Subgroups — C₅×#81800 #14439210

Order 1920.

1104 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#918	C₂	1	4	yes	maximal, complemented
2	C₅×#5725	C₂	1	1	yes	maximal, characteristic
3	C₅×D₃×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₅×#494	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#5190	C₂	1	4	yes	maximal, complemented
6	C₅×#5092	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#5085	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#4693	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄×C₅×ΓL(1,𝔽₂₅)	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#3152	—	3	1	no	maximal, Hall
11	C₂×C₅×#239	C₂²	1	2	yes	—
12	C₂×C₅×D₃×Q₈	C₂²	1	2	yes	—
13	C₂×C₃×C₅×Q₁₆	C₂²	1	4	yes	—
14	C₃×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
15	C₃×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
16	C₅×#947	C₂²	1	2	yes	—
17	C₅×#944	C₂²	1	2	yes	—
18	C₂×C₅×#216	C₂²	1	4	yes	—
19	C₂×C₅×#215	C₂²	1	4	yes	—
20	C₅×#918	—	2	16	no	—
21	C₂×C₅×#204	C₂²	1	4	yes	—
22	C₂×C₅×ΓL(1,𝔽₂₅)	C₂²	1	2	yes	—
23	C₅×#895	—	2	2	no	—
24	C₅×#893	—	2	2	no	—
25	C₅×D₃×C₄⋊C₄	—	2	2	no	—
26	C₅×#888	—	2	2	no	—
27	C₅×#874	C₂²	1	1	yes	characteristic
28	C₄²×C₅×D₃	C₂²	1	1	yes	characteristic
29	C₅×#869	C₂²	1	1	yes	characteristic
30	C₃×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
31	C₅×#815	C₂²	1	2	yes	—
32	C₄×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
33	#81800	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
34	C₂×C₅×#137	—	3	4	no	—
35	C₅×#532	—	3	1	no	—
36	C₂×C₅×C₄⋊Q₈	—	3	1	no	—
37	C₅×#497	—	3	4	no	—
38	C₅×#494	—	3	1	no	—
39	C₅×#494	D₃	1	1	yes	characteristic, complemented
40	C₅×#492	—	3	1	no	—
41	C₅×#492	—	3	1	no	—
42	C₄×C₅×M₁₆	—	3	1	no	—
43	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
44	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
45	C₅×#239	—	2	8	no	—
46	C₅×D₃×Q₈	—	2	8	no	—
47	C₂×C₅×D₁₂	—	2	2	no	—
48	C₂×C₅×D₁₂	—	2	2	no	—
49	C₂×C₅×D₁₂	C₂³	1	2	yes	—
50	C₂×C₄×C₅×D₃	—	2	2	no	—
51	C₂×C₄×C₅×D₃	—	2	2	no	—
52	C₂×C₄×C₅×D₃	D₄	1	2	yes	—
53	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
54	C₂×C₅×Dic₆	—	2	2	no	—
55	C₂×C₅×Dic₆	C₂³	1	2	yes	—
56	C₃×C₅×Q₁₆	—	2	8	no	—
57	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
