Subgroups — C₂×C₅×#5631 #14482682

Order 1920.

3264 conjugacy classes of subgroups.

The subgroup lattice has 672 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₅×#239	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₅×#235	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×C₅×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₅×#944	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₄×C₅×#67	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#5631	C₂	1	16	yes	maximal, direct product factor
7	C₂×C₅×#897	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₅×#894	C₂	1	2	yes	maximal, complemented
9	C₂×C₅×#893	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₅×D₃×C₄⋊C₄	C₂	1	2	yes	maximal, complemented
11	C₂×C₅×#884	C₂	1	2	yes	maximal, complemented
12	C₂×C₅×#883	C₂	1	2	yes	maximal, complemented
13	C₂×C₅×#547	—	3	1	no	maximal, Hall
14	C₂²×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic
15	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
16	C₂²×C₅×#67	C₂²	1	2	yes	—
17	C₂²×C₅×#67	C₂²	1	1	yes	characteristic
18	C₂×C₅×#239	—	2	8	no	—
19	C₂×C₅×#239	C₂²	1	8	yes	complemented
20	C₂×C₅×#235	—	2	8	no	—
21	C₂×C₅×#235	C₂²	1	8	yes	complemented
22	C₂²×C₅×D₁₂	C₂²	1	2	yes	—
23	C₂²×C₅×D₁₂	C₂²	1	1	yes	characteristic
24	C₂²×C₄×C₅×D₃	C₂²	1	2	yes	—
25	C₂²×C₄×C₅×D₃	C₂²	1	2	yes	—
26	C₂²×C₄×C₅×D₃	C₂²	1	1	yes	characteristic
27	C₂²×C₄×C₅×D₃	C₂²	1	2	yes	—
28	C₂²×C₅×Dic₆	C₂²	1	1	yes	characteristic
29	C₃×C₅×C₂²⋊Q₈	C₂²	1	8	yes	complemented
30	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
31	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
32	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
33	C₂×C₅×#217	C₂²	1	1	yes	characteristic
34	C₅×#944	C₂²	1	8	yes	complemented
35	C₄×C₅×#67	C₂²	1	8	yes	complemented
36	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
37	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
38	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
39	C₂×C₅×C₄⋊Dic₃	C₂²	1	2	yes	—
40	C₂×C₅×Dic₃⋊C₄	C₂²	1	2	yes	—
41	C₂×C₅×Dic₃⋊C₄	C₂²	1	2	yes	—
42	C₂×C₅×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
43	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
44	C₅×#897	C₂²	1	8	yes	complemented
45	C₅×#894	C₂²	1	16	yes	complemented
46	C₅×#893	C₂²	1	8	yes	complemented
47	C₅×D₃×C₄⋊C₄	C₂²	1	16	yes	complemented
48	C₅×#884	C₂²	1	16	yes	complemented
49	C₅×#883	C₂²	1	16	yes	complemented
50	C₂×#5631	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
51	C₂²×C₅×#41	—	3	1	no	—
52	C₂²×C₅×#41	—	3	1	no	—
53	C₅×#547	—	3	16	no	—
54	C₂×C₅×C₄⋊Q₈	—	3	1	no	—
55	C₂×C₅×#123	—	3	2	no	—
56	C₂×C₅×#123	—	3	2	no	—
57	C₂×C₅×C₂²⋊Q₈	—	3	1	no	—
58	C₂×C₅×C₂²⋊Q₈	D₃	1	1	yes	characteristic, complemented
59	C₂×C₅×#121	—	3	2	no	—
60	C₂×C₄×C₅×D₄	—	3	1	no	—
61	C₂×C₄×C₅×D₄	—	3	1	no	—
62	C₂²×C₅×C₄⋊C₄	—	3	2	no	—
63	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
64	C₂³×C₅×D₃	C₂³	1	1	yes	characteristic
65	C₂³×C₅×D₃	C₂³	1	2	yes	—
66	C₂×C₃×C₅×Q₈	—	2	4	no	—
