Subgroups — C₅×#29462 #11952182

Order 1280.

766 conjugacy classes of subgroups.

The subgroup lattice has 638 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#2855	C₂	1	1	yes	maximal, characteristic
2	C₄×C₅×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic
3	C₅×#2076	C₂	1	1	yes	maximal, characteristic
4	C₅×#2036	C₂	1	1	yes	maximal, characteristic
5	C₅×#2036	C₂	1	1	yes	maximal, characteristic
6	C₅×#2001	C₂	1	1	yes	maximal, characteristic
7	C₅×#1969	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#1942	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#1933	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#1933	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#1928	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#1921	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅×#1878	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅×#1863	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄×C₅×C₂²⋊C₈	C₂	1	1	yes	maximal, characteristic
16	C₂²×C₅×Q₁₆	C₂²	1	1	yes	characteristic
17	C₂×C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
18	C₂×C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
19	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
20	C₂²×C₄²×C₅	C₂²	1	1	yes	characteristic
21	C₂×C₅×#107	C₂²	1	1	yes	characteristic
22	C₂×C₅×#107	C₂²	1	1	yes	characteristic
23	C₂×C₅×#107	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×#103	C₂²	1	1	yes	characteristic
29	C₂×C₅×#103	C₂²	1	1	yes	characteristic
30	C₂×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic
31	C₂×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic
32	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
33	C₂×C₄×C₅×C₈	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×#389	C₂²	1	1	yes	characteristic
38	C₅×#389	C₂²	1	1	yes	characteristic
39	C₅×#389	C₂²	1	1	yes	characteristic
40	C₅×#387	—	2	1	no	—
41	C₅×#387	—	2	1	no	—
42	C₅×#387	—	2	1	no	—
43	C₅×#385	—	2	1	no	—
44	C₅×#385	—	2	1	no	—
45	C₅×#381	—	2	1	no	—
46	C₅×#380	C₂²	1	1	yes	characteristic
47	C₅×#380	C₂²	1	1	yes	characteristic
48	C₄×C₅×C₄⋊C₄	—	2	1	no	—
49	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
50	C₄×C₅×C₂²⋊C₄	—	2	1	no	—
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×#340	C₂²	1	1	yes	characteristic
56	C₅×#340	C₂²	1	1	yes	characteristic
57	C₅×#336	C₂²	1	1	yes	characteristic
58	C₅×#336	C₂²	1	1	yes	characteristic
59	#29462	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	C₂³×C₄×C₅	D₄	1	1	yes	characteristic
63	C₂³×C₄×C₅	D₄	1	1	yes	characteristic
64	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
65	C₂×C₅×Q₁₆	—	2	2	no	—
66	C₂×C₅×Q₁₆	—	2	2	no	—
67	C₂×C₅×Q₁₆	—	4	1	no	—
68	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
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	C₅×C₂²⋊Q₈	—	2	2	no	—
73	C₅×C₂²⋊Q₈	—	2	2	no	—
74	C₅×C₂²⋊Q₈	—	4	1	no	—
75	C₅×C₂²⋊Q₈	—	4	1	no	—
76	C₄×C₅×Q₈	—	4	1	no	—
