Subgroups — C₅×#23690 #11946410

Order 1280.

908 conjugacy classes of subgroups.

The subgroup lattice has 684 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#440	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄×C₅×SD₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#2328	C₂	1	1	yes	maximal, characteristic
4	C₅×#2320	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#2085	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#2074	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#2067	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#2065	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#2055	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#2055	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#2041	C₂	1	1	yes	maximal, characteristic
12	C₅×#2014	C₂	1	1	yes	maximal, characteristic
13	C₅×#1768	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅×#1762	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄×C₅×#102	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₅×SD₁₆	C₂²	1	1	yes	characteristic
17	C₂²×C₅×SD₁₆	C₂²	1	1	yes	characteristic
18	C₂×C₅×#127	C₂²	1	1	yes	characteristic
19	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
20	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
21	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
22	C₅×#440	—	2	4	no	—
23	C₄×C₅×SD₁₆	—	2	4	no	—
24	C₂×C₅×#107	C₂²	1	1	yes	characteristic
25	C₂×C₅×#106	C₂²	1	1	yes	characteristic
26	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
27	C₂×C₅×C₄⋊C₈	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×#102	C₂²	1	1	yes	characteristic
31	C₂×C₅×#102	C₂²	1	1	yes	characteristic
32	C₂×C₅×#102	C₂²	1	1	yes	characteristic
33	C₂×C₅×#102	C₂²	1	1	yes	characteristic
34	C₂×C₅×#102	C₂²	1	1	yes	characteristic
35	C₂×C₅×#102	C₂²	1	1	yes	characteristic
36	C₂×C₅×#97	C₂²	1	1	yes	characteristic
37	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
38	C₅×#391	C₂²	1	1	yes	characteristic
39	C₅×#391	C₂²	1	1	yes	characteristic
40	C₅×#390	C₂²	1	1	yes	characteristic
41	C₅×#390	C₂²	1	1	yes	characteristic
42	C₅×#389	C₂²	1	1	yes	characteristic
43	C₅×#389	C₂²	1	1	yes	characteristic
44	C₅×#387	—	2	1	no	—
45	C₅×#387	—	2	1	no	—
46	C₅×#386	—	2	1	no	—
47	C₅×#386	—	2	1	no	—
48	C₅×#386	—	2	1	no	—
49	C₅×#386	—	2	1	no	—
50	C₅×#383	—	2	1	no	—
51	C₅×#382	—	2	1	no	—
52	C₅×#382	C₂²	1	1	yes	characteristic
53	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
54	C₅×#376	C₂²	1	1	yes	characteristic
55	C₅×#340	C₂²	1	1	yes	characteristic
56	C₅×#340	C₂²	1	1	yes	characteristic
57	C₅×#340	C₂²	1	1	yes	characteristic
58	C₅×#340	C₂²	1	1	yes	characteristic
59	C₅×#336	C₂²	1	1	yes	characteristic
60	C₅×#336	C₂²	1	1	yes	characteristic
