Subgroups — C₅×#21704 #11944424

Order 1280.

1174 conjugacy classes of subgroups.

The subgroup lattice has 660 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#496	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×#442	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×#440	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₄×C₅×SD₁₆	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₄×C₅×D₈	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#2328	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#2326	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#1973	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#1972	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#1970	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#1968	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#1958	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅×#1957	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅×#1847	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅×#1726	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₅×SD₁₆	C₂²	1	1	yes	characteristic
17	C₂²×C₅×SD₁₆	C₂²	1	1	yes	characteristic
18	C₂²×C₅×D₈	C₂²	1	1	yes	characteristic
19	C₂²×C₅×D₈	C₂²	1	1	yes	characteristic
20	C₂×C₅×#127	C₂²	1	1	yes	characteristic
21	C₂×C₅×#124	C₂²	1	1	yes	characteristic
22	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
23	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
24	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
25	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
26	C₅×#496	C₄	1	8	yes	complemented
27	C₅×#442	—	2	4	no	—
28	C₅×#440	—	2	4	no	—
29	C₄×C₅×SD₁₆	—	2	4	no	—
30	C₄×C₅×D₈	—	2	4	no	—
31	C₂×C₅×#107	C₂²	1	1	yes	characteristic
32	C₂×C₅×#107	C₂²	1	1	yes	characteristic
33	C₂×C₅×#106	C₂²	1	1	yes	characteristic
34	C₂×C₅×#106	C₂²	1	1	yes	characteristic
35	C₂×C₅×#103	C₂²	1	1	yes	characteristic
36	C₂×C₅×#103	C₂²	1	1	yes	characteristic
37	C₂×C₅×#102	C₂²	1	1	yes	characteristic
38	C₂×C₅×#102	C₂²	1	1	yes	characteristic
39	C₂×C₅×#102	C₂²	1	1	yes	characteristic
40	C₂×C₅×#102	C₂²	1	1	yes	characteristic
41	C₂×C₅×#102	C₂²	1	1	yes	characteristic
42	C₂×C₅×#102	C₂²	1	1	yes	characteristic
43	C₂×C₅×#97	C₂²	1	1	yes	characteristic
44	C₂×C₅×#97	C₂²	1	1	yes	characteristic
45	C₂×C₅×#97	C₂²	1	1	yes	characteristic
46	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
47	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
48	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
49	C₅×#391	C₂²	1	1	yes	characteristic
50	C₅×#390	C₂²	1	1	yes	characteristic
51	C₅×#390	C₂²	1	1	yes	characteristic
52	C₅×#390	C₂²	1	1	yes	characteristic
53	C₅×#388	—	2	2	no	—
54	C₅×#386	—	2	2	no	—
55	C₅×#386	—	2	2	no	—
56	C₅×#385	—	2	2	no	—
57	C₅×#384	C₂²	1	1	yes	characteristic
58	C₅×#382	C₂²	1	1	yes	characteristic
59	C₅×#376	C₂²	1	1	yes	characteristic
