Subgroups — C₂×C₄×C₅×#215 #14416052

Order 1920.

1104 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₄×C₅×Q₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₅×#215	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×C₅×D₁₂	C₂	1	1	yes	maximal, characteristic
4	C₂×C₅×#835	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄×C₅×#215	C₂	1	8	yes	maximal, direct product factor
6	C₂×C₅×#809	C₂	1	1	yes	maximal, characteristic
7	C₂×C₅×#808	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₄×C₅×C₃⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₄×C₅×SD₁₆	—	3	1	no	maximal, Hall
10	C₂²×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic
11	C₂²×C₅×D₁₂	C₂²	1	1	yes	characteristic
12	C₂²×C₄×C₅×D₃	—	2	1	no	—
13	C₃×C₄×C₅×Q₈	—	2	2	no	—
14	C₃×C₄×C₅×Q₈	C₂²	1	4	yes	complemented
15	C₂×C₃×C₅×C₄⋊C₄	—	2	1	no	—
16	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
17	C₂×C₃×C₄²×C₅	—	2	1	no	—
18	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
19	C₂×C₅×#215	C₄	1	8	yes	direct product factor
20	C₂×C₅×#215	C₂²	1	4	yes	—
21	C₂×C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
22	C₂×C₅×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
23	C₂²×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
24	C₂²×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
25	C₄×C₅×D₁₂	—	2	2	no	—
26	C₄×C₅×D₁₂	C₂²	1	4	yes	—
27	C₅×#835	C₂²	1	4	yes	complemented
28	C₅×#809	C₂²	1	4	yes	—
29	C₅×#808	C₂²	1	4	yes	complemented
30	C₄×C₅×C₃⋊C₈	C₂²	1	4	yes	complemented
31	C₂×C₄×#215	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
32	C₂²×C₅×SD₁₆	—	3	1	no	—
33	C₂×C₄×C₅×Q₈	D₃	1	1	yes	characteristic, complemented
34	C₂×C₄×C₅×D₄	—	3	1	no	—
35	C₄×C₅×SD₁₆	—	3	8	no	—
36	C₂×C₅×#106	—	3	1	no	—
37	C₂×C₅×#103	—	3	1	no	—
38	C₂×C₅×#102	—	3	1	no	—
39	C₂×C₄×C₅×C₈	—	3	1	no	—
40	C₂³×C₅×D₃	—	2	1	no	—
41	C₂×C₃×C₅×Q₈	—	2	1	no	—
42	C₂×C₃×C₅×Q₈	—	2	2	no	—
43	C₂×C₃×C₅×Q₈	C₂×C₄	1	4	yes	complemented
44	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
45	C₂²×C₃×C₄×C₅	—	2	1	no	—
46	C₂²×C₃×C₄×C₅	—	2	1	no	—
47	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
48	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
