Subgroups — C₅×#60372 #11983092

Order 1280.

5126 conjugacy classes of subgroups.

The subgroup lattice has 674 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₅×H(5,𝔽₂)	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅×#576	C₂	1	2	yes	maximal, complemented
3	C₅×#3488	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#3012	C₂	1	6	yes	maximal, complemented
5	C₅×#3008	C₂	1	6	yes	maximal, complemented
6	C₅×#3006	C₂	1	3	yes	maximal, complemented
7	C₅×#3003	C₂	1	3	yes	maximal, complemented
8	C₅×#3002	C₂	1	3	yes	maximal, complemented
9	C₂×C₅×#447	C₂	1	3	yes	maximal, complemented
10	C₅×#2897	C₂	1	2	yes	maximal, complemented
11	C₅×#2880	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₅×H(5,𝔽₂)	—	2	16	no	—
13	C₂×C₅×H(5,𝔽₂)	—	2	3	no	—
14	C₂×C₅×H(5,𝔽₂)	—	2	1	no	—
15	C₂×C₅×H(5,𝔽₂)	C₂²	1	2	yes	—
16	C₂×C₅×H(5,𝔽₂)	C₂²	1	6	yes	complemented
17	C₂×C₅×H(5,𝔽₂)	C₂²	1	1	yes	characteristic, complemented
18	C₂²×C₅×#41	—	2	1	no	—
19	C₂²×C₅×#41	C₂²	1	1	yes	characteristic
20	C₂²×C₅×#41	C₂²	1	3	yes	complemented
21	C₂³×C₅×D₄	—	2	3	no	—
22	C₂³×C₅×D₄	C₂²	1	3	yes	complemented
23	C₅×#576	—	2	16	no	—
24	C₂×C₅×AGL(1,ℤ/8)	C₂²	1	6	yes	complemented
25	C₂×C₅×AGL(1,ℤ/8)	C₂²	1	6	yes	complemented
26	C₂×C₅×#135	C₂²	1	6	yes	complemented
27	C₂²×C₅×D₈	C₂²	1	6	yes	complemented
28	C₂×C₅×#131	C₂²	1	2	yes	complemented
29	C₅×#550	—	2	1	no	—
30	C₅×#548	—	2	1	no	—
31	C₅×#546	—	2	3	no	—
32	C₅×D₄²	—	2	3	no	—
33	C₅×#537	C₂²	1	3	yes	complemented
34	C₅×#535	C₂²	1	3	yes	complemented
35	C₅×#525	C₂²	1	3	yes	complemented
36	C₂×C₅×#121	C₂²	1	3	yes	complemented
37	C₅×#520	C₂²	1	1	yes	characteristic, complemented
38	C₅×#452	C₂²	1	6	yes	complemented
39	C₅×#451	C₂²	1	1	yes	characteristic, complemented
40	C₅×#450	C₂²	1	3	yes	complemented
41	C₅×#450	C₂²	1	6	yes	complemented
42	C₅×#449	C₂²	1	6	yes	complemented
43	C₅×#449	C₂²	1	12	yes	complemented
44	C₅×#448	C₂²	1	3	yes	complemented
45	C₅×#447	C₂²	1	3	yes	complemented
46	C₅×#447	C₂²	1	6	yes	complemented
47	C₅×#447	C₂²	1	12	yes	complemented
48	C₅×#447	C₂²	1	6	yes	complemented
49	C₅×#418	C₂²	1	6	yes	complemented
50	C₅×#417	C₂²	1	6	yes	complemented
51	C₅×#416	C₂²	1	6	yes	complemented
52	C₂×C₅×#102	C₂²	1	6	yes	complemented
53	C₅×#408	C₂²	1	6	yes	complemented
54	C₅×#407	C₂²	1	3	yes	complemented
55	C₂×C₅×C₂²⋊C₈	C₂²	1	3	yes	complemented
56	#60372	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
57	C₂⁵×C₅	—	2	3	no	—
58	C₅×H(5,𝔽₂)	—	2	16	no	—
59	C₅×H(5,𝔽₂)	—	2	48	no	—
60	C₅×H(5,𝔽₂)	—	2	8	no	—
61	C₅×H(5,𝔽₂)	—	2	24	no	—
62	C₅×H(5,𝔽₂)	—	2	24	no	—
63	C₅×H(5,𝔽₂)	—	2	8	no	—
64	C₅×H(5,𝔽₂)	D₄	1	16	yes	complemented
65	C₂×C₅×#41	—	2	16	no	—
66	C₂×C₅×#41	—	2	8	no	—
67	C₂×C₅×#41	—	2	24	no	—
68	C₂×C₅×#41	—	2	2	no	—
69	C₂×C₅×#41	—	2	6	no	—
70	C₂×C₅×#41	—	2	1	no	—
71	C₂×C₅×#41	—	2	3	no	—
72	C₂×C₅×#41	—	2	3	no	—
73	C₂×C₅×#41	D₄	1	3	yes	—
74	C₂×C₅×#41	D₄	1	1	yes	characteristic
75	C₂×C₅×#41	C₂³	1	6	yes	—
76	C₂×C₅×#41	C₂³	1	6	yes	—
77	C₂×C₅×#41	C₂³	1	3	yes	—
