Subgroups — C₂×C₅×#5083 #14425863

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×C₅×#215	C₂	1	2	yes	maximal
3	C₂×C₄×C₅×D₁₂	C₂	1	1	yes	maximal, characteristic
4	C₂×C₅×#835	C₂	1	2	yes	maximal, complemented
5	C₅×#5083	C₂	1	8	yes	maximal, direct product factor
6	C₂×C₅×C₄⋊(C₃⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₅×#461	—	3	1	no	maximal, Hall
8	C₂²×C₃×C₅×Q₈	C₂²	1	2	yes	—
9	C₂²×C₅×D₁₂	C₂²	1	1	yes	characteristic
10	C₂²×C₄×C₅×D₃	—	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×C₅×#215	—	2	8	no	—
17	C₂×C₅×#215	C₂²	1	8	yes	—
18	C₂×C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
19	C₂×C₅×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
20	C₂²×C₅×C₃⋊C₈	C₂²	1	2	yes	—
21	C₄×C₅×D₁₂	—	2	2	no	—
22	C₄×C₅×D₁₂	C₂²	1	4	yes	—
23	C₅×#835	C₂²	1	8	yes	complemented
24	C₅×C₄⋊(C₃⋊C₈)	C₂²	1	4	yes	complemented
25	C₂×#5083	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
26	C₂²×C₅×SD₁₆	—	3	2	no	—
27	C₂×C₅×C₄⋊Q₈	D₃	1	1	yes	characteristic, complemented
28	C₂×C₄×C₅×D₄	—	3	1	no	—
29	C₅×#461	—	3	8	no	—
30	C₂×C₅×C₄⋊C₈	—	3	1	no	—
31	C₂×C₅×#103	—	3	2	no	—
32	C₂³×C₅×D₃	—	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×C₅×Dic₃	—	2	1	no	—
42	C₂×C₅×D₁₂	—	2	1	no	—
43	C₂×C₅×D₁₂	—	2	2	no	—
44	C₂×C₅×D₁₂	D₄	1	4	yes	—
45	C₂×C₅×D₁₂	C₂³	1	2	yes	—
46	C₂×C₄×C₅×D₃	—	2	4	no	—
47	C₂×C₄×C₅×D₃	—	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	C₅×#215	—	2	16	no	—
53	C₅×(C₂×D₃)⋊C₄	—	2	4	no	—
54	C₅×C₄⋊Dic₃	—	2	1	no	—
55	C₅×C₄⋊Dic₃	C₂³	1	2	yes	—
56	C₂×C₅×C₃⋊C₈	—	2	4	no	—
57	C₂×C₅×C₃⋊C₈	C₂³	1	4	yes	—
58	C₂×C₃×C₄⋊Q₈	C₂×C₅	1	1	yes	characteristic, complemented
59	C₂²×#215	C₂×C₅	1	2	yes	—
60	C₂×C₄×D₁₂	C₂×C₅	1	1	yes	characteristic
61	C₂×#835	C₂×C₅	1	2	yes	complemented
62	#5083	C₂×C₅	1	8	yes	direct product factor
63	C₂×C₄⋊(C₃⋊C₈)	C₂×C₅	1	1	yes	characteristic, complemented
64	C₂²×C₅×Q₈	C₂×D₃	1	2	yes	—
65	C₂²×C₅×D₄	—	3	1	no	—
66	C₂³×C₄×C₅	—	6	1	no	—
67	C₂×C₅×SD₁₆	—	3	8	no	—
68	C₂×C₅×SD₁₆	—	6	8	no	—
69	C₂²×C₅×C₈	—	3	2	no	—
70	C₅×C₄⋊Q₈	—	2	2	no	—
71	C₅×C₄⋊Q₈	C₂×D₃	1	4	yes	complemented
72	C₄×C₅×D₄	—	3	4	no	—
73	C₄×C₅×D₄	—	6	2	no	—
74	C₂×C₅×C₄⋊C₄	—	2	1	no	—
75	C₂×C₅×C₄⋊C₄	—	2	1	no	—
76	C₂×C₅×C₄⋊C₄	—	3	1	no	—
77	C₂×C₅×C₂²⋊C₄	—	6	1	no	—
78	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
79	C₅×C₄⋊C₈	—	3	4	no	—
80	C₅×#103	—	3	8	no	—
81	C₂×#461	—	3	1	no	Sylow
82	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
83	C₂²×C₅×D₃	—	2	4	no	—
84	C₂²×C₅×D₃	—	2	2	no	—