49	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
50	C₂²×C₅×Dic₃	—	2	1	no	—
51	C₂×C₅×D₁₂	—	2	1	no	—
52	C₂×C₅×D₁₂	—	2	2	no	—
53	C₂×C₅×D₁₂	C₂×C₄	1	4	yes	—
54	C₂×C₅×D₁₂	C₂³	1	2	yes	—
55	C₂×C₄×C₅×D₃	—	2	4	no	—
56	C₂×C₄×C₅×D₃	—	4	4	no	—
57	C₃×C₅×C₄⋊C₄	—	2	4	no	—
58	C₃×C₅×C₄⋊C₄	—	2	1	no	—
59	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
60	C₃×C₄²×C₅	—	2	4	no	—
61	C₃×C₄²×C₅	D₄	1	2	yes	—
62	C₃×C₄²×C₅	C₂³	1	2	yes	—
63	C₅×#215	C₂×C₄	1	16	yes	direct product factor
64	C₅×(C₂×D₃)⋊C₄	—	2	4	no	—
65	C₅×C₄⋊Dic₃	—	2	1	no	—
66	C₅×C₄⋊Dic₃	C₂³	1	2	yes	—
67	C₂×C₅×C₃⋊C₈	—	2	2	no	—
68	C₂×C₅×C₃⋊C₈	C₂×C₄	1	4	yes	complemented
69	C₂×C₅×C₃⋊C₈	C₂³	1	2	yes	—
70	C₂×C₅×C₃⋊C₈	C₂³	1	2	yes	—
71	C₂×C₃×C₄×Q₈	C₂×C₅	1	1	yes	characteristic, complemented
72	C₂²×#215	C₂×C₅	1	1	yes	characteristic
73	C₂×C₄×D₁₂	C₂×C₅	1	1	yes	characteristic
74	C₂×#835	C₂×C₅	1	1	yes	characteristic, complemented
75	C₄×#215	C₂×C₅	1	8	yes	direct product factor
76	C₂×#809	C₂×C₅	1	1	yes	characteristic
77	C₂×#808	C₂×C₅	1	1	yes	characteristic, complemented
78	C₂×C₄×C₃⋊C₈	C₂×C₅	1	1	yes	characteristic, complemented
79	C₂²×C₅×Q₈	C₂×D₃	1	1	yes	characteristic
80	C₂²×C₅×D₄	—	3	1	no	—
81	C₂³×C₄×C₅	—	6	1	no	—
82	C₂×C₅×SD₁₆	—	3	8	no	—
83	C₂×C₅×SD₁₆	—	3	4	no	—
84	C₂²×C₅×C₈	—	3	1	no	—
85	C₂²×C₅×C₈	—	3	1	no	—
86	C₄×C₅×Q₈	—	2	2	no	—
87	C₄×C₅×Q₈	C₂×D₃	1	4	yes	complemented
88	C₄×C₅×D₄	—	3	4	no	—
89	C₄×C₅×D₄	—	6	2	no	—
90	C₂×C₅×C₄⋊C₄	—	2	1	no	—
91	C₂×C₅×C₄⋊C₄	—	3	1	no	—
92	C₂×C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
93	C₂×C₅×C₂²⋊C₄	—	6	1	no	—
94	C₂×C₄²×C₅	—	2	1	no	—
95	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
96	C₅×#106	—	3	4	no	—
97	C₅×#103	—	3	4	no	—
98	C₅×#102	—	3	4	no	—
99	C₄×C₅×C₈	—	3	4	no	—
100	C₂×C₄×SD₁₆	—	3	1	no	Sylow
101	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
102	C₂²×C₅×D₃	—	2	4	no	—
103	C₂²×C₅×D₃	—	2	2	no	—
104	C₂²×C₅×D₃	—	4	2	no	—
105	C₂²×C₅×D₃	—	4	2	no	—
106	C₃×C₅×Q₈	—	2	4	no	—
107	C₃×C₅×Q₈	—	2	2	no	—
108	C₃×C₅×Q₈	C₂²×C₄	1	4	yes	complemented
109	C₂×C₃×C₄×C₅	—	2	4	no	—
110	C₂×C₃×C₄×C₅	—	2	2	no	—
111	C₂×C₃×C₄×C₅	—	2	2	no	—
112	C₂×C₃×C₄×C₅	—	2	2	no	—
113	C₂×C₃×C₄×C₅	—	4	2	no	—
