Subgroups — C₅×#29557 #11952277

Order 1280.

742 conjugacy classes of subgroups.

The subgroup lattice has 630 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#2861	C₂	1	1	yes	maximal, characteristic
2	C₅×#2295	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#2059	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#2042	C₂	1	1	yes	maximal, characteristic
5	C₅×#2026	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#2015	C₂	1	1	yes	maximal, characteristic
7	C₅×#1969	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#1968	C₂	1	1	yes	maximal, characteristic
9	C₅×#1934	C₂	1	1	yes	maximal, characteristic
10	C₅×#1933	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#1927	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#1925	C₂	1	1	yes	maximal, characteristic
13	C₅×#1880	C₂	1	1	yes	maximal, characteristic
14	C₅×#1878	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅×#1744	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₅×Q₁₆	C₂²	1	1	yes	characteristic
17	C₂²×C₅×SD₁₆	C₂²	1	1	yes	characteristic
18	C₂×C₅×#125	C₂²	1	1	yes	characteristic
19	C₂×C₅×#124	C₂²	1	1	yes	characteristic
20	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
21	C₂×C₅×#107	C₂²	1	1	yes	characteristic
22	C₂×C₅×#106	C₂²	1	1	yes	characteristic
23	C₂×C₅×#103	C₂²	1	1	yes	characteristic
24	C₂×C₅×#103	C₂²	1	1	yes	characteristic
25	C₂×C₅×#103	C₂²	1	1	yes	characteristic
26	C₂×C₅×#103	C₂²	1	1	yes	characteristic
27	C₂×C₅×#103	C₂²	1	1	yes	characteristic
28	C₂×C₅×#102	C₂²	1	1	yes	characteristic
29	C₂×C₅×#102	C₂²	1	1	yes	characteristic
30	C₂×C₅×#102	C₂²	1	1	yes	characteristic
31	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
32	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
33	C₅×#391	C₂²	1	1	yes	characteristic
34	C₅×#391	C₂²	1	1	yes	characteristic
35	C₅×#391	C₂²	1	1	yes	characteristic
36	C₅×#391	C₂²	1	1	yes	characteristic
37	C₅×#390	C₂²	1	1	yes	characteristic
38	C₅×#390	C₂²	1	1	yes	characteristic
39	C₅×#389	C₂²	1	1	yes	characteristic
40	C₅×#389	C₂²	1	1	yes	characteristic
41	C₅×#388	—	2	1	no	—
42	C₅×#388	—	2	1	no	—
43	C₅×#388	—	2	1	no	—
44	C₅×#388	—	2	1	no	—
45	C₅×#387	—	2	1	no	—
46	C₅×#387	—	2	1	no	—
47	C₄×C₅×C₄⋊C₄	—	2	1	no	—
48	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
49	C₅×#376	—	2	1	no	—
50	C₄³×C₅	C₂²	1	1	yes	characteristic
51	C₅×#340	C₂²	1	1	yes	characteristic
52	C₅×#340	C₂²	1	1	yes	characteristic
53	C₅×#340	C₂²	1	1	yes	characteristic
54	C₅×#340	C₂²	1	1	yes	characteristic
55	C₅×#336	C₂²	1	1	yes	characteristic
