Subgroups — C₂×C₅×#5046 #14423235

Order 1920.

1992 conjugacy classes of subgroups.

The subgroup lattice has 448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₅×D₁₂	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×C₅×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₅×#215	C₂	1	2	yes	maximal, complemented
4	C₂×C₅×#830	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#5046	C₂	1	8	yes	maximal, direct product factor
6	C₂×C₅×#809	C₂	1	2	yes	maximal, complemented
7	C₂×C₅×#450	—	3	1	no	maximal, Hall
8	C₂⁴×C₅×D₃	—	2	1	no	—
9	C₂²×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic, complemented
10	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
11	C₂²×C₅×D₁₂	—	2	1	no	—
12	C₂²×C₅×D₁₂	—	2	2	no	—
13	C₂²×C₅×D₁₂	—	2	8	no	—
14	C₂²×C₅×D₁₂	C₂²	1	4	yes	—
15	C₂²×C₅×D₁₂	C₂²	1	2	yes	—
16	C₃×C₅×C₂²⋊Q₈	—	2	2	no	—
17	C₃×C₅×C₂²⋊Q₈	C₂²	1	4	yes	complemented
18	C₂×C₃×C₅×C₄⋊C₄	—	2	1	no	—
19	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
20	C₂×C₃×C₅×C₂²⋊C₄	—	2	1	no	—
21	C₂×C₅×#215	—	2	8	no	—
22	C₂×C₅×#215	C₂²	1	8	yes	complemented
23	C₂²×C₅×C₃⋊C₈	C₂²	1	2	yes	complemented
24	C₅×#830	C₂²	1	4	yes	complemented
25	C₅×#809	C₂²	1	8	yes	complemented
26	C₂×#5046	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
27	C₂³×C₅×D₄	—	3	1	no	—
28	C₂²×C₅×SD₁₆	—	3	2	no	—
29	C₂×C₅×C₂²⋊Q₈	D₃	1	1	yes	characteristic, complemented
30	C₅×#450	—	3	8	no	—
31	C₂×C₅×#102	—	3	2	no	—
32	C₂×C₅×C₂²⋊C₈	—	3	1	no	—
33	C₂⁴×C₃×C₅	D₄	1	1	yes	characteristic
34	C₂³×C₅×D₃	—	2	8	no	—
35	C₂³×C₅×D₃	—	2	4	no	—
36	C₂³×C₅×D₃	—	2	2	no	—
37	C₂³×C₅×D₃	—	4	4	no	—
38	C₂³×C₅×D₃	—	4	4	no	—
39	C₂×C₃×C₅×Q₈	—	2	1	no	—
40	C₂×C₃×C₅×Q₈	—	2	4	no	—
41	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	complemented
42	C₂²×C₃×C₄×C₅	—	2	4	no	—
43	C₂²×C₃×C₄×C₅	—	2	1	no	—
44	C₂²×C₃×C₄×C₅	—	2	1	no	—
45	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
46	C₂²×C₃×C₄×C₅	D₄	1	2	yes	—
47	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
48	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
49	C₂×C₅×D₁₂	—	2	8	no	—
50	C₂×C₅×D₁₂	—	2	16	no	—
51	C₂×C₅×D₁₂	—	2	4	no	—
52	C₂×C₅×D₁₂	—	2	2	no	—
53	C₂×C₅×D₁₂	—	2	4	no	—
54	C₂×C₅×D₁₂	—	2	16	no	—
55	C₂×C₅×D₁₂	D₄	1	8	yes	—
56	C₂×C₅×D₁₂	C₂³	1	4	yes	—
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	complemented
60	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
