Subgroups — C₅×#23115 #11945835

Order 1280.

762 conjugacy classes of subgroups.

The subgroup lattice has 728 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	C₅×#2935	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#2925	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#1975	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#1974	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#1963	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×#1768	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅×#1765	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅×#1764	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅×#1759	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	C₅×#532	C₂²	1	1	yes	characteristic
21	C₄×C₅×#41	C₂²	1	1	yes	characteristic
22	C₅×#464	C₄	1	1	yes	characteristic, complemented
23	C₅×#464	C₄	1	1	yes	characteristic, complemented
24	C₅×#463	C₄	1	1	yes	characteristic, complemented
25	C₅×#463	C₄	1	1	yes	characteristic, complemented
26	C₅×#462	C₄	1	1	yes	characteristic, complemented
27	C₅×#461	C₄	1	1	yes	characteristic, complemented
28	C₅×#460	C₄	1	1	yes	characteristic, complemented
29	C₅×#459	C₄	1	1	yes	characteristic, complemented
30	C₅×#436	—	2	1	no	—
31	C₅×#435	—	2	1	no	—
32	C₅×#435	—	2	1	no	—
33	C₅×C₈×D₄	—	2	1	no	—
34	C₅×#433	—	2	1	no	—
35	C₅×#433	—	2	1	no	—
36	C₅×#432	—	2	1	no	—
37	C₅×#431	—	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×C₄⋊C₈	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	C₂×C₅×#104	C₂²	1	1	yes	characteristic
49	C₅×#416	C₂²	1	1	yes	characteristic
50	C₅×#416	C₂²	1	1	yes	characteristic
51	C₅×#408	C₂²	1	1	yes	characteristic
52	C₅×#408	C₂²	1	1	yes	characteristic
53	C₅×#408	C₂²	1	1	yes	characteristic
54	C₅×#408	C₂²	1	1	yes	characteristic
55	C₅×#405	C₂²	1	1	yes	characteristic
56	C₅×#405	C₂²	1	1	yes	characteristic
57	C₄×C₅×M₁₆	C₂²	1	1	yes	characteristic
58	C₂×C₅×#97	C₂²	1	1	yes	characteristic
59	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
60	C₅×#376	C₂²	1	1	yes	characteristic
61	C₅×#341	C₂²	1	1	yes	characteristic
62	C₅×#341	C₂²	1	1	yes	characteristic
63	C₅×#339	C₂²	1	1	yes	characteristic
64	C₅×#339	C₂²	1	1	yes	characteristic
65	C₅×#336	C₂²	1	1	yes	characteristic
66	C₅×#336	C₂²	1	1	yes	characteristic
67	#23115	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
68	C₂×C₅×#41	C₂³	1	1	yes	characteristic
69	C₂×C₅×#41	C₂³	1	1	yes	characteristic
70	C₂×C₅×#41	C₂³	1	1	yes	characteristic
71	C₅×#135	—	4	1	no	—
72	C₅×#135	—	4	1	no	—
73	C₅×#135	—	4	1	no	—
74	C₅×#135	—	4	1	no	—
75	C₂×C₅×Q₁₆	C₂×C₄	1	1	yes	characteristic
76	C₂×C₅×Q₁₆	C₂×C₄	1	1	yes	characteristic
77	C₂×C₅×SD₁₆	C₂×C₄	1	1	yes	characteristic
78	C₂×C₅×SD₁₆	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×D₈	C₂×C₄	1	1	yes	characteristic
82	C₂×C₅×D₈	C₂×C₄	1	1	yes	characteristic
83	C₅×#131	—	2	2	no	—
84	C₅×#131	—	2	2	no	—
85	C₅×#131	—	4	1	no	—
86	C₅×#131	—	4	1	no	—
87	C₂×C₅×M₁₆	—	2	1	no	—
88	C₂×C₅×M₁₆	—	2	1	no	—
89	C₂×C₅×M₁₆	C₂³	1	1	yes	characteristic
90	C₂×C₅×M₁₆	C₂³	1	1	yes	characteristic