67	C₂×C₃×C₅×Q₈	C₂³	1	4	yes	—
68	C₂²×C₃×C₄×C₅	—	2	4	no	—
69	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
70	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
71	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
72	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
73	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
74	C₂×C₅×#67	—	2	8	no	—
75	C₂×C₅×#67	—	2	4	no	—
76	C₂×C₅×#67	C₂³	1	8	yes	—
77	C₂×C₅×#67	C₂³	1	4	yes	—
78	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
79	C₂²×C₅×Dic₃	C₂³	1	2	yes	—
80	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
81	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
82	C₅×#239	—	2	32	no	—
83	C₅×#235	—	2	32	no	—
84	C₂×C₅×D₁₂	—	2	8	no	—
85	C₂×C₅×D₁₂	D₄	1	8	yes	complemented
86	C₂×C₅×D₁₂	C₂³	1	8	yes	—
87	C₂×C₅×D₁₂	C₂³	1	4	yes	—
88	C₂×C₄×C₅×D₃	—	2	8	no	—
89	C₂×C₄×C₅×D₃	—	2	8	no	—
90	C₂×C₄×C₅×D₃	—	2	4	no	—
91	C₂×C₄×C₅×D₃	—	2	8	no	—
92	C₂×C₄×C₅×D₃	C₂³	1	8	yes	—
93	C₂×C₄×C₅×D₃	C₂³	1	8	yes	—
94	C₂×C₄×C₅×D₃	C₂³	1	8	yes	—
95	C₂×C₄×C₅×D₃	C₂³	1	4	yes	—
96	C₂×C₅×Dic₆	—	2	4	no	—
97	C₂×C₅×Dic₆	C₂³	1	4	yes	—
98	C₃×C₅×C₄⋊C₄	C₂³	1	8	yes	—
99	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	—
100	C₃×C₅×C₂²⋊C₄	C₂³	1	8	yes	—
101	C₅×#217	C₂³	1	4	yes	—
102	C₅×(C₂×D₃)⋊C₄	C₂³	1	8	yes	—
103	C₅×(C₂×D₃)⋊C₄	C₂³	1	8	yes	—
104	C₅×(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
105	C₅×C₄⋊Dic₃	C₂³	1	8	yes	—
106	C₅×Dic₃⋊C₄	C₂³	1	8	yes	—
107	C₅×Dic₃⋊C₄	C₂³	1	8	yes	—
108	C₅×Dic₃⋊C₄	C₂³	1	4	yes	—
109	C₄×C₅×Dic₃	C₂³	1	4	yes	—
110	C₂²×#239	C₂×C₅	1	1	yes	characteristic, complemented
111	C₂²×#235	C₂×C₅	1	1	yes	characteristic, complemented
112	C₂×C₃×C₂²⋊Q₈	C₂×C₅	1	1	yes	characteristic, complemented
113	C₂×#944	C₂×C₅	1	1	yes	characteristic, complemented
114	C₂×C₄×#67	C₂×C₅	1	1	yes	characteristic, complemented
115	#5631	C₂×C₅	1	16	yes	direct product factor
116	C₂×#897	C₂×C₅	1	1	yes	characteristic, complemented
117	C₂×#894	C₂×C₅	1	2	yes	complemented
118	C₂×#893	C₂×C₅	1	1	yes	characteristic, complemented
119	C₂×D₃×C₄⋊C₄	C₂×C₅	1	2	yes	complemented
120	C₂×#884	C₂×C₅	1	2	yes	complemented
121	C₂×#883	C₂×C₅	1	2	yes	complemented
122	C₂×C₅×#41	—	3	8	no	—
123	C₂×C₅×#41	—	3	8	no	—
124	C₂×C₅×#41	—	6	8	no	—
125	C₂×C₅×#41	—	6	8	no	—
126	C₂²×C₅×Q₈	—	3	1	no	—
127	C₂²×C₅×Q₈	C₂×D₃	1	1	yes	characteristic
128	C₂²×C₅×D₄	—	3	1	no	—
129	C₂²×C₅×D₄	—	3	2	no	—
130	C₂²×C₅×D₄	—	3	1	no	—
131	C₂²×C₅×D₄	—	3	2	no	—
132	C₂³×C₄×C₅	—	3	2	no	—
133	C₂³×C₄×C₅	—	3	2	no	—
134	C₂³×C₄×C₅	—	3	2	no	—
135	C₂³×C₄×C₅	—	3	1	no	—
136	C₂³×C₄×C₅	C₂×D₃	1	1	yes	characteristic
137	C₅×C₄⋊Q₈	—	3	8	no	—
138	C₅×#123	—	3	16	no	—
139	C₅×#123	—	3	16	no	—
140	C₅×C₂²⋊Q₈	—	3	8	no	—
141	C₅×C₂²⋊Q₈	C₂×D₃	1	8	yes	complemented
142	C₅×#121	—	3	16	no	—
143	C₄×C₅×D₄	—	3	8	no	—
144	C₄×C₅×D₄	—	3	8	no	—
145	C₂×C₅×C₄⋊C₄	—	3	1	no	—
146	C₂×C₅×C₄⋊C₄	—	3	2	no	—
147	C₂×C₅×C₄⋊C₄	—	3	2	no	—
148	C₂×C₅×C₄⋊C₄	—	3	2	no	—
149	C₂×C₅×C₄⋊C₄	—	3	16	no	—
150	C₂×C₅×C₄⋊C₄	C₂×D₃	1	2	yes	—
151	C₂×C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
