Subgroups — C₅×#34938 #11957658

Order 1280.

2290 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#533	C₂	1	2	yes	maximal
2	C₅×#2552	C₂	1	2	yes	maximal, complemented
3	C₅×#2551	C₂	1	2	yes	maximal, complemented
4	C₅×#2550	C₂	1	4	yes	maximal, complemented
5	C₅×#2549	C₂	1	4	yes	maximal
6	C₅×#2440	C₂	1	4	yes	maximal
7	C₅×#2399	C₂	1	4	yes	maximal, complemented
8	C₄×C₅×C₄⋊Q₈	C₂	1	4	yes	maximal, complemented
9	C₅×#2296	C₂	1	2	yes	maximal
10	C₅×#2285	C₂	1	1	yes	maximal, characteristic
11	C₄×C₅×#117	C₂	1	1	yes	maximal, characteristic
12	C₂×C₄×C₅×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
13	C₅×#533	—	2	16	no	—
14	C₂×C₅×C₄⋊Q₈	C₂²	1	4	yes	—
15	C₂×C₅×C₄⋊Q₈	C₂²	1	4	yes	—
16	C₂×C₅×#125	C₂²	1	4	yes	—
17	C₂×C₅×C₂²⋊Q₈	C₂²	1	8	yes	—
18	C₂×C₄×C₅×Q₈	C₂²	1	8	yes	—
19	C₂×C₅×#117	C₂²	1	2	yes	—
20	C₂×C₅×#117	C₂²	1	1	yes	characteristic
21	C₂×C₅×#117	C₂²	1	1	yes	characteristic
22	C₂²×C₅×C₄⋊C₄	C₂²	1	2	yes	—
23	C₂²×C₄²×C₅	C₂²	1	2	yes	—
24	C₂²×C₄²×C₅	C₂²	1	1	yes	characteristic
25	C₅×#398	C₂²	1	8	yes	—
26	C₅×#398	C₂²	1	8	yes	—
27	C₅×#395	C₂²	1	8	yes	—
28	C₅×#395	C₂²	1	8	yes	—
29	C₅×#391	C₂²	1	8	yes	—
30	C₅×#389	C₂²	1	8	yes	—
31	C₅×#389	C₂²	1	4	yes	—
32	C₅×#389	C₂²	1	4	yes	—
33	C₅×#389	C₂²	1	4	yes	—
34	C₅×#389	C₂²	1	4	yes	—
35	C₅×#385	C₂²	1	8	yes	—
36	C₅×#384	C₂²	1	2	yes	—
37	C₅×#384	C₂²	1	4	yes	—
38	C₅×#382	C₂²	1	2	yes	—
39	C₅×#380	C₂²	1	2	yes	—
40	C₅×#380	C₂²	1	2	yes	—
41	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
42	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
43	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
44	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
45	C₄×C₅×C₄⋊C₄	C₂²	1	2	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	2	yes	—
49	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
50	C₄×C₅×C₄⋊C₄	C₂²	1	8	yes	—
51	C₄×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
52	C₄×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
53	C₅×#376	C₂²	1	2	yes	—
54	C₂×C₅×#95	C₂²	1	2	yes	—
55	C₄³×C₅	C₂²	1	2	yes	—
56	#34938	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
57	C₂²×C₅×Q₈	C₂³	1	8	yes	—
58	C₂³×C₄×C₅	C₂³	1	4	yes	—
59	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
60	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