85	C₂²×C₅×D₃	—	4	2	no	—
86	C₂²×C₅×D₃	—	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×C₅×Dic₃	—	2	2	no	—
101	C₂×C₅×Dic₃	—	4	2	no	—
102	C₅×D₁₂	—	2	4	no	—
103	C₅×D₁₂	—	2	2	no	—
104	C₅×D₁₂	C₂×D₄	1	4	yes	—
105	C₄×C₅×D₃	—	4	8	no	—
106	C₅×C₃⋊C₈	—	2	4	no	—
107	C₂²×C₃×Q₈	C₂²×C₅	1	2	yes	—
108	C₂²×D₁₂	C₂²×C₅	1	1	yes	characteristic
109	C₂²×C₄×D₃	—	2	1	no	—
110	C₃×C₄⋊Q₈	—	2	2	no	—
111	C₃×C₄⋊Q₈	C₂²×C₅	1	4	yes	complemented
112	C₂×C₃×C₄⋊C₄	—	2	1	no	—
113	C₂×C₃×C₄⋊C₄	—	2	1	no	—
114	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
115	C₂×#215	—	2	8	no	—
116	C₂×#215	C₂²×C₅	1	8	yes	—
117	C₂×(C₂×D₃)⋊C₄	—	2	1	no	—
118	C₂×C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic
119	C₂²×C₃⋊C₈	C₂²×C₅	1	2	yes	—
120	C₄×D₁₂	—	2	2	no	—
121	C₄×D₁₂	C₂²×C₅	1	4	yes	—
122	#835	C₂²×C₅	1	8	yes	complemented
123	C₄⋊(C₃⋊C₈)	C₂²×C₅	1	4	yes	complemented
124	C₂⁴×C₅	—	6	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	C₂²×D₃	1	4	yes	—
129	C₂×C₅×D₄	—	3	4	no	—
130	C₂×C₅×D₄	—	3	2	no	—
131	C₂×C₅×D₄	—	6	2	no	—
132	C₂×C₅×D₄	—	6	1	no	—
133	C₂²×C₄×C₅	—	2	2	no	—
134	C₂²×C₄×C₅	—	6	1	no	—
135	C₂²×C₄×C₅	—	6	4	no	—
136	C₂²×C₄×C₅	—	12	4	no	—
137	C₂²×C₄×C₅	#67	1	1	yes	characteristic
138	C₂²×C₄×C₅	#67	1	1	yes	characteristic
139	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
140	C₅×SD₁₆	—	6	16	no	—
141	C₂×C₅×C₈	—	3	4	no	—
142	C₂×C₅×C₈	—	6	4	no	—
143	C₅×C₄⋊C₄	—	2	4	no	—
144	C₅×C₄⋊C₄	—	2	4	no	—
145	C₅×C₄⋊C₄	—	3	2	no	—
146	C₅×C₄⋊C₄	—	6	1	no	—
147	C₅×C₂²⋊C₄	—	6	4	no	—
148	C₄²×C₅	#67	1	2	yes	—
149	C₄²×C₅	C₂²×D₃	1	2	yes	—
150	C₂²×SD₁₆	—	3	2	no	—
151	C₂×C₄⋊Q₈	C₅×D₃	1	1	yes	characteristic, complemented
152	C₂×C₄×D₄	—	3	1	no	—
153	#461	—	3	8	no	—
154	C₂×C₄⋊C₈	—	3	1	no	—
155	C₂×#103	—	3	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×C₅×D₃	—	2	4	no	—
161	C₂×C₅×D₃	—	4	2	no	—
162	C₂×C₅×D₃	—	4	2	no	—
163	C₂×C₅×D₃	—	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	C₅×Dic₃	—	4	2	no	—
171	C₂³×D₃	—	2	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	C₂³×C₅	1	4	yes	—
176	C₂²×C₃×C₄	—	2	2	no	—
177	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
178	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
179	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
180	C₂²×Dic₃	—	2	1	no	—
181	C₂×D₁₂	—	2	1	no	—
182	C₂×D₁₂	—	2	2	no	—
183	C₂×D₁₂	C₅×D₄	1	4	yes	—
184	C₂×D₁₂	C₂³×C₅	1	2	yes	—
185	C₂×C₄×D₃	—	2	4	no	—
186	C₂×C₄×D₃	—	4	4	no	—
187	C₃×C₄⋊C₄	—	2	4	no	—
188	C₃×C₄⋊C₄	—	2	4	no	—
