Subgroups — C₂²×C₃×#4042 #14479418

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	C₂³×C₃×C₄×D₅	C₂	1	1	yes	maximal, characteristic
2	C₂³×C₃×Dic₁₀	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₃×C₅×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×C₃×#685	C₂	1	1	yes	maximal, characteristic
5	C₂²×C₃×#685	C₂	1	1	yes	maximal, characteristic
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×#4042	C₂	1	24	yes	maximal, direct product factor
9	C₂²×#4042	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂⁴×C₃×D₅	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×C₄×C₅	C₂²	1	1	yes	characteristic
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	C₂²×C₃×C₄×D₅	—	2	8	no	—
18	C₂²×C₃×C₄×D₅	C₂²	1	12	yes	—
19	C₂²×C₃×Dic₁₀	—	2	8	no	—
20	C₂²×C₃×Dic₁₀	C₂²	1	12	yes	complemented
21	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	12	yes	complemented
22	C₂×C₃×#685	C₂²	1	12	yes	—
23	C₂×C₃×#685	C₂²	1	12	yes	—
24	C₂×C₃×#683	C₂²	1	12	yes	complemented
25	C₂×C₃×#683	C₂²	1	12	yes	complemented
26	C₃×#4042	C₂²	1	64	yes	direct product factor
27	C₂²×C₃×C₂²⋊Q₈	—	5	1	no	maximal, Hall
28	C₂³×C₄×D₅	C₂×C₃	1	1	yes	characteristic
29	C₂³×Dic₁₀	C₂×C₃	1	1	yes	characteristic, complemented
30	C₂²×C₅×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic, complemented
31	C₂²×#685	C₂×C₃	1	1	yes	characteristic
32	C₂²×#685	C₂×C₃	1	1	yes	characteristic
33	C₂²×#683	C₂×C₃	1	1	yes	characteristic, complemented
34	C₂²×#683	C₂×C₃	1	1	yes	characteristic, complemented
35	C₂×#4042	C₂×C₃	1	24	yes	direct product factor
36	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
37	C₂³×C₃×D₅	—	2	4	no	—
38	C₂³×C₃×D₅	—	2	4	no	—
39	C₂³×C₃×D₅	Q₈	1	8	yes	complemented
40	C₂³×C₃×D₅	C₂³	1	6	yes	—
41	C₂²×C₃×C₄×C₅	—	2	4	no	—
42	C₂²×C₃×C₄×C₅	—	2	4	no	—
43	C₂²×C₃×C₄×C₅	—	2	4	no	—
44	C₂²×C₃×C₄×C₅	C₂³	1	6	yes	—
45	C₂²×C₃×C₄×C₅	C₂³	1	6	yes	—
46	C₂²×C₃×C₄×C₅	C₂³	1	6	yes	—
47	C₂²×C₃×Dic₅	—	2	4	no	—
48	C₂²×C₃×Dic₅	—	2	4	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	6	yes	—
53	C₂×C₃×C₄×D₅	—	2	48	no	—
54	C₂×C₃×C₄×D₅	C₂³	1	16	yes	—
55	C₂×C₃×Dic₁₀	—	2	48	no	—
56	C₂×C₃×Dic₁₀	C₂³	1	16	yes	complemented
57	C₃×C₅×C₄⋊C₄	C₂³	1	16	yes	complemented
58	C₃×#685	C₂³	1	16	yes	—
59	C₃×#685	C₂³	1	16	yes	—
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	D₅	1	1	yes	characteristic, complemented
68	C₂²×C₃×C₂²⋊C₄	—	5	1	no	—
69	C₂²×C₃×C₂²⋊C₄	—	5	1	no	—
