Subgroups — C₅×#17479 #11940199

Order 1280.

988 conjugacy classes of subgroups.

The subgroup lattice has 508 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	1	yes	maximal, characteristic
2	C₅×#2920	C₂	1	1	yes	maximal, characteristic
3	C₂×C₅×#431	C₂	1	1	yes	maximal, characteristic
4	C₅×#1497	C₂	1	4	yes	maximal, complemented
5	C₅×#1493	C₂	1	4	yes	maximal, complemented
6	C₅×#1479	C₂	1	4	yes	maximal, complemented
7	C₅×#533	—	2	1	no	—
8	C₅×#533	—	2	1	no	—
9	C₅×#533	—	2	1	no	—
10	C₅×#533	—	2	1	no	—
11	C₅×#533	C₄	1	2	yes	—
12	C₅×#533	C₄	1	2	yes	—
13	C₅×#533	C₂²	1	2	yes	—
14	C₅×#533	C₂²	1	2	yes	—
15	C₂×C₅×C₄⋊Q₈	C₄	1	1	yes	characteristic
16	C₂×C₅×C₄⋊Q₈	C₄	1	1	yes	characteristic
17	C₂×C₅×#125	—	2	1	no	—
18	C₂×C₅×C₂²⋊Q₈	—	2	1	no	—
19	C₂×C₅×C₂²⋊Q₈	C₄	1	2	yes	—
20	C₂×C₄×C₅×Q₈	—	2	1	no	—
21	C₂×C₄×C₅×Q₈	C₂²	1	2	yes	—
22	C₂×C₅×#117	—	2	1	no	—
23	C₂²×C₄²×C₅	C₂²	1	1	yes	characteristic
24	C₅×#432	—	2	1	no	—
25	C₅×#432	C₂²	1	2	yes	—
26	C₅×#431	—	2	1	no	—
27	C₅×#431	—	2	1	no	—
28	C₅×#431	—	2	1	no	—
29	C₅×#431	C₂²	1	2	yes	—
30	C₅×#431	C₂²	1	2	yes	—
31	C₅×#431	C₂²	1	2	yes	—
32	C₅×#423	C₂²	1	2	yes	—
33	C₂×C₅×C₄⋊C₈	—	2	1	no	—
34	C₅×#407	—	2	1	no	—
35	C₂×C₅×C₂²⋊C₈	—	2	1	no	—
36	C₄×C₅×M₁₆	—	2	1	no	—
37	C₂×C₄×C₅×C₈	C₂²	1	2	yes	—
38	C₅×Q₈⋊C₈	C₂²	1	16	yes	complemented
39	#17479	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
40	C₂²×C₅×Q₈	—	2	1	no	—
41	C₂²×C₅×Q₈	C₂×C₄	1	2	yes	—
42	C₂³×C₄×C₅	C₂×C₄	1	1	yes	characteristic
43	C₂³×C₄×C₅	D₄	1	1	yes	characteristic
44	C₂³×C₄×C₅	D₄	1	1	yes	characteristic
45	C₂×C₅×M₁₆	—	2	2	no	—
46	C₂²×C₅×C₈	—	2	2	no	—
47	C₅×C₄⋊Q₈	—	2	1	no	—
48	C₅×C₄⋊Q₈	—	2	1	no	—
49	C₅×C₄⋊Q₈	—	2	1	no	—
50	C₅×C₄⋊Q₈	—	2	1	no	—
51	C₅×C₄⋊Q₈	C₂×C₄	1	2	yes	—
52	C₅×C₄⋊Q₈	C₂×C₄	1	2	yes	—
53	C₅×C₄⋊Q₈	C₂×C₄	1	2	yes	—
54	C₅×C₄⋊Q₈	C₂×C₄	1	2	yes	—
55	C₅×#125	—	2	2	no	—
56	C₅×#125	—	2	2	no	—
57	C₅×#125	—	2	2	no	—
58	C₅×#125	—	2	2	no	—
59	C₅×C₂²⋊Q₈	—	2	2	no	—
60	C₅×C₂²⋊Q₈	—	2	2	no	—
61	C₅×C₂²⋊Q₈	—	2	2	no	—
62	C₅×C₂²⋊Q₈	—	2	2	no	—
63	C₅×C₂²⋊Q₈	—	2	2	no	—
64	C₅×C₂²⋊Q₈	—	2	2	no	—
65	C₅×C₂²⋊Q₈	C₂×C₄	1	4	yes	—
66	C₅×C₂²⋊Q₈	C₂×C₄	1	4	yes	—
67	C₄×C₅×Q₈	—	2	2	no	—
68	C₄×C₅×Q₈	—	2	2	no	—
69	C₄×C₅×Q₈	—	2	2	no	—
70	C₄×C₅×Q₈	—	2	2	no	—
71	C₄×C₅×Q₈	—	2	2	no	—
72	C₄×C₅×Q₈	—	2	2	no	—
73	C₄×C₅×Q₈	C₂×C₄	1	4	yes	—
74	C₄×C₅×Q₈	C₂³	1	4	yes	—
75	C₅×#117	—	2	2	no	—
76	C₅×#117	—	2	2	no	—
77	C₅×#117	—	2	2	no	—
78	C₅×#117	—	2	2	no	—
79	C₂×C₅×C₄⋊C₄	—	2	1	no	—
80	C₂×C₅×C₄⋊C₄	—	2	1	no	—
81	C₂×C₅×C₄⋊C₄	—	2	1	no	—
82	C₂×C₅×C₄⋊C₄	—	2	2	no	—
83	C₂×C₅×C₄⋊C₄	—	2	2	no	—
84	C₂×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
85	C₂×C₅×C₂²⋊C₄	—	2	2	no	—
86	C₂×C₄²×C₅	—	2	2	no	—
87	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
88	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
89	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
90	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
91	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
92	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