78	C₂×C₅×#41	C₂³	1	1	yes	characteristic
79	C₂×C₅×#41	C₂³	1	3	yes	complemented
80	C₂²×C₅×Q₈	D₄	1	1	yes	characteristic
81	C₂²×C₅×Q₈	C₂³	1	1	yes	characteristic
82	C₂²×C₅×D₄	—	2	48	no	—
83	C₂²×C₅×D₄	—	2	3	no	—
84	C₂²×C₅×D₄	—	2	6	no	—
85	C₂²×C₅×D₄	—	2	12	no	—
86	C₂²×C₅×D₄	—	2	6	no	—
87	C₂²×C₅×D₄	—	2	24	no	—
88	C₂²×C₅×D₄	—	2	3	no	—
89	C₂²×C₅×D₄	—	2	3	no	—
90	C₂²×C₅×D₄	—	2	3	no	—
91	C₂²×C₅×D₄	—	2	3	no	—
92	C₂²×C₅×D₄	—	2	3	no	—
93	C₂²×C₅×D₄	D₄	1	3	yes	—
94	C₂²×C₅×D₄	C₂³	1	3	yes	—
95	C₂²×C₅×D₄	C₂³	1	6	yes	—
96	C₂²×C₅×D₄	C₂³	1	6	yes	—
97	C₂²×C₅×D₄	C₂³	1	3	yes	complemented
98	C₂³×C₄×C₅	—	2	3	no	—
99	C₂³×C₄×C₅	C₂³	1	3	yes	—
100	C₅×AGL(1,ℤ/8)	—	2	24	no	—
101	C₅×AGL(1,ℤ/8)	—	2	24	no	—
102	C₅×#135	—	2	24	no	—
103	C₂×C₅×Q₁₆	C₂³	1	2	yes	complemented
104	C₂×C₅×SD₁₆	C₂³	1	6	yes	complemented
105	C₂×C₅×SD₁₆	C₂³	1	6	yes	complemented
106	C₂×C₅×D₈	—	2	24	no	—
107	C₂×C₅×D₈	C₂³	1	6	yes	complemented
108	C₂×C₅×D₈	C₂³	1	12	yes	complemented
109	C₅×#131	—	2	8	no	—
110	C₂×C₅×M₁₆	C₂³	1	6	yes	complemented
111	C₂²×C₅×C₈	C₂³	1	6	yes	complemented
112	C₅×#127	—	2	3	no	—
113	C₅×#124	—	2	3	no	—
114	C₅×#123	—	2	3	no	—
115	C₅×C₂²⋊Q₈	—	2	3	no	—
116	C₅×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
117	C₅×C₂²⋊Q₈	C₂³	1	3	yes	complemented
118	C₅×#121	—	2	6	no	—
119	C₅×#121	—	2	3	no	—
120	C₅×#121	—	2	3	no	—
121	C₅×#121	—	2	3	no	—
122	C₅×#121	C₂³	1	3	yes	—
123	C₅×#121	C₂³	1	6	yes	complemented
124	C₅×#121	C₂³	1	3	yes	complemented
125	C₅×#120	—	2	3	no	—
126	C₅×#120	—	2	6	no	—
127	C₄×C₅×Q₈	—	2	1	no	—
128	C₄×C₅×D₄	—	2	3	no	—
129	C₄×C₅×D₄	—	2	3	no	—
130	C₄×C₅×D₄	—	2	3	no	—
131	C₅×#117	C₂³	1	3	yes	complemented
132	C₂×C₅×C₄⋊C₄	C₂³	1	3	yes	complemented
133	C₂×C₅×C₂²⋊C₄	—	2	3	no	—
134	C₅×#103	C₂³	1	2	yes	complemented
135	C₅×#103	C₂³	1	6	yes	complemented
136	C₅×#102	C₂³	1	6	yes	complemented
137	C₅×#102	C₂³	1	12	yes	complemented
138	C₅×#102	C₂³	1	6	yes	complemented
139	C₅×C₂²⋊C₈	C₂³	1	1	yes	characteristic
140	C₅×C₂²⋊C₈	C₂³	1	3	yes	—
141	C₅×C₂²⋊C₈	C₂³	1	6	yes	complemented
142	C₅×C₂²⋊C₈	C₂³	1	6	yes	complemented
143	C₂²×H(5,𝔽₂)	C₂×C₅	1	1	yes	characteristic, complemented
144	C₂×#576	C₂×C₅	1	2	yes	complemented
145	#3488	C₂×C₅	1	1	yes	characteristic, complemented
146	#3012	C₂×C₅	1	6	yes	complemented
147	#3008	C₂×C₅	1	6	yes	complemented
148	#3006	C₂×C₅	1	3	yes	complemented
149	#3003	C₂×C₅	1	3	yes	complemented
150	#3002	C₂×C₅	1	3	yes	complemented
151	C₂×#447	C₂×C₅	1	3	yes	complemented
152	#2897	C₂×C₅	1	2	yes	complemented
153	#2880	C₂×C₅	1	1	yes	characteristic, complemented
154	C₂⁴×C₅	—	2	24	no	—
155	C₂⁴×C₅	—	2	3	no	—
156	C₂⁴×C₅	—	2	6	no	—
157	C₂⁴×C₅	—	2	6	no	—
158	C₂⁴×C₅	—	2	3	no	—
159	C₂⁴×C₅	—	8	6	no	—
160	C₂⁴×C₅	—	8	6	no	—
161	C₂⁴×C₅	C₂×D₄	1	3	yes	—
162	C₅×#41	—	2	24	no	—
163	C₅×#41	—	2	48	no	—
164	C₅×#41	—	2	24	no	—
165	C₅×#41	—	2	16	no	—
166	C₅×#41	—	2	4	no	—
167	C₅×#41	—	2	12	no	—
168	C₅×#41	—	2	12	no	—
169	C₅×#41	—	2	12	no	—
170	C₅×#41	—	2	12	no	—
171	C₅×#41	—	2	12	no	—
172	C₅×#41	—	2	12	no	—
173	C₅×#41	—	4	4	no	—
