Subgroups — C₅×#68766 #14301570

Order 1920.

688 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#5516	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅×#875	C₂	1	1	yes	maximal, characteristic
3	C₂×C₅×#824	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#5131	C₂	1	1	yes	maximal, characteristic
5	C₅×#5001	C₂	1	1	yes	maximal, characteristic
6	C₃×C₅×#339	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#4523	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#1888	—	3	1	no	maximal, Hall
9	C₂²×C₅×D₁₂	C₂²	1	1	yes	characteristic
10	C₂²×C₅×Dic₆	C₂²	1	1	yes	characteristic
11	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
12	C₃×C₅×#117	C₂²	1	1	yes	characteristic
13	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
14	C₂×C₅×(C₂×D₃)⋊C₄	—	2	2	no	—
15	C₅×#926	C₂²	1	1	yes	characteristic
16	C₂×C₅×#208	C₂²	1	1	yes	characteristic
17	C₅×#887	—	2	2	no	—
18	C₅×#877	—	2	2	no	—
19	C₅×#875	—	2	2	no	—
20	C₅×#875	C₄	1	4	yes	complemented
21	C₄×C₅×Dic₆	—	2	2	no	—
22	C₅×#824	—	2	2	no	—
23	C₅×#821	—	2	2	no	—
24	C₅×#809	—	2	2	no	—
25	#68766	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
26	C₂×C₅×#124	—	3	1	no	—
27	C₅×#519	—	3	1	no	—
28	C₅×#418	—	3	1	no	—
29	C₅×#418	—	3	1	no	—
30	C₂×C₅×#101	—	3	1	no	—
31	C₅×#339	—	3	1	no	—
32	C₅×#339	D₃	1	1	yes	characteristic, complemented
33	C₂³×C₅×D₃	—	2	1	no	—
34	C₂²×C₃×C₄×C₅	—	2	1	no	—
35	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
36	C₂²×C₅×Dic₃	D₄	1	2	yes	—
37	C₂×C₅×D₁₂	—	2	1	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	—	2	1	no	—
42	C₂×C₅×D₁₂	C₂×C₄	1	2	yes	—
43	C₂×C₅×Dic₆	—	2	1	no	—
44	C₂×C₅×Dic₆	—	2	1	no	—
45	C₂×C₅×Dic₆	—	2	1	no	—
46	C₂×C₅×Dic₆	—	2	1	no	—
47	C₂×C₅×Dic₆	C₂×C₄	1	2	yes	—
48	C₂×C₅×Dic₆	D₄	1	2	yes	—
49	C₃×C₅×M₁₆	—	2	1	no	—
50	C₃×C₅×M₁₆	—	2	1	no	—
51	C₂×C₃×C₅×C₈	—	2	1	no	—
52	C₃×C₅×C₄⋊C₄	D₄	1	2	yes	—
53	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
54	C₃×C₄²×C₅	—	2	1	no	—
55	C₃×C₄²×C₅	—	2	1	no	—
56	C₃×C₄²×C₅	C₂×C₄	1	2	yes	—
57	C₅×#217	—	2	1	no	—
58	C₅×(C₂×D₃)⋊C₄	—	2	8	no	—
59	C₅×C₄⋊Dic₃	D₄	1	2	yes	—
60	C₅×Dic₃⋊C₄	—	2	4	no	—
61	C₄×C₅×Dic₃	—	2	4	no	—
62	C₄×C₅×Dic₃	—	2	1	no	—
63	C₅×#208	—	2	1	no	—
64	C₅×#208	—	2	1	no	—
65	C₂×C₅×C₃⋊C₈	—	2	1	no	—
66	#5516	C₂×C₅	1	1	yes	characteristic, complemented
67	C₂×#875	C₂×C₅	1	1	yes	characteristic
68	C₂×#824	C₂×C₅	1	1	yes	characteristic, complemented
69	#5131	C₂×C₅	1	1	yes	characteristic
70	#5001	C₂×C₅	1	1	yes	characteristic
71	C₃×#339	C₂×C₅	1	1	yes	characteristic, complemented
72	#4523	C₂×C₅	1	1	yes	characteristic, complemented
