Subgroups — C₅×#34493 #11957213

Order 1280.

3076 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×D₄²	C₂	1	1	yes	maximal, characteristic
2	C₅×#2375	C₂	1	4	yes	maximal, complemented
3	C₅×#2366	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#2363	C₂	1	4	yes	maximal, complemented
5	C₅×#2354	C₂	1	2	yes	maximal, complemented
6	C₅×D₄×C₂²⋊C₄	C₂	1	4	yes	maximal, complemented
7	C₅×#2324	C₂	1	4	yes	maximal, complemented
8	C₅×#2321	C₂	1	4	yes	maximal, complemented
9	C₅×#2309	C₂	1	4	yes	maximal, complemented
10	C₄×C₅×#127	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#2293	C₂	1	2	yes	maximal, complemented
12	C₂³×C₅×D₄	C₂²	1	4	yes	—
13	C₅×D₄²	C₄	1	16	yes	complemented
14	C₂×C₅×#127	C₂²	1	1	yes	characteristic
15	C₂×C₅×#121	C₂²	1	4	yes	—
16	C₂×C₅×#120	C₂²	1	4	yes	—
17	C₂×C₄×C₅×D₄	C₂²	1	2	yes	—
18	C₂×C₄×C₅×D₄	C₂²	1	2	yes	complemented
19	C₂×C₄×C₅×D₄	C₂²	1	4	yes	complemented
20	C₂×C₄×C₅×D₄	C₂²	1	4	yes	complemented
21	C₂×C₅×#117	C₂²	1	4	yes	complemented
22	C₂×C₅×#117	C₂²	1	4	yes	complemented
23	C₂²×C₅×C₂²⋊C₄	C₂²	1	4	yes	complemented
24	C₅×#390	C₂²	1	2	yes	—
25	C₅×#390	C₂²	1	2	yes	—
26	C₅×#390	C₂²	1	4	yes	—
27	C₅×#390	C₂²	1	4	yes	complemented
28	C₅×#390	C₂²	1	2	yes	complemented
29	C₅×#390	C₂²	1	8	yes	complemented
30	C₅×#390	C₂²	1	4	yes	complemented
31	C₅×#390	C₂²	1	8	yes	complemented
32	C₅×#389	C₂²	1	2	yes	complemented
33	C₅×#389	C₂²	1	2	yes	complemented
34	C₅×#388	C₂²	1	4	yes	complemented
35	C₅×#388	C₂²	1	4	yes	complemented
36	C₅×#388	C₂²	1	8	yes	complemented
37	C₅×#388	C₂²	1	8	yes	complemented
38	C₅×#386	C₂²	1	8	yes	complemented
39	C₅×#386	C₂²	1	4	yes	complemented
40	C₅×#386	C₂²	1	8	yes	complemented
41	C₅×#385	C₂²	1	4	yes	complemented
42	C₅×#384	C₂²	1	1	yes	characteristic, complemented
43	C₅×#380	C₂²	1	4	yes	complemented
44	C₅×#379	C₂²	1	4	yes	complemented
45	C₅×#379	C₂²	1	8	yes	complemented
46	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	complemented
47	C₄×C₅×C₄⋊C₄	C₂²	1	4	yes	complemented
48	C₄×C₅×C₂²⋊C₄	C₂²	1	4	yes	complemented
49	C₄×C₅×C₂²⋊C₄	C₂²	1	4	yes	complemented
50	C₄³×C₅	C₂²	1	1	yes	characteristic, complemented
51	#34493	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
52	C₂⁵×C₅	C₂³	1	4	yes	—
53	C₂²×C₅×D₄	—	4	8	no	—
54	C₂²×C₅×D₄	—	4	8	no	—
55	C₂²×C₅×D₄	C₂×C₄	1	32	yes	complemented
56	C₂²×C₅×D₄	C₂³	1	2	yes	—
57	C₂²×C₅×D₄	C₂³	1	4	yes	—