58	C₃×C₅×C₄⋊C₄	—	2	2	no	—
59	C₃×C₅×C₄⋊C₄	—	2	2	no	—
60	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
61	C₅×#216	—	2	8	no	—
62	C₅×#215	—	2	8	no	—
63	C₅×(C₂×D₃)⋊C₄	—	2	4	no	—
64	C₅×C₄⋊Dic₃	—	2	2	no	—
65	C₅×Dic₃⋊C₄	—	2	4	no	—
66	C₄×C₅×Dic₃	D₄	1	2	yes	—
67	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
68	C₂×C₅×C₃⋊C₈	C₂³	1	2	yes	—
69	C₅×#204	—	2	8	no	—
70	C₅×ΓL(1,𝔽₂₅)	D₄	1	8	yes	complemented
71	C₂×#918	C₂×C₅	1	4	yes	complemented
72	#5725	C₂×C₅	1	1	yes	characteristic
73	D₃×C₄⋊Q₈	C₂×C₅	1	1	yes	characteristic, complemented
74	C₃×#494	C₂×C₅	1	1	yes	characteristic, complemented
75	#5190	C₂×C₅	1	4	yes	complemented
76	#5092	C₂×C₅	1	1	yes	characteristic, complemented
77	#5085	C₂×C₅	1	1	yes	characteristic, complemented
78	#4693	C₂×C₅	1	1	yes	characteristic, complemented
79	C₄×ΓL(1,𝔽₂₅)	C₂×C₅	1	1	yes	characteristic, complemented
80	C₂×C₅×#41	—	3	2	no	—
81	C₂²×C₅×Q₈	—	3	2	no	—
82	C₅×#137	—	6	16	no	—
83	C₂×C₅×Q₁₆	—	3	4	no	—
84	C₂×C₅×Q₁₆	C₂×D₃	1	4	yes	—
85	C₂×C₅×SD₁₆	—	3	4	no	—
86	C₂×C₅×SD₁₆	—	3	4	no	—
87	C₂×C₅×M₁₆	—	3	2	no	—
88	C₅×C₄⋊Q₈	—	3	2	no	—
89	C₅×C₄⋊Q₈	—	3	1	no	—
90	C₅×C₄⋊Q₈	—	6	2	no	—
91	C₅×C₄⋊Q₈	C₂×D₃	1	1	yes	characteristic
92	C₅×C₄⋊Q₈	C₂×D₃	1	1	yes	characteristic
93	C₅×#127	—	3	1	no	—
94	C₅×#124	—	3	2	no	—
95	C₅×#121	—	6	2	no	—
96	C₄×C₅×D₄	—	6	2	no	—
97	C₂×C₅×C₄⋊C₄	—	6	2	no	—
98	C₂×C₄²×C₅	—	3	1	no	—
99	C₅×#97	—	3	2	no	—
100	C₄×C₅×C₈	—	3	1	no	—
101	C₄×C₅×C₈	C₂×D₃	1	1	yes	characteristic
102	#3152	—	3	1	no	Sylow
103	C₂²×C₅×D₃	—	2	2	no	—
104	C₂²×C₅×D₃	C₂×D₄	1	1	yes	characteristic
105	C₃×C₅×Q₈	—	2	4	no	—
106	C₃×C₅×Q₈	—	2	4	no	—
107	C₂×C₃×C₄×C₅	—	2	2	no	—
108	C₂×C₃×C₄×C₅	—	2	2	no	—
109	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
110	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
111	C₂×C₅×Dic₃	—	2	2	no	—
112	C₂×C₅×Dic₃	C₂×D₄	1	2	yes	—
113	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
114	C₅×D₁₂	—	2	4	no	—
115	C₅×D₁₂	—	4	4	no	—
116	C₅×D₁₂	—	4	4	no	—
117	C₄×C₅×D₃	—	2	4	no	—
118	C₄×C₅×D₃	—	4	4	no	—
119	C₄×C₅×D₃	—	4	4	no	—
120	C₄×C₅×D₃	C₂×D₄	1	4	yes	—
121	C₅×Dic₆	—	2	4	no	—
122	C₅×Dic₆	—	4	4	no	—
123	C₃×C₅×C₈	C₂×D₄	1	4	yes	—
124	C₅×C₃⋊C₈	C₂×D₄	1	4	yes	—
125	C₂×#239	C₂²×C₅	1	2	yes	—