91	C₂×C₅×M₁₆	C₂³	1	1	yes	characteristic
92	C₂×C₅×M₁₆	C₂³	1	1	yes	characteristic
93	C₂²×C₅×C₈	—	2	1	no	—
94	C₂²×C₅×C₈	—	2	1	no	—
95	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
96	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
97	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
98	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
99	C₅×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
100	C₅×#127	C₂×C₄	1	1	yes	characteristic
101	C₅×#124	C₂×C₄	1	1	yes	characteristic
102	C₅×#124	C₂×C₄	1	1	yes	characteristic
103	C₅×#121	—	2	1	no	—
104	C₅×#121	—	2	1	no	—
105	C₄×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
106	C₄×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
107	C₄×C₅×D₄	—	2	1	no	—
108	C₄×C₅×D₄	—	2	1	no	—
109	C₄×C₅×D₄	—	2	1	no	—
110	C₄×C₅×D₄	—	2	1	no	—
111	C₄×C₅×D₄	C₂×C₄	1	1	yes	characteristic
112	C₄×C₅×D₄	C₂×C₄	1	1	yes	characteristic
113	C₅×#117	—	2	1	no	—
114	C₅×#117	C₂³	1	1	yes	characteristic
115	C₂×C₄²×C₅	—	2	1	no	—
116	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
117	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
118	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
119	C₅×#108	—	4	1	no	—
120	C₅×#108	—	4	1	no	—
121	C₅×C₄⋊C₈	—	2	1	no	—
122	C₅×C₄⋊C₈	—	2	1	no	—
123	C₅×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
124	C₅×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
125	C₅×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
126	C₅×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
127	C₅×C₄⋊C₈	D₄	1	1	yes	characteristic
128	C₅×C₄⋊C₈	D₄	1	1	yes	characteristic
129	C₅×C₄⋊C₈	D₄	1	1	yes	characteristic
130	C₅×C₄⋊C₈	D₄	1	1	yes	characteristic
131	C₅×#104	—	2	2	no	—
132	C₅×#104	—	2	2	no	—
133	C₅×#104	—	2	2	no	—
134	C₅×#104	—	2	2	no	—
135	C₅×#104	—	4	1	no	—
136	C₅×#104	—	4	1	no	—
137	C₅×#103	C₂×C₄	1	1	yes	characteristic
138	C₅×#103	C₂×C₄	1	1	yes	characteristic
139	C₅×#103	C₂×C₄	1	1	yes	characteristic
140	C₅×#103	C₂×C₄	1	1	yes	characteristic
141	C₅×#102	C₂×C₄	1	1	yes	characteristic
142	C₅×#102	C₂×C₄	1	1	yes	characteristic
143	C₅×#102	C₂×C₄	1	1	yes	characteristic
144	C₅×#102	C₂×C₄	1	1	yes	characteristic
145	C₅×C₂²⋊C₈	—	2	1	no	—
146	C₅×C₂²⋊C₈	—	2	1	no	—
147	C₅×C₂²⋊C₈	—	2	1	no	—
148	C₅×C₂²⋊C₈	—	2	1	no	—
149	C₅×C₂²⋊C₈	—	2	1	no	—
150	C₅×C₂²⋊C₈	—	2	1	no	—
151	C₅×C₂²⋊C₈	—	2	1	no	—
152	C₅×C₂²⋊C₈	—	2	1	no	—
153	C₅×#97	—	2	1	no	—
154	C₅×#97	—	2	1	no	—
155	C₅×#97	—	2	1	no	—
156	C₅×#97	—	4	1	no	—
157	C₄×C₅×C₈	—	2	1	no	—
158	C₄×C₅×C₈	—	2	1	no	—
159	C₄×C₅×C₈	—	2	1	no	—
160	C₄×C₅×C₈	—	4	1	no	—
161	C₅×#95	—	2	1	no	—
162	C₅×#95	—	2	1	no	—
163	#3035	C₂×C₅	1	1	yes	characteristic
164	#2935	C₂×C₅	1	1	yes	characteristic, complemented
165	#2925	C₂×C₅	1	1	yes	characteristic, complemented
166	#1975	C₂×C₅	1	1	yes	characteristic, complemented
167	#1974	C₂×C₅	1	1	yes	characteristic, complemented
168	#1963	C₂×C₅	1	1	yes	characteristic, complemented
169	#1950	C₂×C₅	1	1	yes	characteristic, complemented
170	#1929	C₂×C₅	1	1	yes	characteristic, complemented
171	#1929	C₂×C₅	1	1	yes	characteristic, complemented