60	#21704	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
61	C₂²×C₅×Q₈	C₂³	1	1	yes	characteristic
62	C₂²×C₅×D₄	—	2	2	no	—
63	C₂²×C₅×D₄	C₂³	1	1	yes	characteristic
64	C₂²×C₅×D₄	C₂³	1	1	yes	characteristic
65	C₂²×C₅×D₄	C₂³	1	1	yes	characteristic
66	C₂³×C₄×C₅	—	2	1	no	—
67	C₂³×C₄×C₅	—	2	1	no	—
68	C₂³×C₄×C₅	—	2	1	no	—
69	C₂×C₅×SD₁₆	—	2	2	no	—
70	C₂×C₅×SD₁₆	—	2	2	no	—
71	C₂×C₅×SD₁₆	—	2	2	no	—
72	C₂×C₅×SD₁₆	—	2	2	no	—
73	C₂×C₅×SD₁₆	C₂×C₄	1	4	yes	complemented
74	C₂×C₅×SD₁₆	C₂×C₄	1	4	yes	complemented
75	C₂×C₅×D₈	—	2	2	no	—
76	C₂×C₅×D₈	—	2	2	no	—
77	C₂×C₅×D₈	—	2	2	no	—
78	C₂×C₅×D₈	—	2	2	no	—
79	C₂×C₅×D₈	C₂×C₄	1	4	yes	complemented
80	C₂×C₅×D₈	C₂×C₄	1	4	yes	complemented
81	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
82	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
83	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
84	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
85	C₅×#127	—	2	2	no	—
86	C₅×#127	C₂×C₄	1	4	yes	complemented
87	C₅×#124	—	2	2	no	—
88	C₅×#124	C₂×C₄	1	4	yes	complemented
89	C₄×C₅×Q₈	—	2	2	no	—
90	C₄×C₅×Q₈	—	2	2	no	—
91	C₄×C₅×D₄	—	2	2	no	—
92	C₄×C₅×D₄	—	2	2	no	—
93	C₄×C₅×D₄	—	2	2	no	—
94	C₄×C₅×D₄	—	2	2	no	—
95	C₄×C₅×D₄	—	2	2	no	—
96	C₄×C₅×D₄	—	2	2	no	—
97	C₂×C₅×C₄⋊C₄	—	2	1	no	—
98	C₂×C₅×C₄⋊C₄	—	2	2	no	—
99	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
100	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
101	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
102	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
103	C₂×C₅×C₂²⋊C₄	—	2	2	no	—
104	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
105	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
106	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
107	C₂×C₅×C₂²⋊C₄	—	2	2	no	—
108	C₂×C₅×C₂²⋊C₄	—	2	2	no	—
109	C₂×C₅×C₂²⋊C₄	—	2	2	no	—
110	C₂×C₄²×C₅	—	2	1	no	—
111	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
112	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
113	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
114	C₅×#107	—	2	2	no	—
115	C₅×#107	—	2	2	no	—
116	C₅×#106	—	2	2	no	—
117	C₅×#106	—	2	2	no	—
118	C₅×#103	—	2	2	no	—
119	C₅×#103	—	2	2	no	—
120	C₅×#102	—	2	2	no	—
121	C₅×#102	—	2	2	no	—
122	C₅×#102	—	2	2	no	—
123	C₅×#102	—	2	2	no	—
124	C₅×#102	—	2	2	no	—
125	C₅×#102	—	2	2	no	—
126	C₅×#97	—	2	2	no	—
127	C₅×#97	C₂×C₄	1	4	yes	complemented
128	C₅×#97	D₄	1	4	yes	complemented
129	C₄×C₅×C₈	—	2	2	no	—
130	C₄×C₅×C₈	—	2	2	no	—
131	C₄×C₅×C₈	D₄	1	4	yes	complemented
132	C₅×#95	—	2	2	no	—
133	C₅×#95	—	2	2	no	—
134	C₅×#95	D₄	1	2	yes	—
135	C₅×#95	D₄	1	2	yes	—
136	C₂×#496	C₂×C₅	1	1	yes	characteristic
137	C₂×#442	C₂×C₅	1	1	yes	characteristic, complemented
138	C₂×#440	C₂×C₅	1	1	yes	characteristic, complemented
139	C₂×C₄×SD₁₆	C₂×C₅	1	1	yes	characteristic, complemented
140	C₂×C₄×D₈	C₂×C₅	1	1	yes	characteristic, complemented
