Subgroups — C₂×C₂₃×#2321 #19181687

Order 5888.

5094 conjugacy classes of subgroups.

The subgroup lattice has 672 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₂₃×#120	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₄×D₄×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂³×C₂²⋊C₄×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₃×#2321	C₂	1	16	yes	maximal, direct product factor
5	C₂×C₂₃×#390	C₂	1	2	yes	maximal, complemented
6	C₂×C₂₃×#388	C₂	1	2	yes	maximal, complemented
7	C₂×C₂₃×#388	C₂	1	2	yes	maximal, complemented
8	C₂×C₂₃×#386	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₂₃×#386	C₂	1	2	yes	maximal, complemented
10	C₂×C₂₃×#385	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₂₃×#379	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₄×C₂²⋊C₄×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂⁶×C₂₃	C₂²	1	1	yes	characteristic
14	C₂³×D₄×C₂₃	C₂²	1	1	yes	characteristic
15	C₂³×D₄×C₂₃	C₂²	1	2	yes	—
16	C₂⁴×C₄×C₂₃	C₂²	1	1	yes	characteristic
17	C₂⁴×C₄×C₂₃	C₂²	1	1	yes	characteristic
18	C₂⁴×C₄×C₂₃	C₂²	1	1	yes	characteristic, complemented
19	C₂×C₂₃×#120	C₄	1	16	yes	complemented
20	C₂×C₂₃×#120	C₂²	1	8	yes	—
21	C₂×C₄×D₄×C₂₃	—	2	8	no	—
22	C₂×C₄×D₄×C₂₃	C₂²	1	8	yes	complemented
23	C₂²×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic, complemented
24	C₂²×C₄⋊C₄×C₂₃	C₂²	1	2	yes	complemented
25	C₂²×C₂²⋊C₄×C₂₃	—	2	8	no	—
26	C₂²×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
27	C₂²×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
28	C₂²×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	—
29	C₂²×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	—
30	C₂²×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	—
31	C₂²×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	—
32	C₂²×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
33	C₂²×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	—
34	C₂²×C₂²⋊C₄×C₂₃	C₂²	1	8	yes	complemented
35	C₂²×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic, complemented
36	C₂²×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	complemented
37	C₂²×C₄²×C₂₃	C₂²	1	1	yes	characteristic, complemented
38	C₂²×C₄²×C₂₃	C₂²	1	2	yes	complemented
39	C₂₃×#390	C₂²	1	16	yes	complemented
40	C₂₃×#388	C₂²	1	16	yes	complemented
41	C₂₃×#388	C₂²	1	16	yes	complemented
42	C₂₃×#386	C₂²	1	16	yes	complemented
43	C₂₃×#386	C₂²	1	8	yes	complemented
44	C₂₃×#385	C₂²	1	8	yes	complemented
45	C₂₃×#379	C₂²	1	8	yes	complemented
46	C₄×C₂²⋊C₄×C₂₃	C₂²	1	8	yes	complemented
47	C₂×C₂₃×#95	C₂²	1	2	yes	complemented
48	C₂×C₂₃×#95	C₂²	1	2	yes	complemented
49	C₂×C₂₃×#95	C₂²	1	2	yes	complemented
50	C₂⁵×C₂₃	—	2	4	no	—
51	C₂⁵×C₂₃	—	2	4	no	—
52	C₂⁵×C₂₃	—	4	4	no	—
53	C₂⁵×C₂₃	—	4	4	no	—
54	C₂⁵×C₂₃	C₂×C₄	1	8	yes	complemented
55	C₂⁵×C₂₃	C₂³	1	1	yes	characteristic
56	C₂⁵×C₂₃	C₂³	1	2	yes	—
57	C₂⁵×C₂₃	C₂³	1	1	yes	characteristic
58	C₂⁵×C₂₃	C₂³	1	4	yes	—
59	C₂²×D₄×C₂₃	—	2	4	no	—
60	C₂²×D₄×C₂₃	—	2	4	no	—
61	C₂²×D₄×C₂₃	—	4	4	no	—
62	C₂²×D₄×C₂₃	—	4	4	no	—
63	C₂²×D₄×C₂₃	C₂×C₄	1	8	yes	—
64	C₂²×D₄×C₂₃	C₂×C₄	1	16	yes	complemented
65	C₂²×D₄×C₂₃	C₂³	1	4	yes	—
66	C₂²×D₄×C₂₃	C₂³	1	8	yes	—
67	C₂³×C₄×C₂₃	—	2	4	no	—
68	C₂³×C₄×C₂₃	—	2	4	no	—
69	C₂³×C₄×C₂₃	—	4	4	no	—
