Subgroups — C₂×C₅×#3512 #11985529

Order 1280.

7238 conjugacy classes of subgroups.

The subgroup lattice has 544 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#3512	C₂	1	32	yes	maximal, direct product factor
2	C₂×C₅×#553	C₂	1	4	yes	maximal, complemented
3	C₂×C₅×#553	C₂	1	8	yes	maximal, complemented
4	C₂×C₅×#552	C₂	1	4	yes	maximal, complemented
5	C₂×C₅×#541	C₂	1	2	yes	maximal, complemented
6	C₂×C₅×#540	C₂	1	2	yes	maximal, complemented
7	C₂×C₅×#537	C₂	1	2	yes	maximal, complemented
8	C₂×C₅×#532	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₅×#529	C₂	1	4	yes	maximal, complemented
10	C₂²×C₅×#125	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₅×#520	C₂	1	2	yes	maximal, complemented
12	C₂×C₄×C₅×#41	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂²×C₅×#41	C₂²	1	1	yes	characteristic
14	C₂²×C₅×#41	C₂²	1	2	yes	—
15	C₅×#553	C₂²	1	64	yes	complemented
16	C₅×#553	C₂²	1	128	yes	complemented
17	C₅×#552	C₂²	1	64	yes	complemented
18	C₅×#541	C₂²	1	32	yes	complemented
19	C₅×#540	C₂²	1	32	yes	complemented
20	C₅×#537	C₂²	1	32	yes	complemented
21	C₅×#532	C₂²	1	16	yes	complemented
22	C₂×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
23	C₂×C₅×#127	C₂²	1	1	yes	characteristic
24	C₅×#529	C₂²	1	64	yes	complemented
25	C₂×C₅×#126	C₂²	1	8	yes	—
26	C₂×C₅×#126	C₂²	1	8	yes	—
27	C₂×C₅×#125	C₂²	1	2	yes	—
28	C₂×C₅×#125	C₂²	1	2	yes	—
29	C₂×C₅×#125	C₂²	1	4	yes	—
30	C₂×C₅×#125	C₂²	1	8	yes	—
31	C₂×C₅×#125	C₂²	1	16	yes	complemented
32	C₂×C₅×#124	C₂²	1	2	yes	—
33	C₂×C₅×#123	C₂²	1	8	yes	—
34	C₂×C₅×#123	C₂²	1	8	yes	—
35	C₂×C₅×C₂²⋊Q₈	C₂²	1	4	yes	—
36	C₂×C₅×C₂²⋊Q₈	C₂²	1	4	yes	—
37	C₂×C₅×#121	C₂²	1	4	yes	—
38	C₂×C₅×#121	C₂²	1	4	yes	—
39	C₂×C₅×#121	C₂²	1	8	yes	—
40	C₂×C₅×#121	C₂²	1	4	yes	—
41	C₂×C₅×#121	C₂²	1	8	yes	—
42	C₅×#520	C₂²	1	32	yes	complemented
43	C₄×C₅×#41	C₂²	1	16	yes	complemented
44	C₂×C₄×C₅×Q₈	C₂²	1	2	yes	—
45	C₂×C₄×C₅×Q₈	C₂²	1	4	yes	—
46	C₂×C₄×C₅×D₄	C₂²	1	4	yes	—
47	C₂×C₄×C₅×D₄	C₂²	1	2	yes	—
48	C₂×C₄×C₅×D₄	C₂²	1	4	yes	—
49	C₂×C₄×C₅×D₄	C₂²	1	8	yes	—
50	C₂×C₄×C₅×D₄	C₂²	1	8	yes	—
51	C₂×C₄×C₅×D₄	C₂²	1	4	yes	—
52	C₂×C₅×#117	C₂²	1	1	yes	characteristic
53	C₂×C₅×#117	C₂²	1	2	yes	—
54	C₂×C₅×#117	C₂²	1	4	yes	—
55	C₂×C₅×#117	C₂²	1	8	yes	—
56	C₂²×C₅×C₄⋊C₄	C₂²	1	2	yes	—
57	C₂²×C₅×C₄⋊C₄	C₂²	1	4	yes	—
58	C₂²×C₅×C₄⋊C₄	C₂²	1	4	yes	—
59	C₂²×C₄²×C₅	C₂²	1	1	yes	characteristic
