Subgroups — C₂×C₂₃×#3495 #19210429

Order 5888.

7206 conjugacy classes of subgroups.

The subgroup lattice has 904 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3495	C₂	1	32	yes	maximal, direct product factor
2	C₂×C₂₃×#556	C₂	1	2	yes	maximal, complemented
3	C₂×C₂₃×#554	C₂	1	2	yes	maximal, complemented
4	C₂×C₂₃×#552	C₂	1	2	yes	maximal, complemented
5	C₂×C₂₃×#552	C₂	1	4	yes	maximal, complemented
6	C₂×C₂₃×#552	C₂	1	2	yes	maximal, complemented
7	C₂×C₂₃×#551	C₂	1	4	yes	maximal, complemented
8	C₂×C₂₃×#544	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₂₃×#542	C₂	1	2	yes	maximal, complemented
10	C₂×C₂₃×#541	C₂	1	2	yes	maximal, complemented
11	C₂×C₂₃×#536	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₂₃×#533	C₂	1	2	yes	maximal, complemented
13	C₂×C₂₃×#529	C₂	1	2	yes	maximal, complemented
14	C₂×C₂₃×#525	C₂	1	1	yes	maximal, characteristic
15	C₂²×C₂₃×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₂₃×#520	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×C₂₃×#519	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂²×C₂₃×#117	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂²×#41×C₂₃	C₂²	1	1	yes	characteristic
20	C₂³×Q₈×C₂₃	C₂²	1	1	yes	characteristic
21	C₂⁴×C₄×C₂₃	C₂²	1	1	yes	characteristic
22	C₂₃×#556	C₂²	1	32	yes	complemented
23	C₂₃×#554	C₂²	1	32	yes	complemented
24	C₂₃×#552	C₂²	1	32	yes	complemented
25	C₂₃×#552	C₂²	1	64	yes	complemented
26	C₂₃×#552	C₂²	1	32	yes	complemented
27	C₂₃×#551	C₂²	1	64	yes	complemented
28	C₂₃×#544	C₂²	1	16	yes	complemented
29	C₂₃×#542	C₂²	1	32	yes	complemented
30	C₂₃×#541	C₂²	1	32	yes	complemented
31	C₂₃×#536	C₂²	1	16	yes	complemented
32	C₂₃×#533	C₂²	1	32	yes	complemented
33	C₂×C₂₃×C₄⋊Q₈	C₂²	1	2	yes	complemented
34	C₂×C₂₃×C₄⋊Q₈	C₂²	1	2	yes	complemented
35	C₂×C₂₃×C₄⋊Q₈	C₂²	1	2	yes	complemented
36	C₂₃×#529	C₂²	1	32	yes	complemented
37	C₂×C₂₃×#126	C₂²	1	4	yes	—
38	C₂×C₂₃×#126	C₂²	1	4	yes	—
39	C₂×C₂₃×#126	C₂²	1	4	yes	complemented
40	C₂×C₂₃×#126	C₂²	1	4	yes	complemented
41	C₂×C₂₃×#125	C₂²	1	2	yes	complemented
42	C₂×C₂₃×#125	C₂²	1	4	yes	complemented
43	C₂×C₂₃×#125	C₂²	1	4	yes	complemented
44	C₂×C₂₃×#125	C₂²	1	4	yes	complemented
45	C₂×C₂₃×#125	C₂²	1	2	yes	complemented
46	C₂×C₂₃×#124	C₂²	1	4	yes	—
47	C₂×C₂₃×#124	C₂²	1	2	yes	complemented
48	C₂₃×#525	C₂²	1	16	yes	—
49	C₂×C₂₃×#123	C₂²	1	2	yes	—
50	C₂×C₂₃×#123	C₂²	1	4	yes	—
51	C₂×C₂₃×#123	C₂²	1	4	yes	—
52	C₂×C₂₃×#123	C₂²	1	4	yes	—
53	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	2	yes	—
54	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	2	yes	—
55	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	2	yes	—
56	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	2	yes	—
57	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
58	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
59	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	4	yes	—
60	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	4	yes	—
61	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	16	yes	complemented
62	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
63	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
64	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	4	yes	complemented
65	C₂×C₂₃×#121	C₂²	1	1	yes	characteristic
66	C₂×C₂₃×#121	C₂²	1	1	yes	characteristic
67	C₂×C₂₃×#120	C₂²	1	2	yes	—
68	C₂₃×#520	C₂²	1	16	yes	complemented
69	C₂₃×#519	C₂²	1	16	yes	complemented
70	C₂×C₄×Q₈×C₂₃	C₂²	1	2	yes	complemented
71	C₂×C₄×Q₈×C₂₃	C₂²	1	2	yes	complemented
72	C₂×C₄×Q₈×C₂₃	C₂²	1	2	yes	complemented
73	C₂×C₄×Q₈×C₂₃	C₂²	1	2	yes	complemented
74	C₂×C₄×Q₈×C₂₃	C₂²	1	2	yes	complemented
75	C₂×C₄×Q₈×C₂₃	C₂²	1	4	yes	complemented
76	C₂×C₄×D₄×C₂₃	C₂²	1	4	yes	—
77	C₂×C₄×D₄×C₂₃	C₂²	1	2	yes	—
78	C₂×C₄×D₄×C₂₃	C₂²	1	2	yes	—
79	C₂×C₄×D₄×C₂₃	C₂²	1	4	yes	—
80	C₂×C₄×D₄×C₂₃	C₂²	1	2	yes	complemented
81	C₂×C₂₃×#117	C₂²	1	1	yes	characteristic
82	C₂×C₂₃×#117	C₂²	1	1	yes	characteristic
83	C₂×C₂₃×#117	C₂²	1	2	yes	—
84	C₂×C₂₃×#117	C₂²	1	1	yes	characteristic
85	C₂×C₂₃×#117	C₂²	1	2	yes	—
86	C₂×C₂₃×#117	C₂²	1	1	yes	characteristic
87	C₂×C₂₃×#117	C₂²	1	1	yes	characteristic
88	C₂×C₂₃×#117	C₂²	1	4	yes	—
89	C₂×C₂₃×#117	C₂²	1	4	yes	—
90	C₂×C₂₃×#117	C₂²	1	16	yes	complemented
91	C₂×C₂₃×#117	C₂²	1	2	yes	complemented
92	C₂×C₂₃×#117	C₂²	1	4	yes	complemented
93	C₂²×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
94	C₂²×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
95	C₂²×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
96	C₂²×C₄⋊C₄×C₂₃	C₂²	1	2	yes	—
97	C₂²×C₄⋊C₄×C₂₃	C₂²	1	2	yes	complemented
98	C₂²×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	—
99	C₂²×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	—
100	C₂²×C₄²×C₂₃	C₂²	1	2	yes	—
101	C₂⁵×C₂₃	C₂³	1	1	yes	characteristic
102	C₂×#41×C₂₃	—	2	8	no	—
103	C₂×#41×C₂₃	C₂³	1	8	yes	—
104	C₂²×Q₈×C₂₃	—	2	8	no	—
105	C₂²×Q₈×C₂₃	C₂³	1	2	yes	—