58	C₂²×C₅×D₄	C₂³	1	8	yes	—
59	C₂²×C₅×D₄	C₂³	1	2	yes	—
60	C₂³×C₄×C₅	C₂³	1	4	yes	—
61	C₂³×C₄×C₅	C₂³	1	4	yes	—
62	C₂³×C₄×C₅	C₂³	1	4	yes	—
63	C₅×#127	C₂×C₄	1	8	yes	—
64	C₅×#121	C₂×C₄	1	32	yes	complemented
65	C₅×#120	C₂×C₄	1	32	yes	complemented
66	C₄×C₅×D₄	—	4	8	no	—
67	C₄×C₅×D₄	—	4	8	no	—
68	C₄×C₅×D₄	—	4	4	no	—
69	C₄×C₅×D₄	C₂×C₄	1	16	yes	complemented
70	C₅×#117	—	4	8	no	—
71	C₅×#117	—	4	8	no	—
72	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
73	C₂×C₅×C₄⋊C₄	C₂³	1	4	yes	—
74	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
75	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
76	C₂×C₅×C₄⋊C₄	C₂³	1	4	yes	—
77	C₂×C₅×C₄⋊C₄	C₂³	1	4	yes	—
78	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
79	C₂×C₅×C₂²⋊C₄	—	4	8	no	—
80	C₂×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
81	C₂×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
82	C₂×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
83	C₂×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
84	C₂×C₅×C₂²⋊C₄	C₂³	1	8	yes	—
85	C₂×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
86	C₂×C₅×C₂²⋊C₄	C₂³	1	8	yes	—
87	C₂×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
88	C₂×C₅×C₂²⋊C₄	C₂³	1	8	yes	—
89	C₂×C₅×C₂²⋊C₄	C₂³	1	8	yes	—
90	C₂×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
91	C₂×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
92	C₂×C₄²×C₅	C₂³	1	2	yes	—
93	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
94	C₂×C₄²×C₅	C₂³	1	2	yes	—
95	C₂×C₄²×C₅	C₂³	1	4	yes	—
96	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
97	C₂×C₄²×C₅	C₂³	1	8	yes	—
98	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
99	C₅×#95	C₂³	1	4	yes	—
100	C₅×#95	C₂³	1	4	yes	—
101	C₅×#95	C₂³	1	8	yes	—
102	C₅×#95	C₂³	1	4	yes	—
103	C₂×D₄²	C₂×C₅	1	1	yes	characteristic
104	#2375	C₂×C₅	1	4	yes	complemented
105	#2366	C₂×C₅	1	1	yes	characteristic, complemented
106	#2363	C₂×C₅	1	4	yes	complemented
107	#2354	C₂×C₅	1	2	yes	complemented
108	D₄×C₂²⋊C₄	C₂×C₅	1	4	yes	complemented
109	#2324	C₂×C₅	1	4	yes	complemented
110	#2321	C₂×C₅	1	4	yes	complemented
111	#2309	C₂×C₅	1	4	yes	complemented
112	C₄×#127	C₂×C₅	1	1	yes	characteristic, complemented
113	#2293	C₂×C₅	1	2	yes	complemented
114	C₂⁴×C₅	—	4	4	no	—
115	C₂⁴×C₅	—	4	8	no	—
116	C₂⁴×C₅	—	4	8	no	—
117	C₂⁴×C₅	—	4	4	no	—
118	C₂⁴×C₅	C₂²×C₄	1	16	yes	—