61	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
62	C₅×C₄⋊Q₈	—	2	16	no	—
63	C₅×C₄⋊Q₈	—	2	16	no	—
64	C₅×#125	—	2	16	no	—
65	C₅×C₂²⋊Q₈	—	2	32	no	—
66	C₄×C₅×Q₈	—	2	32	no	—
67	C₅×#117	—	2	8	no	—
68	C₅×#117	D₄	1	8	yes	—
69	C₅×#117	Q₈	1	8	yes	complemented
70	C₂×C₅×C₄⋊C₄	—	2	8	no	—
71	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
72	C₂×C₅×C₄⋊C₄	C₂³	1	4	yes	—
73	C₂×C₅×C₄⋊C₄	C₂³	1	4	yes	—
74	C₂×C₅×C₄⋊C₄	C₂³	1	8	yes	—
75	C₂×C₅×C₄⋊C₄	C₂³	1	4	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	8	yes	—
79	C₂×C₅×C₄⋊C₄	C₂³	1	4	yes	—
80	C₂×C₅×C₄⋊C₄	C₂³	1	8	yes	—
81	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
82	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
83	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
84	C₂×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
85	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
86	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
87	C₂×C₄²×C₅	—	2	8	no	—
88	C₂×C₄²×C₅	Q₈	1	8	yes	complemented
89	C₂×C₄²×C₅	C₂³	1	4	yes	—
90	C₂×C₄²×C₅	C₂³	1	2	yes	—
91	C₂×C₄²×C₅	C₂³	1	2	yes	—
92	C₂×C₄²×C₅	C₂³	1	4	yes	—
93	C₂×C₄²×C₅	C₂³	1	4	yes	—
94	C₂×C₄²×C₅	C₂³	1	4	yes	—
95	C₂×C₄²×C₅	C₂³	1	2	yes	—
96	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
97	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
98	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
99	C₂×C₄²×C₅	C₂³	1	2	yes	—
100	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
101	C₅×#95	C₂³	1	4	yes	—
102	C₅×#95	C₂³	1	2	yes	—
103	C₅×#95	C₂³	1	2	yes	—
104	C₅×#95	C₂³	1	4	yes	—
105	C₅×#95	C₂³	1	4	yes	—
106	C₅×#95	C₂³	1	4	yes	—
107	C₅×#95	C₂³	1	4	yes	—
108	C₅×#95	C₂³	1	8	yes	—
109	C₅×#95	C₂³	1	8	yes	—
110	C₂×#533	C₂×C₅	1	2	yes	—
111	#2552	C₂×C₅	1	2	yes	complemented
112	#2551	C₂×C₅	1	2	yes	complemented
113	#2550	C₂×C₅	1	4	yes	complemented
114	#2549	C₂×C₅	1	4	yes	—
115	#2440	C₂×C₅	1	4	yes	—
116	#2399	C₂×C₅	1	4	yes	complemented
117	C₄×C₄⋊Q₈	C₂×C₅	1	4	yes	complemented
118	#2296	C₂×C₅	1	2	yes	—
119	#2285	C₂×C₅	1	1	yes	characteristic
120	C₄×#117	C₂×C₅	1	1	yes	characteristic
121	C₂×C₄×C₄⋊C₄	C₂×C₅	1	1	yes	characteristic
122	C₂⁴×C₅	C₂⁴	1	1	yes	characteristic
123	C₂×C₅×Q₈	—	2	16	no	—
124	C₂×C₅×Q₈	—	2	16	no	—
125	C₂×C₅×Q₈	—	4	8	no	—
126	C₂²×C₄×C₅	—	2	4	no	—
127	C₂²×C₄×C₅	—	2	8	no	—
