Subgroups — C₅×#68432 #14289097

Order 1920.

512 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#5726	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×#5088	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#4843	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#4843	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×C₅×#332	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#4483	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#4483	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#1625	—	3	1	no	maximal, Hall
9	C₂×C₅×#239	—	2	1	no	—
10	C₃×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
11	C₅×#946	—	2	1	no	—
12	C₂×C₅×D₂₄	—	2	1	no	—
13	C₂×C₅×D₂₄	—	2	1	no	—
14	C₅×#895	—	2	1	no	—
15	C₅×#894	—	2	2	no	—
16	C₅×D₃×C₄⋊C₄	—	2	1	no	—
17	C₅×#874	C₂²	1	1	yes	characteristic
18	C₄×C₅×D₁₂	C₂²	1	1	yes	characteristic
19	C₄×C₅×D₁₂	C₂²	1	1	yes	characteristic
20	C₃×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
21	C₃×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
22	C₅×#821	—	2	1	no	—
23	C₅×#821	—	2	1	no	—
24	C₅×#809	—	2	2	no	—
25	C₄×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
26	#68432	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
27	C₅×#547	—	3	1	no	—
28	C₅×#486	—	3	1	no	—
29	C₅×#459	—	3	1	no	—
30	C₅×#459	—	3	1	no	—
31	C₅×#332	D₃	1	1	yes	characteristic, complemented
32	C₅×D₄⋊C₈	—	3	1	no	—
33	C₅×D₄⋊C₈	—	3	1	no	—
34	C₂×C₃×C₅×Q₈	—	2	1	no	—
35	C₅×#239	—	4	2	no	—
36	C₅×#239	—	4	2	no	—
37	C₂×C₅×D₁₂	—	2	2	no	—
38	C₂×C₅×D₁₂	—	2	1	no	—
39	C₂×C₅×D₁₂	—	2	1	no	—
40	C₂×C₅×D₁₂	—	2	1	no	—
41	C₂×C₅×D₁₂	D₄	1	1	yes	characteristic
42	C₂×C₅×D₁₂	D₄	1	1	yes	characteristic
43	C₂×C₄×C₅×D₃	—	2	2	no	—
44	C₂×C₄×C₅×D₃	—	2	1	no	—
45	C₂×C₄×C₅×D₃	—	2	1	no	—
46	C₂×C₃×C₅×C₈	—	2	1	no	—
47	C₂×C₃×C₅×C₈	—	2	1	no	—
48	C₃×C₅×C₄⋊C₄	—	2	1	no	—
49	C₃×C₅×C₄⋊C₄	D₄	1	2	yes	—
50	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
51	C₅×(C₂×D₃)⋊C₄	—	2	2	no	—
52	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
53	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
54	C₅×C₄⋊Dic₃	D₄	1	1	yes	characteristic
55	C₅×C₄⋊Dic₃	D₄	1	1	yes	characteristic
56	C₅×Dic₃⋊C₄	—	2	2	no	—
57	C₂×C₅×C₃⋊C₈	—	2	1	no	—
58	C₅×D₂₄	—	4	2	no	—
59	C₅×D₂₄	—	4	2	no	—