70	C₂³×C₄×C₂₃	—	4	4	no	—
71	C₂³×C₄×C₂₃	—	4	4	no	—
72	C₂³×C₄×C₂₃	D₄	1	8	yes	complemented
73	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
74	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
75	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
76	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
77	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
78	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
79	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
80	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
81	C₂³×C₄×C₂₃	C₂³	1	4	yes	—
82	C₂³×C₄×C₂₃	C₂³	1	4	yes	—
83	C₂³×C₄×C₂₃	C₂³	1	4	yes	complemented
84	C₂₃×#120	C₂×C₄	1	64	yes	complemented
85	C₄×D₄×C₂₃	—	2	32	no	—
86	C₂×C₄⋊C₄×C₂₃	—	2	4	no	—
87	C₂×C₄⋊C₄×C₂₃	—	4	4	no	—
88	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	complemented
89	C₂×C₄⋊C₄×C₂₃	C₂³	1	8	yes	complemented
90	C₂×C₂²⋊C₄×C₂₃	—	2	4	no	—
91	C₂×C₂²⋊C₄×C₂₃	—	2	4	no	—
92	C₂×C₂²⋊C₄×C₂₃	—	2	8	no	—
93	C₂×C₂²⋊C₄×C₂₃	—	2	8	no	—
94	C₂×C₂²⋊C₄×C₂₃	—	2	4	no	—
95	C₂×C₂²⋊C₄×C₂₃	—	2	32	no	—
96	C₂×C₂²⋊C₄×C₂₃	—	4	4	no	—
97	C₂×C₂²⋊C₄×C₂₃	—	4	4	no	—
98	C₂×C₂²⋊C₄×C₂₃	—	4	4	no	—
99	C₂×C₂²⋊C₄×C₂₃	C₂×C₄	1	16	yes	complemented
100	C₂×C₂²⋊C₄×C₂₃	C₂×C₄	1	8	yes	complemented
101	C₂×C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
102	C₂×C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
103	C₂×C₂²⋊C₄×C₂₃	C₂³	1	8	yes	—
104	C₂×C₂²⋊C₄×C₂₃	C₂³	1	8	yes	—
105	C₂×C₂²⋊C₄×C₂₃	C₂³	1	8	yes	—
106	C₂×C₂²⋊C₄×C₂₃	C₂³	1	8	yes	—
107	C₂×C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
108	C₂×C₂²⋊C₄×C₂₃	C₂³	1	8	yes	—
109	C₂×C₂²⋊C₄×C₂₃	C₂³	1	4	yes	complemented
110	C₂×C₂²⋊C₄×C₂₃	C₂³	1	8	yes	complemented
111	C₂×C₄²×C₂₃	—	2	4	no	—
112	C₂×C₄²×C₂₃	—	4	4	no	—
113	C₂×C₄²×C₂₃	C₂³	1	4	yes	complemented
114	C₂×C₄²×C₂₃	C₂³	1	8	yes	complemented
115	C₂₃×#95	C₂³	1	8	yes	complemented
116	C₂₃×#95	C₂³	1	8	yes	complemented
117	C₂₃×#95	C₂³	1	8	yes	complemented
118	C₂⁴×C₂₃	—	2	4	no	—
119	C₂⁴×C₂₃	—	2	4	no	—
120	C₂⁴×C₂₃	—	2	32	no	—
121	C₂⁴×C₂₃	—	2	4	no	—
122	C₂⁴×C₂₃	—	2	8	no	—
123	C₂⁴×C₂₃	—	2	2	no	—
124	C₂⁴×C₂₃	—	2	2	no	—
125	C₂⁴×C₂₃	—	2	4	no	—
126	C₂⁴×C₂₃	—	2	8	no	—
127	C₂⁴×C₂₃	—	2	4	no	—
128	C₂⁴×C₂₃	—	2	4	no	—
129	C₂⁴×C₂₃	—	2	4	no	—
130	C₂⁴×C₂₃	—	2	4	no	—
131	C₂⁴×C₂₃	—	2	4	no	—
132	C₂⁴×C₂₃	—	2	4	no	—
133	C₂⁴×C₂₃	—	4	32	no	—
134	C₂⁴×C₂₃	—	4	8	no	—
135	C₂⁴×C₂₃	—	4	8	no	—
136	C₂⁴×C₂₃	—	4	16	no	—
137	C₂⁴×C₂₃	—	4	16	no	—
138	C₂⁴×C₂₃	—	4	32	no	—
139	C₂⁴×C₂₃	C₂²×C₄	1	8	yes	—
140	C₂⁴×C₂₃	C₂²×C₄	1	4	yes	—
141	C₂⁴×C₂₃	C₂²×C₄	1	4	yes	—
142	C₂⁴×C₂₃	C₂²×C₄	1	16	yes	complemented
143	C₂⁴×C₂₃	C₂×D₄	1	4	yes	—
144	C₂⁴×C₂₃	#41	1	4	yes	—
145	C₂⁴×C₂₃	C₂⁴	1	4	yes	—
146	C₂⁴×C₂₃	C₂⁴	1	2	yes	—
147	C₂⁴×C₂₃	C₂⁴	1	2	yes	—
148	C₂⁴×C₂₃	C₂⁴	1	1	yes	characteristic
149	C₂×D₄×C₂₃	—	2	32	no	—
150	C₂×D₄×C₂₃	—	2	8	no	—
151	C₂×D₄×C₂₃	—	2	8	no	—
152	C₂×D₄×C₂₃	—	4	32	no	—
153	C₂×D₄×C₂₃	—	4	8	no	—
154	C₂×D₄×C₂₃	—	4	8	no	—
155	C₂×D₄×C₂₃	C₂²×C₄	1	16	yes	—
156	C₂×D₄×C₂₃	C₂²×C₄	1	32	yes	complemented
157	C₂²×C₄×C₂₃	—	2	2	no	—
158	C₂²×C₄×C₂₃	—	2	2	no	—
159	C₂²×C₄×C₂₃	—	2	4	no	—
160	C₂²×C₄×C₂₃	—	2	4	no	—
161	C₂²×C₄×C₂₃	—	2	4	no	—
162	C₂²×C₄×C₂₃	—	2	4	no	—
163	C₂²×C₄×C₂₃	—	2	2	no	—
164	C₂²×C₄×C₂₃	—	2	8	no	—
165	C₂²×C₄×C₂₃	—	2	4	no	—
