Subgroups — C₅×#21879 #11944599

Order 1280.

1044 conjugacy classes of subgroups.

The subgroup lattice has 536 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×#423	C₂	1	1	yes	maximal, characteristic
4	C₅×#1997	C₂	1	2	yes	maximal, complemented
5	C₅×#1966	C₂	1	2	yes	maximal, complemented
6	C₅×#1901	C₂	1	4	yes	maximal
7	C₅×#1801	C₂	1	4	yes	maximal, complemented
8	C₂²×C₅×M₁₆	C₂²	1	2	yes	—
9	C₅×#533	—	2	1	no	—
10	C₅×#533	—	2	1	no	—
11	C₅×#533	—	2	1	no	—
12	C₅×#533	—	2	1	no	—
13	C₅×#533	—	2	1	no	—
14	C₅×#533	—	2	1	no	—
15	C₅×#533	—	2	1	no	—
16	C₅×#533	—	2	1	no	—
17	C₂×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
18	C₂×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
19	C₂×C₅×#125	C₄	1	2	yes	—
20	C₂×C₅×C₂²⋊Q₈	C₄	1	2	yes	—
21	C₂×C₅×C₂²⋊Q₈	C₂²	1	2	yes	—
22	C₂×C₄×C₅×Q₈	C₄	1	2	yes	—
23	C₂×C₄×C₅×Q₈	C₂²	1	2	yes	—
24	C₂×C₅×#117	C₄	1	2	yes	—
25	C₂²×C₄²×C₅	C₂²	1	1	yes	characteristic
26	C₅×#432	—	2	1	no	—
27	C₅×#432	—	2	1	no	—
28	C₅×#431	—	2	1	no	—
29	C₅×#431	—	2	1	no	—
30	C₅×#423	—	2	1	no	—
31	C₅×#423	—	2	1	no	—
32	C₅×#423	C₂²	1	2	yes	—
33	C₅×#423	C₂²	1	2	yes	—
34	C₅×#423	C₂²	1	2	yes	—
35	C₂×C₅×C₄⋊C₈	—	2	1	no	—
36	C₂×C₅×C₄⋊C₈	—	2	1	no	—
37	C₂×C₅×#101	C₂²	1	8	yes	—
38	C₅×#407	C₂²	1	2	yes	—
39	C₄×C₅×M₁₆	C₂²	1	2	yes	—
40	C₅×#343	C₂²	1	8	yes	—
41	#21879	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
42	C₂²×C₅×Q₈	C₂×C₄	1	2	yes	—
43	C₂²×C₅×Q₈	C₂³	1	2	yes	—
44	C₂³×C₄×C₅	C₂×C₄	1	1	yes	characteristic
45	C₂³×C₄×C₅	C₂×C₄	1	1	yes	characteristic
46	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
47	C₂×C₅×M₁₆	—	2	2	no	—
48	C₂×C₅×M₁₆	—	4	4	no	—
49	C₂×C₅×M₁₆	C₂³	1	4	yes	—
50	C₂×C₅×M₁₆	C₂³	1	4	yes	—
51	C₂²×C₅×C₈	—	2	2	no	—
52	C₅×C₄⋊Q₈	—	2	1	no	—
53	C₅×C₄⋊Q₈	—	2	1	no	—
54	C₅×C₄⋊Q₈	—	2	1	no	—
55	C₅×C₄⋊Q₈	—	2	1	no	—
56	C₅×C₄⋊Q₈	—	2	1	no	—
57	C₅×C₄⋊Q₈	—	2	1	no	—
58	C₅×C₄⋊Q₈	—	2	1	no	—
59	C₅×C₄⋊Q₈	—	2	1	no	—
60	C₅×#125	—	2	2	no	—
61	C₅×#125	—	2	2	no	—
62	C₅×#125	—	2	2	no	—
63	C₅×#125	—	2	2	no	—
64	C₅×C₂²⋊Q₈	—	2	2	no	—
65	C₅×C₂²⋊Q₈	—	2	2	no	—
66	C₅×C₂²⋊Q₈	—	2	2	no	—
67	C₅×C₂²⋊Q₈	—	2	2	no	—
68	C₅×C₂²⋊Q₈	—	2	2	no	—
69	C₅×C₂²⋊Q₈	—	2	2	no	—
70	C₅×C₂²⋊Q₈	—	2	2	no	—
71	C₅×C₂²⋊Q₈	—	2	2	no	—
72	C₄×C₅×Q₈	—	2	2	no	—
73	C₄×C₅×Q₈	—	2	2	no	—
74	C₄×C₅×Q₈	—	2	2	no	—
75	C₄×C₅×Q₈	—	2	2	no	—
76	C₄×C₅×Q₈	—	2	2	no	—
77	C₄×C₅×Q₈	—	2	2	no	—
78	C₄×C₅×Q₈	—	2	2	no	—
79	C₄×C₅×Q₈	—	2	2	no	—
80	C₅×#117	—	2	2	no	—
81	C₅×#117	—	2	2	no	—
82	C₅×#117	—	2	2	no	—
83	C₅×#117	—	2	2	no	—
84	C₂×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
85	C₂×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