174	C₅×#41	C₂×D₄	1	8	yes	—
175	C₅×#41	C₂×D₄	1	24	yes	complemented
176	C₂×C₅×Q₈	—	2	4	no	—
177	C₂×C₅×Q₈	—	2	4	no	—
178	C₂×C₅×Q₈	—	2	1	no	—
179	C₂×C₅×Q₈	C₂×D₄	1	3	yes	—
180	C₂×C₅×Q₈	C₂×D₄	1	1	yes	characteristic
181	C₂×C₅×Q₈	C₂⁴	1	1	yes	characteristic
182	C₂×C₅×Q₈	C₂⁴	1	2	yes	—
183	C₂×C₅×D₄	—	2	24	no	—
184	C₂×C₅×D₄	—	2	24	no	—
185	C₂×C₅×D₄	—	2	96	no	—
186	C₂×C₅×D₄	—	2	24	no	—
187	C₂×C₅×D₄	—	2	48	no	—
188	C₂×C₅×D₄	—	2	24	no	—
189	C₂×C₅×D₄	—	2	6	no	—
190	C₂×C₅×D₄	—	2	6	no	—
191	C₂×C₅×D₄	—	2	12	no	—
192	C₂×C₅×D₄	—	2	48	no	—
193	C₂×C₅×D₄	—	2	12	no	—
194	C₂×C₅×D₄	—	2	24	no	—
195	C₂×C₅×D₄	—	2	3	no	—
196	C₂×C₅×D₄	—	2	3	no	—
197	C₂×C₅×D₄	—	2	3	no	—
198	C₂×C₅×D₄	—	2	6	no	—
199	C₂×C₅×D₄	—	2	6	no	—
200	C₂×C₅×D₄	—	2	3	no	—
201	C₂×C₅×D₄	—	2	6	no	—
202	C₂×C₅×D₄	—	2	12	no	—
203	C₂×C₅×D₄	—	2	12	no	—
204	C₂×C₅×D₄	—	2	3	no	—
205	C₂×C₅×D₄	—	4	12	no	—
206	C₂×C₅×D₄	—	8	6	no	—
207	C₂×C₅×D₄	C₂×D₄	1	6	yes	—
208	C₂×C₅×D₄	C₂×D₄	1	3	yes	—
209	C₂×C₅×D₄	C₂×D₄	1	3	yes	—
210	C₂×C₅×D₄	C₂×D₄	1	24	yes	complemented
211	C₂×C₅×D₄	C₂⁴	1	3	yes	—
212	C₂×C₅×D₄	C₂⁴	1	6	yes	—
213	C₂²×C₄×C₅	—	2	24	no	—
214	C₂²×C₄×C₅	—	2	1	no	—
215	C₂²×C₄×C₅	—	2	6	no	—
216	C₂²×C₄×C₅	—	2	6	no	—
217	C₂²×C₄×C₅	—	2	12	no	—
218	C₂²×C₄×C₅	—	2	3	no	—
219	C₂²×C₄×C₅	—	2	3	no	—
220	C₂²×C₄×C₅	C₂×D₄	1	3	yes	—
221	C₂²×C₄×C₅	C₂×D₄	1	3	yes	—
222	C₂²×C₄×C₅	C₂×D₄	1	3	yes	—
223	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
224	C₂²×C₄×C₅	C₂⁴	1	3	yes	—
225	C₂²×C₄×C₅	C₂⁴	1	3	yes	—
226	C₅×Q₁₆	—	2	4	no	—
227	C₅×SD₁₆	—	2	12	no	—
228	C₅×SD₁₆	—	2	12	no	—
229	C₅×D₈	—	2	12	no	—
230	C₅×D₈	—	2	24	no	—
231	C₅×M₁₆	—	2	12	no	—
232	C₂×C₅×C₈	—	2	12	no	—
233	C₂×C₅×C₈	C₂⁴	1	2	yes	—
234	C₂×C₅×C₈	C₂⁴	1	6	yes	—
235	C₅×C₄⋊C₄	—	2	3	no	—
236	C₅×C₄⋊C₄	—	2	1	no	—
237	C₅×C₄⋊C₄	—	2	3	no	—
238	C₅×C₄⋊C₄	C₂⁴	1	3	yes	—
239	C₅×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
240	C₅×C₂²⋊C₄	—	2	3	no	—
241	C₅×C₂²⋊C₄	—	2	1	no	—
242	C₅×C₂²⋊C₄	—	2	3	no	—
243	C₅×C₂²⋊C₄	—	2	3	no	—
244	C₅×C₂²⋊C₄	—	2	6	no	—
245	C₅×C₂²⋊C₄	—	2	3	no	—
246	C₄²×C₅	—	2	3	no	—
247	C₂×H(5,𝔽₂)	—	2	16	no	—
248	C₂×H(5,𝔽₂)	—	2	3	no	—
249	C₂×H(5,𝔽₂)	—	2	1	no	—
250	C₂×H(5,𝔽₂)	C₂²×C₅	1	2	yes	—
251	C₂×H(5,𝔽₂)	C₂²×C₅	1	6	yes	complemented
252	C₂×H(5,𝔽₂)	C₂²×C₅	1	1	yes	characteristic, complemented
253	C₂²×#41	—	2	1	no	—
254	C₂²×#41	C₂²×C₅	1	1	yes	characteristic
255	C₂²×#41	C₂²×C₅	1	3	yes	complemented
256	C₂³×D₄	—	2	3	no	—
257	C₂³×D₄	C₂²×C₅	1	3	yes	complemented
258	#576	—	2	16	no	—
259	C₂×AGL(1,ℤ/8)	C₂²×C₅	1	6	yes	complemented
260	C₂×AGL(1,ℤ/8)	C₂²×C₅	1	6	yes	complemented
261	C₂×#135	C₂²×C₅	1	6	yes	complemented
262	C₂²×D₈	C₂²×C₅	1	6	yes	complemented
263	C₂×#131	C₂²×C₅	1	2	yes	complemented
264	#550	—	2	1	no	—
265	#548	—	2	1	no	—
266	#546	—	2	3	no	—
267	D₄²	—	2	3	no	—
268	#537	C₂²×C₅	1	3	yes	complemented
269	#535	C₂²×C₅	1	3	yes	complemented
270	#525	C₂²×C₅	1	3	yes	complemented
271	C₂×#121	C₂²×C₅	1	3	yes	complemented
272	#520	C₂²×C₅	1	1	yes	characteristic, complemented
273	#452	C₂²×C₅	1	6	yes	complemented
