Subgroups — C₅×#19418 #11942138

Order 1280.

594 conjugacy classes of subgroups.

The subgroup lattice has 560 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#3231	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×#3116	C₂	1	1	yes	maximal, characteristic
3	C₅×#3107	C₂	1	1	yes	maximal, characteristic
4	C₅×#2988	C₂	1	1	yes	maximal, characteristic
5	C₅×#1684	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#1683	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#1680	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#1679	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#1674	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#1673	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#1672	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#1671	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅×#1572	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅×#1552	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅×#1542	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅×#533	C₂²	1	1	yes	characteristic
17	C₅×#533	C₂²	1	1	yes	characteristic
18	C₄×C₅×#41	C₂²	1	1	yes	characteristic
19	C₅×#500	C₂²	1	1	yes	characteristic
20	C₅×#498	C₂²	1	1	yes	characteristic
21	C₅×#487	C₂²	1	1	yes	characteristic
22	C₅×#487	C₂²	1	1	yes	characteristic
23	C₅×#485	—	2	1	no	—
24	C₅×#485	—	2	1	no	—
25	C₅×#485	—	2	1	no	—
26	C₅×#485	—	2	1	no	—
27	C₅×#479	—	2	1	no	—
28	C₅×#479	—	2	1	no	—
29	C₅×#477	C₂²	1	1	yes	characteristic
30	C₅×#476	C₂²	1	1	yes	characteristic
31	C₅×#475	C₂²	1	1	yes	characteristic
32	C₅×#474	C₂²	1	1	yes	characteristic
33	C₅×#462	C₂²	1	1	yes	characteristic
34	C₅×#462	C₂²	1	1	yes	characteristic
35	C₅×#461	C₂²	1	1	yes	characteristic
36	C₅×#461	C₂²	1	1	yes	characteristic
37	C₅×#452	—	2	1	no	—
38	C₅×#452	—	2	1	no	—
39	C₅×C₈×Q₈	C₂²	1	1	yes	characteristic
40	C₅×C₈×Q₈	C₂²	1	1	yes	characteristic
41	C₅×#441	—	2	1	no	—
42	C₅×#440	—	2	1	no	—
43	C₄×C₅×Q₁₆	—	2	1	no	—
44	C₄×C₅×SD₁₆	—	2	1	no	—
45	C₅×C₈×D₄	—	2	1	no	—
46	C₅×C₈×D₄	—	2	1	no	—
47	C₅×C₈×D₄	C₂²	1	1	yes	characteristic
48	C₅×C₈×D₄	C₂²	1	1	yes	characteristic
49	C₅×#432	C₂²	1	1	yes	characteristic
50	C₅×#431	—	2	1	no	—
51	C₅×#431	C₂²	1	1	yes	characteristic
52	C₅×#431	C₂²	1	1	yes	characteristic
53	C₂×C₅×C₄⋊C₈	—	2	1	no	—
54	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
55	C₅×#335	C₂²	1	1	yes	characteristic
