Subgroups — C₂×C₂₃×#3511 #19210425

Order 5888.

7758 conjugacy classes of subgroups.

The subgroup lattice has 708 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3511	C₂	1	32	yes	maximal, direct product factor
2	C₂×C₂₃×#556	C₂	1	2	yes	maximal, complemented
3	C₂×C₂₃×#555	C₂	1	2	yes	maximal, complemented
4	C₂×C₂₃×#554	C₂	1	2	yes	maximal, complemented
5	C₂×C₂₃×#553	C₂	1	4	yes	maximal, complemented
6	C₂×C₂₃×#548	C₂	1	4	yes	maximal, complemented
7	C₂×C₂₃×#547	C₂	1	2	yes	maximal, complemented
8	C₂×C₂₃×#542	C₂	1	4	yes	maximal, complemented
9	C₂×C₂₃×#537	C₂	1	2	yes	maximal, complemented
10	C₂×C₂₃×#533	C₂	1	2	yes	maximal, complemented
11	C₂×C₂₃×#532	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₂₃×#532	C₂	1	2	yes	maximal, complemented
13	C₂²×C₂₃×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₂₃×#520	C₂	1	2	yes	maximal, complemented
15	C₂×C₄×#41×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×#41×C₂₃	C₂²	1	1	yes	characteristic
17	C₂²×#41×C₂₃	C₂²	1	2	yes	—
18	C₂²×#41×C₂₃	C₂²	1	4	yes	—
19	C₂³×Q₈×C₂₃	C₂²	1	2	yes	—
20	C₂₃×#556	C₂²	1	32	yes	complemented
21	C₂₃×#555	C₂²	1	32	yes	complemented
22	C₂₃×#554	C₂²	1	32	yes	complemented
23	C₂₃×#553	C₂²	1	64	yes	complemented
24	C₂₃×#548	C₂²	1	64	yes	complemented
25	C₂₃×#547	C₂²	1	32	yes	complemented
26	C₂₃×#542	C₂²	1	64	yes	complemented
27	C₂₃×#537	C₂²	1	32	yes	complemented
28	C₂₃×#533	C₂²	1	32	yes	complemented
29	C₂₃×#532	C₂²	1	16	yes	complemented
30	C₂₃×#532	C₂²	1	32	yes	complemented
31	C₂×C₂₃×C₄⋊Q₈	C₂²	1	2	yes	—
32	C₂×C₂₃×C₄⋊Q₈	C₂²	1	2	yes	—
33	C₂×C₂₃×C₄⋊Q₈	C₂²	1	2	yes	—
34	C₂×C₂₃×C₄⋊Q₈	C₂²	1	2	yes	—
35	C₂×C₂₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
36	C₂×C₂₃×C₄⋊Q₈	C₂²	1	16	yes	complemented
37	C₂×C₂₃×#127	C₂²	1	1	yes	characteristic
38	C₂×C₂₃×#126	C₂²	1	8	yes	—
39	C₂×C₂₃×#125	C₂²	1	4	yes	—
40	C₂×C₂₃×#124	C₂²	1	2	yes	—
41	C₂×C₂₃×#124	C₂²	1	4	yes	—
42	C₂×C₂₃×#124	C₂²	1	8	yes	—
43	C₂×C₂₃×#123	C₂²	1	8	yes	—
44	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	4	yes	—
45	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	4	yes	—
46	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	4	yes	—
47	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	8	yes	—
48	C₂×C₂₃×#121	C₂²	1	4	yes	—
49	C₂×C₂₃×#121	C₂²	1	2	yes	—
50	C₂×C₂₃×#121	C₂²	1	2	yes	—
51	C₂×C₂₃×#121	C₂²	1	4	yes	—
52	C₂×C₂₃×#121	C₂²	1	4	yes	—
53	C₂×C₂₃×#121	C₂²	1	8	yes	—
54	C₂₃×#520	C₂²	1	32	yes	complemented
55	C₄×#41×C₂₃	C₂²	1	16	yes	complemented
56	C₂×C₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic
57	C₂×C₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic
58	C₂×C₄×Q₈×C₂₃	C₂²	1	4	yes	—
59	C₂×C₄×Q₈×C₂₃	C₂²	1	4	yes	—
60	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
61	C₂×C₄×D₄×C₂₃	C₂²	1	2	yes	—
62	C₂×C₄×D₄×C₂₃	C₂²	1	2	yes	—
63	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
64	C₂×C₄×D₄×C₂₃	C₂²	1	4	yes	—
65	C₂×C₄×D₄×C₂₃	C₂²	1	8	yes	—
66	C₂×C₄×D₄×C₂₃	C₂²	1	2	yes	—
67	C₂×C₄×D₄×C₂₃	C₂²	1	4	yes	—
68	C₂×C₄×D₄×C₂₃	C₂²	1	2	yes	—
69	C₂×C₂₃×#117	C₂²	1	1	yes	characteristic
70	C₂×C₂₃×#117	C₂²	1	2	yes	—
71	C₂×C₂₃×#117	C₂²	1	4	yes	—
72	C₂×C₂₃×#117	C₂²	1	4	yes	—
73	C₂²×C₄⋊C₄×C₂₃	C₂²	1	2	yes	—
74	C₂²×C₄⋊C₄×C₂₃	C₂²	1	4	yes	—
75	C₂²×C₄⋊C₄×C₂₃	C₂²	1	2	yes	—
76	C₂²×C₄²×C₂₃	C₂²	1	1	yes	characteristic
77	C₂²×C₄²×C₂₃	C₂²	1	2	yes	—
78	C₂×#41×C₂₃	—	2	8	no	—
79	C₂×#41×C₂₃	—	2	16	no	—
80	C₂×#41×C₂₃	—	4	16	no	—