152	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
153	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
154	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
155	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
156	C₂×C₅×C₂²⋊C₄	C₂×D₃	1	2	yes	—
157	C₂×C₄²×C₅	—	3	1	no	—
158	C₂×#547	—	3	1	no	Sylow
159	C₂³×C₃×C₅	—	2	2	no	—
160	C₂³×C₃×C₅	—	2	2	no	—
161	C₂³×C₃×C₅	—	2	2	no	—
162	C₂³×C₃×C₅	C₂⁴	1	2	yes	—
163	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
164	C₂²×C₅×D₃	—	2	4	no	—
165	C₂²×C₅×D₃	—	2	4	no	—
166	C₂²×C₅×D₃	—	2	2	no	—
167	C₂²×C₅×D₃	—	2	2	no	—
168	C₂²×C₅×D₃	—	2	2	no	—
169	C₂²×C₅×D₃	C₂×D₄	1	8	yes	—
170	C₂²×C₅×D₃	C₂⁴	1	2	yes	—
171	C₂²×C₅×D₃	C₂⁴	1	4	yes	—
172	C₃×C₅×Q₈	—	2	8	no	—
173	C₂×C₃×C₄×C₅	—	2	2	no	—
174	C₂×C₃×C₄×C₅	—	2	4	no	—
175	C₂×C₃×C₄×C₅	—	2	4	no	—
176	C₂×C₃×C₄×C₅	—	2	8	no	—
177	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
178	C₂×C₃×C₄×C₅	C₂⁴	1	4	yes	—
179	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
180	C₂×C₃×C₄×C₅	C₂⁴	1	4	yes	—
181	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
182	C₅×#67	—	2	16	no	—
183	C₅×#67	—	2	8	no	—
184	C₂×C₅×Dic₃	—	2	4	no	—
185	C₂×C₅×Dic₃	—	2	2	no	—
186	C₂×C₅×Dic₃	—	2	2	no	—
187	C₂×C₅×Dic₃	#41	1	4	yes	complemented
188	C₂×C₅×Dic₃	C₂⁴	1	2	yes	—
189	C₂×C₅×Dic₃	C₂⁴	1	4	yes	—
190	C₂×C₅×Dic₃	C₂⁴	1	2	yes	—
191	C₂×C₅×Dic₃	C₂⁴	1	2	yes	—
192	C₅×D₁₂	—	2	16	no	—
193	C₅×D₁₂	C₂×D₄	1	16	yes	complemented
194	C₄×C₅×D₃	—	2	16	no	—
195	C₄×C₅×D₃	—	2	16	no	—
196	C₄×C₅×D₃	—	2	8	no	—
197	C₄×C₅×D₃	—	2	16	no	—
198	C₅×Dic₆	—	2	8	no	—
199	C₂²×C₃×Q₈	C₂²×C₅	1	1	yes	characteristic
200	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
201	C₂²×#67	C₂²×C₅	1	2	yes	—
202	C₂²×#67	C₂²×C₅	1	1	yes	characteristic
203	C₂×#239	—	2	8	no	—
204	C₂×#239	C₂²×C₅	1	8	yes	complemented
205	C₂×#235	—	2	8	no	—
206	C₂×#235	C₂²×C₅	1	8	yes	complemented
207	C₂²×D₁₂	C₂²×C₅	1	2	yes	—
208	C₂²×D₁₂	C₂²×C₅	1	1	yes	characteristic
209	C₂²×C₄×D₃	C₂²×C₅	1	2	yes	—
210	C₂²×C₄×D₃	C₂²×C₅	1	2	yes	—
211	C₂²×C₄×D₃	C₂²×C₅	1	1	yes	characteristic
212	C₂²×C₄×D₃	C₂²×C₅	1	2	yes	—
213	C₂²×Dic₆	C₂²×C₅	1	1	yes	characteristic
214	C₃×C₂²⋊Q₈	C₂²×C₅	1	8	yes	complemented
215	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
216	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
217	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
218	C₂×#217	C₂²×C₅	1	1	yes	characteristic
219	#944	C₂²×C₅	1	8	yes	complemented
220	C₄×#67	C₂²×C₅	1	8	yes	complemented
221	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	2	yes	—
222	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	2	yes	—
223	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	1	yes	characteristic
224	C₂×C₄⋊Dic₃	C₂²×C₅	1	2	yes	—
225	C₂×Dic₃⋊C₄	C₂²×C₅	1	2	yes	—
226	C₂×Dic₃⋊C₄	C₂²×C₅	1	2	yes	—
227	C₂×Dic₃⋊C₄	C₂²×C₅	1	1	yes	characteristic
228	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
229	#897	C₂²×C₅	1	8	yes	complemented
230	#894	C₂²×C₅	1	16	yes	complemented