114	C₂×C₃×C₄×C₅	SD₁₆	1	4	yes	complemented
115	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
116	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
117	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
118	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
119	C₂×C₃×C₄×C₅	#41	1	2	yes	—
120	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
121	C₂×C₅×Dic₃	—	2	2	no	—
122	C₂×C₅×Dic₃	—	4	2	no	—
123	C₅×D₁₂	—	2	4	no	—
124	C₅×D₁₂	—	2	2	no	—
125	C₅×D₁₂	C₂²×C₄	1	4	yes	—
126	C₄×C₅×D₃	—	4	8	no	—
127	C₅×C₃⋊C₈	—	2	2	no	—
128	C₅×C₃⋊C₈	C₂²×C₄	1	4	yes	complemented
129	C₂²×C₃×Q₈	C₂²×C₅	1	1	yes	characteristic
130	C₂²×D₁₂	C₂²×C₅	1	1	yes	characteristic
131	C₂²×C₄×D₃	—	2	1	no	—
132	C₃×C₄×Q₈	—	2	2	no	—
133	C₃×C₄×Q₈	C₂²×C₅	1	4	yes	complemented
134	C₂×C₃×C₄⋊C₄	—	2	1	no	—
135	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
136	C₂×C₃×C₄²	—	2	1	no	—
137	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
138	C₂×#215	C₄×C₅	1	8	yes	direct product factor
139	C₂×#215	C₂²×C₅	1	4	yes	—
140	C₂×(C₂×D₃)⋊C₄	—	2	1	no	—
141	C₂×C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic
142	C₂²×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic
143	C₂²×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic
144	C₄×D₁₂	—	2	2	no	—
145	C₄×D₁₂	C₂²×C₅	1	4	yes	—
146	#835	C₂²×C₅	1	4	yes	complemented
147	#809	C₂²×C₅	1	4	yes	—
148	#808	C₂²×C₅	1	4	yes	complemented
149	C₄×C₃⋊C₈	C₂²×C₅	1	4	yes	complemented
150	C₂⁴×C₅	—	6	1	no	—
151	C₂×C₅×Q₈	—	2	2	no	—
152	C₂×C₅×Q₈	—	2	1	no	—
153	C₂×C₅×Q₈	C₄×D₃	1	4	yes	complemented
154	C₂×C₅×Q₈	C₂²×D₃	1	2	yes	—
155	C₂×C₅×D₄	—	3	4	no	—
156	C₂×C₅×D₄	—	3	2	no	—
157	C₂×C₅×D₄	—	6	2	no	—
158	C₂×C₅×D₄	—	6	1	no	—
159	C₂²×C₄×C₅	—	2	1	no	—
160	C₂²×C₄×C₅	—	2	1	no	—
161	C₂²×C₄×C₅	—	6	1	no	—
162	C₂²×C₄×C₅	—	6	4	no	—
163	C₂²×C₄×C₅	—	12	4	no	—
164	C₂²×C₄×C₅	#67	1	1	yes	characteristic
165	C₂²×C₄×C₅	#67	1	1	yes	characteristic
166	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
167	C₅×SD₁₆	—	3	16	no	—
168	C₂×C₅×C₈	—	3	4	no	—
169	C₂×C₅×C₈	—	3	2	no	—
170	C₂×C₅×C₈	—	3	2	no	—
171	C₂×C₅×C₈	—	6	2	no	—
172	C₅×C₄⋊C₄	—	2	4	no	—
173	C₅×C₄⋊C₄	—	2	1	no	—
