Subgroups — C₅×#35284 #11958004

Order 1280.

1722 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#2868	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×#2859	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#2857	C₂	1	2	yes	maximal
4	C₅×#2647	C₂	1	2	yes	maximal, complemented
5	C₅×#2629	C₂	1	2	yes	maximal
6	C₅×#2507	C₂	1	4	yes	maximal, complemented
7	C₅×#2497	C₂	1	4	yes	maximal
8	C₅×#2446	C₂	1	4	yes	maximal, complemented
9	C₅×#2429	C₂	1	4	yes	maximal
10	C₅×#2330	C₂	1	2	yes	maximal, complemented
11	C₅×#2314	C₂	1	2	yes	maximal
12	C₄×C₅×C₄⋊Q₈	C₂	1	2	yes	maximal, complemented
13	C₄×C₅×#117	C₂	1	1	yes	maximal, characteristic
14	C₂×C₅×C₄⋊Q₈	C₂²	1	2	yes	—
15	C₂×C₅×C₄⋊Q₈	C₂²	1	4	yes	—
16	C₂×C₅×#125	C₂²	1	2	yes	—
17	C₂×C₅×C₂²⋊Q₈	C₂²	1	4	yes	—
18	C₂×C₄×C₅×Q₈	C₂²	1	4	yes	—
19	C₂×C₅×#117	C₂²	1	1	yes	characteristic
20	C₂×C₅×#117	C₂²	1	1	yes	characteristic
21	C₂²×C₄²×C₅	C₂²	1	1	yes	characteristic
22	C₅×#400	C₂²	1	8	yes	—
23	C₅×#398	C₂²	1	8	yes	—
24	C₅×#398	C₂²	1	8	yes	—
25	C₅×#396	C₂²	1	8	yes	—
26	C₅×#391	C₂²	1	4	yes	—
27	C₅×#391	C₂²	1	4	yes	—
28	C₅×#389	C₂²	1	4	yes	—
29	C₅×#389	C₂²	1	4	yes	—
30	C₅×#389	C₂²	1	4	yes	—
31	C₅×#389	C₂²	1	8	yes	—
32	C₅×#389	C₂²	1	4	yes	—
33	C₅×#389	C₂²	1	4	yes	—
34	C₅×#389	C₂²	1	4	yes	—
35	C₅×#388	C₂²	1	8	yes	—
36	C₅×#387	C₂²	1	8	yes	—
37	C₅×#387	C₂²	1	8	yes	—
38	C₅×#384	C₂²	1	4	yes	—
39	C₅×#384	C₂²	1	2	yes	—
40	C₅×#384	C₂²	1	2	yes	—
41	C₅×#384	C₂²	1	2	yes	—
42	C₅×#382	C₂²	1	2	yes	—
43	C₅×#380	C₂²	1	4	yes	—
44	C₅×#380	C₂²	1	4	yes	—
45	C₄×C₅×C₄⋊C₄	C₂²	1	4	yes	—
46	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
47	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
48	C₄×C₅×C₄⋊C₄	C₂²	1	4	yes	—
49	C₄×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
50	C₄×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
51	C₅×#376	C₂²	1	1	yes	characteristic
52	C₅×#376	C₂²	1	1	yes	characteristic
53	C₄³×C₅	C₂²	1	1	yes	characteristic
54	C₄³×C₅	C₂²	1	1	yes	characteristic
55	#35284	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
56	C₂²×C₅×Q₈	C₂³	1	4	yes	—
57	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
58	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
59	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
60	C₅×C₄⋊Q₈	—	2	8	no	—
61	C₅×C₄⋊Q₈	—	4	8	no	—
62	C₅×#125	—	2	8	no	—
63	C₅×C₂²⋊Q₈	—	4	8	no	—
64	C₄×C₅×Q₈	—	4	8	no	—
65	C₅×#117	—	2	4	no	—
66	C₅×#117	Q₈	1	8	yes	complemented
67	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
68	C₂×C₅×C₄⋊C₄	C₂³	1	4	yes	—
69	C₂×C₅×C₄⋊C₄	C₂³	1	4	yes	—
70	C₂×C₅×C₄⋊C₄	C₂³	1	4	yes	—
