Subgroups — C₅×#70411 #14302926

Order 1920.

628 conjugacy classes of subgroups.

The subgroup lattice has 440 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#5825	C₂	1	1	yes	maximal, characteristic
2	C₅×#5516	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×#421	C₂	1	1	yes	maximal, characteristic
4	C₅×#5236	C₂	1	1	yes	maximal, characteristic
5	C₂×C₅×#824	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#4557	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#4531	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#1912	—	3	1	no	maximal, Hall
9	C₂×C₃×C₅×#41	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	C₅×#944	C₄	1	2	yes	complemented
14	C₅×#936	C₄	1	2	yes	complemented
15	C₅×#935	—	2	2	no	—
16	C₅×#926	C₂²	1	1	yes	characteristic
17	C₅×#926	C₂²	1	1	yes	characteristic
18	C₅×#924	—	2	2	no	—
19	C₂×C₅×#208	C₂²	1	1	yes	characteristic
20	C₅×#887	—	2	2	no	—
21	C₅×#877	—	2	2	no	—
22	C₄×C₅×Dic₆	—	2	2	no	—
23	C₃×C₅×#104	—	2	2	no	—
24	C₅×#837	—	2	2	no	—
25	C₅×#824	—	2	2	no	—
26	#70411	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
27	C₅×#536	—	3	1	no	—
28	C₅×#519	—	3	1	no	—
29	C₅×#421	—	3	1	no	—
30	C₅×#421	D₃	1	1	yes	characteristic
31	C₂×C₅×#101	—	3	1	no	—
32	C₅×H(3,ℤ/4)	—	3	1	no	—
33	C₅×H(3,ℤ/4)	—	3	1	no	—
34	C₃×C₅×#41	—	2	1	no	—
35	C₃×C₅×#41	—	2	1	no	—
36	C₃×C₅×#41	—	2	1	no	—
37	C₃×C₅×#41	—	2	1	no	—
38	C₂×C₃×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
39	C₂×C₃×C₅×D₄	—	2	1	no	—
40	C₂×C₃×C₅×D₄	C₂×C₄	1	1	yes	characteristic
41	C₂²×C₃×C₄×C₅	—	2	1	no	—
42	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
43	C₂²×C₅×Dic₃	D₄	1	2	yes	—
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	—	2	1	no	—
48	C₂×C₅×Dic₆	C₂×C₄	1	2	yes	—
49	C₂×C₅×Dic₆	D₄	1	2	yes	—
50	C₃×C₅×M₁₆	—	2	1	no	—
51	C₃×C₅×M₁₆	—	2	1	no	—
52	C₂×C₃×C₅×C₈	—	2	1	no	—
53	C₃×C₅×C₄⋊C₄	—	2	1	no	—
54	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
55	C₃×C₄²×C₅	D₄	1	2	yes	—
56	C₅×#217	—	2	1	no	—
57	C₅×#217	—	2	1	no	—
58	C₅×#217	—	2	4	no	—
59	C₅×C₄⋊Dic₃	—	2	1	no	—
60	C₅×C₄⋊Dic₃	—	2	1	no	—
61	C₅×Dic₃⋊C₄	—	2	4	no	—
62	C₅×Dic₃⋊C₄	—	2	4	no	—
63	C₄×C₅×Dic₃	—	2	4	no	—
64	C₄×C₅×Dic₃	C₂×C₄	1	2	yes	—
65	C₄×C₅×Dic₃	D₄	1	2	yes	—
66	C₅×#208	—	2	1	no	—
67	C₅×#208	—	2	1	no	—
68	C₂×C₅×C₃⋊C₈	—	2	1	no	—
69	#5825	C₂×C₅	1	1	yes	characteristic
70	#5516	C₂×C₅	1	1	yes	characteristic, complemented
