Subgroups — C₂×C₅×#5585 #14484708

Order 1920.

2480 conjugacy classes of subgroups.

The subgroup lattice has 440 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	C₂×C₅×#947	C₂	1	2	yes	maximal, complemented
3	C₅×#5585	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₅×#894	C₂	1	4	yes	maximal, complemented
5	C₂×C₅×#893	C₂	1	2	yes	maximal, complemented
6	C₂×C₅×#875	C₂	1	2	yes	maximal, complemented
7	C₂×C₅×#874	C₂	1	1	yes	maximal, characteristic
8	C₂×C₄×C₅×D₁₂	C₂	1	2	yes	maximal, complemented
9	C₂×C₄×C₅×Dic₆	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₅×#559	—	3	1	no	maximal, Hall
11	C₂²×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic
12	C₂²×C₅×D₁₂	C₂²	1	2	yes	—
13	C₂²×C₅×D₁₂	C₂²	1	2	yes	—
14	C₂²×C₅×D₁₂	C₂²	1	2	yes	—
15	C₂²×C₄×C₅×D₃	C₂²	1	4	yes	—
16	C₂²×C₅×Dic₆	C₂²	1	1	yes	characteristic
17	C₃×C₄×C₅×Q₈	C₂²	1	8	yes	complemented
18	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
19	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
20	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
21	C₂×C₃×C₄²×C₅	C₂²	1	2	yes	—
22	C₅×#947	C₂²	1	16	yes	complemented
23	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	4	yes	—
24	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	4	yes	—
25	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	4	yes	—
26	C₂×C₅×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
27	C₂×C₅×Dic₃⋊C₄	C₂²	1	2	yes	—
28	C₂×C₄×C₅×Dic₃	C₂²	1	2	yes	—
29	C₅×#894	C₂²	1	32	yes	complemented
30	C₅×#893	C₂²	1	16	yes	complemented
31	C₅×#875	C₂²	1	16	yes	complemented
32	C₅×#874	C₂²	1	8	yes	—
33	C₄×C₅×D₁₂	C₂²	1	16	yes	complemented
34	C₄×C₅×Dic₆	C₂²	1	8	yes	complemented
35	C₂×#5585	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
36	C₅×#559	—	3	16	no	—
37	C₂×C₅×#127	—	3	1	no	—
38	C₂×C₅×#124	—	3	2	no	—
39	C₂×C₅×#124	—	3	2	no	—
40	C₂×C₅×#123	—	3	4	no	—
41	C₂×C₄×C₅×Q₈	—	3	1	no	—
42	C₂×C₄×C₅×Q₈	D₃	1	1	yes	characteristic, complemented
43	C₂×C₄×C₅×D₄	—	3	2	no	—
44	C₂×C₄×C₅×D₄	—	3	2	no	—
45	C₂³×C₅×D₃	C₂³	1	4	yes	—
46	C₂×C₃×C₅×Q₈	—	2	4	no	—
47	C₂×C₃×C₅×Q₈	C₂³	1	4	yes	—
48	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
49	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
50	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
51	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