60	C₂²×C₄²×C₅	C₂²	1	2	yes	—
61	C₂×#3512	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
62	C₂×C₅×#41	—	2	8	no	—
63	C₂×C₅×#41	—	2	16	no	—
64	C₂×C₅×#41	C₂³	1	8	yes	—
65	C₂×C₅×#41	C₂³	1	16	yes	—
66	C₂²×C₅×Q₈	C₂³	1	1	yes	characteristic
67	C₂²×C₅×Q₈	C₂³	1	2	yes	—
68	C₂²×C₅×D₄	C₂³	1	2	yes	—
69	C₂²×C₅×D₄	C₂³	1	4	yes	—
70	C₂²×C₅×D₄	C₂³	1	1	yes	characteristic
71	C₂²×C₅×D₄	C₂³	1	2	yes	—
72	C₂²×C₅×D₄	C₂³	1	8	yes	—
73	C₂²×C₅×D₄	C₂³	1	4	yes	—
74	C₂³×C₄×C₅	C₂³	1	2	yes	—
75	C₂³×C₄×C₅	C₂³	1	4	yes	—
76	C₂³×C₄×C₅	C₂³	1	2	yes	—
77	C₂³×C₄×C₅	C₂³	1	4	yes	—
78	C₂³×C₄×C₅	C₂³	1	4	yes	—
79	C₂³×C₄×C₅	C₂³	1	8	yes	—
80	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
81	C₅×C₄⋊Q₈	C₂³	1	8	yes	—
82	C₅×#127	C₂³	1	8	yes	—
83	C₅×#126	C₂³	1	64	yes	—
84	C₅×#126	C₂³	1	64	yes	—
85	C₅×#125	C₂³	1	16	yes	—
86	C₅×#125	C₂³	1	16	yes	—
87	C₅×#125	C₂³	1	32	yes	—
88	C₅×#125	C₂³	1	64	yes	—
89	C₅×#124	C₂³	1	16	yes	—
90	C₅×#123	C₂³	1	64	yes	—
91	C₅×#123	C₂³	1	64	yes	—
92	C₅×C₂²⋊Q₈	C₂³	1	32	yes	—
93	C₅×C₂²⋊Q₈	C₂³	1	32	yes	—
94	C₅×#121	C₂³	1	32	yes	—
95	C₅×#121	C₂³	1	32	yes	—
96	C₅×#121	C₂³	1	64	yes	—
97	C₅×#121	C₂³	1	32	yes	—
98	C₅×#121	C₂³	1	64	yes	—
99	C₄×C₅×Q₈	C₂³	1	16	yes	—
100	C₄×C₅×Q₈	C₂³	1	32	yes	—
101	C₄×C₅×D₄	C₂³	1	32	yes	—
102	C₄×C₅×D₄	C₂³	1	16	yes	—
103	C₄×C₅×D₄	C₂³	1	32	yes	—
104	C₄×C₅×D₄	C₂³	1	64	yes	—
105	C₄×C₅×D₄	C₂³	1	64	yes	—
106	C₄×C₅×D₄	C₂³	1	32	yes	—
107	C₅×#117	C₂³	1	8	yes	—
108	C₅×#117	C₂³	1	16	yes	—
109	C₅×#117	C₂³	1	32	yes	—
110	C₅×#117	C₂³	1	64	yes	—
111	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
112	C₂×C₅×C₄⋊C₄	C₂³	1	4	yes	—
113	C₂×C₅×C₄⋊C₄	C₂³	1	8	yes	—
114	C₂×C₅×C₄⋊C₄	C₂³	1	4	yes	—
115	C₂×C₅×C₄⋊C₄	C₂³	1	8	yes	—
116	C₂×C₅×C₄⋊C₄	C₂³	1	16	yes	—
117	C₂×C₅×C₄⋊C₄	C₂³	1	32	yes	—
118	C₂×C₅×C₄⋊C₄	C₂³	1	8	yes	—
119	C₂×C₅×C₄⋊C₄	C₂³	1	32	yes	—
120	C₂×C₅×C₄⋊C₄	C₂³	1	4	yes	—
121	C₂×C₅×C₄⋊C₄	C₂³	1	8	yes	—
122	C₂×C₅×C₄⋊C₄	C₂³	1	4	yes	—
123	C₂×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
124	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
125	C₂×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
126	C₂×C₅×C₂²⋊C₄	C₂³	1	8	yes	—
127	C₂×C₅×C₂²⋊C₄	C₂³	1	8	yes	—
128	C₂×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
129	C₂×C₅×C₂²⋊C₄	C₂³	1	8	yes	—
130	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
131	C₂×C₄²×C₅	C₂³	1	2	yes	—