274	#451	C₂²×C₅	1	1	yes	characteristic, complemented
275	#450	C₂²×C₅	1	3	yes	complemented
276	#450	C₂²×C₅	1	6	yes	complemented
277	#449	C₂²×C₅	1	6	yes	complemented
278	#449	C₂²×C₅	1	12	yes	complemented
279	#448	C₂²×C₅	1	3	yes	complemented
280	#447	C₂²×C₅	1	3	yes	complemented
281	#447	C₂²×C₅	1	6	yes	complemented
282	#447	C₂²×C₅	1	12	yes	complemented
283	#447	C₂²×C₅	1	6	yes	complemented
284	#418	C₂²×C₅	1	6	yes	complemented
285	#417	C₂²×C₅	1	6	yes	complemented
286	#416	C₂²×C₅	1	6	yes	complemented
287	C₂×#102	C₂²×C₅	1	6	yes	complemented
288	#408	C₂²×C₅	1	6	yes	complemented
289	#407	C₂²×C₅	1	3	yes	complemented
290	C₂×C₂²⋊C₈	C₂²×C₅	1	3	yes	complemented
291	C₂³×C₅	—	2	12	no	—
292	C₂³×C₅	—	2	24	no	—
293	C₂³×C₅	—	2	6	no	—
294	C₂³×C₅	—	2	6	no	—
295	C₂³×C₅	—	2	6	no	—
296	C₂³×C₅	—	2	24	no	—
297	C₂³×C₅	—	2	3	no	—
298	C₂³×C₅	—	4	3	no	—
299	C₂³×C₅	—	4	6	no	—
300	C₂³×C₅	—	4	6	no	—
301	C₂³×C₅	—	4	6	no	—
302	C₂³×C₅	—	8	6	no	—
303	C₂³×C₅	—	8	6	no	—
304	C₂³×C₅	—	8	6	no	—
305	C₂³×C₅	—	8	6	no	—
306	C₂³×C₅	—	8	3	no	—
307	C₂³×C₅	—	8	3	no	—
308	C₂³×C₅	—	8	48	no	—
309	C₂³×C₅	C₂²×D₄	1	3	yes	—
310	C₂³×C₅	C₂²×D₄	1	3	yes	—
311	C₂³×C₅	C₂²×D₄	1	1	yes	characteristic
312	C₅×Q₈	—	2	4	no	—
313	C₅×Q₈	—	2	6	no	—
314	C₅×Q₈	—	2	2	no	—
315	C₅×Q₈	—	2	2	no	—
316	C₅×Q₈	#120	1	4	yes	—
317	C₅×Q₈	C₂²×D₄	1	4	yes	—
318	C₅×D₄	—	2	24	no	—
319	C₅×D₄	—	2	24	no	—
320	C₅×D₄	—	2	12	no	—
321	C₅×D₄	—	2	24	no	—
322	C₅×D₄	—	2	12	no	—
323	C₅×D₄	—	2	6	no	—
324	C₅×D₄	—	2	24	no	—
325	C₅×D₄	—	2	6	no	—
326	C₅×D₄	—	2	6	no	—
327	C₅×D₄	—	4	6	no	—
328	C₅×D₄	—	4	6	no	—
329	C₅×D₄	—	4	6	no	—
330	C₅×D₄	—	8	3	no	—
331	C₅×D₄	—	8	6	no	—
332	C₅×D₄	#120	1	12	yes	—
333	C₅×D₄	C₂²×D₄	1	12	yes	—
334	C₂×C₄×C₅	—	2	4	no	—
335	C₂×C₄×C₅	—	2	24	no	—
336	C₂×C₄×C₅	—	2	6	no	—
337	C₂×C₄×C₅	—	2	2	no	—
338	C₂×C₄×C₅	—	2	6	no	—
339	C₂×C₄×C₅	—	2	24	no	—
340	C₂×C₄×C₅	—	2	6	no	—
341	C₂×C₄×C₅	—	2	2	no	—
342	C₂×C₄×C₅	—	2	6	no	—
343	C₂×C₄×C₅	—	2	1	no	—
344	C₂×C₄×C₅	—	2	3	no	—
345	C₂×C₄×C₅	—	2	1	no	—
346	C₂×C₄×C₅	—	4	6	no	—
347	C₂×C₄×C₅	—	8	3	no	—
348	C₂×C₄×C₅	C₂²×D₄	1	3	yes	—
349	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
350	C₂×C₄×C₅	C₂²×D₄	1	3	yes	—
351	C₂×C₄×C₅	C₂²×D₄	1	12	yes	—
352	C₂×C₄×C₅	C₂⁵	1	1	yes	characteristic
353	C₅×C₈	—	2	2	no	—
354	C₅×C₈	—	2	6	no	—
355	C₂⁵	—	2	3	no	—
356	H(5,𝔽₂)	—	2	16	no	—
357	H(5,𝔽₂)	—	2	48	no	—
358	H(5,𝔽₂)	—	2	8	no	—
359	H(5,𝔽₂)	—	2	24	no	—
360	H(5,𝔽₂)	—	2	24	no	—
361	H(5,𝔽₂)	—	2	8	no	—
362	H(5,𝔽₂)	C₅×D₄	1	16	yes	complemented
363	C₂×#41	—	2	16	no	—
364	C₂×#41	—	2	8	no	—
365	C₂×#41	—	2	24	no	—
366	C₂×#41	—	2	2	no	—
367	C₂×#41	—	2	6	no	—
368	C₂×#41	—	2	1	no	—
369	C₂×#41	—	2	3	no	—
370	C₂×#41	—	2	3	no	—
371	C₂×#41	C₅×D₄	1	3	yes	—
372	C₂×#41	C₅×D₄	1	1	yes	characteristic
373	C₂×#41	C₂³×C₅	1	6	yes	—
374	C₂×#41	C₂³×C₅	1	6	yes	—
375	C₂×#41	C₂³×C₅	1	3	yes	—
376	C₂×#41	C₂³×C₅	1	1	yes	characteristic
377	C₂×#41	C₂³×C₅	1	3	yes	complemented
378	C₂²×Q₈	C₅×D₄	1	1	yes	characteristic
379	C₂²×Q₈	C₂³×C₅	1	1	yes	characteristic
380	C₂²×D₄	—	2	48	no	—