174	C₅×C₄⋊C₄	—	3	2	no	—
175	C₅×C₄⋊C₄	—	6	1	no	—
176	C₅×C₄⋊C₄	C₂²×D₃	1	2	yes	—
177	C₅×C₂²⋊C₄	—	6	4	no	—
178	C₄²×C₅	—	2	4	no	—
179	C₄²×C₅	#67	1	2	yes	—
180	C₄²×C₅	C₂²×D₃	1	2	yes	—
181	C₂²×SD₁₆	—	3	1	no	—
182	C₂×C₄×Q₈	C₅×D₃	1	1	yes	characteristic, complemented
183	C₂×C₄×D₄	—	3	1	no	—
184	C₄×SD₁₆	—	3	8	no	—
185	C₂×#106	—	3	1	no	—
186	C₂×#103	—	3	1	no	—
187	C₂×#102	—	3	1	no	—
188	C₂×C₄×C₈	—	3	1	no	—
189	C₂²×C₃×C₅	C₄×D₄	1	2	yes	—
190	C₂²×C₃×C₅	C₂×SD₁₆	1	2	yes	—
191	C₂²×C₃×C₅	#135	1	2	yes	—
192	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
193	C₂×C₅×D₃	—	2	4	no	—
194	C₂×C₅×D₃	—	4	2	no	—
195	C₂×C₅×D₃	—	4	2	no	—
196	C₂×C₅×D₃	—	4	8	no	—
197	C₃×C₄×C₅	—	2	4	no	—
198	C₃×C₄×C₅	—	2	2	no	—
199	C₃×C₄×C₅	—	4	2	no	—
200	C₃×C₄×C₅	C₄×D₄	1	2	yes	—
201	C₃×C₄×C₅	C₂×SD₁₆	1	4	yes	complemented
202	C₃×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
203	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
204	C₅×Dic₃	—	4	2	no	—
205	C₂³×D₃	—	2	1	no	—
206	C₂×C₃×Q₈	—	2	1	no	—
207	C₂×C₃×Q₈	—	2	2	no	—
208	C₂×C₃×Q₈	C₂×C₄×C₅	1	4	yes	complemented
209	C₂×C₃×Q₈	C₂³×C₅	1	2	yes	—
210	C₂²×C₃×C₄	—	2	1	no	—
211	C₂²×C₃×C₄	—	2	1	no	—
212	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
213	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
214	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
215	C₂²×Dic₃	—	2	1	no	—
216	C₂×D₁₂	—	2	1	no	—
217	C₂×D₁₂	—	2	2	no	—
218	C₂×D₁₂	C₂×C₄×C₅	1	4	yes	—
219	C₂×D₁₂	C₂³×C₅	1	2	yes	—
220	C₂×C₄×D₃	—	2	4	no	—
221	C₂×C₄×D₃	—	4	4	no	—
222	C₃×C₄⋊C₄	—	2	4	no	—
223	C₃×C₄⋊C₄	—	2	1	no	—
224	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
225	C₃×C₄²	—	2	4	no	—
226	C₃×C₄²	C₅×D₄	1	2	yes	—
227	C₃×C₄²	C₂³×C₅	1	2	yes	—
228	#215	C₂×C₄×C₅	1	16	yes	direct product factor
229	(C₂×D₃)⋊C₄	—	2	4	no	—
230	C₄⋊Dic₃	—	2	1	no	—
231	C₄⋊Dic₃	C₂³×C₅	1	2	yes	—
232	C₂×C₃⋊C₈	—	2	2	no	—
233	C₂×C₃⋊C₈	C₂×C₄×C₅	1	4	yes	complemented
234	C₂×C₃⋊C₈	C₂³×C₅	1	2	yes	—
235	C₂×C₃⋊C₈	C₂³×C₅	1	2	yes	—
236	C₂³×C₅	—	6	4	no	—
237	C₂³×C₅	—	6	2	no	—
238	C₂³×C₅	—	12	2	no	—
239	C₂³×C₅	—	12	2	no	—
240	C₂³×C₅	C₂×#67	1	1	yes	characteristic
241	C₅×Q₈	—	2	4	no	—
242	C₅×Q₈	—	2	2	no	—
243	C₅×Q₈	C₂×C₄×D₃	1	4	yes	complemented
