Subgroups — C₂×C₂₃×#2435 #19182318

Order 5888.

7606 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴×D₄×C₂₃	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₂₃×#124	C₂	1	2	yes	maximal, complemented
3	C₂²×C₂₃×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₃×#2435	C₂	1	16	yes	maximal, direct product factor
5	C₂×C₂₃×#394	C₂	1	4	yes	maximal, complemented
6	C₂×C₂₃×#390	C₂	1	2	yes	maximal, complemented
7	C₂×C₂₃×#379	C₂	1	4	yes	maximal, complemented
8	C₂×C₄×C₂²⋊C₄×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂⁶×C₂₃	C₂²	1	2	yes	—
10	C₂³×Q₈×C₂₃	C₂²	1	1	yes	characteristic, complemented
11	C₂³×D₄×C₂₃	—	2	16	no	—
12	C₂³×D₄×C₂₃	—	2	8	no	—
13	C₂³×D₄×C₂₃	C₂²	1	8	yes	—
14	C₂³×D₄×C₂₃	C₂²	1	2	yes	—
15	C₂³×D₄×C₂₃	C₂²	1	2	yes	—
16	C₂⁴×C₄×C₂₃	C₂²	1	1	yes	characteristic
17	C₂×C₂₃×#124	—	2	16	no	—
18	C₂×C₂₃×#124	C₂²	1	16	yes	complemented
19	C₂×C₂₃×C₂²⋊Q₈	—	2	8	no	—
20	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	8	yes	complemented
21	C₂²×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic, complemented
22	C₂²×C₄⋊C₄×C₂₃	C₂²	1	2	yes	complemented
23	C₂²×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	—
24	C₂²×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	—
25	C₂²×C₂²⋊C₄×C₂₃	C₂²	1	8	yes	complemented
26	C₂²×C₂²⋊C₄×C₂₃	C₂²	1	8	yes	complemented
27	C₂²×C₄²×C₂₃	C₂²	1	2	yes	complemented
28	C₂₃×#394	C₂²	1	32	yes	complemented
29	C₂₃×#390	C₂²	1	16	yes	complemented
30	C₂₃×#379	C₂²	1	32	yes	complemented
31	C₄×C₂²⋊C₄×C₂₃	C₂²	1	8	yes	complemented
32	C₂×C₂₃×#95	C₂²	1	2	yes	complemented
33	C₂⁵×C₂₃	—	2	16	no	—
34	C₂⁵×C₂₃	—	2	8	no	—
35	C₂⁵×C₂₃	—	2	16	no	—
36	C₂⁵×C₂₃	—	4	8	no	—
37	C₂⁵×C₂₃	C₂³	1	4	yes	—
38	C₂⁵×C₂₃	C₂³	1	8	yes	—
39	C₂⁵×C₂₃	C₂³	1	1	yes	characteristic
40	C₂²×Q₈×C₂₃	—	2	4	no	—
41	C₂²×Q₈×C₂₃	—	2	8	no	—
42	C₂²×Q₈×C₂₃	C₂³	1	4	yes	complemented
43	C₂²×D₄×C₂₃	—	2	128	no	—
44	C₂²×D₄×C₂₃	—	2	16	no	—
45	C₂²×D₄×C₂₃	—	2	64	no	—
46	C₂²×D₄×C₂₃	—	2	8	no	—
47	C₂²×D₄×C₂₃	—	2	32	no	—
48	C₂²×D₄×C₂₃	—	2	8	no	—