126	C₂×D₃×Q₈	C₂²×C₅	1	2	yes	—
127	C₂×C₃×Q₁₆	C₂²×C₅	1	4	yes	—
128	C₃×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
129	C₃×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
130	#947	C₂²×C₅	1	2	yes	—
131	#944	C₂²×C₅	1	2	yes	—
132	C₂×#216	C₂²×C₅	1	4	yes	—
133	C₂×#215	C₂²×C₅	1	4	yes	—
134	#918	—	2	16	no	—
135	C₂×#204	C₂²×C₅	1	4	yes	—
136	C₂×ΓL(1,𝔽₂₅)	C₂²×C₅	1	2	yes	—
137	#895	—	2	2	no	—
138	#893	—	2	2	no	—
139	D₃×C₄⋊C₄	—	2	2	no	—
140	#888	—	2	2	no	—
141	#874	C₂²×C₅	1	1	yes	characteristic
142	C₄²×D₃	C₂²×C₅	1	1	yes	characteristic
143	#869	C₂²×C₅	1	1	yes	characteristic
144	C₃×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
145	#815	C₂²×C₅	1	2	yes	—
146	C₄×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic
147	C₅×#41	—	6	8	no	—
148	C₂×C₅×Q₈	—	3	2	no	—
149	C₂×C₅×Q₈	—	6	2	no	—
150	C₂×C₅×Q₈	—	6	8	no	—
151	C₂×C₅×Q₈	C₂²×D₃	1	2	yes	—
152	C₂×C₅×Q₈	C₂²×D₃	1	2	yes	—
153	C₂×C₅×D₄	—	3	2	no	—
154	C₂×C₅×D₄	—	6	2	no	—
155	C₂×C₅×D₄	—	6	2	no	—
156	C₂²×C₄×C₅	—	3	1	no	—
157	C₂²×C₄×C₅	—	3	2	no	—
158	C₂²×C₄×C₅	—	6	2	no	—
159	C₂²×C₄×C₅	—	6	2	no	—
160	C₅×Q₁₆	—	2	8	no	—
161	C₅×Q₁₆	—	6	8	no	—
162	C₅×SD₁₆	—	6	8	no	—
163	C₅×SD₁₆	—	6	8	no	—
164	C₅×M₁₆	—	3	8	no	—
165	C₂×C₅×C₈	—	3	2	no	—
166	C₂×C₅×C₈	C₂²×D₃	1	2	yes	—
167	C₅×C₄⋊C₄	—	2	2	no	—
168	C₅×C₄⋊C₄	—	2	2	no	—
169	C₅×C₄⋊C₄	—	6	4	no	—
170	C₅×C₄⋊C₄	—	6	2	no	—
171	C₅×C₂²⋊C₄	—	6	4	no	—
172	C₄²×C₅	—	3	2	no	—
173	C₄²×C₅	—	3	1	no	—
174	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
175	C₂×#137	—	3	4	no	—
176	#532	—	3	1	no	—
177	C₂×C₄⋊Q₈	—	3	1	no	—
178	#497	—	3	4	no	—
179	#494	—	3	1	no	—
180	#494	C₅×D₃	1	1	yes	characteristic, complemented
181	#492	—	3	1	no	—
182	#492	—	3	1	no	—
183	C₄×M₁₆	—	3	1	no	—
184	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
185	C₂×C₅×D₃	—	2	2	no	—
186	C₂×C₅×D₃	—	4	2	no	—
187	C₂×C₅×D₃	—	4	4	no	—
188	C₂×C₅×D₃	#127	1	2	yes	—
189	C₃×C₄×C₅	—	4	2	no	—
190	C₃×C₄×C₅	—	4	2	no	—
191	C₃×C₄×C₅	#137	1	4	yes	complemented
192	C₃×C₄×C₅	C₂²×D₄	1	2	yes	—
193	C₅×Dic₃	—	2	2	no	—
194	C₅×Dic₃	—	4	2	no	—
195	C₅×Dic₃	#127	1	2	yes	—
196	C₂×C₃×Q₈	C₂³×C₅	1	2	yes	—
197	C₂×C₃×Q₈	C₂³×C₅	1	2	yes	—
198	#239	—	2	8	no	—
199	D₃×Q₈	—	2	8	no	—
200	C₂×D₁₂	—	2	2	no	—
201	C₂×D₁₂	—	2	2	no	—
202	C₂×D₁₂	C₂³×C₅	1	2	yes	—