106	C₂²×Q₈×C₂₃	C₂³	1	2	yes	—
107	C₂²×Q₈×C₂₃	C₂³	1	8	yes	—
108	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
109	C₂²×Q₈×C₂₃	C₂³	1	4	yes	—
110	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
111	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
112	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
113	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
114	C₂³×C₄×C₂₃	—	2	8	no	—
115	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
116	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
117	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
118	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
119	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
120	C₂³×C₄×C₂₃	C₂³	1	8	yes	—
121	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
122	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
123	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
124	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
125	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
126	C₂³×C₄×C₂₃	C₂³	1	4	yes	—
127	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
128	C₂₃×C₄⋊Q₈	C₂³	1	16	yes	complemented
129	C₂₃×C₄⋊Q₈	C₂³	1	16	yes	complemented
130	C₂₃×C₄⋊Q₈	C₂³	1	16	yes	complemented
131	C₂₃×#126	C₂³	1	32	yes	—
132	C₂₃×#126	C₂³	1	32	yes	—
133	C₂₃×#126	C₂³	1	32	yes	complemented
134	C₂₃×#126	C₂³	1	32	yes	complemented
135	C₂₃×#125	C₂³	1	32	yes	complemented
136	C₂₃×#125	C₂³	1	32	yes	complemented
137	C₂₃×#125	C₂³	1	16	yes	complemented
138	C₂₃×#125	C₂³	1	32	yes	complemented
139	C₂₃×#125	C₂³	1	16	yes	complemented
140	C₂₃×#124	C₂³	1	32	yes	—
141	C₂₃×#124	C₂³	1	16	yes	complemented
142	C₂₃×#123	C₂³	1	32	yes	—
143	C₂₃×#123	C₂³	1	32	yes	—
144	C₂₃×#123	C₂³	1	32	yes	—
145	C₂₃×#123	C₂³	1	16	yes	—
146	C₂₃×C₂²⋊Q₈	C₂³	1	32	yes	—
147	C₂₃×C₂²⋊Q₈	C₂³	1	32	yes	—
148	C₂₃×C₂²⋊Q₈	C₂³	1	16	yes	—
149	C₂₃×C₂²⋊Q₈	C₂³	1	16	yes	—
150	C₂₃×C₂²⋊Q₈	C₂³	1	16	yes	—
151	C₂₃×C₂²⋊Q₈	C₂³	1	16	yes	—
152	C₂₃×C₂²⋊Q₈	C₂³	1	8	yes	—
153	C₂₃×C₂²⋊Q₈	C₂³	1	8	yes	—
154	C₂₃×C₂²⋊Q₈	C₂³	1	16	yes	complemented
155	C₂₃×C₂²⋊Q₈	C₂³	1	32	yes	complemented
156	C₂₃×C₂²⋊Q₈	C₂³	1	16	yes	complemented
157	C₂₃×#121	C₂³	1	8	yes	—
158	C₂₃×#121	C₂³	1	8	yes	—
159	C₂₃×#120	C₂³	1	16	yes	—
160	C₄×Q₈×C₂₃	C₂³	1	16	yes	complemented
161	C₄×Q₈×C₂₃	C₂³	1	16	yes	complemented
162	C₄×Q₈×C₂₃	C₂³	1	32	yes	complemented
163	C₄×Q₈×C₂₃	C₂³	1	16	yes	complemented
164	C₄×Q₈×C₂₃	C₂³	1	16	yes	complemented
165	C₄×Q₈×C₂₃	C₂³	1	16	yes	complemented
166	C₄×D₄×C₂₃	C₂³	1	32	yes	—
167	C₄×D₄×C₂₃	C₂³	1	32	yes	—
168	C₄×D₄×C₂₃	C₂³	1	16	yes	—
169	C₄×D₄×C₂₃	C₂³	1	16	yes	—
170	C₄×D₄×C₂₃	C₂³	1	16	yes	complemented
171	C₂₃×#117	C₂³	1	32	yes	—
172	C₂₃×#117	C₂³	1	32	yes	—
173	C₂₃×#117	C₂³	1	8	yes	—
174	C₂₃×#117	C₂³	1	16	yes	—
175	C₂₃×#117	C₂³	1	8	yes	—
176	C₂₃×#117	C₂³	1	8	yes	—
177	C₂₃×#117	C₂³	1	8	yes	—
178	C₂₃×#117	C₂³	1	16	yes	—
179	C₂₃×#117	C₂³	1	8	yes	—
180	C₂₃×#117	C₂³	1	32	yes	complemented
181	C₂₃×#117	C₂³	1	16	yes	complemented
182	C₂×C₄⋊C₄×C₂₃	C₂³	1	8	yes	—
183	C₂×C₄⋊C₄×C₂₃	C₂³	1	16	yes	—
184	C₂×C₄⋊C₄×C₂₃	C₂³	1	8	yes	—
185	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
186	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
187	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
188	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
189	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
190	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
191	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
192	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
193	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
194	C₂×C₄⋊C₄×C₂₃	C₂³	1	8	yes	—
195	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
196	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
197	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
198	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
199	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
200	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
201	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
202	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
203	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
204	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
205	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
206	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
207	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
208	C₂×C₄⋊C₄×C₂₃	C₂³	1	16	yes	complemented
209	C₂×C₂²⋊C₄×C₂₃	C₂³	1	16	yes	—
210	C₂×C₂²⋊C₄×C₂₃	C₂³	1	16	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	4	yes	—
216	C₂×C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
217	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
218	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
219	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
220	C₂×C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