49	C₂²×D₄×C₂₃	—	2	8	no	—
50	C₂²×D₄×C₂₃	D₄	1	16	yes	—
51	C₂²×D₄×C₂₃	C₂³	1	8	yes	—
52	C₂²×D₄×C₂₃	C₂³	1	8	yes	—
53	C₂³×C₄×C₂₃	—	2	8	no	—
54	C₂³×C₄×C₂₃	D₄	1	8	yes	—
55	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
56	C₂³×C₄×C₂₃	C₂³	1	4	yes	—
57	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
58	C₂³×C₄×C₂₃	C₂³	1	4	yes	—
59	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
60	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
61	C₂₃×#124	—	2	64	no	—
62	C₂₃×C₂²⋊Q₈	—	2	32	no	—
63	C₂×C₄⋊C₄×C₂₃	—	2	4	no	—
64	C₂×C₄⋊C₄×C₂₃	—	2	8	no	—
65	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	complemented
66	C₂×C₄⋊C₄×C₂₃	C₂³	1	8	yes	complemented
67	C₂×C₂²⋊C₄×C₂₃	—	2	8	no	—
68	C₂×C₂²⋊C₄×C₂₃	—	2	32	no	—
69	C₂×C₂²⋊C₄×C₂₃	—	2	8	no	—
70	C₂×C₂²⋊C₄×C₂₃	—	4	16	no	—
71	C₂×C₂²⋊C₄×C₂₃	C₂³	1	8	yes	—
72	C₂×C₂²⋊C₄×C₂₃	C₂³	1	8	yes	—
73	C₂×C₂²⋊C₄×C₂₃	C₂³	1	32	yes	complemented
74	C₂×C₂²⋊C₄×C₂₃	C₂³	1	32	yes	complemented
75	C₂×C₄²×C₂₃	—	2	8	no	—
76	C₂×C₄²×C₂₃	C₂³	1	8	yes	complemented
77	C₂₃×#95	C₂³	1	8	yes	complemented
78	C₂⁴×C₂₃	—	2	4	no	—
79	C₂⁴×C₂₃	—	2	4	no	—
80	C₂⁴×C₂₃	—	2	64	no	—
81	C₂⁴×C₂₃	—	2	32	no	—
82	C₂⁴×C₂₃	—	2	16	no	—
83	C₂⁴×C₂₃	—	2	8	no	—
84	C₂⁴×C₂₃	—	2	8	no	—
85	C₂⁴×C₂₃	—	2	16	no	—
86	C₂⁴×C₂₃	—	2	16	no	—
87	C₂⁴×C₂₃	—	2	32	no	—
88	C₂⁴×C₂₃	—	4	16	no	—
89	C₂⁴×C₂₃	—	4	128	no	—
90	C₂⁴×C₂₃	—	4	32	no	—
91	C₂⁴×C₂₃	—	4	32	no	—
92	C₂⁴×C₂₃	C₂×D₄	1	16	yes	—
93	C₂⁴×C₂₃	C₂×D₄	1	4	yes	—
94	C₂⁴×C₂₃	#41	1	8	yes	—
95	C₂⁴×C₂₃	C₂⁴	1	8	yes	—
96	C₂⁴×C₂₃	C₂⁴	1	2	yes	—
97	C₂⁴×C₂₃	C₂⁴	1	1	yes	characteristic
98	C₂×Q₈×C₂₃	—	2	8	no	—
99	C₂×Q₈×C₂₃	—	2	16	no	—
100	C₂×Q₈×C₂₃	—	4	16	no	—
101	C₂×D₄×C₂₃	—	2	64	no	—
102	C₂×D₄×C₂₃	—	2	256	no	—
103	C₂×D₄×C₂₃	—	2	32	no	—
104	C₂×D₄×C₂₃	—	2	64	no	—
105	C₂×D₄×C₂₃	—	2	16	no	—
106	C₂×D₄×C₂₃	—	2	16	no	—
107	C₂×D₄×C₂₃	—	2	16	no	—
108	C₂×D₄×C₂₃	C₂×D₄	1	32	yes	—
109	C₂²×C₄×C₂₃	—	2	4	no	—
110	C₂²×C₄×C₂₃	—	2	32	no	—
111	C₂²×C₄×C₂₃	—	2	16	no	—
112	C₂²×C₄×C₂₃	—	2	8	no	—
113	C₂²×C₄×C₂₃	—	2	8	no	—
