Subgroups — C₂×C₃×#65372 #14425864

Order 1920.

1088 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	C₂×C₃×C₅×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₃×#688	C₂	1	2	yes	maximal
3	C₂×C₃×C₄×D₂₀	C₂	1	1	yes	maximal, characteristic
4	C₂×C₃×#3967	C₂	1	2	yes	maximal, complemented
5	C₃×#65372	C₂	1	8	yes	maximal, direct product factor
6	C₂×C₃×C₄⋊#168	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#65372	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₂²×C₃×C₅×Q₈	C₂²	1	2	yes	—
9	C₂²×C₃×D₂₀	C₂²	1	1	yes	characteristic
10	C₂²×C₃×C₄×D₅	—	2	1	no	—
11	C₃×C₅×C₄⋊Q₈	—	2	2	no	—
12	C₃×C₅×C₄⋊Q₈	C₂²	1	4	yes	complemented
13	C₂×C₃×C₅×C₄⋊C₄	—	2	1	no	—
14	C₂×C₃×C₅×C₄⋊C₄	—	2	1	no	—
15	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
16	C₂×C₃×#688	—	2	8	no	—
17	C₂×C₃×#688	C₂²	1	8	yes	—
18	C₂×C₃×#685	—	2	1	no	—
19	C₂×C₃×C₄⋊Dic₅	C₂²	1	1	yes	characteristic
20	C₂²×C₃×#168	C₂²	1	2	yes	—
21	C₃×C₄×D₂₀	—	2	2	no	—
22	C₃×C₄×D₂₀	C₂²	1	4	yes	—
23	C₃×#3967	C₂²	1	8	yes	complemented
24	C₃×C₄⋊#168	C₂²	1	4	yes	complemented
25	C₂×C₃×#461	—	5	1	no	maximal, Hall
26	C₂×C₅×C₄⋊Q₈	C₂×C₃	1	1	yes	characteristic, complemented
27	C₂²×#688	C₂×C₃	1	2	yes	—
28	C₂×C₄×D₂₀	C₂×C₃	1	1	yes	characteristic
29	C₂×#3967	C₂×C₃	1	2	yes	complemented
30	#65372	C₂×C₃	1	8	yes	direct product factor
31	C₂×C₄⋊#168	C₂×C₃	1	1	yes	characteristic, complemented
32	C₂³×C₃×D₅	—	2	1	no	—
33	C₂×C₃×C₅×Q₈	—	2	2	no	—
34	C₂×C₃×C₅×Q₈	—	2	4	no	—
35	C₂×C₃×C₅×Q₈	—	2	4	no	—
36	C₂×C₃×C₅×Q₈	C₂³	1	4	yes	—
37	C₂²×C₃×C₄×C₅	—	2	2	no	—
38	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
39	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
40	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
41	C₂²×C₃×Dic₅	—	2	1	no	—
42	C₂×C₃×D₂₀	—	2	1	no	—
43	C₂×C₃×D₂₀	—	2	2	no	—
44	C₂×C₃×D₂₀	D₄	1	4	yes	—
45	C₂×C₃×D₂₀	C₂³	1	2	yes	—
46	C₂×C₃×C₄×D₅	—	2	4	no	—
47	C₂×C₃×C₄×D₅	—	4	4	no	—
48	C₃×C₅×C₄⋊C₄	—	2	4	no	—
49	C₃×C₅×C₄⋊C₄	—	2	4	no	—
50	C₃×C₄²×C₅	D₄	1	2	yes	—
51	C₃×C₄²×C₅	C₂³	1	2	yes	—
52	C₃×#688	—	2	16	no	—
53	C₃×#685	—	2	4	no	—
54	C₃×C₄⋊Dic₅	—	2	1	no	—
55	C₃×C₄⋊Dic₅	C₂³	1	2	yes	—
56	C₂×C₃×#168	—	2	4	no	—
57	C₂×C₃×#168	C₂³	1	4	yes	—
58	C₂²×C₃×SD₁₆	—	5	2	no	—
59	C₂×C₃×C₄⋊Q₈	D₅	1	1	yes	characteristic, complemented
60	C₂×C₃×C₄×D₄	—	5	1	no	—
61	C₃×#461	—	5	8	no	—
62	C₂×C₃×C₄⋊C₈	—	5	1	no	—
63	C₂×C₃×#103	—	5	2	no	—
