yes	—
384	#391	C₂²×C₂₃	1	2	yes	—
385	#391	C₂²×C₂₃	1	4	yes	—
386	#391	C₂²×C₂₃	1	1	yes	characteristic
387	#389	C₂²×C₂₃	1	2	yes	—
388	#389	C₂²×C₂₃	1	2	yes	—
389	#389	C₂²×C₂₃	1	4	yes	—
390	#389	C₂²×C₂₃	1	2	yes	—
391	#389	C₂²×C₂₃	1	2	yes	—
392	#389	C₂²×C₂₃	1	1	yes	characteristic
393	#389	C₂²×C₂₃	1	1	yes	characteristic
394	#387	C₂²×C₂₃	1	2	yes	—
395	#387	C₂²×C₂₃	1	4	yes	—
396	#387	C₂²×C₂₃	1	4	yes	—
397	#387	C₂²×C₂₃	1	4	yes	—
398	#387	C₂²×C₂₃	1	4	yes	—
399	#387	C₂²×C₂₃	1	2	yes	—
400	#385	C₂²×C₂₃	1	4	yes	—
401	#385	C₂²×C₂₃	1	4	yes	—
402	#385	C₂²×C₂₃	1	4	yes	—
403	#384	C₂²×C₂₃	1	1	yes	characteristic
404	#382	C₂²×C₂₃	1	2	yes	—
405	#380	C₂²×C₂₃	1	4	yes	—
406	#380	C₂²×C₂₃	1	2	yes	—
407	C₄×C₄⋊C₄	C₂²×C₂₃	1	2	yes	—
408	C₄×C₄⋊C₄	C₂²×C₂₃	1	2	yes	—
409	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
410	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
411	C₄×C₄⋊C₄	C₂²×C₂₃	1	2	yes	—
412	C₄×C₄⋊C₄	C₂²×C₂₃	1	2	yes	—
413	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
414	C₄×C₄⋊C₄	C₂²×C₂₃	1	2	yes	—
415	C₄×C₄⋊C₄	C₂²×C₂₃	1	2	yes	—
416	C₄×C₄⋊C₄	C₂²×C₂₃	1	4	yes	—
417	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
418	C₄×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
419	C₄×C₂²⋊C₄	C₂²×C₂₃	1	4	yes	—
420	C₄×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
421	C₄×C₂²⋊C₄	C₂²×C₂₃	1	4	yes	—
422	C₄×C₂²⋊C₄	C₂²×C₂₃	1	4	yes	—
423	C₄×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
424	#376	C₂²×C₂₃	1	2	yes	—
425	C₂×#95	C₂²×C₂₃	1	4	yes	—
426	C₂×#95	C₂²×C₂₃	1	4	yes	—
427	C₄³	C₂²×C₂₃	1	1	yes	characteristic
428	C₂×C₂₃	—	2	8	no	—
429	C₂×C₂₃	C₂²×C₄×Q₈	1	1	yes	characteristic
430	C₂×C₂₃	C₂×#518	1	1	yes	characteristic
431	C₂×C₂₃	C₄×2₋¹⁺⁴	1	1	yes	characteristic
432	C₂×C₂₃	#3501	1	1	yes	characteristic
433	C₂×C₂₃	#3503	1	1	yes	characteristic
434	C₂×C₂₃	#3514	1	1	yes	characteristic
435	C₂×C₂₃	#3520	1	1	yes	characteristic
436	C₂²×Q₈	—	4	4	no	—
437	C₂²×Q₈	—	4	4	no	—
438	C₂²×Q₈	C₂×C₄×C₂₃	1	16	yes	complemented
439	C₂²×Q₈	C₂³×C₂₃	1	2	yes	—
440	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
441	C₂²×Q₈	C₂³×C₂₃	1	4	yes	—
442	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
443	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
444	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
445	C₂³×C₄	C₂³×C₂₃	1	4	yes	—
446	C₂³×C₄	C₂³×C₂₃	1	4	yes	—
447	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
448	C₄⋊Q₈	C₂×C₄×C₂₃	1	8	yes	complemented
449	C₄⋊Q₈	C₂×C₄×C₂₃	1	16	yes	complemented
450	C₂²⋊Q₈	C₂×C₄×C₂₃	1	16	yes	complemented
451	C₂²⋊Q₈	C₂×C₄×C₂₃	1	32	yes	complemented
452	C₄×Q₈	—	4	4	no	—
453	C₄×Q₈	—	4	4	no	—
454	C₄×Q₈	C₂×C₄×C₂₃	1	8	yes	complemented