73	C₂²×C₅×Q₈	—	3	1	no	—
74	C₂²×C₅×D₄	—	3	1	no	—
75	C₂×C₅×M₁₆	—	3	1	no	—
76	C₂×C₅×M₁₆	C₂×D₃	1	1	yes	characteristic
77	C₅×#124	—	3	4	no	—
78	C₅×#124	—	6	2	no	—
79	C₄×C₅×Q₈	—	6	2	no	—
80	C₄×C₅×Q₈	—	6	2	no	—
81	C₅×#117	—	3	1	no	—
82	C₅×#117	—	6	2	no	—
83	C₅×#117	C₂×D₃	1	1	yes	characteristic
84	C₂×C₅×C₂²⋊C₄	—	6	2	no	—
85	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
86	C₅×#102	—	6	2	no	—
87	C₅×#102	—	6	2	no	—
88	C₅×#101	—	6	2	no	—
89	#1888	—	3	1	no	Sylow
90	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
91	C₂²×C₅×D₃	—	2	2	no	—
92	C₂²×C₅×D₃	—	4	4	no	—
93	C₂²×C₅×D₃	—	4	1	no	—
94	C₂²×C₅×D₃	—	4	1	no	—
95	C₂×C₃×C₄×C₅	—	2	2	no	—
96	C₂×C₃×C₄×C₅	—	2	2	no	—
97	C₂×C₃×C₄×C₅	—	4	2	no	—
98	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
99	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
100	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
101	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
102	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
103	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
104	C₂×C₅×Dic₃	—	2	2	no	—
105	C₂×C₅×Dic₃	—	2	2	no	—
106	C₂×C₅×Dic₃	—	2	2	no	—
107	C₂×C₅×Dic₃	C₂²⋊C₄	1	4	yes	—
108	C₅×D₁₂	—	2	2	no	—
109	C₅×D₁₂	—	2	2	no	—
110	C₅×D₁₂	—	4	1	no	—
111	C₅×D₁₂	—	4	1	no	—
112	C₅×Dic₆	—	2	2	no	—
113	C₅×Dic₆	—	2	2	no	—
114	C₅×Dic₆	—	2	2	no	—
115	C₅×Dic₆	—	2	2	no	—
116	C₃×C₅×C₈	—	4	1	no	—
117	C₅×C₃⋊C₈	—	4	1	no	—
118	C₂²×D₁₂	C₂²×C₅	1	1	yes	characteristic
119	C₂²×Dic₆	C₂²×C₅	1	1	yes	characteristic
120	C₂×C₃×M₁₆	C₂²×C₅	1	1	yes	characteristic
121	C₃×#117	C₂²×C₅	1	1	yes	characteristic
122	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
123	C₂×(C₂×D₃)⋊C₄	—	2	2	no	—
124	#926	C₂²×C₅	1	1	yes	characteristic
125	C₂×#208	C₂²×C₅	1	1	yes	characteristic
126	#887	—	2	2	no	—
127	#877	—	2	2	no	—
128	#875	—	2	2	no	—
129	#875	C₄×C₅	1	4	yes	complemented
130	C₄×Dic₆	—	2	2	no	—
131	#824	—	2	2	no	—
132	#821	—	2	2	no	—
133	#809	—	2	2	no	—
134	C₂⁴×C₅	—	6	1	no	—
135	C₂×C₅×Q₈	—	3	2	no	—
136	C₂×C₅×Q₈	—	3	2	no	—
137	C₂×C₅×Q₈	—	6	1	no	—
138	C₂×C₅×Q₈	—	6	1	no	—
139	C₂×C₅×Q₈	—	6	1	no	—
140	C₂×C₅×Q₈	—	6	1	no	—
141	C₂×C₅×D₄	—	3	2	no	—
142	C₂×C₅×D₄	—	6	1	no	—
143	C₂×C₅×D₄	—	6	1	no	—
144	C₂×C₅×D₄	—	6	1	no	—
145	C₂×C₅×D₄	—	6	1	no	—
146	C₂×C₅×D₄	—	6	1	no	—
147	C₂²×C₄×C₅	—	2	1	no	—
148	C₂²×C₄×C₅	—	3	2	no	—
149	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
150	C₅×M₁₆	—	2	1	no	—
151	C₅×M₁₆	—	2	1	no	—
152	C₅×M₁₆	—	6	1	no	—
153	C₅×M₁₆	—	6	1	no	—
154	C₂×C₅×C₈	—	2	1	no	—
155	C₂×C₅×C₈	—	6	1	no	—
