Subgroups — C₅×#21628 #11944348

Order 1280.

738 conjugacy classes of subgroups.

The subgroup lattice has 506 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#3076	C₂	1	1	yes	maximal, characteristic
2	C₅×#2960	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×C₅×#131	C₂	1	1	yes	maximal, characteristic
4	C₅×#1986	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#1950	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#1922	C₂	1	2	yes	maximal, complemented
7	C₅×#1866	C₂	1	2	yes	maximal
8	C₅×#1806	C₂	1	1	yes	maximal, characteristic
9	C₅×#1773	C₂	1	2	yes	maximal, complemented
10	C₅×#1770	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#1765	C₂	1	2	yes	maximal
12	C₂×C₅×#131	C₂²	1	1	yes	characteristic
13	C₂×C₅×#131	C₂²	1	1	yes	characteristic
14	C₅×#533	C₂²	1	1	yes	characteristic
15	C₄×C₅×#41	C₂²	1	1	yes	characteristic
16	C₅×#479	C₄	1	2	yes	complemented
17	C₅×#478	C₄	1	2	yes	complemented
18	C₅×#477	C₄	1	1	yes	characteristic, complemented
19	C₅×#476	C₄	1	1	yes	characteristic, complemented
20	C₅×#475	C₄	1	1	yes	characteristic, complemented
21	C₅×#474	C₄	1	1	yes	characteristic, complemented
22	C₅×#446	—	2	1	no	—
23	C₅×#446	—	2	1	no	—
24	C₅×C₈×Q₈	—	2	1	no	—
25	C₅×C₈×Q₈	—	2	1	no	—
26	C₂×C₅×#108	C₂²	1	2	yes	—
27	C₅×#427	C₂²	1	2	yes	—
28	C₅×#424	C₂²	1	2	yes	—
29	C₅×#423	C₂²	1	1	yes	characteristic
30	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
31	C₂×C₅×#104	C₂²	1	2	yes	—
32	C₅×#416	C₂²	1	2	yes	—
33	C₅×#405	—	2	1	no	—
34	C₅×#405	—	2	1	no	—
35	C₅×#405	C₂²	1	2	yes	—
36	C₅×#405	C₂²	1	1	yes	characteristic
37	C₅×#405	C₂²	1	1	yes	characteristic
38	C₄×C₅×M₁₆	—	2	1	no	—
39	C₄×C₅×M₁₆	C₂²	1	1	yes	characteristic
40	C₂×C₅×#97	C₂²	1	2	yes	—
41	C₂×C₄×C₅×C₈	—	2	1	no	—
42	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
43	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
44	C₅×#341	C₂²	1	2	yes	—
45	C₅×#339	C₂²	1	2	yes	—
46	C₅×#339	C₂²	1	2	yes	—
47	C₅×#339	C₂²	1	2	yes	—
48	C₅×#336	C₂²	1	2	yes	—
49	#21628	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
50	C₂×C₅×#41	C₂³	1	1	yes	characteristic
51	C₅×#131	—	2	2	no	—
52	C₅×#131	—	2	2	no	—
53	C₅×#131	—	2	2	no	—
54	C₅×#131	Q₈	1	4	yes	complemented
55	C₂×C₅×M₁₆	—	2	1	no	—
56	C₂×C₅×M₁₆	—	2	1	no	—
57	C₂×C₅×M₁₆	C₂³	1	2	yes	—
58	C₂×C₅×M₁₆	C₂³	1	1	yes	characteristic
59	C₂×C₅×M₁₆	C₂³	1	1	yes	characteristic
60	C₂²×C₅×C₈	—	2	1	no	—
61	C₂²×C₅×C₈	—	2	1	no	—
62	C₂²×C₅×C₈	C₂³	1	2	yes	—
63	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
64	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
