Subgroups — C₂×C₂₃×#2424 #19182276

Order 5888.

5898 conjugacy classes of subgroups.

The subgroup lattice has 1112 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₂₃×#121	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₂₃×#121	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₂₃×#120	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×C₂₃×#120	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×C₄×D₄×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂³×C₂²⋊C₄×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₃×#2424	C₂	1	16	yes	maximal, direct product factor
8	C₂×C₂₃×#396	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₂₃×#394	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₂₃×#394	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₂₃×#392	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₂₃×#390	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₂₃×#388	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₂₃×#386	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₂₃×#386	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₂₃×#385	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂⁶×C₂₃	C₂²	1	1	yes	characteristic
18	C₂³×D₄×C₂₃	C₂²	1	1	yes	characteristic
19	C₂³×D₄×C₂₃	C₂²	1	1	yes	characteristic
20	C₂³×D₄×C₂₃	C₂²	1	1	yes	characteristic
21	C₂³×D₄×C₂₃	C₂²	1	1	yes	characteristic
22	C₂³×D₄×C₂₃	C₂²	1	1	yes	characteristic
23	C₂³×D₄×C₂₃	C₂²	1	1	yes	characteristic
24	C₂³×D₄×C₂₃	C₂²	1	1	yes	characteristic, complemented
25	C₂⁴×C₄×C₂₃	C₂²	1	1	yes	characteristic
26	C₂⁴×C₄×C₂₃	C₂²	1	1	yes	characteristic
27	C₂⁴×C₄×C₂₃	C₂²	1	1	yes	characteristic, complemented
28	C₂×C₂₃×#121	—	2	8	no	—
29	C₂×C₂₃×#121	—	2	8	no	—
30	C₂×C₂₃×#121	C₂²	1	8	yes	complemented
31	C₂×C₂₃×#121	C₂²	1	8	yes	complemented
32	C₂×C₂₃×#120	—	2	8	no	—
33	C₂×C₂₃×#120	—	2	8	no	—
34	C₂×C₂₃×#120	C₂²	1	8	yes	complemented
35	C₂×C₂₃×#120	C₂²	1	8	yes	complemented
36	C₂×C₄×D₄×C₂₃	—	2	8	no	—
37	C₂×C₄×D₄×C₂₃	C₂²	1	8	yes	complemented
38	C₂²×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic, complemented
39	C₂²×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic, complemented
40	C₂²×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic, complemented
41	C₂²×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic, complemented
42	C₂²×C₂²⋊C₄×C₂₃	—	2	8	no	—
43	C₂²×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
44	C₂²×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
45	C₂²×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
46	C₂²×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
47	C₂²×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
48	C₂²×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
49	C₂²×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
50	C₂²×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
51	C₂²×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
52	C₂²×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
53	C₂²×C₂²⋊C₄×C₂₃	C₂²	1	8	yes	complemented
54	C₂²×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic, complemented
55	C₂²×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic, complemented
56	C₂²×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic, complemented
57	C₂²×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic, complemented
58	C₂²×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic, complemented
59	C₂²×C₄²×C₂₃	C₂²	1	1	yes	characteristic, complemented
60	C₂₃×#396	C₂²	1	8	yes	complemented
61	C₂₃×#394	C₂²	1	8	yes	complemented
62	C₂₃×#394	C₂²	1	8	yes	complemented
63	C₂₃×#392	C₂²	1	8	yes	complemented
64	C₂₃×#390	C₂²	1	8	yes	complemented
65	C₂₃×#388	C₂²	1	8	yes	complemented
66	C₂₃×#386	C₂²	1	8	yes	complemented
67	C₂₃×#386	C₂²	1	8	yes	complemented
68	C₂₃×#385	C₂²	1	8	yes	complemented
69	C₂×C₂₃×#95	C₂²	1	1	yes	characteristic, complemented
70	C₂×C₂₃×#95	C₂²	1	1	yes	characteristic, complemented
71	C₂×C₂₃×#95	C₂²	1	1	yes	characteristic, complemented
72	C₂×C₂₃×#95	C₂²	1	1	yes	characteristic, complemented
73	C₂⁵×C₂₃	—	2	4	no	—
74	C₂⁵×C₂₃	—	2	4	no	—
75	C₂⁵×C₂₃	—	2	4	no	—
76	C₂⁵×C₂₃	—	2	4	no	—
77	C₂⁵×C₂₃	—	2	4	no	—
78	C₂⁵×C₂₃	—	4	2	no	—
79	C₂⁵×C₂₃	—	4	2	no	—
80	C₂⁵×C₂₃	C₂³	1	1	yes	characteristic
81	C₂⁵×C₂₃	C₂³	1	1	yes	characteristic
82	C₂⁵×C₂₃	C₂³	1	1	yes	characteristic
83	C₂⁵×C₂₃	C₂³	1	1	yes	characteristic
84	C₂⁵×C₂₃	C₂³	1	4	yes	—
85	C₂⁵×C₂₃	C₂³	1	1	yes	characteristic
86	C₂²×D₄×C₂₃	—	2	4	no	—
87	C₂²×D₄×C₂₃	—	2	4	no	—
88	C₂²×D₄×C₂₃	—	2	4	no	—
89	C₂²×D₄×C₂₃	—	2	4	no	—
90	C₂²×D₄×C₂₃	—	2	4	no	—
91	C₂²×D₄×C₂₃	—	2	4	no	—
92	C₂²×D₄×C₂₃	—	2	4	no	—
93	C₂²×D₄×C₂₃	—	2	4	no	—
94	C₂²×D₄×C₂₃	—	2	4	no	—
95	C₂²×D₄×C₂₃	—	2	4	no	—
96	C₂²×D₄×C₂₃	—	2	4	no	—
97	C₂²×D₄×C₂₃	—	2	4	no	—
98	C₂²×D₄×C₂₃	—	2	4	no	—
99	C₂²×D₄×C₂₃	—	2	4	no	—
100	C₂²×D₄×C₂₃	—	2	4	no	—
101	C₂²×D₄×C₂₃	—	4	2	no	—
102	C₂²×D₄×C₂₃	—	4	2	no	—
103	C₂²×D₄×C₂₃	—	4	2	no	—
104	C₂²×D₄×C₂₃	—	4	2	no	—
105	C₂²×D₄×C₂₃	—	4	2	no	—
