Subgroups — C₅×#29495 #11952215

Order 1280.

728 conjugacy classes of subgroups.

The subgroup lattice has 442 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#2863	C₂	1	1	yes	maximal, characteristic
2	C₄×C₅×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic
3	C₅×#2083	C₂	1	1	yes	maximal, characteristic
4	C₅×#2072	C₂	1	1	yes	maximal, characteristic
5	C₅×#2043	C₂	1	1	yes	maximal, characteristic
6	C₅×#2016	C₂	1	1	yes	maximal, characteristic
7	C₅×#1969	C₂	1	2	yes	maximal
8	C₅×#1933	C₂	1	2	yes	maximal
9	C₅×#1878	C₂	1	2	yes	maximal
10	C₅×#1863	C₂	1	2	yes	maximal
11	C₅×#1744	C₂	1	1	yes	maximal, characteristic
12	C₂²×C₅×Q₁₆	C₂²	1	2	yes	—
13	C₂×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
14	C₂×C₄×C₅×Q₈	C₂²	1	2	yes	—
15	C₂×C₅×#107	C₂²	1	2	yes	—
16	C₂×C₅×#103	C₂²	1	2	yes	—
17	C₂×C₅×#103	C₂²	1	2	yes	—
18	C₂×C₅×#103	C₂²	1	2	yes	—
19	C₂×C₅×#103	C₂²	1	2	yes	—
20	C₂×C₄×C₅×C₈	C₂²	1	2	yes	—
21	C₅×#391	C₂²	1	1	yes	characteristic
22	C₅×#391	C₂²	1	2	yes	—
23	C₅×#391	C₂²	1	1	yes	characteristic
24	C₅×#391	C₂²	1	1	yes	characteristic
25	C₅×#389	—	2	1	no	—
26	C₅×#389	—	2	1	no	—
27	C₅×#389	C₂²	1	1	yes	characteristic
28	C₅×#389	C₂²	1	1	yes	characteristic
29	C₅×#389	C₂²	1	1	yes	characteristic
30	C₅×#387	—	2	1	no	—
31	C₅×#387	—	2	1	no	—
32	C₅×#387	—	2	1	no	—
33	C₅×#384	C₂²	1	1	yes	characteristic
34	C₅×#383	—	2	1	no	—
35	C₄×C₅×C₄⋊C₄	—	2	1	no	—
36	C₄×C₅×C₄⋊C₄	—	2	1	no	—
37	C₄³×C₅	C₂²	1	1	yes	characteristic
38	C₅×#340	C₂²	1	2	yes	—
39	C₅×#340	C₂²	1	2	yes	—
40	C₅×#336	C₂²	1	1	yes	characteristic
41	C₅×#336	C₂²	1	1	yes	characteristic
42	C₅×#336	C₂²	1	2	yes	—
43	#29495	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
44	C₂²×C₅×Q₈	C₂³	1	1	yes	characteristic
45	C₂²×C₅×Q₈	C₂³	1	2	yes	—
46	C₂×C₅×Q₁₆	—	2	4	no	—
47	C₂×C₅×Q₁₆	—	2	4	no	—
48	C₂×C₅×Q₁₆	—	4	2	no	—
49	C₂²×C₅×C₈	C₂³	1	2	yes	—
50	C₂²×C₅×C₈	C₂³	1	2	yes	—
51	C₅×C₄⋊Q₈	—	2	4	no	—
52	C₄×C₅×Q₈	—	4	2	no	—
53	C₄×C₅×Q₈	—	4	2	no	—
54	C₂×C₅×C₄⋊C₄	—	2	1	no	—
55	C₂×C₅×C₄⋊C₄	—	2	1	no	—
56	C₂×C₅×C₄⋊C₄	—	2	1	no	—
57	C₂×C₅×C₄⋊C₄	—	2	1	no	—
58	C₂×C₅×C₄⋊C₄	—	2	1	no	—
59	C₂×C₅×C₄⋊C₄	—	2	1	no	—
60	C₂×C₅×C₄⋊C₄	—	2	1	no	—
61	C₂×C₅×C₄⋊C₄	—	2	2	no	—
62	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
63	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
64	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
