Subgroups — C₅×#2681 #10616276

Order 640.

618 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#123	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₅×#121	C₂	1	1	yes	maximal, characteristic
5	C₅×#398	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#396	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#394	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#394	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#394	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#393	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#390	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#389	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅×#388	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅×#386	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅×#385	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₅×Q₈	C₂²	1	1	yes	characteristic
17	C₂²×C₅×D₄	C₂²	1	1	yes	characteristic
18	C₂²×C₅×D₄	C₂²	1	1	yes	characteristic
19	C₂²×C₅×D₄	C₂²	1	1	yes	characteristic
20	C₂³×C₄×C₅	C₂²	1	1	yes	characteristic
21	C₂³×C₄×C₅	C₂²	1	1	yes	characteristic
22	C₅×#123	—	2	4	no	—
23	C₅×C₂²⋊Q₈	—	2	4	no	—
24	C₅×C₂²⋊Q₈	—	2	4	no	—
25	C₅×#121	—	2	4	no	—
26	C₂×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
27	C₂×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
28	C₂×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
29	C₂×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
30	C₂×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
31	C₂×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
32	C₂×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
33	C₂×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
34	C₂×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
35	C₂×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
36	C₂×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
37	C₂×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
38	C₂×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
39	C₂×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
40	C₂×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
41	C₂×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
42	C₂×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
43	C₂×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
44	C₂×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
45	C₂×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
46	C₂×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
47	C₂×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
48	C₂×C₄²×C₅	C₂²	1	1	yes	characteristic
49	C₅×#95	C₂²	1	1	yes	characteristic
