Subgroups — C₅×#19181 #11941901

Order 1280.

594 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#3185	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×#3107	C₂	1	1	yes	maximal, characteristic
3	C₅×#3076	C₂	1	1	yes	maximal, characteristic
4	C₅×#2970	C₂	1	1	yes	maximal, characteristic
5	C₅×#1704	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#1700	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#1692	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#1690	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#1683	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#1679	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#1671	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#1669	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅×#1565	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅×#1554	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅×#1552	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×#498	C₂²	1	1	yes	characteristic
20	C₅×#494	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×#479	—	2	1	no	—
25	C₅×#478	—	2	1	no	—
26	C₅×#477	C₂²	1	1	yes	characteristic
27	C₅×#476	C₂²	1	1	yes	characteristic
28	C₅×#475	C₂²	1	1	yes	characteristic
29	C₅×#475	C₂²	1	1	yes	characteristic
30	C₅×#474	C₂²	1	1	yes	characteristic
31	C₅×#474	C₂²	1	1	yes	characteristic
32	C₅×#470	—	2	1	no	—
33	C₅×#470	—	2	1	no	—
34	C₅×#462	C₂²	1	1	yes	characteristic
35	C₅×#461	C₂²	1	1	yes	characteristic
36	C₅×#452	—	2	1	no	—
37	C₅×#446	C₂²	1	1	yes	characteristic
38	C₅×#446	C₂²	1	1	yes	characteristic
39	C₅×#441	—	2	1	no	—
40	C₅×#441	—	2	1	no	—
41	C₄×C₅×Q₁₆	—	2	1	no	—
42	C₄×C₅×SD₁₆	—	2	1	no	—
43	C₅×#435	—	2	1	no	—
44	C₅×#435	—	2	1	no	—
45	C₅×C₈×D₄	C₂²	1	1	yes	characteristic
46	C₅×C₈×D₄	C₂²	1	1	yes	characteristic
47	C₅×#432	—	2	1	no	—
48	C₅×#432	C₂²	1	1	yes	characteristic
49	C₅×#431	C₂²	1	1	yes	characteristic
50	C₅×#427	—	2	1	no	—
51	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
52	C₅×#416	—	2	1	no	—
53	C₄×C₅×M₁₆	C₂²	1	1	yes	characteristic
54	C₂×C₅×#97	—	2	1	no	—
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	#19181	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×Q₁₆	—	2	1	no	—
72	C₂×C₅×SD₁₆	—	2	1	no	—
73	C₂×C₅×M₁₆	D₄	1	1	yes	characteristic
74	C₂×C₅×M₁₆	D₄	1	1	yes	characteristic
75	C₂²×C₅×C₈	—	2	1	no	—
76	C₂²×C₅×C₈	—	2	1	no	—
77	C₂²×C₅×C₈	—	2	1	no	—
78	C₅×C₄⋊Q₈	C₂³	1	1	yes	characteristic
79	C₅×C₄⋊Q₈	C₂³	1	1	yes	characteristic
80	C₅×C₄⋊Q₈	C₂³	1	1	yes	characteristic
81	C₅×C₄⋊Q₈	C₂³	1	1	yes	characteristic
82	C₅×#125	—	2	1	no	—
83	C₅×#125	—	2	1	no	—
84	C₅×C₂²⋊Q₈	—	2	1	no	—
85	C₅×C₂²⋊Q₈	—	2	1	no	—