64	C₂²×C₅×Q₈	C₂²×C₃	1	2	yes	—
65	C₂²×D₂₀	C₂²×C₃	1	1	yes	characteristic
66	C₂²×C₄×D₅	—	2	1	no	—
67	C₅×C₄⋊Q₈	—	2	2	no	—
68	C₅×C₄⋊Q₈	C₂²×C₃	1	4	yes	complemented
69	C₂×C₅×C₄⋊C₄	—	2	1	no	—
70	C₂×C₅×C₄⋊C₄	—	2	1	no	—
71	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
72	C₂×#688	—	2	8	no	—
73	C₂×#688	C₂²×C₃	1	8	yes	—
74	C₂×#685	—	2	1	no	—
75	C₂×C₄⋊Dic₅	C₂²×C₃	1	1	yes	characteristic
76	C₂²×#168	C₂²×C₃	1	2	yes	—
77	C₄×D₂₀	—	2	2	no	—
78	C₄×D₂₀	C₂²×C₃	1	4	yes	—
79	#3967	C₂²×C₃	1	8	yes	complemented
80	C₄⋊#168	C₂²×C₃	1	4	yes	complemented
81	C₂×#461	—	5	1	no	Sylow
82	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
83	C₂²×C₃×D₅	—	2	4	no	—
84	C₂²×C₃×D₅	—	2	2	no	—
85	C₂²×C₃×D₅	—	4	2	no	—
86	C₂²×C₃×D₅	—	4	2	no	—
87	C₃×C₅×Q₈	—	2	4	no	—
88	C₃×C₅×Q₈	—	2	4	no	—
89	C₃×C₅×Q₈	—	4	4	no	—
90	C₂×C₃×C₄×C₅	—	2	2	no	—
91	C₂×C₃×C₄×C₅	—	2	4	no	—
92	C₂×C₃×C₄×C₅	—	4	4	no	—
93	C₂×C₃×C₄×C₅	SD₁₆	1	4	yes	complemented
94	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
95	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
96	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
97	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
98	C₂×C₃×C₄×C₅	#41	1	2	yes	—
99	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
100	C₂×C₃×Dic₅	—	2	2	no	—
101	C₂×C₃×Dic₅	—	4	2	no	—
102	C₃×D₂₀	—	2	4	no	—
103	C₃×D₂₀	—	2	2	no	—
104	C₃×D₂₀	C₂×D₄	1	4	yes	—
105	C₃×C₄×D₅	—	4	8	no	—
106	C₃×#168	—	2	4	no	—
107	C₂²×C₃×Q₈	C₂×D₅	1	2	yes	—
108	C₂²×C₃×D₄	—	5	1	no	—
109	C₂³×C₃×C₄	—	10	1	no	—
110	C₂×C₃×SD₁₆	—	5	8	no	—
111	C₂×C₃×SD₁₆	—	10	8	no	—
112	C₂²×C₃×C₈	—	5	2	no	—
113	C₃×C₄⋊Q₈	—	2	2	no	—
114	C₃×C₄⋊Q₈	C₂×D₅	1	4	yes	complemented
115	C₃×C₄×D₄	—	5	4	no	—
116	C₃×C₄×D₄	—	10	2	no	—
117	C₂×C₃×C₄⋊C₄	—	2	1	no	—
118	C₂×C₃×C₄⋊C₄	—	2	1	no	—
119	C₂×C₃×C₄⋊C₄	—	5	1	no	—
120	C₂×C₃×C₂²⋊C₄	—	10	1	no	—
121	C₂×C₃×C₄²	C₂×D₅	1	1	yes	characteristic
122	C₃×C₄⋊C₈	—	5	4	no	—
123	C₃×#103	—	5	8	no	—
124	C₂³×D₅	—	2	1	no	—
125	C₂×C₅×Q₈	—	2	2	no	—
126	C₂×C₅×Q₈	—	2	4	no	—
127	C₂×C₅×Q₈	—	2	4	no	—
128	C₂×C₅×Q₈	C₂³×C₃	1	4	yes	—
129	C₂²×C₄×C₅	—	2	2	no	—
130	C₂²×C₄×C₅	C₃×D₄	1	1	yes	characteristic
131	C₂²×C₄×C₅	C₃×D₄	1	1	yes	characteristic
132	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
133	C₂²×Dic₅	—	2	1	no	—
134	C₂×D₂₀	—	2	1	no	—
135	C₂×D₂₀	—	2	2	no	—
136	C₂×D₂₀	C₃×D₄	1	4	yes	—
