Subgroups — C₅×#60325 #11983045

Order 1280.

2130 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	C₄×C₅×H(5,𝔽₂)	C₂	1	1	yes	maximal, characteristic
2	C₅×#2991	C₂	1	2	yes	maximal, complemented
3	C₅×#2989	C₂	1	3	yes	maximal, complemented
4	C₅×#2988	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#2975	C₂	1	3	yes	maximal, complemented
6	C₅×#2974	C₂	1	6	yes	maximal, complemented
7	C₅×#2971	C₂	1	2	yes	maximal, complemented
8	C₅×#2965	C₂	1	3	yes	maximal, complemented
9	C₅×C₈×#41	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×D₄×M₁₆	C₂	1	6	yes	maximal, complemented
11	C₂×C₅×#436	C₂	1	3	yes	maximal, complemented
12	C₂×C₅×H(5,𝔽₂)	C₄	1	1	yes	characteristic
13	C₂²×C₅×M₁₆	C₂²	1	6	yes	complemented
14	C₅×#520	C₄	1	2	yes	—
15	C₅×#520	C₄	1	3	yes	—
16	C₅×#520	C₄	1	1	yes	characteristic
17	C₅×#518	C₄	1	6	yes	—
18	C₅×#518	C₄	1	3	yes	—
19	C₄×C₅×#41	C₂²	1	1	yes	characteristic
20	C₄×C₅×#41	C₂²	1	3	yes	—
21	C₄×C₅×#41	C₂²	1	2	yes	—
22	C₂×C₄×C₅×D₄	C₂²	1	3	yes	—
23	C₂×C₄×C₅×D₄	C₂²	1	6	yes	—
24	C₅×#446	C₂²	1	3	yes	complemented
25	C₅×#446	C₂²	1	1	yes	characteristic, complemented
26	C₅×C₈×Q₈	C₂²	1	2	yes	complemented
27	C₅×C₈×Q₈	C₂²	1	1	yes	characteristic, complemented
28	C₅×C₈×Q₈	C₂²	1	1	yes	characteristic, complemented
29	C₅×#436	C₂²	1	6	yes	complemented
30	C₅×#436	C₂²	1	6	yes	complemented
31	C₅×#436	C₂²	1	6	yes	complemented
32	C₅×#436	C₂²	1	3	yes	complemented
33	C₅×#436	C₂²	1	6	yes	complemented
34	C₅×#436	C₂²	1	3	yes	complemented
35	C₅×#436	C₂²	1	6	yes	complemented
36	C₅×#435	C₂²	1	12	yes	complemented
37	C₅×#435	C₂²	1	6	yes	complemented
38	C₅×#435	C₂²	1	6	yes	complemented
39	C₅×C₈×D₄	C₂²	1	6	yes	complemented
40	C₅×C₈×D₄	C₂²	1	3	yes	complemented
41	C₅×C₈×D₄	C₂²	1	3	yes	complemented
42	C₅×#432	C₂²	1	6	yes	complemented
43	C₅×#431	C₂²	1	3	yes	complemented
44	C₅×#431	C₂²	1	3	yes	complemented
45	C₅×#431	C₂²	1	6	yes	complemented
46	C₅×#423	C₂²	1	6	yes	complemented
47	C₂×C₅×C₄⋊C₈	C₂²	1	3	yes	complemented
48	C₅×#407	C₂²	1	12	yes	complemented
49	C₂×C₅×C₂²⋊C₈	C₂²	1	6	yes	complemented
50	C₄×C₅×M₁₆	C₂²	1	6	yes	complemented
51	C₂×C₄×C₅×C₈	C₂²	1	3	yes	complemented
52	#60325	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
53	C₅×H(5,𝔽₂)	—	2	8	no	—