231	#893	C₂²×C₅	1	8	yes	complemented
232	D₃×C₄⋊C₄	C₂²×C₅	1	16	yes	complemented
233	#884	C₂²×C₅	1	16	yes	complemented
234	#883	C₂²×C₅	1	16	yes	complemented
235	C₂⁴×C₅	—	3	2	no	—
236	C₂⁴×C₅	—	3	1	no	—
237	C₂⁴×C₅	C₂²×D₃	1	1	yes	characteristic
238	C₅×#41	—	6	32	no	—
239	C₅×#41	—	6	32	no	—
240	C₂×C₅×Q₈	—	2	4	no	—
241	C₂×C₅×Q₈	—	3	4	no	—
242	C₂×C₅×Q₈	—	6	4	no	—
243	C₂×C₅×Q₈	C₂²×D₃	1	4	yes	—
244	C₂×C₅×D₄	—	3	4	no	—
245	C₂×C₅×D₄	—	3	8	no	—
246	C₂×C₅×D₄	—	3	8	no	—
247	C₂×C₅×D₄	—	3	4	no	—
248	C₂×C₅×D₄	—	3	8	no	—
249	C₂×C₅×D₄	—	6	8	no	—
250	C₂×C₅×D₄	—	6	4	no	—
251	C₂×C₅×D₄	—	6	8	no	—
252	C₂²×C₄×C₅	—	2	4	no	—
253	C₂²×C₄×C₅	—	3	1	no	—
254	C₂²×C₄×C₅	—	3	1	no	—
255	C₂²×C₄×C₅	—	3	1	no	—
256	C₂²×C₄×C₅	—	3	2	no	—
257	C₂²×C₄×C₅	—	3	8	no	—
258	C₂²×C₄×C₅	—	3	8	no	—
259	C₂²×C₄×C₅	—	3	8	no	—
260	C₂²×C₄×C₅	—	3	4	no	—
261	C₂²×C₄×C₅	—	6	8	no	—
262	C₂²×C₄×C₅	—	6	8	no	—
263	C₂²×C₄×C₅	—	6	8	no	—
264	C₂²×C₄×C₅	—	6	4	no	—
265	C₂²×C₄×C₅	C₂²×D₃	1	4	yes	—
266	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
267	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
268	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
269	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
270	C₅×C₄⋊C₄	—	3	4	no	—
271	C₅×C₄⋊C₄	—	3	8	no	—
272	C₅×C₄⋊C₄	—	3	8	no	—
273	C₅×C₄⋊C₄	—	3	8	no	—
274	C₅×C₄⋊C₄	C₂²×D₃	1	8	yes	—
275	C₅×C₄⋊C₄	C₂²×D₃	1	4	yes	—
276	C₅×C₂²⋊C₄	—	3	4	no	—
277	C₅×C₂²⋊C₄	—	3	8	no	—
278	C₅×C₂²⋊C₄	—	3	4	no	—
279	C₅×C₂²⋊C₄	—	3	8	no	—
280	C₅×C₂²⋊C₄	C₂²×D₃	1	8	yes	—
281	C₄²×C₅	—	3	4	no	—
282	C₂²×#41	—	3	1	no	—
283	C₂²×#41	—	3	1	no	—
284	#547	—	3	16	no	—
285	C₂×C₄⋊Q₈	—	3	1	no	—
286	C₂×#123	—	3	2	no	—
287	C₂×#123	—	3	2	no	—
288	C₂×C₂²⋊Q₈	—	3	1	no	—
289	C₂×C₂²⋊Q₈	C₅×D₃	1	1	yes	characteristic, complemented
290	C₂×#121	—	3	2	no	—
291	C₂×C₄×D₄	—	3	1	no	—
292	C₂×C₄×D₄	—	3	1	no	—
293	C₂²×C₄⋊C₄	—	3	2	no	—
294	C₂²×C₃×C₅	—	2	2	no	—
295	C₂²×C₃×C₅	—	2	2	no	—
296	C₂²×C₃×C₅	—	2	2	no	—
297	C₂²×C₃×C₅	—	4	4	no	—
298	C₂²×C₃×C₅	C₂²×D₄	1	2	yes	—
299	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
300	C₂²×C₃×C₅	2₋¹⁺⁴	1	2	yes	—
301	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
302	C₂×C₅×D₃	—	2	16	no	—
303	C₂×C₅×D₃	—	2	4	no	—
304	C₂×C₅×D₃	—	2	4	no	—
305	C₂×C₅×D₃	—	2	2	no	—
306	C₂×C₅×D₃	—	2	2	no	—
307	C₂×C₅×D₃	—	2	2	no	—
308	C₂×C₅×D₃	—	4	4	no	—
309	C₂×C₅×D₃	C₂²×D₄	1	8	yes	—
310	C₃×C₄×C₅	—	2	2	no	—
311	C₃×C₄×C₅	—	2	4	no	—
312	C₃×C₄×C₅	—	2	4	no	—
313	C₃×C₄×C₅	C₂²×D₄	1	4	yes	—
314	C₅×Dic₃	—	2	4	no	—
315	C₅×Dic₃	—	2	2	no	—
316	C₅×Dic₃	—	2	2	no	—
317	C₅×Dic₃	C₂×#41	1	4	yes	complemented
318	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
319	C₂³×D₃	C₂³×C₅	1	1	yes	characteristic
320	C₂³×D₃	C₂³×C₅	1	2	yes	—
321	C₂×C₃×Q₈	—	2	4	no	—
322	C₂×C₃×Q₈	C₂³×C₅	1	4	yes	—
323	C₂²×C₃×C₄	—	2	4	no	—
324	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
325	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
326	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
327	C₂²×C₃×C₄	C₂³×C₅	1	4	yes	—