141	#2328	C₂×C₅	1	1	yes	characteristic, complemented
142	#2326	C₂×C₅	1	1	yes	characteristic, complemented
143	#1973	C₂×C₅	1	1	yes	characteristic, complemented
144	#1972	C₂×C₅	1	1	yes	characteristic, complemented
145	#1970	C₂×C₅	1	1	yes	characteristic, complemented
146	#1968	C₂×C₅	1	1	yes	characteristic, complemented
147	#1958	C₂×C₅	1	1	yes	characteristic, complemented
148	#1957	C₂×C₅	1	1	yes	characteristic, complemented
149	#1847	C₂×C₅	1	1	yes	characteristic, complemented
150	#1726	C₂×C₅	1	1	yes	characteristic, complemented
151	C₂⁴×C₅	—	2	1	no	—
152	C₂⁴×C₅	—	2	1	no	—
153	C₂⁴×C₅	—	2	1	no	—
154	C₂×C₅×Q₈	—	2	1	no	—
155	C₂×C₅×Q₈	—	2	1	no	—
156	C₂×C₅×Q₈	—	2	1	no	—
157	C₂×C₅×Q₈	—	2	1	no	—
158	C₂×C₅×Q₈	—	2	1	no	—
159	C₂×C₅×Q₈	C₂²×C₄	1	2	yes	—
160	C₂×C₅×D₄	—	2	8	no	—
161	C₂×C₅×D₄	—	2	1	no	—
162	C₂×C₅×D₄	—	2	1	no	—
163	C₂×C₅×D₄	—	2	1	no	—
164	C₂×C₅×D₄	—	2	1	no	—
165	C₂×C₅×D₄	—	2	1	no	—
166	C₂×C₅×D₄	—	2	1	no	—
167	C₂×C₅×D₄	—	2	1	no	—
168	C₂×C₅×D₄	—	2	1	no	—
169	C₂×C₅×D₄	—	2	1	no	—
170	C₂×C₅×D₄	—	2	1	no	—
171	C₂×C₅×D₄	—	2	1	no	—
172	C₂×C₅×D₄	—	2	1	no	—
173	C₂×C₅×D₄	—	2	1	no	—
174	C₂×C₅×D₄	—	2	1	no	—
175	C₂×C₅×D₄	—	2	1	no	—
176	C₂×C₅×D₄	—	8	2	no	—
177	C₂×C₅×D₄	—	8	2	no	—
178	C₂×C₅×D₄	C₂²×C₄	1	2	yes	—
179	C₂×C₅×D₄	C₂²×C₄	1	2	yes	—
180	C₂×C₅×D₄	C₂²×C₄	1	2	yes	—
181	C₂²×C₄×C₅	—	2	1	no	—
182	C₂²×C₄×C₅	—	2	1	no	—
183	C₂²×C₄×C₅	—	2	1	no	—
184	C₂²×C₄×C₅	—	2	1	no	—
185	C₂²×C₄×C₅	—	2	1	no	—
186	C₂²×C₄×C₅	—	4	2	no	—
187	C₂²×C₄×C₅	—	4	2	no	—
188	C₂²×C₄×C₅	—	4	2	no	—
189	C₂²×C₄×C₅	—	8	2	no	—
190	C₂²×C₄×C₅	—	8	2	no	—
191	C₂²×C₄×C₅	—	8	2	no	—
192	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
193	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
194	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
195	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
196	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
197	C₅×SD₁₆	—	2	8	no	—
198	C₅×SD₁₆	—	2	8	no	—
199	C₅×D₈	—	2	8	no	—
200	C₅×D₈	—	2	8	no	—
201	C₂×C₅×C₈	—	2	1	no	—
202	C₂×C₅×C₈	—	2	1	no	—
203	C₂×C₅×C₈	—	2	1	no	—
204	C₂×C₅×C₈	—	2	1	no	—
205	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
206	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
207	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
208	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
209	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
210	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
211	C₂×C₅×C₈	#41	1	2	yes	—
212	C₂×C₅×C₈	#41	1	2	yes	—
213	C₅×C₄⋊C₄	—	2	1	no	—
214	C₅×C₄⋊C₄	—	2	1	no	—
215	C₅×C₄⋊C₄	—	2	1	no	—
216	C₅×C₄⋊C₄	—	2	1	no	—
217	C₅×C₄⋊C₄	—	2	1	no	—
218	C₅×C₄⋊C₄	—	2	1	no	—
219	C₅×C₄⋊C₄	—	2	1	no	—
220	C₅×C₄⋊C₄	—	2	1	no	—
221	C₅×C₄⋊C₄	—	4	2	no	—
222	C₅×C₄⋊C₄	—	8	2	no	—
223	C₅×C₂²⋊C₄	—	2	8	no	—
224	C₅×C₂²⋊C₄	—	4	2	no	—
225	C₅×C₂²⋊C₄	—	4	2	no	—
226	C₅×C₂²⋊C₄	—	4	2	no	—
227	C₅×C₂²⋊C₄	—	8	2	no	—
228	C₅×C₂²⋊C₄	—	8	2	no	—