54	C₂×C₅×#41	C₂×C₄	1	2	yes	—
55	C₂×C₅×#41	C₂×C₄	1	3	yes	—
56	C₂×C₅×#41	C₂×C₄	1	1	yes	characteristic
57	C₂²×C₅×D₄	C₂×C₄	1	6	yes	—
58	C₂²×C₅×D₄	C₂×C₄	1	3	yes	—
59	C₂³×C₄×C₅	C₂³	1	6	yes	—
60	C₂×C₅×M₁₆	—	4	12	no	—
61	C₂×C₅×M₁₆	C₂³	1	6	yes	—
62	C₂×C₅×M₁₆	C₂³	1	6	yes	—
63	C₂×C₅×M₁₆	C₂³	1	12	yes	—
64	C₂²×C₅×C₈	C₂³	1	3	yes	—
65	C₂²×C₅×C₈	C₂³	1	3	yes	—
66	C₂²×C₅×C₈	C₂³	1	6	yes	—
67	C₄×C₅×Q₈	C₂×C₄	1	3	yes	—
68	C₄×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
69	C₄×C₅×Q₈	C₂×C₄	1	2	yes	—
70	C₄×C₅×Q₈	C₂³	1	1	yes	characteristic
71	C₄×C₅×Q₈	C₂³	1	1	yes	characteristic
72	C₄×C₅×D₄	C₂×C₄	1	6	yes	—
73	C₄×C₅×D₄	C₂×C₄	1	6	yes	—
74	C₄×C₅×D₄	C₂×C₄	1	12	yes	—
75	C₄×C₅×D₄	C₂×C₄	1	6	yes	—
76	C₄×C₅×D₄	C₂×C₄	1	6	yes	—
77	C₄×C₅×D₄	C₂×C₄	1	6	yes	—
78	C₄×C₅×D₄	C₂×C₄	1	3	yes	—
79	C₄×C₅×D₄	C₂×C₄	1	6	yes	—
80	C₄×C₅×D₄	C₂×C₄	1	3	yes	—
81	C₄×C₅×D₄	C₂³	1	3	yes	—
82	C₄×C₅×D₄	C₂³	1	6	yes	—
83	C₄×C₅×D₄	C₂³	1	3	yes	—
84	C₄×C₅×D₄	C₂³	1	6	yes	—
85	C₅×#117	C₂×C₄	1	6	yes	—
86	C₅×#117	C₂×C₄	1	6	yes	—
87	C₅×#117	C₂×C₄	1	3	yes	—
88	C₅×#117	C₂×C₄	1	3	yes	—
89	C₂×C₅×C₄⋊C₄	C₂×C₄	1	6	yes	—
90	C₂×C₅×C₄⋊C₄	C₂×C₄	1	3	yes	—
91	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	6	yes	—
92	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	12	yes	—
93	C₂×C₄²×C₅	C₂³	1	3	yes	—
94	C₂×C₄²×C₅	C₂³	1	6	yes	—
95	C₅×C₄⋊C₈	C₂³	1	3	yes	—
96	C₅×C₄⋊C₈	C₂³	1	6	yes	—
97	C₅×C₄⋊C₈	C₂³	1	3	yes	—
98	C₅×C₄⋊C₈	C₂³	1	6	yes	—
99	C₅×C₄⋊C₈	C₂³	1	2	yes	—
100	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
101	C₅×C₄⋊C₈	C₂³	1	3	yes	—
102	C₅×C₂²⋊C₈	C₂³	1	6	yes	—
103	C₅×C₂²⋊C₈	C₂³	1	12	yes	—
104	C₅×C₂²⋊C₈	C₂³	1	6	yes	—
105	C₅×C₂²⋊C₈	C₂³	1	6	yes	—
106	C₅×C₂²⋊C₈	C₂³	1	6	yes	—
107	C₅×#97	C₂³	1	2	yes	—
108	C₅×#97	C₂³	1	6	yes	—
109	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
110	C₄×C₅×C₈	C₂³	1	3	yes	—
111	C₄×C₅×C₈	C₂³	1	3	yes	—
112	C₄×C₅×C₈	C₂³	1	3	yes	—
113	C₄×C₅×C₈	C₂³	1	6	yes	—
114	C₄×H(5,𝔽₂)	C₂×C₅	1	1	yes	characteristic
115	#2991	C₂×C₅	1	2	yes	complemented
116	#2989	C₂×C₅	1	3	yes	complemented
117	#2988	C₂×C₅	1	1	yes	characteristic, complemented
118	#2975	C₂×C₅	1	3	yes	complemented
119	#2974	C₂×C₅	1	6	yes	complemented
120	#2971	C₂×C₅	1	2	yes	complemented
121	#2965	C₂×C₅	1	3	yes	complemented