221	C₂×C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
222	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
223	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
224	C₂×C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
225	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
226	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
227	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
228	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
229	C₂×C₄²×C₂₃	C₂³	1	16	yes	—
230	C₂×C₄²×C₂₃	C₂³	1	4	yes	—
231	C₂×C₄²×C₂₃	C₂³	1	4	yes	—
232	C₂×C₄²×C₂₃	C₂³	1	4	yes	—
233	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
234	C₂⁴×C₂₃	—	2	4	no	—
235	C₂⁴×C₂₃	—	2	4	no	—
236	C₂⁴×C₂₃	—	4	2	no	—
237	C₂⁴×C₂₃	C₂⁴	1	1	yes	characteristic
238	C₂⁴×C₂₃	C₂⁴	1	2	yes	—
239	C₂⁴×C₂₃	C₂⁴	1	4	yes	—
240	C₂⁴×C₂₃	C₂⁴	1	1	yes	characteristic
241	C₂⁴×C₂₃	C₂⁴	1	1	yes	characteristic
242	#41×C₂₃	—	2	32	no	—
243	C₂×Q₈×C₂₃	—	2	8	no	—
244	C₂×Q₈×C₂₃	—	2	8	no	—
245	C₂×Q₈×C₂₃	—	2	32	no	—
246	C₂×Q₈×C₂₃	—	2	4	no	—
247	C₂×Q₈×C₂₃	—	4	8	no	—
248	C₂×Q₈×C₂₃	C₂⁴	1	8	yes	—
249	C₂×Q₈×C₂₃	C₂⁴	1	8	yes	—
250	C₂×Q₈×C₂₃	C₂⁴	1	4	yes	—
251	C₂×Q₈×C₂₃	C₂⁴	1	16	yes	—
252	C₂×D₄×C₂₃	—	2	8	no	—
253	C₂×D₄×C₂₃	—	2	8	no	—
254	C₂×D₄×C₂₃	—	2	4	no	—
255	C₂×D₄×C₂₃	—	4	4	no	—
256	C₂×D₄×C₂₃	C₂⁴	1	8	yes	—
257	C₂×D₄×C₂₃	C₂⁴	1	8	yes	—
258	C₂×D₄×C₂₃	C₂⁴	1	4	yes	—
259	C₂×D₄×C₂₃	C₂⁴	1	8	yes	—
260	C₂²×C₄×C₂₃	—	2	4	no	—
261	C₂²×C₄×C₂₃	—	2	8	no	—
262	C₂²×C₄×C₂₃	—	2	8	no	—
263	C₂²×C₄×C₂₃	—	2	4	no	—
264	C₂²×C₄×C₂₃	—	2	4	no	—
265	C₂²×C₄×C₂₃	—	2	4	no	—
266	C₂²×C₄×C₂₃	—	2	4	no	—
267	C₂²×C₄×C₂₃	—	2	32	no	—
268	C₂²×C₄×C₂₃	—	2	8	no	—
269	C₂²×C₄×C₂₃	—	4	8	no	—
270	C₂²×C₄×C₂₃	—	4	4	no	—
271	C₂²×C₄×C₂₃	—	4	4	no	—
272	C₂²×C₄×C₂₃	#41	1	8	yes	—
273	C₂²×C₄×C₂₃	C₂⁴	1	4	yes	—
274	C₂²×C₄×C₂₃	C₂⁴	1	8	yes	—
275	C₂²×C₄×C₂₃	C₂⁴	1	8	yes	—
276	C₂²×C₄×C₂₃	C₂⁴	1	4	yes	—
277	C₂²×C₄×C₂₃	C₂⁴	1	4	yes	—
278	C₂²×C₄×C₂₃	C₂⁴	1	8	yes	—
279	C₂²×C₄×C₂₃	C₂⁴	1	4	yes	—
280	C₂²×C₄×C₂₃	C₂⁴	1	4	yes	—
281	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
282	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
283	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
284	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
285	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
286	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
287	C₂²×C₄×C₂₃	C₂⁴	1	4	yes	—
288	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
289	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
290	C₂²×C₄×C₂₃	C₂⁴	1	4	yes	—
291	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
292	C₂²×C₄×C₂₃	C₂⁴	1	8	yes	—
293	C₂²×C₄×C₂₃	C₂⁴	1	8	yes	—
294	C₂²×C₄×C₂₃	C₂⁴	1	16	yes	—
295	C₂²×C₄×C₂₃	C₂⁴	1	4	yes	—
296	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
297	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
298	C₄⋊C₄×C₂₃	C₂⁴	1	4	yes	—
299	C₄⋊C₄×C₂₃	C₂⁴	1	8	yes	—
300	C₄⋊C₄×C₂₃	C₂⁴	1	4	yes	—
301	C₄⋊C₄×C₂₃	C₂⁴	1	8	yes	—
302	C₄⋊C₄×C₂₃	C₂⁴	1	4	yes	—
303	C₄⋊C₄×C₂₃	C₂⁴	1	4	yes	—
304	C₄⋊C₄×C₂₃	C₂⁴	1	8	yes	—
305	C₄⋊C₄×C₂₃	C₂⁴	1	16	yes	—
306	C₄⋊C₄×C₂₃	C₂⁴	1	8	yes	—
307	C₄⋊C₄×C₂₃	C₂⁴	1	16	yes	—
308	C₄⋊C₄×C₂₃	C₂⁴	1	16	yes	—
309	C₄⋊C₄×C₂₃	C₂⁴	1	4	yes	—
310	C₄⋊C₄×C₂₃	C₂⁴	1	4	yes	—
311	C₄⋊C₄×C₂₃	C₂⁴	1	16	yes	—
312	C₄⋊C₄×C₂₃	C₂⁴	1	16	yes	—
313	C₄⋊C₄×C₂₃	C₂⁴	1	16	yes	—
314	C₄⋊C₄×C₂₃	C₂⁴	1	16	yes	—
315	C₄⋊C₄×C₂₃	C₂⁴	1	16	yes	—
316	C₄⋊C₄×C₂₃	C₂⁴	1	8	yes	—
317	C₄⋊C₄×C₂₃	C₂⁴	1	8	yes	—
318	C₄⋊C₄×C₂₃	C₂⁴	1	16	yes	—
319	C₄⋊C₄×C₂₃	C₂⁴	1	16	yes	—
320	C₂²⋊C₄×C₂₃	C₂⁴	1	8	yes	—
321	C₂²⋊C₄×C₂₃	C₂⁴	1	8	yes	—
322	C₂²⋊C₄×C₂₃	C₂⁴	1	8	yes	—
323	C₂²⋊C₄×C₂₃	C₂⁴	1	8	yes	—
324	C₂²⋊C₄×C₂₃	C₂⁴	1	16	yes	—
325	C₂²⋊C₄×C₂₃	C₂⁴	1	16	yes	—
326	C₂²⋊C₄×C₂₃	C₂⁴	1	8	yes	—
327	C₂²⋊C₄×C₂₃	C₂⁴	1	8	yes	—
328	C₂²⋊C₄×C₂₃	C₂⁴	1	8	yes	—
329	C₂²⋊C₄×C₂₃	C₂⁴	1	16	yes	—
330	C₂²⋊C₄×C₂₃	C₂⁴	1	16	yes	—
331	C₂²⋊C₄×C₂₃	C₂⁴	1	8	yes	—
332	C₂²⋊C₄×C₂₃	C₂⁴	1	8	yes	—
333	C₂²⋊C₄×C₂₃	C₂⁴	1	16	yes	—
334	C₄²×C₂₃	C₂⁴	1	8	yes	—
335	C₄²×C₂₃	C₂⁴	1	8	yes	—
336	C₄²×C₂₃	C₂⁴	1	8	yes	—
337	C₄²×C₂₃	C₂⁴	1	8	yes	—
338	C₄²×C₂₃	C₂⁴	1	16	yes	—
339	C₄²×C₂₃	C₂⁴	1	16	yes	—
340	C₄²×C₂₃	C₂⁴	1	16	yes	—
341	C₄²×C₂₃	C₂⁴	1	8	yes	—
342	C₂×#3495	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
343	C₂³×C₂₃	—	2	2	no	—
344	C₂³×C₂₃	—	2	2	no	—
345	C₂³×C₂₃	—	2	2	no	—
346	C₂³×C₂₃	—	2	2	no	—
347	C₂³×C₂₃	—	2	8	no	—
348	C₂³×C₂₃	—	2	2	no	—
349	C₂³×C₂₃	—	2	4	no	—
350	C₂³×C₂₃	—	2	4	no	—
351	C₂³×C₂₃	—	2	8	no	—
352	C₂³×C₂₃	—	2	2	no	—
353	C₂³×C₂₃	—	2	4	no	—
354	C₂³×C₂₃	—	2	2	no	—
355	C₂³×C₂₃	—	4	4	no	—
356	C₂³×C₂₃	—	4	16	no	—
357	C₂³×C₂₃	C₂×#41	1	4	yes	—
358	C₂³×C₂₃	2₋¹⁺⁴	1	4	yes	—
359	C₂³×C₂₃	C₂⁵	1	2	yes	—
360	C₂³×C₂₃	C₂⁵	1	4	yes	—
361	C₂³×C₂₃	C₂⁵	1	2	yes	—
362	C₂³×C₂₃	C₂⁵	1	2	yes	—
363	C₂³×C₂₃	C₂⁵	1	1	yes	characteristic
364	Q₈×C₂₃	—	2	16	no	—
365	Q₈×C₂₃	—	2	16	no	—
366	Q₈×C₂₃	—	2	8	no	—
367	Q₈×C₂₃	—	4	16	no	—
368	D₄×C₂₃	—	2	16	no	—
