Subgroups — C₅×#69852 #14281927

Order 1920.

468 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#5479	C₂	1	1	yes	maximal, characteristic
2	C₃×C₄×C₅×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×C₄⋊(C₃⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#4459	C₂	1	2	yes	maximal, complemented
5	C₅×#4456	C₂	1	2	yes	maximal, complemented
6	C₅×#1483	—	3	1	no	maximal, Hall
7	C₂×C₃×C₅×M₁₆	—	2	1	no	—
8	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
9	C₅×#930	C₄	1	1	yes	characteristic
10	C₅×#929	—	2	1	no	—
11	C₄×C₅×#67	—	2	1	no	—
12	C₅×#924	C₄	1	1	yes	characteristic
13	C₂²×C₅×C₃⋊C₈	—	2	1	no	—
14	C₅×#876	—	2	1	no	—
15	C₅×#875	C₄	1	1	yes	characteristic
16	C₄×C₅×D₁₂	C₂²	1	1	yes	characteristic
17	C₅×#872	—	2	1	no	—
18	C₅×#870	C₄	1	1	yes	characteristic
19	C₄×C₅×Dic₆	C₂²	1	1	yes	characteristic
20	C₃×C₅×#97	—	2	1	no	—
21	C₃×C₄×C₅×C₈	C₂²	1	2	yes	—
22	C₅×C₄⋊(C₃⋊C₈)	—	2	1	no	—
23	C₅×C₄⋊(C₃⋊C₈)	C₂²	1	2	yes	—
24	#69852	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
25	C₅×#529	—	3	1	no	—
26	C₂×C₅×C₄⋊C₈	—	3	1	no	—
27	C₄×C₅×M₁₆	D₃	1	1	yes	characteristic, complemented
28	C₅×Q₈⋊C₈	—	3	2	no	—
29	C₅×D₄⋊C₈	—	3	2	no	—
30	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
31	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
32	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
33	C₂×C₅×#67	—	2	1	no	—
34	C₂×C₅×D₁₂	C₂×C₄	1	1	yes	characteristic
35	C₂×C₄×C₅×D₃	—	2	1	no	—
36	C₂×C₅×Dic₆	C₂×C₄	1	1	yes	characteristic
37	C₃×C₅×M₁₆	—	2	4	no	—
38	C₂×C₃×C₅×C₈	—	2	2	no	—
39	C₃×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
40	C₃×C₄²×C₅	D₄	1	1	yes	characteristic
41	C₃×C₄²×C₅	D₄	1	1	yes	characteristic
42	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
43	C₅×#217	—	2	1	no	—
44	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
45	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
46	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
47	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
48	C₅×C₄⋊Dic₃	C₂×C₄	1	1	yes	characteristic
49	C₅×C₄⋊Dic₃	C₂×C₄	1	1	yes	characteristic
50	C₅×Dic₃⋊C₄	—	2	1	no	—
51	C₅×Dic₃⋊C₄	—	2	1	no	—
52	C₅×Dic₃⋊C₄	—	2	1	no	—
53	C₅×Dic₃⋊C₄	—	2	1	no	—
54	C₄×C₅×Dic₃	—	2	1	no	—