122	C₈×#41	C₂×C₅	1	1	yes	characteristic, complemented
123	D₄×M₁₆	C₂×C₅	1	6	yes	complemented
124	C₂×#436	C₂×C₅	1	3	yes	complemented
125	C₂⁴×C₅	C₂²×C₄	1	6	yes	—
126	C₅×#41	—	2	8	no	—
127	C₅×#41	—	2	12	no	—
128	C₅×#41	M₁₆	1	8	yes	complemented
129	C₂×C₅×Q₈	C₂²×C₄	1	1	yes	characteristic
130	C₂×C₅×Q₈	C₂²×C₄	1	1	yes	characteristic
131	C₂×C₅×D₄	—	2	24	no	—
132	C₂×C₅×D₄	—	2	12	no	—
133	C₂×C₅×D₄	C₂²×C₄	1	6	yes	—
134	C₂×C₅×D₄	C₂²×C₄	1	6	yes	—
135	C₂×C₅×D₄	C₂²×C₄	1	3	yes	—
136	C₂×C₅×D₄	C₂²×C₄	1	3	yes	—
137	C₂²×C₄×C₅	—	4	6	no	—
138	C₂²×C₄×C₅	—	4	6	no	—
139	C₂²×C₄×C₅	C₂²×C₄	1	6	yes	—
140	C₂²×C₄×C₅	C₂²×C₄	1	6	yes	—
141	C₂²×C₄×C₅	C₂²×C₄	1	3	yes	—
142	C₂²×C₄×C₅	C₂²×C₄	1	12	yes	—
143	C₂²×C₄×C₅	C₂²×C₄	1	6	yes	—
144	C₂²×C₄×C₅	C₂²×C₄	1	3	yes	—
145	C₂²×C₄×C₅	C₂⁴	1	3	yes	—
146	C₂²×C₄×C₅	C₂⁴	1	6	yes	—
147	C₅×M₁₆	—	2	12	no	—
148	C₅×M₁₆	—	4	12	no	—
149	C₅×M₁₆	—	4	6	no	—
150	C₂×C₅×C₈	—	2	6	no	—
151	C₂×C₅×C₈	—	4	3	no	—
152	C₂×C₅×C₈	—	4	6	no	—
153	C₂×C₅×C₈	C₂⁴	1	1	yes	characteristic
154	C₂×C₅×C₈	C₂⁴	1	6	yes	—
155	C₂×C₅×C₈	C₂⁴	1	3	yes	—
156	C₂×C₅×C₈	C₂⁴	1	3	yes	—
157	C₂×C₅×C₈	C₂⁴	1	2	yes	—
158	C₂×C₅×C₈	C₂⁴	1	1	yes	characteristic
159	C₅×C₄⋊C₄	C₂²×C₄	1	6	yes	—
160	C₅×C₄⋊C₄	C₂²×C₄	1	3	yes	—
161	C₅×C₄⋊C₄	C₂²×C₄	1	6	yes	—
162	C₅×C₄⋊C₄	C₂²×C₄	1	3	yes	—
163	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
164	C₅×C₄⋊C₄	C₂²×C₄	1	3	yes	—
165	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
166	C₅×C₂²⋊C₄	C₂²×C₄	1	6	yes	—
167	C₅×C₂²⋊C₄	C₂²×C₄	1	6	yes	—
168	C₅×C₂²⋊C₄	C₂²×C₄	1	12	yes	—
169	C₅×C₂²⋊C₄	C₂²×C₄	1	6	yes	—
170	C₅×C₂²⋊C₄	C₂²×C₄	1	6	yes	—
171	C₄²×C₅	C₂²×C₄	1	6	yes	—
172	C₄²×C₅	C₂²×C₄	1	3	yes	—
173	C₄²×C₅	C₂²×C₄	1	3	yes	—
174	C₄²×C₅	C₂²×C₄	1	6	yes	—
175	C₄²×C₅	C₂⁴	1	1	yes	characteristic
176	C₄²×C₅	C₂⁴	1	3	yes	—
177	C₄²×C₅	C₂⁴	1	2	yes	—
178	C₂×H(5,𝔽₂)	C₄×C₅	1	1	yes	characteristic
179	C₂²×M₁₆	C₂²×C₅	1	6	yes	complemented
180	#520	C₄×C₅	1	2	yes	—
181	#520	C₄×C₅	1	3	yes	—
182	#520	C₄×C₅	1	1	yes	characteristic
183	#518	C₄×C₅	1	6	yes	—
184	#518	C₄×C₅	1	3	yes	—
185	C₄×#41	C₂²×C₅	1	1	yes	characteristic
186	C₄×#41	C₂²×C₅	1	3	yes	—
187	C₄×#41	C₂²×C₅	1	2	yes	—
188	C₂×C₄×D₄	C₂²×C₅	1	3	yes	—
189	C₂×C₄×D₄	C₂²×C₅	1	6	yes	—
190	#446	C₂²×C₅	1	1	yes	characteristic, complemented