229	C₅×C₂²⋊C₄	—	8	2	no	—
230	C₄²×C₅	—	2	1	no	—
231	C₄²×C₅	—	2	1	no	—
232	C₄²×C₅	—	4	2	no	—
233	C₄²×C₅	C₂²×C₄	1	2	yes	—
234	C₄²×C₅	C₂×D₄	1	2	yes	—
235	C₄²×C₅	C₂×D₄	1	2	yes	—
236	C₄²×C₅	#41	1	2	yes	—
237	C₂²×SD₁₆	C₂²×C₅	1	1	yes	characteristic
238	C₂²×SD₁₆	C₂²×C₅	1	1	yes	characteristic
239	C₂²×D₈	C₂²×C₅	1	1	yes	characteristic
240	C₂²×D₈	C₂²×C₅	1	1	yes	characteristic
241	C₂×#127	C₂²×C₅	1	1	yes	characteristic
242	C₂×#124	C₂²×C₅	1	1	yes	characteristic
243	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
244	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
245	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
246	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
247	#496	C₄×C₅	1	8	yes	complemented
248	#442	—	2	4	no	—
249	#440	—	2	4	no	—
250	C₄×SD₁₆	—	2	4	no	—
251	C₄×D₈	—	2	4	no	—
252	C₂×#107	C₂²×C₅	1	1	yes	characteristic
253	C₂×#107	C₂²×C₅	1	1	yes	characteristic
254	C₂×#106	C₂²×C₅	1	1	yes	characteristic
255	C₂×#106	C₂²×C₅	1	1	yes	characteristic
256	C₂×#103	C₂²×C₅	1	1	yes	characteristic
257	C₂×#103	C₂²×C₅	1	1	yes	characteristic
258	C₂×#102	C₂²×C₅	1	1	yes	characteristic
259	C₂×#102	C₂²×C₅	1	1	yes	characteristic
260	C₂×#102	C₂²×C₅	1	1	yes	characteristic
261	C₂×#102	C₂²×C₅	1	1	yes	characteristic
262	C₂×#102	C₂²×C₅	1	1	yes	characteristic
263	C₂×#102	C₂²×C₅	1	1	yes	characteristic
264	C₂×#97	C₂²×C₅	1	1	yes	characteristic
265	C₂×#97	C₂²×C₅	1	1	yes	characteristic
266	C₂×#97	C₂²×C₅	1	1	yes	characteristic
267	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
268	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
269	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
270	#391	C₂²×C₅	1	1	yes	characteristic
271	#390	C₂²×C₅	1	1	yes	characteristic
272	#390	C₂²×C₅	1	1	yes	characteristic
273	#390	C₂²×C₅	1	1	yes	characteristic
274	#388	—	2	2	no	—
275	#386	—	2	2	no	—
276	#386	—	2	2	no	—
277	#385	—	2	2	no	—
278	#384	C₂²×C₅	1	1	yes	characteristic
279	#382	C₂²×C₅	1	1	yes	characteristic
280	#376	C₂²×C₅	1	1	yes	characteristic
281	C₂³×C₅	—	2	2	no	—
282	C₂³×C₅	—	2	2	no	—
283	C₂³×C₅	—	2	2	no	—
284	C₂³×C₅	—	4	1	no	—
285	C₂³×C₅	—	4	1	no	—
286	C₂³×C₅	—	4	1	no	—
287	C₂³×C₅	—	4	1	no	—
288	C₂³×C₅	—	4	1	no	—
289	C₂³×C₅	—	4	1	no	—
290	C₂³×C₅	—	4	2	no	—
291	C₂³×C₅	—	4	2	no	—
292	C₂³×C₅	—	4	2	no	—
293	C₂³×C₅	—	4	2	no	—
294	C₂³×C₅	—	4	2	no	—
295	C₂³×C₅	—	4	2	no	—
296	C₂³×C₅	C₂²×D₄	1	1	yes	characteristic
297	C₅×Q₈	—	2	2	no	—
298	C₅×Q₈	—	2	2	no	—
299	C₅×Q₈	—	4	1	no	—
300	C₅×Q₈	—	4	1	no	—
301	C₅×D₄	—	2	2	no	—
302	C₅×D₄	—	2	2	no	—
303	C₅×D₄	—	2	2	no	—
304	C₅×D₄	—	2	2	no	—
305	C₅×D₄	—	2	2	no	—
306	C₅×D₄	—	2	2	no	—
307	C₅×D₄	—	4	1	no	—
308	C₅×D₄	—	4	1	no	—
309	C₅×D₄	—	4	1	no	—
310	C₅×D₄	—	4	1	no	—
311	C₅×D₄	—	4	1	no	—
312	C₅×D₄	—	4	1	no	—
313	C₅×D₄	—	8	8	no	—
314	C₂×C₄×C₅	—	2	2	no	—
315	C₂×C₄×C₅	—	2	2	no	—
316	C₂×C₄×C₅	—	2	2	no	—
317	C₂×C₄×C₅	—	2	2	no	—
318	C₂×C₄×C₅	—	2	2	no	—