455	C₄×D₄	—	2	4	no	—
456	C₄×D₄	—	2	8	no	—
457	C₄×D₄	C₂×C₄×C₂₃	1	8	yes	—
458	C₄×D₄	C₂×C₄×C₂₃	1	16	yes	—
459	C₄×D₄	Q₈×C₂₃	1	8	yes	complemented
460	C₂×C₄⋊C₄	—	4	4	no	—
461	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
462	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
463	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
464	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
465	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
466	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
467	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
468	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
469	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
470	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
471	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
472	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
473	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
474	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
475	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
476	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
477	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
478	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
479	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
480	C₂×C₂²⋊C₄	C₂³×C₂₃	1	4	yes	—
481	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
482	C₂×C₂²⋊C₄	C₂³×C₂₃	1	4	yes	—
483	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
484	C₂×C₄²	—	4	4	no	—
485	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
486	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
487	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
488	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
489	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
490	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
491	C₂×C₄²	C₂³×C₂₃	1	4	yes	—
492	C₂×C₄²	C₂³×C₂₃	1	4	yes	—
493	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
494	C₂×C₄²	C₂³×C₂₃	1	4	yes	—
495	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
496	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
497	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
498	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
499	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
500	#95	C₂³×C₂₃	1	2	yes	—
501	#95	C₂³×C₂₃	1	2	yes	—
502	#95	C₂³×C₂₃	1	4	yes	—
503	#95	C₂³×C₂₃	1	4	yes	—
504	#95	C₂³×C₂₃	1	4	yes	—
505	#95	C₂³×C₂₃	1	4	yes	—
506	#95	C₂³×C₂₃	1	4	yes	—
507	#95	C₂³×C₂₃	1	4	yes	—
508	#95	C₂³×C₂₃	1	2	yes	—
509	#95	C₂³×C₂₃	1	2	yes	—
510	#95	C₂³×C₂₃	1	2	yes	—
511	#95	C₂³×C₂₃	1	2	yes	—