77	C₄×C₅×Q₈	—	4	1	no	—
78	C₂×C₅×C₄⋊C₄	—	2	1	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×C₄⋊C₄	C₂³	1	1	yes	characteristic
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×C₄²×C₅	—	2	1	no	—
95	C₂×C₄²×C₅	—	2	1	no	—
96	C₂×C₄²×C₅	—	4	1	no	—
97	C₂×C₄²×C₅	—	4	1	no	—
98	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
99	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
100	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
101	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
102	C₅×#107	—	2	2	no	—
103	C₅×#107	—	2	2	no	—
104	C₅×#107	—	4	1	no	—
105	C₅×#103	—	2	2	no	—
106	C₅×#103	—	2	2	no	—
107	C₅×#103	—	2	2	no	—
108	C₅×#103	—	2	2	no	—
109	C₅×#103	—	4	1	no	—
110	C₅×#103	—	4	1	no	—
111	C₅×C₂²⋊C₈	—	2	2	no	—
112	C₅×C₂²⋊C₈	—	2	2	no	—
113	C₄×C₅×C₈	—	4	1	no	—
114	C₄×C₅×C₈	—	4	1	no	—
115	C₅×#95	—	2	1	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	#2855	C₂×C₅	1	1	yes	characteristic
128	C₄×C₂²⋊Q₈	C₂×C₅	1	1	yes	characteristic
129	#2076	C₂×C₅	1	1	yes	characteristic
130	#2036	C₂×C₅	1	1	yes	characteristic
131	#2036	C₂×C₅	1	1	yes	characteristic
132	#2001	C₂×C₅	1	1	yes	characteristic
133	#1969	C₂×C₅	1	1	yes	characteristic, complemented
134	#1942	C₂×C₅	1	1	yes	characteristic, complemented
135	#1933	C₂×C₅	1	1	yes	characteristic, complemented
136	#1933	C₂×C₅	1	1	yes	characteristic, complemented
137	#1928	C₂×C₅	1	1	yes	characteristic, complemented
138	#1921	C₂×C₅	1	1	yes	characteristic, complemented
139	#1878	C₂×C₅	1	1	yes	characteristic, complemented
140	#1863	C₂×C₅	1	1	yes	characteristic, complemented
141	C₄×C₂²⋊C₈	C₂×C₅	1	1	yes	characteristic
142	C₂⁴×C₅	C₂×D₄	1	1	yes	characteristic
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	C₂²×C₄×C₅	—	2	1	no	—
156	C₂²×C₄×C₅	—	2	1	no	—
157	C₂²×C₄×C₅	—	2	2	no	—
158	C₂²×C₄×C₅	—	2	1	no	—
159	C₂²×C₄×C₅	—	2	1	no	—
160	C₂²×C₄×C₅	—	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	—	2	1	no	—
169	C₂²×C₄×C₅	—	2	1	no	—
170	C₂²×C₄×C₅	—	4	1	no	—
171	C₂²×C₄×C₅	—	4	1	no	—
172	C₂²×C₄×C₅	—	4	1	no	—
173	C₂²×C₄×C₅	—	4	1	no	—
174	C₂²×C₄×C₅	Q₁₆	1	4	yes	complemented
175	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
176	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
177	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
178	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
179	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
180	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
181	C₅×Q₁₆	—	4	4	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	—	2	1	no	—
188	C₂×C₅×C₈	—	2	1	no	—
189	C₂×C₅×C₈	—	2	1	no	—
190	C₂×C₅×C₈	—	2	1	no	—
191	C₂×C₅×C₈	—	2	1	no	—
192	C₂×C₅×C₈	#41	1	2	yes	—
193	C₂×C₅×C₈	#41	1	2	yes	—
194	C₅×C₄⋊C₄	—	2	4	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	—	2	1	no	—
200	C₅×C₄⋊C₄	—	2	1	no	—
201	C₅×C₄⋊C₄	—	2	1	no	—
202	C₅×C₄⋊C₄	—	2	1	no	—
203	C₅×C₄⋊C₄	—	2	1	no	—
204	C₅×C₄⋊C₄	—	2	1	no	—
205	C₅×C₄⋊C₄	—	2	1	no	—