86	C₅×C₂²⋊Q₈	—	2	1	no	—
87	C₅×C₂²⋊Q₈	—	2	1	no	—
88	C₄×C₅×Q₈	—	2	1	no	—
89	C₄×C₅×Q₈	—	2	1	no	—
90	C₄×C₅×Q₈	—	2	1	no	—
91	C₄×C₅×Q₈	—	2	1	no	—
92	C₄×C₅×Q₈	D₄	1	1	yes	characteristic
93	C₄×C₅×Q₈	C₂³	1	1	yes	characteristic
94	C₄×C₅×D₄	—	2	1	no	—
95	C₄×C₅×D₄	—	2	1	no	—
96	C₄×C₅×D₄	D₄	1	1	yes	characteristic
97	C₄×C₅×D₄	C₂³	1	1	yes	characteristic
98	C₅×#117	—	2	1	no	—
99	C₅×#117	—	2	1	no	—
100	C₅×#117	—	2	1	no	—
101	C₅×#117	D₄	1	1	yes	characteristic
102	C₂×C₄²×C₅	—	2	1	no	—
103	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
104	C₅×#107	—	2	1	no	—
105	C₅×#107	—	2	1	no	—
106	C₅×#107	—	2	1	no	—
107	C₅×#106	—	2	1	no	—
108	C₅×#106	—	2	1	no	—
109	C₅×#106	—	2	1	no	—
110	C₅×#106	—	2	1	no	—
111	C₅×#106	—	2	1	no	—
112	C₅×C₄⋊C₈	—	2	1	no	—
113	C₅×C₄⋊C₈	—	2	1	no	—
114	C₅×C₄⋊C₈	—	2	1	no	—
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×#102	—	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×#97	—	2	1	no	—
138	C₅×#97	—	2	1	no	—
139	C₅×#97	—	2	1	no	—
140	C₅×#97	D₄	1	1	yes	characteristic
141	C₅×#97	D₄	1	1	yes	characteristic
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	#3185	C₂×C₅	1	1	yes	characteristic, complemented
146	#3107	C₂×C₅	1	1	yes	characteristic
147	#3076	C₂×C₅	1	1	yes	characteristic
148	#2970	C₂×C₅	1	1	yes	characteristic
149	#1704	C₂×C₅	1	1	yes	characteristic, complemented
150	#1700	C₂×C₅	1	1	yes	characteristic, complemented
151	#1692	C₂×C₅	1	1	yes	characteristic, complemented
152	#1690	C₂×C₅	1	1	yes	characteristic, complemented
153	#1683	C₂×C₅	1	1	yes	characteristic, complemented
154	#1679	C₂×C₅	1	1	yes	characteristic, complemented
155	#1671	C₂×C₅	1	1	yes	characteristic, complemented
156	#1669	C₂×C₅	1	1	yes	characteristic, complemented
157	#1565	C₂×C₅	1	1	yes	characteristic, complemented
158	#1554	C₂×C₅	1	1	yes	characteristic, complemented
159	#1552	C₂×C₅	1	1	yes	characteristic, complemented
160	C₅×#41	—	2	2	no	—
161	C₅×#41	—	4	1	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×Q₁₆	—	4	2	no	—
178	C₅×SD₁₆	—	4	2	no	—
179	C₅×M₁₆	—	2	2	no	—
180	C₅×M₁₆	—	4	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	—	2	1	no	—
186	C₂×C₅×C₈	—	2	1	no	—
187	C₂×C₅×C₈	—	4	2	no	—
188	C₂×C₅×C₈	—	4	2	no	—
189	C₂×C₅×C₈	—	4	2	no	—
190	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
191	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
192	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
193	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
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	—	2	1	no	—
203	C₅×C₄⋊C₄	—	2	1	no	—
204	C₅×C₄⋊C₄	—	4	1	no	—
205	C₅×C₄⋊C₄	—	4	1	no	—
206	C₅×C₄⋊C₄	—	4	1	no	—
