Subgroups — C₂×C₅×#3137 #11983331

Order 1280.

2070 conjugacy classes of subgroups.

The subgroup lattice has 566 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#544	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅×#536	C₂	1	1	yes	maximal, characteristic
3	C₅×#3137	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₅×#491	C₂	1	2	yes	maximal, complemented
5	C₂×C₅×#489	C₂	1	2	yes	maximal, complemented
6	C₂×C₅×#488	C₂	1	2	yes	maximal, complemented
7	C₂×C₅×#487	C₂	1	2	yes	maximal, complemented
8	C₂×C₅×#417	C₂	1	1	yes	maximal, characteristic
9	C₂×C₅×#419	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₅×#416	C₂	1	1	yes	maximal, characteristic
11	C₂²×C₅×#103	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₅×#405	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂²×C₅×#41	C₂²	1	1	yes	characteristic
14	C₂³×C₅×Q₈	C₂²	1	1	yes	characteristic
15	C₂²×C₅×M₁₆	C₂²	1	1	yes	characteristic
16	C₂³×C₅×C₈	C₂²	1	1	yes	characteristic
17	C₅×#544	—	2	4	no	—
18	C₅×#544	C₂²	1	8	yes	complemented
19	C₅×#536	—	2	4	no	—
20	C₅×#536	C₂²	1	8	yes	—
21	C₂×C₅×C₄⋊Q₈	—	2	1	no	—
22	C₂×C₅×C₄⋊Q₈	C₂²	1	2	yes	—
23	C₂×C₅×C₄⋊Q₈	C₂²	1	2	yes	—
24	C₂×C₅×#125	—	2	1	no	—
25	C₂×C₅×#125	C₂²	1	2	yes	—
26	C₂×C₅×#124	C₂²	1	2	yes	—
27	C₂×C₅×#123	—	2	2	no	—
28	C₂×C₅×C₂²⋊Q₈	—	2	1	no	—
29	C₂×C₅×C₂²⋊Q₈	—	2	1	no	—
30	C₂×C₅×C₂²⋊Q₈	—	2	2	no	—
31	C₂×C₅×#117	C₂²	1	1	yes	characteristic
32	C₂×C₅×#117	C₂²	1	1	yes	characteristic
33	C₂²×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
34	C₅×#491	C₂²	1	16	yes	complemented
35	C₅×#489	C₂²	1	16	yes	complemented
36	C₅×#488	C₂²	1	16	yes	complemented
37	C₅×#487	C₂²	1	16	yes	complemented
38	C₅×#419	C₂²	1	8	yes	complemented
39	C₅×#417	C₂²	1	8	yes	—
40	C₅×#416	C₂²	1	8	yes	—
41	C₂×C₅×#103	C₂²	1	1	yes	characteristic
42	C₂×C₅×#103	C₂²	1	2	yes	—
43	C₂×C₅×#103	C₂²	1	2	yes	—
44	C₂×C₅×#103	C₂²	1	2	yes	—
45	C₂×C₅×#103	C₂²	1	2	yes	—
46	C₂×C₅×#103	C₂²	1	2	yes	—
47	C₂×C₅×#103	C₂²	1	1	yes	characteristic
48	C₂×C₅×#103	C₂²	1	8	yes	complemented
49	C₂×C₅×#102	C₂²	1	1	yes	characteristic
50	C₂×C₅×#102	C₂²	1	2	yes	—
51	C₂×C₅×#102	C₂²	1	1	yes	characteristic
52	C₅×#405	C₂²	1	8	yes	complemented
53	C₂×C₅×#97	C₂²	1	2	yes	—
54	C₂×C₄×C₅×C₈	C₂²	1	2	yes	—
55	C₂×#3137	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
56	C₂×C₅×#41	—	2	2	no	—
