Subgroups — C₅×#3546 #10619331

Order 640.

1150 conjugacy classes of subgroups.

The subgroup lattice has 482 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#560	C₂	1	4	yes	maximal, complemented
2	C₅×#556	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#553	C₂	1	2	yes	maximal, complemented
4	C₅×#550	C₂	1	2	yes	maximal, complemented
5	C₅×#550	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#547	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#546	C₂	1	2	yes	maximal, complemented
8	C₅×#546	C₂	1	2	yes	maximal, complemented
9	C₅×D₄²	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#542	C₂	1	2	yes	maximal, complemented
11	C₅×#538	C₂	1	4	yes	maximal, complemented
12	C₅×#537	C₂	1	2	yes	maximal, complemented
13	C₅×#535	C₂	1	2	yes	maximal, complemented
14	C₅×#535	C₂	1	2	yes	maximal, complemented
15	C₅×#532	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅×#532	C₂	1	1	yes	maximal, characteristic, complemented
17	C₅×#529	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₅×#41	C₂²	1	2	yes	complemented
19	C₂×C₅×#41	C₂²	1	2	yes	complemented
20	C₂×C₅×#41	C₂²	1	2	yes	complemented
21	C₂×C₅×#41	C₂²	1	2	yes	complemented
22	C₂²×C₅×D₄	C₂²	1	2	yes	—
23	C₂²×C₅×D₄	C₂²	1	2	yes	—
24	C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
25	C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
26	C₅×#127	C₂²	1	1	yes	characteristic
27	C₅×#127	C₂²	1	1	yes	characteristic
28	C₅×#127	C₂²	1	2	yes	complemented
29	C₅×#127	C₂²	1	4	yes	complemented
30	C₅×#126	C₂²	1	2	yes	complemented
31	C₅×#126	C₂²	1	4	yes	complemented
32	C₅×#126	C₂²	1	4	yes	complemented
33	C₅×#125	C₂²	1	1	yes	characteristic, complemented
34	C₅×#124	C₂²	1	1	yes	characteristic
35	C₅×#124	C₂²	1	2	yes	—
36	C₅×#124	C₂²	1	2	yes	complemented
37	C₅×#124	C₂²	1	2	yes	complemented
38	C₅×#124	C₂²	1	4	yes	complemented
39	C₅×#123	C₂²	1	2	yes	complemented
40	C₅×#123	C₂²	1	4	yes	complemented
41	C₅×#123	C₂²	1	4	yes	complemented
42	C₅×#123	C₂²	1	4	yes	complemented
43	C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
44	C₅×C₂²⋊Q₈	C₂²	1	4	yes	complemented
45	C₅×C₂²⋊Q₈	C₂²	1	2	yes	complemented
46	C₅×C₂²⋊Q₈	C₂²	1	2	yes	complemented
47	C₅×#121	C₂²	1	1	yes	characteristic
48	C₅×#121	C₂²	1	1	yes	characteristic
49	C₅×#121	C₂²	1	2	yes	—
50	C₅×#121	C₂²	1	2	yes	—
51	C₅×#121	C₂²	1	2	yes	—
52	C₅×#121	C₂²	1	2	yes	complemented
53	C₅×#121	C₂²	1	1	yes	characteristic, complemented
54	C₅×#121	C₂²	1	2	yes	complemented
55	C₅×#121	C₂²	1	2	yes	complemented
