Subgroups — C₂×C₅×#3522 #11985506

Order 1280.

7758 conjugacy classes of subgroups.

The subgroup lattice has 516 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#3522	C₂	1	32	yes	maximal, direct product factor
2	C₂×C₅×#559	C₂	1	3	yes	maximal, complemented
3	C₂×C₅×Q₈²	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₅×#554	C₂	1	3	yes	maximal, complemented
5	C₂×C₅×#550	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₅×#548	C₂	1	2	yes	maximal, complemented
7	C₂×C₅×#547	C₂	1	6	yes	maximal, complemented
8	C₂×C₅×#542	C₂	1	6	yes	maximal, complemented
9	C₂×C₅×#532	C₂	1	3	yes	maximal, complemented
10	C₂×C₅×#529	C₂	1	3	yes	maximal, complemented
11	C₂×C₅×#520	C₂	1	2	yes	maximal, complemented
12	C₂²×C₄×C₅×Q₈	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂²×C₅×#41	C₂²	1	2	yes	—
14	C₂²×C₅×#41	C₂²	1	6	yes	—
15	C₂³×C₅×Q₈	C₂²	1	1	yes	characteristic
16	C₅×#559	C₂²	1	48	yes	complemented
17	C₅×Q₈²	C₂²	1	16	yes	complemented
18	C₅×#554	C₂²	1	48	yes	complemented
19	C₅×#550	C₂²	1	16	yes	complemented
20	C₅×#548	C₂²	1	32	yes	complemented
21	C₅×#547	C₂²	1	96	yes	complemented
22	C₅×#542	C₂²	1	96	yes	complemented
23	C₅×#532	C₂²	1	48	yes	complemented
24	C₂×C₅×C₄⋊Q₈	C₂²	1	3	yes	—
25	C₂×C₅×C₄⋊Q₈	C₂²	1	6	yes	—
26	C₂×C₅×#127	C₂²	1	3	yes	—
27	C₅×#529	C₂²	1	48	yes	complemented
28	C₂×C₅×#126	C₂²	1	6	yes	—
29	C₂×C₅×#125	C₂²	1	3	yes	—
30	C₂×C₅×#124	C₂²	1	3	yes	—
31	C₂×C₅×#124	C₂²	1	6	yes	—
32	C₂×C₅×#124	C₂²	1	6	yes	—
33	C₂×C₅×#123	C₂²	1	6	yes	—
34	C₂×C₅×#123	C₂²	1	12	yes	—
35	C₂×C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
36	C₂×C₅×C₂²⋊Q₈	C₂²	1	12	yes	—
37	C₂×C₅×C₂²⋊Q₈	C₂²	1	6	yes	—
38	C₂×C₅×#121	C₂²	1	3	yes	—
39	C₂×C₅×#121	C₂²	1	6	yes	—
40	C₂×C₅×#121	C₂²	1	6	yes	—
41	C₅×#520	C₂²	1	32	yes	complemented
42	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
43	C₂×C₄×C₅×Q₈	C₂²	1	3	yes	—
44	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
45	C₂×C₄×C₅×Q₈	C₂²	1	3	yes	—
46	C₂×C₄×C₅×Q₈	C₂²	1	2	yes	—
47	C₂×C₄×C₅×Q₈	C₂²	1	3	yes	—
48	C₂×C₄×C₅×Q₈	C₂²	1	16	yes	complemented
49	C₂×C₄×C₅×D₄	C₂²	1	6	yes	—
50	C₂×C₄×C₅×D₄	C₂²	1	6	yes	—
51	C₂×C₄×C₅×D₄	C₂²	1	6	yes	—
52	C₂×C₄×C₅×D₄	C₂²	1	3	yes	—
53	C₂×C₄×C₅×D₄	C₂²	1	6	yes	—
54	C₂×C₅×#117	C₂²	1	6	yes	—
55	C₂²×C₅×C₄⋊C₄	C₂²	1	3	yes	—
