Subgroups — C₅×#78916 #14417431

Order 1920.

984 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#5798	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₅×#214	C₂	1	1	yes	maximal, characteristic
3	C₅×#5516	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₅×#418	C₂	1	1	yes	maximal, characteristic
5	C₅×#5122	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#5120	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#4998	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#4758	C₂	1	4	yes	maximal, complemented
9	C₅×#4757	C₂	1	4	yes	maximal, complemented
10	C₅×#2949	—	3	1	no	maximal, Hall
11	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
12	C₂²×C₅×Dic₆	C₂²	1	1	yes	characteristic
13	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
14	C₃×C₅×#117	C₂²	1	1	yes	characteristic
15	C₂×C₅×#217	—	2	2	no	—
16	C₅×D₄×Dic₃	—	2	2	no	—
17	C₅×D₄×Dic₃	C₂²	1	4	yes	—
18	C₂×C₅×#214	C₄	1	8	yes	complemented
19	C₂×C₅×#214	C₂²	1	2	yes	—
20	C₂×C₅×#214	C₂²	1	2	yes	—
21	C₅×#926	C₂²	1	1	yes	characteristic
22	C₅×#926	C₂²	1	1	yes	characteristic
23	C₂²×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
24	C₅×#887	C₂²	1	4	yes	complemented
25	C₅×#877	—	2	2	no	—
26	C₄×C₅×Dic₆	—	2	2	no	—
27	C₃×C₅×#102	C₂²	1	4	yes	—
28	C₅×#816	C₂²	1	4	yes	complemented
29	C₅×#815	C₂²	1	2	yes	complemented
30	C₅×C₈×Dic₃	C₂²	1	2	yes	complemented
31	C₅×#808	C₂²	1	2	yes	complemented
32	C₅×#807	C₂²	1	2	yes	complemented
33	#78916	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
34	C₂²×C₅×SD₁₆	—	3	1	no	—
35	C₅×#519	—	3	1	no	—
36	C₅×#518	—	3	1	no	—
37	C₅×#440	—	3	4	no	—
38	C₄×C₅×SD₁₆	—	3	4	no	—
39	C₅×#427	—	3	1	no	—
40	C₅×#419	—	3	1	no	—
41	C₅×#418	D₃	1	1	yes	characteristic
42	C₅×#405	—	3	1	no	—
43	C₂⁴×C₃×C₅	—	2	1	no	—
44	C₂×C₃×C₅×D₄	—	2	1	no	—
45	C₂×C₃×C₅×D₄	—	2	2	no	—
46	C₂×C₃×C₅×D₄	C₂×C₄	1	4	yes	—
47	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
48	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
49	C₂²×C₅×Dic₃	—	2	1	no	—
50	C₂²×C₅×Dic₃	—	2	4	no	—
51	C₂×C₅×Dic₆	—	2	1	no	—
52	C₂×C₅×Dic₆	—	2	2	no	—
53	C₂×C₅×Dic₆	C₂×C₄	1	4	yes	complemented
54	C₂×C₅×Dic₆	C₂³	1	2	yes	—
55	C₃×C₅×M₁₆	—	2	2	no	—
56	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
57	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
58	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
59	C₃×C₄²×C₅	—	2	1	no	—
60	C₅×#217	—	2	1	no	—
61	C₅×#217	—	2	4	no	—
62	C₅×#217	D₄	1	2	yes	—
63	C₅×#214	C₂×C₄	1	8	yes	complemented
64	C₅×#214	C₂×C₄	1	8	yes	complemented
65	C₅×C₄⋊Dic₃	D₄	1	2	yes	—
66	C₅×C₄⋊Dic₃	C₂³	1	2	yes	—
67	C₅×Dic₃⋊C₄	—	2	4	no	—
