Subgroups — C₅×#21844 #11944564

Order 1280.

1100 conjugacy classes of subgroups.

The subgroup lattice has 524 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	C₄×C₅×#117	C₂	1	1	yes	maximal, characteristic
4	C₅×#1994	C₂	1	4	yes	maximal, complemented
5	C₅×#1986	C₂	1	4	yes	maximal, complemented
6	C₅×#1826	C₂	1	4	yes	maximal
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	complemented
12	C₅×#533	C₄	1	2	yes	complemented
13	C₅×#533	C₂²	1	2	yes	—
14	C₅×#533	C₂²	1	2	yes	—
15	C₂×C₅×C₄⋊Q₈	C₄	1	1	yes	characteristic, complemented
16	C₂×C₅×C₄⋊Q₈	C₄	1	1	yes	characteristic, complemented
17	C₂×C₅×#125	C₄	1	2	yes	complemented
18	C₂×C₅×C₂²⋊Q₈	—	2	1	no	—
19	C₂×C₅×C₂²⋊Q₈	—	2	1	no	—
20	C₂×C₄×C₅×Q₈	—	2	1	no	—
21	C₂×C₄×C₅×Q₈	—	2	1	no	—
22	C₂×C₅×#117	—	2	1	no	—
23	C₂×C₅×#117	C₂²	1	2	yes	—
24	C₂²×C₄²×C₅	C₂²	1	1	yes	characteristic
25	C₅×#432	—	2	1	no	—
26	C₅×#432	—	2	1	no	—
27	C₅×#431	—	2	1	no	—
28	C₅×#431	—	2	1	no	—
29	C₅×#423	C₂²	1	2	yes	—
30	C₅×#407	C₂²	1	2	yes	—
31	C₄×C₅×M₁₆	C₂²	1	2	yes	—
32	C₄×C₅×C₄⋊C₄	—	2	1	no	—
33	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
34	C₄×C₅×C₂²⋊C₄	—	2	1	no	—
35	C₄×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
36	C₅×#376	—	2	1	no	—
37	C₄³×C₅	C₂²	1	2	yes	—
38	C₅×#339	C₂²	1	16	yes	—
39	#21844	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
40	C₂²×C₅×Q₈	—	2	1	no	—
41	C₂²×C₅×Q₈	—	2	1	no	—
42	C₂³×C₄×C₅	D₄	1	1	yes	characteristic
43	C₂³×C₄×C₅	D₄	1	1	yes	characteristic
44	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
45	C₂×C₅×M₁₆	C₂³	1	4	yes	—
46	C₅×C₄⋊Q₈	—	2	1	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	C₂×C₄	1	2	yes	—
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×#125	—	2	2	no	—
55	C₅×#125	—	2	2	no	—
56	C₅×#125	C₂×C₄	1	4	yes	—
57	C₅×#125	C₂×C₄	1	4	yes	—
58	C₅×C₂²⋊Q₈	—	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	—	2	2	no	—
66	C₄×C₅×Q₈	—	2	2	no	—
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	—	2	2	no	—
74	C₅×#117	—	2	8	no	—
75	C₅×#117	—	2	2	no	—
76	C₅×#117	—	2	2	no	—
77	C₅×#117	C₂×C₄	1	4	yes	—
78	C₅×#117	C₂³	1	4	yes	—
79	C₂×C₅×C₄⋊C₄	—	2	2	no	—
80	C₂×C₅×C₄⋊C₄	—	2	2	no	—
81	C₂×C₅×C₄⋊C₄	—	2	1	no	—
82	C₂×C₅×C₄⋊C₄	—	2	1	no	—
83	C₂×C₅×C₄⋊C₄	—	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×C₂²⋊C₄	—	2	2	no	—
87	C₂×C₅×C₂²⋊C₄	—	2	2	no	—
88	C₂×C₄²×C₅	—	2	2	no	—
89	C₂×C₄²×C₅	—	2	2	no	—
90	C₂×C₄²×C₅	—	2	2	no	—
91	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
92	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
93	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