65	C₅×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
66	C₅×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
67	C₅×#125	C₂×C₄	1	2	yes	—
68	C₅×C₂²⋊Q₈	—	2	1	no	—
69	C₅×C₂²⋊Q₈	—	2	1	no	—
70	C₄×C₅×Q₈	—	2	1	no	—
71	C₄×C₅×Q₈	—	2	1	no	—
72	C₄×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
73	C₄×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
74	C₄×C₅×D₄	—	2	1	no	—
75	C₄×C₅×D₄	—	2	1	no	—
76	C₄×C₅×D₄	C₂×C₄	1	1	yes	characteristic
77	C₄×C₅×D₄	C₂×C₄	1	1	yes	characteristic
78	C₅×#117	—	2	1	no	—
79	C₅×#117	C₂³	1	1	yes	characteristic
80	C₅×#117	C₂³	1	2	yes	—
81	C₂×C₅×C₄⋊C₄	—	2	1	no	—
82	C₂×C₄²×C₅	—	2	1	no	—
83	C₂×C₄²×C₅	C₂³	1	2	yes	—
84	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
85	C₅×#108	—	2	4	no	—
86	C₅×#107	C₂×C₄	1	2	yes	—
87	C₅×#107	C₂×C₄	1	2	yes	—
88	C₅×#106	C₂×C₄	1	2	yes	—
89	C₅×#106	C₂×C₄	1	2	yes	—
90	C₅×C₄⋊C₈	—	2	2	no	—
91	C₅×C₄⋊C₈	—	2	2	no	—
92	C₅×C₄⋊C₈	—	2	1	no	—
93	C₅×C₄⋊C₈	—	2	1	no	—
94	C₅×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
95	C₅×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
96	C₅×C₄⋊C₈	C₂×C₄	1	2	yes	—
97	C₅×#104	—	2	4	no	—
98	C₅×#103	C₂×C₄	1	2	yes	—
99	C₅×#103	C₂×C₄	1	2	yes	—
100	C₅×#102	C₂×C₄	1	2	yes	—
101	C₅×#102	C₂×C₄	1	2	yes	—
102	C₅×#97	—	2	1	no	—
103	C₅×#97	—	2	1	no	—
104	C₅×#97	—	2	2	no	—
105	C₅×#97	—	2	4	no	—
106	C₅×#97	—	2	1	no	—
107	C₄×C₅×C₈	—	2	1	no	—
108	C₄×C₅×C₈	—	2	1	no	—
109	C₄×C₅×C₈	—	2	2	no	—
110	C₄×C₅×C₈	—	2	1	no	—
111	C₄×C₅×C₈	D₄	1	1	yes	characteristic
112	C₄×C₅×C₈	D₄	1	1	yes	characteristic
113	C₄×C₅×C₈	D₄	1	1	yes	characteristic
114	C₄×C₅×C₈	D₄	1	1	yes	characteristic
115	C₅×#95	—	2	1	no	—
116	#3076	C₂×C₅	1	1	yes	characteristic
117	#2960	C₂×C₅	1	1	yes	characteristic, complemented
118	C₄×#131	C₂×C₅	1	1	yes	characteristic
119	#1986	C₂×C₅	1	1	yes	characteristic, complemented
120	#1950	C₂×C₅	1	1	yes	characteristic, complemented
121	#1922	C₂×C₅	1	2	yes	complemented
122	#1866	C₂×C₅	1	2	yes	—
123	#1806	C₂×C₅	1	1	yes	characteristic
124	#1773	C₂×C₅	1	2	yes	complemented
125	#1770	C₂×C₅	1	1	yes	characteristic, complemented
126	#1765	C₂×C₅	1	2	yes	—
127	C₅×#41	—	2	1	no	—
128	C₅×#41	—	2	1	no	—
129	C₅×#41	C₂×Q₈	1	2	yes	—
130	C₅×#41	#41	1	2	yes	—
131	C₂×C₅×Q₈	—	2	1	no	—
132	C₂×C₅×Q₈	—	2	1	no	—
133	C₂×C₅×Q₈	C₂²×C₄	1	1	yes	characteristic
134	C₂×C₅×D₄	—	2	1	no	—
135	C₂×C₅×D₄	C₂²×C₄	1	1	yes	characteristic
136	C₂²×C₄×C₅	—	2	1	no	—
137	C₂²×C₄×C₅	—	2	1	no	—
138	C₂²×C₄×C₅	—	2	1	no	—
139	C₂²×C₄×C₅	—	2	2	no	—
140	C₂²×C₄×C₅	#41	1	1	yes	characteristic
141	C₂²×C₄×C₅	#41	1	1	yes	characteristic