319	C₂×C₄×C₅	—	2	2	no	—
320	C₂×C₄×C₅	—	2	2	no	—
321	C₂×C₄×C₅	—	2	2	no	—
322	C₂×C₄×C₅	—	4	1	no	—
323	C₂×C₄×C₅	—	4	1	no	—
324	C₂×C₄×C₅	—	4	1	no	—
325	C₂×C₄×C₅	—	4	1	no	—
326	C₂×C₄×C₅	—	4	1	no	—
327	C₂×C₄×C₅	—	4	1	no	—
328	C₂×C₄×C₅	—	4	2	no	—
329	C₂×C₄×C₅	—	4	2	no	—
330	C₂×C₄×C₅	—	4	2	no	—
331	C₂×C₄×C₅	—	4	2	no	—
332	C₂×C₄×C₅	—	8	4	no	—
333	C₂×C₄×C₅	—	8	4	no	—
334	C₂×C₄×C₅	—	8	4	no	—
335	C₂×C₄×C₅	C₄×D₄	1	4	yes	—
336	C₂×C₄×C₅	#127	1	2	yes	—
337	C₂×C₄×C₅	#127	1	2	yes	—
338	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
339	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
340	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
341	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
342	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
343	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
344	C₅×C₈	—	2	2	no	—
345	C₅×C₈	—	2	2	no	—
346	C₅×C₈	C₄×D₄	1	4	yes	—
347	C₅×C₈	C₄×D₄	1	4	yes	—
348	C₂²×Q₈	C₂³×C₅	1	1	yes	characteristic
349	C₂²×D₄	—	2	2	no	—
350	C₂²×D₄	C₂³×C₅	1	1	yes	characteristic
351	C₂²×D₄	C₂³×C₅	1	1	yes	characteristic
352	C₂²×D₄	C₂³×C₅	1	1	yes	characteristic
353	C₂³×C₄	—	2	1	no	—
354	C₂³×C₄	—	2	1	no	—
355	C₂³×C₄	—	2	1	no	—
356	C₂×SD₁₆	—	2	2	no	—
357	C₂×SD₁₆	—	2	2	no	—
358	C₂×SD₁₆	—	2	2	no	—
359	C₂×SD₁₆	—	2	2	no	—
360	C₂×SD₁₆	C₂×C₄×C₅	1	4	yes	complemented
361	C₂×SD₁₆	C₂×C₄×C₅	1	4	yes	complemented
362	C₂×D₈	—	2	2	no	—
363	C₂×D₈	—	2	2	no	—
364	C₂×D₈	—	2	2	no	—
365	C₂×D₈	—	2	2	no	—
366	C₂×D₈	C₂×C₄×C₅	1	4	yes	complemented
367	C₂×D₈	C₂×C₄×C₅	1	4	yes	complemented
368	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
369	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
370	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
371	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
372	#127	—	2	2	no	—
373	#127	C₂×C₄×C₅	1	4	yes	complemented
374	#124	—	2	2	no	—
375	#124	C₂×C₄×C₅	1	4	yes	complemented
376	C₄×Q₈	—	2	2	no	—
377	C₄×Q₈	—	2	2	no	—
378	C₄×D₄	—	2	2	no	—
379	C₄×D₄	—	2	2	no	—
380	C₄×D₄	—	2	2	no	—
381	C₄×D₄	—	2	2	no	—
382	C₄×D₄	—	2	2	no	—
383	C₄×D₄	—	2	2	no	—
384	C₂×C₄⋊C₄	—	2	1	no	—
385	C₂×C₄⋊C₄	—	2	2	no	—
386	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
387	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
388	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
389	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
390	C₂×C₂²⋊C₄	—	2	2	no	—
391	C₂×C₂²⋊C₄	—	2	1	no	—
392	C₂×C₂²⋊C₄	—	2	1	no	—
393	C₂×C₂²⋊C₄	—	2	1	no	—
394	C₂×C₂²⋊C₄	—	2	2	no	—
395	C₂×C₂²⋊C₄	—	2	2	no	—
396	C₂×C₂²⋊C₄	—	2	2	no	—
397	C₂×C₄²	—	2	1	no	—
398	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
399	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
400	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
401	#107	—	2	2	no	—
402	#107	—	2	2	no	—
403	#106	—	2	2	no	—
404	#106	—	2	2	no	—
405	#103	—	2	2	no	—
406	#103	—	2	2	no	—
