Subgroups — C₅×C₂²⋊C₄×Dic₆ #14326117

Order 1920.

1640 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₅×Dic₆	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×C₅×Dic₆	C₂	1	2	yes	maximal, complemented
3	C₃×C₄×C₅×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic
4	C₅×#5212	C₂	1	1	yes	maximal, characteristic
5	C₅×#4942	C₂	1	2	yes	maximal
6	C₅×Dic₃×C₂²⋊C₄	C₂	1	2	yes	maximal
7	C₅×#4929	C₂	1	2	yes	maximal, complemented
8	C₅×#4646	C₂	1	4	yes	maximal, complemented
9	C₅×Q₈×C₂²⋊C₄	—	3	1	no	maximal, Hall
10	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
11	C₂³×C₅×Dic₃	C₂²	1	2	yes	—
12	C₂²×C₅×Dic₆	—	2	8	no	—
13	C₂²×C₅×Dic₆	C₄	1	8	yes	complemented
14	C₂²×C₅×Dic₆	C₂²	1	2	yes	—
15	C₂²×C₅×Dic₆	C₂²	1	1	yes	characteristic
16	C₂²×C₅×Dic₆	C₂²	1	1	yes	characteristic
17	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
18	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
19	C₂×C₃×C₄²×C₅	C₂²	1	2	yes	—
20	C₂×C₅×#217	C₂²	1	2	yes	—
21	C₂×C₅×C₄⋊Dic₃	C₂²	1	2	yes	—
22	C₂×C₅×Dic₃⋊C₄	C₂²	1	4	yes	—
23	C₂×C₄×C₅×Dic₃	C₂²	1	4	yes	—
24	C₄×C₅×Dic₆	—	2	8	no	—
25	C₃×C₅×#95	C₂²	1	2	yes	—
26	C₅×C₃⋊#95	C₂²	1	2	yes	—
27	C₅×C₃⋊#95	C₂²	1	4	yes	—
28	C₅×C₃⋊#95	C₂²	1	4	yes	—
29	C₂²⋊C₄×Dic₆	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
30	C₂³×C₅×Q₈	—	3	1	no	—
31	C₂×C₄×C₅×Q₈	—	3	2	no	—
32	C₅×#391	—	3	4	no	—
33	C₅×#391	—	3	2	no	—
34	C₅×#380	—	3	1	no	—
35	C₅×#380	—	3	2	no	—
36	C₄×C₅×C₂²⋊C₄	—	3	2	no	—
37	C₄×C₅×C₂²⋊C₄	D₃	1	1	yes	characteristic
38	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
39	C₂²×C₃×C₄×C₅	—	2	4	no	—
40	C₂²×C₃×C₄×C₅	C₂×C₄	1	4	yes	—
41	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
42	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
43	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
44	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
45	C₂²×C₅×Dic₃	—	2	8	no	—
46	C₂²×C₅×Dic₃	C₂×C₄	1	8	yes	—
47	C₂²×C₅×Dic₃	C₂³	1	4	yes	—
48	C₂²×C₅×Dic₃	C₂³	1	2	yes	—
49	C₂²×C₅×Dic₃	C₂³	1	2	yes	—
50	C₂×C₅×Dic₆	—	2	4	no	—
51	C₂×C₅×Dic₆	—	2	8	no	—
52	C₂×C₅×Dic₆	—	2	32	no	—
53	C₂×C₅×Dic₆	C₂×C₄	1	4	yes	—
54	C₂×C₅×Dic₆	C₂×C₄	1	8	yes	—
55	C₂×C₅×Dic₆	C₂×C₄	1	4	yes	—
