Subgroups — C₅×#23082 #11945802

Order 1280.

646 conjugacy classes of subgroups.

The subgroup lattice has 620 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#3076	C₂	1	1	yes	maximal, characteristic
2	C₅×#2962	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#2925	C₂	1	1	yes	maximal, characteristic
4	C₅×#1995	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#1950	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#1938	C₂	1	1	yes	maximal, characteristic
7	C₅×#1937	C₂	1	1	yes	maximal, characteristic
8	C₅×#1929	C₂	1	1	yes	maximal, characteristic
9	C₅×#1929	C₂	1	1	yes	maximal, characteristic
10	C₅×#1922	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#1922	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#1773	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅×#1772	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅×#1768	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅×#1759	C₂	1	1	yes	maximal, characteristic
16	C₅×#533	C₂²	1	1	yes	characteristic
17	C₄×C₅×#41	C₂²	1	1	yes	characteristic
18	C₅×#479	C₄	1	1	yes	characteristic, complemented
19	C₅×#479	C₄	1	1	yes	characteristic, complemented
20	C₅×#478	C₄	1	1	yes	characteristic, complemented
21	C₅×#478	C₄	1	1	yes	characteristic, complemented
22	C₅×#477	C₄	1	1	yes	characteristic, complemented
23	C₅×#476	C₄	1	1	yes	characteristic, complemented
24	C₅×#475	C₄	1	1	yes	characteristic, complemented
25	C₅×#474	C₄	1	1	yes	characteristic, complemented
26	C₅×#446	—	2	1	no	—
27	C₅×#446	—	2	1	no	—
28	C₅×#446	—	2	1	no	—
29	C₅×C₈×Q₈	—	2	1	no	—
30	C₅×#433	—	2	1	no	—
31	C₅×#433	—	2	1	no	—
32	C₅×#432	—	2	1	no	—
33	C₅×#431	—	2	1	no	—
34	C₂×C₅×#108	C₂²	1	1	yes	characteristic
35	C₂×C₅×#108	C₂²	1	1	yes	characteristic
36	C₅×#427	C₂²	1	1	yes	characteristic
37	C₅×#427	C₂²	1	1	yes	characteristic
38	C₅×#424	C₂²	1	1	yes	characteristic
39	C₅×#424	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	C₅×#416	C₂²	1	1	yes	characteristic
46	C₅×#416	C₂²	1	1	yes	characteristic
47	C₅×#408	C₂²	1	1	yes	characteristic
48	C₅×#408	C₂²	1	1	yes	characteristic
49	C₅×#405	C₂²	1	1	yes	characteristic
50	C₅×#405	C₂²	1	1	yes	characteristic
51	C₅×#405	C₂²	1	1	yes	characteristic
52	C₅×#405	C₂²	1	1	yes	characteristic
53	C₄×C₅×M₁₆	C₂²	1	1	yes	characteristic
54	C₂×C₅×#97	C₂²	1	1	yes	characteristic
55	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
56	C₅×#376	C₂²	1	1	yes	characteristic
57	C₅×#341	C₂²	1	1	yes	characteristic
58	C₅×#341	C₂²	1	1	yes	characteristic
59	C₅×#339	C₂²	1	1	yes	characteristic
60	C₅×#339	C₂²	1	1	yes	characteristic
61	C₅×#339	C₂²	1	1	yes	characteristic
62	C₅×#339	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	#23082	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
