Subgroups — C₂²×C₃×#4024 #14479415

Order 1920.

3680 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴×C₃×Dic₅	C₂	1	1	yes	maximal, characteristic
2	C₂³×C₃×Dic₁₀	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₃×C₅×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic
4	C₂²×C₃×C₂²⋊Dic₅	C₂	1	1	yes	maximal, characteristic
5	C₂²×C₃×C₄⋊Dic₅	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×C₃×#683	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂²×C₃×#683	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₃×#4024	C₂	1	24	yes	maximal, direct product factor
9	C₂²×#4024	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂⁵×C₃×C₅	C₂²	1	1	yes	characteristic
11	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
12	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
13	C₂³×C₃×Dic₅	—	2	8	no	—
14	C₂³×C₃×Dic₅	C₂²	1	1	yes	characteristic
15	C₂³×C₃×Dic₅	C₂²	1	1	yes	characteristic
16	C₂³×C₃×Dic₅	C₂²	1	1	yes	characteristic
17	C₂³×C₃×Dic₅	C₂²	1	12	yes	—
18	C₂³×C₃×Dic₅	C₂²	1	1	yes	characteristic
19	C₂²×C₃×Dic₁₀	—	2	8	no	—
20	C₂²×C₃×Dic₁₀	C₂²	1	12	yes	complemented
21	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	12	yes	—
22	C₂×C₃×C₂²⋊Dic₅	C₂²	1	12	yes	—
23	C₂×C₃×C₄⋊Dic₅	C₂²	1	12	yes	complemented
24	C₂×C₃×#683	C₂²	1	12	yes	complemented
25	C₂×C₃×#683	C₂²	1	12	yes	complemented
26	C₃×#4024	C₂²	1	64	yes	direct product factor
27	C₂²×C₃×C₂²⋊Q₈	—	5	1	no	maximal, Hall
28	C₂⁴×Dic₅	C₂×C₃	1	1	yes	characteristic
29	C₂³×Dic₁₀	C₂×C₃	1	1	yes	characteristic, complemented
30	C₂²×C₅×C₂²⋊C₄	C₂×C₃	1	1	yes	characteristic
31	C₂²×C₂²⋊Dic₅	C₂×C₃	1	1	yes	characteristic
32	C₂²×C₄⋊Dic₅	C₂×C₃	1	1	yes	characteristic, complemented
33	C₂²×#683	C₂×C₃	1	1	yes	characteristic, complemented
34	C₂²×#683	C₂×C₃	1	1	yes	characteristic, complemented
35	C₂×#4024	C₂×C₃	1	24	yes	direct product factor
36	C₂⁴×C₃×C₅	—	2	4	no	—
37	C₂⁴×C₃×C₅	—	2	4	no	—
38	C₂⁴×C₃×C₅	Q₈	1	8	yes	complemented
39	C₂⁴×C₃×C₅	C₂³	1	6	yes	—
40	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
41	C₂²×C₃×C₄×C₅	—	2	4	no	—
42	C₂²×C₃×C₄×C₅	—	2	4	no	—
43	C₂²×C₃×C₄×C₅	C₂³	1	6	yes	—
