Subgroups — C₅×#68309 #14282915

Order 1920.

480 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×#5622	C₂	1	1	yes	maximal, characteristic
2	C₅×#4718	C₂	1	1	yes	maximal, characteristic
3	C₅×#4649	C₂	1	1	yes	maximal, characteristic
4	C₃×C₅×#328	C₂	1	1	yes	maximal, characteristic
5	C₅×#4538	C₂	1	1	yes	maximal, characteristic
6	C₅×#4467	C₂	1	1	yes	maximal, characteristic
7	C₅×#4452	C₂	1	1	yes	maximal, characteristic
8	C₅×#1503	—	3	1	no	maximal, Hall
9	C₃×C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
10	C₅×Q₈×Dic₃	C₄	1	1	yes	characteristic, complemented
11	C₅×#944	C₄	1	1	yes	characteristic, complemented
12	C₅×#924	C₂²	1	1	yes	characteristic
13	C₂×C₅×Dic₃⋊C₄	—	2	1	no	—
14	C₂×C₄×C₅×Dic₃	—	2	1	no	—
15	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
16	C₅×#889	—	2	1	no	—
17	C₅×#888	C₄	1	1	yes	characteristic, complemented
18	C₅×#887	—	2	1	no	—
19	C₅×#887	C₄	1	1	yes	characteristic, complemented
20	C₅×#878	—	2	1	no	—
21	C₅×#877	—	2	1	no	—
22	C₃×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic
23	C₃×C₅×#95	C₂²	1	1	yes	characteristic
24	C₅×C₃⋊#95	C₂²	1	1	yes	characteristic
25	C₅×#830	C₂²	1	1	yes	characteristic
26	C₅×Dic₃⋊C₈	—	2	1	no	—
27	C₅×C₈×Dic₃	—	2	1	no	—
28	#68309	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
29	C₅×#533	—	3	1	no	—
30	C₅×#431	—	3	1	no	—
31	C₄×C₅×C₄⋊C₄	—	3	1	no	—
32	C₅×#328	—	3	1	no	—
33	C₅×#328	—	3	1	no	—
34	C₅×#328	—	3	1	no	—
35	C₅×#328	D₃	1	1	yes	characteristic
36	C₂×C₃×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
37	C₂²×C₃×C₄×C₅	—	2	1	no	—
38	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
39	C₂²×C₅×Dic₃	—	2	1	no	—
40	C₂²×C₅×Dic₃	D₄	1	1	yes	characteristic
41	C₂²×C₅×Dic₃	D₄	1	1	yes	characteristic
42	C₂×C₅×Dic₆	—	2	1	no	—
43	C₂×C₅×Dic₆	C₂×C₄	1	1	yes	characteristic
44	C₂×C₃×C₅×C₈	—	2	1	no	—
45	C₃×C₅×C₄⋊C₄	—	2	1	no	—
46	C₃×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
47	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
48	C₅×#217	—	2	1	no	—
49	C₅×C₄⋊Dic₃	—	2	1	no	—
50	C₅×C₄⋊Dic₃	C₂×C₄	1	1	yes	characteristic
51	C₅×Dic₃⋊C₄	—	2	4	no	—
52	C₅×Dic₃⋊C₄	—	2	1	no	—
53	C₅×Dic₃⋊C₄	—	2	1	no	—
54	C₅×Dic₃⋊C₄	—	2	1	no	—
55	C₅×Dic₃⋊C₄	—	2	1	no	—
56	C₅×Dic₃⋊C₄	—	2	1	no	—
57	C₄×C₅×Dic₃	—	2	1	no	—
58	C₄×C₅×Dic₃	—	2	1	no	—
59	C₄×C₅×Dic₃	—	4	2	no	—