93	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
94	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
95	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
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	C₅×C₄⋊C₈	—	2	2	no	—
100	C₅×C₄⋊C₈	—	2	2	no	—
101	C₅×C₄⋊C₈	—	2	2	no	—
102	C₅×C₄⋊C₈	C₂³	1	4	yes	—
103	C₅×C₂²⋊C₈	—	2	2	no	—
104	C₅×C₂²⋊C₈	—	2	2	no	—
105	C₅×C₂²⋊C₈	—	2	2	no	—
106	C₅×C₂²⋊C₈	—	2	2	no	—
107	C₅×#97	—	2	2	no	—
108	C₄×C₅×C₈	—	2	2	no	—
109	C₄×C₅×C₈	—	2	2	no	—
110	C₄×C₅×C₈	C₂³	1	4	yes	—
111	C₂×#533	C₂×C₅	1	1	yes	characteristic
112	#2920	C₂×C₅	1	1	yes	characteristic
113	C₂×#431	C₂×C₅	1	1	yes	characteristic
114	#1497	C₂×C₅	1	4	yes	complemented
115	#1493	C₂×C₅	1	4	yes	complemented
116	#1479	C₂×C₅	1	4	yes	complemented
117	C₂⁴×C₅	C₂²⋊C₄	1	1	yes	characteristic
118	C₂×C₅×Q₈	—	2	2	no	—
119	C₂×C₅×Q₈	—	2	2	no	—
120	C₂×C₅×Q₈	—	2	2	no	—
121	C₂×C₅×Q₈	—	2	8	no	—
122	C₂×C₅×Q₈	—	4	4	no	—
123	C₂×C₅×Q₈	C₂²×C₄	1	4	yes	—
124	C₂²×C₄×C₅	—	2	4	no	—
125	C₂²×C₄×C₅	—	2	4	no	—
126	C₂²×C₄×C₅	—	2	2	no	—
127	C₂²×C₄×C₅	—	2	2	no	—
128	C₂²×C₄×C₅	—	4	2	no	—
129	C₂²×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
130	C₂²×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
131	C₂²×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
132	C₂²×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
133	C₂²×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
134	C₂²×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
135	C₂²×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
136	C₂²×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
137	C₂²×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
138	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
139	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
140	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
141	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
142	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
143	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
144	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
145	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
146	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
147	C₅×M₁₆	—	4	4	no	—
148	C₂×C₅×C₈	—	2	4	no	—
149	C₂×C₅×C₈	—	2	4	no	—
150	C₂×C₅×C₈	—	4	4	no	—
151	C₅×C₄⋊C₄	—	2	2	no	—
152	C₅×C₄⋊C₄	—	2	2	no	—
153	C₅×C₄⋊C₄	—	2	2	no	—
154	C₅×C₄⋊C₄	—	2	2	no	—
155	C₅×C₄⋊C₄	—	2	2	no	—
156	C₅×C₄⋊C₄	—	2	2	no	—
157	C₅×C₄⋊C₄	—	2	4	no	—
158	C₅×C₄⋊C₄	—	2	4	no	—
159	C₅×C₄⋊C₄	—	2	4	no	—
160	C₅×C₄⋊C₄	—	2	2	no	—
161	C₅×C₄⋊C₄	—	2	4	no	—
162	C₅×C₄⋊C₄	C₂²×C₄	1	4	yes	—
163	C₅×C₂²⋊C₄	—	2	4	no	—
164	C₅×C₂²⋊C₄	—	2	4	no	—
165	C₄²×C₅	—	2	4	no	—
166	C₄²×C₅	—	2	4	no	—
167	C₄²×C₅	C₂²⋊C₄	1	1	yes	characteristic
168	C₄²×C₅	C₂²⋊C₄	1	1	yes	characteristic
169	C₄²×C₅	C₂²⋊C₄	1	1	yes	characteristic
170	C₄²×C₅	C₂²⋊C₄	1	1	yes	characteristic
171	C₄²×C₅	C₂²⋊C₄	1	1	yes	characteristic
172	C₄²×C₅	C₂²⋊C₄	1	1	yes	characteristic