44	C₂²×C₃×C₄×C₅	C₂³	1	6	yes	—
45	C₂²×C₃×Dic₅	—	2	4	no	—
46	C₂²×C₃×Dic₅	—	2	4	no	—
47	C₂²×C₃×Dic₅	—	2	4	no	—
48	C₂²×C₃×Dic₅	—	2	48	no	—
49	C₂²×C₃×Dic₅	D₄	1	8	yes	—
50	C₂²×C₃×Dic₅	C₂³	1	6	yes	—
51	C₂²×C₃×Dic₅	C₂³	1	6	yes	—
52	C₂²×C₃×Dic₅	C₂³	1	16	yes	—
53	C₂²×C₃×Dic₅	C₂³	1	6	yes	—
54	C₂²×C₃×Dic₅	C₂³	1	6	yes	—
55	C₂×C₃×Dic₁₀	—	2	48	no	—
56	C₂×C₃×Dic₁₀	C₂³	1	16	yes	complemented
57	C₃×C₅×C₂²⋊C₄	C₂³	1	16	yes	—
58	C₃×C₂²⋊Dic₅	C₂³	1	16	yes	—
59	C₃×C₄⋊Dic₅	C₂³	1	16	yes	complemented
60	C₃×#683	C₂³	1	16	yes	complemented
61	C₃×#683	C₂³	1	16	yes	complemented
62	C₂³×C₃×Q₈	—	5	1	no	—
63	C₂⁴×C₃×C₄	—	5	1	no	—
64	C₂×C₃×C₂²⋊Q₈	—	5	24	no	—
65	C₂²×C₃×C₄⋊C₄	—	5	1	no	—
66	C₂²×C₃×C₄⋊C₄	—	5	1	no	—
67	C₂²×C₃×C₄⋊C₄	—	5	1	no	—
68	C₂²×C₃×C₂²⋊C₄	—	5	1	no	—
69	C₂²×C₃×C₂²⋊C₄	D₅	1	1	yes	characteristic
70	C₂⁵×C₅	C₂²×C₃	1	1	yes	characteristic
71	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
72	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
73	C₂³×Dic₅	—	2	8	no	—
74	C₂³×Dic₅	C₂²×C₃	1	12	yes	—
75	C₂³×Dic₅	C₂²×C₃	1	1	yes	characteristic
76	C₂³×Dic₅	C₂²×C₃	1	1	yes	characteristic
77	C₂³×Dic₅	C₂²×C₃	1	1	yes	characteristic
78	C₂³×Dic₅	C₂²×C₃	1	1	yes	characteristic
79	C₂²×Dic₁₀	—	2	8	no	—
80	C₂²×Dic₁₀	C₂²×C₃	1	12	yes	complemented
81	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	12	yes	—
82	C₂×C₂²⋊Dic₅	C₂²×C₃	1	12	yes	—
83	C₂×C₄⋊Dic₅	C₂²×C₃	1	12	yes	complemented
84	C₂×#683	C₂²×C₃	1	12	yes	complemented
85	C₂×#683	C₂²×C₃	1	12	yes	complemented
86	#4024	C₂²×C₃	1	64	yes	direct product factor
87	C₂²×C₂²⋊Q₈	—	5	1	no	Sylow
88	C₂³×C₃×C₅	—	2	32	no	—
89	C₂³×C₃×C₅	—	2	12	no	—
90	C₂³×C₃×C₅	—	2	12	no	—
91	C₂³×C₃×C₅	C₂×D₄	1	4	yes	—
92	C₂³×C₃×C₅	C₂×Q₈	1	4	yes	—
93	C₂³×C₃×C₅	C₂×Q₈	1	24	yes	complemented
94	C₂³×C₃×C₅	#41	1	4	yes	—
95	C₂³×C₃×C₅	C₂⁴	1	4	yes	—
96	C₂³×C₃×C₅	C₂⁴	1	3	yes	—
97	C₂×C₃×C₄×C₅	—	2	12	no	—
98	C₂×C₃×C₄×C₅	—	2	12	no	—
99	C₂×C₃×C₄×C₅	C₂⁴	1	4	yes	—
100	C₂×C₃×C₄×C₅	C₂⁴	1	4	yes	—
101	C₂×C₃×Dic₅	—	2	12	no	—
102	C₂×C₃×Dic₅	—	2	12	no	—
103	C₂×C₃×Dic₅	—	2	12	no	—
104	C₂×C₃×Dic₅	—	2	32	no	—
105	C₂×C₃×Dic₅	C₂×D₄	1	24	yes	—