94	C₂×C₄²×C₅	C₂×C₄	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	C₂³	1	4	yes	—
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×C₂²⋊C₈	—	2	2	no	—
107	C₅×C₂²⋊C₈	—	2	2	no	—
108	C₅×#97	—	2	2	no	—
109	C₄×C₅×C₈	—	2	2	no	—
110	C₅×#95	—	2	2	no	—
111	C₅×#95	—	2	2	no	—
112	C₂×#533	C₂×C₅	1	1	yes	characteristic
113	#2920	C₂×C₅	1	1	yes	characteristic
114	C₄×#117	C₂×C₅	1	1	yes	characteristic
115	#1994	C₂×C₅	1	4	yes	complemented
116	#1986	C₂×C₅	1	4	yes	complemented
117	#1826	C₂×C₅	1	4	yes	—
118	C₂⁴×C₅	C₂×D₄	1	1	yes	characteristic
119	C₂×C₅×Q₈	—	2	2	no	—
120	C₂×C₅×Q₈	—	2	2	no	—
121	C₂×C₅×Q₈	—	2	2	no	—
122	C₂×C₅×Q₈	—	2	2	no	—
123	C₂×C₅×Q₈	—	4	4	no	—
124	C₂×C₅×Q₈	—	4	4	no	—
125	C₂²×C₄×C₅	—	2	4	no	—
126	C₂²×C₄×C₅	—	2	4	no	—
127	C₂²×C₄×C₅	—	2	2	no	—
128	C₂²×C₄×C₅	—	2	2	no	—
129	C₂²×C₄×C₅	—	2	4	no	—
130	C₂²×C₄×C₅	—	4	2	no	—
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	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
148	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
149	C₅×M₁₆	—	2	8	no	—
150	C₂×C₅×C₈	—	2	4	no	—
151	C₅×C₄⋊C₄	—	2	8	no	—
152	C₅×C₄⋊C₄	—	2	4	no	—
153	C₅×C₄⋊C₄	—	2	4	no	—
154	C₅×C₄⋊C₄	—	2	4	no	—
155	C₅×C₄⋊C₄	—	2	4	no	—
156	C₅×C₄⋊C₄	—	2	2	no	—
157	C₅×C₄⋊C₄	—	2	2	no	—
158	C₅×C₄⋊C₄	—	2	2	no	—
159	C₅×C₄⋊C₄	—	2	2	no	—
160	C₅×C₄⋊C₄	—	2	2	no	—
161	C₅×C₄⋊C₄	—	2	2	no	—
162	C₅×C₄⋊C₄	C₂²×C₄	1	4	yes	—
163	C₅×C₄⋊C₄	C₂²×C₄	1	4	yes	—
164	C₅×C₂²⋊C₄	—	2	8	no	—
165	C₅×C₂²⋊C₄	—	2	4	no	—
166	C₅×C₂²⋊C₄	—	2	4	no	—
167	C₄²×C₅	—	2	8	no	—
168	C₄²×C₅	—	2	4	no	—
169	C₄²×C₅	—	2	4	no	—
170	C₄²×C₅	—	2	8	no	—
171	C₄²×C₅	—	4	4	no	—
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	C₂²⋊C₄	1	1	yes	characteristic
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	C₂×D₄	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	#533	—	2	1	no	—
189	#533	—	2	1	no	—
190	#533	—	2	1	no	—
191	#533	—	2	1	no	—
192	#533	C₄×C₅	1	2	yes	complemented
193	#533	C₄×C₅	1	2	yes	complemented
194	#533	C₂²×C₅	1	2	yes	—
195	#533	C₂²×C₅	1	2	yes	—
196	C₂×C₄⋊Q₈	C₄×C₅	1	1	yes	characteristic, complemented
197	C₂×C₄⋊Q₈	C₄×C₅	1	1	yes	characteristic, complemented
198	C₂×#125	C₄×C₅	1	2	yes	complemented
199	C₂×C₂²⋊Q₈	—	2	1	no	—
200	C₂×C₂²⋊Q₈	—	2	1	no	—
201	C₂×C₄×Q₈	—	2	1	no	—
202	C₂×C₄×Q₈	—	2	1	no	—
203	C₂×#117	—	2	1	no	—
204	C₂×#117	C₂²×C₅	1	2	yes	—
205	C₂²×C₄²	C₂²×C₅	1	1	yes	characteristic
206	#432	—	2	1	no	—
207	#432	—	2	1	no	—
208	#431	—	2	1	no	—
209	#431	—	2	1	no	—
210	#423	C₂²×C₅	1	2	yes	—
211	#407	C₂²×C₅	1	2	yes	—
212	C₄×M₁₆	C₂²×C₅	1	2	yes	—
213	C₄×C₄⋊C₄	—	2	1	no	—
214	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
215	C₄×C₂²⋊C₄	—	2	1	no	—