81	C₂×#41×C₂₃	C₂³	1	8	yes	—
82	C₂×#41×C₂₃	C₂³	1	16	yes	—
83	C₂×#41×C₂₃	C₂³	1	32	yes	—
84	C₂²×Q₈×C₂₃	—	4	8	no	—
85	C₂²×Q₈×C₂₃	C₂³	1	4	yes	—
86	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
87	C₂²×Q₈×C₂₃	C₂³	1	2	yes	—
88	C₂²×Q₈×C₂₃	C₂³	1	16	yes	—
89	C₂²×Q₈×C₂₃	C₂³	1	4	yes	—
90	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
91	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
92	C₂²×D₄×C₂₃	C₂³	1	4	yes	—
93	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
94	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
95	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
96	C₂²×D₄×C₂₃	C₂³	1	8	yes	—
97	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
98	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
99	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
100	C₂³×C₄×C₂₃	C₂³	1	4	yes	—
101	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
102	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
103	C₂³×C₄×C₂₃	C₂³	1	4	yes	—
104	C₂³×C₄×C₂₃	C₂³	1	8	yes	—
105	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
106	C₂₃×C₄⋊Q₈	C₂³	1	16	yes	—
107	C₂₃×C₄⋊Q₈	C₂³	1	16	yes	—
108	C₂₃×C₄⋊Q₈	C₂³	1	16	yes	—
109	C₂₃×C₄⋊Q₈	C₂³	1	16	yes	—
110	C₂₃×C₄⋊Q₈	C₂³	1	8	yes	—
111	C₂₃×#127	C₂³	1	8	yes	—
112	C₂₃×#126	C₂³	1	64	yes	—
113	C₂₃×#125	C₂³	1	32	yes	—
114	C₂₃×#124	C₂³	1	64	yes	—
115	C₂₃×#124	C₂³	1	32	yes	—
116	C₂₃×#124	C₂³	1	16	yes	—
117	C₂₃×#123	C₂³	1	64	yes	—
118	C₂₃×C₂²⋊Q₈	C₂³	1	32	yes	—
119	C₂₃×C₂²⋊Q₈	C₂³	1	64	yes	—
120	C₂₃×C₂²⋊Q₈	C₂³	1	32	yes	—
121	C₂₃×C₂²⋊Q₈	C₂³	1	32	yes	—
122	C₂₃×#121	C₂³	1	32	yes	—
123	C₂₃×#121	C₂³	1	16	yes	—
124	C₂₃×#121	C₂³	1	64	yes	—
125	C₂₃×#121	C₂³	1	16	yes	—
126	C₂₃×#121	C₂³	1	32	yes	—
127	C₂₃×#121	C₂³	1	32	yes	—
128	C₄×Q₈×C₂₃	C₂³	1	32	yes	—
129	C₄×Q₈×C₂₃	C₂³	1	8	yes	—
130	C₄×Q₈×C₂₃	C₂³	1	8	yes	—
131	C₄×Q₈×C₂₃	C₂³	1	32	yes	—
132	C₄×D₄×C₂₃	C₂³	1	8	yes	—
133	C₄×D₄×C₂₃	C₂³	1	16	yes	—
134	C₄×D₄×C₂₃	C₂³	1	16	yes	—
135	C₄×D₄×C₂₃	C₂³	1	64	yes	—
136	C₄×D₄×C₂₃	C₂³	1	16	yes	—
137	C₄×D₄×C₂₃	C₂³	1	32	yes	—
138	C₄×D₄×C₂₃	C₂³	1	16	yes	—
139	C₄×D₄×C₂₃	C₂³	1	8	yes	—
140	C₄×D₄×C₂₃	C₂³	1	32	yes	—
141	C₂₃×#117	C₂³	1	32	yes	—
142	C₂₃×#117	C₂³	1	32	yes	—
143	C₂₃×#117	C₂³	1	8	yes	—
144	C₂₃×#117	C₂³	1	16	yes	—
145	C₂×C₄⋊C₄×C₂₃	C₂³	1	32	yes	—
146	C₂×C₄⋊C₄×C₂₃	C₂³	1	16	yes	—
147	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
148	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
149	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
150	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
151	C₂×C₄⋊C₄×C₂₃	C₂³	1	8	yes	—
152	C₂×C₄⋊C₄×C₂₃	C₂³	1	16	yes	—
153	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
154	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
155	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
156	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
157	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
158	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
159	C₂×C₄⋊C₄×C₂₃	C₂³	1	8	yes	—
160	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
161	C₂×C₂²⋊C₄×C₂₃	C₂³	1	8	yes	—
162	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
163	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
164	C₂×C₂²⋊C₄×C₂₃	C₂³	1	8	yes	—
165	C₂×C₂²⋊C₄×C₂₃	C₂³	1	8	yes	—
166	C₂×C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
167	C₂×C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