206	C₅×C₄⋊C₄	—	4	2	no	—
207	C₅×C₄⋊C₄	—	4	2	no	—
208	C₅×C₄⋊C₄	—	4	2	no	—
209	C₅×C₄⋊C₄	—	4	2	no	—
210	C₅×C₄⋊C₄	—	4	2	no	—
211	C₅×C₄⋊C₄	#41	1	2	yes	—
212	C₅×C₂²⋊C₄	—	2	4	no	—
213	C₅×C₂²⋊C₄	—	4	2	no	—
214	C₅×C₂²⋊C₄	—	4	2	no	—
215	C₅×C₂²⋊C₄	—	4	2	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	1	no	—
222	C₄²×C₅	—	4	2	no	—
223	C₄²×C₅	—	4	2	no	—
224	C₂²×Q₁₆	C₂²×C₅	1	1	yes	characteristic
225	C₂×C₂²⋊Q₈	C₂²×C₅	1	1	yes	characteristic
226	C₂×C₂²⋊Q₈	C₂²×C₅	1	1	yes	characteristic
227	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
228	C₂²×C₄²	C₂²×C₅	1	1	yes	characteristic
229	C₂×#107	C₂²×C₅	1	1	yes	characteristic
230	C₂×#107	C₂²×C₅	1	1	yes	characteristic
231	C₂×#107	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×#103	C₂²×C₅	1	1	yes	characteristic
235	C₂×#103	C₂²×C₅	1	1	yes	characteristic
236	C₂×#103	C₂²×C₅	1	1	yes	characteristic
237	C₂×#103	C₂²×C₅	1	1	yes	characteristic
238	C₂×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
239	C₂×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
240	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
241	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
242	#391	C₂²×C₅	1	1	yes	characteristic
243	#391	C₂²×C₅	1	1	yes	characteristic
244	#391	C₂²×C₅	1	1	yes	characteristic
245	#389	C₂²×C₅	1	1	yes	characteristic
246	#389	C₂²×C₅	1	1	yes	characteristic
247	#389	C₂²×C₅	1	1	yes	characteristic
248	#387	—	2	1	no	—
249	#387	—	2	1	no	—
250	#387	—	2	1	no	—
251	#385	—	2	1	no	—
252	#385	—	2	1	no	—
253	#381	—	2	1	no	—
254	#380	C₂²×C₅	1	1	yes	characteristic
255	#380	C₂²×C₅	1	1	yes	characteristic
256	C₄×C₄⋊C₄	—	2	1	no	—
257	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
258	C₄×C₂²⋊C₄	—	2	1	no	—
259	#340	C₂²×C₅	1	1	yes	characteristic
260	#340	C₂²×C₅	1	1	yes	characteristic
261	#340	C₂²×C₅	1	1	yes	characteristic
262	#340	C₂²×C₅	1	1	yes	characteristic
263	#340	C₂²×C₅	1	1	yes	characteristic
264	#340	C₂²×C₅	1	1	yes	characteristic
265	#336	C₂²×C₅	1	1	yes	characteristic
266	#336	C₂²×C₅	1	1	yes	characteristic
267	C₂³×C₅	—	2	1	no	—
268	C₂³×C₅	—	2	1	no	—
269	C₂³×C₅	—	2	1	no	—
270	C₂³×C₅	—	2	1	no	—
271	C₂³×C₅	—	2	1	no	—
272	C₂³×C₅	—	2	1	no	—
273	C₂³×C₅	C₂×Q₁₆	1	2	yes	—
274	C₂³×C₅	C₂²×D₄	1	1	yes	characteristic
275	C₅×Q₈	—	2	2	no	—
276	C₅×Q₈	—	2	2	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×Q₈	—	4	1	no	—
282	C₅×Q₈	—	4	1	no	—
283	C₂×C₄×C₅	—	2	1	no	—
284	C₂×C₄×C₅	—	2	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	2	no	—
290	C₂×C₄×C₅	—	2	2	no	—
291	C₂×C₄×C₅	—	2	1	no	—
292	C₂×C₄×C₅	—	2	1	no	—
293	C₂×C₄×C₅	—	2	1	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	—	4	4	no	—
298	C₂×C₄×C₅	—	4	4	no	—
299	C₂×C₄×C₅	—	4	1	no	—
300	C₂×C₄×C₅	—	4	1	no	—
301	C₂×C₄×C₅	—	4	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	—	4	1	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	C₂×Q₁₆	1	2	yes	—
326	C₂×C₄×C₅	C₂×Q₁₆	1	2	yes	—
327	C₂×C₄×C₅	#135	1	2	yes	—