68	C₄×C₅×Dic₃	—	2	1	no	—
69	C₄×C₅×Dic₃	—	2	4	no	—
70	C₄×C₅×Dic₃	C₂³	1	2	yes	—
71	C₂×C₅×C₃⋊C₈	C₂×C₄	1	4	yes	complemented
72	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
73	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
74	#5798	C₂×C₅	1	1	yes	characteristic
75	C₂²×#214	C₂×C₅	1	1	yes	characteristic
76	#5516	C₂×C₅	1	1	yes	characteristic, complemented
77	C₃×#418	C₂×C₅	1	1	yes	characteristic
78	#5122	C₂×C₅	1	1	yes	characteristic, complemented
79	#5120	C₂×C₅	1	1	yes	characteristic, complemented
80	#4998	C₂×C₅	1	1	yes	characteristic, complemented
81	#4758	C₂×C₅	1	4	yes	complemented
82	#4757	C₂×C₅	1	4	yes	complemented
83	C₂²×C₅×Q₈	—	3	1	no	—
84	C₂²×C₅×D₄	C₂×D₃	1	1	yes	characteristic
85	C₂×C₅×SD₁₆	—	3	8	no	—
86	C₂×C₅×SD₁₆	—	3	2	no	—
87	C₂×C₅×SD₁₆	—	3	2	no	—
88	C₂×C₅×M₁₆	C₂×D₃	1	1	yes	characteristic
89	C₂²×C₅×C₈	—	3	1	no	—
90	C₄×C₅×Q₈	—	3	4	no	—
91	C₄×C₅×Q₈	—	6	2	no	—
92	C₄×C₅×D₄	—	3	4	no	—
93	C₄×C₅×D₄	—	6	2	no	—
94	C₅×#117	—	3	1	no	—
95	C₅×#117	—	3	1	no	—
96	C₅×#117	—	6	2	no	—
97	C₅×#117	C₂×D₃	1	1	yes	characteristic
98	C₂×C₅×C₂²⋊C₄	—	6	2	no	—
99	C₅×#107	—	3	2	no	—
100	C₅×#106	—	3	2	no	—
101	C₅×#103	—	3	4	no	—
102	C₅×#102	C₂×D₃	1	4	yes	—
103	C₅×#97	—	3	2	no	—
104	C₄×C₅×C₈	—	3	2	no	—
105	#2949	—	3	1	no	Sylow
106	C₂³×C₃×C₅	—	2	2	no	—
107	C₂³×C₃×C₅	—	2	4	no	—
108	C₂³×C₃×C₅	—	8	2	no	—
109	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
110	C₃×C₅×D₄	—	2	4	no	—
111	C₃×C₅×D₄	—	2	2	no	—
112	C₃×C₅×D₄	C₂²×C₄	1	4	yes	—
113	C₂×C₃×C₄×C₅	—	2	2	no	—
114	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
115	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
116	C₂×C₃×C₄×C₅	#41	1	2	yes	—
117	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
118	C₂×C₅×Dic₃	—	2	4	no	—
119	C₂×C₅×Dic₃	—	2	2	no	—
120	C₂×C₅×Dic₃	—	2	2	no	—
121	C₂×C₅×Dic₃	—	8	4	no	—
122	C₂×C₅×Dic₃	C₂×D₄	1	4	yes	—
123	C₅×Dic₆	—	2	4	no	—
124	C₅×Dic₆	—	2	2	no	—
125	C₅×Dic₆	C₂²×C₄	1	4	yes	—
126	C₃×C₅×C₈	—	2	2	no	—
127	C₅×C₃⋊C₈	C₂²×C₄	1	2	yes	—
128	C₅×C₃⋊C₈	C₂²×C₄	1	2	yes	—
129	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
130	C₂²×Dic₆	C₂²×C₅	1	1	yes	characteristic
131	C₂×C₃×M₁₆	C₂²×C₅	1	1	yes	characteristic
132	C₃×#117	C₂²×C₅	1	1	yes	characteristic
133	C₂×#217	—	2	2	no	—
134	D₄×Dic₃	—	2	2	no	—
135	D₄×Dic₃	C₂²×C₅	1	4	yes	—
136	C₂×#214	C₄×C₅	1	8	yes	complemented
137	C₂×#214	C₂²×C₅	1	2	yes	—
138	C₂×#214	C₂²×C₅	1	2	yes	—
139	#926	C₂²×C₅	1	1	yes	characteristic
140	#926	C₂²×C₅	1	1	yes	characteristic
141	C₂²×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic
142	#887	C₂²×C₅	1	4	yes	complemented
143	#877	—	2	2	no	—
144	C₄×Dic₆	—	2	2	no	—