56	C₅×#121	C₂²	1	4	yes	complemented
57	C₅×#121	C₂²	1	2	yes	complemented
58	C₅×#121	C₂²	1	4	yes	complemented
59	C₅×#121	C₂²	1	4	yes	complemented
60	C₅×#121	C₂²	1	4	yes	complemented
61	C₅×#121	C₂²	1	4	yes	complemented
62	C₅×#121	C₂²	1	4	yes	complemented
63	C₅×#120	C₂²	1	4	yes	—
64	C₅×#120	C₂²	1	4	yes	complemented
65	C₅×#120	C₂²	1	4	yes	complemented
66	C₅×#120	C₂²	1	4	yes	complemented
67	C₄×C₅×Q₈	C₂²	1	1	yes	characteristic, complemented
68	C₄×C₅×Q₈	C₂²	1	2	yes	complemented
69	C₄×C₅×D₄	C₂²	1	1	yes	characteristic
70	C₄×C₅×D₄	C₂²	1	1	yes	characteristic
71	C₄×C₅×D₄	C₂²	1	2	yes	complemented
72	C₄×C₅×D₄	C₂²	1	2	yes	complemented
73	C₄×C₅×D₄	C₂²	1	2	yes	complemented
74	C₄×C₅×D₄	C₂²	1	2	yes	complemented
75	C₄×C₅×D₄	C₂²	1	1	yes	characteristic, complemented
76	C₄×C₅×D₄	C₂²	1	4	yes	complemented
77	C₄×C₅×D₄	C₂²	1	2	yes	complemented
78	C₅×#117	C₂²	1	2	yes	complemented
79	C₅×#117	C₂²	1	2	yes	complemented
80	C₂×C₅×C₄⋊C₄	C₂²	1	2	yes	complemented
81	C₂×C₅×C₂²⋊C₄	C₂²	1	4	yes	complemented
82	C₂×C₄²×C₅	C₂²	1	1	yes	characteristic, complemented
83	#3546	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
84	C₂⁴×C₅	C₂³	1	4	yes	—
85	C₅×#41	—	4	4	no	—
86	C₅×#41	—	4	4	no	—
87	C₅×#41	—	4	4	no	—
88	C₅×#41	—	4	4	no	—
89	C₂×C₅×Q₈	C₂³	1	1	yes	characteristic
90	C₂×C₅×Q₈	C₂³	1	2	yes	—
91	C₂×C₅×Q₈	C₂³	1	2	yes	—
92	C₂×C₅×D₄	—	4	4	no	—
93	C₂×C₅×D₄	—	4	4	no	—
94	C₂×C₅×D₄	C₂³	1	1	yes	characteristic
95	C₂×C₅×D₄	C₂³	1	1	yes	characteristic
96	C₂×C₅×D₄	C₂³	1	2	yes	—
97	C₂×C₅×D₄	C₂³	1	2	yes	—
98	C₂×C₅×D₄	C₂³	1	1	yes	characteristic
99	C₂×C₅×D₄	C₂³	1	2	yes	—
100	C₂×C₅×D₄	C₂³	1	2	yes	—
101	C₂×C₅×D₄	C₂³	1	2	yes	—
102	C₂×C₅×D₄	C₂³	1	4	yes	—
103	C₂×C₅×D₄	C₂³	1	4	yes	—
104	C₂×C₅×D₄	C₂³	1	4	yes	—
105	C₂×C₅×D₄	C₂³	1	2	yes	—
106	C₂×C₅×D₄	C₂³	1	4	yes	—
107	C₂×C₅×D₄	C₂³	1	2	yes	—
108	C₂×C₅×D₄	C₂³	1	4	yes	—
109	C₂×C₅×D₄	C₂³	1	4	yes	—
110	C₂×C₅×D₄	C₂³	1	2	yes	—
111	C₂²×C₄×C₅	C₂³	1	1	yes	characteristic
112	C₂²×C₄×C₅	C₂³	1	1	yes	characteristic
113	C₂²×C₄×C₅	C₂³	1	2	yes	—
114	C₂²×C₄×C₅	C₂³	1	2	yes	—
115	C₂²×C₄×C₅	C₂³	1	2	yes	—
116	C₂²×C₄×C₅	C₂³	1	1	yes	characteristic
117	C₂²×C₄×C₅	C₂³	1	4	yes	—
118	C₂²×C₄×C₅	C₂³	1	4	yes	—
119	C₂²×C₄×C₅	C₂³	1	4	yes	—
120	C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
121	C₅×C₄⋊C₄	C₂³	1	2	yes	—
122	C₅×C₄⋊C₄	C₂³	1	4	yes	—
123	C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
124	C₅×C₄⋊C₄	C₂³	1	2	yes	—
125	C₅×C₄⋊C₄	C₂³	1	2	yes	—
126	C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
127	C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