172	#1876	C₂×C₅	1	1	yes	characteristic, complemented
173	#1876	C₂×C₅	1	1	yes	characteristic, complemented
174	#1768	C₂×C₅	1	1	yes	characteristic, complemented
175	#1765	C₂×C₅	1	1	yes	characteristic, complemented
176	#1764	C₂×C₅	1	1	yes	characteristic, complemented
177	#1759	C₂×C₅	1	1	yes	characteristic, complemented
178	C₅×#41	—	2	1	no	—
179	C₅×#41	—	2	1	no	—
180	C₅×#41	—	2	1	no	—
181	C₅×#41	—	2	1	no	—
182	C₅×#41	—	2	1	no	—
183	C₅×#41	—	2	1	no	—
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	C₂×C₅×Q₈	C₂²×C₄	1	1	yes	characteristic
191	C₂×C₅×Q₈	C₂²×C₄	1	1	yes	characteristic
192	C₂×C₅×Q₈	C₂²×C₄	1	1	yes	characteristic
193	C₂×C₅×D₄	—	2	1	no	—
194	C₂×C₅×D₄	—	2	1	no	—
195	C₂×C₅×D₄	—	2	1	no	—
196	C₂×C₅×D₄	—	2	1	no	—
197	C₂×C₅×D₄	—	2	1	no	—
198	C₂×C₅×D₄	C₂²×C₄	1	1	yes	characteristic
199	C₂×C₅×D₄	C₂²×C₄	1	1	yes	characteristic
200	C₂×C₅×D₄	C₂²×C₄	1	1	yes	characteristic
201	C₂²×C₄×C₅	—	2	1	no	—
202	C₂²×C₄×C₅	—	2	1	no	—
203	C₂²×C₄×C₅	—	2	1	no	—
204	C₂²×C₄×C₅	—	2	1	no	—
205	C₂²×C₄×C₅	—	2	1	no	—
206	C₂²×C₄×C₅	—	2	1	no	—
207	C₂²×C₄×C₅	—	2	1	no	—
208	C₂²×C₄×C₅	#41	1	1	yes	characteristic
209	C₂²×C₄×C₅	#41	1	1	yes	characteristic
210	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
211	C₅×Q₁₆	—	4	1	no	—
212	C₅×Q₁₆	—	4	1	no	—
213	C₅×SD₁₆	—	4	1	no	—
214	C₅×SD₁₆	—	4	1	no	—
215	C₅×SD₁₆	—	4	1	no	—
216	C₅×SD₁₆	—	4	1	no	—
217	C₅×D₈	—	4	1	no	—
218	C₅×D₈	—	4	1	no	—
219	C₅×M₁₆	—	2	1	no	—
220	C₅×M₁₆	—	2	1	no	—
221	C₅×M₁₆	—	2	1	no	—
222	C₅×M₁₆	—	2	1	no	—
223	C₅×M₁₆	—	2	1	no	—
224	C₅×M₁₆	—	2	1	no	—
225	C₅×M₁₆	—	2	1	no	—
226	C₅×M₁₆	—	4	2	no	—
227	C₅×M₁₆	—	4	2	no	—
228	C₅×M₁₆	#41	1	2	yes	—
229	C₂×C₅×C₈	—	2	1	no	—
230	C₂×C₅×C₈	—	2	1	no	—
231	C₂×C₅×C₈	—	2	1	no	—
232	C₂×C₅×C₈	—	2	1	no	—
233	C₂×C₅×C₈	—	2	1	no	—
234	C₂×C₅×C₈	—	2	1	no	—
235	C₂×C₅×C₈	—	2	1	no	—
236	C₂×C₅×C₈	—	2	1	no	—
237	C₂×C₅×C₈	—	2	1	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	—	4	2	no	—
242	C₂×C₅×C₈	—	4	2	no	—
243	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
244	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
245	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
246	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
247	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
248	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
249	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
250	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
251	C₅×C₄⋊C₄	—	2	1	no	—
252	C₅×C₄⋊C₄	—	2	1	no	—
253	C₅×C₄⋊C₄	—	2	1	no	—
254	C₅×C₄⋊C₄	—	2	1	no	—
255	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
256	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
257	C₅×C₂²⋊C₄	—	2	1	no	—
258	C₅×C₂²⋊C₄	—	2	1	no	—
259	C₅×C₂²⋊C₄	—	2	1	no	—
260	C₅×C₂²⋊C₄	—	2	1	no	—
261	C₅×C₂²⋊C₄	—	2	1	no	—
262	C₅×C₂²⋊C₄	—	2	1	no	—
263	C₅×C₂²⋊C₄	—	2	1	no	—
264	C₄²×C₅	—	2	1	no	—
265	C₄²×C₅	—	2	1	no	—
266	C₄²×C₅	—	2	1	no	—
267	C₄²×C₅	—	2	1	no	—
268	C₄²×C₅	—	2	1	no	—
269	C₄²×C₅	—	2	1	no	—
270	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