168	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
169	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
170	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
171	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
172	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
173	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
174	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
175	C₂×C₄²×C₂₃	C₂³	1	8	yes	—
176	C₂×C₄²×C₂₃	C₂³	1	16	yes	—
177	C₂×C₄²×C₂₃	C₂³	1	8	yes	—
178	C₂⁴×C₂₃	C₂⁴	1	2	yes	—
179	C₂⁴×C₂₃	C₂⁴	1	4	yes	—
180	C₂⁴×C₂₃	C₂⁴	1	1	yes	characteristic
181	#41×C₂₃	—	2	32	no	—
182	#41×C₂₃	—	2	64	no	—
183	#41×C₂₃	—	4	64	no	—
184	C₂×Q₈×C₂₃	—	2	4	no	—
185	C₂×Q₈×C₂₃	—	2	8	no	—
186	C₂×Q₈×C₂₃	—	2	16	no	—
187	C₂×Q₈×C₂₃	—	4	8	no	—
188	C₂×Q₈×C₂₃	—	4	32	no	—
189	C₂×Q₈×C₂₃	C₂⁴	1	4	yes	—
190	C₂×Q₈×C₂₃	C₂⁴	1	8	yes	—
191	C₂×Q₈×C₂₃	C₂⁴	1	16	yes	—
192	C₂×Q₈×C₂₃	C₂⁴	1	16	yes	—
193	C₂×D₄×C₂₃	—	2	8	no	—
194	C₂×D₄×C₂₃	—	2	16	no	—
195	C₂×D₄×C₂₃	—	2	4	no	—
196	C₂×D₄×C₂₃	—	2	8	no	—
197	C₂×D₄×C₂₃	—	2	8	no	—
198	C₂×D₄×C₂₃	—	2	8	no	—
199	C₂×D₄×C₂₃	—	4	16	no	—
200	C₂×D₄×C₂₃	C₂⁴	1	8	yes	—
201	C₂×D₄×C₂₃	C₂⁴	1	8	yes	—
202	C₂×D₄×C₂₃	C₂⁴	1	16	yes	—
203	C₂×D₄×C₂₃	C₂⁴	1	4	yes	—
204	C₂×D₄×C₂₃	C₂⁴	1	8	yes	—
205	C₂×D₄×C₂₃	C₂⁴	1	8	yes	—
206	C₂×D₄×C₂₃	C₂⁴	1	32	yes	—
207	C₂²×C₄×C₂₃	—	2	16	no	—
208	C₂²×C₄×C₂₃	—	2	8	no	—
209	C₂²×C₄×C₂₃	—	2	4	no	—
210	C₂²×C₄×C₂₃	—	2	8	no	—
211	C₂²×C₄×C₂₃	—	2	4	no	—
212	C₂²×C₄×C₂₃	—	2	8	no	—
213	C₂²×C₄×C₂₃	—	4	8	no	—
214	C₂²×C₄×C₂₃	—	4	16	no	—
215	C₂²×C₄×C₂₃	#41	1	8	yes	complemented
216	C₂²×C₄×C₂₃	C₂⁴	1	4	yes	—
217	C₂²×C₄×C₂₃	C₂⁴	1	8	yes	—
218	C₂²×C₄×C₂₃	C₂⁴	1	8	yes	—
219	C₂²×C₄×C₂₃	C₂⁴	1	4	yes	—
220	C₂²×C₄×C₂₃	C₂⁴	1	8	yes	—
221	C₂²×C₄×C₂₃	C₂⁴	1	16	yes	—
222	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
223	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
224	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
225	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
226	C₂²×C₄×C₂₃	C₂⁴	1	4	yes	—
227	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
228	C₂²×C₄×C₂₃	C₂⁴	1	8	yes	—
229	C₂²×C₄×C₂₃	C₂⁴	1	16	yes	—
230	C₂²×C₄×C₂₃	C₂⁴	1	32	yes	—
231	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
232	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
233	C₂²×C₄×C₂₃	C₂⁴	1	4	yes	—
234	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
235	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
236	C₄⋊C₄×C₂₃	C₂⁴	1	4	yes	—
237	C₄⋊C₄×C₂₃	C₂⁴	1	16	yes	—
238	C₄⋊C₄×C₂₃	C₂⁴	1	16	yes	—
239	C₄⋊C₄×C₂₃	C₂⁴	1	16	yes	—
240	C₄⋊C₄×C₂₃	C₂⁴	1	32	yes	—
241	C₄⋊C₄×C₂₃	C₂⁴	1	16	yes	—
242	C₄⋊C₄×C₂₃	C₂⁴	1	4	yes	—
243	C₄⋊C₄×C₂₃	C₂⁴	1	8	yes	—
244	C₄⋊C₄×C₂₃	C₂⁴	1	8	yes	—
245	C₄⋊C₄×C₂₃	C₂⁴	1	8	yes	—
246	C₄⋊C₄×C₂₃	C₂⁴	1	8	yes	—
247	C₄⋊C₄×C₂₃	C₂⁴	1	32	yes	—
248	C₂²⋊C₄×C₂₃	C₂⁴	1	8	yes	—
249	C₂²⋊C₄×C₂₃	C₂⁴	1	32	yes	—
250	C₂²⋊C₄×C₂₃	C₂⁴	1	8	yes	—
251	C₂²⋊C₄×C₂₃	C₂⁴	1	8	yes	—
252	C₂²⋊C₄×C₂₃	C₂⁴	1	32	yes	—
253	C₂²⋊C₄×C₂₃	C₂⁴	1	32	yes	—
254	C₂²⋊C₄×C₂₃	C₂⁴	1	16	yes	—
255	C₂²⋊C₄×C₂₃	C₂⁴	1	16	yes	—
256	C₄²×C₂₃	C₂⁴	1	4	yes	—
257	C₄²×C₂₃	C₂⁴	1	8	yes	—
258	C₄²×C₂₃	C₂⁴	1	4	yes	—
259	C₄²×C₂₃	C₂⁴	1	8	yes	—
260	C₄²×C₂₃	C₂⁴	1	4	yes	—
261	C₄²×C₂₃	C₂⁴	1	4	yes	—
262	C₄²×C₂₃	C₂⁴	1	8	yes	—
263	C₄²×C₂₃	C₂⁴	1	32	yes	—
264	C₂×#3511	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
265	C₂³×C₂₃	—	2	2	no	—
266	C₂³×C₂₃	—	2	2	no	—
267	C₂³×C₂₃	—	2	4	no	—