61	#23690	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
62	C₂²×C₅×Q₈	C₂³	1	1	yes	characteristic
63	C₂²×C₅×D₄	—	2	1	no	—
64	C₂²×C₅×D₄	—	2	1	no	—
65	C₂²×C₅×D₄	C₂³	1	1	yes	characteristic
66	C₂²×C₅×D₄	C₂³	1	1	yes	characteristic
67	C₂³×C₄×C₅	—	2	1	no	—
68	C₂³×C₄×C₅	—	2	1	no	—
69	C₂×C₅×SD₁₆	—	2	2	no	—
70	C₂×C₅×SD₁₆	—	2	2	no	—
71	C₂×C₅×SD₁₆	—	2	2	no	—
72	C₂×C₅×SD₁₆	—	2	2	no	—
73	C₂×C₅×SD₁₆	—	2	2	no	—
74	C₂×C₅×SD₁₆	—	2	2	no	—
75	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
76	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
77	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
78	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
79	C₅×#127	—	2	2	no	—
80	C₅×#127	—	2	2	no	—
81	C₄×C₅×Q₈	—	2	2	no	—
82	C₄×C₅×Q₈	D₄	1	4	yes	complemented
83	C₄×C₅×D₄	—	2	2	no	—
84	C₄×C₅×D₄	—	2	2	no	—
85	C₄×C₅×D₄	—	2	2	no	—
86	C₄×C₅×D₄	—	2	2	no	—
87	C₂×C₅×C₄⋊C₄	—	2	1	no	—
88	C₂×C₅×C₄⋊C₄	—	2	1	no	—
89	C₂×C₅×C₄⋊C₄	—	2	1	no	—
90	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
91	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
92	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
93	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
94	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
95	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
96	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
97	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
98	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
99	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
100	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
101	C₂×C₄²×C₅	—	2	1	no	—
102	C₂×C₄²×C₅	—	2	1	no	—
103	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
104	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
105	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
106	C₅×#107	—	2	2	no	—
107	C₅×#106	—	2	2	no	—
108	C₅×C₄⋊C₈	—	2	2	no	—
109	C₅×C₄⋊C₈	—	2	2	no	—
110	C₅×#103	—	2	2	no	—
111	C₅×#103	—	2	2	no	—
112	C₅×#102	—	2	2	no	—
113	C₅×#102	—	2	2	no	—
114	C₅×#102	—	2	2	no	—
115	C₅×#102	—	2	2	no	—
116	C₅×#102	—	2	2	no	—
117	C₅×#102	—	2	2	no	—
118	C₅×#97	—	2	2	no	—
119	C₄×C₅×C₈	—	2	2	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	C₅×#95	—	2	1	no	—
128	C₅×#95	—	2	1	no	—
129	C₅×#95	D₄	1	1	yes	characteristic
130	C₅×#95	D₄	1	1	yes	characteristic
131	C₅×#95	D₄	1	1	yes	characteristic
132	C₅×#95	D₄	1	1	yes	characteristic
133	C₂×#440	C₂×C₅	1	1	yes	characteristic, complemented
134	C₂×C₄×SD₁₆	C₂×C₅	1	1	yes	characteristic, complemented
135	#2328	C₂×C₅	1	1	yes	characteristic
136	#2320	C₂×C₅	1	1	yes	characteristic, complemented
137	#2085	C₂×C₅	1	1	yes	characteristic, complemented
138	#2074	C₂×C₅	1	1	yes	characteristic, complemented