128	C₂²×C₄×C₅	—	2	8	no	—
129	C₂²×C₄×C₅	—	4	2	no	—
130	C₂²×C₄×C₅	—	4	4	no	—
131	C₂²×C₄×C₅	C₂×D₄	1	4	yes	—
132	C₂²×C₄×C₅	C₂×Q₈	1	4	yes	—
133	C₂²×C₄×C₅	C₂×Q₈	1	4	yes	—
134	C₂²×C₄×C₅	C₂×Q₈	1	4	yes	—
135	C₂²×C₄×C₅	C₂×Q₈	1	4	yes	—
136	C₂²×C₄×C₅	C₂⁴	1	4	yes	—
137	C₂²×C₄×C₅	C₂⁴	1	8	yes	—
138	C₂²×C₄×C₅	C₂⁴	1	4	yes	—
139	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
140	C₂²×C₄×C₅	C₂⁴	1	4	yes	—
141	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
142	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
143	C₂²×C₄×C₅	C₂⁴	1	4	yes	—
144	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
145	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
146	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
147	C₅×C₄⋊C₄	—	2	8	no	—
148	C₅×C₄⋊C₄	—	2	16	no	—
149	C₅×C₄⋊C₄	—	2	16	no	—
150	C₅×C₄⋊C₄	—	2	16	no	—
151	C₅×C₄⋊C₄	—	2	8	no	—
152	C₅×C₄⋊C₄	—	2	4	no	—
153	C₅×C₄⋊C₄	—	2	16	no	—
154	C₅×C₄⋊C₄	—	2	8	no	—
155	C₅×C₄⋊C₄	—	4	8	no	—
156	C₅×C₄⋊C₄	—	4	4	no	—
157	C₅×C₄⋊C₄	C₂×D₄	1	8	yes	—
158	C₅×C₄⋊C₄	C₂×Q₈	1	8	yes	—
159	C₅×C₄⋊C₄	#41	1	8	yes	—
160	C₅×C₂²⋊C₄	—	2	8	no	—
161	C₅×C₂²⋊C₄	C₂×D₄	1	8	yes	—
162	C₅×C₂²⋊C₄	C₂×Q₈	1	8	yes	—
163	C₄²×C₅	—	2	8	no	—
164	C₄²×C₅	—	2	4	no	—
165	C₄²×C₅	—	2	4	no	—
166	C₄²×C₅	—	2	8	no	—
167	C₄²×C₅	—	2	8	no	—
168	C₄²×C₅	—	4	4	no	—
169	C₄²×C₅	C₂×D₄	1	8	yes	—
170	C₄²×C₅	C₂×Q₈	1	4	yes	—
171	C₄²×C₅	C₂×Q₈	1	4	yes	—
172	C₄²×C₅	C₂×Q₈	1	4	yes	—
173	C₄²×C₅	C₂×Q₈	1	4	yes	—
174	C₄²×C₅	C₂×Q₈	1	8	yes	—
175	#533	—	2	16	no	—
176	C₂×C₄⋊Q₈	C₂²×C₅	1	4	yes	—
177	C₂×C₄⋊Q₈	C₂²×C₅	1	4	yes	—
178	C₂×#125	C₂²×C₅	1	4	yes	—
179	C₂×C₂²⋊Q₈	C₂²×C₅	1	8	yes	—
180	C₂×C₄×Q₈	C₂²×C₅	1	8	yes	—
181	C₂×#117	C₂²×C₅	1	2	yes	—
182	C₂×#117	C₂²×C₅	1	1	yes	characteristic
183	C₂×#117	C₂²×C₅	1	1	yes	characteristic
184	C₂²×C₄⋊C₄	C₂²×C₅	1	2	yes	—
185	C₂²×C₄²	C₂²×C₅	1	2	yes	—
186	C₂²×C₄²	C₂²×C₅	1	1	yes	characteristic
187	#398	C₂²×C₅	1	8	yes	—
188	#398	C₂²×C₅	1	8	yes	—
189	#395	C₂²×C₅	1	8	yes	—
190	#395	C₂²×C₅	1	8	yes	—
191	#391	C₂²×C₅	1	8	yes	—
192	#389	C₂²×C₅	1	4	yes	—
193	#389	C₂²×C₅	1	4	yes	—
194	#389	C₂²×C₅	1	8	yes	—
195	#389	C₂²×C₅	1	4	yes	—
196	#389	C₂²×C₅	1	4	yes	—
197	#385	C₂²×C₅	1	8	yes	—
198	#384	C₂²×C₅	1	4	yes	—
199	#384	C₂²×C₅	1	2	yes	—
200	#382	C₂²×C₅	1	2	yes	—
201	#380	C₂²×C₅	1	2	yes	—
