Subgroups — C₅×#21519 #11944239

Order 1280.

902 conjugacy classes of subgroups.

The subgroup lattice has 750 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#3035	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×#444	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×#443	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#2932	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#2875	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#1980	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#1950	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#1929	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#1929	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#1876	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#1876	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#1806	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅×#1771	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅×#1765	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅×#1764	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₅×#135	C₂²	1	1	yes	characteristic
17	C₂×C₅×#135	C₂²	1	1	yes	characteristic
18	C₂×C₅×#131	C₂²	1	1	yes	characteristic
19	C₂×C₅×#131	C₂²	1	1	yes	characteristic
20	C₂×C₅×#131	C₂²	1	1	yes	characteristic
21	C₂×C₅×#131	C₂²	1	1	yes	characteristic
22	C₅×#532	C₂²	1	1	yes	characteristic
23	C₄×C₅×#41	C₂²	1	1	yes	characteristic
24	C₅×#464	C₄	1	1	yes	characteristic, complemented
25	C₅×#464	C₄	1	1	yes	characteristic, complemented
26	C₅×#463	C₄	1	1	yes	characteristic, complemented
27	C₅×#463	C₄	1	1	yes	characteristic, complemented
28	C₅×#462	C₄	1	1	yes	characteristic, complemented
29	C₅×#461	C₄	1	1	yes	characteristic, complemented
30	C₅×#460	C₄	1	1	yes	characteristic, complemented
31	C₅×#459	C₄	1	1	yes	characteristic, complemented
32	C₅×#444	—	2	4	no	—
33	C₅×#443	—	2	4	no	—
34	C₅×#435	—	2	1	no	—
35	C₅×#435	—	2	1	no	—
36	C₅×#435	—	2	1	no	—
37	C₅×#435	—	2	1	no	—
38	C₂×C₅×#108	C₂²	1	1	yes	characteristic
39	C₂×C₅×#108	C₂²	1	1	yes	characteristic
40	C₅×#423	C₂²	1	1	yes	characteristic
41	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
42	C₂×C₅×#104	C₂²	1	1	yes	characteristic
43	C₂×C₅×#104	C₂²	1	1	yes	characteristic
44	C₂×C₅×#104	C₂²	1	1	yes	characteristic
45	C₂×C₅×#104	C₂²	1	1	yes	characteristic
46	C₂×C₅×#104	C₂²	1	1	yes	characteristic
47	C₂×C₅×#104	C₂²	1	1	yes	characteristic
48	C₅×#416	C₂²	1	1	yes	characteristic
49	C₅×#416	C₂²	1	1	yes	characteristic
50	C₅×#408	C₂²	1	1	yes	characteristic
51	C₅×#408	C₂²	1	1	yes	characteristic
52	C₅×#405	—	2	1	no	—
53	C₅×#405	—	2	1	no	—
54	C₅×#405	C₂²	1	1	yes	characteristic
55	C₅×#405	C₂²	1	1	yes	characteristic
56	C₄×C₅×M₁₆	—	2	1	no	—
57	C₄×C₅×M₁₆	C₂²	1	1	yes	characteristic
58	C₂×C₅×#97	—	2	1	no	—
59	C₂×C₅×#97	C₂²	1	1	yes	characteristic
60	C₂×C₅×#97	C₂²	1	1	yes	characteristic
61	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
62	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
63	C₅×#341	C₂²	1	1	yes	characteristic
64	C₅×#341	C₂²	1	1	yes	characteristic
65	C₅×#339	C₂²	1	1	yes	characteristic
66	C₅×#339	C₂²	1	1	yes	characteristic
67	C₅×#336	C₂²	1	1	yes	characteristic
68	C₅×#336	C₂²	1	1	yes	characteristic
69	#21519	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
70	C₂×C₅×#41	C₂³	1	1	yes	characteristic