106	C₂×C₃×Dic₅	C₂⁴	1	4	yes	—
107	C₂×C₃×Dic₅	C₂⁴	1	4	yes	—
108	C₂×C₃×Dic₅	C₂⁴	1	4	yes	—
109	C₂×C₃×Dic₅	C₂⁴	1	4	yes	—
110	C₃×Dic₁₀	—	2	32	no	—
111	C₂⁵×C₃	C₂×D₅	1	1	yes	characteristic
112	C₂²×C₃×Q₈	—	5	12	no	—
113	C₂²×C₃×Q₈	—	10	8	no	—
114	C₂³×C₃×C₄	—	5	1	no	—
115	C₂³×C₃×C₄	—	5	12	no	—
116	C₂³×C₃×C₄	—	5	1	no	—
117	C₂³×C₃×C₄	—	5	1	no	—
118	C₂³×C₃×C₄	—	5	1	no	—
119	C₂³×C₃×C₄	—	10	8	no	—
120	C₂³×C₃×C₄	C₂×D₅	1	1	yes	characteristic
121	C₂³×C₃×C₄	C₂×D₅	1	1	yes	characteristic
122	C₃×C₂²⋊Q₈	—	5	64	no	—
123	C₂×C₃×C₄⋊C₄	—	5	12	no	—
124	C₂×C₃×C₄⋊C₄	—	5	12	no	—
125	C₂×C₃×C₄⋊C₄	—	5	12	no	—
126	C₂×C₃×C₂²⋊C₄	—	5	12	no	—
127	C₂×C₃×C₂²⋊C₄	C₂×D₅	1	12	yes	—
128	C₂⁴×C₅	—	2	4	no	—
129	C₂⁴×C₅	—	2	4	no	—
130	C₂⁴×C₅	C₃×Q₈	1	8	yes	complemented
131	C₂⁴×C₅	C₂³×C₃	1	6	yes	—
132	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
133	C₂²×C₄×C₅	—	2	4	no	—
134	C₂²×C₄×C₅	—	2	4	no	—
135	C₂²×C₄×C₅	C₂³×C₃	1	6	yes	—
136	C₂²×C₄×C₅	C₂³×C₃	1	6	yes	—
137	C₂²×Dic₅	—	2	4	no	—
138	C₂²×Dic₅	—	2	4	no	—
139	C₂²×Dic₅	—	2	4	no	—
140	C₂²×Dic₅	—	2	48	no	—
141	C₂²×Dic₅	C₃×D₄	1	8	yes	—
142	C₂²×Dic₅	C₂³×C₃	1	6	yes	—
143	C₂²×Dic₅	C₂³×C₃	1	6	yes	—
144	C₂²×Dic₅	C₂³×C₃	1	16	yes	—
145	C₂²×Dic₅	C₂³×C₃	1	6	yes	—
146	C₂²×Dic₅	C₂³×C₃	1	6	yes	—
147	C₂×Dic₁₀	—	2	48	no	—
148	C₂×Dic₁₀	C₂³×C₃	1	16	yes	complemented
149	C₅×C₂²⋊C₄	C₂³×C₃	1	16	yes	—
150	C₂²⋊Dic₅	C₂³×C₃	1	16	yes	—
151	C₄⋊Dic₅	C₂³×C₃	1	16	yes	complemented
152	#683	C₂³×C₃	1	16	yes	complemented
153	#683	C₂³×C₃	1	16	yes	complemented
154	C₂³×Q₈	—	5	1	no	—
155	C₂⁴×C₄	—	5	1	no	—
156	C₂×C₂²⋊Q₈	—	5	24	no	—
157	C₂²×C₄⋊C₄	—	5	1	no	—
158	C₂²×C₄⋊C₄	—	5	1	no	—
159	C₂²×C₄⋊C₄	—	5	1	no	—
160	C₂²×C₂²⋊C₄	—	5	1	no	—
161	C₂²×C₂²⋊C₄	C₃×D₅	1	1	yes	characteristic
162	C₂²×C₃×C₅	—	2	48	no	—
163	C₂²×C₃×C₅	—	2	4	no	—
164	C₂²×C₃×C₅	—	2	4	no	—
165	C₂²×C₃×C₅	C₂²⋊Q₈	1	16	yes	complemented
166	C₂²×C₃×C₅	C₂²×D₄	1	6	yes	—
167	C₂²×C₃×C₅	C₂²×Q₈	1	6	yes	—
168	C₂²×C₃×C₅	C₂²×Q₈	1	8	yes	complemented
169	C₂²×C₃×C₅	C₂×#41	1	6	yes	—
170	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
171	C₃×C₄×C₅	—	2	4	no	—
172	C₃×C₄×C₅	—	2	4	no	—
173	C₃×Dic₅	—	2	4	no	—
174	C₃×Dic₅	—	2	4	no	—