61	C₅×#215	—	2	16	no	—
62	C₂×C₅×C₃⋊C₈	—	2	4	no	—
63	C₂×C₅×C₃⋊C₈	C₂³	1	4	yes	complemented
64	C₂³×D₁₂	C₂×C₅	1	1	yes	characteristic
65	C₂×C₃×C₂²⋊Q₈	C₂×C₅	1	1	yes	characteristic, complemented
66	C₂²×#215	C₂×C₅	1	2	yes	complemented
67	C₂×#830	C₂×C₅	1	1	yes	characteristic, complemented
68	#5046	C₂×C₅	1	8	yes	direct product factor
69	C₂×#809	C₂×C₅	1	2	yes	complemented
70	C₂⁵×C₅	—	6	1	no	—
71	C₂²×C₅×Q₈	C₂×D₃	1	1	yes	characteristic, complemented
72	C₂²×C₅×D₄	—	3	2	no	—
73	C₂²×C₅×D₄	—	3	4	no	—
74	C₂²×C₅×D₄	—	6	8	no	—
75	C₂²×C₅×D₄	—	6	2	no	—
76	C₂²×C₅×D₄	—	6	1	no	—
77	C₂³×C₄×C₅	C₂×D₃	1	1	yes	characteristic
78	C₂×C₅×SD₁₆	—	3	8	no	—
79	C₂×C₅×SD₁₆	—	6	8	no	—
80	C₂²×C₅×C₈	—	3	2	no	—
81	C₅×C₂²⋊Q₈	—	2	2	no	—
82	C₅×C₂²⋊Q₈	C₂×D₃	1	4	yes	complemented
83	C₂×C₅×C₄⋊C₄	—	2	1	no	—
84	C₂×C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic, complemented
85	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
86	C₅×#102	—	3	8	no	—
87	C₅×C₂²⋊C₈	—	3	4	no	—
88	C₂×#450	—	3	1	no	Sylow
89	C₂³×C₃×C₅	—	2	2	no	—
90	C₂³×C₃×C₅	—	2	2	no	—
91	C₂³×C₃×C₅	SD₁₆	1	4	yes	complemented
92	C₂³×C₃×C₅	C₂×D₄	1	2	yes	—
93	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
94	C₂²×C₅×D₃	—	2	16	no	—
95	C₂²×C₅×D₃	—	2	8	no	—
96	C₂²×C₅×D₃	—	2	4	no	—
97	C₂²×C₅×D₃	—	4	8	no	—
98	C₂²×C₅×D₃	—	4	32	no	—
99	C₂²×C₅×D₃	—	4	4	no	—
100	C₂²×C₅×D₃	—	4	8	no	—
101	C₂²×C₅×D₃	—	4	4	no	—
102	C₃×C₅×Q₈	—	2	4	no	—
103	C₃×C₅×Q₈	—	4	2	no	—
104	C₂×C₃×C₄×C₅	—	2	2	no	—
105	C₂×C₃×C₄×C₅	—	2	4	no	—
106	C₂×C₃×C₄×C₅	—	2	4	no	—
107	C₂×C₃×C₄×C₅	—	2	2	no	—
108	C₂×C₃×C₄×C₅	—	2	2	no	—
109	C₂×C₃×C₄×C₅	—	4	2	no	—
110	C₂×C₃×C₄×C₅	—	4	2	no	—
111	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
112	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
113	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
114	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
115	C₅×D₁₂	—	2	16	no	—
116	C₅×D₁₂	—	2	8	no	—
117	C₅×D₁₂	—	2	4	no	—
118	C₅×D₁₂	C₂×D₄	1	8	yes	—
119	C₅×C₃⋊C₈	—	2	4	no	—
120	C₂⁴×D₃	—	2	1	no	—
121	C₂²×C₃×Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
122	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
123	C₂²×D₁₂	—	2	1	no	—
124	C₂²×D₁₂	—	2	2	no	—
125	C₂²×D₁₂	—	2	8	no	—
126	C₂²×D₁₂	C₂²×C₅	1	4	yes	—
127	C₂²×D₁₂	C₂²×C₅	1	2	yes	—
128	C₃×C₂²⋊Q₈	—	2	2	no	—
129	C₃×C₂²⋊Q₈	C₂²×C₅	1	4	yes	complemented