156	C₅×C₄⋊C₄	—	3	2	no	—
157	C₅×C₄⋊C₄	—	6	4	no	—
158	C₅×C₄⋊C₄	D₁₂	1	2	yes	—
159	C₅×C₂²⋊C₄	—	2	1	no	—
160	C₅×C₂²⋊C₄	—	6	8	no	—
161	C₅×C₂²⋊C₄	—	6	1	no	—
162	C₄²×C₅	—	2	1	no	—
163	C₄²×C₅	—	2	1	no	—
164	C₄²×C₅	—	6	4	no	—
165	C₄²×C₅	—	6	1	no	—
166	C₄²×C₅	C₄×D₃	1	2	yes	—
167	C₂×#124	—	3	1	no	—
168	#519	—	3	1	no	—
169	#418	—	3	1	no	—
170	#418	—	3	1	no	—
171	C₂×#101	—	3	1	no	—
172	#339	—	3	1	no	—
173	#339	C₅×D₃	1	1	yes	characteristic, complemented
174	C₂²×C₃×C₅	—	2	2	no	—
175	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
176	C₂²×C₃×C₅	#120	1	1	yes	characteristic
177	C₂²×C₃×C₅	#123	1	1	yes	characteristic
178	C₂×C₅×D₃	—	4	4	no	—
179	C₂×C₅×D₃	—	4	2	no	—
180	C₂×C₅×D₃	—	8	2	no	—
181	C₂×C₅×D₃	—	8	2	no	—
182	C₃×C₄×C₅	—	4	2	no	—
183	C₃×C₄×C₅	—	4	2	no	—
184	C₃×C₄×C₅	C₄×D₄	1	1	yes	characteristic
185	C₃×C₄×C₅	C₄×D₄	1	1	yes	characteristic
186	C₃×C₄×C₅	#121	1	1	yes	characteristic
187	C₃×C₄×C₅	#121	1	1	yes	characteristic
188	C₅×Dic₃	—	2	4	no	—
189	C₅×Dic₃	—	4	2	no	—
190	C₂³×D₃	—	2	1	no	—
191	C₂²×C₃×C₄	—	2	1	no	—
192	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
193	C₂²×Dic₃	C₅×D₄	1	2	yes	—
194	C₂×D₁₂	—	2	1	no	—
195	C₂×D₁₂	—	2	1	no	—
196	C₂×D₁₂	—	2	1	no	—
197	C₂×D₁₂	—	2	1	no	—
198	C₂×D₁₂	—	2	1	no	—
199	C₂×D₁₂	C₂×C₄×C₅	1	2	yes	—
200	C₂×Dic₆	—	2	1	no	—
201	C₂×Dic₆	—	2	1	no	—
202	C₂×Dic₆	—	2	1	no	—
203	C₂×Dic₆	—	2	1	no	—
204	C₂×Dic₆	C₂×C₄×C₅	1	2	yes	—
205	C₂×Dic₆	C₅×D₄	1	2	yes	—
206	C₃×M₁₆	—	2	1	no	—
207	C₃×M₁₆	—	2	1	no	—
208	C₂×C₃×C₈	—	2	1	no	—
209	C₃×C₄⋊C₄	C₅×D₄	1	2	yes	—
210	C₃×C₂²⋊C₄	—	2	1	no	—
211	C₃×C₄²	—	2	1	no	—
212	C₃×C₄²	—	2	1	no	—
213	C₃×C₄²	C₂×C₄×C₅	1	2	yes	—
214	#217	—	2	1	no	—
215	(C₂×D₃)⋊C₄	—	2	8	no	—
216	C₄⋊Dic₃	C₅×D₄	1	2	yes	—
217	Dic₃⋊C₄	—	2	4	no	—
218	C₄×Dic₃	—	2	4	no	—
219	C₄×Dic₃	—	2	1	no	—
220	#208	—	2	1	no	—
221	#208	—	2	1	no	—
222	C₂×C₃⋊C₈	—	2	1	no	—
223	C₂³×C₅	—	6	2	no	—
224	C₂³×C₅	—	12	4	no	—
225	C₂³×C₅	—	12	1	no	—
226	C₂³×C₅	—	12	1	no	—
227	C₂³×C₅	D₃×D₄	1	1	yes	characteristic
228	C₅×Q₈	—	6	2	no	—
229	C₅×Q₈	—	6	2	no	—
230	C₅×Q₈	—	6	2	no	—
231	C₅×Q₈	—	6	2	no	—
232	C₅×D₄	—	6	2	no	—
233	C₅×D₄	—	6	2	no	—
234	C₅×D₄	—	12	1	no	—
235	C₅×D₄	—	12	1	no	—
236	C₂×C₄×C₅	—	2	2	no	—
237	C₂×C₄×C₅	—	2	2	no	—
238	C₂×C₄×C₅	—	3	4	no	—
239	C₂×C₄×C₅	—	4	2	no	—
240	C₂×C₄×C₅	—	6	2	no	—
241	C₂×C₄×C₅	—	6	2	no	—
242	C₂×C₄×C₅	—	6	2	no	—
243	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
244	C₂×C₄×C₅	C₂×D₁₂	1	1	yes	characteristic
245	C₂×C₄×C₅	#235	1	1	yes	characteristic
246	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