86	C₂×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
87	C₂×C₅×C₄⋊C₄	C₂×C₄	1	4	yes	—
88	C₂×C₅×C₄⋊C₄	C₂×C₄	1	4	yes	—
89	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
90	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	4	yes	—
91	C₂×C₄²×C₅	C₂×C₄	1	4	yes	—
92	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
93	C₂×C₄²×C₅	C₂×C₄	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	D₄	1	1	yes	characteristic
97	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
98	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
99	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
100	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
101	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
102	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
103	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
104	C₅×C₄⋊C₈	—	2	2	no	—
105	C₅×C₄⋊C₈	—	2	2	no	—
106	C₅×C₄⋊C₈	—	2	2	no	—
107	C₅×C₄⋊C₈	—	2	2	no	—
108	C₅×C₄⋊C₈	—	2	2	no	—
109	C₅×C₄⋊C₈	—	2	2	no	—
110	C₅×#101	—	4	8	no	—
111	C₅×C₂²⋊C₈	—	2	2	no	—
112	C₅×C₂²⋊C₈	—	2	2	no	—
113	C₅×#97	—	2	2	no	—
114	C₄×C₅×C₈	—	2	2	no	—
115	C₂×#533	C₂×C₅	1	1	yes	characteristic
116	#2920	C₂×C₅	1	1	yes	characteristic
117	C₂×#423	C₂×C₅	1	1	yes	characteristic
118	#1997	C₂×C₅	1	2	yes	complemented
119	#1966	C₂×C₅	1	2	yes	complemented
120	#1901	C₂×C₅	1	4	yes	—
121	#1801	C₂×C₅	1	4	yes	complemented
122	C₂⁴×C₅	C₂²×C₄	1	1	yes	characteristic
123	C₂×C₅×Q₈	—	2	2	no	—
124	C₂×C₅×Q₈	—	2	2	no	—
125	C₂×C₅×Q₈	—	2	2	no	—
126	C₂×C₅×Q₈	—	2	2	no	—
127	C₂×C₅×Q₈	—	2	4	no	—
128	C₂×C₅×Q₈	—	2	4	no	—
129	C₂×C₅×Q₈	—	4	4	no	—
130	C₂²×C₄×C₅	—	2	4	no	—
131	C₂²×C₄×C₅	—	2	2	no	—
132	C₂²×C₄×C₅	—	2	2	no	—
133	C₂²×C₄×C₅	—	4	2	no	—
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	C₂²⋊C₄	1	1	yes	characteristic
142	C₂²×C₄×C₅	C₂²×C₄	1	4	yes	—
143	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
144	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
145	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
146	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
147	C₂²×C₄×C₅	C₂²×C₄	1	4	yes	—
148	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
149	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
150	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
151	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
152	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
153	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
154	C₅×M₁₆	—	2	8	no	—
155	C₅×M₁₆	—	2	4	no	—
156	C₅×M₁₆	—	2	4	no	—
157	C₅×M₁₆	—	4	4	no	—
158	C₂×C₅×C₈	—	2	4	no	—