130	C₂×C₃×C₄⋊C₄	—	2	1	no	—
131	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
132	C₂×C₃×C₂²⋊C₄	—	2	1	no	—
133	C₂×#215	—	2	8	no	—
134	C₂×#215	C₂²×C₅	1	8	yes	complemented
135	C₂²×C₃⋊C₈	C₂²×C₅	1	2	yes	complemented
136	#830	C₂²×C₅	1	4	yes	complemented
137	#809	C₂²×C₅	1	8	yes	complemented
138	C₂⁴×C₅	—	6	8	no	—
139	C₂⁴×C₅	—	6	4	no	—
140	C₂⁴×C₅	—	6	2	no	—
141	C₂⁴×C₅	—	12	4	no	—
142	C₂⁴×C₅	—	12	4	no	—
143	C₂⁴×C₅	#67	1	1	yes	characteristic
144	C₂×C₅×Q₈	—	2	1	no	—
145	C₂×C₅×Q₈	—	2	4	no	—
146	C₂×C₅×Q₈	C₂²×D₃	1	2	yes	complemented
147	C₂×C₅×D₄	—	3	8	no	—
148	C₂×C₅×D₄	—	3	4	no	—
149	C₂×C₅×D₄	—	6	16	no	—
150	C₂×C₅×D₄	—	6	8	no	—
151	C₂×C₅×D₄	—	6	16	no	—
152	C₂×C₅×D₄	—	6	4	no	—
153	C₂×C₅×D₄	—	6	4	no	—
154	C₂×C₅×D₄	—	6	2	no	—
155	C₂²×C₄×C₅	—	2	4	no	—
156	C₂²×C₄×C₅	—	2	1	no	—
157	C₂²×C₄×C₅	—	2	1	no	—
158	C₂²×C₄×C₅	#67	1	2	yes	—
159	C₂²×C₄×C₅	#67	1	1	yes	characteristic
160	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
161	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
162	C₅×SD₁₆	—	6	16	no	—
163	C₂×C₅×C₈	—	3	4	no	—
164	C₂×C₅×C₈	—	6	4	no	—
165	C₅×C₄⋊C₄	—	2	4	no	—
166	C₅×C₄⋊C₄	—	2	1	no	—
167	C₅×C₄⋊C₄	C₂²×D₃	1	2	yes	complemented
168	C₅×C₂²⋊C₄	—	2	4	no	—
169	C₂³×D₄	—	3	1	no	—
170	C₂²×SD₁₆	—	3	2	no	—
171	C₂×C₂²⋊Q₈	C₅×D₃	1	1	yes	characteristic, complemented
172	#450	—	3	8	no	—
173	C₂×#102	—	3	2	no	—
174	C₂×C₂²⋊C₈	—	3	1	no	—
175	C₂²×C₃×C₅	—	2	2	no	—
176	C₂²×C₃×C₅	—	2	2	no	—
177	C₂²×C₃×C₅	—	2	8	no	—
178	C₂²×C₃×C₅	#120	1	2	yes	—
179	C₂²×C₃×C₅	C₂×SD₁₆	1	2	yes	—
180	C₂²×C₃×C₅	C₂×SD₁₆	1	4	yes	complemented
181	C₂²×C₃×C₅	AGL(1,ℤ/8)	1	2	yes	—
182	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
183	C₂×C₅×D₃	—	2	8	no	—
184	C₂×C₅×D₃	—	4	32	no	—
185	C₂×C₅×D₃	—	4	4	no	—
186	C₂×C₅×D₃	—	4	4	no	—
187	C₂×C₅×D₃	—	4	16	no	—
188	C₃×C₄×C₅	—	2	2	no	—
189	C₃×C₄×C₅	—	4	2	no	—
190	C₃×C₄×C₅	—	4	2	no	—
191	C₃×C₄×C₅	#120	1	2	yes	—
192	C₃×C₄×C₅	C₂²×D₄	1	2	yes	—
193	C₂⁴×C₃	C₅×D₄	1	1	yes	characteristic
194	C₂³×D₃	—	2	8	no	—
195	C₂³×D₃	—	2	4	no	—
196	C₂³×D₃	—	2	2	no	—
197	C₂³×D₃	—	4	4	no	—
198	C₂³×D₃	—	4	4	no	—
199	C₂×C₃×Q₈	—	2	1	no	—
200	C₂×C₃×Q₈	—	2	4	no	—
201	C₂×C₃×Q₈	C₂³×C₅	1	2	yes	complemented
202	C₂²×C₃×C₄	—	2	4	no	—
203	C₂²×C₃×C₄	—	2	1	no	—
204	C₂²×C₃×C₄	—	2	1	no	—
205	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
206	C₂²×C₃×C₄	C₅×D₄	1	2	yes	—