216	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
217	#376	—	2	1	no	—
218	C₄³	C₂²×C₅	1	2	yes	—
219	#339	C₂²×C₅	1	16	yes	—
220	C₂³×C₅	—	2	2	no	—
221	C₂³×C₅	—	2	2	no	—
222	C₂³×C₅	—	4	1	no	—
223	C₂³×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
224	C₂³×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
225	C₂³×C₅	C₂²×D₄	1	1	yes	characteristic
226	C₅×Q₈	—	4	4	no	—
227	C₅×Q₈	—	4	4	no	—
228	C₅×Q₈	—	4	4	no	—
229	C₅×Q₈	—	4	4	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	2	no	—
239	C₂×C₄×C₅	—	2	2	no	—
240	C₂×C₄×C₅	—	2	2	no	—
241	C₂×C₄×C₅	—	2	2	no	—
242	C₂×C₄×C₅	—	2	2	no	—
243	C₂×C₄×C₅	—	2	8	no	—
244	C₂×C₄×C₅	—	2	4	no	—
245	C₂×C₄×C₅	—	2	4	no	—
246	C₂×C₄×C₅	—	4	1	no	—
247	C₂×C₄×C₅	—	4	1	no	—
248	C₂×C₄×C₅	—	4	1	no	—
249	C₂×C₄×C₅	—	4	4	no	—
250	C₂×C₄×C₅	—	4	4	no	—
251	C₂×C₄×C₅	—	4	4	no	—
252	C₂×C₄×C₅	—	4	4	no	—
253	C₂×C₄×C₅	#104	1	4	yes	—
254	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
255	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
256	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
257	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
258	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
259	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
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	C₂³×C₄	1	1	yes	characteristic
265	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
266	C₂×C₄×C₅	2₋¹⁺⁴	1	4	yes	—
267	C₅×C₈	—	4	4	no	—
268	C₂²×Q₈	—	2	1	no	—
269	C₂²×Q₈	—	2	1	no	—
270	C₂³×C₄	C₅×D₄	1	1	yes	characteristic
271	C₂³×C₄	C₅×D₄	1	1	yes	characteristic
272	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
273	C₂×M₁₆	C₂³×C₅	1	4	yes	—
274	C₄⋊Q₈	—	2	1	no	—
275	C₄⋊Q₈	—	2	1	no	—
276	C₄⋊Q₈	—	2	1	no	—
277	C₄⋊Q₈	—	2	1	no	—
278	C₄⋊Q₈	C₂×C₄×C₅	1	2	yes	—
279	C₄⋊Q₈	C₂×C₄×C₅	1	2	yes	—
280	C₄⋊Q₈	C₂×C₄×C₅	1	2	yes	—
281	C₄⋊Q₈	C₂×C₄×C₅	1	2	yes	—
282	#125	—	2	2	no	—
283	#125	—	2	2	no	—
284	#125	C₂×C₄×C₅	1	4	yes	—
285	#125	C₂×C₄×C₅	1	4	yes	—
286	C₂²⋊Q₈	—	2	2	no	—
287	C₂²⋊Q₈	—	2	2	no	—
288	C₂²⋊Q₈	—	2	2	no	—
289	C₂²⋊Q₈	—	2	2	no	—
290	C₂²⋊Q₈	—	2	2	no	—
291	C₂²⋊Q₈	—	2	2	no	—
292	C₂²⋊Q₈	—	2	2	no	—
293	C₂²⋊Q₈	—	2	2	no	—
294	C₄×Q₈	—	2	2	no	—
295	C₄×Q₈	—	2	2	no	—
296	C₄×Q₈	—	2	2	no	—
297	C₄×Q₈	—	2	2	no	—
298	C₄×Q₈	—	2	2	no	—
299	C₄×Q₈	—	2	2	no	—
300	C₄×Q₈	—	2	2	no	—
301	C₄×Q₈	—	2	2	no	—
302	#117	—	2	8	no	—
303	#117	—	2	2	no	—
304	#117	—	2	2	no	—
305	#117	C₂×C₄×C₅	1	4	yes	—
306	#117	C₂³×C₅	1	4	yes	—
307	C₂×C₄⋊C₄	—	2	2	no	—
308	C₂×C₄⋊C₄	—	2	2	no	—
309	C₂×C₄⋊C₄	—	2	1	no	—
310	C₂×C₄⋊C₄	—	2	1	no	—
311	C₂×C₄⋊C₄	—	2	2	no	—
312	C₂×C₄⋊C₄	C₂×C₄×C₅	1	2	yes	—
313	C₂×C₄⋊C₄	C₂×C₄×C₅	1	2	yes	—