71	C₂×C₅×C₄⋊C₄	C₂³	1	4	yes	—
72	C₂×C₅×C₄⋊C₄	C₂³	1	4	yes	—
73	C₂×C₅×C₄⋊C₄	C₂³	1	8	yes	—
74	C₂×C₅×C₄⋊C₄	C₂³	1	8	yes	—
75	C₂×C₅×C₄⋊C₄	C₂³	1	8	yes	—
76	C₂×C₅×C₄⋊C₄	C₂³	1	8	yes	—
77	C₂×C₅×C₄⋊C₄	C₂³	1	8	yes	—
78	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
79	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
80	C₂×C₅×C₂²⋊C₄	C₂³	1	8	yes	—
81	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
82	C₂×C₄²×C₅	—	2	4	no	—
83	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
84	C₂×C₄²×C₅	C₂³	1	2	yes	—
85	C₂×C₄²×C₅	C₂³	1	2	yes	—
86	C₂×C₄²×C₅	C₂³	1	2	yes	—
87	C₂×C₄²×C₅	C₂³	1	2	yes	—
88	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
89	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
90	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
91	C₂×C₄²×C₅	C₂³	1	8	yes	—
92	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
93	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
94	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
95	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
96	C₅×#95	C₂³	1	2	yes	—
97	C₅×#95	C₂³	1	2	yes	—
98	C₅×#95	C₂³	1	2	yes	—
99	C₅×#95	C₂³	1	2	yes	—
100	C₅×#95	C₂³	1	8	yes	—
101	C₅×#95	C₂³	1	8	yes	—
102	C₅×#95	C₂³	1	8	yes	—
103	C₅×#95	C₂³	1	8	yes	—
104	C₅×#95	C₂³	1	8	yes	—
105	#2868	C₂×C₅	1	1	yes	characteristic, complemented
106	#2859	C₂×C₅	1	1	yes	characteristic, complemented
107	#2857	C₂×C₅	1	2	yes	—
108	#2647	C₂×C₅	1	2	yes	complemented
109	#2629	C₂×C₅	1	2	yes	—
110	#2507	C₂×C₅	1	4	yes	complemented
111	#2497	C₂×C₅	1	4	yes	—
112	#2446	C₂×C₅	1	4	yes	complemented
113	#2429	C₂×C₅	1	4	yes	—
114	#2330	C₂×C₅	1	2	yes	complemented
115	#2314	C₂×C₅	1	2	yes	—
116	C₄×C₄⋊Q₈	C₂×C₅	1	2	yes	complemented
117	C₄×#117	C₂×C₅	1	1	yes	characteristic
118	C₂⁴×C₅	C₂⁴	1	1	yes	characteristic
119	C₂×C₅×Q₈	—	2	8	no	—
120	C₂×C₅×Q₈	—	2	8	no	—
121	C₂×C₅×Q₈	—	2	8	no	—
122	C₂²×C₄×C₅	—	2	2	no	—
123	C₂²×C₄×C₅	—	2	2	no	—
124	C₂²×C₄×C₅	—	2	2	no	—
125	C₂²×C₄×C₅	—	2	2	no	—
126	C₂²×C₄×C₅	—	2	4	no	—
127	C₂²×C₄×C₅	—	2	4	no	—
128	C₂²×C₄×C₅	C₂×Q₈	1	4	yes	—
129	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
130	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
131	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
132	C₂²×C₄×C₅	C₂⁴	1	8	yes	—
133	C₂²×C₄×C₅	C₂⁴	1	8	yes	—
134	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
135	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
136	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
137	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
138	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