57	C₂×C₅×#41	—	2	4	no	—
58	C₂×C₅×#41	—	2	4	no	—
59	C₂×C₅×#41	C₂³	1	4	yes	—
60	C₂²×C₅×Q₈	—	2	1	no	—
61	C₂²×C₅×Q₈	—	2	2	no	—
62	C₂²×C₅×Q₈	—	2	2	no	—
63	C₂²×C₅×Q₈	—	2	4	no	—
64	C₂²×C₅×Q₈	—	2	4	no	—
65	C₂²×C₅×Q₈	C₂³	1	2	yes	—
66	C₂²×C₅×Q₈	C₂³	1	1	yes	characteristic
67	C₂²×C₅×Q₈	C₂³	1	4	yes	—
68	C₂²×C₅×D₄	—	2	1	no	—
69	C₂²×C₅×D₄	C₂³	1	1	yes	characteristic
70	C₂³×C₄×C₅	—	2	1	no	—
71	C₂³×C₄×C₅	—	2	1	no	—
72	C₂³×C₄×C₅	—	2	1	no	—
73	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
74	C₂×C₅×M₁₆	—	2	4	no	—
75	C₂×C₅×M₁₆	C₂³	1	4	yes	—
76	C₂²×C₅×C₈	—	2	4	no	—
77	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
78	C₂²×C₅×C₈	C₂³	1	2	yes	—
79	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
80	C₂²×C₅×C₈	C₂³	1	4	yes	—
81	C₅×C₄⋊Q₈	—	2	8	no	—
82	C₅×C₄⋊Q₈	—	2	4	no	—
83	C₅×C₄⋊Q₈	—	2	4	no	—
84	C₅×C₄⋊Q₈	C₂³	1	8	yes	—
85	C₅×C₄⋊Q₈	C₂³	1	8	yes	—
86	C₅×#125	—	2	8	no	—
87	C₅×#125	—	2	4	no	—
88	C₅×#125	C₂³	1	8	yes	—
89	C₅×#124	—	2	4	no	—
90	C₅×#124	C₂³	1	8	yes	—
91	C₅×#123	—	2	16	no	—
92	C₅×C₂²⋊Q₈	—	2	8	no	—
93	C₅×C₂²⋊Q₈	—	2	8	no	—
94	C₅×C₂²⋊Q₈	—	2	16	no	—
95	C₅×#117	—	2	2	no	—
96	C₅×#117	D₄	1	4	yes	—
97	C₅×#117	C₂³	1	4	yes	—
98	C₅×#117	C₂³	1	4	yes	—
99	C₂×C₅×C₄⋊C₄	—	2	1	no	—
100	C₂×C₅×C₄⋊C₄	—	2	2	no	—
101	C₂×C₅×C₄⋊C₄	—	2	2	no	—
102	C₂×C₅×C₄⋊C₄	—	2	2	no	—
103	C₂×C₅×C₄⋊C₄	—	2	2	no	—
104	C₂×C₅×C₄⋊C₄	—	2	2	no	—
105	C₂×C₅×C₄⋊C₄	—	2	2	no	—
106	C₂×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
107	C₂×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
108	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
109	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
110	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
111	C₂×C₅×C₄⋊C₄	C₂³	1	4	yes	—
112	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
113	C₂×C₅×C₂²⋊C₄	—	2	2	no	—
114	C₂×C₅×C₂²⋊C₄	—	2	2	no	—
115	C₂×C₅×C₂²⋊C₄	D₄	1	2	yes	—
116	C₂×C₄²×C₅	—	2	1	no	—
117	C₂×C₄²×C₅	C₂³	1	2	yes	—
118	C₅×#103	C₂³	1	8	yes	—
119	C₅×#103	C₂³	1	8	yes	—
120	C₅×#103	C₂³	1	4	yes	—
121	C₅×#103	C₂³	1	4	yes	—
122	C₅×#103	C₂³	1	8	yes	—
123	C₅×#103	C₂³	1	8	yes	—
124	C₅×#103	C₂³	1	8	yes	—
125	C₅×#102	C₂³	1	4	yes	—
126	C₅×#102	C₂³	1	4	yes	—
127	C₅×#102	C₂³	1	8	yes	—
128	C₅×#97	C₂³	1	8	yes	—
129	C₄×C₅×C₈	C₂³	1	8	yes	—
130	C₂×#544	C₂×C₅	1	1	yes	characteristic, complemented
131	C₂×#536	C₂×C₅	1	1	yes	characteristic