512	#95	C₂³×C₂₃	1	2	yes	—
513	#95	C₂³×C₂₃	1	2	yes	—
514	#95	C₂³×C₂₃	1	2	yes	—
515	#95	C₂³×C₂₃	1	4	yes	—
516	#95	C₂³×C₂₃	1	4	yes	—
517	#95	C₂³×C₂₃	1	2	yes	—
518	C₂₃	#34334	1	1	yes	characteristic, direct product factor, Sylow
519	C₂⁴	C₂⁴×C₂₃	1	2	yes	—
520	C₂×Q₈	—	2	4	no	—
521	C₂×Q₈	—	2	4	no	—
522	C₂×Q₈	—	2	2	no	—
523	C₂×Q₈	—	2	2	no	—
524	C₂×Q₈	—	4	4	no	—
525	C₂×Q₈	—	4	4	no	—
526	C₂×Q₈	—	4	32	no	—
527	C₂×Q₈	C₂²×C₄×C₂₃	1	4	yes	—
528	C₂×Q₈	C₂²×C₄×C₂₃	1	8	yes	—
529	C₂×Q₈	C₂²×C₄×C₂₃	1	16	yes	—
530	C₂×D₄	C₂²×C₄×C₂₃	1	4	yes	—
531	C₂×D₄	C₂×Q₈×C₂₃	1	4	yes	—
532	C₂×D₄	#41×C₂₃	1	4	yes	—
533	C₂²×C₄	—	2	4	no	—
534	C₂²×C₄	—	2	4	no	—
535	C₂²×C₄	—	2	4	no	—
536	C₂²×C₄	—	2	8	no	—
537	C₂²×C₄	—	2	4	no	—
538	C₂²×C₄	—	4	2	no	—
539	C₂²×C₄	—	4	2	no	—
540	C₂²×C₄	—	4	4	no	—
541	C₂²×C₄	—	4	4	no	—
542	C₂²×C₄	—	4	2	no	—
543	C₂²×C₄	—	4	4	no	—
544	C₂²×C₄	—	4	4	no	—
545	C₂²×C₄	C₂²×C₄×C₂₃	1	8	yes	—
546	C₂²×C₄	C₂²×C₄×C₂₃	1	16	yes	—
547	C₂²×C₄	C₂×Q₈×C₂₃	1	8	yes	complemented
548	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
549	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
550	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
551	C₂²×C₄	C₂⁴×C₂₃	1	4	yes	—
552	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
553	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
554	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
555	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
556	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
557	C₂²×C₄	C₂⁴×C₂₃	1	4	yes	—
558	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
559	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
560	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
561	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
562	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
563	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
564	C₄⋊C₄	—	2	2	no	—
565	C₄⋊C₄	—	2	4	no	—
566	C₄⋊C₄	—	2	2	no	—
567	C₄⋊C₄	—	2	4	no	—
568	C₄⋊C₄	—	2	2	no	—
569	C₄⋊C₄	—	2	4	no	—
570	C₄⋊C₄	—	4	4	no	—
571	C₄⋊C₄	—	4	4	no	—
572	C₄⋊C₄	—	4	4	no	—
573	C₄⋊C₄	—	4	2	no	—
574	C₄⋊C₄	—	4	2	no	—
575	C₄⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
576	C₄⋊C₄	C₂²×C₄×C₂₃	1	8	yes	—
577	C₄⋊C₄	C₂²×C₄×C₂₃	1	8	yes	—
578	C₄⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
579	C₄⋊C₄	C₂²×C₄×C₂₃	1	16	yes	—
580	C₄⋊C₄	C₂²×C₄×C₂₃	1	8	yes	—
581	C₄⋊C₄	C₂×Q₈×C₂₃	1	4	yes	complemented
582	C₂²⋊C₄	—	2	4	no	—
583	C₂²⋊C₄	—	2	8	no	—
584	C₂²⋊C₄	C₂²×C₄×C₂₃	1	8	yes	—
585	C₂²⋊C₄	C₂²×C₄×C₂₃	1	16	yes	—
586	C₂²⋊C₄	C₂×Q₈×C₂₃	1	8	yes	complemented
587	C₄²	—	2	2	no	—
588	C₄²	—	2	4	no	—
589	C₄²	—	2	2	no	—
590	C₄²	—	2	4	no	—
591	C₄²	—	2	2	no	—