70	C₂⁴×D₅	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×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
74	C₂³×Dic₅	C₂²×C₃	1	1	yes	characteristic
75	C₂³×Dic₅	C₂²×C₃	1	1	yes	characteristic
76	C₂³×Dic₅	C₂²×C₃	1	1	yes	characteristic
77	C₂²×C₄×D₅	—	2	8	no	—
78	C₂²×C₄×D₅	C₂²×C₃	1	12	yes	—
79	C₂²×Dic₁₀	—	2	8	no	—
80	C₂²×Dic₁₀	C₂²×C₃	1	12	yes	complemented
81	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	12	yes	complemented
82	C₂×#685	C₂²×C₃	1	12	yes	—
83	C₂×#685	C₂²×C₃	1	12	yes	—
84	C₂×#683	C₂²×C₃	1	12	yes	complemented
85	C₂×#683	C₂²×C₃	1	12	yes	complemented
86	#4042	C₂²×C₃	1	64	yes	direct product factor
87	C₂²×C₂²⋊Q₈	—	5	1	no	Sylow
88	C₂³×C₃×C₅	C₂×D₄	1	4	yes	—
89	C₂³×C₃×C₅	C₂×Q₈	1	4	yes	—
90	C₂³×C₃×C₅	#41	1	4	yes	—
91	C₂³×C₃×C₅	C₂⁴	1	3	yes	—
92	C₂²×C₃×D₅	—	2	32	no	—
93	C₂²×C₃×D₅	—	2	12	no	—
94	C₂²×C₃×D₅	—	2	12	no	—
95	C₂²×C₃×D₅	C₂×Q₈	1	24	yes	complemented
96	C₂²×C₃×D₅	C₂⁴	1	4	yes	—
97	C₂×C₃×C₄×C₅	—	2	12	no	—
98	C₂×C₃×C₄×C₅	—	2	12	no	—
99	C₂×C₃×C₄×C₅	—	2	12	no	—
100	C₂×C₃×C₄×C₅	C₂⁴	1	4	yes	—
101	C₂×C₃×C₄×C₅	C₂⁴	1	4	yes	—
102	C₂×C₃×C₄×C₅	C₂⁴	1	4	yes	—
103	C₂×C₃×Dic₅	—	2	12	no	—
104	C₂×C₃×Dic₅	—	2	12	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	C₃×C₄×D₅	—	2	32	no	—
110	C₃×Dic₁₀	—	2	32	no	—
111	C₂⁵×C₃	—	5	1	no	—
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	1	no	—
116	C₂³×C₃×C₄	—	5	1	no	—
117	C₂³×C₃×C₄	—	5	12	no	—
118	C₂³×C₃×C₄	—	10	8	no	—
119	C₂³×C₃×C₄	C₂×D₅	1	1	yes	characteristic
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	C₂×D₅	1	12	yes	complemented
126	C₂×C₃×C₂²⋊C₄	—	5	12	no	—
127	C₂×C₃×C₂²⋊C₄	—	5	12	no	—
128	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
129	C₂³×D₅	—	2	4	no	—
130	C₂³×D₅	—	2	4	no	—
131	C₂³×D₅	C₃×Q₈	1	8	yes	complemented
132	C₂³×D₅	C₂³×C₃	1	6	yes	—
133	C₂²×C₄×C₅	—	2	4	no	—
134	C₂²×C₄×C₅	—	2	4	no	—
135	C₂²×C₄×C₅	—	2	4	no	—
136	C₂²×C₄×C₅	C₂³×C₃	1	6	yes	—
137	C₂²×C₄×C₅	C₂³×C₃	1	6	yes	—
138	C₂²×C₄×C₅	C₂³×C₃	1	6	yes	—
139	C₂²×Dic₅	—	2	4	no	—
140	C₂²×Dic₅	—	2	4	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	6	yes	—
145	C₂×C₄×D₅	—	2	48	no	—
146	C₂×C₄×D₅	C₂³×C₃	1	16	yes	—
147	C₂×Dic₁₀	—	2	48	no	—
148	C₂×Dic₁₀	C₂³×C₃	1	16	yes	complemented
149	C₅×C₄⋊C₄	C₂³×C₃	1	16	yes	complemented
150	#685	C₂³×C₃	1	16	yes	—
151	#685	C₂³×C₃	1	16	yes	—
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	C₃×D₅	1	1	yes	characteristic, complemented
160	C₂²×C₂²⋊C₄	—	5	1	no	—
161	C₂²×C₂²⋊C₄	—	5	1	no	—