114	C₂²×C₄×C₂₃	—	2	4	no	—
115	C₂²×C₄×C₂₃	—	2	4	no	—
116	C₂²×C₄×C₂₃	—	2	8	no	—
117	C₂²×C₄×C₂₃	—	2	8	no	—
118	C₂²×C₄×C₂₃	—	2	8	no	—
119	C₂²×C₄×C₂₃	C₂×D₄	1	4	yes	—
120	C₂²×C₄×C₂₃	C₂×D₄	1	16	yes	—
121	C₂²×C₄×C₂₃	C₂×D₄	1	8	yes	—
122	C₂²×C₄×C₂₃	C₂×D₄	1	4	yes	—
123	C₂²×C₄×C₂₃	C₂⁴	1	8	yes	—
124	C₂²×C₄×C₂₃	C₂⁴	1	4	yes	—
125	C₂²×C₄×C₂₃	C₂⁴	1	4	yes	—
126	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
127	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
128	C₄⋊C₄×C₂₃	—	2	8	no	—
129	C₄⋊C₄×C₂₃	—	2	16	no	—
130	C₂²⋊C₄×C₂₃	—	2	16	no	—
131	C₂²⋊C₄×C₂₃	—	2	64	no	—
132	C₂²⋊C₄×C₂₃	—	2	16	no	—
133	C₂²⋊C₄×C₂₃	—	4	32	no	—
134	C₄²×C₂₃	—	2	16	no	—
135	C₂×#2435	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
136	C₂³×C₂₃	—	2	8	no	—
137	C₂³×C₂₃	—	2	8	no	—
138	C₂³×C₂₃	—	2	32	no	—
139	C₂³×C₂₃	—	2	4	no	—
140	C₂³×C₂₃	—	2	4	no	—
141	C₂³×C₂₃	—	2	64	no	—
142	C₂³×C₂₃	—	2	32	no	—
143	C₂³×C₂₃	—	2	64	no	—
144	C₂³×C₂₃	—	2	8	no	—
145	C₂³×C₂₃	—	2	8	no	—
146	C₂³×C₂₃	—	2	16	no	—
147	C₂³×C₂₃	—	2	16	no	—
148	C₂³×C₂₃	—	4	128	no	—
149	C₂³×C₂₃	—	4	32	no	—
150	C₂³×C₂₃	—	4	256	no	—
151	C₂³×C₂₃	—	4	16	no	—
152	C₂³×C₂₃	—	4	32	no	—
153	C₂³×C₂₃	—	4	16	no	—
154	C₂³×C₂₃	—	4	32	no	—
155	C₂³×C₂₃	#124	1	16	yes	complemented
156	C₂³×C₂₃	C₂²×D₄	1	16	yes	—
157	C₂³×C₂₃	C₂²×D₄	1	4	yes	—
158	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
159	C₂³×C₂₃	C₂²×D₄	1	4	yes	—
160	C₂³×C₂₃	C₂×#41	1	8	yes	—
161	C₂³×C₂₃	C₂×#41	1	4	yes	—
162	C₂³×C₂₃	H(5,𝔽₂)	1	4	yes	—
163	C₂³×C₂₃	C₂⁵	1	1	yes	characteristic
164	Q₈×C₂₃	—	4	16	no	—
165	D₄×C₂₃	—	2	64	no	—
166	D₄×C₂₃	—	2	64	no	—
167	C₂×C₄×C₂₃	—	2	8	no	—
168	C₂×C₄×C₂₃	—	2	4	no	—
169	C₂×C₄×C₂₃	—	2	32	no	—
170	C₂×C₄×C₂₃	—	2	8	no	—
171	C₂×C₄×C₂₃	—	2	8	no	—
172	C₂×C₄×C₂₃	—	2	4	no	—
173	C₂×C₄×C₂₃	—	2	4	no	—
174	C₂×C₄×C₂₃	—	2	8	no	—
175	C₂×C₄×C₂₃	—	2	8	no	—
176	C₂×C₄×C₂₃	—	2	8	no	—
177	C₂×C₄×C₂₃	—	4	8	no	—
178	C₂×C₄×C₂₃	—	4	8	no	—
179	C₂×C₄×C₂₃	—	4	16	no	—
180	C₂×C₄×C₂₃	#120	1	16	yes	—
181	C₂×C₄×C₂₃	C₂²×D₄	1	4	yes	—