407	#102	—	2	2	no	—
408	#102	—	2	2	no	—
409	#102	—	2	2	no	—
410	#102	—	2	2	no	—
411	#102	—	2	2	no	—
412	#102	—	2	2	no	—
413	#97	—	2	2	no	—
414	#97	C₂×C₄×C₅	1	4	yes	complemented
415	#97	C₅×D₄	1	4	yes	complemented
416	C₄×C₈	—	2	2	no	—
417	C₄×C₈	—	2	2	no	—
418	C₄×C₈	C₅×D₄	1	4	yes	complemented
419	#95	—	2	2	no	—
420	#95	—	2	2	no	—
421	#95	C₅×D₄	1	2	yes	—
422	#95	C₅×D₄	1	2	yes	—
423	C₂²×C₅	—	4	2	no	—
424	C₂²×C₅	—	4	2	no	—
425	C₂²×C₅	—	4	2	no	—
426	C₂²×C₅	—	4	4	no	—
427	C₂²×C₅	—	4	4	no	—
428	C₂²×C₅	—	4	4	no	—
429	C₂²×C₅	—	8	1	no	—
430	C₂²×C₅	—	8	1	no	—
431	C₂²×C₅	—	8	1	no	—
432	C₂²×C₅	—	8	1	no	—
433	C₂²×C₅	—	8	1	no	—
434	C₂²×C₅	—	8	1	no	—
435	C₂²×C₅	—	8	2	no	—
436	C₂²×C₅	—	8	2	no	—
437	C₂²×C₅	—	8	2	no	—
438	C₂²×C₅	C₂×C₄×D₄	1	1	yes	characteristic
439	C₂²×C₅	C₂×#127	1	1	yes	characteristic
440	C₂²×C₅	#532	1	1	yes	characteristic
441	C₂²×C₅	#576	1	2	yes	—
442	C₂²×C₅	#577	1	2	yes	—
443	C₄×C₅	—	2	2	no	—
444	C₄×C₅	—	2	2	no	—
445	C₄×C₅	—	2	4	no	—
446	C₄×C₅	—	4	2	no	—
447	C₄×C₅	—	4	2	no	—
448	C₄×C₅	—	8	1	no	—
449	C₄×C₅	—	8	1	no	—
450	C₄×C₅	—	8	1	no	—
451	C₄×C₅	—	8	1	no	—
452	C₄×C₅	C₂×C₄×D₄	1	1	yes	characteristic
453	C₄×C₅	C₂×C₄×D₄	1	1	yes	characteristic
454	C₄×C₅	#532	1	1	yes	characteristic
455	C₄×C₅	#532	1	1	yes	characteristic
456	C₂⁴	—	2	1	no	—
457	C₂⁴	—	2	1	no	—
458	C₂⁴	—	2	1	no	—
459	C₂×Q₈	—	2	1	no	—
460	C₂×Q₈	—	2	1	no	—
461	C₂×Q₈	—	2	1	no	—
462	C₂×Q₈	—	2	1	no	—
463	C₂×Q₈	—	2	1	no	—
464	C₂×Q₈	C₂²×C₄×C₅	1	2	yes	—
465	C₂×D₄	—	2	8	no	—
466	C₂×D₄	—	2	1	no	—
467	C₂×D₄	—	2	1	no	—
468	C₂×D₄	—	2	1	no	—
469	C₂×D₄	—	2	1	no	—
470	C₂×D₄	—	2	1	no	—
471	C₂×D₄	—	2	1	no	—
472	C₂×D₄	—	2	1	no	—
473	C₂×D₄	—	2	1	no	—
474	C₂×D₄	—	2	1	no	—
475	C₂×D₄	—	2	1	no	—
476	C₂×D₄	—	2	1	no	—
477	C₂×D₄	—	2	1	no	—
478	C₂×D₄	—	2	1	no	—
479	C₂×D₄	—	2	1	no	—
480	C₂×D₄	—	2	1	no	—
481	C₂×D₄	—	8	2	no	—
482	C₂×D₄	—	8	2	no	—
483	C₂×D₄	C₂²×C₄×C₅	1	2	yes	—
484	C₂×D₄	C₂²×C₄×C₅	1	2	yes	—
485	C₂×D₄	C₂²×C₄×C₅	1	2	yes	—
486	C₂²×C₄	—	2	1	no	—
487	C₂²×C₄	—	2	1	no	—
488	C₂²×C₄	—	2	1	no	—
489	C₂²×C₄	—	2	1	no	—
490	C₂²×C₄	—	2	1	no	—
491	C₂²×C₄	—	4	2	no	—
492	C₂²×C₄	—	4	2	no	—
493	C₂²×C₄	—	4	2	no	—
494	C₂²×C₄	—	8	2	no	—
495	C₂²×C₄	—	8	2	no	—
496	C₂²×C₄	—	8	2	no	—
497	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
498	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
499	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
500	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
501	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
502	SD₁₆	—	2	8	no	—
503	SD₁₆	—	2	8	no	—
504	D₈	—	2	8	no	—
505	D₈	—	2	8	no	—
506	C₂×C₈	—	2	1	no	—
507	C₂×C₈	—	2	1	no	—
508	C₂×C₈	—	2	1	no	—
509	C₂×C₈	—	2	1	no	—
510	C₂×C₈	C₂²×C₄×C₅	1	2	yes	—
511	C₂×C₈	C₂²×C₄×C₅	1	2	yes	—
512	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
513	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
514	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