106	C₂²×D₄×C₂₃	D₄	1	8	yes	complemented
107	C₂²×D₄×C₂₃	C₂³	1	4	yes	—
108	C₂²×D₄×C₂₃	C₂³	1	4	yes	—
109	C₂²×D₄×C₂₃	C₂³	1	4	yes	—
110	C₂²×D₄×C₂₃	C₂³	1	4	yes	—
111	C₂²×D₄×C₂₃	C₂³	1	4	yes	—
112	C₂²×D₄×C₂₃	C₂³	1	4	yes	—
113	C₂²×D₄×C₂₃	C₂³	1	4	yes	complemented
114	C₂³×C₄×C₂₃	—	2	4	no	—
115	C₂³×C₄×C₂₃	—	2	4	no	—
116	C₂³×C₄×C₂₃	—	2	4	no	—
117	C₂³×C₄×C₂₃	—	2	4	no	—
118	C₂³×C₄×C₂₃	—	2	4	no	—
119	C₂³×C₄×C₂₃	—	2	4	no	—
120	C₂³×C₄×C₂₃	—	4	2	no	—
121	C₂³×C₄×C₂₃	—	4	2	no	—
122	C₂³×C₄×C₂₃	—	4	2	no	—
123	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
124	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
125	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
126	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
127	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
128	C₂³×C₄×C₂₃	C₂³	1	4	yes	—
129	C₂³×C₄×C₂₃	C₂³	1	4	yes	—
130	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
131	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
132	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
133	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
134	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
135	C₂³×C₄×C₂₃	C₂³	1	4	yes	complemented
136	C₂₃×#121	—	2	32	no	—
137	C₂₃×#121	—	2	32	no	—
138	C₂₃×#120	—	2	32	no	—
139	C₂₃×#120	—	2	32	no	—
140	C₄×D₄×C₂₃	—	2	32	no	—
141	C₂×C₄⋊C₄×C₂₃	—	2	4	no	—
142	C₂×C₄⋊C₄×C₂₃	—	2	4	no	—
143	C₂×C₄⋊C₄×C₂₃	—	2	4	no	—
144	C₂×C₄⋊C₄×C₂₃	—	4	2	no	—
145	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	complemented
146	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	complemented
147	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	complemented
148	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	complemented
149	C₂×C₂²⋊C₄×C₂₃	—	2	4	no	—
150	C₂×C₂²⋊C₄×C₂₃	—	2	4	no	—
151	C₂×C₂²⋊C₄×C₂₃	—	2	4	no	—
152	C₂×C₂²⋊C₄×C₂₃	—	2	4	no	—
153	C₂×C₂²⋊C₄×C₂₃	—	2	4	no	—
154	C₂×C₂²⋊C₄×C₂₃	—	2	4	no	—
155	C₂×C₂²⋊C₄×C₂₃	—	2	4	no	—
156	C₂×C₂²⋊C₄×C₂₃	—	2	4	no	—
157	C₂×C₂²⋊C₄×C₂₃	—	2	4	no	—
158	C₂×C₂²⋊C₄×C₂₃	—	2	4	no	—
159	C₂×C₂²⋊C₄×C₂₃	—	2	4	no	—
160	C₂×C₂²⋊C₄×C₂₃	—	2	4	no	—
161	C₂×C₂²⋊C₄×C₂₃	—	2	32	no	—
162	C₂×C₂²⋊C₄×C₂₃	—	4	2	no	—
163	C₂×C₂²⋊C₄×C₂₃	D₄	1	8	yes	complemented
164	C₂×C₂²⋊C₄×C₂₃	D₄	1	8	yes	complemented
165	C₂×C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
166	C₂×C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
167	C₂×C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
168	C₂×C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
169	C₂×C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
170	C₂×C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
171	C₂×C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
172	C₂×C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
173	C₂×C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
174	C₂×C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
175	C₂×C₂²⋊C₄×C₂₃	C₂³	1	4	yes	complemented
176	C₂×C₂²⋊C₄×C₂₃	C₂³	1	4	yes	complemented
177	C₂×C₂²⋊C₄×C₂₃	C₂³	1	4	yes	complemented
178	C₂×C₂²⋊C₄×C₂₃	C₂³	1	4	yes	complemented
179	C₂×C₂²⋊C₄×C₂₃	C₂³	1	4	yes	complemented
180	C₂×C₄²×C₂₃	—	2	4	no	—
181	C₂×C₄²×C₂₃	C₂³	1	4	yes	complemented
182	C₂₃×#95	C₂³	1	4	yes	complemented
183	C₂₃×#95	C₂³	1	4	yes	complemented
184	C₂₃×#95	C₂³	1	4	yes	complemented
185	C₂₃×#95	C₂³	1	4	yes	complemented
186	C₂⁴×C₂₃	—	2	2	no	—
187	C₂⁴×C₂₃	—	2	2	no	—
188	C₂⁴×C₂₃	—	2	2	no	—
189	C₂⁴×C₂₃	—	2	2	no	—
190	C₂⁴×C₂₃	—	2	32	no	—
191	C₂⁴×C₂₃	—	2	8	no	—
192	C₂⁴×C₂₃	—	2	2	no	—
193	C₂⁴×C₂₃	—	2	2	no	—
194	C₂⁴×C₂₃	—	2	2	no	—
195	C₂⁴×C₂₃	—	2	2	no	—
196	C₂⁴×C₂₃	—	2	2	no	—
197	C₂⁴×C₂₃	—	2	2	no	—
198	C₂⁴×C₂₃	—	2	2	no	—
199	C₂⁴×C₂₃	—	2	2	no	—
200	C₂⁴×C₂₃	—	2	2	no	—
201	C₂⁴×C₂₃	—	2	8	no	—
202	C₂⁴×C₂₃	—	2	8	no	—
203	C₂⁴×C₂₃	—	2	2	no	—
204	C₂⁴×C₂₃	—	2	2	no	—
205	C₂⁴×C₂₃	—	2	2	no	—
206	C₂⁴×C₂₃	—	2	2	no	—
207	C₂⁴×C₂₃	—	2	2	no	—
208	C₂⁴×C₂₃	—	2	2	no	—
209	C₂⁴×C₂₃	—	2	2	no	—
210	C₂⁴×C₂₃	—	2	2	no	—
211	C₂⁴×C₂₃	—	2	2	no	—
212	C₂⁴×C₂₃	—	2	2	no	—
213	C₂⁴×C₂₃	—	2	2	no	—
214	C₂⁴×C₂₃	—	2	8	no	—
215	C₂⁴×C₂₃	—	2	8	no	—
216	C₂⁴×C₂₃	—	2	2	no	—
217	C₂⁴×C₂₃	—	2	2	no	—
218	C₂⁴×C₂₃	—	2	2	no	—
219	C₂⁴×C₂₃	—	2	2	no	—
220	C₂⁴×C₂₃	—	2	2	no	—
221	C₂⁴×C₂₃	—	4	4	no	—
222	C₂⁴×C₂₃	—	4	4	no	—
223	C₂⁴×C₂₃	—	4	16	no	—
224	C₂⁴×C₂₃	—	4	16	no	—
225	C₂⁴×C₂₃	—	4	16	no	—
226	C₂⁴×C₂₃	—	4	16	no	—
227	C₂⁴×C₂₃	—	4	16	no	—
228	C₂⁴×C₂₃	—	4	16	no	—
229	C₂⁴×C₂₃	C₂×D₄	1	4	yes	—
230	C₂⁴×C₂₃	C₂×D₄	1	4	yes	—
231	C₂⁴×C₂₃	C₂×D₄	1	4	yes	—
232	C₂⁴×C₂₃	C₂×D₄	1	4	yes	—
233	C₂⁴×C₂₃	#41	1	4	yes	—
234	C₂⁴×C₂₃	#41	1	4	yes	—
235	C₂⁴×C₂₃	C₂⁴	1	2	yes	—
236	C₂⁴×C₂₃	C₂⁴	1	2	yes	—
237	C₂⁴×C₂₃	C₂⁴	1	2	yes	—
238	C₂⁴×C₂₃	C₂⁴	1	2	yes	—
239	C₂⁴×C₂₃	C₂⁴	1	2	yes	—
240	C₂⁴×C₂₃	C₂⁴	1	1	yes	characteristic
241	C₂×D₄×C₂₃	—	2	32	no	—
242	C₂×D₄×C₂₃	—	2	8	no	—
243	C₂×D₄×C₂₃	—	2	8	no	—
244	C₂×D₄×C₂₃	—	2	8	no	—
245	C₂×D₄×C₂₃	—	2	8	no	—
246	C₂×D₄×C₂₃	—	2	8	no	—
247	C₂×D₄×C₂₃	—	2	8	no	—
248	C₂×D₄×C₂₃	—	2	8	no	—
249	C₂×D₄×C₂₃	—	2	8	no	—
250	C₂×D₄×C₂₃	—	2	8	no	—
