Subgroups — C₅×#19309 #11942029

Order 1280.

600 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#3182	C₂	1	1	yes	maximal, characteristic
2	C₅×#3112	C₂	1	1	yes	maximal, characteristic
3	C₅×#3078	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×Q₈×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#1704	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#1698	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#1696	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#1686	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#1684	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#1678	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#1676	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#1666	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅×#1569	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅×#1560	C₂	1	1	yes	maximal, characteristic
15	C₅×#1559	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅×#533	C₂²	1	1	yes	characteristic
17	C₅×#532	C₂²	1	1	yes	characteristic
18	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
19	C₅×#500	C₂²	1	1	yes	characteristic
20	C₅×#492	C₂²	1	1	yes	characteristic
21	C₅×#487	C₂²	1	1	yes	characteristic
22	C₅×#486	C₂²	1	1	yes	characteristic
23	C₅×#480	—	2	1	no	—
24	C₅×#479	—	2	1	no	—
25	C₅×#479	—	2	1	no	—
26	C₅×#477	C₂²	1	1	yes	characteristic
27	C₅×#477	C₂²	1	1	yes	characteristic
28	C₅×#477	C₂²	1	1	yes	characteristic
29	C₅×#477	C₂²	1	1	yes	characteristic
30	C₅×#475	C₂²	1	1	yes	characteristic
31	C₅×#475	C₂²	1	1	yes	characteristic
32	C₅×#468	—	2	1	no	—
33	C₅×#468	—	2	1	no	—
34	C₅×#460	C₂²	1	1	yes	characteristic
35	C₅×#460	C₂²	1	1	yes	characteristic
36	C₅×#448	—	2	1	no	—
37	C₅×#446	—	2	1	no	—
38	C₅×#446	—	2	1	no	—
39	C₅×#446	C₂²	1	1	yes	characteristic
40	C₅×#446	C₂²	1	1	yes	characteristic
41	C₅×C₈×Q₈	C₂²	1	1	yes	characteristic
42	C₅×C₈×Q₈	C₂²	1	1	yes	characteristic
43	C₅×#440	—	2	1	no	—
44	C₅×#440	—	2	1	no	—
45	C₅×#440	—	2	1	no	—
46	C₅×#440	—	2	1	no	—
47	C₅×#432	C₂²	1	1	yes	characteristic
48	C₅×#428	—	2	1	no	—
49	C₅×#423	—	2	1	no	—
50	C₅×#423	C₂²	1	1	yes	characteristic
51	C₅×#423	C₂²	1	1	yes	characteristic
52	C₅×#419	—	2	1	no	—
53	C₄×C₅×M₁₆	—	2	1	no	—
54	C₄×C₅×M₁₆	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×#333	C₂²	1	1	yes	characteristic
62	C₅×#333	C₂²	1	1	yes	characteristic
63	C₅×#332	C₂²	1	1	yes	characteristic
64	C₅×#332	C₂²	1	1	yes	characteristic
65	C₅×#331	C₂²	1	1	yes	characteristic
66	C₅×#331	C₂²	1	1	yes	characteristic
67	#19309	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
68	C₂×C₅×#41	—	2	1	no	—
69	C₂²×C₅×Q₈	D₄	1	1	yes	characteristic
70	C₂×C₅×SD₁₆	—	2	1	no	—
71	C₂×C₅×SD₁₆	—	2	1	no	—
72	C₂×C₅×SD₁₆	—	2	1	no	—
73	C₂×C₅×SD₁₆	—	2	1	no	—
74	C₂×C₅×M₁₆	—	2	1	no	—
75	C₂×C₅×M₁₆	—	2	1	no	—
76	C₂×C₅×M₁₆	D₄	1	1	yes	characteristic