52	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
53	C₂²×C₅×Dic₃	C₂³	1	2	yes	—
54	C₂²×C₅×Dic₃	C₂³	1	2	yes	—
55	C₂×C₅×D₁₂	—	2	8	no	—
56	C₂×C₅×D₁₂	—	2	8	no	—
57	C₂×C₅×D₁₂	—	4	4	no	—
58	C₂×C₅×D₁₂	C₂³	1	8	yes	—
59	C₂×C₅×D₁₂	C₂³	1	8	yes	—
60	C₂×C₅×D₁₂	C₂³	1	8	yes	—
61	C₂×C₄×C₅×D₃	—	4	8	no	—
62	C₂×C₄×C₅×D₃	C₂³	1	16	yes	—
63	C₂×C₅×Dic₆	—	2	4	no	—
64	C₂×C₅×Dic₆	C₂³	1	4	yes	—
65	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	—
66	C₃×C₅×C₄⋊C₄	C₂³	1	8	yes	—
67	C₃×C₄²×C₅	C₂³	1	4	yes	—
68	C₃×C₄²×C₅	C₂³	1	8	yes	—
69	C₅×(C₂×D₃)⋊C₄	C₂³	1	16	yes	—
70	C₅×(C₂×D₃)⋊C₄	C₂³	1	16	yes	—
71	C₅×(C₂×D₃)⋊C₄	C₂³	1	16	yes	—
72	C₅×C₄⋊Dic₃	C₂³	1	4	yes	—
73	C₅×Dic₃⋊C₄	C₂³	1	8	yes	—
74	C₄×C₅×Dic₃	C₂³	1	8	yes	—
75	C₂×C₃×C₄×Q₈	C₂×C₅	1	1	yes	characteristic, complemented
76	C₂×#947	C₂×C₅	1	2	yes	complemented
77	#5585	C₂×C₅	1	16	yes	direct product factor
78	C₂×#894	C₂×C₅	1	4	yes	complemented
79	C₂×#893	C₂×C₅	1	2	yes	complemented
80	C₂×#875	C₂×C₅	1	2	yes	complemented
81	C₂×#874	C₂×C₅	1	1	yes	characteristic
82	C₂×C₄×D₁₂	C₂×C₅	1	2	yes	complemented
83	C₂×C₄×Dic₆	C₂×C₅	1	1	yes	characteristic, complemented
84	C₂²×C₅×Q₈	—	3	1	no	—
85	C₂²×C₅×Q₈	C₂×D₃	1	1	yes	characteristic
86	C₂²×C₅×D₄	—	3	2	no	—
87	C₂²×C₅×D₄	—	3	2	no	—
88	C₂²×C₅×D₄	—	3	2	no	—
89	C₂³×C₄×C₅	—	3	4	no	—
90	C₅×#127	—	3	8	no	—
91	C₅×#124	—	3	16	no	—
92	C₅×#124	—	3	16	no	—
93	C₅×#123	—	3	32	no	—
94	C₄×C₅×Q₈	—	3	8	no	—
95	C₄×C₅×Q₈	C₂×D₃	1	8	yes	complemented
96	C₄×C₅×D₄	—	3	16	no	—
97	C₄×C₅×D₄	—	3	16	no	—
98	C₂×C₅×C₄⋊C₄	—	3	2	no	—
99	C₂×C₅×C₄⋊C₄	—	3	1	no	—
100	C₂×C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
101	C₂×C₅×C₄⋊C₄	C₂×D₃	1	2	yes	—
102	C₂×C₅×C₂²⋊C₄	—	3	4	no	—
103	C₂×C₅×C₂²⋊C₄	—	3	4	no	—
104	C₂×C₅×C₂²⋊C₄	—	3	4	no	—
105	C₂×C₄²×C₅	—	3	2	no	—
106	C₂×C₄²×C₅	C₂×D₃	1	2	yes	—
107	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
108	C₂×#559	—	3	1	no	Sylow
109	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
110	C₂²×C₅×D₃	—	2	8	no	—
111	C₂²×C₅×D₃	—	2	8	no	—
112	C₂²×C₅×D₃	—	2	8	no	—
113	C₂²×C₅×D₃	C₂⁴	1	8	yes	—
114	C₃×C₅×Q₈	—	2	8	no	—
115	C₂×C₃×C₄×C₅	—	2	4	no	—
116	C₂×C₃×C₄×C₅	—	2	4	no	—
117	C₂×C₃×C₄×C₅	—	2	2	no	—
118	C₂×C₃×C₄×C₅	#41	1	4	yes	—
119	C₂×C₃×C₄×C₅	#41	1	4	yes	—
120	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
121	C₂×C₃×C₄×C₅	C₂⁴	1	4	yes	—
122	C₂×C₃×C₄×C₅	C₂⁴	1	4	yes	—
123	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