268	C₂³×C₂₃	—	2	8	no	—
269	C₂³×C₂₃	—	2	4	no	—
270	C₂³×C₂₃	—	2	8	no	—
271	C₂³×C₂₃	—	2	4	no	—
272	C₂³×C₂₃	—	2	8	no	—
273	C₂³×C₂₃	C₂×#41	1	4	yes	—
274	C₂³×C₂₃	C₂⁵	1	4	yes	—
275	C₂³×C₂₃	C₂⁵	1	8	yes	—
276	C₂³×C₂₃	C₂⁵	1	2	yes	—
277	C₂³×C₂₃	C₂⁵	1	1	yes	characteristic
278	Q₈×C₂₃	—	2	8	no	—
279	Q₈×C₂₃	—	2	16	no	—
280	Q₈×C₂₃	—	2	32	no	—
281	Q₈×C₂₃	—	4	16	no	—
282	D₄×C₂₃	—	2	16	no	—
283	D₄×C₂₃	—	2	32	no	—
284	D₄×C₂₃	—	2	8	no	—
285	D₄×C₂₃	—	2	16	no	—
286	D₄×C₂₃	—	2	16	no	—
287	D₄×C₂₃	—	2	16	no	—
288	D₄×C₂₃	—	4	32	no	—
289	C₂×C₄×C₂₃	—	2	8	no	—
290	C₂×C₄×C₂₃	—	2	4	no	—
291	C₂×C₄×C₂₃	—	2	4	no	—
292	C₂×C₄×C₂₃	—	2	2	no	—
293	C₂×C₄×C₂₃	—	2	16	no	—
294	C₂×C₄×C₂₃	—	2	4	no	—
295	C₂×C₄×C₂₃	—	2	2	no	—
296	C₂×C₄×C₂₃	—	2	32	no	—
297	C₂×C₄×C₂₃	—	2	16	no	—
298	C₂×C₄×C₂₃	—	2	8	no	—
299	C₂×C₄×C₂₃	—	2	16	no	—
300	C₂×C₄×C₂₃	—	2	8	no	—
301	C₂×C₄×C₂₃	—	2	16	no	—
302	C₂×C₄×C₂₃	—	4	16	no	—
303	C₂×C₄×C₂₃	—	4	32	no	—
304	C₂×C₄×C₂₃	C₂×#41	1	4	yes	—
305	C₂×C₄×C₂₃	C₂×#41	1	4	yes	—
306	C₂×C₄×C₂₃	C₂×#41	1	16	yes	complemented
307	C₂×C₄×C₂₃	H(5,𝔽₂)	1	4	yes	—
308	C₂×C₄×C₂₃	2₋¹⁺⁴	1	4	yes	—
309	C₂×C₄×C₂₃	C₂⁵	1	4	yes	—
310	C₂×C₄×C₂₃	C₂⁵	1	2	yes	—
311	C₂×C₄×C₂₃	C₂⁵	1	2	yes	—
312	C₂×C₄×C₂₃	C₂⁵	1	4	yes	—
313	C₂×C₄×C₂₃	C₂⁵	1	8	yes	—
314	C₂×C₄×C₂₃	C₂⁵	1	4	yes	—
315	C₂×C₄×C₂₃	C₂⁵	1	16	yes	—
316	C₂×C₄×C₂₃	C₂⁵	1	2	yes	—
317	C₂×C₄×C₂₃	C₂⁵	1	2	yes	—
318	C₂×C₄×C₂₃	C₂⁵	1	2	yes	—
319	C₂×C₄×C₂₃	C₂⁵	1	2	yes	—
320	#3511	C₂×C₂₃	1	32	yes	direct product factor
321	C₂×#556	C₂×C₂₃	1	2	yes	complemented
322	C₂×#555	C₂×C₂₃	1	2	yes	complemented
323	C₂×#554	C₂×C₂₃	1	2	yes	complemented
324	C₂×#553	C₂×C₂₃	1	4	yes	complemented
325	C₂×#548	C₂×C₂₃	1	4	yes	complemented
326	C₂×#547	C₂×C₂₃	1	2	yes	complemented
327	C₂×#542	C₂×C₂₃	1	4	yes	complemented
328	C₂×#537	C₂×C₂₃	1	2	yes	complemented
329	C₂×#533	C₂×C₂₃	1	2	yes	complemented
330	C₂×#532	C₂×C₂₃	1	2	yes	complemented
331	C₂×#532	C₂×C₂₃	1	1	yes	characteristic, complemented
332	C₂²×C₄⋊Q₈	C₂×C₂₃	1	1	yes	characteristic, complemented
333	C₂×#520	C₂×C₂₃	1	2	yes	complemented
334	C₂×C₄×#41	C₂×C₂₃	1	1	yes	characteristic, complemented
335	C₂²×C₂₃	—	2	2	no	—
336	C₂²×C₂₃	—	2	2	no	—
337	C₂²×C₂₃	—	2	8	no	—
338	C₂²×C₂₃	—	2	4	no	—
339	C₂²×C₂₃	—	2	8	no	—
340	C₂²×C₂₃	—	2	4	no	—
341	C₂²×C₂₃	—	2	8	no	—
342	C₂²×C₂₃	—	2	4	no	—
343	C₂²×C₂₃	—	2	8	no	—
344	C₂²×C₂₃	—	4	8	no	—
345	C₂²×C₂₃	—	4	16	no	—
346	C₂²×C₂₃	C₂²×#41	1	4	yes	—
347	C₂²×C₂₃	C₂²×#41	1	2	yes	—
348	C₂²×C₂₃	C₂×H(5,𝔽₂)	1	2	yes	—
349	C₂²×C₂₃	C₂×2₋¹⁺⁴	1	2	yes	—
350	C₂²×C₂₃	C₂⁶	1	1	yes	characteristic
351	C₄×C₂₃	—	2	8	no	—
352	C₄×C₂₃	—	2	4	no	—
353	C₄×C₂₃	—	2	4	no	—
354	C₄×C₂₃	—	2	2	no	—
355	C₄×C₂₃	—	2	16	no	—
356	C₄×C₂₃	—	2	4	no	—
357	C₄×C₂₃	—	2	2	no	—
358	C₄×C₂₃	C₂²×#41	1	4	yes	—
359	C₄×C₂₃	C₂²×#41	1	4	yes	—
360	C₄×C₂₃	C₂×H(5,𝔽₂)	1	4	yes	—
361	C₄×C₂₃	C₂×2₋¹⁺⁴	1	4	yes	—
362	C₂²×#41	C₂²×C₂₃	1	1	yes	characteristic
363	C₂²×#41	C₂²×C₂₃	1	2	yes	—
364	C₂²×#41	C₂²×C₂₃	1	4	yes	—
365	C₂³×Q₈	C₂²×C₂₃	1	2	yes	—
366	#556	C₂²×C₂₃	1	32	yes	complemented
367	#555	C₂²×C₂₃	1	32	yes	complemented
368	#554	C₂²×C₂₃	1	32	yes	complemented
369	#553	C₂²×C₂₃	1	64	yes	complemented
370	#548	C₂²×C₂₃	1	64	yes	complemented
371	#547	C₂²×C₂₃	1	32	yes	complemented
372	#542	C₂²×C₂₃	1	64	yes	complemented
373	#537	C₂²×C₂₃	1	32	yes	complemented
374	#533	C₂²×C₂₃	1	32	yes	complemented
375	#532	C₂²×C₂₃	1	16	yes	complemented
376	#532	C₂²×C₂₃	1	32	yes	complemented