369	D₄×C₂₃	—	2	16	no	—
370	D₄×C₂₃	—	2	8	no	—
371	D₄×C₂₃	—	4	8	no	—
372	C₂×C₄×C₂₃	—	2	8	no	—
373	C₂×C₄×C₂₃	—	2	2	no	—
374	C₂×C₄×C₂₃	—	2	2	no	—
375	C₂×C₄×C₂₃	—	2	4	no	—
376	C₂×C₄×C₂₃	—	2	16	no	—
377	C₂×C₄×C₂₃	—	2	8	no	—
378	C₂×C₄×C₂₃	—	2	16	no	—
379	C₂×C₄×C₂₃	—	2	4	no	—
380	C₂×C₄×C₂₃	—	2	4	no	—
381	C₂×C₄×C₂₃	—	2	4	no	—
382	C₂×C₄×C₂₃	—	2	4	no	—
383	C₂×C₄×C₂₃	—	2	8	no	—
384	C₂×C₄×C₂₃	—	2	4	no	—
385	C₂×C₄×C₂₃	—	2	4	no	—
386	C₂×C₄×C₂₃	—	2	8	no	—
387	C₂×C₄×C₂₃	—	2	8	no	—
388	C₂×C₄×C₂₃	—	2	8	no	—
389	C₂×C₄×C₂₃	—	2	8	no	—
390	C₂×C₄×C₂₃	—	2	16	no	—
391	C₂×C₄×C₂₃	—	4	16	no	—
392	C₂×C₄×C₂₃	—	4	8	no	—
393	C₂×C₄×C₂₃	—	4	8	no	—
394	C₂×C₄×C₂₃	C₂×#41	1	4	yes	—
395	C₂×C₄×C₂₃	C₂×#41	1	4	yes	—
396	C₂×C₄×C₂₃	C₂×#41	1	16	yes	—
397	C₂×C₄×C₂₃	C₂⁵	1	4	yes	—
398	C₂×C₄×C₂₃	C₂⁵	1	2	yes	—
399	C₂×C₄×C₂₃	C₂⁵	1	4	yes	—
400	C₂×C₄×C₂₃	C₂⁵	1	4	yes	—
401	C₂×C₄×C₂₃	C₂⁵	1	4	yes	—
402	C₂×C₄×C₂₃	C₂⁵	1	4	yes	—
403	C₂×C₄×C₂₃	C₂⁵	1	8	yes	—
404	C₂×C₄×C₂₃	C₂⁵	1	4	yes	—
405	C₂×C₄×C₂₃	C₂⁵	1	4	yes	—
406	C₂×C₄×C₂₃	C₂⁵	1	8	yes	—
407	C₂×C₄×C₂₃	C₂⁵	1	2	yes	—
408	C₂×C₄×C₂₃	C₂⁵	1	2	yes	—
409	C₂×C₄×C₂₃	C₂⁵	1	2	yes	—
410	#3495	C₂×C₂₃	1	32	yes	direct product factor
411	C₂×#556	C₂×C₂₃	1	2	yes	complemented
412	C₂×#554	C₂×C₂₃	1	2	yes	complemented
413	C₂×#552	C₂×C₂₃	1	2	yes	complemented
414	C₂×#552	C₂×C₂₃	1	4	yes	complemented
415	C₂×#552	C₂×C₂₃	1	2	yes	complemented
416	C₂×#551	C₂×C₂₃	1	4	yes	complemented
417	C₂×#544	C₂×C₂₃	1	1	yes	characteristic, complemented
418	C₂×#542	C₂×C₂₃	1	2	yes	complemented
419	C₂×#541	C₂×C₂₃	1	2	yes	complemented
420	C₂×#536	C₂×C₂₃	1	1	yes	characteristic, complemented
421	C₂×#533	C₂×C₂₃	1	2	yes	complemented
422	C₂×#529	C₂×C₂₃	1	2	yes	complemented
423	C₂×#525	C₂×C₂₃	1	1	yes	characteristic
424	C₂²×C₂²⋊Q₈	C₂×C₂₃	1	1	yes	characteristic, complemented
425	C₂×#520	C₂×C₂₃	1	1	yes	characteristic, complemented
426	C₂×#519	C₂×C₂₃	1	1	yes	characteristic, complemented
427	C₂²×#117	C₂×C₂₃	1	1	yes	characteristic, complemented
428	C₂²×C₂₃	—	2	2	no	—
429	C₂²×C₂₃	—	2	2	no	—
430	C₂²×C₂₃	—	2	2	no	—
431	C₂²×C₂₃	—	2	2	no	—
432	C₂²×C₂₃	—	2	8	no	—
433	C₂²×C₂₃	—	2	8	no	—
434	C₂²×C₂₃	—	2	2	no	—
435	C₂²×C₂₃	—	2	4	no	—
436	C₂²×C₂₃	—	2	4	no	—
437	C₂²×C₂₃	—	2	2	no	—
438	C₂²×C₂₃	—	2	4	no	—
439	C₂²×C₂₃	—	2	2	no	—
440	C₂²×C₂₃	—	4	16	no	—
441	C₂²×C₂₃	—	4	8	no	—
442	C₂²×C₂₃	—	4	4	no	—
443	C₂²×C₂₃	C₂²×#41	1	4	yes	—
444	C₂²×C₂₃	C₂²×#41	1	2	yes	—
445	C₂²×C₂₃	C₂×2₋¹⁺⁴	1	4	yes	—
446	C₂²×C₂₃	C₂×2₋¹⁺⁴	1	2	yes	—
447	C₂²×C₂₃	#585	1	2	yes	—
448	C₂²×C₂₃	C₂⁶	1	1	yes	characteristic
449	C₄×C₂₃	—	2	2	no	—
450	C₄×C₂₃	—	2	2	no	—
451	C₄×C₂₃	—	2	4	no	—
452	C₄×C₂₃	—	2	8	no	—
453	C₄×C₂₃	—	2	4	no	—
454	C₄×C₂₃	—	2	4	no	—
455	C₄×C₂₃	—	2	4	no	—
456	C₄×C₂₃	—	2	4	no	—
457	C₄×C₂₃	—	2	8	no	—
458	C₄×C₂₃	—	2	4	no	—
459	C₄×C₂₃	—	2	4	no	—
460	C₄×C₂₃	C₂²×#41	1	4	yes	—
461	C₄×C₂₃	C₂²×#41	1	4	yes	—
462	C₂²×#41	C₂²×C₂₃	1	1	yes	characteristic
463	C₂³×Q₈	C₂²×C₂₃	1	1	yes	characteristic
464	C₂⁴×C₄	C₂²×C₂₃	1	1	yes	characteristic
465	#556	C₂²×C₂₃	1	32	yes	complemented
466	#554	C₂²×C₂₃	1	32	yes	complemented
467	#552	C₂²×C₂₃	1	32	yes	complemented
468	#552	C₂²×C₂₃	1	64	yes	complemented
469	#552	C₂²×C₂₃	1	32	yes	complemented
470	#551	C₂²×C₂₃	1	64	yes	complemented
471	#544	C₂²×C₂₃	1	16	yes	complemented
472	#542	C₂²×C₂₃	1	32	yes	complemented
473	#541	C₂²×C₂₃	1	32	yes	complemented
474	#536	C₂²×C₂₃	1	16	yes	complemented
475	#533	C₂²×C₂₃	1	32	yes	complemented
476	C₂×C₄⋊Q₈	C₂²×C₂₃	1	2	yes	complemented
477	C₂×C₄⋊Q₈	C₂²×C₂₃	1	2	yes	complemented
478	C₂×C₄⋊Q₈	C₂²×C₂₃	1	2	yes	complemented
479	#529	C₂²×C₂₃	1	32	yes	complemented
480	C₂×#126	C₂²×C₂₃	1	4	yes	—
481	C₂×#126	C₂²×C₂₃	1	4	yes	—
482	C₂×#126	C₂²×C₂₃	1	4	yes	complemented
483	C₂×#126	C₂²×C₂₃	1	4	yes	complemented
484	C₂×#125	C₂²×C₂₃	1	2	yes	complemented
485	C₂×#125	C₂²×C₂₃	1	4	yes	complemented
486	C₂×#125	C₂²×C₂₃	1	4	yes	complemented
487	C₂×#125	C₂²×C₂₃	1	4	yes	complemented
488	C₂×#125	C₂²×C₂₃	1	2	yes	complemented
489	C₂×#124	C₂²×C₂₃	1	4	yes	—
490	C₂×#124	C₂²×C₂₃	1	2	yes	complemented
491	#525	C₂²×C₂₃	1	16	yes	—
492	C₂×#123	C₂²×C₂₃	1	2	yes	—
493	C₂×#123	C₂²×C₂₃	1	4	yes	—
494	C₂×#123	C₂²×C₂₃	1	4	yes	—
495	C₂×#123	C₂²×C₂₃	1	4	yes	—
496	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	2	yes	—
497	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	2	yes	—
498	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	2	yes	—
499	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	2	yes	—
500	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
501	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
502	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	4	yes	—
503	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	4	yes	—
504	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	16	yes	complemented
505	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	2	yes	complemented
506	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	2	yes	complemented