56	C₅×#335	C₂²	1	1	yes	characteristic
57	C₅×#334	C₂²	1	1	yes	characteristic
58	C₅×#334	C₂²	1	1	yes	characteristic
59	C₅×#333	C₂²	1	1	yes	characteristic
60	C₅×#333	C₂²	1	1	yes	characteristic
61	C₅×#332	C₂²	1	1	yes	characteristic
62	C₅×#332	C₂²	1	1	yes	characteristic
63	C₅×#332	C₂²	1	1	yes	characteristic
64	C₅×#332	C₂²	1	1	yes	characteristic
65	C₅×#332	C₂²	1	1	yes	characteristic
66	C₅×#332	C₂²	1	1	yes	characteristic
67	#19418	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
68	C₂×C₅×#41	D₄	1	1	yes	characteristic
69	C₂×C₅×Q₁₆	—	2	1	no	—
70	C₂×C₅×Q₁₆	—	2	1	no	—
71	C₂×C₅×SD₁₆	—	2	1	no	—
72	C₂×C₅×SD₁₆	—	2	1	no	—
73	C₂²×C₅×C₈	—	2	1	no	—
74	C₂²×C₅×C₈	—	2	1	no	—
75	C₂²×C₅×C₈	—	2	1	no	—
76	C₅×C₄⋊Q₈	C₂³	1	1	yes	characteristic
77	C₅×C₄⋊Q₈	C₂³	1	1	yes	characteristic
78	C₅×C₄⋊Q₈	C₂³	1	1	yes	characteristic
79	C₅×C₄⋊Q₈	C₂³	1	1	yes	characteristic
80	C₅×#125	—	2	1	no	—
81	C₅×#125	—	2	1	no	—
82	C₅×C₂²⋊Q₈	—	2	1	no	—
83	C₅×C₂²⋊Q₈	—	2	1	no	—
84	C₅×C₂²⋊Q₈	—	2	1	no	—
85	C₅×C₂²⋊Q₈	—	2	1	no	—
86	C₄×C₅×Q₈	—	2	1	no	—
87	C₄×C₅×Q₈	—	2	1	no	—
88	C₄×C₅×Q₈	—	2	1	no	—
89	C₄×C₅×Q₈	—	2	1	no	—
90	C₄×C₅×Q₈	D₄	1	1	yes	characteristic
91	C₄×C₅×Q₈	C₂³	1	1	yes	characteristic
92	C₄×C₅×D₄	—	2	1	no	—
93	C₄×C₅×D₄	—	2	1	no	—
94	C₄×C₅×D₄	D₄	1	1	yes	characteristic
95	C₄×C₅×D₄	C₂³	1	1	yes	characteristic
96	C₅×#117	—	2	1	no	—
97	C₅×#117	—	2	1	no	—
98	C₅×#117	—	2	1	no	—
99	C₅×#117	D₄	1	1	yes	characteristic
100	C₂×C₄²×C₅	—	2	1	no	—
101	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
102	C₅×#107	—	2	1	no	—
103	C₅×#107	—	2	1	no	—
104	C₅×#107	—	2	1	no	—
105	C₅×#107	—	2	1	no	—
106	C₅×#106	—	2	1	no	—
107	C₅×#106	—	2	1	no	—
108	C₅×#106	—	2	1	no	—
109	C₅×#106	—	2	1	no	—
110	C₅×C₄⋊C₈	—	2	1	no	—
111	C₅×C₄⋊C₈	—	2	1	no	—
112	C₅×C₄⋊C₈	—	2	1	no	—
113	C₅×C₄⋊C₈	D₄	1	1	yes	characteristic
114	C₅×C₄⋊C₈	D₄	1	1	yes	characteristic
115	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
116	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
117	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
118	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
119	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
120	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
121	C₅×#103	—	2	1	no	—
122	C₅×#103	—	2	1	no	—
123	C₅×#103	—	2	1	no	—
124	C₅×#103	—	2	1	no	—
125	C₅×#103	—	2	1	no	—
126	C₅×#103	—	2	1	no	—
127	C₅×#103	—	2	1	no	—