207	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
208	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
209	C₂×D₁₂	—	2	8	no	—
210	C₂×D₁₂	—	2	16	no	—
211	C₂×D₁₂	—	2	4	no	—
212	C₂×D₁₂	—	2	4	no	—
213	C₂×D₁₂	—	2	2	no	—
214	C₂×D₁₂	—	2	16	no	—
215	C₂×D₁₂	C₅×D₄	1	8	yes	—
216	C₂×D₁₂	C₂³×C₅	1	4	yes	—
217	C₃×C₄⋊C₄	—	2	4	no	—
218	C₃×C₄⋊C₄	—	2	1	no	—
219	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	complemented
220	C₃×C₂²⋊C₄	—	2	4	no	—
221	#215	—	2	16	no	—
222	C₂×C₃⋊C₈	—	2	4	no	—
223	C₂×C₃⋊C₈	C₂³×C₅	1	4	yes	complemented
224	C₂³×C₅	—	2	2	no	—
225	C₂³×C₅	—	2	2	no	—
226	C₂³×C₅	—	6	16	no	—
227	C₂³×C₅	—	6	8	no	—
228	C₂³×C₅	—	6	4	no	—
229	C₂³×C₅	—	12	32	no	—
230	C₂³×C₅	—	12	8	no	—
231	C₂³×C₅	—	12	4	no	—
232	C₂³×C₅	—	12	8	no	—
233	C₂³×C₅	—	12	4	no	—
234	C₂³×C₅	#215	1	4	yes	complemented
235	C₂³×C₅	C₂×#67	1	2	yes	—
236	C₂³×C₅	C₂×#67	1	1	yes	characteristic
237	C₅×Q₈	—	2	4	no	—
238	C₅×Q₈	—	4	2	no	—
239	C₅×D₄	—	3	8	no	—
240	C₅×D₄	—	6	16	no	—
241	C₅×D₄	—	6	8	no	—
242	C₅×D₄	—	6	4	no	—
243	C₂×C₄×C₅	—	2	2	no	—
244	C₂×C₄×C₅	—	2	4	no	—
245	C₂×C₄×C₅	—	2	4	no	—
246	C₂×C₄×C₅	—	2	2	no	—
247	C₂×C₄×C₅	—	2	2	no	—
248	C₂×C₄×C₅	—	4	2	no	—
249	C₂×C₄×C₅	—	4	2	no	—
250	C₂×C₄×C₅	D₃×D₄	1	4	yes	—
251	C₂×C₄×C₅	C₂×#67	1	2	yes	—
252	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
253	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
254	C₅×C₈	—	6	4	no	—
255	C₂⁵	—	6	1	no	—
256	C₂²×Q₈	C₂×C₅×D₃	1	1	yes	characteristic, complemented
257	C₂²×D₄	—	3	2	no	—
258	C₂²×D₄	—	3	4	no	—
259	C₂²×D₄	—	6	8	no	—
260	C₂²×D₄	—	6	1	no	—
261	C₂²×D₄	—	6	2	no	—
262	C₂³×C₄	C₂×C₅×D₃	1	1	yes	characteristic
263	C₂×SD₁₆	—	3	8	no	—
264	C₂×SD₁₆	—	6	8	no	—
265	C₂²×C₈	—	3	2	no	—
266	C₂²⋊Q₈	—	2	2	no	—
267	C₂²⋊Q₈	C₂×C₅×D₃	1	4	yes	complemented
268	C₂×C₄⋊C₄	—	2	1	no	—
269	C₂×C₄⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic, complemented
270	C₂×C₂²⋊C₄	—	2	1	no	—
271	#102	—	3	8	no	—
272	C₂²⋊C₈	—	3	4	no	—
273	C₂×C₃×C₅	—	2	4	no	—
274	C₂×C₃×C₅	#450	1	4	yes	complemented
275	C₂×C₃×C₅	C₂×#120	1	1	yes	characteristic
276	C₂×C₃×C₅	C₂²×SD₁₆	1	1	yes	characteristic
277	C₂×C₃×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
278	C₅×D₃	—	4	8	no	—
279	C₂³×C₃	—	2	2	no	—
280	C₂³×C₃	—	2	2	no	—
281	C₂³×C₃	C₅×SD₁₆	1	4	yes	complemented
282	C₂³×C₃	C₂×C₅×D₄	1	2	yes	—
283	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