65	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
66	C₂×C₄²×C₅	—	2	2	no	—
67	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
68	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
69	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
70	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
71	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
72	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
73	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
74	C₅×#107	—	4	2	no	—
75	C₅×#103	—	2	4	no	—
76	C₅×#103	—	2	4	no	—
77	C₅×#103	—	4	2	no	—
78	C₅×#103	—	4	2	no	—
79	C₄×C₅×C₈	—	2	4	no	—
80	C₅×#95	—	2	2	no	—
81	C₅×#95	—	2	2	no	—
82	C₅×#95	—	2	1	no	—
83	C₅×#95	—	2	1	no	—
84	C₅×#95	—	2	1	no	—
85	C₅×#95	—	2	1	no	—
86	C₅×#95	—	2	1	no	—
87	C₅×#95	—	2	1	no	—
88	C₅×#95	—	2	1	no	—
89	C₅×#95	—	2	1	no	—
90	C₅×#95	—	2	1	no	—
91	#2863	C₂×C₅	1	1	yes	characteristic
92	C₄×C₄⋊Q₈	C₂×C₅	1	1	yes	characteristic
93	#2083	C₂×C₅	1	1	yes	characteristic
94	#2072	C₂×C₅	1	1	yes	characteristic
95	#2043	C₂×C₅	1	1	yes	characteristic
96	#2016	C₂×C₅	1	1	yes	characteristic
97	#1969	C₂×C₅	1	2	yes	—
98	#1933	C₂×C₅	1	2	yes	—
99	#1878	C₂×C₅	1	2	yes	—
100	#1863	C₂×C₅	1	2	yes	—
101	#1744	C₂×C₅	1	1	yes	characteristic
102	C₂×C₅×Q₈	—	2	2	no	—
103	C₂×C₅×Q₈	—	2	2	no	—
104	C₂×C₅×Q₈	—	2	2	no	—
105	C₂×C₅×Q₈	—	2	2	no	—
106	C₂×C₅×Q₈	—	2	2	no	—
107	C₂×C₅×Q₈	—	2	2	no	—
108	C₂×C₅×Q₈	—	2	2	no	—
109	C₂×C₅×Q₈	—	2	1	no	—
110	C₂×C₅×Q₈	—	2	1	no	—
111	C₂×C₅×Q₈	#41	1	4	yes	—
112	C₂²×C₄×C₅	—	2	2	no	—
113	C₂²×C₄×C₅	—	2	2	no	—
114	C₂²×C₄×C₅	—	2	1	no	—
115	C₂²×C₄×C₅	—	2	1	no	—
116	C₂²×C₄×C₅	—	2	1	no	—
117	C₂²×C₄×C₅	—	2	1	no	—
118	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
119	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
120	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
121	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
122	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
123	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
124	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
125	C₅×Q₁₆	—	4	8	no	—
126	C₂×C₅×C₈	—	2	2	no	—
127	C₂×C₅×C₈	—	2	2	no	—
128	C₂×C₅×C₈	—	2	2	no	—
129	C₂×C₅×C₈	—	2	2	no	—
130	C₂×C₅×C₈	—	2	2	no	—
131	C₂×C₅×C₈	#41	1	4	yes	—
132	C₅×C₄⋊C₄	—	2	4	no	—
133	C₅×C₄⋊C₄	—	2	4	no	—