251	C₂×D₄×C₂₃	—	2	8	no	—
252	C₂×D₄×C₂₃	—	2	8	no	—
253	C₂×D₄×C₂₃	—	2	8	no	—
254	C₂×D₄×C₂₃	—	2	8	no	—
255	C₂×D₄×C₂₃	—	2	8	no	—
256	C₂×D₄×C₂₃	—	2	8	no	—
257	C₂×D₄×C₂₃	—	4	4	no	—
258	C₂×D₄×C₂₃	—	4	4	no	—
259	C₂×D₄×C₂₃	—	4	4	no	—
260	C₂×D₄×C₂₃	—	4	4	no	—
261	C₂×D₄×C₂₃	—	4	4	no	—
262	C₂×D₄×C₂₃	—	4	16	no	—
263	C₂×D₄×C₂₃	—	4	16	no	—
264	C₂×D₄×C₂₃	—	4	16	no	—
265	C₂×D₄×C₂₃	—	4	16	no	—
266	C₂×D₄×C₂₃	—	4	16	no	—
267	C₂×D₄×C₂₃	—	4	16	no	—
268	C₂×D₄×C₂₃	C₂×D₄	1	16	yes	complemented
269	C₂²×C₄×C₂₃	—	2	2	no	—
270	C₂²×C₄×C₂₃	—	2	2	no	—
271	C₂²×C₄×C₂₃	—	2	2	no	—
272	C₂²×C₄×C₂₃	—	2	2	no	—
273	C₂²×C₄×C₂₃	—	2	2	no	—
274	C₂²×C₄×C₂₃	—	2	2	no	—
275	C₂²×C₄×C₂₃	—	2	2	no	—
276	C₂²×C₄×C₂₃	—	2	2	no	—
277	C₂²×C₄×C₂₃	—	2	2	no	—
278	C₂²×C₄×C₂₃	—	2	2	no	—
279	C₂²×C₄×C₂₃	—	2	2	no	—
280	C₂²×C₄×C₂₃	—	2	2	no	—
281	C₂²×C₄×C₂₃	—	2	2	no	—
282	C₂²×C₄×C₂₃	—	2	2	no	—
283	C₂²×C₄×C₂₃	—	2	2	no	—
284	C₂²×C₄×C₂₃	—	2	2	no	—
285	C₂²×C₄×C₂₃	—	2	2	no	—
286	C₂²×C₄×C₂₃	—	2	2	no	—
287	C₂²×C₄×C₂₃	—	2	2	no	—
288	C₂²×C₄×C₂₃	—	2	8	no	—
289	C₂²×C₄×C₂₃	—	2	8	no	—
290	C₂²×C₄×C₂₃	—	2	2	no	—
291	C₂²×C₄×C₂₃	—	2	2	no	—
292	C₂²×C₄×C₂₃	—	2	2	no	—
293	C₂²×C₄×C₂₃	—	2	2	no	—
294	C₂²×C₄×C₂₃	—	2	2	no	—
295	C₂²×C₄×C₂₃	—	2	2	no	—
296	C₂²×C₄×C₂₃	—	2	8	no	—
297	C₂²×C₄×C₂₃	—	2	8	no	—
298	C₂²×C₄×C₂₃	—	2	8	no	—
299	C₂²×C₄×C₂₃	—	2	8	no	—
300	C₂²×C₄×C₂₃	—	4	4	no	—
301	C₂²×C₄×C₂₃	—	4	4	no	—
302	C₂²×C₄×C₂₃	—	4	4	no	—
303	C₂²×C₄×C₂₃	—	4	16	no	—
304	C₂²×C₄×C₂₃	—	4	16	no	—
305	C₂²×C₄×C₂₃	—	4	16	no	—
306	C₂²×C₄×C₂₃	C₂×D₄	1	4	yes	—
307	C₂²×C₄×C₂₃	C₂×D₄	1	4	yes	—
308	C₂²×C₄×C₂₃	C₂×D₄	1	4	yes	—
309	C₂²×C₄×C₂₃	C₂×D₄	1	4	yes	—
310	C₂²×C₄×C₂₃	C₂×D₄	1	4	yes	—
311	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
312	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
313	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
314	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
315	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
316	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
317	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
318	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
319	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
320	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
321	C₄⋊C₄×C₂₃	—	2	8	no	—
322	C₄⋊C₄×C₂₃	—	2	8	no	—
323	C₄⋊C₄×C₂₃	—	2	8	no	—
324	C₄⋊C₄×C₂₃	—	4	4	no	—
325	C₂²⋊C₄×C₂₃	—	2	8	no	—
326	C₂²⋊C₄×C₂₃	—	2	8	no	—
327	C₂²⋊C₄×C₂₃	—	2	8	no	—
328	C₂²⋊C₄×C₂₃	—	2	8	no	—
329	C₂²⋊C₄×C₂₃	—	2	8	no	—
330	C₂²⋊C₄×C₂₃	—	2	8	no	—
331	C₂²⋊C₄×C₂₃	—	2	8	no	—
332	C₂²⋊C₄×C₂₃	—	2	8	no	—
333	C₂²⋊C₄×C₂₃	—	2	8	no	—
334	C₂²⋊C₄×C₂₃	—	2	8	no	—
335	C₂²⋊C₄×C₂₃	—	2	8	no	—
336	C₂²⋊C₄×C₂₃	—	2	8	no	—
337	C₂²⋊C₄×C₂₃	—	4	4	no	—
338	C₂²⋊C₄×C₂₃	C₂×D₄	1	16	yes	complemented
339	C₂²⋊C₄×C₂₃	C₂×D₄	1	16	yes	complemented
340	C₄²×C₂₃	—	2	8	no	—
341	C₂×#2424	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
342	C₂³×C₂₃	—	2	8	no	—
343	C₂³×C₂₃	—	2	8	no	—
344	C₂³×C₂₃	—	2	8	no	—
345	C₂³×C₂₃	—	2	8	no	—
346	C₂³×C₂₃	—	2	8	no	—
347	C₂³×C₂₃	—	2	8	no	—
348	C₂³×C₂₃	—	2	2	no	—
349	C₂³×C₂₃	—	2	2	no	—
350	C₂³×C₂₃	—	2	2	no	—
351	C₂³×C₂₃	—	2	2	no	—
352	C₂³×C₂₃	—	2	32	no	—
353	C₂³×C₂₃	—	2	8	no	—
354	C₂³×C₂₃	—	2	8	no	—
355	C₂³×C₂₃	—	2	8	no	—
356	C₂³×C₂₃	—	2	8	no	—
357	C₂³×C₂₃	—	2	8	no	—
358	C₂³×C₂₃	—	2	8	no	—
359	C₂³×C₂₃	—	2	8	no	—
360	C₂³×C₂₃	—	2	8	no	—
361	C₂³×C₂₃	—	2	8	no	—
362	C₂³×C₂₃	—	2	2	no	—
363	C₂³×C₂₃	—	2	2	no	—
364	C₂³×C₂₃	—	2	2	no	—
365	C₂³×C₂₃	—	2	2	no	—
366	C₂³×C₂₃	—	2	2	no	—
367	C₂³×C₂₃	—	2	2	no	—
368	C₂³×C₂₃	—	2	2	no	—
369	C₂³×C₂₃	—	2	2	no	—
370	C₂³×C₂₃	—	2	2	no	—
371	C₂³×C₂₃	—	2	2	no	—
372	C₂³×C₂₃	—	2	2	no	—
373	C₂³×C₂₃	—	2	2	no	—
374	C₂³×C₂₃	—	2	2	no	—
375	C₂³×C₂₃	—	2	2	no	—
376	C₂³×C₂₃	—	2	2	no	—
377	C₂³×C₂₃	—	2	2	no	—
378	C₂³×C₂₃	—	2	2	no	—
379	C₂³×C₂₃	—	2	2	no	—
380	C₂³×C₂₃	—	2	2	no	—
381	C₂³×C₂₃	—	2	2	no	—
382	C₂³×C₂₃	—	2	2	no	—
383	C₂³×C₂₃	—	2	2	no	—
384	C₂³×C₂₃	—	2	2	no	—
385	C₂³×C₂₃	—	2	2	no	—
386	C₂³×C₂₃	—	2	2	no	—
387	C₂³×C₂₃	—	4	16	no	—
388	C₂³×C₂₃	—	4	16	no	—
389	C₂³×C₂₃	—	4	16	no	—
390	C₂³×C₂₃	—	4	16	no	—
391	C₂³×C₂₃	—	4	128	no	—
392	C₂³×C₂₃	—	4	16	no	—
393	C₂³×C₂₃	—	4	4	no	—
394	C₂³×C₂₃	—	4	4	no	—
395	C₂³×C₂₃	—	4	16	no	—
396	C₂³×C₂₃	—	4	4	no	—
397	C₂³×C₂₃	—	4	4	no	—
398	C₂³×C₂₃	—	4	4	no	—
399	C₂³×C₂₃	—	4	4	no	—
400	C₂³×C₂₃	—	4	4	no	—
401	C₂³×C₂₃	—	4	4	no	—
402	C₂³×C₂₃	—	4	4	no	—
403	C₂³×C₂₃	—	4	4	no	—
404	C₂³×C₂₃	—	4	4	no	—
405	C₂³×C₂₃	—	4	4	no	—
406	C₂³×C₂₃	—	4	4	no	—
407	C₂³×C₂₃	—	4	4	no	—
408	C₂³×C₂₃	—	4	4	no	—
409	C₂³×C₂₃	—	4	4	no	—
410	C₂³×C₂₃	—	4	4	no	—
411	C₂³×C₂₃	—	4	4	no	—
412	C₂³×C₂₃	—	4	4	no	—
413	C₂³×C₂₃	#121	1	16	yes	complemented
414	C₂³×C₂₃	C₂²×D₄	1	4	yes	—
415	C₂³×C₂₃	C₂²×D₄	1	4	yes	—
416	C₂³×C₂₃	C₂²×D₄	1	4	yes	—
417	C₂³×C₂₃	C₂²×D₄	1	4	yes	—
418	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
419	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
420	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
421	C₂³×C₂₃	C₂×#41	1	4	yes	—
422	C₂³×C₂₃	C₂×#41	1	4	yes	—