56	C₂²×C₅×C₄⋊C₄	C₂²	1	6	yes	—
57	C₂²×C₄²×C₅	C₂²	1	3	yes	—
58	C₂×#3522	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
59	C₂×C₅×#41	—	2	16	no	—
60	C₂×C₅×#41	—	4	24	no	—
61	C₂×C₅×#41	C₂³	1	16	yes	—
62	C₂×C₅×#41	C₂³	1	48	yes	—
63	C₂²×C₅×Q₈	—	2	8	no	—
64	C₂²×C₅×Q₈	C₂³	1	1	yes	characteristic
65	C₂²×C₅×Q₈	C₂³	1	3	yes	—
66	C₂²×C₅×Q₈	C₂³	1	8	yes	—
67	C₂²×C₅×Q₈	C₂³	1	6	yes	—
68	C₂²×C₅×Q₈	C₂³	1	1	yes	characteristic
69	C₂²×C₅×D₄	C₂³	1	3	yes	—
70	C₂²×C₅×D₄	C₂³	1	6	yes	—
71	C₂²×C₅×D₄	C₂³	1	6	yes	—
72	C₂²×C₅×D₄	C₂³	1	6	yes	—
73	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
74	C₂³×C₄×C₅	C₂³	1	3	yes	—
75	C₂³×C₄×C₅	C₂³	1	3	yes	—
76	C₂³×C₄×C₅	C₂³	1	6	yes	—
77	C₂³×C₄×C₅	C₂³	1	12	yes	—
78	C₅×C₄⋊Q₈	C₂³	1	24	yes	—
79	C₅×C₄⋊Q₈	C₂³	1	48	yes	—
80	C₅×#127	C₂³	1	24	yes	—
81	C₅×#126	C₂³	1	48	yes	—
82	C₅×#125	C₂³	1	24	yes	—
83	C₅×#124	C₂³	1	24	yes	—
84	C₅×#124	C₂³	1	48	yes	—
85	C₅×#124	C₂³	1	48	yes	—
86	C₅×#123	C₂³	1	48	yes	—
87	C₅×#123	C₂³	1	96	yes	—
88	C₅×C₂²⋊Q₈	C₂³	1	8	yes	—
89	C₅×C₂²⋊Q₈	C₂³	1	96	yes	—
90	C₅×C₂²⋊Q₈	C₂³	1	48	yes	—
91	C₅×#121	C₂³	1	24	yes	—
92	C₅×#121	C₂³	1	48	yes	—
93	C₅×#121	C₂³	1	48	yes	—
94	C₄×C₅×Q₈	C₂³	1	8	yes	—
95	C₄×C₅×Q₈	C₂³	1	24	yes	—
96	C₄×C₅×Q₈	C₂³	1	8	yes	—
97	C₄×C₅×Q₈	C₂³	1	24	yes	—
98	C₄×C₅×Q₈	C₂³	1	16	yes	—
99	C₄×C₅×Q₈	C₂³	1	24	yes	—
100	C₄×C₅×D₄	C₂³	1	48	yes	—
101	C₄×C₅×D₄	C₂³	1	48	yes	—
102	C₄×C₅×D₄	C₂³	1	48	yes	—
103	C₄×C₅×D₄	C₂³	1	24	yes	—
104	C₄×C₅×D₄	C₂³	1	48	yes	—
105	C₅×#117	C₂³	1	48	yes	—
106	C₂×C₅×C₄⋊C₄	C₂³	1	3	yes	—
107	C₂×C₅×C₄⋊C₄	C₂³	1	6	yes	—
108	C₂×C₅×C₄⋊C₄	C₂³	1	6	yes	—
109	C₂×C₅×C₄⋊C₄	C₂³	1	3	yes	—
110	C₂×C₅×C₄⋊C₄	C₂³	1	6	yes	—
111	C₂×C₅×C₄⋊C₄	C₂³	1	24	yes	—
112	C₂×C₅×C₄⋊C₄	C₂³	1	48	yes	—
113	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
114	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
115	C₂×C₅×C₄⋊C₄	C₂³	1	3	yes	—
116	C₂×C₅×C₄⋊C₄	C₂³	1	6	yes	—
117	C₂×C₅×C₄⋊C₄	C₂³	1	6	yes	—
118	C₂×C₅×C₂²⋊C₄	C₂³	1	6	yes	—
119	C₂×C₅×C₂²⋊C₄	C₂³	1	6	yes	—
120	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
121	C₂×C₅×C₂²⋊C₄	C₂³	1	6	yes	—
122	C₂×C₅×C₂²⋊C₄	C₂³	1	12	yes	—
123	C₂×C₅×C₂²⋊C₄	C₂³	1	6	yes	—
124	C₂×C₄²×C₅	C₂³	1	3	yes	—
125	C₂×C₄²×C₅	C₂³	1	3	yes	—
126	C₂×C₄²×C₅	C₂³	1	3	yes	—
127	C₂×C₄²×C₅	C₂³	1	3	yes	—
128	C₂×C₄²×C₅	C₂³	1	24	yes	—