71	C₃×#421	C₂×C₅	1	1	yes	characteristic
72	#5236	C₂×C₅	1	1	yes	characteristic
73	C₂×#824	C₂×C₅	1	1	yes	characteristic, complemented
74	#4557	C₂×C₅	1	1	yes	characteristic, complemented
75	#4531	C₂×C₅	1	1	yes	characteristic, complemented
76	C₂×C₅×#41	C₂×D₃	1	1	yes	characteristic
77	C₂²×C₅×Q₈	—	3	1	no	—
78	C₂×C₅×M₁₆	—	3	1	no	—
79	C₂×C₅×M₁₆	C₂×D₃	1	1	yes	characteristic
80	C₅×C₄⋊Q₈	—	3	2	no	—
81	C₅×#124	—	3	2	no	—
82	C₅×#123	—	6	2	no	—
83	C₅×C₂²⋊Q₈	—	6	2	no	—
84	C₄×C₅×Q₈	—	6	2	no	—
85	C₄×C₅×Q₈	—	6	2	no	—
86	C₅×#117	—	3	1	no	—
87	C₅×#117	—	3	1	no	—
88	C₅×#117	—	6	2	no	—
89	C₅×#117	C₂×D₃	1	1	yes	characteristic
90	C₅×#104	—	2	2	no	—
91	C₅×#104	—	6	2	no	—
92	C₅×#101	—	6	2	no	—
93	#1912	—	3	1	no	Sylow
94	C₂³×C₃×C₅	—	2	1	no	—
95	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
96	C₃×C₅×Q₈	—	2	1	no	—
97	C₃×C₅×Q₈	—	2	1	no	—
98	C₃×C₅×D₄	—	2	1	no	—
99	C₃×C₅×D₄	—	2	1	no	—
100	C₃×C₅×D₄	—	4	1	no	—
101	C₃×C₅×D₄	—	4	1	no	—
102	C₂×C₃×C₄×C₅	—	2	1	no	—
103	C₂×C₃×C₄×C₅	—	2	2	no	—
104	C₂×C₃×C₄×C₅	—	4	1	no	—
105	C₂×C₃×C₄×C₅	—	4	1	no	—
106	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
107	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
108	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
109	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
110	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
111	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
112	C₂×C₅×Dic₃	—	2	2	no	—
113	C₂×C₅×Dic₃	—	2	2	no	—
114	C₂×C₅×Dic₃	—	2	2	no	—
115	C₂×C₅×Dic₃	—	2	2	no	—
116	C₂×C₅×Dic₃	C₂²⋊C₄	1	4	yes	—
117	C₅×Dic₆	—	2	2	no	—
118	C₅×Dic₆	—	2	2	no	—
119	C₅×Dic₆	—	2	2	no	—
120	C₅×Dic₆	—	2	2	no	—
121	C₃×C₅×C₈	—	4	1	no	—
122	C₅×C₃⋊C₈	—	4	1	no	—
123	C₂×C₃×#41	C₂²×C₅	1	1	yes	characteristic
124	C₂²×Dic₆	C₂²×C₅	1	1	yes	characteristic
125	C₂×C₃×M₁₆	C₂²×C₅	1	1	yes	characteristic
126	C₃×#117	C₂²×C₅	1	1	yes	characteristic
127	#944	C₄×C₅	1	2	yes	complemented
128	#936	C₄×C₅	1	2	yes	complemented
129	#935	—	2	2	no	—
130	#926	C₂²×C₅	1	1	yes	characteristic
131	#926	C₂²×C₅	1	1	yes	characteristic
132	#924	—	2	2	no	—
133	C₂×#208	C₂²×C₅	1	1	yes	characteristic
134	#887	—	2	2	no	—
135	#877	—	2	2	no	—
136	C₄×Dic₆	—	2	2	no	—
137	C₃×#104	—	2	2	no	—
138	#837	—	2	2	no	—
139	#824	—	2	2	no	—
140	C₅×#41	—	2	1	no	—
141	C₅×#41	—	2	1	no	—
142	C₅×#41	—	2	1	no	—
143	C₅×#41	—	2	1	no	—
144	C₂×C₅×Q₈	—	3	2	no	—