128	C₅×C₄⋊C₄	C₂³	1	2	yes	—
129	C₅×C₄⋊C₄	C₂³	1	2	yes	—
130	C₅×C₄⋊C₄	C₂³	1	2	yes	—
131	C₅×C₄⋊C₄	C₂³	1	4	yes	—
132	C₅×C₄⋊C₄	C₂³	1	2	yes	—
133	C₅×C₂²⋊C₄	C₂³	1	2	yes	—
134	C₅×C₂²⋊C₄	C₂³	1	2	yes	—
135	C₅×C₂²⋊C₄	C₂³	1	4	yes	—
136	C₅×C₂²⋊C₄	C₂³	1	4	yes	—
137	C₅×C₂²⋊C₄	C₂³	1	2	yes	—
138	C₅×C₂²⋊C₄	C₂³	1	4	yes	—
139	C₅×C₂²⋊C₄	C₂³	1	2	yes	—
140	C₅×C₂²⋊C₄	C₂³	1	2	yes	—
141	C₅×C₂²⋊C₄	C₂³	1	2	yes	—
142	C₅×C₂²⋊C₄	C₂³	1	2	yes	—
143	C₅×C₂²⋊C₄	C₂³	1	4	yes	—
144	C₅×C₂²⋊C₄	C₂³	1	4	yes	—
145	C₅×C₂²⋊C₄	C₂³	1	4	yes	—
146	C₅×C₂²⋊C₄	C₂³	1	4	yes	—
147	C₅×C₂²⋊C₄	C₂³	1	2	yes	—
148	C₅×C₂²⋊C₄	C₂³	1	2	yes	—
149	C₄²×C₅	C₂³	1	1	yes	characteristic
150	C₄²×C₅	C₂³	1	1	yes	characteristic
151	C₄²×C₅	C₂³	1	1	yes	characteristic
152	C₄²×C₅	C₂³	1	1	yes	characteristic
153	C₄²×C₅	C₂³	1	2	yes	—
154	C₄²×C₅	C₂³	1	4	yes	—
155	#560	C₂×C₅	1	4	yes	complemented
156	#556	C₂×C₅	1	1	yes	characteristic, complemented
157	#553	C₂×C₅	1	2	yes	complemented
158	#550	C₂×C₅	1	2	yes	complemented
159	#550	C₂×C₅	1	1	yes	characteristic, complemented
160	#547	C₂×C₅	1	1	yes	characteristic, complemented
161	#546	C₂×C₅	1	2	yes	complemented
162	#546	C₂×C₅	1	2	yes	complemented
163	D₄²	C₂×C₅	1	1	yes	characteristic, complemented
164	#542	C₂×C₅	1	2	yes	complemented
165	#538	C₂×C₅	1	4	yes	complemented
166	#537	C₂×C₅	1	2	yes	complemented
167	#535	C₂×C₅	1	2	yes	complemented
168	#535	C₂×C₅	1	2	yes	complemented
169	#532	C₂×C₅	1	1	yes	characteristic, complemented
170	#532	C₂×C₅	1	1	yes	characteristic, complemented
171	#529	C₂×C₅	1	1	yes	characteristic, complemented
172	C₂³×C₅	—	4	4	no	—
173	C₂³×C₅	—	4	4	no	—
174	C₂³×C₅	—	4	4	no	—
175	C₂³×C₅	C₂⁴	1	2	yes	—
176	C₂³×C₅	C₂⁴	1	2	yes	—
177	C₂³×C₅	C₂⁴	1	4	yes	—
178	C₂³×C₅	C₂⁴	1	1	yes	characteristic
179	C₂³×C₅	C₂⁴	1	2	yes	—
180	C₅×Q₈	—	2	2	no	—
181	C₅×Q₈	—	2	4	no	—
182	C₅×Q₈	—	4	2	no	—
183	C₅×D₄	—	2	2	no	—
184	C₅×D₄	—	2	2	no	—
185	C₅×D₄	—	2	4	no	—
186	C₅×D₄	—	2	4	no	—
187	C₅×D₄	—	2	2	no	—
188	C₅×D₄	—	4	4	no	—
189	C₅×D₄	—	4	4	no	—
190	C₅×D₄	—	4	2	no	—
191	C₅×D₄	—	4	2	no	—
192	C₅×D₄	—	4	2	no	—
193	C₅×D₄	—	4	4	no	—
194	C₅×D₄	—	4	2	no	—
195	C₅×D₄	—	4	2	no	—
196	C₅×D₄	—	4	2	no	—
197	C₅×D₄	—	4	4	no	—
198	C₅×D₄	—	4	4	no	—
199	C₅×D₄	—	4	4	no	—
200	C₂×C₄×C₅	—	2	4	no	—
201	C₂×C₄×C₅	—	2	4	no	—
202	C₂×C₄×C₅	—	2	2	no	—
203	C₂×C₄×C₅	—	2	4	no	—
204	C₂×C₄×C₅	—	2	2	no	—
205	C₂×C₄×C₅	—	4	1	no	—
206	C₂×C₄×C₅	—	4	4	no	—
207	C₂×C₄×C₅	—	4	4	no	—
208	C₂×C₄×C₅	—	4	4	no	—
209	C₂×C₄×C₅	C₂⁴	1	2	yes	—
210	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