202	#380	C₂²×C₅	1	2	yes	—
203	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
204	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
205	C₄×C₄⋊C₄	C₂²×C₅	1	8	yes	—
206	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
207	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
208	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
209	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
210	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
211	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
212	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
213	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
214	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
215	#376	C₂²×C₅	1	2	yes	—
216	C₂×#95	C₂²×C₅	1	2	yes	—
217	C₄³	C₂²×C₅	1	2	yes	—
218	C₂³×C₅	—	2	2	no	—
219	C₂³×C₅	—	2	2	no	—
220	C₂³×C₅	C₂²×D₄	1	2	yes	—
221	C₂³×C₅	C₂²×Q₈	1	2	yes	—
222	C₂³×C₅	C₂²×Q₈	1	2	yes	—
223	C₂³×C₅	C₂⁵	1	1	yes	characteristic
224	C₅×Q₈	—	4	32	no	—
225	C₂×C₄×C₅	—	2	4	no	—
226	C₂×C₄×C₅	—	2	4	no	—
227	C₂×C₄×C₅	—	2	4	no	—
228	C₂×C₄×C₅	—	2	2	no	—
229	C₂×C₄×C₅	—	2	2	no	—
230	C₂×C₄×C₅	—	2	4	no	—
231	C₂×C₄×C₅	—	2	4	no	—
232	C₂×C₄×C₅	—	2	2	no	—
233	C₂×C₄×C₅	—	2	4	no	—
234	C₂×C₄×C₅	—	2	8	no	—
235	C₂×C₄×C₅	—	2	4	no	—
236	C₂×C₄×C₅	—	2	8	no	—
237	C₂×C₄×C₅	—	2	4	no	—
238	C₂×C₄×C₅	—	2	8	no	—
239	C₂×C₄×C₅	—	2	4	no	—
240	C₂×C₄×C₅	—	2	8	no	—
241	C₂×C₄×C₅	—	4	4	no	—
242	C₂×C₄×C₅	—	4	16	no	—
243	C₂×C₄×C₅	C₄⋊Q₈	1	16	yes	complemented
244	C₂×C₄×C₅	C₂²×D₄	1	8	yes	—
245	C₂×C₄×C₅	C₂²×D₄	1	2	yes	—
246	C₂×C₄×C₅	C₂²×D₄	1	2	yes	—
247	C₂×C₄×C₅	C₂²×Q₈	1	2	yes	—
248	C₂×C₄×C₅	C₂²×Q₈	1	2	yes	—
249	C₂×C₄×C₅	C₂²×Q₈	1	2	yes	—
250	C₂×C₄×C₅	C₂²×Q₈	1	8	yes	—
251	C₂×C₄×C₅	C₂²×Q₈	1	2	yes	—
252	C₂×C₄×C₅	C₂²×Q₈	1	2	yes	—
253	C₂×C₄×C₅	C₂²×Q₈	1	2	yes	—
254	C₂×C₄×C₅	C₂²×Q₈	1	2	yes	—
255	C₂×C₄×C₅	C₂²×Q₈	1	2	yes	—
256	C₂×C₄×C₅	C₂×#41	1	8	yes	—
257	C₂×C₄×C₅	C₂×#41	1	4	yes	—
258	C₂²×Q₈	C₂³×C₅	1	8	yes	—
259	C₂³×C₄	C₂³×C₅	1	4	yes	—
260	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
261	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
262	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
263	C₄⋊Q₈	—	2	16	no	—
264	C₄⋊Q₈	—	2	16	no	—
265	#125	—	2	16	no	—
266	C₂²⋊Q₈	—	2	32	no	—
267	C₄×Q₈	—	2	32	no	—
268	#117	—	2	8	no	—