124	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
125	C₂×C₅×Dic₃	—	2	4	no	—
126	C₂×C₅×Dic₃	—	2	4	no	—
127	C₂×C₅×Dic₃	C₂⁴	1	4	yes	—
128	C₂×C₅×Dic₃	C₂⁴	1	4	yes	—
129	C₅×D₁₂	—	2	16	no	—
130	C₅×D₁₂	—	2	16	no	—
131	C₅×D₁₂	—	4	8	no	—
132	C₄×C₅×D₃	—	4	16	no	—
133	C₅×Dic₆	—	2	8	no	—
134	C₂²×C₃×Q₈	C₂²×C₅	1	1	yes	characteristic
135	C₂²×D₁₂	C₂²×C₅	1	2	yes	—
136	C₂²×D₁₂	C₂²×C₅	1	2	yes	—
137	C₂²×D₁₂	C₂²×C₅	1	2	yes	—
138	C₂²×C₄×D₃	C₂²×C₅	1	4	yes	—
139	C₂²×Dic₆	C₂²×C₅	1	1	yes	characteristic
140	C₃×C₄×Q₈	C₂²×C₅	1	8	yes	complemented
141	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
142	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
143	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
144	C₂×C₃×C₄²	C₂²×C₅	1	2	yes	—
145	#947	C₂²×C₅	1	16	yes	complemented
146	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	4	yes	—
147	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	4	yes	—
148	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	4	yes	—
149	C₂×C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic
150	C₂×Dic₃⋊C₄	C₂²×C₅	1	2	yes	—
151	C₂×C₄×Dic₃	C₂²×C₅	1	2	yes	—
152	#894	C₂²×C₅	1	32	yes	complemented
153	#893	C₂²×C₅	1	16	yes	complemented
154	#875	C₂²×C₅	1	16	yes	complemented
155	#874	C₂²×C₅	1	8	yes	—
156	C₄×D₁₂	C₂²×C₅	1	16	yes	complemented
157	C₄×Dic₆	C₂²×C₅	1	8	yes	complemented
158	C₂⁴×C₅	—	3	4	no	—
159	C₂×C₅×Q₈	—	2	4	no	—
160	C₂×C₅×Q₈	—	3	4	no	—
161	C₂×C₅×Q₈	—	6	4	no	—
162	C₂×C₅×Q₈	C₂²×D₃	1	4	yes	—
163	C₂×C₅×D₄	—	3	8	no	—
164	C₂×C₅×D₄	—	3	8	no	—
165	C₂×C₅×D₄	—	3	8	no	—
166	C₂×C₅×D₄	—	6	8	no	—
167	C₂×C₅×D₄	—	6	8	no	—
168	C₂×C₅×D₄	—	12	4	no	—
169	C₂²×C₄×C₅	—	3	2	no	—
170	C₂²×C₄×C₅	—	3	2	no	—
171	C₂²×C₄×C₅	—	3	16	no	—
172	C₂²×C₄×C₅	—	12	8	no	—
173	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
174	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
175	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
176	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
177	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
178	C₅×C₄⋊C₄	—	3	4	no	—
179	C₅×C₄⋊C₄	—	3	8	no	—
180	C₅×C₄⋊C₄	C₂²×D₃	1	4	yes	—
181	C₅×C₄⋊C₄	C₂²×D₃	1	8	yes	—
182	C₅×C₂²⋊C₄	—	3	16	no	—
183	C₅×C₂²⋊C₄	—	3	16	no	—
184	C₅×C₂²⋊C₄	—	3	16	no	—
185	C₄²×C₅	—	3	8	no	—
186	C₄²×C₅	C₂²×D₃	1	8	yes	—
187	C₄²×C₅	C₂²×D₃	1	4	yes	—
188	#559	—	3	16	no	—
189	C₂×#127	—	3	1	no	—