71	C₂×C₅×#41	C₂³	1	1	yes	characteristic
72	C₂×C₅×#41	C₂³	1	1	yes	characteristic
73	C₅×#135	—	2	2	no	—
74	C₅×#135	—	2	2	no	—
75	C₅×#135	—	2	2	no	—
76	C₅×#135	—	2	2	no	—
77	C₂×C₅×Q₁₆	C₂×C₄	1	1	yes	characteristic
78	C₂×C₅×Q₁₆	C₂×C₄	1	1	yes	characteristic
79	C₂×C₅×SD₁₆	C₂×C₄	1	1	yes	characteristic
80	C₂×C₅×SD₁₆	C₂×C₄	1	1	yes	characteristic
81	C₂×C₅×SD₁₆	C₂×C₄	1	1	yes	characteristic
82	C₂×C₅×SD₁₆	C₂×C₄	1	1	yes	characteristic
83	C₂×C₅×D₈	C₂×C₄	1	1	yes	characteristic
84	C₂×C₅×D₈	C₂×C₄	1	1	yes	characteristic
85	C₅×#131	—	2	2	no	—
86	C₅×#131	—	2	2	no	—
87	C₅×#131	—	2	2	no	—
88	C₅×#131	—	2	2	no	—
89	C₅×#131	—	2	2	no	—
90	C₅×#131	—	2	2	no	—
91	C₅×#131	—	2	2	no	—
92	C₅×#131	D₄	1	4	yes	complemented
93	C₂×C₅×M₁₆	—	2	1	no	—
94	C₂×C₅×M₁₆	—	2	1	no	—
95	C₂×C₅×M₁₆	—	2	1	no	—
96	C₂×C₅×M₁₆	—	2	1	no	—
97	C₂×C₅×M₁₆	C₂³	1	1	yes	characteristic
98	C₂×C₅×M₁₆	C₂³	1	1	yes	characteristic
99	C₂×C₅×M₁₆	C₂³	1	1	yes	characteristic
100	C₂×C₅×M₁₆	C₂³	1	1	yes	characteristic
101	C₂²×C₅×C₈	—	2	1	no	—
102	C₂²×C₅×C₈	—	2	1	no	—
103	C₂²×C₅×C₈	—	2	1	no	—
104	C₂²×C₅×C₈	—	2	1	no	—
105	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
106	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
107	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
108	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
109	C₅×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
110	C₅×#127	C₂×C₄	1	1	yes	characteristic
111	C₅×#124	C₂×C₄	1	1	yes	characteristic
112	C₅×#124	C₂×C₄	1	1	yes	characteristic
113	C₅×#121	—	2	1	no	—
114	C₅×#121	—	2	1	no	—
115	C₄×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
116	C₄×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
117	C₄×C₅×D₄	—	2	1	no	—
118	C₄×C₅×D₄	—	2	1	no	—
119	C₄×C₅×D₄	—	2	1	no	—
120	C₄×C₅×D₄	—	2	1	no	—
121	C₄×C₅×D₄	C₂×C₄	1	1	yes	characteristic
122	C₄×C₅×D₄	C₂×C₄	1	1	yes	characteristic
123	C₅×#117	—	2	1	no	—
124	C₅×#117	C₂³	1	1	yes	characteristic
125	C₂×C₅×C₄⋊C₄	—	2	1	no	—
126	C₂×C₄²×C₅	—	2	1	no	—
127	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
128	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
129	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
130	C₅×#108	—	2	2	no	—
131	C₅×#108	—	2	2	no	—
132	C₅×C₄⋊C₈	—	2	1	no	—
133	C₅×C₄⋊C₈	—	2	1	no	—
134	C₅×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
135	C₅×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
136	C₅×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
137	C₅×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
138	C₅×#104	—	2	2	no	—
139	C₅×#104	—	2	2	no	—
140	C₅×#104	—	2	2	no	—
141	C₅×#104	—	2	2	no	—
142	C₅×#104	—	2	2	no	—
143	C₅×#104	—	2	2	no	—
144	C₅×#103	C₂×C₄	1	1	yes	characteristic
145	C₅×#103	C₂×C₄	1	1	yes	characteristic
146	C₅×#103	C₂×C₄	1	1	yes	characteristic
147	C₅×#103	C₂×C₄	1	1	yes	characteristic
148	C₅×#102	C₂×C₄	1	1	yes	characteristic
149	C₅×#102	C₂×C₄	1	1	yes	characteristic
150	C₅×#102	C₂×C₄	1	1	yes	characteristic
151	C₅×#102	C₂×C₄	1	1	yes	characteristic
152	C₅×C₂²⋊C₈	—	2	1	no	—
153	C₅×C₂²⋊C₈	—	2	1	no	—
154	C₅×C₂²⋊C₈	—	2	1	no	—
155	C₅×C₂²⋊C₈	—	2	1	no	—
156	C₅×#97	—	2	1	no	—
157	C₅×#97	—	2	1	no	—
158	C₅×#97	—	2	2	no	—
159	C₅×#97	—	2	1	no	—
160	C₅×#97	D₄	1	1	yes	characteristic
161	C₅×#97	D₄	1	1	yes	characteristic
162	C₅×#97	D₄	1	1	yes	characteristic
163	C₅×#97	D₄	1	1	yes	characteristic