60	C₄×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
61	C₄×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
62	C₄×C₅×Dic₃	D₄	1	1	yes	characteristic
63	C₄×C₅×Dic₃	D₄	1	1	yes	characteristic
64	C₂×C₅×C₃⋊C₈	—	2	1	no	—
65	#5622	C₂×C₅	1	1	yes	characteristic
66	#4718	C₂×C₅	1	1	yes	characteristic
67	#4649	C₂×C₅	1	1	yes	characteristic
68	C₃×#328	C₂×C₅	1	1	yes	characteristic
69	#4538	C₂×C₅	1	1	yes	characteristic
70	#4467	C₂×C₅	1	1	yes	characteristic
71	#4452	C₂×C₅	1	1	yes	characteristic
72	C₅×C₄⋊Q₈	—	3	1	no	—
73	C₅×C₄⋊Q₈	—	3	1	no	—
74	C₅×#125	—	6	1	no	—
75	C₅×C₂²⋊Q₈	—	3	1	no	—
76	C₅×C₂²⋊Q₈	—	6	1	no	—
77	C₅×C₂²⋊Q₈	C₂×D₃	1	1	yes	characteristic
78	C₄×C₅×Q₈	—	3	1	no	—
79	C₄×C₅×Q₈	—	3	1	no	—
80	C₄×C₅×Q₈	—	6	1	no	—
81	C₅×#117	—	6	1	no	—
82	C₂×C₅×C₄⋊C₄	—	6	1	no	—
83	C₂×C₄²×C₅	—	3	1	no	—
84	C₂×C₄²×C₅	—	6	1	no	—
85	C₅×C₄⋊C₈	—	6	1	no	—
86	C₅×C₂²⋊C₈	—	3	1	no	—
87	C₅×C₂²⋊C₈	C₂×D₃	1	1	yes	characteristic
88	C₄×C₅×C₈	—	6	1	no	—
89	C₅×#95	—	3	1	no	—
90	C₅×#95	C₂×D₃	1	1	yes	characteristic
91	#1503	—	3	1	no	Sylow
92	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
93	C₃×C₅×Q₈	—	4	1	no	—
94	C₂×C₃×C₄×C₅	—	2	2	no	—
95	C₂×C₃×C₄×C₅	—	2	1	no	—
96	C₂×C₃×C₄×C₅	—	2	1	no	—
97	C₂×C₃×C₄×C₅	—	4	1	no	—
98	C₂×C₃×C₄×C₅	—	4	1	no	—
99	C₂×C₃×C₄×C₅	—	4	1	no	—
100	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
101	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
102	C₂×C₅×Dic₃	—	2	2	no	—
103	C₂×C₅×Dic₃	—	2	2	no	—
104	C₂×C₅×Dic₃	—	2	1	no	—
105	C₂×C₅×Dic₃	—	2	1	no	—
106	C₂×C₅×Dic₃	—	4	1	no	—
107	C₂×C₅×Dic₃	—	4	1	no	—
108	C₂×C₅×Dic₃	C₂²⋊C₄	1	1	yes	characteristic
109	C₂×C₅×Dic₃	C₂²⋊C₄	1	1	yes	characteristic
110	C₂×C₅×Dic₃	C₂²⋊C₄	1	1	yes	characteristic
111	C₂×C₅×Dic₃	C₂²⋊C₄	1	1	yes	characteristic
112	C₂×C₅×Dic₃	SD₁₆	1	2	yes	—
113	C₂×C₅×Dic₃	Q₁₆	1	2	yes	—
114	C₅×Dic₆	—	4	2	no	—
115	C₅×Dic₆	—	4	1	no	—
116	C₃×C₅×C₈	—	4	1	no	—
117	C₅×C₃⋊C₈	—	4	1	no	—
118	C₃×C₂²⋊Q₈	C₂²×C₅	1	1	yes	characteristic
119	Q₈×Dic₃	C₄×C₅	1	1	yes	characteristic, complemented
120	#944	C₄×C₅	1	1	yes	characteristic, complemented
121	#924	C₂²×C₅	1	1	yes	characteristic
122	C₂×Dic₃⋊C₄	—	2	1	no	—
123	C₂×C₄×Dic₃	—	2	1	no	—
124	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
125	#889	—	2	1	no	—
126	#888	C₄×C₅	1	1	yes	characteristic, complemented
127	#887	—	2	1	no	—
128	#887	C₄×C₅	1	1	yes	characteristic, complemented