191	#446	C₂²×C₅	1	3	yes	complemented
192	C₈×Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
193	C₈×Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
194	C₈×Q₈	C₂²×C₅	1	2	yes	complemented
195	#436	C₂²×C₅	1	3	yes	complemented
196	#436	C₂²×C₅	1	6	yes	complemented
197	#436	C₂²×C₅	1	6	yes	complemented
198	#436	C₂²×C₅	1	6	yes	complemented
199	#436	C₂²×C₅	1	6	yes	complemented
200	#436	C₂²×C₅	1	3	yes	complemented
201	#436	C₂²×C₅	1	6	yes	complemented
202	#435	C₂²×C₅	1	6	yes	complemented
203	#435	C₂²×C₅	1	12	yes	complemented
204	#435	C₂²×C₅	1	6	yes	complemented
205	C₈×D₄	C₂²×C₅	1	3	yes	complemented
206	C₈×D₄	C₂²×C₅	1	6	yes	complemented
207	C₈×D₄	C₂²×C₅	1	3	yes	complemented
208	#432	C₂²×C₅	1	6	yes	complemented
209	#431	C₂²×C₅	1	3	yes	complemented
210	#431	C₂²×C₅	1	6	yes	complemented
211	#431	C₂²×C₅	1	3	yes	complemented
212	#423	C₂²×C₅	1	6	yes	complemented
213	C₂×C₄⋊C₈	C₂²×C₅	1	3	yes	complemented
214	#407	C₂²×C₅	1	12	yes	complemented
215	C₂×C₂²⋊C₈	C₂²×C₅	1	6	yes	complemented
216	C₄×M₁₆	C₂²×C₅	1	6	yes	complemented
217	C₂×C₄×C₈	C₂²×C₅	1	3	yes	complemented
218	C₂³×C₅	—	2	12	no	—
219	C₂³×C₅	—	4	6	no	—
220	C₂³×C₅	—	4	6	no	—
221	C₂³×C₅	C₂³×C₄	1	6	yes	—
222	C₂³×C₅	C₂³×C₄	1	3	yes	—
223	C₅×Q₈	—	2	2	no	—
224	C₅×Q₈	C₂×M₁₆	1	4	yes	complemented
225	C₅×D₄	—	2	12	no	—
226	C₅×D₄	—	2	12	no	—
227	C₅×D₄	—	2	6	no	—
228	C₅×D₄	C₂×M₁₆	1	12	yes	complemented
229	C₂×C₄×C₅	—	2	12	no	—
230	C₂×C₄×C₅	—	2	3	no	—
231	C₂×C₄×C₅	—	2	6	no	—
232	C₂×C₄×C₅	—	2	3	no	—
233	C₂×C₄×C₅	—	2	6	no	—
234	C₂×C₄×C₅	—	4	6	no	—
235	C₂×C₄×C₅	—	4	12	no	—
236	C₂×C₄×C₅	—	4	3	no	—
237	C₂×C₄×C₅	—	4	6	no	—
238	C₂×C₄×C₅	C₂×M₁₆	1	12	yes	complemented
239	C₂×C₄×C₅	C₂³×C₄	1	3	yes	—
240	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
241	C₂×C₄×C₅	C₂³×C₄	1	2	yes	—
242	C₂×C₄×C₅	C₂³×C₄	1	2	yes	—
243	C₂×C₄×C₅	C₂³×C₄	1	3	yes	—
244	C₂×C₄×C₅	C₂³×C₄	1	6	yes	—
245	C₂×C₄×C₅	C₂³×C₄	1	3	yes	—
246	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
247	C₂×C₄×C₅	C₂⁵	1	1	yes	characteristic
248	C₅×C₈	—	2	3	no	—
249	C₅×C₈	—	2	6	no	—
250	C₅×C₈	—	2	1	no	—
251	C₅×C₈	—	2	3	no	—
252	C₅×C₈	—	2	2	no	—
253	C₅×C₈	H(5,𝔽₂)	1	2	yes	complemented
254	H(5,𝔽₂)	—	2	8	no	—
255	C₂×#41	C₂×C₄×C₅	1	2	yes	—
256	C₂×#41	C₂×C₄×C₅	1	3	yes	—