68	C₂×C₅×#41	C₂³	1	1	yes	characteristic
69	C₂×C₅×M₁₆	C₂³	1	1	yes	characteristic
70	C₂×C₅×M₁₆	C₂³	1	1	yes	characteristic
71	C₂×C₅×M₁₆	C₂³	1	1	yes	characteristic
72	C₂×C₅×M₁₆	C₂³	1	1	yes	characteristic
73	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
74	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
75	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
76	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
77	C₅×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
78	C₅×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
79	C₅×#125	C₂×C₄	1	1	yes	characteristic
80	C₅×#125	C₂×C₄	1	1	yes	characteristic
81	C₅×C₂²⋊Q₈	—	2	1	no	—
82	C₅×C₂²⋊Q₈	—	2	1	no	—
83	C₄×C₅×Q₈	—	2	1	no	—
84	C₄×C₅×Q₈	—	2	1	no	—
85	C₄×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
86	C₄×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
87	C₄×C₅×D₄	—	2	1	no	—
88	C₄×C₅×D₄	—	2	1	no	—
89	C₄×C₅×D₄	C₂×C₄	1	1	yes	characteristic
90	C₄×C₅×D₄	C₂×C₄	1	1	yes	characteristic
91	C₅×#117	—	2	1	no	—
92	C₅×#117	C₂³	1	1	yes	characteristic
93	C₅×#117	C₂³	1	1	yes	characteristic
94	C₅×#117	C₂³	1	1	yes	characteristic
95	C₂×C₄²×C₅	—	2	1	no	—
96	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
97	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
98	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
99	C₅×#108	—	2	2	no	—
100	C₅×#108	—	2	2	no	—
101	C₅×#107	C₂×C₄	1	1	yes	characteristic
102	C₅×#107	C₂×C₄	1	1	yes	characteristic
103	C₅×#107	C₂×C₄	1	1	yes	characteristic
104	C₅×#107	C₂×C₄	1	1	yes	characteristic
105	C₅×#106	C₂×C₄	1	1	yes	characteristic
106	C₅×#106	C₂×C₄	1	1	yes	characteristic
107	C₅×#106	C₂×C₄	1	1	yes	characteristic
108	C₅×#106	C₂×C₄	1	1	yes	characteristic
109	C₅×C₄⋊C₈	—	2	1	no	—
110	C₅×C₄⋊C₈	—	2	1	no	—
111	C₅×C₄⋊C₈	—	2	1	no	—
112	C₅×C₄⋊C₈	—	2	1	no	—
113	C₅×C₄⋊C₈	—	2	1	no	—
114	C₅×C₄⋊C₈	—	2	1	no	—
115	C₅×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
116	C₅×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
117	C₅×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
118	C₅×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
119	C₅×C₄⋊C₈	D₄	1	1	yes	characteristic
120	C₅×C₄⋊C₈	D₄	1	1	yes	characteristic
121	C₅×C₄⋊C₈	D₄	1	1	yes	characteristic
122	C₅×C₄⋊C₈	D₄	1	1	yes	characteristic
123	C₅×#104	—	2	2	no	—
124	C₅×#104	—	2	2	no	—
125	C₅×#103	C₂×C₄	1	1	yes	characteristic
126	C₅×#103	C₂×C₄	1	1	yes	characteristic
127	C₅×#103	C₂×C₄	1	1	yes	characteristic
128	C₅×#103	C₂×C₄	1	1	yes	characteristic
129	C₅×#102	C₂×C₄	1	1	yes	characteristic
130	C₅×#102	C₂×C₄	1	1	yes	characteristic
131	C₅×#102	C₂×C₄	1	1	yes	characteristic
132	C₅×#102	C₂×C₄	1	1	yes	characteristic
133	C₅×C₂²⋊C₈	—	2	1	no	—
134	C₅×C₂²⋊C₈	—	2	1	no	—
135	C₅×C₂²⋊C₈	—	2	1	no	—
136	C₅×C₂²⋊C₈	—	2	1	no	—
137	C₅×#97	—	2	1	no	—