190	C₂×#124	—	3	2	no	—
191	C₂×#124	—	3	2	no	—
192	C₂×#123	—	3	4	no	—
193	C₂×C₄×Q₈	—	3	1	no	—
194	C₂×C₄×Q₈	C₅×D₃	1	1	yes	characteristic, complemented
195	C₂×C₄×D₄	—	3	2	no	—
196	C₂×C₄×D₄	—	3	2	no	—
197	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
198	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
199	C₂²×C₃×C₅	H(5,𝔽₂)	1	2	yes	—
200	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
201	C₂×C₅×D₃	—	2	8	no	—
202	C₂×C₅×D₃	—	2	8	no	—
203	C₂×C₅×D₃	—	2	8	no	—
204	C₂×C₅×D₃	—	4	16	no	—
205	C₃×C₄×C₅	—	2	4	no	—
206	C₃×C₄×C₅	—	2	4	no	—
207	C₃×C₄×C₅	—	2	2	no	—
208	C₃×C₄×C₅	C₂×#41	1	4	yes	—
209	C₃×C₄×C₅	C₂×#41	1	4	yes	—
210	C₅×Dic₃	—	2	4	no	—
211	C₅×Dic₃	—	2	4	no	—
212	C₂³×D₃	C₂³×C₅	1	4	yes	—
213	C₂×C₃×Q₈	—	2	4	no	—
214	C₂×C₃×Q₈	C₂³×C₅	1	4	yes	—
215	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
216	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
217	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
218	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
219	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
220	C₂²×Dic₃	C₂³×C₅	1	2	yes	—
221	C₂²×Dic₃	C₂³×C₅	1	2	yes	—
222	C₂×D₁₂	—	2	8	no	—
223	C₂×D₁₂	—	2	8	no	—
224	C₂×D₁₂	—	4	4	no	—
225	C₂×D₁₂	C₂³×C₅	1	8	yes	—
226	C₂×D₁₂	C₂³×C₅	1	8	yes	—
227	C₂×D₁₂	C₂³×C₅	1	8	yes	—
228	C₂×C₄×D₃	—	4	8	no	—
229	C₂×C₄×D₃	C₂³×C₅	1	16	yes	—
230	C₂×Dic₆	—	2	4	no	—
231	C₂×Dic₆	C₂³×C₅	1	4	yes	—
232	C₃×C₄⋊C₄	C₂³×C₅	1	4	yes	—
233	C₃×C₄⋊C₄	C₂³×C₅	1	8	yes	—
234	C₃×C₄²	C₂³×C₅	1	4	yes	—
235	C₃×C₄²	C₂³×C₅	1	8	yes	—
236	(C₂×D₃)⋊C₄	C₂³×C₅	1	16	yes	—
237	(C₂×D₃)⋊C₄	C₂³×C₅	1	16	yes	—
238	(C₂×D₃)⋊C₄	C₂³×C₅	1	16	yes	—
239	C₄⋊Dic₃	C₂³×C₅	1	4	yes	—
240	Dic₃⋊C₄	C₂³×C₅	1	8	yes	—
241	C₄×Dic₃	C₂³×C₅	1	8	yes	—
242	C₂³×C₅	—	3	8	no	—
243	C₂³×C₅	—	6	8	no	—
244	C₂³×C₅	—	6	8	no	—
245	C₂³×C₅	—	6	8	no	—
246	C₂³×C₅	C₂³×D₃	1	1	yes	characteristic
247	C₅×Q₈	—	2	8	no	—
248	C₅×Q₈	—	6	8	no	—
249	C₅×D₄	—	6	16	no	—
250	C₅×D₄	—	6	16	no	—
251	C₅×D₄	—	12	8	no	—
252	C₂×C₄×C₅	—	2	4	no	—
253	C₂×C₄×C₅	—	2	4	no	—
254	C₂×C₄×C₅	—	2	2	no	—
255	C₂×C₄×C₅	—	3	4	no	—
256	C₂×C₄×C₅	—	3	4	no	—
257	C₂×C₄×C₅	—	6	4	no	—
258	C₂×C₄×C₅	—	6	4	no	—
259	C₂×C₄×C₅	—	12	16	no	—
260	C₂×C₄×C₅	#235	1	4	yes	—
261	C₂×C₄×C₅	#239	1	4	yes	—
262	C₂×C₄×C₅	C₂³×D₃	1	4	yes	—
263	C₂×C₄×C₅	C₂³×D₃	1	4	yes	—
264	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