257	C₂×#41	C₂×C₄×C₅	1	1	yes	characteristic
258	C₂²×D₄	C₂×C₄×C₅	1	6	yes	—
259	C₂²×D₄	C₂×C₄×C₅	1	3	yes	—
260	C₂³×C₄	C₂³×C₅	1	6	yes	—
261	C₂×M₁₆	—	4	12	no	—
262	C₂×M₁₆	C₂³×C₅	1	6	yes	—
263	C₂×M₁₆	C₂³×C₅	1	12	yes	—
264	C₂×M₁₆	C₂³×C₅	1	6	yes	—
265	C₂²×C₈	C₂³×C₅	1	3	yes	—
266	C₂²×C₈	C₂³×C₅	1	6	yes	—
267	C₂²×C₈	C₂³×C₅	1	3	yes	—
268	C₄×Q₈	C₂×C₄×C₅	1	3	yes	—
269	C₄×Q₈	C₂×C₄×C₅	1	1	yes	characteristic
270	C₄×Q₈	C₂×C₄×C₅	1	2	yes	—
271	C₄×Q₈	C₂³×C₅	1	1	yes	characteristic
272	C₄×Q₈	C₂³×C₅	1	1	yes	characteristic
273	C₄×D₄	C₂×C₄×C₅	1	6	yes	—
274	C₄×D₄	C₂×C₄×C₅	1	6	yes	—
275	C₄×D₄	C₂×C₄×C₅	1	12	yes	—
276	C₄×D₄	C₂×C₄×C₅	1	6	yes	—
277	C₄×D₄	C₂×C₄×C₅	1	6	yes	—
278	C₄×D₄	C₂×C₄×C₅	1	6	yes	—
279	C₄×D₄	C₂×C₄×C₅	1	3	yes	—
280	C₄×D₄	C₂×C₄×C₅	1	6	yes	—
281	C₄×D₄	C₂×C₄×C₅	1	3	yes	—
282	C₄×D₄	C₂³×C₅	1	3	yes	—
283	C₄×D₄	C₂³×C₅	1	6	yes	—
284	C₄×D₄	C₂³×C₅	1	3	yes	—
285	C₄×D₄	C₂³×C₅	1	6	yes	—
286	#117	C₂×C₄×C₅	1	6	yes	—
287	#117	C₂×C₄×C₅	1	6	yes	—
288	#117	C₂×C₄×C₅	1	3	yes	—
289	#117	C₂×C₄×C₅	1	3	yes	—
290	C₂×C₄⋊C₄	C₂×C₄×C₅	1	6	yes	—
291	C₂×C₄⋊C₄	C₂×C₄×C₅	1	3	yes	—
292	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	6	yes	—
293	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	12	yes	—
294	C₂×C₄²	C₂³×C₅	1	3	yes	—
295	C₂×C₄²	C₂³×C₅	1	6	yes	—
296	C₄⋊C₈	C₂³×C₅	1	3	yes	—
297	C₄⋊C₈	C₂³×C₅	1	6	yes	—
298	C₄⋊C₈	C₂³×C₅	1	3	yes	—
299	C₄⋊C₈	C₂³×C₅	1	6	yes	—
300	C₄⋊C₈	C₂³×C₅	1	2	yes	—
301	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
302	C₄⋊C₈	C₂³×C₅	1	3	yes	—
303	C₂²⋊C₈	C₂³×C₅	1	6	yes	—
304	C₂²⋊C₈	C₂³×C₅	1	12	yes	—
305	C₂²⋊C₈	C₂³×C₅	1	6	yes	—
306	C₂²⋊C₈	C₂³×C₅	1	6	yes	—
307	C₂²⋊C₈	C₂³×C₅	1	6	yes	—
308	#97	C₂³×C₅	1	2	yes	—
309	#97	C₂³×C₅	1	6	yes	—
310	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
311	C₄×C₈	C₂³×C₅	1	3	yes	—
312	C₄×C₈	C₂³×C₅	1	3	yes	—
313	C₄×C₈	C₂³×C₅	1	3	yes	—
314	C₄×C₈	C₂³×C₅	1	6	yes	—
315	C₂²×C₅	—	2	3	no	—
316	C₂²×C₅	—	2	3	no	—
317	C₂²×C₅	—	2	6	no	—
318	C₂²×C₅	—	2	6	no	—
319	C₂²×C₅	—	2	6	no	—
320	C₂²×C₅	—	8	12	no	—
321	C₂²×C₅	C₂²×M₁₆	1	6	yes	—
322	C₂²×C₅	C₂⁴×C₄	1	1	yes	characteristic
323	C₄×C₅	—	2	3	no	—
324	C₄×C₅	—	2	6	no	—
325	C₄×C₅	—	2	2	no	—
326	C₄×C₅	—	2	1	no	—
327	C₄×C₅	—	2	3	no	—
328	C₄×C₅	—	2	2	no	—
329	C₄×C₅	C₂²×M₁₆	1	6	yes	—