162	C₂²×C₃×C₅	C₂²⋊Q₈	1	16	yes	complemented
163	C₂²×C₃×C₅	C₂²×D₄	1	6	yes	—
164	C₂²×C₃×C₅	C₂²×Q₈	1	6	yes	—
165	C₂²×C₃×C₅	C₂×#41	1	6	yes	—
166	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
167	C₂×C₃×D₅	—	2	48	no	—
168	C₂×C₃×D₅	—	2	4	no	—
169	C₂×C₃×D₅	—	2	4	no	—
170	C₂×C₃×D₅	C₂²×Q₈	1	8	yes	complemented
171	C₃×C₄×C₅	—	2	4	no	—
172	C₃×C₄×C₅	—	2	4	no	—
173	C₃×C₄×C₅	—	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	—	5	8	no	—
178	C₂⁴×C₃	—	5	6	no	—
179	C₂⁴×C₃	—	10	4	no	—
180	C₂⁴×C₃	—	10	4	no	—
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	—	2	4	no	—
187	C₂²×C₃×C₄	—	5	8	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	C₂²×D₅	1	6	yes	—
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	C₂²×D₅	1	16	yes	complemented
201	C₃×C₂²⋊C₄	—	5	16	no	—
202	C₃×C₂²⋊C₄	—	5	16	no	—
203	C₂³×C₅	C₂×C₃×D₄	1	4	yes	—
204	C₂³×C₅	C₂×C₃×Q₈	1	4	yes	—
205	C₂³×C₅	C₃×#41	1	4	yes	—
206	C₂³×C₅	C₂⁴×C₃	1	3	yes	—
207	C₂²×D₅	—	2	32	no	—
208	C₂²×D₅	—	2	12	no	—
209	C₂²×D₅	—	2	12	no	—
210	C₂²×D₅	C₂×C₃×Q₈	1	24	yes	complemented
211	C₂²×D₅	C₂⁴×C₃	1	4	yes	—
212	C₂×C₄×C₅	—	2	12	no	—
213	C₂×C₄×C₅	—	2	12	no	—
214	C₂×C₄×C₅	—	2	12	no	—
215	C₂×C₄×C₅	C₂⁴×C₃	1	4	yes	—
216	C₂×C₄×C₅	C₂⁴×C₃	1	4	yes	—
217	C₂×C₄×C₅	C₂⁴×C₃	1	4	yes	—
218	C₂×Dic₅	—	2	12	no	—
219	C₂×Dic₅	—	2	12	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	C₄×D₅	—	2	32	no	—
225	Dic₁₀	—	2	32	no	—
226	C₂⁵	—	5	1	no	—
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	12	no	—
233	C₂³×C₄	—	10	8	no	—
234	C₂³×C₄	C₂×C₃×D₅	1	1	yes	characteristic
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	C₂×C₃×D₅	1	12	yes	complemented
241	C₂×C₂²⋊C₄	—	5	12	no	—
242	C₂×C₂²⋊C₄	—	5	12	no	—
243	C₂×C₃×C₅	C₂×C₂²⋊Q₈	1	12	yes	complemented
244	C₂×C₃×C₅	C₂³×D₄	1	1	yes	characteristic
245	C₂×C₃×C₅	C₂³×Q₈	1	1	yes	characteristic
246	C₂×C₃×C₅	C₂²×#41	1	1	yes	characteristic
247	C₃×D₅	—	2	8	no	—
248	C₂³×C₃	—	5	24	no	—
249	C₂³×C₃	—	5	4	no	—
250	C₂³×C₃	—	10	12	no	—
251	C₂³×C₃	—	10	12	no	—
252	C₂³×C₃	—	10	32	no	—
253	C₂³×C₃	#709	1	4	yes	—
254	C₂³×C₃	D₄×D₅	1	4	yes	—
255	C₂³×C₃	Q₈×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	—	2	12	no	—
261	C₂×C₃×C₄	—	5	24	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	C₂³×D₅	1	4	yes	—
269	C₂×C₃×C₄	C₂³×D₅	1	4	yes	—
270	C₂×C₃×C₄	C₂³×D₅	1	4	yes	—
271	C₂²×C₅	C₃×C₂²⋊Q₈	1	16	yes	complemented
272	C₂²×C₅	C₂²×C₃×D₄	1	6	yes	—
273	C₂²×C₅	C₂²×C₃×Q₈	1	6	yes	—
274	C₂²×C₅	C₂×C₃×#41	1	6	yes	—