189	C₃×C₄²	C₅×D₄	1	2	yes	—
190	C₃×C₄²	C₂³×C₅	1	2	yes	—
191	#215	—	2	16	no	—
192	(C₂×D₃)⋊C₄	—	2	4	no	—
193	C₄⋊Dic₃	—	2	1	no	—
194	C₄⋊Dic₃	C₂³×C₅	1	2	yes	—
195	C₂×C₃⋊C₈	—	2	4	no	—
196	C₂×C₃⋊C₈	C₂³×C₅	1	4	yes	—
197	C₂³×C₅	—	6	4	no	—
198	C₂³×C₅	—	6	2	no	—
199	C₂³×C₅	—	12	2	no	—
200	C₂³×C₅	—	12	2	no	—
201	C₂³×C₅	C₂×#67	1	1	yes	characteristic
202	C₅×Q₈	—	2	4	no	—
203	C₅×Q₈	—	2	4	no	—
204	C₅×Q₈	—	4	4	no	—
205	C₅×D₄	—	3	4	no	—
206	C₅×D₄	—	6	4	no	—
207	C₅×D₄	—	6	2	no	—
208	C₂×C₄×C₅	—	2	2	no	—
209	C₂×C₄×C₅	—	2	4	no	—
210	C₂×C₄×C₅	—	4	4	no	—
211	C₂×C₄×C₅	—	6	2	no	—
212	C₂×C₄×C₅	—	12	2	no	—
213	C₂×C₄×C₅	—	12	8	no	—
214	C₂×C₄×C₅	#215	1	4	yes	complemented
215	C₂×C₄×C₅	D₃×D₄	1	2	yes	—
216	C₂×C₄×C₅	#237	1	2	yes	—
217	C₂×C₄×C₅	C₂×#67	1	2	yes	—
218	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
219	C₂×C₄×C₅	C₂×#67	1	2	yes	—
220	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
221	C₅×C₈	—	6	4	no	—
222	C₂²×Q₈	C₂×C₅×D₃	1	2	yes	—
223	C₂²×D₄	—	3	1	no	—
224	C₂³×C₄	—	6	1	no	—
225	C₂×SD₁₆	—	3	8	no	—
226	C₂×SD₁₆	—	6	8	no	—
227	C₂²×C₈	—	3	2	no	—
228	C₄⋊Q₈	—	2	2	no	—
229	C₄⋊Q₈	C₂×C₅×D₃	1	4	yes	complemented
230	C₄×D₄	—	3	4	no	—
231	C₄×D₄	—	6	2	no	—
232	C₂×C₄⋊C₄	—	2	1	no	—
233	C₂×C₄⋊C₄	—	2	1	no	—
234	C₂×C₄⋊C₄	—	3	1	no	—
235	C₂×C₂²⋊C₄	—	6	1	no	—
236	C₂×C₄²	C₂×C₅×D₃	1	1	yes	characteristic
237	C₄⋊C₈	—	3	4	no	—
238	#103	—	3	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	C₅×D₃	—	4	4	no	—
244	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
245	C₂²×D₃	—	2	4	no	—
246	C₂²×D₃	—	2	2	no	—
247	C₂²×D₃	—	4	2	no	—
248	C₂²×D₃	—	4	2	no	—
249	C₃×Q₈	—	2	4	no	—
250	C₃×Q₈	—	2	4	no	—
251	C₃×Q₈	—	4	4	no	—
252	C₂×C₃×C₄	—	2	2	no	—
253	C₂×C₃×C₄	—	2	4	no	—
254	C₂×C₃×C₄	—	4	4	no	—
255	C₂×C₃×C₄	C₅×SD₁₆	1	4	yes	complemented
256	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
257	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
258	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
259	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
260	C₂×C₃×C₄	C₅×#41	1	2	yes	—
261	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
262	C₂×Dic₃	—	2	2	no	—
263	C₂×Dic₃	—	4	2	no	—
264	D₁₂	—	2	4	no	—
265	D₁₂	—	2	2	no	—
266	D₁₂	C₂×C₅×D₄	1	4	yes	—
267	C₄×D₃	—	4	8	no	—
268	C₃⋊C₈	—	2	4	no	—
269	C₂²×C₅	—	6	4	no	—
270	C₂²×C₅	—	12	2	no	—
271	C₂²×C₅	—	12	2	no	—
272	C₂²×C₅	—	12	8	no	—
273	C₂²×C₅	#938	1	2	yes	—
274	C₂²×C₅	C₂×#215	1	2	yes	—
275	C₂²×C₅	#942	1	2	yes	—