173	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
174	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
175	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
176	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
177	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
178	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
179	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
180	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
181	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
182	C₄²×C₅	C₂⁴	1	1	yes	characteristic
183	#533	—	2	1	no	—
184	#533	—	2	1	no	—
185	#533	—	2	1	no	—
186	#533	—	2	1	no	—
187	#533	C₄×C₅	1	2	yes	—
188	#533	C₄×C₅	1	2	yes	—
189	#533	C₂²×C₅	1	2	yes	—
190	#533	C₂²×C₅	1	2	yes	—
191	C₂×C₄⋊Q₈	C₄×C₅	1	1	yes	characteristic
192	C₂×C₄⋊Q₈	C₄×C₅	1	1	yes	characteristic
193	C₂×#125	—	2	1	no	—
194	C₂×C₂²⋊Q₈	—	2	1	no	—
195	C₂×C₂²⋊Q₈	C₄×C₅	1	2	yes	—
196	C₂×C₄×Q₈	—	2	1	no	—
197	C₂×C₄×Q₈	C₂²×C₅	1	2	yes	—
198	C₂×#117	—	2	1	no	—
199	C₂²×C₄²	C₂²×C₅	1	1	yes	characteristic
200	#432	—	2	1	no	—
201	#432	C₂²×C₅	1	2	yes	—
202	#431	—	2	1	no	—
203	#431	—	2	1	no	—
204	#431	—	2	1	no	—
205	#431	C₂²×C₅	1	2	yes	—
206	#431	C₂²×C₅	1	2	yes	—
207	#431	C₂²×C₅	1	2	yes	—
208	#423	C₂²×C₅	1	2	yes	—
209	C₂×C₄⋊C₈	—	2	1	no	—
210	#407	—	2	1	no	—
211	C₂×C₂²⋊C₈	—	2	1	no	—
212	C₄×M₁₆	—	2	1	no	—
213	C₂×C₄×C₈	C₂²×C₅	1	2	yes	—
214	Q₈⋊C₈	C₂²×C₅	1	16	yes	complemented
215	C₂³×C₅	—	2	2	no	—
216	C₂³×C₅	—	2	2	no	—
217	C₂³×C₅	—	4	1	no	—
218	C₂³×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
219	C₂³×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
220	C₂³×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
221	C₅×Q₈	—	2	8	no	—
222	C₅×Q₈	—	4	4	no	—
223	C₅×Q₈	—	4	4	no	—
224	C₅×Q₈	—	4	4	no	—
225	C₂×C₄×C₅	—	2	2	no	—
226	C₂×C₄×C₅	—	2	2	no	—
227	C₂×C₄×C₅	—	2	2	no	—
228	C₂×C₄×C₅	—	2	2	no	—
229	C₂×C₄×C₅	—	2	2	no	—
230	C₂×C₄×C₅	—	2	2	no	—
231	C₂×C₄×C₅	—	2	2	no	—
232	C₂×C₄×C₅	—	2	2	no	—
233	C₂×C₄×C₅	—	2	2	no	—
234	C₂×C₄×C₅	—	2	2	no	—
235	C₂×C₄×C₅	—	2	2	no	—
236	C₂×C₄×C₅	—	2	2	no	—
237	C₂×C₄×C₅	—	2	2	no	—
238	C₂×C₄×C₅	—	2	4	no	—
239	C₂×C₄×C₅	—	2	4	no	—
240	C₂×C₄×C₅	—	4	1	no	—
241	C₂×C₄×C₅	—	4	1	no	—
242	C₂×C₄×C₅	—	4	1	no	—
243	C₂×C₄×C₅	—	4	4	no	—
244	C₂×C₄×C₅	—	4	4	no	—
245	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
246	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
247	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
248	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
249	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
250	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
251	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
252	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
253	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
254	C₂×C₄×C₅	#131	1	4	yes	—
255	C₂×C₄×C₅	#137	1	4	yes	—
256	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
257	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