139	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
140	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
141	C₅×C₄⋊C₄	—	2	4	no	—
142	C₅×C₄⋊C₄	—	2	16	no	—
143	C₅×C₄⋊C₄	—	2	8	no	—
144	C₅×C₄⋊C₄	—	2	8	no	—
145	C₅×C₄⋊C₄	—	2	8	no	—
146	C₅×C₄⋊C₄	—	2	8	no	—
147	C₅×C₄⋊C₄	—	2	8	no	—
148	C₅×C₄⋊C₄	—	4	8	no	—
149	C₅×C₄⋊C₄	—	4	8	no	—
150	C₅×C₄⋊C₄	—	4	8	no	—
151	C₅×C₄⋊C₄	—	4	8	no	—
152	C₅×C₄⋊C₄	C₂×Q₈	1	8	yes	—
153	C₅×C₂²⋊C₄	—	2	4	no	—
154	C₅×C₂²⋊C₄	—	4	8	no	—
155	C₅×C₂²⋊C₄	C₂×Q₈	1	8	yes	—
156	C₄²×C₅	—	2	2	no	—
157	C₄²×C₅	—	2	2	no	—
158	C₄²×C₅	—	2	2	no	—
159	C₄²×C₅	—	2	2	no	—
160	C₄²×C₅	—	2	4	no	—
161	C₄²×C₅	—	2	4	no	—
162	C₄²×C₅	—	2	4	no	—
163	C₄²×C₅	—	2	4	no	—
164	C₄²×C₅	—	4	8	no	—
165	C₄²×C₅	C₂×Q₈	1	4	yes	—
166	C₄²×C₅	C₂×Q₈	1	4	yes	—
167	C₄²×C₅	#41	1	4	yes	—
168	C₄²×C₅	#41	1	4	yes	—
169	C₂×C₄⋊Q₈	C₂²×C₅	1	2	yes	—
170	C₂×C₄⋊Q₈	C₂²×C₅	1	4	yes	—
171	C₂×#125	C₂²×C₅	1	2	yes	—
172	C₂×C₂²⋊Q₈	C₂²×C₅	1	4	yes	—
173	C₂×C₄×Q₈	C₂²×C₅	1	4	yes	—
174	C₂×#117	C₂²×C₅	1	1	yes	characteristic
175	C₂×#117	C₂²×C₅	1	1	yes	characteristic
176	C₂²×C₄²	C₂²×C₅	1	1	yes	characteristic
177	#400	C₂²×C₅	1	8	yes	—
178	#398	C₂²×C₅	1	8	yes	—
179	#398	C₂²×C₅	1	8	yes	—
180	#396	C₂²×C₅	1	8	yes	—
181	#391	C₂²×C₅	1	4	yes	—
182	#391	C₂²×C₅	1	4	yes	—
183	#389	C₂²×C₅	1	4	yes	—
184	#389	C₂²×C₅	1	4	yes	—
185	#389	C₂²×C₅	1	4	yes	—
186	#389	C₂²×C₅	1	8	yes	—
187	#389	C₂²×C₅	1	4	yes	—
188	#389	C₂²×C₅	1	4	yes	—
189	#389	C₂²×C₅	1	4	yes	—
190	#388	C₂²×C₅	1	8	yes	—
191	#387	C₂²×C₅	1	8	yes	—
192	#387	C₂²×C₅	1	8	yes	—
193	#384	C₂²×C₅	1	2	yes	—
194	#384	C₂²×C₅	1	2	yes	—
195	#384	C₂²×C₅	1	2	yes	—
196	#384	C₂²×C₅	1	4	yes	—
197	#382	C₂²×C₅	1	2	yes	—
198	#380	C₂²×C₅	1	4	yes	—
199	#380	C₂²×C₅	1	4	yes	—
200	C₄×C₄⋊C₄	C₂²×C₅	1	4	yes	—
201	C₄×C₄⋊C₄	C₂²×C₅	1	4	yes	—
202	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
203	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
204	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
205	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
206	#376	C₂²×C₅	1	1	yes	characteristic
207	#376	C₂²×C₅	1	1	yes	characteristic
208	C₄³	C₂²×C₅	1	1	yes	characteristic
209	C₄³	C₂²×C₅	1	1	yes	characteristic
210	C₂³×C₅	—	2	1	no	—
211	C₂³×C₅	—	2	1	no	—
212	C₂³×C₅	—	2	2	no	—
213	C₂³×C₅	—	2	2	no	—
214	C₂³×C₅	C₂²×Q₈	1	2	yes	—
215	C₂³×C₅	C₂⁵	1	1	yes	characteristic
216	C₅×Q₈	—	4	16	no	—
217	C₂×C₄×C₅	—	2	1	no	—
218	C₂×C₄×C₅	—	2	1	no	—
219	C₂×C₄×C₅	—	2	2	no	—
220	C₂×C₄×C₅	—	2	2	no	—
221	C₂×C₄×C₅	—	2	2	no	—
222	C₂×C₄×C₅	—	2	2	no	—
223	C₂×C₄×C₅	—	2	2	no	—
224	C₂×C₄×C₅	—	2	2	no	—