247	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
248	C₂×C₄×C₅	#239	1	1	yes	characteristic
249	C₅×C₈	—	4	1	no	—
250	C₅×C₈	—	12	1	no	—
251	C₂²×Q₈	—	3	1	no	—
252	C₂²×D₄	—	3	1	no	—
253	C₂×M₁₆	—	3	1	no	—
254	C₂×M₁₆	C₂×C₅×D₃	1	1	yes	characteristic
255	#124	—	3	4	no	—
256	#124	—	6	2	no	—
257	C₄×Q₈	—	6	2	no	—
258	C₄×Q₈	—	6	2	no	—
259	#117	—	3	1	no	—
260	#117	—	6	2	no	—
261	#117	C₂×C₅×D₃	1	1	yes	characteristic
262	C₂×C₂²⋊C₄	—	6	2	no	—
263	C₂×C₄²	C₂×C₅×D₃	1	1	yes	characteristic
264	#102	—	6	2	no	—
265	#102	—	6	2	no	—
266	#101	—	6	2	no	—
267	C₂×C₃×C₅	—	2	1	no	—
268	C₂×C₃×C₅	—	2	1	no	—
269	C₂×C₃×C₅	#386	1	1	yes	characteristic
270	C₂×C₃×C₅	#454	1	2	yes	—
271	C₅×D₃	—	8	2	no	—
272	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
273	C₂²×D₃	—	2	2	no	—
274	C₂²×D₃	—	4	4	no	—
275	C₂²×D₃	—	4	1	no	—
276	C₂²×D₃	—	4	1	no	—
277	C₂×C₃×C₄	—	2	2	no	—
278	C₂×C₃×C₄	—	2	2	no	—
279	C₂×C₃×C₄	—	4	2	no	—
280	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
281	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
282	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
283	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
284	C₂×C₃×C₄	C₅×#41	1	1	yes	characteristic
285	C₂×C₃×C₄	C₅×#41	1	1	yes	characteristic
286	C₂×Dic₃	—	2	2	no	—
287	C₂×Dic₃	—	2	2	no	—
288	C₂×Dic₃	—	2	2	no	—
289	C₂×Dic₃	C₅×C₂²⋊C₄	1	4	yes	—
290	D₁₂	—	2	2	no	—
291	D₁₂	—	2	2	no	—
292	D₁₂	—	4	1	no	—
293	D₁₂	—	4	1	no	—
294	Dic₆	—	2	2	no	—
295	Dic₆	—	2	2	no	—
296	Dic₆	—	2	2	no	—
297	Dic₆	—	2	2	no	—
298	C₃×C₈	—	4	1	no	—
299	C₃⋊C₈	—	4	1	no	—
300	C₂²×C₅	—	2	2	no	—
301	C₂²×C₅	—	12	4	no	—
302	C₂²×C₅	—	12	2	no	—
303	C₂²×C₅	—	24	2	no	—
304	C₂²×C₅	—	24	2	no	—
305	C₂²×C₅	D₃×C₂²⋊C₄	1	1	yes	characteristic
306	C₂²×C₅	#882	1	1	yes	characteristic
307	C₂²×C₅	#894	1	1	yes	characteristic
308	C₄×C₅	—	4	2	no	—
309	C₄×C₅	—	4	2	no	—
310	C₄×C₅	—	6	4	no	—
311	C₄×C₅	—	12	2	no	—
312	C₄×C₅	C₄×D₁₂	1	1	yes	characteristic
313	C₄×C₅	#884	1	1	yes	characteristic
314	C₄×C₅	#893	1	1	yes	characteristic
315	C₄×C₅	#895	1	1	yes	characteristic
316	C₂⁴	—	6	1	no	—
317	C₂×Q₈	—	3	2	no	—
318	C₂×Q₈	—	3	2	no	—
319	C₂×Q₈	—	6	1	no	—
320	C₂×Q₈	—	6	1	no	—
321	C₂×Q₈	—	6	1	no	—
322	C₂×Q₈	—	6	1	no	—
323	C₂×D₄	—	3	2	no	—
324	C₂×D₄	—	6	1	no	—
325	C₂×D₄	—	6	1	no	—
326	C₂×D₄	—	6	1	no	—
327	C₂×D₄	—	6	1	no	—
328	C₂×D₄	—	6	1	no	—
329	C₂²×C₄	—	2	1	no	—
330	C₂²×C₄	—	3	2	no	—
331	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
332	M₁₆	—	2	1	no	—
333	M₁₆	—	2	1	no	—
334	M₁₆	—	6	1	no	—
335	M₁₆	—	6	1	no	—
336	C₂×C₈	—	2	1	no	—
337	C₂×C₈	—	6	1	no	—
338	C₄⋊C₄	—	3	2	no	—