182	C₂×C₄×C₂₃	C₂²×D₄	1	8	yes	—
183	C₂×C₄×C₂₃	C₂²×D₄	1	4	yes	—
184	C₂⁴×D₄	C₂×C₂₃	1	1	yes	characteristic
185	C₂²×#124	C₂×C₂₃	1	2	yes	complemented
186	C₂²×C₂²⋊Q₈	C₂×C₂₃	1	1	yes	characteristic, complemented
187	#2435	C₂×C₂₃	1	16	yes	direct product factor
188	C₂×#394	C₂×C₂₃	1	4	yes	complemented
189	C₂×#390	C₂×C₂₃	1	2	yes	complemented
190	C₂×#379	C₂×C₂₃	1	4	yes	complemented
191	C₂×C₄×C₂²⋊C₄	C₂×C₂₃	1	1	yes	characteristic, complemented
192	C₂²×C₂₃	—	2	4	no	—
193	C₂²×C₂₃	—	2	4	no	—
194	C₂²×C₂₃	—	2	32	no	—
195	C₂²×C₂₃	—	2	16	no	—
196	C₂²×C₂₃	—	2	16	no	—
197	C₂²×C₂₃	—	2	32	no	—
198	C₂²×C₂₃	—	4	128	no	—
199	C₂²×C₂₃	—	4	8	no	—
200	C₂²×C₂₃	—	4	8	no	—
201	C₂²×C₂₃	—	4	64	no	—
202	C₂²×C₂₃	—	4	16	no	—
203	C₂²×C₂₃	C₂×#120	1	4	yes	—
204	C₂²×C₂₃	C₂×#124	1	4	yes	—
205	C₂²×C₂₃	C₂×#124	1	8	yes	complemented
206	C₂²×C₂₃	#535	1	4	yes	—
207	C₂²×C₂₃	#546	1	16	yes	—
208	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
209	C₂²×C₂₃	C₂³×D₄	1	2	yes	—
210	C₂²×C₂₃	C₂²×#41	1	2	yes	—
211	C₂²×C₂₃	C₂×H(5,𝔽₂)	1	2	yes	—
212	C₄×C₂₃	—	2	4	no	—
213	C₄×C₂₃	—	4	4	no	—
214	C₄×C₂₃	—	4	4	no	—
215	C₄×C₂₃	—	4	8	no	—
216	C₄×C₂₃	C₂×#120	1	8	yes	—
217	C₂⁶	C₂²×C₂₃	1	2	yes	—
218	C₂³×Q₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
219	C₂³×D₄	—	2	16	no	—
220	C₂³×D₄	—	2	8	no	—
221	C₂³×D₄	C₂²×C₂₃	1	2	yes	—
222	C₂³×D₄	C₂²×C₂₃	1	8	yes	—
223	C₂³×D₄	C₂²×C₂₃	1	2	yes	—
224	C₂⁴×C₄	C₂²×C₂₃	1	1	yes	characteristic
225	C₂×#124	—	2	16	no	—
226	C₂×#124	C₂²×C₂₃	1	16	yes	complemented
227	C₂×C₂²⋊Q₈	—	2	8	no	—
228	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	8	yes	complemented
229	C₂²×C₄⋊C₄	C₂²×C₂₃	1	2	yes	complemented
230	C₂²×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic, complemented
231	C₂²×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
232	C₂²×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
233	C₂²×C₂²⋊C₄	C₂²×C₂₃	1	8	yes	complemented
234	C₂²×C₂²⋊C₄	C₂²×C₂₃	1	8	yes	complemented
235	C₂²×C₄²	C₂²×C₂₃	1	2	yes	complemented