164	C₄×C₅×C₈	—	2	2	no	—
165	C₄×C₅×C₈	—	2	1	no	—
166	C₄×C₅×C₈	—	2	1	no	—
167	C₄×C₅×C₈	—	2	1	no	—
168	C₅×#95	—	2	1	no	—
169	#3035	C₂×C₅	1	1	yes	characteristic
170	C₂×#444	C₂×C₅	1	1	yes	characteristic, complemented
171	C₂×#443	C₂×C₅	1	1	yes	characteristic, complemented
172	#2932	C₂×C₅	1	1	yes	characteristic, complemented
173	#2875	C₂×C₅	1	1	yes	characteristic, complemented
174	#1980	C₂×C₅	1	1	yes	characteristic, complemented
175	#1950	C₂×C₅	1	1	yes	characteristic, complemented
176	#1929	C₂×C₅	1	1	yes	characteristic, complemented
177	#1929	C₂×C₅	1	1	yes	characteristic, complemented
178	#1876	C₂×C₅	1	1	yes	characteristic, complemented
179	#1876	C₂×C₅	1	1	yes	characteristic, complemented
180	#1806	C₂×C₅	1	1	yes	characteristic, complemented
181	#1771	C₂×C₅	1	1	yes	characteristic, complemented
182	#1765	C₂×C₅	1	1	yes	characteristic, complemented
183	#1764	C₂×C₅	1	1	yes	characteristic, complemented
184	C₅×#41	—	2	1	no	—
185	C₅×#41	—	2	1	no	—
186	C₅×#41	—	2	1	no	—
187	C₅×#41	—	2	1	no	—
188	C₅×#41	—	2	1	no	—
189	C₅×#41	—	2	1	no	—
190	C₅×#41	—	2	1	no	—
191	C₅×#41	—	2	1	no	—
192	C₅×#41	—	2	1	no	—
193	C₅×#41	—	2	1	no	—
194	C₅×#41	C₂×D₄	1	2	yes	—
195	C₅×#41	#41	1	2	yes	—
196	C₂×C₅×Q₈	C₂²×C₄	1	1	yes	characteristic
197	C₂×C₅×Q₈	C₂²×C₄	1	1	yes	characteristic
198	C₂×C₅×Q₈	C₂²×C₄	1	1	yes	characteristic
199	C₂×C₅×D₄	—	2	1	no	—
200	C₂×C₅×D₄	—	2	1	no	—
201	C₂×C₅×D₄	—	2	1	no	—
202	C₂×C₅×D₄	—	2	1	no	—
203	C₂×C₅×D₄	—	2	1	no	—
204	C₂×C₅×D₄	C₂²×C₄	1	1	yes	characteristic
205	C₂×C₅×D₄	C₂²×C₄	1	1	yes	characteristic
206	C₂×C₅×D₄	C₂²×C₄	1	1	yes	characteristic
207	C₂²×C₄×C₅	—	2	1	no	—
208	C₂²×C₄×C₅	—	2	1	no	—
209	C₂²×C₄×C₅	—	2	1	no	—
210	C₂²×C₄×C₅	—	2	1	no	—
211	C₂²×C₄×C₅	—	2	1	no	—
212	C₂²×C₄×C₅	—	2	1	no	—
213	C₂²×C₄×C₅	—	2	1	no	—
214	C₂²×C₄×C₅	#41	1	1	yes	characteristic
215	C₂²×C₄×C₅	#41	1	1	yes	characteristic
216	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
217	C₅×Q₁₆	—	2	2	no	—
218	C₅×Q₁₆	—	2	2	no	—
219	C₅×SD₁₆	—	2	2	no	—
220	C₅×SD₁₆	—	2	2	no	—
221	C₅×SD₁₆	—	2	2	no	—
222	C₅×SD₁₆	—	2	2	no	—
223	C₅×D₈	—	2	2	no	—
224	C₅×D₈	—	2	2	no	—
225	C₅×M₁₆	—	2	4	no	—
226	C₅×M₁₆	—	2	1	no	—
227	C₅×M₁₆	—	2	1	no	—
228	C₅×M₁₆	—	2	4	no	—
229	C₅×M₁₆	—	2	1	no	—
230	C₅×M₁₆	—	2	1	no	—
231	C₅×M₁₆	—	2	1	no	—
232	C₅×M₁₆	—	2	1	no	—
233	C₅×M₁₆	—	4	2	no	—
234	C₅×M₁₆	—	4	2	no	—
235	C₅×M₁₆	C₂×D₄	1	2	yes	—
236	C₅×M₁₆	#41	1	2	yes	—
237	C₂×C₅×C₈	—	2	4	no	—
238	C₂×C₅×C₈	—	2	1	no	—
239	C₂×C₅×C₈	—	2	1	no	—
240	C₂×C₅×C₈	—	2	1	no	—
241	C₂×C₅×C₈	—	2	1	no	—
242	C₂×C₅×C₈	—	2	1	no	—
243	C₂×C₅×C₈	—	2	1	no	—
244	C₂×C₅×C₈	—	2	1	no	—
245	C₂×C₅×C₈	—	2	1	no	—
246	C₂×C₅×C₈	—	2	4	no	—
247	C₂×C₅×C₈	—	2	1	no	—
248	C₂×C₅×C₈	—	2	1	no	—
249	C₂×C₅×C₈	—	4	2	no	—
250	C₂×C₅×C₈	—	4	2	no	—
251	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
252	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
253	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
254	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
255	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
256	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
257	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
258	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
259	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
260	C₂×C₅×C₈	#41	1	2	yes	—
261	C₅×C₄⋊C₄	—	2	1	no	—