592	C₄²	—	2	2	no	—
593	C₄²	—	4	2	no	—
594	C₄²	—	4	2	no	—
595	C₄²	—	4	4	no	—
596	C₄²	—	4	4	no	—
597	C₄²	—	4	4	no	—
598	C₄²	—	4	1	no	—
599	C₄²	C₂²×C₄×C₂₃	1	8	yes	—
600	C₄²	C₂²×C₄×C₂₃	1	4	yes	—
601	C₄²	C₂×Q₈×C₂₃	1	4	yes	complemented
602	C₂³	—	2	2	no	—
603	C₂³	—	2	2	no	—
604	C₂³	—	2	2	no	—
605	C₂³	—	2	2	no	—
606	C₂³	C₂³×C₄×C₂₃	1	4	yes	—
607	C₂³	C₂²×Q₈×C₂₃	1	4	yes	—
608	C₂³	C₂×#41×C₂₃	1	4	yes	—
609	C₂³	C₂⁵×C₂₃	1	1	yes	characteristic
610	Q₈	—	2	8	no	—
611	Q₈	—	2	16	no	—
612	Q₈	—	4	16	no	—
613	D₄	C₄×Q₈×C₂₃	1	16	yes	complemented
614	C₂×C₄	—	2	1	no	—
615	C₂×C₄	—	2	1	no	—
616	C₂×C₄	—	2	2	no	—
617	C₂×C₄	—	2	1	no	—
618	C₂×C₄	—	2	1	no	—
619	C₂×C₄	—	2	2	no	—
620	C₂×C₄	—	2	4	no	—
621	C₂×C₄	—	2	4	no	—
622	C₂×C₄	—	2	2	no	—
623	C₂×C₄	—	2	2	no	—
624	C₂×C₄	—	2	2	no	—
625	C₂×C₄	—	2	1	no	—
626	C₂×C₄	—	2	1	no	—
627	C₂×C₄	—	2	2	no	—
628	C₂×C₄	—	2	2	no	—
629	C₂×C₄	—	2	2	no	—
630	C₂×C₄	—	2	1	no	—
631	C₂×C₄	—	2	1	no	—
632	C₂×C₄	—	2	16	no	—
633	C₂×C₄	—	2	1	no	—
634	C₂×C₄	—	2	2	no	—
635	C₂×C₄	—	2	2	no	—
636	C₂×C₄	—	2	4	no	—
637	C₂×C₄	—	2	2	no	—
638	C₂×C₄	—	2	2	no	—
639	C₂×C₄	—	2	1	no	—
640	C₂×C₄	—	2	2	no	—
641	C₂×C₄	—	2	4	no	—
642	C₂×C₄	—	2	2	no	—
643	C₂×C₄	—	2	2	no	—
644	C₂×C₄	—	2	2	no	—
645	C₂×C₄	—	2	1	no	—
646	C₂×C₄	—	2	4	no	—
647	C₂×C₄	—	2	2	no	—
648	C₂×C₄	—	4	16	no	—
649	C₂×C₄	—	4	8	no	—
650	C₂×C₄	—	4	8	no	—
651	C₂×C₄	—	8	8	no	—
652	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
653	C₂×C₄	C₂³×C₄×C₂₃	1	4	yes	—
654	C₂×C₄	C₂³×C₄×C₂₃	1	4	yes	—
655	C₂×C₄	C₂³×C₄×C₂₃	1	4	yes	—
656	C₂×C₄	C₂³×C₄×C₂₃	1	8	yes	—
657	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
658	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
659	C₂×C₄	C₂²×Q₈×C₂₃	1	2	yes	—
660	C₂×C₄	C₂²×Q₈×C₂₃	1	2	yes	—
661	C₂×C₄	C₂²×Q₈×C₂₃	1	4	yes	—
662	C₂×C₄	C₂²×Q₈×C₂₃	1	2	yes	—
663	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
664	C₂×C₄	C₂₃×H(5,𝔽₂)	1	2	yes	—
665	C₂×C₄	C₂₃×H(5,𝔽₂)	1	2	yes	—
666	C₂×C₄	C₂₃×2₋¹⁺⁴	1	2	yes	—
667	C₂²	—	2	4	no	—
668	C₂²	—	2	4	no	—
669	C₂²	—	2	4	no	—
670	C₂²	—	2	4	no	—
671	C₂²	—	2	4	no	—
672	C₂²	—	2	4	no	—
673	C₂²	C₂×C₄×Q₈×C₂₃	1	8	yes	—
674	C₂²	C₂⁴×C₄×C₂₃	1	1	yes	characteristic
675	C₂²	C₂³×Q₈×C₂₃	1	1	yes	characteristic
676	C₂²	C₂²×#41×C₂₃	1	1	yes	characteristic
677	C₂²	C₂×C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
678	C₂²	C₂×C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
679	C₂²	C₂×C₂₃×2₋¹⁺⁴	1	1	yes	characteristic
680	C₂²	C₂₃×#585	1	1	yes	characteristic
681	C₄	—	2	4	no	—
682	C₄	—	2	4	no	—
683	C₄	—	2	8	no	—
684	C₄	—	2	2	no	—
685	C₄	—	2	4	no	—
686	C₄	—	2	2	no	—
687	C₄	—	2	4	no	—
688	C₄	—	2	2	no	—
689	C₄	—	2	2	no	—
690	C₄	—	4	2	no	—