56	C₂×C₅×Dic₆	D₄	1	8	yes	—
57	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
58	C₃×C₅×C₂²⋊C₄	Q₈	1	4	yes	complemented
59	C₃×C₄²×C₅	—	2	4	no	—
60	C₅×#217	—	2	4	no	—
61	C₅×C₄⋊Dic₃	—	2	4	no	—
62	C₅×Dic₃⋊C₄	—	2	8	no	—
63	C₄×C₅×Dic₃	—	2	8	no	—
64	C₂³×Dic₆	C₂×C₅	1	1	yes	characteristic
65	C₂×C₄×Dic₆	C₂×C₅	1	2	yes	complemented
66	C₃×C₄×C₂²⋊C₄	C₂×C₅	1	1	yes	characteristic
67	#5212	C₂×C₅	1	1	yes	characteristic
68	#4942	C₂×C₅	1	2	yes	—
69	Dic₃×C₂²⋊C₄	C₂×C₅	1	2	yes	—
70	#4929	C₂×C₅	1	2	yes	complemented
71	#4646	C₂×C₅	1	4	yes	complemented
72	C₂²×C₅×Q₈	—	3	8	no	—
73	C₂²×C₅×Q₈	—	3	1	no	—
74	C₂²×C₅×Q₈	—	3	2	no	—
75	C₂²×C₅×Q₈	—	3	1	no	—
76	C₂²×C₅×Q₈	—	6	8	no	—
77	C₂³×C₄×C₅	—	3	2	no	—
78	C₂³×C₄×C₅	C₂×D₃	1	1	yes	characteristic
79	C₄×C₅×Q₈	—	6	8	no	—
80	C₂×C₅×C₄⋊C₄	—	3	4	no	—
81	C₂×C₅×C₄⋊C₄	—	3	2	no	—
82	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
83	C₂×C₅×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic
84	C₂×C₅×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic
85	C₂×C₄²×C₅	—	3	4	no	—
86	C₂×C₄²×C₅	C₂×D₃	1	2	yes	—
87	C₅×#95	—	3	4	no	—
88	C₅×#95	—	3	4	no	—
89	C₅×#95	—	3	2	no	—
90	C₅×#95	C₂×D₃	1	2	yes	—
91	Q₈×C₂²⋊C₄	—	3	1	no	Sylow
92	C₂³×C₃×C₅	—	2	2	no	—
93	C₂³×C₃×C₅	—	2	2	no	—
94	C₂³×C₃×C₅	C₂²×C₄	1	2	yes	—
95	C₂³×C₃×C₅	C₂×Q₈	1	2	yes	—
96	C₂³×C₃×C₅	#41	1	2	yes	—
97	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
98	C₂×C₃×C₄×C₅	—	2	2	no	—
99	C₂×C₃×C₄×C₅	—	2	2	no	—
100	C₂×C₃×C₄×C₅	—	2	2	no	—
101	C₂×C₃×C₄×C₅	—	2	8	no	—
102	C₂×C₃×C₄×C₅	—	2	2	no	—
103	C₂×C₃×C₄×C₅	—	2	2	no	—
104	C₂×C₃×C₄×C₅	—	2	2	no	—
105	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
106	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
107	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
108	C₂×C₃×C₄×C₅	C₂×Q₈	1	4	yes	complemented
109	C₂×C₅×Dic₃	—	2	4	no	—
110	C₂×C₅×Dic₃	—	2	16	no	—
111	C₂×C₅×Dic₃	—	2	4	no	—
112	C₂×C₅×Dic₃	—	2	4	no	—
113	C₂×C₅×Dic₃	—	2	4	no	—
114	C₂×C₅×Dic₃	C₂²×C₄	1	4	yes	—
115	C₂×C₅×Dic₃	C₂²×C₄	1	4	yes	—
116	C₂×C₅×Dic₃	C₂×D₄	1	8	yes	—
117	C₅×Dic₆	—	2	8	no	—
118	C₅×Dic₆	—	2	16	no	—
119	C₅×Dic₆	C₂²⋊C₄	1	16	yes	direct product factor
120	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