339	C₄⋊C₄	—	6	4	no	—
340	C₄⋊C₄	C₅×D₁₂	1	2	yes	—
341	C₂²⋊C₄	—	2	1	no	—
342	C₂²⋊C₄	—	6	8	no	—
343	C₂²⋊C₄	—	6	1	no	—
344	C₄²	—	2	1	no	—
345	C₄²	—	2	1	no	—
346	C₄²	—	6	4	no	—
347	C₄²	—	6	1	no	—
348	C₄²	C₄×C₅×D₃	1	2	yes	—
349	C₃×C₅	#1888	1	1	yes	characteristic, complemented, Hall
350	C₂²×C₃	—	2	2	no	—
351	C₂²×C₃	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
352	C₂²×C₃	C₅×#120	1	1	yes	characteristic
353	C₂²×C₃	C₅×#123	1	1	yes	characteristic
354	C₂×D₃	—	4	4	no	—
355	C₂×D₃	—	4	2	no	—
356	C₂×D₃	—	8	2	no	—
357	C₂×D₃	—	8	2	no	—
358	C₃×C₄	—	4	2	no	—
359	C₃×C₄	—	4	2	no	—
360	C₃×C₄	C₄×C₅×D₄	1	1	yes	characteristic
361	C₃×C₄	C₄×C₅×D₄	1	1	yes	characteristic
362	C₃×C₄	C₅×#121	1	1	yes	characteristic
363	C₃×C₄	C₅×#121	1	1	yes	characteristic
364	Dic₃	—	2	4	no	—
365	Dic₃	—	4	2	no	—
366	C₂×C₅	—	2	1	no	—
367	C₂×C₅	—	2	1	no	—
368	C₂×C₅	—	24	2	no	—
369	C₂×C₅	#4665	1	1	yes	characteristic
370	C₂×C₅	#4827	1	2	yes	—
371	C₂³	—	6	2	no	—
372	C₂³	—	12	4	no	—
373	C₂³	—	12	1	no	—
374	C₂³	—	12	1	no	—
375	C₂³	C₅×D₃×D₄	1	1	yes	characteristic
376	Q₈	—	6	2	no	—
377	Q₈	—	6	2	no	—
378	Q₈	—	6	2	no	—
379	Q₈	—	6	2	no	—
380	D₄	—	6	2	no	—
381	D₄	—	6	2	no	—
382	D₄	—	12	1	no	—
383	D₄	—	12	1	no	—
384	C₂×C₄	—	2	2	no	—
385	C₂×C₄	—	2	2	no	—
386	C₂×C₄	—	3	4	no	—
387	C₂×C₄	—	4	2	no	—
388	C₂×C₄	—	6	2	no	—
389	C₂×C₄	—	6	2	no	—
390	C₂×C₄	—	6	2	no	—
391	C₂×C₄	C₂×C₄×C₅×D₃	1	1	yes	characteristic
392	C₂×C₄	C₂×C₅×D₁₂	1	1	yes	characteristic
393	C₂×C₄	C₅×#235	1	1	yes	characteristic
394	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
395	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
396	C₂×C₄	C₅×#239	1	1	yes	characteristic
397	C₈	—	4	1	no	—
398	C₈	—	12	1	no	—
399	C₂×C₃	—	2	1	no	—
400	C₂×C₃	—	2	1	no	—
401	C₂×C₃	C₅×#386	1	1	yes	characteristic
402	C₂×C₃	C₅×#454	1	2	yes	—
403	D₃	—	8	2	no	—
404	C₅	#68766	1	1	yes	characteristic, direct product factor, Sylow
405	C₂²	—	2	2	no	—
406	C₂²	—	12	4	no	—
407	C₂²	—	12	2	no	—
408	C₂²	—	24	2	no	—
409	C₂²	—	24	2	no	—
410	C₂²	C₅×D₃×C₂²⋊C₄	1	1	yes	characteristic
411	C₂²	C₅×#882	1	1	yes	characteristic
412	C₂²	C₅×#894	1	1	yes	characteristic
413	C₄	—	4	2	no	—
414	C₄	—	4	2	no	—
415	C₄	—	6	4	no	—
416	C₄	—	12	2	no	—
417	C₄	C₄×C₅×D₁₂	1	1	yes	characteristic
418	C₄	C₅×#884	1	1	yes	characteristic
419	C₄	C₅×#893	1	1	yes	characteristic
420	C₄	C₅×#895	1	1	yes	characteristic
421	C₃	C₅×#1888	1	1	yes	characteristic, complemented, Sylow
422	C₂	—	2	1	no	—
423	C₂	—	2	1	no	—
424	C₂	—	24	2	no	—
425	C₂	C₅×#4665	1	1	yes	characteristic
426	C₂	C₅×#4827	1	2	yes	—