134	C₅×C₄⋊C₄	—	2	2	no	—
135	C₅×C₄⋊C₄	—	2	2	no	—
136	C₅×C₄⋊C₄	—	2	2	no	—
137	C₅×C₄⋊C₄	—	2	2	no	—
138	C₅×C₄⋊C₄	—	2	1	no	—
139	C₅×C₄⋊C₄	—	2	1	no	—
140	C₅×C₄⋊C₄	—	4	2	no	—
141	C₅×C₄⋊C₄	—	4	2	no	—
142	C₅×C₄⋊C₄	—	4	4	no	—
143	C₅×C₄⋊C₄	—	4	2	no	—
144	C₅×C₄⋊C₄	—	4	2	no	—
145	C₅×C₄⋊C₄	—	4	2	no	—
146	C₄²×C₅	—	2	2	no	—
147	C₄²×C₅	—	2	2	no	—
148	C₄²×C₅	—	2	2	no	—
149	C₄²×C₅	—	2	2	no	—
150	C₄²×C₅	—	2	1	no	—
151	C₄²×C₅	—	2	1	no	—
152	C₄²×C₅	—	4	1	no	—
153	C₄²×C₅	—	4	4	no	—
154	C₄²×C₅	Q₁₆	1	4	yes	complemented
155	C₂²×Q₁₆	C₂²×C₅	1	2	yes	—
156	C₂×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
157	C₂×C₄×Q₈	C₂²×C₅	1	2	yes	—
158	C₂×#107	C₂²×C₅	1	2	yes	—
159	C₂×#103	C₂²×C₅	1	2	yes	—
160	C₂×#103	C₂²×C₅	1	2	yes	—
161	C₂×#103	C₂²×C₅	1	2	yes	—
162	C₂×#103	C₂²×C₅	1	2	yes	—
163	C₂×C₄×C₈	C₂²×C₅	1	2	yes	—
164	#391	C₂²×C₅	1	2	yes	—
165	#391	C₂²×C₅	1	1	yes	characteristic
166	#391	C₂²×C₅	1	1	yes	characteristic
167	#391	C₂²×C₅	1	1	yes	characteristic
168	#389	—	2	1	no	—
169	#389	—	2	1	no	—
170	#389	C₂²×C₅	1	1	yes	characteristic
171	#389	C₂²×C₅	1	1	yes	characteristic
172	#389	C₂²×C₅	1	1	yes	characteristic
173	#387	—	2	1	no	—
174	#387	—	2	1	no	—
175	#387	—	2	1	no	—
176	#384	C₂²×C₅	1	1	yes	characteristic
177	#383	—	2	1	no	—
178	C₄×C₄⋊C₄	—	2	1	no	—
179	C₄×C₄⋊C₄	—	2	1	no	—
180	C₄³	C₂²×C₅	1	1	yes	characteristic
181	#340	C₂²×C₅	1	2	yes	—
182	#340	C₂²×C₅	1	2	yes	—
183	#336	C₂²×C₅	1	1	yes	characteristic
184	#336	C₂²×C₅	1	1	yes	characteristic
185	#336	C₂²×C₅	1	2	yes	—
186	C₂³×C₅	C₂²×D₄	1	1	yes	characteristic
187	C₅×Q₈	—	2	4	no	—
188	C₅×Q₈	—	2	4	no	—
189	C₅×Q₈	—	4	2	no	—
190	C₅×Q₈	—	4	2	no	—
191	C₅×Q₈	—	4	2	no	—
192	C₅×Q₈	—	4	2	no	—
193	C₂×C₄×C₅	—	2	1	no	—
194	C₂×C₄×C₅	—	2	1	no	—
195	C₂×C₄×C₅	—	2	1	no	—
196	C₂×C₄×C₅	—	2	1	no	—
197	C₂×C₄×C₅	—	2	1	no	—
198	C₂×C₄×C₅	—	2	1	no	—
199	C₂×C₄×C₅	—	2	1	no	—
200	C₂×C₄×C₅	—	2	1	no	—
201	C₂×C₄×C₅	—	2	1	no	—
202	C₂×C₄×C₅	—	2	1	no	—
203	C₂×C₄×C₅	—	2	4	no	—
204	C₂×C₄×C₅	—	2	1	no	—
205	C₂×C₄×C₅	—	2	1	no	—
206	C₂×C₄×C₅	—	2	1	no	—
207	C₂×C₄×C₅	—	4	2	no	—
208	C₂×C₄×C₅	—	4	2	no	—
209	C₂×C₄×C₅	—	4	1	no	—
210	C₂×C₄×C₅	—	4	1	no	—
211	C₂×C₄×C₅	—	4	1	no	—
212	C₂×C₄×C₅	—	4	1	no	—
213	C₂×C₄×C₅	—	4	2	no	—
214	C₂×C₄×C₅	—	4	1	no	—
215	C₂×C₄×C₅	—	4	1	no	—
216	C₂×C₄×C₅	—	4	1	no	—
217	C₂×C₄×C₅	—	4	2	no	—
218	C₂×C₄×C₅	—	4	1	no	—
219	C₂×C₄×C₅	—	4	1	no	—