50	C₅×#95	C₂²	1	1	yes	characteristic
51	C₅×#95	C₂²	1	1	yes	characteristic
52	C₅×#95	C₂²	1	1	yes	characteristic
53	C₅×#95	C₂²	1	1	yes	characteristic
54	C₅×#95	C₂²	1	1	yes	characteristic
55	#2681	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
56	C₂⁴×C₅	C₂³	1	1	yes	characteristic
57	C₂⁴×C₅	C₂³	1	1	yes	characteristic
58	C₂⁴×C₅	C₂³	1	1	yes	characteristic
59	C₂×C₅×Q₈	—	2	2	no	—
60	C₂×C₅×Q₈	—	2	2	no	—
61	C₂×C₅×Q₈	—	4	1	no	—
62	C₂×C₅×D₄	—	2	2	no	—
63	C₂×C₅×D₄	—	2	2	no	—
64	C₂×C₅×D₄	—	2	2	no	—
65	C₂×C₅×D₄	—	2	2	no	—
66	C₂×C₅×D₄	—	2	2	no	—
67	C₂×C₅×D₄	—	2	2	no	—
68	C₂×C₅×D₄	—	4	1	no	—
69	C₂×C₅×D₄	—	4	1	no	—
70	C₂×C₅×D₄	—	4	1	no	—
71	C₂²×C₄×C₅	—	2	2	no	—
72	C₂²×C₄×C₅	—	2	2	no	—
73	C₂²×C₄×C₅	—	2	2	no	—
74	C₂²×C₄×C₅	—	2	2	no	—
75	C₂²×C₄×C₅	—	4	1	no	—
76	C₂²×C₄×C₅	—	4	1	no	—
77	C₂²×C₄×C₅	C₂³	1	1	yes	characteristic
78	C₂²×C₄×C₅	C₂³	1	1	yes	characteristic
79	C₂²×C₄×C₅	C₂³	1	1	yes	characteristic
80	C₂²×C₄×C₅	C₂³	1	1	yes	characteristic
81	C₂²×C₄×C₅	C₂³	1	1	yes	characteristic
82	C₂²×C₄×C₅	C₂³	1	1	yes	characteristic
83	C₂²×C₄×C₅	C₂³	1	1	yes	characteristic
84	C₂²×C₄×C₅	C₂³	1	1	yes	characteristic
85	C₂²×C₄×C₅	C₂³	1	1	yes	characteristic
86	C₂²×C₄×C₅	C₂³	1	1	yes	characteristic
87	C₂²×C₄×C₅	C₂³	1	1	yes	characteristic
88	C₂²×C₄×C₅	C₂³	1	1	yes	characteristic
89	C₅×C₄⋊C₄	—	2	2	no	—
90	C₅×C₄⋊C₄	—	2	2	no	—
91	C₅×C₄⋊C₄	—	2	2	no	—
92	C₅×C₄⋊C₄	—	2	2	no	—
93	C₅×C₄⋊C₄	—	2	2	no	—
94	C₅×C₄⋊C₄	—	2	2	no	—
95	C₅×C₄⋊C₄	—	2	2	no	—
96	C₅×C₄⋊C₄	—	4	1	no	—
97	C₅×C₄⋊C₄	D₄	1	4	yes	complemented
98	C₅×C₂²⋊C₄	—	2	2	no	—
99	C₅×C₂²⋊C₄	—	2	2	no	—
100	C₅×C₂²⋊C₄	—	2	2	no	—
101	C₅×C₂²⋊C₄	—	2	2	no	—
102	C₅×C₂²⋊C₄	—	2	2	no	—
103	C₅×C₂²⋊C₄	—	2	2	no	—
104	C₅×C₂²⋊C₄	—	2	2	no	—
105	C₅×C₂²⋊C₄	—	2	2	no	—
106	C₅×C₂²⋊C₄	—	4	1	no	—
107	C₅×C₂²⋊C₄	—	4	1	no	—
108	C₅×C₂²⋊C₄	—	4	1	no	—
109	C₅×C₂²⋊C₄	—	4	1	no	—
110	C₅×C₂²⋊C₄	D₄	1	4	yes	—
111	C₄²×C₅	—	4	1	no	—
112	C₂×#123	C₂×C₅	1	1	yes	characteristic, complemented
113	C₂×C₂²⋊Q₈	C₂×C₅	1	1	yes	characteristic, complemented
114	C₂×C₂²⋊Q₈	C₂×C₅	1	1	yes	characteristic, complemented
115	C₂×#121	C₂×C₅	1	1	yes	characteristic
116	#398	C₂×C₅	1	1	yes	characteristic, complemented
117	#396	C₂×C₅	1	1	yes	characteristic, complemented
118	#394	C₂×C₅	1	1	yes	characteristic, complemented
119	#394	C₂×C₅	1	1	yes	characteristic, complemented
120	#394	C₂×C₅	1	1	yes	characteristic, complemented
121	#393	C₂×C₅	1	1	yes	characteristic, complemented
122	#390	C₂×C₅	1	1	yes	characteristic, complemented
123	#389	C₂×C₅	1	1	yes	characteristic, complemented
124	#388	C₂×C₅	1	1	yes	characteristic, complemented
125	#386	C₂×C₅	1	1	yes	characteristic, complemented