284	C₂²×D₃	—	2	16	no	—
285	C₂²×D₃	—	2	8	no	—
286	C₂²×D₃	—	2	4	no	—
287	C₂²×D₃	—	4	32	no	—
288	C₂²×D₃	—	4	8	no	—
289	C₂²×D₃	—	4	4	no	—
290	C₂²×D₃	—	4	8	no	—
291	C₂²×D₃	—	4	4	no	—
292	C₃×Q₈	—	2	4	no	—
293	C₃×Q₈	—	4	2	no	—
294	C₂×C₃×C₄	—	2	2	no	—
295	C₂×C₃×C₄	—	2	4	no	—
296	C₂×C₃×C₄	—	2	4	no	—
297	C₂×C₃×C₄	—	2	2	no	—
298	C₂×C₃×C₄	—	2	2	no	—
299	C₂×C₃×C₄	—	4	2	no	—
300	C₂×C₃×C₄	—	4	2	no	—
301	C₂×C₃×C₄	C₂×C₅×D₄	1	4	yes	—
302	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
303	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
304	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
305	D₁₂	—	2	16	no	—
306	D₁₂	—	2	8	no	—
307	D₁₂	—	2	4	no	—
308	D₁₂	C₂×C₅×D₄	1	8	yes	—
309	C₃⋊C₈	—	2	4	no	—
310	C₂²×C₅	—	2	2	no	—
311	C₂²×C₅	—	2	8	no	—
312	C₂²×C₅	—	2	2	no	—
313	C₂²×C₅	—	6	8	no	—
314	C₂²×C₅	—	12	32	no	—
315	C₂²×C₅	—	12	4	no	—
316	C₂²×C₅	—	12	16	no	—
317	C₂²×C₅	—	12	4	no	—
318	C₂²×C₅	#937	1	2	yes	—
319	C₂²×C₅	C₂×#215	1	2	yes	—
320	C₂²×C₅	C₂×#215	1	4	yes	complemented
321	C₂²×C₅	#949	1	2	yes	—
322	C₂²×C₅	C₂²×#67	1	1	yes	characteristic
323	C₄×C₅	—	2	2	no	—
324	C₄×C₅	—	4	2	no	—
325	C₄×C₅	—	4	2	no	—
326	C₄×C₅	#937	1	2	yes	—
327	C₄×C₅	C₂×D₃×D₄	1	2	yes	—
328	C₂⁴	—	6	8	no	—
329	C₂⁴	—	6	4	no	—
330	C₂⁴	—	6	2	no	—
331	C₂⁴	—	12	4	no	—
332	C₂⁴	—	12	4	no	—
333	C₂⁴	C₅×#67	1	1	yes	characteristic
334	C₂×Q₈	—	2	1	no	—
335	C₂×Q₈	—	2	4	no	—
336	C₂×Q₈	C₂²×C₅×D₃	1	2	yes	complemented
337	C₂×D₄	—	3	8	no	—
338	C₂×D₄	—	3	4	no	—
339	C₂×D₄	—	6	16	no	—
340	C₂×D₄	—	6	8	no	—
341	C₂×D₄	—	6	16	no	—
342	C₂×D₄	—	6	4	no	—
343	C₂×D₄	—	6	4	no	—
344	C₂×D₄	—	6	2	no	—
345	C₂²×C₄	—	2	4	no	—
346	C₂²×C₄	—	2	1	no	—
347	C₂²×C₄	—	2	1	no	—
348	C₂²×C₄	C₅×#67	1	1	yes	characteristic
349	C₂²×C₄	C₅×#67	1	2	yes	—
350	C₂²×C₄	C₂²×C₅×D₃	1	2	yes	—
351	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
352	SD₁₆	—	6	16	no	—
353	C₂×C₈	—	3	4	no	—
354	C₂×C₈	—	6	4	no	—
355	C₄⋊C₄	—	2	4	no	—
356	C₄⋊C₄	—	2	1	no	—
357	C₄⋊C₄	C₂²×C₅×D₃	1	2	yes	complemented
358	C₂²⋊C₄	—	2	4	no	—
359	C₃×C₅	C₂×#450	1	1	yes	characteristic, complemented, Hall
360	C₂²×C₃	—	2	8	no	—
361	C₂²×C₃	—	2	2	no	—
362	C₂²×C₃	—	2	2	no	—
363	C₂²×C₃	C₅×#120	1	2	yes	—
364	C₂²×C₃	C₂×C₅×SD₁₆	1	2	yes	—
365	C₂²×C₃	C₂×C₅×SD₁₆	1	4	yes	complemented
366	C₂²×C₃	C₅×AGL(1,ℤ/8)	1	2	yes	—
367	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