129	#878	—	2	1	no	—
130	#877	—	2	1	no	—
131	C₃×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
132	C₃×#95	C₂²×C₅	1	1	yes	characteristic
133	C₃⋊#95	C₂²×C₅	1	1	yes	characteristic
134	#830	C₂²×C₅	1	1	yes	characteristic
135	Dic₃⋊C₈	—	2	1	no	—
136	C₈×Dic₃	—	2	1	no	—
137	C₂×C₅×Q₈	—	3	1	no	—
138	C₂×C₅×Q₈	—	6	1	no	—
139	C₂×C₅×Q₈	C₄×D₃	1	1	yes	characteristic
140	C₂²×C₄×C₅	—	2	1	no	—
141	C₂²×C₄×C₅	—	3	1	no	—
142	C₂²×C₄×C₅	—	3	1	no	—
143	C₂²×C₄×C₅	—	6	1	no	—
144	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
145	C₂×C₅×C₈	—	2	1	no	—
146	C₂×C₅×C₈	—	6	1	no	—
147	C₅×C₄⋊C₄	—	2	1	no	—
148	C₅×C₄⋊C₄	—	3	1	no	—
149	C₅×C₄⋊C₄	—	6	1	no	—
150	C₅×C₄⋊C₄	—	6	1	no	—
151	C₅×C₄⋊C₄	—	6	1	no	—
152	C₅×C₄⋊C₄	—	6	1	no	—
153	C₅×C₄⋊C₄	—	6	1	no	—
154	C₅×C₄⋊C₄	—	6	4	no	—
155	C₅×C₄⋊C₄	—	6	1	no	—
156	C₅×C₄⋊C₄	C₄×D₃	1	1	yes	characteristic
157	C₅×C₂²⋊C₄	—	2	1	no	—
158	C₅×C₂²⋊C₄	—	6	1	no	—
159	C₄²×C₅	—	3	1	no	—
160	C₄²×C₅	—	3	1	no	—
161	C₄²×C₅	—	3	1	no	—
162	C₄²×C₅	—	3	1	no	—
163	C₄²×C₅	—	6	1	no	—
164	C₄²×C₅	—	6	1	no	—
165	C₄²×C₅	—	12	2	no	—
166	#533	—	3	1	no	—
167	#431	—	3	1	no	—
168	C₄×C₄⋊C₄	—	3	1	no	—
169	#328	—	3	1	no	—
170	#328	—	3	1	no	—
171	#328	—	3	1	no	—
172	#328	C₅×D₃	1	1	yes	characteristic
173	C₂²×C₃×C₅	—	2	1	no	—
174	C₂²×C₃×C₅	—	2	1	no	—
175	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
176	C₂²×C₃×C₅	C₂×SD₁₆	1	1	yes	characteristic
177	C₂²×C₃×C₅	C₂×Q₁₆	1	1	yes	characteristic
178	C₃×C₄×C₅	—	2	1	no	—
179	C₃×C₄×C₅	—	2	1	no	—
180	C₃×C₄×C₅	—	4	2	no	—
181	C₃×C₄×C₅	—	4	1	no	—
182	C₃×C₄×C₅	—	4	1	no	—
183	C₅×Dic₃	—	2	1	no	—
184	C₅×Dic₃	—	4	2	no	—
185	C₅×Dic₃	—	4	1	no	—
186	C₅×Dic₃	—	4	1	no	—
187	C₅×Dic₃	#103	1	2	yes	—
188	C₅×Dic₃	#103	1	2	yes	—
189	C₅×Dic₃	#104	1	2	yes	—
190	C₂×C₃×Q₈	C₂×C₄×C₅	1	1	yes	characteristic
191	C₂²×C₃×C₄	—	2	1	no	—
192	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
193	C₂²×Dic₃	—	2	1	no	—
194	C₂²×Dic₃	C₅×D₄	1	1	yes	characteristic
195	C₂²×Dic₃	C₅×D₄	1	1	yes	characteristic
196	C₂×Dic₆	—	2	1	no	—
197	C₂×Dic₆	C₂×C₄×C₅	1	1	yes	characteristic
198	C₂×C₃×C₈	—	2	1	no	—
199	C₃×C₄⋊C₄	—	2	1	no	—
200	C₃×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
201	C₃×C₂²⋊C₄	—	2	1	no	—
202	#217	—	2	1	no	—
203	C₄⋊Dic₃	—	2	1	no	—
204	C₄⋊Dic₃	C₂×C₄×C₅	1	1	yes	characteristic
205	Dic₃⋊C₄	—	2	4	no	—
206	Dic₃⋊C₄	—	2	1	no	—