381	C₂²×D₄	—	2	3	no	—
382	C₂²×D₄	—	2	6	no	—
383	C₂²×D₄	—	2	12	no	—
384	C₂²×D₄	—	2	6	no	—
385	C₂²×D₄	—	2	24	no	—
386	C₂²×D₄	—	2	3	no	—
387	C₂²×D₄	—	2	3	no	—
388	C₂²×D₄	—	2	3	no	—
389	C₂²×D₄	—	2	3	no	—
390	C₂²×D₄	—	2	3	no	—
391	C₂²×D₄	C₅×D₄	1	3	yes	—
392	C₂²×D₄	C₂³×C₅	1	3	yes	—
393	C₂²×D₄	C₂³×C₅	1	6	yes	—
394	C₂²×D₄	C₂³×C₅	1	6	yes	—
395	C₂²×D₄	C₂³×C₅	1	3	yes	complemented
396	C₂³×C₄	—	2	3	no	—
397	C₂³×C₄	C₂³×C₅	1	3	yes	—
398	AGL(1,ℤ/8)	—	2	24	no	—
399	AGL(1,ℤ/8)	—	2	24	no	—
400	#135	—	2	24	no	—
401	C₂×Q₁₆	C₂³×C₅	1	2	yes	complemented
402	C₂×SD₁₆	C₂³×C₅	1	6	yes	complemented
403	C₂×SD₁₆	C₂³×C₅	1	6	yes	complemented
404	C₂×D₈	—	2	24	no	—
405	C₂×D₈	C₂³×C₅	1	6	yes	complemented
406	C₂×D₈	C₂³×C₅	1	12	yes	complemented
407	#131	—	2	8	no	—
408	C₂×M₁₆	C₂³×C₅	1	6	yes	complemented
409	C₂²×C₈	C₂³×C₅	1	6	yes	complemented
410	#127	—	2	3	no	—
411	#124	—	2	3	no	—
412	#123	—	2	3	no	—
413	C₂²⋊Q₈	—	2	3	no	—
414	C₂²⋊Q₈	C₂³×C₅	1	1	yes	characteristic
415	C₂²⋊Q₈	C₂³×C₅	1	3	yes	complemented
416	#121	—	2	6	no	—
417	#121	—	2	3	no	—
418	#121	—	2	3	no	—
419	#121	—	2	3	no	—
420	#121	C₂³×C₅	1	3	yes	—
421	#121	C₂³×C₅	1	6	yes	complemented
422	#121	C₂³×C₅	1	3	yes	complemented
423	#120	—	2	3	no	—
424	#120	—	2	6	no	—
425	C₄×Q₈	—	2	1	no	—
426	C₄×D₄	—	2	3	no	—
427	C₄×D₄	—	2	3	no	—
428	C₄×D₄	—	2	3	no	—
429	#117	C₂³×C₅	1	3	yes	complemented
430	C₂×C₄⋊C₄	C₂³×C₅	1	3	yes	complemented
431	C₂×C₂²⋊C₄	—	2	3	no	—
432	#103	C₂³×C₅	1	2	yes	complemented
433	#103	C₂³×C₅	1	6	yes	complemented
434	#102	C₂³×C₅	1	6	yes	complemented
435	#102	C₂³×C₅	1	12	yes	complemented
436	#102	C₂³×C₅	1	6	yes	complemented
437	C₂²⋊C₈	C₂³×C₅	1	1	yes	characteristic
438	C₂²⋊C₈	C₂³×C₅	1	3	yes	—
439	C₂²⋊C₈	C₂³×C₅	1	6	yes	complemented
440	C₂²⋊C₈	C₂³×C₅	1	6	yes	complemented
441	C₂²×C₅	—	2	1	no	—
442	C₂²×C₅	—	2	3	no	—
443	C₂²×C₅	—	2	1	no	—
444	C₂²×C₅	—	2	3	no	—
445	C₂²×C₅	—	2	3	no	—
446	C₂²×C₅	—	2	3	no	—
447	C₂²×C₅	—	2	12	no	—
448	C₂²×C₅	—	2	3	no	—
449	C₂²×C₅	—	4	12	no	—
450	C₂²×C₅	—	4	24	no	—
451	C₂²×C₅	—	4	6	no	—
452	C₂²×C₅	—	4	6	no	—
453	C₂²×C₅	—	4	3	no	—
454	C₂²×C₅	—	4	3	no	—
455	C₂²×C₅	—	4	3	no	—
456	C₂²×C₅	—	8	24	no	—
457	C₂²×C₅	—	8	24	no	—
458	C₂²×C₅	—	16	6	no	—
459	C₂²×C₅	C₂×#120	1	6	yes	—
460	C₂²×C₅	#576	1	2	yes	complemented
461	C₂²×C₅	C₂³×D₄	1	1	yes	characteristic
462	C₄×C₅	—	2	4	no	—
463	C₄×C₅	—	2	3	no	—
464	C₄×C₅	—	2	1	no	—
465	C₄×C₅	—	4	1	no	—
466	C₄×C₅	—	4	1	no	—
467	C₄×C₅	—	4	3	no	—
468	C₄×C₅	C₂×#120	1	6	yes	—
469	C₄×C₅	C₂³×D₄	1	2	yes	—
470	C₂⁴	—	2	24	no	—
471	C₂⁴	—	2	3	no	—
472	C₂⁴	—	2	6	no	—
473	C₂⁴	—	2	6	no	—
474	C₂⁴	—	2	3	no	—
475	C₂⁴	—	8	6	no	—
476	C₂⁴	—	8	6	no	—
477	C₂⁴	C₂×C₅×D₄	1	3	yes	—
478	#41	—	2	24	no	—
479	#41	—	2	48	no	—
480	#41	—	2	24	no	—
481	#41	—	2	16	no	—
482	#41	—	2	4	no	—
483	#41	—	2	12	no	—
484	#41	—	2	12	no	—
485	#41	—	2	12	no	—
486	#41	—	2	12	no	—
487	#41	—	2	12	no	—
488	#41	—	2	12	no	—
489	#41	—	4	4	no	—
490	#41	C₂×C₅×D₄	1	8	yes	—
491	#41	C₂×C₅×D₄	1	24	yes	complemented
492	C₂×Q₈	—	2	4	no	—
