Subgroups — C₅×#68711 #14298578

Order 1920.

524 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#5522	C₂	1	1	yes	maximal, characteristic
2	C₅×#5132	C₂	1	1	yes	maximal, characteristic
3	C₅×#5006	C₂	1	1	yes	maximal, characteristic
4	C₃×C₅×H(3,ℤ/4)	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#4555	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#4532	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#4531	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#1827	—	3	1	no	maximal, Hall
9	C₂×C₅×#235	C₂²	1	1	yes	characteristic
10	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
11	C₃×C₅×#117	C₂²	1	1	yes	characteristic
12	C₃×C₅×#117	C₂²	1	1	yes	characteristic
13	C₅×#926	C₂²	1	1	yes	characteristic
14	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
15	C₂×C₅×#208	C₂²	1	1	yes	characteristic
16	C₅×#893	—	2	1	no	—
17	C₅×#887	—	2	1	no	—
18	C₅×#67⋊C₄	—	2	2	no	—
19	C₅×#872	C₄	1	2	yes	complemented
20	C₄²×C₅×D₃	C₄	1	2	yes	complemented
21	C₅×#824	—	2	1	no	—
22	C₅×#823	—	2	1	no	—
23	C₅×#806	—	2	2	no	—
24	#68711	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
25	C₄×C₅×#41	—	3	1	no	—
26	C₅×#413	—	3	1	no	—
27	C₅×#410	—	3	1	no	—
28	C₅×#339	—	3	1	no	—
29	C₅×#339	—	3	1	no	—
30	C₅×H(3,ℤ/4)	—	3	1	no	—
31	C₅×H(3,ℤ/4)	D₃	1	1	yes	characteristic, complemented
32	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
33	C₂×C₅×#67	D₄	1	2	yes	—
34	C₂²×C₅×Dic₃	—	2	1	no	—
35	C₅×#235	—	2	1	no	—
36	C₅×#235	—	2	1	no	—
37	C₅×#235	—	2	1	no	—
38	C₅×#235	—	2	1	no	—
39	C₂×C₅×D₁₂	D₄	1	1	yes	characteristic
40	C₂×C₄×C₅×D₃	—	2	2	no	—
41	C₂×C₄×C₅×D₃	C₂×C₄	1	2	yes	—
42	C₂×C₅×Dic₆	D₄	1	1	yes	characteristic
43	C₃×C₅×M₁₆	—	2	1	no	—
44	C₃×C₅×M₁₆	—	2	1	no	—
45	C₂×C₃×C₅×C₈	—	2	1	no	—
46	C₃×C₅×C₄⋊C₄	—	2	1	no	—
47	C₃×C₅×C₄⋊C₄	—	2	1	no	—
48	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
49	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
50	C₃×C₄²×C₅	—	2	1	no	—
51	C₃×C₄²×C₅	C₂×C₄	1	2	yes	—
52	C₅×#217	—	2	1	no	—
53	C₅×(C₂×D₃)⋊C₄	—	2	2	no	—
54	C₅×C₄⋊Dic₃	—	2	1	no	—
55	C₅×Dic₃⋊C₄	—	2	2	no	—
56	C₄×C₅×Dic₃	—	2	1	no	—
57	C₄×C₅×Dic₃	—	2	2	no	—
58	C₄×C₅×Dic₃	—	2	1	no	—
59	C₄×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
60	C₄×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
61	C₅×#208	—	2	1	no	—
62	C₅×#208	—	2	1	no	—
63	C₂×C₅×C₃⋊C₈	—	2	1	no	—
64	#5522	C₂×C₅	1	1	yes	characteristic
65	#5132	C₂×C₅	1	1	yes	characteristic
66	#5006	C₂×C₅	1	1	yes	characteristic