132	#3137	C₂×C₅	1	16	yes	direct product factor
133	C₂×#491	C₂×C₅	1	2	yes	complemented
134	C₂×#489	C₂×C₅	1	2	yes	complemented
135	C₂×#488	C₂×C₅	1	2	yes	complemented
136	C₂×#487	C₂×C₅	1	2	yes	complemented
137	C₂×#417	C₂×C₅	1	1	yes	characteristic
138	C₂×#419	C₂×C₅	1	1	yes	characteristic, complemented
139	C₂×#416	C₂×C₅	1	1	yes	characteristic
140	C₂²×#103	C₂×C₅	1	1	yes	characteristic, complemented
141	C₂×#405	C₂×C₅	1	1	yes	characteristic, complemented
142	C₂⁴×C₅	—	2	1	no	—
143	C₂⁴×C₅	C₂×D₄	1	1	yes	characteristic
144	C₅×#41	—	2	8	no	—
145	C₅×#41	—	2	8	no	—
146	C₅×#41	—	4	8	no	—
147	C₂×C₅×Q₈	—	2	4	no	—
148	C₂×C₅×Q₈	—	2	2	no	—
149	C₂×C₅×Q₈	—	2	1	no	—
150	C₂×C₅×Q₈	—	2	8	no	—
151	C₂×C₅×Q₈	—	2	4	no	—
152	C₂×C₅×Q₈	—	2	4	no	—
153	C₂×C₅×Q₈	—	2	8	no	—
154	C₂×C₅×Q₈	—	2	8	no	—
155	C₂×C₅×Q₈	—	2	2	no	—
156	C₂×C₅×Q₈	—	2	2	no	—
157	C₂×C₅×Q₈	—	4	4	no	—
158	C₂×C₅×Q₈	—	4	8	no	—
159	C₂×C₅×Q₈	—	8	4	no	—
160	C₂×C₅×Q₈	C₂⁴	1	4	yes	—
161	C₂×C₅×Q₈	C₂⁴	1	2	yes	—
162	C₂×C₅×D₄	—	2	4	no	—
163	C₂×C₅×D₄	—	2	1	no	—
164	C₂×C₅×D₄	—	2	2	no	—
165	C₂×C₅×D₄	—	2	2	no	—
166	C₂×C₅×D₄	—	4	4	no	—
167	C₂×C₅×D₄	C₂⁴	1	2	yes	—
168	C₂²×C₄×C₅	—	2	4	no	—
169	C₂²×C₄×C₅	—	2	1	no	—
170	C₂²×C₄×C₅	—	2	1	no	—
171	C₂²×C₄×C₅	—	2	2	no	—
172	C₂²×C₄×C₅	—	2	2	no	—
173	C₂²×C₄×C₅	—	2	1	no	—
174	C₂²×C₄×C₅	—	2	4	no	—
175	C₂²×C₄×C₅	—	2	4	no	—
176	C₂²×C₄×C₅	—	4	4	no	—
177	C₂²×C₄×C₅	—	4	4	no	—
178	C₂²×C₄×C₅	—	8	2	no	—
179	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
180	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
181	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
182	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
183	C₂²×C₄×C₅	#41	1	4	yes	—
184	C₂²×C₄×C₅	#41	1	4	yes	—
185	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
186	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
187	C₅×M₁₆	—	2	8	no	—
188	C₂×C₅×C₈	—	2	2	no	—
189	C₂×C₅×C₈	—	2	2	no	—
190	C₂×C₅×C₈	—	2	8	no	—
191	C₂×C₅×C₈	—	2	4	no	—
192	C₂×C₅×C₈	C₂⁴	1	2	yes	—
193	C₂×C₅×C₈	C₂⁴	1	2	yes	—
194	C₂×C₅×C₈	C₂⁴	1	4	yes	—
195	C₅×C₄⋊C₄	—	2	4	no	—
196	C₅×C₄⋊C₄	—	2	2	no	—
197	C₅×C₄⋊C₄	—	2	8	no	—
198	C₅×C₄⋊C₄	—	2	8	no	—
199	C₅×C₄⋊C₄	—	2	8	no	—
200	C₅×C₄⋊C₄	—	2	8	no	—
201	C₅×C₄⋊C₄	—	2	8	no	—
202	C₅×C₄⋊C₄	—	2	1	no	—
203	C₅×C₄⋊C₄	—	2	1	no	—
204	C₅×C₄⋊C₄	C₂×D₄	1	4	yes	—
205	C₅×C₄⋊C₄	C₂×D₄	1	4	yes	—
206	C₅×C₄⋊C₄	C₂⁴	1	4	yes	—