493	C₂×Q₈	—	2	4	no	—
494	C₂×Q₈	—	2	1	no	—
495	C₂×Q₈	C₂×C₅×D₄	1	3	yes	—
496	C₂×Q₈	C₂×C₅×D₄	1	1	yes	characteristic
497	C₂×Q₈	C₂⁴×C₅	1	1	yes	characteristic
498	C₂×Q₈	C₂⁴×C₅	1	2	yes	—
499	C₂×D₄	—	2	24	no	—
500	C₂×D₄	—	2	24	no	—
501	C₂×D₄	—	2	96	no	—
502	C₂×D₄	—	2	24	no	—
503	C₂×D₄	—	2	48	no	—
504	C₂×D₄	—	2	24	no	—
505	C₂×D₄	—	2	6	no	—
506	C₂×D₄	—	2	6	no	—
507	C₂×D₄	—	2	12	no	—
508	C₂×D₄	—	2	48	no	—
509	C₂×D₄	—	2	12	no	—
510	C₂×D₄	—	2	24	no	—
511	C₂×D₄	—	2	3	no	—
512	C₂×D₄	—	2	3	no	—
513	C₂×D₄	—	2	3	no	—
514	C₂×D₄	—	2	6	no	—
515	C₂×D₄	—	2	6	no	—
516	C₂×D₄	—	2	3	no	—
517	C₂×D₄	—	2	6	no	—
518	C₂×D₄	—	2	12	no	—
519	C₂×D₄	—	2	12	no	—
520	C₂×D₄	—	2	3	no	—
521	C₂×D₄	—	4	12	no	—
522	C₂×D₄	—	8	6	no	—
523	C₂×D₄	C₂×C₅×D₄	1	6	yes	—
524	C₂×D₄	C₂×C₅×D₄	1	3	yes	—
525	C₂×D₄	C₂×C₅×D₄	1	3	yes	—
526	C₂×D₄	C₂×C₅×D₄	1	24	yes	complemented
527	C₂×D₄	C₂⁴×C₅	1	3	yes	—
528	C₂×D₄	C₂⁴×C₅	1	6	yes	—
529	C₂²×C₄	—	2	24	no	—
530	C₂²×C₄	—	2	1	no	—
531	C₂²×C₄	—	2	6	no	—
532	C₂²×C₄	—	2	6	no	—
533	C₂²×C₄	—	2	12	no	—
534	C₂²×C₄	—	2	3	no	—
535	C₂²×C₄	—	2	3	no	—
536	C₂²×C₄	C₂×C₅×D₄	1	3	yes	—
537	C₂²×C₄	C₂×C₅×D₄	1	3	yes	—
538	C₂²×C₄	C₂×C₅×D₄	1	3	yes	—
539	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
540	C₂²×C₄	C₂⁴×C₅	1	3	yes	—
541	C₂²×C₄	C₂⁴×C₅	1	3	yes	—
542	Q₁₆	—	2	4	no	—
543	SD₁₆	—	2	12	no	—
544	SD₁₆	—	2	12	no	—
545	D₈	—	2	12	no	—
546	D₈	—	2	24	no	—
547	M₁₆	—	2	12	no	—
548	C₂×C₈	—	2	12	no	—
549	C₂×C₈	C₂⁴×C₅	1	2	yes	—
550	C₂×C₈	C₂⁴×C₅	1	6	yes	—
551	C₄⋊C₄	—	2	3	no	—
552	C₄⋊C₄	—	2	1	no	—
553	C₄⋊C₄	—	2	3	no	—
554	C₄⋊C₄	C₂⁴×C₅	1	3	yes	—
555	C₄⋊C₄	C₂⁴×C₅	1	1	yes	characteristic
556	C₂²⋊C₄	—	2	3	no	—
557	C₂²⋊C₄	—	2	1	no	—
558	C₂²⋊C₄	—	2	3	no	—
559	C₂²⋊C₄	—	2	3	no	—
560	C₂²⋊C₄	—	2	6	no	—
561	C₂²⋊C₄	—	2	3	no	—
562	C₄²	—	2	3	no	—
563	C₂×C₅	—	2	2	no	—
564	C₂×C₅	—	2	6	no	—
565	C₂×C₅	—	4	3	no	—
566	C₂×C₅	—	4	12	no	—
567	C₂×C₅	—	8	3	no	—
568	C₂×C₅	C₂²×#120	1	1	yes	characteristic
569	C₂×C₅	C₂×#576	1	1	yes	characteristic
570	C₂×C₅	#3585	1	1	yes	characteristic
571	C₂³	—	2	12	no	—
572	C₂³	—	2	24	no	—
573	C₂³	—	2	6	no	—
574	C₂³	—	2	6	no	—
575	C₂³	—	2	6	no	—
576	C₂³	—	2	24	no	—
577	C₂³	—	2	3	no	—
578	C₂³	—	4	3	no	—
579	C₂³	—	4	6	no	—
580	C₂³	—	4	6	no	—
581	C₂³	—	4	6	no	—
582	C₂³	—	8	6	no	—
583	C₂³	—	8	6	no	—
584	C₂³	—	8	6	no	—
585	C₂³	—	8	6	no	—
586	C₂³	—	8	3	no	—
587	C₂³	—	8	3	no	—
588	C₂³	—	8	48	no	—
589	C₂³	C₂²×C₅×D₄	1	3	yes	—
590	C₂³	C₂²×C₅×D₄	1	3	yes	—
591	C₂³	C₂²×C₅×D₄	1	1	yes	characteristic
592	Q₈	—	2	4	no	—
593	Q₈	—	2	6	no	—
594	Q₈	—	2	2	no	—
595	Q₈	—	2	2	no	—
596	Q₈	C₅×#120	1	4	yes	—
597	Q₈	C₂²×C₅×D₄	1	4	yes	—
598	D₄	—	2	24	no	—
599	D₄	—	2	24	no	—
600	D₄	—	2	12	no	—
601	D₄	—	2	24	no	—
602	D₄	—	2	12	no	—
603	D₄	—	2	6	no	—
604	D₄	—	2	24	no	—
605	D₄	—	2	6	no	—
606	D₄	—	2	6	no	—
607	D₄	—	4	6	no	—
608	D₄	—	4	6	no	—
609	D₄	—	4	6	no	—
610	D₄	—	8	6	no	—
611	D₄	—	8	3	no	—
612	D₄	C₅×#120	1	12	yes	—
613	D₄	C₂²×C₅×D₄	1	12	yes	—
614	C₂×C₄	—	2	4	no	—
615	C₂×C₄	—	2	24	no	—
616	C₂×C₄	—	2	6	no	—
617	C₂×C₄	—	2	2	no	—