207	Dic₃⋊C₄	—	2	1	no	—
208	Dic₃⋊C₄	—	2	1	no	—
209	Dic₃⋊C₄	—	2	1	no	—
210	Dic₃⋊C₄	—	2	1	no	—
211	C₄×Dic₃	—	2	1	no	—
212	C₄×Dic₃	—	2	1	no	—
213	C₄×Dic₃	—	4	2	no	—
214	C₄×Dic₃	C₂×C₄×C₅	1	1	yes	characteristic
215	C₄×Dic₃	C₂×C₄×C₅	1	1	yes	characteristic
216	C₄×Dic₃	C₅×D₄	1	1	yes	characteristic
217	C₄×Dic₃	C₅×D₄	1	1	yes	characteristic
218	C₂×C₃⋊C₈	—	2	1	no	—
219	C₂³×C₅	D₃×D₄	1	1	yes	characteristic
220	C₅×Q₈	—	4	1	no	—
221	C₅×Q₈	—	12	1	no	—
222	C₅×Q₈	—	12	2	no	—
223	C₂×C₄×C₅	—	2	2	no	—
224	C₂×C₄×C₅	—	2	1	no	—
225	C₂×C₄×C₅	—	2	1	no	—
226	C₂×C₄×C₅	—	3	1	no	—
227	C₂×C₄×C₅	—	3	1	no	—
228	C₂×C₄×C₅	—	3	1	no	—
229	C₂×C₄×C₅	—	3	2	no	—
230	C₂×C₄×C₅	—	3	2	no	—
231	C₂×C₄×C₅	—	3	1	no	—
232	C₂×C₄×C₅	—	4	1	no	—
233	C₂×C₄×C₅	—	4	1	no	—
234	C₂×C₄×C₅	—	4	1	no	—
235	C₂×C₄×C₅	—	6	2	no	—
236	C₂×C₄×C₅	—	6	2	no	—
237	C₂×C₄×C₅	—	6	1	no	—
238	C₂×C₄×C₅	—	6	1	no	—
239	C₂×C₄×C₅	—	12	1	no	—
240	C₂×C₄×C₅	—	12	1	no	—
241	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
242	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
243	C₅×C₈	—	4	1	no	—
244	C₅×C₈	—	12	1	no	—
245	C₄⋊Q₈	—	3	1	no	—
246	C₄⋊Q₈	—	3	1	no	—
247	#125	—	6	1	no	—
248	C₂²⋊Q₈	—	3	1	no	—
249	C₂²⋊Q₈	—	6	1	no	—
250	C₂²⋊Q₈	C₂×C₅×D₃	1	1	yes	characteristic
251	C₄×Q₈	—	3	1	no	—
252	C₄×Q₈	—	3	1	no	—
253	C₄×Q₈	—	6	1	no	—
254	#117	—	6	1	no	—
255	C₂×C₄⋊C₄	—	6	1	no	—
256	C₂×C₄²	—	3	1	no	—
257	C₂×C₄²	—	6	1	no	—
258	C₄⋊C₈	—	6	1	no	—
259	C₂²⋊C₈	—	3	1	no	—
260	C₂²⋊C₈	C₂×C₅×D₃	1	1	yes	characteristic
261	C₄×C₈	—	6	1	no	—
262	#95	—	3	1	no	—
263	#95	C₂×C₅×D₃	1	1	yes	characteristic
264	C₂×C₃×C₅	—	2	1	no	—
265	C₂×C₃×C₅	—	2	1	no	—
266	C₂×C₃×C₅	#410	1	1	yes	characteristic
267	C₂×C₃×C₅	C₂×#103	1	1	yes	characteristic
268	C₂×C₃×C₅	C₂×#104	1	1	yes	characteristic
269	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
270	C₃×Q₈	—	4	1	no	—
271	C₂×C₃×C₄	—	2	2	no	—
272	C₂×C₃×C₄	—	2	1	no	—
273	C₂×C₃×C₄	—	2	1	no	—
274	C₂×C₃×C₄	—	4	1	no	—
275	C₂×C₃×C₄	—	4	1	no	—
276	C₂×C₃×C₄	—	4	1	no	—
277	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
278	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
279	C₂×Dic₃	—	2	2	no	—
280	C₂×Dic₃	—	2	2	no	—
281	C₂×Dic₃	—	2	1	no	—
282	C₂×Dic₃	—	2	1	no	—
283	C₂×Dic₃	—	4	1	no	—
284	C₂×Dic₃	—	4	1	no	—
285	C₂×Dic₃	C₅×C₂²⋊C₄	1	1	yes	characteristic
286	C₂×Dic₃	C₅×C₂²⋊C₄	1	1	yes	characteristic