211	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
212	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
213	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
214	C₂×C₄×C₅	C₂⁴	1	2	yes	—
215	C₂×C₄×C₅	C₂⁴	1	2	yes	—
216	C₂×C₄×C₅	C₂⁴	1	4	yes	—
217	C₂×C₄×C₅	C₂⁴	1	2	yes	—
218	C₂×C₄×C₅	C₂⁴	1	2	yes	—
219	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
220	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
221	C₂×#41	C₂²×C₅	1	2	yes	complemented
222	C₂×#41	C₂²×C₅	1	2	yes	complemented
223	C₂×#41	C₂²×C₅	1	2	yes	complemented
224	C₂×#41	C₂²×C₅	1	2	yes	complemented
225	C₂²×D₄	C₂²×C₅	1	2	yes	—
226	C₂²×D₄	C₂²×C₅	1	2	yes	—
227	C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
228	C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
229	#127	C₂²×C₅	1	1	yes	characteristic
230	#127	C₂²×C₅	1	1	yes	characteristic
231	#127	C₂²×C₅	1	2	yes	complemented
232	#127	C₂²×C₅	1	4	yes	complemented
233	#126	C₂²×C₅	1	2	yes	complemented
234	#126	C₂²×C₅	1	4	yes	complemented
235	#126	C₂²×C₅	1	4	yes	complemented
236	#125	C₂²×C₅	1	1	yes	characteristic, complemented
237	#124	C₂²×C₅	1	1	yes	characteristic
238	#124	C₂²×C₅	1	2	yes	—
239	#124	C₂²×C₅	1	2	yes	complemented
240	#124	C₂²×C₅	1	2	yes	complemented
241	#124	C₂²×C₅	1	4	yes	complemented
242	#123	C₂²×C₅	1	2	yes	complemented
243	#123	C₂²×C₅	1	4	yes	complemented
244	#123	C₂²×C₅	1	4	yes	complemented
245	#123	C₂²×C₅	1	4	yes	complemented
246	C₂²⋊Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
247	C₂²⋊Q₈	C₂²×C₅	1	4	yes	complemented
248	C₂²⋊Q₈	C₂²×C₅	1	2	yes	complemented
249	C₂²⋊Q₈	C₂²×C₅	1	2	yes	complemented
250	#121	C₂²×C₅	1	1	yes	characteristic
251	#121	C₂²×C₅	1	1	yes	characteristic
252	#121	C₂²×C₅	1	2	yes	—
253	#121	C₂²×C₅	1	2	yes	—
254	#121	C₂²×C₅	1	2	yes	—
255	#121	C₂²×C₅	1	2	yes	complemented
256	#121	C₂²×C₅	1	1	yes	characteristic, complemented
257	#121	C₂²×C₅	1	2	yes	complemented
258	#121	C₂²×C₅	1	2	yes	complemented
259	#121	C₂²×C₅	1	4	yes	complemented
260	#121	C₂²×C₅	1	2	yes	complemented
261	#121	C₂²×C₅	1	4	yes	complemented
262	#121	C₂²×C₅	1	4	yes	complemented
263	#121	C₂²×C₅	1	4	yes	complemented
264	#121	C₂²×C₅	1	4	yes	complemented
265	#121	C₂²×C₅	1	4	yes	complemented
266	#120	C₂²×C₅	1	4	yes	—
267	#120	C₂²×C₅	1	4	yes	complemented
268	#120	C₂²×C₅	1	4	yes	complemented
269	#120	C₂²×C₅	1	4	yes	complemented
270	C₄×Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
271	C₄×Q₈	C₂²×C₅	1	2	yes	complemented
272	C₄×D₄	C₂²×C₅	1	1	yes	characteristic
273	C₄×D₄	C₂²×C₅	1	1	yes	characteristic