119	C₂⁴×C₅	C₂⁴	1	4	yes	—
120	C₂⁴×C₅	C₂⁴	1	4	yes	—
121	C₂×C₅×D₄	—	2	8	no	—
122	C₂×C₅×D₄	—	2	8	no	—
123	C₂×C₅×D₄	—	2	4	no	—
124	C₂×C₅×D₄	—	2	4	no	—
125	C₂×C₅×D₄	—	4	64	no	—
126	C₂×C₅×D₄	—	4	2	no	—
127	C₂×C₅×D₄	—	4	8	no	—
128	C₂×C₅×D₄	—	4	8	no	—
129	C₂×C₅×D₄	—	4	2	no	—
130	C₂×C₅×D₄	C₂²×C₄	1	8	yes	—
131	C₂×C₅×D₄	C₂²×C₄	1	16	yes	—
132	C₂×C₅×D₄	C₂²×C₄	1	8	yes	—
133	C₂×C₅×D₄	C₂²×C₄	1	32	yes	—
134	C₂²×C₄×C₅	—	2	8	no	—
135	C₂²×C₄×C₅	—	2	8	no	—
136	C₂²×C₄×C₅	—	2	8	no	—
137	C₂²×C₄×C₅	—	4	4	no	—
138	C₂²×C₄×C₅	—	4	8	no	—
139	C₂²×C₄×C₅	—	4	8	no	—
140	C₂²×C₄×C₅	C₂²×C₄	1	16	yes	—
141	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
142	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
143	C₂²×C₄×C₅	C₂⁴	1	4	yes	—
144	C₂²×C₄×C₅	C₂⁴	1	4	yes	—
145	C₂²×C₄×C₅	C₂⁴	1	4	yes	—
146	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
147	C₂²×C₄×C₅	C₂⁴	1	4	yes	—
148	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
149	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
150	C₅×C₄⋊C₄	—	2	4	no	—
151	C₅×C₄⋊C₄	—	2	8	no	—
152	C₅×C₄⋊C₄	—	2	4	no	—
153	C₅×C₄⋊C₄	—	4	4	no	—
154	C₅×C₄⋊C₄	—	4	4	no	—
155	C₅×C₄⋊C₄	—	4	2	no	—
156	C₅×C₄⋊C₄	C₂²×C₄	1	8	yes	—
157	C₅×C₂²⋊C₄	—	2	8	no	—
158	C₅×C₂²⋊C₄	—	4	8	no	—
159	C₅×C₂²⋊C₄	—	4	4	no	—
160	C₅×C₂²⋊C₄	—	4	4	no	—
161	C₅×C₂²⋊C₄	—	4	4	no	—
162	C₅×C₂²⋊C₄	—	4	4	no	—
163	C₅×C₂²⋊C₄	—	4	8	no	—
164	C₅×C₂²⋊C₄	—	4	8	no	—
165	C₅×C₂²⋊C₄	—	4	4	no	—
166	C₅×C₂²⋊C₄	—	4	8	no	—
167	C₅×C₂²⋊C₄	C₂²×C₄	1	16	yes	—
168	C₅×C₂²⋊C₄	C₂²×C₄	1	16	yes	—
169	C₄²×C₅	—	2	4	no	—
170	C₄²×C₅	—	2	8	no	—
171	C₄²×C₅	—	2	2	no	—
172	C₄²×C₅	—	2	4	no	—
173	C₄²×C₅	—	4	1	no	—
174	C₄²×C₅	—	4	8	no	—
175	C₄²×C₅	C₂²×C₄	1	4	yes	—
176	C₂³×D₄	C₂²×C₅	1	4	yes	—
177	D₄²	C₄×C₅	1	16	yes	complemented
178	C₂×#127	C₂²×C₅	1	1	yes	characteristic
179	C₂×#121	C₂²×C₅	1	4	yes	—
180	C₂×#120	C₂²×C₅	1	4	yes	—
181	C₂×C₄×D₄	C₂²×C₅	1	2	yes	—
182	C₂×C₄×D₄	C₂²×C₅	1	2	yes	complemented
183	C₂×C₄×D₄	C₂²×C₅	1	4	yes	complemented
184	C₂×C₄×D₄	C₂²×C₅	1	4	yes	complemented
185	C₂×#117	C₂²×C₅	1	4	yes	complemented
186	C₂×#117	C₂²×C₅	1	4	yes	complemented
187	C₂²×C₂²⋊C₄	C₂²×C₅	1	4	yes	complemented
188	#390	C₂²×C₅	1	2	yes	—
189	#390	C₂²×C₅	1	4	yes	—
190	#390	C₂²×C₅	1	2	yes	—
191	#390	C₂²×C₅	1	4	yes	complemented
192	#390	C₂²×C₅	1	2	yes	complemented
193	#390	C₂²×C₅	1	8	yes	complemented
194	#390	C₂²×C₅	1	4	yes	complemented