262	C₅×C₄⋊C₄	—	2	1	no	—
263	C₅×C₄⋊C₄	—	2	1	no	—
264	C₅×C₄⋊C₄	—	2	1	no	—
265	C₅×C₄⋊C₄	—	4	2	no	—
266	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
267	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
268	C₅×C₂²⋊C₄	—	2	1	no	—
269	C₅×C₂²⋊C₄	—	2	1	no	—
270	C₅×C₂²⋊C₄	—	2	1	no	—
271	C₅×C₂²⋊C₄	—	2	1	no	—
272	C₅×C₂²⋊C₄	—	2	1	no	—
273	C₅×C₂²⋊C₄	—	2	1	no	—
274	C₅×C₂²⋊C₄	—	2	1	no	—
275	C₄²×C₅	—	2	1	no	—
276	C₄²×C₅	—	2	1	no	—
277	C₄²×C₅	—	2	1	no	—
278	C₄²×C₅	—	2	1	no	—
279	C₄²×C₅	—	2	1	no	—
280	C₄²×C₅	—	2	1	no	—
281	C₄²×C₅	—	2	1	no	—
282	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
283	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
284	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
285	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
286	C₂×#135	C₂²×C₅	1	1	yes	characteristic
287	C₂×#135	C₂²×C₅	1	1	yes	characteristic
288	C₂×#131	C₂²×C₅	1	1	yes	characteristic
289	C₂×#131	C₂²×C₅	1	1	yes	characteristic
290	C₂×#131	C₂²×C₅	1	1	yes	characteristic
291	C₂×#131	C₂²×C₅	1	1	yes	characteristic
292	#532	C₂²×C₅	1	1	yes	characteristic
293	C₄×#41	C₂²×C₅	1	1	yes	characteristic
294	#464	C₄×C₅	1	1	yes	characteristic, complemented
295	#464	C₄×C₅	1	1	yes	characteristic, complemented
296	#463	C₄×C₅	1	1	yes	characteristic, complemented
297	#463	C₄×C₅	1	1	yes	characteristic, complemented
298	#462	C₄×C₅	1	1	yes	characteristic, complemented
299	#461	C₄×C₅	1	1	yes	characteristic, complemented
300	#460	C₄×C₅	1	1	yes	characteristic, complemented
301	#459	C₄×C₅	1	1	yes	characteristic, complemented
302	#444	—	2	4	no	—
303	#443	—	2	4	no	—
304	#435	—	2	1	no	—
305	#435	—	2	1	no	—
306	#435	—	2	1	no	—
307	#435	—	2	1	no	—
308	C₂×#108	C₂²×C₅	1	1	yes	characteristic
309	C₂×#108	C₂²×C₅	1	1	yes	characteristic
310	#423	C₂²×C₅	1	1	yes	characteristic
311	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
312	C₂×#104	C₂²×C₅	1	1	yes	characteristic
313	C₂×#104	C₂²×C₅	1	1	yes	characteristic
314	C₂×#104	C₂²×C₅	1	1	yes	characteristic
315	C₂×#104	C₂²×C₅	1	1	yes	characteristic
316	C₂×#104	C₂²×C₅	1	1	yes	characteristic
317	C₂×#104	C₂²×C₅	1	1	yes	characteristic
318	#416	C₂²×C₅	1	1	yes	characteristic
319	#416	C₂²×C₅	1	1	yes	characteristic
320	#408	C₂²×C₅	1	1	yes	characteristic
321	#408	C₂²×C₅	1	1	yes	characteristic
322	#405	—	2	1	no	—
323	#405	—	2	1	no	—
324	#405	C₂²×C₅	1	1	yes	characteristic
325	#405	C₂²×C₅	1	1	yes	characteristic
326	C₄×M₁₆	—	2	1	no	—
327	C₄×M₁₆	C₂²×C₅	1	1	yes	characteristic
328	C₂×#97	—	2	1	no	—
329	C₂×#97	C₂²×C₅	1	1	yes	characteristic
330	C₂×#97	C₂²×C₅	1	1	yes	characteristic
331	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
332	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
333	#341	C₂²×C₅	1	1	yes	characteristic
334	#341	C₂²×C₅	1	1	yes	characteristic
335	#339	C₂²×C₅	1	1	yes	characteristic
336	#339	C₂²×C₅	1	1	yes	characteristic
337	#336	C₂²×C₅	1	1	yes	characteristic
338	#336	C₂²×C₅	1	1	yes	characteristic
339	C₂³×C₅	—	2	1	no	—
340	C₂³×C₅	—	2	1	no	—
341	C₂³×C₅	—	2	1	no	—
342	C₂³×C₅	C₂×#41	1	1	yes	characteristic
343	C₅×Q₈	—	2	1	no	—
344	C₅×Q₈	—	2	1	no	—
345	C₅×Q₈	—	2	1	no	—
346	C₅×Q₈	—	2	1	no	—
347	C₅×Q₈	—	2	1	no	—
348	C₅×Q₈	C₄×D₄	1	2	yes	—
349	C₅×D₄	—	2	2	no	—
350	C₅×D₄	—	2	2	no	—
351	C₅×D₄	—	2	1	no	—
352	C₅×D₄	—	2	1	no	—
353	C₅×D₄	—	2	1	no	—