423	C₂³×C₂₃	C₂×#41	1	2	yes	—
424	C₂³×C₂₃	C₂×#41	1	2	yes	—
425	C₂³×C₂₃	H(5,𝔽₂)	1	2	yes	—
426	C₂³×C₂₃	H(5,𝔽₂)	1	2	yes	—
427	C₂³×C₂₃	C₂⁵	1	1	yes	characteristic
428	D₄×C₂₃	—	2	32	no	—
429	D₄×C₂₃	—	4	16	no	—
430	D₄×C₂₃	—	4	16	no	—
431	D₄×C₂₃	—	4	16	no	—
432	D₄×C₂₃	—	4	16	no	—
433	D₄×C₂₃	—	4	16	no	—
434	D₄×C₂₃	—	4	16	no	—
435	C₂×C₄×C₂₃	—	2	8	no	—
436	C₂×C₄×C₂₃	—	2	8	no	—
437	C₂×C₄×C₂₃	—	2	8	no	—
438	C₂×C₄×C₂₃	—	2	8	no	—
439	C₂×C₄×C₂₃	—	2	8	no	—
440	C₂×C₄×C₂₃	—	2	2	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	2	no	—
452	C₂×C₄×C₂₃	—	2	2	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	2	no	—
463	C₂×C₄×C₂₃	—	2	2	no	—
464	C₂×C₄×C₂₃	—	2	2	no	—
465	C₂×C₄×C₂₃	—	4	16	no	—
466	C₂×C₄×C₂₃	—	4	16	no	—
467	C₂×C₄×C₂₃	—	4	16	no	—
468	C₂×C₄×C₂₃	—	4	4	no	—
469	C₂×C₄×C₂₃	—	4	4	no	—
470	C₂×C₄×C₂₃	—	4	4	no	—
471	C₂×C₄×C₂₃	—	4	4	no	—
472	C₂×C₄×C₂₃	—	4	4	no	—
473	C₂×C₄×C₂₃	C₂²×D₄	1	4	yes	—
474	C₂×C₄×C₂₃	C₂²×D₄	1	4	yes	—
475	C₂×C₄×C₂₃	C₂²×D₄	1	4	yes	—
476	C₂×C₄×C₂₃	C₂²×D₄	1	4	yes	—
477	C₂×C₄×C₂₃	C₂²×D₄	1	4	yes	—
478	C₂²×#121	C₂×C₂₃	1	1	yes	characteristic, complemented
479	C₂²×#121	C₂×C₂₃	1	1	yes	characteristic, complemented
480	C₂²×#120	C₂×C₂₃	1	1	yes	characteristic, complemented
481	C₂²×#120	C₂×C₂₃	1	1	yes	characteristic, complemented
482	C₂²×C₄×D₄	C₂×C₂₃	1	1	yes	characteristic, complemented
483	C₂³×C₂²⋊C₄	C₂×C₂₃	1	1	yes	characteristic, complemented
484	#2424	C₂×C₂₃	1	16	yes	direct product factor
485	C₂×#396	C₂×C₂₃	1	1	yes	characteristic, complemented
486	C₂×#394	C₂×C₂₃	1	1	yes	characteristic, complemented
487	C₂×#394	C₂×C₂₃	1	1	yes	characteristic, complemented
488	C₂×#392	C₂×C₂₃	1	1	yes	characteristic, complemented
489	C₂×#390	C₂×C₂₃	1	1	yes	characteristic, complemented
490	C₂×#388	C₂×C₂₃	1	1	yes	characteristic, complemented
491	C₂×#386	C₂×C₂₃	1	1	yes	characteristic, complemented
492	C₂×#386	C₂×C₂₃	1	1	yes	characteristic, complemented
493	C₂×#385	C₂×C₂₃	1	1	yes	characteristic, complemented
494	C₂²×C₂₃	—	2	4	no	—
495	C₂²×C₂₃	—	2	32	no	—
496	C₂²×C₂₃	—	2	4	no	—
497	C₂²×C₂₃	—	2	4	no	—
498	C₂²×C₂₃	—	2	4	no	—
499	C₂²×C₂₃	—	2	4	no	—
500	C₂²×C₂₃	—	2	4	no	—
501	C₂²×C₂₃	—	2	4	no	—
502	C₂²×C₂₃	—	2	4	no	—
503	C₂²×C₂₃	—	2	4	no	—
504	C₂²×C₂₃	—	2	4	no	—
505	C₂²×C₂₃	—	2	4	no	—
506	C₂²×C₂₃	—	2	4	no	—
507	C₂²×C₂₃	—	2	4	no	—
508	C₂²×C₂₃	—	2	4	no	—
509	C₂²×C₂₃	—	2	4	no	—
510	C₂²×C₂₃	—	4	64	no	—
511	C₂²×C₂₃	—	4	2	no	—
512	C₂²×C₂₃	—	4	2	no	—
513	C₂²×C₂₃	—	4	2	no	—
514	C₂²×C₂₃	—	4	16	no	—
515	C₂²×C₂₃	—	4	16	no	—
516	C₂²×C₂₃	—	4	16	no	—
517	C₂²×C₂₃	—	4	2	no	—
518	C₂²×C₂₃	—	4	2	no	—
519	C₂²×C₂₃	—	4	2	no	—
520	C₂²×C₂₃	—	4	2	no	—
521	C₂²×C₂₃	—	4	2	no	—
522	C₂²×C₂₃	—	4	2	no	—
523	C₂²×C₂₃	—	4	2	no	—
524	C₂²×C₂₃	—	4	2	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	2	no	—
530	C₂²×C₂₃	—	4	2	no	—
531	C₂²×C₂₃	—	4	2	no	—
532	C₂²×C₂₃	—	4	2	no	—
533	C₂²×C₂₃	—	8	8	no	—
534	C₂²×C₂₃	C₂×#121	1	4	yes	—
535	C₂²×C₂₃	C₂×#121	1	8	yes	complemented
536	C₂²×C₂₃	#525	1	4	yes	—
537	C₂²×C₂₃	#538	1	4	yes	—
538	C₂²×C₂₃	D₄²	1	4	yes	—
539	C₂²×C₂₃	D₄²	1	4	yes	—
540	C₂²×C₂₃	#546	1	4	yes	—
541	C₂²×C₂₃	#546	1	4	yes	—
542	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
543	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
544	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
545	C₂²×C₂₃	C₂²×#41	1	1	yes	characteristic
546	C₂²×C₂₃	C₂²×#41	1	1	yes	characteristic
547	C₂²×C₂₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
548	C₂²×C₂₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
549	C₄×C₂₃	—	2	4	no	—
550	C₄×C₂₃	—	2	4	no	—
551	C₄×C₂₃	—	2	4	no	—
552	C₄×C₂₃	—	2	4	no	—
553	C₄×C₂₃	—	2	4	no	—
554	C₄×C₂₃	—	4	2	no	—
555	C₄×C₂₃	—	4	2	no	—
556	C₄×C₂₃	—	4	2	no	—
557	C₄×C₂₃	—	4	2	no	—
558	C₄×C₂₃	—	4	2	no	—
559	C₂⁶	C₂²×C₂₃	1	1	yes	characteristic
560	C₂³×D₄	C₂²×C₂₃	1	1	yes	characteristic
561	C₂³×D₄	C₂²×C₂₃	1	1	yes	characteristic
562	C₂³×D₄	C₂²×C₂₃	1	1	yes	characteristic
563	C₂³×D₄	C₂²×C₂₃	1	1	yes	characteristic
564	C₂³×D₄	C₂²×C₂₃	1	1	yes	characteristic
565	C₂³×D₄	C₂²×C₂₃	1	1	yes	characteristic
566	C₂³×D₄	C₂²×C₂₃	1	1	yes	characteristic, complemented
567	C₂⁴×C₄	C₂²×C₂₃	1	1	yes	characteristic
568	C₂⁴×C₄	C₂²×C₂₃	1	1	yes	characteristic
569	C₂⁴×C₄	C₂²×C₂₃	1	1	yes	characteristic, complemented
570	C₂×#121	—	2	8	no	—
571	C₂×#121	—	2	8	no	—
572	C₂×#121	C₂²×C₂₃	1	8	yes	complemented
573	C₂×#121	C₂²×C₂₃	1	8	yes	complemented
574	C₂×#120	—	2	8	no	—
575	C₂×#120	—	2	8	no	—
576	C₂×#120	C₂²×C₂₃	1	8	yes	complemented
577	C₂×#120	C₂²×C₂₃	1	8	yes	complemented
578	C₂×C₄×D₄	—	2	8	no	—
579	C₂×C₄×D₄	C₂²×C₂₃	1	8	yes	complemented
580	C₂²×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic, complemented
581	C₂²×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic, complemented
582	C₂²×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic, complemented
583	C₂²×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic, complemented
584	C₂²×C₂²⋊C₄	—	2	8	no	—
585	C₂²×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