618	C₂×C₄	—	2	6	no	—
619	C₂×C₄	—	2	24	no	—
620	C₂×C₄	—	2	6	no	—
621	C₂×C₄	—	2	2	no	—
622	C₂×C₄	—	2	6	no	—
623	C₂×C₄	—	2	1	no	—
624	C₂×C₄	—	2	3	no	—
625	C₂×C₄	—	2	1	no	—
626	C₂×C₄	—	4	6	no	—
627	C₂×C₄	—	8	3	no	—
628	C₂×C₄	C₂²×C₅×D₄	1	3	yes	—
629	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
630	C₂×C₄	C₂²×C₅×D₄	1	3	yes	—
631	C₂×C₄	C₂²×C₅×D₄	1	12	yes	—
632	C₂×C₄	C₂⁵×C₅	1	1	yes	characteristic
633	C₈	—	2	2	no	—
634	C₈	—	2	6	no	—
635	C₅	#60372	1	1	yes	characteristic, direct product factor, Sylow
636	C₂²	—	2	1	no	—
637	C₂²	—	2	3	no	—
638	C₂²	—	2	1	no	—
639	C₂²	—	2	3	no	—
640	C₂²	—	2	3	no	—
641	C₂²	—	2	12	no	—
642	C₂²	—	2	3	no	—
643	C₂²	—	2	3	no	—
644	C₂²	—	4	12	no	—
645	C₂²	—	4	24	no	—
646	C₂²	—	4	6	no	—
647	C₂²	—	4	6	no	—
648	C₂²	—	4	3	no	—
649	C₂²	—	4	3	no	—
650	C₂²	—	4	3	no	—
651	C₂²	—	8	24	no	—
652	C₂²	—	8	24	no	—
653	C₂²	—	16	6	no	—
654	C₂²	C₂×C₅×#120	1	6	yes	—
655	C₂²	C₅×#576	1	2	yes	complemented
656	C₂²	C₂³×C₅×D₄	1	1	yes	characteristic
657	C₄	—	2	4	no	—
658	C₄	—	2	3	no	—
659	C₄	—	2	1	no	—
660	C₄	—	4	1	no	—
661	C₄	—	4	3	no	—
662	C₄	—	4	1	no	—
663	C₄	C₂×C₅×#120	1	6	yes	—
664	C₄	C₂³×C₅×D₄	1	2	yes	—
665	C₂	—	2	2	no	—
666	C₂	—	2	6	no	—
667	C₂	—	4	3	no	—
668	C₂	—	4	12	no	—
669	C₂	—	8	3	no	—
670	C₂	C₂²×C₅×#120	1	1	yes	characteristic
671	C₂	C₂×C₅×#576	1	1	yes	characteristic
672	C₂	C₅×#3585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₅	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₅
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₅ ◁ C₂²×C₅×#41 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×C₅×H(5,𝔽₂)	C₂	semidirect
2. C₂×C₅×#576	C₂	semidirect
3. C₅×#3488	C₂	semidirect
4. C₅×#3012	C₂	semidirect
5. C₅×#3008	C₂	semidirect
6. C₅×#3006	C₂	semidirect
7. C₅×#3003	C₂	semidirect
8. C₅×#3002	C₂	semidirect
9. C₂×C₅×#447	C₂	semidirect
10. C₅×#2897	C₂	semidirect
11. C₅×#2880	C₂	semidirect
16. C₂×C₅×H(5,𝔽₂)	C₂²	semidirect
17. C₂×C₅×H(5,𝔽₂)	C₂²	semidirect
20. C₂²×C₅×#41	C₂²	semidirect
22. C₂³×C₅×D₄	C₂²	semidirect
24. C₂×C₅×AGL(1,ℤ/8)	C₂²	semidirect
25. C₂×C₅×AGL(1,ℤ/8)	C₂²	semidirect
26. C₂×C₅×#135	C₂²	semidirect
27. C₂²×C₅×D₈	C₂²	semidirect
28. C₂×C₅×#131	C₂²	semidirect
33. C₅×#537	C₂²	semidirect
34. C₅×#535	C₂²	semidirect
35. C₅×#525	C₂²	semidirect
36. C₂×C₅×#121	C₂²	semidirect
37. C₅×#520	C₂²	semidirect
38. C₅×#452	C₂²	semidirect
39. C₅×#451	C₂²	semidirect
40. C₅×#450	C₂²	semidirect
41. C₅×#450	C₂²	semidirect
42. C₅×#449	C₂²	semidirect
43. C₅×#449	C₂²	semidirect
44. C₅×#448	C₂²	semidirect
45. C₅×#447	C₂²	semidirect
46. C₅×#447	C₂²	semidirect
47. C₅×#447	C₂²	semidirect
48. C₅×#447	C₂²	semidirect
49. C₅×#418	C₂²	semidirect
50. C₅×#417	C₂²	semidirect
51. C₅×#416	C₂²	semidirect
52. C₂×C₅×#102	C₂²	semidirect
53. C₅×#408	C₂²	semidirect
54. C₅×#407	C₂²	semidirect
55. C₂×C₅×C₂²⋊C₈	C₂²	semidirect
56. #60372	C₅	direct (N × H)
64. C₅×H(5,𝔽₂)	D₄	semidirect
79. C₂×C₅×#41	C₂³	semidirect
97. C₂²×C₅×D₄	C₂³	semidirect
103. C₂×C₅×Q₁₆	C₂³	semidirect
104. C₂×C₅×SD₁₆	C₂³	semidirect