138	C₅×#97	—	2	1	no	—
139	C₅×#97	—	2	1	no	—
140	C₅×#97	—	2	1	no	—
141	C₅×#97	—	2	1	no	—
142	C₅×#97	—	2	2	no	—
143	C₄×C₅×C₈	—	2	1	no	—
144	C₄×C₅×C₈	—	2	1	no	—
145	C₄×C₅×C₈	—	2	1	no	—
146	C₄×C₅×C₈	—	2	1	no	—
147	C₄×C₅×C₈	—	2	1	no	—
148	C₄×C₅×C₈	—	2	2	no	—
149	C₅×#95	—	2	1	no	—
150	C₅×#95	—	2	1	no	—
151	#3076	C₂×C₅	1	1	yes	characteristic
152	#2962	C₂×C₅	1	1	yes	characteristic, complemented
153	#2925	C₂×C₅	1	1	yes	characteristic
154	#1995	C₂×C₅	1	1	yes	characteristic, complemented
155	#1950	C₂×C₅	1	1	yes	characteristic, complemented
156	#1938	C₂×C₅	1	1	yes	characteristic
157	#1937	C₂×C₅	1	1	yes	characteristic
158	#1929	C₂×C₅	1	1	yes	characteristic
159	#1929	C₂×C₅	1	1	yes	characteristic
160	#1922	C₂×C₅	1	1	yes	characteristic, complemented
161	#1922	C₂×C₅	1	1	yes	characteristic, complemented
162	#1773	C₂×C₅	1	1	yes	characteristic, complemented
163	#1772	C₂×C₅	1	1	yes	characteristic, complemented
164	#1768	C₂×C₅	1	1	yes	characteristic, complemented
165	#1759	C₂×C₅	1	1	yes	characteristic
166	C₅×#41	—	2	1	no	—
167	C₅×#41	—	2	1	no	—
168	C₅×#41	—	2	1	no	—
169	C₅×#41	—	2	1	no	—
170	C₂×C₅×Q₈	—	2	1	no	—
171	C₂×C₅×Q₈	—	2	1	no	—
172	C₂×C₅×Q₈	C₂²×C₄	1	1	yes	characteristic
173	C₂×C₅×D₄	—	2	1	no	—
174	C₂×C₅×D₄	C₂²×C₄	1	1	yes	characteristic
175	C₂²×C₄×C₅	—	2	1	no	—
176	C₂²×C₄×C₅	—	2	1	no	—
177	C₂²×C₄×C₅	—	2	1	no	—
178	C₂²×C₄×C₅	—	2	1	no	—
179	C₂²×C₄×C₅	—	2	1	no	—
180	C₂²×C₄×C₅	#41	1	1	yes	characteristic
181	C₂²×C₄×C₅	#41	1	1	yes	characteristic
182	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
183	C₅×M₁₆	—	2	1	no	—
184	C₅×M₁₆	—	2	1	no	—
185	C₅×M₁₆	—	2	1	no	—
186	C₅×M₁₆	—	2	1	no	—
187	C₅×M₁₆	—	2	1	no	—
188	C₅×M₁₆	—	2	1	no	—
189	C₅×M₁₆	—	2	1	no	—
190	C₅×M₁₆	#41	1	2	yes	—
191	C₂×C₅×C₈	—	2	1	no	—
192	C₂×C₅×C₈	—	2	1	no	—
193	C₂×C₅×C₈	—	2	1	no	—
194	C₂×C₅×C₈	—	2	1	no	—
195	C₂×C₅×C₈	—	2	1	no	—
196	C₂×C₅×C₈	—	2	1	no	—
197	C₂×C₅×C₈	—	2	1	no	—
198	C₂×C₅×C₈	—	2	1	no	—
199	C₂×C₅×C₈	—	2	1	no	—
200	C₂×C₅×C₈	—	2	1	no	—
201	C₂×C₅×C₈	—	2	1	no	—
202	C₂×C₅×C₈	—	2	1	no	—
203	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
204	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
205	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
206	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
207	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
208	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
209	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
210	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
211	C₅×C₄⋊C₄	—	2	1	no	—
212	C₅×C₄⋊C₄	—	2	1	no	—
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	C₂²×C₄	1	1	yes	characteristic
220	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
221	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