269	#117	C₅×D₄	1	8	yes	—
270	#117	C₅×Q₈	1	8	yes	complemented
271	C₂×C₄⋊C₄	—	2	8	no	—
272	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
273	C₂×C₄⋊C₄	C₂³×C₅	1	4	yes	—
274	C₂×C₄⋊C₄	C₂³×C₅	1	4	yes	—
275	C₂×C₄⋊C₄	C₂³×C₅	1	8	yes	—
276	C₂×C₄⋊C₄	C₂³×C₅	1	8	yes	—
277	C₂×C₄⋊C₄	C₂³×C₅	1	8	yes	—
278	C₂×C₄⋊C₄	C₂³×C₅	1	4	yes	—
279	C₂×C₄⋊C₄	C₂³×C₅	1	8	yes	—
280	C₂×C₄⋊C₄	C₂³×C₅	1	4	yes	—
281	C₂×C₄⋊C₄	C₂³×C₅	1	8	yes	—
282	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
283	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
284	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
285	C₂×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
286	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
287	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
288	C₂×C₄²	—	2	8	no	—
289	C₂×C₄²	C₅×Q₈	1	8	yes	complemented
290	C₂×C₄²	C₂³×C₅	1	4	yes	—
291	C₂×C₄²	C₂³×C₅	1	4	yes	—
292	C₂×C₄²	C₂³×C₅	1	2	yes	—
293	C₂×C₄²	C₂³×C₅	1	2	yes	—
294	C₂×C₄²	C₂³×C₅	1	4	yes	—
295	C₂×C₄²	C₂³×C₅	1	4	yes	—
296	C₂×C₄²	C₂³×C₅	1	2	yes	—
297	C₂×C₄²	C₂³×C₅	1	2	yes	—
298	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
299	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
300	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
301	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
302	#95	C₂³×C₅	1	4	yes	—
303	#95	C₂³×C₅	1	2	yes	—
304	#95	C₂³×C₅	1	2	yes	—
305	#95	C₂³×C₅	1	4	yes	—
306	#95	C₂³×C₅	1	4	yes	—
307	#95	C₂³×C₅	1	4	yes	—
308	#95	C₂³×C₅	1	4	yes	—
309	#95	C₂³×C₅	1	8	yes	—
310	#95	C₂³×C₅	1	8	yes	—
311	C₂²×C₅	—	2	2	no	—
312	C₂²×C₅	—	2	2	no	—
313	C₂²×C₅	—	2	4	no	—
314	C₂²×C₅	—	2	4	no	—
315	C₂²×C₅	C₂×C₄⋊Q₈	1	4	yes	—
316	C₂²×C₅	C₂³×D₄	1	1	yes	characteristic
317	C₂²×C₅	C₂³×Q₈	1	1	yes	characteristic
318	C₂²×C₅	C₂³×Q₈	1	1	yes	characteristic
319	C₂²×C₅	C₂²×#41	1	2	yes	—
320	C₂²×C₅	#585	1	2	yes	—
321	C₄×C₅	—	2	2	no	—
322	C₄×C₅	—	2	2	no	—
323	C₄×C₅	—	2	2	no	—
324	C₄×C₅	—	2	8	no	—
325	C₄×C₅	—	2	8	no	—
326	C₄×C₅	—	2	8	no	—
327	C₄×C₅	—	4	4	no	—
328	C₄×C₅	—	4	8	no	—
329	C₄×C₅	C₂×C₄⋊Q₈	1	4	yes	—
330	C₄×C₅	C₂×C₄⋊Q₈	1	4	yes	—
331	C₄×C₅	#533	1	4	yes	complemented
332	C₂⁴	C₂⁴×C₅	1	1	yes	characteristic
333	C₂×Q₈	—	2	16	no	—
334	C₂×Q₈	—	2	16	no	—
335	C₂×Q₈	—	4	8	no	—
336	C₂²×C₄	—	2	4	no	—
337	C₂²×C₄	—	2	8	no	—