142	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
143	C₅×M₁₆	—	2	4	no	—
144	C₅×M₁₆	—	2	1	no	—
145	C₅×M₁₆	—	2	1	no	—
146	C₅×M₁₆	—	2	4	no	—
147	C₅×M₁₆	—	2	2	no	—
148	C₅×M₁₆	—	2	2	no	—
149	C₅×M₁₆	C₂×Q₈	1	2	yes	—
150	C₅×M₁₆	#41	1	2	yes	—
151	C₂×C₅×C₈	—	2	4	no	—
152	C₂×C₅×C₈	—	2	1	no	—
153	C₂×C₅×C₈	—	2	1	no	—
154	C₂×C₅×C₈	—	2	1	no	—
155	C₂×C₅×C₈	—	2	1	no	—
156	C₂×C₅×C₈	—	2	2	no	—
157	C₂×C₅×C₈	—	2	2	no	—
158	C₂×C₅×C₈	—	2	4	no	—
159	C₂×C₅×C₈	—	2	2	no	—
160	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
161	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
162	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
163	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
164	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
165	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
166	C₂×C₅×C₈	C₂×Q₈	1	2	yes	—
167	C₂×C₅×C₈	#41	1	2	yes	—
168	C₅×C₄⋊C₄	—	2	1	no	—
169	C₅×C₄⋊C₄	—	2	1	no	—
170	C₅×C₄⋊C₄	—	2	2	no	—
171	C₅×C₄⋊C₄	—	2	2	no	—
172	C₅×C₄⋊C₄	—	2	1	no	—
173	C₅×C₄⋊C₄	—	2	1	no	—
174	C₅×C₄⋊C₄	—	4	2	no	—
175	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
176	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
177	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
178	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
179	C₅×C₂²⋊C₄	—	2	1	no	—
180	C₅×C₂²⋊C₄	—	2	2	no	—
181	C₅×C₂²⋊C₄	—	2	1	no	—
182	C₅×C₂²⋊C₄	—	2	1	no	—
183	C₄²×C₅	—	2	1	no	—
184	C₄²×C₅	—	2	1	no	—
185	C₄²×C₅	—	2	1	no	—
186	C₄²×C₅	—	2	2	no	—
187	C₄²×C₅	—	2	2	no	—
188	C₄²×C₅	—	2	2	no	—
189	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
190	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
191	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
192	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
193	C₂×#131	C₂²×C₅	1	1	yes	characteristic
194	C₂×#131	C₂²×C₅	1	1	yes	characteristic
195	#533	C₂²×C₅	1	1	yes	characteristic
196	C₄×#41	C₂²×C₅	1	1	yes	characteristic
197	#479	C₄×C₅	1	2	yes	complemented
198	#478	C₄×C₅	1	2	yes	complemented
199	#477	C₄×C₅	1	1	yes	characteristic, complemented
200	#476	C₄×C₅	1	1	yes	characteristic, complemented
201	#475	C₄×C₅	1	1	yes	characteristic, complemented
202	#474	C₄×C₅	1	1	yes	characteristic, complemented
203	#446	—	2	1	no	—
204	#446	—	2	1	no	—
205	C₈×Q₈	—	2	1	no	—
206	C₈×Q₈	—	2	1	no	—
207	C₂×#108	C₂²×C₅	1	2	yes	—
208	#427	C₂²×C₅	1	2	yes	—
209	#424	C₂²×C₅	1	2	yes	—
210	#423	C₂²×C₅	1	1	yes	characteristic
211	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
212	C₂×#104	C₂²×C₅	1	2	yes	—