121	C₂³×Dic₃	C₂²×C₅	1	2	yes	—
122	C₂²×Dic₆	—	2	8	no	—
123	C₂²×Dic₆	C₄×C₅	1	8	yes	complemented
124	C₂²×Dic₆	C₂²×C₅	1	2	yes	—
125	C₂²×Dic₆	C₂²×C₅	1	1	yes	characteristic
126	C₂²×Dic₆	C₂²×C₅	1	1	yes	characteristic
127	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
128	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
129	C₂×C₃×C₄²	C₂²×C₅	1	2	yes	—
130	C₂×#217	C₂²×C₅	1	2	yes	—
131	C₂×C₄⋊Dic₃	C₂²×C₅	1	2	yes	—
132	C₂×Dic₃⋊C₄	C₂²×C₅	1	4	yes	—
133	C₂×C₄×Dic₃	C₂²×C₅	1	4	yes	—
134	C₄×Dic₆	—	2	8	no	—
135	C₃×#95	C₂²×C₅	1	2	yes	—
136	C₃⋊#95	C₂²×C₅	1	2	yes	—
137	C₃⋊#95	C₂²×C₅	1	4	yes	—
138	C₃⋊#95	C₂²×C₅	1	4	yes	—
139	C₂⁴×C₅	C₂²×D₃	1	1	yes	characteristic
140	C₂×C₅×Q₈	—	3	4	no	—
141	C₂×C₅×Q₈	—	3	8	no	—
142	C₂×C₅×Q₈	—	3	4	no	—
143	C₂×C₅×Q₈	—	3	8	no	—
144	C₂×C₅×Q₈	—	6	8	no	—
145	C₂×C₅×Q₈	—	6	32	no	—
146	C₂×C₅×Q₈	—	6	4	no	—
147	C₂²×C₄×C₅	—	2	4	no	—
148	C₂²×C₄×C₅	—	3	2	no	—
149	C₂²×C₄×C₅	—	3	8	no	—
150	C₂²×C₄×C₅	—	3	2	no	—
151	C₂²×C₄×C₅	—	3	4	no	—
152	C₂²×C₄×C₅	—	6	8	no	—
153	C₂²×C₄×C₅	C₄×D₃	1	4	yes	—
154	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
155	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
156	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
157	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
158	C₅×C₄⋊C₄	—	6	8	no	—
159	C₅×C₄⋊C₄	—	6	4	no	—
160	C₅×C₂²⋊C₄	—	2	2	no	—
161	C₅×C₂²⋊C₄	—	6	4	no	—
162	C₅×C₂²⋊C₄	Dic₆	1	4	yes	direct product factor
163	C₄²×C₅	—	2	4	no	—
164	C₄²×C₅	—	6	8	no	—
165	C₂³×Q₈	—	3	1	no	—
166	C₂×C₄×Q₈	—	3	2	no	—
167	#391	—	3	2	no	—
168	#391	—	3	4	no	—
169	#380	—	3	1	no	—
170	#380	—	3	2	no	—
171	C₄×C₂²⋊C₄	—	3	2	no	—
172	C₄×C₂²⋊C₄	C₅×D₃	1	1	yes	characteristic
173	C₂²×C₃×C₅	—	2	2	no	—
174	C₂²×C₃×C₅	—	2	2	no	—
175	C₂²×C₃×C₅	—	2	4	no	—
176	C₂²×C₃×C₅	—	2	4	no	—
177	C₂²×C₃×C₅	C₄×Q₈	1	4	yes	complemented
178	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
179	C₂²×C₃×C₅	C₂²×D₄	1	2	yes	—
180	C₂²×C₃×C₅	C₂²×Q₈	1	1	yes	characteristic
181	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
182	C₂²×C₃×C₅	2₋¹⁺⁴	1	2	yes	—
183	C₃×C₄×C₅	—	2	2	no	—
184	C₃×C₄×C₅	—	2	4	no	—
185	C₃×C₄×C₅	—	4	2	no	—
186	C₃×C₄×C₅	C₂×C₂²⋊C₄	1	4	yes	—
187	C₅×Dic₃	—	2	4	no	—