377	C₂×C₄⋊Q₈	C₂²×C₂₃	1	2	yes	—
378	C₂×C₄⋊Q₈	C₂²×C₂₃	1	2	yes	—
379	C₂×C₄⋊Q₈	C₂²×C₂₃	1	2	yes	—
380	C₂×C₄⋊Q₈	C₂²×C₂₃	1	2	yes	—
381	C₂×C₄⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
382	C₂×C₄⋊Q₈	C₂²×C₂₃	1	16	yes	complemented
383	C₂×#127	C₂²×C₂₃	1	1	yes	characteristic
384	C₂×#126	C₂²×C₂₃	1	8	yes	—
385	C₂×#125	C₂²×C₂₃	1	4	yes	—
386	C₂×#124	C₂²×C₂₃	1	2	yes	—
387	C₂×#124	C₂²×C₂₃	1	4	yes	—
388	C₂×#124	C₂²×C₂₃	1	8	yes	—
389	C₂×#123	C₂²×C₂₃	1	8	yes	—
390	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	4	yes	—
391	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	4	yes	—
392	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	4	yes	—
393	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	8	yes	—
394	C₂×#121	C₂²×C₂₃	1	4	yes	—
395	C₂×#121	C₂²×C₂₃	1	2	yes	—
396	C₂×#121	C₂²×C₂₃	1	2	yes	—
397	C₂×#121	C₂²×C₂₃	1	4	yes	—
398	C₂×#121	C₂²×C₂₃	1	4	yes	—
399	C₂×#121	C₂²×C₂₃	1	8	yes	—
400	#520	C₂²×C₂₃	1	32	yes	complemented
401	C₄×#41	C₂²×C₂₃	1	16	yes	complemented
402	C₂×C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
403	C₂×C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
404	C₂×C₄×Q₈	C₂²×C₂₃	1	4	yes	—
405	C₂×C₄×Q₈	C₂²×C₂₃	1	4	yes	—
406	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
407	C₂×C₄×D₄	C₂²×C₂₃	1	2	yes	—
408	C₂×C₄×D₄	C₂²×C₂₃	1	2	yes	—
409	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
410	C₂×C₄×D₄	C₂²×C₂₃	1	4	yes	—
411	C₂×C₄×D₄	C₂²×C₂₃	1	8	yes	—
412	C₂×C₄×D₄	C₂²×C₂₃	1	2	yes	—
413	C₂×C₄×D₄	C₂²×C₂₃	1	4	yes	—
414	C₂×C₄×D₄	C₂²×C₂₃	1	2	yes	—
415	C₂×#117	C₂²×C₂₃	1	1	yes	characteristic
416	C₂×#117	C₂²×C₂₃	1	2	yes	—
417	C₂×#117	C₂²×C₂₃	1	4	yes	—
418	C₂×#117	C₂²×C₂₃	1	4	yes	—
419	C₂²×C₄⋊C₄	C₂²×C₂₃	1	2	yes	—
420	C₂²×C₄⋊C₄	C₂²×C₂₃	1	4	yes	—
421	C₂²×C₄⋊C₄	C₂²×C₂₃	1	2	yes	—
422	C₂²×C₄²	C₂²×C₂₃	1	1	yes	characteristic
423	C₂²×C₄²	C₂²×C₂₃	1	2	yes	—
424	C₂×C₂₃	—	2	4	no	—
425	C₂×C₂₃	—	4	4	no	—
426	C₂×C₂₃	—	4	8	no	—
427	C₂×C₂₃	#3511	1	4	yes	direct product factor
428	C₂×C₂₃	C₂³×#41	1	1	yes	characteristic
429	C₂×C₂₃	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
430	C₂×C₂₃	C₂²×2₋¹⁺⁴	1	1	yes	characteristic
431	C₂×#41	—	2	8	no	—
432	C₂×#41	—	2	16	no	—
433	C₂×#41	—	4	16	no	—
434	C₂×#41	C₂³×C₂₃	1	8	yes	—
435	C₂×#41	C₂³×C₂₃	1	16	yes	—
436	C₂×#41	C₂³×C₂₃	1	32	yes	—
437	C₂²×Q₈	—	4	8	no	—
438	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
439	C₂²×Q₈	C₂³×C₂₃	1	2	yes	—
440	C₂²×Q₈	C₂³×C₂₃	1	4	yes	—
441	C₂²×Q₈	C₂³×C₂₃	1	4	yes	—
442	C₂²×Q₈	C₂³×C₂₃	1	16	yes	—
443	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
444	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
445	C₂²×D₄	C₂³×C₂₃	1	4	yes	—
446	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
447	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
448	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
449	C₂²×D₄	C₂³×C₂₃	1	8	yes	—
450	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
451	C₂³×C₄	C₂³×C₂₃	1	4	yes	—
452	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
453	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
454	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
455	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
456	C₂³×C₄	C₂³×C₂₃	1	4	yes	—
457	C₂³×C₄	C₂³×C₂₃	1	8	yes	—
458	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
459	C₄⋊Q₈	C₂³×C₂₃	1	16	yes	—
460	C₄⋊Q₈	C₂³×C₂₃	1	16	yes	—
461	C₄⋊Q₈	C₂³×C₂₃	1	16	yes	—