129	C₂×C₄²×C₅	C₂³	1	6	yes	—
130	#3522	C₂×C₅	1	32	yes	direct product factor
131	C₂×#559	C₂×C₅	1	3	yes	complemented
132	C₂×Q₈²	C₂×C₅	1	1	yes	characteristic, complemented
133	C₂×#554	C₂×C₅	1	3	yes	complemented
134	C₂×#550	C₂×C₅	1	1	yes	characteristic, complemented
135	C₂×#548	C₂×C₅	1	2	yes	complemented
136	C₂×#547	C₂×C₅	1	6	yes	complemented
137	C₂×#542	C₂×C₅	1	6	yes	complemented
138	C₂×#532	C₂×C₅	1	3	yes	complemented
139	C₂×#529	C₂×C₅	1	3	yes	complemented
140	C₂×#520	C₂×C₅	1	2	yes	complemented
141	C₂²×C₄×Q₈	C₂×C₅	1	1	yes	characteristic, complemented
142	C₂⁴×C₅	C₂⁴	1	6	yes	—
143	C₂⁴×C₅	C₂⁴	1	1	yes	characteristic
144	C₅×#41	—	2	64	no	—
145	C₅×#41	—	4	96	no	—
146	C₂×C₅×Q₈	—	2	32	no	—
147	C₂×C₅×Q₈	—	2	12	no	—
148	C₂×C₅×Q₈	—	2	4	no	—
149	C₂×C₅×Q₈	—	4	12	no	—
150	C₂×C₅×Q₈	#41	1	8	yes	complemented
151	C₂×C₅×Q₈	C₂⁴	1	4	yes	—
152	C₂×C₅×Q₈	C₂⁴	1	12	yes	—
153	C₂×C₅×Q₈	C₂⁴	1	24	yes	—
154	C₂×C₅×Q₈	C₂⁴	1	4	yes	—
155	C₂×C₅×D₄	—	2	24	no	—
156	C₂×C₅×D₄	—	2	24	no	—
157	C₂×C₅×D₄	—	2	12	no	—
158	C₂×C₅×D₄	—	4	12	no	—
159	C₂×C₅×D₄	C₂⁴	1	12	yes	—
160	C₂×C₅×D₄	C₂⁴	1	24	yes	—
161	C₂×C₅×D₄	C₂⁴	1	24	yes	—
162	C₂×C₅×D₄	C₂⁴	1	24	yes	—
163	C₂²×C₄×C₅	—	2	12	no	—
164	C₂²×C₄×C₅	—	2	12	no	—
165	C₂²×C₄×C₅	—	2	24	no	—
166	C₂²×C₄×C₅	—	2	4	no	—
167	C₂²×C₄×C₅	—	4	24	no	—
168	C₂²×C₄×C₅	C₂⁴	1	4	yes	—
169	C₂²×C₄×C₅	C₂⁴	1	12	yes	—
170	C₂²×C₄×C₅	C₂⁴	1	12	yes	—
171	C₂²×C₄×C₅	C₂⁴	1	24	yes	—
172	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
173	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
174	C₂²×C₄×C₅	C₂⁴	1	3	yes	—
175	C₂²×C₄×C₅	C₂⁴	1	3	yes	—
176	C₂²×C₄×C₅	C₂⁴	1	3	yes	—
177	C₂²×C₄×C₅	C₂⁴	1	6	yes	—
178	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
179	C₂²×C₄×C₅	C₂⁴	1	48	yes	—
180	C₂²×C₄×C₅	C₂⁴	1	3	yes	—
181	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
182	C₅×C₄⋊C₄	C₂⁴	1	12	yes	—
183	C₅×C₄⋊C₄	C₂⁴	1	24	yes	—
184	C₅×C₄⋊C₄	C₂⁴	1	24	yes	—
185	C₅×C₄⋊C₄	C₂⁴	1	12	yes	—
186	C₅×C₄⋊C₄	C₂⁴	1	24	yes	—
187	C₅×C₄⋊C₄	C₂⁴	1	8	yes	—
188	C₅×C₄⋊C₄	C₂⁴	1	4	yes	—
189	C₅×C₄⋊C₄	C₂⁴	1	12	yes	—
190	C₅×C₄⋊C₄	C₂⁴	1	24	yes	—
191	C₅×C₄⋊C₄	C₂⁴	1	24	yes	—
192	C₅×C₂²⋊C₄	C₂⁴	1	24	yes	—
193	C₅×C₂²⋊C₄	C₂⁴	1	24	yes	—
194	C₅×C₂²⋊C₄	C₂⁴	1	8	yes	—
195	C₅×C₂²⋊C₄	C₂⁴	1	24	yes	—
196	C₅×C₂²⋊C₄	C₂⁴	1	48	yes	—
197	C₅×C₂²⋊C₄	C₂⁴	1	24	yes	—