244	C₅×D₄	—	3	4	no	—
245	C₅×D₄	—	6	4	no	—
246	C₅×D₄	—	6	2	no	—
247	C₂×C₄×C₅	—	2	4	no	—
248	C₂×C₄×C₅	—	2	2	no	—
249	C₂×C₄×C₅	—	2	2	no	—
250	C₂×C₄×C₅	—	2	2	no	—
251	C₂×C₄×C₅	—	4	2	no	—
252	C₂×C₄×C₅	—	6	2	no	—
253	C₂×C₄×C₅	—	12	2	no	—
254	C₂×C₄×C₅	—	12	8	no	—
255	C₂×C₄×C₅	#215	1	4	yes	direct product factor
256	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
257	C₂×C₄×C₅	#235	1	2	yes	—
258	C₂×C₄×C₅	C₂×#67	1	2	yes	—
259	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
260	C₂×C₄×C₅	C₂×#67	1	2	yes	—
261	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
262	C₅×C₈	—	3	4	no	—
263	C₅×C₈	—	6	2	no	—
264	C₂²×Q₈	C₂×C₅×D₃	1	1	yes	characteristic
265	C₂²×D₄	—	3	1	no	—
266	C₂³×C₄	—	6	1	no	—
267	C₂×SD₁₆	—	3	8	no	—
268	C₂×SD₁₆	—	3	4	no	—
269	C₂²×C₈	—	3	1	no	—
270	C₂²×C₈	—	3	1	no	—
271	C₄×Q₈	—	2	2	no	—
272	C₄×Q₈	C₂×C₅×D₃	1	4	yes	complemented
273	C₄×D₄	—	3	4	no	—
274	C₄×D₄	—	6	2	no	—
275	C₂×C₄⋊C₄	—	2	1	no	—
276	C₂×C₄⋊C₄	—	3	1	no	—
277	C₂×C₄⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
278	C₂×C₂²⋊C₄	—	6	1	no	—
279	C₂×C₄²	—	2	1	no	—
280	C₂×C₄²	C₂×C₅×D₃	1	1	yes	characteristic
281	#106	—	3	4	no	—
282	#103	—	3	4	no	—
283	#102	—	3	4	no	—
284	C₄×C₈	—	3	4	no	—
285	C₂×C₃×C₅	C₄×SD₁₆	1	4	yes	complemented
286	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
287	C₂×C₃×C₅	C₂²×SD₁₆	1	1	yes	characteristic
288	C₂×C₃×C₅	C₂×#135	1	1	yes	characteristic
289	C₅×D₃	—	4	4	no	—
290	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
291	C₂²×D₃	—	2	4	no	—
292	C₂²×D₃	—	2	2	no	—
293	C₂²×D₃	—	4	2	no	—
294	C₂²×D₃	—	4	2	no	—
295	C₃×Q₈	—	2	4	no	—
296	C₃×Q₈	—	2	2	no	—
297	C₃×Q₈	C₂²×C₄×C₅	1	4	yes	complemented
298	C₂×C₃×C₄	—	2	4	no	—
299	C₂×C₃×C₄	—	2	2	no	—
300	C₂×C₃×C₄	—	2	2	no	—
301	C₂×C₃×C₄	—	2	2	no	—
302	C₂×C₃×C₄	—	4	2	no	—
303	C₂×C₃×C₄	C₅×SD₁₆	1	4	yes	complemented
304	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
305	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
306	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
307	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
308	C₂×C₃×C₄	C₅×#41	1	2	yes	—
309	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