56	C₅×#336	C₂²	1	1	yes	characteristic
57	C₅×#336	C₂²	1	1	yes	characteristic
58	C₅×#336	C₂²	1	1	yes	characteristic
59	#29557	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
60	C₂²×C₅×Q₈	C₂³	1	1	yes	characteristic
61	C₂²×C₅×Q₈	C₂³	1	1	yes	characteristic
62	C₂²×C₅×D₄	C₂³	1	1	yes	characteristic
63	C₂×C₅×Q₁₆	—	2	2	no	—
64	C₂×C₅×Q₁₆	—	2	2	no	—
65	C₂×C₅×Q₁₆	—	4	1	no	—
66	C₂×C₅×SD₁₆	—	2	2	no	—
67	C₂×C₅×SD₁₆	—	2	2	no	—
68	C₂×C₅×SD₁₆	—	4	1	no	—
69	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
70	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
71	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
72	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
73	C₅×#125	—	4	1	no	—
74	C₅×#125	—	4	1	no	—
75	C₅×#124	—	4	1	no	—
76	C₅×#124	—	4	1	no	—
77	C₄×C₅×Q₈	—	2	2	no	—
78	C₄×C₅×Q₈	—	2	2	no	—
79	C₂×C₅×C₄⋊C₄	—	2	1	no	—
80	C₂×C₅×C₄⋊C₄	—	2	1	no	—
81	C₂×C₅×C₄⋊C₄	—	2	1	no	—
82	C₂×C₅×C₄⋊C₄	—	2	1	no	—
83	C₂×C₅×C₄⋊C₄	—	2	1	no	—
84	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
85	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
86	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
87	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
88	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
89	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
90	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
91	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
92	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
93	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
94	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
95	C₂×C₄²×C₅	—	2	1	no	—
96	C₂×C₄²×C₅	—	2	1	no	—
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	1	yes	characteristic
102	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
103	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
104	C₅×#107	—	4	1	no	—
105	C₅×#106	—	4	1	no	—
106	C₅×#103	—	2	2	no	—
107	C₅×#103	—	2	2	no	—
108	C₅×#103	—	4	1	no	—
109	C₅×#103	—	4	1	no	—
110	C₅×#103	—	4	1	no	—
111	C₅×#102	—	2	2	no	—
112	C₅×#102	—	2	2	no	—
113	C₅×#102	—	4	1	no	—
114	C₄×C₅×C₈	—	2	2	no	—
115	C₄×C₅×C₈	—	2	2	no	—
116	C₅×#95	—	2	1	no	—
117	C₅×#95	—	2	1	no	—
118	C₅×#95	—	2	1	no	—
119	C₅×#95	—	2	1	no	—
120	C₅×#95	—	2	1	no	—
121	C₅×#95	—	2	1	no	—
122	C₅×#95	—	2	1	no	—
123	C₅×#95	—	2	1	no	—
124	C₅×#95	—	2	1	no	—
125	C₅×#95	—	2	1	no	—
126	C₅×#95	—	2	1	no	—
127	#2861	C₂×C₅	1	1	yes	characteristic
128	#2295	C₂×C₅	1	1	yes	characteristic, complemented
129	#2059	C₂×C₅	1	1	yes	characteristic, complemented
130	#2042	C₂×C₅	1	1	yes	characteristic