198	C₄²×C₅	C₂⁴	1	12	yes	—
199	C₄²×C₅	C₂⁴	1	12	yes	—
200	C₄²×C₅	C₂⁴	1	12	yes	—
201	C₄²×C₅	C₂⁴	1	12	yes	—
202	C₄²×C₅	C₂⁴	1	24	yes	—
203	C₂²×#41	C₂²×C₅	1	2	yes	—
204	C₂²×#41	C₂²×C₅	1	6	yes	—
205	C₂³×Q₈	C₂²×C₅	1	1	yes	characteristic
206	#559	C₂²×C₅	1	48	yes	complemented
207	Q₈²	C₂²×C₅	1	16	yes	complemented
208	#554	C₂²×C₅	1	48	yes	complemented
209	#550	C₂²×C₅	1	16	yes	complemented
210	#548	C₂²×C₅	1	32	yes	complemented
211	#547	C₂²×C₅	1	96	yes	complemented
212	#542	C₂²×C₅	1	96	yes	complemented
213	#532	C₂²×C₅	1	48	yes	complemented
214	C₂×C₄⋊Q₈	C₂²×C₅	1	3	yes	—
215	C₂×C₄⋊Q₈	C₂²×C₅	1	6	yes	—
216	C₂×#127	C₂²×C₅	1	3	yes	—
217	#529	C₂²×C₅	1	48	yes	complemented
218	C₂×#126	C₂²×C₅	1	6	yes	—
219	C₂×#125	C₂²×C₅	1	3	yes	—
220	C₂×#124	C₂²×C₅	1	3	yes	—
221	C₂×#124	C₂²×C₅	1	6	yes	—
222	C₂×#124	C₂²×C₅	1	6	yes	—
223	C₂×#123	C₂²×C₅	1	6	yes	—
224	C₂×#123	C₂²×C₅	1	12	yes	—
225	C₂×C₂²⋊Q₈	C₂²×C₅	1	1	yes	characteristic
226	C₂×C₂²⋊Q₈	C₂²×C₅	1	12	yes	—
227	C₂×C₂²⋊Q₈	C₂²×C₅	1	6	yes	—
228	C₂×#121	C₂²×C₅	1	3	yes	—
229	C₂×#121	C₂²×C₅	1	6	yes	—
230	C₂×#121	C₂²×C₅	1	6	yes	—
231	#520	C₂²×C₅	1	32	yes	complemented
232	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
233	C₂×C₄×Q₈	C₂²×C₅	1	3	yes	—
234	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
235	C₂×C₄×Q₈	C₂²×C₅	1	3	yes	—
236	C₂×C₄×Q₈	C₂²×C₅	1	2	yes	—
237	C₂×C₄×Q₈	C₂²×C₅	1	3	yes	—
238	C₂×C₄×Q₈	C₂²×C₅	1	16	yes	complemented
239	C₂×C₄×D₄	C₂²×C₅	1	6	yes	—
240	C₂×C₄×D₄	C₂²×C₅	1	6	yes	—
241	C₂×C₄×D₄	C₂²×C₅	1	6	yes	—
242	C₂×C₄×D₄	C₂²×C₅	1	3	yes	—
243	C₂×C₄×D₄	C₂²×C₅	1	6	yes	—
244	C₂×#117	C₂²×C₅	1	6	yes	—
245	C₂²×C₄⋊C₄	C₂²×C₅	1	3	yes	—
246	C₂²×C₄⋊C₄	C₂²×C₅	1	6	yes	—
247	C₂²×C₄²	C₂²×C₅	1	3	yes	—
248	C₂³×C₅	—	2	2	no	—
249	C₂³×C₅	—	2	2	no	—
250	C₂³×C₅	—	2	12	no	—
251	C₂³×C₅	—	2	12	no	—
252	C₂³×C₅	—	2	12	no	—
253	C₂³×C₅	H(5,𝔽₂)	1	4	yes	—
254	C₂³×C₅	C₂⁵	1	12	yes	—
255	C₂³×C₅	C₂⁵	1	2	yes	—
256	C₂³×C₅	C₂⁵	1	1	yes	characteristic
257	C₅×Q₈	—	2	24	no	—
258	C₅×Q₈	—	2	8	no	—
259	C₅×Q₈	—	4	24	no	—
260	C₅×Q₈	C₂×#41	1	16	yes	complemented
261	C₅×D₄	—	2	48	no	—
262	C₅×D₄	—	2	48	no	—
263	C₅×D₄	—	2	24	no	—
264	C₅×D₄	—	4	24	no	—
265	C₂×C₄×C₅	—	2	4	no	—
266	C₂×C₄×C₅	—	2	6	no	—
267	C₂×C₄×C₅	—	2	6	no	—
268	C₂×C₄×C₅	—	2	6	no	—
269	C₂×C₄×C₅	—	2	24	no	—