207	C₅×C₄⋊C₄	C₂⁴	1	2	yes	—
208	C₅×C₄⋊C₄	C₂⁴	1	2	yes	—
209	C₅×C₂²⋊C₄	—	2	4	no	—
210	C₅×C₂²⋊C₄	—	2	8	no	—
211	C₅×C₂²⋊C₄	—	2	8	no	—
212	C₅×C₂²⋊C₄	C₂×D₄	1	8	yes	—
213	C₄²×C₅	—	2	4	no	—
214	C₄²×C₅	C₂×D₄	1	4	yes	—
215	C₄²×C₅	C₂⁴	1	4	yes	—
216	C₂²×#41	C₂²×C₅	1	1	yes	characteristic
217	C₂³×Q₈	C₂²×C₅	1	1	yes	characteristic
218	C₂²×M₁₆	C₂²×C₅	1	1	yes	characteristic
219	C₂³×C₈	C₂²×C₅	1	1	yes	characteristic
220	#544	—	2	4	no	—
221	#544	C₂²×C₅	1	8	yes	complemented
222	#536	—	2	4	no	—
223	#536	C₂²×C₅	1	8	yes	—
224	C₂×C₄⋊Q₈	—	2	1	no	—
225	C₂×C₄⋊Q₈	C₂²×C₅	1	2	yes	—
226	C₂×C₄⋊Q₈	C₂²×C₅	1	2	yes	—
227	C₂×#125	—	2	1	no	—
228	C₂×#125	C₂²×C₅	1	2	yes	—
229	C₂×#124	C₂²×C₅	1	2	yes	—
230	C₂×#123	—	2	2	no	—
231	C₂×C₂²⋊Q₈	—	2	1	no	—
232	C₂×C₂²⋊Q₈	—	2	1	no	—
233	C₂×C₂²⋊Q₈	—	2	2	no	—
234	C₂×#117	C₂²×C₅	1	1	yes	characteristic
235	C₂×#117	C₂²×C₅	1	1	yes	characteristic
236	C₂²×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
237	#491	C₂²×C₅	1	16	yes	complemented
238	#489	C₂²×C₅	1	16	yes	complemented
239	#488	C₂²×C₅	1	16	yes	complemented
240	#487	C₂²×C₅	1	16	yes	complemented
241	#419	C₂²×C₅	1	8	yes	complemented
242	#417	C₂²×C₅	1	8	yes	—
243	#416	C₂²×C₅	1	8	yes	—
244	C₂×#103	C₂²×C₅	1	1	yes	characteristic
245	C₂×#103	C₂²×C₅	1	2	yes	—
246	C₂×#103	C₂²×C₅	1	2	yes	—
247	C₂×#103	C₂²×C₅	1	2	yes	—
248	C₂×#103	C₂²×C₅	1	2	yes	—
249	C₂×#103	C₂²×C₅	1	2	yes	—
250	C₂×#103	C₂²×C₅	1	1	yes	characteristic
251	C₂×#103	C₂²×C₅	1	8	yes	complemented
252	C₂×#102	C₂²×C₅	1	1	yes	characteristic
253	C₂×#102	C₂²×C₅	1	2	yes	—
254	C₂×#102	C₂²×C₅	1	1	yes	characteristic
255	#405	C₂²×C₅	1	8	yes	complemented
256	C₂×#97	C₂²×C₅	1	2	yes	—
257	C₂×C₄×C₈	C₂²×C₅	1	2	yes	—
258	C₂³×C₅	—	2	2	no	—
259	C₂³×C₅	—	2	2	no	—
260	C₂³×C₅	—	2	2	no	—
261	C₂³×C₅	—	4	2	no	—
262	C₂³×C₅	—	4	2	no	—
263	C₂³×C₅	—	4	2	no	—
264	C₂³×C₅	#124	1	4	yes	—
265	C₂³×C₅	C₂²×D₄	1	2	yes	—
266	C₂³×C₅	C₂²×D₄	1	1	yes	characteristic
267	C₅×Q₈	—	2	4	no	—
268	C₅×Q₈	—	2	4	no	—
269	C₅×Q₈	—	2	2	no	—
270	C₅×Q₈	—	2	2	no	—
271	C₅×Q₈	—	4	8	no	—
272	C₅×Q₈	—	4	4	no	—
273	C₅×Q₈	—	4	2	no	—
274	C₅×Q₈	—	8	8	no	—
275	C₅×D₄	—	2	2	no	—
276	C₅×D₄	—	2	2	no	—
277	C₅×D₄	—	4	8	no	—
278	C₅×D₄	—	4	2	no	—
279	C₂×C₄×C₅	—	2	4	no	—
280	C₂×C₄×C₅	—	2	4	no	—
281	C₂×C₄×C₅	—	2	2	no	—
282	C₂×C₄×C₅	—	2	2	no	—
283	C₂×C₄×C₅	—	2	4	no	—
284	C₂×C₄×C₅	—	2	4	no	—