265	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
266	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
267	C₂²×Q₈	—	3	1	no	—
268	C₂²×Q₈	C₂×C₅×D₃	1	1	yes	characteristic
269	C₂²×D₄	—	3	2	no	—
270	C₂²×D₄	—	3	2	no	—
271	C₂²×D₄	—	3	2	no	—
272	C₂³×C₄	—	3	4	no	—
273	#127	—	3	8	no	—
274	#124	—	3	16	no	—
275	#124	—	3	16	no	—
276	#123	—	3	32	no	—
277	C₄×Q₈	—	3	8	no	—
278	C₄×Q₈	C₂×C₅×D₃	1	8	yes	complemented
279	C₄×D₄	—	3	16	no	—
280	C₄×D₄	—	3	16	no	—
281	C₂×C₄⋊C₄	—	3	1	no	—
282	C₂×C₄⋊C₄	—	3	2	no	—
283	C₂×C₄⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
284	C₂×C₄⋊C₄	C₂×C₅×D₃	1	2	yes	—
285	C₂×C₂²⋊C₄	—	3	4	no	—
286	C₂×C₂²⋊C₄	—	3	4	no	—
287	C₂×C₂²⋊C₄	—	3	4	no	—
288	C₂×C₄²	—	3	2	no	—
289	C₂×C₄²	C₂×C₅×D₃	1	2	yes	—
290	C₂×C₄²	C₂×C₅×D₃	1	1	yes	characteristic
291	C₂×C₃×C₅	#559	1	4	yes	complemented
292	C₂×C₃×C₅	C₂²×#41	1	1	yes	characteristic
293	C₂×C₃×C₅	C₂²×#41	1	1	yes	characteristic
294	C₂×C₃×C₅	C₂×H(5,𝔽₂)	1	1	yes	characteristic
295	C₅×D₃	—	4	8	no	—
296	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
297	C₂²×D₃	—	2	8	no	—
298	C₂²×D₃	—	2	8	no	—
299	C₂²×D₃	—	2	8	no	—
300	C₂²×D₃	C₂⁴×C₅	1	8	yes	—
301	C₃×Q₈	—	2	8	no	—
302	C₂×C₃×C₄	—	2	4	no	—
303	C₂×C₃×C₄	—	2	4	no	—
304	C₂×C₃×C₄	—	2	2	no	—
305	C₂×C₃×C₄	C₅×#41	1	4	yes	—
306	C₂×C₃×C₄	C₅×#41	1	4	yes	—
307	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
308	C₂×C₃×C₄	C₂⁴×C₅	1	4	yes	—
309	C₂×C₃×C₄	C₂⁴×C₅	1	4	yes	—
310	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
311	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
312	C₂×Dic₃	—	2	4	no	—
313	C₂×Dic₃	—	2	4	no	—
314	C₂×Dic₃	C₂⁴×C₅	1	4	yes	—
315	C₂×Dic₃	C₂⁴×C₅	1	4	yes	—
316	D₁₂	—	2	16	no	—
317	D₁₂	—	2	16	no	—
318	D₁₂	—	4	8	no	—
319	C₄×D₃	—	4	16	no	—
320	Dic₆	—	2	8	no	—
321	C₂²×C₅	—	6	8	no	—
322	C₂²×C₅	—	6	8	no	—
323	C₂²×C₅	—	6	8	no	—
324	C₂²×C₅	—	12	16	no	—
325	C₂²×C₅	C₂×#235	1	2	yes	—
326	C₂²×C₅	C₂×#239	1	2	yes	—
327	C₂²×C₅	#1009	1	2	yes	—
328	C₂²×C₅	C₂⁴×D₃	1	1	yes	characteristic
329	C₄×C₅	—	2	4	no	—
330	C₄×C₅	—	2	4	no	—
331	C₄×C₅	—	2	2	no	—
332	C₄×C₅	—	6	4	no	—
333	C₄×C₅	—	6	4	no	—
334	C₄×C₅	C₂×#235	1	4	yes	—
335	C₄×C₅	C₂×#239	1	4	yes	—
336	C₂⁴	—	3	4	no	—
337	C₂×Q₈	—	2	4	no	—
338	C₂×Q₈	—	3	4	no	—
339	C₂×Q₈	—	6	4	no	—
340	C₂×Q₈	C₂²×C₅×D₃	1	4	yes	—
341	C₂×D₄	—	3	8	no	—
342	C₂×D₄	—	3	8	no	—
343	C₂×D₄	—	3	8	no	—
344	C₂×D₄	—	6	8	no	—
345	C₂×D₄	—	6	8	no	—