60	#5726	C₂×C₅	1	1	yes	characteristic, complemented
61	#5088	C₂×C₅	1	1	yes	characteristic, complemented
62	#4843	C₂×C₅	1	1	yes	characteristic, complemented
63	#4843	C₂×C₅	1	1	yes	characteristic, complemented
64	C₃×#332	C₂×C₅	1	1	yes	characteristic, complemented
65	#4483	C₂×C₅	1	1	yes	characteristic, complemented
66	#4483	C₂×C₅	1	1	yes	characteristic, complemented
67	C₂×C₅×#41	—	6	1	no	—
68	C₂×C₅×D₈	—	6	1	no	—
69	C₂×C₅×D₈	—	6	1	no	—
70	C₅×C₄⋊Q₈	C₂×D₃	1	1	yes	characteristic
71	C₅×#127	—	3	1	no	—
72	C₅×#123	—	6	2	no	—
73	C₅×C₂²⋊Q₈	—	6	1	no	—
74	C₅×#121	—	6	1	no	—
75	C₄×C₅×D₄	—	3	1	no	—
76	C₄×C₅×D₄	—	3	1	no	—
77	C₂×C₅×C₄⋊C₄	—	6	1	no	—
78	C₅×C₄⋊C₈	C₂×D₃	1	1	yes	characteristic
79	C₅×C₄⋊C₈	C₂×D₃	1	1	yes	characteristic
80	C₅×#102	—	6	1	no	—
81	C₅×#102	—	6	1	no	—
82	C₅×#102	—	6	2	no	—
83	C₄×C₅×C₈	—	3	1	no	—
84	#1625	—	3	1	no	Sylow
85	C₂²×C₅×D₃	—	2	1	no	—
86	C₂²×C₅×D₃	—	2	1	no	—
87	C₂²×C₅×D₃	—	4	1	no	—
88	C₃×C₅×Q₈	—	4	1	no	—
89	C₃×C₅×Q₈	—	4	1	no	—
90	C₂×C₃×C₄×C₅	—	2	2	no	—
91	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
92	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
93	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
94	C₂×C₅×Dic₃	—	2	1	no	—
95	C₂×C₅×Dic₃	—	2	1	no	—
96	C₅×D₁₂	—	2	1	no	—
97	C₅×D₁₂	—	2	1	no	—
98	C₅×D₁₂	—	2	1	no	—
99	C₅×D₁₂	—	4	2	no	—
100	C₅×D₁₂	—	4	4	no	—
101	C₅×D₁₂	—	4	1	no	—
102	C₅×D₁₂	—	4	1	no	—
103	C₅×D₁₂	—	4	1	no	—
104	C₅×D₁₂	—	4	1	no	—
105	C₅×D₁₂	D₈	1	2	yes	complemented
106	C₄×C₅×D₃	—	4	4	no	—
107	C₄×C₅×D₃	—	4	1	no	—
108	C₄×C₅×D₃	—	4	1	no	—
109	C₄×C₅×D₃	—	4	1	no	—
110	C₄×C₅×D₃	—	4	1	no	—
111	C₃×C₅×C₈	—	4	1	no	—
112	C₃×C₅×C₈	—	4	1	no	—
113	C₅×C₃⋊C₈	—	4	1	no	—
114	C₂×#239	—	2	1	no	—
115	C₃×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
116	#946	—	2	1	no	—
117	C₂×D₂₄	—	2	1	no	—
118	C₂×D₂₄	—	2	1	no	—
119	#895	—	2	1	no	—
120	#894	—	2	2	no	—
121	D₃×C₄⋊C₄	—	2	1	no	—
122	#874	C₂²×C₅	1	1	yes	characteristic
123	C₄×D₁₂	C₂²×C₅	1	1	yes	characteristic
124	C₄×D₁₂	C₂²×C₅	1	1	yes	characteristic
125	C₃×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
126	C₃×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
127	#821	—	2	1	no	—
128	#821	—	2	1	no	—
129	#809	—	2	2	no	—
130	C₄×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic
131	C₅×#41	—	12	2	no	—
132	C₅×#41	—	12	2	no	—
133	C₂×C₅×Q₈	—	2	1	no	—
134	C₂×C₅×D₄	—	3	1	no	—
135	C₂×C₅×D₄	—	3	1	no	—
136	C₂×C₅×D₄	—	6	2	no	—
137	C₂×C₅×D₄	—	6	1	no	—
138	C₂×C₅×D₄	—	6	1	no	—
139	C₂×C₅×D₄	—	6	1	no	—
140	C₂²×C₄×C₅	—	6	2	no	—
141	C₂²×C₄×C₅	—	6	1	no	—
142	C₂²×C₄×C₅	—	6	1	no	—
143	C₅×D₈	—	12	2	no	—
144	C₅×D₈	—	12	2	no	—
145	C₂×C₅×C₈	—	2	1	no	—
146	C₂×C₅×C₈	—	2	1	no	—
147	C₂×C₅×C₈	—	6	1	no	—
148	C₅×C₄⋊C₄	—	2	1	no	—
149	C₅×C₄⋊C₄	—	3	1	no	—
150	C₅×C₄⋊C₄	—	3	1	no	—
151	C₅×C₄⋊C₄	—	6	2	no	—
152	C₅×C₄⋊C₄	D₁₂	1	2	yes	—
153	C₅×C₂²⋊C₄	—	6	2	no	—
154	C₅×C₂²⋊C₄	—	6	1	no	—
155	C₅×C₂²⋊C₄	—	6	1	no	—
156	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
157	#547	—	3	1	no	—
158	#486	—	3	1	no	—
159	#459	—	3	1	no	—
160	#459	—	3	1	no	—
161	#332	C₅×D₃	1	1	yes	characteristic, complemented
162	D₄⋊C₈	—	3	1	no	—
163	D₄⋊C₈	—	3	1	no	—
164	C₂²×C₃×C₅	#120	1	1	yes	characteristic
165	C₂×C₅×D₃	—	2	2	no	—
166	C₂×C₅×D₃	—	4	1	no	—
167	C₂×C₅×D₃	—	4	1	no	—
168	C₂×C₅×D₃	—	4	1	no	—
169	C₂×C₅×D₃	—	4	1	no	—
170	C₂×C₅×D₃	—	4	1	no	—
171	C₂×C₅×D₃	—	8	1	no	—
172	C₂×C₅×D₃	—	8	1	no	—
173	C₂×C₅×D₃	—	8	1	no	—
174	C₃×C₄×C₅	—	2	1	no	—
175	C₃×C₄×C₅	—	4	2	no	—
176	C₃×C₄×C₅	C₂×D₈	1	1	yes	characteristic
177	C₃×C₄×C₅	#135	1	1	yes	characteristic
178	C₃×C₄×C₅	AGL(1,ℤ/8)	1	1	yes	characteristic
179	C₃×C₄×C₅	AGL(1,ℤ/8)	1	1	yes	characteristic
180	C₅×Dic₃	—	4	1	no	—
181	C₅×Dic₃	—	4	1	no	—
182	C₂×C₃×Q₈	—	2	1	no	—
183	#239	—	4	2	no	—
184	#239	—	4	2	no	—
185	C₂×D₁₂	—	2	2	no	—
186	C₂×D₁₂	—	2	1	no	—
187	C₂×D₁₂	—	2	1	no	—
188	C₂×D₁₂	—	2	1	no	—
189	C₂×D₁₂	C₅×D₄	1	1	yes	characteristic
190	C₂×D₁₂	C₅×D₄	1	1	yes	characteristic
191	C₂×C₄×D₃	—	2	2	no	—
192	C₂×C₄×D₃	—	2	1	no	—
193	C₂×C₄×D₃	—	2	1	no	—
194	C₂×C₃×C₈	—	2	1	no	—
195	C₂×C₃×C₈	—	2	1	no	—
196	C₃×C₄⋊C₄	—	2	1	no	—
197	C₃×C₄⋊C₄	C₅×D₄	1	2	yes	—
198	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
199	(C₂×D₃)⋊C₄	—	2	2	no	—
200	(C₂×D₃)⋊C₄	—	2	1	no	—
201	(C₂×D₃)⋊C₄	—	2	1	no	—
202	C₄⋊Dic₃	C₅×D₄	1	1	yes	characteristic
203	C₄⋊Dic₃	C₅×D₄	1	1	yes	characteristic
204	Dic₃⋊C₄	—	2	2	no	—
205	C₂×C₃⋊C₈	—	2	1	no	—
206	D₂₄	—	4	2	no	—
207	D₂₄	—	4	2	no	—
208	C₂³×C₅	—	6	1	no	—
209	C₂³×C₅	—	6	1	no	—
210	C₂³×C₅	—	12	1	no	—
211	C₅×Q₈	—	4	1	no	—
212	C₅×Q₈	—	4	1	no	—
213	C₅×D₄	—	3	2	no	—