126	#385	C₂×C₅	1	1	yes	characteristic, complemented
127	C₂³×C₅	—	2	1	no	—
128	C₂³×C₅	—	2	1	no	—
129	C₂³×C₅	—	2	1	no	—
130	C₂³×C₅	—	2	1	no	—
131	C₂³×C₅	—	2	1	no	—
132	C₂³×C₅	—	2	1	no	—
133	C₂³×C₅	—	2	1	no	—
134	C₂³×C₅	—	2	1	no	—
135	C₂³×C₅	—	2	1	no	—
136	C₂³×C₅	—	2	1	no	—
137	C₂³×C₅	—	2	1	no	—
138	C₂³×C₅	—	2	1	no	—
139	C₂³×C₅	—	2	1	no	—
140	C₂³×C₅	—	2	1	no	—
141	C₂³×C₅	—	2	1	no	—
142	C₂³×C₅	—	2	1	no	—
143	C₂³×C₅	—	2	1	no	—
144	C₂³×C₅	—	2	1	no	—
145	C₂³×C₅	—	2	1	no	—
146	C₂³×C₅	C₂×D₄	1	2	yes	—
147	C₂³×C₅	#41	1	2	yes	—
148	C₂³×C₅	C₂⁴	1	1	yes	characteristic
149	C₅×Q₈	—	4	4	no	—
150	C₅×D₄	—	4	4	no	—
151	C₅×D₄	—	4	4	no	—
152	C₅×D₄	—	4	4	no	—
153	C₂×C₄×C₅	—	2	1	no	—
154	C₂×C₄×C₅	—	2	1	no	—
155	C₂×C₄×C₅	—	2	1	no	—
156	C₂×C₄×C₅	—	2	1	no	—
157	C₂×C₄×C₅	—	2	1	no	—
158	C₂×C₄×C₅	—	2	1	no	—
159	C₂×C₄×C₅	—	2	1	no	—
160	C₂×C₄×C₅	—	2	1	no	—
161	C₂×C₄×C₅	—	2	1	no	—
162	C₂×C₄×C₅	—	2	1	no	—
163	C₂×C₄×C₅	—	2	1	no	—
164	C₂×C₄×C₅	—	2	1	no	—
165	C₂×C₄×C₅	—	2	1	no	—
166	C₂×C₄×C₅	—	2	1	no	—
167	C₂×C₄×C₅	—	2	1	no	—
168	C₂×C₄×C₅	—	2	1	no	—
169	C₂×C₄×C₅	—	2	1	no	—
170	C₂×C₄×C₅	—	2	1	no	—
171	C₂×C₄×C₅	—	2	1	no	—
172	C₂×C₄×C₅	—	2	1	no	—
173	C₂×C₄×C₅	—	2	1	no	—
174	C₂×C₄×C₅	—	2	1	no	—
175	C₂×C₄×C₅	—	2	1	no	—
176	C₂×C₄×C₅	—	2	1	no	—
177	C₂×C₄×C₅	—	2	1	no	—
178	C₂×C₄×C₅	—	2	1	no	—
179	C₂×C₄×C₅	—	2	1	no	—
180	C₂×C₄×C₅	—	2	1	no	—
181	C₂×C₄×C₅	—	2	1	no	—
182	C₂×C₄×C₅	—	2	1	no	—
183	C₂×C₄×C₅	—	2	1	no	—
184	C₂×C₄×C₅	—	4	4	no	—
185	C₂×C₄×C₅	—	4	4	no	—
186	C₂×C₄×C₅	C₂×D₄	1	2	yes	—
187	C₂×C₄×C₅	C₂×D₄	1	2	yes	—
188	C₂×C₄×C₅	C₂×D₄	1	2	yes	—
189	C₂×C₄×C₅	C₂×D₄	1	2	yes	—
190	C₂×C₄×C₅	C₂×D₄	1	2	yes	—
191	C₂²×Q₈	C₂²×C₅	1	1	yes	characteristic
192	C₂²×D₄	C₂²×C₅	1	1	yes	characteristic
193	C₂²×D₄	C₂²×C₅	1	1	yes	characteristic
194	C₂²×D₄	C₂²×C₅	1	1	yes	characteristic
195	C₂³×C₄	C₂²×C₅	1	1	yes	characteristic
196	C₂³×C₄	C₂²×C₅	1	1	yes	characteristic
197	#123	—	2	4	no	—
198	C₂²⋊Q₈	—	2	4	no	—
199	C₂²⋊Q₈	—	2	4	no	—
200	#121	—	2	4	no	—
201	C₂×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
202	C₂×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
203	C₂×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
204	C₂×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
205	C₂×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
206	C₂×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
207	C₂×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
208	C₂×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
209	C₂×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
210	C₂×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
211	C₂×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