67	C₃×H(3,ℤ/4)	C₂×C₅	1	1	yes	characteristic, complemented
68	#4555	C₂×C₅	1	1	yes	characteristic, complemented
69	#4532	C₂×C₅	1	1	yes	characteristic, complemented
70	#4531	C₂×C₅	1	1	yes	characteristic, complemented
71	C₂×C₅×#41	—	3	1	no	—
72	C₂×C₅×M₁₆	—	3	1	no	—
73	C₂×C₅×M₁₆	C₂×D₃	1	1	yes	characteristic
74	C₄×C₅×Q₈	—	6	1	no	—
75	C₄×C₅×D₄	—	6	2	no	—
76	C₄×C₅×D₄	—	6	1	no	—
77	C₅×#117	—	3	2	no	—
78	C₅×#117	—	3	1	no	—
79	C₅×#117	C₂×D₃	1	1	yes	characteristic
80	C₅×#117	C₂×D₃	1	1	yes	characteristic
81	C₂×C₄²×C₅	—	3	1	no	—
82	C₂×C₄²×C₅	—	3	2	no	—
83	C₅×#101	—	6	1	no	—
84	C₅×#100	—	6	1	no	—
85	C₅×#99	—	6	2	no	—
86	#1827	—	3	1	no	Sylow
87	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
88	C₂²×C₅×D₃	C₂²⋊C₄	1	2	yes	—
89	C₂×C₃×C₄×C₅	—	2	2	no	—
90	C₂×C₃×C₄×C₅	—	4	1	no	—
91	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
92	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
93	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
94	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
95	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
96	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
97	C₅×#67	—	2	2	no	—
98	C₅×#67	—	2	2	no	—
99	C₂×C₅×Dic₃	—	2	1	no	—
100	C₂×C₅×Dic₃	—	2	1	no	—
101	C₂×C₅×Dic₃	—	4	2	no	—
102	C₂×C₅×Dic₃	—	4	1	no	—
103	C₂×C₅×Dic₃	C₂²⋊C₄	1	2	yes	—
104	C₅×D₁₂	—	2	1	no	—
105	C₅×D₁₂	—	2	1	no	—
106	C₄×C₅×D₃	—	2	2	no	—
107	C₄×C₅×D₃	—	2	2	no	—
108	C₄×C₅×D₃	—	4	4	no	—
109	C₅×Dic₆	—	2	1	no	—
110	C₅×Dic₆	—	2	1	no	—
111	C₃×C₅×C₈	—	4	1	no	—
112	C₅×C₃⋊C₈	—	4	1	no	—
113	C₂×#235	C₂²×C₅	1	1	yes	characteristic
114	C₂×C₃×M₁₆	C₂²×C₅	1	1	yes	characteristic
115	C₃×#117	C₂²×C₅	1	1	yes	characteristic
116	C₃×#117	C₂²×C₅	1	1	yes	characteristic
117	#926	C₂²×C₅	1	1	yes	characteristic
118	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
119	C₂×#208	C₂²×C₅	1	1	yes	characteristic
120	#893	—	2	1	no	—
121	#887	—	2	1	no	—
122	#67⋊C₄	—	2	2	no	—
123	#872	C₄×C₅	1	2	yes	complemented
124	C₄²×D₃	C₄×C₅	1	2	yes	complemented
125	#824	—	2	1	no	—
126	#823	—	2	1	no	—
127	#806	—	2	2	no	—
128	C₅×#41	—	6	1	no	—
129	C₅×#41	—	6	1	no	—
130	C₅×#41	—	6	1	no	—
131	C₅×#41	—	6	1	no	—
132	C₂×C₅×Q₈	—	3	1	no	—
133	C₂×C₅×D₄	—	3	2	no	—
134	C₂×C₅×D₄	—	3	1	no	—
135	C₂²×C₄×C₅	—	3	2	no	—
136	C₂²×C₄×C₅	—	6	2	no	—
137	C₂²×C₄×C₅	—	6	1	no	—
138	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
139	C₅×M₁₆	—	2	1	no	—
140	C₅×M₁₆	—	2	1	no	—
141	C₅×M₁₆	—	6	1	no	—
142	C₅×M₁₆	—	6	1	no	—
143	C₂×C₅×C₈	—	2	1	no	—
144	C₂×C₅×C₈	—	6	1	no	—
145	C₅×C₄⋊C₄	—	2	1	no	—