188	C₅×Dic₃	—	4	4	no	—
189	C₅×Dic₃	C₂×C₂²⋊C₄	1	8	yes	—
190	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
191	C₂²×C₃×C₄	—	2	4	no	—
192	C₂²×C₃×C₄	C₂×C₄×C₅	1	4	yes	—
193	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
194	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
195	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
196	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
197	C₂²×Dic₃	—	2	8	no	—
198	C₂²×Dic₃	C₂×C₄×C₅	1	8	yes	—
199	C₂²×Dic₃	C₂³×C₅	1	4	yes	—
200	C₂²×Dic₃	C₂³×C₅	1	2	yes	—
201	C₂²×Dic₃	C₂³×C₅	1	2	yes	—
202	C₂×Dic₆	—	2	4	no	—
203	C₂×Dic₆	—	2	8	no	—
204	C₂×Dic₆	—	2	32	no	—
205	C₂×Dic₆	C₂×C₄×C₅	1	4	yes	—
206	C₂×Dic₆	C₂×C₄×C₅	1	8	yes	—
207	C₂×Dic₆	C₂×C₄×C₅	1	4	yes	—
208	C₂×Dic₆	C₅×D₄	1	8	yes	—
209	C₃×C₂²⋊C₄	—	2	2	no	—
210	C₃×C₂²⋊C₄	C₅×Q₈	1	4	yes	complemented
211	C₃×C₄²	—	2	4	no	—
212	#217	—	2	4	no	—
213	C₄⋊Dic₃	—	2	4	no	—
214	Dic₃⋊C₄	—	2	8	no	—
215	C₄×Dic₃	—	2	8	no	—
216	C₂³×C₅	—	2	2	no	—
217	C₂³×C₅	—	2	2	no	—
218	C₂³×C₅	C₂×Dic₆	1	2	yes	—
219	C₂³×C₅	C₂×C₄×D₃	1	2	yes	—
220	C₂³×C₅	#235	1	2	yes	—
221	C₂³×C₅	C₂³×D₃	1	1	yes	characteristic
222	C₅×Q₈	—	3	16	no	—
223	C₅×Q₈	—	6	16	no	—
224	C₅×Q₈	—	6	8	no	—
225	C₂×C₄×C₅	—	2	2	no	—
226	C₂×C₄×C₅	—	2	2	no	—
227	C₂×C₄×C₅	—	2	2	no	—
228	C₂×C₄×C₅	—	2	8	no	—
229	C₂×C₄×C₅	—	2	2	no	—
230	C₂×C₄×C₅	—	2	2	no	—
231	C₂×C₄×C₅	—	2	2	no	—
232	C₂×C₄×C₅	—	3	4	no	—
233	C₂×C₄×C₅	—	3	8	no	—
234	C₂×C₄×C₅	—	3	4	no	—
235	C₂×C₄×C₅	—	6	16	no	—
236	C₂×C₄×C₅	—	6	4	no	—
237	C₂×C₄×C₅	—	6	4	no	—
238	C₂×C₄×C₅	—	6	4	no	—
239	C₂×C₄×C₅	—	6	4	no	—
240	C₂×C₄×C₅	C₂×Dic₆	1	4	yes	complemented
241	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
242	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
243	C₂×C₄×C₅	D₃×D₄	1	4	yes	—
244	C₂²×Q₈	—	3	8	no	—
245	C₂²×Q₈	—	3	1	no	—
246	C₂²×Q₈	—	3	2	no	—
247	C₂²×Q₈	—	3	1	no	—
248	C₂²×Q₈	—	6	8	no	—
249	C₂³×C₄	—	3	2	no	—
250	C₂³×C₄	C₂×C₅×D₃	1	1	yes	characteristic
251	C₄×Q₈	—	6	8	no	—
252	C₂×C₄⋊C₄	—	3	4	no	—
253	C₂×C₄⋊C₄	—	3	2	no	—
254	C₂×C₂²⋊C₄	—	3	2	no	—
255	C₂×C₂²⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
256	C₂×C₂²⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
257	C₂×C₄²	—	3	4	no	—