212	C₂×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
213	C₂×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
214	C₂×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
215	C₂×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
216	C₂×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
217	C₂×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
218	C₂×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
219	C₂×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
220	C₂×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
221	C₂×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
222	C₂×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
223	C₂×C₄²	C₂²×C₅	1	1	yes	characteristic
224	#95	C₂²×C₅	1	1	yes	characteristic
225	#95	C₂²×C₅	1	1	yes	characteristic
226	#95	C₂²×C₅	1	1	yes	characteristic
227	#95	C₂²×C₅	1	1	yes	characteristic
228	#95	C₂²×C₅	1	1	yes	characteristic
229	#95	C₂²×C₅	1	1	yes	characteristic
230	C₂²×C₅	—	2	2	no	—
231	C₂²×C₅	—	2	2	no	—
232	C₂²×C₅	—	2	2	no	—
233	C₂²×C₅	—	2	2	no	—
234	C₂²×C₅	—	2	2	no	—
235	C₂²×C₅	—	2	2	no	—
236	C₂²×C₅	—	4	1	no	—
237	C₂²×C₅	—	4	1	no	—
238	C₂²×C₅	—	4	1	no	—
239	C₂²×C₅	—	4	1	no	—
240	C₂²×C₅	—	4	1	no	—
241	C₂²×C₅	—	4	1	no	—
242	C₂²×C₅	—	4	1	no	—
243	C₂²×C₅	—	4	1	no	—
244	C₂²×C₅	—	4	1	no	—
245	C₂²×C₅	—	4	1	no	—
246	C₂²×C₅	—	4	1	no	—
247	C₂²×C₅	—	4	1	no	—
248	C₂²×C₅	—	4	1	no	—
249	C₂²×C₅	—	4	1	no	—
250	C₂²×C₅	—	4	1	no	—
251	C₂²×C₅	C₂²×D₄	1	1	yes	characteristic
252	C₂²×C₅	C₂²×D₄	1	1	yes	characteristic
253	C₂²×C₅	C₂×#41	1	1	yes	characteristic
254	C₂²×C₅	H(5,𝔽₂)	1	1	yes	characteristic
255	C₂²×C₅	H(5,𝔽₂)	1	1	yes	characteristic
256	C₂²×C₅	2₋¹⁺⁴	1	1	yes	characteristic
257	C₂²×C₅	2₋¹⁺⁴	1	1	yes	characteristic
258	C₄×C₅	—	2	2	no	—
259	C₄×C₅	—	2	2	no	—
260	C₄×C₅	—	2	2	no	—
261	C₄×C₅	—	2	2	no	—
262	C₄×C₅	—	2	2	no	—
263	C₄×C₅	—	4	1	no	—
264	C₄×C₅	—	4	1	no	—
265	C₄×C₅	—	4	1	no	—
266	C₄×C₅	—	4	1	no	—
267	C₄×C₅	—	4	1	no	—
268	C₄×C₅	—	4	1	no	—
269	C₄×C₅	—	4	1	no	—
270	C₂⁴	C₂³×C₅	1	1	yes	characteristic
271	C₂⁴	C₂³×C₅	1	1	yes	characteristic
272	C₂⁴	C₂³×C₅	1	1	yes	characteristic
273	C₂×Q₈	—	2	2	no	—
274	C₂×Q₈	—	2	2	no	—
275	C₂×Q₈	—	4	1	no	—
276	C₂×D₄	—	2	2	no	—
277	C₂×D₄	—	2	2	no	—
278	C₂×D₄	—	2	2	no	—
279	C₂×D₄	—	2	2	no	—
280	C₂×D₄	—	2	2	no	—
281	C₂×D₄	—	2	2	no	—
282	C₂×D₄	—	4	1	no	—
283	C₂×D₄	—	4	1	no	—
284	C₂×D₄	—	4	1	no	—
285	C₂²×C₄	—	2	2	no	—
286	C₂²×C₄	—	2	2	no	—
287	C₂²×C₄	—	2	2	no	—
288	C₂²×C₄	—	2	2	no	—
289	C₂²×C₄	—	4	1	no	—
290	C₂²×C₄	—	4	1	no	—
291	C₂²×C₄	C₂³×C₅	1	1	yes	characteristic
292	C₂²×C₄	C₂³×C₅	1	1	yes	characteristic
293	C₂²×C₄	C₂³×C₅	1	1	yes	characteristic
294	C₂²×C₄	C₂³×C₅	1	1	yes	characteristic