330	C₄×C₅	C₂²×M₁₆	1	2	yes	—
331	C₄×C₅	C₂×H(5,𝔽₂)	1	1	yes	characteristic
332	C₄×C₅	#585	1	1	yes	characteristic
333	C₂⁴	C₂²×C₄×C₅	1	6	yes	—
334	#41	—	2	8	no	—
335	#41	—	2	12	no	—
336	#41	C₅×M₁₆	1	8	yes	complemented
337	C₂×Q₈	C₂²×C₄×C₅	1	1	yes	characteristic
338	C₂×Q₈	C₂²×C₄×C₅	1	1	yes	characteristic
339	C₂×D₄	—	2	24	no	—
340	C₂×D₄	—	2	12	no	—
341	C₂×D₄	C₂²×C₄×C₅	1	6	yes	—
342	C₂×D₄	C₂²×C₄×C₅	1	6	yes	—
343	C₂×D₄	C₂²×C₄×C₅	1	3	yes	—
344	C₂×D₄	C₂²×C₄×C₅	1	3	yes	—
345	C₂²×C₄	—	4	6	no	—
346	C₂²×C₄	—	4	6	no	—
347	C₂²×C₄	C₂²×C₄×C₅	1	6	yes	—
348	C₂²×C₄	C₂²×C₄×C₅	1	6	yes	—
349	C₂²×C₄	C₂²×C₄×C₅	1	3	yes	—
350	C₂²×C₄	C₂²×C₄×C₅	1	12	yes	—
351	C₂²×C₄	C₂²×C₄×C₅	1	6	yes	—
352	C₂²×C₄	C₂²×C₄×C₅	1	3	yes	—
353	C₂²×C₄	C₂⁴×C₅	1	3	yes	—
354	C₂²×C₄	C₂⁴×C₅	1	6	yes	—
355	M₁₆	—	2	12	no	—
356	M₁₆	—	4	12	no	—
357	M₁₆	—	4	6	no	—
358	C₂×C₈	—	2	6	no	—
359	C₂×C₈	—	4	6	no	—
360	C₂×C₈	—	4	3	no	—
361	C₂×C₈	C₂⁴×C₅	1	1	yes	characteristic
362	C₂×C₈	C₂⁴×C₅	1	2	yes	—
363	C₂×C₈	C₂⁴×C₅	1	3	yes	—
364	C₂×C₈	C₂⁴×C₅	1	3	yes	—
365	C₂×C₈	C₂⁴×C₅	1	6	yes	—
366	C₂×C₈	C₂⁴×C₅	1	1	yes	characteristic
367	C₄⋊C₄	C₂²×C₄×C₅	1	6	yes	—
368	C₄⋊C₄	C₂²×C₄×C₅	1	3	yes	—
369	C₄⋊C₄	C₂²×C₄×C₅	1	6	yes	—
370	C₄⋊C₄	C₂²×C₄×C₅	1	3	yes	—
371	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
372	C₄⋊C₄	C₂²×C₄×C₅	1	3	yes	—
373	C₄⋊C₄	C₂²×C₄×C₅	1	1	yes	characteristic
374	C₂²⋊C₄	C₂²×C₄×C₅	1	6	yes	—
375	C₂²⋊C₄	C₂²×C₄×C₅	1	6	yes	—
376	C₂²⋊C₄	C₂²×C₄×C₅	1	12	yes	—
377	C₂²⋊C₄	C₂²×C₄×C₅	1	6	yes	—
378	C₂²⋊C₄	C₂²×C₄×C₅	1	6	yes	—
379	C₄²	C₂²×C₄×C₅	1	6	yes	—
380	C₄²	C₂²×C₄×C₅	1	3	yes	—
381	C₄²	C₂²×C₄×C₅	1	3	yes	—
382	C₄²	C₂²×C₄×C₅	1	6	yes	—
383	C₄²	C₂⁴×C₅	1	1	yes	characteristic
384	C₄²	C₂⁴×C₅	1	3	yes	—
385	C₄²	C₂⁴×C₅	1	2	yes	—
386	C₂×C₅	—	2	6	no	—
387	C₂×C₅	—	4	6	no	—
388	C₂×C₅	C₄×H(5,𝔽₂)	1	1	yes	characteristic
389	C₂×C₅	C₂³×M₁₆	1	1	yes	characteristic
390	C₂×C₅	#3573	1	1	yes	characteristic
391	C₂³	—	2	12	no	—
392	C₂³	—	4	6	no	—
393	C₂³	—	4	6	no	—
394	C₂³	C₂³×C₄×C₅	1	6	yes	—
395	C₂³	C₂³×C₄×C₅	1	3	yes	—
396	Q₈	—	2	2	no	—
397	Q₈	C₂×C₅×M₁₆	1	4	yes	complemented
398	D₄	—	2	12	no	—
399	D₄	—	2	12	no	—
400	D₄	—	2	6	no	—
401	D₄	C₂×C₅×M₁₆	1	12	yes	complemented
402	C₂×C₄	—	2	12	no	—
403	C₂×C₄	—	2	3	no	—
404	C₂×C₄	—	2	6	no	—