270	C₂×C₄×C₅	—	2	12	no	—
271	C₂×C₄×C₅	—	2	2	no	—
272	C₂×C₄×C₅	—	2	4	no	—
273	C₂×C₄×C₅	—	2	24	no	—
274	C₂×C₄×C₅	—	2	48	no	—
275	C₂×C₄×C₅	—	2	8	no	—
276	C₂×C₄×C₅	—	4	48	no	—
277	C₂×C₄×C₅	C₂×#41	1	12	yes	—
278	C₂×C₄×C₅	2₋¹⁺⁴	1	4	yes	—
279	C₂×C₄×C₅	C₂⁵	1	2	yes	—
280	C₂×C₄×C₅	C₂⁵	1	4	yes	—
281	C₂×C₄×C₅	C₂⁵	1	6	yes	—
282	C₂×C₄×C₅	C₂⁵	1	6	yes	—
283	C₂×C₄×C₅	C₂⁵	1	6	yes	—
284	C₂×C₄×C₅	C₂⁵	1	12	yes	—
285	C₂×C₄×C₅	C₂⁵	1	4	yes	—
286	C₂×C₄×C₅	C₂⁵	1	6	yes	—
287	C₂×C₄×C₅	C₂⁵	1	2	yes	—
288	C₂×#41	—	2	16	no	—
289	C₂×#41	—	4	24	no	—
290	C₂×#41	C₂³×C₅	1	16	yes	—
291	C₂×#41	C₂³×C₅	1	48	yes	—
292	C₂²×Q₈	—	2	8	no	—
293	C₂²×Q₈	C₂³×C₅	1	1	yes	characteristic
294	C₂²×Q₈	C₂³×C₅	1	3	yes	—
295	C₂²×Q₈	C₂³×C₅	1	8	yes	—
296	C₂²×Q₈	C₂³×C₅	1	6	yes	—
297	C₂²×Q₈	C₂³×C₅	1	1	yes	characteristic
298	C₂²×D₄	C₂³×C₅	1	3	yes	—
299	C₂²×D₄	C₂³×C₅	1	6	yes	—
300	C₂²×D₄	C₂³×C₅	1	6	yes	—
301	C₂²×D₄	C₂³×C₅	1	6	yes	—
302	C₂³×C₄	C₂³×C₅	1	3	yes	—
303	C₂³×C₄	C₂³×C₅	1	6	yes	—
304	C₂³×C₄	C₂³×C₅	1	3	yes	—
305	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
306	C₂³×C₄	C₂³×C₅	1	12	yes	—
307	C₄⋊Q₈	C₂³×C₅	1	24	yes	—
308	C₄⋊Q₈	C₂³×C₅	1	48	yes	—
309	#127	C₂³×C₅	1	24	yes	—
310	#126	C₂³×C₅	1	48	yes	—
311	#125	C₂³×C₅	1	24	yes	—
312	#124	C₂³×C₅	1	24	yes	—
313	#124	C₂³×C₅	1	48	yes	—
314	#124	C₂³×C₅	1	48	yes	—
315	#123	C₂³×C₅	1	48	yes	—
316	#123	C₂³×C₅	1	96	yes	—
317	C₂²⋊Q₈	C₂³×C₅	1	8	yes	—
318	C₂²⋊Q₈	C₂³×C₅	1	96	yes	—
319	C₂²⋊Q₈	C₂³×C₅	1	48	yes	—
320	#121	C₂³×C₅	1	24	yes	—
321	#121	C₂³×C₅	1	48	yes	—
322	#121	C₂³×C₅	1	48	yes	—
323	C₄×Q₈	C₂³×C₅	1	8	yes	—
324	C₄×Q₈	C₂³×C₅	1	24	yes	—
325	C₄×Q₈	C₂³×C₅	1	8	yes	—
326	C₄×Q₈	C₂³×C₅	1	24	yes	—
327	C₄×Q₈	C₂³×C₅	1	16	yes	—
328	C₄×Q₈	C₂³×C₅	1	24	yes	—
329	C₄×D₄	C₂³×C₅	1	48	yes	—
330	C₄×D₄	C₂³×C₅	1	48	yes	—
331	C₄×D₄	C₂³×C₅	1	48	yes	—
332	C₄×D₄	C₂³×C₅	1	24	yes	—
333	C₄×D₄	C₂³×C₅	1	48	yes	—
334	#117	C₂³×C₅	1	48	yes	—
335	C₂×C₄⋊C₄	C₂³×C₅	1	3	yes	—
336	C₂×C₄⋊C₄	C₂³×C₅	1	6	yes	—
337	C₂×C₄⋊C₄	C₂³×C₅	1	6	yes	—
338	C₂×C₄⋊C₄	C₂³×C₅	1	3	yes	—
339	C₂×C₄⋊C₄	C₂³×C₅	1	6	yes	—
340	C₂×C₄⋊C₄	C₂³×C₅	1	24	yes	—
341	C₂×C₄⋊C₄	C₂³×C₅	1	48	yes	—
342	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
343	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
344	C₂×C₄⋊C₄	C₂³×C₅	1	3	yes	—
345	C₂×C₄⋊C₄	C₂³×C₅	1	6	yes	—