258	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
259	C₅×C₈	—	4	4	no	—
260	C₅×C₈	—	4	4	no	—
261	C₂²×Q₈	—	2	1	no	—
262	C₂²×Q₈	C₂×C₄×C₅	1	2	yes	—
263	C₂³×C₄	C₂×C₄×C₅	1	1	yes	characteristic
264	C₂³×C₄	C₅×D₄	1	1	yes	characteristic
265	C₂³×C₄	C₅×D₄	1	1	yes	characteristic
266	C₂×M₁₆	—	2	2	no	—
267	C₂²×C₈	—	2	2	no	—
268	C₄⋊Q₈	—	2	1	no	—
269	C₄⋊Q₈	—	2	1	no	—
270	C₄⋊Q₈	—	2	1	no	—
271	C₄⋊Q₈	—	2	1	no	—
272	C₄⋊Q₈	C₂×C₄×C₅	1	2	yes	—
273	C₄⋊Q₈	C₂×C₄×C₅	1	2	yes	—
274	C₄⋊Q₈	C₂×C₄×C₅	1	2	yes	—
275	C₄⋊Q₈	C₂×C₄×C₅	1	2	yes	—
276	#125	—	2	2	no	—
277	#125	—	2	2	no	—
278	#125	—	2	2	no	—
279	#125	—	2	2	no	—
280	C₂²⋊Q₈	—	2	2	no	—
281	C₂²⋊Q₈	—	2	2	no	—
282	C₂²⋊Q₈	—	2	2	no	—
283	C₂²⋊Q₈	—	2	2	no	—
284	C₂²⋊Q₈	—	2	2	no	—
285	C₂²⋊Q₈	—	2	2	no	—
286	C₂²⋊Q₈	C₂×C₄×C₅	1	4	yes	—
287	C₂²⋊Q₈	C₂×C₄×C₅	1	4	yes	—
288	C₄×Q₈	—	2	2	no	—
289	C₄×Q₈	—	2	2	no	—
290	C₄×Q₈	—	2	2	no	—
291	C₄×Q₈	—	2	2	no	—
292	C₄×Q₈	—	2	2	no	—
293	C₄×Q₈	—	2	2	no	—
294	C₄×Q₈	C₂×C₄×C₅	1	4	yes	—
295	C₄×Q₈	C₂³×C₅	1	4	yes	—
296	#117	—	2	2	no	—
297	#117	—	2	2	no	—
298	#117	—	2	2	no	—
299	#117	—	2	2	no	—
300	C₂×C₄⋊C₄	—	2	1	no	—
301	C₂×C₄⋊C₄	—	2	1	no	—
302	C₂×C₄⋊C₄	—	2	1	no	—
303	C₂×C₄⋊C₄	—	2	2	no	—
304	C₂×C₄⋊C₄	—	2	2	no	—
305	C₂×C₄⋊C₄	C₂×C₄×C₅	1	2	yes	—
306	C₂×C₂²⋊C₄	—	2	2	no	—
307	C₂×C₄²	—	2	2	no	—
308	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
309	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
310	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
311	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
312	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
313	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
314	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
315	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
316	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
317	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
318	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
319	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
320	C₄⋊C₈	—	2	2	no	—
321	C₄⋊C₈	—	2	2	no	—
322	C₄⋊C₈	—	2	2	no	—
323	C₄⋊C₈	C₂³×C₅	1	4	yes	—
324	C₂²⋊C₈	—	2	2	no	—
325	C₂²⋊C₈	—	2	2	no	—
326	C₂²⋊C₈	—	2	2	no	—
327	C₂²⋊C₈	—	2	2	no	—
328	#97	—	2	2	no	—
329	C₄×C₈	—	2	2	no	—
330	C₄×C₈	—	2	2	no	—
331	C₄×C₈	C₂³×C₅	1	4	yes	—
332	C₂²×C₅	—	2	1	no	—
333	C₂²×C₅	—	2	1	no	—
334	C₂²×C₅	—	2	1	no	—
335	C₂²×C₅	—	2	1	no	—
336	C₂²×C₅	—	2	1	no	—
337	C₂²×C₅	—	2	1	no	—
338	C₂²×C₅	—	2	1	no	—
339	C₂²×C₅	—	4	4	no	—
340	C₂²×C₅	#408	1	2	yes	—
341	C₂²×C₅	#419	1	2	yes	—
342	C₂²×C₅	C₂²×C₂²⋊C₄	1	1	yes	characteristic
343	C₄×C₅	—	2	1	no	—
344	C₄×C₅	—	2	1	no	—
345	C₄×C₅	—	2	1	no	—
346	C₄×C₅	—	2	1	no	—
347	C₄×C₅	—	2	1	no	—
348	C₄×C₅	—	2	1	no	—
349	C₄×C₅	—	2	1	no	—
350	C₄×C₅	—	4	4	no	—
351	C₄×C₅	—	4	4	no	—
352	C₄×C₅	#408	1	2	yes	—
353	C₄×C₅	#419	1	2	yes	—
354	C₄×C₅	#421	1	2	yes	—
355	C₄×C₅	C₂×#131	1	2	yes	—
356	C₄×C₅	C₂×#137	1	2	yes	—
357	C₂⁴	C₅×C₂²⋊C₄	1	1	yes	characteristic
358	C₂×Q₈	—	2	2	no	—
359	C₂×Q₈	—	2	2	no	—