105. C₂×C₅×SD₁₆	C₂³	semidirect
107. C₂×C₅×D₈	C₂³	semidirect
108. C₂×C₅×D₈	C₂³	semidirect
110. C₂×C₅×M₁₆	C₂³	semidirect
111. C₂²×C₅×C₈	C₂³	semidirect
117. C₅×C₂²⋊Q₈	C₂³	semidirect
123. C₅×#121	C₂³	semidirect
124. C₅×#121	C₂³	semidirect
131. C₅×#117	C₂³	semidirect
132. C₂×C₅×C₄⋊C₄	C₂³	semidirect
134. C₅×#103	C₂³	semidirect
135. C₅×#103	C₂³	semidirect
136. C₅×#102	C₂³	semidirect
137. C₅×#102	C₂³	semidirect
138. C₅×#102	C₂³	semidirect
141. C₅×C₂²⋊C₈	C₂³	semidirect
142. C₅×C₂²⋊C₈	C₂³	semidirect
143. C₂²×H(5,𝔽₂)	C₂×C₅	semidirect
144. C₂×#576	C₂×C₅	semidirect
145. #3488	C₂×C₅	semidirect
146. #3012	C₂×C₅	semidirect
147. #3008	C₂×C₅	semidirect
148. #3006	C₂×C₅	semidirect
149. #3003	C₂×C₅	semidirect
150. #3002	C₂×C₅	semidirect
151. C₂×#447	C₂×C₅	semidirect
152. #2897	C₂×C₅	semidirect
153. #2880	C₂×C₅	semidirect
175. C₅×#41	C₂×D₄	semidirect
210. C₂×C₅×D₄	C₂×D₄	semidirect
251. C₂×H(5,𝔽₂)	C₂²×C₅	semidirect
252. C₂×H(5,𝔽₂)	C₂²×C₅	semidirect
255. C₂²×#41	C₂²×C₅	semidirect
257. C₂³×D₄	C₂²×C₅	semidirect
259. C₂×AGL(1,ℤ/8)	C₂²×C₅	semidirect
260. C₂×AGL(1,ℤ/8)	C₂²×C₅	semidirect
261. C₂×#135	C₂²×C₅	semidirect
262. C₂²×D₈	C₂²×C₅	semidirect
263. C₂×#131	C₂²×C₅	semidirect
268. #537	C₂²×C₅	semidirect
269. #535	C₂²×C₅	semidirect
270. #525	C₂²×C₅	semidirect
271. C₂×#121	C₂²×C₅	semidirect
272. #520	C₂²×C₅	semidirect
273. #452	C₂²×C₅	semidirect
274. #451	C₂²×C₅	semidirect
275. #450	C₂²×C₅	semidirect
276. #450	C₂²×C₅	semidirect
277. #449	C₂²×C₅	semidirect
278. #449	C₂²×C₅	semidirect
279. #448	C₂²×C₅	semidirect
280. #447	C₂²×C₅	semidirect
281. #447	C₂²×C₅	semidirect
282. #447	C₂²×C₅	semidirect
283. #447	C₂²×C₅	semidirect
284. #418	C₂²×C₅	semidirect
285. #417	C₂²×C₅	semidirect
286. #416	C₂²×C₅	semidirect
287. C₂×#102	C₂²×C₅	semidirect
288. #408	C₂²×C₅	semidirect
289. #407	C₂²×C₅	semidirect
290. C₂×C₂²⋊C₈	C₂²×C₅	semidirect
362. H(5,𝔽₂)	C₅×D₄	semidirect
377. C₂×#41	C₂³×C₅	semidirect
395. C₂²×D₄	C₂³×C₅	semidirect
401. C₂×Q₁₆	C₂³×C₅	semidirect
402. C₂×SD₁₆	C₂³×C₅	semidirect
403. C₂×SD₁₆	C₂³×C₅	semidirect
405. C₂×D₈	C₂³×C₅	semidirect
406. C₂×D₈	C₂³×C₅	semidirect
408. C₂×M₁₆	C₂³×C₅	semidirect
409. C₂²×C₈	C₂³×C₅	semidirect
415. C₂²⋊Q₈	C₂³×C₅	semidirect
421. #121	C₂³×C₅	semidirect
422. #121	C₂³×C₅	semidirect
429. #117	C₂³×C₅	semidirect
430. C₂×C₄⋊C₄	C₂³×C₅	semidirect
432. #103	C₂³×C₅	semidirect
433. #103	C₂³×C₅	semidirect
434. #102	C₂³×C₅	semidirect
435. #102	C₂³×C₅	semidirect
436. #102	C₂³×C₅	semidirect
439. C₂²⋊C₈	C₂³×C₅	semidirect
440. C₂²⋊C₈	C₂³×C₅	semidirect
460. C₂²×C₅	#576	semidirect
491. #41	C₂×C₅×D₄	semidirect
526. C₂×D₄	C₂×C₅×D₄	semidirect
635. C₅	#60372	direct (N × H)
655. C₂²	C₅×#576	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₅×H(5,𝔽₂)	2
C₂×C₅×#576	2
C₅×#3488	2
C₅×#3012	2
C₅×#3008	2
C₅×#3006	2
C₅×#3003	2
C₅×#3002	2
C₂×C₅×#447	2
C₅×#2897	2
C₅×#2880	2
#60372	5

Subgroups — C5×#60372 #11983092

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#60372 #11983092