271	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
272	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
273	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
274	C₄²×C₅	#41	1	2	yes	—
275	C₂×#135	C₂²×C₅	1	1	yes	characteristic
276	C₂×#135	C₂²×C₅	1	1	yes	characteristic
277	C₂×#131	C₂²×C₅	1	1	yes	characteristic
278	C₂×#131	C₂²×C₅	1	1	yes	characteristic
279	#532	C₂²×C₅	1	1	yes	characteristic
280	C₄×#41	C₂²×C₅	1	1	yes	characteristic
281	#464	C₄×C₅	1	1	yes	characteristic, complemented
282	#464	C₄×C₅	1	1	yes	characteristic, complemented
283	#463	C₄×C₅	1	1	yes	characteristic, complemented
284	#463	C₄×C₅	1	1	yes	characteristic, complemented
285	#462	C₄×C₅	1	1	yes	characteristic, complemented
286	#461	C₄×C₅	1	1	yes	characteristic, complemented
287	#460	C₄×C₅	1	1	yes	characteristic, complemented
288	#459	C₄×C₅	1	1	yes	characteristic, complemented
289	#436	—	2	1	no	—
290	#435	—	2	1	no	—
291	#435	—	2	1	no	—
292	C₈×D₄	—	2	1	no	—
293	#433	—	2	1	no	—
294	#433	—	2	1	no	—
295	#432	—	2	1	no	—
296	#431	—	2	1	no	—
297	C₂×#108	C₂²×C₅	1	1	yes	characteristic
298	C₂×#108	C₂²×C₅	1	1	yes	characteristic
299	#423	C₂²×C₅	1	1	yes	characteristic
300	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
301	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
302	C₂×#104	C₂²×C₅	1	1	yes	characteristic
303	C₂×#104	C₂²×C₅	1	1	yes	characteristic
304	C₂×#104	C₂²×C₅	1	1	yes	characteristic
305	C₂×#104	C₂²×C₅	1	1	yes	characteristic
306	C₂×#104	C₂²×C₅	1	1	yes	characteristic
307	C₂×#104	C₂²×C₅	1	1	yes	characteristic
308	#416	C₂²×C₅	1	1	yes	characteristic
309	#416	C₂²×C₅	1	1	yes	characteristic
310	#408	C₂²×C₅	1	1	yes	characteristic
311	#408	C₂²×C₅	1	1	yes	characteristic
312	#408	C₂²×C₅	1	1	yes	characteristic
313	#408	C₂²×C₅	1	1	yes	characteristic
314	#405	C₂²×C₅	1	1	yes	characteristic
315	#405	C₂²×C₅	1	1	yes	characteristic
316	C₄×M₁₆	C₂²×C₅	1	1	yes	characteristic
317	C₂×#97	C₂²×C₅	1	1	yes	characteristic
318	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
319	#376	C₂²×C₅	1	1	yes	characteristic
320	#341	C₂²×C₅	1	1	yes	characteristic
321	#341	C₂²×C₅	1	1	yes	characteristic
322	#339	C₂²×C₅	1	1	yes	characteristic
323	#339	C₂²×C₅	1	1	yes	characteristic
324	#336	C₂²×C₅	1	1	yes	characteristic
325	#336	C₂²×C₅	1	1	yes	characteristic
326	C₂³×C₅	—	2	1	no	—
327	C₂³×C₅	—	2	1	no	—
328	C₂³×C₅	—	2	1	no	—
329	C₂³×C₅	C₂×#41	1	1	yes	characteristic
330	C₅×Q₈	—	2	1	no	—
331	C₅×Q₈	—	2	1	no	—
332	C₅×Q₈	—	2	1	no	—
333	C₅×Q₈	—	2	1	no	—
334	C₅×Q₈	—	2	1	no	—
335	C₅×Q₈	—	2	1	no	—
336	C₅×D₄	—	2	1	no	—
337	C₅×D₄	—	2	1	no	—
338	C₅×D₄	—	2	1	no	—
339	C₅×D₄	—	2	1	no	—
340	C₅×D₄	—	2	1	no	—
341	C₅×D₄	—	2	1	no	—
342	C₅×D₄	—	4	2	no	—
343	C₅×D₄	—	4	1	no	—
344	C₅×D₄	—	4	1	no	—
345	C₅×D₄	—	4	1	no	—
346	C₅×D₄	—	4	1	no	—
347	C₅×D₄	—	4	1	no	—
348	C₅×D₄	—	4	1	no	—
349	C₅×D₄	—	8	1	no	—
350	C₂×C₄×C₅	—	2	1	no	—
351	C₂×C₄×C₅	—	2	1	no	—
352	C₂×C₄×C₅	—	2	1	no	—
353	C₂×C₄×C₅	—	2	1	no	—
354	C₂×C₄×C₅	—	2	1	no	—
355	C₂×C₄×C₅	—	2	2	no	—
356	C₂×C₄×C₅	—	4	1	no	—
357	C₂×C₄×C₅	—	4	1	no	—
358	C₂×C₄×C₅	—	4	2	no	—
359	C₂×C₄×C₅	—	4	1	no	—