295	C₂²×C₄	C₂³×C₅	1	1	yes	characteristic
296	C₂²×C₄	C₂³×C₅	1	1	yes	characteristic
297	C₂²×C₄	C₂³×C₅	1	1	yes	characteristic
298	C₂²×C₄	C₂³×C₅	1	1	yes	characteristic
299	C₂²×C₄	C₂³×C₅	1	1	yes	characteristic
300	C₂²×C₄	C₂³×C₅	1	1	yes	characteristic
301	C₂²×C₄	C₂³×C₅	1	1	yes	characteristic
302	C₂²×C₄	C₂³×C₅	1	1	yes	characteristic
303	C₄⋊C₄	—	2	2	no	—
304	C₄⋊C₄	—	2	2	no	—
305	C₄⋊C₄	—	2	2	no	—
306	C₄⋊C₄	—	2	2	no	—
307	C₄⋊C₄	—	2	2	no	—
308	C₄⋊C₄	—	2	2	no	—
309	C₄⋊C₄	—	2	2	no	—
310	C₄⋊C₄	—	4	1	no	—
311	C₄⋊C₄	C₅×D₄	1	4	yes	complemented
312	C₂²⋊C₄	—	2	2	no	—
313	C₂²⋊C₄	—	2	2	no	—
314	C₂²⋊C₄	—	2	2	no	—
315	C₂²⋊C₄	—	2	2	no	—
316	C₂²⋊C₄	—	2	2	no	—
317	C₂²⋊C₄	—	2	2	no	—
318	C₂²⋊C₄	—	2	2	no	—
319	C₂²⋊C₄	—	2	2	no	—
320	C₂²⋊C₄	—	4	1	no	—
321	C₂²⋊C₄	—	4	1	no	—
322	C₂²⋊C₄	—	4	1	no	—
323	C₂²⋊C₄	—	4	1	no	—
324	C₂²⋊C₄	C₅×D₄	1	4	yes	—
325	C₄²	—	4	1	no	—
326	C₂×C₅	—	4	2	no	—
327	C₂×C₅	—	4	2	no	—
328	C₂×C₅	—	8	1	no	—
329	C₂×C₅	#536	1	1	yes	characteristic
330	C₂×C₅	#537	1	1	yes	characteristic
331	C₂×C₅	#539	1	1	yes	characteristic
332	C₂×C₅	D₄²	1	1	yes	characteristic
333	C₂×C₅	#546	1	1	yes	characteristic
334	C₂×C₅	#548	1	1	yes	characteristic
335	C₂×C₅	#562	1	1	yes	characteristic
336	C₂³	—	2	1	no	—
337	C₂³	—	2	1	no	—
338	C₂³	—	2	1	no	—
339	C₂³	—	2	1	no	—
340	C₂³	—	2	1	no	—
341	C₂³	—	2	1	no	—
342	C₂³	—	2	1	no	—
343	C₂³	—	2	1	no	—
344	C₂³	—	2	1	no	—
345	C₂³	—	2	1	no	—
346	C₂³	—	2	1	no	—
347	C₂³	—	2	1	no	—
348	C₂³	—	2	1	no	—
349	C₂³	—	2	1	no	—
350	C₂³	—	2	1	no	—
351	C₂³	—	2	1	no	—
352	C₂³	—	2	1	no	—
353	C₂³	—	2	1	no	—
354	C₂³	—	2	1	no	—
355	C₂³	C₂×C₅×D₄	1	2	yes	—
356	C₂³	C₅×#41	1	2	yes	—
357	C₂³	C₂⁴×C₅	1	1	yes	characteristic
358	Q₈	—	4	4	no	—
359	D₄	—	4	4	no	—
360	D₄	—	4	4	no	—
361	D₄	—	4	4	no	—
362	C₂×C₄	—	2	1	no	—
363	C₂×C₄	—	2	1	no	—
364	C₂×C₄	—	2	1	no	—
365	C₂×C₄	—	2	1	no	—
366	C₂×C₄	—	2	1	no	—
367	C₂×C₄	—	2	1	no	—
368	C₂×C₄	—	2	1	no	—
369	C₂×C₄	—	2	1	no	—
370	C₂×C₄	—	2	1	no	—
371	C₂×C₄	—	2	1	no	—
372	C₂×C₄	—	2	1	no	—
373	C₂×C₄	—	2	1	no	—
374	C₂×C₄	—	2	1	no	—
375	C₂×C₄	—	2	1	no	—
376	C₂×C₄	—	2	1	no	—
377	C₂×C₄	—	2	1	no	—
378	C₂×C₄	—	2	1	no	—
379	C₂×C₄	—	2	1	no	—
380	C₂×C₄	—	2	1	no	—
381	C₂×C₄	—	2	1	no	—
382	C₂×C₄	—	2	1	no	—
383	C₂×C₄	—	2	1	no	—
384	C₂×C₄	—	2	1	no	—
385	C₂×C₄	—	2	1	no	—
386	C₂×C₄	—	2	1	no	—
387	C₂×C₄	—	2	1	no	—
388	C₂×C₄	—	2	1	no	—
389	C₂×C₄	—	2	1	no	—
390	C₂×C₄	—	2	1	no	—
391	C₂×C₄	—	2	1	no	—
392	C₂×C₄	—	2	1	no	—
393	C₂×C₄	—	4	4	no	—
394	C₂×C₄	—	4	4	no	—
395	C₂×C₄	C₂×C₅×D₄	1	2	yes	—
396	C₂×C₄	C₂×C₅×D₄	1	2	yes	—
397	C₂×C₄	C₂×C₅×D₄	1	2	yes	—
398	C₂×C₄	C₂×C₅×D₄	1	2	yes	—
399	C₂×C₄	C₂×C₅×D₄	1	2	yes	—