222	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
223	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
224	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
225	C₅×C₂²⋊C₄	—	2	1	no	—
226	C₅×C₂²⋊C₄	—	2	1	no	—
227	C₅×C₂²⋊C₄	—	2	1	no	—
228	C₅×C₂²⋊C₄	—	2	1	no	—
229	C₅×C₂²⋊C₄	—	2	1	no	—
230	C₄²×C₅	—	2	1	no	—
231	C₄²×C₅	—	2	1	no	—
232	C₄²×C₅	—	2	1	no	—
233	C₄²×C₅	—	2	1	no	—
234	C₄²×C₅	—	2	1	no	—
235	C₄²×C₅	—	2	1	no	—
236	C₄²×C₅	—	2	1	no	—
237	C₄²×C₅	—	2	1	no	—
238	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
239	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
240	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
241	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
242	C₄²×C₅	#41	1	2	yes	—
243	#533	C₂²×C₅	1	1	yes	characteristic
244	C₄×#41	C₂²×C₅	1	1	yes	characteristic
245	#479	C₄×C₅	1	1	yes	characteristic, complemented
246	#479	C₄×C₅	1	1	yes	characteristic, complemented
247	#478	C₄×C₅	1	1	yes	characteristic, complemented
248	#478	C₄×C₅	1	1	yes	characteristic, complemented
249	#477	C₄×C₅	1	1	yes	characteristic, complemented
250	#476	C₄×C₅	1	1	yes	characteristic, complemented
251	#475	C₄×C₅	1	1	yes	characteristic, complemented
252	#474	C₄×C₅	1	1	yes	characteristic, complemented
253	#446	—	2	1	no	—
254	#446	—	2	1	no	—
255	#446	—	2	1	no	—
256	C₈×Q₈	—	2	1	no	—
257	#433	—	2	1	no	—
258	#433	—	2	1	no	—
259	#432	—	2	1	no	—
260	#431	—	2	1	no	—
261	C₂×#108	C₂²×C₅	1	1	yes	characteristic
262	C₂×#108	C₂²×C₅	1	1	yes	characteristic
263	#427	C₂²×C₅	1	1	yes	characteristic
264	#427	C₂²×C₅	1	1	yes	characteristic
265	#424	C₂²×C₅	1	1	yes	characteristic
266	#424	C₂²×C₅	1	1	yes	characteristic
267	#423	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	C₂×#104	C₂²×C₅	1	1	yes	characteristic
271	C₂×#104	C₂²×C₅	1	1	yes	characteristic
272	#416	C₂²×C₅	1	1	yes	characteristic
273	#416	C₂²×C₅	1	1	yes	characteristic
274	#408	C₂²×C₅	1	1	yes	characteristic
275	#408	C₂²×C₅	1	1	yes	characteristic
276	#405	C₂²×C₅	1	1	yes	characteristic
277	#405	C₂²×C₅	1	1	yes	characteristic
278	#405	C₂²×C₅	1	1	yes	characteristic
279	#405	C₂²×C₅	1	1	yes	characteristic
280	C₄×M₁₆	C₂²×C₅	1	1	yes	characteristic
281	C₂×#97	C₂²×C₅	1	1	yes	characteristic
282	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
283	#376	C₂²×C₅	1	1	yes	characteristic
284	#341	C₂²×C₅	1	1	yes	characteristic
285	#341	C₂²×C₅	1	1	yes	characteristic
286	#339	C₂²×C₅	1	1	yes	characteristic
287	#339	C₂²×C₅	1	1	yes	characteristic
288	#339	C₂²×C₅	1	1	yes	characteristic
289	#339	C₂²×C₅	1	1	yes	characteristic
290	#339	C₂²×C₅	1	1	yes	characteristic
291	#339	C₂²×C₅	1	1	yes	characteristic
292	#336	C₂²×C₅	1	1	yes	characteristic
293	#336	C₂²×C₅	1	1	yes	characteristic
294	C₂³×C₅	—	2	1	no	—
295	C₂³×C₅	C₂×#41	1	1	yes	characteristic