166	C₂²×C₄×C₂₃	—	2	2	no	—
167	C₂²×C₄×C₂₃	—	2	4	no	—
168	C₂²×C₄×C₂₃	—	2	4	no	—
169	C₂²×C₄×C₂₃	—	2	4	no	—
170	C₂²×C₄×C₂₃	—	2	4	no	—
171	C₂²×C₄×C₂₃	—	2	4	no	—
172	C₂²×C₄×C₂₃	—	2	4	no	—
173	C₂²×C₄×C₂₃	—	2	4	no	—
174	C₂²×C₄×C₂₃	—	2	8	no	—
175	C₂²×C₄×C₂₃	—	4	16	no	—
176	C₂²×C₄×C₂₃	—	4	8	no	—
177	C₂²×C₄×C₂₃	—	4	8	no	—
178	C₂²×C₄×C₂₃	—	4	8	no	—
179	C₂²×C₄×C₂₃	—	4	16	no	—
180	C₂²×C₄×C₂₃	—	4	16	no	—
181	C₂²×C₄×C₂₃	C₂²×C₄	1	4	yes	—
182	C₂²×C₄×C₂₃	C₂²×C₄	1	8	yes	—
183	C₂²×C₄×C₂₃	C₂×D₄	1	4	yes	—
184	C₂²×C₄×C₂₃	C₂×D₄	1	4	yes	—
185	C₂²×C₄×C₂₃	C₂×D₄	1	16	yes	complemented
186	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
187	C₂²×C₄×C₂₃	C₂⁴	1	4	yes	—
188	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
189	C₂²×C₄×C₂₃	C₂⁴	1	4	yes	—
190	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
191	C₂²×C₄×C₂₃	C₂⁴	1	4	yes	—
192	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
193	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
194	C₄⋊C₄×C₂₃	—	2	8	no	—
195	C₄⋊C₄×C₂₃	—	4	8	no	—
196	C₂²⋊C₄×C₂₃	—	2	8	no	—
197	C₂²⋊C₄×C₂₃	—	2	8	no	—
198	C₂²⋊C₄×C₂₃	—	2	16	no	—
199	C₂²⋊C₄×C₂₃	—	2	16	no	—
200	C₂²⋊C₄×C₂₃	—	2	8	no	—
201	C₂²⋊C₄×C₂₃	—	4	8	no	—
202	C₂²⋊C₄×C₂₃	—	4	8	no	—
203	C₂²⋊C₄×C₂₃	—	4	8	no	—
204	C₂²⋊C₄×C₂₃	C₂²×C₄	1	32	yes	complemented
205	C₂²⋊C₄×C₂₃	C₂²×C₄	1	16	yes	complemented
206	C₄²×C₂₃	—	2	8	no	—
207	C₄²×C₂₃	—	4	8	no	—
208	C₂×#2321	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
209	C₂³×C₂₃	—	2	16	no	—
210	C₂³×C₂₃	—	2	8	no	—
211	C₂³×C₂₃	—	2	8	no	—
212	C₂³×C₂₃	—	2	16	no	—
213	C₂³×C₂₃	—	2	4	no	—
214	C₂³×C₂₃	—	2	4	no	—
215	C₂³×C₂₃	—	2	8	no	—
216	C₂³×C₂₃	—	2	16	no	—
217	C₂³×C₂₃	—	2	32	no	—
218	C₂³×C₂₃	—	2	16	no	—
219	C₂³×C₂₃	—	2	16	no	—
220	C₂³×C₂₃	—	2	16	no	—
221	C₂³×C₂₃	—	2	4	no	—
222	C₂³×C₂₃	—	2	2	no	—
223	C₂³×C₂₃	—	2	2	no	—
224	C₂³×C₂₃	—	2	4	no	—
225	C₂³×C₂₃	—	2	4	no	—
226	C₂³×C₂₃	—	2	4	no	—
227	C₂³×C₂₃	—	2	4	no	—
228	C₂³×C₂₃	—	2	4	no	—
229	C₂³×C₂₃	—	2	4	no	—
230	C₂³×C₂₃	—	2	4	no	—
231	C₂³×C₂₃	—	4	32	no	—
232	C₂³×C₂₃	—	4	128	no	—
233	C₂³×C₂₃	—	4	16	no	—
234	C₂³×C₂₃	—	4	16	no	—
235	C₂³×C₂₃	—	4	32	no	—
236	C₂³×C₂₃	—	4	4	no	—
237	C₂³×C₂₃	—	4	8	no	—
238	C₂³×C₂₃	—	4	4	no	—
239	C₂³×C₂₃	—	4	8	no	—
240	C₂³×C₂₃	—	4	8	no	—
241	C₂³×C₂₃	—	4	8	no	—
242	C₂³×C₂₃	—	4	8	no	—
243	C₂³×C₂₃	C₄×D₄	1	16	yes	—
244	C₂³×C₂₃	C₂³×C₄	1	8	yes	—
245	C₂³×C₂₃	C₂³×C₄	1	4	yes	—
246	C₂³×C₂₃	C₂³×C₄	1	4	yes	—
247	C₂³×C₂₃	C₂³×C₄	1	2	yes	—
248	C₂³×C₂₃	C₂²×D₄	1	4	yes	—
249	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
250	C₂³×C₂₃	C₂×#41	1	4	yes	—
251	C₂³×C₂₃	C₂×#41	1	2	yes	—
252	C₂³×C₂₃	H(5,𝔽₂)	1	4	yes	—
253	C₂³×C₂₃	H(5,𝔽₂)	1	4	yes	—
254	C₂³×C₂₃	C₂⁵	1	1	yes	characteristic
255	D₄×C₂₃	—	2	32	no	—
256	D₄×C₂₃	—	4	32	no	—
257	C₂×C₄×C₂₃	—	2	8	no	—
258	C₂×C₄×C₂₃	—	2	16	no	—
259	C₂×C₄×C₂₃	—	2	8	no	—
260	C₂×C₄×C₂₃	—	2	8	no	—
261	C₂×C₄×C₂₃	—	2	2	no	—
262	C₂×C₄×C₂₃	—	2	2	no	—
263	C₂×C₄×C₂₃	—	2	4	no	—
264	C₂×C₄×C₂₃	—	2	4	no	—
265	C₂×C₄×C₂₃	—	2	4	no	—
266	C₂×C₄×C₂₃	—	2	4	no	—
267	C₂×C₄×C₂₃	—	2	2	no	—
268	C₂×C₄×C₂₃	—	2	4	no	—
269	C₂×C₄×C₂₃	—	2	2	no	—
270	C₂×C₄×C₂₃	—	2	4	no	—
271	C₂×C₄×C₂₃	—	2	4	no	—
272	C₂×C₄×C₂₃	—	2	4	no	—
273	C₂×C₄×C₂₃	—	2	4	no	—
274	C₂×C₄×C₂₃	—	2	4	no	—
275	C₂×C₄×C₂₃	—	2	4	no	—