139	#2067	C₂×C₅	1	1	yes	characteristic, complemented
140	#2065	C₂×C₅	1	1	yes	characteristic, complemented
141	#2055	C₂×C₅	1	1	yes	characteristic, complemented
142	#2055	C₂×C₅	1	1	yes	characteristic, complemented
143	#2041	C₂×C₅	1	1	yes	characteristic
144	#2014	C₂×C₅	1	1	yes	characteristic
145	#1768	C₂×C₅	1	1	yes	characteristic, complemented
146	#1762	C₂×C₅	1	1	yes	characteristic, complemented
147	C₄×#102	C₂×C₅	1	1	yes	characteristic, complemented
148	C₂⁴×C₅	—	2	1	no	—
149	C₂⁴×C₅	—	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	—	2	1	no	—
155	C₂×C₅×Q₈	C₂×D₄	1	2	yes	—
156	C₂×C₅×D₄	—	2	4	no	—
157	C₂×C₅×D₄	—	2	4	no	—
158	C₂×C₅×D₄	—	2	1	no	—
159	C₂×C₅×D₄	—	2	1	no	—
160	C₂×C₅×D₄	—	2	1	no	—
161	C₂×C₅×D₄	—	2	1	no	—
162	C₂×C₅×D₄	—	2	1	no	—
163	C₂×C₅×D₄	—	2	1	no	—
164	C₂×C₅×D₄	—	2	1	no	—
165	C₂×C₅×D₄	—	2	1	no	—
166	C₂×C₅×D₄	—	2	1	no	—
167	C₂×C₅×D₄	—	2	1	no	—
168	C₂×C₅×D₄	—	8	1	no	—
169	C₂×C₅×D₄	—	8	1	no	—
170	C₂×C₅×D₄	—	8	1	no	—
171	C₂×C₅×D₄	—	8	1	no	—
172	C₂×C₅×D₄	#41	1	2	yes	—
173	C₂×C₅×D₄	#41	1	2	yes	—
174	C₂²×C₄×C₅	—	2	1	no	—
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	—	4	2	no	—
181	C₂²×C₄×C₅	—	4	2	no	—
182	C₂²×C₄×C₅	—	8	1	no	—
183	C₂²×C₄×C₅	—	8	1	no	—
184	C₂²×C₄×C₅	—	8	1	no	—
185	C₂²×C₄×C₅	—	8	1	no	—
186	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
187	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
188	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
189	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
190	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
191	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
192	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
193	C₅×SD₁₆	—	2	8	no	—
194	C₅×SD₁₆	—	2	8	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	—	2	1	no	—
204	C₂×C₅×C₈	—	2	1	no	—
205	C₂×C₅×C₈	#41	1	2	yes	—
206	C₂×C₅×C₈	#41	1	2	yes	—
207	C₅×C₄⋊C₄	—	2	4	no	—
208	C₅×C₄⋊C₄	—	2	1	no	—
209	C₅×C₄⋊C₄	—	2	1	no	—
210	C₅×C₄⋊C₄	—	2	1	no	—
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	—	8	1	no	—
218	C₅×C₄⋊C₄	—	8	1	no	—
219	C₅×C₄⋊C₄	C₂×D₄	1	2	yes	—
220	C₅×C₂²⋊C₄	—	4	2	no	—
221	C₅×C₂²⋊C₄	—	4	2	no	—
222	C₅×C₂²⋊C₄	—	8	1	no	—
223	C₅×C₂²⋊C₄	—	8	1	no	—
224	C₅×C₂²⋊C₄	—	8	1	no	—
225	C₅×C₂²⋊C₄	—	8	1	no	—
226	C₄²×C₅	—	2	4	no	—
227	C₄²×C₅	—	2	1	no	—
228	C₄²×C₅	—	2	1	no	—
229	C₄²×C₅	—	2	1	no	—
230	C₄²×C₅	—	2	1	no	—
231	C₄²×C₅	—	8	1	no	—
232	C₄²×C₅	C₂×D₄	1	2	yes	—
233	C₄²×C₅	#41	1	2	yes	—
234	C₂²×SD₁₆	C₂²×C₅	1	1	yes	characteristic
235	C₂²×SD₁₆	C₂²×C₅	1	1	yes	characteristic
236	C₂×#127	C₂²×C₅	1	1	yes	characteristic
237	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
238	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
239	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