285	C₂×C₄×C₅	—	2	2	no	—
286	C₂×C₄×C₅	—	4	2	no	—
287	C₂×C₄×C₅	—	4	8	no	—
288	C₂×C₄×C₅	—	4	4	no	—
289	C₂×C₄×C₅	—	4	4	no	—
290	C₂×C₄×C₅	—	4	2	no	—
291	C₂×C₄×C₅	—	4	2	no	—
292	C₂×C₄×C₅	—	4	8	no	—
293	C₂×C₄×C₅	—	8	4	no	—
294	C₂×C₄×C₅	#124	1	4	yes	—
295	C₂×C₄×C₅	#124	1	8	yes	—
296	C₂×C₄×C₅	C₂²×D₄	1	4	yes	—
297	C₂×C₄×C₅	C₂²×D₄	1	4	yes	—
298	C₂×C₄×C₅	C₂²×D₄	1	2	yes	—
299	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
300	C₂×C₄×C₅	C₂×#41	1	2	yes	—
301	C₂×C₄×C₅	C₂×#41	1	2	yes	—
302	C₂×C₄×C₅	C₂×#41	1	4	yes	—
303	C₂×C₄×C₅	C₂×#41	1	4	yes	—
304	C₂×C₄×C₅	C₂⁵	1	1	yes	characteristic
305	C₅×C₈	—	2	2	no	—
306	C₅×C₈	—	2	2	no	—
307	C₅×C₈	—	2	4	no	—
308	C₂×#41	—	2	2	no	—
309	C₂×#41	—	2	4	no	—
310	C₂×#41	—	2	4	no	—
311	C₂×#41	C₂³×C₅	1	4	yes	—
312	C₂²×Q₈	—	2	1	no	—
313	C₂²×Q₈	—	2	2	no	—
314	C₂²×Q₈	—	2	2	no	—
315	C₂²×Q₈	—	2	4	no	—
316	C₂²×Q₈	—	2	4	no	—
317	C₂²×Q₈	C₂³×C₅	1	2	yes	—
318	C₂²×Q₈	C₂³×C₅	1	1	yes	characteristic
319	C₂²×Q₈	C₂³×C₅	1	4	yes	—
320	C₂²×D₄	—	2	1	no	—
321	C₂²×D₄	C₂³×C₅	1	1	yes	characteristic
322	C₂³×C₄	—	2	1	no	—
323	C₂³×C₄	—	2	1	no	—
324	C₂³×C₄	—	2	1	no	—
325	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
326	C₂×M₁₆	—	2	4	no	—
327	C₂×M₁₆	C₂³×C₅	1	4	yes	—
328	C₂²×C₈	—	2	4	no	—
329	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
330	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
331	C₂²×C₈	C₂³×C₅	1	4	yes	—
332	C₂²×C₈	C₂³×C₅	1	2	yes	—
333	C₄⋊Q₈	—	2	8	no	—
334	C₄⋊Q₈	—	2	4	no	—
335	C₄⋊Q₈	—	2	4	no	—
336	C₄⋊Q₈	C₂³×C₅	1	8	yes	—
337	C₄⋊Q₈	C₂³×C₅	1	8	yes	—
338	#125	—	2	8	no	—
339	#125	—	2	4	no	—
340	#125	C₂³×C₅	1	8	yes	—
341	#124	—	2	4	no	—
342	#124	C₂³×C₅	1	8	yes	—
343	#123	—	2	16	no	—
344	C₂²⋊Q₈	—	2	8	no	—
345	C₂²⋊Q₈	—	2	8	no	—
346	C₂²⋊Q₈	—	2	16	no	—
347	#117	—	2	2	no	—
348	#117	C₅×D₄	1	4	yes	—
349	#117	C₂³×C₅	1	4	yes	—
350	#117	C₂³×C₅	1	4	yes	—
351	C₂×C₄⋊C₄	—	2	1	no	—
352	C₂×C₄⋊C₄	—	2	2	no	—
353	C₂×C₄⋊C₄	—	2	2	no	—
354	C₂×C₄⋊C₄	—	2	2	no	—
355	C₂×C₄⋊C₄	—	2	2	no	—
356	C₂×C₄⋊C₄	—	2	2	no	—
357	C₂×C₄⋊C₄	—	2	2	no	—
358	C₂×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
359	C₂×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
360	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
361	C₂×C₄⋊C₄	C₂³×C₅	1	4	yes	—
362	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
363	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