145	C₃×#102	C₂²×C₅	1	4	yes	—
146	#816	C₂²×C₅	1	4	yes	complemented
147	#815	C₂²×C₅	1	2	yes	complemented
148	C₈×Dic₃	C₂²×C₅	1	2	yes	complemented
149	#808	C₂²×C₅	1	2	yes	complemented
150	#807	C₂²×C₅	1	2	yes	complemented
151	C₂⁴×C₅	—	2	1	no	—
152	C₂×C₅×Q₈	—	3	4	no	—
153	C₂×C₅×Q₈	—	3	2	no	—
154	C₂×C₅×Q₈	—	6	1	no	—
155	C₂×C₅×Q₈	—	6	2	no	—
156	C₂×C₅×D₄	—	2	1	no	—
157	C₂×C₅×D₄	—	2	2	no	—
158	C₂×C₅×D₄	C₄×D₃	1	4	yes	—
159	C₂×C₅×D₄	C₂²×D₃	1	2	yes	—
160	C₂²×C₄×C₅	—	6	4	no	—
161	C₂²×C₄×C₅	—	6	1	no	—
162	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
163	C₅×SD₁₆	—	3	8	no	—
164	C₅×SD₁₆	—	3	8	no	—
165	C₅×M₁₆	—	2	2	no	—
166	C₂×C₅×C₈	—	3	4	no	—
167	C₂×C₅×C₈	—	3	1	no	—
168	C₂×C₅×C₈	—	3	1	no	—
169	C₂×C₅×C₈	C₂²×D₃	1	2	yes	—
170	C₅×C₄⋊C₄	—	3	2	no	—
171	C₅×C₄⋊C₄	—	3	2	no	—
172	C₅×C₄⋊C₄	—	6	4	no	—
173	C₅×C₄⋊C₄	C₂²×D₃	1	2	yes	—
174	C₅×C₂²⋊C₄	—	2	1	no	—
175	C₅×C₂²⋊C₄	—	3	2	no	—
176	C₅×C₂²⋊C₄	—	6	4	no	—
177	C₅×C₂²⋊C₄	—	6	1	no	—
178	C₄²×C₅	—	2	1	no	—
179	C₄²×C₅	—	3	2	no	—
180	C₄²×C₅	—	6	4	no	—
181	C₄²×C₅	—	6	1	no	—
182	C₂²×SD₁₆	—	3	1	no	—
183	#519	—	3	1	no	—
184	#518	—	3	1	no	—
185	#440	—	3	4	no	—
186	C₄×SD₁₆	—	3	4	no	—
187	#427	—	3	1	no	—
188	#419	—	3	1	no	—
189	#418	C₅×D₃	1	1	yes	characteristic
190	#405	—	3	1	no	—
191	C₂²×C₃×C₅	—	2	2	no	—
192	C₂²×C₃×C₅	—	2	4	no	—
193	C₂²×C₃×C₅	—	4	4	no	—
194	C₂²×C₃×C₅	—	8	4	no	—
195	C₂²×C₃×C₅	C₄×D₄	1	2	yes	—
196	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
197	C₃×C₄×C₅	—	4	2	no	—
198	C₃×C₄×C₅	C₄×D₄	1	2	yes	—
199	C₃×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
200	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
201	C₅×Dic₃	—	2	4	no	—
202	C₅×Dic₃	—	2	4	no	—
203	C₅×Dic₃	—	4	2	no	—
204	C₂⁴×C₃	—	2	1	no	—
205	C₂×C₃×D₄	—	2	1	no	—
206	C₂×C₃×D₄	—	2	2	no	—
207	C₂×C₃×D₄	C₂×C₄×C₅	1	4	yes	—
208	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
209	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
210	C₂²×Dic₃	—	2	1	no	—
211	C₂²×Dic₃	—	2	4	no	—
212	C₂×Dic₆	—	2	1	no	—
213	C₂×Dic₆	—	2	2	no	—
214	C₂×Dic₆	C₂×C₄×C₅	1	4	yes	complemented
215	C₂×Dic₆	C₂³×C₅	1	2	yes	—
216	C₃×M₁₆	—	2	2	no	—
217	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
218	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
219	C₃×C₂²⋊C₄	—	2	1	no	—
220	C₃×C₄²	—	2	1	no	—
221	#217	—	2	1	no	—
222	#217	—	2	4	no	—
223	#217	C₅×D₄	1	2	yes	—
224	#214	C₂×C₄×C₅	1	8	yes	complemented
225	#214	C₂×C₄×C₅	1	8	yes	complemented
226	C₄⋊Dic₃	C₅×D₄	1	2	yes	—
227	C₄⋊Dic₃	C₂³×C₅	1	2	yes	—
228	Dic₃⋊C₄	—	2	4	no	—
229	C₄×Dic₃	—	2	1	no	—
230	C₄×Dic₃	—	2	4	no	—
231	C₄×Dic₃	C₂³×C₅	1	2	yes	—