203	C₂×C₄×D₃	—	2	2	no	—
204	C₂×C₄×D₃	—	2	2	no	—
205	C₂×C₄×D₃	C₅×D₄	1	2	yes	—
206	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
207	C₂×Dic₆	—	2	2	no	—
208	C₂×Dic₆	C₂³×C₅	1	2	yes	—
209	C₃×Q₁₆	—	2	8	no	—
210	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
211	C₃×C₄⋊C₄	—	2	2	no	—
212	C₃×C₄⋊C₄	—	2	2	no	—
213	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
214	#216	—	2	8	no	—
215	#215	—	2	8	no	—
216	(C₂×D₃)⋊C₄	—	2	4	no	—
217	C₄⋊Dic₃	—	2	2	no	—
218	Dic₃⋊C₄	—	2	4	no	—
219	C₄×Dic₃	C₅×D₄	1	2	yes	—
220	C₄×Dic₃	C₂³×C₅	1	1	yes	characteristic
221	C₂×C₃⋊C₈	C₂³×C₅	1	2	yes	—
222	#204	—	2	8	no	—
223	ΓL(1,𝔽₂₅)	C₅×D₄	1	8	yes	complemented
224	C₂³×C₅	—	3	1	no	—
225	C₂³×C₅	—	6	2	no	—
226	C₅×Q₈	—	2	4	no	—
227	C₅×Q₈	—	2	4	no	—
228	C₅×Q₈	—	6	4	no	—
229	C₅×Q₈	—	12	4	no	—
230	C₅×D₄	—	6	4	no	—
231	C₅×D₄	—	12	4	no	—
232	C₅×D₄	—	12	4	no	—
233	C₂×C₄×C₅	—	2	2	no	—
234	C₂×C₄×C₅	—	2	2	no	—
235	C₂×C₄×C₅	—	3	1	no	—
236	C₂×C₄×C₅	—	3	4	no	—
237	C₂×C₄×C₅	—	3	2	no	—
238	C₂×C₄×C₅	—	6	4	no	—
239	C₂×C₄×C₅	—	6	2	no	—
240	C₂×C₄×C₅	—	12	4	no	—
241	C₂×C₄×C₅	—	12	4	no	—
242	C₂×C₄×C₅	D₃×D₄	1	2	yes	—
243	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
244	C₅×C₈	—	3	4	no	—
245	C₅×C₈	D₃×D₄	1	4	yes	—
246	C₂×#41	—	3	2	no	—
247	C₂²×Q₈	—	3	2	no	—
248	#137	—	6	16	no	—
249	C₂×Q₁₆	—	3	4	no	—
250	C₂×Q₁₆	C₂×C₅×D₃	1	4	yes	—
251	C₂×SD₁₆	—	3	4	no	—
252	C₂×SD₁₆	—	3	4	no	—
253	C₂×M₁₆	—	3	2	no	—
254	C₄⋊Q₈	—	3	2	no	—
255	C₄⋊Q₈	—	3	1	no	—
256	C₄⋊Q₈	—	6	2	no	—
257	C₄⋊Q₈	C₂×C₅×D₃	1	1	yes	characteristic
258	C₄⋊Q₈	C₂×C₅×D₃	1	1	yes	characteristic
259	#127	—	3	1	no	—
260	#124	—	3	2	no	—
261	#121	—	6	2	no	—
262	C₄×D₄	—	6	2	no	—
263	C₂×C₄⋊C₄	—	6	2	no	—
264	C₂×C₄²	—	3	1	no	—
265	#97	—	3	2	no	—
266	C₄×C₈	—	3	1	no	—
267	C₄×C₈	C₂×C₅×D₃	1	1	yes	characteristic
268	C₂×C₃×C₅	C₂×#127	1	1	yes	characteristic
269	C₂×C₃×C₅	C₂×#137	1	2	yes	—
270	C₅×D₃	—	2	2	no	—
271	C₅×D₃	—	8	2	no	—
272	C₂²×D₃	—	2	2	no	—
273	C₂²×D₃	C₂×C₅×D₄	1	1	yes	characteristic
274	C₃×Q₈	—	2	4	no	—
275	C₃×Q₈	—	2	4	no	—
276	C₂×C₃×C₄	—	2	2	no	—
277	C₂×C₃×C₄	—	2	2	no	—
278	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
279	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
280	C₂×Dic₃	—	2	2	no	—
281	C₂×Dic₃	C₂×C₅×D₄	1	2	yes	—