364	C₂×C₂²⋊C₄	—	2	1	no	—
365	C₂×C₂²⋊C₄	—	2	2	no	—
366	C₂×C₂²⋊C₄	—	2	2	no	—
367	C₂×C₂²⋊C₄	C₅×D₄	1	2	yes	—
368	C₂×C₄²	—	2	1	no	—
369	C₂×C₄²	C₂³×C₅	1	2	yes	—
370	#103	C₂³×C₅	1	8	yes	—
371	#103	C₂³×C₅	1	8	yes	—
372	#103	C₂³×C₅	1	4	yes	—
373	#103	C₂³×C₅	1	4	yes	—
374	#103	C₂³×C₅	1	8	yes	—
375	#103	C₂³×C₅	1	8	yes	—
376	#103	C₂³×C₅	1	8	yes	—
377	#102	C₂³×C₅	1	4	yes	—
378	#102	C₂³×C₅	1	4	yes	—
379	#102	C₂³×C₅	1	8	yes	—
380	#97	C₂³×C₅	1	8	yes	—
381	C₄×C₈	C₂³×C₅	1	8	yes	—
382	C₂²×C₅	—	2	8	no	—
383	C₂²×C₅	—	2	2	no	—
384	C₂²×C₅	—	2	2	no	—
385	C₂²×C₅	—	4	2	no	—
386	C₂²×C₅	—	4	2	no	—
387	C₂²×C₅	—	4	2	no	—
388	C₂²×C₅	—	8	4	no	—
389	C₂²×C₅	C₂×#124	1	4	yes	—
390	C₂²×C₅	C₂×#124	1	2	yes	—
391	C₂²×C₅	#577	1	2	yes	—
392	C₂²×C₅	#578	1	2	yes	—
393	C₂²×C₅	C₂³×D₄	1	1	yes	characteristic
394	C₄×C₅	—	2	4	no	—
395	C₄×C₅	—	2	4	no	—
396	C₄×C₅	—	4	2	no	—
397	C₄×C₅	—	4	4	no	—
398	C₄×C₅	—	4	4	no	—
399	C₄×C₅	—	4	2	no	—
400	C₄×C₅	—	4	2	no	—
401	C₄×C₅	C₂×#124	1	4	yes	—
402	C₄×C₅	C₂×#124	1	2	yes	—
403	C₄×C₅	C₂²×#41	1	1	yes	characteristic
404	C₄×C₅	C₂²×#41	1	1	yes	characteristic
405	C₂⁴	—	2	1	no	—
406	C₂⁴	C₂×C₅×D₄	1	1	yes	characteristic
407	#41	—	2	8	no	—
408	#41	—	2	8	no	—
409	#41	—	4	8	no	—
410	C₂×Q₈	—	2	4	no	—
411	C₂×Q₈	—	2	2	no	—
412	C₂×Q₈	—	2	1	no	—
413	C₂×Q₈	—	2	8	no	—
414	C₂×Q₈	—	2	4	no	—
415	C₂×Q₈	—	2	4	no	—
416	C₂×Q₈	—	2	8	no	—
417	C₂×Q₈	—	2	8	no	—
418	C₂×Q₈	—	2	2	no	—
419	C₂×Q₈	—	2	2	no	—
420	C₂×Q₈	—	4	4	no	—
421	C₂×Q₈	—	4	8	no	—
422	C₂×Q₈	—	8	4	no	—
423	C₂×Q₈	C₂⁴×C₅	1	4	yes	—
424	C₂×Q₈	C₂⁴×C₅	1	2	yes	—
425	C₂×D₄	—	2	4	no	—
426	C₂×D₄	—	2	1	no	—
427	C₂×D₄	—	2	2	no	—
428	C₂×D₄	—	2	2	no	—
429	C₂×D₄	—	4	4	no	—
430	C₂×D₄	C₂⁴×C₅	1	2	yes	—
431	C₂²×C₄	—	2	1	no	—
432	C₂²×C₄	—	2	1	no	—
433	C₂²×C₄	—	2	2	no	—
434	C₂²×C₄	—	2	2	no	—
435	C₂²×C₄	—	2	1	no	—
436	C₂²×C₄	—	2	4	no	—
437	C₂²×C₄	—	2	4	no	—
438	C₂²×C₄	—	2	4	no	—
439	C₂²×C₄	—	4	4	no	—
440	C₂²×C₄	—	4	4	no	—
441	C₂²×C₄	—	8	2	no	—
442	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
443	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
444	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
445	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
446	C₂²×C₄	C₅×#41	1	4	yes	—
447	C₂²×C₄	C₅×#41	1	4	yes	—
448	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
449	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