405	C₂×C₄	—	2	3	no	—
406	C₂×C₄	—	2	6	no	—
407	C₂×C₄	—	4	6	no	—
408	C₂×C₄	—	4	12	no	—
409	C₂×C₄	—	4	3	no	—
410	C₂×C₄	—	4	6	no	—
411	C₂×C₄	C₂×C₅×M₁₆	1	12	yes	complemented
412	C₂×C₄	C₂³×C₄×C₅	1	3	yes	—
413	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
414	C₂×C₄	C₂³×C₄×C₅	1	2	yes	—
415	C₂×C₄	C₂³×C₄×C₅	1	2	yes	—
416	C₂×C₄	C₂³×C₄×C₅	1	3	yes	—
417	C₂×C₄	C₂³×C₄×C₅	1	6	yes	—
418	C₂×C₄	C₂³×C₄×C₅	1	3	yes	—
419	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
420	C₂×C₄	C₂⁵×C₅	1	1	yes	characteristic
421	C₈	—	2	3	no	—
422	C₈	—	2	6	no	—
423	C₈	—	2	1	no	—
424	C₈	—	2	3	no	—
425	C₈	—	2	2	no	—
426	C₈	C₅×H(5,𝔽₂)	1	2	yes	complemented
427	C₅	#60325	1	1	yes	characteristic, direct product factor, Sylow
428	C₂²	—	2	3	no	—
429	C₂²	—	2	3	no	—
430	C₂²	—	2	6	no	—
431	C₂²	—	2	6	no	—
432	C₂²	—	2	6	no	—
433	C₂²	—	8	12	no	—
434	C₂²	C₂²×C₅×M₁₆	1	6	yes	—
435	C₂²	C₂⁴×C₄×C₅	1	1	yes	characteristic
436	C₄	—	2	3	no	—
437	C₄	—	2	6	no	—
438	C₄	—	2	2	no	—
439	C₄	—	2	1	no	—
440	C₄	—	2	3	no	—
441	C₄	—	2	2	no	—
442	C₄	C₂²×C₅×M₁₆	1	6	yes	—
443	C₄	C₂²×C₅×M₁₆	1	2	yes	—
444	C₄	C₂×C₅×H(5,𝔽₂)	1	1	yes	characteristic
445	C₄	C₅×#585	1	1	yes	characteristic
446	C₂	—	2	6	no	—
447	C₂	—	4	6	no	—
448	C₂	C₄×C₅×H(5,𝔽₂)	1	1	yes	characteristic
449	C₂	C₂³×C₅×M₁₆	1	1	yes	characteristic
450	C₂	C₅×#3573	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₅	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₅
Frattini, cosocle	C₂×C₄	C₂⁵×C₅
socle	C₂²×C₅	C₂⁴×C₄
prime radical	C₂×C₅×H(5,𝔽₂)	C₄
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₅×#2991	C₂	semidirect
3. C₅×#2989	C₂	semidirect
4. C₅×#2988	C₂	semidirect
5. C₅×#2975	C₂	semidirect
6. C₅×#2974	C₂	semidirect
7. C₅×#2971	C₂	semidirect
8. C₅×#2965	C₂	semidirect
9. C₅×C₈×#41	C₂	semidirect
10. C₅×D₄×M₁₆	C₂	semidirect
11. C₂×C₅×#436	C₂	semidirect
13. C₂²×C₅×M₁₆	C₂²	semidirect
24. C₅×#446	C₂²	semidirect
25. C₅×#446	C₂²	semidirect
26. C₅×C₈×Q₈	C₂²	semidirect
27. C₅×C₈×Q₈	C₂²	semidirect
28. C₅×C₈×Q₈	C₂²	semidirect
29. C₅×#436	C₂²	semidirect
30. C₅×#436	C₂²	semidirect
31. C₅×#436	C₂²	semidirect
32. C₅×#436	C₂²	semidirect
33. C₅×#436	C₂²	semidirect
34. C₅×#436	C₂²	semidirect
35. C₅×#436	C₂²	semidirect
36. C₅×#435	C₂²	semidirect