346	C₂×D₄	—	12	4	no	—
347	C₂²×C₄	—	3	2	no	—
348	C₂²×C₄	—	3	2	no	—
349	C₂²×C₄	—	3	16	no	—
350	C₂²×C₄	—	12	8	no	—
351	C₂²×C₄	C₂²×C₅×D₃	1	2	yes	—
352	C₂²×C₄	C₂²×C₅×D₃	1	2	yes	—
353	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
354	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
355	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
356	C₄⋊C₄	—	3	4	no	—
357	C₄⋊C₄	—	3	8	no	—
358	C₄⋊C₄	C₂²×C₅×D₃	1	4	yes	—
359	C₄⋊C₄	C₂²×C₅×D₃	1	8	yes	—
360	C₂²⋊C₄	—	3	16	no	—
361	C₂²⋊C₄	—	3	16	no	—
362	C₂²⋊C₄	—	3	16	no	—
363	C₄²	—	3	8	no	—
364	C₄²	C₂²×C₅×D₃	1	8	yes	—
365	C₄²	C₂²×C₅×D₃	1	4	yes	—
366	C₃×C₅	C₂×#559	1	1	yes	characteristic, complemented, Hall
367	C₂²×C₃	C₂×C₅×#41	1	2	yes	—
368	C₂²×C₃	C₂×C₅×#41	1	2	yes	—
369	C₂²×C₃	C₅×H(5,𝔽₂)	1	2	yes	—
370	C₂²×C₃	C₂⁵×C₅	1	1	yes	characteristic
371	C₂×D₃	—	2	8	no	—
372	C₂×D₃	—	2	8	no	—
373	C₂×D₃	—	2	8	no	—
374	C₂×D₃	—	4	16	no	—
375	C₃×C₄	—	2	4	no	—
376	C₃×C₄	—	2	4	no	—
377	C₃×C₄	—	2	2	no	—
378	C₃×C₄	C₂×C₅×#41	1	4	yes	—
379	C₃×C₄	C₂×C₅×#41	1	4	yes	—
380	Dic₃	—	2	4	no	—
381	Dic₃	—	2	4	no	—
382	C₂×C₅	—	12	8	no	—
383	C₂×C₅	#5585	1	4	yes	direct product factor
384	C₂×C₅	C₂²×#235	1	1	yes	characteristic
385	C₂×C₅	C₂²×#239	1	1	yes	characteristic
386	C₂×C₅	C₂×#1009	1	1	yes	characteristic
387	C₂³	—	3	8	no	—
388	C₂³	—	6	8	no	—
389	C₂³	—	6	8	no	—
390	C₂³	—	6	8	no	—
391	C₂³	C₂³×C₅×D₃	1	1	yes	characteristic
392	Q₈	—	2	8	no	—
393	Q₈	—	6	8	no	—
394	D₄	—	6	16	no	—
395	D₄	—	6	16	no	—
396	D₄	—	12	8	no	—
397	C₂×C₄	—	2	4	no	—
398	C₂×C₄	—	2	4	no	—
399	C₂×C₄	—	2	2	no	—
400	C₂×C₄	—	3	4	no	—
401	C₂×C₄	—	3	4	no	—
402	C₂×C₄	—	6	4	no	—
403	C₂×C₄	—	6	4	no	—
404	C₂×C₄	—	12	16	no	—
405	C₂×C₄	C₅×#235	1	4	yes	—
406	C₂×C₄	C₅×#239	1	4	yes	—
407	C₂×C₄	C₂³×C₅×D₃	1	4	yes	—
408	C₂×C₄	C₂³×C₅×D₃	1	4	yes	—
409	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
410	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
411	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
412	C₂×C₃	C₅×#559	1	4	yes	complemented
413	C₂×C₃	C₂²×C₅×#41	1	1	yes	characteristic
414	C₂×C₃	C₂²×C₅×#41	1	1	yes	characteristic
415	C₂×C₃	C₂×C₅×H(5,𝔽₂)	1	1	yes	characteristic
416	D₃	—	4	8	no	—
417	C₅	C₂×#5585	1	1	yes	characteristic, direct product factor, Sylow
418	C₂²	—	6	8	no	—
419	C₂²	—	6	8	no	—
420	C₂²	—	6	8	no	—
421	C₂²	—	12	16	no	—
422	C₂²	C₂×C₅×#235	1	2	yes	—
423	C₂²	C₂×C₅×#239	1	2	yes	—