146	C₅×C₄⋊C₄	—	2	1	no	—
147	C₅×C₄⋊C₄	—	6	2	no	—
148	C₅×C₄⋊C₄	—	6	1	no	—
149	C₅×C₂²⋊C₄	—	2	1	no	—
150	C₅×C₂²⋊C₄	—	2	1	no	—
151	C₅×C₂²⋊C₄	—	6	2	no	—
152	C₅×C₂²⋊C₄	—	6	1	no	—
153	C₄²×C₅	—	2	1	no	—
154	C₄²×C₅	—	3	1	no	—
155	C₄²×C₅	—	3	1	no	—
156	C₄²×C₅	—	6	2	no	—
157	C₄²×C₅	—	6	1	no	—
158	C₄²×C₅	—	6	1	no	—
159	C₄²×C₅	C₄×D₃	1	2	yes	—
160	C₄×#41	—	3	1	no	—
161	#413	—	3	1	no	—
162	#410	—	3	1	no	—
163	#339	—	3	1	no	—
164	#339	—	3	1	no	—
165	H(3,ℤ/4)	—	3	1	no	—
166	H(3,ℤ/4)	C₅×D₃	1	1	yes	characteristic, complemented
167	C₂²×C₃×C₅	—	4	1	no	—
168	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
169	C₂²×C₃×C₅	#123	1	1	yes	characteristic
170	C₂²×C₃×C₅	#123	1	1	yes	characteristic
171	C₂×C₅×D₃	—	2	2	no	—
172	C₂×C₅×D₃	—	4	2	no	—
173	C₃×C₄×C₅	—	4	2	no	—
174	C₃×C₄×C₅	—	8	1	no	—
175	C₃×C₄×C₅	#117	1	1	yes	characteristic
176	C₃×C₄×C₅	#117	1	1	yes	characteristic
177	C₃×C₄×C₅	#123	1	1	yes	characteristic
178	C₃×C₄×C₅	#123	1	1	yes	characteristic
179	C₅×Dic₃	—	2	2	no	—
180	C₅×Dic₃	—	2	2	no	—
181	C₅×Dic₃	—	4	1	no	—
182	C₅×Dic₃	—	8	1	no	—
183	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
184	C₂×#67	C₅×D₄	1	2	yes	—
185	C₂²×Dic₃	—	2	1	no	—
186	#235	—	2	1	no	—
187	#235	—	2	1	no	—
188	#235	—	2	1	no	—
189	#235	—	2	1	no	—
190	C₂×D₁₂	C₅×D₄	1	1	yes	characteristic
191	C₂×C₄×D₃	—	2	2	no	—
192	C₂×C₄×D₃	C₂×C₄×C₅	1	2	yes	—
193	C₂×Dic₆	C₅×D₄	1	1	yes	characteristic
194	C₃×M₁₆	—	2	1	no	—
195	C₃×M₁₆	—	2	1	no	—
196	C₂×C₃×C₈	—	2	1	no	—
197	C₃×C₄⋊C₄	—	2	1	no	—
198	C₃×C₄⋊C₄	—	2	1	no	—
199	C₃×C₂²⋊C₄	—	2	1	no	—
200	C₃×C₂²⋊C₄	—	2	1	no	—
201	C₃×C₄²	—	2	1	no	—
202	C₃×C₄²	C₂×C₄×C₅	1	2	yes	—
203	#217	—	2	1	no	—
204	(C₂×D₃)⋊C₄	—	2	2	no	—
205	C₄⋊Dic₃	—	2	1	no	—
206	Dic₃⋊C₄	—	2	2	no	—
207	C₄×Dic₃	—	2	1	no	—
208	C₄×Dic₃	—	2	2	no	—
209	C₄×Dic₃	—	2	1	no	—
210	C₄×Dic₃	C₂×C₄×C₅	1	1	yes	characteristic
211	C₄×Dic₃	C₂×C₄×C₅	1	1	yes	characteristic
212	#208	—	2	1	no	—
213	#208	—	2	1	no	—
214	C₂×C₃⋊C₈	—	2	1	no	—
215	C₂³×C₅	—	3	2	no	—
216	C₂³×C₅	D₃×D₄	1	1	yes	characteristic
217	C₅×Q₈	—	6	1	no	—
218	C₅×Q₈	—	6	1	no	—
219	C₅×D₄	—	6	2	no	—
220	C₅×D₄	—	6	2	no	—
221	C₅×D₄	—	6	1	no	—
222	C₅×D₄	—	6	1	no	—
223	C₂×C₄×C₅	—	2	2	no	—
224	C₂×C₄×C₅	—	3	2	no	—
225	C₂×C₄×C₅	—	4	1	no	—
226	C₂×C₄×C₅	—	6	1	no	—
227	C₂×C₄×C₅	—	6	2	no	—
228	C₂×C₄×C₅	—	6	2	no	—
229	C₂×C₄×C₅	—	6	1	no	—
230	C₂×C₄×C₅	—	12	4	no	—
231	C₂×C₄×C₅	—	12	2	no	—
232	C₂×C₄×C₅	—	12	1	no	—
233	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
234	C₂×C₄×C₅	#235	1	1	yes	characteristic