131	#2026	C₂×C₅	1	1	yes	characteristic, complemented
132	#2015	C₂×C₅	1	1	yes	characteristic
133	#1969	C₂×C₅	1	1	yes	characteristic, complemented
134	#1968	C₂×C₅	1	1	yes	characteristic
135	#1934	C₂×C₅	1	1	yes	characteristic
136	#1933	C₂×C₅	1	1	yes	characteristic, complemented
137	#1927	C₂×C₅	1	1	yes	characteristic, complemented
138	#1925	C₂×C₅	1	1	yes	characteristic
139	#1880	C₂×C₅	1	1	yes	characteristic
140	#1878	C₂×C₅	1	1	yes	characteristic, complemented
141	#1744	C₂×C₅	1	1	yes	characteristic, complemented
142	C₂⁴×C₅	—	2	1	no	—
143	C₂×C₅×Q₈	—	2	1	no	—
144	C₂×C₅×Q₈	—	2	1	no	—
145	C₂×C₅×Q₈	—	2	1	no	—
146	C₂×C₅×Q₈	—	2	1	no	—
147	C₂×C₅×Q₈	—	2	1	no	—
148	C₂×C₅×Q₈	—	2	1	no	—
149	C₂×C₅×Q₈	—	2	1	no	—
150	C₂×C₅×Q₈	—	2	1	no	—
151	C₂×C₅×Q₈	—	2	1	no	—
152	C₂×C₅×Q₈	—	2	1	no	—
153	C₂×C₅×Q₈	—	2	1	no	—
154	C₂×C₅×Q₈	#41	1	2	yes	—
155	C₂×C₅×D₄	—	2	1	no	—
156	C₂×C₅×D₄	—	2	1	no	—
157	C₂×C₅×D₄	—	2	1	no	—
158	C₂×C₅×D₄	—	2	1	no	—
159	C₂×C₅×D₄	—	2	1	no	—
160	C₂×C₅×D₄	—	2	1	no	—
161	C₂²×C₄×C₅	—	2	1	no	—
162	C₂²×C₄×C₅	—	2	1	no	—
163	C₂²×C₄×C₅	—	2	1	no	—
164	C₂²×C₄×C₅	—	2	1	no	—
165	C₂²×C₄×C₅	—	2	1	no	—
166	C₂²×C₄×C₅	—	2	1	no	—
167	C₂²×C₄×C₅	—	2	1	no	—
168	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
169	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
170	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
171	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
172	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
173	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
174	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
175	C₅×Q₁₆	—	4	4	no	—
176	C₅×SD₁₆	—	4	4	no	—
177	C₂×C₅×C₈	—	2	1	no	—
178	C₂×C₅×C₈	—	2	1	no	—
179	C₂×C₅×C₈	—	2	1	no	—
180	C₂×C₅×C₈	—	2	1	no	—
181	C₂×C₅×C₈	—	2	1	no	—
182	C₂×C₅×C₈	—	2	1	no	—
183	C₂×C₅×C₈	—	2	1	no	—
184	C₂×C₅×C₈	—	2	1	no	—
185	C₂×C₅×C₈	—	2	1	no	—
186	C₂×C₅×C₈	—	2	1	no	—
187	C₂×C₅×C₈	#41	1	2	yes	—
188	C₂×C₅×C₈	#41	1	2	yes	—
189	C₅×C₄⋊C₄	—	2	4	no	—
190	C₅×C₄⋊C₄	—	2	1	no	—
191	C₅×C₄⋊C₄	—	2	1	no	—
192	C₅×C₄⋊C₄	—	2	1	no	—
193	C₅×C₄⋊C₄	—	2	1	no	—
194	C₅×C₄⋊C₄	—	2	1	no	—
195	C₅×C₄⋊C₄	—	2	1	no	—
196	C₅×C₄⋊C₄	—	2	1	no	—
197	C₅×C₄⋊C₄	—	2	1	no	—
198	C₅×C₄⋊C₄	—	2	1	no	—
199	C₅×C₄⋊C₄	—	4	2	no	—
200	C₅×C₄⋊C₄	—	4	2	no	—
201	C₅×C₄⋊C₄	—	4	2	no	—
202	C₅×C₄⋊C₄	—	4	2	no	—
203	C₅×C₄⋊C₄	#41	1	2	yes	—
204	C₅×C₂²⋊C₄	—	4	2	no	—
205	C₅×C₂²⋊C₄	—	4	2	no	—
206	C₅×C₂²⋊C₄	—	4	2	no	—
207	C₅×C₂²⋊C₄	—	4	2	no	—
208	C₅×C₂²⋊C₄	—	4	2	no	—
209	C₅×C₂²⋊C₄	—	4	2	no	—
210	C₄²×C₅	—	2	4	no	—
211	C₄²×C₅	—	2	2	no	—
212	C₄²×C₅	—	2	2	no	—