275	C₂²×C₅	C₂⁵×C₃	1	1	yes	characteristic
276	C₂×D₅	—	2	4	no	—
277	C₂×D₅	—	2	4	no	—
278	C₂×D₅	—	2	48	no	—
279	C₂×D₅	C₂²×C₃×Q₈	1	8	yes	complemented
280	C₄×C₅	—	2	4	no	—
281	C₄×C₅	—	2	4	no	—
282	C₄×C₅	—	2	4	no	—
283	Dic₅	—	2	4	no	—
284	Dic₅	—	2	4	no	—
285	Dic₅	C₂²×C₃×D₄	1	8	yes	—
286	C₂⁴	—	5	8	no	—
287	C₂⁴	—	5	6	no	—
288	C₂⁴	—	10	4	no	—
289	C₂⁴	—	10	4	no	—
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	—	2	4	no	—
296	C₂²×C₄	—	5	8	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	C₂²×C₃×D₅	1	6	yes	—
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	C₂²×C₃×D₅	1	16	yes	complemented
310	C₂²⋊C₄	—	5	16	no	—
311	C₂²⋊C₄	—	5	16	no	—
312	C₃×C₅	C₂²×C₂²⋊Q₈	1	1	yes	characteristic, complemented, Hall
313	C₂²×C₃	—	5	8	no	—
314	C₂²×C₃	—	10	48	no	—
315	C₂²×C₃	—	10	4	no	—
316	C₂²×C₃	—	10	4	no	—
317	C₂²×C₃	#4042	1	16	yes	direct product factor
318	C₂²×C₃	C₂×#709	1	6	yes	—
319	C₂²×C₃	C₂×D₄×D₅	1	6	yes	—
320	C₂²×C₃	C₂×Q₈×D₅	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	—	2	4	no	—
325	C₃×C₄	—	5	8	no	—
326	C₃×C₄	—	10	4	no	—
327	C₃×C₄	—	10	4	no	—
328	C₂×C₅	C₂×C₃×C₂²⋊Q₈	1	12	yes	complemented
329	C₂×C₅	C₂³×C₃×D₄	1	1	yes	characteristic
330	C₂×C₅	C₂³×C₃×Q₈	1	1	yes	characteristic
331	C₂×C₅	C₂²×C₃×#41	1	1	yes	characteristic
332	D₅	—	2	8	no	—
333	C₂³	—	5	24	no	—
334	C₂³	—	5	4	no	—
335	C₂³	—	10	12	no	—
336	C₂³	—	10	12	no	—
337	C₂³	—	10	32	no	—
338	C₂³	C₃×#709	1	4	yes	—
339	C₂³	C₃×D₄×D₅	1	4	yes	—
340	C₂³	C₃×Q₈×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	—	2	12	no	—
346	C₂×C₄	—	5	24	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	C₂³×C₃×D₅	1	4	yes	—
354	C₂×C₄	C₂³×C₃×D₅	1	4	yes	—
355	C₂×C₄	C₂³×C₃×D₅	1	4	yes	—
356	C₂×C₃	—	10	8	no	—
357	C₂×C₃	C₂×#4042	1	12	yes	direct product factor
358	C₂×C₃	C₂²×#709	1	1	yes	characteristic
359	C₂×C₃	C₂²×D₄×D₅	1	1	yes	characteristic
360	C₂×C₃	C₂²×Q₈×D₅	1	1	yes	characteristic
361	C₅	C₂²×C₃×C₂²⋊Q₈	1	1	yes	characteristic, complemented, Sylow
362	C₂²	—	5	8	no	—
363	C₂²	—	10	4	no	—
364	C₂²	—	10	4	no	—
365	C₂²	—	10	48	no	—
366	C₂²	C₃×#4042	1	16	yes	direct product factor
367	C₂²	C₂×C₃×#709	1	6	yes	—
368	C₂²	C₂×C₃×D₄×D₅	1	6	yes	—
369	C₂²	C₂×C₃×Q₈×D₅	1	6	yes	—
370	C₂²	C₂⁴×C₃×D₅	1	1	yes	characteristic
371	C₄	—	2	4	no	—
372	C₄	—	2	4	no	—
373	C₄	—	2	4	no	—
374	C₄	—	5	8	no	—
375	C₄	—	10	4	no	—
376	C₄	—	10	4	no	—
377	C₃	C₂²×#4042	1	1	yes	characteristic, direct product factor, Sylow
378	C₂	—	10	8	no	—