276	C₂×C₄×C₂₃	—	2	4	no	—
277	C₂×C₄×C₂₃	—	4	16	no	—
278	C₂×C₄×C₂₃	—	4	16	no	—
279	C₂×C₄×C₂₃	—	4	16	no	—
280	C₂×C₄×C₂₃	—	4	4	no	—
281	C₂×C₄×C₂₃	—	4	4	no	—
282	C₂×C₄×C₂₃	—	4	8	no	—
283	C₂×C₄×C₂₃	—	4	8	no	—
284	C₂×C₄×C₂₃	C₂³×C₄	1	4	yes	—
285	C₂×C₄×C₂₃	C₂³×C₄	1	8	yes	—
286	C₂×C₄×C₂₃	C₂²×D₄	1	4	yes	—
287	C₂×C₄×C₂₃	C₂²×D₄	1	4	yes	—
288	C₂²×#120	C₂×C₂₃	1	1	yes	characteristic
289	C₂²×C₄×D₄	C₂×C₂₃	1	1	yes	characteristic, complemented
290	C₂³×C₂²⋊C₄	C₂×C₂₃	1	1	yes	characteristic, complemented
291	#2321	C₂×C₂₃	1	16	yes	direct product factor
292	C₂×#390	C₂×C₂₃	1	2	yes	complemented
293	C₂×#388	C₂×C₂₃	1	2	yes	complemented
294	C₂×#388	C₂×C₂₃	1	2	yes	complemented
295	C₂×#386	C₂×C₂₃	1	2	yes	complemented
296	C₂×#386	C₂×C₂₃	1	1	yes	characteristic, complemented
297	C₂×#385	C₂×C₂₃	1	1	yes	characteristic, complemented
298	C₂×#379	C₂×C₂₃	1	1	yes	characteristic, complemented
299	C₂×C₄×C₂²⋊C₄	C₂×C₂₃	1	1	yes	characteristic, complemented
300	C₂²×C₂₃	—	2	32	no	—
301	C₂²×C₂₃	—	2	8	no	—
302	C₂²×C₂₃	—	2	4	no	—
303	C₂²×C₂₃	—	2	4	no	—
304	C₂²×C₂₃	—	2	8	no	—
305	C₂²×C₂₃	—	2	4	no	—
306	C₂²×C₂₃	—	2	8	no	—
307	C₂²×C₂₃	—	2	8	no	—
308	C₂²×C₂₃	—	2	8	no	—
309	C₂²×C₂₃	—	2	8	no	—
310	C₂²×C₂₃	—	4	64	no	—
311	C₂²×C₂₃	—	4	16	no	—
312	C₂²×C₂₃	—	4	32	no	—
313	C₂²×C₂₃	—	4	2	no	—
314	C₂²×C₂₃	—	4	4	no	—
315	C₂²×C₂₃	—	4	2	no	—
316	C₂²×C₂₃	—	4	4	no	—
317	C₂²×C₂₃	—	4	4	no	—
318	C₂²×C₂₃	—	4	4	no	—
319	C₂²×C₂₃	—	4	4	no	—
320	C₂²×C₂₃	C₂×C₄×D₄	1	8	yes	—
321	C₂²×C₂₃	C₂×C₄×D₄	1	4	yes	—
322	C₂²×C₂₃	#518	1	8	yes	—
323	C₂²×C₂₃	#534	1	4	yes	—
324	C₂²×C₂₃	#535	1	4	yes	—
325	C₂²×C₂₃	#538	1	8	yes	—
326	C₂²×C₂₃	C₂⁴×C₄	1	1	yes	characteristic
327	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
328	C₂²×C₂₃	C₂²×#41	1	1	yes	characteristic
329	C₂²×C₂₃	C₂×H(5,𝔽₂)	1	2	yes	—
330	C₂²×C₂₃	C₂×H(5,𝔽₂)	1	2	yes	—
331	C₄×C₂₃	—	2	4	no	—
332	C₄×C₂₃	—	2	8	no	—
333	C₄×C₂₃	—	2	4	no	—
334	C₄×C₂₃	—	2	4	no	—
335	C₄×C₂₃	—	4	2	no	—
336	C₄×C₂₃	—	4	2	no	—
337	C₄×C₂₃	—	4	4	no	—
338	C₄×C₂₃	—	4	4	no	—
339	C₂⁶	C₂²×C₂₃	1	1	yes	characteristic
340	C₂³×D₄	C₂²×C₂₃	1	1	yes	characteristic
341	C₂³×D₄	C₂²×C₂₃	1	2	yes	—
342	C₂⁴×C₄	C₂²×C₂₃	1	1	yes	characteristic
343	C₂⁴×C₄	C₂²×C₂₃	1	1	yes	characteristic
344	C₂⁴×C₄	C₂²×C₂₃	1	1	yes	characteristic, complemented
345	C₂×#120	C₄×C₂₃	1	16	yes	complemented
346	C₂×#120	C₂²×C₂₃	1	8	yes	—
347	C₂×C₄×D₄	—	2	8	no	—
348	C₂×C₄×D₄	C₂²×C₂₃	1	8	yes	complemented
349	C₂²×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic, complemented
350	C₂²×C₄⋊C₄	C₂²×C₂₃	1	2	yes	complemented
351	C₂²×C₂²⋊C₄	—	2	8	no	—
352	C₂²×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
353	C₂²×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
354	C₂²×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
355	C₂²×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
356	C₂²×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
357	C₂²×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
358	C₂²×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
359	C₂²×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
360	C₂²×C₂²⋊C₄	C₂²×C₂₃	1	8	yes	complemented
361	C₂²×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic, complemented
362	C₂²×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	complemented