274	C₄×D₄	C₂²×C₅	1	2	yes	complemented
275	C₄×D₄	C₂²×C₅	1	2	yes	complemented
276	C₄×D₄	C₂²×C₅	1	2	yes	complemented
277	C₄×D₄	C₂²×C₅	1	2	yes	complemented
278	C₄×D₄	C₂²×C₅	1	1	yes	characteristic, complemented
279	C₄×D₄	C₂²×C₅	1	4	yes	complemented
280	C₄×D₄	C₂²×C₅	1	2	yes	complemented
281	#117	C₂²×C₅	1	2	yes	complemented
282	#117	C₂²×C₅	1	2	yes	complemented
283	C₂×C₄⋊C₄	C₂²×C₅	1	2	yes	complemented
284	C₂×C₂²⋊C₄	C₂²×C₅	1	4	yes	complemented
285	C₂×C₄²	C₂²×C₅	1	1	yes	characteristic, complemented
286	C₂²×C₅	—	2	1	no	—
287	C₂²×C₅	—	2	1	no	—
288	C₂²×C₅	—	2	2	no	—
289	C₂²×C₅	—	2	2	no	—
290	C₂²×C₅	—	2	2	no	—
291	C₂²×C₅	—	2	2	no	—
292	C₂²×C₅	—	2	4	no	—
293	C₂²×C₅	—	2	4	no	—
294	C₂²×C₅	—	2	2	no	—
295	C₂²×C₅	—	2	2	no	—
296	C₂²×C₅	—	2	1	no	—
297	C₂²×C₅	—	2	2	no	—
298	C₂²×C₅	—	2	4	no	—
299	C₂²×C₅	—	2	2	no	—
300	C₂²×C₅	—	2	2	no	—
301	C₂²×C₅	—	8	8	no	—
302	C₂²×C₅	C₂⁵	1	1	yes	characteristic
303	C₄×C₅	—	2	1	no	—
304	C₄×C₅	—	2	2	no	—
305	C₄×C₅	—	2	2	no	—
306	C₄×C₅	—	2	2	no	—
307	C₄×C₅	—	2	1	no	—
308	C₄×C₅	—	2	4	no	—
309	C₄×C₅	—	2	2	no	—
310	C₄×C₅	—	2	1	no	—
311	C₄×C₅	—	2	1	no	—
312	C₄×C₅	—	2	2	no	—
313	C₄×C₅	H(5,𝔽₂)	1	2	yes	—
314	C₄×C₅	H(5,𝔽₂)	1	2	yes	—
315	C₂⁴	C₂³×C₅	1	4	yes	—
316	#41	—	4	4	no	—
317	#41	—	4	4	no	—
318	#41	—	4	4	no	—
319	#41	—	4	4	no	—
320	C₂×Q₈	C₂³×C₅	1	1	yes	characteristic
321	C₂×Q₈	C₂³×C₅	1	2	yes	—
322	C₂×Q₈	C₂³×C₅	1	2	yes	—
323	C₂×D₄	—	4	4	no	—
324	C₂×D₄	—	4	4	no	—
325	C₂×D₄	C₂³×C₅	1	1	yes	characteristic
326	C₂×D₄	C₂³×C₅	1	1	yes	characteristic
327	C₂×D₄	C₂³×C₅	1	2	yes	—
328	C₂×D₄	C₂³×C₅	1	2	yes	—
329	C₂×D₄	C₂³×C₅	1	1	yes	characteristic
330	C₂×D₄	C₂³×C₅	1	2	yes	—
331	C₂×D₄	C₂³×C₅	1	2	yes	—
332	C₂×D₄	C₂³×C₅	1	2	yes	—
333	C₂×D₄	C₂³×C₅	1	4	yes	—
334	C₂×D₄	C₂³×C₅	1	4	yes	—
335	C₂×D₄	C₂³×C₅	1	4	yes	—
336	C₂×D₄	C₂³×C₅	1	2	yes	—
337	C₂×D₄	C₂³×C₅	1	4	yes	—
338	C₂×D₄	C₂³×C₅	1	2	yes	—
339	C₂×D₄	C₂³×C₅	1	4	yes	—
340	C₂×D₄	C₂³×C₅	1	4	yes	—
341	C₂×D₄	C₂³×C₅	1	2	yes	—
342	C₂²×C₄	C₂³×C₅	1	1	yes	characteristic
343	C₂²×C₄	C₂³×C₅	1	1	yes	characteristic
344	C₂²×C₄	C₂³×C₅	1	2	yes	—
345	C₂²×C₄	C₂³×C₅	1	2	yes	—
346	C₂²×C₄	C₂³×C₅	1	2	yes	—
347	C₂²×C₄	C₂³×C₅	1	1	yes	characteristic
348	C₂²×C₄	C₂³×C₅	1	4	yes	—
349	C₂²×C₄	C₂³×C₅	1	4	yes	—
350	C₂²×C₄	C₂³×C₅	1	4	yes	—
351	C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
352	C₄⋊C₄	C₂³×C₅	1	2	yes	—
353	C₄⋊C₄	C₂³×C₅	1	4	yes	—
354	C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
355	C₄⋊C₄	C₂³×C₅	1	2	yes	—
356	C₄⋊C₄	C₂³×C₅	1	2	yes	—