195	#390	C₂²×C₅	1	8	yes	complemented
196	#389	C₂²×C₅	1	2	yes	complemented
197	#389	C₂²×C₅	1	2	yes	complemented
198	#388	C₂²×C₅	1	4	yes	complemented
199	#388	C₂²×C₅	1	8	yes	complemented
200	#388	C₂²×C₅	1	8	yes	complemented
201	#388	C₂²×C₅	1	4	yes	complemented
202	#386	C₂²×C₅	1	8	yes	complemented
203	#386	C₂²×C₅	1	4	yes	complemented
204	#386	C₂²×C₅	1	8	yes	complemented
205	#385	C₂²×C₅	1	4	yes	complemented
206	#384	C₂²×C₅	1	1	yes	characteristic, complemented
207	#380	C₂²×C₅	1	4	yes	complemented
208	#379	C₂²×C₅	1	4	yes	complemented
209	#379	C₂²×C₅	1	8	yes	complemented
210	C₄×C₄⋊C₄	C₂²×C₅	1	4	yes	complemented
211	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	complemented
212	C₄×C₂²⋊C₄	C₂²×C₅	1	4	yes	complemented
213	C₄×C₂²⋊C₄	C₂²×C₅	1	4	yes	complemented
214	C₄³	C₂²×C₅	1	1	yes	characteristic, complemented
215	C₂³×C₅	—	2	4	no	—
216	C₂³×C₅	—	2	4	no	—
217	C₂³×C₅	—	2	4	no	—
218	C₂³×C₅	—	2	4	no	—
219	C₂³×C₅	—	2	8	no	—
220	C₂³×C₅	—	2	8	no	—
221	C₂³×C₅	—	2	4	no	—
222	C₂³×C₅	—	2	4	no	—
223	C₂³×C₅	—	2	4	no	—
224	C₂³×C₅	—	2	4	no	—
225	C₂³×C₅	—	4	32	no	—
226	C₂³×C₅	—	4	16	no	—
227	C₂³×C₅	—	8	8	no	—
228	C₂³×C₅	—	8	16	no	—
229	C₂³×C₅	—	8	8	no	—
230	C₂³×C₅	C₂³×C₄	1	8	yes	—
231	C₂³×C₅	C₂³×C₄	1	8	yes	—
232	C₂³×C₅	C₂⁵	1	1	yes	characteristic
233	C₅×D₄	—	2	16	no	—
234	C₅×D₄	—	2	32	no	—
235	C₅×D₄	—	4	32	no	—
236	C₅×D₄	—	4	8	no	—
237	C₂×C₄×C₅	—	2	1	no	—
238	C₂×C₄×C₅	—	2	2	no	—
239	C₂×C₄×C₅	—	2	4	no	—
240	C₂×C₄×C₅	—	2	4	no	—
241	C₂×C₄×C₅	—	2	1	no	—
242	C₂×C₄×C₅	—	2	32	no	—
243	C₂×C₄×C₅	—	2	2	no	—
244	C₂×C₄×C₅	—	2	1	no	—
245	C₂×C₄×C₅	—	2	4	no	—
246	C₂×C₄×C₅	—	2	2	no	—
247	C₂×C₄×C₅	—	2	2	no	—
248	C₂×C₄×C₅	—	2	4	no	—
249	C₂×C₄×C₅	—	2	4	no	—
250	C₂×C₄×C₅	—	2	8	no	—
251	C₂×C₄×C₅	—	2	4	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	—	2	4	no	—
256	C₂×C₄×C₅	—	8	8	no	—
257	C₂×C₄×C₅	—	8	8	no	—
258	C₂×C₄×C₅	C₂³×C₄	1	2	yes	—
259	C₂×C₄×C₅	C₂³×C₄	1	8	yes	—
260	C₂×C₄×C₅	C₂³×C₄	1	4	yes	—
261	C₂×C₄×C₅	H(5,𝔽₂)	1	2	yes	—
262	C₂×C₄×C₅	H(5,𝔽₂)	1	4	yes	—
263	C₂×C₄×C₅	H(5,𝔽₂)	1	4	yes	—
264	C₂⁵	C₂³×C₅	1	4	yes	—
265	C₂²×D₄	—	4	8	no	—
266	C₂²×D₄	—	4	8	no	—
267	C₂²×D₄	C₂×C₄×C₅	1	32	yes	complemented
268	C₂²×D₄	C₂³×C₅	1	2	yes	—
269	C₂²×D₄	C₂³×C₅	1	4	yes	—
270	C₂²×D₄	C₂³×C₅	1	2	yes	—
271	C₂²×D₄	C₂³×C₅	1	8	yes	—
272	C₂³×C₄	C₂³×C₅	1	4	yes	—
273	C₂³×C₄	C₂³×C₅	1	4	yes	—
274	C₂³×C₄	C₂³×C₅	1	4	yes	—