159	C₂×C₅×C₈	—	2	4	no	—
160	C₂×C₅×C₈	—	4	4	no	—
161	C₅×C₄⋊C₄	—	2	2	no	—
162	C₅×C₄⋊C₄	—	2	2	no	—
163	C₅×C₄⋊C₄	—	2	2	no	—
164	C₅×C₄⋊C₄	—	2	2	no	—
165	C₅×C₄⋊C₄	—	2	4	no	—
166	C₅×C₄⋊C₄	—	2	4	no	—
167	C₅×C₄⋊C₄	—	2	4	no	—
168	C₅×C₄⋊C₄	—	2	4	no	—
169	C₅×C₄⋊C₄	—	2	2	no	—
170	C₅×C₄⋊C₄	—	2	2	no	—
171	C₅×C₄⋊C₄	—	2	2	no	—
172	C₅×C₄⋊C₄	—	2	2	no	—
173	C₅×C₂²⋊C₄	—	2	4	no	—
174	C₅×C₂²⋊C₄	—	2	4	no	—
175	C₄²×C₅	—	2	4	no	—
176	C₄²×C₅	—	2	4	no	—
177	C₄²×C₅	C₂²⋊C₄	1	1	yes	characteristic
178	C₄²×C₅	C₂²⋊C₄	1	1	yes	characteristic
179	C₄²×C₅	C₂²⋊C₄	1	1	yes	characteristic
180	C₄²×C₅	C₂²⋊C₄	1	1	yes	characteristic
181	C₄²×C₅	C₂²⋊C₄	1	1	yes	characteristic
182	C₄²×C₅	C₂²⋊C₄	1	1	yes	characteristic
183	C₄²×C₅	C₂²⋊C₄	1	1	yes	characteristic
184	C₄²×C₅	C₂²⋊C₄	1	1	yes	characteristic
185	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
186	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
187	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
188	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
189	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
190	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
191	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
192	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
193	C₂²×M₁₆	C₂²×C₅	1	2	yes	—
194	#533	—	2	1	no	—
195	#533	—	2	1	no	—
196	#533	—	2	1	no	—
197	#533	—	2	1	no	—
198	#533	—	2	1	no	—
199	#533	—	2	1	no	—
200	#533	—	2	1	no	—
201	#533	—	2	1	no	—
202	C₂×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
203	C₂×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
204	C₂×#125	C₄×C₅	1	2	yes	—
205	C₂×C₂²⋊Q₈	C₄×C₅	1	2	yes	—
206	C₂×C₂²⋊Q₈	C₂²×C₅	1	2	yes	—
207	C₂×C₄×Q₈	C₄×C₅	1	2	yes	—
208	C₂×C₄×Q₈	C₂²×C₅	1	2	yes	—
209	C₂×#117	C₄×C₅	1	2	yes	—
210	C₂²×C₄²	C₂²×C₅	1	1	yes	characteristic
211	#432	—	2	1	no	—
212	#432	—	2	1	no	—
213	#431	—	2	1	no	—
214	#431	—	2	1	no	—
215	#423	—	2	1	no	—
216	#423	—	2	1	no	—
217	#423	C₂²×C₅	1	2	yes	—
218	#423	C₂²×C₅	1	2	yes	—
219	#423	C₂²×C₅	1	2	yes	—
220	C₂×C₄⋊C₈	—	2	1	no	—
221	C₂×C₄⋊C₈	—	2	1	no	—
222	C₂×#101	C₂²×C₅	1	8	yes	—
223	#407	C₂²×C₅	1	2	yes	—
224	C₄×M₁₆	C₂²×C₅	1	2	yes	—
225	#343	C₂²×C₅	1	8	yes	—
226	C₂³×C₅	—	2	2	no	—
227	C₂³×C₅	—	2	2	no	—
228	C₂³×C₅	—	4	1	no	—
229	C₂³×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
230	C₂³×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
231	C₂³×C₅	C₂³×C₄	1	1	yes	characteristic
232	C₅×Q₈	—	4	4	no	—
233	C₅×Q₈	—	4	2	no	—
234	C₅×Q₈	—	4	2	no	—
235	C₅×Q₈	—	4	4	no	—
236	C₅×Q₈	—	4	4	no	—
237	C₂×C₄×C₅	—	2	2	no	—
238	C₂×C₄×C₅	—	2	2	no	—