213	#416	C₂²×C₅	1	2	yes	—
214	#405	—	2	1	no	—
215	#405	—	2	1	no	—
216	#405	C₂²×C₅	1	1	yes	characteristic
217	#405	C₂²×C₅	1	1	yes	characteristic
218	#405	C₂²×C₅	1	2	yes	—
219	C₄×M₁₆	—	2	1	no	—
220	C₄×M₁₆	C₂²×C₅	1	1	yes	characteristic
221	C₂×#97	C₂²×C₅	1	2	yes	—
222	C₂×C₄×C₈	—	2	1	no	—
223	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
224	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
225	#341	C₂²×C₅	1	2	yes	—
226	#339	C₂²×C₅	1	2	yes	—
227	#339	C₂²×C₅	1	2	yes	—
228	#339	C₂²×C₅	1	2	yes	—
229	#336	C₂²×C₅	1	2	yes	—
230	C₂³×C₅	—	2	1	no	—
231	C₂³×C₅	C₂×#41	1	1	yes	characteristic
232	C₅×Q₈	—	2	1	no	—
233	C₅×Q₈	—	4	2	no	—
234	C₅×Q₈	—	4	2	no	—
235	C₅×Q₈	C₄×Q₈	1	2	yes	—
236	C₅×D₄	—	2	2	no	—
237	C₅×D₄	—	2	2	no	—
238	C₅×D₄	—	2	1	no	—
239	C₅×D₄	C₄×Q₈	1	2	yes	—
240	C₂×C₄×C₅	—	2	1	no	—
241	C₂×C₄×C₅	—	2	2	no	—
242	C₂×C₄×C₅	—	2	2	no	—
243	C₂×C₄×C₅	—	2	2	no	—
244	C₂×C₄×C₅	—	2	1	no	—
245	C₂×C₄×C₅	—	2	1	no	—
246	C₂×C₄×C₅	—	2	2	no	—
247	C₂×C₄×C₅	—	2	2	no	—
248	C₂×C₄×C₅	—	4	1	no	—
249	C₂×C₄×C₅	—	4	2	no	—
250	C₂×C₄×C₅	—	4	2	no	—
251	C₂×C₄×C₅	—	4	2	no	—
252	C₂×C₄×C₅	—	4	2	no	—
253	C₂×C₄×C₅	—	4	2	no	—
254	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
255	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
256	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
257	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
258	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
259	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
260	C₂×C₄×C₅	C₂²×Q₈	1	1	yes	characteristic
261	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
262	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
263	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
264	C₅×C₈	—	2	2	no	—
265	C₅×C₈	—	2	2	no	—
266	C₅×C₈	—	2	2	no	—
267	C₅×C₈	—	2	1	no	—
268	C₅×C₈	—	2	2	no	—
269	C₅×C₈	—	2	1	no	—
270	C₅×C₈	—	4	2	no	—
271	C₅×C₈	C₂²⋊Q₈	1	2	yes	—
272	C₅×C₈	C₂²⋊Q₈	1	2	yes	—
273	C₂×#41	C₂³×C₅	1	1	yes	characteristic
274	#131	—	2	2	no	—
275	#131	—	2	2	no	—
276	#131	—	2	2	no	—
277	#131	C₅×Q₈	1	4	yes	complemented
278	C₂×M₁₆	—	2	1	no	—
279	C₂×M₁₆	—	2	1	no	—
280	C₂×M₁₆	C₂³×C₅	1	2	yes	—
281	C₂×M₁₆	C₂³×C₅	1	1	yes	characteristic
282	C₂×M₁₆	C₂³×C₅	1	1	yes	characteristic
283	C₂²×C₈	—	2	1	no	—
284	C₂²×C₈	—	2	1	no	—
285	C₂²×C₈	C₂³×C₅	1	2	yes	—
286	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
287	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
288	C₄⋊Q₈	C₂×C₄×C₅	1	1	yes	characteristic
289	C₄⋊Q₈	C₂×C₄×C₅	1	1	yes	characteristic
290	#125	C₂×C₄×C₅	1	2	yes	—
291	C₂²⋊Q₈	—	2	1	no	—