275	#127	C₂×C₄×C₅	1	8	yes	—
276	#121	C₂×C₄×C₅	1	32	yes	complemented
277	#120	C₂×C₄×C₅	1	32	yes	complemented
278	C₄×D₄	—	4	8	no	—
279	C₄×D₄	—	4	8	no	—
280	C₄×D₄	—	4	4	no	—
281	C₄×D₄	C₂×C₄×C₅	1	16	yes	complemented
282	#117	—	4	8	no	—
283	#117	—	4	8	no	—
284	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
285	C₂×C₄⋊C₄	C₂³×C₅	1	4	yes	—
286	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
287	C₂×C₄⋊C₄	C₂³×C₅	1	4	yes	—
288	C₂×C₄⋊C₄	C₂³×C₅	1	4	yes	—
289	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
290	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
291	C₂×C₂²⋊C₄	—	4	8	no	—
292	C₂×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
293	C₂×C₂²⋊C₄	C₂³×C₅	1	8	yes	—
294	C₂×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
295	C₂×C₂²⋊C₄	C₂³×C₅	1	8	yes	—
296	C₂×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
297	C₂×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
298	C₂×C₂²⋊C₄	C₂³×C₅	1	8	yes	—
299	C₂×C₂²⋊C₄	C₂³×C₅	1	8	yes	—
300	C₂×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
301	C₂×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
302	C₂×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
303	C₂×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
304	C₂×C₄²	C₂³×C₅	1	2	yes	—
305	C₂×C₄²	C₂³×C₅	1	4	yes	—
306	C₂×C₄²	C₂³×C₅	1	2	yes	—
307	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
308	C₂×C₄²	C₂³×C₅	1	8	yes	—
309	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
310	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
311	#95	C₂³×C₅	1	4	yes	—
312	#95	C₂³×C₅	1	4	yes	—
313	#95	C₂³×C₅	1	8	yes	—
314	#95	C₂³×C₅	1	4	yes	—
315	C₂²×C₅	—	2	8	no	—
316	C₂²×C₅	—	2	8	no	—
317	C₂²×C₅	—	2	16	no	—
318	C₂²×C₅	—	2	8	no	—
319	C₂²×C₅	—	2	8	no	—
320	C₂²×C₅	—	4	4	no	—
321	C₂²×C₅	—	4	4	no	—
322	C₂²×C₅	—	4	8	no	—
323	C₂²×C₅	—	4	4	no	—
324	C₂²×C₅	—	4	4	no	—
325	C₂²×C₅	—	4	4	no	—
326	C₂²×C₅	—	4	4	no	—
327	C₂²×C₅	—	8	32	no	—
328	C₂²×C₅	C₂⁴×C₄	1	1	yes	characteristic
329	C₂²×C₅	C₂×H(5,𝔽₂)	1	2	yes	—
330	C₂²×C₅	C₂×H(5,𝔽₂)	1	2	yes	—
331	C₂²×C₅	C₂×H(5,𝔽₂)	1	1	yes	characteristic
332	C₂²×C₅	#585	1	1	yes	characteristic
333	C₄×C₅	—	2	8	no	—
334	C₄×C₅	—	2	2	no	—
335	C₄×C₅	—	2	2	no	—
336	C₄×C₅	—	4	4	no	—
337	C₄×C₅	—	4	2	no	—
338	C₄×C₅	—	4	4	no	—
339	C₄×C₅	—	4	1	no	—
340	C₄×C₅	—	4	4	no	—
341	C₄×C₅	#518	1	8	yes	—
342	C₂⁴	—	4	4	no	—
343	C₂⁴	—	4	8	no	—