239	C₂×C₄×C₅	—	2	1	no	—
240	C₂×C₄×C₅	—	2	1	no	—
241	C₂×C₄×C₅	—	2	1	no	—
242	C₂×C₄×C₅	—	2	1	no	—
243	C₂×C₄×C₅	—	2	2	no	—
244	C₂×C₄×C₅	—	2	2	no	—
245	C₂×C₄×C₅	—	2	2	no	—
246	C₂×C₄×C₅	—	2	2	no	—
247	C₂×C₄×C₅	—	2	2	no	—
248	C₂×C₄×C₅	—	2	2	no	—
249	C₂×C₄×C₅	—	2	2	no	—
250	C₂×C₄×C₅	—	2	2	no	—
251	C₂×C₄×C₅	—	2	2	no	—
252	C₂×C₄×C₅	—	2	4	no	—
253	C₂×C₄×C₅	—	2	4	no	—
254	C₂×C₄×C₅	—	2	8	no	—
255	C₂×C₄×C₅	—	4	1	no	—
256	C₂×C₄×C₅	—	4	1	no	—
257	C₂×C₄×C₅	—	4	1	no	—
258	C₂×C₄×C₅	—	4	4	no	—
259	C₂×C₄×C₅	#101	1	4	yes	complemented
260	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
261	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
262	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
263	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
264	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
265	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
266	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
267	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
268	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
269	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
270	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
271	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
272	C₂×C₄×C₅	H(5,𝔽₂)	1	2	yes	—
273	C₂×C₄×C₅	2₋¹⁺⁴	1	2	yes	—
274	C₅×C₈	—	4	4	no	—
275	C₅×C₈	—	4	4	no	—
276	C₂²×Q₈	C₂×C₄×C₅	1	2	yes	—
277	C₂²×Q₈	C₂³×C₅	1	2	yes	—
278	C₂³×C₄	C₂×C₄×C₅	1	1	yes	characteristic
279	C₂³×C₄	C₂×C₄×C₅	1	1	yes	characteristic
280	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
281	C₂×M₁₆	—	2	2	no	—
282	C₂×M₁₆	—	4	4	no	—
283	C₂×M₁₆	C₂³×C₅	1	4	yes	—
284	C₂×M₁₆	C₂³×C₅	1	4	yes	—
285	C₂²×C₈	—	2	2	no	—
286	C₄⋊Q₈	—	2	1	no	—
287	C₄⋊Q₈	—	2	1	no	—
288	C₄⋊Q₈	—	2	1	no	—
289	C₄⋊Q₈	—	2	1	no	—
290	C₄⋊Q₈	—	2	1	no	—
291	C₄⋊Q₈	—	2	1	no	—
292	C₄⋊Q₈	—	2	1	no	—
293	C₄⋊Q₈	—	2	1	no	—
294	#125	—	2	2	no	—
295	#125	—	2	2	no	—
296	#125	—	2	2	no	—
297	#125	—	2	2	no	—
298	C₂²⋊Q₈	—	2	2	no	—
299	C₂²⋊Q₈	—	2	2	no	—
300	C₂²⋊Q₈	—	2	2	no	—
301	C₂²⋊Q₈	—	2	2	no	—
302	C₂²⋊Q₈	—	2	2	no	—
303	C₂²⋊Q₈	—	2	2	no	—
304	C₂²⋊Q₈	—	2	2	no	—
305	C₂²⋊Q₈	—	2	2	no	—
306	C₄×Q₈	—	2	2	no	—
307	C₄×Q₈	—	2	2	no	—
308	C₄×Q₈	—	2	2	no	—
309	C₄×Q₈	—	2	2	no	—
310	C₄×Q₈	—	2	2	no	—
311	C₄×Q₈	—	2	2	no	—
312	C₄×Q₈	—	2	2	no	—
313	C₄×Q₈	—	2	2	no	—
314	#117	—	2	2	no	—
315	#117	—	2	2	no	—
316	#117	—	2	2	no	—
317	#117	—	2	2	no	—
318	C₂×C₄⋊C₄	C₂×C₄×C₅	1	2	yes	—
319	C₂×C₄⋊C₄	C₂×C₄×C₅	1	2	yes	—
320	C₂×C₄⋊C₄	C₂×C₄×C₅	1	2	yes	—
321	C₂×C₄⋊C₄	C₂×C₄×C₅	1	4	yes	—
322	C₂×C₄⋊C₄	C₂×C₄×C₅	1	4	yes	—
323	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