310	C₂×Dic₃	—	2	2	no	—
311	C₂×Dic₃	—	4	2	no	—
312	D₁₂	—	2	4	no	—
313	D₁₂	—	2	2	no	—
314	D₁₂	C₂²×C₄×C₅	1	4	yes	—
315	C₄×D₃	—	4	8	no	—
316	C₃⋊C₈	—	2	2	no	—
317	C₃⋊C₈	C₂²×C₄×C₅	1	4	yes	complemented
318	C₂²×C₅	—	6	4	no	—
319	C₂²×C₅	—	12	8	no	—
320	C₂²×C₅	—	12	2	no	—
321	C₂²×C₅	—	12	2	no	—
322	C₂²×C₅	C₄×#67	1	2	yes	—
323	C₂²×C₅	C₂×#215	1	2	yes	—
324	C₂²×C₅	#950	1	2	yes	—
325	C₂²×C₅	C₂²×#67	1	1	yes	characteristic
326	C₄×C₅	—	2	4	no	—
327	C₄×C₅	—	2	2	no	—
328	C₄×C₅	—	4	2	no	—
329	C₄×C₅	—	12	2	no	—
330	C₄×C₅	C₄×#67	1	2	yes	—
331	C₄×C₅	C₂×#215	1	4	yes	direct product factor
332	C₄×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
333	C₄×C₅	C₂×#235	1	1	yes	characteristic
334	C₂⁴	—	6	1	no	—
335	C₂×Q₈	—	2	2	no	—
336	C₂×Q₈	—	2	1	no	—
337	C₂×Q₈	C₄×C₅×D₃	1	4	yes	complemented
338	C₂×Q₈	C₂²×C₅×D₃	1	2	yes	—
339	C₂×D₄	—	3	4	no	—
340	C₂×D₄	—	3	2	no	—
341	C₂×D₄	—	6	2	no	—
342	C₂×D₄	—	6	1	no	—
343	C₂²×C₄	—	2	1	no	—
344	C₂²×C₄	—	2	1	no	—
345	C₂²×C₄	—	6	1	no	—
346	C₂²×C₄	—	6	4	no	—
347	C₂²×C₄	—	12	4	no	—
348	C₂²×C₄	C₅×#67	1	1	yes	characteristic
349	C₂²×C₄	C₅×#67	1	1	yes	characteristic
350	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
351	SD₁₆	—	3	16	no	—
352	C₂×C₈	—	3	4	no	—
353	C₂×C₈	—	3	2	no	—
354	C₂×C₈	—	3	2	no	—
355	C₂×C₈	—	6	2	no	—
356	C₄⋊C₄	—	2	4	no	—
357	C₄⋊C₄	—	2	1	no	—
358	C₄⋊C₄	—	3	2	no	—
359	C₄⋊C₄	—	6	1	no	—
360	C₄⋊C₄	C₂²×C₅×D₃	1	2	yes	—
361	C₂²⋊C₄	—	6	4	no	—
362	C₄²	—	2	4	no	—
363	C₄²	C₅×#67	1	2	yes	—
364	C₄²	C₂²×C₅×D₃	1	2	yes	—
365	C₃×C₅	C₂×C₄×SD₁₆	1	1	yes	characteristic, complemented, Hall
366	C₂²×C₃	C₄×C₅×D₄	1	2	yes	—
367	C₂²×C₃	C₂×C₅×SD₁₆	1	2	yes	—
368	C₂²×C₃	C₅×#135	1	2	yes	—
369	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
370	C₂×D₃	—	2	4	no	—
371	C₂×D₃	—	4	8	no	—
372	C₂×D₃	—	4	2	no	—
373	C₂×D₃	—	4	2	no	—
374	C₃×C₄	—	2	4	no	—
375	C₃×C₄	—	2	2	no	—
376	C₃×C₄	—	4	2	no	—
377	C₃×C₄	C₄×C₅×D₄	1	2	yes	—
378	C₃×C₄	C₂×C₅×SD₁₆	1	4	yes	complemented
379	C₃×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
380	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
381	Dic₃	—	4	2	no	—
382	C₂×C₅	—	12	4	no	—
383	C₂×C₅	C₄×#215	1	4	yes	direct product factor