132	C₂×C₄²×C₅	C₂³	1	4	yes	—
133	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
134	C₂×C₄²×C₅	C₂³	1	2	yes	—
135	C₂×C₄²×C₅	C₂³	1	8	yes	—
136	C₂×C₄²×C₅	C₂³	1	16	yes	—
137	C₂×C₄²×C₅	C₂³	1	8	yes	—
138	#3512	C₂×C₅	1	32	yes	direct product factor
139	C₂×#553	C₂×C₅	1	4	yes	complemented
140	C₂×#553	C₂×C₅	1	8	yes	complemented
141	C₂×#552	C₂×C₅	1	4	yes	complemented
142	C₂×#541	C₂×C₅	1	2	yes	complemented
143	C₂×#540	C₂×C₅	1	2	yes	complemented
144	C₂×#537	C₂×C₅	1	2	yes	complemented
145	C₂×#532	C₂×C₅	1	1	yes	characteristic, complemented
146	C₂×#529	C₂×C₅	1	4	yes	complemented
147	C₂²×#125	C₂×C₅	1	1	yes	characteristic, complemented
148	C₂×#520	C₂×C₅	1	2	yes	complemented
149	C₂×C₄×#41	C₂×C₅	1	1	yes	characteristic, complemented
150	C₂⁴×C₅	C₂⁴	1	4	yes	—
151	C₂⁴×C₅	C₂⁴	1	2	yes	—
152	C₂⁴×C₅	C₂⁴	1	1	yes	characteristic
153	C₅×#41	—	2	32	no	—
154	C₅×#41	—	2	64	no	—
155	C₂×C₅×Q₈	—	2	4	no	—
156	C₂×C₅×Q₈	—	2	8	no	—
157	C₂×C₅×Q₈	C₂⁴	1	4	yes	—
158	C₂×C₅×Q₈	C₂⁴	1	8	yes	—
159	C₂×C₅×D₄	—	2	8	no	—
160	C₂×C₅×D₄	—	2	16	no	—
161	C₂×C₅×D₄	—	2	4	no	—
162	C₂×C₅×D₄	—	2	8	no	—
163	C₂×C₅×D₄	—	4	16	no	—
164	C₂×C₅×D₄	—	4	8	no	—
165	C₂×C₅×D₄	C₂⁴	1	8	yes	—
166	C₂×C₅×D₄	C₂⁴	1	16	yes	—
167	C₂×C₅×D₄	C₂⁴	1	4	yes	—
168	C₂×C₅×D₄	C₂⁴	1	8	yes	—
169	C₂×C₅×D₄	C₂⁴	1	32	yes	—
170	C₂×C₅×D₄	C₂⁴	1	16	yes	—
171	C₂²×C₄×C₅	—	2	16	no	—
172	C₂²×C₄×C₅	—	2	8	no	—
173	C₂²×C₄×C₅	—	4	8	no	—
174	C₂²×C₄×C₅	—	4	16	no	—
175	C₂²×C₄×C₅	—	4	4	no	—
176	C₂²×C₄×C₅	—	4	8	no	—
177	C₂²×C₄×C₅	#41	1	8	yes	—
178	C₂²×C₄×C₅	C₂⁴	1	8	yes	—
179	C₂²×C₄×C₅	C₂⁴	1	16	yes	—
180	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
181	C₂²×C₄×C₅	C₂⁴	1	4	yes	—
182	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
183	C₂²×C₄×C₅	C₂⁴	1	4	yes	—
184	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
185	C₂²×C₄×C₅	C₂⁴	1	8	yes	—
186	C₂²×C₄×C₅	C₂⁴	1	8	yes	—
187	C₂²×C₄×C₅	C₂⁴	1	16	yes	—
188	C₂²×C₄×C₅	C₂⁴	1	16	yes	—
189	C₂²×C₄×C₅	C₂⁴	1	32	yes	—
190	C₂²×C₄×C₅	C₂⁴	1	4	yes	—
191	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
192	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
193	C₅×C₄⋊C₄	C₂⁴	1	8	yes	—
194	C₅×C₄⋊C₄	C₂⁴	1	16	yes	—
195	C₅×C₄⋊C₄	C₂⁴	1	32	yes	—
196	C₅×C₄⋊C₄	C₂⁴	1	16	yes	—
197	C₅×C₄⋊C₄	C₂⁴	1	32	yes	—
198	C₅×C₄⋊C₄	C₂⁴	1	32	yes	—
199	C₅×C₄⋊C₄	C₂⁴	1	16	yes	—
200	C₅×C₄⋊C₄	C₂⁴	1	32	yes	—
201	C₅×C₄⋊C₄	C₂⁴	1	16	yes	—