586	C₂²×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
587	C₂²×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
588	C₂²×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
589	C₂²×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
590	C₂²×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
591	C₂²×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
592	C₂²×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
593	C₂²×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
594	C₂²×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
595	C₂²×C₂²⋊C₄	C₂²×C₂₃	1	8	yes	complemented
596	C₂²×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic, complemented
597	C₂²×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic, complemented
598	C₂²×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic, complemented
599	C₂²×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic, complemented
600	C₂²×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic, complemented
601	C₂²×C₄²	C₂²×C₂₃	1	1	yes	characteristic, complemented
602	#396	C₂²×C₂₃	1	8	yes	complemented
603	#394	C₂²×C₂₃	1	8	yes	complemented
604	#394	C₂²×C₂₃	1	8	yes	complemented
605	#392	C₂²×C₂₃	1	8	yes	complemented
606	#390	C₂²×C₂₃	1	8	yes	complemented
607	#388	C₂²×C₂₃	1	8	yes	complemented
608	#386	C₂²×C₂₃	1	8	yes	complemented
609	#386	C₂²×C₂₃	1	8	yes	complemented
610	#385	C₂²×C₂₃	1	8	yes	complemented
611	C₂×#95	C₂²×C₂₃	1	1	yes	characteristic, complemented
612	C₂×#95	C₂²×C₂₃	1	1	yes	characteristic, complemented
613	C₂×#95	C₂²×C₂₃	1	1	yes	characteristic, complemented
614	C₂×#95	C₂²×C₂₃	1	1	yes	characteristic, complemented
615	C₂×C₂₃	—	2	8	no	—
616	C₂×C₂₃	—	4	4	no	—
617	C₂×C₂₃	—	4	4	no	—
618	C₂×C₂₃	—	4	4	no	—
619	C₂×C₂₃	—	8	2	no	—
620	C₂×C₂₃	#2424	1	8	yes	direct product factor
621	C₂×C₂₃	C₂²×#121	1	1	yes	characteristic
622	C₂×C₂₃	C₂×#525	1	1	yes	characteristic
623	C₂×C₂₃	C₂×#538	1	1	yes	characteristic
624	C₂×C₂₃	C₂×D₄²	1	1	yes	characteristic
625	C₂×C₂₃	C₂×D₄²	1	1	yes	characteristic
626	C₂×C₂₃	C₂×#546	1	1	yes	characteristic
627	C₂×C₂₃	C₂×#546	1	1	yes	characteristic
628	C₂⁵	—	2	4	no	—
629	C₂⁵	—	2	4	no	—
630	C₂⁵	—	2	4	no	—
631	C₂⁵	—	2	4	no	—
632	C₂⁵	—	2	4	no	—
633	C₂⁵	—	4	2	no	—
634	C₂⁵	—	4	2	no	—
635	C₂⁵	C₂³×C₂₃	1	1	yes	characteristic
636	C₂⁵	C₂³×C₂₃	1	1	yes	characteristic
637	C₂⁵	C₂³×C₂₃	1	1	yes	characteristic
638	C₂⁵	C₂³×C₂₃	1	1	yes	characteristic
639	C₂⁵	C₂³×C₂₃	1	4	yes	—
640	C₂⁵	C₂³×C₂₃	1	1	yes	characteristic
641	C₂²×D₄	—	2	4	no	—
642	C₂²×D₄	—	2	4	no	—
643	C₂²×D₄	—	2	4	no	—
644	C₂²×D₄	—	2	4	no	—
645	C₂²×D₄	—	2	4	no	—
646	C₂²×D₄	—	2	4	no	—
647	C₂²×D₄	—	2	4	no	—
648	C₂²×D₄	—	2	4	no	—
649	C₂²×D₄	—	2	4	no	—
650	C₂²×D₄	—	2	4	no	—
651	C₂²×D₄	—	2	4	no	—
652	C₂²×D₄	—	2	4	no	—
653	C₂²×D₄	—	2	4	no	—
654	C₂²×D₄	—	2	4	no	—
655	C₂²×D₄	—	2	4	no	—
656	C₂²×D₄	—	4	2	no	—
657	C₂²×D₄	—	4	2	no	—
658	C₂²×D₄	—	4	2	no	—
659	C₂²×D₄	—	4	2	no	—
660	C₂²×D₄	—	4	2	no	—
661	C₂²×D₄	D₄×C₂₃	1	8	yes	complemented
662	C₂²×D₄	C₂³×C₂₃	1	4	yes	—
663	C₂²×D₄	C₂³×C₂₃	1	4	yes	—
664	C₂²×D₄	C₂³×C₂₃	1	4	yes	—
665	C₂²×D₄	C₂³×C₂₃	1	4	yes	—
666	C₂²×D₄	C₂³×C₂₃	1	4	yes	—
667	C₂²×D₄	C₂³×C₂₃	1	4	yes	—
668	C₂²×D₄	C₂³×C₂₃	1	4	yes	complemented
669	C₂³×C₄	—	2	4	no	—
670	C₂³×C₄	—	2	4	no	—
671	C₂³×C₄	—	2	4	no	—
672	C₂³×C₄	—	2	4	no	—
673	C₂³×C₄	—	2	4	no	—
674	C₂³×C₄	—	2	4	no	—
675	C₂³×C₄	—	4	2	no	—
676	C₂³×C₄	—	4	2	no	—
677	C₂³×C₄	—	4	2	no	—
678	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
679	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
680	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
681	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
682	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
683	C₂³×C₄	C₂³×C₂₃	1	4	yes	—
684	C₂³×C₄	C₂³×C₂₃	1	4	yes	—
685	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
686	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
687	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
688	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
689	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
690	C₂³×C₄	C₂³×C₂₃	1	4	yes	complemented
691	#121	—	2	32	no	—
692	#121	—	2	32	no	—
693	#120	—	2	32	no	—
694	#120	—	2	32	no	—
695	C₄×D₄	—	2	32	no	—
696	C₂×C₄⋊C₄	—	2	4	no	—
697	C₂×C₄⋊C₄	—	2	4	no	—
698	C₂×C₄⋊C₄	—	2	4	no	—
699	C₂×C₄⋊C₄	—	4	2	no	—
700	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	complemented
701	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	complemented
702	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	complemented
703	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	complemented
704	C₂×C₂²⋊C₄	—	2	4	no	—
705	C₂×C₂²⋊C₄	—	2	4	no	—
706	C₂×C₂²⋊C₄	—	2	4	no	—
707	C₂×C₂²⋊C₄	—	2	4	no	—
708	C₂×C₂²⋊C₄	—	2	4	no	—
709	C₂×C₂²⋊C₄	—	2	4	no	—
710	C₂×C₂²⋊C₄	—	2	4	no	—
711	C₂×C₂²⋊C₄	—	2	4	no	—
712	C₂×C₂²⋊C₄	—	2	4	no	—
713	C₂×C₂²⋊C₄	—	2	4	no	—
714	C₂×C₂²⋊C₄	—	2	4	no	—
715	C₂×C₂²⋊C₄	—	2	4	no	—
716	C₂×C₂²⋊C₄	—	2	32	no	—