225	C₂×C₄×C₅	—	2	8	no	—
226	C₂×C₄×C₅	—	2	1	no	—
227	C₂×C₄×C₅	—	2	1	no	—
228	C₂×C₄×C₅	—	2	2	no	—
229	C₂×C₄×C₅	—	2	8	no	—
230	C₂×C₄×C₅	—	2	8	no	—
231	C₂×C₄×C₅	—	2	2	no	—
232	C₂×C₄×C₅	—	2	8	no	—
233	C₂×C₄×C₅	—	2	8	no	—
234	C₂×C₄×C₅	—	2	8	no	—
235	C₂×C₄×C₅	—	2	2	no	—
236	C₂×C₄×C₅	—	2	2	no	—
237	C₂×C₄×C₅	—	2	8	no	—
238	C₂×C₄×C₅	—	2	2	no	—
239	C₂×C₄×C₅	—	4	4	no	—
240	C₂×C₄×C₅	—	4	4	no	—
241	C₂×C₄×C₅	C₂²×Q₈	1	4	yes	—
242	C₂×C₄×C₅	C₂²×Q₈	1	4	yes	—
243	C₂×C₄×C₅	C₂²×Q₈	1	2	yes	—
244	C₂×C₄×C₅	C₂²×Q₈	1	2	yes	—
245	C₂×C₄×C₅	C₂×#41	1	4	yes	—
246	C₂×C₄×C₅	C₂×#41	1	2	yes	—
247	C₂×C₄×C₅	C₂×#41	1	2	yes	—
248	C₂×C₄×C₅	C₂×#41	1	2	yes	—
249	C₂×C₄×C₅	C₂×#41	1	2	yes	—
250	C₂×C₄×C₅	H(5,𝔽₂)	1	4	yes	—
251	C₂×C₄×C₅	2₋¹⁺⁴	1	4	yes	—
252	C₂²×Q₈	C₂³×C₅	1	4	yes	—
253	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
254	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
255	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
256	C₄⋊Q₈	—	2	8	no	—
257	C₄⋊Q₈	—	4	8	no	—
258	#125	—	2	8	no	—
259	C₂²⋊Q₈	—	4	8	no	—
260	C₄×Q₈	—	4	8	no	—
261	#117	—	2	4	no	—
262	#117	C₅×Q₈	1	8	yes	complemented
263	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
264	C₂×C₄⋊C₄	C₂³×C₅	1	4	yes	—
265	C₂×C₄⋊C₄	C₂³×C₅	1	4	yes	—
266	C₂×C₄⋊C₄	C₂³×C₅	1	8	yes	—
267	C₂×C₄⋊C₄	C₂³×C₅	1	4	yes	—
268	C₂×C₄⋊C₄	C₂³×C₅	1	4	yes	—
269	C₂×C₄⋊C₄	C₂³×C₅	1	4	yes	—
270	C₂×C₄⋊C₄	C₂³×C₅	1	8	yes	—
271	C₂×C₄⋊C₄	C₂³×C₅	1	8	yes	—
272	C₂×C₄⋊C₄	C₂³×C₅	1	8	yes	—
273	C₂×C₄⋊C₄	C₂³×C₅	1	8	yes	—
274	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
275	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
276	C₂×C₂²⋊C₄	C₂³×C₅	1	8	yes	—
277	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
278	C₂×C₄²	—	2	4	no	—
279	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
280	C₂×C₄²	C₂³×C₅	1	2	yes	—
281	C₂×C₄²	C₂³×C₅	1	2	yes	—
282	C₂×C₄²	C₂³×C₅	1	2	yes	—
283	C₂×C₄²	C₂³×C₅	1	2	yes	—
284	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
285	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
286	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
287	C₂×C₄²	C₂³×C₅	1	8	yes	—
288	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
289	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
290	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
291	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
292	#95	C₂³×C₅	1	2	yes	—
293	#95	C₂³×C₅	1	2	yes	—
294	#95	C₂³×C₅	1	2	yes	—
295	#95	C₂³×C₅	1	2	yes	—
296	#95	C₂³×C₅	1	8	yes	—
297	#95	C₂³×C₅	1	8	yes	—
298	#95	C₂³×C₅	1	8	yes	—
299	#95	C₂³×C₅	1	8	yes	—
300	#95	C₂³×C₅	1	8	yes	—