240	#440	—	2	4	no	—
241	C₄×SD₁₆	—	2	4	no	—
242	C₂×#107	C₂²×C₅	1	1	yes	characteristic
243	C₂×#106	C₂²×C₅	1	1	yes	characteristic
244	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
245	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
246	C₂×#103	C₂²×C₅	1	1	yes	characteristic
247	C₂×#103	C₂²×C₅	1	1	yes	characteristic
248	C₂×#102	C₂²×C₅	1	1	yes	characteristic
249	C₂×#102	C₂²×C₅	1	1	yes	characteristic
250	C₂×#102	C₂²×C₅	1	1	yes	characteristic
251	C₂×#102	C₂²×C₅	1	1	yes	characteristic
252	C₂×#102	C₂²×C₅	1	1	yes	characteristic
253	C₂×#102	C₂²×C₅	1	1	yes	characteristic
254	C₂×#97	C₂²×C₅	1	1	yes	characteristic
255	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
256	#391	C₂²×C₅	1	1	yes	characteristic
257	#391	C₂²×C₅	1	1	yes	characteristic
258	#390	C₂²×C₅	1	1	yes	characteristic
259	#390	C₂²×C₅	1	1	yes	characteristic
260	#389	C₂²×C₅	1	1	yes	characteristic
261	#389	C₂²×C₅	1	1	yes	characteristic
262	#387	—	2	1	no	—
263	#387	—	2	1	no	—
264	#386	—	2	1	no	—
265	#386	—	2	1	no	—
266	#386	—	2	1	no	—
267	#386	—	2	1	no	—
268	#383	—	2	1	no	—
269	#382	—	2	1	no	—
270	#382	C₂²×C₅	1	1	yes	characteristic
271	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
272	#376	C₂²×C₅	1	1	yes	characteristic
273	#340	C₂²×C₅	1	1	yes	characteristic
274	#340	C₂²×C₅	1	1	yes	characteristic
275	#340	C₂²×C₅	1	1	yes	characteristic
276	#340	C₂²×C₅	1	1	yes	characteristic
277	#336	C₂²×C₅	1	1	yes	characteristic
278	#336	C₂²×C₅	1	1	yes	characteristic
279	C₂³×C₅	—	2	2	no	—
280	C₂³×C₅	—	2	2	no	—
281	C₂³×C₅	—	4	1	no	—
282	C₂³×C₅	—	4	1	no	—
283	C₂³×C₅	—	4	1	no	—
284	C₂³×C₅	—	4	1	no	—
285	C₂³×C₅	—	4	1	no	—
286	C₂³×C₅	—	4	1	no	—
287	C₂³×C₅	—	4	1	no	—
288	C₂³×C₅	—	4	1	no	—
289	C₂³×C₅	—	4	1	no	—
290	C₂³×C₅	—	4	1	no	—
291	C₂³×C₅	—	4	1	no	—
292	C₂³×C₅	—	4	1	no	—
293	C₂³×C₅	C₂²×D₄	1	1	yes	characteristic
294	C₅×Q₈	—	2	2	no	—
295	C₅×Q₈	—	2	2	no	—
296	C₅×Q₈	—	4	1	no	—
297	C₅×Q₈	—	4	1	no	—
298	C₅×D₄	—	2	2	no	—
299	C₅×D₄	—	2	2	no	—
300	C₅×D₄	—	2	2	no	—
301	C₅×D₄	—	2	2	no	—
302	C₅×D₄	—	4	1	no	—
303	C₅×D₄	—	4	1	no	—
304	C₅×D₄	—	4	1	no	—
305	C₅×D₄	—	4	1	no	—
306	C₅×D₄	—	8	4	no	—
307	C₅×D₄	—	8	4	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	1	no	—
312	C₂×C₄×C₅	—	2	2	no	—
313	C₂×C₄×C₅	—	2	2	no	—
314	C₂×C₄×C₅	—	2	1	no	—
315	C₂×C₄×C₅	—	2	1	no	—
316	C₂×C₄×C₅	—	2	1	no	—
317	C₂×C₄×C₅	—	2	1	no	—
318	C₂×C₄×C₅	—	2	1	no	—
319	C₂×C₄×C₅	—	2	1	no	—
320	C₂×C₄×C₅	—	2	1	no	—
321	C₂×C₄×C₅	—	2	1	no	—
322	C₂×C₄×C₅	—	2	1	no	—
323	C₂×C₄×C₅	—	2	1	no	—
324	C₂×C₄×C₅	—	2	1	no	—
325	C₂×C₄×C₅	—	2	1	no	—
326	C₂×C₄×C₅	—	4	1	no	—
327	C₂×C₄×C₅	—	4	1	no	—
328	C₂×C₄×C₅	—	4	1	no	—
329	C₂×C₄×C₅	—	4	1	no	—
330	C₂×C₄×C₅	—	4	1	no	—
331	C₂×C₄×C₅	—	4	1	no	—
332	C₂×C₄×C₅	—	4	1	no	—