236	#394	C₂²×C₂₃	1	32	yes	complemented
237	#390	C₂²×C₂₃	1	16	yes	complemented
238	#379	C₂²×C₂₃	1	32	yes	complemented
239	C₄×C₂²⋊C₄	C₂²×C₂₃	1	8	yes	complemented
240	C₂×#95	C₂²×C₂₃	1	2	yes	complemented
241	C₂×C₂₃	—	2	8	no	—
242	C₂×C₂₃	—	4	16	no	—
243	C₂×C₂₃	#2435	1	8	yes	direct product factor
244	C₂×C₂₃	C₂²×#120	1	1	yes	characteristic
245	C₂×C₂₃	C₂²×#124	1	1	yes	characteristic
246	C₂×C₂₃	C₂×#535	1	1	yes	characteristic
247	C₂×C₂₃	C₂×#546	1	4	yes	—
248	C₂⁵	—	2	16	no	—
249	C₂⁵	—	2	8	no	—
250	C₂⁵	—	2	16	no	—
251	C₂⁵	—	4	8	no	—
252	C₂⁵	C₂³×C₂₃	1	4	yes	—
253	C₂⁵	C₂³×C₂₃	1	8	yes	—
254	C₂⁵	C₂³×C₂₃	1	1	yes	characteristic
255	C₂²×Q₈	—	2	4	no	—
256	C₂²×Q₈	—	2	8	no	—
257	C₂²×Q₈	C₂³×C₂₃	1	4	yes	complemented
258	C₂²×D₄	—	2	128	no	—
259	C₂²×D₄	—	2	16	no	—
260	C₂²×D₄	—	2	64	no	—
261	C₂²×D₄	—	2	8	no	—
262	C₂²×D₄	—	2	32	no	—
263	C₂²×D₄	—	2	8	no	—
264	C₂²×D₄	—	2	8	no	—
265	C₂²×D₄	D₄×C₂₃	1	16	yes	—
266	C₂²×D₄	C₂³×C₂₃	1	8	yes	—
267	C₂²×D₄	C₂³×C₂₃	1	8	yes	—
268	C₂³×C₄	—	2	8	no	—
269	C₂³×C₄	D₄×C₂₃	1	8	yes	—
270	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
271	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
272	C₂³×C₄	C₂³×C₂₃	1	4	yes	—
273	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
274	C₂³×C₄	C₂³×C₂₃	1	4	yes	—
275	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
276	#124	—	2	64	no	—
277	C₂²⋊Q₈	—	2	32	no	—
278	C₂×C₄⋊C₄	—	2	4	no	—
279	C₂×C₄⋊C₄	—	2	8	no	—
280	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	complemented
281	C₂×C₄⋊C₄	C₂³×C₂₃	1	8	yes	complemented
282	C₂×C₂²⋊C₄	—	2	8	no	—
283	C₂×C₂²⋊C₄	—	2	32	no	—
284	C₂×C₂²⋊C₄	—	2	8	no	—
285	C₂×C₂²⋊C₄	—	4	16	no	—
286	C₂×C₂²⋊C₄	C₂³×C₂₃	1	8	yes	—
287	C₂×C₂²⋊C₄	C₂³×C₂₃	1	8	yes	—
288	C₂×C₂²⋊C₄	C₂³×C₂₃	1	32	yes	complemented
289	C₂×C₂²⋊C₄	C₂³×C₂₃	1	32	yes	complemented
290	C₂×C₄²	—	2	8	no	—
291	C₂×C₄²	C₂³×C₂₃	1	8	yes	complemented
292	#95	C₂³×C₂₃	1	8	yes	complemented
293	C₂₃	C₂×#2435	1	1	yes	characteristic, direct product factor, Sylow
294	C₂⁴	—	2	4	no	—