717	C₂×C₂²⋊C₄	—	4	2	no	—
718	C₂×C₂²⋊C₄	D₄×C₂₃	1	8	yes	complemented
719	C₂×C₂²⋊C₄	D₄×C₂₃	1	8	yes	complemented
720	C₂×C₂²⋊C₄	C₂³×C₂₃	1	4	yes	—
721	C₂×C₂²⋊C₄	C₂³×C₂₃	1	4	yes	—
722	C₂×C₂²⋊C₄	C₂³×C₂₃	1	4	yes	—
723	C₂×C₂²⋊C₄	C₂³×C₂₃	1	4	yes	—
724	C₂×C₂²⋊C₄	C₂³×C₂₃	1	4	yes	—
725	C₂×C₂²⋊C₄	C₂³×C₂₃	1	4	yes	—
726	C₂×C₂²⋊C₄	C₂³×C₂₃	1	4	yes	—
727	C₂×C₂²⋊C₄	C₂³×C₂₃	1	4	yes	—
728	C₂×C₂²⋊C₄	C₂³×C₂₃	1	4	yes	—
729	C₂×C₂²⋊C₄	C₂³×C₂₃	1	4	yes	—
730	C₂×C₂²⋊C₄	C₂³×C₂₃	1	4	yes	complemented
731	C₂×C₂²⋊C₄	C₂³×C₂₃	1	4	yes	complemented
732	C₂×C₂²⋊C₄	C₂³×C₂₃	1	4	yes	complemented
733	C₂×C₂²⋊C₄	C₂³×C₂₃	1	4	yes	complemented
734	C₂×C₂²⋊C₄	C₂³×C₂₃	1	4	yes	complemented
735	C₂×C₄²	—	2	4	no	—
736	C₂×C₄²	C₂³×C₂₃	1	4	yes	complemented
737	#95	C₂³×C₂₃	1	4	yes	complemented
738	#95	C₂³×C₂₃	1	4	yes	complemented
739	#95	C₂³×C₂₃	1	4	yes	complemented
740	#95	C₂³×C₂₃	1	4	yes	complemented
741	C₂₃	C₂×#2424	1	1	yes	characteristic, direct product factor, Sylow
742	C₂⁴	—	2	2	no	—
743	C₂⁴	—	2	2	no	—
744	C₂⁴	—	2	2	no	—
745	C₂⁴	—	2	2	no	—
746	C₂⁴	—	2	32	no	—
747	C₂⁴	—	2	8	no	—
748	C₂⁴	—	2	2	no	—
749	C₂⁴	—	2	2	no	—
750	C₂⁴	—	2	2	no	—
751	C₂⁴	—	2	2	no	—
752	C₂⁴	—	2	2	no	—
753	C₂⁴	—	2	2	no	—
754	C₂⁴	—	2	2	no	—
755	C₂⁴	—	2	2	no	—
756	C₂⁴	—	2	2	no	—
757	C₂⁴	—	2	8	no	—
758	C₂⁴	—	2	8	no	—
759	C₂⁴	—	2	2	no	—
760	C₂⁴	—	2	2	no	—
761	C₂⁴	—	2	2	no	—
762	C₂⁴	—	2	2	no	—
763	C₂⁴	—	2	2	no	—
764	C₂⁴	—	2	2	no	—
765	C₂⁴	—	2	2	no	—
766	C₂⁴	—	2	2	no	—
767	C₂⁴	—	2	2	no	—
768	C₂⁴	—	2	2	no	—
769	C₂⁴	—	2	2	no	—
770	C₂⁴	—	2	8	no	—
771	C₂⁴	—	2	8	no	—
772	C₂⁴	—	2	2	no	—
773	C₂⁴	—	2	2	no	—
774	C₂⁴	—	2	2	no	—
775	C₂⁴	—	2	2	no	—
776	C₂⁴	—	2	2	no	—
777	C₂⁴	—	4	4	no	—
778	C₂⁴	—	4	4	no	—
779	C₂⁴	—	4	16	no	—
780	C₂⁴	—	4	16	no	—
781	C₂⁴	—	4	16	no	—
782	C₂⁴	—	4	16	no	—
783	C₂⁴	—	4	16	no	—
784	C₂⁴	—	4	16	no	—
785	C₂⁴	C₂×D₄×C₂₃	1	4	yes	—
786	C₂⁴	C₂×D₄×C₂₃	1	4	yes	—
787	C₂⁴	C₂×D₄×C₂₃	1	4	yes	—
788	C₂⁴	C₂×D₄×C₂₃	1	4	yes	—
789	C₂⁴	#41×C₂₃	1	4	yes	—
790	C₂⁴	#41×C₂₃	1	4	yes	—
791	C₂⁴	C₂⁴×C₂₃	1	2	yes	—
792	C₂⁴	C₂⁴×C₂₃	1	2	yes	—
793	C₂⁴	C₂⁴×C₂₃	1	2	yes	—
794	C₂⁴	C₂⁴×C₂₃	1	2	yes	—
795	C₂⁴	C₂⁴×C₂₃	1	2	yes	—
796	C₂⁴	C₂⁴×C₂₃	1	1	yes	characteristic
797	C₂×D₄	—	2	32	no	—
798	C₂×D₄	—	2	8	no	—
799	C₂×D₄	—	2	8	no	—
800	C₂×D₄	—	2	8	no	—
801	C₂×D₄	—	2	8	no	—
802	C₂×D₄	—	2	8	no	—
803	C₂×D₄	—	2	8	no	—
804	C₂×D₄	—	2	8	no	—
805	C₂×D₄	—	2	8	no	—
806	C₂×D₄	—	2	8	no	—
807	C₂×D₄	—	2	8	no	—
808	C₂×D₄	—	2	8	no	—
809	C₂×D₄	—	2	8	no	—
810	C₂×D₄	—	2	8	no	—
811	C₂×D₄	—	2	8	no	—
812	C₂×D₄	—	2	8	no	—
813	C₂×D₄	—	4	4	no	—
814	C₂×D₄	—	4	4	no	—
815	C₂×D₄	—	4	4	no	—
816	C₂×D₄	—	4	4	no	—
817	C₂×D₄	—	4	4	no	—
818	C₂×D₄	—	4	16	no	—
819	C₂×D₄	—	4	16	no	—
820	C₂×D₄	—	4	16	no	—
821	C₂×D₄	—	4	16	no	—
822	C₂×D₄	—	4	16	no	—
823	C₂×D₄	—	4	16	no	—
824	C₂×D₄	C₂×D₄×C₂₃	1	16	yes	complemented
825	C₂²×C₄	—	2	2	no	—
826	C₂²×C₄	—	2	2	no	—
827	C₂²×C₄	—	2	2	no	—
828	C₂²×C₄	—	2	2	no	—
829	C₂²×C₄	—	2	2	no	—
830	C₂²×C₄	—	2	2	no	—
831	C₂²×C₄	—	2	2	no	—
832	C₂²×C₄	—	2	2	no	—
833	C₂²×C₄	—	2	2	no	—
834	C₂²×C₄	—	2	2	no	—
835	C₂²×C₄	—	2	2	no	—
836	C₂²×C₄	—	2	2	no	—
837	C₂²×C₄	—	2	2	no	—
838	C₂²×C₄	—	2	2	no	—
839	C₂²×C₄	—	2	2	no	—
840	C₂²×C₄	—	2	2	no	—
841	C₂²×C₄	—	2	2	no	—
842	C₂²×C₄	—	2	2	no	—
843	C₂²×C₄	—	2	2	no	—
844	C₂²×C₄	—	2	8	no	—
845	C₂²×C₄	—	2	8	no	—
846	C₂²×C₄	—	2	2	no	—
847	C₂²×C₄	—	2	2	no	—
848	C₂²×C₄	—	2	2	no	—
849	C₂²×C₄	—	2	2	no	—
850	C₂²×C₄	—	2	2	no	—
851	C₂²×C₄	—	2	2	no	—
852	C₂²×C₄	—	2	8	no	—
853	C₂²×C₄	—	2	8	no	—
854	C₂²×C₄	—	2	8	no	—
855	C₂²×C₄	—	2	8	no	—
856	C₂²×C₄	—	4	4	no	—
857	C₂²×C₄	—	4	4	no	—
858	C₂²×C₄	—	4	4	no	—
859	C₂²×C₄	—	4	16	no	—
860	C₂²×C₄	—	4	16	no	—
861	C₂²×C₄	—	4	16	no	—
862	C₂²×C₄	C₂×D₄×C₂₃	1	4	yes	—
863	C₂²×C₄	C₂×D₄×C₂₃	1	4	yes	—
864	C₂²×C₄	C₂×D₄×C₂₃	1	4	yes	—
865	C₂²×C₄	C₂×D₄×C₂₃	1	4	yes	—
866	C₂²×C₄	C₂×D₄×C₂₃	1	4	yes	—
867	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
868	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
869	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
870	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
871	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
872	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
873	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
874	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
875	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
876	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
877	C₄⋊C₄	—	2	8	no	—
878	C₄⋊C₄	—	2	8	no	—
879	C₄⋊C₄	—	2	8	no	—
880	C₄⋊C₄	—	4	4	no	—
881	C₂²⋊C₄	—	2	8	no	—
882	C₂²⋊C₄	—	2	8	no	—
883	C₂²⋊C₄	—	2	8	no	—
884	C₂²⋊C₄	—	2	8	no	—
885	C₂²⋊C₄	—	2	8	no	—
886	C₂²⋊C₄	—	2	8	no	—
887	C₂²⋊C₄	—	2	8	no	—
888	C₂²⋊C₄	—	2	8	no	—
889	C₂²⋊C₄	—	2	8	no	—
890	C₂²⋊C₄	—	2	8	no	—
891	C₂²⋊C₄	—	2	8	no	—
892	C₂²⋊C₄	—	2	8	no	—
893	C₂²⋊C₄	—	4	4	no	—
894	C₂²⋊C₄	C₂×D₄×C₂₃	1	16	yes	complemented
895	C₂²⋊C₄	C₂×D₄×C₂₃	1	16	yes	complemented
896	C₄²	—	2	8	no	—
897	C₂³	—	2	2	no	—
898	C₂³	—	2	2	no	—
899	C₂³	—	2	2	no	—
900	C₂³	—	2	2	no	—