213	C₄²×C₅	—	2	2	no	—
214	C₄²×C₅	—	2	1	no	—
215	C₄²×C₅	—	2	1	no	—
216	C₄²×C₅	—	2	1	no	—
217	C₄²×C₅	—	2	1	no	—
218	C₄²×C₅	—	2	1	no	—
219	C₄²×C₅	—	2	1	no	—
220	C₄²×C₅	—	4	1	no	—
221	C₄²×C₅	—	4	2	no	—
222	C₂²×Q₁₆	C₂²×C₅	1	1	yes	characteristic
223	C₂²×SD₁₆	C₂²×C₅	1	1	yes	characteristic
224	C₂×#125	C₂²×C₅	1	1	yes	characteristic
225	C₂×#124	C₂²×C₅	1	1	yes	characteristic
226	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
227	C₂×#107	C₂²×C₅	1	1	yes	characteristic
228	C₂×#106	C₂²×C₅	1	1	yes	characteristic
229	C₂×#103	C₂²×C₅	1	1	yes	characteristic
230	C₂×#103	C₂²×C₅	1	1	yes	characteristic
231	C₂×#103	C₂²×C₅	1	1	yes	characteristic
232	C₂×#103	C₂²×C₅	1	1	yes	characteristic
233	C₂×#103	C₂²×C₅	1	1	yes	characteristic
234	C₂×#102	C₂²×C₅	1	1	yes	characteristic
235	C₂×#102	C₂²×C₅	1	1	yes	characteristic
236	C₂×#102	C₂²×C₅	1	1	yes	characteristic
237	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
238	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
239	#391	C₂²×C₅	1	1	yes	characteristic
240	#391	C₂²×C₅	1	1	yes	characteristic
241	#391	C₂²×C₅	1	1	yes	characteristic
242	#391	C₂²×C₅	1	1	yes	characteristic
243	#390	C₂²×C₅	1	1	yes	characteristic
244	#390	C₂²×C₅	1	1	yes	characteristic
245	#389	C₂²×C₅	1	1	yes	characteristic
246	#389	C₂²×C₅	1	1	yes	characteristic
247	#388	—	2	1	no	—
248	#388	—	2	1	no	—
249	#388	—	2	1	no	—
250	#388	—	2	1	no	—
251	#387	—	2	1	no	—
252	#387	—	2	1	no	—
253	C₄×C₄⋊C₄	—	2	1	no	—
254	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
255	#376	—	2	1	no	—
256	C₄³	C₂²×C₅	1	1	yes	characteristic
257	#340	C₂²×C₅	1	1	yes	characteristic
258	#340	C₂²×C₅	1	1	yes	characteristic
259	#340	C₂²×C₅	1	1	yes	characteristic
260	#340	C₂²×C₅	1	1	yes	characteristic
261	#336	C₂²×C₅	1	1	yes	characteristic
262	#336	C₂²×C₅	1	1	yes	characteristic
263	#336	C₂²×C₅	1	1	yes	characteristic
264	#336	C₂²×C₅	1	1	yes	characteristic
265	C₂³×C₅	—	4	1	no	—
266	C₂³×C₅	—	4	1	no	—
267	C₂³×C₅	—	4	1	no	—
268	C₂³×C₅	—	4	1	no	—
269	C₂³×C₅	—	4	1	no	—
270	C₂³×C₅	—	4	1	no	—
271	C₂³×C₅	—	4	1	no	—
272	C₂³×C₅	C₂²×D₄	1	1	yes	characteristic
273	C₅×Q₈	—	2	2	no	—
274	C₅×Q₈	—	2	2	no	—
275	C₅×Q₈	—	4	1	no	—
276	C₅×Q₈	—	4	1	no	—
277	C₅×Q₈	—	4	1	no	—
278	C₅×Q₈	—	4	1	no	—
279	C₅×Q₈	—	4	1	no	—
280	C₅×Q₈	—	4	1	no	—
281	C₅×D₄	—	4	1	no	—
282	C₅×D₄	—	4	1	no	—
283	C₅×D₄	—	4	1	no	—
284	C₅×D₄	—	4	1	no	—
285	C₂×C₄×C₅	—	2	1	no	—
286	C₂×C₄×C₅	—	2	1	no	—
287	C₂×C₄×C₅	—	2	1	no	—
288	C₂×C₄×C₅	—	2	1	no	—
289	C₂×C₄×C₅	—	2	1	no	—
290	C₂×C₄×C₅	—	2	1	no	—
291	C₂×C₄×C₅	—	2	1	no	—
292	C₂×C₄×C₅	—	2	2	no	—