368	C₂×D₃	—	2	8	no	—
369	C₂×D₃	—	4	32	no	—
370	C₂×D₃	—	4	16	no	—
371	C₂×D₃	—	4	4	no	—
372	C₂×D₃	—	4	4	no	—
373	C₃×C₄	—	2	2	no	—
374	C₃×C₄	—	4	2	no	—
375	C₃×C₄	—	4	2	no	—
376	C₃×C₄	C₅×#120	1	2	yes	—
377	C₃×C₄	C₂²×C₅×D₄	1	2	yes	—
378	C₂×C₅	—	2	4	no	—
379	C₂×C₅	—	12	8	no	—
380	C₂×C₅	#5046	1	4	yes	direct product factor
381	C₂×C₅	C₂×#937	1	1	yes	characteristic
382	C₂×C₅	C₂²×#215	1	1	yes	characteristic
383	C₂×C₅	C₂×#949	1	1	yes	characteristic
384	C₂³	—	2	2	no	—
385	C₂³	—	2	2	no	—
386	C₂³	—	6	16	no	—
387	C₂³	—	6	8	no	—
388	C₂³	—	6	4	no	—
389	C₂³	—	12	32	no	—
390	C₂³	—	12	8	no	—
391	C₂³	—	12	4	no	—
392	C₂³	—	12	8	no	—
393	C₂³	—	12	4	no	—
394	C₂³	C₅×#215	1	4	yes	complemented
395	C₂³	C₂×C₅×#67	1	2	yes	—
396	C₂³	C₂×C₅×#67	1	1	yes	characteristic
397	Q₈	—	2	4	no	—
398	Q₈	—	4	2	no	—
399	D₄	—	3	8	no	—
400	D₄	—	6	16	no	—
401	D₄	—	6	8	no	—
402	D₄	—	6	4	no	—
403	C₂×C₄	—	2	2	no	—
404	C₂×C₄	—	2	4	no	—
405	C₂×C₄	—	2	4	no	—
406	C₂×C₄	—	2	2	no	—
407	C₂×C₄	—	2	2	no	—
408	C₂×C₄	—	4	2	no	—
409	C₂×C₄	—	4	2	no	—
410	C₂×C₄	C₅×D₃×D₄	1	4	yes	—
411	C₂×C₄	C₂×C₅×#67	1	2	yes	—
412	C₂×C₄	C₂×C₅×#67	1	1	yes	characteristic
413	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
414	C₈	—	6	4	no	—
415	C₂×C₃	—	2	4	no	—
416	C₂×C₃	C₅×#450	1	4	yes	complemented
417	C₂×C₃	C₂×C₅×#120	1	1	yes	characteristic
418	C₂×C₃	C₂²×C₅×SD₁₆	1	1	yes	characteristic
419	C₂×C₃	C₂×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
420	D₃	—	4	8	no	—
421	C₅	C₂×#5046	1	1	yes	characteristic, direct product factor, Sylow
422	C₂²	—	2	8	no	—
423	C₂²	—	2	2	no	—
424	C₂²	—	2	2	no	—
425	C₂²	—	6	8	no	—
426	C₂²	—	12	32	no	—
427	C₂²	—	12	16	no	—
428	C₂²	—	12	4	no	—
429	C₂²	—	12	4	no	—
430	C₂²	C₅×#937	1	2	yes	—
431	C₂²	C₂×C₅×#215	1	2	yes	—
432	C₂²	C₂×C₅×#215	1	4	yes	complemented
433	C₂²	C₅×#949	1	2	yes	—
434	C₂²	C₂²×C₅×#67	1	1	yes	characteristic
435	C₄	—	2	2	no	—
436	C₄	—	4	2	no	—
437	C₄	—	4	2	no	—
438	C₄	C₅×#937	1	2	yes	—
439	C₄	C₂×C₅×D₃×D₄	1	2	yes	—
440	C₃	C₂×C₅×#450	1	1	yes	characteristic, complemented, Sylow
441	C₂	—	2	4	no	—
442	C₂	—	12	8	no	—
443	C₂	C₅×#5046	1	4	yes	direct product factor
444	C₂	C₂×C₅×#937	1	1	yes	characteristic
445	C₂	C₂²×C₅×#215	1	1	yes	characteristic
446	C₂	C₂×C₅×#949	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×C₂²⋊Q₈	C₂
socle	C₂³×C₃×C₅	C₂×D₄
prime radical	C₂³×C₅×D₁₂	C₂