314	C₂×C₂²⋊C₄	—	2	2	no	—
315	C₂×C₂²⋊C₄	—	2	2	no	—
316	C₂×C₄²	—	2	2	no	—
317	C₂×C₄²	—	2	2	no	—
318	C₂×C₄²	—	2	2	no	—
319	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
320	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
321	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
322	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
323	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
324	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
325	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
326	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
327	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
328	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
329	C₂×C₄²	C₂³×C₅	1	4	yes	—
330	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
331	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
332	C₄⋊C₈	—	2	2	no	—
333	C₄⋊C₈	—	2	2	no	—
334	C₂²⋊C₈	—	2	2	no	—
335	C₂²⋊C₈	—	2	2	no	—
336	#97	—	2	2	no	—
337	C₄×C₈	—	2	2	no	—
338	#95	—	2	2	no	—
339	#95	—	2	2	no	—
340	C₂²×C₅	—	2	1	no	—
341	C₂²×C₅	—	2	1	no	—
342	C₂²×C₅	—	2	1	no	—
343	C₂²×C₅	—	2	1	no	—
344	C₂²×C₅	—	2	1	no	—
345	C₂²×C₅	—	2	1	no	—
346	C₂²×C₅	—	2	1	no	—
347	C₂²×C₅	—	4	4	no	—
348	C₂²×C₅	C₂×#104	1	2	yes	—
349	C₂²×C₅	C₂²×C₂²⋊C₄	1	1	yes	characteristic
350	C₂²×C₅	#536	1	2	yes	—
351	C₄×C₅	—	2	1	no	—
352	C₄×C₅	—	2	1	no	—
353	C₄×C₅	—	2	1	no	—
354	C₄×C₅	—	2	1	no	—
355	C₄×C₅	—	2	1	no	—
356	C₄×C₅	—	2	1	no	—
357	C₄×C₅	—	2	1	no	—
358	C₄×C₅	—	4	8	no	—
359	C₄×C₅	—	4	4	no	—
360	C₄×C₅	—	4	4	no	—
361	C₄×C₅	C₂×#104	1	2	yes	—
362	C₄×C₅	C₂×#104	1	2	yes	—
363	C₄×C₅	#421	1	2	yes	—
364	C₄×C₅	#519	1	2	yes	—
365	C₄×C₅	#536	1	2	yes	—
366	C₂⁴	C₂×C₅×D₄	1	1	yes	characteristic
367	C₂×Q₈	—	2	2	no	—
368	C₂×Q₈	—	2	2	no	—
369	C₂×Q₈	—	2	2	no	—
370	C₂×Q₈	—	2	2	no	—
371	C₂×Q₈	—	4	4	no	—
372	C₂×Q₈	—	4	4	no	—
373	C₂²×C₄	—	2	4	no	—
374	C₂²×C₄	—	2	4	no	—
375	C₂²×C₄	—	2	2	no	—
376	C₂²×C₄	—	2	2	no	—
377	C₂²×C₄	—	2	4	no	—
378	C₂²×C₄	—	4	2	no	—
379	C₂²×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
380	C₂²×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
381	C₂²×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
382	C₂²×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
383	C₂²×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
384	C₂²×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
385	C₂²×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
386	C₂²×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
387	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
388	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