328	C₂×C₄×C₅	C₂×#41	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	C₂×#41	1	1	yes	characteristic
332	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
333	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
334	C₅×C₈	—	2	2	no	—
335	C₅×C₈	—	2	2	no	—
336	C₅×C₈	—	4	1	no	—
337	C₅×C₈	—	4	1	no	—
338	C₂²×Q₈	C₂³×C₅	1	1	yes	characteristic
339	C₂²×Q₈	C₂³×C₅	1	1	yes	characteristic
340	C₂³×C₄	C₅×D₄	1	1	yes	characteristic
341	C₂³×C₄	C₅×D₄	1	1	yes	characteristic
342	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
343	C₂×Q₁₆	—	2	2	no	—
344	C₂×Q₁₆	—	2	2	no	—
345	C₂×Q₁₆	—	4	1	no	—
346	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
347	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
348	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
349	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
350	C₂²⋊Q₈	—	2	2	no	—
351	C₂²⋊Q₈	—	2	2	no	—
352	C₂²⋊Q₈	—	4	1	no	—
353	C₂²⋊Q₈	—	4	1	no	—
354	C₄×Q₈	—	4	1	no	—
355	C₄×Q₈	—	4	1	no	—
356	C₂×C₄⋊C₄	—	2	1	no	—
357	C₂×C₄⋊C₄	—	2	1	no	—
358	C₂×C₄⋊C₄	—	2	1	no	—
359	C₂×C₄⋊C₄	—	2	1	no	—
360	C₂×C₄⋊C₄	—	2	1	no	—
361	C₂×C₄⋊C₄	—	2	1	no	—
362	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
363	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
364	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
365	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
366	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
367	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
368	C₂×C₂²⋊C₄	—	2	1	no	—
369	C₂×C₂²⋊C₄	—	2	1	no	—
370	C₂×C₂²⋊C₄	—	2	1	no	—
371	C₂×C₂²⋊C₄	—	2	1	no	—
372	C₂×C₄²	—	2	1	no	—
373	C₂×C₄²	—	2	1	no	—
374	C₂×C₄²	—	4	1	no	—
375	C₂×C₄²	—	4	1	no	—
376	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
377	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
378	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
379	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
380	#107	—	2	2	no	—
381	#107	—	2	2	no	—
382	#107	—	4	1	no	—
383	#103	—	2	2	no	—
384	#103	—	2	2	no	—
385	#103	—	2	2	no	—
386	#103	—	2	2	no	—
387	#103	—	4	1	no	—
388	#103	—	4	1	no	—
389	C₂²⋊C₈	—	2	2	no	—
390	C₂²⋊C₈	—	2	2	no	—
391	C₄×C₈	—	4	1	no	—
392	C₄×C₈	—	4	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	#95	—	2	1	no	—
402	#95	—	2	1	no	—
403	#95	—	2	1	no	—
404	#95	—	2	1	no	—
405	C₂²×C₅	—	2	2	no	—
406	C₂²×C₅	—	2	2	no	—
407	C₂²×C₅	—	2	2	no	—
408	C₂²×C₅	—	4	1	no	—
409	C₂²×C₅	—	4	1	no	—
410	C₂²×C₅	—	4	1	no	—
411	C₂²×C₅	—	4	1	no	—
412	C₂²×C₅	#525	1	1	yes	characteristic
413	C₂²×C₅	#532	1	1	yes	characteristic
414	C₂²×C₅	#534	1	1	yes	characteristic
415	C₂²×C₅	C₂²×Q₁₆	1	1	yes	characteristic
416	C₂²×C₅	C₂×#135	1	1	yes	characteristic
417	C₂²×C₅	#575	1	1	yes	characteristic
418	C₂²×C₅	#575	1	1	yes	characteristic
419	C₄×C₅	—	2	2	no	—
420	C₄×C₅	—	2	2	no	—
421	C₄×C₅	—	2	2	no	—
422	C₄×C₅	—	4	2	no	—
423	C₄×C₅	—	4	1	no	—
424	C₄×C₅	—	4	2	no	—
425	C₄×C₅	—	4	1	no	—
426	C₄×C₅	—	8	1	no	—