901	C₂³	—	2	8	no	—
902	C₂³	—	2	8	no	—
903	C₂³	—	2	8	no	—
904	C₂³	—	2	8	no	—
905	C₂³	—	2	8	no	—
906	C₂³	—	2	8	no	—
907	C₂³	—	2	32	no	—
908	C₂³	—	2	2	no	—
909	C₂³	—	2	2	no	—
910	C₂³	—	2	2	no	—
911	C₂³	—	2	2	no	—
912	C₂³	—	2	2	no	—
913	C₂³	—	2	2	no	—
914	C₂³	—	2	2	no	—
915	C₂³	—	2	2	no	—
916	C₂³	—	2	2	no	—
917	C₂³	—	2	2	no	—
918	C₂³	—	2	2	no	—
919	C₂³	—	2	2	no	—
920	C₂³	—	2	2	no	—
921	C₂³	—	2	2	no	—
922	C₂³	—	2	2	no	—
923	C₂³	—	2	2	no	—
924	C₂³	—	2	2	no	—
925	C₂³	—	2	2	no	—
926	C₂³	—	2	8	no	—
927	C₂³	—	2	8	no	—
928	C₂³	—	2	8	no	—
929	C₂³	—	2	8	no	—
930	C₂³	—	2	8	no	—
931	C₂³	—	2	8	no	—
932	C₂³	—	2	8	no	—
933	C₂³	—	2	8	no	—
934	C₂³	—	2	8	no	—
935	C₂³	—	2	2	no	—
936	C₂³	—	2	2	no	—
937	C₂³	—	2	2	no	—
938	C₂³	—	2	2	no	—
939	C₂³	—	2	2	no	—
940	C₂³	—	2	2	no	—
941	C₂³	—	2	2	no	—
942	C₂³	—	4	16	no	—
943	C₂³	—	4	16	no	—
944	C₂³	—	4	16	no	—
945	C₂³	—	4	16	no	—
946	C₂³	—	4	128	no	—
947	C₂³	—	4	16	no	—
948	C₂³	—	4	4	no	—
949	C₂³	—	4	4	no	—
950	C₂³	—	4	16	no	—
951	C₂³	—	4	4	no	—
952	C₂³	—	4	4	no	—
953	C₂³	—	4	4	no	—
954	C₂³	—	4	4	no	—
955	C₂³	—	4	4	no	—
956	C₂³	—	4	4	no	—
957	C₂³	—	4	4	no	—
958	C₂³	—	4	4	no	—
959	C₂³	—	4	4	no	—
960	C₂³	—	4	4	no	—
961	C₂³	—	4	4	no	—
962	C₂³	—	4	4	no	—
963	C₂³	—	4	4	no	—
964	C₂³	—	4	4	no	—
965	C₂³	—	4	4	no	—
966	C₂³	—	4	4	no	—
967	C₂³	—	4	4	no	—
968	C₂³	C₂₃×#121	1	16	yes	complemented
969	C₂³	C₂²×D₄×C₂₃	1	4	yes	—
970	C₂³	C₂²×D₄×C₂₃	1	4	yes	—
971	C₂³	C₂²×D₄×C₂₃	1	4	yes	—
972	C₂³	C₂²×D₄×C₂₃	1	4	yes	—
973	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
974	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
975	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
976	C₂³	C₂×#41×C₂₃	1	4	yes	—
977	C₂³	C₂×#41×C₂₃	1	4	yes	—
978	C₂³	C₂×#41×C₂₃	1	2	yes	—
979	C₂³	C₂×#41×C₂₃	1	2	yes	—
980	C₂³	C₂₃×H(5,𝔽₂)	1	2	yes	—
981	C₂³	C₂₃×H(5,𝔽₂)	1	2	yes	—
982	C₂³	C₂⁵×C₂₃	1	1	yes	characteristic
983	D₄	—	2	32	no	—
984	D₄	—	4	16	no	—
985	D₄	—	4	16	no	—
986	D₄	—	4	16	no	—
987	D₄	—	4	16	no	—
988	D₄	—	4	16	no	—
989	D₄	—	4	16	no	—
990	C₂×C₄	—	2	2	no	—
991	C₂×C₄	—	2	2	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	8	no	—
1001	C₂×C₄	—	2	8	no	—
1002	C₂×C₄	—	2	8	no	—
1003	C₂×C₄	—	2	8	no	—
1004	C₂×C₄	—	2	8	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	2	no	—
1014	C₂×C₄	—	2	2	no	—
1015	C₂×C₄	—	2	2	no	—
1016	C₂×C₄	—	2	2	no	—
1017	C₂×C₄	—	2	2	no	—
1018	C₂×C₄	—	2	2	no	—
1019	C₂×C₄	—	2	2	no	—
1020	C₂×C₄	—	4	16	no	—
1021	C₂×C₄	—	4	16	no	—
1022	C₂×C₄	—	4	16	no	—
1023	C₂×C₄	—	4	4	no	—
1024	C₂×C₄	—	4	4	no	—
1025	C₂×C₄	—	4	4	no	—
1026	C₂×C₄	—	4	4	no	—
1027	C₂×C₄	—	4	4	no	—
1028	C₂×C₄	C₂²×D₄×C₂₃	1	4	yes	—
1029	C₂×C₄	C₂²×D₄×C₂₃	1	4	yes	—
1030	C₂×C₄	C₂²×D₄×C₂₃	1	4	yes	—
1031	C₂×C₄	C₂²×D₄×C₂₃	1	4	yes	—
1032	C₂×C₄	C₂²×D₄×C₂₃	1	4	yes	—
1033	C₂²	—	2	4	no	—
1034	C₂²	—	2	32	no	—
1035	C₂²	—	2	4	no	—
1036	C₂²	—	2	4	no	—
1037	C₂²	—	2	4	no	—
1038	C₂²	—	2	4	no	—
1039	C₂²	—	2	4	no	—
1040	C₂²	—	2	4	no	—
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	—	4	64	no	—
1050	C₂²	—	4	2	no	—
1051	C₂²	—	4	2	no	—
1052	C₂²	—	4	2	no	—
1053	C₂²	—	4	16	no	—
1054	C₂²	—	4	16	no	—
1055	C₂²	—	4	16	no	—
1056	C₂²	—	4	2	no	—
1057	C₂²	—	4	2	no	—
1058	C₂²	—	4	2	no	—
1059	C₂²	—	4	2	no	—
1060	C₂²	—	4	2	no	—
1061	C₂²	—	4	2	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	2	no	—
1068	C₂²	—	4	2	no	—
1069	C₂²	—	4	2	no	—
1070	C₂²	—	4	2	no	—
1071	C₂²	—	4	2	no	—
1072	C₂²	—	8	8	no	—
1073	C₂²	C₂×C₂₃×#121	1	4	yes	—
1074	C₂²	C₂×C₂₃×#121	1	8	yes	complemented
1075	C₂²	C₂₃×#525	1	4	yes	—
1076	C₂²	C₂₃×#538	1	4	yes	—
1077	C₂²	D₄²×C₂₃	1	4	yes	—
1078	C₂²	D₄²×C₂₃	1	4	yes	—
1079	C₂²	C₂₃×#546	1	4	yes	—
1080	C₂²	C₂₃×#546	1	4	yes	—
1081	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
1082	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
1083	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
1084	C₂²	C₂²×#41×C₂₃	1	1	yes	characteristic
1085	C₂²	C₂²×#41×C₂₃	1	1	yes	characteristic
1086	C₂²	C₂×C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
1087	C₂²	C₂×C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
1088	C₄	—	2	4	no	—
1089	C₄	—	2	4	no	—
1090	C₄	—	2	4	no	—
1091	C₄	—	2	4	no	—
1092	C₄	—	2	4	no	—
1093	C₄	—	4	2	no	—
1094	C₄	—	4	2	no	—
1095	C₄	—	4	2	no	—
1096	C₄	—	4	2	no	—
1097	C₄	—	4	2	no	—
1098	C₂	—	2	8	no	—
1099	C₂	—	4	4	no	—
1100	C₂	—	4	4	no	—
1101	C₂	—	4	4	no	—
1102	C₂	—	8	2	no	—
1103	C₂	C₂₃×#2424	1	8	yes	direct product factor
1104	C₂	C₂²×C₂₃×#121	1	1	yes	characteristic
1105	C₂	C₂×C₂₃×#525	1	1	yes	characteristic
1106	C₂	C₂×C₂₃×#538	1	1	yes	characteristic
1107	C₂	C₂×D₄²×C₂₃	1	1	yes	characteristic
1108	C₂	C₂×D₄²×C₂₃	1	1	yes	characteristic
1109	C₂	C₂×C₂₃×#546	1	1	yes	characteristic
1110	C₂	C₂×C₂₃×#546	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂⁴×C₂₃	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₂₃
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×C₂₃×#121	C₂	semidirect
2. C₂²×C₂₃×#121	C₂	semidirect
3. C₂²×C₂₃×#120	C₂	semidirect