462	C₄⋊Q₈	C₂³×C₂₃	1	16	yes	—
463	C₄⋊Q₈	C₂³×C₂₃	1	8	yes	—
464	#127	C₂³×C₂₃	1	8	yes	—
465	#126	C₂³×C₂₃	1	64	yes	—
466	#125	C₂³×C₂₃	1	32	yes	—
467	#124	C₂³×C₂₃	1	16	yes	—
468	#124	C₂³×C₂₃	1	32	yes	—
469	#124	C₂³×C₂₃	1	64	yes	—
470	#123	C₂³×C₂₃	1	64	yes	—
471	C₂²⋊Q₈	C₂³×C₂₃	1	32	yes	—
472	C₂²⋊Q₈	C₂³×C₂₃	1	32	yes	—
473	C₂²⋊Q₈	C₂³×C₂₃	1	32	yes	—
474	C₂²⋊Q₈	C₂³×C₂₃	1	64	yes	—
475	#121	C₂³×C₂₃	1	32	yes	—
476	#121	C₂³×C₂₃	1	16	yes	—
477	#121	C₂³×C₂₃	1	16	yes	—
478	#121	C₂³×C₂₃	1	32	yes	—
479	#121	C₂³×C₂₃	1	32	yes	—
480	#121	C₂³×C₂₃	1	64	yes	—
481	C₄×Q₈	C₂³×C₂₃	1	8	yes	—
482	C₄×Q₈	C₂³×C₂₃	1	8	yes	—
483	C₄×Q₈	C₂³×C₂₃	1	32	yes	—
484	C₄×Q₈	C₂³×C₂₃	1	32	yes	—
485	C₄×D₄	C₂³×C₂₃	1	8	yes	—
486	C₄×D₄	C₂³×C₂₃	1	16	yes	—
487	C₄×D₄	C₂³×C₂₃	1	16	yes	—
488	C₄×D₄	C₂³×C₂₃	1	8	yes	—
489	C₄×D₄	C₂³×C₂₃	1	32	yes	—
490	C₄×D₄	C₂³×C₂₃	1	64	yes	—
491	C₄×D₄	C₂³×C₂₃	1	16	yes	—
492	C₄×D₄	C₂³×C₂₃	1	32	yes	—
493	C₄×D₄	C₂³×C₂₃	1	16	yes	—
494	#117	C₂³×C₂₃	1	8	yes	—
495	#117	C₂³×C₂₃	1	16	yes	—
496	#117	C₂³×C₂₃	1	32	yes	—
497	#117	C₂³×C₂₃	1	32	yes	—
498	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
499	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
500	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
501	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
502	C₂×C₄⋊C₄	C₂³×C₂₃	1	8	yes	—
503	C₂×C₄⋊C₄	C₂³×C₂₃	1	16	yes	—
504	C₂×C₄⋊C₄	C₂³×C₂₃	1	32	yes	—
505	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
506	C₂×C₄⋊C₄	C₂³×C₂₃	1	16	yes	—
507	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
508	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
509	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
510	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
511	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
512	C₂×C₄⋊C₄	C₂³×C₂₃	1	8	yes	—
513	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
514	C₂×C₂²⋊C₄	C₂³×C₂₃	1	8	yes	—
515	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
516	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
517	C₂×C₂²⋊C₄	C₂³×C₂₃	1	8	yes	—
518	C₂×C₂²⋊C₄	C₂³×C₂₃	1	8	yes	—
519	C₂×C₂²⋊C₄	C₂³×C₂₃	1	4	yes	—
520	C₂×C₂²⋊C₄	C₂³×C₂₃	1	4	yes	—
521	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
522	C₂×C₄²	C₂³×C₂₃	1	8	yes	—
523	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
524	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
525	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
526	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
527	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
528	C₂×C₄²	C₂³×C₂₃	1	8	yes	—
529	C₂×C₄²	C₂³×C₂₃	1	16	yes	—
530	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
531	C₂₃	C₂×#3511	1	1	yes	characteristic, direct product factor, Sylow
532	C₂⁴	C₂⁴×C₂₃	1	2	yes	—
533	C₂⁴	C₂⁴×C₂₃	1	4	yes	—
534	C₂⁴	C₂⁴×C₂₃	1	1	yes	characteristic
535	#41	—	2	32	no	—
536	#41	—	2	64	no	—
537	#41	—	4	64	no	—
538	C₂×Q₈	—	2	4	no	—
539	C₂×Q₈	—	2	8	no	—
540	C₂×Q₈	—	2	16	no	—
541	C₂×Q₈	—	4	8	no	—
542	C₂×Q₈	—	4	32	no	—
543	C₂×Q₈	C₂⁴×C₂₃	1	4	yes	—
544	C₂×Q₈	C₂⁴×C₂₃	1	8	yes	—
545	C₂×Q₈	C₂⁴×C₂₃	1	16	yes	—
546	C₂×Q₈	C₂⁴×C₂₃	1	16	yes	—
547	C₂×D₄	—	2	8	no	—
548	C₂×D₄	—	2	16	no	—
549	C₂×D₄	—	2	4	no	—
550	C₂×D₄	—	2	8	no	—
551	C₂×D₄	—	2	8	no	—
552	C₂×D₄	—	2	8	no	—
553	C₂×D₄	—	4	16	no	—
554	C₂×D₄	C₂⁴×C₂₃	1	8	yes	—
555	C₂×D₄	C₂⁴×C₂₃	1	8	yes	—
556	C₂×D₄	C₂⁴×C₂₃	1	16	yes	—
557	C₂×D₄	C₂⁴×C₂₃	1	4	yes	—