hypercenter	C₂×C₅×C₂²⋊Q₈	D₃
hypocenter	C₃	C₂×C₅×#450
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₅ ◁ C₂³×C₄×C₅ ◁ C₂×C₅×C₂²⋊Q₈

Complements

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

N	H ≅ G/N	type
2. C₂×C₃×C₅×C₂²⋊Q₈	C₂	semidirect
3. C₂²×C₅×#215	C₂	semidirect
4. C₂×C₅×#830	C₂	semidirect
5. C₅×#5046	C₂	direct (N × H)
6. C₂×C₅×#809	C₂	semidirect
9. C₂²×C₃×C₅×Q₈	C₂²	semidirect
17. C₃×C₅×C₂²⋊Q₈	C₂²	semidirect
19. C₂×C₃×C₅×C₄⋊C₄	C₂²	semidirect
22. C₂×C₅×#215	C₂²	semidirect
23. C₂²×C₅×C₃⋊C₈	C₂²	semidirect
24. C₅×#830	C₂²	semidirect
25. C₅×#809	C₂²	semidirect
26. C₂×#5046	C₅	direct (N × H)
29. C₂×C₅×C₂²⋊Q₈	D₃	semidirect
41. C₂×C₃×C₅×Q₈	C₂³	semidirect
59. C₃×C₅×C₄⋊C₄	C₂³	semidirect
63. C₂×C₅×C₃⋊C₈	C₂³	semidirect
65. C₂×C₃×C₂²⋊Q₈	C₂×C₅	semidirect
66. C₂²×#215	C₂×C₅	semidirect
67. C₂×#830	C₂×C₅	semidirect
68. #5046	C₂×C₅	direct (N × H)
69. C₂×#809	C₂×C₅	semidirect
71. C₂²×C₅×Q₈	C₂×D₃	semidirect
82. C₅×C₂²⋊Q₈	C₂×D₃	semidirect
84. C₂×C₅×C₄⋊C₄	C₂×D₃	semidirect
91. C₂³×C₃×C₅	SD₁₆	semidirect
121. C₂²×C₃×Q₈	C₂²×C₅	semidirect
129. C₃×C₂²⋊Q₈	C₂²×C₅	semidirect
131. C₂×C₃×C₄⋊C₄	C₂²×C₅	semidirect
134. C₂×#215	C₂²×C₅	semidirect
135. C₂²×C₃⋊C₈	C₂²×C₅	semidirect
136. #830	C₂²×C₅	semidirect
137. #809	C₂²×C₅	semidirect
146. C₂×C₅×Q₈	C₂²×D₃	semidirect
167. C₅×C₄⋊C₄	C₂²×D₃	semidirect
171. C₂×C₂²⋊Q₈	C₅×D₃	semidirect
180. C₂²×C₃×C₅	C₂×SD₁₆	semidirect
201. C₂×C₃×Q₈	C₂³×C₅	semidirect
219. C₃×C₄⋊C₄	C₂³×C₅	semidirect
223. C₂×C₃⋊C₈	C₂³×C₅	semidirect
234. C₂³×C₅	#215	semidirect
256. C₂²×Q₈	C₂×C₅×D₃	semidirect
267. C₂²⋊Q₈	C₂×C₅×D₃	semidirect
269. C₂×C₄⋊C₄	C₂×C₅×D₃	semidirect
274. C₂×C₃×C₅	#450	semidirect
281. C₂³×C₃	C₅×SD₁₆	semidirect
320. C₂²×C₅	C₂×#215	semidirect
336. C₂×Q₈	C₂²×C₅×D₃	semidirect
357. C₄⋊C₄	C₂²×C₅×D₃	semidirect
359. C₃×C₅	C₂×#450	semidirect
365. C₂²×C₃	C₂×C₅×SD₁₆	semidirect
380. C₂×C₅	#5046	direct (N × H)
394. C₂³	C₅×#215	semidirect
416. C₂×C₃	C₅×#450	semidirect
421. C₅	C₂×#5046	direct (N × H)
432. C₂²	C₂×C₅×#215	semidirect
440. C₃	C₂×C₅×#450	semidirect
443. C₂	C₅×#5046	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×C₅×D₁₂	2
C₂×C₃×C₅×C₂²⋊Q₈	2
C₂²×C₅×#215	2
C₂×C₅×#830	2
C₅×#5046	2
C₂×C₅×#809	2
C₂×C₅×#450	3
C₂×#5046	5

Subgroups — C2×C5×#5046 #14423235

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#5046 #14423235