344	C₂⁴	—	4	8	no	—
345	C₂⁴	—	4	4	no	—
346	C₂⁴	C₂²×C₄×C₅	1	16	yes	—
347	C₂⁴	C₂⁴×C₅	1	4	yes	—
348	C₂⁴	C₂⁴×C₅	1	4	yes	—
349	C₂×D₄	—	2	8	no	—
350	C₂×D₄	—	2	8	no	—
351	C₂×D₄	—	2	4	no	—
352	C₂×D₄	—	2	4	no	—
353	C₂×D₄	—	4	64	no	—
354	C₂×D₄	—	4	2	no	—
355	C₂×D₄	—	4	8	no	—
356	C₂×D₄	—	4	8	no	—
357	C₂×D₄	—	4	2	no	—
358	C₂×D₄	C₂²×C₄×C₅	1	8	yes	—
359	C₂×D₄	C₂²×C₄×C₅	1	16	yes	—
360	C₂×D₄	C₂²×C₄×C₅	1	8	yes	—
361	C₂×D₄	C₂²×C₄×C₅	1	32	yes	—
362	C₂²×C₄	—	2	8	no	—
363	C₂²×C₄	—	2	8	no	—
364	C₂²×C₄	—	2	8	no	—
365	C₂²×C₄	—	4	4	no	—
366	C₂²×C₄	—	4	8	no	—
367	C₂²×C₄	—	4	8	no	—
368	C₂²×C₄	C₂²×C₄×C₅	1	16	yes	—
369	C₂²×C₄	C₂⁴×C₅	1	4	yes	—
370	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
371	C₂²×C₄	C₂⁴×C₅	1	4	yes	—
372	C₂²×C₄	C₂⁴×C₅	1	4	yes	—
373	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
374	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
375	C₂²×C₄	C₂⁴×C₅	1	4	yes	—
376	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
377	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
378	C₄⋊C₄	—	2	4	no	—
379	C₄⋊C₄	—	2	8	no	—
380	C₄⋊C₄	—	2	4	no	—
381	C₄⋊C₄	—	4	4	no	—
382	C₄⋊C₄	—	4	4	no	—
383	C₄⋊C₄	—	4	2	no	—
384	C₄⋊C₄	C₂²×C₄×C₅	1	8	yes	—
385	C₂²⋊C₄	—	2	8	no	—
386	C₂²⋊C₄	—	4	8	no	—
387	C₂²⋊C₄	—	4	4	no	—
388	C₂²⋊C₄	—	4	4	no	—
389	C₂²⋊C₄	—	4	8	no	—
390	C₂²⋊C₄	—	4	8	no	—
391	C₂²⋊C₄	—	4	4	no	—
392	C₂²⋊C₄	—	4	8	no	—
393	C₂²⋊C₄	—	4	4	no	—
394	C₂²⋊C₄	—	4	4	no	—
395	C₂²⋊C₄	C₂²×C₄×C₅	1	16	yes	—
396	C₂²⋊C₄	C₂²×C₄×C₅	1	16	yes	—
397	C₄²	—	2	4	no	—
398	C₄²	—	2	8	no	—
399	C₄²	—	2	2	no	—
400	C₄²	—	2	4	no	—
401	C₄²	—	4	8	no	—
402	C₄²	—	4	1	no	—
403	C₄²	C₂²×C₄×C₅	1	4	yes	—
404	C₂×C₅	—	4	8	no	—
405	C₂×C₅	—	4	8	no	—
406	C₂×C₅	C₂×#518	1	2	yes	—
407	C₂×C₅	C₄×H(5,𝔽₂)	1	1	yes	characteristic
408	C₂×C₅	#3543	1	1	yes	characteristic
409	C₂×C₅	#3546	1	2	yes	—
410	C₂×C₅	#3549	1	1	yes	characteristic
411	C₂³	—	2	4	no	—
412	C₂³	—	2	4	no	—
413	C₂³	—	2	4	no	—
414	C₂³	—	2	4	no	—
415	C₂³	—	2	8	no	—
416	C₂³	—	2	8	no	—
417	C₂³	—	2	4	no	—
418	C₂³	—	2	4	no	—
419	C₂³	—	2	4	no	—
420	C₂³	—	2	4	no	—
421	C₂³	—	4	32	no	—
422	C₂³	—	4	16	no	—
423	C₂³	—	8	8	no	—
424	C₂³	—	8	16	no	—
425	C₂³	—	8	8	no	—
426	C₂³	C₂³×C₄×C₅	1	8	yes	—
427	C₂³	C₂³×C₄×C₅	1	8	yes	—
428	C₂³	C₂⁵×C₅	1	1	yes	characteristic
429	D₄	—	2	16	no	—
430	D₄	—	2	32	no	—
431	D₄	—	4	32	no	—
432	D₄	—	4	8	no	—
433	C₂×C₄	—	2	1	no	—
434	C₂×C₄	—	2	2	no	—