232	C₂×C₃⋊C₈	C₂×C₄×C₅	1	4	yes	complemented
233	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
234	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
235	C₂³×C₅	—	2	2	no	—
236	C₂³×C₅	—	2	4	no	—
237	C₂³×C₅	—	8	2	no	—
238	C₂³×C₅	D₃×D₄	1	1	yes	characteristic
239	C₅×Q₈	—	3	4	no	—
240	C₅×Q₈	—	6	4	no	—
241	C₅×Q₈	—	6	2	no	—
242	C₅×D₄	—	2	4	no	—
243	C₅×D₄	—	2	2	no	—
244	C₅×D₄	C₂×C₄×D₃	1	4	yes	—
245	C₂×C₄×C₅	—	2	2	no	—
246	C₂×C₄×C₅	—	3	4	no	—
247	C₂×C₄×C₅	—	6	4	no	—
248	C₂×C₄×C₅	—	6	2	no	—
249	C₂×C₄×C₅	—	6	2	no	—
250	C₂×C₄×C₅	—	24	4	no	—
251	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
252	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
253	C₂×C₄×C₅	#237	1	2	yes	—
254	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
255	C₅×C₈	—	2	2	no	—
256	C₅×C₈	—	3	2	no	—
257	C₅×C₈	—	3	2	no	—
258	C₂²×Q₈	—	3	1	no	—
259	C₂²×D₄	C₂×C₅×D₃	1	1	yes	characteristic
260	C₂×SD₁₆	—	3	8	no	—
261	C₂×SD₁₆	—	3	2	no	—
262	C₂×SD₁₆	—	3	2	no	—
263	C₂×M₁₆	C₂×C₅×D₃	1	1	yes	characteristic
264	C₂²×C₈	—	3	1	no	—
265	C₄×Q₈	—	3	4	no	—
266	C₄×Q₈	—	6	2	no	—
267	C₄×D₄	—	3	4	no	—
268	C₄×D₄	—	6	2	no	—
269	#117	—	3	1	no	—
270	#117	—	3	1	no	—
271	#117	—	6	2	no	—
272	#117	C₂×C₅×D₃	1	1	yes	characteristic
273	C₂×C₂²⋊C₄	—	6	2	no	—
274	#107	—	3	2	no	—
275	#106	—	3	2	no	—
276	#103	—	3	4	no	—
277	#102	C₂×C₅×D₃	1	4	yes	—
278	#97	—	3	2	no	—
279	C₄×C₈	—	3	2	no	—
280	C₂×C₃×C₅	—	2	2	no	—
281	C₂×C₃×C₅	—	4	4	no	—
282	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
283	C₂×C₃×C₅	#577	1	2	yes	—
284	C₂³×C₃	—	2	2	no	—
285	C₂³×C₃	—	2	4	no	—
286	C₂³×C₃	—	8	2	no	—
287	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
288	C₃×D₄	—	2	4	no	—
289	C₃×D₄	—	2	2	no	—
290	C₃×D₄	C₂²×C₄×C₅	1	4	yes	—
291	C₂×C₃×C₄	—	2	2	no	—
292	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
293	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
294	C₂×C₃×C₄	C₅×#41	1	2	yes	—
295	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
296	C₂×Dic₃	—	2	4	no	—
297	C₂×Dic₃	—	2	2	no	—
298	C₂×Dic₃	—	2	2	no	—
299	C₂×Dic₃	—	8	4	no	—
300	C₂×Dic₃	C₂×C₅×D₄	1	4	yes	—
301	Dic₆	—	2	4	no	—
302	Dic₆	—	2	2	no	—
303	Dic₆	C₂²×C₄×C₅	1	4	yes	—
304	C₃×C₈	—	2	2	no	—
305	C₃⋊C₈	C₂²×C₄×C₅	1	2	yes	—
306	C₃⋊C₈	C₂²×C₄×C₅	1	2	yes	—
307	C₂²×C₅	—	2	2	no	—
308	C₂²×C₅	—	2	4	no	—
309	C₂²×C₅	—	4	4	no	—
310	C₂²×C₅	—	8	4	no	—
311	C₂²×C₅	#67⋊C₄	1	2	yes	—
312	C₂²×C₅	C₂×D₃×D₄	1	1	yes	characteristic
313	C₄×C₅	—	4	2	no	—
314	C₄×C₅	—	6	4	no	—
315	C₄×C₅	—	6	4	no	—
316	C₄×C₅	—	12	2	no	—
317	C₄×C₅	#67⋊C₄	1	2	yes	—
318	C₄×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
319	C₄×C₅	C₂×#237	1	1	yes	characteristic