384	C₂×C₅	C₂×C₄×#67	1	1	yes	characteristic
385	C₂×C₅	C₂²×#215	1	1	yes	characteristic
386	C₂×C₅	C₂×#950	1	1	yes	characteristic
387	C₂³	—	6	4	no	—
388	C₂³	—	6	2	no	—
389	C₂³	—	12	2	no	—
390	C₂³	—	12	2	no	—
391	C₂³	C₂×C₅×#67	1	1	yes	characteristic
392	Q₈	—	2	4	no	—
393	Q₈	—	2	2	no	—
394	Q₈	C₂×C₄×C₅×D₃	1	4	yes	complemented
395	D₄	—	3	4	no	—
396	D₄	—	6	4	no	—
397	D₄	—	6	2	no	—
398	C₂×C₄	—	2	4	no	—
399	C₂×C₄	—	2	2	no	—
400	C₂×C₄	—	2	2	no	—
401	C₂×C₄	—	2	2	no	—
402	C₂×C₄	—	4	2	no	—
403	C₂×C₄	—	6	2	no	—
404	C₂×C₄	—	12	2	no	—
405	C₂×C₄	—	12	8	no	—
406	C₂×C₄	C₅×#215	1	4	yes	direct product factor
407	C₂×C₄	C₂×C₄×C₅×D₃	1	2	yes	—
408	C₂×C₄	C₅×#235	1	2	yes	—
409	C₂×C₄	C₂×C₅×#67	1	2	yes	—
410	C₂×C₄	C₂×C₅×#67	1	1	yes	characteristic
411	C₂×C₄	C₂×C₅×#67	1	2	yes	—
412	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
413	C₈	—	3	4	no	—
414	C₈	—	6	2	no	—
415	C₂×C₃	C₄×C₅×SD₁₆	1	4	yes	complemented
416	C₂×C₃	C₂×C₄×C₅×D₄	1	1	yes	characteristic
417	C₂×C₃	C₂²×C₅×SD₁₆	1	1	yes	characteristic
418	C₂×C₃	C₂×C₅×#135	1	1	yes	characteristic
419	D₃	—	4	4	no	—
420	C₅	C₂×C₄×#215	1	1	yes	characteristic, direct product factor, Sylow
421	C₂²	—	6	4	no	—
422	C₂²	—	12	8	no	—
423	C₂²	—	12	2	no	—
424	C₂²	—	12	2	no	—
425	C₂²	C₄×C₅×#67	1	2	yes	—
426	C₂²	C₂×C₅×#215	1	2	yes	—
427	C₂²	C₅×#950	1	2	yes	—
428	C₂²	C₂²×C₅×#67	1	1	yes	characteristic
429	C₄	—	2	4	no	—
430	C₄	—	2	2	no	—
431	C₄	—	4	2	no	—
432	C₄	—	12	2	no	—
433	C₄	C₄×C₅×#67	1	2	yes	—
434	C₄	C₂×C₅×#215	1	4	yes	direct product factor
435	C₄	C₂²×C₄×C₅×D₃	1	1	yes	characteristic
436	C₄	C₂×C₅×#235	1	1	yes	characteristic
437	C₃	C₂×C₄×C₅×SD₁₆	1	1	yes	characteristic, complemented, Sylow
438	C₂	—	12	4	no	—
439	C₂	C₄×C₅×#215	1	4	yes	direct product factor
440	C₂	C₂×C₄×C₅×#67	1	1	yes	characteristic
441	C₂	C₂²×C₅×#215	1	1	yes	characteristic
442	C₂	C₂×C₅×#950	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₅	#67
commutator	C₃×C₄	C₂³×C₄×C₅
Frattini	C₂×C₄	C₂³×C₅×D₃
Fitting	C₂×C₃×C₄×C₅×Q₈	C₂
socle	C₂³×C₃×C₅	C₂×D₄
prime radical	C₂²×C₅×D₁₂	C₂²
cosocle	C₂×C₃×C₄	C₂⁴×C₅
hypercenter	C₂×C₄×C₅×Q₈	D₃
hypocenter	C₃	C₂×C₄×C₅×SD₁₆