128	C₅×#103	—	2	1	no	—
129	C₅×#103	—	2	1	no	—
130	C₅×#103	—	2	1	no	—
131	C₅×#102	—	2	1	no	—
132	C₅×#102	—	2	1	no	—
133	C₅×C₂²⋊C₈	—	2	1	no	—
134	C₅×C₂²⋊C₈	—	2	1	no	—
135	C₅×C₂²⋊C₈	—	2	1	no	—
136	C₅×C₂²⋊C₈	—	2	1	no	—
137	C₅×C₂²⋊C₈	D₄	1	1	yes	characteristic
138	C₅×C₂²⋊C₈	D₄	1	1	yes	characteristic
139	C₅×#97	—	2	1	no	—
140	C₄×C₅×C₈	—	2	1	no	—
141	C₄×C₅×C₈	—	2	1	no	—
142	C₄×C₅×C₈	—	2	1	no	—
143	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
144	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
145	#3231	C₂×C₅	1	1	yes	characteristic, complemented
146	#3116	C₂×C₅	1	1	yes	characteristic
147	#3107	C₂×C₅	1	1	yes	characteristic
148	#2988	C₂×C₅	1	1	yes	characteristic
149	#1684	C₂×C₅	1	1	yes	characteristic, complemented
150	#1683	C₂×C₅	1	1	yes	characteristic, complemented
151	#1680	C₂×C₅	1	1	yes	characteristic, complemented
152	#1679	C₂×C₅	1	1	yes	characteristic, complemented
153	#1674	C₂×C₅	1	1	yes	characteristic, complemented
154	#1673	C₂×C₅	1	1	yes	characteristic, complemented
155	#1672	C₂×C₅	1	1	yes	characteristic, complemented
156	#1671	C₂×C₅	1	1	yes	characteristic, complemented
157	#1572	C₂×C₅	1	1	yes	characteristic, complemented
158	#1552	C₂×C₅	1	1	yes	characteristic, complemented
159	#1542	C₂×C₅	1	1	yes	characteristic, complemented
160	C₅×#41	—	2	2	no	—
161	C₅×#41	—	2	2	no	—
162	C₂×C₅×Q₈	—	2	1	no	—
163	C₂×C₅×Q₈	—	2	1	no	—
164	C₂×C₅×Q₈	—	2	1	no	—
165	C₂×C₅×Q₈	—	2	1	no	—
166	C₂×C₅×Q₈	C₂×D₄	1	1	yes	characteristic
167	C₂×C₅×D₄	—	2	1	no	—
168	C₂×C₅×D₄	C₂×D₄	1	1	yes	characteristic
169	C₂²×C₄×C₅	—	2	1	no	—
170	C₂²×C₄×C₅	—	2	1	no	—
171	C₂²×C₄×C₅	—	2	1	no	—
172	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
173	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
174	C₂²×C₄×C₅	#41	1	1	yes	characteristic
175	C₅×Q₁₆	—	4	2	no	—
176	C₅×Q₁₆	—	4	2	no	—
177	C₅×SD₁₆	—	4	2	no	—
178	C₅×SD₁₆	—	4	2	no	—
179	C₂×C₅×C₈	—	2	1	no	—
180	C₂×C₅×C₈	—	2	1	no	—
181	C₂×C₅×C₈	—	2	1	no	—
182	C₂×C₅×C₈	—	2	1	no	—
183	C₂×C₅×C₈	—	2	1	no	—
184	C₂×C₅×C₈	—	2	1	no	—
185	C₂×C₅×C₈	—	8	1	no	—
186	C₂×C₅×C₈	—	8	1	no	—
187	C₂×C₅×C₈	—	8	1	no	—
188	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
189	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
190	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
191	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
192	C₅×C₄⋊C₄	—	2	1	no	—