207	C₅×C₄⋊C₄	—	4	1	no	—
208	C₅×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
209	C₅×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
210	C₅×C₂²⋊C₄	—	2	1	no	—
211	C₅×C₂²⋊C₄	—	2	1	no	—
212	C₅×C₂²⋊C₄	—	2	1	no	—
213	C₅×C₂²⋊C₄	—	4	1	no	—
214	C₅×C₂²⋊C₄	—	4	1	no	—
215	C₄²×C₅	—	2	1	no	—
216	C₄²×C₅	—	2	1	no	—
217	C₄²×C₅	—	2	1	no	—
218	C₄²×C₅	—	4	1	no	—
219	C₄²×C₅	—	4	1	no	—
220	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
221	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
222	C₄²×C₅	#41	1	1	yes	characteristic
223	C₄²×C₅	C₂⁴	1	1	yes	characteristic
224	#533	C₂²×C₅	1	1	yes	characteristic
225	#533	C₂²×C₅	1	1	yes	characteristic
226	C₄×#41	C₂²×C₅	1	1	yes	characteristic
227	#498	C₂²×C₅	1	1	yes	characteristic
228	#494	C₂²×C₅	1	1	yes	characteristic
229	#487	C₂²×C₅	1	1	yes	characteristic
230	#487	C₂²×C₅	1	1	yes	characteristic
231	#485	—	2	1	no	—
232	#479	—	2	1	no	—
233	#478	—	2	1	no	—
234	#477	C₂²×C₅	1	1	yes	characteristic
235	#476	C₂²×C₅	1	1	yes	characteristic
236	#475	C₂²×C₅	1	1	yes	characteristic
237	#475	C₂²×C₅	1	1	yes	characteristic
238	#474	C₂²×C₅	1	1	yes	characteristic
239	#474	C₂²×C₅	1	1	yes	characteristic
240	#470	—	2	1	no	—
241	#470	—	2	1	no	—
242	#462	C₂²×C₅	1	1	yes	characteristic
243	#461	C₂²×C₅	1	1	yes	characteristic
244	#452	—	2	1	no	—
245	#446	C₂²×C₅	1	1	yes	characteristic
246	#446	C₂²×C₅	1	1	yes	characteristic
247	#441	—	2	1	no	—
248	#441	—	2	1	no	—
249	C₄×Q₁₆	—	2	1	no	—
250	C₄×SD₁₆	—	2	1	no	—
251	#435	—	2	1	no	—
252	#435	—	2	1	no	—
253	C₈×D₄	C₂²×C₅	1	1	yes	characteristic
254	C₈×D₄	C₂²×C₅	1	1	yes	characteristic
255	#432	—	2	1	no	—
256	#432	C₂²×C₅	1	1	yes	characteristic
257	#431	C₂²×C₅	1	1	yes	characteristic
258	#427	—	2	1	no	—
259	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
260	#416	—	2	1	no	—
261	C₄×M₁₆	C₂²×C₅	1	1	yes	characteristic
262	C₂×#97	—	2	1	no	—
263	#335	C₂²×C₅	1	1	yes	characteristic
264	#335	C₂²×C₅	1	1	yes	characteristic
265	#334	C₂²×C₅	1	1	yes	characteristic
266	#334	C₂²×C₅	1	1	yes	characteristic
267	#333	C₂²×C₅	1	1	yes	characteristic
268	#333	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	#332	C₂²×C₅	1	1	yes	characteristic
274	#332	C₂²×C₅	1	1	yes	characteristic
275	C₂³×C₅	—	2	1	no	—
276	C₂³×C₅	#121	1	1	yes	characteristic
277	C₅×Q₈	—	2	1	no	—
278	C₅×Q₈	—	2	1	no	—
279	C₅×Q₈	—	4	1	no	—
280	C₅×Q₈	—	4	1	no	—
281	C₅×Q₈	—	4	1	no	—
282	C₅×Q₈	—	4	1	no	—
283	C₅×Q₈	—	4	1	no	—
284	C₅×Q₈	—	4	1	no	—
285	C₅×Q₈	—	8	1	no	—
286	C₅×D₄	—	2	1	no	—
287	C₅×D₄	—	4	2	no	—
288	C₅×D₄	#137	1	2	yes	—
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	—	2	1	no	—
296	C₂×C₄×C₅	—	4	1	no	—