357	C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
358	C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
359	C₄⋊C₄	C₂³×C₅	1	2	yes	—
360	C₄⋊C₄	C₂³×C₅	1	2	yes	—
361	C₄⋊C₄	C₂³×C₅	1	2	yes	—
362	C₄⋊C₄	C₂³×C₅	1	4	yes	—
363	C₄⋊C₄	C₂³×C₅	1	2	yes	—
364	C₂²⋊C₄	C₂³×C₅	1	2	yes	—
365	C₂²⋊C₄	C₂³×C₅	1	2	yes	—
366	C₂²⋊C₄	C₂³×C₅	1	4	yes	—
367	C₂²⋊C₄	C₂³×C₅	1	4	yes	—
368	C₂²⋊C₄	C₂³×C₅	1	2	yes	—
369	C₂²⋊C₄	C₂³×C₅	1	4	yes	—
370	C₂²⋊C₄	C₂³×C₅	1	2	yes	—
371	C₂²⋊C₄	C₂³×C₅	1	2	yes	—
372	C₂²⋊C₄	C₂³×C₅	1	2	yes	—
373	C₂²⋊C₄	C₂³×C₅	1	2	yes	—
374	C₂²⋊C₄	C₂³×C₅	1	4	yes	—
375	C₂²⋊C₄	C₂³×C₅	1	4	yes	—
376	C₂²⋊C₄	C₂³×C₅	1	4	yes	—
377	C₂²⋊C₄	C₂³×C₅	1	4	yes	—
378	C₂²⋊C₄	C₂³×C₅	1	2	yes	—
379	C₂²⋊C₄	C₂³×C₅	1	2	yes	—
380	C₄²	C₂³×C₅	1	1	yes	characteristic
381	C₄²	C₂³×C₅	1	1	yes	characteristic
382	C₄²	C₂³×C₅	1	1	yes	characteristic
383	C₄²	C₂³×C₅	1	1	yes	characteristic
384	C₄²	C₂³×C₅	1	2	yes	—
385	C₄²	C₂³×C₅	1	4	yes	—
386	C₂×C₅	—	4	1	no	—
387	C₂×C₅	—	4	2	no	—
388	C₂×C₅	—	4	4	no	—
389	C₂×C₅	—	4	2	no	—
390	C₂×C₅	—	4	2	no	—
391	C₂×C₅	C₂×H(5,𝔽₂)	1	1	yes	characteristic
392	C₂×C₅	C₂×H(5,𝔽₂)	1	1	yes	characteristic
393	C₂×C₅	#585	1	1	yes	characteristic
394	C₂³	—	4	4	no	—
395	C₂³	—	4	4	no	—
396	C₂³	—	4	4	no	—
397	C₂³	C₂⁴×C₅	1	2	yes	—
398	C₂³	C₂⁴×C₅	1	2	yes	—
399	C₂³	C₂⁴×C₅	1	4	yes	—
400	C₂³	C₂⁴×C₅	1	1	yes	characteristic
401	C₂³	C₂⁴×C₅	1	2	yes	—
402	Q₈	—	2	2	no	—
403	Q₈	—	2	4	no	—
404	Q₈	—	4	2	no	—
405	D₄	—	2	2	no	—
406	D₄	—	2	2	no	—
407	D₄	—	2	4	no	—
408	D₄	—	2	4	no	—
409	D₄	—	2	2	no	—
410	D₄	—	4	4	no	—
411	D₄	—	4	4	no	—
412	D₄	—	4	2	no	—
413	D₄	—	4	2	no	—
414	D₄	—	4	2	no	—
415	D₄	—	4	4	no	—
416	D₄	—	4	4	no	—
417	D₄	—	4	4	no	—
418	D₄	—	4	2	no	—
419	D₄	—	4	2	no	—
420	D₄	—	4	2	no	—
421	D₄	—	4	4	no	—
422	C₂×C₄	—	2	4	no	—
423	C₂×C₄	—	2	4	no	—
424	C₂×C₄	—	2	2	no	—
425	C₂×C₄	—	2	4	no	—
426	C₂×C₄	—	2	2	no	—
427	C₂×C₄	—	4	4	no	—
428	C₂×C₄	—	4	4	no	—
429	C₂×C₄	—	4	4	no	—
430	C₂×C₄	—	4	1	no	—
431	C₂×C₄	C₂⁴×C₅	1	2	yes	—
432	C₂×C₄	C₂⁴×C₅	1	1	yes	characteristic
433	C₂×C₄	C₂⁴×C₅	1	1	yes	characteristic
434	C₂×C₄	C₂⁴×C₅	1	1	yes	characteristic
435	C₂×C₄	C₂⁴×C₅	1	1	yes	characteristic
436	C₂×C₄	C₂⁴×C₅	1	2	yes	—
437	C₂×C₄	C₂⁴×C₅	1	2	yes	—
438	C₂×C₄	C₂⁴×C₅	1	4	yes	—
439	C₂×C₄	C₂⁴×C₅	1	2	yes	—
440	C₂×C₄	C₂⁴×C₅	1	2	yes	—
441	C₂×C₄	C₂⁴×C₅	1	1	yes	characteristic
442	C₂×C₄	C₂⁴×C₅	1	1	yes	characteristic
443	C₅	#3546	1	1	yes	characteristic, direct product factor, Sylow
444	C₂²	—	2	1	no	—
445	C₂²	—	2	1	no	—
446	C₂²	—	2	2	no	—
447	C₂²	—	2	2	no	—
448	C₂²	—	2	2	no	—
449	C₂²	—	2	2	no	—
450	C₂²	—	2	4	no	—