193	C₅×C₄⋊C₄	—	2	1	no	—
194	C₅×C₄⋊C₄	—	2	1	no	—
195	C₅×C₄⋊C₄	—	2	1	no	—
196	C₅×C₄⋊C₄	—	2	1	no	—
197	C₅×C₄⋊C₄	—	2	1	no	—
198	C₅×C₄⋊C₄	—	2	1	no	—
199	C₅×C₄⋊C₄	—	2	1	no	—
200	C₅×C₄⋊C₄	—	2	1	no	—
201	C₅×C₄⋊C₄	—	2	1	no	—
202	C₅×C₄⋊C₄	—	4	1	no	—
203	C₅×C₄⋊C₄	—	4	1	no	—
204	C₅×C₄⋊C₄	—	4	1	no	—
205	C₅×C₄⋊C₄	—	4	1	no	—
206	C₅×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
207	C₅×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
208	C₅×C₂²⋊C₄	—	2	1	no	—
209	C₅×C₂²⋊C₄	—	2	1	no	—
210	C₅×C₂²⋊C₄	—	2	1	no	—
211	C₅×C₂²⋊C₄	—	4	1	no	—
212	C₅×C₂²⋊C₄	—	4	1	no	—
213	C₄²×C₅	—	2	1	no	—
214	C₄²×C₅	—	2	1	no	—
215	C₄²×C₅	—	2	1	no	—
216	C₄²×C₅	—	4	1	no	—
217	C₄²×C₅	—	4	1	no	—
218	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
219	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
220	C₄²×C₅	#41	1	1	yes	characteristic
221	C₄²×C₅	C₂⁴	1	1	yes	characteristic
222	#533	C₂²×C₅	1	1	yes	characteristic
223	#533	C₂²×C₅	1	1	yes	characteristic
224	C₄×#41	C₂²×C₅	1	1	yes	characteristic
225	#500	C₂²×C₅	1	1	yes	characteristic
226	#498	C₂²×C₅	1	1	yes	characteristic
227	#487	C₂²×C₅	1	1	yes	characteristic
228	#487	C₂²×C₅	1	1	yes	characteristic
229	#485	—	2	1	no	—
230	#485	—	2	1	no	—
231	#485	—	2	1	no	—
232	#485	—	2	1	no	—
233	#479	—	2	1	no	—
234	#479	—	2	1	no	—
235	#477	C₂²×C₅	1	1	yes	characteristic
236	#476	C₂²×C₅	1	1	yes	characteristic
237	#475	C₂²×C₅	1	1	yes	characteristic
238	#474	C₂²×C₅	1	1	yes	characteristic
239	#462	C₂²×C₅	1	1	yes	characteristic
240	#462	C₂²×C₅	1	1	yes	characteristic
241	#461	C₂²×C₅	1	1	yes	characteristic
242	#461	C₂²×C₅	1	1	yes	characteristic
243	#452	—	2	1	no	—
244	#452	—	2	1	no	—
245	C₈×Q₈	C₂²×C₅	1	1	yes	characteristic
246	C₈×Q₈	C₂²×C₅	1	1	yes	characteristic
247	#441	—	2	1	no	—
248	#440	—	2	1	no	—
249	C₄×Q₁₆	—	2	1	no	—
250	C₄×SD₁₆	—	2	1	no	—
251	C₈×D₄	—	2	1	no	—
252	C₈×D₄	—	2	1	no	—
253	C₈×D₄	C₂²×C₅	1	1	yes	characteristic
254	C₈×D₄	C₂²×C₅	1	1	yes	characteristic
255	#432	C₂²×C₅	1	1	yes	characteristic
256	#431	—	2	1	no	—
257	#431	C₂²×C₅	1	1	yes	characteristic
258	#431	C₂²×C₅	1	1	yes	characteristic
259	C₂×C₄⋊C₈	—	2	1	no	—
260	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
261	#335	C₂²×C₅	1	1	yes	characteristic
262	#335	C₂²×C₅	1	1	yes	characteristic
263	#334	C₂²×C₅	1	1	yes	characteristic
264	#334	C₂²×C₅	1	1	yes	characteristic
265	#333	C₂²×C₅	1	1	yes	characteristic