333	C₂×C₄×C₅	—	4	1	no	—
334	C₂×C₄×C₅	—	4	1	no	—
335	C₂×C₄×C₅	—	4	1	no	—
336	C₂×C₄×C₅	—	4	1	no	—
337	C₂×C₄×C₅	—	4	1	no	—
338	C₂×C₄×C₅	—	4	1	no	—
339	C₂×C₄×C₅	—	4	1	no	—
340	C₂×C₄×C₅	—	4	1	no	—
341	C₂×C₄×C₅	—	4	1	no	—
342	C₂×C₄×C₅	—	8	4	no	—
343	C₂×C₄×C₅	—	8	4	no	—
344	C₂×C₄×C₅	#121	1	2	yes	—
345	C₂×C₄×C₅	#121	1	2	yes	—
346	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
347	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
348	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
349	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
350	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
351	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
352	C₅×C₈	—	2	2	no	—
353	C₅×C₈	—	2	2	no	—
354	C₅×C₈	—	4	1	no	—
355	C₅×C₈	—	4	1	no	—
356	C₂²×Q₈	C₂³×C₅	1	1	yes	characteristic
357	C₂²×D₄	—	2	1	no	—
358	C₂²×D₄	—	2	1	no	—
359	C₂²×D₄	C₂³×C₅	1	1	yes	characteristic
360	C₂²×D₄	C₂³×C₅	1	1	yes	characteristic
361	C₂³×C₄	—	2	1	no	—
362	C₂³×C₄	—	2	1	no	—
363	C₂×SD₁₆	—	2	2	no	—
364	C₂×SD₁₆	—	2	2	no	—
365	C₂×SD₁₆	—	2	2	no	—
366	C₂×SD₁₆	—	2	2	no	—
367	C₂×SD₁₆	—	2	2	no	—
368	C₂×SD₁₆	—	2	2	no	—
369	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
370	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
371	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
372	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
373	#127	—	2	2	no	—
374	#127	—	2	2	no	—
375	C₄×Q₈	—	2	2	no	—
376	C₄×Q₈	C₅×D₄	1	4	yes	complemented
377	C₄×D₄	—	2	2	no	—
378	C₄×D₄	—	2	2	no	—
379	C₄×D₄	—	2	2	no	—
380	C₄×D₄	—	2	2	no	—
381	C₂×C₄⋊C₄	—	2	1	no	—
382	C₂×C₄⋊C₄	—	2	1	no	—
383	C₂×C₄⋊C₄	—	2	1	no	—
384	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
385	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
386	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
387	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
388	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
389	C₂×C₂²⋊C₄	—	2	1	no	—
390	C₂×C₂²⋊C₄	—	2	1	no	—
391	C₂×C₂²⋊C₄	—	2	1	no	—
392	C₂×C₂²⋊C₄	—	2	1	no	—
393	C₂×C₂²⋊C₄	—	2	1	no	—
394	C₂×C₂²⋊C₄	—	2	1	no	—
395	C₂×C₄²	—	2	1	no	—
396	C₂×C₄²	—	2	1	no	—
397	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
398	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
399	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
400	#107	—	2	2	no	—
401	#106	—	2	2	no	—
402	C₄⋊C₈	—	2	2	no	—
403	C₄⋊C₈	—	2	2	no	—
404	#103	—	2	2	no	—
405	#103	—	2	2	no	—
406	#102	—	2	2	no	—
407	#102	—	2	2	no	—
408	#102	—	2	2	no	—
409	#102	—	2	2	no	—
410	#102	—	2	2	no	—
411	#102	—	2	2	no	—
412	#97	—	2	2	no	—
413	C₄×C₈	—	2	2	no	—
414	#95	—	2	1	no	—
415	#95	—	2	1	no	—
416	#95	—	2	1	no	—
417	#95	—	2	1	no	—
418	#95	—	2	1	no	—
419	#95	—	2	1	no	—
420	#95	—	2	1	no	—
421	#95	—	2	1	no	—