389	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
390	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
391	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
392	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
393	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
394	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
395	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
396	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
397	M₁₆	—	2	8	no	—
398	C₂×C₈	—	2	4	no	—
399	C₄⋊C₄	—	2	8	no	—
400	C₄⋊C₄	—	2	4	no	—
401	C₄⋊C₄	—	2	4	no	—
402	C₄⋊C₄	—	2	4	no	—
403	C₄⋊C₄	—	2	4	no	—
404	C₄⋊C₄	—	2	2	no	—
405	C₄⋊C₄	—	2	2	no	—
406	C₄⋊C₄	—	2	2	no	—
407	C₄⋊C₄	—	2	2	no	—
408	C₄⋊C₄	—	2	2	no	—
409	C₄⋊C₄	—	2	2	no	—
410	C₄⋊C₄	C₂²×C₄×C₅	1	4	yes	—
411	C₄⋊C₄	C₂²×C₄×C₅	1	4	yes	—
412	C₂²⋊C₄	—	2	8	no	—
413	C₂²⋊C₄	—	2	4	no	—
414	C₂²⋊C₄	—	2	4	no	—
415	C₄²	—	2	8	no	—
416	C₄²	—	2	4	no	—
417	C₄²	—	2	4	no	—
418	C₄²	—	2	8	no	—
419	C₄²	—	4	4	no	—
420	C₄²	C₅×C₂²⋊C₄	1	1	yes	characteristic
421	C₄²	C₅×C₂²⋊C₄	1	1	yes	characteristic
422	C₄²	C₅×C₂²⋊C₄	1	1	yes	characteristic
423	C₄²	C₅×C₂²⋊C₄	1	1	yes	characteristic
424	C₄²	C₅×C₂²⋊C₄	1	1	yes	characteristic
425	C₄²	C₅×C₂²⋊C₄	1	1	yes	characteristic
426	C₄²	C₅×C₂²⋊C₄	1	1	yes	characteristic
427	C₄²	C₅×C₂²⋊C₄	1	1	yes	characteristic
428	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
429	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
430	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
431	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
432	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
433	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
434	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
435	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
436	C₂×C₅	—	2	2	no	—
437	C₂×C₅	—	2	2	no	—
438	C₂×C₅	—	4	1	no	—
439	C₂×C₅	#2310	1	1	yes	characteristic
440	C₂×C₅	C₂²×#104	1	1	yes	characteristic
441	C₂×C₅	C₂×#421	1	1	yes	characteristic
442	C₂³	—	2	2	no	—
443	C₂³	—	2	2	no	—
444	C₂³	—	4	1	no	—
445	C₂³	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
446	C₂³	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
447	C₂³	C₂²×C₅×D₄	1	1	yes	characteristic
448	Q₈	—	4	4	no	—
449	Q₈	—	4	4	no	—
450	Q₈	—	4	4	no	—
451	Q₈	—	4	4	no	—
452	C₂×C₄	—	2	2	no	—
453	C₂×C₄	—	2	2	no	—
454	C₂×C₄	—	2	2	no	—
455	C₂×C₄	—	2	2	no	—
456	C₂×C₄	—	2	2	no	—
457	C₂×C₄	—	2	2	no	—
458	C₂×C₄	—	2	2	no	—
459	C₂×C₄	—	2	2	no	—
460	C₂×C₄	—	2	2	no	—
461	C₂×C₄	—	2	2	no	—
462	C₂×C₄	—	2	2	no	—
463	C₂×C₄	—	2	2	no	—
464	C₂×C₄	—	2	2	no	—
465	C₂×C₄	—	2	8	no	—
466	C₂×C₄	—	2	4	no	—