145	C₂×C₅×Q₈	—	3	2	no	—
146	C₂×C₅×Q₈	—	6	1	no	—
147	C₂×C₅×Q₈	—	6	1	no	—
148	C₂×C₅×Q₈	—	6	1	no	—
149	C₂×C₅×Q₈	—	6	1	no	—
150	C₂×C₅×Q₈	C₄×D₃	1	1	yes	characteristic
151	C₂×C₅×D₄	—	2	1	no	—
152	C₂×C₅×D₄	C₄×D₃	1	1	yes	characteristic
153	C₂²×C₄×C₅	—	2	1	no	—
154	C₂²×C₄×C₅	—	3	2	no	—
155	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
156	C₅×M₁₆	—	2	1	no	—
157	C₅×M₁₆	—	2	1	no	—
158	C₅×M₁₆	—	6	1	no	—
159	C₅×M₁₆	—	6	1	no	—
160	C₂×C₅×C₈	—	2	1	no	—
161	C₂×C₅×C₈	—	6	1	no	—
162	C₅×C₄⋊C₄	—	2	1	no	—
163	C₅×C₄⋊C₄	—	6	4	no	—
164	C₅×C₄⋊C₄	—	6	4	no	—
165	C₅×C₄⋊C₄	—	6	1	no	—
166	C₅×C₄⋊C₄	—	6	1	no	—
167	C₅×C₂²⋊C₄	—	2	1	no	—
168	C₅×C₂²⋊C₄	—	6	4	no	—
169	C₅×C₂²⋊C₄	—	6	1	no	—
170	C₅×C₂²⋊C₄	—	6	1	no	—
171	C₄²×C₅	—	3	2	no	—
172	C₄²×C₅	—	3	2	no	—
173	C₄²×C₅	—	6	4	no	—
174	C₄²×C₅	#67	1	2	yes	—
175	#536	—	3	1	no	—
176	#519	—	3	1	no	—
177	#421	—	3	1	no	—
178	#421	C₅×D₃	1	1	yes	characteristic
179	C₂×#101	—	3	1	no	—
180	H(3,ℤ/4)	—	3	1	no	—
181	H(3,ℤ/4)	—	3	1	no	—
182	C₂²×C₃×C₅	—	4	1	no	—
183	C₂²×C₃×C₅	—	4	2	no	—
184	C₂²×C₃×C₅	—	4	1	no	—
185	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
186	C₂²×C₃×C₅	#120	1	1	yes	characteristic
187	C₂²×C₃×C₅	#123	1	1	yes	characteristic
188	C₃×C₄×C₅	—	4	2	no	—
189	C₃×C₄×C₅	—	4	1	no	—
190	C₃×C₄×C₅	C₄×D₄	1	1	yes	characteristic
191	C₃×C₄×C₅	C₄×D₄	1	1	yes	characteristic
192	C₃×C₄×C₅	#121	1	1	yes	characteristic
193	C₃×C₄×C₅	#121	1	1	yes	characteristic
194	C₅×Dic₃	—	2	4	no	—
195	C₅×Dic₃	—	4	2	no	—
196	C₅×Dic₃	—	4	2	no	—
197	C₃×#41	—	2	1	no	—
198	C₃×#41	—	2	1	no	—
199	C₃×#41	—	2	1	no	—
200	C₃×#41	—	2	1	no	—
201	C₂×C₃×Q₈	C₂×C₄×C₅	1	1	yes	characteristic
202	C₂×C₃×D₄	—	2	1	no	—
203	C₂×C₃×D₄	C₂×C₄×C₅	1	1	yes	characteristic
204	C₂²×C₃×C₄	—	2	1	no	—
205	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
206	C₂²×Dic₃	C₅×D₄	1	2	yes	—
207	C₂×Dic₆	—	2	1	no	—
208	C₂×Dic₆	—	2	1	no	—
209	C₂×Dic₆	—	2	1	no	—
210	C₂×Dic₆	—	2	1	no	—
211	C₂×Dic₆	C₂×C₄×C₅	1	2	yes	—
212	C₂×Dic₆	C₅×D₄	1	2	yes	—
213	C₃×M₁₆	—	2	1	no	—
214	C₃×M₁₆	—	2	1	no	—
215	C₂×C₃×C₈	—	2	1	no	—
216	C₃×C₄⋊C₄	—	2	1	no	—
217	C₃×C₂²⋊C₄	—	2	1	no	—
218	C₃×C₄²	C₅×D₄	1	2	yes	—
219	#217	—	2	1	no	—
220	#217	—	2	1	no	—
221	#217	—	2	4	no	—
222	C₄⋊Dic₃	—	2	1	no	—
223	C₄⋊Dic₃	—	2	1	no	—
224	Dic₃⋊C₄	—	2	4	no	—
225	Dic₃⋊C₄	—	2	4	no	—
226	C₄×Dic₃	—	2	4	no	—
227	C₄×Dic₃	C₂×C₄×C₅	1	2	yes	—
228	C₄×Dic₃	C₅×D₄	1	2	yes	—
229	#208	—	2	1	no	—