55	C₂×C₅×C₃⋊C₈	—	2	2	no	—
56	C₂×C₅×C₃⋊C₈	—	4	2	no	—
57	#5479	C₂×C₅	1	1	yes	characteristic
58	C₃×C₄×M₁₆	C₂×C₅	1	1	yes	characteristic, complemented
59	C₂×C₄⋊(C₃⋊C₈)	C₂×C₅	1	1	yes	characteristic, complemented
60	#4459	C₂×C₅	1	2	yes	complemented
61	#4456	C₂×C₅	1	2	yes	complemented
62	C₂×C₅×M₁₆	—	2	1	no	—
63	C₂²×C₅×C₈	—	6	1	no	—
64	C₅×#126	—	6	1	no	—
65	C₅×#125	—	3	1	no	—
66	C₅×#124	—	3	1	no	—
67	C₅×#123	—	6	1	no	—
68	C₅×C₂²⋊Q₈	—	3	1	no	—
69	C₅×#121	—	3	1	no	—
70	C₄×C₅×Q₈	—	3	1	no	—
71	C₄×C₅×D₄	—	3	1	no	—
72	C₄×C₅×D₄	—	6	1	no	—
73	C₅×#117	—	6	1	no	—
74	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
75	C₅×C₄⋊C₈	—	3	2	no	—
76	C₅×C₄⋊C₈	—	6	1	no	—
77	C₅×#97	—	2	1	no	—
78	C₄×C₅×C₈	C₂×D₃	1	2	yes	—
79	#1483	—	3	1	no	Sylow
80	C₂³×C₃×C₅	C₂²⋊C₄	1	1	yes	characteristic
81	C₂²×C₅×D₃	—	2	1	no	—
82	C₂×C₃×C₄×C₅	—	2	2	no	—
83	C₂×C₃×C₄×C₅	—	2	2	no	—
84	C₂×C₃×C₄×C₅	—	2	1	no	—
85	C₂×C₃×C₄×C₅	—	2	1	no	—
86	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
87	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
88	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
89	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
90	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
91	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
92	C₅×#67	—	4	2	no	—
93	C₂×C₅×Dic₃	—	2	1	no	—
94	C₂×C₅×Dic₃	—	2	1	no	—
95	C₂×C₅×Dic₃	—	2	1	no	—
96	C₅×D₁₂	—	2	2	no	—
97	C₄×C₅×D₃	—	4	1	no	—
98	C₄×C₅×D₃	—	4	1	no	—
99	C₅×Dic₆	—	2	2	no	—
100	C₃×C₅×C₈	—	2	4	no	—
101	C₅×C₃⋊C₈	—	4	2	no	—
102	C₂×C₃×M₁₆	—	2	1	no	—
103	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
104	#930	C₄×C₅	1	1	yes	characteristic
105	#929	—	2	1	no	—
106	C₄×#67	—	2	1	no	—
107	#924	C₄×C₅	1	1	yes	characteristic
108	C₂²×C₃⋊C₈	—	2	1	no	—
109	#876	—	2	1	no	—
110	#875	C₄×C₅	1	1	yes	characteristic
111	C₄×D₁₂	C₂²×C₅	1	1	yes	characteristic
112	#872	—	2	1	no	—
113	#870	C₄×C₅	1	1	yes	characteristic
114	C₄×Dic₆	C₂²×C₅	1	1	yes	characteristic
115	C₃×#97	—	2	1	no	—
116	C₃×C₄×C₈	C₂²×C₅	1	2	yes	—
117	C₄⋊(C₃⋊C₈)	—	2	1	no	—
118	C₄⋊(C₃⋊C₈)	C₂²×C₅	1	2	yes	—
119	C₂×C₅×Q₈	—	3	1	no	—
120	C₂×C₅×D₄	—	3	1	no	—
121	C₂×C₅×D₄	—	6	1	no	—
122	C₂²×C₄×C₅	—	6	1	no	—
123	C₂²×C₄×C₅	C₄×D₃	1	1	yes	characteristic