202	C₅×C₂²⋊C₄	C₂⁴	1	16	yes	—
203	C₅×C₂²⋊C₄	C₂⁴	1	8	yes	—
204	C₅×C₂²⋊C₄	C₂⁴	1	16	yes	—
205	C₅×C₂²⋊C₄	C₂⁴	1	32	yes	—
206	C₅×C₂²⋊C₄	C₂⁴	1	32	yes	—
207	C₅×C₂²⋊C₄	C₂⁴	1	16	yes	—
208	C₅×C₂²⋊C₄	C₂⁴	1	32	yes	—
209	C₄²×C₅	C₂⁴	1	4	yes	—
210	C₄²×C₅	C₂⁴	1	8	yes	—
211	C₄²×C₅	C₂⁴	1	16	yes	—
212	C₄²×C₅	C₂⁴	1	4	yes	—
213	C₄²×C₅	C₂⁴	1	8	yes	—
214	C₄²×C₅	C₂⁴	1	32	yes	—
215	C₂²×#41	C₂²×C₅	1	1	yes	characteristic
216	C₂²×#41	C₂²×C₅	1	2	yes	—
217	#553	C₂²×C₅	1	64	yes	complemented
218	#553	C₂²×C₅	1	128	yes	complemented
219	#552	C₂²×C₅	1	64	yes	complemented
220	#541	C₂²×C₅	1	32	yes	complemented
221	#540	C₂²×C₅	1	32	yes	complemented
222	#537	C₂²×C₅	1	32	yes	complemented
223	#532	C₂²×C₅	1	16	yes	complemented
224	C₂×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
225	C₂×#127	C₂²×C₅	1	1	yes	characteristic
226	#529	C₂²×C₅	1	64	yes	complemented
227	C₂×#126	C₂²×C₅	1	8	yes	—
228	C₂×#126	C₂²×C₅	1	8	yes	—
229	C₂×#125	C₂²×C₅	1	2	yes	—
230	C₂×#125	C₂²×C₅	1	2	yes	—
231	C₂×#125	C₂²×C₅	1	4	yes	—
232	C₂×#125	C₂²×C₅	1	8	yes	—
233	C₂×#125	C₂²×C₅	1	16	yes	complemented
234	C₂×#124	C₂²×C₅	1	2	yes	—
235	C₂×#123	C₂²×C₅	1	8	yes	—
236	C₂×#123	C₂²×C₅	1	8	yes	—
237	C₂×C₂²⋊Q₈	C₂²×C₅	1	4	yes	—
238	C₂×C₂²⋊Q₈	C₂²×C₅	1	4	yes	—
239	C₂×#121	C₂²×C₅	1	4	yes	—
240	C₂×#121	C₂²×C₅	1	4	yes	—
241	C₂×#121	C₂²×C₅	1	8	yes	—
242	C₂×#121	C₂²×C₅	1	4	yes	—
243	C₂×#121	C₂²×C₅	1	8	yes	—
244	#520	C₂²×C₅	1	32	yes	complemented
245	C₄×#41	C₂²×C₅	1	16	yes	complemented
246	C₂×C₄×Q₈	C₂²×C₅	1	2	yes	—
247	C₂×C₄×Q₈	C₂²×C₅	1	4	yes	—
248	C₂×C₄×D₄	C₂²×C₅	1	4	yes	—
249	C₂×C₄×D₄	C₂²×C₅	1	2	yes	—
250	C₂×C₄×D₄	C₂²×C₅	1	4	yes	—
251	C₂×C₄×D₄	C₂²×C₅	1	8	yes	—
252	C₂×C₄×D₄	C₂²×C₅	1	8	yes	—
253	C₂×C₄×D₄	C₂²×C₅	1	4	yes	—
254	C₂×#117	C₂²×C₅	1	1	yes	characteristic
255	C₂×#117	C₂²×C₅	1	2	yes	—
256	C₂×#117	C₂²×C₅	1	4	yes	—
257	C₂×#117	C₂²×C₅	1	8	yes	—
258	C₂²×C₄⋊C₄	C₂²×C₅	1	2	yes	—
259	C₂²×C₄⋊C₄	C₂²×C₅	1	4	yes	—
260	C₂²×C₄⋊C₄	C₂²×C₅	1	4	yes	—
261	C₂²×C₄²	C₂²×C₅	1	1	yes	characteristic
262	C₂²×C₄²	C₂²×C₅	1	2	yes	—
263	C₂³×C₅	—	2	4	no	—
264	C₂³×C₅	—	2	8	no	—
265	C₂³×C₅	—	2	4	no	—
266	C₂³×C₅	—	2	8	no	—
267	C₂³×C₅	—	2	8	no	—
268	C₂³×C₅	—	2	8	no	—
269	C₂³×C₅	C₂×#41	1	4	yes	—
270	C₂³×C₅	C₂⁵	1	8	yes	—
271	C₂³×C₅	C₂⁵	1	4	yes	—
272	C₂³×C₅	C₂⁵	1	2	yes	—
273	C₂³×C₅	C₂⁵	1	1	yes	characteristic
274	C₅×Q₈	—	2	8	no	—
275	C₅×Q₈	—	2	16	no	—
276	C₅×D₄	—	2	16	no	—