297	C₂×C₄×C₅	—	4	2	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	—	4	1	no	—
303	C₂×C₄×C₅	—	4	1	no	—
304	C₂×C₄×C₅	—	8	1	no	—
305	C₂×C₄×C₅	#121	1	1	yes	characteristic
306	C₂×C₄×C₅	#121	1	1	yes	characteristic
307	C₂×C₄×C₅	#121	1	1	yes	characteristic
308	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
309	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
310	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
311	C₅×C₈	—	2	1	no	—
312	C₅×C₈	—	2	1	no	—
313	C₅×C₈	—	2	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	C₅×C₈	—	4	1	no	—
320	C₅×C₈	#135	1	2	yes	—
321	C₂×#41	C₅×D₄	1	1	yes	characteristic
322	C₂×Q₁₆	—	2	1	no	—
323	C₂×Q₁₆	—	2	1	no	—
324	C₂×Q₁₆	—	2	1	no	—
325	C₂×SD₁₆	—	2	1	no	—
326	C₂×M₁₆	C₅×D₄	1	1	yes	characteristic
327	C₂×M₁₆	C₅×D₄	1	1	yes	characteristic
328	C₂²×C₈	—	2	1	no	—
329	C₂²×C₈	—	2	1	no	—
330	C₂²×C₈	—	2	1	no	—
331	C₄⋊Q₈	C₂³×C₅	1	1	yes	characteristic
332	C₄⋊Q₈	C₂³×C₅	1	1	yes	characteristic
333	C₄⋊Q₈	C₂³×C₅	1	1	yes	characteristic
334	C₄⋊Q₈	C₂³×C₅	1	1	yes	characteristic
335	#125	—	2	1	no	—
336	#125	—	2	1	no	—
337	C₂²⋊Q₈	—	2	1	no	—
338	C₂²⋊Q₈	—	2	1	no	—
339	C₂²⋊Q₈	—	2	1	no	—
340	C₂²⋊Q₈	—	2	1	no	—
341	C₄×Q₈	—	2	1	no	—
342	C₄×Q₈	—	2	1	no	—
343	C₄×Q₈	—	2	1	no	—
344	C₄×Q₈	—	2	1	no	—
345	C₄×Q₈	C₅×D₄	1	1	yes	characteristic
346	C₄×Q₈	C₂³×C₅	1	1	yes	characteristic
347	C₄×D₄	—	2	1	no	—
348	C₄×D₄	—	2	1	no	—
349	C₄×D₄	C₅×D₄	1	1	yes	characteristic
350	C₄×D₄	C₂³×C₅	1	1	yes	characteristic
351	#117	—	2	1	no	—
352	#117	—	2	1	no	—
353	#117	—	2	1	no	—
354	#117	C₅×D₄	1	1	yes	characteristic
355	C₂×C₄²	—	2	1	no	—
356	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
357	#107	—	2	1	no	—
358	#107	—	2	1	no	—
359	#107	—	2	1	no	—
360	#106	—	2	1	no	—
361	#106	—	2	1	no	—
362	#106	—	2	1	no	—
363	#106	—	2	1	no	—
364	#106	—	2	1	no	—
365	C₄⋊C₈	—	2	1	no	—
366	C₄⋊C₈	—	2	1	no	—
367	C₄⋊C₈	—	2	1	no	—
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	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
373	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
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	#103	—	2	1	no	—
383	#102	—	2	1	no	—
384	#102	—	2	1	no	—
385	#102	—	2	1	no	—
386	C₂²⋊C₈	—	2	1	no	—
387	C₂²⋊C₈	—	2	1	no	—
388	C₂²⋊C₈	—	2	1	no	—
389	C₂²⋊C₈	—	2	1	no	—
390	#97	—	2	1	no	—
391	#97	—	2	1	no	—
392	#97	—	2	1	no	—
393	#97	C₅×D₄	1	1	yes	characteristic
394	#97	C₅×D₄	1	1	yes	characteristic
395	C₄×C₈	—	2	1	no	—
396	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
397	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
398	C₂²×C₅	—	2	1	no	—
399	C₂²×C₅	—	2	1	no	—
400	C₂²×C₅	—	2	2	no	—
401	C₂²×C₅	—	2	1	no	—
402	C₂²×C₅	—	4	1	no	—