124	C₂²×C₄×C₅	D₁₂	1	1	yes	characteristic
125	C₂²×C₄×C₅	#67	1	1	yes	characteristic
126	C₅×M₁₆	—	2	4	no	—
127	C₂×C₅×C₈	—	2	2	no	—
128	C₂×C₅×C₈	—	6	2	no	—
129	C₂×C₅×C₈	—	12	2	no	—
130	C₅×C₄⋊C₄	—	3	1	no	—
131	C₅×C₄⋊C₄	—	3	1	no	—
132	C₅×C₄⋊C₄	—	6	1	no	—
133	C₅×C₄⋊C₄	—	6	1	no	—
134	C₅×C₄⋊C₄	—	6	1	no	—
135	C₅×C₄⋊C₄	—	6	1	no	—
136	C₅×C₂²⋊C₄	—	6	1	no	—
137	C₅×C₂²⋊C₄	—	6	1	no	—
138	C₅×C₂²⋊C₄	—	6	1	no	—
139	C₅×C₂²⋊C₄	—	6	1	no	—
140	C₅×C₂²⋊C₄	—	6	1	no	—
141	C₄²×C₅	—	6	1	no	—
142	C₄²×C₅	C₄×D₃	1	1	yes	characteristic
143	C₄²×C₅	D₁₂	1	1	yes	characteristic
144	C₄²×C₅	#67	1	1	yes	characteristic
145	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
146	#529	—	3	1	no	—
147	C₂×C₄⋊C₈	—	3	1	no	—
148	C₄×M₁₆	C₅×D₃	1	1	yes	characteristic, complemented
149	Q₈⋊C₈	—	3	2	no	—
150	D₄⋊C₈	—	3	2	no	—
151	C₂²×C₃×C₅	—	2	1	no	—
152	C₂²×C₃×C₅	—	2	1	no	—
153	C₂²×C₃×C₅	#104	1	2	yes	—
154	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
155	C₂×C₅×D₃	—	4	1	no	—
156	C₂×C₅×D₃	—	4	1	no	—
157	C₂×C₅×D₃	—	4	1	no	—
158	C₃×C₄×C₅	—	2	1	no	—
159	C₃×C₄×C₅	—	2	1	no	—
160	C₃×C₄×C₅	—	2	1	no	—
161	C₃×C₄×C₅	—	2	1	no	—
162	C₃×C₄×C₅	#131	1	2	yes	—
163	C₃×C₄×C₅	AGL(1,ℤ/8)	1	1	yes	characteristic
164	C₃×C₄×C₅	#137	1	1	yes	characteristic
165	C₅×Dic₃	—	4	1	no	—
166	C₅×Dic₃	—	4	1	no	—
167	C₅×Dic₃	—	4	1	no	—
168	C₂²×C₃×C₄	C₂×C₄×C₅	1	1	yes	characteristic
169	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
170	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
171	C₂×#67	—	2	1	no	—
172	C₂×D₁₂	C₂×C₄×C₅	1	1	yes	characteristic
173	C₂×C₄×D₃	—	2	1	no	—
174	C₂×Dic₆	C₂×C₄×C₅	1	1	yes	characteristic
175	C₃×M₁₆	—	2	4	no	—
176	C₂×C₃×C₈	—	2	2	no	—
177	C₃×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
178	C₃×C₄²	C₅×D₄	1	1	yes	characteristic
179	C₃×C₄²	C₅×D₄	1	1	yes	characteristic
180	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
181	#217	—	2	1	no	—
182	(C₂×D₃)⋊C₄	—	2	1	no	—
183	(C₂×D₃)⋊C₄	—	2	1	no	—
184	(C₂×D₃)⋊C₄	—	2	1	no	—
185	(C₂×D₃)⋊C₄	—	2	1	no	—
186	C₄⋊Dic₃	C₂×C₄×C₅	1	1	yes	characteristic
187	C₄⋊Dic₃	C₂×C₄×C₅	1	1	yes	characteristic
188	Dic₃⋊C₄	—	2	1	no	—
189	Dic₃⋊C₄	—	2	1	no	—
190	Dic₃⋊C₄	—	2	1	no	—
191	Dic₃⋊C₄	—	2	1	no	—
192	C₄×Dic₃	—	2	1	no	—
