Subgroups — C₅×#19275 #11941995

Order 1280.

670 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#487	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×#3079	C₂	1	1	yes	maximal, characteristic
3	C₅×#3039	C₂	1	1	yes	maximal, characteristic
4	C₅×C₈×#41	C₂	1	1	yes	maximal, characteristic
5	C₅×#1680	C₂	1	4	yes	maximal, complemented
6	C₅×#1679	C₂	1	4	yes	maximal, complemented
7	C₅×#1566	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#1549	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#1546	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₅×#137	—	2	1	no	—
11	C₂×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
12	C₂×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
13	C₄×C₅×#41	C₂²	1	1	yes	characteristic
14	C₅×#487	—	2	1	no	—
15	C₅×#487	—	2	1	no	—
16	C₅×#487	C₂²	1	4	yes	—
17	C₅×#477	—	2	1	no	—
18	C₅×#476	—	2	1	no	—
19	C₅×#475	C₂²	1	2	yes	—
20	C₅×#474	C₂²	1	2	yes	—
21	C₅×#462	—	2	1	no	—
22	C₅×#462	C₂²	1	2	yes	—
23	C₅×#461	—	2	1	no	—
24	C₅×#461	C₂²	1	2	yes	—
25	C₅×C₈×Q₈	C₂²	1	2	yes	—
26	C₅×C₈×D₄	—	2	2	no	—
27	C₅×C₈×D₄	C₂²	1	2	yes	—
28	C₅×#431	—	2	1	no	—
29	C₅×#431	C₂²	1	1	yes	characteristic
30	C₅×#428	—	2	1	no	—
31	C₅×#423	C₂²	1	1	yes	characteristic
32	C₅×#423	C₂²	1	1	yes	characteristic
33	C₅×#419	—	2	1	no	—
34	C₅×#417	—	2	1	no	—
35	C₂×C₅×#103	—	2	2	no	—
36	C₂×C₄×C₅×C₈	—	2	1	no	—
37	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
38	C₅×#334	C₂²	1	4	yes	—
39	C₅×#332	C₂²	1	4	yes	—
40	C₅×#332	C₂²	1	4	yes	—
41	#19275	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
42	C₂×C₅×#41	D₄	1	1	yes	characteristic
43	C₂²×C₅×Q₈	—	2	1	no	—
44	C₂²×C₅×Q₈	—	2	1	no	—
45	C₅×#137	—	4	4	no	—
46	C₂×C₅×Q₁₆	—	2	2	no	—
47	C₂×C₅×SD₁₆	—	2	2	no	—
48	C₂×C₅×M₁₆	—	2	1	no	—
49	C₂×C₅×M₁₆	—	2	1	no	—
50	C₂²×C₅×C₈	—	2	2	no	—
51	C₂²×C₅×C₈	D₄	1	2	yes	—
52	C₅×C₄⋊Q₈	—	2	1	no	—
53	C₅×C₄⋊Q₈	—	2	1	no	—
54	C₅×C₄⋊Q₈	—	2	1	no	—
55	C₅×C₄⋊Q₈	—	2	1	no	—
56	C₅×C₄⋊Q₈	—	2	1	no	—
57	C₅×C₄⋊Q₈	—	2	1	no	—
58	C₅×C₄⋊Q₈	C₂³	1	2	yes	—
59	C₅×C₄⋊Q₈	C₂³	1	2	yes	—
60	C₄×C₅×Q₈	D₄	1	1	yes	characteristic
61	C₄×C₅×Q₈	C₂³	1	1	yes	characteristic
62	C₄×C₅×D₄	—	2	1	no	—
63	C₄×C₅×D₄	—	2	1	no	—