277	C₅×D₄	—	2	32	no	—
278	C₅×D₄	—	2	8	no	—
279	C₅×D₄	—	2	16	no	—
280	C₅×D₄	—	4	32	no	—
281	C₅×D₄	—	4	16	no	—
282	C₂×C₄×C₅	—	2	8	no	—
283	C₂×C₄×C₅	—	2	4	no	—
284	C₂×C₄×C₅	—	2	4	no	—
285	C₂×C₄×C₅	—	2	8	no	—
286	C₂×C₄×C₅	—	2	16	no	—
287	C₂×C₄×C₅	—	2	4	no	—
288	C₂×C₄×C₅	—	2	32	no	—
289	C₂×C₄×C₅	—	2	16	no	—
290	C₂×C₄×C₅	—	4	16	no	—
291	C₂×C₄×C₅	—	4	32	no	—
292	C₂×C₄×C₅	—	4	8	no	—
293	C₂×C₄×C₅	—	4	16	no	—
294	C₂×C₄×C₅	C₂×#41	1	4	yes	—
295	C₂×C₄×C₅	C₂×#41	1	4	yes	—
296	C₂×C₄×C₅	C₂×#41	1	16	yes	—
297	C₂×C₄×C₅	C₂⁵	1	4	yes	—
298	C₂×C₄×C₅	C₂⁵	1	8	yes	—
299	C₂×C₄×C₅	C₂⁵	1	4	yes	—
300	C₂×C₄×C₅	C₂⁵	1	8	yes	—
301	C₂×C₄×C₅	C₂⁵	1	4	yes	—
302	C₂×C₄×C₅	C₂⁵	1	16	yes	—
303	C₂×C₄×C₅	C₂⁵	1	2	yes	—
304	C₂×C₄×C₅	C₂⁵	1	2	yes	—
305	C₂×#41	—	2	8	no	—
306	C₂×#41	—	2	16	no	—
307	C₂×#41	C₂³×C₅	1	8	yes	—
308	C₂×#41	C₂³×C₅	1	16	yes	—
309	C₂²×Q₈	C₂³×C₅	1	1	yes	characteristic
310	C₂²×Q₈	C₂³×C₅	1	2	yes	—
311	C₂²×D₄	C₂³×C₅	1	2	yes	—
312	C₂²×D₄	C₂³×C₅	1	4	yes	—
313	C₂²×D₄	C₂³×C₅	1	1	yes	characteristic
314	C₂²×D₄	C₂³×C₅	1	2	yes	—
315	C₂²×D₄	C₂³×C₅	1	8	yes	—
316	C₂²×D₄	C₂³×C₅	1	4	yes	—
317	C₂³×C₄	C₂³×C₅	1	4	yes	—
318	C₂³×C₄	C₂³×C₅	1	2	yes	—
319	C₂³×C₄	C₂³×C₅	1	4	yes	—
320	C₂³×C₄	C₂³×C₅	1	2	yes	—
321	C₂³×C₄	C₂³×C₅	1	8	yes	—
322	C₂³×C₄	C₂³×C₅	1	4	yes	—
323	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
324	C₄⋊Q₈	C₂³×C₅	1	8	yes	—
325	#127	C₂³×C₅	1	8	yes	—
326	#126	C₂³×C₅	1	64	yes	—
327	#126	C₂³×C₅	1	64	yes	—
328	#125	C₂³×C₅	1	16	yes	—
329	#125	C₂³×C₅	1	16	yes	—
330	#125	C₂³×C₅	1	32	yes	—
331	#125	C₂³×C₅	1	64	yes	—
332	#124	C₂³×C₅	1	16	yes	—
333	#123	C₂³×C₅	1	64	yes	—
334	#123	C₂³×C₅	1	64	yes	—
335	C₂²⋊Q₈	C₂³×C₅	1	32	yes	—
336	C₂²⋊Q₈	C₂³×C₅	1	32	yes	—
337	#121	C₂³×C₅	1	32	yes	—
338	#121	C₂³×C₅	1	32	yes	—
339	#121	C₂³×C₅	1	64	yes	—
340	#121	C₂³×C₅	1	32	yes	—
341	#121	C₂³×C₅	1	64	yes	—
342	C₄×Q₈	C₂³×C₅	1	16	yes	—
343	C₄×Q₈	C₂³×C₅	1	32	yes	—
344	C₄×D₄	C₂³×C₅	1	32	yes	—
345	C₄×D₄	C₂³×C₅	1	16	yes	—
346	C₄×D₄	C₂³×C₅	1	32	yes	—
347	C₄×D₄	C₂³×C₅	1	64	yes	—
348	C₄×D₄	C₂³×C₅	1	64	yes	—
349	C₄×D₄	C₂³×C₅	1	32	yes	—
350	#117	C₂³×C₅	1	8	yes	—
351	#117	C₂³×C₅	1	16	yes	—
352	#117	C₂³×C₅	1	32	yes	—
353	#117	C₂³×C₅	1	64	yes	—
354	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
355	C₂×C₄⋊C₄	C₂³×C₅	1	4	yes	—
356	C₂×C₄⋊C₄	C₂³×C₅	1	8	yes	—
357	C₂×C₄⋊C₄	C₂³×C₅	1	4	yes	—
358	C₂×C₄⋊C₄	C₂³×C₅	1	8	yes	—