360	C₂×C₄×C₅	—	4	1	no	—
361	C₂×C₄×C₅	—	4	1	no	—
362	C₂×C₄×C₅	—	4	1	no	—
363	C₂×C₄×C₅	—	4	1	no	—
364	C₂×C₄×C₅	—	4	1	no	—
365	C₂×C₄×C₅	—	4	1	no	—
366	C₂×C₄×C₅	—	4	1	no	—
367	C₂×C₄×C₅	—	4	1	no	—
368	C₂×C₄×C₅	—	4	1	no	—
369	C₂×C₄×C₅	—	4	1	no	—
370	C₂×C₄×C₅	—	8	1	no	—
371	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
372	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
373	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
374	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
375	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
376	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
377	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
378	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
379	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
380	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
381	C₅×C₈	—	2	1	no	—
382	C₅×C₈	—	2	1	no	—
383	C₅×C₈	—	2	1	no	—
384	C₅×C₈	—	2	1	no	—
385	C₅×C₈	—	2	1	no	—
386	C₅×C₈	—	2	1	no	—
387	C₅×C₈	—	2	1	no	—
388	C₅×C₈	—	2	1	no	—
389	C₅×C₈	—	2	2	no	—
390	C₅×C₈	—	4	1	no	—
391	C₅×C₈	—	4	1	no	—
392	C₅×C₈	—	4	1	no	—
393	C₂×#41	C₂³×C₅	1	1	yes	characteristic
394	C₂×#41	C₂³×C₅	1	1	yes	characteristic
395	C₂×#41	C₂³×C₅	1	1	yes	characteristic
396	#135	—	4	1	no	—
397	#135	—	4	1	no	—
398	#135	—	4	1	no	—
399	#135	—	4	1	no	—
400	C₂×Q₁₆	C₂×C₄×C₅	1	1	yes	characteristic
401	C₂×Q₁₆	C₂×C₄×C₅	1	1	yes	characteristic
402	C₂×SD₁₆	C₂×C₄×C₅	1	1	yes	characteristic
403	C₂×SD₁₆	C₂×C₄×C₅	1	1	yes	characteristic
404	C₂×SD₁₆	C₂×C₄×C₅	1	1	yes	characteristic
405	C₂×SD₁₆	C₂×C₄×C₅	1	1	yes	characteristic
406	C₂×D₈	C₂×C₄×C₅	1	1	yes	characteristic
407	C₂×D₈	C₂×C₄×C₅	1	1	yes	characteristic
408	#131	—	2	2	no	—
409	#131	—	2	2	no	—
410	#131	—	4	1	no	—
411	#131	—	4	1	no	—
412	C₂×M₁₆	—	2	1	no	—
413	C₂×M₁₆	—	2	1	no	—
414	C₂×M₁₆	C₂³×C₅	1	1	yes	characteristic
415	C₂×M₁₆	C₂³×C₅	1	1	yes	characteristic
416	C₂×M₁₆	C₂³×C₅	1	1	yes	characteristic
417	C₂×M₁₆	C₂³×C₅	1	1	yes	characteristic
418	C₂²×C₈	—	2	1	no	—
419	C₂²×C₈	—	2	1	no	—
420	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
421	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
422	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
423	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
424	C₄⋊Q₈	C₂×C₄×C₅	1	1	yes	characteristic
425	#127	C₂×C₄×C₅	1	1	yes	characteristic
426	#124	C₂×C₄×C₅	1	1	yes	characteristic
427	#124	C₂×C₄×C₅	1	1	yes	characteristic
428	#121	—	2	1	no	—
429	#121	—	2	1	no	—
430	C₄×Q₈	C₂×C₄×C₅	1	1	yes	characteristic
431	C₄×Q₈	C₂×C₄×C₅	1	1	yes	characteristic
432	C₄×D₄	—	2	1	no	—
433	C₄×D₄	—	2	1	no	—
434	C₄×D₄	—	2	1	no	—
435	C₄×D₄	—	2	1	no	—
436	C₄×D₄	C₂×C₄×C₅	1	1	yes	characteristic
437	C₄×D₄	C₂×C₄×C₅	1	1	yes	characteristic
438	#117	—	2	1	no	—
439	#117	C₂³×C₅	1	1	yes	characteristic
440	C₂×C₄²	—	2	1	no	—
441	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
442	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
443	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
444	#108	—	4	1	no	—
445	#108	—	4	1	no	—