64	C₄×C₅×D₄	D₄	1	1	yes	characteristic
65	C₄×C₅×D₄	C₂³	1	1	yes	characteristic
66	C₅×#117	—	2	1	no	—
67	C₅×#117	D₄	1	1	yes	characteristic
68	C₂×C₅×C₄⋊C₄	—	2	1	no	—
69	C₂×C₅×C₄⋊C₄	—	2	1	no	—
70	C₂×C₅×C₄⋊C₄	—	2	1	no	—
71	C₂×C₅×C₄⋊C₄	—	2	1	no	—
72	C₂×C₄²×C₅	—	2	1	no	—
73	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
74	C₅×#107	—	2	2	no	—
75	C₅×#106	—	2	2	no	—
76	C₅×C₄⋊C₈	—	2	2	no	—
77	C₅×C₄⋊C₈	—	2	1	no	—
78	C₅×C₄⋊C₈	—	2	1	no	—
79	C₅×C₄⋊C₈	C₂³	1	2	yes	—
80	C₅×C₄⋊C₈	C₂³	1	2	yes	—
81	C₅×C₄⋊C₈	C₂³	1	2	yes	—
82	C₅×#103	—	2	2	no	—
83	C₅×#103	—	2	4	no	—
84	C₅×#103	—	2	4	no	—
85	C₅×#103	—	2	2	no	—
86	C₅×#103	—	2	2	no	—
87	C₅×#102	—	2	2	no	—
88	C₅×C₂²⋊C₈	—	2	1	no	—
89	C₅×C₂²⋊C₈	—	2	2	no	—
90	C₄×C₅×C₈	—	2	2	no	—
91	C₄×C₅×C₈	—	2	1	no	—
92	C₄×C₅×C₈	D₄	1	1	yes	characteristic
93	C₄×C₅×C₈	D₄	1	1	yes	characteristic
94	C₄×C₅×C₈	C₂³	1	2	yes	—
95	C₂×#487	C₂×C₅	1	1	yes	characteristic, complemented
96	#3079	C₂×C₅	1	1	yes	characteristic
97	#3039	C₂×C₅	1	1	yes	characteristic
98	C₈×#41	C₂×C₅	1	1	yes	characteristic
99	#1680	C₂×C₅	1	4	yes	complemented
100	#1679	C₂×C₅	1	4	yes	complemented
101	#1566	C₂×C₅	1	1	yes	characteristic, complemented
102	#1549	C₂×C₅	1	1	yes	characteristic, complemented
103	#1546	C₂×C₅	1	1	yes	characteristic, complemented
104	C₅×#41	—	2	2	no	—
105	C₅×#41	SD₁₆	1	4	yes	—
106	C₂×C₅×Q₈	—	2	2	no	—
107	C₂×C₅×Q₈	—	2	2	no	—
108	C₂×C₅×Q₈	—	4	4	no	—
109	C₂×C₅×Q₈	—	4	1	no	—
110	C₂×C₅×Q₈	—	4	1	no	—
111	C₂×C₅×Q₈	—	4	2	no	—
112	C₂×C₅×Q₈	—	4	2	no	—
113	C₂×C₅×Q₈	C₂×D₄	1	1	yes	characteristic
114	C₂×C₅×D₄	—	2	1	no	—
115	C₂×C₅×D₄	C₂×D₄	1	1	yes	characteristic
116	C₂²×C₄×C₅	—	2	1	no	—
117	C₂²×C₄×C₅	—	2	1	no	—
118	C₂²×C₄×C₅	—	2	1	no	—
119	C₂²×C₄×C₅	—	4	1	no	—
120	C₂²×C₄×C₅	—	4	1	no	—
121	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
122	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
123	C₂²×C₄×C₅	#41	1	1	yes	characteristic
124	C₅×Q₁₆	—	4	4	no	—
125	C₅×SD₁₆	—	4	4	no	—
126	C₅×M₁₆	—	4	2	no	—
127	C₅×M₁₆	—	4	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	—	4	2	no	—
132	C₂×C₅×C₈	—	4	4	no	—
133	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
134	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