77	C₂×C₅×M₁₆	D₄	1	1	yes	characteristic
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×#127	C₂³	1	1	yes	characteristic
82	C₅×#125	—	2	1	no	—
83	C₅×#124	—	2	1	no	—
84	C₅×C₂²⋊Q₈	—	2	1	no	—
85	C₅×C₂²⋊Q₈	—	2	1	no	—
86	C₅×#121	—	2	1	no	—
87	C₅×#121	—	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	D₄	1	1	yes	characteristic
94	C₄×C₅×Q₈	C₂³	1	1	yes	characteristic
95	C₄×C₅×Q₈	C₂³	1	1	yes	characteristic
96	C₄×C₅×D₄	—	2	1	no	—
97	C₄×C₅×D₄	—	2	1	no	—
98	C₅×#117	—	2	1	no	—
99	C₂×C₅×C₄⋊C₄	—	2	1	no	—
100	C₂×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
101	C₂×C₄²×C₅	—	2	1	no	—
102	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
103	C₅×#107	—	2	1	no	—
104	C₅×#107	—	2	1	no	—
105	C₅×#107	—	2	1	no	—
106	C₅×#107	—	2	1	no	—
107	C₅×#107	—	2	1	no	—
108	C₅×#107	—	2	1	no	—
109	C₅×#106	—	2	1	no	—
110	C₅×#106	—	2	1	no	—
111	C₅×C₄⋊C₈	—	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	—	2	1	no	—
116	C₅×C₄⋊C₈	—	2	1	no	—
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×C₄⋊C₈	C₂³	1	1	yes	characteristic
122	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
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×#102	—	2	1	no	—
134	C₅×#102	—	2	1	no	—
135	C₅×C₂²⋊C₈	—	2	1	no	—
136	C₅×#97	—	2	1	no	—
137	C₅×#97	—	2	1	no	—
138	C₅×#97	—	2	1	no	—
139	C₅×#97	D₄	1	1	yes	characteristic
140	C₅×#97	D₄	1	1	yes	characteristic
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	#3182	C₂×C₅	1	1	yes	characteristic
146	#3112	C₂×C₅	1	1	yes	characteristic
147	#3078	C₂×C₅	1	1	yes	characteristic, complemented
148	Q₈×M₁₆	C₂×C₅	1	1	yes	characteristic, complemented
149	#1704	C₂×C₅	1	1	yes	characteristic, complemented
150	#1698	C₂×C₅	1	1	yes	characteristic, complemented
151	#1696	C₂×C₅	1	1	yes	characteristic, complemented
152	#1686	C₂×C₅	1	1	yes	characteristic, complemented
153	#1684	C₂×C₅	1	1	yes	characteristic, complemented
154	#1678	C₂×C₅	1	1	yes	characteristic, complemented
155	#1676	C₂×C₅	1	1	yes	characteristic, complemented
156	#1666	C₂×C₅	1	1	yes	characteristic, complemented
157	#1569	C₂×C₅	1	1	yes	characteristic, complemented
158	#1560	C₂×C₅	1	1	yes	characteristic
159	#1559	C₂×C₅	1	1	yes	characteristic, complemented
160	C₅×#41	—	8	2	no	—
161	C₂×C₅×Q₈	—	2	1	no	—
162	C₂×C₅×Q₈	—	2	2	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	—	4	1	no	—
167	C₂×C₅×Q₈	C₂×D₄	1	1	yes	characteristic
168	C₂×C₅×Q₈	C₂×D₄	1	1	yes	characteristic
169	C₂×C₅×D₄	—	2	1	no	—
170	C₂×C₅×D₄	—	2	1	no	—
171	C₂×C₅×D₄	—	2	1	no	—
172	C₂×C₅×D₄	—	4	1	no	—
173	C₂²×C₄×C₅	—	2	1	no	—
174	C₂²×C₄×C₅	—	2	1	no	—
175	C₂²×C₄×C₅	—	4	1	no	—
176	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
177	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
178	C₂²×C₄×C₅	#41	1	1	yes	characteristic
179	C₅×SD₁₆	—	4	2	no	—
180	C₅×SD₁₆	—	4	2	no	—
181	C₅×SD₁₆	—	4	2	no	—
182	C₅×SD₁₆	—	4	2	no	—
183	C₅×M₁₆	—	2	2	no	—