175	C₃×Dic₅	—	2	4	no	—
176	C₃×Dic₅	C₂²×D₄	1	8	yes	—
177	C₂⁴×C₃	—	2	4	no	—
178	C₂⁴×C₃	—	2	4	no	—
179	C₂⁴×C₃	Dic₁₀	1	8	yes	complemented
180	C₂⁴×C₃	C₂²×D₅	1	6	yes	—
181	C₂⁴×C₃	C₂²×D₅	1	1	yes	characteristic
182	C₂×C₃×Q₈	—	5	16	no	—
183	C₂×C₃×Q₈	—	10	48	no	—
184	C₂²×C₃×C₄	—	2	4	no	—
185	C₂²×C₃×C₄	—	2	4	no	—
186	C₂²×C₃×C₄	—	5	8	no	—
187	C₂²×C₃×C₄	—	5	6	no	—
188	C₂²×C₃×C₄	—	5	6	no	—
189	C₂²×C₃×C₄	—	5	6	no	—
190	C₂²×C₃×C₄	—	5	6	no	—
191	C₂²×C₃×C₄	—	5	16	no	—
192	C₂²×C₃×C₄	—	10	48	no	—
193	C₂²×C₃×C₄	—	10	4	no	—
194	C₂²×C₃×C₄	—	10	4	no	—
195	C₂²×C₃×C₄	—	10	4	no	—
196	C₂²×C₃×C₄	C₂²×D₅	1	6	yes	—
197	C₂²×C₃×C₄	C₂²×D₅	1	6	yes	—
198	C₃×C₄⋊C₄	—	5	16	no	—
199	C₃×C₄⋊C₄	—	5	16	no	—
200	C₃×C₄⋊C₄	—	5	16	no	—
201	C₃×C₂²⋊C₄	—	5	16	no	—
202	C₃×C₂²⋊C₄	C₂²×D₅	1	16	yes	—
203	C₂³×C₅	—	2	32	no	—
204	C₂³×C₅	—	2	12	no	—
205	C₂³×C₅	—	2	12	no	—
206	C₂³×C₅	C₂×C₃×D₄	1	4	yes	—
207	C₂³×C₅	C₂×C₃×Q₈	1	4	yes	—
208	C₂³×C₅	C₂×C₃×Q₈	1	24	yes	complemented
209	C₂³×C₅	C₃×#41	1	4	yes	—
210	C₂³×C₅	C₂⁴×C₃	1	4	yes	—
211	C₂³×C₅	C₂⁴×C₃	1	3	yes	—
212	C₂×C₄×C₅	—	2	12	no	—
213	C₂×C₄×C₅	—	2	12	no	—
214	C₂×C₄×C₅	C₂⁴×C₃	1	4	yes	—
215	C₂×C₄×C₅	C₂⁴×C₃	1	4	yes	—
216	C₂×Dic₅	—	2	12	no	—
217	C₂×Dic₅	—	2	12	no	—
218	C₂×Dic₅	—	2	12	no	—
219	C₂×Dic₅	—	2	32	no	—
220	C₂×Dic₅	C₂×C₃×D₄	1	24	yes	—
221	C₂×Dic₅	C₂⁴×C₃	1	4	yes	—
222	C₂×Dic₅	C₂⁴×C₃	1	4	yes	—
223	C₂×Dic₅	C₂⁴×C₃	1	4	yes	—
224	C₂×Dic₅	C₂⁴×C₃	1	4	yes	—
225	Dic₁₀	—	2	32	no	—
226	C₂⁵	C₂×C₃×D₅	1	1	yes	characteristic
227	C₂²×Q₈	—	5	12	no	—
228	C₂²×Q₈	—	10	8	no	—
229	C₂³×C₄	—	5	1	no	—
230	C₂³×C₄	—	5	1	no	—
231	C₂³×C₄	—	5	1	no	—
232	C₂³×C₄	—	5	1	no	—
233	C₂³×C₄	—	5	12	no	—
234	C₂³×C₄	—	10	8	no	—
235	C₂³×C₄	C₂×C₃×D₅	1	1	yes	characteristic
236	C₂³×C₄	C₂×C₃×D₅	1	1	yes	characteristic
237	C₂²⋊Q₈	—	5	64	no	—
238	C₂×C₄⋊C₄	—	5	12	no	—
239	C₂×C₄⋊C₄	—	5	12	no	—
240	C₂×C₄⋊C₄	—	5	12	no	—
241	C₂×C₂²⋊C₄	—	5	12	no	—
242	C₂×C₂²⋊C₄	C₂×C₃×D₅	1	12	yes	—
243	C₂×C₃×C₅	—	2	8	no	—
244	C₂×C₃×C₅	C₂×C₂²⋊Q₈	1	12	yes	complemented
245	C₂×C₃×C₅	C₂³×D₄	1	1	yes	characteristic
246	C₂×C₃×C₅	C₂³×Q₈	1	1	yes	characteristic
247	C₂×C₃×C₅	C₂²×#41	1	1	yes	characteristic