354	C₅×D₄	—	2	1	no	—
355	C₅×D₄	—	2	1	no	—
356	C₅×D₄	—	4	1	no	—
357	C₅×D₄	—	4	1	no	—
358	C₅×D₄	—	4	1	no	—
359	C₅×D₄	—	4	1	no	—
360	C₅×D₄	—	8	1	no	—
361	C₅×D₄	—	8	1	no	—
362	C₅×D₄	C₄×D₄	1	2	yes	—
363	C₂×C₄×C₅	—	2	1	no	—
364	C₂×C₄×C₅	—	2	2	no	—
365	C₂×C₄×C₅	—	2	2	no	—
366	C₂×C₄×C₅	—	2	2	no	—
367	C₂×C₄×C₅	—	2	1	no	—
368	C₂×C₄×C₅	—	2	1	no	—
369	C₂×C₄×C₅	—	2	1	no	—
370	C₂×C₄×C₅	—	2	1	no	—
371	C₂×C₄×C₅	—	4	1	no	—
372	C₂×C₄×C₅	—	4	1	no	—
373	C₂×C₄×C₅	—	4	1	no	—
374	C₂×C₄×C₅	—	4	1	no	—
375	C₂×C₄×C₅	—	4	1	no	—
376	C₂×C₄×C₅	—	4	1	no	—
377	C₂×C₄×C₅	—	4	1	no	—
378	C₂×C₄×C₅	—	4	1	no	—
379	C₂×C₄×C₅	—	4	1	no	—
380	C₂×C₄×C₅	—	4	1	no	—
381	C₂×C₄×C₅	—	4	1	no	—
382	C₂×C₄×C₅	—	8	1	no	—
383	C₂×C₄×C₅	—	8	1	no	—
384	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
385	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
386	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
387	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
388	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
389	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
390	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
391	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
392	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
393	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
394	C₅×C₈	—	2	1	no	—
395	C₅×C₈	—	2	1	no	—
396	C₅×C₈	—	2	1	no	—
397	C₅×C₈	—	2	1	no	—
398	C₅×C₈	—	2	2	no	—
399	C₅×C₈	—	2	1	no	—
400	C₅×C₈	—	2	2	no	—
401	C₅×C₈	—	2	1	no	—
402	C₅×C₈	—	4	1	no	—
403	C₅×C₈	—	4	1	no	—
404	C₅×C₈	#121	1	2	yes	—
405	C₅×C₈	#121	1	2	yes	—
406	C₂×#41	C₂³×C₅	1	1	yes	characteristic
407	C₂×#41	C₂³×C₅	1	1	yes	characteristic
408	C₂×#41	C₂³×C₅	1	1	yes	characteristic
409	#135	—	2	2	no	—
410	#135	—	2	2	no	—
411	#135	—	2	2	no	—
412	#135	—	2	2	no	—
413	C₂×Q₁₆	C₂×C₄×C₅	1	1	yes	characteristic
414	C₂×Q₁₆	C₂×C₄×C₅	1	1	yes	characteristic
415	C₂×SD₁₆	C₂×C₄×C₅	1	1	yes	characteristic
416	C₂×SD₁₆	C₂×C₄×C₅	1	1	yes	characteristic
417	C₂×SD₁₆	C₂×C₄×C₅	1	1	yes	characteristic
418	C₂×SD₁₆	C₂×C₄×C₅	1	1	yes	characteristic
419	C₂×D₈	C₂×C₄×C₅	1	1	yes	characteristic
420	C₂×D₈	C₂×C₄×C₅	1	1	yes	characteristic
421	#131	—	2	2	no	—
422	#131	—	2	2	no	—
423	#131	—	2	2	no	—
424	#131	—	2	2	no	—
425	#131	—	2	2	no	—
426	#131	—	2	2	no	—
427	#131	—	2	2	no	—
428	#131	C₅×D₄	1	4	yes	complemented
429	C₂×M₁₆	—	2	1	no	—
430	C₂×M₁₆	—	2	1	no	—
431	C₂×M₁₆	—	2	1	no	—
432	C₂×M₁₆	—	2	1	no	—
433	C₂×M₁₆	C₂³×C₅	1	1	yes	characteristic
434	C₂×M₁₆	C₂³×C₅	1	1	yes	characteristic
435	C₂×M₁₆	C₂³×C₅	1	1	yes	characteristic
436	C₂×M₁₆	C₂³×C₅	1	1	yes	characteristic
437	C₂²×C₈	—	2	1	no	—
438	C₂²×C₈	—	2	1	no	—
439	C₂²×C₈	—	2	1	no	—
440	C₂²×C₈	—	2	1	no	—
441	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
442	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
443	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
444	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
445	C₄⋊Q₈	C₂×C₄×C₅	1	1	yes	characteristic
446	#127	C₂×C₄×C₅	1	1	yes	characteristic
447	#124	C₂×C₄×C₅	1	1	yes	characteristic
448	#124	C₂×C₄×C₅	1	1	yes	characteristic
449	#121	—	2	1	no	—
450	#121	—	2	1	no	—
451	C₄×Q₈	C₂×C₄×C₅	1	1	yes	characteristic
452	C₄×Q₈	C₂×C₄×C₅	1	1	yes	characteristic
453	C₄×D₄	—	2	1	no	—
454	C₄×D₄	—	2	1	no	—
455	C₄×D₄	—	2	1	no	—
456	C₄×D₄	—	2	1	no	—
457	C₄×D₄	C₂×C₄×C₅	1	1	yes	characteristic