328	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
329	C₂×#67	—	2	8	no	—
330	C₂×#67	—	2	4	no	—
331	C₂×#67	C₂³×C₅	1	8	yes	—
332	C₂×#67	C₂³×C₅	1	4	yes	—
333	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
334	C₂²×Dic₃	C₂³×C₅	1	2	yes	—
335	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
336	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
337	#239	—	2	32	no	—
338	#235	—	2	32	no	—
339	C₂×D₁₂	—	2	8	no	—
340	C₂×D₁₂	C₅×D₄	1	8	yes	complemented
341	C₂×D₁₂	C₂³×C₅	1	8	yes	—
342	C₂×D₁₂	C₂³×C₅	1	4	yes	—
343	C₂×C₄×D₃	—	2	8	no	—
344	C₂×C₄×D₃	—	2	8	no	—
345	C₂×C₄×D₃	—	2	4	no	—
346	C₂×C₄×D₃	—	2	8	no	—
347	C₂×C₄×D₃	C₂³×C₅	1	8	yes	—
348	C₂×C₄×D₃	C₂³×C₅	1	8	yes	—
349	C₂×C₄×D₃	C₂³×C₅	1	8	yes	—
350	C₂×C₄×D₃	C₂³×C₅	1	4	yes	—
351	C₂×Dic₆	—	2	4	no	—
352	C₂×Dic₆	C₂³×C₅	1	4	yes	—
353	C₃×C₄⋊C₄	C₂³×C₅	1	8	yes	—
354	C₃×C₄⋊C₄	C₂³×C₅	1	4	yes	—
355	C₃×C₂²⋊C₄	C₂³×C₅	1	8	yes	—
356	#217	C₂³×C₅	1	4	yes	—
357	(C₂×D₃)⋊C₄	C₂³×C₅	1	8	yes	—
358	(C₂×D₃)⋊C₄	C₂³×C₅	1	8	yes	—
359	(C₂×D₃)⋊C₄	C₂³×C₅	1	4	yes	—
360	C₄⋊Dic₃	C₂³×C₅	1	8	yes	—
361	Dic₃⋊C₄	C₂³×C₅	1	8	yes	—
362	Dic₃⋊C₄	C₂³×C₅	1	8	yes	—
363	Dic₃⋊C₄	C₂³×C₅	1	4	yes	—
364	C₄×Dic₃	C₂³×C₅	1	4	yes	—
365	C₂³×C₅	—	2	2	no	—
366	C₂³×C₅	—	2	2	no	—
367	C₂³×C₅	—	2	2	no	—
368	C₂³×C₅	—	3	8	no	—
369	C₂³×C₅	—	3	4	no	—
370	C₂³×C₅	—	3	2	no	—
371	C₂³×C₅	—	6	4	no	—
372	C₂³×C₅	—	6	4	no	—
373	C₂³×C₅	—	6	2	no	—
374	C₂³×C₅	—	6	2	no	—
375	C₂³×C₅	—	6	2	no	—
376	C₂³×C₅	C₂³×D₃	1	2	yes	—
377	C₂³×C₅	C₂³×D₃	1	1	yes	characteristic
378	C₅×Q₈	—	2	8	no	—
379	C₅×Q₈	—	6	8	no	—
380	C₅×D₄	—	3	16	no	—
381	C₅×D₄	—	6	16	no	—
382	C₅×D₄	—	6	8	no	—
383	C₅×D₄	—	6	16	no	—
384	C₂×C₄×C₅	—	2	2	no	—
385	C₂×C₄×C₅	—	2	4	no	—
386	C₂×C₄×C₅	—	2	4	no	—
387	C₂×C₄×C₅	—	2	8	no	—
388	C₂×C₄×C₅	—	3	4	no	—
389	C₂×C₄×C₅	—	3	2	no	—
390	C₂×C₄×C₅	—	3	2	no	—
391	C₂×C₄×C₅	—	3	2	no	—
392	C₂×C₄×C₅	—	3	4	no	—
393	C₂×C₄×C₅	—	6	16	no	—
394	C₂×C₄×C₅	—	6	16	no	—
395	C₂×C₄×C₅	—	6	16	no	—
396	C₂×C₄×C₅	—	6	2	no	—
397	C₂×C₄×C₅	—	6	4	no	—
398	C₂×C₄×C₅	—	6	2	no	—
399	C₂×C₄×C₅	—	6	8	no	—
400	C₂×C₄×C₅	D₃×D₄	1	4	yes	—
401	C₂×C₄×C₅	C₂³×D₃	1	4	yes	—
402	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
403	C₂×C₄×C₅	C₂³×D₃	1	4	yes	—
404	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
405	C₂×#41	—	3	8	no	—
406	C₂×#41	—	3	8	no	—
407	C₂×#41	—	6	8	no	—
408	C₂×#41	—	6	8	no	—
409	C₂²×Q₈	—	3	1	no	—
410	C₂²×Q₈	C₂×C₅×D₃	1	1	yes	characteristic
411	C₂²×D₄	—	3	1	no	—
412	C₂²×D₄	—	3	2	no	—
413	C₂²×D₄	—	3	1	no	—
414	C₂²×D₄	—	3	2	no	—
415	C₂³×C₄	—	3	2	no	—
416	C₂³×C₄	—	3	2	no	—
417	C₂³×C₄	—	3	2	no	—
418	C₂³×C₄	—	3	1	no	—
419	C₂³×C₄	C₂×C₅×D₃	1	1	yes	characteristic
420	C₄⋊Q₈	—	3	8	no	—
421	#123	—	3	16	no	—
422	#123	—	3	16	no	—
423	C₂²⋊Q₈	—	3	8	no	—
424	C₂²⋊Q₈	C₂×C₅×D₃	1	8	yes	complemented
425	#121	—	3	16	no	—
426	C₄×D₄	—	3	8	no	—
427	C₄×D₄	—	3	8	no	—
428	C₂×C₄⋊C₄	—	3	1	no	—
429	C₂×C₄⋊C₄	—	3	2	no	—
430	C₂×C₄⋊C₄	—	3	2	no	—
431	C₂×C₄⋊C₄	—	3	2	no	—
432	C₂×C₄⋊C₄	—	3	16	no	—
433	C₂×C₄⋊C₄	C₂×C₅×D₃	1	2	yes	—
434	C₂×C₄⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