214	C₅×D₄	—	6	1	no	—
215	C₅×D₄	—	6	1	no	—
216	C₅×D₄	—	6	1	no	—
217	C₅×D₄	—	12	2	no	—
218	C₅×D₄	—	12	4	no	—
219	C₅×D₄	—	12	1	no	—
220	C₅×D₄	—	12	1	no	—
221	C₅×D₄	—	12	1	no	—
222	C₅×D₄	—	12	1	no	—
223	C₂×C₄×C₅	—	2	2	no	—
224	C₂×C₄×C₅	—	6	1	no	—
225	C₂×C₄×C₅	—	6	1	no	—
226	C₂×C₄×C₅	—	12	4	no	—
227	C₂×C₄×C₅	—	12	1	no	—
228	C₂×C₄×C₅	—	12	1	no	—
229	C₂×C₄×C₅	—	12	1	no	—
230	C₂×C₄×C₅	—	12	1	no	—
231	C₂×C₄×C₅	C₂×D₁₂	1	1	yes	characteristic
232	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
233	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
234	C₅×C₈	—	4	1	no	—
235	C₅×C₈	—	4	1	no	—
236	C₅×C₈	—	12	1	no	—
237	C₂×#41	—	6	1	no	—
238	C₂×D₈	—	6	1	no	—
239	C₂×D₈	—	6	1	no	—
240	C₄⋊Q₈	C₂×C₅×D₃	1	1	yes	characteristic
241	#127	—	3	1	no	—
242	#123	—	6	2	no	—
243	C₂²⋊Q₈	—	6	1	no	—
244	#121	—	6	1	no	—
245	C₄×D₄	—	3	1	no	—
246	C₄×D₄	—	3	1	no	—
247	C₂×C₄⋊C₄	—	6	1	no	—
248	C₄⋊C₈	C₂×C₅×D₃	1	1	yes	characteristic
249	C₄⋊C₈	C₂×C₅×D₃	1	1	yes	characteristic
250	#102	—	6	1	no	—
251	#102	—	6	1	no	—
252	#102	—	6	2	no	—
253	C₄×C₈	—	3	1	no	—
254	C₂×C₃×C₅	#447	1	1	yes	characteristic
255	C₂×C₃×C₅	#449	1	1	yes	characteristic
256	C₂×C₃×C₅	#454	1	1	yes	characteristic
257	C₅×D₃	—	4	2	no	—
258	C₅×D₃	—	8	1	no	—
259	C₅×D₃	—	16	1	no	—
260	C₂²×D₃	—	2	1	no	—
261	C₂²×D₃	—	2	1	no	—
262	C₂²×D₃	—	4	1	no	—
263	C₃×Q₈	—	4	1	no	—
264	C₃×Q₈	—	4	1	no	—
265	C₂×C₃×C₄	—	2	2	no	—
266	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
267	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
268	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
269	C₂×Dic₃	—	2	1	no	—
270	C₂×Dic₃	—	2	1	no	—
271	D₁₂	—	2	1	no	—
272	D₁₂	—	2	1	no	—
273	D₁₂	—	2	1	no	—
274	D₁₂	—	4	2	no	—
275	D₁₂	—	4	4	no	—
276	D₁₂	—	4	1	no	—
277	D₁₂	—	4	1	no	—
278	D₁₂	—	4	1	no	—
279	D₁₂	—	4	1	no	—
280	D₁₂	C₅×D₈	1	2	yes	complemented
281	C₄×D₃	—	4	4	no	—
282	C₄×D₃	—	4	1	no	—
283	C₄×D₃	—	4	1	no	—
284	C₄×D₃	—	4	1	no	—
285	C₄×D₃	—	4	1	no	—
286	C₃×C₈	—	4	1	no	—
287	C₃×C₈	—	4	1	no	—
288	C₃⋊C₈	—	4	1	no	—
289	C₂²×C₅	—	6	2	no	—
290	C₂²×C₅	—	12	1	no	—
291	C₂²×C₅	—	12	1	no	—
292	C₂²×C₅	—	12	1	no	—
293	C₂²×C₅	—	12	1	no	—
294	C₂²×C₅	—	12	1	no	—
295	C₂²×C₅	—	24	1	no	—
296	C₂²×C₅	—	24	1	no	—
297	C₂²×C₅	—	24	1	no	—
298	C₂²×C₅	#882	1	1	yes	characteristic