230	#208	—	2	1	no	—
231	C₂×C₃⋊C₈	—	2	1	no	—
232	C₂³×C₅	—	2	1	no	—
233	C₂³×C₅	D₃×D₄	1	1	yes	characteristic
234	C₅×Q₈	—	2	1	no	—
235	C₅×Q₈	—	2	1	no	—
236	C₅×Q₈	—	6	2	no	—
237	C₅×Q₈	—	6	2	no	—
238	C₅×Q₈	—	6	2	no	—
239	C₅×Q₈	—	6	2	no	—
240	C₅×D₄	—	2	1	no	—
241	C₅×D₄	—	2	1	no	—
242	C₅×D₄	—	4	1	no	—
243	C₅×D₄	—	4	1	no	—
244	C₂×C₄×C₅	—	2	1	no	—
245	C₂×C₄×C₅	—	2	2	no	—
246	C₂×C₄×C₅	—	3	4	no	—
247	C₂×C₄×C₅	—	4	1	no	—
248	C₂×C₄×C₅	—	4	1	no	—
249	C₂×C₄×C₅	—	6	2	no	—
250	C₂×C₄×C₅	—	6	2	no	—
251	C₂×C₄×C₅	—	6	2	no	—
252	C₂×C₄×C₅	—	6	2	no	—
253	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
254	C₂×C₄×C₅	#235	1	1	yes	characteristic
255	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
256	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
257	C₂×C₄×C₅	#237	1	1	yes	characteristic
258	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
259	C₅×C₈	—	4	1	no	—
260	C₅×C₈	—	12	1	no	—
261	C₂×#41	C₂×C₅×D₃	1	1	yes	characteristic
262	C₂²×Q₈	—	3	1	no	—
263	C₂×M₁₆	—	3	1	no	—
264	C₂×M₁₆	C₂×C₅×D₃	1	1	yes	characteristic
265	C₄⋊Q₈	—	3	2	no	—
266	#124	—	3	2	no	—
267	#123	—	6	2	no	—
268	C₂²⋊Q₈	—	6	2	no	—
269	C₄×Q₈	—	6	2	no	—
270	C₄×Q₈	—	6	2	no	—
271	#117	—	3	1	no	—
272	#117	—	3	1	no	—
273	#117	—	6	2	no	—
274	#117	C₂×C₅×D₃	1	1	yes	characteristic
275	#104	—	2	2	no	—
276	#104	—	6	2	no	—
277	#101	—	6	2	no	—
278	C₂×C₃×C₅	—	2	1	no	—
279	C₂×C₃×C₅	—	2	1	no	—
280	C₂×C₃×C₅	—	2	1	no	—
281	C₂×C₃×C₅	—	8	1	no	—
282	C₂×C₃×C₅	#386	1	1	yes	characteristic
283	C₂³×C₃	—	2	1	no	—
284	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
285	C₃×Q₈	—	2	1	no	—
286	C₃×Q₈	—	2	1	no	—
287	C₃×D₄	—	2	1	no	—
288	C₃×D₄	—	2	1	no	—
289	C₃×D₄	—	4	1	no	—
290	C₃×D₄	—	4	1	no	—
291	C₂×C₃×C₄	—	2	1	no	—
292	C₂×C₃×C₄	—	2	2	no	—
293	C₂×C₃×C₄	—	4	1	no	—
294	C₂×C₃×C₄	—	4	1	no	—
295	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
296	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
297	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
298	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
299	C₂×C₃×C₄	C₅×#41	1	1	yes	characteristic
300	C₂×C₃×C₄	C₅×#41	1	1	yes	characteristic
301	C₂×Dic₃	—	2	2	no	—
302	C₂×Dic₃	—	2	2	no	—
303	C₂×Dic₃	—	2	2	no	—
304	C₂×Dic₃	—	2	2	no	—
305	C₂×Dic₃	C₅×C₂²⋊C₄	1	4	yes	—
306	Dic₆	—	2	2	no	—
307	Dic₆	—	2	2	no	—
308	Dic₆	—	2	2	no	—
309	Dic₆	—	2	2	no	—
310	C₃×C₈	—	4	1	no	—