427	C₄×C₅	—	8	1	no	—
428	C₄×C₅	—	8	1	no	—
429	C₄×C₅	—	8	1	no	—
430	C₄×C₅	—	8	1	no	—
431	C₄×C₅	—	8	1	no	—
432	C₄×C₅	#551	1	1	yes	characteristic
433	C₄×C₅	#553	1	1	yes	characteristic
434	C₄×C₅	#553	1	1	yes	characteristic
435	C₄×C₅	#559	1	1	yes	characteristic
436	C₂⁴	C₂×C₅×D₄	1	1	yes	characteristic
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	—	2	1	no	—
445	C₂×Q₈	—	2	1	no	—
446	C₂×Q₈	—	2	1	no	—
447	C₂×Q₈	—	2	1	no	—
448	C₂×Q₈	C₅×#41	1	2	yes	—
449	C₂²×C₄	—	2	1	no	—
450	C₂²×C₄	—	2	1	no	—
451	C₂²×C₄	—	2	2	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	—	2	1	no	—
459	C₂²×C₄	—	2	1	no	—
460	C₂²×C₄	—	2	1	no	—
461	C₂²×C₄	—	2	1	no	—
462	C₂²×C₄	—	2	1	no	—
463	C₂²×C₄	—	2	1	no	—
464	C₂²×C₄	—	4	1	no	—
465	C₂²×C₄	—	4	1	no	—
466	C₂²×C₄	—	4	1	no	—
467	C₂²×C₄	—	4	1	no	—
468	C₂²×C₄	C₅×Q₁₆	1	4	yes	complemented
469	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
470	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
471	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
472	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
473	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
474	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
475	Q₁₆	—	4	4	no	—
476	C₂×C₈	—	2	1	no	—
477	C₂×C₈	—	2	1	no	—
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	C₅×#41	1	2	yes	—
487	C₂×C₈	C₅×#41	1	2	yes	—
488	C₄⋊C₄	—	2	4	no	—
489	C₄⋊C₄	—	2	1	no	—
490	C₄⋊C₄	—	2	1	no	—
491	C₄⋊C₄	—	2	1	no	—
492	C₄⋊C₄	—	2	1	no	—
493	C₄⋊C₄	—	2	1	no	—
494	C₄⋊C₄	—	2	1	no	—
495	C₄⋊C₄	—	2	1	no	—
496	C₄⋊C₄	—	2	1	no	—
497	C₄⋊C₄	—	2	1	no	—
498	C₄⋊C₄	—	2	1	no	—
499	C₄⋊C₄	—	2	1	no	—
500	C₄⋊C₄	—	4	2	no	—
501	C₄⋊C₄	—	4	2	no	—
502	C₄⋊C₄	—	4	2	no	—
503	C₄⋊C₄	—	4	2	no	—
504	C₄⋊C₄	—	4	2	no	—
505	C₄⋊C₄	C₅×#41	1	2	yes	—
506	C₂²⋊C₄	—	2	4	no	—
507	C₂²⋊C₄	—	4	2	no	—
508	C₂²⋊C₄	—	4	2	no	—
509	C₂²⋊C₄	—	4	2	no	—
510	C₄²	—	2	1	no	—
511	C₄²	—	2	1	no	—
512	C₄²	—	2	1	no	—
513	C₄²	—	2	1	no	—
514	C₄²	—	4	1	no	—
515	C₄²	—	4	1	no	—
516	C₄²	—	4	2	no	—
517	C₄²	—	4	2	no	—
518	C₂×C₅	—	4	2	no	—
519	C₂×C₅	#2602	1	1	yes	characteristic
520	C₂×C₅	#3102	1	1	yes	characteristic
521	C₂×C₅	#3104	1	1	yes	characteristic
522	C₂×C₅	#3170	1	1	yes	characteristic
523	C₂×C₅	#3183	1	1	yes	characteristic
524	C₂×C₅	#3189	1	1	yes	characteristic
525	C₂×C₅	#3191	1	1	yes	characteristic
526	C₂³	—	2	1	no	—
527	C₂³	—	2	1	no	—
528	C₂³	—	2	1	no	—
529	C₂³	—	2	1	no	—
530	C₂³	—	2	1	no	—
531	C₂³	—	2	1	no	—
532	C₂³	C₂×C₅×Q₁₆	1	2	yes	—
533	C₂³	C₂²×C₅×D₄	1	1	yes	characteristic
534	Q₈	—	2	2	no	—
535	Q₈	—	2	2	no	—
536	Q₈	—	4	1	no	—
537	Q₈	—	4	1	no	—
538	Q₈	—	4	1	no	—
539	Q₈	—	4	1	no	—
540	Q₈	—	4	1	no	—
541	Q₈	—	4	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	1	no	—
548	C₂×C₄	—	2	2	no	—
549	C₂×C₄	—	2	2	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	—	4	4	no	—
557	C₂×C₄	—	4	4	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	—	4	1	no	—
577	C₂×C₄	—	4	1	no	—
578	C₂×C₄	—	4	1	no	—