	subgroup	G/H
center	C₂²×C₅	#882
commutator	C₂×C₃×C₄	C₂²×C₄×C₅
Frattini	C₂²×C₄	C₂²×C₅×D₃
Fitting	C₃×C₅×#339	C₂
socle	C₂²×C₃×C₅	#120
prime radical	C₂²×C₅×D₁₂	C₂²
cosocle	C₂²×C₃×C₄	C₂³×C₅
hypercenter	C₅×#339	D₃
hypocenter	C₃	C₅×#1888
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₂²×C₄×C₅ ◁ C₅×#339

Complements

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

N	H ≅ G/N	type
1. C₅×#5516	C₂	semidirect
3. C₂×C₅×#824	C₂	semidirect
6. C₃×C₅×#339	C₂	semidirect
7. C₅×#4523	C₂	semidirect
20. C₅×#875	C₄	semidirect
25. #68766	C₅	direct (N × H)
32. C₅×#339	D₃	semidirect
66. #5516	C₂×C₅	semidirect
68. C₂×#824	C₂×C₅	semidirect
71. C₃×#339	C₂×C₅	semidirect
72. #4523	C₂×C₅	semidirect
129. #875	C₄×C₅	semidirect
173. #339	C₅×D₃	semidirect
349. C₃×C₅	#1888	semidirect
404. C₅	#68766	direct (N × H)
421. C₃	C₅×#1888	semidirect

Maximal subgroups

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

subgroup	index
C₅×#5516	2
C₂×C₅×#875	2
C₂×C₅×#824	2
C₅×#5131	2
C₅×#5001	2
C₃×C₅×#339	2
C₅×#4523	2
C₅×#1888	3
#68766	5

Subgroups — C5×#68766 #14301570

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#68766 #14301570