266	#333	C₂²×C₅	1	1	yes	characteristic
267	#332	C₂²×C₅	1	1	yes	characteristic
268	#332	C₂²×C₅	1	1	yes	characteristic
269	#332	C₂²×C₅	1	1	yes	characteristic
270	#332	C₂²×C₅	1	1	yes	characteristic
271	#332	C₂²×C₅	1	1	yes	characteristic
272	#332	C₂²×C₅	1	1	yes	characteristic
273	C₂³×C₅	—	2	1	no	—
274	C₂³×C₅	#121	1	1	yes	characteristic
275	C₅×Q₈	—	2	1	no	—
276	C₅×Q₈	—	4	1	no	—
277	C₅×Q₈	—	4	1	no	—
278	C₅×Q₈	—	4	1	no	—
279	C₅×Q₈	—	4	1	no	—
280	C₅×Q₈	—	4	1	no	—
281	C₅×Q₈	—	4	1	no	—
282	C₅×Q₈	—	8	1	no	—
283	C₅×Q₈	#135	1	2	yes	—
284	C₅×D₄	—	2	4	no	—
285	C₅×D₄	—	2	1	no	—
286	C₅×D₄	#135	1	2	yes	—
287	C₂×C₄×C₅	—	2	4	no	—
288	C₂×C₄×C₅	—	2	1	no	—
289	C₂×C₄×C₅	—	2	1	no	—
290	C₂×C₄×C₅	—	2	1	no	—
291	C₂×C₄×C₅	—	2	1	no	—
292	C₂×C₄×C₅	—	2	1	no	—
293	C₂×C₄×C₅	—	2	1	no	—
294	C₂×C₄×C₅	—	2	1	no	—
295	C₂×C₄×C₅	—	4	1	no	—
296	C₂×C₄×C₅	—	4	1	no	—
297	C₂×C₄×C₅	—	4	1	no	—
298	C₂×C₄×C₅	—	4	1	no	—
299	C₂×C₄×C₅	—	4	1	no	—
300	C₂×C₄×C₅	—	4	1	no	—
301	C₂×C₄×C₅	—	4	1	no	—
302	C₂×C₄×C₅	—	8	1	no	—
303	C₂×C₄×C₅	#121	1	1	yes	characteristic
304	C₂×C₄×C₅	#121	1	1	yes	characteristic
305	C₂×C₄×C₅	#121	1	1	yes	characteristic
306	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
307	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
308	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
309	C₅×C₈	—	2	1	no	—
310	C₅×C₈	—	2	1	no	—
311	C₅×C₈	—	2	1	no	—
312	C₅×C₈	—	2	1	no	—
313	C₅×C₈	—	4	1	no	—
314	C₅×C₈	—	4	1	no	—
315	C₅×C₈	—	4	1	no	—
316	C₅×C₈	—	4	1	no	—
317	C₅×C₈	—	4	1	no	—
318	C₅×C₈	—	4	1	no	—
319	C₂×#41	C₅×D₄	1	1	yes	characteristic
320	C₂×Q₁₆	—	2	1	no	—
321	C₂×Q₁₆	—	2	1	no	—
322	C₂×SD₁₆	—	2	1	no	—
323	C₂×SD₁₆	—	2	1	no	—
324	C₂²×C₈	—	2	1	no	—
325	C₂²×C₈	—	2	1	no	—
326	C₂²×C₈	—	2	1	no	—
327	C₄⋊Q₈	C₂³×C₅	1	1	yes	characteristic
328	C₄⋊Q₈	C₂³×C₅	1	1	yes	characteristic
329	C₄⋊Q₈	C₂³×C₅	1	1	yes	characteristic
330	C₄⋊Q₈	C₂³×C₅	1	1	yes	characteristic
331	#125	—	2	1	no	—
332	#125	—	2	1	no	—
333	C₂²⋊Q₈	—	2	1	no	—
334	C₂²⋊Q₈	—	2	1	no	—
335	C₂²⋊Q₈	—	2	1	no	—
336	C₂²⋊Q₈	—	2	1	no	—
337	C₄×Q₈	—	2	1	no	—
338	C₄×Q₈	—	2	1	no	—
339	C₄×Q₈	—	2	1	no	—
340	C₄×Q₈	—	2	1	no	—
341	C₄×Q₈	C₅×D₄	1	1	yes	characteristic
342	C₄×Q₈	C₂³×C₅	1	1	yes	characteristic
343	C₄×D₄	—	2	1	no	—
344	C₄×D₄	—	2	1	no	—
345	C₄×D₄	C₅×D₄	1	1	yes	characteristic
346	C₄×D₄	C₂³×C₅	1	1	yes	characteristic
347	#117	—	2	1	no	—
348	#117	—	2	1	no	—