235	C₂×C₄×C₅	#235	1	1	yes	characteristic
236	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
237	C₂×C₄×C₅	#237	1	1	yes	characteristic
238	C₂×C₄×C₅	#239	1	1	yes	characteristic
239	C₅×C₈	—	4	1	no	—
240	C₅×C₈	—	12	1	no	—
241	C₂×#41	—	3	1	no	—
242	C₂×M₁₆	—	3	1	no	—
243	C₂×M₁₆	C₂×C₅×D₃	1	1	yes	characteristic
244	C₄×Q₈	—	6	1	no	—
245	C₄×D₄	—	6	2	no	—
246	C₄×D₄	—	6	1	no	—
247	#117	—	3	2	no	—
248	#117	—	3	1	no	—
249	#117	C₂×C₅×D₃	1	1	yes	characteristic
250	#117	C₂×C₅×D₃	1	1	yes	characteristic
251	C₂×C₄²	—	3	1	no	—
252	C₂×C₄²	—	3	2	no	—
253	#101	—	6	1	no	—
254	#100	—	6	1	no	—
255	#99	—	6	2	no	—
256	C₂×C₃×C₅	—	2	1	no	—
257	C₂×C₃×C₅	—	2	1	no	—
258	C₂×C₃×C₅	—	2	1	no	—
259	C₂×C₃×C₅	#381	1	1	yes	characteristic
260	C₅×D₃	—	4	2	no	—
261	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
262	C₂²×D₃	C₅×C₂²⋊C₄	1	2	yes	—
263	C₂×C₃×C₄	—	2	2	no	—
264	C₂×C₃×C₄	—	4	1	no	—
265	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
266	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
267	C₂×C₃×C₄	C₅×#41	1	1	yes	characteristic
268	C₂×C₃×C₄	C₅×#41	1	1	yes	characteristic
269	C₂×C₃×C₄	C₅×#41	1	1	yes	characteristic
270	C₂×C₃×C₄	C₅×#41	1	1	yes	characteristic
271	#67	—	2	2	no	—
272	#67	—	2	2	no	—
273	C₂×Dic₃	—	2	1	no	—
274	C₂×Dic₃	—	2	1	no	—
275	C₂×Dic₃	—	4	2	no	—
276	C₂×Dic₃	—	4	1	no	—
277	C₂×Dic₃	C₅×C₂²⋊C₄	1	2	yes	—
278	D₁₂	—	2	1	no	—
279	D₁₂	—	2	1	no	—
280	C₄×D₃	—	2	2	no	—
281	C₄×D₃	—	2	2	no	—
282	C₄×D₃	—	4	4	no	—
283	Dic₆	—	2	1	no	—
284	Dic₆	—	2	1	no	—
285	C₃×C₈	—	4	1	no	—
286	C₃⋊C₈	—	4	1	no	—
287	C₂²×C₅	—	4	1	no	—
288	C₂²×C₅	—	6	2	no	—
289	C₂²×C₅	—	12	2	no	—
290	C₂²×C₅	D₃×C₂²⋊C₄	1	1	yes	characteristic
291	C₂²×C₅	#883	1	1	yes	characteristic
292	C₂²×C₅	#894	1	1	yes	characteristic
293	C₄×C₅	—	4	2	no	—
294	C₄×C₅	—	6	2	no	—
295	C₄×C₅	—	6	2	no	—
296	C₄×C₅	—	8	1	no	—
297	C₄×C₅	—	12	1	no	—
298	C₄×C₅	—	24	1	no	—
299	C₄×C₅	#872	1	1	yes	characteristic
300	C₄×C₅	#883	1	1	yes	characteristic
301	C₄×C₅	#892	1	1	yes	characteristic
302	C₄×C₅	#894	1	1	yes	characteristic
303	#41	—	6	1	no	—
304	#41	—	6	1	no	—
305	#41	—	6	1	no	—
306	#41	—	6	1	no	—
307	C₂×Q₈	—	3	1	no	—
308	C₂×D₄	—	3	2	no	—
309	C₂×D₄	—	3	1	no	—
310	C₂²×C₄	—	3	2	no	—
311	C₂²×C₄	—	6	2	no	—
312	C₂²×C₄	—	6	1	no	—
313	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
314	M₁₆	—	2	1	no	—
315	M₁₆	—	2	1	no	—
316	M₁₆	—	6	1	no	—
317	M₁₆	—	6	1	no	—
318	C₂×C₈	—	2	1	no	—
319	C₂×C₈	—	6	1	no	—
320	C₄⋊C₄	—	2	1	no	—
321	C₄⋊C₄	—	2	1	no	—
322	C₄⋊C₄	—	6	2	no	—