446	C₄⋊C₈	—	2	1	no	—
447	C₄⋊C₈	—	2	1	no	—
448	C₄⋊C₈	C₂×C₄×C₅	1	1	yes	characteristic
449	C₄⋊C₈	C₂×C₄×C₅	1	1	yes	characteristic
450	C₄⋊C₈	C₂×C₄×C₅	1	1	yes	characteristic
451	C₄⋊C₈	C₂×C₄×C₅	1	1	yes	characteristic
452	C₄⋊C₈	C₅×D₄	1	1	yes	characteristic
453	C₄⋊C₈	C₅×D₄	1	1	yes	characteristic
454	C₄⋊C₈	C₅×D₄	1	1	yes	characteristic
455	C₄⋊C₈	C₅×D₄	1	1	yes	characteristic
456	#104	—	2	2	no	—
457	#104	—	2	2	no	—
458	#104	—	2	2	no	—
459	#104	—	2	2	no	—
460	#104	—	4	1	no	—
461	#104	—	4	1	no	—
462	#103	C₂×C₄×C₅	1	1	yes	characteristic
463	#103	C₂×C₄×C₅	1	1	yes	characteristic
464	#103	C₂×C₄×C₅	1	1	yes	characteristic
465	#103	C₂×C₄×C₅	1	1	yes	characteristic
466	#102	C₂×C₄×C₅	1	1	yes	characteristic
467	#102	C₂×C₄×C₅	1	1	yes	characteristic
468	#102	C₂×C₄×C₅	1	1	yes	characteristic
469	#102	C₂×C₄×C₅	1	1	yes	characteristic
470	C₂²⋊C₈	—	2	1	no	—
471	C₂²⋊C₈	—	2	1	no	—
472	C₂²⋊C₈	—	2	1	no	—
473	C₂²⋊C₈	—	2	1	no	—
474	C₂²⋊C₈	—	2	1	no	—
475	C₂²⋊C₈	—	2	1	no	—
476	C₂²⋊C₈	—	2	1	no	—
477	C₂²⋊C₈	—	2	1	no	—
478	#97	—	2	1	no	—
479	#97	—	2	1	no	—
480	#97	—	2	1	no	—
481	#97	—	4	1	no	—
482	C₄×C₈	—	2	1	no	—
483	C₄×C₈	—	2	1	no	—
484	C₄×C₈	—	2	1	no	—
485	C₄×C₈	—	4	1	no	—
486	#95	—	2	1	no	—
487	#95	—	2	1	no	—
488	C₂²×C₅	—	2	1	no	—
489	C₂²×C₅	—	2	1	no	—
490	C₂²×C₅	—	4	1	no	—
491	C₂²×C₅	—	4	1	no	—
492	C₂²×C₅	—	4	1	no	—
493	C₂²×C₅	—	4	1	no	—
494	C₂²×C₅	—	4	1	no	—
495	C₂²×C₅	—	4	1	no	—
496	C₂²×C₅	—	4	1	no	—
497	C₂²×C₅	—	4	1	no	—
498	C₂²×C₅	—	4	1	no	—
499	C₂²×C₅	C₂×C₄×D₄	1	1	yes	characteristic
500	C₂²×C₅	#553	1	1	yes	characteristic
501	C₂²×C₅	#555	1	1	yes	characteristic
502	C₄×C₅	—	2	1	no	—
503	C₄×C₅	—	2	1	no	—
504	C₄×C₅	—	2	1	no	—
505	C₄×C₅	—	2	1	no	—
506	C₄×C₅	—	4	2	no	—
507	C₄×C₅	—	4	1	no	—
508	C₄×C₅	—	4	1	no	—
509	C₄×C₅	—	4	1	no	—
510	C₄×C₅	—	4	1	no	—
511	C₄×C₅	—	4	1	no	—
512	C₄×C₅	—	8	1	no	—
513	C₄×C₅	C₄×#41	1	1	yes	characteristic
514	C₄×C₅	#518	1	1	yes	characteristic
515	C₄×C₅	#546	1	1	yes	characteristic
516	C₄×C₅	#550	1	1	yes	characteristic
517	#41	—	2	1	no	—
518	#41	—	2	1	no	—
519	#41	—	2	1	no	—
520	#41	—	2	1	no	—
521	#41	—	2	1	no	—
522	#41	—	2	1	no	—
523	#41	—	2	1	no	—
524	#41	—	2	1	no	—
525	#41	—	2	1	no	—
526	#41	—	2	1	no	—
527	#41	—	2	1	no	—
528	#41	—	2	1	no	—
529	C₂×Q₈	C₂²×C₄×C₅	1	1	yes	characteristic
530	C₂×Q₈	C₂²×C₄×C₅	1	1	yes	characteristic
531	C₂×Q₈	C₂²×C₄×C₅	1	1	yes	characteristic
532	C₂×D₄	—	2	1	no	—
533	C₂×D₄	—	2	1	no	—
534	C₂×D₄	—	2	1	no	—
535	C₂×D₄	—	2	1	no	—
536	C₂×D₄	—	2	1	no	—
537	C₂×D₄	C₂²×C₄×C₅	1	1	yes	characteristic
538	C₂×D₄	C₂²×C₄×C₅	1	1	yes	characteristic
539	C₂×D₄	C₂²×C₄×C₅	1	1	yes	characteristic
540	C₂²×C₄	—	2	1	no	—
541	C₂²×C₄	—	2	1	no	—
542	C₂²×C₄	—	2	1	no	—
543	C₂²×C₄	—	2	1	no	—
544	C₂²×C₄	—	2	1	no	—
545	C₂²×C₄	—	2	1	no	—
546	C₂²×C₄	—	2	1	no	—
547	C₂²×C₄	C₅×#41	1	1	yes	characteristic
548	C₂²×C₄	C₅×#41	1	1	yes	characteristic
549	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
550	Q₁₆	—	4	1	no	—
551	Q₁₆	—	4	1	no	—
552	SD₁₆	—	4	1	no	—
553	SD₁₆	—	4	1	no	—
554	SD₁₆	—	4	1	no	—
555	SD₁₆	—	4	1	no	—
556	D₈	—	4	1	no	—
557	D₈	—	4	1	no	—
558	M₁₆	—	2	1	no	—