338	C₂²×C₄	—	2	8	no	—
339	C₂²×C₄	—	4	2	no	—
340	C₂²×C₄	—	4	4	no	—
341	C₂²×C₄	C₂×C₅×D₄	1	4	yes	—
342	C₂²×C₄	C₂×C₅×Q₈	1	4	yes	—
343	C₂²×C₄	C₂×C₅×Q₈	1	4	yes	—
344	C₂²×C₄	C₂×C₅×Q₈	1	4	yes	—
345	C₂²×C₄	C₂×C₅×Q₈	1	4	yes	—
346	C₂²×C₄	C₂⁴×C₅	1	4	yes	—
347	C₂²×C₄	C₂⁴×C₅	1	8	yes	—
348	C₂²×C₄	C₂⁴×C₅	1	4	yes	—
349	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
350	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
351	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
352	C₂²×C₄	C₂⁴×C₅	1	4	yes	—
353	C₂²×C₄	C₂⁴×C₅	1	4	yes	—
354	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
355	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
356	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
357	C₄⋊C₄	—	2	8	no	—
358	C₄⋊C₄	—	2	16	no	—
359	C₄⋊C₄	—	2	16	no	—
360	C₄⋊C₄	—	2	16	no	—
361	C₄⋊C₄	—	2	8	no	—
362	C₄⋊C₄	—	2	4	no	—
363	C₄⋊C₄	—	2	16	no	—
364	C₄⋊C₄	—	2	8	no	—
365	C₄⋊C₄	—	4	8	no	—
366	C₄⋊C₄	—	4	4	no	—
367	C₄⋊C₄	C₂×C₅×D₄	1	8	yes	—
368	C₄⋊C₄	C₂×C₅×Q₈	1	8	yes	—
369	C₄⋊C₄	C₅×#41	1	8	yes	—
370	C₂²⋊C₄	—	2	8	no	—
371	C₂²⋊C₄	C₂×C₅×D₄	1	8	yes	—
372	C₂²⋊C₄	C₂×C₅×Q₈	1	8	yes	—
373	C₄²	—	2	8	no	—
374	C₄²	—	2	4	no	—
375	C₄²	—	2	4	no	—
376	C₄²	—	2	8	no	—
377	C₄²	—	2	8	no	—
378	C₄²	—	4	4	no	—
379	C₄²	C₂×C₅×D₄	1	8	yes	—
380	C₄²	C₂×C₅×Q₈	1	4	yes	—
381	C₄²	C₂×C₅×Q₈	1	4	yes	—
382	C₄²	C₂×C₅×Q₈	1	4	yes	—
383	C₄²	C₂×C₅×Q₈	1	4	yes	—
384	C₄²	C₂×C₅×Q₈	1	8	yes	—
385	C₂×C₅	—	2	4	no	—
386	C₂×C₅	C₂²×C₄⋊Q₈	1	1	yes	characteristic
387	C₂×C₅	C₂×#533	1	1	yes	characteristic
388	C₂×C₅	#3458	1	1	yes	characteristic
389	C₂×C₅	D₄×#41	1	2	yes	—
390	C₂×C₅	Q₈×#41	1	2	yes	—
391	C₂³	—	2	2	no	—
392	C₂³	—	2	2	no	—
393	C₂³	C₂²×C₅×D₄	1	2	yes	—
394	C₂³	C₂²×C₅×Q₈	1	2	yes	—
395	C₂³	C₂²×C₅×Q₈	1	2	yes	—
396	C₂³	C₂⁵×C₅	1	1	yes	characteristic
397	Q₈	—	4	32	no	—
398	C₂×C₄	—	2	4	no	—
399	C₂×C₄	—	2	4	no	—
400	C₂×C₄	—	2	4	no	—
401	C₂×C₄	—	2	2	no	—
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	2	4	no	—
404	C₂×C₄	—	2	4	no	—
405	C₂×C₄	—	2	2	no	—
406	C₂×C₄	—	2	4	no	—
407	C₂×C₄	—	2	8	no	—
408	C₂×C₄	—	2	4	no	—
409	C₂×C₄	—	2	8	no	—
410	C₂×C₄	—	2	4	no	—
411	C₂×C₄	—	2	8	no	—
412	C₂×C₄	—	2	4	no	—
413	C₂×C₄	—	2	8	no	—
414	C₂×C₄	—	4	4	no	—
415	C₂×C₄	—	4	16	no	—
416	C₂×C₄	C₅×C₄⋊Q₈	1	16	yes	complemented
417	C₂×C₄	C₂²×C₅×D₄	1	8	yes	—