507	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	4	yes	complemented
508	C₂×#121	C₂²×C₂₃	1	1	yes	characteristic
509	C₂×#121	C₂²×C₂₃	1	1	yes	characteristic
510	C₂×#120	C₂²×C₂₃	1	2	yes	—
511	#520	C₂²×C₂₃	1	16	yes	complemented
512	#519	C₂²×C₂₃	1	16	yes	complemented
513	C₂×C₄×Q₈	C₂²×C₂₃	1	2	yes	complemented
514	C₂×C₄×Q₈	C₂²×C₂₃	1	2	yes	complemented
515	C₂×C₄×Q₈	C₂²×C₂₃	1	2	yes	complemented
516	C₂×C₄×Q₈	C₂²×C₂₃	1	2	yes	complemented
517	C₂×C₄×Q₈	C₂²×C₂₃	1	2	yes	complemented
518	C₂×C₄×Q₈	C₂²×C₂₃	1	4	yes	complemented
519	C₂×C₄×D₄	C₂²×C₂₃	1	4	yes	—
520	C₂×C₄×D₄	C₂²×C₂₃	1	2	yes	—
521	C₂×C₄×D₄	C₂²×C₂₃	1	2	yes	—
522	C₂×C₄×D₄	C₂²×C₂₃	1	4	yes	—
523	C₂×C₄×D₄	C₂²×C₂₃	1	2	yes	complemented
524	C₂×#117	C₂²×C₂₃	1	1	yes	characteristic
525	C₂×#117	C₂²×C₂₃	1	1	yes	characteristic
526	C₂×#117	C₂²×C₂₃	1	2	yes	—
527	C₂×#117	C₂²×C₂₃	1	1	yes	characteristic
528	C₂×#117	C₂²×C₂₃	1	2	yes	—
529	C₂×#117	C₂²×C₂₃	1	1	yes	characteristic
530	C₂×#117	C₂²×C₂₃	1	1	yes	characteristic
531	C₂×#117	C₂²×C₂₃	1	4	yes	—
532	C₂×#117	C₂²×C₂₃	1	4	yes	—
533	C₂×#117	C₂²×C₂₃	1	16	yes	complemented
534	C₂×#117	C₂²×C₂₃	1	2	yes	complemented
535	C₂×#117	C₂²×C₂₃	1	4	yes	complemented
536	C₂²×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
537	C₂²×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
538	C₂²×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
539	C₂²×C₄⋊C₄	C₂²×C₂₃	1	2	yes	—
540	C₂²×C₄⋊C₄	C₂²×C₂₃	1	2	yes	complemented
541	C₂²×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
542	C₂²×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
543	C₂²×C₄²	C₂²×C₂₃	1	2	yes	—
544	C₂×C₂₃	—	2	4	no	—
545	C₂×C₂₃	—	2	4	no	—
546	C₂×C₂₃	—	4	4	no	—
547	C₂×C₂₃	—	4	2	no	—
548	C₂×C₂₃	#3495	1	4	yes	direct product factor
549	C₂×C₂₃	C₂³×#41	1	1	yes	characteristic
550	C₂×C₂₃	C₂²×2₋¹⁺⁴	1	1	yes	characteristic
551	C₂×C₂₃	C₂×#585	1	1	yes	characteristic
552	C₂⁵	C₂³×C₂₃	1	1	yes	characteristic
553	C₂×#41	—	2	8	no	—
554	C₂×#41	C₂³×C₂₃	1	8	yes	—
555	C₂²×Q₈	—	2	8	no	—
556	C₂²×Q₈	C₂³×C₂₃	1	2	yes	—
557	C₂²×Q₈	C₂³×C₂₃	1	2	yes	—
558	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
559	C₂²×Q₈	C₂³×C₂₃	1	8	yes	—
560	C₂²×Q₈	C₂³×C₂₃	1	4	yes	—
561	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
562	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
563	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
564	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
565	C₂³×C₄	—	2	8	no	—
566	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
567	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
568	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
569	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
570	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
571	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
572	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
573	C₂³×C₄	C₂³×C₂₃	1	8	yes	—
574	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
575	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
576	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
577	C₂³×C₄	C₂³×C₂₃	1	4	yes	—
578	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
579	C₄⋊Q₈	C₂³×C₂₃	1	16	yes	complemented
580	C₄⋊Q₈	C₂³×C₂₃	1	16	yes	complemented
581	C₄⋊Q₈	C₂³×C₂₃	1	16	yes	complemented
582	#126	C₂³×C₂₃	1	32	yes	—
583	#126	C₂³×C₂₃	1	32	yes	—
584	#126	C₂³×C₂₃	1	32	yes	complemented
585	#126	C₂³×C₂₃	1	32	yes	complemented
586	#125	C₂³×C₂₃	1	16	yes	complemented
587	#125	C₂³×C₂₃	1	32	yes	complemented
588	#125	C₂³×C₂₃	1	32	yes	complemented
589	#125	C₂³×C₂₃	1	32	yes	complemented
590	#125	C₂³×C₂₃	1	16	yes	complemented
591	#124	C₂³×C₂₃	1	32	yes	—
592	#124	C₂³×C₂₃	1	16	yes	complemented
593	#123	C₂³×C₂₃	1	16	yes	—
594	#123	C₂³×C₂₃	1	32	yes	—
595	#123	C₂³×C₂₃	1	32	yes	—
596	#123	C₂³×C₂₃	1	32	yes	—
597	C₂²⋊Q₈	C₂³×C₂₃	1	16	yes	—
598	C₂²⋊Q₈	C₂³×C₂₃	1	16	yes	—
599	C₂²⋊Q₈	C₂³×C₂₃	1	16	yes	—
600	C₂²⋊Q₈	C₂³×C₂₃	1	16	yes	—
601	C₂²⋊Q₈	C₂³×C₂₃	1	8	yes	—
602	C₂²⋊Q₈	C₂³×C₂₃	1	8	yes	—
603	C₂²⋊Q₈	C₂³×C₂₃	1	32	yes	—
604	C₂²⋊Q₈	C₂³×C₂₃	1	32	yes	—
605	C₂²⋊Q₈	C₂³×C₂₃	1	16	yes	complemented
606	C₂²⋊Q₈	C₂³×C₂₃	1	16	yes	complemented
607	C₂²⋊Q₈	C₂³×C₂₃	1	32	yes	complemented
608	#121	C₂³×C₂₃	1	8	yes	—
609	#121	C₂³×C₂₃	1	8	yes	—
610	#120	C₂³×C₂₃	1	16	yes	—
611	C₄×Q₈	C₂³×C₂₃	1	16	yes	complemented
612	C₄×Q₈	C₂³×C₂₃	1	16	yes	complemented
613	C₄×Q₈	C₂³×C₂₃	1	16	yes	complemented
614	C₄×Q₈	C₂³×C₂₃	1	16	yes	complemented
615	C₄×Q₈	C₂³×C₂₃	1	16	yes	complemented
616	C₄×Q₈	C₂³×C₂₃	1	32	yes	complemented
617	C₄×D₄	C₂³×C₂₃	1	32	yes	—
618	C₄×D₄	C₂³×C₂₃	1	16	yes	—
619	C₄×D₄	C₂³×C₂₃	1	16	yes	—
620	C₄×D₄	C₂³×C₂₃	1	32	yes	—
621	C₄×D₄	C₂³×C₂₃	1	16	yes	complemented
622	#117	C₂³×C₂₃	1	8	yes	—
623	#117	C₂³×C₂₃	1	8	yes	—
624	#117	C₂³×C₂₃	1	16	yes	—
625	#117	C₂³×C₂₃	1	8	yes	—
626	#117	C₂³×C₂₃	1	16	yes	—
627	#117	C₂³×C₂₃	1	8	yes	—