301	C₂²×C₅	—	2	2	no	—
302	C₂²×C₅	—	2	4	no	—
303	C₂²×C₅	—	4	1	no	—
304	C₂²×C₅	—	4	1	no	—
305	C₂²×C₅	—	4	2	no	—
306	C₂²×C₅	C₂³×Q₈	1	1	yes	characteristic
307	C₂²×C₅	C₂²×#41	1	1	yes	characteristic
308	C₂²×C₅	C₂²×#41	1	1	yes	characteristic
309	C₂²×C₅	C₂×H(5,𝔽₂)	1	2	yes	—
310	C₂²×C₅	C₂×2₋¹⁺⁴	1	2	yes	—
311	C₄×C₅	—	2	2	no	—
312	C₄×C₅	—	2	4	no	—
313	C₄×C₅	—	2	4	no	—
314	C₄×C₅	—	2	4	no	—
315	C₄×C₅	—	4	1	no	—
316	C₄×C₅	—	4	8	no	—
317	C₄×C₅	—	4	1	no	—
318	C₄×C₅	—	4	2	no	—
319	C₄×C₅	—	4	8	no	—
320	C₄×C₅	#533	1	4	yes	—
321	C₄×C₅	#540	1	4	yes	—
322	C₄×C₅	#541	1	4	yes	—
323	C₂⁴	C₂⁴×C₅	1	1	yes	characteristic
324	C₂×Q₈	—	2	8	no	—
325	C₂×Q₈	—	2	8	no	—
326	C₂×Q₈	—	2	8	no	—
327	C₂²×C₄	—	2	2	no	—
328	C₂²×C₄	—	2	2	no	—
329	C₂²×C₄	—	2	2	no	—
330	C₂²×C₄	—	2	2	no	—
331	C₂²×C₄	—	2	4	no	—
332	C₂²×C₄	—	2	4	no	—
333	C₂²×C₄	C₂×C₅×Q₈	1	4	yes	—
334	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
335	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
336	C₂²×C₄	C₂⁴×C₅	1	8	yes	—
337	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
338	C₂²×C₄	C₂⁴×C₅	1	8	yes	—
339	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
340	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
341	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
342	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
343	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
344	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
345	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
346	C₄⋊C₄	—	2	4	no	—
347	C₄⋊C₄	—	2	16	no	—
348	C₄⋊C₄	—	2	8	no	—
349	C₄⋊C₄	—	2	8	no	—
350	C₄⋊C₄	—	2	8	no	—
351	C₄⋊C₄	—	2	8	no	—
352	C₄⋊C₄	—	2	8	no	—
353	C₄⋊C₄	—	4	8	no	—
354	C₄⋊C₄	—	4	8	no	—
355	C₄⋊C₄	—	4	8	no	—
356	C₄⋊C₄	—	4	8	no	—
357	C₄⋊C₄	C₂×C₅×Q₈	1	8	yes	—
358	C₂²⋊C₄	—	2	4	no	—
359	C₂²⋊C₄	—	4	8	no	—
360	C₂²⋊C₄	C₂×C₅×Q₈	1	8	yes	—
361	C₄²	—	2	2	no	—
362	C₄²	—	2	2	no	—
363	C₄²	—	2	2	no	—
364	C₄²	—	2	2	no	—
365	C₄²	—	2	4	no	—
366	C₄²	—	2	4	no	—
367	C₄²	—	2	4	no	—
368	C₄²	—	2	4	no	—
369	C₄²	—	4	8	no	—
370	C₄²	C₂×C₅×Q₈	1	4	yes	—
371	C₄²	C₂×C₅×Q₈	1	4	yes	—
372	C₄²	C₅×#41	1	4	yes	—
373	C₄²	C₅×#41	1	4	yes	—
374	C₂×C₅	—	4	2	no	—
375	C₂×C₅	C₂×#533	1	1	yes	characteristic
376	C₂×C₅	C₂×#540	1	1	yes	characteristic
377	C₂×C₅	C₂×#541	1	1	yes	characteristic
378	C₂×C₅	#3503	1	2	yes	—
379	C₂×C₅	#3511	1	2	yes	—
380	C₂³	—	2	1	no	—
381	C₂³	—	2	1	no	—
382	C₂³	—	2	2	no	—
383	C₂³	—	2	2	no	—
384	C₂³	C₂²×C₅×Q₈	1	2	yes	—
385	C₂³	C₂⁵×C₅	1	1	yes	characteristic
386	Q₈	—	4	16	no	—
387	C₂×C₄	—	2	1	no	—
388	C₂×C₄	—	2	1	no	—
389	C₂×C₄	—	2	2	no	—
390	C₂×C₄	—	2	2	no	—