299	C₄×C₅	—	2	1	no	—
300	C₄×C₅	—	4	2	no	—
301	C₄×C₅	—	12	1	no	—
302	C₄×C₅	—	12	1	no	—
303	C₄×C₅	D₃×D₈	1	1	yes	characteristic
304	C₄×C₅	#914	1	1	yes	characteristic
305	C₄×C₅	#914	1	1	yes	characteristic
306	C₄×C₅	#919	1	1	yes	characteristic
307	#41	—	12	2	no	—
308	#41	—	12	2	no	—
309	C₂×Q₈	—	2	1	no	—
310	C₂×D₄	—	3	1	no	—
311	C₂×D₄	—	3	1	no	—
312	C₂×D₄	—	6	2	no	—
313	C₂×D₄	—	6	1	no	—
314	C₂×D₄	—	6	1	no	—
315	C₂×D₄	—	6	1	no	—
316	C₂²×C₄	—	6	2	no	—
317	C₂²×C₄	—	6	1	no	—
318	C₂²×C₄	—	6	1	no	—
319	D₈	—	12	2	no	—
320	D₈	—	12	2	no	—
321	C₂×C₈	—	2	1	no	—
322	C₂×C₈	—	2	1	no	—
323	C₂×C₈	—	6	1	no	—
324	C₄⋊C₄	—	2	1	no	—
325	C₄⋊C₄	—	3	1	no	—
326	C₄⋊C₄	—	3	1	no	—
327	C₄⋊C₄	—	6	2	no	—
328	C₄⋊C₄	C₅×D₁₂	1	2	yes	—
329	C₂²⋊C₄	—	6	2	no	—
330	C₂²⋊C₄	—	6	1	no	—
331	C₂²⋊C₄	—	6	1	no	—
332	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
333	C₃×C₅	#1625	1	1	yes	characteristic, complemented, Hall
334	C₂²×C₃	C₅×#120	1	1	yes	characteristic
335	C₂×D₃	—	2	2	no	—
336	C₂×D₃	—	4	1	no	—
337	C₂×D₃	—	4	1	no	—
338	C₂×D₃	—	4	1	no	—
339	C₂×D₃	—	4	1	no	—
340	C₂×D₃	—	4	1	no	—
341	C₂×D₃	—	8	1	no	—
342	C₂×D₃	—	8	1	no	—
343	C₂×D₃	—	8	1	no	—
344	C₃×C₄	—	2	1	no	—
345	C₃×C₄	—	4	2	no	—
346	C₃×C₄	C₂×C₅×D₈	1	1	yes	characteristic
347	C₃×C₄	C₅×#135	1	1	yes	characteristic
348	C₃×C₄	C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
349	C₃×C₄	C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
350	Dic₃	—	4	1	no	—
351	Dic₃	—	4	1	no	—
352	C₂×C₅	—	12	2	no	—
353	C₂×C₅	—	24	1	no	—
354	C₂×C₅	—	48	1	no	—
355	C₂×C₅	#4753	1	1	yes	characteristic
356	C₂×C₅	#4773	1	1	yes	characteristic
357	C₂×C₅	#4810	1	1	yes	characteristic
358	C₂³	—	6	1	no	—
359	C₂³	—	6	1	no	—
360	C₂³	—	12	1	no	—
361	Q₈	—	4	1	no	—
362	Q₈	—	4	1	no	—
363	D₄	—	3	2	no	—
364	D₄	—	6	1	no	—
365	D₄	—	6	1	no	—
366	D₄	—	6	1	no	—
367	D₄	—	12	2	no	—
368	D₄	—	12	4	no	—
369	D₄	—	12	1	no	—
370	D₄	—	12	1	no	—
371	D₄	—	12	1	no	—
372	D₄	—	12	1	no	—
373	C₂×C₄	—	2	2	no	—
374	C₂×C₄	—	6	1	no	—
375	C₂×C₄	—	6	1	no	—
376	C₂×C₄	—	12	4	no	—
377	C₂×C₄	—	12	1	no	—
378	C₂×C₄	—	12	1	no	—
379	C₂×C₄	—	12	1	no	—
380	C₂×C₄	—	12	1	no	—
381	C₂×C₄	C₂×C₅×D₁₂	1	1	yes	characteristic
382	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
383	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