400	C₅	#2681	1	1	yes	characteristic, direct product factor, Sylow
401	C₂²	—	2	2	no	—
402	C₂²	—	2	2	no	—
403	C₂²	—	2	2	no	—
404	C₂²	—	2	2	no	—
405	C₂²	—	2	2	no	—
406	C₂²	—	2	2	no	—
407	C₂²	—	4	1	no	—
408	C₂²	—	4	1	no	—
409	C₂²	—	4	1	no	—
410	C₂²	—	4	1	no	—
411	C₂²	—	4	1	no	—
412	C₂²	—	4	1	no	—
413	C₂²	—	4	1	no	—
414	C₂²	—	4	1	no	—
415	C₂²	—	4	1	no	—
416	C₂²	—	4	1	no	—
417	C₂²	—	4	1	no	—
418	C₂²	—	4	1	no	—
419	C₂²	—	4	1	no	—
420	C₂²	—	4	1	no	—
421	C₂²	—	4	1	no	—
422	C₂²	C₂²×C₅×D₄	1	1	yes	characteristic
423	C₂²	C₂²×C₅×D₄	1	1	yes	characteristic
424	C₂²	C₂×C₅×#41	1	1	yes	characteristic
425	C₂²	C₅×H(5,𝔽₂)	1	1	yes	characteristic
426	C₂²	C₅×H(5,𝔽₂)	1	1	yes	characteristic
427	C₂²	C₅×2₋¹⁺⁴	1	1	yes	characteristic
428	C₂²	C₅×2₋¹⁺⁴	1	1	yes	characteristic
429	C₄	—	2	2	no	—
430	C₄	—	2	2	no	—
431	C₄	—	2	2	no	—
432	C₄	—	2	2	no	—
433	C₄	—	2	2	no	—
434	C₄	—	4	1	no	—
435	C₄	—	4	1	no	—
436	C₄	—	4	1	no	—
437	C₄	—	4	1	no	—
438	C₄	—	4	1	no	—
439	C₄	—	4	1	no	—
440	C₄	—	4	1	no	—
441	C₂	—	4	2	no	—
442	C₂	—	4	2	no	—
443	C₂	—	8	1	no	—
444	C₂	C₅×#536	1	1	yes	characteristic
445	C₂	C₅×#537	1	1	yes	characteristic
446	C₂	C₅×#539	1	1	yes	characteristic
447	C₂	C₅×D₄²	1	1	yes	characteristic
448	C₂	C₅×#546	1	1	yes	characteristic
449	C₂	C₅×#548	1	1	yes	characteristic
450	C₂	C₅×#562	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₅	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁴×C₅
prime radical	C₂×C₅×#121	C₂
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₅×#123	C₂	semidirect
2. C₂×C₅×C₂²⋊Q₈	C₂	semidirect
3. C₂×C₅×C₂²⋊Q₈	C₂	semidirect
5. C₅×#398	C₂	semidirect
6. C₅×#396	C₂	semidirect
7. C₅×#394	C₂	semidirect
8. C₅×#394	C₂	semidirect
9. C₅×#394	C₂	semidirect
10. C₅×#393	C₂	semidirect
11. C₅×#390	C₂	semidirect
12. C₅×#389	C₂	semidirect
13. C₅×#388	C₂	semidirect
14. C₅×#386	C₂	semidirect
15. C₅×#385	C₂	semidirect
55. #2681	C₅	direct (N × H)
97. C₅×C₄⋊C₄	D₄	semidirect
112. C₂×#123	C₂×C₅	semidirect
113. C₂×C₂²⋊Q₈	C₂×C₅	semidirect
114. C₂×C₂²⋊Q₈	C₂×C₅	semidirect
116. #398	C₂×C₅	semidirect
117. #396	C₂×C₅	semidirect
118. #394	C₂×C₅	semidirect
119. #394	C₂×C₅	semidirect
120. #394	C₂×C₅	semidirect
121. #393	C₂×C₅	semidirect
122. #390	C₂×C₅	semidirect
123. #389	C₂×C₅	semidirect
124. #388	C₂×C₅	semidirect
125. #386	C₂×C₅	semidirect
126. #385	C₂×C₅	semidirect
311. C₄⋊C₄	C₅×D₄	semidirect
400. C₅	#2681	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×#123	2
C₂×C₅×C₂²⋊Q₈	2
C₂×C₅×#121	2
C₅×#398	2
C₅×#396	2
C₅×#394	2
C₅×#393	2
C₅×#390	2
C₅×#389	2
C₅×#388	2
C₅×#386	2
C₅×#385	2
#2681	5

Subgroups — C5×#2681 #10616276

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#2681 #10616276