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₄×C₅ ◁ C₂×C₄²×C₅ ◁ C₂×C₄×C₅×Q₈

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×C₄×C₅×Q₈	C₂	semidirect
4. C₂×C₅×#835	C₂	semidirect
5. C₄×C₅×#215	C₂	direct (N × H)
7. C₂×C₅×#808	C₂	semidirect
8. C₂×C₄×C₅×C₃⋊C₈	C₂	semidirect
14. C₃×C₄×C₅×Q₈	C₂²	semidirect
19. C₂×C₅×#215	C₄	direct (N × H)
27. C₅×#835	C₂²	semidirect
29. C₅×#808	C₂²	semidirect
30. C₄×C₅×C₃⋊C₈	C₂²	semidirect
31. C₂×C₄×#215	C₅	direct (N × H)
33. C₂×C₄×C₅×Q₈	D₃	semidirect
43. C₂×C₃×C₅×Q₈	C₂×C₄	semidirect
63. C₅×#215	C₂×C₄	direct (N × H)
68. C₂×C₅×C₃⋊C₈	C₂×C₄	semidirect
71. C₂×C₃×C₄×Q₈	C₂×C₅	semidirect
74. C₂×#835	C₂×C₅	semidirect
75. C₄×#215	C₂×C₅	direct (N × H)
77. C₂×#808	C₂×C₅	semidirect
78. C₂×C₄×C₃⋊C₈	C₂×C₅	semidirect
87. C₄×C₅×Q₈	C₂×D₃	semidirect
108. C₃×C₅×Q₈	C₂²×C₄	semidirect
114. C₂×C₃×C₄×C₅	SD₁₆	semidirect
128. C₅×C₃⋊C₈	C₂²×C₄	semidirect
133. C₃×C₄×Q₈	C₂²×C₅	semidirect
138. C₂×#215	C₄×C₅	direct (N × H)
146. #835	C₂²×C₅	semidirect
148. #808	C₂²×C₅	semidirect
149. C₄×C₃⋊C₈	C₂²×C₅	semidirect
153. C₂×C₅×Q₈	C₄×D₃	semidirect
182. C₂×C₄×Q₈	C₅×D₃	semidirect
201. C₃×C₄×C₅	C₂×SD₁₆	semidirect
208. C₂×C₃×Q₈	C₂×C₄×C₅	semidirect
228. #215	C₂×C₄×C₅	direct (N × H)
233. C₂×C₃⋊C₈	C₂×C₄×C₅	semidirect
243. C₅×Q₈	C₂×C₄×D₃	semidirect
255. C₂×C₄×C₅	#215	direct (N × H)
272. C₄×Q₈	C₂×C₅×D₃	semidirect
285. C₂×C₃×C₅	C₄×SD₁₆	semidirect
297. C₃×Q₈	C₂²×C₄×C₅	semidirect
303. C₂×C₃×C₄	C₅×SD₁₆	semidirect
317. C₃⋊C₈	C₂²×C₄×C₅	semidirect
331. C₄×C₅	C₂×#215	direct (N × H)
337. C₂×Q₈	C₄×C₅×D₃	semidirect
365. C₃×C₅	C₂×C₄×SD₁₆	semidirect
378. C₃×C₄	C₂×C₅×SD₁₆	semidirect
383. C₂×C₅	C₄×#215	direct (N × H)
394. Q₈	C₂×C₄×C₅×D₃	semidirect
406. C₂×C₄	C₅×#215	direct (N × H)
415. C₂×C₃	C₄×C₅×SD₁₆	semidirect
420. C₅	C₂×C₄×#215	direct (N × H)
434. C₄	C₂×C₅×#215	direct (N × H)
437. C₃	C₂×C₄×C₅×SD₁₆	semidirect
439. C₂	C₄×C₅×#215	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×C₄×C₅×Q₈	2
C₂²×C₅×#215	2
C₂×C₄×C₅×D₁₂	2
C₂×C₅×#835	2
C₄×C₅×#215	2
C₂×C₅×#809	2
C₂×C₅×#808	2
C₂×C₄×C₅×C₃⋊C₈	2
C₂×C₄×C₅×SD₁₆	3
C₂×C₄×#215	5

Subgroups — C2×C4×C5×#215 #14416052

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄×C₅×#215 #14416052