220	C₂×C₄×C₅	—	4	1	no	—
221	C₂×C₄×C₅	—	4	1	no	—
222	C₂×C₄×C₅	—	4	2	no	—
223	C₂×C₄×C₅	—	4	1	no	—
224	C₂×C₄×C₅	C₂×Q₁₆	1	2	yes	—
225	C₂×C₄×C₅	C₂×Q₁₆	1	2	yes	—
226	C₂×C₄×C₅	C₂×Q₁₆	1	2	yes	—
227	C₂×C₄×C₅	#135	1	2	yes	—
228	C₂×C₄×C₅	#137	1	2	yes	—
229	C₂×C₄×C₅	C₂×#41	1	2	yes	—
230	C₂×C₄×C₅	C₂×#41	1	2	yes	—
231	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
232	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
233	C₅×C₈	—	2	4	no	—
234	C₅×C₈	—	4	2	no	—
235	C₂²×Q₈	C₂³×C₅	1	1	yes	characteristic
236	C₂²×Q₈	C₂³×C₅	1	2	yes	—
237	C₂×Q₁₆	—	2	4	no	—
238	C₂×Q₁₆	—	2	4	no	—
239	C₂×Q₁₆	—	4	2	no	—
240	C₂²×C₈	C₂³×C₅	1	2	yes	—
241	C₂²×C₈	C₂³×C₅	1	2	yes	—
242	C₄⋊Q₈	—	2	4	no	—
243	C₄×Q₈	—	4	2	no	—
244	C₄×Q₈	—	4	2	no	—
245	C₂×C₄⋊C₄	—	2	1	no	—
246	C₂×C₄⋊C₄	—	2	1	no	—
247	C₂×C₄⋊C₄	—	2	2	no	—
248	C₂×C₄⋊C₄	—	2	1	no	—
249	C₂×C₄⋊C₄	—	2	1	no	—
250	C₂×C₄⋊C₄	—	2	1	no	—
251	C₂×C₄⋊C₄	—	2	1	no	—
252	C₂×C₄⋊C₄	—	2	1	no	—
253	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
254	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
255	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
256	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
257	C₂×C₄²	—	2	2	no	—
258	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
259	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
260	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
261	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
262	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
263	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
264	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
265	#107	—	4	2	no	—
266	#103	—	2	4	no	—
267	#103	—	2	4	no	—
268	#103	—	4	2	no	—
269	#103	—	4	2	no	—
270	C₄×C₈	—	2	4	no	—
271	#95	—	2	2	no	—
272	#95	—	2	2	no	—
273	#95	—	2	1	no	—
274	#95	—	2	1	no	—
275	#95	—	2	1	no	—
276	#95	—	2	1	no	—
277	#95	—	2	1	no	—
278	#95	—	2	1	no	—
279	#95	—	2	1	no	—
280	#95	—	2	1	no	—
281	#95	—	2	1	no	—
282	C₂²×C₅	#525	1	1	yes	characteristic
283	C₂²×C₅	#532	1	1	yes	characteristic
284	C₂²×C₅	#535	1	1	yes	characteristic
285	C₂²×C₅	C₂²×Q₁₆	1	1	yes	characteristic
286	C₂²×C₅	C₂×#135	1	1	yes	characteristic
287	C₂²×C₅	C₂×#137	1	1	yes	characteristic
288	C₂²×C₅	#575	1	1	yes	characteristic
289	C₄×C₅	—	2	2	no	—
290	C₄×C₅	—	2	2	no	—
291	C₄×C₅	—	2	2	no	—
292	C₄×C₅	—	2	2	no	—