276	C₂²×C₅	C₂²×#67	1	1	yes	characteristic
277	C₄×C₅	—	2	2	no	—
278	C₄×C₅	—	4	4	no	—
279	C₄×C₅	—	12	2	no	—
280	C₄×C₅	#938	1	2	yes	—
281	C₄×C₅	C₂×#215	1	4	yes	complemented
282	C₄×C₅	C₂×D₃×D₄	1	1	yes	characteristic
283	C₄×C₅	C₂×#237	1	1	yes	characteristic
284	C₂⁴	—	6	1	no	—
285	C₂×Q₈	—	2	2	no	—
286	C₂×Q₈	—	2	4	no	—
287	C₂×Q₈	—	2	4	no	—
288	C₂×Q₈	C₂²×C₅×D₃	1	4	yes	—
289	C₂×D₄	—	3	4	no	—
290	C₂×D₄	—	3	2	no	—
291	C₂×D₄	—	6	2	no	—
292	C₂×D₄	—	6	1	no	—
293	C₂²×C₄	—	2	2	no	—
294	C₂²×C₄	—	6	1	no	—
295	C₂²×C₄	—	6	4	no	—
296	C₂²×C₄	—	12	4	no	—
297	C₂²×C₄	C₅×#67	1	1	yes	characteristic
298	C₂²×C₄	C₅×#67	1	1	yes	characteristic
299	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
300	SD₁₆	—	6	16	no	—
301	C₂×C₈	—	3	4	no	—
302	C₂×C₈	—	6	4	no	—
303	C₄⋊C₄	—	2	4	no	—
304	C₄⋊C₄	—	2	4	no	—
305	C₄⋊C₄	—	3	2	no	—
306	C₄⋊C₄	—	6	1	no	—
307	C₂²⋊C₄	—	6	4	no	—
308	C₄²	C₅×#67	1	2	yes	—
309	C₄²	C₂²×C₅×D₃	1	2	yes	—
310	C₃×C₅	C₂×#461	1	1	yes	characteristic, complemented, Hall
311	C₂²×C₃	C₅×#121	1	2	yes	—
312	C₂²×C₃	C₂×C₅×SD₁₆	1	2	yes	—
313	C₂²×C₃	C₅×#137	1	2	yes	—
314	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
315	C₂×D₃	—	2	4	no	—
316	C₂×D₃	—	4	8	no	—
317	C₂×D₃	—	4	2	no	—
318	C₂×D₃	—	4	2	no	—
319	C₃×C₄	—	2	2	no	—
320	C₃×C₄	—	4	4	no	—
321	C₃×C₄	C₅×#121	1	2	yes	—
322	C₃×C₄	C₂×C₅×SD₁₆	1	4	yes	complemented
323	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
324	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
325	Dic₃	—	4	2	no	—
326	C₂×C₅	—	12	4	no	—
327	C₂×C₅	#5083	1	4	yes	direct product factor
328	C₂×C₅	C₂×#938	1	1	yes	characteristic
329	C₂×C₅	C₂²×#215	1	1	yes	characteristic
330	C₂×C₅	C₂×#942	1	1	yes	characteristic
331	C₂³	—	6	4	no	—
332	C₂³	—	6	2	no	—
333	C₂³	—	12	2	no	—
334	C₂³	—	12	2	no	—
335	C₂³	C₂×C₅×#67	1	1	yes	characteristic
336	Q₈	—	2	4	no	—
337	Q₈	—	2	4	no	—
338	Q₈	—	4	4	no	—
339	D₄	—	3	4	no	—
340	D₄	—	6	4	no	—
341	D₄	—	6	2	no	—
342	C₂×C₄	—	2	2	no	—
343	C₂×C₄	—	2	4	no	—
344	C₂×C₄	—	4	4	no	—
345	C₂×C₄	—	6	2	no	—
346	C₂×C₄	—	12	2	no	—
347	C₂×C₄	—	12	8	no	—
348	C₂×C₄	C₅×#215	1	4	yes	complemented
349	C₂×C₄	C₅×D₃×D₄	1	2	yes	—
350	C₂×C₄	C₅×#237	1	2	yes	—
351	C₂×C₄	C₂×C₅×#67	1	2	yes	—
352	C₂×C₄	C₂×C₅×#67	1	1	yes	characteristic
353	C₂×C₄	C₂×C₅×#67	1	2	yes	—
354	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
355	C₈	—	6	4	no	—
356	C₂×C₃	C₅×#461	1	4	yes	complemented
357	C₂×C₃	C₂×C₅×#121	1	1	yes	characteristic
358	C₂×C₃	C₂²×C₅×SD₁₆	1	1	yes	characteristic