293	C₂×C₄×C₅	—	2	2	no	—
294	C₂×C₄×C₅	—	2	1	no	—
295	C₂×C₄×C₅	—	2	1	no	—
296	C₂×C₄×C₅	—	2	1	no	—
297	C₂×C₄×C₅	—	2	1	no	—
298	C₂×C₄×C₅	—	2	1	no	—
299	C₂×C₄×C₅	—	2	1	no	—
300	C₂×C₄×C₅	—	2	1	no	—
301	C₂×C₄×C₅	—	2	1	no	—
302	C₂×C₄×C₅	—	4	1	no	—
303	C₂×C₄×C₅	—	4	1	no	—
304	C₂×C₄×C₅	—	4	1	no	—
305	C₂×C₄×C₅	—	4	1	no	—
306	C₂×C₄×C₅	—	4	1	no	—
307	C₂×C₄×C₅	—	4	1	no	—
308	C₂×C₄×C₅	—	4	1	no	—
309	C₂×C₄×C₅	—	4	1	no	—
310	C₂×C₄×C₅	—	4	1	no	—
311	C₂×C₄×C₅	—	4	1	no	—
312	C₂×C₄×C₅	—	4	1	no	—
313	C₂×C₄×C₅	—	4	1	no	—
314	C₂×C₄×C₅	—	4	1	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	#135	1	2	yes	—
322	C₂×C₄×C₅	#135	1	2	yes	—
323	C₂×C₄×C₅	#137	1	2	yes	—
324	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
325	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
326	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
327	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
328	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
329	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
330	C₅×C₈	—	2	2	no	—
331	C₅×C₈	—	2	2	no	—
332	C₅×C₈	—	4	1	no	—
333	C₅×C₈	—	4	1	no	—
334	C₂²×Q₈	C₂³×C₅	1	1	yes	characteristic
335	C₂²×Q₈	C₂³×C₅	1	1	yes	characteristic
336	C₂²×D₄	C₂³×C₅	1	1	yes	characteristic
337	C₂×Q₁₆	—	2	2	no	—
338	C₂×Q₁₆	—	2	2	no	—
339	C₂×Q₁₆	—	4	1	no	—
340	C₂×SD₁₆	—	2	2	no	—
341	C₂×SD₁₆	—	2	2	no	—
342	C₂×SD₁₆	—	4	1	no	—
343	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
344	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
345	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
346	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
347	#125	—	4	1	no	—
348	#125	—	4	1	no	—
349	#124	—	4	1	no	—
350	#124	—	4	1	no	—
351	C₄×Q₈	—	2	2	no	—
352	C₄×Q₈	—	2	2	no	—
353	C₂×C₄⋊C₄	—	2	1	no	—
354	C₂×C₄⋊C₄	—	2	1	no	—
355	C₂×C₄⋊C₄	—	2	1	no	—
356	C₂×C₄⋊C₄	—	2	1	no	—
357	C₂×C₄⋊C₄	—	2	1	no	—
358	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
359	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
360	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
361	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
362	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
363	C₂×C₂²⋊C₄	—	2	1	no	—
364	C₂×C₂²⋊C₄	—	2	1	no	—
365	C₂×C₂²⋊C₄	—	2	1	no	—
366	C₂×C₂²⋊C₄	—	2	1	no	—
367	C₂×C₂²⋊C₄	—	2	1	no	—
368	C₂×C₂²⋊C₄	—	2	1	no	—
369	C₂×C₄²	—	2	1	no	—
370	C₂×C₄²	—	2	1	no	—
371	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
372	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
373	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