184	C₅×M₁₆	—	4	1	no	—
185	C₅×M₁₆	—	4	2	no	—
186	C₅×M₁₆	—	4	2	no	—
187	C₂×C₅×C₈	—	2	1	no	—
188	C₂×C₅×C₈	—	2	1	no	—
189	C₂×C₅×C₈	—	2	1	no	—
190	C₂×C₅×C₈	—	2	1	no	—
191	C₂×C₅×C₈	—	2	1	no	—
192	C₂×C₅×C₈	—	2	1	no	—
193	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
194	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
195	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
196	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
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	—	2	1	no	—
205	C₅×C₄⋊C₄	—	2	1	no	—
206	C₅×C₄⋊C₄	—	2	1	no	—
207	C₅×C₄⋊C₄	—	2	1	no	—
208	C₅×C₄⋊C₄	—	4	1	no	—
209	C₅×C₄⋊C₄	—	4	1	no	—
210	C₅×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
211	C₅×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
212	C₅×C₂²⋊C₄	—	4	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	—	2	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	#532	C₂²×C₅	1	1	yes	characteristic
226	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
227	#500	C₂²×C₅	1	1	yes	characteristic
228	#492	C₂²×C₅	1	1	yes	characteristic
229	#487	C₂²×C₅	1	1	yes	characteristic
230	#486	C₂²×C₅	1	1	yes	characteristic
231	#480	—	2	1	no	—
232	#479	—	2	1	no	—
233	#479	—	2	1	no	—
234	#477	C₂²×C₅	1	1	yes	characteristic
235	#477	C₂²×C₅	1	1	yes	characteristic
236	#477	C₂²×C₅	1	1	yes	characteristic
237	#477	C₂²×C₅	1	1	yes	characteristic
238	#475	C₂²×C₅	1	1	yes	characteristic
239	#475	C₂²×C₅	1	1	yes	characteristic
240	#468	—	2	1	no	—
241	#468	—	2	1	no	—
242	#460	C₂²×C₅	1	1	yes	characteristic
243	#460	C₂²×C₅	1	1	yes	characteristic
244	#448	—	2	1	no	—
245	#446	—	2	1	no	—
246	#446	—	2	1	no	—
247	#446	C₂²×C₅	1	1	yes	characteristic
248	#446	C₂²×C₅	1	1	yes	characteristic
249	C₈×Q₈	C₂²×C₅	1	1	yes	characteristic
250	C₈×Q₈	C₂²×C₅	1	1	yes	characteristic
251	#440	—	2	1	no	—
252	#440	—	2	1	no	—
253	#440	—	2	1	no	—
254	#440	—	2	1	no	—
255	#432	C₂²×C₅	1	1	yes	characteristic
256	#428	—	2	1	no	—
257	#423	—	2	1	no	—
258	#423	C₂²×C₅	1	1	yes	characteristic
259	#423	C₂²×C₅	1	1	yes	characteristic
260	#419	—	2	1	no	—
261	C₄×M₁₆	—	2	1	no	—
262	C₄×M₁₆	C₂²×C₅	1	1	yes	characteristic
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	#333	C₂²×C₅	1	1	yes	characteristic
270	#333	C₂²×C₅	1	1	yes	characteristic
271	#332	C₂²×C₅	1	1	yes	characteristic
272	#332	C₂²×C₅	1	1	yes	characteristic
273	#331	C₂²×C₅	1	1	yes	characteristic
274	#331	C₂²×C₅	1	1	yes	characteristic
275	C₂³×C₅	—	4	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	—	2	1	no	—
280	C₅×Q₈	—	4	2	no	—
281	C₅×Q₈	—	4	1	no	—
282	C₅×Q₈	—	4	1	no	—
283	C₅×Q₈	—	8	1	no	—
284	C₅×Q₈	—	8	1	no	—
285	C₅×Q₈	#137	1	2	yes	—
286	C₅×D₄	—	4	1	no	—
287	C₅×D₄	—	4	1	no	—
288	C₅×D₄	—	4	1	no	—
289	C₅×D₄	—	4	1	no	—
290	C₅×D₄	—	8	1	no	—
291	C₅×D₄	—	8	2	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	—	2	1	no	—
297	C₂×C₄×C₅	—	2	1	no	—