293	C₄×C₅	—	2	2	no	—
294	C₄×C₅	—	4	4	no	—
295	C₄×C₅	—	4	1	no	—
296	C₄×C₅	—	8	1	no	—
297	C₄×C₅	—	8	1	no	—
298	C₄×C₅	—	8	1	no	—
299	C₄×C₅	—	8	2	no	—
300	C₄×C₅	—	8	1	no	—
301	C₄×C₅	#551	1	2	yes	—
302	C₄×C₅	#553	1	2	yes	—
303	C₂×Q₈	—	2	2	no	—
304	C₂×Q₈	—	2	2	no	—
305	C₂×Q₈	—	2	2	no	—
306	C₂×Q₈	—	2	2	no	—
307	C₂×Q₈	—	2	2	no	—
308	C₂×Q₈	—	2	2	no	—
309	C₂×Q₈	—	2	2	no	—
310	C₂×Q₈	—	2	1	no	—
311	C₂×Q₈	—	2	1	no	—
312	C₂×Q₈	C₅×#41	1	4	yes	—
313	C₂²×C₄	—	2	2	no	—
314	C₂²×C₄	—	2	1	no	—
315	C₂²×C₄	—	2	1	no	—
316	C₂²×C₄	—	2	1	no	—
317	C₂²×C₄	—	2	1	no	—
318	C₂²×C₄	—	2	2	no	—
319	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
320	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
321	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
322	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
323	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
324	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
325	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
326	Q₁₆	—	4	8	no	—
327	C₂×C₈	—	2	2	no	—
328	C₂×C₈	—	2	2	no	—
329	C₂×C₈	—	2	2	no	—
330	C₂×C₈	—	2	2	no	—
331	C₂×C₈	—	2	2	no	—
332	C₂×C₈	C₅×#41	1	4	yes	—
333	C₄⋊C₄	—	2	4	no	—
334	C₄⋊C₄	—	2	4	no	—
335	C₄⋊C₄	—	2	2	no	—
336	C₄⋊C₄	—	2	2	no	—
337	C₄⋊C₄	—	2	1	no	—
338	C₄⋊C₄	—	2	2	no	—
339	C₄⋊C₄	—	2	1	no	—
340	C₄⋊C₄	—	2	2	no	—
341	C₄⋊C₄	—	4	4	no	—
342	C₄⋊C₄	—	4	2	no	—
343	C₄⋊C₄	—	4	2	no	—
344	C₄⋊C₄	—	4	2	no	—
345	C₄⋊C₄	—	4	2	no	—
346	C₄⋊C₄	—	4	2	no	—
347	C₄²	—	2	2	no	—
348	C₄²	—	2	2	no	—
349	C₄²	—	2	2	no	—
350	C₄²	—	2	2	no	—
351	C₄²	—	2	1	no	—
352	C₄²	—	2	1	no	—
353	C₄²	—	4	1	no	—
354	C₄²	—	4	4	no	—
355	C₄²	C₅×Q₁₆	1	4	yes	complemented
356	C₂×C₅	#2603	1	1	yes	characteristic
357	C₂×C₅	#3104	1	1	yes	characteristic
358	C₂×C₅	#3108	1	1	yes	characteristic
359	C₂×C₅	#3170	1	1	yes	characteristic
360	C₂×C₅	#3181	1	1	yes	characteristic
361	C₂×C₅	#3209	1	1	yes	characteristic
362	C₂×C₅	#3212	1	1	yes	characteristic
363	C₂³	C₂²×C₅×D₄	1	1	yes	characteristic
364	Q₈	—	2	4	no	—
365	Q₈	—	2	4	no	—
366	Q₈	—	4	2	no	—
367	Q₈	—	4	2	no	—
368	Q₈	—	4	2	no	—
369	Q₈	—	4	2	no	—
370	C₂×C₄	—	2	1	no	—
371	C₂×C₄	—	2	1	no	—
372	C₂×C₄	—	2	1	no	—
373	C₂×C₄	—	2	1	no	—
374	C₂×C₄	—	2	1	no	—
375	C₂×C₄	—	2	1	no	—
376	C₂×C₄	—	2	1	no	—
377	C₂×C₄	—	2	1	no	—
378	C₂×C₄	—	2	1	no	—
379	C₂×C₄	—	2	1	no	—
380	C₂×C₄	—	2	4	no	—