296	C₅×Q₈	—	2	1	no	—
297	C₅×Q₈	—	2	1	no	—
298	C₅×Q₈	—	4	2	no	—
299	C₅×Q₈	—	8	1	no	—
300	C₅×D₄	—	2	1	no	—
301	C₅×D₄	—	2	1	no	—
302	C₅×D₄	—	4	1	no	—
303	C₅×D₄	—	4	1	no	—
304	C₂×C₄×C₅	—	2	1	no	—
305	C₂×C₄×C₅	—	2	1	no	—
306	C₂×C₄×C₅	—	2	1	no	—
307	C₂×C₄×C₅	—	2	1	no	—
308	C₂×C₄×C₅	—	2	1	no	—
309	C₂×C₄×C₅	—	2	1	no	—
310	C₂×C₄×C₅	—	2	1	no	—
311	C₂×C₄×C₅	—	2	2	no	—
312	C₂×C₄×C₅	—	4	1	no	—
313	C₂×C₄×C₅	—	4	1	no	—
314	C₂×C₄×C₅	—	4	2	no	—
315	C₂×C₄×C₅	—	4	1	no	—
316	C₂×C₄×C₅	—	4	1	no	—
317	C₂×C₄×C₅	—	4	1	no	—
318	C₂×C₄×C₅	—	4	1	no	—
319	C₂×C₄×C₅	—	4	1	no	—
320	C₂×C₄×C₅	—	4	1	no	—
321	C₂×C₄×C₅	—	4	1	no	—
322	C₂×C₄×C₅	—	8	1	no	—
323	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
324	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
325	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
326	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
327	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
328	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
329	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
330	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
331	C₂×C₄×C₅	2₋¹⁺⁴	1	1	yes	characteristic
332	C₂×C₄×C₅	2₋¹⁺⁴	1	1	yes	characteristic
333	C₅×C₈	—	2	1	no	—
334	C₅×C₈	—	2	1	no	—
335	C₅×C₈	—	2	1	no	—
336	C₅×C₈	—	2	1	no	—
337	C₅×C₈	—	2	1	no	—
338	C₅×C₈	—	2	1	no	—
339	C₅×C₈	—	2	1	no	—
340	C₅×C₈	—	2	1	no	—
341	C₅×C₈	—	2	2	no	—
342	C₅×C₈	—	4	1	no	—
343	C₅×C₈	—	4	1	no	—
344	C₅×C₈	—	4	1	no	—
345	C₂×#41	C₂³×C₅	1	1	yes	characteristic
346	C₂×M₁₆	C₂³×C₅	1	1	yes	characteristic
347	C₂×M₁₆	C₂³×C₅	1	1	yes	characteristic
348	C₂×M₁₆	C₂³×C₅	1	1	yes	characteristic
349	C₂×M₁₆	C₂³×C₅	1	1	yes	characteristic
350	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
351	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
352	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
353	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
354	C₄⋊Q₈	C₂×C₄×C₅	1	1	yes	characteristic
355	C₄⋊Q₈	C₂×C₄×C₅	1	1	yes	characteristic
356	#125	C₂×C₄×C₅	1	1	yes	characteristic
357	#125	C₂×C₄×C₅	1	1	yes	characteristic
358	C₂²⋊Q₈	—	2	1	no	—
359	C₂²⋊Q₈	—	2	1	no	—
360	C₄×Q₈	—	2	1	no	—
361	C₄×Q₈	—	2	1	no	—
362	C₄×Q₈	C₂×C₄×C₅	1	1	yes	characteristic
363	C₄×Q₈	C₂×C₄×C₅	1	1	yes	characteristic
364	C₄×D₄	—	2	1	no	—
365	C₄×D₄	—	2	1	no	—
366	C₄×D₄	C₂×C₄×C₅	1	1	yes	characteristic
367	C₄×D₄	C₂×C₄×C₅	1	1	yes	characteristic
368	#117	—	2	1	no	—
369	#117	C₂³×C₅	1	1	yes	characteristic
370	#117	C₂³×C₅	1	1	yes	characteristic
371	#117	C₂³×C₅	1	1	yes	characteristic
372	C₂×C₄²	—	2	1	no	—
373	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
374	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
375	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
376	#108	—	2	2	no	—
377	#108	—	2	2	no	—