282	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
283	D₁₂	—	2	4	no	—
284	D₁₂	—	4	4	no	—
285	D₁₂	—	4	4	no	—
286	C₄×D₃	—	2	4	no	—
287	C₄×D₃	—	4	4	no	—
288	C₄×D₃	—	4	4	no	—
289	C₄×D₃	C₂×C₅×D₄	1	4	yes	—
290	Dic₆	—	2	4	no	—
291	Dic₆	—	4	4	no	—
292	C₃×C₈	C₂×C₅×D₄	1	4	yes	—
293	C₃⋊C₈	C₂×C₅×D₄	1	4	yes	—
294	C₂²×C₅	—	3	2	no	—
295	C₂²×C₅	—	6	2	no	—
296	C₂²×C₅	—	12	2	no	—
297	C₂²×C₅	—	12	4	no	—
298	C₂²×C₅	C₂×D₃×D₄	1	1	yes	characteristic
299	C₄×C₅	—	3	2	no	—
300	C₄×C₅	—	4	2	no	—
301	C₄×C₅	—	4	2	no	—
302	C₄×C₅	—	6	2	no	—
303	C₄×C₅	—	12	2	no	—
304	C₄×C₅	#918	1	4	yes	complemented
305	C₄×C₅	C₂×D₃×D₄	1	2	yes	—
306	#41	—	6	8	no	—
307	C₂×Q₈	—	3	2	no	—
308	C₂×Q₈	—	6	2	no	—
309	C₂×Q₈	—	6	8	no	—
310	C₂×Q₈	C₂²×C₅×D₃	1	2	yes	—
311	C₂×Q₈	C₂²×C₅×D₃	1	2	yes	—
312	C₂×D₄	—	3	2	no	—
313	C₂×D₄	—	6	2	no	—
314	C₂×D₄	—	6	2	no	—
315	C₂²×C₄	—	3	1	no	—
316	C₂²×C₄	—	3	2	no	—
317	C₂²×C₄	—	6	2	no	—
318	C₂²×C₄	—	6	2	no	—
319	Q₁₆	—	2	8	no	—
320	Q₁₆	—	6	8	no	—
321	SD₁₆	—	6	8	no	—
322	SD₁₆	—	6	8	no	—
323	M₁₆	—	3	8	no	—
324	C₂×C₈	—	3	2	no	—
325	C₂×C₈	C₂²×C₅×D₃	1	2	yes	—
326	C₄⋊C₄	—	2	2	no	—
327	C₄⋊C₄	—	2	2	no	—
328	C₄⋊C₄	—	6	4	no	—
329	C₄⋊C₄	—	6	2	no	—
330	C₂²⋊C₄	—	6	4	no	—
331	C₄²	—	3	2	no	—
332	C₄²	—	3	1	no	—
333	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
334	C₃×C₅	#3152	1	1	yes	characteristic, complemented, Hall
335	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
336	C₂×D₃	—	2	2	no	—
337	C₂×D₃	—	4	2	no	—
338	C₂×D₃	—	4	4	no	—
339	C₂×D₃	C₅×#127	1	2	yes	—
340	C₃×C₄	—	4	2	no	—
341	C₃×C₄	—	4	2	no	—
342	C₃×C₄	C₅×#137	1	4	yes	complemented
343	C₃×C₄	C₂²×C₅×D₄	1	2	yes	—
344	Dic₃	—	2	2	no	—
345	Dic₃	—	4	2	no	—
346	Dic₃	C₅×#127	1	2	yes	—
347	C₂×C₅	—	6	2	no	—
348	C₂×C₅	—	24	2	no	—
349	C₂×C₅	D₃×#127	1	1	yes	characteristic
350	C₂×C₅	C₂×#918	1	2	yes	—
351	C₂³	—	3	1	no	—
352	C₂³	—	6	2	no	—
353	Q₈	—	2	4	no	—
354	Q₈	—	2	4	no	—
355	Q₈	—	6	4	no	—
356	Q₈	—	12	4	no	—
357	D₄	—	6	4	no	—
358	D₄	—	12	4	no	—
359	D₄	—	12	4	no	—
360	C₂×C₄	—	2	2	no	—
361	C₂×C₄	—	2	2	no	—
362	C₂×C₄	—	3	1	no	—
363	C₂×C₄	—	3	4	no	—
364	C₂×C₄	—	3	2	no	—
365	C₂×C₄	—	6	4	no	—
366	C₂×C₄	—	6	2	no	—
367	C₂×C₄	—	12	4	no	—
368	C₂×C₄	—	12	4	no	—
369	C₂×C₄	C₅×D₃×D₄	1	2	yes	—