359	C₂×C₄⋊C₄	C₂³×C₅	1	16	yes	—
360	C₂×C₄⋊C₄	C₂³×C₅	1	32	yes	—
361	C₂×C₄⋊C₄	C₂³×C₅	1	8	yes	—
362	C₂×C₄⋊C₄	C₂³×C₅	1	32	yes	—
363	C₂×C₄⋊C₄	C₂³×C₅	1	4	yes	—
364	C₂×C₄⋊C₄	C₂³×C₅	1	8	yes	—
365	C₂×C₄⋊C₄	C₂³×C₅	1	4	yes	—
366	C₂×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
367	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
368	C₂×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
369	C₂×C₂²⋊C₄	C₂³×C₅	1	8	yes	—
370	C₂×C₂²⋊C₄	C₂³×C₅	1	8	yes	—
371	C₂×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
372	C₂×C₂²⋊C₄	C₂³×C₅	1	8	yes	—
373	C₂×C₄²	C₂³×C₅	1	2	yes	—
374	C₂×C₄²	C₂³×C₅	1	8	yes	—
375	C₂×C₄²	C₂³×C₅	1	4	yes	—
376	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
377	C₂×C₄²	C₂³×C₅	1	2	yes	—
378	C₂×C₄²	C₂³×C₅	1	8	yes	—
379	C₂×C₄²	C₂³×C₅	1	16	yes	—
380	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
381	C₂²×C₅	—	2	4	no	—
382	C₂²×C₅	—	2	8	no	—
383	C₂²×C₅	—	2	8	no	—
384	C₂²×C₅	—	2	4	no	—
385	C₂²×C₅	—	2	8	no	—
386	C₂²×C₅	—	2	8	no	—
387	C₂²×C₅	—	2	8	no	—
388	C₂²×C₅	—	4	16	no	—
389	C₂²×C₅	—	4	8	no	—
390	C₂²×C₅	C₂²×#41	1	4	yes	—
391	C₂²×C₅	C₂²×#41	1	2	yes	—
392	C₂²×C₅	#585	1	4	yes	—
393	C₂²×C₅	C₂⁶	1	1	yes	characteristic
394	C₄×C₅	—	2	8	no	—
395	C₄×C₅	—	2	4	no	—
396	C₄×C₅	—	2	4	no	—
397	C₄×C₅	—	2	8	no	—
398	C₄×C₅	—	2	16	no	—
399	C₄×C₅	—	2	4	no	—
400	C₄×C₅	C₂²×#41	1	4	yes	—
401	C₄×C₅	C₂²×#41	1	4	yes	—
402	C₂⁴	C₂⁴×C₅	1	4	yes	—
403	C₂⁴	C₂⁴×C₅	1	2	yes	—
404	C₂⁴	C₂⁴×C₅	1	1	yes	characteristic
405	#41	—	2	32	no	—
406	#41	—	2	64	no	—
407	C₂×Q₈	—	2	4	no	—
408	C₂×Q₈	—	2	8	no	—
409	C₂×Q₈	C₂⁴×C₅	1	4	yes	—
410	C₂×Q₈	C₂⁴×C₅	1	8	yes	—
411	C₂×D₄	—	2	8	no	—
412	C₂×D₄	—	2	16	no	—
413	C₂×D₄	—	2	4	no	—
414	C₂×D₄	—	2	8	no	—
415	C₂×D₄	—	4	16	no	—
416	C₂×D₄	—	4	8	no	—
417	C₂×D₄	C₂⁴×C₅	1	8	yes	—
418	C₂×D₄	C₂⁴×C₅	1	16	yes	—
419	C₂×D₄	C₂⁴×C₅	1	4	yes	—
420	C₂×D₄	C₂⁴×C₅	1	8	yes	—
421	C₂×D₄	C₂⁴×C₅	1	32	yes	—
422	C₂×D₄	C₂⁴×C₅	1	16	yes	—
423	C₂²×C₄	—	2	16	no	—
424	C₂²×C₄	—	2	8	no	—
425	C₂²×C₄	—	4	8	no	—
426	C₂²×C₄	—	4	16	no	—
427	C₂²×C₄	—	4	4	no	—
428	C₂²×C₄	—	4	8	no	—
429	C₂²×C₄	C₅×#41	1	8	yes	—
430	C₂²×C₄	C₂⁴×C₅	1	4	yes	—
431	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
432	C₂²×C₄	C₂⁴×C₅	1	4	yes	—
433	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
434	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
435	C₂²×C₄	C₂⁴×C₅	1	8	yes	—