360	C₂×Q₈	—	2	2	no	—
361	C₂×Q₈	—	2	8	no	—
362	C₂×Q₈	—	4	4	no	—
363	C₂×Q₈	C₂²×C₄×C₅	1	4	yes	—
364	C₂²×C₄	—	2	4	no	—
365	C₂²×C₄	—	2	4	no	—
366	C₂²×C₄	—	2	2	no	—
367	C₂²×C₄	—	2	2	no	—
368	C₂²×C₄	—	4	2	no	—
369	C₂²×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
370	C₂²×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
371	C₂²×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
372	C₂²×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
373	C₂²×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
374	C₂²×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
375	C₂²×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
376	C₂²×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
377	C₂²×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
378	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
379	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
380	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
381	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
382	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
383	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
384	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
385	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
386	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
387	M₁₆	—	4	4	no	—
388	C₂×C₈	—	2	4	no	—
389	C₂×C₈	—	2	4	no	—
390	C₂×C₈	—	4	4	no	—
391	C₄⋊C₄	—	2	2	no	—
392	C₄⋊C₄	—	2	2	no	—
393	C₄⋊C₄	—	2	2	no	—
394	C₄⋊C₄	—	2	2	no	—
395	C₄⋊C₄	—	2	2	no	—
396	C₄⋊C₄	—	2	2	no	—
397	C₄⋊C₄	—	2	4	no	—
398	C₄⋊C₄	—	2	4	no	—
399	C₄⋊C₄	—	2	4	no	—
400	C₄⋊C₄	—	2	2	no	—
401	C₄⋊C₄	—	2	4	no	—
402	C₄⋊C₄	C₂²×C₄×C₅	1	4	yes	—
403	C₂²⋊C₄	—	2	4	no	—
404	C₂²⋊C₄	—	2	4	no	—
405	C₄²	—	2	4	no	—
406	C₄²	—	2	4	no	—
407	C₄²	C₅×C₂²⋊C₄	1	1	yes	characteristic
408	C₄²	C₅×C₂²⋊C₄	1	1	yes	characteristic
409	C₄²	C₅×C₂²⋊C₄	1	1	yes	characteristic
410	C₄²	C₅×C₂²⋊C₄	1	1	yes	characteristic
411	C₄²	C₅×C₂²⋊C₄	1	1	yes	characteristic
412	C₄²	C₅×C₂²⋊C₄	1	1	yes	characteristic
413	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
414	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
415	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
416	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
417	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
418	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
419	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
420	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
421	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
422	C₄²	C₂⁴×C₅	1	1	yes	characteristic
423	C₂×C₅	—	2	2	no	—
424	C₂×C₅	—	2	2	no	—
425	C₂×C₅	—	4	1	no	—
426	C₂×C₅	C₂×#408	1	1	yes	characteristic
427	C₂×C₅	C₂×#419	1	1	yes	characteristic
428	C₂×C₅	C₂×#421	1	1	yes	characteristic
429	C₂³	—	2	2	no	—
430	C₂³	—	2	2	no	—
431	C₂³	—	4	1	no	—
432	C₂³	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
433	C₂³	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