515	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
516	C₂×C₈	C₅×#41	1	2	yes	—
517	C₂×C₈	C₅×#41	1	2	yes	—
518	C₄⋊C₄	—	2	1	no	—
519	C₄⋊C₄	—	2	1	no	—
520	C₄⋊C₄	—	2	1	no	—
521	C₄⋊C₄	—	2	1	no	—
522	C₄⋊C₄	—	2	1	no	—
523	C₄⋊C₄	—	2	1	no	—
524	C₄⋊C₄	—	2	1	no	—
525	C₄⋊C₄	—	2	1	no	—
526	C₄⋊C₄	—	4	2	no	—
527	C₄⋊C₄	—	8	2	no	—
528	C₂²⋊C₄	—	2	8	no	—
529	C₂²⋊C₄	—	4	2	no	—
530	C₂²⋊C₄	—	4	2	no	—
531	C₂²⋊C₄	—	4	2	no	—
532	C₂²⋊C₄	—	8	2	no	—
533	C₂²⋊C₄	—	8	2	no	—
534	C₂²⋊C₄	—	8	2	no	—
535	C₄²	—	2	1	no	—
536	C₄²	—	2	1	no	—
537	C₄²	—	4	2	no	—
538	C₄²	C₂²×C₄×C₅	1	2	yes	—
539	C₄²	C₂×C₅×D₄	1	2	yes	—
540	C₄²	C₂×C₅×D₄	1	2	yes	—
541	C₄²	C₅×#41	1	2	yes	—
542	C₂×C₅	—	8	2	no	—
543	C₂×C₅	—	8	2	no	—
544	C₂×C₅	—	8	2	no	—
545	C₂×C₅	C₄×#127	1	1	yes	characteristic
546	C₂×C₅	#2946	1	2	yes	—
547	C₂×C₅	#3154	1	1	yes	characteristic
548	C₂×C₅	#3155	1	1	yes	characteristic
549	C₂×C₅	#3179	1	2	yes	—
550	C₂³	—	2	2	no	—
551	C₂³	—	2	2	no	—
552	C₂³	—	2	2	no	—
553	C₂³	—	4	1	no	—
554	C₂³	—	4	1	no	—
555	C₂³	—	4	1	no	—
556	C₂³	—	4	1	no	—
557	C₂³	—	4	1	no	—
558	C₂³	—	4	1	no	—
559	C₂³	—	4	2	no	—
560	C₂³	—	4	2	no	—
561	C₂³	—	4	2	no	—
562	C₂³	—	4	2	no	—
563	C₂³	—	4	2	no	—
564	C₂³	—	4	2	no	—
565	C₂³	C₂²×C₅×D₄	1	1	yes	characteristic
566	Q₈	—	2	2	no	—
567	Q₈	—	2	2	no	—
568	Q₈	—	4	1	no	—
569	Q₈	—	4	1	no	—
570	D₄	—	2	2	no	—
571	D₄	—	2	2	no	—
572	D₄	—	2	2	no	—
573	D₄	—	2	2	no	—
574	D₄	—	2	2	no	—
575	D₄	—	2	2	no	—
576	D₄	—	4	1	no	—
577	D₄	—	4	1	no	—
578	D₄	—	4	1	no	—
579	D₄	—	4	1	no	—
580	D₄	—	4	1	no	—
581	D₄	—	4	1	no	—
582	D₄	—	8	8	no	—
583	C₂×C₄	—	2	2	no	—
584	C₂×C₄	—	2	2	no	—
585	C₂×C₄	—	2	2	no	—
586	C₂×C₄	—	2	2	no	—
587	C₂×C₄	—	2	2	no	—
588	C₂×C₄	—	2	2	no	—
589	C₂×C₄	—	2	2	no	—
590	C₂×C₄	—	2	2	no	—
591	C₂×C₄	—	4	1	no	—
592	C₂×C₄	—	4	1	no	—
593	C₂×C₄	—	4	1	no	—
594	C₂×C₄	—	4	1	no	—
595	C₂×C₄	—	4	1	no	—
596	C₂×C₄	—	4	1	no	—
597	C₂×C₄	—	4	2	no	—
598	C₂×C₄	—	4	2	no	—
599	C₂×C₄	—	4	2	no	—
600	C₂×C₄	—	4	2	no	—
601	C₂×C₄	—	8	4	no	—
602	C₂×C₄	—	8	4	no	—
603	C₂×C₄	—	8	4	no	—
604	C₂×C₄	C₄×C₅×D₄	1	4	yes	—
605	C₂×C₄	C₅×#127	1	2	yes	—
606	C₂×C₄	C₅×#127	1	2	yes	—
607	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
608	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
609	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
610	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
611	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
612	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
613	C₈	—	2	2	no	—
614	C₈	—	2	2	no	—
615	C₈	C₄×C₅×D₄	1	4	yes	—
616	C₈	C₄×C₅×D₄	1	4	yes	—
617	C₅	#21704	1	1	yes	characteristic, direct product factor, Sylow
618	C₂²	—	4	2	no	—
619	C₂²	—	4	2	no	—
620	C₂²	—	4	2	no	—
621	C₂²	—	4	4	no	—
622	C₂²	—	4	4	no	—
623	C₂²	—	4	4	no	—
624	C₂²	—	8	1	no	—
625	C₂²	—	8	1	no	—
626	C₂²	—	8	1	no	—
627	C₂²	—	8	1	no	—
628	C₂²	—	8	1	no	—
629	C₂²	—	8	1	no	—
630	C₂²	—	8	2	no	—