258	C₂×C₄²	C₂×C₅×D₃	1	2	yes	—
259	#95	—	3	4	no	—
260	#95	—	3	4	no	—
261	#95	—	3	2	no	—
262	#95	C₂×C₅×D₃	1	2	yes	—
263	C₂×C₃×C₅	—	2	4	no	—
264	C₂×C₃×C₅	C₂²×C₂²⋊C₄	1	1	yes	characteristic
265	C₂×C₃×C₅	C₂×C₄×Q₈	1	1	yes	characteristic
266	C₂×C₃×C₅	#519	1	1	yes	characteristic
267	C₂×C₃×C₅	#548	1	2	yes	—
268	C₂×C₃×C₅	D₄×Q₈	1	2	yes	—
269	C₂³×C₃	—	2	2	no	—
270	C₂³×C₃	—	2	2	no	—
271	C₂³×C₃	C₂²×C₄×C₅	1	2	yes	—
272	C₂³×C₃	C₂×C₅×Q₈	1	2	yes	—
273	C₂³×C₃	C₅×#41	1	2	yes	—
274	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
275	C₂×C₃×C₄	—	2	2	no	—
276	C₂×C₃×C₄	—	2	2	no	—
277	C₂×C₃×C₄	—	2	2	no	—
278	C₂×C₃×C₄	—	2	8	no	—
279	C₂×C₃×C₄	—	2	2	no	—
280	C₂×C₃×C₄	—	2	2	no	—
281	C₂×C₃×C₄	—	2	2	no	—
282	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
283	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
284	C₂×C₃×C₄	C₂×C₅×D₄	1	4	yes	—
285	C₂×C₃×C₄	C₂×C₅×Q₈	1	4	yes	complemented
286	C₂×Dic₃	—	2	4	no	—
287	C₂×Dic₃	—	2	16	no	—
288	C₂×Dic₃	—	2	4	no	—
289	C₂×Dic₃	—	2	4	no	—
290	C₂×Dic₃	—	2	4	no	—
291	C₂×Dic₃	C₂²×C₄×C₅	1	4	yes	—
292	C₂×Dic₃	C₂²×C₄×C₅	1	4	yes	—
293	C₂×Dic₃	C₂×C₅×D₄	1	8	yes	—
294	Dic₆	—	2	8	no	—
295	Dic₆	—	2	16	no	—
296	Dic₆	C₅×C₂²⋊C₄	1	16	yes	direct product factor
297	C₂²×C₅	—	2	2	no	—
298	C₂²×C₅	—	2	2	no	—
299	C₂²×C₅	—	2	4	no	—
300	C₂²×C₅	—	2	4	no	—
301	C₂²×C₅	C₄×Dic₆	1	4	yes	complemented
302	C₂²×C₅	C₂²×Dic₆	1	1	yes	characteristic
303	C₂²×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
304	C₂²×C₅	C₂×#235	1	1	yes	characteristic
305	C₂²×C₅	C₂×D₃×D₄	1	2	yes	—
306	C₂²×C₅	#1010	1	2	yes	—
307	C₄×C₅	—	2	2	no	—
308	C₄×C₅	—	2	4	no	—
309	C₄×C₅	—	3	8	no	—
310	C₄×C₅	—	4	2	no	—
311	C₄×C₅	—	6	4	no	—
312	C₄×C₅	—	12	4	no	—
313	C₄×C₅	D₃×C₂²⋊C₄	1	4	yes	—
314	C₂⁴	C₂²×C₅×D₃	1	1	yes	characteristic
315	C₂×Q₈	—	3	4	no	—
316	C₂×Q₈	—	3	8	no	—
317	C₂×Q₈	—	3	4	no	—
318	C₂×Q₈	—	3	8	no	—
319	C₂×Q₈	—	6	8	no	—
320	C₂×Q₈	—	6	32	no	—
321	C₂×Q₈	—	6	4	no	—
322	C₂²×C₄	—	2	4	no	—
323	C₂²×C₄	—	3	2	no	—
324	C₂²×C₄	—	3	8	no	—
325	C₂²×C₄	—	3	2	no	—
326	C₂²×C₄	—	3	4	no	—
327	C₂²×C₄	—	6	8	no	—
328	C₂²×C₄	C₄×C₅×D₃	1	4	yes	—
329	C₂²×C₄	C₂²×C₅×D₃	1	2	yes	—
330	C₂²×C₄	C₂²×C₅×D₃	1	2	yes	—
331	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