363	C₂²×C₄²	C₂²×C₂₃	1	1	yes	characteristic, complemented
364	C₂²×C₄²	C₂²×C₂₃	1	2	yes	complemented
365	#390	C₂²×C₂₃	1	16	yes	complemented
366	#388	C₂²×C₂₃	1	16	yes	complemented
367	#388	C₂²×C₂₃	1	16	yes	complemented
368	#386	C₂²×C₂₃	1	16	yes	complemented
369	#386	C₂²×C₂₃	1	8	yes	complemented
370	#385	C₂²×C₂₃	1	8	yes	complemented
371	#379	C₂²×C₂₃	1	8	yes	complemented
372	C₄×C₂²⋊C₄	C₂²×C₂₃	1	8	yes	complemented
373	C₂×#95	C₂²×C₂₃	1	2	yes	complemented
374	C₂×#95	C₂²×C₂₃	1	2	yes	complemented
375	C₂×#95	C₂²×C₂₃	1	2	yes	complemented
376	C₂×C₂₃	—	2	8	no	—
377	C₂×C₂₃	—	4	4	no	—
378	C₂×C₂₃	—	4	8	no	—
379	C₂×C₂₃	#2321	1	8	yes	direct product factor
380	C₂×C₂₃	C₂²×C₄×D₄	1	1	yes	characteristic
381	C₂×C₂₃	C₂×#518	1	2	yes	—
382	C₂×C₂₃	C₂×#534	1	1	yes	characteristic
383	C₂×C₂₃	C₂×#535	1	1	yes	characteristic
384	C₂×C₂₃	C₂×#538	1	2	yes	—
385	C₂⁵	—	2	4	no	—
386	C₂⁵	—	2	4	no	—
387	C₂⁵	—	4	4	no	—
388	C₂⁵	—	4	4	no	—
389	C₂⁵	C₂×C₄×C₂₃	1	8	yes	complemented
390	C₂⁵	C₂³×C₂₃	1	2	yes	—
391	C₂⁵	C₂³×C₂₃	1	1	yes	characteristic
392	C₂⁵	C₂³×C₂₃	1	1	yes	characteristic
393	C₂⁵	C₂³×C₂₃	1	4	yes	—
394	C₂²×D₄	—	2	4	no	—
395	C₂²×D₄	—	2	4	no	—
396	C₂²×D₄	—	4	4	no	—
397	C₂²×D₄	—	4	4	no	—
398	C₂²×D₄	C₂×C₄×C₂₃	1	8	yes	—
399	C₂²×D₄	C₂×C₄×C₂₃	1	16	yes	complemented
400	C₂²×D₄	C₂³×C₂₃	1	4	yes	—
401	C₂²×D₄	C₂³×C₂₃	1	8	yes	—
402	C₂³×C₄	—	2	4	no	—
403	C₂³×C₄	—	2	4	no	—
404	C₂³×C₄	—	4	4	no	—
405	C₂³×C₄	—	4	4	no	—
406	C₂³×C₄	—	4	4	no	—
407	C₂³×C₄	D₄×C₂₃	1	8	yes	complemented
408	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
409	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
410	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
411	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
412	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
413	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
414	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
415	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
416	C₂³×C₄	C₂³×C₂₃	1	4	yes	—
417	C₂³×C₄	C₂³×C₂₃	1	4	yes	—
418	C₂³×C₄	C₂³×C₂₃	1	4	yes	complemented
419	#120	C₂×C₄×C₂₃	1	64	yes	complemented
420	C₄×D₄	—	2	32	no	—
421	C₂×C₄⋊C₄	—	2	4	no	—
422	C₂×C₄⋊C₄	—	4	4	no	—
423	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	complemented
424	C₂×C₄⋊C₄	C₂³×C₂₃	1	8	yes	complemented
425	C₂×C₂²⋊C₄	—	2	4	no	—
426	C₂×C₂²⋊C₄	—	2	4	no	—
427	C₂×C₂²⋊C₄	—	2	8	no	—
428	C₂×C₂²⋊C₄	—	2	8	no	—
429	C₂×C₂²⋊C₄	—	2	4	no	—
430	C₂×C₂²⋊C₄	—	2	32	no	—
431	C₂×C₂²⋊C₄	—	4	4	no	—
432	C₂×C₂²⋊C₄	—	4	4	no	—
433	C₂×C₂²⋊C₄	—	4	4	no	—
434	C₂×C₂²⋊C₄	C₂×C₄×C₂₃	1	16	yes	complemented
435	C₂×C₂²⋊C₄	C₂×C₄×C₂₃	1	8	yes	complemented
436	C₂×C₂²⋊C₄	C₂³×C₂₃	1	8	yes	—
437	C₂×C₂²⋊C₄	C₂³×C₂₃	1	8	yes	—
438	C₂×C₂²⋊C₄	C₂³×C₂₃	1	4	yes	—
439	C₂×C₂²⋊C₄	C₂³×C₂₃	1	4	yes	—
440	C₂×C₂²⋊C₄	C₂³×C₂₃	1	8	yes	—
441	C₂×C₂²⋊C₄	C₂³×C₂₃	1	8	yes	—
442	C₂×C₂²⋊C₄	C₂³×C₂₃	1	4	yes	—
443	C₂×C₂²⋊C₄	C₂³×C₂₃	1	8	yes	—
444	C₂×C₂²⋊C₄	C₂³×C₂₃	1	4	yes	complemented
445	C₂×C₂²⋊C₄	C₂³×C₂₃	1	8	yes	complemented
446	C₂×C₄²	—	2	4	no	—
447	C₂×C₄²	—	4	4	no	—
448	C₂×C₄²	C₂³×C₂₃	1	4	yes	complemented
449	C₂×C₄²	C₂³×C₂₃	1	8	yes	complemented
450	#95	C₂³×C₂₃	1	8	yes	complemented
451	#95	C₂³×C₂₃	1	8	yes	complemented