384	C₈	—	4	1	no	—
385	C₈	—	4	1	no	—
386	C₈	—	12	1	no	—
387	C₂×C₃	C₅×#447	1	1	yes	characteristic
388	C₂×C₃	C₅×#449	1	1	yes	characteristic
389	C₂×C₃	C₅×#454	1	1	yes	characteristic
390	D₃	—	4	2	no	—
391	D₃	—	8	1	no	—
392	D₃	—	16	1	no	—
393	C₅	#68432	1	1	yes	characteristic, direct product factor, Sylow
394	C₂²	—	6	2	no	—
395	C₂²	—	12	1	no	—
396	C₂²	—	12	1	no	—
397	C₂²	—	12	1	no	—
398	C₂²	—	12	1	no	—
399	C₂²	—	12	1	no	—
400	C₂²	—	24	1	no	—
401	C₂²	—	24	1	no	—
402	C₂²	—	24	1	no	—
403	C₂²	C₅×#882	1	1	yes	characteristic
404	C₄	—	2	1	no	—
405	C₄	—	4	2	no	—
406	C₄	—	12	1	no	—
407	C₄	—	12	1	no	—
408	C₄	C₅×D₃×D₈	1	1	yes	characteristic
409	C₄	C₅×#914	1	1	yes	characteristic
410	C₄	C₅×#914	1	1	yes	characteristic
411	C₄	C₅×#919	1	1	yes	characteristic
412	C₃	C₅×#1625	1	1	yes	characteristic, complemented, Sylow
413	C₂	—	12	2	no	—
414	C₂	—	24	1	no	—
415	C₂	—	48	1	no	—
416	C₂	C₅×#4753	1	1	yes	characteristic
417	C₂	C₅×#4773	1	1	yes	characteristic
418	C₂	C₅×#4810	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₅	#882
commutator, cosocle	C₃×C₄²	C₂³×C₅
Frattini	C₄²	C₂²×C₅×D₃
Fitting	C₃×C₅×#332	C₂
socle	C₂²×C₃×C₅	#120
hypercenter	C₅×#332	D₃
hypocenter	C₃	C₅×#1625
LCS	G ▷ C₃×C₄² ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₄²×C₅ ◁ C₅×#332

Complements

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

N	H ≅ G/N	type
1. C₅×#5726	C₂	semidirect
2. C₅×#5088	C₂	semidirect
3. C₅×#4843	C₂	semidirect
4. C₅×#4843	C₂	semidirect
5. C₃×C₅×#332	C₂	semidirect
6. C₅×#4483	C₂	semidirect
7. C₅×#4483	C₂	semidirect
26. #68432	C₅	direct (N × H)
31. C₅×#332	D₃	semidirect
60. #5726	C₂×C₅	semidirect
61. #5088	C₂×C₅	semidirect
62. #4843	C₂×C₅	semidirect
63. #4843	C₂×C₅	semidirect
64. C₃×#332	C₂×C₅	semidirect
65. #4483	C₂×C₅	semidirect
66. #4483	C₂×C₅	semidirect
105. C₅×D₁₂	D₈	semidirect
161. #332	C₅×D₃	semidirect
280. D₁₂	C₅×D₈	semidirect
333. C₃×C₅	#1625	semidirect
393. C₅	#68432	direct (N × H)
412. C₃	C₅×#1625	semidirect

Maximal subgroups

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

subgroup	index
C₅×#5726	2
C₅×#5088	2
C₅×#4843	2
C₃×C₅×#332	2
C₅×#4483	2
C₅×#1625	3
#68432	5

Subgroups — C5×#68432 #14289097

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#68432 #14289097