422	#95	—	2	1	no	—
423	#95	C₅×D₄	1	1	yes	characteristic
424	#95	C₅×D₄	1	1	yes	characteristic
425	#95	C₅×D₄	1	1	yes	characteristic
426	#95	C₅×D₄	1	1	yes	characteristic
427	C₂²×C₅	—	4	2	no	—
428	C₂²×C₅	—	4	2	no	—
429	C₂²×C₅	—	4	2	no	—
430	C₂²×C₅	—	4	2	no	—
431	C₂²×C₅	—	4	2	no	—
432	C₂²×C₅	—	4	2	no	—
433	C₂²×C₅	—	8	1	no	—
434	C₂²×C₅	—	8	1	no	—
435	C₂²×C₅	—	8	1	no	—
436	C₂²×C₅	—	8	1	no	—
437	C₂²×C₅	—	8	1	no	—
438	C₂²×C₅	—	8	1	no	—
439	C₂²×C₅	—	8	1	no	—
440	C₂²×C₅	—	8	1	no	—
441	C₂²×C₅	C₂×#121	1	1	yes	characteristic
442	C₂²×C₅	#525	1	1	yes	characteristic
443	C₂²×C₅	#532	1	1	yes	characteristic
444	C₂²×C₅	#576	1	1	yes	characteristic
445	C₂²×C₅	#577	1	1	yes	characteristic
446	C₂²×C₅	#577	1	1	yes	characteristic
447	C₂²×C₅	#577	1	1	yes	characteristic
448	C₄×C₅	—	2	2	no	—
449	C₄×C₅	—	2	2	no	—
450	C₄×C₅	—	4	1	no	—
451	C₄×C₅	—	4	1	no	—
452	C₄×C₅	—	4	2	no	—
453	C₄×C₅	—	4	1	no	—
454	C₄×C₅	—	4	1	no	—
455	C₄×C₅	—	4	2	no	—
456	C₄×C₅	—	8	1	no	—
457	C₄×C₅	—	8	1	no	—
458	C₄×C₅	—	8	1	no	—
459	C₄×C₅	—	8	1	no	—
460	C₄×C₅	#525	1	1	yes	characteristic
461	C₄×C₅	#525	1	1	yes	characteristic
462	C₄×C₅	#529	1	1	yes	characteristic
463	C₄×C₅	#529	1	1	yes	characteristic
464	C₂⁴	—	2	1	no	—
465	C₂⁴	—	2	1	no	—
466	C₂×Q₈	—	2	1	no	—
467	C₂×Q₈	—	2	1	no	—
468	C₂×Q₈	—	2	1	no	—
469	C₂×Q₈	—	2	1	no	—
470	C₂×Q₈	—	2	1	no	—
471	C₂×Q₈	C₂×C₅×D₄	1	2	yes	—
472	C₂×D₄	—	2	4	no	—
473	C₂×D₄	—	2	4	no	—
474	C₂×D₄	—	2	1	no	—
475	C₂×D₄	—	2	1	no	—
476	C₂×D₄	—	2	1	no	—
477	C₂×D₄	—	2	1	no	—
478	C₂×D₄	—	2	1	no	—
479	C₂×D₄	—	2	1	no	—
480	C₂×D₄	—	2	1	no	—
481	C₂×D₄	—	2	1	no	—
482	C₂×D₄	—	2	1	no	—
483	C₂×D₄	—	2	1	no	—
484	C₂×D₄	—	8	1	no	—
485	C₂×D₄	—	8	1	no	—
486	C₂×D₄	—	8	1	no	—
487	C₂×D₄	—	8	1	no	—
488	C₂×D₄	C₅×#41	1	2	yes	—
489	C₂×D₄	C₅×#41	1	2	yes	—
490	C₂²×C₄	—	2	1	no	—
491	C₂²×C₄	—	2	1	no	—
492	C₂²×C₄	—	2	1	no	—
493	C₂²×C₄	—	2	1	no	—
494	C₂²×C₄	—	2	1	no	—
495	C₂²×C₄	—	2	1	no	—
496	C₂²×C₄	—	4	2	no	—
497	C₂²×C₄	—	4	2	no	—
498	C₂²×C₄	—	8	1	no	—
499	C₂²×C₄	—	8	1	no	—
500	C₂²×C₄	—	8	1	no	—
501	C₂²×C₄	—	8	1	no	—
502	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
503	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
504	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
505	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
506	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
507	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
508	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
509	SD₁₆	—	2	8	no	—
510	SD₁₆	—	2	8	no	—
511	C₂×C₈	—	2	1	no	—
512	C₂×C₈	—	2	1	no	—
513	C₂×C₈	—	2	1	no	—
514	C₂×C₈	—	2	1	no	—
515	C₂×C₈	—	2	1	no	—
516	C₂×C₈	—	2	1	no	—
517	C₂×C₈	—	2	1	no	—
518	C₂×C₈	—	2	1	no	—
519	C₂×C₈	—	2	1	no	—
520	C₂×C₈	—	2	1	no	—
521	C₂×C₈	C₅×#41	1	2	yes	—