137	C₂×D₂₀	C₂³×C₃	1	2	yes	—
138	C₂×C₄×D₅	—	2	4	no	—
139	C₂×C₄×D₅	—	4	4	no	—
140	C₅×C₄⋊C₄	—	2	4	no	—
141	C₅×C₄⋊C₄	—	2	4	no	—
142	C₄²×C₅	C₃×D₄	1	2	yes	—
143	C₄²×C₅	C₂³×C₃	1	2	yes	—
144	#688	—	2	16	no	—
145	#685	—	2	4	no	—
146	C₄⋊Dic₅	—	2	1	no	—
147	C₄⋊Dic₅	C₂³×C₃	1	2	yes	—
148	C₂×#168	—	2	4	no	—
149	C₂×#168	C₂³×C₃	1	4	yes	—
150	C₂²×SD₁₆	—	5	2	no	—
151	C₂×C₄⋊Q₈	C₃×D₅	1	1	yes	characteristic, complemented
152	C₂×C₄×D₄	—	5	1	no	—
153	#461	—	5	8	no	—
154	C₂×C₄⋊C₈	—	5	1	no	—
155	C₂×#103	—	5	2	no	—
156	C₂²×C₃×C₅	#121	1	2	yes	—
157	C₂²×C₃×C₅	C₂×SD₁₆	1	2	yes	—
158	C₂²×C₃×C₅	#137	1	2	yes	—
159	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
160	C₂×C₃×D₅	—	2	4	no	—
161	C₂×C₃×D₅	—	4	2	no	—
162	C₂×C₃×D₅	—	4	2	no	—
163	C₂×C₃×D₅	—	4	8	no	—
164	C₃×C₄×C₅	—	2	2	no	—
165	C₃×C₄×C₅	—	4	4	no	—
166	C₃×C₄×C₅	#121	1	2	yes	—
167	C₃×C₄×C₅	C₂×SD₁₆	1	4	yes	complemented
168	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
169	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
170	C₃×Dic₅	—	4	2	no	—
171	C₂⁴×C₃	—	10	1	no	—
172	C₂×C₃×Q₈	—	2	2	no	—
173	C₂×C₃×Q₈	—	2	4	no	—
174	C₂×C₃×Q₈	—	2	4	no	—
175	C₂×C₃×Q₈	C₂²×D₅	1	4	yes	—
176	C₂×C₃×D₄	—	5	4	no	—
177	C₂×C₃×D₄	—	5	2	no	—
178	C₂×C₃×D₄	—	10	2	no	—
179	C₂×C₃×D₄	—	10	1	no	—
180	C₂²×C₃×C₄	—	2	2	no	—
181	C₂²×C₃×C₄	—	10	1	no	—
182	C₂²×C₃×C₄	—	10	4	no	—
183	C₂²×C₃×C₄	—	20	4	no	—
184	C₂²×C₃×C₄	C₂²⋊D₅	1	1	yes	characteristic
185	C₂²×C₃×C₄	C₂²⋊D₅	1	1	yes	characteristic
186	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
187	C₃×SD₁₆	—	10	16	no	—
188	C₂×C₃×C₈	—	5	4	no	—
189	C₂×C₃×C₈	—	10	4	no	—
190	C₃×C₄⋊C₄	—	2	4	no	—
191	C₃×C₄⋊C₄	—	2	4	no	—
192	C₃×C₄⋊C₄	—	5	2	no	—
193	C₃×C₄⋊C₄	—	10	1	no	—
194	C₃×C₂²⋊C₄	—	10	4	no	—
195	C₃×C₄²	C₂²⋊D₅	1	2	yes	—
196	C₃×C₄²	C₂²×D₅	1	2	yes	—
197	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
198	C₂²×D₅	—	2	4	no	—
199	C₂²×D₅	—	2	2	no	—
200	C₂²×D₅	—	4	2	no	—
201	C₂²×D₅	—	4	2	no	—
202	C₅×Q₈	—	2	4	no	—
203	C₅×Q₈	—	2	4	no	—
204	C₅×Q₈	—	4	4	no	—
205	C₂×C₄×C₅	—	2	2	no	—
206	C₂×C₄×C₅	—	2	4	no	—
207	C₂×C₄×C₅	—	4	4	no	—
208	C₂×C₄×C₅	C₃×SD₁₆	1	4	yes	complemented
209	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
210	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
211	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
212	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