374	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
375	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
376	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
377	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
378	#107	—	4	1	no	—
379	#106	—	4	1	no	—
380	#103	—	2	2	no	—
381	#103	—	2	2	no	—
382	#103	—	4	1	no	—
383	#103	—	4	1	no	—
384	#103	—	4	1	no	—
385	#102	—	2	2	no	—
386	#102	—	2	2	no	—
387	#102	—	4	1	no	—
388	C₄×C₈	—	2	2	no	—
389	C₄×C₈	—	2	2	no	—
390	#95	—	2	1	no	—
391	#95	—	2	1	no	—
392	#95	—	2	1	no	—
393	#95	—	2	1	no	—
394	#95	—	2	1	no	—
395	#95	—	2	1	no	—
396	#95	—	2	1	no	—
397	#95	—	2	1	no	—
398	#95	—	2	1	no	—
399	#95	—	2	1	no	—
400	#95	—	2	1	no	—
401	C₂²×C₅	—	8	1	no	—
402	C₂²×C₅	—	8	1	no	—
403	C₂²×C₅	—	8	1	no	—
404	C₂²×C₅	—	8	1	no	—
405	C₂²×C₅	—	8	1	no	—
406	C₂²×C₅	—	8	1	no	—
407	C₂²×C₅	—	8	1	no	—
408	C₂²×C₅	#525	1	1	yes	characteristic
409	C₂²×C₅	#532	1	1	yes	characteristic
410	C₂²×C₅	#535	1	1	yes	characteristic
411	C₂²×C₅	C₂×#135	1	1	yes	characteristic
412	C₂²×C₅	C₂×#135	1	1	yes	characteristic
413	C₂²×C₅	C₂×#137	1	1	yes	characteristic
414	C₂²×C₅	#575	1	1	yes	characteristic
415	C₄×C₅	—	2	2	no	—
416	C₄×C₅	—	2	2	no	—
417	C₄×C₅	—	2	2	no	—
418	C₄×C₅	—	4	1	no	—
419	C₄×C₅	—	4	2	no	—
420	C₄×C₅	—	4	2	no	—
421	C₄×C₅	—	4	1	no	—
422	C₄×C₅	—	4	1	no	—
423	C₄×C₅	—	8	1	no	—
424	C₄×C₅	—	8	1	no	—
425	C₄×C₅	—	8	1	no	—
426	C₄×C₅	—	8	1	no	—
427	C₄×C₅	—	8	1	no	—
428	C₄×C₅	#551	1	1	yes	characteristic
429	C₄×C₅	#551	1	1	yes	characteristic
430	C₄×C₅	#555	1	1	yes	characteristic
431	C₄×C₅	#555	1	1	yes	characteristic
432	C₂⁴	—	2	1	no	—
433	C₂×Q₈	—	2	1	no	—
434	C₂×Q₈	—	2	1	no	—
435	C₂×Q₈	—	2	1	no	—
436	C₂×Q₈	—	2	1	no	—
437	C₂×Q₈	—	2	1	no	—
438	C₂×Q₈	—	2	1	no	—
439	C₂×Q₈	—	2	1	no	—
440	C₂×Q₈	—	2	1	no	—
441	C₂×Q₈	—	2	1	no	—
442	C₂×Q₈	—	2	1	no	—
443	C₂×Q₈	—	2	1	no	—
444	C₂×Q₈	C₅×#41	1	2	yes	—
445	C₂×D₄	—	2	1	no	—
446	C₂×D₄	—	2	1	no	—
447	C₂×D₄	—	2	1	no	—
448	C₂×D₄	—	2	1	no	—
449	C₂×D₄	—	2	1	no	—
450	C₂×D₄	—	2	1	no	—
451	C₂²×C₄	—	2	1	no	—
452	C₂²×C₄	—	2	1	no	—
453	C₂²×C₄	—	2	1	no	—
454	C₂²×C₄	—	2	1	no	—
455	C₂²×C₄	—	2	1	no	—
456	C₂²×C₄	—	2	1	no	—
457	C₂²×C₄	—	2	1	no	—
458	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
459	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
460	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
461	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
462	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
463	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
464	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