458	C₄×D₄	C₂×C₄×C₅	1	1	yes	characteristic
459	#117	—	2	1	no	—
460	#117	C₂³×C₅	1	1	yes	characteristic
461	C₂×C₄⋊C₄	—	2	1	no	—
462	C₂×C₄²	—	2	1	no	—
463	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
464	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
465	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
466	#108	—	2	2	no	—
467	#108	—	2	2	no	—
468	C₄⋊C₈	—	2	1	no	—
469	C₄⋊C₈	—	2	1	no	—
470	C₄⋊C₈	C₂×C₄×C₅	1	1	yes	characteristic
471	C₄⋊C₈	C₂×C₄×C₅	1	1	yes	characteristic
472	C₄⋊C₈	C₂×C₄×C₅	1	1	yes	characteristic
473	C₄⋊C₈	C₂×C₄×C₅	1	1	yes	characteristic
474	#104	—	2	2	no	—
475	#104	—	2	2	no	—
476	#104	—	2	2	no	—
477	#104	—	2	2	no	—
478	#104	—	2	2	no	—
479	#104	—	2	2	no	—
480	#103	C₂×C₄×C₅	1	1	yes	characteristic
481	#103	C₂×C₄×C₅	1	1	yes	characteristic
482	#103	C₂×C₄×C₅	1	1	yes	characteristic
483	#103	C₂×C₄×C₅	1	1	yes	characteristic
484	#102	C₂×C₄×C₅	1	1	yes	characteristic
485	#102	C₂×C₄×C₅	1	1	yes	characteristic
486	#102	C₂×C₄×C₅	1	1	yes	characteristic
487	#102	C₂×C₄×C₅	1	1	yes	characteristic
488	C₂²⋊C₈	—	2	1	no	—
489	C₂²⋊C₈	—	2	1	no	—
490	C₂²⋊C₈	—	2	1	no	—
491	C₂²⋊C₈	—	2	1	no	—
492	#97	—	2	1	no	—
493	#97	—	2	1	no	—
494	#97	—	2	2	no	—
495	#97	—	2	1	no	—
496	#97	C₅×D₄	1	1	yes	characteristic
497	#97	C₅×D₄	1	1	yes	characteristic
498	#97	C₅×D₄	1	1	yes	characteristic
499	#97	C₅×D₄	1	1	yes	characteristic
500	C₄×C₈	—	2	2	no	—
501	C₄×C₈	—	2	1	no	—
502	C₄×C₈	—	2	1	no	—
503	C₄×C₈	—	2	1	no	—
504	#95	—	2	1	no	—
505	C₂²×C₅	—	2	1	no	—
506	C₂²×C₅	—	2	1	no	—
507	C₂²×C₅	—	2	2	no	—
508	C₂²×C₅	—	4	1	no	—
509	C₂²×C₅	—	4	1	no	—
510	C₂²×C₅	—	4	1	no	—
511	C₂²×C₅	—	4	1	no	—
512	C₂²×C₅	—	4	1	no	—
513	C₂²×C₅	—	4	1	no	—
514	C₂²×C₅	—	4	1	no	—
515	C₂²×C₅	—	4	1	no	—
516	C₂²×C₅	C₂×C₄×D₄	1	1	yes	characteristic
517	C₂²×C₅	#529	1	1	yes	characteristic
518	C₂²×C₅	#532	1	1	yes	characteristic
519	C₄×C₅	—	2	1	no	—
520	C₄×C₅	—	2	1	no	—
521	C₄×C₅	—	2	1	no	—
522	C₄×C₅	—	2	1	no	—
523	C₄×C₅	—	2	2	no	—
524	C₄×C₅	—	4	2	no	—
525	C₄×C₅	—	4	1	no	—
526	C₄×C₅	—	4	1	no	—
527	C₄×C₅	—	4	1	no	—
528	C₄×C₅	—	4	1	no	—
529	C₄×C₅	—	8	1	no	—
530	C₄×C₅	C₂×C₄×D₄	1	1	yes	characteristic
531	C₄×C₅	C₄×#41	1	1	yes	characteristic
532	C₄×C₅	C₂×#121	1	1	yes	characteristic
533	C₄×C₅	#525	1	1	yes	characteristic
534	#41	—	2	1	no	—
535	#41	—	2	1	no	—
536	#41	—	2	1	no	—
537	#41	—	2	1	no	—
538	#41	—	2	1	no	—
539	#41	—	2	1	no	—
540	#41	—	2	1	no	—
541	#41	—	2	1	no	—
542	#41	—	2	1	no	—
543	#41	—	2	1	no	—
544	#41	C₂×C₅×D₄	1	2	yes	—
545	#41	C₅×#41	1	2	yes	—
546	C₂×Q₈	C₂²×C₄×C₅	1	1	yes	characteristic
547	C₂×Q₈	C₂²×C₄×C₅	1	1	yes	characteristic
548	C₂×Q₈	C₂²×C₄×C₅	1	1	yes	characteristic
549	C₂×D₄	—	2	1	no	—
550	C₂×D₄	—	2	1	no	—
551	C₂×D₄	—	2	1	no	—
552	C₂×D₄	—	2	1	no	—
553	C₂×D₄	—	2	1	no	—
554	C₂×D₄	C₂²×C₄×C₅	1	1	yes	characteristic
555	C₂×D₄	C₂²×C₄×C₅	1	1	yes	characteristic
556	C₂×D₄	C₂²×C₄×C₅	1	1	yes	characteristic
557	C₂²×C₄	—	2	1	no	—
558	C₂²×C₄	—	2	1	no	—
559	C₂²×C₄	—	2	1	no	—
560	C₂²×C₄	—	2	1	no	—
561	C₂²×C₄	—	2	1	no	—
562	C₂²×C₄	—	2	1	no	—
563	C₂²×C₄	—	2	1	no	—
564	C₂²×C₄	C₅×#41	1	1	yes	characteristic
565	C₂²×C₄	C₅×#41	1	1	yes	characteristic
566	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
567	Q₁₆	—	2	2	no	—
568	Q₁₆	—	2	2	no	—
569	SD₁₆	—	2	2	no	—
570	SD₁₆	—	2	2	no	—
571	SD₁₆	—	2	2	no	—
572	SD₁₆	—	2	2	no	—