691	C₄	—	4	4	no	—
692	C₄	—	4	1	no	—
693	C₄	—	4	2	no	—
694	C₄	—	4	2	no	—
695	C₄	C₂×C₄×Q₈×C₂₃	1	4	yes	—
696	C₄	C₂₃×#518	1	4	yes	—
697	C₂	—	2	8	no	—
698	C₂	C₂²×C₄×Q₈×C₂₃	1	1	yes	characteristic
699	C₂	C₂×C₂₃×#518	1	1	yes	characteristic
700	C₂	C₄×C₂₃×2₋¹⁺⁴	1	1	yes	characteristic
701	C₂	C₂₃×#3501	1	1	yes	characteristic
702	C₂	C₂₃×#3503	1	1	yes	characteristic
703	C₂	C₂₃×#3514	1	1	yes	characteristic
704	C₂	C₂₃×#3520	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₂₃	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₂₃
Frattini, cosocle	C₂³	C₂⁵×C₂₃
prime radical	C₂²×D₄×C₂₃	C₂³
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂₃×#2369	C₂	semidirect
3. C₂₃×#2368	C₂	semidirect
4. C₂₃×#2365	C₂	semidirect
5. C₂₃×#2360	C₂	semidirect
6. C₂₃×#2355	C₂	semidirect
9. Q₈×C₂²⋊C₄×C₂₃	C₂	semidirect
10. C₂₃×#2331	C₂	semidirect
11. C₂₃×#2329	C₂	semidirect
12. C₄×C₂₃×C₄⋊Q₈	C₂	semidirect
13. C₄×C₂₃×C₂²⋊Q₈	C₂	semidirect
14. C₂₃×#2295	C₂	semidirect
15. C₂×C₂₃×#391	C₂	semidirect
19. D₄×Q₈×C₂₃	C₄	semidirect
86. C₂²×Q₈×C₂₃	C₂×C₄	semidirect
96. C₂₃×C₄⋊Q₈	C₂×C₄	semidirect
97. C₂₃×C₄⋊Q₈	C₂×C₄	semidirect
98. C₂₃×C₂²⋊Q₈	C₂×C₄	semidirect
99. C₂₃×C₂²⋊Q₈	C₂×C₄	semidirect
102. C₄×Q₈×C₂₃	C₂×C₄	semidirect
107. C₄×D₄×C₂₃	Q₈	semidirect
194. C₂²×C₄×C₂₃	C₂×Q₈	semidirect
228. C₄⋊C₄×C₂₃	C₂×Q₈	semidirect
233. C₂²⋊C₄×C₂₃	C₂×Q₈	semidirect
248. C₄²×C₂₃	C₂×Q₈	semidirect
249. #34334	C₂₃	direct (N × H)
261. D₄×C₂₃	C₄×Q₈	semidirect
316. #2369	C₂×C₂₃	semidirect
317. #2368	C₂×C₂₃	semidirect
318. #2365	C₂×C₂₃	semidirect
319. #2360	C₂×C₂₃	semidirect
320. #2355	C₂×C₂₃	semidirect
323. Q₈×C₂²⋊C₄	C₂×C₂₃	semidirect
324. #2331	C₂×C₂₃	semidirect
325. #2329	C₂×C₂₃	semidirect
326. C₄×C₄⋊Q₈	C₂×C₂₃	semidirect
327. C₄×C₂²⋊Q₈	C₂×C₂₃	semidirect
328. #2295	C₂×C₂₃	semidirect
329. C₂×#391	C₂×C₂₃	semidirect
363. D₄×Q₈	C₄×C₂₃	semidirect
438. C₂²×Q₈	C₂×C₄×C₂₃	semidirect
448. C₄⋊Q₈	C₂×C₄×C₂₃	semidirect
449. C₄⋊Q₈	C₂×C₄×C₂₃	semidirect
450. C₂²⋊Q₈	C₂×C₄×C₂₃	semidirect
451. C₂²⋊Q₈	C₂×C₄×C₂₃	semidirect
454. C₄×Q₈	C₂×C₄×C₂₃	semidirect
459. C₄×D₄	Q₈×C₂₃	semidirect
518. C₂₃	#34334	direct (N × H)
547. C₂²×C₄	C₂×Q₈×C₂₃	semidirect
581. C₄⋊C₄	C₂×Q₈×C₂₃	semidirect
586. C₂²⋊C₄	C₂×Q₈×C₂₃	semidirect
601. C₄²	C₂×Q₈×C₂₃	semidirect
613. D₄	C₄×Q₈×C₂₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₄×Q₈×C₂₃	2
C₂₃×#2369	2
C₂₃×#2368	2
C₂₃×#2365	2
C₂₃×#2360	2
C₂₃×#2355	2
C₂₃×#2349	2
D₄×C₄⋊C₄×C₂₃	2
Q₈×C₂²⋊C₄×C₂₃	2
C₂₃×#2331	2
C₂₃×#2329	2
C₄×C₂₃×C₄⋊Q₈	2
C₄×C₂₃×C₂²⋊Q₈	2
C₂₃×#2295	2
C₂×C₂₃×#391	2
C₂₃×#2275	2
C₄²×D₄×C₂₃	2
#34334	23

Subgroups — C23×#34334 #19181960

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#34334 #19181960