452	#95	C₂³×C₂₃	1	8	yes	complemented
453	C₂₃	C₂×#2321	1	1	yes	characteristic, direct product factor, Sylow
454	C₂⁴	—	2	4	no	—
455	C₂⁴	—	2	4	no	—
456	C₂⁴	—	2	32	no	—
457	C₂⁴	—	2	4	no	—
458	C₂⁴	—	2	8	no	—
459	C₂⁴	—	2	2	no	—
460	C₂⁴	—	2	2	no	—
461	C₂⁴	—	2	4	no	—
462	C₂⁴	—	2	8	no	—
463	C₂⁴	—	2	4	no	—
464	C₂⁴	—	2	4	no	—
465	C₂⁴	—	2	4	no	—
466	C₂⁴	—	2	4	no	—
467	C₂⁴	—	2	4	no	—
468	C₂⁴	—	2	4	no	—
469	C₂⁴	—	4	32	no	—
470	C₂⁴	—	4	8	no	—
471	C₂⁴	—	4	8	no	—
472	C₂⁴	—	4	16	no	—
473	C₂⁴	—	4	16	no	—
474	C₂⁴	—	4	32	no	—
475	C₂⁴	C₂²×C₄×C₂₃	1	8	yes	—
476	C₂⁴	C₂²×C₄×C₂₃	1	4	yes	—
477	C₂⁴	C₂²×C₄×C₂₃	1	4	yes	—
478	C₂⁴	C₂²×C₄×C₂₃	1	16	yes	complemented
479	C₂⁴	C₂×D₄×C₂₃	1	4	yes	—
480	C₂⁴	#41×C₂₃	1	4	yes	—
481	C₂⁴	C₂⁴×C₂₃	1	4	yes	—
482	C₂⁴	C₂⁴×C₂₃	1	2	yes	—
483	C₂⁴	C₂⁴×C₂₃	1	2	yes	—
484	C₂⁴	C₂⁴×C₂₃	1	1	yes	characteristic
485	C₂×D₄	—	2	32	no	—
486	C₂×D₄	—	2	8	no	—
487	C₂×D₄	—	2	8	no	—
488	C₂×D₄	—	4	32	no	—
489	C₂×D₄	—	4	8	no	—
490	C₂×D₄	—	4	8	no	—
491	C₂×D₄	C₂²×C₄×C₂₃	1	16	yes	—
492	C₂×D₄	C₂²×C₄×C₂₃	1	32	yes	complemented
493	C₂²×C₄	—	2	2	no	—
494	C₂²×C₄	—	2	2	no	—
495	C₂²×C₄	—	2	4	no	—
496	C₂²×C₄	—	2	4	no	—
497	C₂²×C₄	—	2	4	no	—
498	C₂²×C₄	—	2	4	no	—
499	C₂²×C₄	—	2	2	no	—
500	C₂²×C₄	—	2	8	no	—
501	C₂²×C₄	—	2	4	no	—
502	C₂²×C₄	—	2	2	no	—
503	C₂²×C₄	—	2	4	no	—
504	C₂²×C₄	—	2	4	no	—
505	C₂²×C₄	—	2	4	no	—
506	C₂²×C₄	—	2	4	no	—
507	C₂²×C₄	—	2	4	no	—
508	C₂²×C₄	—	2	4	no	—
509	C₂²×C₄	—	2	4	no	—
510	C₂²×C₄	—	2	8	no	—
511	C₂²×C₄	—	4	16	no	—
512	C₂²×C₄	—	4	8	no	—
513	C₂²×C₄	—	4	8	no	—
514	C₂²×C₄	—	4	8	no	—
515	C₂²×C₄	—	4	16	no	—
516	C₂²×C₄	—	4	16	no	—
517	C₂²×C₄	C₂²×C₄×C₂₃	1	4	yes	—
518	C₂²×C₄	C₂²×C₄×C₂₃	1	8	yes	—
519	C₂²×C₄	C₂×D₄×C₂₃	1	4	yes	—
520	C₂²×C₄	C₂×D₄×C₂₃	1	4	yes	—
521	C₂²×C₄	C₂×D₄×C₂₃	1	16	yes	complemented
522	C₂²×C₄	C₂⁴×C₂₃	1	4	yes	—
523	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
524	C₂²×C₄	C₂⁴×C₂₃	1	4	yes	—
525	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
526	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
527	C₂²×C₄	C₂⁴×C₂₃	1	4	yes	—
528	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
529	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
530	C₄⋊C₄	—	2	8	no	—
531	C₄⋊C₄	—	4	8	no	—
532	C₂²⋊C₄	—	2	8	no	—
533	C₂²⋊C₄	—	2	8	no	—
534	C₂²⋊C₄	—	2	16	no	—
535	C₂²⋊C₄	—	2	16	no	—
536	C₂²⋊C₄	—	2	8	no	—
537	C₂²⋊C₄	—	4	8	no	—
538	C₂²⋊C₄	—	4	8	no	—
539	C₂²⋊C₄	—	4	8	no	—
540	C₂²⋊C₄	C₂²×C₄×C₂₃	1	32	yes	complemented
541	C₂²⋊C₄	C₂²×C₄×C₂₃	1	16	yes	complemented
542	C₄²	—	2	8	no	—
543	C₄²	—	4	8	no	—
544	C₂³	—	2	4	no	—
545	C₂³	—	2	4	no	—
546	C₂³	—	2	16	no	—
547	C₂³	—	2	8	no	—
548	C₂³	—	2	8	no	—
549	C₂³	—	2	16	no	—
550	C₂³	—	2	4	no	—
551	C₂³	—	2	2	no	—
552	C₂³	—	2	2	no	—
553	C₂³	—	2	4	no	—
554	C₂³	—	2	4	no	—
555	C₂³	—	2	4	no	—
556	C₂³	—	2	4	no	—
557	C₂³	—	2	4	no	—
558	C₂³	—	2	4	no	—
559	C₂³	—	2	4	no	—
560	C₂³	—	2	8	no	—
561	C₂³	—	2	16	no	—
562	C₂³	—	2	32	no	—
563	C₂³	—	2	16	no	—
564	C₂³	—	2	16	no	—
565	C₂³	—	2	16	no	—
566	C₂³	—	4	32	no	—
567	C₂³	—	4	16	no	—
568	C₂³	—	4	16	no	—
569	C₂³	—	4	32	no	—
570	C₂³	—	4	128	no	—
571	C₂³	—	4	4	no	—
572	C₂³	—	4	8	no	—
573	C₂³	—	4	8	no	—
574	C₂³	—	4	4	no	—
575	C₂³	—	4	8	no	—
576	C₂³	—	4	8	no	—
577	C₂³	—	4	8	no	—
578	C₂³	C₄×D₄×C₂₃	1	16	yes	—
579	C₂³	C₂³×C₄×C₂₃	1	8	yes	—