295	C₂⁴	—	2	4	no	—
296	C₂⁴	—	2	64	no	—
297	C₂⁴	—	2	32	no	—
298	C₂⁴	—	2	16	no	—
299	C₂⁴	—	2	8	no	—
300	C₂⁴	—	2	8	no	—
301	C₂⁴	—	2	16	no	—
302	C₂⁴	—	2	16	no	—
303	C₂⁴	—	2	32	no	—
304	C₂⁴	—	4	16	no	—
305	C₂⁴	—	4	128	no	—
306	C₂⁴	—	4	32	no	—
307	C₂⁴	—	4	32	no	—
308	C₂⁴	C₂×D₄×C₂₃	1	16	yes	—
309	C₂⁴	C₂×D₄×C₂₃	1	4	yes	—
310	C₂⁴	#41×C₂₃	1	8	yes	—
311	C₂⁴	C₂⁴×C₂₃	1	8	yes	—
312	C₂⁴	C₂⁴×C₂₃	1	2	yes	—
313	C₂⁴	C₂⁴×C₂₃	1	1	yes	characteristic
314	C₂×Q₈	—	2	8	no	—
315	C₂×Q₈	—	2	16	no	—
316	C₂×Q₈	—	4	16	no	—
317	C₂×D₄	—	2	64	no	—
318	C₂×D₄	—	2	256	no	—
319	C₂×D₄	—	2	32	no	—
320	C₂×D₄	—	2	64	no	—
321	C₂×D₄	—	2	16	no	—
322	C₂×D₄	—	2	16	no	—
323	C₂×D₄	—	2	16	no	—
324	C₂×D₄	C₂×D₄×C₂₃	1	32	yes	—
325	C₂²×C₄	—	2	4	no	—
326	C₂²×C₄	—	2	32	no	—
327	C₂²×C₄	—	2	16	no	—
328	C₂²×C₄	—	2	8	no	—
329	C₂²×C₄	—	2	8	no	—
330	C₂²×C₄	—	2	4	no	—
331	C₂²×C₄	—	2	4	no	—
332	C₂²×C₄	—	2	8	no	—
333	C₂²×C₄	—	2	8	no	—
334	C₂²×C₄	—	2	8	no	—
335	C₂²×C₄	C₂×D₄×C₂₃	1	4	yes	—
336	C₂²×C₄	C₂×D₄×C₂₃	1	16	yes	—
337	C₂²×C₄	C₂×D₄×C₂₃	1	8	yes	—
338	C₂²×C₄	C₂×D₄×C₂₃	1	4	yes	—
339	C₂²×C₄	C₂⁴×C₂₃	1	8	yes	—
340	C₂²×C₄	C₂⁴×C₂₃	1	4	yes	—
341	C₂²×C₄	C₂⁴×C₂₃	1	4	yes	—
342	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
343	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
344	C₄⋊C₄	—	2	8	no	—
345	C₄⋊C₄	—	2	16	no	—
346	C₂²⋊C₄	—	2	16	no	—
347	C₂²⋊C₄	—	2	64	no	—
348	C₂²⋊C₄	—	2	16	no	—
349	C₂²⋊C₄	—	4	32	no	—
350	C₄²	—	2	16	no	—
351	C₂³	—	2	4	no	—
352	C₂³	—	2	4	no	—
353	C₂³	—	2	8	no	—
354	C₂³	—	2	8	no	—
355	C₂³	—	2	32	no	—
356	C₂³	—	2	64	no	—
357	C₂³	—	2	8	no	—
358	C₂³	—	2	8	no	—
359	C₂³	—	2	16	no	—
360	C₂³	—	2	16	no	—
361	C₂³	—	2	32	no	—
362	C₂³	—	2	64	no	—
363	C₂³	—	4	128	no	—
364	C₂³	—	4	32	no	—
365	C₂³	—	4	256	no	—
366	C₂³	—	4	16	no	—
367	C₂³	—	4	32	no	—
368	C₂³	—	4	16	no	—
369	C₂³	—	4	32	no	—
370	C₂³	C₂₃×#124	1	16	yes	complemented
371	C₂³	C₂²×D₄×C₂₃	1	16	yes	—
372	C₂³	C₂²×D₄×C₂₃	1	4	yes	—
373	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
374	C₂³	C₂²×D₄×C₂₃	1	4	yes	—