193	C₂×C₃⋊C₈	—	2	2	no	—
194	C₂×C₃⋊C₈	—	4	2	no	—
195	C₂³×C₅	—	6	1	no	—
196	C₂³×C₅	(C₂×D₃)⋊C₄	1	1	yes	characteristic
197	C₅×Q₈	—	6	2	no	—
198	C₅×D₄	—	6	2	no	—
199	C₅×D₄	—	12	2	no	—
200	C₂×C₄×C₅	—	2	2	no	—
201	C₂×C₄×C₅	—	2	2	no	—
202	C₂×C₄×C₅	—	2	1	no	—
203	C₂×C₄×C₅	—	2	1	no	—
204	C₂×C₄×C₅	—	6	1	no	—
205	C₂×C₄×C₅	—	6	1	no	—
206	C₂×C₄×C₅	—	6	1	no	—
207	C₂×C₄×C₅	—	12	1	no	—
208	C₂×C₄×C₅	—	12	1	no	—
209	C₂×C₄×C₅	(C₂×D₃)⋊C₄	1	1	yes	characteristic
210	C₂×C₄×C₅	(C₂×D₃)⋊C₄	1	1	yes	characteristic
211	C₂×C₄×C₅	(C₂×D₃)⋊C₄	1	1	yes	characteristic
212	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
213	C₂×C₄×C₅	C₂×D₁₂	1	1	yes	characteristic
214	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
215	C₅×C₈	—	2	4	no	—
216	C₅×C₈	—	12	2	no	—
217	C₂×M₁₆	—	2	1	no	—
218	C₂²×C₈	—	6	1	no	—
219	#126	—	6	1	no	—
220	#125	—	3	1	no	—
221	#124	—	3	1	no	—
222	#123	—	6	1	no	—
223	C₂²⋊Q₈	—	3	1	no	—
224	#121	—	3	1	no	—
225	C₄×Q₈	—	3	1	no	—
226	C₄×D₄	—	3	1	no	—
227	C₄×D₄	—	6	1	no	—
228	#117	—	6	1	no	—
229	C₂×C₄²	C₂×C₅×D₃	1	1	yes	characteristic
230	C₄⋊C₈	—	3	2	no	—
231	C₄⋊C₈	—	6	1	no	—
232	#97	—	2	1	no	—
233	C₄×C₈	C₂×C₅×D₃	1	2	yes	—
234	C₂×C₃×C₅	—	2	2	no	—
235	C₂×C₃×C₅	#408	1	1	yes	characteristic
236	C₂×C₃×C₅	#417	1	1	yes	characteristic
237	C₂×C₃×C₅	C₂×#104	1	1	yes	characteristic
238	C₅×D₃	—	8	1	no	—
239	C₂³×C₃	C₅×C₂²⋊C₄	1	1	yes	characteristic
240	C₂²×D₃	—	2	1	no	—
241	C₂×C₃×C₄	—	2	2	no	—
242	C₂×C₃×C₄	—	2	2	no	—
243	C₂×C₃×C₄	—	2	1	no	—
244	C₂×C₃×C₄	—	2	1	no	—
245	C₂×C₃×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
246	C₂×C₃×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
247	C₂×C₃×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
248	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
249	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
250	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
251	#67	—	4	2	no	—
252	C₂×Dic₃	—	2	1	no	—
253	C₂×Dic₃	—	2	1	no	—
254	C₂×Dic₃	—	2	1	no	—
255	D₁₂	—	2	2	no	—
256	C₄×D₃	—	4	1	no	—
257	C₄×D₃	—	4	1	no	—
258	Dic₆	—	2	2	no	—
259	C₃×C₈	—	2	4	no	—
260	C₃⋊C₈	—	4	2	no	—
261	C₂²×C₅	—	2	1	no	—
262	C₂²×C₅	—	2	1	no	—
263	C₂²×C₅	—	12	1	no	—
264	C₂²×C₅	—	12	1	no	—
265	C₂²×C₅	—	12	1	no	—