37. C₅×#435	C₂²	semidirect
38. C₅×#435	C₂²	semidirect
39. C₅×C₈×D₄	C₂²	semidirect
40. C₅×C₈×D₄	C₂²	semidirect
41. C₅×C₈×D₄	C₂²	semidirect
42. C₅×#432	C₂²	semidirect
43. C₅×#431	C₂²	semidirect
44. C₅×#431	C₂²	semidirect
45. C₅×#431	C₂²	semidirect
46. C₅×#423	C₂²	semidirect
47. C₂×C₅×C₄⋊C₈	C₂²	semidirect
48. C₅×#407	C₂²	semidirect
49. C₂×C₅×C₂²⋊C₈	C₂²	semidirect
50. C₄×C₅×M₁₆	C₂²	semidirect
51. C₂×C₄×C₅×C₈	C₂²	semidirect
52. #60325	C₅	direct (N × H)
115. #2991	C₂×C₅	semidirect
116. #2989	C₂×C₅	semidirect
117. #2988	C₂×C₅	semidirect
118. #2975	C₂×C₅	semidirect
119. #2974	C₂×C₅	semidirect
120. #2971	C₂×C₅	semidirect
121. #2965	C₂×C₅	semidirect
122. C₈×#41	C₂×C₅	semidirect
123. D₄×M₁₆	C₂×C₅	semidirect
124. C₂×#436	C₂×C₅	semidirect
128. C₅×#41	M₁₆	semidirect
179. C₂²×M₁₆	C₂²×C₅	semidirect
190. #446	C₂²×C₅	semidirect
191. #446	C₂²×C₅	semidirect
192. C₈×Q₈	C₂²×C₅	semidirect
193. C₈×Q₈	C₂²×C₅	semidirect
194. C₈×Q₈	C₂²×C₅	semidirect
195. #436	C₂²×C₅	semidirect
196. #436	C₂²×C₅	semidirect
197. #436	C₂²×C₅	semidirect
198. #436	C₂²×C₅	semidirect
199. #436	C₂²×C₅	semidirect
200. #436	C₂²×C₅	semidirect
201. #436	C₂²×C₅	semidirect
202. #435	C₂²×C₅	semidirect
203. #435	C₂²×C₅	semidirect
204. #435	C₂²×C₅	semidirect
205. C₈×D₄	C₂²×C₅	semidirect
206. C₈×D₄	C₂²×C₅	semidirect
207. C₈×D₄	C₂²×C₅	semidirect
208. #432	C₂²×C₅	semidirect
209. #431	C₂²×C₅	semidirect
210. #431	C₂²×C₅	semidirect
211. #431	C₂²×C₅	semidirect
212. #423	C₂²×C₅	semidirect
213. C₂×C₄⋊C₈	C₂²×C₅	semidirect
214. #407	C₂²×C₅	semidirect
215. C₂×C₂²⋊C₈	C₂²×C₅	semidirect
216. C₄×M₁₆	C₂²×C₅	semidirect
217. C₂×C₄×C₈	C₂²×C₅	semidirect
224. C₅×Q₈	C₂×M₁₆	semidirect
228. C₅×D₄	C₂×M₁₆	semidirect
238. C₂×C₄×C₅	C₂×M₁₆	semidirect
253. C₅×C₈	H(5,𝔽₂)	semidirect
336. #41	C₅×M₁₆	semidirect
397. Q₈	C₂×C₅×M₁₆	semidirect
401. D₄	C₂×C₅×M₁₆	semidirect
411. C₂×C₄	C₂×C₅×M₁₆	semidirect
426. C₈	C₅×H(5,𝔽₂)	semidirect
427. C₅	#60325	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄×C₅×H(5,𝔽₂)	2
C₅×#2991	2
C₅×#2989	2
C₅×#2988	2
C₅×#2975	2
C₅×#2974	2
C₅×#2971	2
C₅×#2965	2
C₅×C₈×#41	2
C₅×D₄×M₁₆	2
C₂×C₅×#436	2
#60325	5

Subgroups — C5×#60325 #11983045

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#60325 #11983045