628	#117	C₂³×C₂₃	1	8	yes	—
629	#117	C₂³×C₂₃	1	32	yes	—
630	#117	C₂³×C₂₃	1	32	yes	—
631	#117	C₂³×C₂₃	1	16	yes	complemented
632	#117	C₂³×C₂₃	1	32	yes	complemented
633	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
634	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
635	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
636	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
637	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
638	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
639	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
640	C₂×C₄⋊C₄	C₂³×C₂₃	1	8	yes	—
641	C₂×C₄⋊C₄	C₂³×C₂₃	1	8	yes	—
642	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
643	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
644	C₂×C₄⋊C₄	C₂³×C₂₃	1	8	yes	—
645	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
646	C₂×C₄⋊C₄	C₂³×C₂₃	1	16	yes	—
647	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
648	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
649	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
650	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
651	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
652	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
653	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
654	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
655	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
656	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
657	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
658	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
659	C₂×C₄⋊C₄	C₂³×C₂₃	1	16	yes	complemented
660	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
661	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
662	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
663	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
664	C₂×C₂²⋊C₄	C₂³×C₂₃	1	4	yes	—
665	C₂×C₂²⋊C₄	C₂³×C₂₃	1	16	yes	—
666	C₂×C₂²⋊C₄	C₂³×C₂₃	1	4	yes	—
667	C₂×C₂²⋊C₄	C₂³×C₂₃	1	16	yes	—
668	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
669	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
670	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
671	C₂×C₂²⋊C₄	C₂³×C₂₃	1	4	yes	—
672	C₂×C₂²⋊C₄	C₂³×C₂₃	1	4	yes	—
673	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
674	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
675	C₂×C₂²⋊C₄	C₂³×C₂₃	1	4	yes	—
676	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
677	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
678	C₂×C₄²	C₂³×C₂₃	1	4	yes	—
679	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
680	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
681	C₂×C₄²	C₂³×C₂₃	1	4	yes	—
682	C₂×C₄²	C₂³×C₂₃	1	4	yes	—
683	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
684	C₂×C₄²	C₂³×C₂₃	1	16	yes	—
685	C₂₃	C₂×#3495	1	1	yes	characteristic, direct product factor, Sylow
686	C₂⁴	—	2	4	no	—
687	C₂⁴	—	2	4	no	—
688	C₂⁴	—	4	2	no	—
689	C₂⁴	C₂⁴×C₂₃	1	1	yes	characteristic
690	C₂⁴	C₂⁴×C₂₃	1	2	yes	—
691	C₂⁴	C₂⁴×C₂₃	1	4	yes	—
692	C₂⁴	C₂⁴×C₂₃	1	1	yes	characteristic
693	C₂⁴	C₂⁴×C₂₃	1	1	yes	characteristic
694	#41	—	2	32	no	—
695	C₂×Q₈	—	2	8	no	—
696	C₂×Q₈	—	2	8	no	—
697	C₂×Q₈	—	2	32	no	—
698	C₂×Q₈	—	2	4	no	—
699	C₂×Q₈	—	4	8	no	—
700	C₂×Q₈	C₂⁴×C₂₃	1	8	yes	—
701	C₂×Q₈	C₂⁴×C₂₃	1	8	yes	—
702	C₂×Q₈	C₂⁴×C₂₃	1	4	yes	—
703	C₂×Q₈	C₂⁴×C₂₃	1	16	yes	—
704	C₂×D₄	—	2	8	no	—
705	C₂×D₄	—	2	8	no	—
706	C₂×D₄	—	2	4	no	—
707	C₂×D₄	—	4	4	no	—
708	C₂×D₄	C₂⁴×C₂₃	1	8	yes	—
709	C₂×D₄	C₂⁴×C₂₃	1	8	yes	—
710	C₂×D₄	C₂⁴×C₂₃	1	4	yes	—
711	C₂×D₄	C₂⁴×C₂₃	1	8	yes	—
712	C₂²×C₄	—	2	4	no	—
713	C₂²×C₄	—	2	8	no	—
714	C₂²×C₄	—	2	8	no	—
715	C₂²×C₄	—	2	4	no	—
716	C₂²×C₄	—	2	4	no	—
717	C₂²×C₄	—	2	4	no	—
718	C₂²×C₄	—	2	4	no	—
719	C₂²×C₄	—	2	32	no	—
720	C₂²×C₄	—	2	8	no	—
721	C₂²×C₄	—	4	8	no	—
722	C₂²×C₄	—	4	4	no	—
723	C₂²×C₄	—	4	4	no	—
724	C₂²×C₄	#41×C₂₃	1	8	yes	—
725	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
726	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
727	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
728	C₂²×C₄	C₂⁴×C₂₃	1	4	yes	—
729	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
730	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
731	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
732	C₂²×C₄	C₂⁴×C₂₃	1	4	yes	—
733	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
734	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
735	C₂²×C₄	C₂⁴×C₂₃	1	8	yes	—
736	C₂²×C₄	C₂⁴×C₂₃	1	4	yes	—
737	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
738	C₂²×C₄	C₂⁴×C₂₃	1	8	yes	—
739	C₂²×C₄	C₂⁴×C₂₃	1	4	yes	—
740	C₂²×C₄	C₂⁴×C₂₃	1	4	yes	—
741	C₂²×C₄	C₂⁴×C₂₃	1	8	yes	—
742	C₂²×C₄	C₂⁴×C₂₃	1	4	yes	—
743	C₂²×C₄	C₂⁴×C₂₃	1	4	yes	—
744	C₂²×C₄	C₂⁴×C₂₃	1	8	yes	—
745	C₂²×C₄	C₂⁴×C₂₃	1	8	yes	—
746	C₂²×C₄	C₂⁴×C₂₃	1	16	yes	—
747	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