435	C₂×C₂²⋊C₄	—	3	1	no	—
436	C₂×C₂²⋊C₄	—	3	2	no	—
437	C₂×C₂²⋊C₄	—	3	1	no	—
438	C₂×C₂²⋊C₄	—	3	2	no	—
439	C₂×C₂²⋊C₄	C₂×C₅×D₃	1	2	yes	—
440	C₂×C₄²	—	3	1	no	—
441	C₂×C₃×C₅	—	4	2	no	—
442	C₂×C₃×C₅	#547	1	4	yes	complemented
443	C₂×C₃×C₅	C₂³×D₄	1	1	yes	characteristic
444	C₂×C₃×C₅	C₂²×#41	1	1	yes	characteristic
445	C₂×C₃×C₅	C₂×2₋¹⁺⁴	1	1	yes	characteristic
446	C₅×D₃	—	2	8	no	—
447	C₅×D₃	—	4	2	no	—
448	C₂³×C₃	—	2	2	no	—
449	C₂³×C₃	—	2	2	no	—
450	C₂³×C₃	—	2	2	no	—
451	C₂³×C₃	C₂⁴×C₅	1	2	yes	—
452	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
453	C₂²×D₃	—	2	4	no	—
454	C₂²×D₃	—	2	4	no	—
455	C₂²×D₃	—	2	2	no	—
456	C₂²×D₃	—	2	2	no	—
457	C₂²×D₃	—	2	2	no	—
458	C₂²×D₃	C₂×C₅×D₄	1	8	yes	—
459	C₂²×D₃	C₂⁴×C₅	1	2	yes	—
460	C₂²×D₃	C₂⁴×C₅	1	4	yes	—
461	C₃×Q₈	—	2	8	no	—
462	C₂×C₃×C₄	—	2	2	no	—
463	C₂×C₃×C₄	—	2	4	no	—
464	C₂×C₃×C₄	—	2	4	no	—
465	C₂×C₃×C₄	—	2	8	no	—
466	C₂×C₃×C₄	C₂×C₅×D₄	1	4	yes	—
467	C₂×C₃×C₄	C₂⁴×C₅	1	4	yes	—
468	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
469	C₂×C₃×C₄	C₂⁴×C₅	1	4	yes	—
470	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
471	#67	—	2	16	no	—
472	#67	—	2	8	no	—
473	C₂×Dic₃	—	2	4	no	—
474	C₂×Dic₃	—	2	2	no	—
475	C₂×Dic₃	—	2	2	no	—
476	C₂×Dic₃	C₅×#41	1	4	yes	complemented
477	C₂×Dic₃	C₂⁴×C₅	1	2	yes	—
478	C₂×Dic₃	C₂⁴×C₅	1	4	yes	—
479	C₂×Dic₃	C₂⁴×C₅	1	2	yes	—
480	C₂×Dic₃	C₂⁴×C₅	1	2	yes	—
481	D₁₂	—	2	16	no	—
482	D₁₂	C₂×C₅×D₄	1	16	yes	complemented
483	C₄×D₃	—	2	16	no	—
484	C₄×D₃	—	2	16	no	—
485	C₄×D₃	—	2	8	no	—
486	C₄×D₃	—	2	16	no	—
487	Dic₆	—	2	8	no	—
488	C₂²×C₅	—	2	2	no	—
489	C₂²×C₅	—	2	2	no	—
490	C₂²×C₅	—	2	2	no	—
491	C₂²×C₅	—	3	8	no	—
492	C₂²×C₅	—	4	4	no	—
493	C₂²×C₅	—	6	4	no	—
494	C₂²×C₅	—	6	4	no	—
495	C₂²×C₅	—	6	16	no	—
496	C₂²×C₅	—	6	2	no	—
497	C₂²×C₅	—	6	2	no	—
498	C₂²×C₅	—	6	2	no	—
499	C₂²×C₅	—	12	4	no	—
500	C₂²×C₅	C₂×D₃×D₄	1	2	yes	—
501	C₂²×C₅	#1007	1	2	yes	—
502	C₂²×C₅	D₃×#41	1	2	yes	—
503	C₂²×C₅	C₂⁴×D₃	1	1	yes	characteristic
504	C₄×C₅	—	2	2	no	—
505	C₄×C₅	—	2	4	no	—
506	C₄×C₅	—	2	4	no	—
507	C₄×C₅	—	3	4	no	—
508	C₄×C₅	—	6	2	no	—
509	C₄×C₅	—	6	4	no	—
510	C₄×C₅	—	6	2	no	—
511	C₄×C₅	C₂×D₃×D₄	1	4	yes	—
512	C₂⁴	—	3	2	no	—
513	C₂⁴	—	3	1	no	—
514	C₂⁴	C₂²×C₅×D₃	1	1	yes	characteristic
515	#41	—	6	32	no	—
516	#41	—	6	32	no	—
517	C₂×Q₈	—	2	4	no	—
518	C₂×Q₈	—	3	4	no	—
519	C₂×Q₈	—	6	4	no	—
520	C₂×Q₈	C₂²×C₅×D₃	1	4	yes	—
521	C₂×D₄	—	3	4	no	—
522	C₂×D₄	—	3	8	no	—
523	C₂×D₄	—	3	8	no	—
524	C₂×D₄	—	3	4	no	—
525	C₂×D₄	—	3	8	no	—
526	C₂×D₄	—	6	8	no	—
527	C₂×D₄	—	6	4	no	—
528	C₂×D₄	—	6	8	no	—
529	C₂²×C₄	—	2	4	no	—
530	C₂²×C₄	—	3	1	no	—
531	C₂²×C₄	—	3	1	no	—
532	C₂²×C₄	—	3	1	no	—
533	C₂²×C₄	—	3	2	no	—
534	C₂²×C₄	—	3	8	no	—
535	C₂²×C₄	—	3	8	no	—
536	C₂²×C₄	—	3	8	no	—
537	C₂²×C₄	—	3	4	no	—
538	C₂²×C₄	—	6	8	no	—
539	C₂²×C₄	—	6	8	no	—
540	C₂²×C₄	—	6	8	no	—
541	C₂²×C₄	—	6	4	no	—
542	C₂²×C₄	C₂²×C₅×D₃	1	2	yes	—
543	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
544	C₂²×C₄	C₂²×C₅×D₃	1	2	yes	—
545	C₂²×C₄	C₂²×C₅×D₃	1	4	yes	—