450	M₁₆	—	2	8	no	—
451	C₂×C₈	—	2	2	no	—
452	C₂×C₈	—	2	2	no	—
453	C₂×C₈	—	2	8	no	—
454	C₂×C₈	—	2	4	no	—
455	C₂×C₈	C₂⁴×C₅	1	2	yes	—
456	C₂×C₈	C₂⁴×C₅	1	4	yes	—
457	C₂×C₈	C₂⁴×C₅	1	2	yes	—
458	C₄⋊C₄	—	2	4	no	—
459	C₄⋊C₄	—	2	2	no	—
460	C₄⋊C₄	—	2	8	no	—
461	C₄⋊C₄	—	2	8	no	—
462	C₄⋊C₄	—	2	8	no	—
463	C₄⋊C₄	—	2	8	no	—
464	C₄⋊C₄	—	2	8	no	—
465	C₄⋊C₄	—	2	1	no	—
466	C₄⋊C₄	—	2	1	no	—
467	C₄⋊C₄	C₂×C₅×D₄	1	4	yes	—
468	C₄⋊C₄	C₂×C₅×D₄	1	4	yes	—
469	C₄⋊C₄	C₂⁴×C₅	1	4	yes	—
470	C₄⋊C₄	C₂⁴×C₅	1	2	yes	—
471	C₄⋊C₄	C₂⁴×C₅	1	2	yes	—
472	C₂²⋊C₄	—	2	4	no	—
473	C₂²⋊C₄	—	2	8	no	—
474	C₂²⋊C₄	—	2	8	no	—
475	C₂²⋊C₄	C₂×C₅×D₄	1	8	yes	—
476	C₄²	—	2	4	no	—
477	C₄²	C₂×C₅×D₄	1	4	yes	—
478	C₄²	C₂⁴×C₅	1	4	yes	—
479	C₂×C₅	—	2	4	no	—
480	C₂×C₅	—	8	2	no	—
481	C₂×C₅	#3137	1	4	yes	direct product factor
482	C₂×C₅	C₂²×#124	1	1	yes	characteristic
483	C₂×C₅	C₂×#577	1	1	yes	characteristic
484	C₂×C₅	C₂×#578	1	1	yes	characteristic
485	C₂³	—	2	2	no	—
486	C₂³	—	2	2	no	—
487	C₂³	—	2	2	no	—
488	C₂³	—	4	2	no	—
489	C₂³	—	4	2	no	—
490	C₂³	—	4	2	no	—
491	C₂³	C₅×#124	1	4	yes	—
492	C₂³	C₂²×C₅×D₄	1	2	yes	—
493	C₂³	C₂²×C₅×D₄	1	1	yes	characteristic
494	Q₈	—	2	4	no	—
495	Q₈	—	2	4	no	—
496	Q₈	—	2	2	no	—
497	Q₈	—	2	2	no	—
498	Q₈	—	4	8	no	—
499	Q₈	—	4	4	no	—
500	Q₈	—	4	2	no	—
501	Q₈	—	8	8	no	—
502	D₄	—	2	2	no	—
503	D₄	—	2	2	no	—
504	D₄	—	4	8	no	—
505	D₄	—	4	2	no	—
506	C₂×C₄	—	2	4	no	—
507	C₂×C₄	—	2	4	no	—
508	C₂×C₄	—	2	2	no	—
509	C₂×C₄	—	2	2	no	—
510	C₂×C₄	—	2	4	no	—
511	C₂×C₄	—	2	4	no	—
512	C₂×C₄	—	2	2	no	—
513	C₂×C₄	—	4	2	no	—
514	C₂×C₄	—	4	8	no	—
515	C₂×C₄	—	4	4	no	—
516	C₂×C₄	—	4	4	no	—
517	C₂×C₄	—	4	2	no	—
518	C₂×C₄	—	4	2	no	—
519	C₂×C₄	—	4	8	no	—
520	C₂×C₄	—	8	4	no	—
521	C₂×C₄	C₅×#124	1	4	yes	—
522	C₂×C₄	C₅×#124	1	8	yes	—
523	C₂×C₄	C₂²×C₅×D₄	1	4	yes	—
524	C₂×C₄	C₂²×C₅×D₄	1	4	yes	—
525	C₂×C₄	C₂²×C₅×D₄	1	2	yes	—
526	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
527	C₂×C₄	C₂×C₅×#41	1	2	yes	—
528	C₂×C₄	C₂×C₅×#41	1	2	yes	—
529	C₂×C₄	C₂×C₅×#41	1	4	yes	—
530	C₂×C₄	C₂×C₅×#41	1	4	yes	—
531	C₂×C₄	C₂⁵×C₅	1	1	yes	characteristic
532	C₈	—	2	2	no	—
533	C₈	—	2	2	no	—
534	C₈	—	2	4	no	—
535	C₅	C₂×#3137	1	1	yes	characteristic, direct product factor, Sylow
536	C₂²	—	2	8	no	—
537	C₂²	—	2	2	no	—
538	C₂²	—	2	2	no	—
539	C₂²	—	4	2	no	—
540	C₂²	—	4	2	no	—
541	C₂²	—	4	2	no	—
542	C₂²	—	8	4	no	—