248	C₂³×C₃	—	2	12	no	—
249	C₂³×C₃	—	2	12	no	—
250	C₂³×C₃	—	2	32	no	—
251	C₂³×C₃	C₂×Dic₁₀	1	4	yes	—
252	C₂³×C₃	C₂×Dic₁₀	1	24	yes	complemented
253	C₂³×C₃	D₄×D₅	1	4	yes	—
254	C₂³×C₃	#711	1	4	yes	—
255	C₂³×C₃	C₂³×D₅	1	4	yes	—
256	C₂³×C₃	C₂³×D₅	1	3	yes	—
257	C₃×Q₈	—	10	32	no	—
258	C₂×C₃×C₄	—	2	12	no	—
259	C₂×C₃×C₄	—	2	12	no	—
260	C₂×C₃×C₄	—	5	24	no	—
261	C₂×C₃×C₄	—	5	4	no	—
262	C₂×C₃×C₄	—	5	4	no	—
263	C₂×C₃×C₄	—	5	4	no	—
264	C₂×C₃×C₄	—	5	4	no	—
265	C₂×C₃×C₄	—	10	32	no	—
266	C₂×C₃×C₄	—	10	12	no	—
267	C₂×C₃×C₄	—	10	12	no	—
268	C₂×C₃×C₄	—	10	12	no	—
269	C₂×C₃×C₄	C₂³×D₅	1	4	yes	—
270	C₂×C₃×C₄	C₂³×D₅	1	4	yes	—
271	C₂²×C₅	—	2	4	no	—
272	C₂²×C₅	—	2	4	no	—
273	C₂²×C₅	—	2	48	no	—
274	C₂²×C₅	C₃×C₂²⋊Q₈	1	16	yes	complemented
275	C₂²×C₅	C₂²×C₃×D₄	1	6	yes	—
276	C₂²×C₅	C₂²×C₃×Q₈	1	6	yes	—
277	C₂²×C₅	C₂²×C₃×Q₈	1	8	yes	complemented
278	C₂²×C₅	C₂×C₃×#41	1	6	yes	—
279	C₂²×C₅	C₂⁵×C₃	1	1	yes	characteristic
280	C₄×C₅	—	2	4	no	—
281	C₄×C₅	—	2	4	no	—
282	Dic₅	—	2	4	no	—
283	Dic₅	—	2	4	no	—
284	Dic₅	—	2	4	no	—
285	Dic₅	C₂²×C₃×D₄	1	8	yes	—
286	C₂⁴	—	2	4	no	—
287	C₂⁴	—	2	4	no	—
288	C₂⁴	C₃×Dic₁₀	1	8	yes	complemented
289	C₂⁴	C₂²×C₃×D₅	1	6	yes	—
290	C₂⁴	C₂²×C₃×D₅	1	1	yes	characteristic
291	C₂×Q₈	—	5	16	no	—
292	C₂×Q₈	—	10	48	no	—
293	C₂²×C₄	—	2	4	no	—
294	C₂²×C₄	—	2	4	no	—
295	C₂²×C₄	—	5	8	no	—
296	C₂²×C₄	—	5	6	no	—
297	C₂²×C₄	—	5	6	no	—
298	C₂²×C₄	—	5	6	no	—
299	C₂²×C₄	—	5	6	no	—
300	C₂²×C₄	—	5	16	no	—
301	C₂²×C₄	—	10	48	no	—
302	C₂²×C₄	—	10	4	no	—
303	C₂²×C₄	—	10	4	no	—
304	C₂²×C₄	—	10	4	no	—
305	C₂²×C₄	C₂²×C₃×D₅	1	6	yes	—
306	C₂²×C₄	C₂²×C₃×D₅	1	6	yes	—
307	C₄⋊C₄	—	5	16	no	—
308	C₄⋊C₄	—	5	16	no	—
309	C₄⋊C₄	—	5	16	no	—
310	C₂²⋊C₄	—	5	16	no	—
311	C₂²⋊C₄	C₂²×C₃×D₅	1	16	yes	—
312	C₃×C₅	C₂²×C₂²⋊Q₈	1	1	yes	characteristic, complemented, Hall
313	C₂²×C₃	—	2	48	no	—
314	C₂²×C₃	—	2	4	no	—
315	C₂²×C₃	—	2	4	no	—
316	C₂²×C₃	#4024	1	16	yes	direct product factor
317	C₂²×C₃	C₂²×Dic₁₀	1	6	yes	—
318	C₂²×C₃	C₂²×Dic₁₀	1	8	yes	complemented
319	C₂²×C₃	C₂×D₄×D₅	1	6	yes	—
320	C₂²×C₃	C₂×#711	1	6	yes	—
321	C₂²×C₃	C₂⁴×D₅	1	1	yes	characteristic
322	C₃×C₄	—	2	4	no	—