546	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
547	C₄⋊C₄	—	3	4	no	—
548	C₄⋊C₄	—	3	8	no	—
549	C₄⋊C₄	—	3	8	no	—
550	C₄⋊C₄	—	3	8	no	—
551	C₄⋊C₄	C₂²×C₅×D₃	1	8	yes	—
552	C₄⋊C₄	C₂²×C₅×D₃	1	4	yes	—
553	C₂²⋊C₄	—	3	4	no	—
554	C₂²⋊C₄	—	3	8	no	—
555	C₂²⋊C₄	—	3	4	no	—
556	C₂²⋊C₄	—	3	8	no	—
557	C₂²⋊C₄	C₂²×C₅×D₃	1	8	yes	—
558	C₄²	—	3	4	no	—
559	C₃×C₅	C₂×#547	1	1	yes	characteristic, complemented, Hall
560	C₂²×C₃	—	2	2	no	—
561	C₂²×C₃	—	2	2	no	—
562	C₂²×C₃	—	2	2	no	—
563	C₂²×C₃	—	4	4	no	—
564	C₂²×C₃	C₂²×C₅×D₄	1	2	yes	—
565	C₂²×C₃	C₂×C₅×#41	1	2	yes	—
566	C₂²×C₃	C₅×2₋¹⁺⁴	1	2	yes	—
567	C₂²×C₃	C₂⁵×C₅	1	1	yes	characteristic
568	C₂×D₃	—	2	16	no	—
569	C₂×D₃	—	2	4	no	—
570	C₂×D₃	—	2	4	no	—
571	C₂×D₃	—	2	2	no	—
572	C₂×D₃	—	2	2	no	—
573	C₂×D₃	—	2	2	no	—
574	C₂×D₃	—	4	4	no	—
575	C₂×D₃	C₂²×C₅×D₄	1	8	yes	—
576	C₃×C₄	—	2	2	no	—
577	C₃×C₄	—	2	4	no	—
578	C₃×C₄	—	2	4	no	—
579	C₃×C₄	C₂²×C₅×D₄	1	4	yes	—
580	Dic₃	—	2	4	no	—
581	Dic₃	—	2	2	no	—
582	Dic₃	—	2	2	no	—
583	Dic₃	C₂×C₅×#41	1	4	yes	complemented
584	C₂×C₅	—	4	2	no	—
585	C₂×C₅	—	6	8	no	—
586	C₂×C₅	—	12	2	no	—
587	C₂×C₅	#5631	1	4	yes	direct product factor
588	C₂×C₅	C₂²×D₃×D₄	1	1	yes	characteristic
589	C₂×C₅	C₂×#1007	1	1	yes	characteristic
590	C₂×C₅	C₂×D₃×#41	1	1	yes	characteristic
591	C₂³	—	2	2	no	—
592	C₂³	—	2	2	no	—
593	C₂³	—	2	2	no	—
594	C₂³	—	3	8	no	—
595	C₂³	—	3	4	no	—
596	C₂³	—	3	2	no	—
597	C₂³	—	6	4	no	—
598	C₂³	—	6	4	no	—
599	C₂³	—	6	2	no	—
600	C₂³	—	6	2	no	—
601	C₂³	—	6	2	no	—
602	C₂³	C₂³×C₅×D₃	1	2	yes	—
603	C₂³	C₂³×C₅×D₃	1	1	yes	characteristic
604	Q₈	—	2	8	no	—
605	Q₈	—	6	8	no	—
606	D₄	—	3	16	no	—
607	D₄	—	6	16	no	—
608	D₄	—	6	8	no	—
609	D₄	—	6	16	no	—
610	C₂×C₄	—	2	2	no	—
611	C₂×C₄	—	2	4	no	—
612	C₂×C₄	—	2	4	no	—
613	C₂×C₄	—	2	8	no	—
614	C₂×C₄	—	3	4	no	—
615	C₂×C₄	—	3	2	no	—
616	C₂×C₄	—	3	2	no	—
617	C₂×C₄	—	3	2	no	—
618	C₂×C₄	—	3	4	no	—
619	C₂×C₄	—	6	16	no	—
620	C₂×C₄	—	6	16	no	—
621	C₂×C₄	—	6	16	no	—
622	C₂×C₄	—	6	2	no	—
623	C₂×C₄	—	6	4	no	—
624	C₂×C₄	—	6	2	no	—
625	C₂×C₄	—	6	8	no	—
626	C₂×C₄	C₅×D₃×D₄	1	4	yes	—
627	C₂×C₄	C₂³×C₅×D₃	1	4	yes	—
628	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
629	C₂×C₄	C₂³×C₅×D₃	1	4	yes	—
630	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
631	C₂×C₃	—	4	2	no	—
632	C₂×C₃	C₅×#547	1	4	yes	complemented
633	C₂×C₃	C₂³×C₅×D₄	1	1	yes	characteristic
634	C₂×C₃	C₂²×C₅×#41	1	1	yes	characteristic
635	C₂×C₃	C₂×C₅×2₋¹⁺⁴	1	1	yes	characteristic
636	D₃	—	2	8	no	—
637	D₃	—	4	2	no	—
638	C₅	C₂×#5631	1	1	yes	characteristic, direct product factor, Sylow
639	C₂²	—	2	2	no	—
640	C₂²	—	2	2	no	—
641	C₂²	—	2	2	no	—
642	C₂²	—	3	8	no	—
643	C₂²	—	4	4	no	—
644	C₂²	—	6	4	no	—
645	C₂²	—	6	4	no	—
646	C₂²	—	6	16	no	—
647	C₂²	—	6	2	no	—
648	C₂²	—	6	2	no	—
649	C₂²	—	6	2	no	—
650	C₂²	—	12	4	no	—
651	C₂²	C₂×C₅×D₃×D₄	1	2	yes	—
652	C₂²	C₅×#1007	1	2	yes	—
653	C₂²	C₅×D₃×#41	1	2	yes	—
654	C₂²	C₂⁴×C₅×D₃	1	1	yes	characteristic
655	C₄	—	2	2	no	—
656	C₄	—	2	4	no	—
657	C₄	—	2	4	no	—
658	C₄	—	3	4	no	—
659	C₄	—	6	2	no	—
660	C₄	—	6	4	no	—