346	C₂×C₄⋊C₄	C₂³×C₅	1	6	yes	—
347	C₂×C₂²⋊C₄	C₂³×C₅	1	6	yes	—
348	C₂×C₂²⋊C₄	C₂³×C₅	1	6	yes	—
349	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
350	C₂×C₂²⋊C₄	C₂³×C₅	1	6	yes	—
351	C₂×C₂²⋊C₄	C₂³×C₅	1	12	yes	—
352	C₂×C₂²⋊C₄	C₂³×C₅	1	6	yes	—
353	C₂×C₄²	C₂³×C₅	1	3	yes	—
354	C₂×C₄²	C₂³×C₅	1	6	yes	—
355	C₂×C₄²	C₂³×C₅	1	3	yes	—
356	C₂×C₄²	C₂³×C₅	1	3	yes	—
357	C₂×C₄²	C₂³×C₅	1	3	yes	—
358	C₂×C₄²	C₂³×C₅	1	24	yes	—
359	C₂²×C₅	—	2	2	no	—
360	C₂²×C₅	—	2	2	no	—
361	C₂²×C₅	—	2	8	no	—
362	C₂²×C₅	—	2	12	no	—
363	C₂²×C₅	—	2	12	no	—
364	C₂²×C₅	—	2	12	no	—
365	C₂²×C₅	—	4	24	no	—
366	C₂²×C₅	C₂²×#41	1	2	yes	—
367	C₂²×C₅	C₂×H(5,𝔽₂)	1	4	yes	—
368	C₂²×C₅	C₂×H(5,𝔽₂)	1	2	yes	—
369	C₂²×C₅	C₂×2₋¹⁺⁴	1	2	yes	—
370	C₂²×C₅	C₂⁶	1	1	yes	characteristic
371	C₄×C₅	—	2	4	no	—
372	C₄×C₅	—	2	6	no	—
373	C₄×C₅	—	2	6	no	—
374	C₄×C₅	—	2	6	no	—
375	C₄×C₅	—	2	12	no	—
376	C₄×C₅	—	2	2	no	—
377	C₄×C₅	—	2	4	no	—
378	C₄×C₅	C₂²×#41	1	12	yes	—
379	C₄×C₅	C₂×2₋¹⁺⁴	1	4	yes	—
380	C₂⁴	C₂⁴×C₅	1	6	yes	—
381	C₂⁴	C₂⁴×C₅	1	1	yes	characteristic
382	#41	—	2	64	no	—
383	#41	—	4	96	no	—
384	C₂×Q₈	—	2	32	no	—
385	C₂×Q₈	—	2	12	no	—
386	C₂×Q₈	—	2	4	no	—
387	C₂×Q₈	—	4	12	no	—
388	C₂×Q₈	C₅×#41	1	8	yes	complemented
389	C₂×Q₈	C₂⁴×C₅	1	4	yes	—
390	C₂×Q₈	C₂⁴×C₅	1	12	yes	—
391	C₂×Q₈	C₂⁴×C₅	1	24	yes	—
392	C₂×Q₈	C₂⁴×C₅	1	4	yes	—
393	C₂×D₄	—	2	24	no	—
394	C₂×D₄	—	2	24	no	—
395	C₂×D₄	—	2	12	no	—
396	C₂×D₄	—	4	12	no	—
397	C₂×D₄	C₂⁴×C₅	1	12	yes	—
398	C₂×D₄	C₂⁴×C₅	1	24	yes	—
399	C₂×D₄	C₂⁴×C₅	1	24	yes	—
400	C₂×D₄	C₂⁴×C₅	1	24	yes	—
401	C₂²×C₄	—	2	12	no	—
402	C₂²×C₄	—	2	12	no	—
403	C₂²×C₄	—	2	24	no	—
404	C₂²×C₄	—	2	4	no	—
405	C₂²×C₄	—	4	24	no	—
406	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
407	C₂²×C₄	C₂⁴×C₅	1	4	yes	—
408	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
409	C₂²×C₄	C₂⁴×C₅	1	3	yes	—
410	C₂²×C₄	C₂⁴×C₅	1	3	yes	—
411	C₂²×C₄	C₂⁴×C₅	1	3	yes	—
412	C₂²×C₄	C₂⁴×C₅	1	12	yes	—
413	C₂²×C₄	C₂⁴×C₅	1	12	yes	—
414	C₂²×C₄	C₂⁴×C₅	1	6	yes	—
415	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
416	C₂²×C₄	C₂⁴×C₅	1	24	yes	—
417	C₂²×C₄	C₂⁴×C₅	1	48	yes	—
418	C₂²×C₄	C₂⁴×C₅	1	3	yes	—
419	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
420	C₄⋊C₄	C₂⁴×C₅	1	12	yes	—
421	C₄⋊C₄	C₂⁴×C₅	1	24	yes	—
422	C₄⋊C₄	C₂⁴×C₅	1	24	yes	—
423	C₄⋊C₄	C₂⁴×C₅	1	12	yes	—