465	Q₁₆	—	4	4	no	—
466	SD₁₆	—	4	4	no	—
467	C₂×C₈	—	2	1	no	—
468	C₂×C₈	—	2	1	no	—
469	C₂×C₈	—	2	1	no	—
470	C₂×C₈	—	2	1	no	—
471	C₂×C₈	—	2	1	no	—
472	C₂×C₈	—	2	1	no	—
473	C₂×C₈	—	2	1	no	—
474	C₂×C₈	—	2	1	no	—
475	C₂×C₈	—	2	1	no	—
476	C₂×C₈	—	2	1	no	—
477	C₂×C₈	C₅×#41	1	2	yes	—
478	C₂×C₈	C₅×#41	1	2	yes	—
479	C₄⋊C₄	—	2	4	no	—
480	C₄⋊C₄	—	2	1	no	—
481	C₄⋊C₄	—	2	1	no	—
482	C₄⋊C₄	—	2	1	no	—
483	C₄⋊C₄	—	2	1	no	—
484	C₄⋊C₄	—	2	1	no	—
485	C₄⋊C₄	—	2	1	no	—
486	C₄⋊C₄	—	2	1	no	—
487	C₄⋊C₄	—	2	1	no	—
488	C₄⋊C₄	—	2	1	no	—
489	C₄⋊C₄	—	4	2	no	—
490	C₄⋊C₄	—	4	2	no	—
491	C₄⋊C₄	—	4	2	no	—
492	C₄⋊C₄	—	4	2	no	—
493	C₄⋊C₄	C₅×#41	1	2	yes	—
494	C₂²⋊C₄	—	4	2	no	—
495	C₂²⋊C₄	—	4	2	no	—
496	C₂²⋊C₄	—	4	2	no	—
497	C₂²⋊C₄	—	4	2	no	—
498	C₂²⋊C₄	—	4	2	no	—
499	C₂²⋊C₄	—	4	2	no	—
500	C₄²	—	2	4	no	—
501	C₄²	—	2	2	no	—
502	C₄²	—	2	2	no	—
503	C₄²	—	2	2	no	—
504	C₄²	—	2	1	no	—
505	C₄²	—	2	1	no	—
506	C₄²	—	2	1	no	—
507	C₄²	—	2	1	no	—
508	C₄²	—	2	1	no	—
509	C₄²	—	2	1	no	—
510	C₄²	—	4	1	no	—
511	C₄²	—	4	2	no	—
512	C₂×C₅	—	16	1	no	—
513	C₂×C₅	#2610	1	1	yes	characteristic
514	C₂×C₅	#3102	1	1	yes	characteristic
515	C₂×C₅	#3108	1	1	yes	characteristic
516	C₂×C₅	#3168	1	1	yes	characteristic
517	C₂×C₅	#3181	1	1	yes	characteristic
518	C₂×C₅	#3210	1	1	yes	characteristic
519	C₂×C₅	#3212	1	1	yes	characteristic
520	C₂³	—	4	1	no	—
521	C₂³	—	4	1	no	—
522	C₂³	—	4	1	no	—
523	C₂³	—	4	1	no	—
524	C₂³	—	4	1	no	—
525	C₂³	—	4	1	no	—
526	C₂³	—	4	1	no	—
527	C₂³	C₂²×C₅×D₄	1	1	yes	characteristic
528	Q₈	—	2	2	no	—
529	Q₈	—	2	2	no	—
530	Q₈	—	4	1	no	—
531	Q₈	—	4	1	no	—
532	Q₈	—	4	1	no	—
533	Q₈	—	4	1	no	—
534	Q₈	—	4	1	no	—
535	Q₈	—	4	1	no	—
536	D₄	—	4	1	no	—
537	D₄	—	4	1	no	—
538	D₄	—	4	1	no	—
539	D₄	—	4	1	no	—
540	C₂×C₄	—	2	1	no	—
541	C₂×C₄	—	2	1	no	—
542	C₂×C₄	—	2	1	no	—
543	C₂×C₄	—	2	1	no	—
544	C₂×C₄	—	2	1	no	—
545	C₂×C₄	—	2	1	no	—
546	C₂×C₄	—	2	1	no	—
547	C₂×C₄	—	2	2	no	—
548	C₂×C₄	—	2	2	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	1	no	—
554	C₂×C₄	—	2	1	no	—
555	C₂×C₄	—	2	1	no	—
556	C₂×C₄	—	2	1	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	—	4	1	no	—
565	C₂×C₄	—	4	1	no	—
566	C₂×C₄	—	4	1	no	—
567	C₂×C₄	—	4	1	no	—
568	C₂×C₄	—	4	1	no	—
569	C₂×C₄	—	4	1	no	—
570	C₂×C₄	—	4	1	no	—
571	C₂×C₄	—	4	1	no	—
572	C₂×C₄	—	4	1	no	—
573	C₂×C₄	—	4	1	no	—
574	C₂×C₄	—	4	1	no	—
575	C₂×C₄	—	4	1	no	—
576	C₂×C₄	C₅×#135	1	2	yes	—
577	C₂×C₄	C₅×#135	1	2	yes	—
578	C₂×C₄	C₅×#137	1	2	yes	—
579	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
580	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