324	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	4	yes	—
325	C₂×C₄²	C₂×C₄×C₅	1	4	yes	—
326	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
327	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
328	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
329	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
330	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
331	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
332	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
333	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
334	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
335	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
336	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
337	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
338	C₄⋊C₈	—	2	2	no	—
339	C₄⋊C₈	—	2	2	no	—
340	C₄⋊C₈	—	2	2	no	—
341	C₄⋊C₈	—	2	2	no	—
342	C₄⋊C₈	—	2	2	no	—
343	C₄⋊C₈	—	2	2	no	—
344	#101	—	4	8	no	—
345	C₂²⋊C₈	—	2	2	no	—
346	C₂²⋊C₈	—	2	2	no	—
347	#97	—	2	2	no	—
348	C₄×C₈	—	2	2	no	—
349	C₂²×C₅	—	2	1	no	—
350	C₂²×C₅	—	2	1	no	—
351	C₂²×C₅	—	2	1	no	—
352	C₂²×C₅	—	2	1	no	—
353	C₂²×C₅	—	2	1	no	—
354	C₂²×C₅	—	2	1	no	—
355	C₂²×C₅	—	2	1	no	—
356	C₂²×C₅	—	4	4	no	—
357	C₂²×C₅	C₂×#101	1	2	yes	—
358	C₂²×C₅	C₂²×C₂²⋊C₄	1	1	yes	characteristic
359	C₂²×C₅	#520	1	2	yes	—
360	C₄×C₅	—	2	1	no	—
361	C₄×C₅	—	2	1	no	—
362	C₄×C₅	—	2	1	no	—
363	C₄×C₅	—	2	1	no	—
364	C₄×C₅	—	2	1	no	—
365	C₄×C₅	—	2	1	no	—
366	C₄×C₅	—	2	1	no	—
367	C₄×C₅	—	4	4	no	—
368	C₄×C₅	—	4	4	no	—
369	C₄×C₅	C₂×#101	1	2	yes	—
370	C₄×C₅	C₂×#101	1	2	yes	—
371	C₄×C₅	#413	1	2	yes	—
372	C₄×C₅	#535	1	1	yes	characteristic
373	C₄×C₅	#536	1	1	yes	characteristic
374	C₄×C₅	#537	1	2	yes	—
375	C₂⁴	C₂²×C₄×C₅	1	1	yes	characteristic
376	C₂×Q₈	—	2	2	no	—
377	C₂×Q₈	—	2	2	no	—
378	C₂×Q₈	—	2	2	no	—
379	C₂×Q₈	—	2	2	no	—
380	C₂×Q₈	—	2	4	no	—
381	C₂×Q₈	—	2	4	no	—
382	C₂×Q₈	—	4	4	no	—
383	C₂²×C₄	—	2	2	no	—
384	C₂²×C₄	—	2	2	no	—
385	C₂²×C₄	—	2	4	no	—
386	C₂²×C₄	—	4	2	no	—
387	C₂²×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
388	C₂²×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
389	C₂²×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
390	C₂²×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
391	C₂²×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
392	C₂²×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
393	C₂²×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
394	C₂²×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
395	C₂²×C₄	C₂²×C₄×C₅	1	4	yes	—