332	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
333	C₄⋊C₄	—	6	8	no	—
334	C₄⋊C₄	—	6	4	no	—
335	C₂²⋊C₄	—	2	2	no	—
336	C₂²⋊C₄	—	6	4	no	—
337	C₂²⋊C₄	C₅×Dic₆	1	4	yes	direct product factor
338	C₄²	—	2	4	no	—
339	C₄²	—	6	8	no	—
340	C₃×C₅	Q₈×C₂²⋊C₄	1	1	yes	characteristic, complemented, Hall
341	C₂²×C₃	—	2	2	no	—
342	C₂²×C₃	—	2	2	no	—
343	C₂²×C₃	—	2	4	no	—
344	C₂²×C₃	—	2	4	no	—
345	C₂²×C₃	C₄×C₅×Q₈	1	4	yes	complemented
346	C₂²×C₃	C₂³×C₄×C₅	1	1	yes	characteristic
347	C₂²×C₃	C₂²×C₅×D₄	1	2	yes	—
348	C₂²×C₃	C₂²×C₅×Q₈	1	1	yes	characteristic
349	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
350	C₂²×C₃	C₅×2₋¹⁺⁴	1	2	yes	—
351	C₃×C₄	—	2	2	no	—
352	C₃×C₄	—	2	4	no	—
353	C₃×C₄	—	4	2	no	—
354	C₃×C₄	C₂×C₅×C₂²⋊C₄	1	4	yes	—
355	Dic₃	—	2	4	no	—
356	Dic₃	—	4	4	no	—
357	Dic₃	C₂×C₅×C₂²⋊C₄	1	8	yes	—
358	C₂×C₅	—	2	4	no	—
359	C₂×C₅	C₂×C₄×Dic₆	1	1	yes	characteristic
360	C₂×C₅	C₂×D₃×C₂²⋊C₄	1	1	yes	characteristic
361	C₂×C₅	#5516	1	1	yes	characteristic
362	C₂×C₅	D₄×Dic₆	1	2	yes	—
363	C₂×C₅	#5552	1	2	yes	—
364	C₂³	—	2	2	no	—
365	C₂³	—	2	2	no	—
366	C₂³	C₂×C₅×Dic₆	1	2	yes	—
367	C₂³	C₂×C₄×C₅×D₃	1	2	yes	—
368	C₂³	C₅×#235	1	2	yes	—
369	C₂³	C₂³×C₅×D₃	1	1	yes	characteristic
370	Q₈	—	3	16	no	—
371	Q₈	—	6	16	no	—
372	Q₈	—	6	8	no	—
373	C₂×C₄	—	2	2	no	—
374	C₂×C₄	—	2	2	no	—
375	C₂×C₄	—	2	2	no	—
376	C₂×C₄	—	2	8	no	—
377	C₂×C₄	—	2	2	no	—
378	C₂×C₄	—	2	2	no	—
379	C₂×C₄	—	2	2	no	—
380	C₂×C₄	—	3	4	no	—
381	C₂×C₄	—	3	8	no	—
382	C₂×C₄	—	3	4	no	—
383	C₂×C₄	—	6	16	no	—
384	C₂×C₄	—	6	4	no	—
385	C₂×C₄	—	6	4	no	—
386	C₂×C₄	—	6	4	no	—
387	C₂×C₄	—	6	4	no	—
388	C₂×C₄	C₂×C₅×Dic₆	1	4	yes	complemented
389	C₂×C₄	C₂×C₄×C₅×D₃	1	2	yes	—
390	C₂×C₄	C₂×C₄×C₅×D₃	1	2	yes	—
391	C₂×C₄	C₅×D₃×D₄	1	4	yes	—
392	C₂×C₃	—	2	4	no	—
393	C₂×C₃	C₂²×C₅×C₂²⋊C₄	1	1	yes	characteristic
394	C₂×C₃	C₂×C₄×C₅×Q₈	1	1	yes	characteristic
395	C₂×C₃	C₅×#519	1	1	yes	characteristic
396	C₂×C₃	C₅×#548	1	2	yes	—
397	C₂×C₃	C₅×D₄×Q₈	1	2	yes	—
398	C₅	C₂²⋊C₄×Dic₆	1	1	yes	characteristic, direct product factor, Sylow
399	C₂²	—	2	2	no	—
400	C₂²	—	2	2	no	—
401	C₂²	—	2	4	no	—
402	C₂²	—	2	4	no	—
403	C₂²	C₄×C₅×Dic₆	1	4	yes	complemented
404	C₂²	C₂²×C₅×Dic₆	1	1	yes	characteristic