543	C₂²	C₂×C₅×#124	1	4	yes	—
544	C₂²	C₂×C₅×#124	1	2	yes	—
545	C₂²	C₅×#577	1	2	yes	—
546	C₂²	C₅×#578	1	2	yes	—
547	C₂²	C₂³×C₅×D₄	1	1	yes	characteristic
548	C₄	—	2	4	no	—
549	C₄	—	2	4	no	—
550	C₄	—	4	2	no	—
551	C₄	—	4	4	no	—
552	C₄	—	4	4	no	—
553	C₄	—	4	2	no	—
554	C₄	—	4	2	no	—
555	C₄	C₂×C₅×#124	1	4	yes	—
556	C₄	C₂×C₅×#124	1	2	yes	—
557	C₄	C₂²×C₅×#41	1	1	yes	characteristic
558	C₄	C₂²×C₅×#41	1	1	yes	characteristic
559	C₂	—	2	4	no	—
560	C₂	—	8	2	no	—
561	C₂	C₅×#3137	1	4	yes	direct product factor
562	C₂	C₂²×C₅×#124	1	1	yes	characteristic
563	C₂	C₂×C₅×#577	1	1	yes	characteristic
564	C₂	C₂×C₅×#578	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₅	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₅
prime radical	C₂²×C₅×#41	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₅ ◁ C₂×C₅×#117 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₅×#544	C₂	semidirect
3. C₅×#3137	C₂	direct (N × H)
4. C₂×C₅×#491	C₂	semidirect
5. C₂×C₅×#489	C₂	semidirect
6. C₂×C₅×#488	C₂	semidirect
7. C₂×C₅×#487	C₂	semidirect
9. C₂×C₅×#419	C₂	semidirect
11. C₂²×C₅×#103	C₂	semidirect
12. C₂×C₅×#405	C₂	semidirect
18. C₅×#544	C₂²	semidirect
34. C₅×#491	C₂²	semidirect
35. C₅×#489	C₂²	semidirect
36. C₅×#488	C₂²	semidirect
37. C₅×#487	C₂²	semidirect
38. C₅×#419	C₂²	semidirect
48. C₂×C₅×#103	C₂²	semidirect
52. C₅×#405	C₂²	semidirect
55. C₂×#3137	C₅	direct (N × H)
130. C₂×#544	C₂×C₅	semidirect
132. #3137	C₂×C₅	direct (N × H)
133. C₂×#491	C₂×C₅	semidirect
134. C₂×#489	C₂×C₅	semidirect
135. C₂×#488	C₂×C₅	semidirect
136. C₂×#487	C₂×C₅	semidirect
138. C₂×#419	C₂×C₅	semidirect
140. C₂²×#103	C₂×C₅	semidirect
141. C₂×#405	C₂×C₅	semidirect
221. #544	C₂²×C₅	semidirect
237. #491	C₂²×C₅	semidirect
238. #489	C₂²×C₅	semidirect
239. #488	C₂²×C₅	semidirect
240. #487	C₂²×C₅	semidirect
241. #419	C₂²×C₅	semidirect
251. C₂×#103	C₂²×C₅	semidirect
255. #405	C₂²×C₅	semidirect
481. C₂×C₅	#3137	direct (N × H)
535. C₅	C₂×#3137	direct (N × H)
561. C₂	C₅×#3137	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×C₅×#544	2
C₂×C₅×#536	2
C₅×#3137	2
C₂×C₅×#491	2
C₂×C₅×#489	2
C₂×C₅×#488	2
C₂×C₅×#487	2
C₂×C₅×#417	2
C₂×C₅×#419	2
C₂×C₅×#416	2
C₂²×C₅×#103	2
C₂×C₅×#405	2
C₂×#3137	5

Subgroups — C2×C5×#3137 #11983331

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#3137 #11983331