379	C₂	C₂×C₃×#4042	1	12	yes	direct product factor
380	C₂	C₂²×C₃×#709	1	1	yes	characteristic
381	C₂	C₂²×C₃×D₄×D₅	1	1	yes	characteristic
382	C₂	C₂²×C₃×Q₈×D₅	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×C₄⋊C₄	C₂
socle	C₂⁴×C₃×C₅	C₂³
prime radical	C₂⁴×C₃×D₅	C₂²
hypercenter	C₂²×C₃×C₄⋊C₄	D₅
hypocenter	C₅	C₂²×C₃×C₂²⋊Q₈
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂⁴×C₃ ◁ C₂²×C₃×C₄⋊C₄

Complements

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

N	H ≅ G/N	type
2. C₂³×C₃×Dic₁₀	C₂	semidirect
3. C₂²×C₃×C₅×C₄⋊C₄	C₂	semidirect
6. C₂²×C₃×#683	C₂	semidirect
7. C₂²×C₃×#683	C₂	semidirect
8. C₂×C₃×#4042	C₂	direct (N × H)
9. C₂²×#4042	C₃	direct (N × H)
20. C₂²×C₃×Dic₁₀	C₂²	semidirect
21. C₂×C₃×C₅×C₄⋊C₄	C₂²	semidirect
24. C₂×C₃×#683	C₂²	semidirect
25. C₂×C₃×#683	C₂²	semidirect
26. C₃×#4042	C₂²	direct (N × H)
29. C₂³×Dic₁₀	C₂×C₃	semidirect
30. C₂²×C₅×C₄⋊C₄	C₂×C₃	semidirect
33. C₂²×#683	C₂×C₃	semidirect
34. C₂²×#683	C₂×C₃	semidirect
35. C₂×#4042	C₂×C₃	direct (N × H)
39. C₂³×C₃×D₅	Q₈	semidirect
56. C₂×C₃×Dic₁₀	C₂³	semidirect
57. C₃×C₅×C₄⋊C₄	C₂³	semidirect
60. C₃×#683	C₂³	semidirect
61. C₃×#683	C₂³	semidirect
67. C₂²×C₃×C₄⋊C₄	D₅	semidirect
80. C₂²×Dic₁₀	C₂²×C₃	semidirect
81. C₂×C₅×C₄⋊C₄	C₂²×C₃	semidirect
84. C₂×#683	C₂²×C₃	semidirect
85. C₂×#683	C₂²×C₃	semidirect
86. #4042	C₂²×C₃	direct (N × H)
95. C₂²×C₃×D₅	C₂×Q₈	semidirect
125. C₂×C₃×C₄⋊C₄	C₂×D₅	semidirect
131. C₂³×D₅	C₃×Q₈	semidirect
148. C₂×Dic₁₀	C₂³×C₃	semidirect
149. C₅×C₄⋊C₄	C₂³×C₃	semidirect
152. #683	C₂³×C₃	semidirect
153. #683	C₂³×C₃	semidirect
159. C₂²×C₄⋊C₄	C₃×D₅	semidirect
162. C₂²×C₃×C₅	C₂²⋊Q₈	semidirect
170. C₂×C₃×D₅	C₂²×Q₈	semidirect
200. C₃×C₄⋊C₄	C₂²×D₅	semidirect
210. C₂²×D₅	C₂×C₃×Q₈	semidirect
240. C₂×C₄⋊C₄	C₂×C₃×D₅	semidirect
243. C₂×C₃×C₅	C₂×C₂²⋊Q₈	semidirect
271. C₂²×C₅	C₃×C₂²⋊Q₈	semidirect
279. C₂×D₅	C₂²×C₃×Q₈	semidirect
309. C₄⋊C₄	C₂²×C₃×D₅	semidirect
312. C₃×C₅	C₂²×C₂²⋊Q₈	semidirect
317. C₂²×C₃	#4042	direct (N × H)
328. C₂×C₅	C₂×C₃×C₂²⋊Q₈	semidirect
357. C₂×C₃	C₂×#4042	direct (N × H)
361. C₅	C₂²×C₃×C₂²⋊Q₈	semidirect
366. C₂²	C₃×#4042	direct (N × H)
377. C₃	C₂²×#4042	direct (N × H)
379. C₂	C₂×C₃×#4042	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×C₃×C₄×D₅	2
C₂³×C₃×Dic₁₀	2
C₂²×C₃×C₅×C₄⋊C₄	2
C₂²×C₃×#685	2
C₂²×C₃×#683	2
C₂×C₃×#4042	2
C₂²×#4042	3
C₂²×C₃×C₂²⋊Q₈	5

Subgroups — C22×C3×#4042 #14479418

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₃×#4042 #14479418