436	C₂²×C₄	C₂⁴×C₅	1	8	yes	—
437	C₂²×C₄	C₂⁴×C₅	1	16	yes	—
438	C₂²×C₄	C₂⁴×C₅	1	8	yes	—
439	C₂²×C₄	C₂⁴×C₅	1	16	yes	—
440	C₂²×C₄	C₂⁴×C₅	1	16	yes	—
441	C₂²×C₄	C₂⁴×C₅	1	32	yes	—
442	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
443	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
444	C₂²×C₄	C₂⁴×C₅	1	4	yes	—
445	C₄⋊C₄	C₂⁴×C₅	1	8	yes	—
446	C₄⋊C₄	C₂⁴×C₅	1	16	yes	—
447	C₄⋊C₄	C₂⁴×C₅	1	32	yes	—
448	C₄⋊C₄	C₂⁴×C₅	1	16	yes	—
449	C₄⋊C₄	C₂⁴×C₅	1	32	yes	—
450	C₄⋊C₄	C₂⁴×C₅	1	32	yes	—
451	C₄⋊C₄	C₂⁴×C₅	1	16	yes	—
452	C₄⋊C₄	C₂⁴×C₅	1	32	yes	—
453	C₄⋊C₄	C₂⁴×C₅	1	16	yes	—
454	C₂²⋊C₄	C₂⁴×C₅	1	16	yes	—
455	C₂²⋊C₄	C₂⁴×C₅	1	8	yes	—
456	C₂²⋊C₄	C₂⁴×C₅	1	16	yes	—
457	C₂²⋊C₄	C₂⁴×C₅	1	32	yes	—
458	C₂²⋊C₄	C₂⁴×C₅	1	32	yes	—
459	C₂²⋊C₄	C₂⁴×C₅	1	16	yes	—
460	C₂²⋊C₄	C₂⁴×C₅	1	32	yes	—
461	C₄²	C₂⁴×C₅	1	4	yes	—
462	C₄²	C₂⁴×C₅	1	8	yes	—
463	C₄²	C₂⁴×C₅	1	16	yes	—
464	C₄²	C₂⁴×C₅	1	4	yes	—
465	C₄²	C₂⁴×C₅	1	8	yes	—
466	C₄²	C₂⁴×C₅	1	32	yes	—
467	C₂×C₅	—	2	4	no	—
468	C₂×C₅	—	4	8	no	—
469	C₂×C₅	—	4	4	no	—
470	C₂×C₅	#3512	1	4	yes	direct product factor
471	C₂×C₅	C₂³×#41	1	1	yes	characteristic
472	C₂×C₅	C₂×#585	1	2	yes	—
473	C₂³	—	2	4	no	—
474	C₂³	—	2	8	no	—
475	C₂³	—	2	4	no	—
476	C₂³	—	2	8	no	—
477	C₂³	—	2	8	no	—
478	C₂³	—	2	8	no	—
479	C₂³	C₂×C₅×#41	1	4	yes	—
480	C₂³	C₂⁵×C₅	1	8	yes	—
481	C₂³	C₂⁵×C₅	1	4	yes	—
482	C₂³	C₂⁵×C₅	1	2	yes	—
483	C₂³	C₂⁵×C₅	1	1	yes	characteristic
484	Q₈	—	2	8	no	—
485	Q₈	—	2	16	no	—
486	D₄	—	2	16	no	—
487	D₄	—	2	32	no	—
488	D₄	—	2	8	no	—
489	D₄	—	2	16	no	—
490	D₄	—	4	32	no	—
491	D₄	—	4	16	no	—
492	C₂×C₄	—	2	8	no	—
493	C₂×C₄	—	2	4	no	—
494	C₂×C₄	—	2	4	no	—
495	C₂×C₄	—	2	8	no	—
496	C₂×C₄	—	2	16	no	—
497	C₂×C₄	—	2	4	no	—
498	C₂×C₄	—	2	32	no	—
499	C₂×C₄	—	2	16	no	—
500	C₂×C₄	—	4	16	no	—
501	C₂×C₄	—	4	32	no	—
502	C₂×C₄	—	4	8	no	—
503	C₂×C₄	—	4	16	no	—
504	C₂×C₄	C₂×C₅×#41	1	4	yes	—
505	C₂×C₄	C₂×C₅×#41	1	4	yes	—
506	C₂×C₄	C₂×C₅×#41	1	16	yes	—
507	C₂×C₄	C₂⁵×C₅	1	4	yes	—
508	C₂×C₄	C₂⁵×C₅	1	8	yes	—
509	C₂×C₄	C₂⁵×C₅	1	4	yes	—
510	C₂×C₄	C₂⁵×C₅	1	8	yes	—
511	C₂×C₄	C₂⁵×C₅	1	4	yes	—
512	C₂×C₄	C₂⁵×C₅	1	16	yes	—
513	C₂×C₄	C₂⁵×C₅	1	2	yes	—
514	C₂×C₄	C₂⁵×C₅	1	2	yes	—
515	C₅	C₂×#3512	1	1	yes	characteristic, direct product factor, Sylow
516	C₂²	—	2	4	no	—
517	C₂²	—	2	8	no	—
518	C₂²	—	2	8	no	—
519	C₂²	—	2	4	no	—
520	C₂²	—	2	8	no	—
521	C₂²	—	2	8	no	—
522	C₂²	—	2	8	no	—