631	C₂²	—	8	2	no	—
632	C₂²	—	8	2	no	—
633	C₂²	C₂×C₄×C₅×D₄	1	1	yes	characteristic
634	C₂²	C₂×C₅×#127	1	1	yes	characteristic
635	C₂²	C₅×#532	1	1	yes	characteristic
636	C₂²	C₅×#576	1	2	yes	—
637	C₂²	C₅×#577	1	2	yes	—
638	C₄	—	2	2	no	—
639	C₄	—	2	2	no	—
640	C₄	—	2	4	no	—
641	C₄	—	4	2	no	—
642	C₄	—	4	2	no	—
643	C₄	—	8	1	no	—
644	C₄	—	8	1	no	—
645	C₄	—	8	1	no	—
646	C₄	—	8	1	no	—
647	C₄	C₂×C₄×C₅×D₄	1	1	yes	characteristic
648	C₄	C₂×C₄×C₅×D₄	1	1	yes	characteristic
649	C₄	C₅×#532	1	1	yes	characteristic
650	C₄	C₅×#532	1	1	yes	characteristic
651	C₂	—	8	2	no	—
652	C₂	—	8	2	no	—
653	C₂	—	8	2	no	—
654	C₂	C₄×C₅×#127	1	1	yes	characteristic
655	C₂	C₅×#2946	1	2	yes	—
656	C₂	C₅×#3154	1	1	yes	characteristic
657	C₂	C₅×#3155	1	1	yes	characteristic
658	C₂	C₅×#3179	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₅	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₅
Frattini, cosocle	C₂²×C₄	C₂⁴×C₅
prime radical	C₂×C₅×#496	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₅ ◁ C₅×#376 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₅×#442	C₂	semidirect
3. C₂×C₅×#440	C₂	semidirect
4. C₂×C₄×C₅×SD₁₆	C₂	semidirect
5. C₂×C₄×C₅×D₈	C₂	semidirect
6. C₅×#2328	C₂	semidirect
7. C₅×#2326	C₂	semidirect
8. C₅×#1973	C₂	semidirect
9. C₅×#1972	C₂	semidirect
10. C₅×#1970	C₂	semidirect
11. C₅×#1968	C₂	semidirect
12. C₅×#1958	C₂	semidirect
13. C₅×#1957	C₂	semidirect
14. C₅×#1847	C₂	semidirect
15. C₅×#1726	C₂	semidirect
26. C₅×#496	C₄	semidirect
60. #21704	C₅	direct (N × H)
73. C₂×C₅×SD₁₆	C₂×C₄	semidirect
74. C₂×C₅×SD₁₆	C₂×C₄	semidirect
79. C₂×C₅×D₈	C₂×C₄	semidirect
80. C₂×C₅×D₈	C₂×C₄	semidirect
86. C₅×#127	C₂×C₄	semidirect
88. C₅×#124	C₂×C₄	semidirect
127. C₅×#97	C₂×C₄	semidirect
128. C₅×#97	D₄	semidirect
131. C₄×C₅×C₈	D₄	semidirect
137. C₂×#442	C₂×C₅	semidirect
138. C₂×#440	C₂×C₅	semidirect
139. C₂×C₄×SD₁₆	C₂×C₅	semidirect
140. C₂×C₄×D₈	C₂×C₅	semidirect
141. #2328	C₂×C₅	semidirect
142. #2326	C₂×C₅	semidirect
143. #1973	C₂×C₅	semidirect
144. #1972	C₂×C₅	semidirect
145. #1970	C₂×C₅	semidirect
146. #1968	C₂×C₅	semidirect
147. #1958	C₂×C₅	semidirect
148. #1957	C₂×C₅	semidirect
149. #1847	C₂×C₅	semidirect
150. #1726	C₂×C₅	semidirect
247. #496	C₄×C₅	semidirect
360. C₂×SD₁₆	C₂×C₄×C₅	semidirect
361. C₂×SD₁₆	C₂×C₄×C₅	semidirect
366. C₂×D₈	C₂×C₄×C₅	semidirect
367. C₂×D₈	C₂×C₄×C₅	semidirect
373. #127	C₂×C₄×C₅	semidirect
375. #124	C₂×C₄×C₅	semidirect
414. #97	C₂×C₄×C₅	semidirect
415. #97	C₅×D₄	semidirect
418. C₄×C₈	C₅×D₄	semidirect
617. C₅	#21704	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×#496	2
C₂×C₅×#442	2
C₂×C₅×#440	2
C₂×C₄×C₅×SD₁₆	2
C₂×C₄×C₅×D₈	2
C₅×#2328	2
C₅×#2326	2
C₅×#1973	2
C₅×#1972	2
C₅×#1970	2
C₅×#1968	2
C₅×#1958	2
C₅×#1957	2
C₅×#1847	2
C₅×#1726	2
#21704	5

Subgroups — C5×#21704 #11944424

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#21704 #11944424