292	C₂²⋊Q₈	—	2	1	no	—
293	C₄×Q₈	—	2	1	no	—
294	C₄×Q₈	—	2	1	no	—
295	C₄×Q₈	C₂×C₄×C₅	1	1	yes	characteristic
296	C₄×Q₈	C₂×C₄×C₅	1	1	yes	characteristic
297	C₄×D₄	—	2	1	no	—
298	C₄×D₄	—	2	1	no	—
299	C₄×D₄	C₂×C₄×C₅	1	1	yes	characteristic
300	C₄×D₄	C₂×C₄×C₅	1	1	yes	characteristic
301	#117	—	2	1	no	—
302	#117	C₂³×C₅	1	1	yes	characteristic
303	#117	C₂³×C₅	1	2	yes	—
304	C₂×C₄⋊C₄	—	2	1	no	—
305	C₂×C₄²	—	2	1	no	—
306	C₂×C₄²	C₂³×C₅	1	2	yes	—
307	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
308	#108	—	2	4	no	—
309	#107	C₂×C₄×C₅	1	2	yes	—
310	#107	C₂×C₄×C₅	1	2	yes	—
311	#106	C₂×C₄×C₅	1	2	yes	—
312	#106	C₂×C₄×C₅	1	2	yes	—
313	C₄⋊C₈	—	2	2	no	—
314	C₄⋊C₈	—	2	2	no	—
315	C₄⋊C₈	—	2	1	no	—
316	C₄⋊C₈	—	2	1	no	—
317	C₄⋊C₈	C₂×C₄×C₅	1	1	yes	characteristic
318	C₄⋊C₈	C₂×C₄×C₅	1	1	yes	characteristic
319	C₄⋊C₈	C₂×C₄×C₅	1	2	yes	—
320	#104	—	2	4	no	—
321	#103	C₂×C₄×C₅	1	2	yes	—
322	#103	C₂×C₄×C₅	1	2	yes	—
323	#102	C₂×C₄×C₅	1	2	yes	—
324	#102	C₂×C₄×C₅	1	2	yes	—
325	#97	—	2	1	no	—
326	#97	—	2	1	no	—
327	#97	—	2	2	no	—
328	#97	—	2	4	no	—
329	#97	—	2	1	no	—
330	C₄×C₈	—	2	1	no	—
331	C₄×C₈	—	2	1	no	—
332	C₄×C₈	—	2	2	no	—
333	C₄×C₈	—	2	1	no	—
334	C₄×C₈	C₅×D₄	1	1	yes	characteristic
335	C₄×C₈	C₅×D₄	1	1	yes	characteristic
336	C₄×C₈	C₅×D₄	1	1	yes	characteristic
337	C₄×C₈	C₅×D₄	1	1	yes	characteristic
338	#95	—	2	1	no	—
339	C₂²×C₅	—	2	1	no	—
340	C₂²×C₅	—	2	1	no	—
341	C₂²×C₅	—	2	2	no	—
342	C₂²×C₅	—	4	1	no	—
343	C₂²×C₅	—	4	1	no	—
344	C₂²×C₅	C₂×C₄×D₄	1	1	yes	characteristic
345	C₂²×C₅	#529	1	1	yes	characteristic
346	C₂²×C₅	#533	1	1	yes	characteristic
347	C₄×C₅	—	2	1	no	—
348	C₄×C₅	—	2	1	no	—
349	C₄×C₅	—	2	1	no	—
350	C₄×C₅	—	2	2	no	—
351	C₄×C₅	—	4	1	no	—
352	C₄×C₅	—	4	2	no	—
353	C₄×C₅	—	4	1	no	—
354	C₄×C₅	—	4	2	no	—
355	C₄×C₅	—	8	2	no	—
356	C₄×C₅	#444	1	2	yes	—
357	C₄×C₅	C₂×C₄×Q₈	1	1	yes	characteristic
358	C₄×C₅	C₄×#41	1	1	yes	characteristic
359	C₄×C₅	C₂×C₂²⋊Q₈	1	1	yes	characteristic
360	C₄×C₅	#525	1	1	yes	characteristic
361	#41	—	2	1	no	—
362	#41	—	2	1	no	—
363	#41	C₂×C₅×Q₈	1	2	yes	—
364	#41	C₅×#41	1	2	yes	—
365	C₂×Q₈	—	2	1	no	—
366	C₂×Q₈	—	2	1	no	—
367	C₂×Q₈	C₂²×C₄×C₅	1	1	yes	characteristic
368	C₂×D₄	—	2	1	no	—
369	C₂×D₄	C₂²×C₄×C₅	1	1	yes	characteristic
370	C₂²×C₄	—	2	1	no	—
371	C₂²×C₄	—	2	1	no	—
372	C₂²×C₄	—	2	1	no	—
373	C₂²×C₄	—	2	2	no	—
374	C₂²×C₄	C₅×#41	1	1	yes	characteristic
375	C₂²×C₄	C₅×#41	1	1	yes	characteristic
376	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
377	M₁₆	—	2	4	no	—
378	M₁₆	—	2	1	no	—
379	M₁₆	—	2	1	no	—
380	M₁₆	—	2	4	no	—
381	M₁₆	—	2	2	no	—