523	C₂²	—	4	16	no	—
524	C₂²	—	4	8	no	—
525	C₂²	C₂²×C₅×#41	1	4	yes	—
526	C₂²	C₂²×C₅×#41	1	2	yes	—
527	C₂²	C₅×#585	1	4	yes	—
528	C₂²	C₂⁶×C₅	1	1	yes	characteristic
529	C₄	—	2	8	no	—
530	C₄	—	2	4	no	—
531	C₄	—	2	4	no	—
532	C₄	—	2	8	no	—
533	C₄	—	2	16	no	—
534	C₄	—	2	4	no	—
535	C₄	C₂²×C₅×#41	1	4	yes	—
536	C₄	C₂²×C₅×#41	1	4	yes	—
537	C₂	—	2	4	no	—
538	C₂	—	4	8	no	—
539	C₂	—	4	4	no	—
540	C₂	C₅×#3512	1	4	yes	direct product factor
541	C₂	C₂³×C₅×#41	1	1	yes	characteristic
542	C₂	C₂×C₅×#585	1	2	yes	—

	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×#3512	C₂	direct (N × H)
2. C₂×C₅×#553	C₂	semidirect
3. C₂×C₅×#553	C₂	semidirect
4. C₂×C₅×#552	C₂	semidirect
5. C₂×C₅×#541	C₂	semidirect
6. C₂×C₅×#540	C₂	semidirect
7. C₂×C₅×#537	C₂	semidirect
8. C₂×C₅×#532	C₂	semidirect
9. C₂×C₅×#529	C₂	semidirect
10. C₂²×C₅×#125	C₂	semidirect
11. C₂×C₅×#520	C₂	semidirect
12. C₂×C₄×C₅×#41	C₂	semidirect
15. C₅×#553	C₂²	semidirect
16. C₅×#553	C₂²	semidirect
17. C₅×#552	C₂²	semidirect
18. C₅×#541	C₂²	semidirect
19. C₅×#540	C₂²	semidirect
20. C₅×#537	C₂²	semidirect
21. C₅×#532	C₂²	semidirect
24. C₅×#529	C₂²	semidirect
31. C₂×C₅×#125	C₂²	semidirect
42. C₅×#520	C₂²	semidirect
43. C₄×C₅×#41	C₂²	semidirect
61. C₂×#3512	C₅	direct (N × H)
138. #3512	C₂×C₅	direct (N × H)
139. C₂×#553	C₂×C₅	semidirect
140. C₂×#553	C₂×C₅	semidirect
141. C₂×#552	C₂×C₅	semidirect
142. C₂×#541	C₂×C₅	semidirect
143. C₂×#540	C₂×C₅	semidirect
144. C₂×#537	C₂×C₅	semidirect
145. C₂×#532	C₂×C₅	semidirect
146. C₂×#529	C₂×C₅	semidirect
147. C₂²×#125	C₂×C₅	semidirect
148. C₂×#520	C₂×C₅	semidirect
149. C₂×C₄×#41	C₂×C₅	semidirect
217. #553	C₂²×C₅	semidirect
218. #553	C₂²×C₅	semidirect
219. #552	C₂²×C₅	semidirect
220. #541	C₂²×C₅	semidirect
221. #540	C₂²×C₅	semidirect
222. #537	C₂²×C₅	semidirect
223. #532	C₂²×C₅	semidirect
226. #529	C₂²×C₅	semidirect
233. C₂×#125	C₂²×C₅	semidirect
244. #520	C₂²×C₅	semidirect
245. C₄×#41	C₂²×C₅	semidirect
470. C₂×C₅	#3512	direct (N × H)
515. C₅	C₂×#3512	direct (N × H)
540. C₂	C₅×#3512	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×#3512	2
C₂×C₅×#553	2
C₂×C₅×#552	2
C₂×C₅×#541	2
C₂×C₅×#540	2
C₂×C₅×#537	2
C₂×C₅×#532	2
C₂×C₅×#529	2
C₂²×C₅×#125	2
C₂×C₅×#520	2
C₂×C₄×C₅×#41	2
C₂×#3512	5

Subgroups — C2×C5×#3512 #11985529

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#3512 #11985529