370	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
371	C₈	—	3	4	no	—
372	C₈	C₅×D₃×D₄	1	4	yes	—
373	C₂×C₃	C₂×C₅×#127	1	1	yes	characteristic
374	C₂×C₃	C₂×C₅×#137	1	2	yes	—
375	D₃	—	2	2	no	—
376	D₃	—	8	2	no	—
377	C₅	#81800	1	1	yes	characteristic, direct product factor, Sylow
378	C₂²	—	3	2	no	—
379	C₂²	—	6	2	no	—
380	C₂²	—	12	2	no	—
381	C₂²	—	12	4	no	—
382	C₂²	C₂×C₅×D₃×D₄	1	1	yes	characteristic
383	C₄	—	3	2	no	—
384	C₄	—	4	2	no	—
385	C₄	—	4	2	no	—
386	C₄	—	6	2	no	—
387	C₄	—	12	2	no	—
388	C₄	C₅×#918	1	4	yes	complemented
389	C₄	C₂×C₅×D₃×D₄	1	2	yes	—
390	C₃	C₅×#3152	1	1	yes	characteristic, complemented, Sylow
391	C₂	—	6	2	no	—
392	C₂	—	24	2	no	—
393	C₂	C₅×D₃×#127	1	1	yes	characteristic
394	C₂	C₂×C₅×#918	1	2	yes	—

	subgroup	G/H
center	C₂²×C₅	C₂×D₃×D₄
commutator, cosocle	C₂×C₃×C₄	C₂⁴×C₅
Frattini	C₂×C₄	C₂³×C₅×D₃
Fitting	C₃×C₅×#494	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
prime radical	C₅×#5725	C₂
hypercenter	C₅×#494	D₃
hypocenter	C₃	C₅×#3152
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₄²×C₅ ◁ C₅×#494

Complements

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

N	H ≅ G/N	type
1. C₂×C₅×#918	C₂	semidirect
3. C₅×D₃×C₄⋊Q₈	C₂	semidirect
4. C₃×C₅×#494	C₂	semidirect
5. C₅×#5190	C₂	semidirect
6. C₅×#5092	C₂	semidirect
7. C₅×#5085	C₂	semidirect
8. C₅×#4693	C₂	semidirect
9. C₄×C₅×ΓL(1,𝔽₂₅)	C₂	semidirect
33. #81800	C₅	direct (N × H)
39. C₅×#494	D₃	semidirect
70. C₅×ΓL(1,𝔽₂₅)	D₄	semidirect
71. C₂×#918	C₂×C₅	semidirect
73. D₃×C₄⋊Q₈	C₂×C₅	semidirect
74. C₃×#494	C₂×C₅	semidirect
75. #5190	C₂×C₅	semidirect
76. #5092	C₂×C₅	semidirect
77. #5085	C₂×C₅	semidirect
78. #4693	C₂×C₅	semidirect
79. C₄×ΓL(1,𝔽₂₅)	C₂×C₅	semidirect
180. #494	C₅×D₃	semidirect
191. C₃×C₄×C₅	#137	semidirect
223. ΓL(1,𝔽₂₅)	C₅×D₄	semidirect
304. C₄×C₅	#918	semidirect
334. C₃×C₅	#3152	semidirect
342. C₃×C₄	C₅×#137	semidirect
377. C₅	#81800	direct (N × H)
388. C₄	C₅×#918	semidirect
390. C₃	C₅×#3152	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×#918	2
C₅×#5725	2
C₅×D₃×C₄⋊Q₈	2
C₃×C₅×#494	2
C₅×#5190	2
C₅×#5092	2
C₅×#5085	2
C₅×#4693	2
C₄×C₅×ΓL(1,𝔽₂₅)	2
C₅×#3152	3
#81800	5

Subgroups — C5×#81800 #14439210

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#81800 #14439210