287	C₂×Dic₃	C₅×C₂²⋊C₄	1	1	yes	characteristic
288	C₂×Dic₃	C₅×C₂²⋊C₄	1	1	yes	characteristic
289	C₂×Dic₃	C₅×SD₁₆	1	2	yes	—
290	C₂×Dic₃	C₅×Q₁₆	1	2	yes	—
291	Dic₆	—	4	2	no	—
292	Dic₆	—	4	1	no	—
293	C₃×C₈	—	4	1	no	—
294	C₃⋊C₈	—	4	1	no	—
295	C₂²×C₅	—	2	1	no	—
296	C₂²×C₅	—	2	1	no	—
297	C₂²×C₅	D₃×C₂²⋊C₄	1	1	yes	characteristic
298	C₂²×C₅	D₃×SD₁₆	1	1	yes	characteristic
299	C₂²×C₅	D₃×Q₁₆	1	1	yes	characteristic
300	C₄×C₅	—	2	1	no	—
301	C₄×C₅	—	2	1	no	—
302	C₄×C₅	—	3	2	no	—
303	C₄×C₅	—	3	2	no	—
304	C₄×C₅	—	3	2	no	—
305	C₄×C₅	—	4	2	no	—
306	C₄×C₅	—	4	1	no	—
307	C₄×C₅	—	4	1	no	—
308	C₄×C₅	—	6	1	no	—
309	C₄×C₅	—	12	2	no	—
310	C₄×C₅	—	12	1	no	—
311	C₄×C₅	—	12	1	no	—
312	C₂×Q₈	—	3	1	no	—
313	C₂×Q₈	—	6	1	no	—
314	C₂×Q₈	C₄×C₅×D₃	1	1	yes	characteristic
315	C₂²×C₄	—	2	1	no	—
316	C₂²×C₄	—	3	1	no	—
317	C₂²×C₄	—	3	1	no	—
318	C₂²×C₄	—	6	1	no	—
319	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
320	C₂×C₈	—	2	1	no	—
321	C₂×C₈	—	6	1	no	—
322	C₄⋊C₄	—	2	1	no	—
323	C₄⋊C₄	—	3	1	no	—
324	C₄⋊C₄	—	6	1	no	—
325	C₄⋊C₄	—	6	1	no	—
326	C₄⋊C₄	—	6	1	no	—
327	C₄⋊C₄	—	6	1	no	—
328	C₄⋊C₄	—	6	1	no	—
329	C₄⋊C₄	—	6	4	no	—
330	C₄⋊C₄	—	6	1	no	—
331	C₄⋊C₄	C₄×C₅×D₃	1	1	yes	characteristic
332	C₂²⋊C₄	—	2	1	no	—
333	C₂²⋊C₄	—	6	1	no	—
334	C₄²	—	3	1	no	—
335	C₄²	—	3	1	no	—
336	C₄²	—	3	1	no	—
337	C₄²	—	3	1	no	—
338	C₄²	—	6	1	no	—
339	C₄²	—	6	1	no	—
340	C₄²	—	12	2	no	—
341	C₃×C₅	#1503	1	1	yes	characteristic, complemented, Hall
342	C₂²×C₃	—	2	1	no	—
343	C₂²×C₃	—	2	1	no	—
344	C₂²×C₃	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
345	C₂²×C₃	C₂×C₅×SD₁₆	1	1	yes	characteristic
346	C₂²×C₃	C₂×C₅×Q₁₆	1	1	yes	characteristic
347	C₃×C₄	—	2	1	no	—
348	C₃×C₄	—	2	1	no	—
349	C₃×C₄	—	4	2	no	—
350	C₃×C₄	—	4	1	no	—
351	C₃×C₄	—	4	1	no	—
352	Dic₃	—	2	1	no	—
353	Dic₃	—	4	2	no	—
354	Dic₃	—	4	1	no	—
355	Dic₃	—	4	1	no	—
356	Dic₃	C₅×#103	1	2	yes	—
357	Dic₃	C₅×#103	1	2	yes	—
358	Dic₃	C₅×#104	1	2	yes	—
359	C₂×C₅	—	2	1	no	—
360	C₂×C₅	—	2	1	no	—
361	C₂×C₅	#4740	1	1	yes	characteristic
362	C₂×C₅	D₃×#103	1	1	yes	characteristic
363	C₂×C₅	D₃×#104	1	1	yes	characteristic
364	C₂³	C₅×D₃×D₄	1	1	yes	characteristic
365	Q₈	—	4	1	no	—
366	Q₈	—	12	1	no	—
367	Q₈	—	12	2	no	—
368	C₂×C₄	—	2	2	no	—
369	C₂×C₄	—	2	1	no	—
370	C₂×C₄	—	2	1	no	—
371	C₂×C₄	—	3	1	no	—
372	C₂×C₄	—	3	1	no	—
373	C₂×C₄	—	3	1	no	—
374	C₂×C₄	—	3	2	no	—