661	C₄	—	6	2	no	—
662	C₄	C₂×C₅×D₃×D₄	1	4	yes	—
663	C₃	C₂×C₅×#547	1	1	yes	characteristic, complemented, Sylow
664	C₂	—	4	2	no	—
665	C₂	—	6	8	no	—
666	C₂	—	12	2	no	—
667	C₂	C₅×#5631	1	4	yes	direct product factor
668	C₂	C₂²×C₅×D₃×D₄	1	1	yes	characteristic
669	C₂	C₂×C₅×#1007	1	1	yes	characteristic
670	C₂	C₂×C₅×D₃×#41	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×C₅×C₂²⋊Q₈	C₂
socle	C₂³×C₃×C₅	C₂⁴
hypercenter	C₂×C₅×C₂²⋊Q₈	D₃
hypocenter	C₃	C₂×C₅×#547
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₅ ◁ C₂×C₅×C₂²⋊Q₈

Complements

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

N	H ≅ G/N	type
1. C₂²×C₅×#239	C₂	semidirect
2. C₂²×C₅×#235	C₂	semidirect
3. C₂×C₃×C₅×C₂²⋊Q₈	C₂	semidirect
4. C₂×C₅×#944	C₂	semidirect
5. C₂×C₄×C₅×#67	C₂	semidirect
6. C₅×#5631	C₂	direct (N × H)
7. C₂×C₅×#897	C₂	semidirect
8. C₂×C₅×#894	C₂	semidirect
9. C₂×C₅×#893	C₂	semidirect
10. C₂×C₅×D₃×C₄⋊C₄	C₂	semidirect
11. C₂×C₅×#884	C₂	semidirect
12. C₂×C₅×#883	C₂	semidirect
19. C₂×C₅×#239	C₂²	semidirect
21. C₂×C₅×#235	C₂²	semidirect
29. C₃×C₅×C₂²⋊Q₈	C₂²	semidirect
34. C₅×#944	C₂²	semidirect
35. C₄×C₅×#67	C₂²	semidirect
44. C₅×#897	C₂²	semidirect
45. C₅×#894	C₂²	semidirect
46. C₅×#893	C₂²	semidirect
47. C₅×D₃×C₄⋊C₄	C₂²	semidirect
48. C₅×#884	C₂²	semidirect
49. C₅×#883	C₂²	semidirect
50. C₂×#5631	C₅	direct (N × H)
58. C₂×C₅×C₂²⋊Q₈	D₃	semidirect
85. C₂×C₅×D₁₂	D₄	semidirect
110. C₂²×#239	C₂×C₅	semidirect
111. C₂²×#235	C₂×C₅	semidirect
112. C₂×C₃×C₂²⋊Q₈	C₂×C₅	semidirect
113. C₂×#944	C₂×C₅	semidirect
114. C₂×C₄×#67	C₂×C₅	semidirect
115. #5631	C₂×C₅	direct (N × H)
116. C₂×#897	C₂×C₅	semidirect
117. C₂×#894	C₂×C₅	semidirect
118. C₂×#893	C₂×C₅	semidirect
119. C₂×D₃×C₄⋊C₄	C₂×C₅	semidirect
120. C₂×#884	C₂×C₅	semidirect
121. C₂×#883	C₂×C₅	semidirect
141. C₅×C₂²⋊Q₈	C₂×D₃	semidirect
187. C₂×C₅×Dic₃	#41	semidirect
193. C₅×D₁₂	C₂×D₄	semidirect
204. C₂×#239	C₂²×C₅	semidirect
206. C₂×#235	C₂²×C₅	semidirect
214. C₃×C₂²⋊Q₈	C₂²×C₅	semidirect
219. #944	C₂²×C₅	semidirect
220. C₄×#67	C₂²×C₅	semidirect
229. #897	C₂²×C₅	semidirect
230. #894	C₂²×C₅	semidirect
231. #893	C₂²×C₅	semidirect
232. D₃×C₄⋊C₄	C₂²×C₅	semidirect
233. #884	C₂²×C₅	semidirect
234. #883	C₂²×C₅	semidirect
289. C₂×C₂²⋊Q₈	C₅×D₃	semidirect
317. C₅×Dic₃	C₂×#41	semidirect
340. C₂×D₁₂	C₅×D₄	semidirect
424. C₂²⋊Q₈	C₂×C₅×D₃	semidirect
442. C₂×C₃×C₅	#547	semidirect
476. C₂×Dic₃	C₅×#41	semidirect
482. D₁₂	C₂×C₅×D₄	semidirect
559. C₃×C₅	C₂×#547	semidirect
583. Dic₃	C₂×C₅×#41	semidirect
587. C₂×C₅	#5631	direct (N × H)
632. C₂×C₃	C₅×#547	semidirect
638. C₅	C₂×#5631	direct (N × H)
663. C₃	C₂×C₅×#547	semidirect
667. C₂	C₅×#5631	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₅×#239	2
C₂²×C₅×#235	2
C₂×C₃×C₅×C₂²⋊Q₈	2
C₂×C₅×#944	2
C₂×C₄×C₅×#67	2
C₅×#5631	2
C₂×C₅×#897	2
C₂×C₅×#894	2
C₂×C₅×#893	2
C₂×C₅×D₃×C₄⋊C₄	2
C₂×C₅×#884	2
C₂×C₅×#883	2
C₂×C₅×#547	3
C₂×#5631	5

Subgroups — C2×C5×#5631 #14482682

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#5631 #14482682