580	C₂³	C₂³×C₄×C₂₃	1	4	yes	—
581	C₂³	C₂³×C₄×C₂₃	1	4	yes	—
582	C₂³	C₂³×C₄×C₂₃	1	2	yes	—
583	C₂³	C₂²×D₄×C₂₃	1	4	yes	—
584	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
585	C₂³	C₂×#41×C₂₃	1	4	yes	—
586	C₂³	C₂×#41×C₂₃	1	2	yes	—
587	C₂³	C₂₃×H(5,𝔽₂)	1	4	yes	—
588	C₂³	C₂₃×H(5,𝔽₂)	1	4	yes	—
589	C₂³	C₂⁵×C₂₃	1	1	yes	characteristic
590	D₄	—	2	32	no	—
591	D₄	—	4	32	no	—
592	C₂×C₄	—	2	2	no	—
593	C₂×C₄	—	2	2	no	—
594	C₂×C₄	—	2	4	no	—
595	C₂×C₄	—	2	4	no	—
596	C₂×C₄	—	2	4	no	—
597	C₂×C₄	—	2	4	no	—
598	C₂×C₄	—	2	8	no	—
599	C₂×C₄	—	2	16	no	—
600	C₂×C₄	—	2	8	no	—
601	C₂×C₄	—	2	8	no	—
602	C₂×C₄	—	2	2	no	—
603	C₂×C₄	—	2	4	no	—
604	C₂×C₄	—	2	2	no	—
605	C₂×C₄	—	2	4	no	—
606	C₂×C₄	—	2	4	no	—
607	C₂×C₄	—	2	4	no	—
608	C₂×C₄	—	2	4	no	—
609	C₂×C₄	—	2	4	no	—
610	C₂×C₄	—	2	4	no	—
611	C₂×C₄	—	2	4	no	—
612	C₂×C₄	—	4	16	no	—
613	C₂×C₄	—	4	16	no	—
614	C₂×C₄	—	4	16	no	—
615	C₂×C₄	—	4	4	no	—
616	C₂×C₄	—	4	8	no	—
617	C₂×C₄	—	4	4	no	—
618	C₂×C₄	—	4	8	no	—
619	C₂×C₄	C₂³×C₄×C₂₃	1	4	yes	—
620	C₂×C₄	C₂³×C₄×C₂₃	1	8	yes	—
621	C₂×C₄	C₂²×D₄×C₂₃	1	4	yes	—
622	C₂×C₄	C₂²×D₄×C₂₃	1	4	yes	—
623	C₂²	—	2	8	no	—
624	C₂²	—	2	4	no	—
625	C₂²	—	2	4	no	—
626	C₂²	—	2	8	no	—
627	C₂²	—	2	32	no	—
628	C₂²	—	2	4	no	—
629	C₂²	—	2	8	no	—
630	C₂²	—	2	8	no	—
631	C₂²	—	2	8	no	—
632	C₂²	—	2	8	no	—
633	C₂²	—	4	64	no	—
634	C₂²	—	4	2	no	—
635	C₂²	—	4	4	no	—
636	C₂²	—	4	4	no	—
637	C₂²	—	4	2	no	—
638	C₂²	—	4	4	no	—
639	C₂²	—	4	4	no	—
640	C₂²	—	4	4	no	—
641	C₂²	—	4	32	no	—
642	C₂²	—	4	16	no	—
643	C₂²	C₂×C₄×D₄×C₂₃	1	8	yes	—
644	C₂²	C₂×C₄×D₄×C₂₃	1	4	yes	—
645	C₂²	C₂₃×#518	1	8	yes	—
646	C₂²	C₂₃×#534	1	4	yes	—
647	C₂²	C₂₃×#535	1	4	yes	—
648	C₂²	C₂₃×#538	1	8	yes	—
649	C₂²	C₂⁴×C₄×C₂₃	1	1	yes	characteristic
650	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
651	C₂²	C₂²×#41×C₂₃	1	1	yes	characteristic
652	C₂²	C₂×C₂₃×H(5,𝔽₂)	1	2	yes	—
653	C₂²	C₂×C₂₃×H(5,𝔽₂)	1	2	yes	—
654	C₄	—	2	4	no	—
655	C₄	—	2	8	no	—
656	C₄	—	2	4	no	—
657	C₄	—	2	4	no	—
658	C₄	—	4	2	no	—
659	C₄	—	4	4	no	—
660	C₄	—	4	2	no	—
661	C₄	—	4	4	no	—
662	C₂	—	2	8	no	—
663	C₂	—	4	8	no	—
664	C₂	—	4	4	no	—
665	C₂	C₂₃×#2321	1	8	yes	direct product factor
666	C₂	C₂²×C₄×D₄×C₂₃	1	1	yes	characteristic
667	C₂	C₂×C₂₃×#518	1	2	yes	—
668	C₂	C₂×C₂₃×#534	1	1	yes	characteristic
669	C₂	C₂×C₂₃×#535	1	1	yes	characteristic
670	C₂	C₂×C₂₃×#538	1	2	yes	—

	subgroup	G/H
center, socle	C₂⁴×C₂₃	C₂⁴
commutator	C₂²	C₂⁴×C₄×C₂₃
Frattini, cosocle	C₂³	C₂⁵×C₂₃
prime radical	C₂²×C₂₃×#120	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂⁴×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂²×C₄×D₄×C₂₃	C₂	semidirect
3. C₂³×C₂²⋊C₄×C₂₃	C₂	semidirect
4. C₂₃×#2321	C₂	direct (N × H)
5. C₂×C₂₃×#390	C₂	semidirect
6. C₂×C₂₃×#388	C₂	semidirect
7. C₂×C₂₃×#388	C₂	semidirect
8. C₂×C₂₃×#386	C₂	semidirect
9. C₂×C₂₃×#386	C₂	semidirect
10. C₂×C₂₃×#385	C₂	semidirect
11. C₂×C₂₃×#379	C₂	semidirect
12. C₂×C₄×C₂²⋊C₄×C₂₃	C₂	semidirect
18. C₂⁴×C₄×C₂₃	C₂²	semidirect
19. C₂×C₂₃×#120	C₄	semidirect
22. C₂×C₄×D₄×C₂₃	C₂²	semidirect
23. C₂²×C₄⋊C₄×C₂₃	C₂²	semidirect
24. C₂²×C₄⋊C₄×C₂₃	C₂²	semidirect
34. C₂²×C₂²⋊C₄×C₂₃	C₂²	semidirect
35. C₂²×C₂²⋊C₄×C₂₃	C₂²	semidirect
36. C₂²×C₂²⋊C₄×C₂₃	C₂²	semidirect
37. C₂²×C₄²×C₂₃	C₂²	semidirect