266	C₂²×C₅	#805	1	2	yes	—
267	C₂²×C₅	C₂×(C₂×D₃)⋊C₄	1	1	yes	characteristic
268	C₄×C₅	—	2	1	no	—
269	C₄×C₅	—	2	1	no	—
270	C₄×C₅	—	2	1	no	—
271	C₄×C₅	—	2	1	no	—
272	C₄×C₅	—	12	1	no	—
273	C₄×C₅	—	12	1	no	—
274	C₄×C₅	—	12	1	no	—
275	C₄×C₅	#907	1	2	yes	—
276	C₄×C₅	#908	1	1	yes	characteristic
277	C₄×C₅	#909	1	1	yes	characteristic
278	C₂×Q₈	—	3	1	no	—
279	C₂×D₄	—	3	1	no	—
280	C₂×D₄	—	6	1	no	—
281	C₂²×C₄	—	6	1	no	—
282	C₂²×C₄	C₄×C₅×D₃	1	1	yes	characteristic
283	C₂²×C₄	C₅×D₁₂	1	1	yes	characteristic
284	C₂²×C₄	C₅×#67	1	1	yes	characteristic
285	M₁₆	—	2	4	no	—
286	C₂×C₈	—	2	2	no	—
287	C₂×C₈	—	6	2	no	—
288	C₂×C₈	—	12	2	no	—
289	C₄⋊C₄	—	3	1	no	—
290	C₄⋊C₄	—	3	1	no	—
291	C₄⋊C₄	—	6	1	no	—
292	C₄⋊C₄	—	6	1	no	—
293	C₄⋊C₄	—	6	1	no	—
294	C₄⋊C₄	—	6	1	no	—
295	C₂²⋊C₄	—	6	1	no	—
296	C₂²⋊C₄	—	6	1	no	—
297	C₂²⋊C₄	—	6	1	no	—
298	C₂²⋊C₄	—	6	1	no	—
299	C₂²⋊C₄	—	6	1	no	—
300	C₄²	—	6	1	no	—
301	C₄²	C₄×C₅×D₃	1	1	yes	characteristic
302	C₄²	C₅×D₁₂	1	1	yes	characteristic
303	C₄²	C₅×#67	1	1	yes	characteristic
304	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
305	C₃×C₅	#1483	1	1	yes	characteristic, complemented, Hall
306	C₂²×C₃	—	2	1	no	—
307	C₂²×C₃	—	2	1	no	—
308	C₂²×C₃	C₅×#104	1	2	yes	—
309	C₂²×C₃	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
310	C₂×D₃	—	4	1	no	—
311	C₂×D₃	—	4	1	no	—
312	C₂×D₃	—	4	1	no	—
313	C₃×C₄	—	2	1	no	—
314	C₃×C₄	—	2	1	no	—
315	C₃×C₄	—	2	1	no	—
316	C₃×C₄	—	2	1	no	—
317	C₃×C₄	C₅×#131	1	2	yes	—
318	C₃×C₄	C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
319	C₃×C₄	C₅×#137	1	1	yes	characteristic
320	Dic₃	—	4	1	no	—
321	Dic₃	—	4	1	no	—
322	Dic₃	—	4	1	no	—
323	C₂×C₅	—	2	2	no	—
324	C₂×C₅	—	24	1	no	—
325	C₂×C₅	C₂×#805	1	1	yes	characteristic
326	C₂×C₅	#5129	1	1	yes	characteristic
327	C₂×C₅	#5133	1	1	yes	characteristic
328	C₂³	—	6	1	no	—
329	C₂³	C₅×(C₂×D₃)⋊C₄	1	1	yes	characteristic
330	Q₈	—	6	2	no	—
331	D₄	—	6	2	no	—
332	D₄	—	12	2	no	—
333	C₂×C₄	—	2	2	no	—
334	C₂×C₄	—	2	2	no	—
335	C₂×C₄	—	2	1	no	—
336	C₂×C₄	—	2	1	no	—
337	C₂×C₄	—	6	1	no	—
338	C₂×C₄	—	6	1	no	—
339	C₂×C₄	—	6	1	no	—
340	C₂×C₄	—	12	1	no	—
341	C₂×C₄	—	12	1	no	—
342	C₂×C₄	C₅×(C₂×D₃)⋊C₄	1	1	yes	characteristic
343	C₂×C₄	C₅×(C₂×D₃)⋊C₄	1	1	yes	characteristic