323	C₄⋊C₄	—	6	1	no	—
324	C₂²⋊C₄	—	2	1	no	—
325	C₂²⋊C₄	—	2	1	no	—
326	C₂²⋊C₄	—	6	2	no	—
327	C₂²⋊C₄	—	6	1	no	—
328	C₄²	—	2	1	no	—
329	C₄²	—	3	1	no	—
330	C₄²	—	3	1	no	—
331	C₄²	—	6	2	no	—
332	C₄²	—	6	1	no	—
333	C₄²	—	6	1	no	—
334	C₄²	C₄×C₅×D₃	1	2	yes	—
335	C₃×C₅	#1827	1	1	yes	characteristic, complemented, Hall
336	C₂²×C₃	—	4	1	no	—
337	C₂²×C₃	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
338	C₂²×C₃	C₅×#123	1	1	yes	characteristic
339	C₂²×C₃	C₅×#123	1	1	yes	characteristic
340	C₂×D₃	—	2	2	no	—
341	C₂×D₃	—	4	2	no	—
342	C₃×C₄	—	4	2	no	—
343	C₃×C₄	—	8	1	no	—
344	C₃×C₄	C₅×#117	1	1	yes	characteristic
345	C₃×C₄	C₅×#117	1	1	yes	characteristic
346	C₃×C₄	C₅×#123	1	1	yes	characteristic
347	C₃×C₄	C₅×#123	1	1	yes	characteristic
348	Dic₃	—	2	2	no	—
349	Dic₃	—	2	2	no	—
350	Dic₃	—	4	1	no	—
351	Dic₃	—	8	1	no	—
352	C₂×C₅	—	2	1	no	—
353	C₂×C₅	—	2	1	no	—
354	C₂×C₅	—	2	1	no	—
355	C₂×C₅	—	12	2	no	—
356	C₂×C₅	#4664	1	1	yes	characteristic
357	C₂³	—	3	2	no	—
358	C₂³	C₅×D₃×D₄	1	1	yes	characteristic
359	Q₈	—	6	1	no	—
360	Q₈	—	6	1	no	—
361	D₄	—	6	2	no	—
362	D₄	—	6	2	no	—
363	D₄	—	6	1	no	—
364	D₄	—	6	1	no	—
365	C₂×C₄	—	2	2	no	—
366	C₂×C₄	—	3	2	no	—
367	C₂×C₄	—	4	1	no	—
368	C₂×C₄	—	6	1	no	—
369	C₂×C₄	—	6	2	no	—
370	C₂×C₄	—	6	2	no	—
371	C₂×C₄	—	6	1	no	—
372	C₂×C₄	—	12	4	no	—
373	C₂×C₄	—	12	2	no	—
374	C₂×C₄	—	12	1	no	—
375	C₂×C₄	C₂×C₄×C₅×D₃	1	1	yes	characteristic
376	C₂×C₄	C₅×#235	1	1	yes	characteristic
377	C₂×C₄	C₅×#235	1	1	yes	characteristic
378	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
379	C₂×C₄	C₅×#237	1	1	yes	characteristic
380	C₂×C₄	C₅×#239	1	1	yes	characteristic
381	C₈	—	4	1	no	—
382	C₈	—	12	1	no	—
383	C₂×C₃	—	2	1	no	—
384	C₂×C₃	—	2	1	no	—
385	C₂×C₃	—	2	1	no	—
386	C₂×C₃	C₅×#381	1	1	yes	characteristic
387	D₃	—	4	2	no	—
388	C₅	#68711	1	1	yes	characteristic, direct product factor, Sylow
389	C₂²	—	4	1	no	—
390	C₂²	—	6	2	no	—
391	C₂²	—	12	2	no	—
392	C₂²	C₅×D₃×C₂²⋊C₄	1	1	yes	characteristic
393	C₂²	C₅×#883	1	1	yes	characteristic
394	C₂²	C₅×#894	1	1	yes	characteristic
395	C₄	—	4	2	no	—
396	C₄	—	6	2	no	—
397	C₄	—	6	2	no	—
398	C₄	—	8	1	no	—
399	C₄	—	12	1	no	—
400	C₄	—	24	1	no	—
401	C₄	C₅×#872	1	1	yes	characteristic
402	C₄	C₅×#883	1	1	yes	characteristic
403	C₄	C₅×#892	1	1	yes	characteristic
404	C₄	C₅×#894	1	1	yes	characteristic
405	C₃	C₅×#1827	1	1	yes	characteristic, complemented, Sylow
406	C₂	—	2	1	no	—
407	C₂	—	2	1	no	—
408	C₂	—	2	1	no	—
409	C₂	—	12	2	no	—
410	C₂	C₅×#4664	1	1	yes	characteristic