403	C₂²×C₅	—	4	1	no	—
404	C₂²×C₅	C₂×#121	1	1	yes	characteristic
405	C₄×C₅	—	2	1	no	—
406	C₄×C₅	—	2	1	no	—
407	C₄×C₅	—	2	1	no	—
408	C₄×C₅	—	2	1	no	—
409	C₄×C₅	—	4	1	no	—
410	C₄×C₅	—	4	1	no	—
411	C₄×C₅	—	4	1	no	—
412	C₄×C₅	—	8	1	no	—
413	C₄×C₅	—	8	1	no	—
414	C₄×C₅	—	8	1	no	—
415	C₄×C₅	—	8	1	no	—
416	C₄×C₅	C₂×#135	1	1	yes	characteristic
417	C₄×C₅	C₂×#137	1	1	yes	characteristic
418	C₄×C₅	#575	1	1	yes	characteristic
419	C₄×C₅	#575	1	1	yes	characteristic
420	#41	—	2	2	no	—
421	#41	—	4	1	no	—
422	C₂×Q₈	—	2	1	no	—
423	C₂×Q₈	—	2	1	no	—
424	C₂×Q₈	—	2	1	no	—
425	C₂×Q₈	—	2	1	no	—
426	C₂×Q₈	C₂×C₅×D₄	1	1	yes	characteristic
427	C₂×D₄	—	2	1	no	—
428	C₂×D₄	C₂×C₅×D₄	1	1	yes	characteristic
429	C₂²×C₄	—	2	1	no	—
430	C₂²×C₄	—	2	1	no	—
431	C₂²×C₄	—	2	1	no	—
432	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
433	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
434	C₂²×C₄	C₅×#41	1	1	yes	characteristic
435	Q₁₆	—	4	2	no	—
436	Q₁₆	—	4	2	no	—
437	Q₁₆	—	4	2	no	—
438	SD₁₆	—	4	2	no	—
439	M₁₆	—	2	2	no	—
440	M₁₆	—	4	1	no	—
441	C₂×C₈	—	2	1	no	—
442	C₂×C₈	—	2	1	no	—
443	C₂×C₈	—	2	1	no	—
444	C₂×C₈	—	2	1	no	—
445	C₂×C₈	—	2	1	no	—
446	C₂×C₈	—	2	1	no	—
447	C₂×C₈	—	4	2	no	—
448	C₂×C₈	—	4	2	no	—
449	C₂×C₈	—	4	2	no	—
450	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
451	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
452	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
453	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
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	—	2	1	no	—
461	C₄⋊C₄	—	2	1	no	—
462	C₄⋊C₄	—	2	1	no	—
463	C₄⋊C₄	—	2	1	no	—
464	C₄⋊C₄	—	4	1	no	—
465	C₄⋊C₄	—	4	1	no	—
466	C₄⋊C₄	—	4	1	no	—
467	C₄⋊C₄	—	4	1	no	—
468	C₄⋊C₄	C₂×C₅×D₄	1	1	yes	characteristic
469	C₄⋊C₄	C₂×C₅×D₄	1	1	yes	characteristic
470	C₂²⋊C₄	—	2	1	no	—
471	C₂²⋊C₄	—	2	1	no	—
472	C₂²⋊C₄	—	2	1	no	—
473	C₂²⋊C₄	—	4	1	no	—
474	C₂²⋊C₄	—	4	1	no	—
475	C₄²	—	2	1	no	—
476	C₄²	—	2	1	no	—
477	C₄²	—	2	1	no	—
478	C₄²	—	4	1	no	—
479	C₄²	—	4	1	no	—
480	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
481	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
482	C₄²	C₅×#41	1	1	yes	characteristic
483	C₄²	C₂⁴×C₅	1	1	yes	characteristic
484	C₂×C₅	—	4	1	no	—
485	C₂×C₅	—	4	2	no	—
486	C₂×C₅	#3035	1	1	yes	characteristic
487	C₂×C₅	#3056	1	1	yes	characteristic
488	C₂×C₅	#3069	1	1	yes	characteristic
489	C₂³	—	2	1	no	—
490	C₂³	C₅×#121	1	1	yes	characteristic
491	Q₈	—	2	1	no	—
492	Q₈	—	2	1	no	—
493	Q₈	—	4	1	no	—
494	Q₈	—	4	1	no	—
495	Q₈	—	4	1	no	—
496	Q₈	—	4	1	no	—
497	Q₈	—	4	1	no	—
498	Q₈	—	4	1	no	—
499	Q₈	—	8	1	no	—
500	D₄	—	2	1	no	—
501	D₄	—	4	2	no	—