405	C₂²	C₂²×C₄×C₅×D₃	1	1	yes	characteristic
406	C₂²	C₂×C₅×#235	1	1	yes	characteristic
407	C₂²	C₂×C₅×D₃×D₄	1	2	yes	—
408	C₂²	C₅×#1010	1	2	yes	—
409	C₄	—	2	2	no	—
410	C₄	—	2	4	no	—
411	C₄	—	3	8	no	—
412	C₄	—	4	2	no	—
413	C₄	—	6	4	no	—
414	C₄	—	12	4	no	—
415	C₄	C₅×D₃×C₂²⋊C₄	1	4	yes	—
416	C₃	C₅×Q₈×C₂²⋊C₄	1	1	yes	characteristic, complemented, Sylow
417	C₂	—	2	4	no	—
418	C₂	C₂×C₄×C₅×Dic₆	1	1	yes	characteristic
419	C₂	C₂×C₅×D₃×C₂²⋊C₄	1	1	yes	characteristic
420	C₂	C₅×#5516	1	1	yes	characteristic
421	C₂	C₅×D₄×Dic₆	1	2	yes	—
422	C₂	C₅×#5552	1	2	yes	—

	subgroup	G/H
center	C₂³×C₅	C₂³×D₃
commutator	C₂²×C₃	C₂³×C₄×C₅
Frattini	C₂³	C₂³×C₅×D₃
Fitting	C₃×C₄×C₅×C₂²⋊C₄	C₂
socle	C₂³×C₃×C₅	C₂⁴
prime radical	C₂⁴×C₃×C₅	C₂³
cosocle	C₂³×C₃	C₂⁴×C₅
hypercenter	C₄×C₅×C₂²⋊C₄	D₃
hypocenter	C₃	C₅×Q₈×C₂²⋊C₄
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₅ ◁ C₄×C₅×C₂²⋊C₄

Complements

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

N	H ≅ G/N	type
2. C₂×C₄×C₅×Dic₆	C₂	semidirect
7. C₅×#4929	C₂	semidirect
8. C₅×#4646	C₂	semidirect
13. C₂²×C₅×Dic₆	C₄	semidirect
29. C₂²⋊C₄×Dic₆	C₅	direct (N × H)
58. C₃×C₅×C₂²⋊C₄	Q₈	semidirect
65. C₂×C₄×Dic₆	C₂×C₅	semidirect
70. #4929	C₂×C₅	semidirect
71. #4646	C₂×C₅	semidirect
108. C₂×C₃×C₄×C₅	C₂×Q₈	semidirect
119. C₅×Dic₆	C₂²⋊C₄	direct (N × H)
123. C₂²×Dic₆	C₄×C₅	semidirect
162. C₅×C₂²⋊C₄	Dic₆	direct (N × H)
177. C₂²×C₃×C₅	C₄×Q₈	semidirect
210. C₃×C₂²⋊C₄	C₅×Q₈	semidirect
240. C₂×C₄×C₅	C₂×Dic₆	semidirect
285. C₂×C₃×C₄	C₂×C₅×Q₈	semidirect
296. Dic₆	C₅×C₂²⋊C₄	direct (N × H)
301. C₂²×C₅	C₄×Dic₆	semidirect
337. C₂²⋊C₄	C₅×Dic₆	direct (N × H)
340. C₃×C₅	Q₈×C₂²⋊C₄	semidirect
345. C₂²×C₃	C₄×C₅×Q₈	semidirect
388. C₂×C₄	C₂×C₅×Dic₆	semidirect
398. C₅	C₂²⋊C₄×Dic₆	direct (N × H)
403. C₂²	C₄×C₅×Dic₆	semidirect
416. C₃	C₅×Q₈×C₂²⋊C₄	semidirect

Maximal subgroups

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

subgroup	index
C₂³×C₅×Dic₆	2
C₂×C₄×C₅×Dic₆	2
C₃×C₄×C₅×C₂²⋊C₄	2
C₅×#5212	2
C₅×#4942	2
C₅×Dic₃×C₂²⋊C₄	2
C₅×#4929	2
C₅×#4646	2
C₅×Q₈×C₂²⋊C₄	3
C₂²⋊C₄×Dic₆	5

Subgroups — C5×C22⋊C4×Dic6 #14326117

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×C₂²⋊C₄×Dic₆ #14326117