311	C₃⋊C₈	—	4	1	no	—
312	C₂²×C₅	—	4	1	no	—
313	C₂²×C₅	—	4	2	no	—
314	C₂²×C₅	—	4	1	no	—
315	C₂²×C₅	D₃×C₂²⋊C₄	1	1	yes	characteristic
316	C₂²×C₅	#883	1	1	yes	characteristic
317	C₂²×C₅	#937	1	1	yes	characteristic
318	C₄×C₅	—	4	2	no	—
319	C₄×C₅	—	4	1	no	—
320	C₄×C₅	—	6	4	no	—
321	C₄×C₅	—	12	2	no	—
322	C₄×C₅	—	12	2	no	—
323	C₄×C₅	#67⋊C₄	1	1	yes	characteristic
324	C₄×C₅	#884	1	1	yes	characteristic
325	C₄×C₅	C₄×#67	1	1	yes	characteristic
326	C₄×C₅	#938	1	1	yes	characteristic
327	#41	—	2	1	no	—
328	#41	—	2	1	no	—
329	#41	—	2	1	no	—
330	#41	—	2	1	no	—
331	C₂×Q₈	—	3	2	no	—
332	C₂×Q₈	—	3	2	no	—
333	C₂×Q₈	—	6	1	no	—
334	C₂×Q₈	—	6	1	no	—
335	C₂×Q₈	—	6	1	no	—
336	C₂×Q₈	—	6	1	no	—
337	C₂×Q₈	C₄×C₅×D₃	1	1	yes	characteristic
338	C₂×D₄	—	2	1	no	—
339	C₂×D₄	C₄×C₅×D₃	1	1	yes	characteristic
340	C₂²×C₄	—	2	1	no	—
341	C₂²×C₄	—	3	2	no	—
342	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
343	M₁₆	—	2	1	no	—
344	M₁₆	—	2	1	no	—
345	M₁₆	—	6	1	no	—
346	M₁₆	—	6	1	no	—
347	C₂×C₈	—	2	1	no	—
348	C₂×C₈	—	6	1	no	—
349	C₄⋊C₄	—	2	1	no	—
350	C₄⋊C₄	—	6	4	no	—
351	C₄⋊C₄	—	6	4	no	—
352	C₄⋊C₄	—	6	1	no	—
353	C₄⋊C₄	—	6	1	no	—
354	C₂²⋊C₄	—	2	1	no	—
355	C₂²⋊C₄	—	6	4	no	—
356	C₂²⋊C₄	—	6	1	no	—
357	C₂²⋊C₄	—	6	1	no	—
358	C₄²	—	3	2	no	—
359	C₄²	—	3	2	no	—
360	C₄²	—	6	4	no	—
361	C₄²	C₅×#67	1	2	yes	—
362	C₃×C₅	#1912	1	1	yes	characteristic, complemented, Hall
363	C₂²×C₃	—	4	1	no	—
364	C₂²×C₃	—	4	2	no	—
365	C₂²×C₃	—	4	1	no	—
366	C₂²×C₃	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
367	C₂²×C₃	C₅×#120	1	1	yes	characteristic
368	C₂²×C₃	C₅×#123	1	1	yes	characteristic
369	C₃×C₄	—	4	2	no	—
370	C₃×C₄	—	4	1	no	—
371	C₃×C₄	C₄×C₅×D₄	1	1	yes	characteristic
372	C₃×C₄	C₄×C₅×D₄	1	1	yes	characteristic
373	C₃×C₄	C₅×#121	1	1	yes	characteristic
374	C₃×C₄	C₅×#121	1	1	yes	characteristic
375	Dic₃	—	2	4	no	—
376	Dic₃	—	4	2	no	—
377	Dic₃	—	4	2	no	—
378	C₂×C₅	—	2	1	no	—
379	C₂×C₅	—	2	1	no	—
380	C₂×C₅	—	2	1	no	—
381	C₂×C₅	—	8	1	no	—
382	C₂×C₅	#4956	1	1	yes	characteristic
383	C₂³	—	2	1	no	—
384	C₂³	C₅×D₃×D₄	1	1	yes	characteristic
385	Q₈	—	2	1	no	—
386	Q₈	—	2	1	no	—
387	Q₈	—	6	2	no	—
388	Q₈	—	6	2	no	—
389	Q₈	—	6	2	no	—
390	Q₈	—	6	2	no	—
391	D₄	—	2	1	no	—
392	D₄	—	2	1	no	—
393	D₄	—	4	1	no	—
394	D₄	—	4	1	no	—
395	C₂×C₄	—	2	1	no	—
396	C₂×C₄	—	2	2	no	—
397	C₂×C₄	—	3	4	no	—
398	C₂×C₄	—	4	1	no	—
399	C₂×C₄	—	4	1	no	—
400	C₂×C₄	—	6	2	no	—