502	D₄	C₅×#137	1	2	yes	—
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	—	2	1	no	—
508	C₂×C₄	—	2	1	no	—
509	C₂×C₄	—	2	1	no	—
510	C₂×C₄	—	4	1	no	—
511	C₂×C₄	—	4	2	no	—
512	C₂×C₄	—	4	1	no	—
513	C₂×C₄	—	4	1	no	—
514	C₂×C₄	—	4	1	no	—
515	C₂×C₄	—	4	1	no	—
516	C₂×C₄	—	4	1	no	—
517	C₂×C₄	—	4	1	no	—
518	C₂×C₄	—	8	1	no	—
519	C₂×C₄	C₅×#121	1	1	yes	characteristic
520	C₂×C₄	C₅×#121	1	1	yes	characteristic
521	C₂×C₄	C₅×#121	1	1	yes	characteristic
522	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
523	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
524	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
525	C₈	—	2	1	no	—
526	C₈	—	2	1	no	—
527	C₈	—	2	1	no	—
528	C₈	—	4	1	no	—
529	C₈	—	4	1	no	—
530	C₈	—	4	1	no	—
531	C₈	—	4	1	no	—
532	C₈	—	4	1	no	—
533	C₈	—	4	1	no	—
534	C₈	C₅×#135	1	2	yes	—
535	C₅	#19181	1	1	yes	characteristic, direct product factor, Sylow
536	C₂²	—	2	1	no	—
537	C₂²	—	2	1	no	—
538	C₂²	—	2	2	no	—
539	C₂²	—	2	1	no	—
540	C₂²	—	4	1	no	—
541	C₂²	—	4	1	no	—
542	C₂²	C₂×C₅×#121	1	1	yes	characteristic
543	C₄	—	2	1	no	—
544	C₄	—	2	1	no	—
545	C₄	—	2	1	no	—
546	C₄	—	2	1	no	—
547	C₄	—	4	1	no	—
548	C₄	—	4	1	no	—
549	C₄	—	4	1	no	—
550	C₄	—	8	1	no	—
551	C₄	—	8	1	no	—
552	C₄	—	8	1	no	—
553	C₄	—	8	1	no	—
554	C₄	C₂×C₅×#135	1	1	yes	characteristic
555	C₄	C₂×C₅×#137	1	1	yes	characteristic
556	C₄	C₅×#575	1	1	yes	characteristic
557	C₄	C₅×#575	1	1	yes	characteristic
558	C₂	—	4	1	no	—
559	C₂	—	4	2	no	—
560	C₂	C₅×#3035	1	1	yes	characteristic
561	C₂	C₅×#3056	1	1	yes	characteristic
562	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×#3185	C₂	semidirect
5. C₅×#1704	C₂	semidirect
6. C₅×#1700	C₂	semidirect
7. C₅×#1692	C₂	semidirect
8. C₅×#1690	C₂	semidirect
9. C₅×#1683	C₂	semidirect
10. C₅×#1679	C₂	semidirect
11. C₅×#1671	C₂	semidirect
12. C₅×#1669	C₂	semidirect
13. C₅×#1565	C₂	semidirect
14. C₅×#1554	C₂	semidirect
15. C₅×#1552	C₂	semidirect
67. #19181	C₅	direct (N × H)
145. #3185	C₂×C₅	semidirect
149. #1704	C₂×C₅	semidirect
150. #1700	C₂×C₅	semidirect
151. #1692	C₂×C₅	semidirect
152. #1690	C₂×C₅	semidirect
153. #1683	C₂×C₅	semidirect
154. #1679	C₂×C₅	semidirect
155. #1671	C₂×C₅	semidirect
156. #1669	C₂×C₅	semidirect
157. #1565	C₂×C₅	semidirect
158. #1554	C₂×C₅	semidirect
159. #1552	C₂×C₅	semidirect
535. C₅	#19181	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×#3185	2
C₅×#3107	2
C₅×#3076	2
C₅×#2970	2
C₅×#1704	2
C₅×#1700	2
C₅×#1692	2
C₅×#1690	2
C₅×#1683	2
C₅×#1679	2
C₅×#1671	2
C₅×#1669	2
C₅×#1565	2
C₅×#1554	2
C₅×#1552	2
#19181	5

Subgroups — C5×#19181 #11941901

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#19181 #11941901