378	#107	C₂×C₄×C₅	1	1	yes	characteristic
379	#107	C₂×C₄×C₅	1	1	yes	characteristic
380	#107	C₂×C₄×C₅	1	1	yes	characteristic
381	#107	C₂×C₄×C₅	1	1	yes	characteristic
382	#106	C₂×C₄×C₅	1	1	yes	characteristic
383	#106	C₂×C₄×C₅	1	1	yes	characteristic
384	#106	C₂×C₄×C₅	1	1	yes	characteristic
385	#106	C₂×C₄×C₅	1	1	yes	characteristic
386	C₄⋊C₈	—	2	1	no	—
387	C₄⋊C₈	—	2	1	no	—
388	C₄⋊C₈	—	2	1	no	—
389	C₄⋊C₈	—	2	1	no	—
390	C₄⋊C₈	—	2	1	no	—
391	C₄⋊C₈	—	2	1	no	—
392	C₄⋊C₈	C₂×C₄×C₅	1	1	yes	characteristic
393	C₄⋊C₈	C₂×C₄×C₅	1	1	yes	characteristic
394	C₄⋊C₈	C₂×C₄×C₅	1	1	yes	characteristic
395	C₄⋊C₈	C₂×C₄×C₅	1	1	yes	characteristic
396	C₄⋊C₈	C₅×D₄	1	1	yes	characteristic
397	C₄⋊C₈	C₅×D₄	1	1	yes	characteristic
398	C₄⋊C₈	C₅×D₄	1	1	yes	characteristic
399	C₄⋊C₈	C₅×D₄	1	1	yes	characteristic
400	#104	—	2	2	no	—
401	#104	—	2	2	no	—
402	#103	C₂×C₄×C₅	1	1	yes	characteristic
403	#103	C₂×C₄×C₅	1	1	yes	characteristic
404	#103	C₂×C₄×C₅	1	1	yes	characteristic
405	#103	C₂×C₄×C₅	1	1	yes	characteristic
406	#102	C₂×C₄×C₅	1	1	yes	characteristic
407	#102	C₂×C₄×C₅	1	1	yes	characteristic
408	#102	C₂×C₄×C₅	1	1	yes	characteristic
409	#102	C₂×C₄×C₅	1	1	yes	characteristic
410	C₂²⋊C₈	—	2	1	no	—
411	C₂²⋊C₈	—	2	1	no	—
412	C₂²⋊C₈	—	2	1	no	—
413	C₂²⋊C₈	—	2	1	no	—
414	#97	—	2	1	no	—
415	#97	—	2	1	no	—
416	#97	—	2	1	no	—
417	#97	—	2	1	no	—
418	#97	—	2	1	no	—
419	#97	—	2	2	no	—
420	C₄×C₈	—	2	1	no	—
421	C₄×C₈	—	2	1	no	—
422	C₄×C₈	—	2	1	no	—
423	C₄×C₈	—	2	1	no	—
424	C₄×C₈	—	2	1	no	—
425	C₄×C₈	—	2	2	no	—
426	#95	—	2	1	no	—
427	#95	—	2	1	no	—
428	C₂²×C₅	—	2	1	no	—
429	C₂²×C₅	—	2	1	no	—
430	C₂²×C₅	—	4	1	no	—
431	C₂²×C₅	—	4	1	no	—
432	C₂²×C₅	—	4	1	no	—
433	C₂²×C₅	C₂×C₄×D₄	1	1	yes	characteristic
434	C₂²×C₅	#552	1	1	yes	characteristic
435	C₂²×C₅	#556	1	1	yes	characteristic
436	C₄×C₅	—	2	1	no	—
437	C₄×C₅	—	2	1	no	—
438	C₄×C₅	—	2	1	no	—
439	C₄×C₅	—	2	1	no	—
440	C₄×C₅	—	4	2	no	—
441	C₄×C₅	—	4	1	no	—
442	C₄×C₅	—	4	1	no	—
443	C₄×C₅	—	4	1	no	—
444	C₄×C₅	—	4	1	no	—
445	C₄×C₅	—	4	1	no	—
446	C₄×C₅	—	4	1	no	—
447	C₄×C₅	—	4	1	no	—
448	C₄×C₅	—	8	1	no	—
449	C₄×C₅	C₄×#41	1	1	yes	characteristic
450	C₄×C₅	#519	1	1	yes	characteristic
451	C₄×C₅	#547	1	1	yes	characteristic
452	C₄×C₅	#548	1	1	yes	characteristic
453	#41	—	2	1	no	—
454	#41	—	2	1	no	—
455	#41	—	2	1	no	—
456	#41	—	2	1	no	—
457	C₂×Q₈	—	2	1	no	—
458	C₂×Q₈	—	2	1	no	—
459	C₂×Q₈	C₂²×C₄×C₅	1	1	yes	characteristic
460	C₂×D₄	—	2	1	no	—
461	C₂×D₄	C₂²×C₄×C₅	1	1	yes	characteristic
462	C₂²×C₄	—	2	1	no	—
463	C₂²×C₄	—	2	1	no	—
464	C₂²×C₄	—	2	1	no	—
465	C₂²×C₄	—	2	1	no	—
466	C₂²×C₄	—	2	1	no	—
467	C₂²×C₄	C₅×#41	1	1	yes	characteristic
468	C₂²×C₄	C₅×#41	1	1	yes	characteristic
469	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
470	M₁₆	—	2	1	no	—
471	M₁₆	—	2	1	no	—