391	C₂×C₄	—	2	2	no	—
392	C₂×C₄	—	2	2	no	—
393	C₂×C₄	—	2	2	no	—
394	C₂×C₄	—	2	2	no	—
395	C₂×C₄	—	2	8	no	—
396	C₂×C₄	—	2	1	no	—
397	C₂×C₄	—	2	1	no	—
398	C₂×C₄	—	2	2	no	—
399	C₂×C₄	—	2	8	no	—
400	C₂×C₄	—	2	8	no	—
401	C₂×C₄	—	2	2	no	—
402	C₂×C₄	—	2	8	no	—
403	C₂×C₄	—	2	8	no	—
404	C₂×C₄	—	2	8	no	—
405	C₂×C₄	—	2	2	no	—
406	C₂×C₄	—	2	2	no	—
407	C₂×C₄	—	2	8	no	—
408	C₂×C₄	—	2	2	no	—
409	C₂×C₄	—	4	4	no	—
410	C₂×C₄	—	4	4	no	—
411	C₂×C₄	C₂²×C₅×Q₈	1	4	yes	—
412	C₂×C₄	C₂²×C₅×Q₈	1	4	yes	—
413	C₂×C₄	C₂²×C₅×Q₈	1	2	yes	—
414	C₂×C₄	C₂²×C₅×Q₈	1	2	yes	—
415	C₂×C₄	C₂×C₅×#41	1	4	yes	—
416	C₂×C₄	C₂×C₅×#41	1	2	yes	—
417	C₂×C₄	C₂×C₅×#41	1	2	yes	—
418	C₂×C₄	C₂×C₅×#41	1	2	yes	—
419	C₂×C₄	C₂×C₅×#41	1	2	yes	—
420	C₂×C₄	C₅×H(5,𝔽₂)	1	4	yes	—
421	C₂×C₄	C₅×2₋¹⁺⁴	1	4	yes	—
422	C₅	#35284	1	1	yes	characteristic, direct product factor, Sylow
423	C₂²	—	2	2	no	—
424	C₂²	—	2	4	no	—
425	C₂²	—	4	1	no	—
426	C₂²	—	4	1	no	—
427	C₂²	—	4	2	no	—
428	C₂²	C₂³×C₅×Q₈	1	1	yes	characteristic
429	C₂²	C₂²×C₅×#41	1	1	yes	characteristic
430	C₂²	C₂²×C₅×#41	1	1	yes	characteristic
431	C₂²	C₂×C₅×H(5,𝔽₂)	1	2	yes	—
432	C₂²	C₂×C₅×2₋¹⁺⁴	1	2	yes	—
433	C₄	—	2	2	no	—
434	C₄	—	2	4	no	—
435	C₄	—	2	4	no	—
436	C₄	—	2	4	no	—
437	C₄	—	4	1	no	—
438	C₄	—	4	8	no	—
439	C₄	—	4	1	no	—
440	C₄	—	4	2	no	—
441	C₄	—	4	8	no	—
442	C₄	C₅×#533	1	4	yes	—
443	C₄	C₅×#540	1	4	yes	—
444	C₄	C₅×#541	1	4	yes	—
445	C₂	—	4	2	no	—
446	C₂	C₂×C₅×#533	1	1	yes	characteristic
447	C₂	C₂×C₅×#540	1	1	yes	characteristic
448	C₂	C₂×C₅×#541	1	1	yes	characteristic
449	C₂	C₅×#3503	1	2	yes	—
450	C₂	C₅×#3511	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₅	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₅
prime radical	C₂⁴×C₅	C₂⁴
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₅×#2868	C₂	semidirect
2. C₅×#2859	C₂	semidirect
4. C₅×#2647	C₂	semidirect
6. C₅×#2507	C₂	semidirect
8. C₅×#2446	C₂	semidirect
10. C₅×#2330	C₂	semidirect
12. C₄×C₅×C₄⋊Q₈	C₂	semidirect
55. #35284	C₅	direct (N × H)
66. C₅×#117	Q₈	semidirect
105. #2868	C₂×C₅	semidirect
106. #2859	C₂×C₅	semidirect
108. #2647	C₂×C₅	semidirect
110. #2507	C₂×C₅	semidirect
112. #2446	C₂×C₅	semidirect
114. #2330	C₂×C₅	semidirect
116. C₄×C₄⋊Q₈	C₂×C₅	semidirect
262. #117	C₅×Q₈	semidirect
422. C₅	#35284	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×#2868	2
C₅×#2859	2
C₅×#2857	2
C₅×#2647	2
C₅×#2629	2
C₅×#2507	2
C₅×#2497	2
C₅×#2446	2
C₅×#2429	2
C₅×#2330	2
C₅×#2314	2
C₄×C₅×C₄⋊Q₈	2
C₄×C₅×#117	2
#35284	5

Subgroups — C5×#35284 #11958004

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#35284 #11958004