559	M₁₆	—	2	1	no	—
560	M₁₆	—	2	1	no	—
561	M₁₆	—	2	1	no	—
562	M₁₆	—	2	1	no	—
563	M₁₆	—	2	1	no	—
564	M₁₆	—	2	1	no	—
565	M₁₆	—	4	2	no	—
566	M₁₆	—	4	2	no	—
567	M₁₆	C₅×#41	1	2	yes	—
568	C₂×C₈	—	2	1	no	—
569	C₂×C₈	—	2	1	no	—
570	C₂×C₈	—	2	1	no	—
571	C₂×C₈	—	2	1	no	—
572	C₂×C₈	—	2	1	no	—
573	C₂×C₈	—	2	1	no	—
574	C₂×C₈	—	2	1	no	—
575	C₂×C₈	—	2	1	no	—
576	C₂×C₈	—	2	1	no	—
577	C₂×C₈	—	2	1	no	—
578	C₂×C₈	—	2	1	no	—
579	C₂×C₈	—	2	1	no	—
580	C₂×C₈	—	4	2	no	—
581	C₂×C₈	—	4	2	no	—
582	C₂×C₈	C₂²×C₄×C₅	1	1	yes	characteristic
583	C₂×C₈	C₂²×C₄×C₅	1	1	yes	characteristic
584	C₂×C₈	C₂²×C₄×C₅	1	1	yes	characteristic
585	C₂×C₈	C₂²×C₄×C₅	1	1	yes	characteristic
586	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
587	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
588	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
589	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
590	C₄⋊C₄	—	2	1	no	—
591	C₄⋊C₄	—	2	1	no	—
592	C₄⋊C₄	—	2	1	no	—
593	C₄⋊C₄	—	2	1	no	—
594	C₄⋊C₄	C₂²×C₄×C₅	1	1	yes	characteristic
595	C₄⋊C₄	C₂²×C₄×C₅	1	1	yes	characteristic
596	C₂²⋊C₄	—	2	1	no	—
597	C₂²⋊C₄	—	2	1	no	—
598	C₂²⋊C₄	—	2	1	no	—
599	C₂²⋊C₄	—	2	1	no	—
600	C₂²⋊C₄	—	2	1	no	—
601	C₂²⋊C₄	—	2	1	no	—
602	C₂²⋊C₄	—	2	1	no	—
603	C₄²	—	2	1	no	—
604	C₄²	—	2	1	no	—
605	C₄²	—	2	1	no	—
606	C₄²	—	2	1	no	—
607	C₄²	—	2	1	no	—
608	C₄²	—	2	1	no	—
609	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
610	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
611	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
612	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
613	C₄²	C₅×#41	1	2	yes	—
614	C₂×C₅	—	2	1	no	—
615	C₂×C₅	—	2	1	no	—
616	C₂×C₅	—	8	1	no	—
617	C₂×C₅	—	8	1	no	—
618	C₂×C₅	—	8	1	no	—
619	C₂×C₅	#2363	1	1	yes	characteristic
620	C₂×C₅	#2955	1	1	yes	characteristic
621	C₂×C₅	#2957	1	1	yes	characteristic
622	C₂³	—	2	1	no	—
623	C₂³	—	2	1	no	—
624	C₂³	—	2	1	no	—
625	C₂³	C₂×C₅×#41	1	1	yes	characteristic
626	Q₈	—	2	1	no	—
627	Q₈	—	2	1	no	—
628	Q₈	—	2	1	no	—
629	Q₈	—	2	1	no	—
630	Q₈	—	2	1	no	—
631	Q₈	—	2	1	no	—
632	D₄	—	2	1	no	—
633	D₄	—	2	1	no	—
634	D₄	—	2	1	no	—
635	D₄	—	2	1	no	—
636	D₄	—	2	1	no	—
637	D₄	—	2	1	no	—
638	D₄	—	4	2	no	—
639	D₄	—	4	1	no	—
640	D₄	—	4	1	no	—
641	D₄	—	4	1	no	—
642	D₄	—	4	1	no	—
643	D₄	—	4	1	no	—
644	D₄	—	4	1	no	—
645	D₄	—	8	1	no	—
646	C₂×C₄	—	2	1	no	—
647	C₂×C₄	—	2	1	no	—
648	C₂×C₄	—	2	1	no	—
649	C₂×C₄	—	2	1	no	—
650	C₂×C₄	—	2	1	no	—
651	C₂×C₄	—	2	2	no	—
652	C₂×C₄	—	4	1	no	—
653	C₂×C₄	—	4	1	no	—
654	C₂×C₄	—	4	2	no	—
655	C₂×C₄	—	4	1	no	—
656	C₂×C₄	—	4	1	no	—
657	C₂×C₄	—	4	1	no	—
658	C₂×C₄	—	4	1	no	—
659	C₂×C₄	—	4	1	no	—
660	C₂×C₄	—	4	1	no	—
661	C₂×C₄	—	4	1	no	—
662	C₂×C₄	—	4	1	no	—
663	C₂×C₄	—	4	1	no	—
664	C₂×C₄	—	4	1	no	—
665	C₂×C₄	—	4	1	no	—
666	C₂×C₄	—	8	1	no	—
667	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
668	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
669	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
670	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
671	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