213	C₂×C₄×C₅	C₃×#41	1	2	yes	—
214	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
215	C₂×Dic₅	—	2	2	no	—
216	C₂×Dic₅	—	4	2	no	—
217	D₂₀	—	2	4	no	—
218	D₂₀	—	2	2	no	—
219	D₂₀	C₂×C₃×D₄	1	4	yes	—
220	C₄×D₅	—	4	8	no	—
221	#168	—	2	4	no	—
222	C₂²×Q₈	C₂×C₃×D₅	1	2	yes	—
223	C₂²×D₄	—	5	1	no	—
224	C₂³×C₄	—	10	1	no	—
225	C₂×SD₁₆	—	5	8	no	—
226	C₂×SD₁₆	—	10	8	no	—
227	C₂²×C₈	—	5	2	no	—
228	C₄⋊Q₈	—	2	2	no	—
229	C₄⋊Q₈	C₂×C₃×D₅	1	4	yes	complemented
230	C₄×D₄	—	5	4	no	—
231	C₄×D₄	—	10	2	no	—
232	C₂×C₄⋊C₄	—	2	1	no	—
233	C₂×C₄⋊C₄	—	2	1	no	—
234	C₂×C₄⋊C₄	—	5	1	no	—
235	C₂×C₂²⋊C₄	—	10	1	no	—
236	C₂×C₄²	C₂×C₃×D₅	1	1	yes	characteristic
237	C₄⋊C₈	—	5	4	no	—
238	#103	—	5	8	no	—
239	C₂×C₃×C₅	#461	1	4	yes	complemented
240	C₂×C₃×C₅	C₂×#121	1	1	yes	characteristic
241	C₂×C₃×C₅	C₂²×SD₁₆	1	1	yes	characteristic
242	C₂×C₃×C₅	C₂×#137	1	1	yes	characteristic
243	C₃×D₅	—	4	4	no	—
244	C₂³×C₃	—	10	2	no	—
245	C₂³×C₃	—	10	4	no	—
246	C₂³×C₃	—	20	2	no	—
247	C₂³×C₃	—	20	2	no	—
248	C₂³×C₃	C₂×C₂²⋊D₅	1	1	yes	characteristic
249	C₃×Q₈	—	2	4	no	—
250	C₃×Q₈	—	2	4	no	—
251	C₃×Q₈	—	4	4	no	—
252	C₃×D₄	—	5	4	no	—
253	C₃×D₄	—	10	2	no	—
254	C₃×D₄	—	10	4	no	—
255	C₂×C₃×C₄	—	2	2	no	—
256	C₂×C₃×C₄	—	2	4	no	—
257	C₂×C₃×C₄	—	4	4	no	—
258	C₂×C₃×C₄	—	10	2	no	—
259	C₂×C₃×C₄	—	20	2	no	—
260	C₂×C₃×C₄	—	20	8	no	—
261	C₂×C₃×C₄	#688	1	4	yes	complemented
262	C₂×C₃×C₄	D₄×D₅	1	2	yes	—
263	C₂×C₃×C₄	#711	1	2	yes	—
264	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	2	yes	—
265	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
266	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	2	yes	—
267	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
268	C₃×C₈	—	10	4	no	—
269	C₂²×C₅	C₃×#121	1	2	yes	—
270	C₂²×C₅	C₂×C₃×SD₁₆	1	2	yes	—
271	C₂²×C₅	C₃×#137	1	2	yes	—
272	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
273	C₂×D₅	—	2	4	no	—
274	C₂×D₅	—	4	2	no	—
275	C₂×D₅	—	4	2	no	—
276	C₂×D₅	—	4	8	no	—
277	C₄×C₅	—	2	2	no	—
278	C₄×C₅	—	4	4	no	—
279	C₄×C₅	C₃×#121	1	2	yes	—
280	C₄×C₅	C₂×C₃×SD₁₆	1	4	yes	complemented
281	C₄×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
282	C₄×C₅	C₂×C₃×#41	1	1	yes	characteristic
283	Dic₅	—	4	2	no	—
284	C₂⁴	—	10	1	no	—
285	C₂×Q₈	—	2	2	no	—
286	C₂×Q₈	—	2	4	no	—
287	C₂×Q₈	—	2	4	no	—
288	C₂×Q₈	C₂²×C₃×D₅	1	4	yes	—
289	C₂×D₄	—	5	4	no	—
290	C₂×D₄	—	5	2	no	—