349	#117	—	2	1	no	—
350	#117	C₅×D₄	1	1	yes	characteristic
351	C₂×C₄²	—	2	1	no	—
352	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
353	#107	—	2	1	no	—
354	#107	—	2	1	no	—
355	#107	—	2	1	no	—
356	#107	—	2	1	no	—
357	#106	—	2	1	no	—
358	#106	—	2	1	no	—
359	#106	—	2	1	no	—
360	#106	—	2	1	no	—
361	C₄⋊C₈	—	2	1	no	—
362	C₄⋊C₈	—	2	1	no	—
363	C₄⋊C₈	—	2	1	no	—
364	C₄⋊C₈	C₅×D₄	1	1	yes	characteristic
365	C₄⋊C₈	C₅×D₄	1	1	yes	characteristic
366	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
367	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
368	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
369	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
370	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
371	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
372	#103	—	2	1	no	—
373	#103	—	2	1	no	—
374	#103	—	2	1	no	—
375	#103	—	2	1	no	—
376	#103	—	2	1	no	—
377	#103	—	2	1	no	—
378	#103	—	2	1	no	—
379	#103	—	2	1	no	—
380	#103	—	2	1	no	—
381	#103	—	2	1	no	—
382	#102	—	2	1	no	—
383	#102	—	2	1	no	—
384	C₂²⋊C₈	—	2	1	no	—
385	C₂²⋊C₈	—	2	1	no	—
386	C₂²⋊C₈	—	2	1	no	—
387	C₂²⋊C₈	—	2	1	no	—
388	C₂²⋊C₈	C₅×D₄	1	1	yes	characteristic
389	C₂²⋊C₈	C₅×D₄	1	1	yes	characteristic
390	#97	—	2	1	no	—
391	C₄×C₈	—	2	1	no	—
392	C₄×C₈	—	2	1	no	—
393	C₄×C₈	—	2	1	no	—
394	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
395	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
396	C₂²×C₅	—	2	1	no	—
397	C₂²×C₅	—	2	1	no	—
398	C₂²×C₅	—	2	2	no	—
399	C₂²×C₅	—	2	1	no	—
400	C₂²×C₅	—	4	1	no	—
401	C₂²×C₅	—	4	1	no	—
402	C₂²×C₅	C₂×#121	1	1	yes	characteristic
403	C₄×C₅	—	2	1	no	—
404	C₄×C₅	—	2	1	no	—
405	C₄×C₅	—	2	2	no	—
406	C₄×C₅	—	2	1	no	—
407	C₄×C₅	—	2	1	no	—
408	C₄×C₅	—	4	1	no	—
409	C₄×C₅	—	4	1	no	—
410	C₄×C₅	—	8	1	no	—
411	C₄×C₅	—	8	1	no	—
412	C₄×C₅	—	8	1	no	—
413	C₄×C₅	—	8	1	no	—
414	C₄×C₅	C₂×#135	1	1	yes	characteristic
415	C₄×C₅	C₂×#135	1	1	yes	characteristic
416	C₄×C₅	#577	1	1	yes	characteristic
417	C₄×C₅	#578	1	1	yes	characteristic
418	#41	—	2	2	no	—
419	#41	—	2	2	no	—
420	C₂×Q₈	—	2	1	no	—
421	C₂×Q₈	—	2	1	no	—
422	C₂×Q₈	—	2	1	no	—
423	C₂×Q₈	—	2	1	no	—
424	C₂×Q₈	C₂×C₅×D₄	1	1	yes	characteristic
425	C₂×D₄	—	2	1	no	—
426	C₂×D₄	C₂×C₅×D₄	1	1	yes	characteristic
427	C₂²×C₄	—	2	1	no	—
428	C₂²×C₄	—	2	1	no	—
429	C₂²×C₄	—	2	1	no	—
430	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