135	C₅×C₄⋊C₄	—	2	1	no	—
136	C₅×C₄⋊C₄	—	2	1	no	—
137	C₅×C₄⋊C₄	—	2	2	no	—
138	C₅×C₄⋊C₄	—	2	2	no	—
139	C₅×C₄⋊C₄	—	2	2	no	—
140	C₅×C₄⋊C₄	—	2	2	no	—
141	C₅×C₄⋊C₄	—	4	1	no	—
142	C₅×C₄⋊C₄	—	4	1	no	—
143	C₅×C₄⋊C₄	—	4	1	no	—
144	C₅×C₄⋊C₄	—	4	1	no	—
145	C₅×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
146	C₅×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
147	C₅×C₂²⋊C₄	—	2	1	no	—
148	C₅×C₂²⋊C₄	—	2	1	no	—
149	C₅×C₂²⋊C₄	—	2	1	no	—
150	C₄²×C₅	—	2	1	no	—
151	C₄²×C₅	—	2	1	no	—
152	C₄²×C₅	—	2	1	no	—
153	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
154	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
155	C₄²×C₅	#41	1	1	yes	characteristic
156	C₄²×C₅	C₂⁴	1	1	yes	characteristic
157	C₂×#137	—	2	1	no	—
158	C₂×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
159	C₂×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
160	C₄×#41	C₂²×C₅	1	1	yes	characteristic
161	#487	—	2	1	no	—
162	#487	—	2	1	no	—
163	#487	C₂²×C₅	1	4	yes	—
164	#477	—	2	1	no	—
165	#476	—	2	1	no	—
166	#475	C₂²×C₅	1	2	yes	—
167	#474	C₂²×C₅	1	2	yes	—
168	#462	—	2	1	no	—
169	#462	C₂²×C₅	1	2	yes	—
170	#461	—	2	1	no	—
171	#461	C₂²×C₅	1	2	yes	—
172	C₈×Q₈	C₂²×C₅	1	2	yes	—
173	C₈×D₄	—	2	2	no	—
174	C₈×D₄	C₂²×C₅	1	2	yes	—
175	#431	—	2	1	no	—
176	#431	C₂²×C₅	1	1	yes	characteristic
177	#428	—	2	1	no	—
178	#423	C₂²×C₅	1	1	yes	characteristic
179	#423	C₂²×C₅	1	1	yes	characteristic
180	#419	—	2	1	no	—
181	#417	—	2	1	no	—
182	C₂×#103	—	2	2	no	—
183	C₂×C₄×C₈	—	2	1	no	—
184	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
185	#334	C₂²×C₅	1	4	yes	—
186	#332	C₂²×C₅	1	4	yes	—
187	#332	C₂²×C₅	1	4	yes	—
188	C₂³×C₅	—	2	1	no	—
189	C₂³×C₅	#121	1	1	yes	characteristic
190	C₅×Q₈	—	2	1	no	—
191	C₅×Q₈	—	4	2	no	—
192	C₅×Q₈	—	4	2	no	—
193	C₅×Q₈	—	4	4	no	—
194	C₅×Q₈	—	8	2	no	—
195	C₅×Q₈	—	8	2	no	—
196	C₅×Q₈	C₂×SD₁₆	1	2	yes	—
197	C₅×D₄	—	2	4	no	—
198	C₅×D₄	—	2	1	no	—
199	C₅×D₄	C₂×SD₁₆	1	2	yes	—
200	C₂×C₄×C₅	—	2	1	no	—
201	C₂×C₄×C₅	—	2	2	no	—
202	C₂×C₄×C₅	—	2	4	no	—
203	C₂×C₄×C₅	—	2	2	no	—
204	C₂×C₄×C₅	—	2	1	no	—
205	C₂×C₄×C₅	—	2	1	no	—
206	C₂×C₄×C₅	—	4	2	no	—
207	C₂×C₄×C₅	—	4	2	no	—