298	C₂×C₄×C₅	—	2	1	no	—
299	C₂×C₄×C₅	—	2	1	no	—
300	C₂×C₄×C₅	—	4	1	no	—
301	C₂×C₄×C₅	—	4	2	no	—
302	C₂×C₄×C₅	—	4	1	no	—
303	C₂×C₄×C₅	—	4	1	no	—
304	C₂×C₄×C₅	—	4	1	no	—
305	C₂×C₄×C₅	—	8	2	no	—
306	C₂×C₄×C₅	—	8	1	no	—
307	C₂×C₄×C₅	#121	1	1	yes	characteristic
308	C₂×C₄×C₅	#121	1	1	yes	characteristic
309	C₂×C₄×C₅	#121	1	1	yes	characteristic
310	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
311	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
312	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
313	C₅×C₈	—	2	1	no	—
314	C₅×C₈	—	2	1	no	—
315	C₅×C₈	—	2	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	—	4	1	no	—
321	C₅×C₈	—	4	1	no	—
322	C₅×C₈	#137	1	2	yes	—
323	C₂×#41	—	2	1	no	—
324	C₂²×Q₈	C₅×D₄	1	1	yes	characteristic
325	C₂×SD₁₆	—	2	1	no	—
326	C₂×SD₁₆	—	2	1	no	—
327	C₂×SD₁₆	—	2	1	no	—
328	C₂×SD₁₆	—	2	1	no	—
329	C₂×M₁₆	—	2	1	no	—
330	C₂×M₁₆	—	2	1	no	—
331	C₂×M₁₆	C₅×D₄	1	1	yes	characteristic
332	C₂×M₁₆	C₅×D₄	1	1	yes	characteristic
333	C₄⋊Q₈	C₂³×C₅	1	1	yes	characteristic
334	C₄⋊Q₈	C₂³×C₅	1	1	yes	characteristic
335	C₄⋊Q₈	C₂³×C₅	1	1	yes	characteristic
336	#127	C₂³×C₅	1	1	yes	characteristic
337	#125	—	2	1	no	—
338	#124	—	2	1	no	—
339	C₂²⋊Q₈	—	2	1	no	—
340	C₂²⋊Q₈	—	2	1	no	—
341	#121	—	2	1	no	—
342	#121	—	2	1	no	—
343	C₄×Q₈	—	2	1	no	—
344	C₄×Q₈	—	2	1	no	—
345	C₄×Q₈	—	2	1	no	—
346	C₄×Q₈	—	2	1	no	—
347	C₄×Q₈	C₅×D₄	1	1	yes	characteristic
348	C₄×Q₈	C₅×D₄	1	1	yes	characteristic
349	C₄×Q₈	C₂³×C₅	1	1	yes	characteristic
350	C₄×Q₈	C₂³×C₅	1	1	yes	characteristic
351	C₄×D₄	—	2	1	no	—
352	C₄×D₄	—	2	1	no	—
353	#117	—	2	1	no	—
354	C₂×C₄⋊C₄	—	2	1	no	—
355	C₂×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
356	C₂×C₄²	—	2	1	no	—
357	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
358	#107	—	2	1	no	—
359	#107	—	2	1	no	—
360	#107	—	2	1	no	—
361	#107	—	2	1	no	—
362	#107	—	2	1	no	—
363	#107	—	2	1	no	—
364	#106	—	2	1	no	—
365	#106	—	2	1	no	—
366	C₄⋊C₈	—	2	1	no	—
367	C₄⋊C₈	—	2	1	no	—
368	C₄⋊C₈	—	2	1	no	—
369	C₄⋊C₈	—	2	1	no	—
370	C₄⋊C₈	—	2	1	no	—
371	C₄⋊C₈	—	2	1	no	—
372	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
373	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
374	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
375	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
376	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
377	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
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	#103	—	2	1	no	—
384	#103	—	2	1	no	—
385	#103	—	2	1	no	—
386	#102	—	2	1	no	—
387	#102	—	2	1	no	—
388	#102	—	2	1	no	—
389	#102	—	2	1	no	—
390	C₂²⋊C₈	—	2	1	no	—
391	#97	—	2	1	no	—
392	#97	—	2	1	no	—
393	#97	—	2	1	no	—
394	#97	C₅×D₄	1	1	yes	characteristic
395	#97	C₅×D₄	1	1	yes	characteristic
396	C₄×C₈	—	2	1	no	—
397	C₄×C₈	—	2	1	no	—
398	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