375	C₂³	C₂×#41×C₂₃	1	8	yes	—
376	C₂³	C₂×#41×C₂₃	1	4	yes	—
377	C₂³	C₂₃×H(5,𝔽₂)	1	4	yes	—
378	C₂³	C₂⁵×C₂₃	1	1	yes	characteristic
379	Q₈	—	4	16	no	—
380	D₄	—	2	64	no	—
381	D₄	—	2	64	no	—
382	C₂×C₄	—	2	4	no	—
383	C₂×C₄	—	2	8	no	—
384	C₂×C₄	—	2	32	no	—
385	C₂×C₄	—	2	8	no	—
386	C₂×C₄	—	2	8	no	—
387	C₂×C₄	—	2	4	no	—
388	C₂×C₄	—	2	4	no	—
389	C₂×C₄	—	2	8	no	—
390	C₂×C₄	—	2	8	no	—
391	C₂×C₄	—	2	8	no	—
392	C₂×C₄	—	4	8	no	—
393	C₂×C₄	—	4	8	no	—
394	C₂×C₄	—	4	16	no	—
395	C₂×C₄	C₂₃×#120	1	16	yes	—
396	C₂×C₄	C₂²×D₄×C₂₃	1	4	yes	—
397	C₂×C₄	C₂²×D₄×C₂₃	1	8	yes	—
398	C₂×C₄	C₂²×D₄×C₂₃	1	4	yes	—
399	C₂²	—	2	4	no	—
400	C₂²	—	2	4	no	—
401	C₂²	—	2	32	no	—
402	C₂²	—	2	16	no	—
403	C₂²	—	2	16	no	—
404	C₂²	—	2	32	no	—
405	C₂²	—	4	128	no	—
406	C₂²	—	4	8	no	—
407	C₂²	—	4	8	no	—
408	C₂²	—	4	64	no	—
409	C₂²	—	4	16	no	—
410	C₂²	C₂×C₂₃×#120	1	4	yes	—
411	C₂²	C₂×C₂₃×#124	1	4	yes	—
412	C₂²	C₂×C₂₃×#124	1	8	yes	complemented
413	C₂²	C₂₃×#535	1	4	yes	—
414	C₂²	C₂₃×#546	1	16	yes	—
415	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
416	C₂²	C₂³×D₄×C₂₃	1	2	yes	—
417	C₂²	C₂²×#41×C₂₃	1	2	yes	—
418	C₂²	C₂×C₂₃×H(5,𝔽₂)	1	2	yes	—
419	C₄	—	2	4	no	—
420	C₄	—	4	4	no	—
421	C₄	—	4	4	no	—
422	C₄	—	4	8	no	—
423	C₄	C₂×C₂₃×#120	1	8	yes	—
424	C₂	—	2	8	no	—
425	C₂	—	4	16	no	—
426	C₂	C₂₃×#2435	1	8	yes	direct product factor
427	C₂	C₂²×C₂₃×#120	1	1	yes	characteristic
428	C₂	C₂²×C₂₃×#124	1	1	yes	characteristic
429	C₂	C₂×C₂₃×#535	1	1	yes	characteristic
430	C₂	C₂×C₂₃×#546	1	4	yes	—

	subgroup	G/H
center, socle	C₂⁴×C₂₃	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₂₃
prime radical	C₂⁴×D₄×C₂₃	C₂
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
2. C₂²×C₂₃×#124	C₂	semidirect
3. C₂²×C₂₃×C₂²⋊Q₈	C₂	semidirect
4. C₂₃×#2435	C₂	direct (N × H)
5. C₂×C₂₃×#394	C₂	semidirect
6. C₂×C₂₃×#390	C₂	semidirect
7. C₂×C₂₃×#379	C₂	semidirect
8. C₂×C₄×C₂²⋊C₄×C₂₃	C₂	semidirect
10. C₂³×Q₈×C₂₃	C₂²	semidirect
18. C₂×C₂₃×#124	C₂²	semidirect
20. C₂×C₂₃×C₂²⋊Q₈	C₂²	semidirect