435	C₂×C₄	—	2	4	no	—
436	C₂×C₄	—	2	4	no	—
437	C₂×C₄	—	2	1	no	—
438	C₂×C₄	—	2	32	no	—
439	C₂×C₄	—	2	2	no	—
440	C₂×C₄	—	2	1	no	—
441	C₂×C₄	—	2	4	no	—
442	C₂×C₄	—	2	2	no	—
443	C₂×C₄	—	2	2	no	—
444	C₂×C₄	—	2	4	no	—
445	C₂×C₄	—	2	4	no	—
446	C₂×C₄	—	2	8	no	—
447	C₂×C₄	—	2	4	no	—
448	C₂×C₄	—	2	4	no	—
449	C₂×C₄	—	2	4	no	—
450	C₂×C₄	—	2	2	no	—
451	C₂×C₄	—	2	4	no	—
452	C₂×C₄	—	8	8	no	—
453	C₂×C₄	—	8	8	no	—
454	C₂×C₄	C₂³×C₄×C₅	1	2	yes	—
455	C₂×C₄	C₂³×C₄×C₅	1	8	yes	—
456	C₂×C₄	C₂³×C₄×C₅	1	4	yes	—
457	C₂×C₄	C₅×H(5,𝔽₂)	1	2	yes	—
458	C₂×C₄	C₅×H(5,𝔽₂)	1	4	yes	—
459	C₂×C₄	C₅×H(5,𝔽₂)	1	4	yes	—
460	C₅	#34493	1	1	yes	characteristic, direct product factor, Sylow
461	C₂²	—	2	8	no	—
462	C₂²	—	2	8	no	—
463	C₂²	—	2	16	no	—
464	C₂²	—	2	8	no	—
465	C₂²	—	2	8	no	—
466	C₂²	—	4	4	no	—
467	C₂²	—	4	4	no	—
468	C₂²	—	4	4	no	—
469	C₂²	—	4	4	no	—
470	C₂²	—	4	8	no	—
471	C₂²	—	4	4	no	—
472	C₂²	—	4	4	no	—
473	C₂²	—	8	32	no	—
474	C₂²	C₂⁴×C₄×C₅	1	1	yes	characteristic
475	C₂²	C₂×C₅×H(5,𝔽₂)	1	2	yes	—
476	C₂²	C₂×C₅×H(5,𝔽₂)	1	2	yes	—
477	C₂²	C₂×C₅×H(5,𝔽₂)	1	1	yes	characteristic
478	C₂²	C₅×#585	1	1	yes	characteristic
479	C₄	—	2	8	no	—
480	C₄	—	2	2	no	—
481	C₄	—	2	2	no	—
482	C₄	—	4	4	no	—
483	C₄	—	4	2	no	—
484	C₄	—	4	4	no	—
485	C₄	—	4	4	no	—
486	C₄	—	4	1	no	—
487	C₄	C₅×#518	1	8	yes	—
488	C₂	—	4	8	no	—
489	C₂	—	4	8	no	—
490	C₂	C₂×C₅×#518	1	2	yes	—
491	C₂	C₄×C₅×H(5,𝔽₂)	1	1	yes	characteristic
492	C₂	C₅×#3543	1	1	yes	characteristic
493	C₂	C₅×#3546	1	2	yes	—
494	C₂	C₅×#3549	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₅	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₅
Frattini, cosocle	C₂³	C₂⁵×C₅
prime radical	C₂×C₅×D₄²	C₂
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
2. C₅×#2375	C₂	semidirect
3. C₅×#2366	C₂	semidirect
4. C₅×#2363	C₂	semidirect
5. C₅×#2354	C₂	semidirect
6. C₅×D₄×C₂²⋊C₄	C₂	semidirect
7. C₅×#2324	C₂	semidirect
8. C₅×#2321	C₂	semidirect
9. C₅×#2309	C₂	semidirect
10. C₄×C₅×#127	C₂	semidirect
11. C₅×#2293	C₂	semidirect
13. C₅×D₄²	C₄	semidirect
18. C₂×C₄×C₅×D₄	C₂²	semidirect
19. C₂×C₄×C₅×D₄	C₂²	semidirect
20. C₂×C₄×C₅×D₄	C₂²	semidirect
21. C₂×C₅×#117	C₂²	semidirect
22. C₂×C₅×#117	C₂²	semidirect
23. C₂²×C₅×C₂²⋊C₄	C₂²	semidirect
27. C₅×#390	C₂²	semidirect
28. C₅×#390	C₂²	semidirect
29. C₅×#390	C₂²	semidirect
30. C₅×#390	C₂²	semidirect
31. C₅×#390	C₂²	semidirect