401	C₂×C₄	—	6	2	no	—
402	C₂×C₄	—	6	2	no	—
403	C₂×C₄	—	6	2	no	—
404	C₂×C₄	C₂×C₄×C₅×D₃	1	1	yes	characteristic
405	C₂×C₄	C₅×#235	1	1	yes	characteristic
406	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
407	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
408	C₂×C₄	C₅×#237	1	1	yes	characteristic
409	C₂×C₄	C₂×C₅×#67	1	1	yes	characteristic
410	C₈	—	4	1	no	—
411	C₈	—	12	1	no	—
412	C₂×C₃	—	2	1	no	—
413	C₂×C₃	—	2	1	no	—
414	C₂×C₃	—	2	1	no	—
415	C₂×C₃	—	8	1	no	—
416	C₂×C₃	C₅×#386	1	1	yes	characteristic
417	C₅	#70411	1	1	yes	characteristic, direct product factor, Sylow
418	C₂²	—	4	1	no	—
419	C₂²	—	4	2	no	—
420	C₂²	—	4	1	no	—
421	C₂²	C₅×D₃×C₂²⋊C₄	1	1	yes	characteristic
422	C₂²	C₅×#883	1	1	yes	characteristic
423	C₂²	C₅×#937	1	1	yes	characteristic
424	C₄	—	4	2	no	—
425	C₄	—	4	1	no	—
426	C₄	—	6	4	no	—
427	C₄	—	12	2	no	—
428	C₄	—	12	2	no	—
429	C₄	C₅×#67⋊C₄	1	1	yes	characteristic
430	C₄	C₅×#884	1	1	yes	characteristic
431	C₄	C₄×C₅×#67	1	1	yes	characteristic
432	C₄	C₅×#938	1	1	yes	characteristic
433	C₃	C₅×#1912	1	1	yes	characteristic, complemented, Sylow
434	C₂	—	2	1	no	—
435	C₂	—	2	1	no	—
436	C₂	—	2	1	no	—
437	C₂	—	8	1	no	—
438	C₂	C₅×#4956	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₅	#4956
commutator	C₂×C₃×C₄	C₂²×C₄×C₅
Frattini	C₂²×C₄	C₂²×C₅×D₃
Fitting	C₃×C₅×#421	C₂
socle	C₂×C₃×C₅	#386
prime radical	C₂×C₃×C₅×#41	C₂²
cosocle	C₂²×C₃×C₄	C₂³×C₅
hypercenter	C₅×#421	D₃
hypocenter	C₃	C₅×#1912
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₅ ◁ C₂²×C₄×C₅ ◁ C₅×#421

Complements

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

N	H ≅ G/N	type
2. C₅×#5516	C₂	semidirect
5. C₂×C₅×#824	C₂	semidirect
6. C₅×#4557	C₂	semidirect
7. C₅×#4531	C₂	semidirect
13. C₅×#944	C₄	semidirect
14. C₅×#936	C₄	semidirect
26. #70411	C₅	direct (N × H)
70. #5516	C₂×C₅	semidirect
73. C₂×#824	C₂×C₅	semidirect
74. #4557	C₂×C₅	semidirect
75. #4531	C₂×C₅	semidirect
127. #944	C₄×C₅	semidirect
128. #936	C₄×C₅	semidirect
362. C₃×C₅	#1912	semidirect
417. C₅	#70411	direct (N × H)
433. C₃	C₅×#1912	semidirect

Maximal subgroups

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

subgroup	index
C₅×#5825	2
C₅×#5516	2
C₃×C₅×#421	2
C₅×#5236	2
C₂×C₅×#824	2
C₅×#4557	2
C₅×#4531	2
C₅×#1912	3
#70411	5

Subgroups — C5×#70411 #14302926

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#70411 #14302926