424	C₂²	C₅×#1009	1	2	yes	—
425	C₂²	C₂⁴×C₅×D₃	1	1	yes	characteristic
426	C₄	—	2	4	no	—
427	C₄	—	2	4	no	—
428	C₄	—	2	2	no	—
429	C₄	—	6	4	no	—
430	C₄	—	6	4	no	—
431	C₄	C₂×C₅×#235	1	4	yes	—
432	C₄	C₂×C₅×#239	1	4	yes	—
433	C₃	C₂×C₅×#559	1	1	yes	characteristic, complemented, Sylow
434	C₂	—	12	8	no	—
435	C₂	C₅×#5585	1	4	yes	direct product factor
436	C₂	C₂²×C₅×#235	1	1	yes	characteristic
437	C₂	C₂²×C₅×#239	1	1	yes	characteristic
438	C₂	C₂×C₅×#1009	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₅	C₂³×D₃
commutator, cosocle	C₂²×C₃	C₂⁵×C₅
Frattini	C₂²	C₂⁴×C₅×D₃
Fitting	C₂×C₃×C₄×C₅×Q₈	C₂
socle	C₂³×C₃×C₅	C₂⁴
prime radical	C₂×C₅×#874	C₂
hypercenter	C₂×C₄×C₅×Q₈	D₃
hypocenter	C₃	C₂×C₅×#559
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×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
2. C₂×C₅×#947	C₂	semidirect
3. C₅×#5585	C₂	direct (N × H)
4. C₂×C₅×#894	C₂	semidirect
5. C₂×C₅×#893	C₂	semidirect
6. C₂×C₅×#875	C₂	semidirect
8. C₂×C₄×C₅×D₁₂	C₂	semidirect
9. C₂×C₄×C₅×Dic₆	C₂	semidirect
17. C₃×C₄×C₅×Q₈	C₂²	semidirect
22. C₅×#947	C₂²	semidirect
29. C₅×#894	C₂²	semidirect
30. C₅×#893	C₂²	semidirect
31. C₅×#875	C₂²	semidirect
33. C₄×C₅×D₁₂	C₂²	semidirect
34. C₄×C₅×Dic₆	C₂²	semidirect
35. C₂×#5585	C₅	direct (N × H)
42. C₂×C₄×C₅×Q₈	D₃	semidirect
75. C₂×C₃×C₄×Q₈	C₂×C₅	semidirect
76. C₂×#947	C₂×C₅	semidirect
77. #5585	C₂×C₅	direct (N × H)
78. C₂×#894	C₂×C₅	semidirect
79. C₂×#893	C₂×C₅	semidirect
80. C₂×#875	C₂×C₅	semidirect
82. C₂×C₄×D₁₂	C₂×C₅	semidirect
83. C₂×C₄×Dic₆	C₂×C₅	semidirect
95. C₄×C₅×Q₈	C₂×D₃	semidirect
140. C₃×C₄×Q₈	C₂²×C₅	semidirect
145. #947	C₂²×C₅	semidirect
152. #894	C₂²×C₅	semidirect
153. #893	C₂²×C₅	semidirect
154. #875	C₂²×C₅	semidirect
156. C₄×D₁₂	C₂²×C₅	semidirect
157. C₄×Dic₆	C₂²×C₅	semidirect
194. C₂×C₄×Q₈	C₅×D₃	semidirect
278. C₄×Q₈	C₂×C₅×D₃	semidirect
291. C₂×C₃×C₅	#559	semidirect
366. C₃×C₅	C₂×#559	semidirect
383. C₂×C₅	#5585	direct (N × H)
412. C₂×C₃	C₅×#559	semidirect
417. C₅	C₂×#5585	direct (N × H)
433. C₃	C₂×C₅×#559	semidirect
435. C₂	C₅×#5585	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
C₂×C₅×#947	2
C₅×#5585	2
C₂×C₅×#894	2
C₂×C₅×#893	2
C₂×C₅×#875	2
C₂×C₅×#874	2
C₂×C₄×C₅×D₁₂	2
C₂×C₄×C₅×Dic₆	2
C₂×C₅×#559	3
C₂×#5585	5

Subgroups — C2×C5×#5585 #14484708

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#5585 #14484708