581	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
582	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
583	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
584	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
585	C₈	—	2	2	no	—
586	C₈	—	2	2	no	—
587	C₈	—	4	1	no	—
588	C₈	—	4	1	no	—
589	C₅	#29557	1	1	yes	characteristic, direct product factor, Sylow
590	C₂²	—	8	1	no	—
591	C₂²	—	8	1	no	—
592	C₂²	—	8	1	no	—
593	C₂²	—	8	1	no	—
594	C₂²	—	8	1	no	—
595	C₂²	—	8	1	no	—
596	C₂²	—	8	1	no	—
597	C₂²	C₅×#525	1	1	yes	characteristic
598	C₂²	C₅×#532	1	1	yes	characteristic
599	C₂²	C₅×#535	1	1	yes	characteristic
600	C₂²	C₂×C₅×#135	1	1	yes	characteristic
601	C₂²	C₂×C₅×#135	1	1	yes	characteristic
602	C₂²	C₂×C₅×#137	1	1	yes	characteristic
603	C₂²	C₅×#575	1	1	yes	characteristic
604	C₄	—	2	2	no	—
605	C₄	—	2	2	no	—
606	C₄	—	2	2	no	—
607	C₄	—	4	1	no	—
608	C₄	—	4	2	no	—
609	C₄	—	4	2	no	—
610	C₄	—	4	1	no	—
611	C₄	—	4	1	no	—
612	C₄	—	8	1	no	—
613	C₄	—	8	1	no	—
614	C₄	—	8	1	no	—
615	C₄	—	8	1	no	—
616	C₄	—	8	1	no	—
617	C₄	C₅×#551	1	1	yes	characteristic
618	C₄	C₅×#551	1	1	yes	characteristic
619	C₄	C₅×#555	1	1	yes	characteristic
620	C₄	C₅×#555	1	1	yes	characteristic
621	C₂	—	16	1	no	—
622	C₂	C₅×#2610	1	1	yes	characteristic
623	C₂	C₅×#3102	1	1	yes	characteristic
624	C₂	C₅×#3108	1	1	yes	characteristic
625	C₂	C₅×#3168	1	1	yes	characteristic
626	C₂	C₅×#3181	1	1	yes	characteristic
627	C₂	C₅×#3210	1	1	yes	characteristic
628	C₂	C₅×#3212	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₅	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₅
prime radical	C₂²×C₅×D₄	C₂³
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₅ ◁ C₄³×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₅×#2295	C₂	semidirect
3. C₅×#2059	C₂	semidirect
5. C₅×#2026	C₂	semidirect
7. C₅×#1969	C₂	semidirect
10. C₅×#1933	C₂	semidirect
11. C₅×#1927	C₂	semidirect
14. C₅×#1878	C₂	semidirect
15. C₅×#1744	C₂	semidirect
59. #29557	C₅	direct (N × H)
128. #2295	C₂×C₅	semidirect
129. #2059	C₂×C₅	semidirect
131. #2026	C₂×C₅	semidirect
133. #1969	C₂×C₅	semidirect
136. #1933	C₂×C₅	semidirect
137. #1927	C₂×C₅	semidirect
140. #1878	C₂×C₅	semidirect
141. #1744	C₂×C₅	semidirect
589. C₅	#29557	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×#2861	2
C₅×#2295	2
C₅×#2059	2
C₅×#2042	2
C₅×#2026	2
C₅×#2015	2
C₅×#1969	2
C₅×#1968	2
C₅×#1934	2
C₅×#1933	2
C₅×#1927	2
C₅×#1925	2
C₅×#1880	2
C₅×#1878	2
C₅×#1744	2
#29557	5

Subgroups — C5×#29557 #11952277

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#29557 #11952277