522	C₂×C₈	C₅×#41	1	2	yes	—
523	C₄⋊C₄	—	2	4	no	—
524	C₄⋊C₄	—	2	1	no	—
525	C₄⋊C₄	—	2	1	no	—
526	C₄⋊C₄	—	2	1	no	—
527	C₄⋊C₄	—	2	1	no	—
528	C₄⋊C₄	—	2	1	no	—
529	C₄⋊C₄	—	2	1	no	—
530	C₄⋊C₄	—	2	1	no	—
531	C₄⋊C₄	—	2	1	no	—
532	C₄⋊C₄	—	2	1	no	—
533	C₄⋊C₄	—	8	1	no	—
534	C₄⋊C₄	—	8	1	no	—
535	C₄⋊C₄	C₂×C₅×D₄	1	2	yes	—
536	C₂²⋊C₄	—	4	2	no	—
537	C₂²⋊C₄	—	4	2	no	—
538	C₂²⋊C₄	—	8	1	no	—
539	C₂²⋊C₄	—	8	1	no	—
540	C₂²⋊C₄	—	8	1	no	—
541	C₂²⋊C₄	—	8	1	no	—
542	C₄²	—	2	4	no	—
543	C₄²	—	2	1	no	—
544	C₄²	—	2	1	no	—
545	C₄²	—	2	1	no	—
546	C₄²	—	2	1	no	—
547	C₄²	—	8	1	no	—
548	C₄²	C₂×C₅×D₄	1	2	yes	—
549	C₄²	C₅×#41	1	2	yes	—
550	C₂×C₅	—	8	2	no	—
551	C₂×C₅	—	8	2	no	—
552	C₂×C₅	#2392	1	1	yes	characteristic
553	C₂×C₅	#3043	1	1	yes	characteristic
554	C₂×C₅	#3045	1	1	yes	characteristic
555	C₂×C₅	#3118	1	1	yes	characteristic
556	C₂×C₅	#3123	1	1	yes	characteristic
557	C₂×C₅	#3174	1	1	yes	characteristic
558	C₂×C₅	#3179	1	1	yes	characteristic
559	C₂³	—	2	2	no	—
560	C₂³	—	2	2	no	—
561	C₂³	—	4	1	no	—
562	C₂³	—	4	1	no	—
563	C₂³	—	4	1	no	—
564	C₂³	—	4	1	no	—
565	C₂³	—	4	1	no	—
566	C₂³	—	4	1	no	—
567	C₂³	—	4	1	no	—
568	C₂³	—	4	1	no	—
569	C₂³	—	4	1	no	—
570	C₂³	—	4	1	no	—
571	C₂³	—	4	1	no	—
572	C₂³	—	4	1	no	—
573	C₂³	C₂²×C₅×D₄	1	1	yes	characteristic
574	Q₈	—	2	2	no	—
575	Q₈	—	2	2	no	—
576	Q₈	—	4	1	no	—
577	Q₈	—	4	1	no	—
578	D₄	—	2	2	no	—
579	D₄	—	2	2	no	—
580	D₄	—	2	2	no	—
581	D₄	—	2	2	no	—
582	D₄	—	4	1	no	—
583	D₄	—	4	1	no	—
584	D₄	—	4	1	no	—
585	D₄	—	4	1	no	—
586	D₄	—	8	4	no	—
587	D₄	—	8	4	no	—
588	C₂×C₄	—	2	1	no	—
589	C₂×C₄	—	2	1	no	—
590	C₂×C₄	—	2	1	no	—
591	C₂×C₄	—	2	1	no	—
592	C₂×C₄	—	2	2	no	—
593	C₂×C₄	—	2	2	no	—
594	C₂×C₄	—	2	1	no	—
595	C₂×C₄	—	2	1	no	—
596	C₂×C₄	—	2	1	no	—
597	C₂×C₄	—	2	1	no	—
598	C₂×C₄	—	2	1	no	—
599	C₂×C₄	—	2	1	no	—
600	C₂×C₄	—	2	1	no	—
601	C₂×C₄	—	2	1	no	—
602	C₂×C₄	—	2	1	no	—
603	C₂×C₄	—	2	1	no	—
604	C₂×C₄	—	2	1	no	—
605	C₂×C₄	—	2	1	no	—
606	C₂×C₄	—	4	1	no	—
607	C₂×C₄	—	4	1	no	—
608	C₂×C₄	—	4	1	no	—
609	C₂×C₄	—	4	1	no	—
610	C₂×C₄	—	4	1	no	—
611	C₂×C₄	—	4	1	no	—
612	C₂×C₄	—	4	1	no	—
613	C₂×C₄	—	4	1	no	—
614	C₂×C₄	—	4	1	no	—
615	C₂×C₄	—	4	1	no	—
616	C₂×C₄	—	4	1	no	—
617	C₂×C₄	—	4	1	no	—
618	C₂×C₄	—	4	1	no	—
619	C₂×C₄	—	4	1	no	—
620	C₂×C₄	—	4	1	no	—
621	C₂×C₄	—	4	1	no	—
622	C₂×C₄	—	8	4	no	—
623	C₂×C₄	—	8	4	no	—
624	C₂×C₄	C₅×#121	1	2	yes	—
625	C₂×C₄	C₅×#121	1	2	yes	—
626	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
627	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
628	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
629	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
630	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
631	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
632	C₈	—	2	2	no	—