573	D₈	—	2	2	no	—
574	D₈	—	2	2	no	—
575	M₁₆	—	2	4	no	—
576	M₁₆	—	2	1	no	—
577	M₁₆	—	2	1	no	—
578	M₁₆	—	2	4	no	—
579	M₁₆	—	2	1	no	—
580	M₁₆	—	2	1	no	—
581	M₁₆	—	2	1	no	—
582	M₁₆	—	2	1	no	—
583	M₁₆	—	4	2	no	—
584	M₁₆	—	4	2	no	—
585	M₁₆	C₂×C₅×D₄	1	2	yes	—
586	M₁₆	C₅×#41	1	2	yes	—
587	C₂×C₈	—	2	4	no	—
588	C₂×C₈	—	2	1	no	—
589	C₂×C₈	—	2	1	no	—
590	C₂×C₈	—	2	1	no	—
591	C₂×C₈	—	2	1	no	—
592	C₂×C₈	—	2	1	no	—
593	C₂×C₈	—	2	1	no	—
594	C₂×C₈	—	2	1	no	—
595	C₂×C₈	—	2	1	no	—
596	C₂×C₈	—	2	4	no	—
597	C₂×C₈	—	2	1	no	—
598	C₂×C₈	—	2	1	no	—
599	C₂×C₈	—	4	2	no	—
600	C₂×C₈	—	4	2	no	—
601	C₂×C₈	C₂²×C₄×C₅	1	1	yes	characteristic
602	C₂×C₈	C₂²×C₄×C₅	1	1	yes	characteristic
603	C₂×C₈	C₂²×C₄×C₅	1	1	yes	characteristic
604	C₂×C₈	C₂²×C₄×C₅	1	1	yes	characteristic
605	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
606	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
607	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
608	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
609	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
610	C₂×C₈	C₅×#41	1	2	yes	—
611	C₄⋊C₄	—	2	1	no	—
612	C₄⋊C₄	—	2	1	no	—
613	C₄⋊C₄	—	2	1	no	—
614	C₄⋊C₄	—	2	1	no	—
615	C₄⋊C₄	—	4	2	no	—
616	C₄⋊C₄	C₂²×C₄×C₅	1	1	yes	characteristic
617	C₄⋊C₄	C₂²×C₄×C₅	1	1	yes	characteristic
618	C₂²⋊C₄	—	2	1	no	—
619	C₂²⋊C₄	—	2	1	no	—
620	C₂²⋊C₄	—	2	1	no	—
621	C₂²⋊C₄	—	2	1	no	—
622	C₂²⋊C₄	—	2	1	no	—
623	C₂²⋊C₄	—	2	1	no	—
624	C₂²⋊C₄	—	2	1	no	—
625	C₄²	—	2	1	no	—
626	C₄²	—	2	1	no	—
627	C₄²	—	2	1	no	—
628	C₄²	—	2	1	no	—
629	C₄²	—	2	1	no	—
630	C₄²	—	2	1	no	—
631	C₄²	—	2	1	no	—
632	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
633	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
634	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
635	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
636	C₂×C₅	—	2	1	no	—
637	C₂×C₅	—	2	1	no	—
638	C₂×C₅	—	4	2	no	—
639	C₂×C₅	—	8	1	no	—
640	C₂×C₅	—	8	1	no	—
641	C₂×C₅	C₄×#121	1	1	yes	characteristic
642	C₂×C₅	#2956	1	1	yes	characteristic
643	C₂×C₅	#2957	1	1	yes	characteristic
644	C₂³	—	2	1	no	—
645	C₂³	—	2	1	no	—
646	C₂³	—	2	1	no	—
647	C₂³	C₂×C₅×#41	1	1	yes	characteristic
648	Q₈	—	2	1	no	—
649	Q₈	—	2	1	no	—
650	Q₈	—	2	1	no	—
651	Q₈	—	2	1	no	—
652	Q₈	—	2	1	no	—
653	Q₈	C₄×C₅×D₄	1	2	yes	—
654	D₄	—	2	2	no	—
655	D₄	—	2	2	no	—
656	D₄	—	2	1	no	—
657	D₄	—	2	1	no	—
658	D₄	—	2	1	no	—
659	D₄	—	2	1	no	—
660	D₄	—	2	1	no	—
661	D₄	—	4	1	no	—
662	D₄	—	4	1	no	—
663	D₄	—	4	1	no	—
664	D₄	—	4	1	no	—
665	D₄	—	8	1	no	—
666	D₄	—	8	1	no	—
667	D₄	C₄×C₅×D₄	1	2	yes	—
668	C₂×C₄	—	2	1	no	—
669	C₂×C₄	—	2	2	no	—
670	C₂×C₄	—	2	2	no	—
671	C₂×C₄	—	2	2	no	—
672	C₂×C₄	—	2	1	no	—
673	C₂×C₄	—	2	1	no	—
674	C₂×C₄	—	2	1	no	—
675	C₂×C₄	—	2	1	no	—
676	C₂×C₄	—	4	1	no	—
677	C₂×C₄	—	4	1	no	—
678	C₂×C₄	—	4	1	no	—
679	C₂×C₄	—	4	1	no	—
680	C₂×C₄	—	4	1	no	—
681	C₂×C₄	—	4	1	no	—
682	C₂×C₄	—	4	1	no	—
683	C₂×C₄	—	4	1	no	—
684	C₂×C₄	—	4	1	no	—
685	C₂×C₄	—	4	1	no	—
686	C₂×C₄	—	4	1	no	—
687	C₂×C₄	—	8	1	no	—
688	C₂×C₄	—	8	1	no	—
689	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
690	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
691	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
692	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
693	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
694	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