208	C₂×C₄×C₅	—	4	2	no	—
209	C₂×C₄×C₅	—	4	2	no	—
210	C₂×C₄×C₅	—	8	2	no	—
211	C₂×C₄×C₅	—	8	2	no	—
212	C₂×C₄×C₅	#121	1	1	yes	characteristic
213	C₂×C₄×C₅	#121	1	1	yes	characteristic
214	C₂×C₄×C₅	#121	1	1	yes	characteristic
215	C₂×C₄×C₅	C₂×SD₁₆	1	2	yes	—
216	C₂×C₄×C₅	#135	1	2	yes	—
217	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
218	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
219	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
220	C₅×C₈	—	2	2	no	—
221	C₅×C₈	—	2	2	no	—
222	C₅×C₈	—	4	2	no	—
223	C₅×C₈	—	4	2	no	—
224	C₅×C₈	—	4	2	no	—
225	C₂×#41	C₅×D₄	1	1	yes	characteristic
226	C₂²×Q₈	—	2	1	no	—
227	C₂²×Q₈	—	2	1	no	—
228	#137	—	4	4	no	—
229	C₂×Q₁₆	—	2	2	no	—
230	C₂×SD₁₆	—	2	2	no	—
231	C₂×M₁₆	—	2	1	no	—
232	C₂×M₁₆	—	2	1	no	—
233	C₂²×C₈	—	2	2	no	—
234	C₂²×C₈	C₅×D₄	1	2	yes	—
235	C₄⋊Q₈	—	2	1	no	—
236	C₄⋊Q₈	—	2	1	no	—
237	C₄⋊Q₈	—	2	1	no	—
238	C₄⋊Q₈	—	2	1	no	—
239	C₄⋊Q₈	—	2	1	no	—
240	C₄⋊Q₈	—	2	1	no	—
241	C₄⋊Q₈	C₂³×C₅	1	2	yes	—
242	C₄⋊Q₈	C₂³×C₅	1	2	yes	—
243	C₄×Q₈	C₅×D₄	1	1	yes	characteristic
244	C₄×Q₈	C₂³×C₅	1	1	yes	characteristic
245	C₄×D₄	—	2	1	no	—
246	C₄×D₄	—	2	1	no	—
247	C₄×D₄	C₅×D₄	1	1	yes	characteristic
248	C₄×D₄	C₂³×C₅	1	1	yes	characteristic
249	#117	—	2	1	no	—
250	#117	C₅×D₄	1	1	yes	characteristic
251	C₂×C₄⋊C₄	—	2	1	no	—
252	C₂×C₄⋊C₄	—	2	1	no	—
253	C₂×C₄⋊C₄	—	2	1	no	—
254	C₂×C₄⋊C₄	—	2	1	no	—
255	C₂×C₄²	—	2	1	no	—
256	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
257	#107	—	2	2	no	—
258	#106	—	2	2	no	—
259	C₄⋊C₈	—	2	2	no	—
260	C₄⋊C₈	—	2	1	no	—
261	C₄⋊C₈	—	2	1	no	—
262	C₄⋊C₈	C₂³×C₅	1	2	yes	—
263	C₄⋊C₈	C₂³×C₅	1	2	yes	—
264	C₄⋊C₈	C₂³×C₅	1	2	yes	—
265	#103	—	2	2	no	—
266	#103	—	2	4	no	—
267	#103	—	2	4	no	—
268	#103	—	2	2	no	—
269	#103	—	2	2	no	—
270	#102	—	2	2	no	—
271	C₂²⋊C₈	—	2	1	no	—
272	C₂²⋊C₈	—	2	2	no	—
273	C₄×C₈	—	2	2	no	—
274	C₄×C₈	—	2	1	no	—
275	C₄×C₈	C₅×D₄	1	1	yes	characteristic
276	C₄×C₈	C₅×D₄	1	1	yes	characteristic
277	C₄×C₈	C₂³×C₅	1	2	yes	—
278	C₂²×C₅	—	2	1	no	—
279	C₂²×C₅	—	2	1	no	—
280	C₂²×C₅	—	2	2	no	—
281	C₂²×C₅	—	4	1	no	—
282	C₂²×C₅	—	4	1	no	—
283	C₂²×C₅	#465	1	2	yes	—
284	C₂²×C₅	C₂×#121	1	1	yes	characteristic
285	C₄×C₅	—	2	1	no	—