396	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
397	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
398	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
399	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
400	C₂²×C₄	C₂²×C₄×C₅	1	4	yes	—
401	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
402	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
403	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
404	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
405	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
406	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
407	M₁₆	—	2	4	no	—
408	M₁₆	—	2	8	no	—
409	M₁₆	—	2	4	no	—
410	M₁₆	—	4	4	no	—
411	C₂×C₈	—	2	4	no	—
412	C₂×C₈	—	2	4	no	—
413	C₂×C₈	—	4	4	no	—
414	C₄⋊C₄	—	2	2	no	—
415	C₄⋊C₄	—	2	2	no	—
416	C₄⋊C₄	—	2	2	no	—
417	C₄⋊C₄	—	2	2	no	—
418	C₄⋊C₄	—	2	4	no	—
419	C₄⋊C₄	—	2	4	no	—
420	C₄⋊C₄	—	2	4	no	—
421	C₄⋊C₄	—	2	4	no	—
422	C₄⋊C₄	—	2	2	no	—
423	C₄⋊C₄	—	2	2	no	—
424	C₄⋊C₄	—	2	2	no	—
425	C₄⋊C₄	—	2	2	no	—
426	C₂²⋊C₄	—	2	4	no	—
427	C₂²⋊C₄	—	2	4	no	—
428	C₄²	—	2	4	no	—
429	C₄²	—	2	4	no	—
430	C₄²	C₅×C₂²⋊C₄	1	1	yes	characteristic
431	C₄²	C₅×C₂²⋊C₄	1	1	yes	characteristic
432	C₄²	C₅×C₂²⋊C₄	1	1	yes	characteristic
433	C₄²	C₅×C₂²⋊C₄	1	1	yes	characteristic
434	C₄²	C₅×C₂²⋊C₄	1	1	yes	characteristic
435	C₄²	C₅×C₂²⋊C₄	1	1	yes	characteristic
436	C₄²	C₅×C₂²⋊C₄	1	1	yes	characteristic
437	C₄²	C₅×C₂²⋊C₄	1	1	yes	characteristic
438	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
439	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
440	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
441	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
442	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
443	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
444	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
445	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
446	C₂×C₅	—	2	2	no	—
447	C₂×C₅	—	2	2	no	—
448	C₂×C₅	—	4	1	no	—
449	C₂×C₅	#2311	1	1	yes	characteristic
450	C₂×C₅	C₂²×#101	1	1	yes	characteristic
451	C₂×C₅	C₂×#413	1	1	yes	characteristic
452	C₂³	—	2	2	no	—
453	C₂³	—	2	2	no	—
454	C₂³	—	4	1	no	—
455	C₂³	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
456	C₂³	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
457	C₂³	C₂³×C₄×C₅	1	1	yes	characteristic
458	Q₈	—	4	4	no	—
459	Q₈	—	4	4	no	—
460	Q₈	—	4	2	no	—
461	Q₈	—	4	2	no	—
462	Q₈	—	4	4	no	—
463	C₂×C₄	—	2	2	no	—
464	C₂×C₄	—	2	2	no	—
465	C₂×C₄	—	2	2	no	—
466	C₂×C₄	—	2	2	no	—
467	C₂×C₄	—	2	2	no	—
468	C₂×C₄	—	2	2	no	—
469	C₂×C₄	—	2	2	no	—