431	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
432	C₂²×C₄	C₅×#41	1	1	yes	characteristic
433	Q₁₆	—	4	2	no	—
434	Q₁₆	—	4	2	no	—
435	SD₁₆	—	4	2	no	—
436	SD₁₆	—	4	2	no	—
437	C₂×C₈	—	2	1	no	—
438	C₂×C₈	—	2	1	no	—
439	C₂×C₈	—	2	1	no	—
440	C₂×C₈	—	2	1	no	—
441	C₂×C₈	—	2	1	no	—
442	C₂×C₈	—	2	1	no	—
443	C₂×C₈	—	8	1	no	—
444	C₂×C₈	—	8	1	no	—
445	C₂×C₈	—	8	1	no	—
446	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
447	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
448	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
449	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
450	C₄⋊C₄	—	2	1	no	—
451	C₄⋊C₄	—	2	1	no	—
452	C₄⋊C₄	—	2	1	no	—
453	C₄⋊C₄	—	2	1	no	—
454	C₄⋊C₄	—	2	1	no	—
455	C₄⋊C₄	—	2	1	no	—
456	C₄⋊C₄	—	2	1	no	—
457	C₄⋊C₄	—	2	1	no	—
458	C₄⋊C₄	—	2	1	no	—
459	C₄⋊C₄	—	2	1	no	—
460	C₄⋊C₄	—	4	1	no	—
461	C₄⋊C₄	—	4	1	no	—
462	C₄⋊C₄	—	4	1	no	—
463	C₄⋊C₄	—	4	1	no	—
464	C₄⋊C₄	C₂×C₅×D₄	1	1	yes	characteristic
465	C₄⋊C₄	C₂×C₅×D₄	1	1	yes	characteristic
466	C₂²⋊C₄	—	2	1	no	—
467	C₂²⋊C₄	—	2	1	no	—
468	C₂²⋊C₄	—	2	1	no	—
469	C₂²⋊C₄	—	4	1	no	—
470	C₂²⋊C₄	—	4	1	no	—
471	C₄²	—	2	1	no	—
472	C₄²	—	2	1	no	—
473	C₄²	—	2	1	no	—
474	C₄²	—	4	1	no	—
475	C₄²	—	4	1	no	—
476	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
477	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
478	C₄²	C₅×#41	1	1	yes	characteristic
479	C₄²	C₂⁴×C₅	1	1	yes	characteristic
480	C₂×C₅	—	4	1	no	—
481	C₂×C₅	—	4	2	no	—
482	C₂×C₅	#3046	1	1	yes	characteristic
483	C₂×C₅	#3050	1	1	yes	characteristic
484	C₂×C₅	#3069	1	1	yes	characteristic
485	C₂³	—	2	1	no	—
486	C₂³	C₅×#121	1	1	yes	characteristic
487	Q₈	—	2	1	no	—
488	Q₈	—	4	1	no	—
489	Q₈	—	4	1	no	—
490	Q₈	—	4	1	no	—
491	Q₈	—	4	1	no	—
492	Q₈	—	4	1	no	—
493	Q₈	—	4	1	no	—
494	Q₈	—	8	1	no	—
495	Q₈	C₅×#135	1	2	yes	—
496	D₄	—	2	4	no	—
497	D₄	—	2	1	no	—
498	D₄	C₅×#135	1	2	yes	—
499	C₂×C₄	—	2	4	no	—
500	C₂×C₄	—	2	1	no	—
501	C₂×C₄	—	2	1	no	—
502	C₂×C₄	—	2	1	no	—
503	C₂×C₄	—	2	1	no	—
504	C₂×C₄	—	2	1	no	—
505	C₂×C₄	—	2	1	no	—
506	C₂×C₄	—	2	1	no	—
507	C₂×C₄	—	4	1	no	—
508	C₂×C₄	—	4	1	no	—
509	C₂×C₄	—	4	1	no	—
510	C₂×C₄	—	4	1	no	—
511	C₂×C₄	—	4	1	no	—
512	C₂×C₄	—	4	1	no	—
513	C₂×C₄	—	4	1	no	—
514	C₂×C₄	—	8	1	no	—
515	C₂×C₄	C₅×#121	1	1	yes	characteristic
516	C₂×C₄	C₅×#121	1	1	yes	characteristic
517	C₂×C₄	C₅×#121	1	1	yes	characteristic
518	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