579	C₂×C₄	—	4	1	no	—
580	C₂×C₄	—	4	1	no	—
581	C₂×C₄	—	4	1	no	—
582	C₂×C₄	—	4	1	no	—
583	C₂×C₄	—	4	1	no	—
584	C₂×C₄	C₂×C₅×Q₁₆	1	2	yes	—
585	C₂×C₄	C₂×C₅×Q₁₆	1	2	yes	—
586	C₂×C₄	C₅×#135	1	2	yes	—
587	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
588	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
589	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
590	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
591	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
592	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
593	C₈	—	2	2	no	—
594	C₈	—	2	2	no	—
595	C₈	—	4	1	no	—
596	C₈	—	4	1	no	—
597	C₅	#29462	1	1	yes	characteristic, direct product factor, Sylow
598	C₂²	—	2	2	no	—
599	C₂²	—	2	2	no	—
600	C₂²	—	2	2	no	—
601	C₂²	—	4	1	no	—
602	C₂²	—	4	1	no	—
603	C₂²	—	4	1	no	—
604	C₂²	—	4	1	no	—
605	C₂²	C₅×#525	1	1	yes	characteristic
606	C₂²	C₅×#532	1	1	yes	characteristic
607	C₂²	C₅×#534	1	1	yes	characteristic
608	C₂²	C₂²×C₅×Q₁₆	1	1	yes	characteristic
609	C₂²	C₂×C₅×#135	1	1	yes	characteristic
610	C₂²	C₅×#575	1	1	yes	characteristic
611	C₂²	C₅×#575	1	1	yes	characteristic
612	C₄	—	2	2	no	—
613	C₄	—	2	2	no	—
614	C₄	—	2	2	no	—
615	C₄	—	4	2	no	—
616	C₄	—	4	1	no	—
617	C₄	—	4	2	no	—
618	C₄	—	4	1	no	—
619	C₄	—	8	1	no	—
620	C₄	—	8	1	no	—
621	C₄	—	8	1	no	—
622	C₄	—	8	1	no	—
623	C₄	—	8	1	no	—
624	C₄	—	8	1	no	—
625	C₄	C₅×#551	1	1	yes	characteristic
626	C₄	C₅×#553	1	1	yes	characteristic
627	C₄	C₅×#553	1	1	yes	characteristic
628	C₄	C₅×#559	1	1	yes	characteristic
629	C₂	—	4	2	no	—
630	C₂	C₅×#2602	1	1	yes	characteristic
631	C₂	C₅×#3102	1	1	yes	characteristic
632	C₂	C₅×#3104	1	1	yes	characteristic
633	C₂	C₅×#3170	1	1	yes	characteristic
634	C₂	C₅×#3183	1	1	yes	characteristic
635	C₂	C₅×#3189	1	1	yes	characteristic
636	C₂	C₅×#3191	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₅	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₅
prime radical	C₂⁴×C₅	C₂×D₄
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₅ ◁ C₂²×C₄²×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
7. C₅×#1969	C₂	semidirect
8. C₅×#1942	C₂	semidirect
9. C₅×#1933	C₂	semidirect
10. C₅×#1933	C₂	semidirect
11. C₅×#1928	C₂	semidirect
12. C₅×#1921	C₂	semidirect
13. C₅×#1878	C₂	semidirect
14. C₅×#1863	C₂	semidirect
59. #29462	C₅	direct (N × H)
133. #1969	C₂×C₅	semidirect
134. #1942	C₂×C₅	semidirect
135. #1933	C₂×C₅	semidirect
136. #1933	C₂×C₅	semidirect
137. #1928	C₂×C₅	semidirect
138. #1921	C₂×C₅	semidirect
139. #1878	C₂×C₅	semidirect
140. #1863	C₂×C₅	semidirect
174. C₂²×C₄×C₅	Q₁₆	semidirect
468. C₂²×C₄	C₅×Q₁₆	semidirect
597. C₅	#29462	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×#2855	2
C₄×C₅×C₂²⋊Q₈	2
C₅×#2076	2
C₅×#2036	2
C₅×#2001	2
C₅×#1969	2
C₅×#1942	2
C₅×#1933	2
C₅×#1928	2
C₅×#1921	2
C₅×#1878	2
C₅×#1863	2
C₄×C₅×C₂²⋊C₈	2
#29462	5

Subgroups — C5×#29462 #11952182

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#29462 #11952182