451	C₂²	—	2	4	no	—
452	C₂²	—	2	2	no	—
453	C₂²	—	2	2	no	—
454	C₂²	—	2	1	no	—
455	C₂²	—	2	2	no	—
456	C₂²	—	2	4	no	—
457	C₂²	—	2	2	no	—
458	C₂²	—	2	2	no	—
459	C₂²	—	8	8	no	—
460	C₂²	C₂⁵×C₅	1	1	yes	characteristic
461	C₄	—	2	1	no	—
462	C₄	—	2	2	no	—
463	C₄	—	2	2	no	—
464	C₄	—	2	2	no	—
465	C₄	—	2	1	no	—
466	C₄	—	2	4	no	—
467	C₄	—	2	2	no	—
468	C₄	—	2	1	no	—
469	C₄	—	2	1	no	—
470	C₄	—	2	2	no	—
471	C₄	C₅×H(5,𝔽₂)	1	2	yes	—
472	C₄	C₅×H(5,𝔽₂)	1	2	yes	—
473	C₂	—	4	2	no	—
474	C₂	—	4	2	no	—
475	C₂	—	4	4	no	—
476	C₂	—	4	1	no	—
477	C₂	—	4	2	no	—
478	C₂	C₂×C₅×H(5,𝔽₂)	1	1	yes	characteristic
479	C₂	C₂×C₅×H(5,𝔽₂)	1	1	yes	characteristic
480	C₂	C₅×#585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₅	C₂⁵
commutator, Frattini, cosocle	C₂²	C₂⁵×C₅
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₅×#560	C₂	semidirect
2. C₅×#556	C₂	semidirect
3. C₅×#553	C₂	semidirect
4. C₅×#550	C₂	semidirect
5. C₅×#550	C₂	semidirect
6. C₅×#547	C₂	semidirect
7. C₅×#546	C₂	semidirect
8. C₅×#546	C₂	semidirect
9. C₅×D₄²	C₂	semidirect
10. C₅×#542	C₂	semidirect
11. C₅×#538	C₂	semidirect
12. C₅×#537	C₂	semidirect
13. C₅×#535	C₂	semidirect
14. C₅×#535	C₂	semidirect
15. C₅×#532	C₂	semidirect
16. C₅×#532	C₂	semidirect
17. C₅×#529	C₂	semidirect
18. C₂×C₅×#41	C₂²	semidirect
19. C₂×C₅×#41	C₂²	semidirect
20. C₂×C₅×#41	C₂²	semidirect
21. C₂×C₅×#41	C₂²	semidirect
24. C₅×C₄⋊Q₈	C₂²	semidirect
25. C₅×C₄⋊Q₈	C₂²	semidirect
28. C₅×#127	C₂²	semidirect
29. C₅×#127	C₂²	semidirect
30. C₅×#126	C₂²	semidirect
31. C₅×#126	C₂²	semidirect
32. C₅×#126	C₂²	semidirect
33. C₅×#125	C₂²	semidirect
36. C₅×#124	C₂²	semidirect
37. C₅×#124	C₂²	semidirect
38. C₅×#124	C₂²	semidirect
39. C₅×#123	C₂²	semidirect
40. C₅×#123	C₂²	semidirect
41. C₅×#123	C₂²	semidirect
42. C₅×#123	C₂²	semidirect
43. C₅×C₂²⋊Q₈	C₂²	semidirect
44. C₅×C₂²⋊Q₈	C₂²	semidirect
45. C₅×C₂²⋊Q₈	C₂²	semidirect
46. C₅×C₂²⋊Q₈	C₂²	semidirect
52. C₅×#121	C₂²	semidirect
53. C₅×#121	C₂²	semidirect
54. C₅×#121	C₂²	semidirect
55. C₅×#121	C₂²	semidirect
56. C₅×#121	C₂²	semidirect
57. C₅×#121	C₂²	semidirect
58. C₅×#121	C₂²	semidirect
59. C₅×#121	C₂²	semidirect
60. C₅×#121	C₂²	semidirect
61. C₅×#121	C₂²	semidirect
62. C₅×#121	C₂²	semidirect
64. C₅×#120	C₂²	semidirect
65. C₅×#120	C₂²	semidirect
66. C₅×#120	C₂²	semidirect
67. C₄×C₅×Q₈	C₂²	semidirect
68. C₄×C₅×Q₈	C₂²	semidirect
71. C₄×C₅×D₄	C₂²	semidirect
72. C₄×C₅×D₄	C₂²	semidirect
73. C₄×C₅×D₄	C₂²	semidirect
74. C₄×C₅×D₄	C₂²	semidirect
75. C₄×C₅×D₄	C₂²	semidirect