434	C₂³	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
435	Q₈	—	2	8	no	—
436	Q₈	—	4	4	no	—
437	Q₈	—	4	4	no	—
438	Q₈	—	4	4	no	—
439	C₂×C₄	—	2	2	no	—
440	C₂×C₄	—	2	2	no	—
441	C₂×C₄	—	2	2	no	—
442	C₂×C₄	—	2	2	no	—
443	C₂×C₄	—	2	2	no	—
444	C₂×C₄	—	2	2	no	—
445	C₂×C₄	—	2	2	no	—
446	C₂×C₄	—	2	2	no	—
447	C₂×C₄	—	2	2	no	—
448	C₂×C₄	—	2	2	no	—
449	C₂×C₄	—	2	2	no	—
450	C₂×C₄	—	2	2	no	—
451	C₂×C₄	—	2	2	no	—
452	C₂×C₄	—	2	4	no	—
453	C₂×C₄	—	2	4	no	—
454	C₂×C₄	—	4	1	no	—
455	C₂×C₄	—	4	1	no	—
456	C₂×C₄	—	4	1	no	—
457	C₂×C₄	—	4	4	no	—
458	C₂×C₄	—	4	4	no	—
459	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
460	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
461	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
462	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
463	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
464	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
465	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
466	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
467	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
468	C₂×C₄	C₅×#131	1	4	yes	—
469	C₂×C₄	C₅×#137	1	4	yes	—
470	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
471	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
472	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
473	C₈	—	4	4	no	—
474	C₈	—	4	4	no	—
475	C₅	#17479	1	1	yes	characteristic, direct product factor, Sylow
476	C₂²	—	2	1	no	—
477	C₂²	—	2	1	no	—
478	C₂²	—	2	1	no	—
479	C₂²	—	2	1	no	—
480	C₂²	—	2	1	no	—
481	C₂²	—	2	1	no	—
482	C₂²	—	2	1	no	—
483	C₂²	—	4	4	no	—
484	C₂²	C₅×#408	1	2	yes	—
485	C₂²	C₅×#419	1	2	yes	—
486	C₂²	C₂²×C₅×C₂²⋊C₄	1	1	yes	characteristic
487	C₄	—	2	1	no	—
488	C₄	—	2	1	no	—
489	C₄	—	2	1	no	—
490	C₄	—	2	1	no	—
491	C₄	—	2	1	no	—
492	C₄	—	2	1	no	—
493	C₄	—	2	1	no	—
494	C₄	—	4	4	no	—
495	C₄	—	4	4	no	—
496	C₄	C₅×#408	1	2	yes	—
497	C₄	C₅×#419	1	2	yes	—
498	C₄	C₅×#421	1	2	yes	—
499	C₄	C₂×C₅×#131	1	2	yes	—
500	C₄	C₂×C₅×#137	1	2	yes	—
501	C₂	—	2	2	no	—
502	C₂	—	2	2	no	—
503	C₂	—	4	1	no	—
504	C₂	C₂×C₅×#408	1	1	yes	characteristic
505	C₂	C₂×C₅×#419	1	1	yes	characteristic
506	C₂	C₂×C₅×#421	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₅	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₅
Frattini, cosocle	C₄²	C₂⁴×C₅
socle	C₂²×C₅	C₂²×C₂²⋊C₄
prime radical	C₂⁴×C₅	C₂²⋊C₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₅ ◁ C₂²×C₄²×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₅×#1497	C₂	semidirect
5. C₅×#1493	C₂	semidirect
6. C₅×#1479	C₂	semidirect
38. C₅×Q₈⋊C₈	C₂²	semidirect
39. #17479	C₅	direct (N × H)
114. #1497	C₂×C₅	semidirect
115. #1493	C₂×C₅	semidirect
116. #1479	C₂×C₅	semidirect
214. Q₈⋊C₈	C₂²×C₅	semidirect
475. C₅	#17479	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×#533	2
C₅×#2920	2
C₂×C₅×#431	2
C₅×#1497	2
C₅×#1493	2
C₅×#1479	2
#17479	5

Subgroups — C5×#17479 #11940199

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#17479 #11940199