	subgroup	G/H
center	C₄×C₅	#872
commutator	C₂×C₃×C₄	C₂²×C₄×C₅
Frattini	C₂²×C₄	C₂²×C₅×D₃
Fitting	C₃×C₅×H(3,ℤ/4)	C₂
socle	C₂×C₃×C₅	#381
prime radical	C₂×C₅×#235	C₂²
cosocle	C₂²×C₃×C₄	C₂³×C₅
hypercenter	C₅×H(3,ℤ/4)	D₃
hypocenter	C₃	C₅×#1827
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₄×C₅ ◁ C₅×#117 ◁ C₅×H(3,ℤ/4)

Complements

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

N	H ≅ G/N	type
4. C₃×C₅×H(3,ℤ/4)	C₂	semidirect
5. C₅×#4555	C₂	semidirect
6. C₅×#4532	C₂	semidirect
7. C₅×#4531	C₂	semidirect
19. C₅×#872	C₄	semidirect
20. C₄²×C₅×D₃	C₄	semidirect
24. #68711	C₅	direct (N × H)
31. C₅×H(3,ℤ/4)	D₃	semidirect
67. C₃×H(3,ℤ/4)	C₂×C₅	semidirect
68. #4555	C₂×C₅	semidirect
69. #4532	C₂×C₅	semidirect
70. #4531	C₂×C₅	semidirect
123. #872	C₄×C₅	semidirect
124. C₄²×D₃	C₄×C₅	semidirect
166. H(3,ℤ/4)	C₅×D₃	semidirect
335. C₃×C₅	#1827	semidirect
388. C₅	#68711	direct (N × H)
405. C₃	C₅×#1827	semidirect

Maximal subgroups

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

subgroup	index
C₅×#5522	2
C₅×#5132	2
C₅×#5006	2
C₃×C₅×H(3,ℤ/4)	2
C₅×#4555	2
C₅×#4532	2
C₅×#4531	2
C₅×#1827	3
#68711	5

Subgroups — C5×#68711 #14298578

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#68711 #14298578