286	C₄×C₅	—	2	2	no	—
287	C₄×C₅	—	2	1	no	—
288	C₄×C₅	—	4	1	no	—
289	C₄×C₅	—	4	1	no	—
290	C₄×C₅	—	8	2	no	—
291	C₄×C₅	—	8	2	no	—
292	C₄×C₅	#465	1	2	yes	—
293	C₄×C₅	#473	1	2	yes	—
294	C₄×C₅	C₂²×SD₁₆	1	1	yes	characteristic
295	C₄×C₅	C₂×#135	1	1	yes	characteristic
296	C₄×C₅	#575	1	2	yes	—
297	#41	—	2	2	no	—
298	#41	C₅×SD₁₆	1	4	yes	—
299	C₂×Q₈	—	2	2	no	—
300	C₂×Q₈	—	2	2	no	—
301	C₂×Q₈	—	4	4	no	—
302	C₂×Q₈	—	4	1	no	—
303	C₂×Q₈	—	4	1	no	—
304	C₂×Q₈	—	4	2	no	—
305	C₂×Q₈	—	4	2	no	—
306	C₂×Q₈	C₂×C₅×D₄	1	1	yes	characteristic
307	C₂×D₄	—	2	1	no	—
308	C₂×D₄	C₂×C₅×D₄	1	1	yes	characteristic
309	C₂²×C₄	—	2	1	no	—
310	C₂²×C₄	—	2	1	no	—
311	C₂²×C₄	—	2	1	no	—
312	C₂²×C₄	—	4	1	no	—
313	C₂²×C₄	—	4	1	no	—
314	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
315	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
316	C₂²×C₄	C₅×#41	1	1	yes	characteristic
317	Q₁₆	—	4	4	no	—
318	SD₁₆	—	4	4	no	—
319	M₁₆	—	4	2	no	—
320	M₁₆	—	4	2	no	—
321	C₂×C₈	—	2	2	no	—
322	C₂×C₈	—	2	2	no	—
323	C₂×C₈	—	2	2	no	—
324	C₂×C₈	—	4	2	no	—
325	C₂×C₈	—	4	4	no	—
326	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
327	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
328	C₄⋊C₄	—	2	1	no	—
329	C₄⋊C₄	—	2	1	no	—
330	C₄⋊C₄	—	2	2	no	—
331	C₄⋊C₄	—	2	2	no	—
332	C₄⋊C₄	—	2	2	no	—
333	C₄⋊C₄	—	2	2	no	—
334	C₄⋊C₄	—	4	1	no	—
335	C₄⋊C₄	—	4	1	no	—
336	C₄⋊C₄	—	4	1	no	—
337	C₄⋊C₄	—	4	1	no	—
338	C₄⋊C₄	C₂×C₅×D₄	1	1	yes	characteristic
339	C₄⋊C₄	C₂×C₅×D₄	1	1	yes	characteristic
340	C₂²⋊C₄	—	2	1	no	—
341	C₂²⋊C₄	—	2	1	no	—
342	C₂²⋊C₄	—	2	1	no	—
343	C₄²	—	2	1	no	—
344	C₄²	—	2	1	no	—
345	C₄²	—	2	1	no	—
346	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
347	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
348	C₄²	C₅×#41	1	1	yes	characteristic
349	C₄²	C₂⁴×C₅	1	1	yes	characteristic
350	C₂×C₅	—	2	2	no	—
351	C₂×C₅	—	4	2	no	—
352	C₂×C₅	#3040	1	1	yes	characteristic
353	C₂×C₅	C₂×#465	1	1	yes	characteristic
354	C₂×C₅	C₂×#473	1	1	yes	characteristic
355	C₂³	—	2	1	no	—
356	C₂³	C₅×#121	1	1	yes	characteristic
357	Q₈	—	2	1	no	—
358	Q₈	—	4	2	no	—
359	Q₈	—	4	2	no	—
360	Q₈	—	4	4	no	—
361	Q₈	—	8	2	no	—
362	Q₈	—	8	2	no	—
363	Q₈	C₂×C₅×SD₁₆	1	2	yes	—