382	M₁₆	—	2	2	no	—
383	M₁₆	C₂×C₅×Q₈	1	2	yes	—
384	M₁₆	C₅×#41	1	2	yes	—
385	C₂×C₈	—	2	4	no	—
386	C₂×C₈	—	2	1	no	—
387	C₂×C₈	—	2	1	no	—
388	C₂×C₈	—	2	2	no	—
389	C₂×C₈	—	2	2	no	—
390	C₂×C₈	—	2	1	no	—
391	C₂×C₈	—	2	1	no	—
392	C₂×C₈	—	2	4	no	—
393	C₂×C₈	—	2	2	no	—
394	C₂×C₈	C₂²×C₄×C₅	1	2	yes	—
395	C₂×C₈	C₂²×C₄×C₅	1	2	yes	—
396	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
397	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
398	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
399	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
400	C₂×C₈	C₂×C₅×Q₈	1	2	yes	—
401	C₂×C₈	C₅×#41	1	2	yes	—
402	C₄⋊C₄	—	2	1	no	—
403	C₄⋊C₄	—	2	1	no	—
404	C₄⋊C₄	—	2	2	no	—
405	C₄⋊C₄	—	2	2	no	—
406	C₄⋊C₄	—	2	1	no	—
407	C₄⋊C₄	—	2	1	no	—
408	C₄⋊C₄	—	4	2	no	—
409	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
410	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
411	C₄⋊C₄	C₂²×C₄×C₅	1	1	yes	characteristic
412	C₄⋊C₄	C₂²×C₄×C₅	1	1	yes	characteristic
413	C₂²⋊C₄	—	2	1	no	—
414	C₂²⋊C₄	—	2	2	no	—
415	C₂²⋊C₄	—	2	1	no	—
416	C₂²⋊C₄	—	2	1	no	—
417	C₄²	—	2	1	no	—
418	C₄²	—	2	1	no	—
419	C₄²	—	2	1	no	—
420	C₄²	—	2	2	no	—
421	C₄²	—	2	2	no	—
422	C₄²	—	2	2	no	—
423	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
424	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
425	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
426	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
427	C₂×C₅	—	2	1	no	—
428	C₂×C₅	—	2	1	no	—
429	C₂×C₅	—	4	2	no	—
430	C₂×C₅	C₄×C₂²⋊Q₈	1	1	yes	characteristic
431	C₂×C₅	C₂×#444	1	1	yes	characteristic
432	C₂×C₅	#2955	1	1	yes	characteristic
433	C₂³	—	2	1	no	—
434	C₂³	C₂×C₅×#41	1	1	yes	characteristic
435	Q₈	—	2	1	no	—
436	Q₈	—	4	2	no	—
437	Q₈	—	4	2	no	—
438	Q₈	C₄×C₅×Q₈	1	2	yes	—
439	D₄	—	2	2	no	—
440	D₄	—	2	2	no	—
441	D₄	—	2	1	no	—
442	D₄	C₄×C₅×Q₈	1	2	yes	—
443	C₂×C₄	—	2	1	no	—
444	C₂×C₄	—	2	2	no	—
445	C₂×C₄	—	2	2	no	—
446	C₂×C₄	—	2	2	no	—
447	C₂×C₄	—	2	1	no	—
448	C₂×C₄	—	2	1	no	—
449	C₂×C₄	—	2	2	no	—
450	C₂×C₄	—	2	2	no	—
451	C₂×C₄	—	4	1	no	—
452	C₂×C₄	—	4	2	no	—
453	C₂×C₄	—	4	2	no	—
454	C₂×C₄	—	4	2	no	—
455	C₂×C₄	—	4	2	no	—
456	C₂×C₄	—	4	2	no	—
457	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
458	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
459	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
460	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
461	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
462	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
463	C₂×C₄	C₂²×C₅×Q₈	1	1	yes	characteristic