291	C₂×D₄	—	10	2	no	—
292	C₂×D₄	—	10	1	no	—
293	C₂²×C₄	—	2	2	no	—
294	C₂²×C₄	—	10	1	no	—
295	C₂²×C₄	—	10	4	no	—
296	C₂²×C₄	—	20	4	no	—
297	C₂²×C₄	C₃×C₂²⋊D₅	1	1	yes	characteristic
298	C₂²×C₄	C₃×C₂²⋊D₅	1	1	yes	characteristic
299	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
300	SD₁₆	—	10	16	no	—
301	C₂×C₈	—	5	4	no	—
302	C₂×C₈	—	10	4	no	—
303	C₄⋊C₄	—	2	4	no	—
304	C₄⋊C₄	—	2	4	no	—
305	C₄⋊C₄	—	5	2	no	—
306	C₄⋊C₄	—	10	1	no	—
307	C₂²⋊C₄	—	10	4	no	—
308	C₄²	C₃×C₂²⋊D₅	1	2	yes	—
309	C₄²	C₂²×C₃×D₅	1	2	yes	—
310	C₃×C₅	C₂×#461	1	1	yes	characteristic, complemented, Hall
311	C₂²×C₃	—	10	4	no	—
312	C₂²×C₃	—	20	8	no	—
313	C₂²×C₃	—	20	2	no	—
314	C₂²×C₃	—	20	2	no	—
315	C₂²×C₃	#4084	1	2	yes	—
316	C₂²×C₃	C₂×#688	1	2	yes	—
317	C₂²×C₃	#4088	1	2	yes	—
318	C₂²×C₃	C₂²×C₂²⋊D₅	1	1	yes	characteristic
319	C₃×C₄	—	2	2	no	—
320	C₃×C₄	—	4	4	no	—
321	C₃×C₄	—	20	2	no	—
322	C₃×C₄	#4084	1	2	yes	—
323	C₃×C₄	C₂×#688	1	4	yes	complemented
324	C₃×C₄	C₂×D₄×D₅	1	1	yes	characteristic
325	C₃×C₄	C₂×#711	1	1	yes	characteristic
326	C₂×C₅	C₃×#461	1	4	yes	complemented
327	C₂×C₅	C₂×C₃×#121	1	1	yes	characteristic
328	C₂×C₅	C₂²×C₃×SD₁₆	1	1	yes	characteristic
329	C₂×C₅	C₂×C₃×#137	1	1	yes	characteristic
330	D₅	—	4	4	no	—
331	C₂³	—	10	4	no	—
332	C₂³	—	10	2	no	—
333	C₂³	—	20	2	no	—
334	C₂³	—	20	2	no	—
335	C₂³	C₂×C₃×C₂²⋊D₅	1	1	yes	characteristic
336	Q₈	—	2	4	no	—
337	Q₈	—	2	4	no	—
338	Q₈	—	4	4	no	—
339	D₄	—	5	4	no	—
340	D₄	—	10	4	no	—
341	D₄	—	10	2	no	—
342	C₂×C₄	—	2	2	no	—
343	C₂×C₄	—	2	4	no	—
344	C₂×C₄	—	4	4	no	—
345	C₂×C₄	—	10	2	no	—
346	C₂×C₄	—	20	2	no	—
347	C₂×C₄	—	20	8	no	—
348	C₂×C₄	C₃×#688	1	4	yes	complemented
349	C₂×C₄	C₃×D₄×D₅	1	2	yes	—
350	C₂×C₄	C₃×#711	1	2	yes	—
351	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	2	yes	—
352	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	1	yes	characteristic
353	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	2	yes	—
354	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
355	C₈	—	10	4	no	—
356	C₂×C₃	—	20	4	no	—
357	C₂×C₃	#65372	1	4	yes	direct product factor
358	C₂×C₃	C₂×#4084	1	1	yes	characteristic
359	C₂×C₃	C₂²×#688	1	1	yes	characteristic
360	C₂×C₃	C₂×#4088	1	1	yes	characteristic
361	C₅	C₂×C₃×#461	1	1	yes	characteristic, complemented, Sylow
362	C₂²	—	10	4	no	—
363	C₂²	—	20	2	no	—
364	C₂²	—	20	2	no	—
365	C₂²	—	20	8	no	—