424	C₄⋊C₄	C₂⁴×C₅	1	24	yes	—
425	C₄⋊C₄	C₂⁴×C₅	1	8	yes	—
426	C₄⋊C₄	C₂⁴×C₅	1	4	yes	—
427	C₄⋊C₄	C₂⁴×C₅	1	12	yes	—
428	C₄⋊C₄	C₂⁴×C₅	1	24	yes	—
429	C₄⋊C₄	C₂⁴×C₅	1	24	yes	—
430	C₂²⋊C₄	C₂⁴×C₅	1	24	yes	—
431	C₂²⋊C₄	C₂⁴×C₅	1	24	yes	—
432	C₂²⋊C₄	C₂⁴×C₅	1	8	yes	—
433	C₂²⋊C₄	C₂⁴×C₅	1	24	yes	—
434	C₂²⋊C₄	C₂⁴×C₅	1	48	yes	—
435	C₂²⋊C₄	C₂⁴×C₅	1	24	yes	—
436	C₄²	C₂⁴×C₅	1	12	yes	—
437	C₄²	C₂⁴×C₅	1	12	yes	—
438	C₄²	C₂⁴×C₅	1	12	yes	—
439	C₄²	C₂⁴×C₅	1	12	yes	—
440	C₄²	C₂⁴×C₅	1	24	yes	—
441	C₂×C₅	—	2	4	no	—
442	C₂×C₅	—	4	12	no	—
443	C₂×C₅	#3522	1	4	yes	direct product factor
444	C₂×C₅	C₂³×#41	1	1	yes	characteristic
445	C₂×C₅	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
446	C₂×C₅	C₂²×2₋¹⁺⁴	1	1	yes	characteristic
447	C₂³	—	2	2	no	—
448	C₂³	—	2	2	no	—
449	C₂³	—	2	12	no	—
450	C₂³	—	2	12	no	—
451	C₂³	—	2	12	no	—
452	C₂³	C₅×H(5,𝔽₂)	1	4	yes	—
453	C₂³	C₂⁵×C₅	1	12	yes	—
454	C₂³	C₂⁵×C₅	1	2	yes	—
455	C₂³	C₂⁵×C₅	1	1	yes	characteristic
456	Q₈	—	2	24	no	—
457	Q₈	—	2	8	no	—
458	Q₈	—	4	24	no	—
459	Q₈	C₂×C₅×#41	1	16	yes	complemented
460	D₄	—	2	48	no	—
461	D₄	—	2	48	no	—
462	D₄	—	2	24	no	—
463	D₄	—	4	24	no	—
464	C₂×C₄	—	2	4	no	—
465	C₂×C₄	—	2	6	no	—
466	C₂×C₄	—	2	6	no	—
467	C₂×C₄	—	2	6	no	—
468	C₂×C₄	—	2	24	no	—
469	C₂×C₄	—	2	12	no	—
470	C₂×C₄	—	2	2	no	—
471	C₂×C₄	—	2	4	no	—
472	C₂×C₄	—	2	24	no	—
473	C₂×C₄	—	2	48	no	—
474	C₂×C₄	—	2	8	no	—
475	C₂×C₄	—	4	48	no	—
476	C₂×C₄	C₂×C₅×#41	1	12	yes	—
477	C₂×C₄	C₅×2₋¹⁺⁴	1	4	yes	—
478	C₂×C₄	C₂⁵×C₅	1	2	yes	—
479	C₂×C₄	C₂⁵×C₅	1	4	yes	—
480	C₂×C₄	C₂⁵×C₅	1	6	yes	—
481	C₂×C₄	C₂⁵×C₅	1	6	yes	—
482	C₂×C₄	C₂⁵×C₅	1	6	yes	—
483	C₂×C₄	C₂⁵×C₅	1	12	yes	—
484	C₂×C₄	C₂⁵×C₅	1	4	yes	—
485	C₂×C₄	C₂⁵×C₅	1	6	yes	—
486	C₂×C₄	C₂⁵×C₅	1	2	yes	—
487	C₅	C₂×#3522	1	1	yes	characteristic, direct product factor, Sylow
488	C₂²	—	2	2	no	—
489	C₂²	—	2	2	no	—
490	C₂²	—	2	8	no	—
491	C₂²	—	2	12	no	—
492	C₂²	—	2	12	no	—
493	C₂²	—	2	12	no	—
494	C₂²	—	4	24	no	—
495	C₂²	C₂²×C₅×#41	1	2	yes	—
496	C₂²	C₂×C₅×H(5,𝔽₂)	1	4	yes	—
497	C₂²	C₂×C₅×H(5,𝔽₂)	1	2	yes	—
498	C₂²	C₂×C₅×2₋¹⁺⁴	1	2	yes	—
499	C₂²	C₂⁶×C₅	1	1	yes	characteristic
500	C₄	—	2	4	no	—
501	C₄	—	2	6	no	—
502	C₄	—	2	6	no	—
503	C₄	—	2	6	no	—
504	C₄	—	2	12	no	—
505	C₄	—	2	2	no	—
506	C₄	—	2	4	no	—
507	C₄	C₂²×C₅×#41	1	12	yes	—
508	C₄	C₂×C₅×2₋¹⁺⁴	1	4	yes	—