472	M₁₆	—	2	1	no	—
473	M₁₆	—	2	1	no	—
474	M₁₆	—	2	1	no	—
475	M₁₆	—	2	1	no	—
476	M₁₆	—	2	1	no	—
477	M₁₆	C₅×#41	1	2	yes	—
478	C₂×C₈	—	2	1	no	—
479	C₂×C₈	—	2	1	no	—
480	C₂×C₈	—	2	1	no	—
481	C₂×C₈	—	2	1	no	—
482	C₂×C₈	—	2	1	no	—
483	C₂×C₈	—	2	1	no	—
484	C₂×C₈	—	2	1	no	—
485	C₂×C₈	—	2	1	no	—
486	C₂×C₈	—	2	1	no	—
487	C₂×C₈	—	2	1	no	—
488	C₂×C₈	—	2	1	no	—
489	C₂×C₈	—	2	1	no	—
490	C₂×C₈	C₂²×C₄×C₅	1	1	yes	characteristic
491	C₂×C₈	C₂²×C₄×C₅	1	1	yes	characteristic
492	C₂×C₈	C₂²×C₄×C₅	1	1	yes	characteristic
493	C₂×C₈	C₂²×C₄×C₅	1	1	yes	characteristic
494	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
495	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
496	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
497	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
498	C₄⋊C₄	—	2	1	no	—
499	C₄⋊C₄	—	2	1	no	—
500	C₄⋊C₄	—	2	1	no	—
501	C₄⋊C₄	—	2	1	no	—
502	C₄⋊C₄	—	2	1	no	—
503	C₄⋊C₄	—	2	1	no	—
504	C₄⋊C₄	—	2	1	no	—
505	C₄⋊C₄	—	2	1	no	—
506	C₄⋊C₄	C₂²×C₄×C₅	1	1	yes	characteristic
507	C₄⋊C₄	C₂²×C₄×C₅	1	1	yes	characteristic
508	C₄⋊C₄	C₂²×C₄×C₅	1	1	yes	characteristic
509	C₄⋊C₄	C₂²×C₄×C₅	1	1	yes	characteristic
510	C₄⋊C₄	C₂²×C₄×C₅	1	1	yes	characteristic
511	C₄⋊C₄	C₂²×C₄×C₅	1	1	yes	characteristic
512	C₂²⋊C₄	—	2	1	no	—
513	C₂²⋊C₄	—	2	1	no	—
514	C₂²⋊C₄	—	2	1	no	—
515	C₂²⋊C₄	—	2	1	no	—
516	C₂²⋊C₄	—	2	1	no	—
517	C₄²	—	2	1	no	—
518	C₄²	—	2	1	no	—
519	C₄²	—	2	1	no	—
520	C₄²	—	2	1	no	—
521	C₄²	—	2	1	no	—
522	C₄²	—	2	1	no	—
523	C₄²	—	2	1	no	—
524	C₄²	—	2	1	no	—
525	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
526	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
527	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
528	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
529	C₄²	C₅×#41	1	2	yes	—
530	C₂×C₅	—	2	1	no	—
531	C₂×C₅	—	2	1	no	—
532	C₂×C₅	—	8	1	no	—
533	C₂×C₅	#2362	1	1	yes	characteristic
534	C₂×C₅	#2955	1	1	yes	characteristic
535	C₂×C₅	#2957	1	1	yes	characteristic
536	C₂³	—	2	1	no	—
537	C₂³	C₂×C₅×#41	1	1	yes	characteristic
538	Q₈	—	2	1	no	—
539	Q₈	—	2	1	no	—
540	Q₈	—	4	2	no	—
541	Q₈	—	8	1	no	—
542	D₄	—	2	1	no	—
543	D₄	—	2	1	no	—
544	D₄	—	4	1	no	—
545	D₄	—	4	1	no	—
546	C₂×C₄	—	2	1	no	—
547	C₂×C₄	—	2	1	no	—
548	C₂×C₄	—	2	1	no	—
549	C₂×C₄	—	2	1	no	—
550	C₂×C₄	—	2	1	no	—
551	C₂×C₄	—	2	1	no	—
552	C₂×C₄	—	2	1	no	—
553	C₂×C₄	—	2	2	no	—
554	C₂×C₄	—	4	1	no	—
555	C₂×C₄	—	4	1	no	—
556	C₂×C₄	—	4	2	no	—
557	C₂×C₄	—	4	1	no	—
558	C₂×C₄	—	4	1	no	—
559	C₂×C₄	—	4	1	no	—
560	C₂×C₄	—	4	1	no	—
561	C₂×C₄	—	4	1	no	—
562	C₂×C₄	—	4	1	no	—
563	C₂×C₄	—	4	1	no	—
564	C₂×C₄	—	8	1	no	—
565	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
566	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
567	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