323	C₃×C₄	—	2	4	no	—
324	C₃×C₄	—	5	8	no	—
325	C₃×C₄	—	10	4	no	—
326	C₃×C₄	—	10	4	no	—
327	C₃×C₄	—	10	4	no	—
328	C₂×C₅	—	2	8	no	—
329	C₂×C₅	C₂×C₃×C₂²⋊Q₈	1	12	yes	complemented
330	C₂×C₅	C₂³×C₃×D₄	1	1	yes	characteristic
331	C₂×C₅	C₂³×C₃×Q₈	1	1	yes	characteristic
332	C₂×C₅	C₂²×C₃×#41	1	1	yes	characteristic
333	C₂³	—	2	12	no	—
334	C₂³	—	2	12	no	—
335	C₂³	—	2	32	no	—
336	C₂³	C₂×C₃×Dic₁₀	1	4	yes	—
337	C₂³	C₂×C₃×Dic₁₀	1	24	yes	complemented
338	C₂³	C₃×D₄×D₅	1	4	yes	—
339	C₂³	C₃×#711	1	4	yes	—
340	C₂³	C₂³×C₃×D₅	1	4	yes	—
341	C₂³	C₂³×C₃×D₅	1	3	yes	—
342	Q₈	—	10	32	no	—
343	C₂×C₄	—	2	12	no	—
344	C₂×C₄	—	2	12	no	—
345	C₂×C₄	—	5	24	no	—
346	C₂×C₄	—	5	4	no	—
347	C₂×C₄	—	5	4	no	—
348	C₂×C₄	—	5	4	no	—
349	C₂×C₄	—	5	4	no	—
350	C₂×C₄	—	10	32	no	—
351	C₂×C₄	—	10	12	no	—
352	C₂×C₄	—	10	12	no	—
353	C₂×C₄	—	10	12	no	—
354	C₂×C₄	C₂³×C₃×D₅	1	4	yes	—
355	C₂×C₄	C₂³×C₃×D₅	1	4	yes	—
356	C₂×C₃	—	2	8	no	—
357	C₂×C₃	C₂×#4024	1	12	yes	direct product factor
358	C₂×C₃	C₂³×Dic₁₀	1	1	yes	characteristic
359	C₂×C₃	C₂²×D₄×D₅	1	1	yes	characteristic
360	C₂×C₃	C₂²×#711	1	1	yes	characteristic
361	C₅	C₂²×C₃×C₂²⋊Q₈	1	1	yes	characteristic, complemented, Sylow
362	C₂²	—	2	4	no	—
363	C₂²	—	2	4	no	—
364	C₂²	—	2	48	no	—
365	C₂²	C₃×#4024	1	16	yes	direct product factor
366	C₂²	C₂²×C₃×Dic₁₀	1	6	yes	—
367	C₂²	C₂²×C₃×Dic₁₀	1	8	yes	complemented
368	C₂²	C₂×C₃×D₄×D₅	1	6	yes	—
369	C₂²	C₂×C₃×#711	1	6	yes	—
370	C₂²	C₂⁴×C₃×D₅	1	1	yes	characteristic
371	C₄	—	2	4	no	—
372	C₄	—	2	4	no	—
373	C₄	—	5	8	no	—
374	C₄	—	10	4	no	—
375	C₄	—	10	4	no	—
376	C₄	—	10	4	no	—
377	C₃	C₂²×#4024	1	1	yes	characteristic, direct product factor, Sylow
378	C₂	—	2	8	no	—
379	C₂	C₂×C₃×#4024	1	12	yes	direct product factor
380	C₂	C₂³×C₃×Dic₁₀	1	1	yes	characteristic
381	C₂	C₂²×C₃×D₄×D₅	1	1	yes	characteristic
382	C₂	C₂²×C₃×#711	1	1	yes	characteristic

	subgroup	G/H
center	C₂⁴×C₃	C₂²×D₅
commutator, cosocle	C₂²×C₅	C₂⁵×C₃
Frattini	C₂²	C₂⁴×C₃×D₅
Fitting	C₂²×C₃×C₅×C₂²⋊C₄	C₂
socle	C₂⁴×C₃×C₅	C₂³
prime radical	C₂⁵×C₃×C₅	C₂²
hypercenter	C₂²×C₃×C₂²⋊C₄	D₅
hypocenter	C₅	C₂²×C₃×C₂²⋊Q₈