32. C₅×#389	C₂²	semidirect
33. C₅×#389	C₂²	semidirect
34. C₅×#388	C₂²	semidirect
35. C₅×#388	C₂²	semidirect
36. C₅×#388	C₂²	semidirect
37. C₅×#388	C₂²	semidirect
38. C₅×#386	C₂²	semidirect
39. C₅×#386	C₂²	semidirect
40. C₅×#386	C₂²	semidirect
41. C₅×#385	C₂²	semidirect
42. C₅×#384	C₂²	semidirect
43. C₅×#380	C₂²	semidirect
44. C₅×#379	C₂²	semidirect
45. C₅×#379	C₂²	semidirect
46. C₄×C₅×C₄⋊C₄	C₂²	semidirect
47. C₄×C₅×C₄⋊C₄	C₂²	semidirect
48. C₄×C₅×C₂²⋊C₄	C₂²	semidirect
49. C₄×C₅×C₂²⋊C₄	C₂²	semidirect
50. C₄³×C₅	C₂²	semidirect
51. #34493	C₅	direct (N × H)
55. C₂²×C₅×D₄	C₂×C₄	semidirect
64. C₅×#121	C₂×C₄	semidirect
65. C₅×#120	C₂×C₄	semidirect
69. C₄×C₅×D₄	C₂×C₄	semidirect
104. #2375	C₂×C₅	semidirect
105. #2366	C₂×C₅	semidirect
106. #2363	C₂×C₅	semidirect
107. #2354	C₂×C₅	semidirect
108. D₄×C₂²⋊C₄	C₂×C₅	semidirect
109. #2324	C₂×C₅	semidirect
110. #2321	C₂×C₅	semidirect
111. #2309	C₂×C₅	semidirect
112. C₄×#127	C₂×C₅	semidirect
113. #2293	C₂×C₅	semidirect
177. D₄²	C₄×C₅	semidirect
182. C₂×C₄×D₄	C₂²×C₅	semidirect
183. C₂×C₄×D₄	C₂²×C₅	semidirect
184. C₂×C₄×D₄	C₂²×C₅	semidirect
185. C₂×#117	C₂²×C₅	semidirect
186. C₂×#117	C₂²×C₅	semidirect
187. C₂²×C₂²⋊C₄	C₂²×C₅	semidirect
191. #390	C₂²×C₅	semidirect
192. #390	C₂²×C₅	semidirect
193. #390	C₂²×C₅	semidirect
194. #390	C₂²×C₅	semidirect
195. #390	C₂²×C₅	semidirect
196. #389	C₂²×C₅	semidirect
197. #389	C₂²×C₅	semidirect
198. #388	C₂²×C₅	semidirect
199. #388	C₂²×C₅	semidirect
200. #388	C₂²×C₅	semidirect
201. #388	C₂²×C₅	semidirect
202. #386	C₂²×C₅	semidirect
203. #386	C₂²×C₅	semidirect
204. #386	C₂²×C₅	semidirect
205. #385	C₂²×C₅	semidirect
206. #384	C₂²×C₅	semidirect
207. #380	C₂²×C₅	semidirect
208. #379	C₂²×C₅	semidirect
209. #379	C₂²×C₅	semidirect
210. C₄×C₄⋊C₄	C₂²×C₅	semidirect
211. C₄×C₄⋊C₄	C₂²×C₅	semidirect
212. C₄×C₂²⋊C₄	C₂²×C₅	semidirect
213. C₄×C₂²⋊C₄	C₂²×C₅	semidirect
214. C₄³	C₂²×C₅	semidirect
267. C₂²×D₄	C₂×C₄×C₅	semidirect
276. #121	C₂×C₄×C₅	semidirect
277. #120	C₂×C₄×C₅	semidirect
281. C₄×D₄	C₂×C₄×C₅	semidirect
460. C₅	#34493	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×D₄²	2
C₅×#2375	2
C₅×#2366	2
C₅×#2363	2
C₅×#2354	2
C₅×D₄×C₂²⋊C₄	2
C₅×#2324	2
C₅×#2321	2
C₅×#2309	2
C₄×C₅×#127	2
C₅×#2293	2
#34493	5

Subgroups — C5×#34493 #11957213

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#34493 #11957213