519	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
520	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
521	C₈	—	2	1	no	—
522	C₈	—	2	1	no	—
523	C₈	—	2	1	no	—
524	C₈	—	2	1	no	—
525	C₈	—	4	1	no	—
526	C₈	—	4	1	no	—
527	C₈	—	4	1	no	—
528	C₈	—	4	1	no	—
529	C₈	—	4	1	no	—
530	C₈	—	4	1	no	—
531	C₅	#19418	1	1	yes	characteristic, direct product factor, Sylow
532	C₂²	—	2	1	no	—
533	C₂²	—	2	1	no	—
534	C₂²	—	2	2	no	—
535	C₂²	—	2	1	no	—
536	C₂²	—	4	1	no	—
537	C₂²	—	4	1	no	—
538	C₂²	C₂×C₅×#121	1	1	yes	characteristic
539	C₄	—	2	1	no	—
540	C₄	—	2	1	no	—
541	C₄	—	2	2	no	—
542	C₄	—	2	1	no	—
543	C₄	—	2	1	no	—
544	C₄	—	4	1	no	—
545	C₄	—	4	1	no	—
546	C₄	—	8	1	no	—
547	C₄	—	8	1	no	—
548	C₄	—	8	1	no	—
549	C₄	—	8	1	no	—
550	C₄	C₂×C₅×#135	1	1	yes	characteristic
551	C₄	C₂×C₅×#135	1	1	yes	characteristic
552	C₄	C₅×#577	1	1	yes	characteristic
553	C₄	C₅×#578	1	1	yes	characteristic
554	C₂	—	4	1	no	—
555	C₂	—	4	2	no	—
556	C₂	C₅×#3046	1	1	yes	characteristic
557	C₂	C₅×#3050	1	1	yes	characteristic
558	C₂	C₅×#3069	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₅	C₂×#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₅
prime radical	C₂×C₅×#41	D₄
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₅ ◁ C₂×C₄²×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₅×#3231	C₂	semidirect
5. C₅×#1684	C₂	semidirect
6. C₅×#1683	C₂	semidirect
7. C₅×#1680	C₂	semidirect
8. C₅×#1679	C₂	semidirect
9. C₅×#1674	C₂	semidirect
10. C₅×#1673	C₂	semidirect
11. C₅×#1672	C₂	semidirect
12. C₅×#1671	C₂	semidirect
13. C₅×#1572	C₂	semidirect
14. C₅×#1552	C₂	semidirect
15. C₅×#1542	C₂	semidirect
67. #19418	C₅	direct (N × H)
145. #3231	C₂×C₅	semidirect
149. #1684	C₂×C₅	semidirect
150. #1683	C₂×C₅	semidirect
151. #1680	C₂×C₅	semidirect
152. #1679	C₂×C₅	semidirect
153. #1674	C₂×C₅	semidirect
154. #1673	C₂×C₅	semidirect
155. #1672	C₂×C₅	semidirect
156. #1671	C₂×C₅	semidirect
157. #1572	C₂×C₅	semidirect
158. #1552	C₂×C₅	semidirect
159. #1542	C₂×C₅	semidirect
531. C₅	#19418	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×#3231	2
C₅×#3116	2
C₅×#3107	2
C₅×#2988	2
C₅×#1684	2
C₅×#1683	2
C₅×#1680	2
C₅×#1679	2
C₅×#1674	2
C₅×#1673	2
C₅×#1672	2
C₅×#1671	2
C₅×#1572	2
C₅×#1552	2
C₅×#1542	2
#19418	5

Subgroups — C5×#19418 #11942138

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#19418 #11942138