418	C₂×C₄	C₂²×C₅×D₄	1	2	yes	—
419	C₂×C₄	C₂²×C₅×D₄	1	2	yes	—
420	C₂×C₄	C₂²×C₅×Q₈	1	2	yes	—
421	C₂×C₄	C₂²×C₅×Q₈	1	2	yes	—
422	C₂×C₄	C₂²×C₅×Q₈	1	2	yes	—
423	C₂×C₄	C₂²×C₅×Q₈	1	8	yes	—
424	C₂×C₄	C₂²×C₅×Q₈	1	2	yes	—
425	C₂×C₄	C₂²×C₅×Q₈	1	2	yes	—
426	C₂×C₄	C₂²×C₅×Q₈	1	2	yes	—
427	C₂×C₄	C₂²×C₅×Q₈	1	2	yes	—
428	C₂×C₄	C₂²×C₅×Q₈	1	2	yes	—
429	C₂×C₄	C₂×C₅×#41	1	8	yes	—
430	C₂×C₄	C₂×C₅×#41	1	4	yes	—
431	C₅	#34938	1	1	yes	characteristic, direct product factor, Sylow
432	C₂²	—	2	2	no	—
433	C₂²	—	2	2	no	—
434	C₂²	—	2	4	no	—
435	C₂²	—	2	4	no	—
436	C₂²	C₂×C₅×C₄⋊Q₈	1	4	yes	—
437	C₂²	C₂³×C₅×D₄	1	1	yes	characteristic
438	C₂²	C₂³×C₅×Q₈	1	1	yes	characteristic
439	C₂²	C₂³×C₅×Q₈	1	1	yes	characteristic
440	C₂²	C₂²×C₅×#41	1	2	yes	—
441	C₂²	C₅×#585	1	2	yes	—
442	C₄	—	2	2	no	—
443	C₄	—	2	2	no	—
444	C₄	—	2	2	no	—
445	C₄	—	2	8	no	—
446	C₄	—	2	8	no	—
447	C₄	—	2	8	no	—
448	C₄	—	4	4	no	—
449	C₄	—	4	8	no	—
450	C₄	C₂×C₅×C₄⋊Q₈	1	4	yes	—
451	C₄	C₂×C₅×C₄⋊Q₈	1	4	yes	—
452	C₄	C₅×#533	1	4	yes	complemented
453	C₂	—	2	4	no	—
454	C₂	C₂²×C₅×C₄⋊Q₈	1	1	yes	characteristic
455	C₂	C₂×C₅×#533	1	1	yes	characteristic
456	C₂	C₅×#3458	1	1	yes	characteristic
457	C₂	C₅×D₄×#41	1	2	yes	—
458	C₂	C₅×Q₈×#41	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄×C₅	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₅
socle	C₂³×C₅	C₂⁵
prime radical	C₂⁴×C₅	C₂⁴
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₅×#2552	C₂	semidirect
3. C₅×#2551	C₂	semidirect
4. C₅×#2550	C₂	semidirect
7. C₅×#2399	C₂	semidirect
8. C₄×C₅×C₄⋊Q₈	C₂	semidirect
56. #34938	C₅	direct (N × H)
69. C₅×#117	Q₈	semidirect
88. C₂×C₄²×C₅	Q₈	semidirect
111. #2552	C₂×C₅	semidirect
112. #2551	C₂×C₅	semidirect
113. #2550	C₂×C₅	semidirect
116. #2399	C₂×C₅	semidirect
117. C₄×C₄⋊Q₈	C₂×C₅	semidirect
243. C₂×C₄×C₅	C₄⋊Q₈	semidirect
270. #117	C₅×Q₈	semidirect
289. C₂×C₄²	C₅×Q₈	semidirect
331. C₄×C₅	#533	semidirect
416. C₂×C₄	C₅×C₄⋊Q₈	semidirect
431. C₅	#34938	direct (N × H)
452. C₄	C₅×#533	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×#533	2
C₅×#2552	2
C₅×#2551	2
C₅×#2550	2
C₅×#2549	2
C₅×#2440	2
C₅×#2399	2
C₄×C₅×C₄⋊Q₈	2
C₅×#2296	2
C₅×#2285	2
C₄×C₅×#117	2
C₂×C₄×C₅×C₄⋊C₄	2
#34938	5

Subgroups — C5×#34938 #11957658

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#34938 #11957658