748	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
749	C₂²×C₄	C₂⁴×C₂₃	1	4	yes	—
750	C₄⋊C₄	C₂⁴×C₂₃	1	4	yes	—
751	C₄⋊C₄	C₂⁴×C₂₃	1	8	yes	—
752	C₄⋊C₄	C₂⁴×C₂₃	1	4	yes	—
753	C₄⋊C₄	C₂⁴×C₂₃	1	8	yes	—
754	C₄⋊C₄	C₂⁴×C₂₃	1	4	yes	—
755	C₄⋊C₄	C₂⁴×C₂₃	1	4	yes	—
756	C₄⋊C₄	C₂⁴×C₂₃	1	8	yes	—
757	C₄⋊C₄	C₂⁴×C₂₃	1	16	yes	—
758	C₄⋊C₄	C₂⁴×C₂₃	1	8	yes	—
759	C₄⋊C₄	C₂⁴×C₂₃	1	16	yes	—
760	C₄⋊C₄	C₂⁴×C₂₃	1	16	yes	—
761	C₄⋊C₄	C₂⁴×C₂₃	1	4	yes	—
762	C₄⋊C₄	C₂⁴×C₂₃	1	4	yes	—
763	C₄⋊C₄	C₂⁴×C₂₃	1	16	yes	—
764	C₄⋊C₄	C₂⁴×C₂₃	1	16	yes	—
765	C₄⋊C₄	C₂⁴×C₂₃	1	16	yes	—
766	C₄⋊C₄	C₂⁴×C₂₃	1	16	yes	—
767	C₄⋊C₄	C₂⁴×C₂₃	1	16	yes	—
768	C₄⋊C₄	C₂⁴×C₂₃	1	8	yes	—
769	C₄⋊C₄	C₂⁴×C₂₃	1	8	yes	—
770	C₄⋊C₄	C₂⁴×C₂₃	1	16	yes	—
771	C₄⋊C₄	C₂⁴×C₂₃	1	16	yes	—
772	C₂²⋊C₄	C₂⁴×C₂₃	1	8	yes	—
773	C₂²⋊C₄	C₂⁴×C₂₃	1	8	yes	—
774	C₂²⋊C₄	C₂⁴×C₂₃	1	8	yes	—
775	C₂²⋊C₄	C₂⁴×C₂₃	1	8	yes	—
776	C₂²⋊C₄	C₂⁴×C₂₃	1	16	yes	—
777	C₂²⋊C₄	C₂⁴×C₂₃	1	16	yes	—
778	C₂²⋊C₄	C₂⁴×C₂₃	1	8	yes	—
779	C₂²⋊C₄	C₂⁴×C₂₃	1	8	yes	—
780	C₂²⋊C₄	C₂⁴×C₂₃	1	8	yes	—
781	C₂²⋊C₄	C₂⁴×C₂₃	1	16	yes	—
782	C₂²⋊C₄	C₂⁴×C₂₃	1	16	yes	—
783	C₂²⋊C₄	C₂⁴×C₂₃	1	8	yes	—
784	C₂²⋊C₄	C₂⁴×C₂₃	1	8	yes	—
785	C₂²⋊C₄	C₂⁴×C₂₃	1	16	yes	—
786	C₄²	C₂⁴×C₂₃	1	8	yes	—
787	C₄²	C₂⁴×C₂₃	1	8	yes	—
788	C₄²	C₂⁴×C₂₃	1	8	yes	—
789	C₄²	C₂⁴×C₂₃	1	8	yes	—
790	C₄²	C₂⁴×C₂₃	1	16	yes	—
791	C₄²	C₂⁴×C₂₃	1	16	yes	—
792	C₄²	C₂⁴×C₂₃	1	16	yes	—
793	C₄²	C₂⁴×C₂₃	1	8	yes	—
794	C₂³	—	2	2	no	—
795	C₂³	—	2	2	no	—
796	C₂³	—	2	2	no	—
797	C₂³	—	2	2	no	—
798	C₂³	—	2	8	no	—
799	C₂³	—	2	2	no	—
800	C₂³	—	2	4	no	—
801	C₂³	—	2	4	no	—
802	C₂³	—	2	8	no	—
803	C₂³	—	2	2	no	—
804	C₂³	—	2	4	no	—
805	C₂³	—	2	2	no	—
806	C₂³	—	4	4	no	—
807	C₂³	—	4	16	no	—
808	C₂³	C₂×#41×C₂₃	1	4	yes	—
809	C₂³	C₂₃×2₋¹⁺⁴	1	4	yes	—
810	C₂³	C₂⁵×C₂₃	1	2	yes	—
811	C₂³	C₂⁵×C₂₃	1	4	yes	—
812	C₂³	C₂⁵×C₂₃	1	2	yes	—
813	C₂³	C₂⁵×C₂₃	1	2	yes	—
814	C₂³	C₂⁵×C₂₃	1	1	yes	characteristic
815	Q₈	—	2	16	no	—
816	Q₈	—	2	16	no	—
817	Q₈	—	2	8	no	—
818	Q₈	—	4	16	no	—
819	D₄	—	2	16	no	—
820	D₄	—	2	16	no	—
821	D₄	—	2	8	no	—
822	D₄	—	4	8	no	—
823	C₂×C₄	—	2	8	no	—
824	C₂×C₄	—	2	2	no	—
825	C₂×C₄	—	2	2	no	—
826	C₂×C₄	—	2	4	no	—
827	C₂×C₄	—	2	16	no	—
828	C₂×C₄	—	2	8	no	—
829	C₂×C₄	—	2	16	no	—
830	C₂×C₄	—	2	4	no	—
831	C₂×C₄	—	2	4	no	—
832	C₂×C₄	—	2	4	no	—
833	C₂×C₄	—	2	4	no	—
834	C₂×C₄	—	2	8	no	—
835	C₂×C₄	—	2	4	no	—
836	C₂×C₄	—	2	4	no	—
837	C₂×C₄	—	2	8	no	—
838	C₂×C₄	—	2	8	no	—
839	C₂×C₄	—	2	8	no	—
840	C₂×C₄	—	2	8	no	—
841	C₂×C₄	—	2	16	no	—
842	C₂×C₄	—	4	16	no	—
843	C₂×C₄	—	4	8	no	—
844	C₂×C₄	—	4	8	no	—
845	C₂×C₄	C₂×#41×C₂₃	1	4	yes	—
846	C₂×C₄	C₂×#41×C₂₃	1	4	yes	—
847	C₂×C₄	C₂×#41×C₂₃	1	16	yes	—
848	C₂×C₄	C₂⁵×C₂₃	1	4	yes	—
849	C₂×C₄	C₂⁵×C₂₃	1	2	yes	—
850	C₂×C₄	C₂⁵×C₂₃	1	4	yes	—
851	C₂×C₄	C₂⁵×C₂₃	1	4	yes	—
852	C₂×C₄	C₂⁵×C₂₃	1	4	yes	—
853	C₂×C₄	C₂⁵×C₂₃	1	4	yes	—
854	C₂×C₄	C₂⁵×C₂₃	1	8	yes	—
855	C₂×C₄	C₂⁵×C₂₃	1	4	yes	—
856	C₂×C₄	C₂⁵×C₂₃	1	4	yes	—
857	C₂×C₄	C₂⁵×C₂₃	1	8	yes	—
858	C₂×C₄	C₂⁵×C₂₃	1	2	yes	—
859	C₂×C₄	C₂⁵×C₂₃	1	2	yes	—
860	C₂×C₄	C₂⁵×C₂₃	1	2	yes	—
861	C₂²	—	2	8	no	—
862	C₂²	—	2	8	no	—
863	C₂²	—	2	2	no	—
864	C₂²	—	2	2	no	—
865	C₂²	—	2	2	no	—
866	C₂²	—	2	2	no	—
867	C₂²	—	2	2	no	—
868	C₂²	—	2	4	no	—
869	C₂²	—	2	4	no	—
870	C₂²	—	2	2	no	—
871	C₂²	—	2	4	no	—
872	C₂²	—	2	2	no	—
873	C₂²	—	4	16	no	—
874	C₂²	—	4	4	no	—
875	C₂²	—	4	8	no	—
876	C₂²	C₂²×#41×C₂₃	1	4	yes	—
877	C₂²	C₂²×#41×C₂₃	1	2	yes	—
878	C₂²	C₂×C₂₃×2₋¹⁺⁴	1	4	yes	—
879	C₂²	C₂×C₂₃×2₋¹⁺⁴	1	2	yes	—
880	C₂²	C₂₃×#585	1	2	yes	—
881	C₂²	C₂⁶×C₂₃	1	1	yes	characteristic
882	C₄	—	2	2	no	—
883	C₄	—	2	2	no	—
884	C₄	—	2	4	no	—
885	C₄	—	2	8	no	—
886	C₄	—	2	4	no	—
887	C₄	—	2	4	no	—
888	C₄	—	2	4	no	—
889	C₄	—	2	4	no	—
890	C₄	—	2	8	no	—
891	C₄	—	2	4	no	—
892	C₄	—	2	4	no	—
893	C₄	C₂²×#41×C₂₃	1	4	yes	—
894	C₄	C₂²×#41×C₂₃	1	4	yes	—
895	C₂	—	2	4	no	—
896	C₂	—	2	4	no	—
897	C₂	—	4	2	no	—
898	C₂	—	4	4	no	—
899	C₂	C₂₃×#3495	1	4	yes	direct product factor
900	C₂	C₂³×#41×C₂₃	1	1	yes	characteristic
901	C₂	C₂²×C₂₃×2₋¹⁺⁴	1	1	yes	characteristic
902	C₂	C₂×C₂₃×#585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₂₃	C₂⁵
commutator, Frattini, cosocle	C₂²	C₂⁶×C₂₃
prime radical	C₂×C₂₃×#525	C₂
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×#3495	C₂	direct (N × H)
2. C₂×C₂₃×#556	C₂	semidirect
3. C₂×C₂₃×#554	C₂	semidirect
4. C₂×C₂₃×#552	C₂	semidirect
5. C₂×C₂₃×#552	C₂	semidirect
6. C₂×C₂₃×#552	C₂	semidirect
7. C₂×C₂₃×#551	C₂	semidirect
8. C₂×C₂₃×#544	C₂	semidirect
9. C₂×C₂₃×#542	C₂	semidirect
10. C₂×C₂₃×#541	C₂	semidirect
11. C₂×C₂₃×#536	C₂	semidirect
12. C₂×C₂₃×#533	C₂	semidirect
13. C₂×C₂₃×#529	C₂	semidirect
15. C₂²×C₂₃×C₂²⋊Q₈	C₂	semidirect
16. C₂×C₂₃×#520	C₂	semidirect
17. C₂×C₂₃×#519	C₂	semidirect
18. C₂²×C₂₃×#117	C₂	semidirect
22. C₂₃×#556	C₂²	semidirect
23. C₂₃×#554	C₂²	semidirect
24. C₂₃×#552	C₂²	semidirect
25. C₂₃×#552	C₂²	semidirect
26. C₂₃×#552	C₂²	semidirect
27. C₂₃×#551	C₂²	semidirect
28. C₂₃×#544	C₂²	semidirect
29. C₂₃×#542	C₂²	semidirect