467	C₂×C₄	—	2	4	no	—
468	C₂×C₄	—	4	1	no	—
469	C₂×C₄	—	4	1	no	—
470	C₂×C₄	—	4	1	no	—
471	C₂×C₄	—	4	4	no	—
472	C₂×C₄	—	4	4	no	—
473	C₂×C₄	—	4	4	no	—
474	C₂×C₄	—	4	4	no	—
475	C₂×C₄	C₅×#104	1	4	yes	—
476	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
477	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
478	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
479	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
480	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
481	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
482	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
483	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
484	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
485	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
486	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
487	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
488	C₂×C₄	C₅×2₋¹⁺⁴	1	4	yes	—
489	C₈	—	4	4	no	—
490	C₅	#21844	1	1	yes	characteristic, direct product factor, Sylow
491	C₂²	—	2	1	no	—
492	C₂²	—	2	1	no	—
493	C₂²	—	2	1	no	—
494	C₂²	—	2	1	no	—
495	C₂²	—	2	1	no	—
496	C₂²	—	2	1	no	—
497	C₂²	—	2	1	no	—
498	C₂²	—	4	4	no	—
499	C₂²	C₂×C₅×#104	1	2	yes	—
500	C₂²	C₂²×C₅×C₂²⋊C₄	1	1	yes	characteristic
501	C₂²	C₅×#536	1	2	yes	—
502	C₄	—	2	1	no	—
503	C₄	—	2	1	no	—
504	C₄	—	2	1	no	—
505	C₄	—	2	1	no	—
506	C₄	—	2	1	no	—
507	C₄	—	2	1	no	—
508	C₄	—	2	1	no	—
509	C₄	—	4	8	no	—
510	C₄	—	4	4	no	—
511	C₄	—	4	4	no	—
512	C₄	C₂×C₅×#104	1	2	yes	—
513	C₄	C₂×C₅×#104	1	2	yes	—
514	C₄	C₅×#421	1	2	yes	—
515	C₄	C₅×#519	1	2	yes	—
516	C₄	C₅×#536	1	2	yes	—
517	C₂	—	2	2	no	—
518	C₂	—	2	2	no	—
519	C₂	—	4	1	no	—
520	C₂	C₅×#2310	1	1	yes	characteristic
521	C₂	C₂²×C₅×#104	1	1	yes	characteristic
522	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	C₂²×C₄	C₂⁴×C₅
socle	C₂²×C₅	C₂²×C₂²⋊C₄
prime radical	C₂⁴×C₅	C₂×D₄
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×#1994	C₂	semidirect
5. C₅×#1986	C₂	semidirect
11. C₅×#533	C₄	semidirect
12. C₅×#533	C₄	semidirect
15. C₂×C₅×C₄⋊Q₈	C₄	semidirect
16. C₂×C₅×C₄⋊Q₈	C₄	semidirect
17. C₂×C₅×#125	C₄	semidirect
39. #21844	C₅	direct (N × H)
115. #1994	C₂×C₅	semidirect
116. #1986	C₂×C₅	semidirect
192. #533	C₄×C₅	semidirect
193. #533	C₄×C₅	semidirect
196. C₂×C₄⋊Q₈	C₄×C₅	semidirect
197. C₂×C₄⋊Q₈	C₄×C₅	semidirect
198. C₂×#125	C₄×C₅	semidirect
490. C₅	#21844	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
C₄×C₅×#117	2
C₅×#1994	2
C₅×#1986	2
C₅×#1826	2
#21844	5

Subgroups — C5×#21844 #11944564

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#21844 #11944564