21. C₂²×C₄⋊C₄×C₂₃	C₂²	semidirect
22. C₂²×C₄⋊C₄×C₂₃	C₂²	semidirect
25. C₂²×C₂²⋊C₄×C₂₃	C₂²	semidirect
26. C₂²×C₂²⋊C₄×C₂₃	C₂²	semidirect
27. C₂²×C₄²×C₂₃	C₂²	semidirect
28. C₂₃×#394	C₂²	semidirect
29. C₂₃×#390	C₂²	semidirect
30. C₂₃×#379	C₂²	semidirect
31. C₄×C₂²⋊C₄×C₂₃	C₂²	semidirect
32. C₂×C₂₃×#95	C₂²	semidirect
42. C₂²×Q₈×C₂₃	C₂³	semidirect
65. C₂×C₄⋊C₄×C₂₃	C₂³	semidirect
66. C₂×C₄⋊C₄×C₂₃	C₂³	semidirect
73. C₂×C₂²⋊C₄×C₂₃	C₂³	semidirect
74. C₂×C₂²⋊C₄×C₂₃	C₂³	semidirect
76. C₂×C₄²×C₂₃	C₂³	semidirect
77. C₂₃×#95	C₂³	semidirect
135. C₂×#2435	C₂₃	direct (N × H)
155. C₂³×C₂₃	#124	semidirect
185. C₂²×#124	C₂×C₂₃	semidirect
186. C₂²×C₂²⋊Q₈	C₂×C₂₃	semidirect
187. #2435	C₂×C₂₃	direct (N × H)
188. C₂×#394	C₂×C₂₃	semidirect
189. C₂×#390	C₂×C₂₃	semidirect
190. C₂×#379	C₂×C₂₃	semidirect
191. C₂×C₄×C₂²⋊C₄	C₂×C₂₃	semidirect
205. C₂²×C₂₃	C₂×#124	semidirect
218. C₂³×Q₈	C₂²×C₂₃	semidirect
226. C₂×#124	C₂²×C₂₃	semidirect
228. C₂×C₂²⋊Q₈	C₂²×C₂₃	semidirect
229. C₂²×C₄⋊C₄	C₂²×C₂₃	semidirect
230. C₂²×C₄⋊C₄	C₂²×C₂₃	semidirect
233. C₂²×C₂²⋊C₄	C₂²×C₂₃	semidirect
234. C₂²×C₂²⋊C₄	C₂²×C₂₃	semidirect
235. C₂²×C₄²	C₂²×C₂₃	semidirect
236. #394	C₂²×C₂₃	semidirect
237. #390	C₂²×C₂₃	semidirect
238. #379	C₂²×C₂₃	semidirect
239. C₄×C₂²⋊C₄	C₂²×C₂₃	semidirect
240. C₂×#95	C₂²×C₂₃	semidirect
243. C₂×C₂₃	#2435	direct (N × H)
257. C₂²×Q₈	C₂³×C₂₃	semidirect
280. C₂×C₄⋊C₄	C₂³×C₂₃	semidirect
281. C₂×C₄⋊C₄	C₂³×C₂₃	semidirect
288. C₂×C₂²⋊C₄	C₂³×C₂₃	semidirect
289. C₂×C₂²⋊C₄	C₂³×C₂₃	semidirect
291. C₂×C₄²	C₂³×C₂₃	semidirect
292. #95	C₂³×C₂₃	semidirect
293. C₂₃	C₂×#2435	direct (N × H)
370. C₂³	C₂₃×#124	semidirect
412. C₂²	C₂×C₂₃×#124	semidirect
426. C₂	C₂₃×#2435	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂⁴×D₄×C₂₃	2
C₂²×C₂₃×#124	2
C₂²×C₂₃×C₂²⋊Q₈	2
C₂₃×#2435	2
C₂×C₂₃×#394	2
C₂×C₂₃×#390	2
C₂×C₂₃×#379	2
C₂×C₄×C₂²⋊C₄×C₂₃	2
C₂×#2435	23

Subgroups — C2×C23×#2435 #19182318

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₂₃×#2435 #19182318