320	C₂⁴	—	2	1	no	—
321	C₂×Q₈	—	3	4	no	—
322	C₂×Q₈	—	3	2	no	—
323	C₂×Q₈	—	6	1	no	—
324	C₂×Q₈	—	6	2	no	—
325	C₂×D₄	—	2	1	no	—
326	C₂×D₄	—	2	2	no	—
327	C₂×D₄	C₄×C₅×D₃	1	4	yes	—
328	C₂×D₄	C₂²×C₅×D₃	1	2	yes	—
329	C₂²×C₄	—	6	4	no	—
330	C₂²×C₄	—	6	1	no	—
331	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
332	SD₁₆	—	3	8	no	—
333	SD₁₆	—	3	8	no	—
334	M₁₆	—	2	2	no	—
335	C₂×C₈	—	3	4	no	—
336	C₂×C₈	—	3	1	no	—
337	C₂×C₈	—	3	1	no	—
338	C₂×C₈	C₂²×C₅×D₃	1	2	yes	—
339	C₄⋊C₄	—	3	2	no	—
340	C₄⋊C₄	—	3	2	no	—
341	C₄⋊C₄	—	6	4	no	—
342	C₄⋊C₄	C₂²×C₅×D₃	1	2	yes	—
343	C₂²⋊C₄	—	2	1	no	—
344	C₂²⋊C₄	—	3	2	no	—
345	C₂²⋊C₄	—	6	4	no	—
346	C₂²⋊C₄	—	6	1	no	—
347	C₄²	—	2	1	no	—
348	C₄²	—	3	2	no	—
349	C₄²	—	6	4	no	—
350	C₄²	—	6	1	no	—
351	C₃×C₅	#2949	1	1	yes	characteristic, complemented, Hall
352	C₂²×C₃	—	2	2	no	—
353	C₂²×C₃	—	2	4	no	—
354	C₂²×C₃	—	4	4	no	—
355	C₂²×C₃	—	8	4	no	—
356	C₂²×C₃	C₄×C₅×D₄	1	2	yes	—
357	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
358	C₃×C₄	—	4	2	no	—
359	C₃×C₄	C₄×C₅×D₄	1	2	yes	—
360	C₃×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
361	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
362	Dic₃	—	2	4	no	—
363	Dic₃	—	2	4	no	—
364	Dic₃	—	4	2	no	—
365	C₂×C₅	—	2	2	no	—
366	C₂×C₅	—	4	4	no	—
367	C₂×C₅	C₂×#67⋊C₄	1	1	yes	characteristic
368	C₂×C₅	#5775	1	2	yes	—
369	C₂³	—	2	2	no	—
370	C₂³	—	2	4	no	—
371	C₂³	—	8	2	no	—
372	C₂³	C₅×D₃×D₄	1	1	yes	characteristic
373	Q₈	—	3	4	no	—
374	Q₈	—	6	4	no	—
375	Q₈	—	6	2	no	—
376	D₄	—	2	4	no	—
377	D₄	—	2	2	no	—
378	D₄	C₂×C₄×C₅×D₃	1	4	yes	—
379	C₂×C₄	—	2	2	no	—
380	C₂×C₄	—	3	4	no	—
381	C₂×C₄	—	6	4	no	—
382	C₂×C₄	—	6	2	no	—
383	C₂×C₄	—	6	2	no	—
384	C₂×C₄	—	24	4	no	—
385	C₂×C₄	C₂×C₄×C₅×D₃	1	2	yes	—
386	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
387	C₂×C₄	C₅×#237	1	2	yes	—
388	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
389	C₈	—	2	2	no	—
390	C₈	—	3	2	no	—
391	C₈	—	3	2	no	—
392	C₂×C₃	—	2	2	no	—
393	C₂×C₃	—	4	4	no	—
394	C₂×C₃	C₂×C₄×C₅×D₄	1	1	yes	characteristic
395	C₂×C₃	C₅×#577	1	2	yes	—
396	C₅	#78916	1	1	yes	characteristic, direct product factor, Sylow
397	C₂²	—	2	2	no	—
398	C₂²	—	2	4	no	—
399	C₂²	—	4	4	no	—
400	C₂²	—	8	4	no	—
401	C₂²	C₅×#67⋊C₄	1	2	yes	—
402	C₂²	C₂×C₅×D₃×D₄	1	1	yes	characteristic
403	C₄	—	4	2	no	—
404	C₄	—	6	4	no	—
405	C₄	—	6	4	no	—
406	C₄	—	12	2	no	—
407	C₄	C₅×#67⋊C₄	1	2	yes	—
408	C₄	C₂²×C₄×C₅×D₃	1	1	yes	characteristic
409	C₄	C₂×C₅×#237	1	1	yes	characteristic
410	C₃	C₅×#2949	1	1	yes	characteristic, complemented, Sylow
411	C₂	—	2	2	no	—
412	C₂	—	4	4	no	—
413	C₂	C₂×C₅×#67⋊C₄	1	1	yes	characteristic
414	C₂	C₅×#5775	1	2	yes	—