375	C₂×C₄	—	3	2	no	—
376	C₂×C₄	—	3	1	no	—
377	C₂×C₄	—	4	1	no	—
378	C₂×C₄	—	4	1	no	—
379	C₂×C₄	—	4	1	no	—
380	C₂×C₄	—	6	2	no	—
381	C₂×C₄	—	6	2	no	—
382	C₂×C₄	—	6	1	no	—
383	C₂×C₄	—	6	1	no	—
384	C₂×C₄	—	12	1	no	—
385	C₂×C₄	—	12	1	no	—
386	C₂×C₄	C₂×C₄×C₅×D₃	1	1	yes	characteristic
387	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
388	C₈	—	4	1	no	—
389	C₈	—	12	1	no	—
390	C₂×C₃	—	2	1	no	—
391	C₂×C₃	—	2	1	no	—
392	C₂×C₃	C₅×#410	1	1	yes	characteristic
393	C₂×C₃	C₂×C₅×#103	1	1	yes	characteristic
394	C₂×C₃	C₂×C₅×#104	1	1	yes	characteristic
395	C₅	#68309	1	1	yes	characteristic, direct product factor, Sylow
396	C₂²	—	2	1	no	—
397	C₂²	—	2	1	no	—
398	C₂²	C₅×D₃×C₂²⋊C₄	1	1	yes	characteristic
399	C₂²	C₅×D₃×SD₁₆	1	1	yes	characteristic
400	C₂²	C₅×D₃×Q₁₆	1	1	yes	characteristic
401	C₄	—	2	1	no	—
402	C₄	—	2	1	no	—
403	C₄	—	3	2	no	—
404	C₄	—	3	2	no	—
405	C₄	—	3	2	no	—
406	C₄	—	4	2	no	—
407	C₄	—	4	1	no	—
408	C₄	—	4	1	no	—
409	C₄	—	6	1	no	—
410	C₄	—	12	2	no	—
411	C₄	—	12	1	no	—
412	C₄	—	12	1	no	—
413	C₃	C₅×#1503	1	1	yes	characteristic, complemented, Sylow
414	C₂	—	2	1	no	—
415	C₂	—	2	1	no	—
416	C₂	C₅×#4740	1	1	yes	characteristic
417	C₂	C₅×D₃×#103	1	1	yes	characteristic
418	C₂	C₅×D₃×#104	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₅	D₃×C₂²⋊C₄
commutator	C₂×C₃×C₄	C₂²×C₄×C₅
Frattini	C₂²×C₄	C₂²×C₅×D₃
Fitting	C₃×C₅×#328	C₂
socle	C₂²×C₃×C₅	C₂×C₂²⋊C₄
prime radical	C₂³×C₃×C₅	C₂×D₄
cosocle	C₂²×C₃×C₄	C₂³×C₅
hypercenter	C₅×#328	D₃
hypocenter	C₃	C₅×#1503
LCS	G ▷ C₂×C₃×C₄ ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₂²×C₄×C₅ ◁ C₅×#328

Complements

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

N	H ≅ G/N	type
10. C₅×Q₈×Dic₃	C₄	semidirect
11. C₅×#944	C₄	semidirect
17. C₅×#888	C₄	semidirect
19. C₅×#887	C₄	semidirect
28. #68309	C₅	direct (N × H)
119. Q₈×Dic₃	C₄×C₅	semidirect
120. #944	C₄×C₅	semidirect
126. #888	C₄×C₅	semidirect
128. #887	C₄×C₅	semidirect
341. C₃×C₅	#1503	semidirect
395. C₅	#68309	direct (N × H)
413. C₃	C₅×#1503	semidirect

Maximal subgroups

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

subgroup	index
C₅×#5622	2
C₅×#4718	2
C₅×#4649	2
C₃×C₅×#328	2
C₅×#4538	2
C₅×#4467	2
C₅×#4452	2
C₅×#1503	3
#68309	5

Subgroups — C5×#68309 #14282915

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#68309 #14282915