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂⁴×C₃ ◁ C₂²×C₃×C₂²⋊C₄

Complements

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

N	H ≅ G/N	type
2. C₂³×C₃×Dic₁₀	C₂	semidirect
5. C₂²×C₃×C₄⋊Dic₅	C₂	semidirect
6. C₂²×C₃×#683	C₂	semidirect
7. C₂²×C₃×#683	C₂	semidirect
8. C₂×C₃×#4024	C₂	direct (N × H)
9. C₂²×#4024	C₃	direct (N × H)
20. C₂²×C₃×Dic₁₀	C₂²	semidirect
23. C₂×C₃×C₄⋊Dic₅	C₂²	semidirect
24. C₂×C₃×#683	C₂²	semidirect
25. C₂×C₃×#683	C₂²	semidirect
26. C₃×#4024	C₂²	direct (N × H)
29. C₂³×Dic₁₀	C₂×C₃	semidirect
32. C₂²×C₄⋊Dic₅	C₂×C₃	semidirect
33. C₂²×#683	C₂×C₃	semidirect
34. C₂²×#683	C₂×C₃	semidirect
35. C₂×#4024	C₂×C₃	direct (N × H)
38. C₂⁴×C₃×C₅	Q₈	semidirect
56. C₂×C₃×Dic₁₀	C₂³	semidirect
59. C₃×C₄⋊Dic₅	C₂³	semidirect
60. C₃×#683	C₂³	semidirect
61. C₃×#683	C₂³	semidirect
80. C₂²×Dic₁₀	C₂²×C₃	semidirect
83. C₂×C₄⋊Dic₅	C₂²×C₃	semidirect
84. C₂×#683	C₂²×C₃	semidirect
85. C₂×#683	C₂²×C₃	semidirect
86. #4024	C₂²×C₃	direct (N × H)
93. C₂³×C₃×C₅	C₂×Q₈	semidirect
130. C₂⁴×C₅	C₃×Q₈	semidirect
148. C₂×Dic₁₀	C₂³×C₃	semidirect
151. C₄⋊Dic₅	C₂³×C₃	semidirect
152. #683	C₂³×C₃	semidirect
153. #683	C₂³×C₃	semidirect
165. C₂²×C₃×C₅	C₂²⋊Q₈	semidirect
168. C₂²×C₃×C₅	C₂²×Q₈	semidirect
179. C₂⁴×C₃	Dic₁₀	semidirect
208. C₂³×C₅	C₂×C₃×Q₈	semidirect
244. C₂×C₃×C₅	C₂×C₂²⋊Q₈	semidirect
252. C₂³×C₃	C₂×Dic₁₀	semidirect
274. C₂²×C₅	C₃×C₂²⋊Q₈	semidirect
277. C₂²×C₅	C₂²×C₃×Q₈	semidirect
288. C₂⁴	C₃×Dic₁₀	semidirect
312. C₃×C₅	C₂²×C₂²⋊Q₈	semidirect
316. C₂²×C₃	#4024	direct (N × H)
318. C₂²×C₃	C₂²×Dic₁₀	semidirect
329. C₂×C₅	C₂×C₃×C₂²⋊Q₈	semidirect
337. C₂³	C₂×C₃×Dic₁₀	semidirect
357. C₂×C₃	C₂×#4024	direct (N × H)
361. C₅	C₂²×C₃×C₂²⋊Q₈	semidirect
365. C₂²	C₃×#4024	direct (N × H)
367. C₂²	C₂²×C₃×Dic₁₀	semidirect
377. C₃	C₂²×#4024	direct (N × H)
379. C₂	C₂×C₃×#4024	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×C₃×Dic₅	2
C₂³×C₃×Dic₁₀	2
C₂²×C₃×C₅×C₂²⋊C₄	2
C₂²×C₃×C₂²⋊Dic₅	2
C₂²×C₃×C₄⋊Dic₅	2
C₂²×C₃×#683	2
C₂×C₃×#4024	2
C₂²×#4024	3
C₂²×C₃×C₂²⋊Q₈	5

Subgroups — C22×C3×#4024 #14479415

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₃×#4024 #14479415