695	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
696	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
697	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
698	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
699	C₈	—	2	1	no	—
700	C₈	—	2	1	no	—
701	C₈	—	2	1	no	—
702	C₈	—	2	1	no	—
703	C₈	—	2	2	no	—
704	C₈	—	2	1	no	—
705	C₈	—	2	2	no	—
706	C₈	—	2	1	no	—
707	C₈	—	4	1	no	—
708	C₈	—	4	1	no	—
709	C₈	C₅×#121	1	2	yes	—
710	C₈	C₅×#121	1	2	yes	—
711	C₅	#21519	1	1	yes	characteristic, direct product factor, Sylow
712	C₂²	—	2	1	no	—
713	C₂²	—	2	1	no	—
714	C₂²	—	2	2	no	—
715	C₂²	—	4	1	no	—
716	C₂²	—	4	1	no	—
717	C₂²	—	4	1	no	—
718	C₂²	—	4	1	no	—
719	C₂²	—	4	1	no	—
720	C₂²	—	4	1	no	—
721	C₂²	—	4	1	no	—
722	C₂²	—	4	1	no	—
723	C₂²	C₂×C₄×C₅×D₄	1	1	yes	characteristic
724	C₂²	C₅×#529	1	1	yes	characteristic
725	C₂²	C₅×#532	1	1	yes	characteristic
726	C₄	—	2	2	no	—
727	C₄	—	2	1	no	—
728	C₄	—	2	1	no	—
729	C₄	—	2	1	no	—
730	C₄	—	2	1	no	—
731	C₄	—	4	2	no	—
732	C₄	—	4	1	no	—
733	C₄	—	4	1	no	—
734	C₄	—	4	1	no	—
735	C₄	—	4	1	no	—
736	C₄	—	8	1	no	—
737	C₄	C₂×C₄×C₅×D₄	1	1	yes	characteristic
738	C₄	C₄×C₅×#41	1	1	yes	characteristic
739	C₄	C₂×C₅×#121	1	1	yes	characteristic
740	C₄	C₅×#525	1	1	yes	characteristic
741	C₂	—	2	1	no	—
742	C₂	—	2	1	no	—
743	C₂	—	4	2	no	—
744	C₂	—	8	1	no	—
745	C₂	—	8	1	no	—
746	C₂	C₄×C₅×#121	1	1	yes	characteristic
747	C₂	C₅×#2956	1	1	yes	characteristic
748	C₂	C₅×#2957	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	C₂×C₄×D₄
prime radical	C₅×#3035	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₅ ◁ C₂×C₅×#97 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₅×#444	C₂	semidirect
3. C₂×C₅×#443	C₂	semidirect
4. C₅×#2932	C₂	semidirect
5. C₅×#2875	C₂	semidirect
6. C₅×#1980	C₂	semidirect
7. C₅×#1950	C₂	semidirect
8. C₅×#1929	C₂	semidirect
9. C₅×#1929	C₂	semidirect
10. C₅×#1876	C₂	semidirect
11. C₅×#1876	C₂	semidirect
12. C₅×#1806	C₂	semidirect
13. C₅×#1771	C₂	semidirect
14. C₅×#1765	C₂	semidirect
15. C₅×#1764	C₂	semidirect
24. C₅×#464	C₄	semidirect
25. C₅×#464	C₄	semidirect
26. C₅×#463	C₄	semidirect
27. C₅×#463	C₄	semidirect
28. C₅×#462	C₄	semidirect
29. C₅×#461	C₄	semidirect
30. C₅×#460	C₄	semidirect
31. C₅×#459	C₄	semidirect
69. #21519	C₅	direct (N × H)
92. C₅×#131	D₄	semidirect
170. C₂×#444	C₂×C₅	semidirect
171. C₂×#443	C₂×C₅	semidirect
172. #2932	C₂×C₅	semidirect
173. #2875	C₂×C₅	semidirect
174. #1980	C₂×C₅	semidirect
175. #1950	C₂×C₅	semidirect
176. #1929	C₂×C₅	semidirect
177. #1929	C₂×C₅	semidirect
178. #1876	C₂×C₅	semidirect
179. #1876	C₂×C₅	semidirect
180. #1806	C₂×C₅	semidirect
181. #1771	C₂×C₅	semidirect
182. #1765	C₂×C₅	semidirect
183. #1764	C₂×C₅	semidirect
294. #464	C₄×C₅	semidirect
295. #464	C₄×C₅	semidirect
296. #463	C₄×C₅	semidirect
297. #463	C₄×C₅	semidirect
298. #462	C₄×C₅	semidirect
299. #461	C₄×C₅	semidirect
300. #460	C₄×C₅	semidirect
301. #459	C₄×C₅	semidirect
428. #131	C₅×D₄	semidirect
711. C₅	#21519	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅×#3035	2
C₂×C₅×#444	2
C₂×C₅×#443	2
C₅×#2932	2
C₅×#2875	2
C₅×#1980	2
C₅×#1950	2
C₅×#1929	2
C₅×#1876	2
C₅×#1806	2
C₅×#1771	2
C₅×#1765	2
C₅×#1764	2
#21519	5

Subgroups — C5×#21519 #11944239

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#21519 #11944239