359	C₂×C₃	C₂×C₅×#137	1	1	yes	characteristic
360	D₃	—	4	4	no	—
361	C₅	C₂×#5083	1	1	yes	characteristic, direct product factor, Sylow
362	C₂²	—	6	4	no	—
363	C₂²	—	12	2	no	—
364	C₂²	—	12	2	no	—
365	C₂²	—	12	8	no	—
366	C₂²	C₅×#938	1	2	yes	—
367	C₂²	C₂×C₅×#215	1	2	yes	—
368	C₂²	C₅×#942	1	2	yes	—
369	C₂²	C₂²×C₅×#67	1	1	yes	characteristic
370	C₄	—	2	2	no	—
371	C₄	—	4	4	no	—
372	C₄	—	12	2	no	—
373	C₄	C₅×#938	1	2	yes	—
374	C₄	C₂×C₅×#215	1	4	yes	complemented
375	C₄	C₂×C₅×D₃×D₄	1	1	yes	characteristic
376	C₄	C₂×C₅×#237	1	1	yes	characteristic
377	C₃	C₂×C₅×#461	1	1	yes	characteristic, complemented, Sylow
378	C₂	—	12	4	no	—
379	C₂	C₅×#5083	1	4	yes	direct product factor
380	C₂	C₂×C₅×#938	1	1	yes	characteristic
381	C₂	C₂²×C₅×#215	1	1	yes	characteristic
382	C₂	C₂×C₅×#942	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₅	C₂×#67
commutator, cosocle	C₂×C₃×C₄	C₂⁴×C₅
Frattini	C₂×C₄	C₂³×C₅×D₃
Fitting	C₂×C₃×C₅×C₄⋊Q₈	C₂
socle	C₂³×C₃×C₅	C₂×D₄
prime radical	C₂²×C₅×D₁₂	C₂²
hypercenter	C₂×C₅×C₄⋊Q₈	D₃
hypocenter	C₃	C₂×C₅×#461
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₅ ◁ C₂×C₄²×C₅ ◁ C₂×C₅×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×C₅×#835	C₂	semidirect
5. C₅×#5083	C₂	direct (N × H)
6. C₂×C₅×C₄⋊(C₃⋊C₈)	C₂	semidirect
12. C₃×C₅×C₄⋊Q₈	C₂²	semidirect
23. C₅×#835	C₂²	semidirect
24. C₅×C₄⋊(C₃⋊C₈)	C₂²	semidirect
25. C₂×#5083	C₅	direct (N × H)
27. C₂×C₅×C₄⋊Q₈	D₃	semidirect
58. C₂×C₃×C₄⋊Q₈	C₂×C₅	semidirect
61. C₂×#835	C₂×C₅	semidirect
62. #5083	C₂×C₅	direct (N × H)
63. C₂×C₄⋊(C₃⋊C₈)	C₂×C₅	semidirect
71. C₅×C₄⋊Q₈	C₂×D₃	semidirect
93. C₂×C₃×C₄×C₅	SD₁₆	semidirect
111. C₃×C₄⋊Q₈	C₂²×C₅	semidirect
122. #835	C₂²×C₅	semidirect
123. C₄⋊(C₃⋊C₈)	C₂²×C₅	semidirect
151. C₂×C₄⋊Q₈	C₅×D₃	semidirect
167. C₃×C₄×C₅	C₂×SD₁₆	semidirect
214. C₂×C₄×C₅	#215	semidirect
229. C₄⋊Q₈	C₂×C₅×D₃	semidirect
239. C₂×C₃×C₅	#461	semidirect
255. C₂×C₃×C₄	C₅×SD₁₆	semidirect
281. C₄×C₅	C₂×#215	semidirect
310. C₃×C₅	C₂×#461	semidirect
322. C₃×C₄	C₂×C₅×SD₁₆	semidirect
327. C₂×C₅	#5083	direct (N × H)
348. C₂×C₄	C₅×#215	semidirect
356. C₂×C₃	C₅×#461	semidirect
361. C₅	C₂×#5083	direct (N × H)
374. C₄	C₂×C₅×#215	semidirect
377. C₃	C₂×C₅×#461	semidirect
379. C₂	C₅×#5083	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×C₅×#215	2
C₂×C₄×C₅×D₁₂	2
C₂×C₅×#835	2
C₅×#5083	2
C₂×C₅×C₄⋊(C₃⋊C₈)	2
C₂×C₅×#461	3
C₂×#5083	5

Subgroups — C2×C5×#5083 #14425863

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#5083 #14425863