558	C₂×D₄	C₂⁴×C₂₃	1	8	yes	—
559	C₂×D₄	C₂⁴×C₂₃	1	8	yes	—
560	C₂×D₄	C₂⁴×C₂₃	1	32	yes	—
561	C₂²×C₄	—	2	16	no	—
562	C₂²×C₄	—	2	8	no	—
563	C₂²×C₄	—	2	4	no	—
564	C₂²×C₄	—	2	8	no	—
565	C₂²×C₄	—	2	4	no	—
566	C₂²×C₄	—	2	8	no	—
567	C₂²×C₄	—	4	8	no	—
568	C₂²×C₄	—	4	16	no	—
569	C₂²×C₄	#41×C₂₃	1	8	yes	complemented
570	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
571	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
572	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
573	C₂²×C₄	C₂⁴×C₂₃	1	4	yes	—
574	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
575	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
576	C₂²×C₄	C₂⁴×C₂₃	1	4	yes	—
577	C₂²×C₄	C₂⁴×C₂₃	1	8	yes	—
578	C₂²×C₄	C₂⁴×C₂₃	1	8	yes	—
579	C₂²×C₄	C₂⁴×C₂₃	1	4	yes	—
580	C₂²×C₄	C₂⁴×C₂₃	1	8	yes	—
581	C₂²×C₄	C₂⁴×C₂₃	1	8	yes	—
582	C₂²×C₄	C₂⁴×C₂₃	1	16	yes	—
583	C₂²×C₄	C₂⁴×C₂₃	1	16	yes	—
584	C₂²×C₄	C₂⁴×C₂₃	1	32	yes	—
585	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
586	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
587	C₂²×C₄	C₂⁴×C₂₃	1	4	yes	—
588	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
589	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
590	C₄⋊C₄	C₂⁴×C₂₃	1	4	yes	—
591	C₄⋊C₄	C₂⁴×C₂₃	1	16	yes	—
592	C₄⋊C₄	C₂⁴×C₂₃	1	16	yes	—
593	C₄⋊C₄	C₂⁴×C₂₃	1	16	yes	—
594	C₄⋊C₄	C₂⁴×C₂₃	1	32	yes	—
595	C₄⋊C₄	C₂⁴×C₂₃	1	16	yes	—
596	C₄⋊C₄	C₂⁴×C₂₃	1	4	yes	—
597	C₄⋊C₄	C₂⁴×C₂₃	1	8	yes	—
598	C₄⋊C₄	C₂⁴×C₂₃	1	8	yes	—
599	C₄⋊C₄	C₂⁴×C₂₃	1	8	yes	—
600	C₄⋊C₄	C₂⁴×C₂₃	1	8	yes	—
601	C₄⋊C₄	C₂⁴×C₂₃	1	32	yes	—
602	C₂²⋊C₄	C₂⁴×C₂₃	1	8	yes	—
603	C₂²⋊C₄	C₂⁴×C₂₃	1	32	yes	—
604	C₂²⋊C₄	C₂⁴×C₂₃	1	8	yes	—
605	C₂²⋊C₄	C₂⁴×C₂₃	1	8	yes	—
606	C₂²⋊C₄	C₂⁴×C₂₃	1	32	yes	—
607	C₂²⋊C₄	C₂⁴×C₂₃	1	32	yes	—
608	C₂²⋊C₄	C₂⁴×C₂₃	1	16	yes	—
609	C₂²⋊C₄	C₂⁴×C₂₃	1	16	yes	—
610	C₄²	C₂⁴×C₂₃	1	4	yes	—
611	C₄²	C₂⁴×C₂₃	1	8	yes	—
612	C₄²	C₂⁴×C₂₃	1	4	yes	—
613	C₄²	C₂⁴×C₂₃	1	8	yes	—
614	C₄²	C₂⁴×C₂₃	1	4	yes	—
615	C₄²	C₂⁴×C₂₃	1	4	yes	—
616	C₄²	C₂⁴×C₂₃	1	8	yes	—
617	C₄²	C₂⁴×C₂₃	1	32	yes	—
618	C₂³	—	2	2	no	—
619	C₂³	—	2	2	no	—
620	C₂³	—	2	4	no	—
621	C₂³	—	2	8	no	—
622	C₂³	—	2	4	no	—
623	C₂³	—	2	8	no	—
624	C₂³	—	2	4	no	—
625	C₂³	—	2	8	no	—
626	C₂³	C₂×#41×C₂₃	1	4	yes	—
627	C₂³	C₂⁵×C₂₃	1	4	yes	—
628	C₂³	C₂⁵×C₂₃	1	8	yes	—
629	C₂³	C₂⁵×C₂₃	1	2	yes	—
630	C₂³	C₂⁵×C₂₃	1	1	yes	characteristic
631	Q₈	—	2	8	no	—
632	Q₈	—	2	16	no	—
633	Q₈	—	2	32	no	—
634	Q₈	—	4	16	no	—
635	D₄	—	2	16	no	—
636	D₄	—	2	32	no	—
637	D₄	—	2	8	no	—
638	D₄	—	2	16	no	—
639	D₄	—	2	16	no	—
640	D₄	—	2	16	no	—
641	D₄	—	4	32	no	—
642	C₂×C₄	—	2	8	no	—
643	C₂×C₄	—	2	4	no	—
644	C₂×C₄	—	2	4	no	—
645	C₂×C₄	—	2	2	no	—
646	C₂×C₄	—	2	16	no	—
647	C₂×C₄	—	2	4	no	—
648	C₂×C₄	—	2	2	no	—
649	C₂×C₄	—	2	32	no	—
650	C₂×C₄	—	2	16	no	—
651	C₂×C₄	—	2	8	no	—
652	C₂×C₄	—	2	16	no	—
653	C₂×C₄	—	2	8	no	—
654	C₂×C₄	—	2	16	no	—
655	C₂×C₄	—	4	16	no	—
656	C₂×C₄	—	4	32	no	—
657	C₂×C₄	C₂×#41×C₂₃	1	4	yes	—
658	C₂×C₄	C₂×#41×C₂₃	1	4	yes	—
659	C₂×C₄	C₂×#41×C₂₃	1	16	yes	complemented
660	C₂×C₄	C₂₃×H(5,𝔽₂)	1	4	yes	—
661	C₂×C₄	C₂₃×2₋¹⁺⁴	1	4	yes	—
662	C₂×C₄	C₂⁵×C₂₃	1	4	yes	—
663	C₂×C₄	C₂⁵×C₂₃	1	2	yes	—
664	C₂×C₄	C₂⁵×C₂₃	1	2	yes	—
665	C₂×C₄	C₂⁵×C₂₃	1	4	yes	—
666	C₂×C₄	C₂⁵×C₂₃	1	8	yes	—
667	C₂×C₄	C₂⁵×C₂₃	1	4	yes	—
668	C₂×C₄	C₂⁵×C₂₃	1	16	yes	—
669	C₂×C₄	C₂⁵×C₂₃	1	2	yes	—
670	C₂×C₄	C₂⁵×C₂₃	1	2	yes	—
671	C₂×C₄	C₂⁵×C₂₃	1	2	yes	—
672	C₂×C₄	C₂⁵×C₂₃	1	2	yes	—
673	C₂²	—	2	8	no	—
674	C₂²	—	2	2	no	—
675	C₂²	—	2	2	no	—