4. C₂²×C₂₃×#120	C₂	semidirect
5. C₂²×C₄×D₄×C₂₃	C₂	semidirect
6. C₂³×C₂²⋊C₄×C₂₃	C₂	semidirect
7. C₂₃×#2424	C₂	direct (N × H)
8. C₂×C₂₃×#396	C₂	semidirect
9. C₂×C₂₃×#394	C₂	semidirect
10. C₂×C₂₃×#394	C₂	semidirect
11. C₂×C₂₃×#392	C₂	semidirect
12. C₂×C₂₃×#390	C₂	semidirect
13. C₂×C₂₃×#388	C₂	semidirect
14. C₂×C₂₃×#386	C₂	semidirect
15. C₂×C₂₃×#386	C₂	semidirect
16. C₂×C₂₃×#385	C₂	semidirect
24. C₂³×D₄×C₂₃	C₂²	semidirect
27. C₂⁴×C₄×C₂₃	C₂²	semidirect
30. C₂×C₂₃×#121	C₂²	semidirect
31. C₂×C₂₃×#121	C₂²	semidirect
34. C₂×C₂₃×#120	C₂²	semidirect
35. C₂×C₂₃×#120	C₂²	semidirect
37. C₂×C₄×D₄×C₂₃	C₂²	semidirect
38. C₂²×C₄⋊C₄×C₂₃	C₂²	semidirect
39. C₂²×C₄⋊C₄×C₂₃	C₂²	semidirect
40. C₂²×C₄⋊C₄×C₂₃	C₂²	semidirect
41. C₂²×C₄⋊C₄×C₂₃	C₂²	semidirect
53. C₂²×C₂²⋊C₄×C₂₃	C₂²	semidirect
54. C₂²×C₂²⋊C₄×C₂₃	C₂²	semidirect
55. C₂²×C₂²⋊C₄×C₂₃	C₂²	semidirect
56. C₂²×C₂²⋊C₄×C₂₃	C₂²	semidirect
57. C₂²×C₂²⋊C₄×C₂₃	C₂²	semidirect
58. C₂²×C₂²⋊C₄×C₂₃	C₂²	semidirect
59. C₂²×C₄²×C₂₃	C₂²	semidirect
60. C₂₃×#396	C₂²	semidirect
61. C₂₃×#394	C₂²	semidirect
62. C₂₃×#394	C₂²	semidirect
63. C₂₃×#392	C₂²	semidirect
64. C₂₃×#390	C₂²	semidirect
65. C₂₃×#388	C₂²	semidirect
66. C₂₃×#386	C₂²	semidirect
67. C₂₃×#386	C₂²	semidirect
68. C₂₃×#385	C₂²	semidirect
69. C₂×C₂₃×#95	C₂²	semidirect
70. C₂×C₂₃×#95	C₂²	semidirect
71. C₂×C₂₃×#95	C₂²	semidirect
72. C₂×C₂₃×#95	C₂²	semidirect
106. C₂²×D₄×C₂₃	D₄	semidirect
113. C₂²×D₄×C₂₃	C₂³	semidirect
135. C₂³×C₄×C₂₃	C₂³	semidirect
145. C₂×C₄⋊C₄×C₂₃	C₂³	semidirect
146. C₂×C₄⋊C₄×C₂₃	C₂³	semidirect
147. C₂×C₄⋊C₄×C₂₃	C₂³	semidirect
148. C₂×C₄⋊C₄×C₂₃	C₂³	semidirect
163. C₂×C₂²⋊C₄×C₂₃	D₄	semidirect
164. C₂×C₂²⋊C₄×C₂₃	D₄	semidirect
175. C₂×C₂²⋊C₄×C₂₃	C₂³	semidirect
176. C₂×C₂²⋊C₄×C₂₃	C₂³	semidirect
177. C₂×C₂²⋊C₄×C₂₃	C₂³	semidirect
178. C₂×C₂²⋊C₄×C₂₃	C₂³	semidirect
179. C₂×C₂²⋊C₄×C₂₃	C₂³	semidirect
181. C₂×C₄²×C₂₃	C₂³	semidirect
182. C₂₃×#95	C₂³	semidirect
183. C₂₃×#95	C₂³	semidirect
184. C₂₃×#95	C₂³	semidirect
185. C₂₃×#95	C₂³	semidirect
268. C₂×D₄×C₂₃	C₂×D₄	semidirect
338. C₂²⋊C₄×C₂₃	C₂×D₄	semidirect
339. C₂²⋊C₄×C₂₃	C₂×D₄	semidirect
341. C₂×#2424	C₂₃	direct (N × H)
413. C₂³×C₂₃	#121	semidirect
478. C₂²×#121	C₂×C₂₃	semidirect
479. C₂²×#121	C₂×C₂₃	semidirect
480. C₂²×#120	C₂×C₂₃	semidirect
481. C₂²×#120	C₂×C₂₃	semidirect
482. C₂²×C₄×D₄	C₂×C₂₃	semidirect
483. C₂³×C₂²⋊C₄	C₂×C₂₃	semidirect
484. #2424	C₂×C₂₃	direct (N × H)
485. C₂×#396	C₂×C₂₃	semidirect
486. C₂×#394	C₂×C₂₃	semidirect
487. C₂×#394	C₂×C₂₃	semidirect
488. C₂×#392	C₂×C₂₃	semidirect
489. C₂×#390	C₂×C₂₃	semidirect
490. C₂×#388	C₂×C₂₃	semidirect
491. C₂×#386	C₂×C₂₃	semidirect
492. C₂×#386	C₂×C₂₃	semidirect
493. C₂×#385	C₂×C₂₃	semidirect
535. C₂²×C₂₃	C₂×#121	semidirect
566. C₂³×D₄	C₂²×C₂₃	semidirect
569. C₂⁴×C₄	C₂²×C₂₃	semidirect
572. C₂×#121	C₂²×C₂₃	semidirect
573. C₂×#121	C₂²×C₂₃	semidirect
576. C₂×#120	C₂²×C₂₃	semidirect
577. C₂×#120	C₂²×C₂₃	semidirect
579. C₂×C₄×D₄	C₂²×C₂₃	semidirect
580. C₂²×C₄⋊C₄	C₂²×C₂₃	semidirect
581. C₂²×C₄⋊C₄	C₂²×C₂₃	semidirect
582. C₂²×C₄⋊C₄	C₂²×C₂₃	semidirect
583. C₂²×C₄⋊C₄	C₂²×C₂₃	semidirect
595. C₂²×C₂²⋊C₄	C₂²×C₂₃	semidirect
596. C₂²×C₂²⋊C₄	C₂²×C₂₃	semidirect
597. C₂²×C₂²⋊C₄	C₂²×C₂₃	semidirect
598. C₂²×C₂²⋊C₄	C₂²×C₂₃	semidirect
599. C₂²×C₂²⋊C₄	C₂²×C₂₃	semidirect
600. C₂²×C₂²⋊C₄	C₂²×C₂₃	semidirect
601. C₂²×C₄²	C₂²×C₂₃	semidirect
602. #396	C₂²×C₂₃	semidirect
603. #394	C₂²×C₂₃	semidirect
604. #394	C₂²×C₂₃	semidirect
605. #392	C₂²×C₂₃	semidirect
606. #390	C₂²×C₂₃	semidirect
607. #388	C₂²×C₂₃	semidirect
608. #386	C₂²×C₂₃	semidirect
609. #386	C₂²×C₂₃	semidirect
610. #385	C₂²×C₂₃	semidirect
611. C₂×#95	C₂²×C₂₃	semidirect
612. C₂×#95	C₂²×C₂₃	semidirect
613. C₂×#95	C₂²×C₂₃	semidirect
614. C₂×#95	C₂²×C₂₃	semidirect
620. C₂×C₂₃	#2424	direct (N × H)
661. C₂²×D₄	D₄×C₂₃	semidirect
668. C₂²×D₄	C₂³×C₂₃	semidirect
690. C₂³×C₄	C₂³×C₂₃	semidirect
700. C₂×C₄⋊C₄	C₂³×C₂₃	semidirect
701. C₂×C₄⋊C₄	C₂³×C₂₃	semidirect
702. C₂×C₄⋊C₄	C₂³×C₂₃	semidirect
703. C₂×C₄⋊C₄	C₂³×C₂₃	semidirect
718. C₂×C₂²⋊C₄	D₄×C₂₃	semidirect
719. C₂×C₂²⋊C₄	D₄×C₂₃	semidirect
730. C₂×C₂²⋊C₄	C₂³×C₂₃	semidirect
731. C₂×C₂²⋊C₄	C₂³×C₂₃	semidirect
732. C₂×C₂²⋊C₄	C₂³×C₂₃	semidirect
733. C₂×C₂²⋊C₄	C₂³×C₂₃	semidirect
734. C₂×C₂²⋊C₄	C₂³×C₂₃	semidirect
736. C₂×C₄²	C₂³×C₂₃	semidirect
737. #95	C₂³×C₂₃	semidirect
738. #95	C₂³×C₂₃	semidirect
739. #95	C₂³×C₂₃	semidirect
740. #95	C₂³×C₂₃	semidirect
741. C₂₃	C₂×#2424	direct (N × H)
824. C₂×D₄	C₂×D₄×C₂₃	semidirect
894. C₂²⋊C₄	C₂×D₄×C₂₃	semidirect
895. C₂²⋊C₄	C₂×D₄×C₂₃	semidirect
968. C₂³	C₂₃×#121	semidirect
1074. C₂²	C₂×C₂₃×#121	semidirect
1103. C₂	C₂₃×#2424	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₂₃×#121	2
C₂²×C₂₃×#120	2
C₂²×C₄×D₄×C₂₃	2
C₂³×C₂²⋊C₄×C₂₃	2
C₂₃×#2424	2
C₂×C₂₃×#396	2
C₂×C₂₃×#394	2
C₂×C₂₃×#392	2
C₂×C₂₃×#390	2
C₂×C₂₃×#388	2
C₂×C₂₃×#386	2
C₂×C₂₃×#385	2
C₂×#2424	23

Subgroups — C2×C23×#2424 #19182276

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₂₃×#2424 #19182276