364	D₄	—	2	4	no	—
365	D₄	—	2	1	no	—
366	D₄	C₂×C₅×SD₁₆	1	2	yes	—
367	C₂×C₄	—	2	1	no	—
368	C₂×C₄	—	2	4	no	—
369	C₂×C₄	—	2	2	no	—
370	C₂×C₄	—	2	2	no	—
371	C₂×C₄	—	2	1	no	—
372	C₂×C₄	—	2	1	no	—
373	C₂×C₄	—	4	2	no	—
374	C₂×C₄	—	4	2	no	—
375	C₂×C₄	—	4	2	no	—
376	C₂×C₄	—	4	2	no	—
377	C₂×C₄	—	8	2	no	—
378	C₂×C₄	—	8	2	no	—
379	C₂×C₄	C₅×#121	1	1	yes	characteristic
380	C₂×C₄	C₅×#121	1	1	yes	characteristic
381	C₂×C₄	C₅×#121	1	1	yes	characteristic
382	C₂×C₄	C₂×C₅×SD₁₆	1	2	yes	—
383	C₂×C₄	C₅×#135	1	2	yes	—
384	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
385	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
386	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
387	C₈	—	2	2	no	—
388	C₈	—	2	2	no	—
389	C₈	—	4	2	no	—
390	C₈	—	4	2	no	—
391	C₈	—	4	2	no	—
392	C₅	#19275	1	1	yes	characteristic, direct product factor, Sylow
393	C₂²	—	2	1	no	—
394	C₂²	—	2	1	no	—
395	C₂²	—	2	2	no	—
396	C₂²	—	4	1	no	—
397	C₂²	—	4	1	no	—
398	C₂²	C₅×#465	1	2	yes	—
399	C₂²	C₂×C₅×#121	1	1	yes	characteristic
400	C₄	—	2	1	no	—
401	C₄	—	2	2	no	—
402	C₄	—	2	1	no	—
403	C₄	—	4	1	no	—
404	C₄	—	4	1	no	—
405	C₄	—	8	2	no	—
406	C₄	—	8	2	no	—
407	C₄	C₅×#465	1	2	yes	—
408	C₄	C₅×#473	1	2	yes	—
409	C₄	C₂²×C₅×SD₁₆	1	1	yes	characteristic
410	C₄	C₂×C₅×#135	1	1	yes	characteristic
411	C₄	C₅×#575	1	2	yes	—
412	C₂	—	2	2	no	—
413	C₂	—	4	2	no	—
414	C₂	C₅×#3040	1	1	yes	characteristic
415	C₂	C₂×C₅×#465	1	1	yes	characteristic
416	C₂	C₂×C₅×#473	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. C₂×C₅×#487	C₂	semidirect
5. C₅×#1680	C₂	semidirect
6. C₅×#1679	C₂	semidirect
7. C₅×#1566	C₂	semidirect
8. C₅×#1549	C₂	semidirect
9. C₅×#1546	C₂	semidirect
41. #19275	C₅	direct (N × H)
95. C₂×#487	C₂×C₅	semidirect
99. #1680	C₂×C₅	semidirect
100. #1679	C₂×C₅	semidirect
101. #1566	C₂×C₅	semidirect
102. #1549	C₂×C₅	semidirect
103. #1546	C₂×C₅	semidirect
392. C₅	#19275	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₅×#487	2
C₅×#3079	2
C₅×#3039	2
C₅×C₈×#41	2
C₅×#1680	2
C₅×#1679	2
C₅×#1566	2
C₅×#1549	2
C₅×#1546	2
#19275	5

Subgroups — C5×#19275 #11941995

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#19275 #11941995