381	C₂×C₄	—	2	1	no	—
382	C₂×C₄	—	2	1	no	—
383	C₂×C₄	—	2	1	no	—
384	C₂×C₄	—	4	2	no	—
385	C₂×C₄	—	4	2	no	—
386	C₂×C₄	—	4	1	no	—
387	C₂×C₄	—	4	1	no	—
388	C₂×C₄	—	4	1	no	—
389	C₂×C₄	—	4	1	no	—
390	C₂×C₄	—	4	2	no	—
391	C₂×C₄	—	4	1	no	—
392	C₂×C₄	—	4	1	no	—
393	C₂×C₄	—	4	1	no	—
394	C₂×C₄	—	4	1	no	—
395	C₂×C₄	—	4	2	no	—
396	C₂×C₄	—	4	1	no	—
397	C₂×C₄	—	4	1	no	—
398	C₂×C₄	—	4	1	no	—
399	C₂×C₄	—	4	1	no	—
400	C₂×C₄	—	4	2	no	—
401	C₂×C₄	C₂×C₅×Q₁₆	1	2	yes	—
402	C₂×C₄	C₂×C₅×Q₁₆	1	2	yes	—
403	C₂×C₄	C₂×C₅×Q₁₆	1	2	yes	—
404	C₂×C₄	C₅×#135	1	2	yes	—
405	C₂×C₄	C₅×#137	1	2	yes	—
406	C₂×C₄	C₂×C₅×#41	1	2	yes	—
407	C₂×C₄	C₂×C₅×#41	1	2	yes	—
408	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
409	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
410	C₈	—	2	4	no	—
411	C₈	—	4	2	no	—
412	C₅	#29495	1	1	yes	characteristic, direct product factor, Sylow
413	C₂²	C₅×#525	1	1	yes	characteristic
414	C₂²	C₅×#532	1	1	yes	characteristic
415	C₂²	C₅×#535	1	1	yes	characteristic
416	C₂²	C₂²×C₅×Q₁₆	1	1	yes	characteristic
417	C₂²	C₂×C₅×#135	1	1	yes	characteristic
418	C₂²	C₂×C₅×#137	1	1	yes	characteristic
419	C₂²	C₅×#575	1	1	yes	characteristic
420	C₄	—	2	2	no	—
421	C₄	—	2	2	no	—
422	C₄	—	2	2	no	—
423	C₄	—	2	2	no	—
424	C₄	—	2	2	no	—
425	C₄	—	4	4	no	—
426	C₄	—	4	1	no	—
427	C₄	—	8	1	no	—
428	C₄	—	8	1	no	—
429	C₄	—	8	1	no	—
430	C₄	—	8	2	no	—
431	C₄	—	8	1	no	—
432	C₄	C₅×#551	1	2	yes	—
433	C₄	C₅×#553	1	2	yes	—
434	C₂	C₅×#2603	1	1	yes	characteristic
435	C₂	C₅×#3104	1	1	yes	characteristic
436	C₂	C₅×#3108	1	1	yes	characteristic
437	C₂	C₅×#3170	1	1	yes	characteristic
438	C₂	C₅×#3181	1	1	yes	characteristic
439	C₂	C₅×#3209	1	1	yes	characteristic
440	C₂	C₅×#3212	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂³×C₅	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₅
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₅ ◁ C₄³×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
43. #29495	C₅	direct (N × H)
154. C₄²×C₅	Q₁₆	semidirect
355. C₄²	C₅×Q₁₆	semidirect
412. C₅	#29495	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×#2863	2
C₄×C₅×C₄⋊Q₈	2
C₅×#2083	2
C₅×#2072	2
C₅×#2043	2
C₅×#2016	2
C₅×#1969	2
C₅×#1933	2
C₅×#1878	2
C₅×#1863	2
C₅×#1744	2
#29495	5

Subgroups — C5×#29495 #11952215

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#29495 #11952215