568	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
569	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
570	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
571	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
572	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
573	C₂×C₄	C₅×2₋¹⁺⁴	1	1	yes	characteristic
574	C₂×C₄	C₅×2₋¹⁺⁴	1	1	yes	characteristic
575	C₈	—	2	1	no	—
576	C₈	—	2	1	no	—
577	C₈	—	2	1	no	—
578	C₈	—	2	1	no	—
579	C₈	—	2	1	no	—
580	C₈	—	2	1	no	—
581	C₈	—	2	1	no	—
582	C₈	—	2	1	no	—
583	C₈	—	2	2	no	—
584	C₈	—	4	1	no	—
585	C₈	—	4	1	no	—
586	C₈	—	4	1	no	—
587	C₅	#23082	1	1	yes	characteristic, direct product factor, Sylow
588	C₂²	—	2	1	no	—
589	C₂²	—	2	1	no	—
590	C₂²	—	4	1	no	—
591	C₂²	—	4	1	no	—
592	C₂²	—	4	1	no	—
593	C₂²	C₂×C₄×C₅×D₄	1	1	yes	characteristic
594	C₂²	C₅×#552	1	1	yes	characteristic
595	C₂²	C₅×#556	1	1	yes	characteristic
596	C₄	—	2	1	no	—
597	C₄	—	2	1	no	—
598	C₄	—	2	1	no	—
599	C₄	—	2	1	no	—
600	C₄	—	4	2	no	—
601	C₄	—	4	1	no	—
602	C₄	—	4	1	no	—
603	C₄	—	4	1	no	—
604	C₄	—	4	1	no	—
605	C₄	—	4	1	no	—
606	C₄	—	4	1	no	—
607	C₄	—	4	1	no	—
608	C₄	—	8	1	no	—
609	C₄	C₄×C₅×#41	1	1	yes	characteristic
610	C₄	C₅×#519	1	1	yes	characteristic
611	C₄	C₅×#547	1	1	yes	characteristic
612	C₄	C₅×#548	1	1	yes	characteristic
613	C₂	—	2	1	no	—
614	C₂	—	2	1	no	—
615	C₂	—	8	1	no	—
616	C₂	C₅×#2362	1	1	yes	characteristic
617	C₂	C₅×#2955	1	1	yes	characteristic
618	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	C₂×C₅×#41	C₂³
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×#2962	C₂	semidirect
4. C₅×#1995	C₂	semidirect
5. C₅×#1950	C₂	semidirect
10. C₅×#1922	C₂	semidirect
11. C₅×#1922	C₂	semidirect
12. C₅×#1773	C₂	semidirect
13. C₅×#1772	C₂	semidirect
14. C₅×#1768	C₂	semidirect
18. C₅×#479	C₄	semidirect
19. C₅×#479	C₄	semidirect
20. C₅×#478	C₄	semidirect
21. C₅×#478	C₄	semidirect
22. C₅×#477	C₄	semidirect
23. C₅×#476	C₄	semidirect
24. C₅×#475	C₄	semidirect
25. C₅×#474	C₄	semidirect
67. #23082	C₅	direct (N × H)
152. #2962	C₂×C₅	semidirect
154. #1995	C₂×C₅	semidirect
155. #1950	C₂×C₅	semidirect
160. #1922	C₂×C₅	semidirect
161. #1922	C₂×C₅	semidirect
162. #1773	C₂×C₅	semidirect
163. #1772	C₂×C₅	semidirect
164. #1768	C₂×C₅	semidirect
245. #479	C₄×C₅	semidirect
246. #479	C₄×C₅	semidirect
247. #478	C₄×C₅	semidirect
248. #478	C₄×C₅	semidirect
249. #477	C₄×C₅	semidirect
250. #476	C₄×C₅	semidirect
251. #475	C₄×C₅	semidirect
252. #474	C₄×C₅	semidirect
587. C₅	#23082	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×#3076	2
C₅×#2962	2
C₅×#2925	2
C₅×#1995	2
C₅×#1950	2
C₅×#1938	2
C₅×#1937	2
C₅×#1929	2
C₅×#1922	2
C₅×#1773	2
C₅×#1772	2
C₅×#1768	2
C₅×#1759	2
#23082	5

Subgroups — C5×#23082 #11945802

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#23082 #11945802