344	C₂×C₄	C₅×(C₂×D₃)⋊C₄	1	1	yes	characteristic
345	C₂×C₄	C₂×C₄×C₅×D₃	1	1	yes	characteristic
346	C₂×C₄	C₂×C₅×D₁₂	1	1	yes	characteristic
347	C₂×C₄	C₂×C₅×#67	1	1	yes	characteristic
348	C₈	—	2	4	no	—
349	C₈	—	12	2	no	—
350	C₂×C₃	—	2	2	no	—
351	C₂×C₃	C₅×#408	1	1	yes	characteristic
352	C₂×C₃	C₅×#417	1	1	yes	characteristic
353	C₂×C₃	C₂×C₅×#104	1	1	yes	characteristic
354	D₃	—	8	1	no	—
355	C₅	#69852	1	1	yes	characteristic, direct product factor, Sylow
356	C₂²	—	2	1	no	—
357	C₂²	—	2	1	no	—
358	C₂²	—	12	1	no	—
359	C₂²	—	12	1	no	—
360	C₂²	—	12	1	no	—
361	C₂²	C₅×#805	1	2	yes	—
362	C₂²	C₂×C₅×(C₂×D₃)⋊C₄	1	1	yes	characteristic
363	C₄	—	2	1	no	—
364	C₄	—	2	1	no	—
365	C₄	—	2	1	no	—
366	C₄	—	2	1	no	—
367	C₄	—	12	1	no	—
368	C₄	—	12	1	no	—
369	C₄	—	12	1	no	—
370	C₄	C₅×#907	1	2	yes	—
371	C₄	C₅×#908	1	1	yes	characteristic
372	C₄	C₅×#909	1	1	yes	characteristic
373	C₃	C₅×#1483	1	1	yes	characteristic, complemented, Sylow
374	C₂	—	2	2	no	—
375	C₂	—	24	1	no	—
376	C₂	C₂×C₅×#805	1	1	yes	characteristic
377	C₂	C₅×#5129	1	1	yes	characteristic
378	C₂	C₅×#5133	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₅	C₂×D₁₂
commutator	C₂×C₃×C₄	C₂²×C₄×C₅
Frattini	C₄²	C₂²×C₅×D₃
Fitting	C₃×C₄×C₅×M₁₆	C₂
socle	C₂²×C₃×C₅	C₂×C₂²⋊C₄
prime radical	C₅×#930	C₄
cosocle	C₃×C₄²	C₂³×C₅
hypercenter	C₄×C₅×M₁₆	D₃
hypocenter	C₃	C₅×#1483
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₄×C₅ ◁ C₂×C₄²×C₅ ◁ C₄×C₅×M₁₆

Complements

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

N	H ≅ G/N	type
2. C₃×C₄×C₅×M₁₆	C₂	semidirect
3. C₂×C₅×C₄⋊(C₃⋊C₈)	C₂	semidirect
4. C₅×#4459	C₂	semidirect
5. C₅×#4456	C₂	semidirect
24. #69852	C₅	direct (N × H)
27. C₄×C₅×M₁₆	D₃	semidirect
58. C₃×C₄×M₁₆	C₂×C₅	semidirect
59. C₂×C₄⋊(C₃⋊C₈)	C₂×C₅	semidirect
60. #4459	C₂×C₅	semidirect
61. #4456	C₂×C₅	semidirect
148. C₄×M₁₆	C₅×D₃	semidirect
305. C₃×C₅	#1483	semidirect
355. C₅	#69852	direct (N × H)
373. C₃	C₅×#1483	semidirect

Maximal subgroups

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

subgroup	index
C₅×#5479	2
C₃×C₄×C₅×M₁₆	2
C₂×C₅×C₄⋊(C₃⋊C₈)	2
C₅×#4459	2
C₅×#4456	2
C₅×#1483	3
#69852	5

Subgroups — C5×#69852 #14281927

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#69852 #14281927