676	C₂²	—	2	4	no	—
677	C₂²	—	2	8	no	—
678	C₂²	—	2	4	no	—
679	C₂²	—	2	8	no	—
680	C₂²	—	2	4	no	—
681	C₂²	—	2	8	no	—
682	C₂²	—	4	8	no	—
683	C₂²	—	4	16	no	—
684	C₂²	C₂²×#41×C₂₃	1	4	yes	—
685	C₂²	C₂²×#41×C₂₃	1	2	yes	—
686	C₂²	C₂×C₂₃×H(5,𝔽₂)	1	2	yes	—
687	C₂²	C₂×C₂₃×2₋¹⁺⁴	1	2	yes	—
688	C₂²	C₂⁶×C₂₃	1	1	yes	characteristic
689	C₄	—	2	8	no	—
690	C₄	—	2	4	no	—
691	C₄	—	2	4	no	—
692	C₄	—	2	2	no	—
693	C₄	—	2	16	no	—
694	C₄	—	2	4	no	—
695	C₄	—	2	2	no	—
696	C₄	C₂²×#41×C₂₃	1	4	yes	—
697	C₄	C₂²×#41×C₂₃	1	4	yes	—
698	C₄	C₂×C₂₃×H(5,𝔽₂)	1	4	yes	—
699	C₄	C₂×C₂₃×2₋¹⁺⁴	1	4	yes	—
700	C₂	—	2	4	no	—
701	C₂	—	4	4	no	—
702	C₂	—	4	8	no	—
703	C₂	C₂₃×#3511	1	4	yes	direct product factor
704	C₂	C₂³×#41×C₂₃	1	1	yes	characteristic
705	C₂	C₂²×C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
706	C₂	C₂²×C₂₃×2₋¹⁺⁴	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₂₃	C₂⁵
commutator, Frattini, cosocle	C₂²	C₂⁶×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
1. C₂₃×#3511	C₂	direct (N × H)
2. C₂×C₂₃×#556	C₂	semidirect
3. C₂×C₂₃×#555	C₂	semidirect
4. C₂×C₂₃×#554	C₂	semidirect
5. C₂×C₂₃×#553	C₂	semidirect
6. C₂×C₂₃×#548	C₂	semidirect
7. C₂×C₂₃×#547	C₂	semidirect
8. C₂×C₂₃×#542	C₂	semidirect
9. C₂×C₂₃×#537	C₂	semidirect
10. C₂×C₂₃×#533	C₂	semidirect
11. C₂×C₂₃×#532	C₂	semidirect
12. C₂×C₂₃×#532	C₂	semidirect
13. C₂²×C₂₃×C₄⋊Q₈	C₂	semidirect
14. C₂×C₂₃×#520	C₂	semidirect
15. C₂×C₄×#41×C₂₃	C₂	semidirect
20. C₂₃×#556	C₂²	semidirect
21. C₂₃×#555	C₂²	semidirect
22. C₂₃×#554	C₂²	semidirect
23. C₂₃×#553	C₂²	semidirect
24. C₂₃×#548	C₂²	semidirect
25. C₂₃×#547	C₂²	semidirect
26. C₂₃×#542	C₂²	semidirect
27. C₂₃×#537	C₂²	semidirect
28. C₂₃×#533	C₂²	semidirect
29. C₂₃×#532	C₂²	semidirect
30. C₂₃×#532	C₂²	semidirect
36. C₂×C₂₃×C₄⋊Q₈	C₂²	semidirect
54. C₂₃×#520	C₂²	semidirect
55. C₄×#41×C₂₃	C₂²	semidirect
215. C₂²×C₄×C₂₃	#41	semidirect
264. C₂×#3511	C₂₃	direct (N × H)
306. C₂×C₄×C₂₃	C₂×#41	semidirect
320. #3511	C₂×C₂₃	direct (N × H)
321. C₂×#556	C₂×C₂₃	semidirect
322. C₂×#555	C₂×C₂₃	semidirect
323. C₂×#554	C₂×C₂₃	semidirect
324. C₂×#553	C₂×C₂₃	semidirect
325. C₂×#548	C₂×C₂₃	semidirect
326. C₂×#547	C₂×C₂₃	semidirect
327. C₂×#542	C₂×C₂₃	semidirect
328. C₂×#537	C₂×C₂₃	semidirect
329. C₂×#533	C₂×C₂₃	semidirect
330. C₂×#532	C₂×C₂₃	semidirect
331. C₂×#532	C₂×C₂₃	semidirect
332. C₂²×C₄⋊Q₈	C₂×C₂₃	semidirect
333. C₂×#520	C₂×C₂₃	semidirect
334. C₂×C₄×#41	C₂×C₂₃	semidirect
366. #556	C₂²×C₂₃	semidirect
367. #555	C₂²×C₂₃	semidirect
368. #554	C₂²×C₂₃	semidirect
369. #553	C₂²×C₂₃	semidirect
370. #548	C₂²×C₂₃	semidirect
371. #547	C₂²×C₂₃	semidirect
372. #542	C₂²×C₂₃	semidirect
373. #537	C₂²×C₂₃	semidirect
374. #533	C₂²×C₂₃	semidirect
375. #532	C₂²×C₂₃	semidirect
376. #532	C₂²×C₂₃	semidirect
382. C₂×C₄⋊Q₈	C₂²×C₂₃	semidirect
400. #520	C₂²×C₂₃	semidirect
401. C₄×#41	C₂²×C₂₃	semidirect
427. C₂×C₂₃	#3511	direct (N × H)
531. C₂₃	C₂×#3511	direct (N × H)
569. C₂²×C₄	#41×C₂₃	semidirect
659. C₂×C₄	C₂×#41×C₂₃	semidirect
703. C₂	C₂₃×#3511	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂₃×#3511	2
C₂×C₂₃×#556	2
C₂×C₂₃×#555	2
C₂×C₂₃×#554	2
C₂×C₂₃×#553	2
C₂×C₂₃×#548	2
C₂×C₂₃×#547	2
C₂×C₂₃×#542	2
C₂×C₂₃×#537	2
C₂×C₂₃×#533	2
C₂×C₂₃×#532	2
C₂²×C₂₃×C₄⋊Q₈	2
C₂×C₂₃×#520	2
C₂×C₄×#41×C₂₃	2
C₂×#3511	23

Subgroups — C2×C23×#3511 #19210425

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₂₃×#3511 #19210425