399	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
400	C₂²×C₅	—	2	1	no	—
401	C₂²×C₅	—	2	1	no	—
402	C₂²×C₅	—	2	1	no	—
403	C₂²×C₅	—	8	1	no	—
404	C₂²×C₅	—	8	1	no	—
405	C₂²×C₅	—	8	1	no	—
406	C₂²×C₅	C₂×#121	1	1	yes	characteristic
407	C₄×C₅	—	2	1	no	—
408	C₄×C₅	—	2	1	no	—
409	C₄×C₅	—	2	2	no	—
410	C₄×C₅	—	2	1	no	—
411	C₄×C₅	—	2	1	no	—
412	C₄×C₅	—	4	1	no	—
413	C₄×C₅	—	4	1	no	—
414	C₄×C₅	—	4	1	no	—
415	C₄×C₅	—	8	1	no	—
416	C₄×C₅	—	8	1	no	—
417	C₄×C₅	—	8	1	no	—
418	C₄×C₅	C₂×#137	1	1	yes	characteristic
419	C₄×C₅	C₂×#137	1	1	yes	characteristic
420	C₄×C₅	#575	1	1	yes	characteristic
421	C₄×C₅	#575	1	1	yes	characteristic
422	#41	—	8	2	no	—
423	C₂×Q₈	—	2	1	no	—
424	C₂×Q₈	—	2	2	no	—
425	C₂×Q₈	—	2	1	no	—
426	C₂×Q₈	—	2	1	no	—
427	C₂×Q₈	—	2	1	no	—
428	C₂×Q₈	—	4	1	no	—
429	C₂×Q₈	C₂×C₅×D₄	1	1	yes	characteristic
430	C₂×Q₈	C₂×C₅×D₄	1	1	yes	characteristic
431	C₂×D₄	—	2	1	no	—
432	C₂×D₄	—	2	1	no	—
433	C₂×D₄	—	2	1	no	—
434	C₂×D₄	—	4	1	no	—
435	C₂²×C₄	—	2	1	no	—
436	C₂²×C₄	—	2	1	no	—
437	C₂²×C₄	—	4	1	no	—
438	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
439	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
440	C₂²×C₄	C₅×#41	1	1	yes	characteristic
441	SD₁₆	—	4	2	no	—
442	SD₁₆	—	4	2	no	—
443	SD₁₆	—	4	2	no	—
444	SD₁₆	—	4	2	no	—
445	M₁₆	—	2	2	no	—
446	M₁₆	—	4	1	no	—
447	M₁₆	—	4	2	no	—
448	M₁₆	—	4	2	no	—
449	C₂×C₈	—	2	1	no	—
450	C₂×C₈	—	2	1	no	—
451	C₂×C₈	—	2	1	no	—
452	C₂×C₈	—	2	1	no	—
453	C₂×C₈	—	2	1	no	—
454	C₂×C₈	—	2	1	no	—
455	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
456	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
457	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
458	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
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	—	2	1	no	—
465	C₄⋊C₄	—	2	1	no	—
466	C₄⋊C₄	—	2	1	no	—
467	C₄⋊C₄	—	2	1	no	—
468	C₄⋊C₄	—	2	1	no	—
469	C₄⋊C₄	—	2	1	no	—
470	C₄⋊C₄	—	4	1	no	—
471	C₄⋊C₄	—	4	1	no	—
472	C₄⋊C₄	C₂×C₅×D₄	1	1	yes	characteristic
473	C₄⋊C₄	C₂×C₅×D₄	1	1	yes	characteristic
474	C₂²⋊C₄	—	4	1	no	—
475	C₂²⋊C₄	—	4	1	no	—
476	C₂²⋊C₄	—	4	1	no	—
477	C₄²	—	2	1	no	—
478	C₄²	—	2	1	no	—
479	C₄²	—	2	1	no	—
480	C₄²	—	2	1	no	—
481	C₄²	—	4	1	no	—
482	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
483	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
484	C₄²	C₅×#41	1	1	yes	characteristic
485	C₄²	C₂⁴×C₅	1	1	yes	characteristic
486	C₂×C₅	—	4	1	no	—
487	C₂×C₅	—	16	1	no	—
488	C₂×C₅	#3037	1	1	yes	characteristic
489	C₂×C₅	#3056	1	1	yes	characteristic
490	C₂×C₅	#3068	1	1	yes	characteristic
491	C₂³	—	4	1	no	—
492	C₂³	C₅×#121	1	1	yes	characteristic
493	Q₈	—	2	1	no	—
494	Q₈	—	2	1	no	—
495	Q₈	—	2	1	no	—
496	Q₈	—	4	2	no	—
497	Q₈	—	4	1	no	—
498	Q₈	—	4	1	no	—
499	Q₈	—	8	1	no	—
500	Q₈	—	8	1	no	—
501	Q₈	C₅×#137	1	2	yes	—
502	D₄	—	4	1	no	—
503	D₄	—	4	1	no	—
504	D₄	—	4	1	no	—