470	C₂×C₄	—	2	2	no	—
471	C₂×C₄	—	2	2	no	—
472	C₂×C₄	—	2	1	no	—
473	C₂×C₄	—	2	1	no	—
474	C₂×C₄	—	2	1	no	—
475	C₂×C₄	—	2	1	no	—
476	C₂×C₄	—	2	2	no	—
477	C₂×C₄	—	2	2	no	—
478	C₂×C₄	—	2	4	no	—
479	C₂×C₄	—	2	4	no	—
480	C₂×C₄	—	2	8	no	—
481	C₂×C₄	—	4	1	no	—
482	C₂×C₄	—	4	1	no	—
483	C₂×C₄	—	4	1	no	—
484	C₂×C₄	—	4	4	no	—
485	C₂×C₄	C₅×#101	1	4	yes	complemented
486	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
487	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
488	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
489	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
490	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
491	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
492	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
493	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
494	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
495	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
496	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
497	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
498	C₂×C₄	C₅×H(5,𝔽₂)	1	2	yes	—
499	C₂×C₄	C₅×2₋¹⁺⁴	1	2	yes	—
500	C₈	—	4	4	no	—
501	C₈	—	4	4	no	—
502	C₅	#21879	1	1	yes	characteristic, direct product factor, Sylow
503	C₂²	—	2	1	no	—
504	C₂²	—	2	1	no	—
505	C₂²	—	2	1	no	—
506	C₂²	—	2	1	no	—
507	C₂²	—	2	1	no	—
508	C₂²	—	2	1	no	—
509	C₂²	—	2	1	no	—
510	C₂²	—	4	4	no	—
511	C₂²	C₂×C₅×#101	1	2	yes	—
512	C₂²	C₂²×C₅×C₂²⋊C₄	1	1	yes	characteristic
513	C₂²	C₅×#520	1	2	yes	—
514	C₄	—	2	1	no	—
515	C₄	—	2	1	no	—
516	C₄	—	2	1	no	—
517	C₄	—	2	1	no	—
518	C₄	—	2	1	no	—
519	C₄	—	2	1	no	—
520	C₄	—	2	1	no	—
521	C₄	—	4	4	no	—
522	C₄	—	4	4	no	—
523	C₄	C₂×C₅×#101	1	2	yes	—
524	C₄	C₂×C₅×#101	1	2	yes	—
525	C₄	C₅×#413	1	2	yes	—
526	C₄	C₅×#535	1	1	yes	characteristic
527	C₄	C₅×#536	1	1	yes	characteristic
528	C₄	C₅×#537	1	2	yes	—
529	C₂	—	2	2	no	—
530	C₂	—	2	2	no	—
531	C₂	—	4	1	no	—
532	C₂	C₅×#2311	1	1	yes	characteristic
533	C₂	C₂²×C₅×#101	1	1	yes	characteristic
534	C₂	C₂×C₅×#413	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
4. C₅×#1997	C₂	semidirect
5. C₅×#1966	C₂	semidirect
7. C₅×#1801	C₂	semidirect
41. #21879	C₅	direct (N × H)
118. #1997	C₂×C₅	semidirect
119. #1966	C₂×C₅	semidirect
121. #1801	C₂×C₅	semidirect
259. C₂×C₄×C₅	#101	semidirect
485. C₂×C₄	C₅×#101	semidirect
502. C₅	#21879	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×#423	2
C₅×#1997	2
C₅×#1966	2
C₅×#1901	2
C₅×#1801	2
#21879	5

Subgroups — C5×#21879 #11944599

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#21879 #11944599