30. C₂₃×#541	C₂²	semidirect
31. C₂₃×#536	C₂²	semidirect
32. C₂₃×#533	C₂²	semidirect
33. C₂×C₂₃×C₄⋊Q₈	C₂²	semidirect
34. C₂×C₂₃×C₄⋊Q₈	C₂²	semidirect
35. C₂×C₂₃×C₄⋊Q₈	C₂²	semidirect
36. C₂₃×#529	C₂²	semidirect
39. C₂×C₂₃×#126	C₂²	semidirect
40. C₂×C₂₃×#126	C₂²	semidirect
41. C₂×C₂₃×#125	C₂²	semidirect
42. C₂×C₂₃×#125	C₂²	semidirect
43. C₂×C₂₃×#125	C₂²	semidirect
44. C₂×C₂₃×#125	C₂²	semidirect
45. C₂×C₂₃×#125	C₂²	semidirect
47. C₂×C₂₃×#124	C₂²	semidirect
61. C₂×C₂₃×C₂²⋊Q₈	C₂²	semidirect
62. C₂×C₂₃×C₂²⋊Q₈	C₂²	semidirect
63. C₂×C₂₃×C₂²⋊Q₈	C₂²	semidirect
64. C₂×C₂₃×C₂²⋊Q₈	C₂²	semidirect
68. C₂₃×#520	C₂²	semidirect
69. C₂₃×#519	C₂²	semidirect
70. C₂×C₄×Q₈×C₂₃	C₂²	semidirect
71. C₂×C₄×Q₈×C₂₃	C₂²	semidirect
72. C₂×C₄×Q₈×C₂₃	C₂²	semidirect
73. C₂×C₄×Q₈×C₂₃	C₂²	semidirect
74. C₂×C₄×Q₈×C₂₃	C₂²	semidirect
75. C₂×C₄×Q₈×C₂₃	C₂²	semidirect
80. C₂×C₄×D₄×C₂₃	C₂²	semidirect
90. C₂×C₂₃×#117	C₂²	semidirect
91. C₂×C₂₃×#117	C₂²	semidirect
92. C₂×C₂₃×#117	C₂²	semidirect
97. C₂²×C₄⋊C₄×C₂₃	C₂²	semidirect
128. C₂₃×C₄⋊Q₈	C₂³	semidirect
129. C₂₃×C₄⋊Q₈	C₂³	semidirect
130. C₂₃×C₄⋊Q₈	C₂³	semidirect
133. C₂₃×#126	C₂³	semidirect
134. C₂₃×#126	C₂³	semidirect
135. C₂₃×#125	C₂³	semidirect
136. C₂₃×#125	C₂³	semidirect
137. C₂₃×#125	C₂³	semidirect
138. C₂₃×#125	C₂³	semidirect
139. C₂₃×#125	C₂³	semidirect
141. C₂₃×#124	C₂³	semidirect
154. C₂₃×C₂²⋊Q₈	C₂³	semidirect
155. C₂₃×C₂²⋊Q₈	C₂³	semidirect
156. C₂₃×C₂²⋊Q₈	C₂³	semidirect
160. C₄×Q₈×C₂₃	C₂³	semidirect
161. C₄×Q₈×C₂₃	C₂³	semidirect
162. C₄×Q₈×C₂₃	C₂³	semidirect
163. C₄×Q₈×C₂₃	C₂³	semidirect
164. C₄×Q₈×C₂₃	C₂³	semidirect
165. C₄×Q₈×C₂₃	C₂³	semidirect
170. C₄×D₄×C₂₃	C₂³	semidirect
180. C₂₃×#117	C₂³	semidirect
181. C₂₃×#117	C₂³	semidirect
208. C₂×C₄⋊C₄×C₂₃	C₂³	semidirect
342. C₂×#3495	C₂₃	direct (N × H)
410. #3495	C₂×C₂₃	direct (N × H)
411. C₂×#556	C₂×C₂₃	semidirect
412. C₂×#554	C₂×C₂₃	semidirect
413. C₂×#552	C₂×C₂₃	semidirect
414. C₂×#552	C₂×C₂₃	semidirect
415. C₂×#552	C₂×C₂₃	semidirect
416. C₂×#551	C₂×C₂₃	semidirect
417. C₂×#544	C₂×C₂₃	semidirect
418. C₂×#542	C₂×C₂₃	semidirect
419. C₂×#541	C₂×C₂₃	semidirect
420. C₂×#536	C₂×C₂₃	semidirect
421. C₂×#533	C₂×C₂₃	semidirect
422. C₂×#529	C₂×C₂₃	semidirect
424. C₂²×C₂²⋊Q₈	C₂×C₂₃	semidirect
425. C₂×#520	C₂×C₂₃	semidirect
426. C₂×#519	C₂×C₂₃	semidirect
427. C₂²×#117	C₂×C₂₃	semidirect
465. #556	C₂²×C₂₃	semidirect
466. #554	C₂²×C₂₃	semidirect
467. #552	C₂²×C₂₃	semidirect
468. #552	C₂²×C₂₃	semidirect
469. #552	C₂²×C₂₃	semidirect
470. #551	C₂²×C₂₃	semidirect
471. #544	C₂²×C₂₃	semidirect
472. #542	C₂²×C₂₃	semidirect
473. #541	C₂²×C₂₃	semidirect
474. #536	C₂²×C₂₃	semidirect
475. #533	C₂²×C₂₃	semidirect
476. C₂×C₄⋊Q₈	C₂²×C₂₃	semidirect
477. C₂×C₄⋊Q₈	C₂²×C₂₃	semidirect
478. C₂×C₄⋊Q₈	C₂²×C₂₃	semidirect
479. #529	C₂²×C₂₃	semidirect
482. C₂×#126	C₂²×C₂₃	semidirect
483. C₂×#126	C₂²×C₂₃	semidirect
484. C₂×#125	C₂²×C₂₃	semidirect
485. C₂×#125	C₂²×C₂₃	semidirect
486. C₂×#125	C₂²×C₂₃	semidirect
487. C₂×#125	C₂²×C₂₃	semidirect
488. C₂×#125	C₂²×C₂₃	semidirect
490. C₂×#124	C₂²×C₂₃	semidirect
504. C₂×C₂²⋊Q₈	C₂²×C₂₃	semidirect
505. C₂×C₂²⋊Q₈	C₂²×C₂₃	semidirect
506. C₂×C₂²⋊Q₈	C₂²×C₂₃	semidirect
507. C₂×C₂²⋊Q₈	C₂²×C₂₃	semidirect
511. #520	C₂²×C₂₃	semidirect
512. #519	C₂²×C₂₃	semidirect
513. C₂×C₄×Q₈	C₂²×C₂₃	semidirect
514. C₂×C₄×Q₈	C₂²×C₂₃	semidirect
515. C₂×C₄×Q₈	C₂²×C₂₃	semidirect
516. C₂×C₄×Q₈	C₂²×C₂₃	semidirect
517. C₂×C₄×Q₈	C₂²×C₂₃	semidirect
518. C₂×C₄×Q₈	C₂²×C₂₃	semidirect
523. C₂×C₄×D₄	C₂²×C₂₃	semidirect
533. C₂×#117	C₂²×C₂₃	semidirect
534. C₂×#117	C₂²×C₂₃	semidirect
535. C₂×#117	C₂²×C₂₃	semidirect
540. C₂²×C₄⋊C₄	C₂²×C₂₃	semidirect
548. C₂×C₂₃	#3495	direct (N × H)
579. C₄⋊Q₈	C₂³×C₂₃	semidirect
580. C₄⋊Q₈	C₂³×C₂₃	semidirect
581. C₄⋊Q₈	C₂³×C₂₃	semidirect
584. #126	C₂³×C₂₃	semidirect
585. #126	C₂³×C₂₃	semidirect
586. #125	C₂³×C₂₃	semidirect
587. #125	C₂³×C₂₃	semidirect
588. #125	C₂³×C₂₃	semidirect
589. #125	C₂³×C₂₃	semidirect
590. #125	C₂³×C₂₃	semidirect
592. #124	C₂³×C₂₃	semidirect
605. C₂²⋊Q₈	C₂³×C₂₃	semidirect
606. C₂²⋊Q₈	C₂³×C₂₃	semidirect
607. C₂²⋊Q₈	C₂³×C₂₃	semidirect
611. C₄×Q₈	C₂³×C₂₃	semidirect
612. C₄×Q₈	C₂³×C₂₃	semidirect
613. C₄×Q₈	C₂³×C₂₃	semidirect
614. C₄×Q₈	C₂³×C₂₃	semidirect
615. C₄×Q₈	C₂³×C₂₃	semidirect
616. C₄×Q₈	C₂³×C₂₃	semidirect
621. C₄×D₄	C₂³×C₂₃	semidirect
631. #117	C₂³×C₂₃	semidirect
632. #117	C₂³×C₂₃	semidirect
659. C₂×C₄⋊C₄	C₂³×C₂₃	semidirect
685. C₂₃	C₂×#3495	direct (N × H)
899. C₂	C₂₃×#3495	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×#3495	2
C₂×C₂₃×#556	2
C₂×C₂₃×#554	2
C₂×C₂₃×#552	2
C₂×C₂₃×#551	2
C₂×C₂₃×#544	2
C₂×C₂₃×#542	2
C₂×C₂₃×#541	2
C₂×C₂₃×#536	2
C₂×C₂₃×#533	2
C₂×C₂₃×#529	2
C₂×C₂₃×#525	2
C₂²×C₂₃×C₂²⋊Q₈	2
C₂×C₂₃×#520	2
C₂×C₂₃×#519	2
C₂²×C₂₃×#117	2
C₂×#3495	23

Subgroups — C2×C23×#3495 #19210429

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₂₃×#3495 #19210429