672	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
673	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
674	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
675	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
676	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
677	C₈	—	2	1	no	—
678	C₈	—	2	1	no	—
679	C₈	—	2	1	no	—
680	C₈	—	2	1	no	—
681	C₈	—	2	1	no	—
682	C₈	—	2	1	no	—
683	C₈	—	2	1	no	—
684	C₈	—	2	1	no	—
685	C₈	—	2	2	no	—
686	C₈	—	4	1	no	—
687	C₈	—	4	1	no	—
688	C₈	—	4	1	no	—
689	C₅	#23115	1	1	yes	characteristic, direct product factor, Sylow
690	C₂²	—	2	1	no	—
691	C₂²	—	2	1	no	—
692	C₂²	—	4	1	no	—
693	C₂²	—	4	1	no	—
694	C₂²	—	4	1	no	—
695	C₂²	—	4	1	no	—
696	C₂²	—	4	1	no	—
697	C₂²	—	4	1	no	—
698	C₂²	—	4	1	no	—
699	C₂²	—	4	1	no	—
700	C₂²	—	4	1	no	—
701	C₂²	C₂×C₄×C₅×D₄	1	1	yes	characteristic
702	C₂²	C₅×#553	1	1	yes	characteristic
703	C₂²	C₅×#555	1	1	yes	characteristic
704	C₄	—	2	1	no	—
705	C₄	—	2	1	no	—
706	C₄	—	2	1	no	—
707	C₄	—	2	1	no	—
708	C₄	—	4	2	no	—
709	C₄	—	4	1	no	—
710	C₄	—	4	1	no	—
711	C₄	—	4	1	no	—
712	C₄	—	4	1	no	—
713	C₄	—	4	1	no	—
714	C₄	—	8	1	no	—
715	C₄	C₄×C₅×#41	1	1	yes	characteristic
716	C₄	C₅×#518	1	1	yes	characteristic
717	C₄	C₅×#546	1	1	yes	characteristic
718	C₄	C₅×#550	1	1	yes	characteristic
719	C₂	—	2	1	no	—
720	C₂	—	2	1	no	—
721	C₂	—	8	1	no	—
722	C₂	—	8	1	no	—
723	C₂	—	8	1	no	—
724	C₂	C₅×#2363	1	1	yes	characteristic
725	C₂	C₅×#2955	1	1	yes	characteristic
726	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×C₄⋊C₈ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₅×#2935	C₂	semidirect
3. C₅×#2925	C₂	semidirect
4. C₅×#1975	C₂	semidirect
5. C₅×#1974	C₂	semidirect
6. C₅×#1963	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×#1768	C₂	semidirect
13. C₅×#1765	C₂	semidirect
14. C₅×#1764	C₂	semidirect
15. C₅×#1759	C₂	semidirect
22. C₅×#464	C₄	semidirect
23. C₅×#464	C₄	semidirect
24. C₅×#463	C₄	semidirect
25. C₅×#463	C₄	semidirect
26. C₅×#462	C₄	semidirect
27. C₅×#461	C₄	semidirect
28. C₅×#460	C₄	semidirect
29. C₅×#459	C₄	semidirect
67. #23115	C₅	direct (N × H)
164. #2935	C₂×C₅	semidirect
165. #2925	C₂×C₅	semidirect
166. #1975	C₂×C₅	semidirect
167. #1974	C₂×C₅	semidirect
168. #1963	C₂×C₅	semidirect
169. #1950	C₂×C₅	semidirect
170. #1929	C₂×C₅	semidirect
171. #1929	C₂×C₅	semidirect
172. #1876	C₂×C₅	semidirect
173. #1876	C₂×C₅	semidirect
174. #1768	C₂×C₅	semidirect
175. #1765	C₂×C₅	semidirect
176. #1764	C₂×C₅	semidirect
177. #1759	C₂×C₅	semidirect
281. #464	C₄×C₅	semidirect
282. #464	C₄×C₅	semidirect
283. #463	C₄×C₅	semidirect
284. #463	C₄×C₅	semidirect
285. #462	C₄×C₅	semidirect
286. #461	C₄×C₅	semidirect
287. #460	C₄×C₅	semidirect
288. #459	C₄×C₅	semidirect
689. C₅	#23115	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
C₅×#2935	2
C₅×#2925	2
C₅×#1975	2
C₅×#1974	2
C₅×#1963	2
C₅×#1950	2
C₅×#1929	2
C₅×#1876	2
C₅×#1768	2
C₅×#1765	2
C₅×#1764	2
C₅×#1759	2
#23115	5

Subgroups — C5×#23115 #11945835

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#23115 #11945835