509	C₂	—	2	4	no	—
510	C₂	—	4	12	no	—
511	C₂	C₅×#3522	1	4	yes	direct product factor
512	C₂	C₂³×C₅×#41	1	1	yes	characteristic
513	C₂	C₂²×C₅×H(5,𝔽₂)	1	1	yes	characteristic
514	C₂	C₂²×C₅×2₋¹⁺⁴	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₅	C₂⁵
commutator, Frattini, cosocle	C₂²	C₂⁶×C₅
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₅×#3522	C₂	direct (N × H)
2. C₂×C₅×#559	C₂	semidirect
3. C₂×C₅×Q₈²	C₂	semidirect
4. C₂×C₅×#554	C₂	semidirect
5. C₂×C₅×#550	C₂	semidirect
6. C₂×C₅×#548	C₂	semidirect
7. C₂×C₅×#547	C₂	semidirect
8. C₂×C₅×#542	C₂	semidirect
9. C₂×C₅×#532	C₂	semidirect
10. C₂×C₅×#529	C₂	semidirect
11. C₂×C₅×#520	C₂	semidirect
12. C₂²×C₄×C₅×Q₈	C₂	semidirect
16. C₅×#559	C₂²	semidirect
17. C₅×Q₈²	C₂²	semidirect
18. C₅×#554	C₂²	semidirect
19. C₅×#550	C₂²	semidirect
20. C₅×#548	C₂²	semidirect
21. C₅×#547	C₂²	semidirect
22. C₅×#542	C₂²	semidirect
23. C₅×#532	C₂²	semidirect
27. C₅×#529	C₂²	semidirect
41. C₅×#520	C₂²	semidirect
48. C₂×C₄×C₅×Q₈	C₂²	semidirect
58. C₂×#3522	C₅	direct (N × H)
130. #3522	C₂×C₅	direct (N × H)
131. C₂×#559	C₂×C₅	semidirect
132. C₂×Q₈²	C₂×C₅	semidirect
133. C₂×#554	C₂×C₅	semidirect
134. C₂×#550	C₂×C₅	semidirect
135. C₂×#548	C₂×C₅	semidirect
136. C₂×#547	C₂×C₅	semidirect
137. C₂×#542	C₂×C₅	semidirect
138. C₂×#532	C₂×C₅	semidirect
139. C₂×#529	C₂×C₅	semidirect
140. C₂×#520	C₂×C₅	semidirect
141. C₂²×C₄×Q₈	C₂×C₅	semidirect
150. C₂×C₅×Q₈	#41	semidirect
206. #559	C₂²×C₅	semidirect
207. Q₈²	C₂²×C₅	semidirect
208. #554	C₂²×C₅	semidirect
209. #550	C₂²×C₅	semidirect
210. #548	C₂²×C₅	semidirect
211. #547	C₂²×C₅	semidirect
212. #542	C₂²×C₅	semidirect
213. #532	C₂²×C₅	semidirect
217. #529	C₂²×C₅	semidirect
231. #520	C₂²×C₅	semidirect
238. C₂×C₄×Q₈	C₂²×C₅	semidirect
260. C₅×Q₈	C₂×#41	semidirect
388. C₂×Q₈	C₅×#41	semidirect
443. C₂×C₅	#3522	direct (N × H)
459. Q₈	C₂×C₅×#41	semidirect
487. C₅	C₂×#3522	direct (N × H)
511. C₂	C₅×#3522	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅×#3522	2
C₂×C₅×#559	2
C₂×C₅×Q₈²	2
C₂×C₅×#554	2
C₂×C₅×#550	2
C₂×C₅×#548	2
C₂×C₅×#547	2
C₂×C₅×#542	2
C₂×C₅×#532	2
C₂×C₅×#529	2
C₂×C₅×#520	2
C₂²×C₄×C₅×Q₈	2
C₂×#3522	5

Subgroups — C2×C5×#3522 #11985506

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#3522 #11985506