	subgroup	G/H
center	C₂²×C₅	C₂×D₃×D₄
commutator	C₃×C₄	C₂³×C₄×C₅
Frattini	C₂×C₄	C₂³×C₅×D₃
Fitting	C₃×C₅×#418	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
prime radical	C₂²×C₃×C₅×D₄	C₂²
cosocle	C₂×C₃×C₄	C₂⁴×C₅
hypercenter	C₅×#418	D₃
hypocenter	C₃	C₅×#2949
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₂²×C₄×C₅ ◁ C₅×#418

Complements

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

N	H ≅ G/N	type
3. C₅×#5516	C₂	semidirect
5. C₅×#5122	C₂	semidirect
6. C₅×#5120	C₂	semidirect
7. C₅×#4998	C₂	semidirect
8. C₅×#4758	C₂	semidirect
9. C₅×#4757	C₂	semidirect
18. C₂×C₅×#214	C₄	semidirect
24. C₅×#887	C₂²	semidirect
28. C₅×#816	C₂²	semidirect
29. C₅×#815	C₂²	semidirect
30. C₅×C₈×Dic₃	C₂²	semidirect
31. C₅×#808	C₂²	semidirect
32. C₅×#807	C₂²	semidirect
33. #78916	C₅	direct (N × H)
53. C₂×C₅×Dic₆	C₂×C₄	semidirect
63. C₅×#214	C₂×C₄	semidirect
64. C₅×#214	C₂×C₄	semidirect
71. C₂×C₅×C₃⋊C₈	C₂×C₄	semidirect
76. #5516	C₂×C₅	semidirect
78. #5122	C₂×C₅	semidirect
79. #5120	C₂×C₅	semidirect
80. #4998	C₂×C₅	semidirect
81. #4758	C₂×C₅	semidirect
82. #4757	C₂×C₅	semidirect
136. C₂×#214	C₄×C₅	semidirect
142. #887	C₂²×C₅	semidirect
146. #816	C₂²×C₅	semidirect
147. #815	C₂²×C₅	semidirect
148. C₈×Dic₃	C₂²×C₅	semidirect
149. #808	C₂²×C₅	semidirect
150. #807	C₂²×C₅	semidirect
214. C₂×Dic₆	C₂×C₄×C₅	semidirect
224. #214	C₂×C₄×C₅	semidirect
225. #214	C₂×C₄×C₅	semidirect
232. C₂×C₃⋊C₈	C₂×C₄×C₅	semidirect
351. C₃×C₅	#2949	semidirect
396. C₅	#78916	direct (N × H)
410. C₃	C₅×#2949	semidirect

Maximal subgroups

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

subgroup	index
C₅×#5798	2
C₂²×C₅×#214	2
C₅×#5516	2
C₃×C₅×#418	2
C₅×#5122	2
C₅×#5120	2
C₅×#4998	2
C₅×#4758	2
C₅×#4757	2
C₅×#2949	3
#78916	5

Subgroups — C5×#78916 #14417431

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#78916 #14417431