76. C₄×C₅×D₄	C₂²	semidirect
77. C₄×C₅×D₄	C₂²	semidirect
78. C₅×#117	C₂²	semidirect
79. C₅×#117	C₂²	semidirect
80. C₂×C₅×C₄⋊C₄	C₂²	semidirect
81. C₂×C₅×C₂²⋊C₄	C₂²	semidirect
82. C₂×C₄²×C₅	C₂²	semidirect
83. #3546	C₅	direct (N × H)
155. #560	C₂×C₅	semidirect
156. #556	C₂×C₅	semidirect
157. #553	C₂×C₅	semidirect
158. #550	C₂×C₅	semidirect
159. #550	C₂×C₅	semidirect
160. #547	C₂×C₅	semidirect
161. #546	C₂×C₅	semidirect
162. #546	C₂×C₅	semidirect
163. D₄²	C₂×C₅	semidirect
164. #542	C₂×C₅	semidirect
165. #538	C₂×C₅	semidirect
166. #537	C₂×C₅	semidirect
167. #535	C₂×C₅	semidirect
168. #535	C₂×C₅	semidirect
169. #532	C₂×C₅	semidirect
170. #532	C₂×C₅	semidirect
171. #529	C₂×C₅	semidirect
221. C₂×#41	C₂²×C₅	semidirect
222. C₂×#41	C₂²×C₅	semidirect
223. C₂×#41	C₂²×C₅	semidirect
224. C₂×#41	C₂²×C₅	semidirect
227. C₄⋊Q₈	C₂²×C₅	semidirect
228. C₄⋊Q₈	C₂²×C₅	semidirect
231. #127	C₂²×C₅	semidirect
232. #127	C₂²×C₅	semidirect
233. #126	C₂²×C₅	semidirect
234. #126	C₂²×C₅	semidirect
235. #126	C₂²×C₅	semidirect
236. #125	C₂²×C₅	semidirect
239. #124	C₂²×C₅	semidirect
240. #124	C₂²×C₅	semidirect
241. #124	C₂²×C₅	semidirect
242. #123	C₂²×C₅	semidirect
243. #123	C₂²×C₅	semidirect
244. #123	C₂²×C₅	semidirect
245. #123	C₂²×C₅	semidirect
246. C₂²⋊Q₈	C₂²×C₅	semidirect
247. C₂²⋊Q₈	C₂²×C₅	semidirect
248. C₂²⋊Q₈	C₂²×C₅	semidirect
249. C₂²⋊Q₈	C₂²×C₅	semidirect
255. #121	C₂²×C₅	semidirect
256. #121	C₂²×C₅	semidirect
257. #121	C₂²×C₅	semidirect
258. #121	C₂²×C₅	semidirect
259. #121	C₂²×C₅	semidirect
260. #121	C₂²×C₅	semidirect
261. #121	C₂²×C₅	semidirect
262. #121	C₂²×C₅	semidirect
263. #121	C₂²×C₅	semidirect
264. #121	C₂²×C₅	semidirect
265. #121	C₂²×C₅	semidirect
267. #120	C₂²×C₅	semidirect
268. #120	C₂²×C₅	semidirect
269. #120	C₂²×C₅	semidirect
270. C₄×Q₈	C₂²×C₅	semidirect
271. C₄×Q₈	C₂²×C₅	semidirect
274. C₄×D₄	C₂²×C₅	semidirect
275. C₄×D₄	C₂²×C₅	semidirect
276. C₄×D₄	C₂²×C₅	semidirect
277. C₄×D₄	C₂²×C₅	semidirect
278. C₄×D₄	C₂²×C₅	semidirect
279. C₄×D₄	C₂²×C₅	semidirect
280. C₄×D₄	C₂²×C₅	semidirect
281. #117	C₂²×C₅	semidirect
282. #117	C₂²×C₅	semidirect
283. C₂×C₄⋊C₄	C₂²×C₅	semidirect
284. C₂×C₂²⋊C₄	C₂²×C₅	semidirect
285. C₂×C₄²	C₂²×C₅	semidirect
443. C₅	#3546	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×#560	2
C₅×#556	2
C₅×#553	2
C₅×#550	2
C₅×#547	2
C₅×#546	2
C₅×D₄²	2
C₅×#542	2
C₅×#538	2
C₅×#537	2
C₅×#535	2
C₅×#532	2
C₅×#529	2
#3546	5

Subgroups — C5×#3546 #10619331

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#3546 #10619331