505	D₄	—	4	1	no	—
506	D₄	—	8	1	no	—
507	D₄	—	8	2	no	—
508	C₂×C₄	—	2	1	no	—
509	C₂×C₄	—	2	1	no	—
510	C₂×C₄	—	2	1	no	—
511	C₂×C₄	—	2	1	no	—
512	C₂×C₄	—	2	1	no	—
513	C₂×C₄	—	2	1	no	—
514	C₂×C₄	—	2	1	no	—
515	C₂×C₄	—	2	1	no	—
516	C₂×C₄	—	4	1	no	—
517	C₂×C₄	—	4	2	no	—
518	C₂×C₄	—	4	1	no	—
519	C₂×C₄	—	4	1	no	—
520	C₂×C₄	—	4	1	no	—
521	C₂×C₄	—	8	2	no	—
522	C₂×C₄	—	8	1	no	—
523	C₂×C₄	C₅×#121	1	1	yes	characteristic
524	C₂×C₄	C₅×#121	1	1	yes	characteristic
525	C₂×C₄	C₅×#121	1	1	yes	characteristic
526	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
527	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
528	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
529	C₈	—	2	1	no	—
530	C₈	—	2	1	no	—
531	C₈	—	2	1	no	—
532	C₈	—	4	1	no	—
533	C₈	—	4	1	no	—
534	C₈	—	4	1	no	—
535	C₈	—	4	1	no	—
536	C₈	—	4	1	no	—
537	C₈	—	4	1	no	—
538	C₈	C₅×#137	1	2	yes	—
539	C₅	#19309	1	1	yes	characteristic, direct product factor, Sylow
540	C₂²	—	2	1	no	—
541	C₂²	—	2	1	no	—
542	C₂²	—	2	1	no	—
543	C₂²	—	8	1	no	—
544	C₂²	—	8	1	no	—
545	C₂²	—	8	1	no	—
546	C₂²	C₂×C₅×#121	1	1	yes	characteristic
547	C₄	—	2	1	no	—
548	C₄	—	2	1	no	—
549	C₄	—	2	2	no	—
550	C₄	—	2	1	no	—
551	C₄	—	2	1	no	—
552	C₄	—	4	1	no	—
553	C₄	—	4	1	no	—
554	C₄	—	4	1	no	—
555	C₄	—	8	1	no	—
556	C₄	—	8	1	no	—
557	C₄	—	8	1	no	—
558	C₄	C₂×C₅×#137	1	1	yes	characteristic
559	C₄	C₂×C₅×#137	1	1	yes	characteristic
560	C₄	C₅×#575	1	1	yes	characteristic
561	C₄	C₅×#575	1	1	yes	characteristic
562	C₂	—	4	1	no	—
563	C₂	—	16	1	no	—
564	C₂	C₅×#3037	1	1	yes	characteristic
565	C₂	C₅×#3056	1	1	yes	characteristic
566	C₂	C₅×#3068	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₅	C₂×#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₅
prime radical	C₅×#532	C₂²
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
3. C₅×#3078	C₂	semidirect
4. C₅×Q₈×M₁₆	C₂	semidirect
5. C₅×#1704	C₂	semidirect
6. C₅×#1698	C₂	semidirect
7. C₅×#1696	C₂	semidirect
8. C₅×#1686	C₂	semidirect
9. C₅×#1684	C₂	semidirect
10. C₅×#1678	C₂	semidirect
11. C₅×#1676	C₂	semidirect
12. C₅×#1666	C₂	semidirect
13. C₅×#1569	C₂	semidirect
15. C₅×#1559	C₂	semidirect
67. #19309	C₅	direct (N × H)
147. #3078	C₂×C₅	semidirect
148. Q₈×M₁₆	C₂×C₅	semidirect
149. #1704	C₂×C₅	semidirect
150. #1698	C₂×C₅	semidirect
151. #1696	C₂×C₅	semidirect
152. #1686	C₂×C₅	semidirect
153. #1684	C₂×C₅	semidirect
154. #1678	C₂×C₅	semidirect
155. #1676	C₂×C₅	semidirect
156. #1666	C₂×C₅	semidirect
157. #1569	C₂×C₅	semidirect
159. #1559	C₂×C₅	semidirect
539. C₅	#19309	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×#3182	2
C₅×#3112	2
C₅×#3078	2
C₅×Q₈×M₁₆	2
C₅×#1704	2
C₅×#1698	2
C₅×#1696	2
C₅×#1686	2
C₅×#1684	2
C₅×#1678	2
C₅×#1676	2
C₅×#1666	2
C₅×#1569	2
C₅×#1560	2
C₅×#1559	2
#19309	5

Subgroups — C5×#19309 #11942029

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#19309 #11942029