633	C₈	—	2	2	no	—
634	C₈	—	4	1	no	—
635	C₈	—	4	1	no	—
636	C₅	#23690	1	1	yes	characteristic, direct product factor, Sylow
637	C₂²	—	4	2	no	—
638	C₂²	—	4	2	no	—
639	C₂²	—	4	2	no	—
640	C₂²	—	4	2	no	—
641	C₂²	—	4	2	no	—
642	C₂²	—	4	2	no	—
643	C₂²	—	8	1	no	—
644	C₂²	—	8	1	no	—
645	C₂²	—	8	1	no	—
646	C₂²	—	8	1	no	—
647	C₂²	—	8	1	no	—
648	C₂²	—	8	1	no	—
649	C₂²	—	8	1	no	—
650	C₂²	—	8	1	no	—
651	C₂²	C₂×C₅×#121	1	1	yes	characteristic
652	C₂²	C₅×#525	1	1	yes	characteristic
653	C₂²	C₅×#532	1	1	yes	characteristic
654	C₂²	C₅×#576	1	1	yes	characteristic
655	C₂²	C₅×#577	1	1	yes	characteristic
656	C₂²	C₅×#577	1	1	yes	characteristic
657	C₂²	C₅×#577	1	1	yes	characteristic
658	C₄	—	2	2	no	—
659	C₄	—	2	2	no	—
660	C₄	—	4	2	no	—
661	C₄	—	4	1	no	—
662	C₄	—	4	1	no	—
663	C₄	—	4	2	no	—
664	C₄	—	4	1	no	—
665	C₄	—	4	1	no	—
666	C₄	—	8	1	no	—
667	C₄	—	8	1	no	—
668	C₄	—	8	1	no	—
669	C₄	—	8	1	no	—
670	C₄	C₅×#525	1	1	yes	characteristic
671	C₄	C₅×#525	1	1	yes	characteristic
672	C₄	C₅×#529	1	1	yes	characteristic
673	C₄	C₅×#529	1	1	yes	characteristic
674	C₂	—	8	2	no	—
675	C₂	—	8	2	no	—
676	C₂	C₅×#2392	1	1	yes	characteristic
677	C₂	C₅×#3043	1	1	yes	characteristic
678	C₂	C₅×#3045	1	1	yes	characteristic
679	C₂	C₅×#3118	1	1	yes	characteristic
680	C₂	C₅×#3123	1	1	yes	characteristic
681	C₂	C₅×#3174	1	1	yes	characteristic
682	C₂	C₅×#3179	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₅	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₅
prime radical	C₂×C₅×#127	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₅ ◁ C₅×#376 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₅×#440	C₂	semidirect
2. C₂×C₄×C₅×SD₁₆	C₂	semidirect
4. C₅×#2320	C₂	semidirect
5. C₅×#2085	C₂	semidirect
6. C₅×#2074	C₂	semidirect
7. C₅×#2067	C₂	semidirect
8. C₅×#2065	C₂	semidirect
9. C₅×#2055	C₂	semidirect
10. C₅×#2055	C₂	semidirect
13. C₅×#1768	C₂	semidirect
14. C₅×#1762	C₂	semidirect
15. C₄×C₅×#102	C₂	semidirect
61. #23690	C₅	direct (N × H)
82. C₄×C₅×Q₈	D₄	semidirect
133. C₂×#440	C₂×C₅	semidirect
134. C₂×C₄×SD₁₆	C₂×C₅	semidirect
136. #2320	C₂×C₅	semidirect
137. #2085	C₂×C₅	semidirect
138. #2074	C₂×C₅	semidirect
139. #2067	C₂×C₅	semidirect
140. #2065	C₂×C₅	semidirect
141. #2055	C₂×C₅	semidirect
142. #2055	C₂×C₅	semidirect
145. #1768	C₂×C₅	semidirect
146. #1762	C₂×C₅	semidirect
147. C₄×#102	C₂×C₅	semidirect
376. C₄×Q₈	C₅×D₄	semidirect
636. C₅	#23690	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₅×#440	2
C₂×C₄×C₅×SD₁₆	2
C₅×#2328	2
C₅×#2320	2
C₅×#2085	2
C₅×#2074	2
C₅×#2067	2
C₅×#2065	2
C₅×#2055	2
C₅×#2041	2
C₅×#2014	2
C₅×#1768	2
C₅×#1762	2
C₄×C₅×#102	2
#23690	5

Subgroups — C5×#23690 #11946410

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#23690 #11946410