464	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
465	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
466	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
467	C₈	—	2	2	no	—
468	C₈	—	2	2	no	—
469	C₈	—	2	2	no	—
470	C₈	—	2	1	no	—
471	C₈	—	2	2	no	—
472	C₈	—	2	1	no	—
473	C₈	—	4	2	no	—
474	C₈	C₅×C₂²⋊Q₈	1	2	yes	—
475	C₈	C₅×C₂²⋊Q₈	1	2	yes	—
476	C₅	#21628	1	1	yes	characteristic, direct product factor, Sylow
477	C₂²	—	2	1	no	—
478	C₂²	—	2	1	no	—
479	C₂²	—	2	2	no	—
480	C₂²	—	4	1	no	—
481	C₂²	—	4	1	no	—
482	C₂²	C₂×C₄×C₅×D₄	1	1	yes	characteristic
483	C₂²	C₅×#529	1	1	yes	characteristic
484	C₂²	C₅×#533	1	1	yes	characteristic
485	C₄	—	2	2	no	—
486	C₄	—	2	1	no	—
487	C₄	—	2	1	no	—
488	C₄	—	2	1	no	—
489	C₄	—	4	1	no	—
490	C₄	—	4	2	no	—
491	C₄	—	4	1	no	—
492	C₄	—	4	2	no	—
493	C₄	—	8	2	no	—
494	C₄	C₅×#444	1	2	yes	—
495	C₄	C₂×C₄×C₅×Q₈	1	1	yes	characteristic
496	C₄	C₄×C₅×#41	1	1	yes	characteristic
497	C₄	C₂×C₅×C₂²⋊Q₈	1	1	yes	characteristic
498	C₄	C₅×#525	1	1	yes	characteristic
499	C₂	—	2	1	no	—
500	C₂	—	2	1	no	—
501	C₂	—	4	2	no	—
502	C₂	C₄×C₅×C₂²⋊Q₈	1	1	yes	characteristic
503	C₂	C₂×C₅×#444	1	1	yes	characteristic
504	C₂	C₅×#2955	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₅	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₅
Frattini, cosocle	C₂²×C₄	C₂⁴×C₅
socle	C₂²×C₅	C₂×C₄×D₄
prime radical	C₂×C₅×#41	C₂³
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₅ ◁ C₂×C₄×C₅×C₈ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₅×#2960	C₂	semidirect
4. C₅×#1986	C₂	semidirect
5. C₅×#1950	C₂	semidirect
6. C₅×#1922	C₂	semidirect
9. C₅×#1773	C₂	semidirect
10. C₅×#1770	C₂	semidirect
16. C₅×#479	C₄	semidirect
17. C₅×#478	C₄	semidirect
18. C₅×#477	C₄	semidirect
19. C₅×#476	C₄	semidirect
20. C₅×#475	C₄	semidirect
21. C₅×#474	C₄	semidirect
49. #21628	C₅	direct (N × H)
54. C₅×#131	Q₈	semidirect
117. #2960	C₂×C₅	semidirect
119. #1986	C₂×C₅	semidirect
120. #1950	C₂×C₅	semidirect
121. #1922	C₂×C₅	semidirect
124. #1773	C₂×C₅	semidirect
125. #1770	C₂×C₅	semidirect
197. #479	C₄×C₅	semidirect
198. #478	C₄×C₅	semidirect
199. #477	C₄×C₅	semidirect
200. #476	C₄×C₅	semidirect
201. #475	C₄×C₅	semidirect
202. #474	C₄×C₅	semidirect
277. #131	C₅×Q₈	semidirect
476. C₅	#21628	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×#3076	2
C₅×#2960	2
C₄×C₅×#131	2
C₅×#1986	2
C₅×#1950	2
C₅×#1922	2
C₅×#1866	2
C₅×#1806	2
C₅×#1773	2
C₅×#1770	2
C₅×#1765	2
#21628	5

Subgroups — C5×#21628 #11944348

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#21628 #11944348