38. C₂²×C₄²×C₂₃	C₂²	semidirect
39. C₂₃×#390	C₂²	semidirect
40. C₂₃×#388	C₂²	semidirect
41. C₂₃×#388	C₂²	semidirect
42. C₂₃×#386	C₂²	semidirect
43. C₂₃×#386	C₂²	semidirect
44. C₂₃×#385	C₂²	semidirect
45. C₂₃×#379	C₂²	semidirect
46. C₄×C₂²⋊C₄×C₂₃	C₂²	semidirect
47. C₂×C₂₃×#95	C₂²	semidirect
48. C₂×C₂₃×#95	C₂²	semidirect
49. C₂×C₂₃×#95	C₂²	semidirect
54. C₂⁵×C₂₃	C₂×C₄	semidirect
64. C₂²×D₄×C₂₃	C₂×C₄	semidirect
72. C₂³×C₄×C₂₃	D₄	semidirect
83. C₂³×C₄×C₂₃	C₂³	semidirect
84. C₂₃×#120	C₂×C₄	semidirect
88. C₂×C₄⋊C₄×C₂₃	C₂³	semidirect
89. C₂×C₄⋊C₄×C₂₃	C₂³	semidirect
99. C₂×C₂²⋊C₄×C₂₃	C₂×C₄	semidirect
100. C₂×C₂²⋊C₄×C₂₃	C₂×C₄	semidirect
109. C₂×C₂²⋊C₄×C₂₃	C₂³	semidirect
110. C₂×C₂²⋊C₄×C₂₃	C₂³	semidirect
113. C₂×C₄²×C₂₃	C₂³	semidirect
114. C₂×C₄²×C₂₃	C₂³	semidirect
115. C₂₃×#95	C₂³	semidirect
116. C₂₃×#95	C₂³	semidirect
117. C₂₃×#95	C₂³	semidirect
142. C₂⁴×C₂₃	C₂²×C₄	semidirect
156. C₂×D₄×C₂₃	C₂²×C₄	semidirect
185. C₂²×C₄×C₂₃	C₂×D₄	semidirect
204. C₂²⋊C₄×C₂₃	C₂²×C₄	semidirect
205. C₂²⋊C₄×C₂₃	C₂²×C₄	semidirect
208. C₂×#2321	C₂₃	direct (N × H)
289. C₂²×C₄×D₄	C₂×C₂₃	semidirect
290. C₂³×C₂²⋊C₄	C₂×C₂₃	semidirect
291. #2321	C₂×C₂₃	direct (N × H)
292. C₂×#390	C₂×C₂₃	semidirect
293. C₂×#388	C₂×C₂₃	semidirect
294. C₂×#388	C₂×C₂₃	semidirect
295. C₂×#386	C₂×C₂₃	semidirect
296. C₂×#386	C₂×C₂₃	semidirect
297. C₂×#385	C₂×C₂₃	semidirect
298. C₂×#379	C₂×C₂₃	semidirect
299. C₂×C₄×C₂²⋊C₄	C₂×C₂₃	semidirect
344. C₂⁴×C₄	C₂²×C₂₃	semidirect
345. C₂×#120	C₄×C₂₃	semidirect
348. C₂×C₄×D₄	C₂²×C₂₃	semidirect
349. C₂²×C₄⋊C₄	C₂²×C₂₃	semidirect
350. C₂²×C₄⋊C₄	C₂²×C₂₃	semidirect
360. C₂²×C₂²⋊C₄	C₂²×C₂₃	semidirect
361. C₂²×C₂²⋊C₄	C₂²×C₂₃	semidirect
362. C₂²×C₂²⋊C₄	C₂²×C₂₃	semidirect
363. C₂²×C₄²	C₂²×C₂₃	semidirect
364. C₂²×C₄²	C₂²×C₂₃	semidirect
365. #390	C₂²×C₂₃	semidirect
366. #388	C₂²×C₂₃	semidirect
367. #388	C₂²×C₂₃	semidirect
368. #386	C₂²×C₂₃	semidirect
369. #386	C₂²×C₂₃	semidirect
370. #385	C₂²×C₂₃	semidirect
371. #379	C₂²×C₂₃	semidirect
372. C₄×C₂²⋊C₄	C₂²×C₂₃	semidirect
373. C₂×#95	C₂²×C₂₃	semidirect
374. C₂×#95	C₂²×C₂₃	semidirect
375. C₂×#95	C₂²×C₂₃	semidirect
379. C₂×C₂₃	#2321	direct (N × H)
389. C₂⁵	C₂×C₄×C₂₃	semidirect
399. C₂²×D₄	C₂×C₄×C₂₃	semidirect
407. C₂³×C₄	D₄×C₂₃	semidirect
418. C₂³×C₄	C₂³×C₂₃	semidirect
419. #120	C₂×C₄×C₂₃	semidirect
423. C₂×C₄⋊C₄	C₂³×C₂₃	semidirect
424. C₂×C₄⋊C₄	C₂³×C₂₃	semidirect
434. C₂×C₂²⋊C₄	C₂×C₄×C₂₃	semidirect
435. C₂×C₂²⋊C₄	C₂×C₄×C₂₃	semidirect
444. C₂×C₂²⋊C₄	C₂³×C₂₃	semidirect
445. C₂×C₂²⋊C₄	C₂³×C₂₃	semidirect
448. C₂×C₄²	C₂³×C₂₃	semidirect
449. C₂×C₄²	C₂³×C₂₃	semidirect
450. #95	C₂³×C₂₃	semidirect
451. #95	C₂³×C₂₃	semidirect
452. #95	C₂³×C₂₃	semidirect
453. C₂₃	C₂×#2321	direct (N × H)
478. C₂⁴	C₂²×C₄×C₂₃	semidirect
492. C₂×D₄	C₂²×C₄×C₂₃	semidirect
521. C₂²×C₄	C₂×D₄×C₂₃	semidirect
540. C₂²⋊C₄	C₂²×C₄×C₂₃	semidirect
541. C₂²⋊C₄	C₂²×C₄×C₂₃	semidirect
665. C₂	C₂₃×#2321	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×#120	2
C₂²×C₄×D₄×C₂₃	2
C₂³×C₂²⋊C₄×C₂₃	2
C₂₃×#2321	2
C₂×C₂₃×#390	2
C₂×C₂₃×#388	2
C₂×C₂₃×#386	2
C₂×C₂₃×#385	2
C₂×C₂₃×#379	2
C₂×C₄×C₂²⋊C₄×C₂₃	2
C₂×#2321	23

Subgroups — C2×C23×#2321 #19181687

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₂₃×#2321 #19181687