366	C₂²	C₃×#4084	1	2	yes	—
367	C₂²	C₂×C₃×#688	1	2	yes	—
368	C₂²	C₃×#4088	1	2	yes	—
369	C₂²	C₂²×C₃×C₂²⋊D₅	1	1	yes	characteristic
370	C₄	—	2	2	no	—
371	C₄	—	4	4	no	—
372	C₄	—	20	2	no	—
373	C₄	C₃×#4084	1	2	yes	—
374	C₄	C₂×C₃×#688	1	4	yes	complemented
375	C₄	C₂×C₃×D₄×D₅	1	1	yes	characteristic
376	C₄	C₂×C₃×#711	1	1	yes	characteristic
377	C₃	C₂×#65372	1	1	yes	characteristic, direct product factor, Sylow
378	C₂	—	20	4	no	—
379	C₂	C₃×#65372	1	4	yes	direct product factor
380	C₂	C₂×C₃×#4084	1	1	yes	characteristic
381	C₂	C₂²×C₃×#688	1	1	yes	characteristic
382	C₂	C₂×C₃×#4088	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₃	C₂×C₂²⋊D₅
commutator, cosocle	C₂×C₄×C₅	C₂⁴×C₃
Frattini	C₂×C₄	C₂³×C₃×D₅
Fitting	C₂×C₃×C₅×C₄⋊Q₈	C₂
socle	C₂³×C₃×C₅	C₂×D₄
prime radical	C₂²×C₃×D₂₀	C₂²
hypercenter	C₂×C₃×C₄⋊Q₈	D₅
hypocenter	C₅	C₂×C₃×#461
LCS	G ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂³×C₃ ◁ C₂×C₃×C₄² ◁ C₂×C₃×C₄⋊Q₈

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×C₅×C₄⋊Q₈	C₂	semidirect
4. C₂×C₃×#3967	C₂	semidirect
5. C₃×#65372	C₂	direct (N × H)
6. C₂×C₃×C₄⋊#168	C₂	semidirect
7. C₂×#65372	C₃	direct (N × H)
12. C₃×C₅×C₄⋊Q₈	C₂²	semidirect
23. C₃×#3967	C₂²	semidirect
24. C₃×C₄⋊#168	C₂²	semidirect
26. C₂×C₅×C₄⋊Q₈	C₂×C₃	semidirect
29. C₂×#3967	C₂×C₃	semidirect
30. #65372	C₂×C₃	direct (N × H)
31. C₂×C₄⋊#168	C₂×C₃	semidirect
59. C₂×C₃×C₄⋊Q₈	D₅	semidirect
68. C₅×C₄⋊Q₈	C₂²×C₃	semidirect
79. #3967	C₂²×C₃	semidirect
80. C₄⋊#168	C₂²×C₃	semidirect
93. C₂×C₃×C₄×C₅	SD₁₆	semidirect
114. C₃×C₄⋊Q₈	C₂×D₅	semidirect
151. C₂×C₄⋊Q₈	C₃×D₅	semidirect
167. C₃×C₄×C₅	C₂×SD₁₆	semidirect
208. C₂×C₄×C₅	C₃×SD₁₆	semidirect
229. C₄⋊Q₈	C₂×C₃×D₅	semidirect
239. C₂×C₃×C₅	#461	semidirect
261. C₂×C₃×C₄	#688	semidirect
280. C₄×C₅	C₂×C₃×SD₁₆	semidirect
310. C₃×C₅	C₂×#461	semidirect
323. C₃×C₄	C₂×#688	semidirect
326. C₂×C₅	C₃×#461	semidirect
348. C₂×C₄	C₃×#688	semidirect
357. C₂×C₃	#65372	direct (N × H)
361. C₅	C₂×C₃×#461	semidirect
374. C₄	C₂×C₃×#688	semidirect
377. C₃	C₂×#65372	direct (N × H)
379. C₂	C₃×#65372	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃×C₅×C₄⋊Q₈	2
C₂²×C₃×#688	2
C₂×C₃×C₄×D₂₀	2
C₂×C₃×#3967	2
C₃×#65372	2
C₂×C₃×C₄⋊#168	2
C₂×#65372	3
C₂×C₃×#461	5

Subgroups — C2×C3×#65372 #14425864

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#65372 #14425864