Subgroups — C₅×#78915 #14417327

Order 1920.

1056 conjugacy classes of subgroups.

The subgroup lattice has 436 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, complemented
2	C₂²×C₅×#213	C₂	1	1	yes	maximal, characteristic
3	C₅×#5521	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₅×#418	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#5131	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#5122	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#4998	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#4785	C₂	1	4	yes	maximal, complemented
9	C₅×#4756	C₂	1	4	yes	maximal, complemented
10	C₅×#2948	—	3	1	no	maximal, Hall
11	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
12	C₂²×C₅×D₁₂	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	complemented
18	C₂×C₅×#213	C₄	1	8	yes	complemented
19	C₂×C₅×#213	C₂²	1	2	yes	—
20	C₂×C₅×#213	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×#893	C₂²	1	4	yes	complemented
25	C₅×D₃×C₂²⋊C₄	—	2	2	no	—
26	C₄×C₅×D₁₂	—	2	2	no	—
27	C₃×C₅×#102	C₂²	1	4	yes	complemented
28	C₅×#821	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	#78915	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
34	C₂²×C₅×D₈	—	3	1	no	—
35	C₅×#518	—	3	1	no	—
36	C₅×#518	—	3	1	no	—
37	C₅×#442	—	3	4	no	—
38	C₄×C₅×D₈	—	3	4	no	—
39	C₅×#427	—	3	1	no	—
40	C₅×#418	—	3	1	no	—
41	C₅×#418	D₃	1	1	yes	characteristic, complemented
42	C₅×#405	—	3	1	no	—
43	C₂⁴×C₃×C₅	—	2	1	no	—
44	C₂³×C₅×D₃	—	2	1	no	—
45	C₂×C₃×C₅×D₄	—	2	1	no	—
46	C₂×C₃×C₅×D₄	—	2	2	no	—
47	C₂×C₃×C₅×D₄	C₂×C₄	1	4	yes	complemented
48	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
49	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
50	C₂²×C₅×Dic₃	—	2	4	no	—
51	C₂×C₅×D₁₂	—	2	1	no	—
52	C₂×C₅×D₁₂	—	2	2	no	—
53	C₂×C₅×D₁₂	C₂×C₄	1	4	yes	complemented
54	C₂×C₅×D₁₂	C₂³	1	2	yes	—
55	C₂×C₄×C₅×D₃	—	2	4	no	—
56	C₃×C₅×M₁₆	—	2	2	no	—
57	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
58	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
59	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
60	C₃×C₄²×C₅	—	2	1	no	—
61	C₅×#217	—	2	1	no	—
62	C₅×#217	—	2	4	no	—
63	C₅×#217	D₄	1	2	yes	—
64	C₅×#213	C₂×C₄	1	8	yes	complemented
65	C₅×#213	C₂×C₄	1	8	yes	complemented
66	C₅×(C₂×D₃)⋊C₄	—	2	4	no	—
67	C₅×C₄⋊Dic₃	D₄	1	2	yes	—
68	C₅×C₄⋊Dic₃	C₂³	1	2	yes	—
69	C₄×C₅×Dic₃	—	2	1	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, complemented
75	C₂²×#213	C₂×C₅	1	1	yes	characteristic
76	#5521	C₂×C₅	1	1	yes	characteristic, complemented
77	C₃×#418	C₂×C₅	1	1	yes	characteristic, complemented
78	#5131	C₂×C₅	1	1	yes	characteristic, complemented
79	#5122	C₂×C₅	1	1	yes	characteristic, complemented
80	#4998	C₂×C₅	1	1	yes	characteristic, complemented
81	#4785	C₂×C₅	1	4	yes	complemented
82	#4756	C₂×C₅	1	4	yes	complemented
83	C₂²×C₅×D₄	—	3	1	no	—
84	C₂²×C₅×D₄	C₂×D₃	1	1	yes	characteristic
85	C₂×C₅×D₈	—	3	8	no	—
86	C₂×C₅×D₈	—	3	2	no	—
87	C₂×C₅×D₈	—	3	2	no	—
88	C₂×C₅×M₁₆	C₂×D₃	1	1	yes	characteristic
89	C₂²×C₅×C₈	—	3	1	no	—
90	C₄×C₅×D₄	—	3	4	no	—
91	C₄×C₅×D₄	—	3	4	no	—
92	C₄×C₅×D₄	—	6	2	no	—
93	C₄×C₅×D₄	—	6	2	no	—
94	C₅×#117	—	3	1	no	—
95	C₅×#117	—	3	1	no	—
96	C₅×#117	C₂×D₃	1	1	yes	characteristic
97	C₂×C₅×C₂²⋊C₄	—	6	2	no	—
98	C₂×C₅×C₂²⋊C₄	—	6	2	no	—
99	C₅×#107	—	3	2	no	—
100	C₅×#106	—	3	2	no	—
101	C₅×#102	—	3	4	no	—
102	C₅×#102	C₂×D₃	1	4	yes	complemented
103	C₅×#97	—	3	2	no	—
104	C₄×C₅×C₈	—	3	2	no	—
105	#2948	—	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	C₂²×C₅×D₃	—	2	2	no	—
111	C₂²×C₅×D₃	—	2	4	no	—
112	C₂²×C₅×D₃	—	8	2	no	—
113	C₃×C₅×D₄	—	2	4	no	—
114	C₃×C₅×D₄	—	2	2	no	—
115	C₃×C₅×D₄	C₂²×C₄	1	4	yes	—
116	C₂×C₃×C₄×C₅	—	2	2	no	—
117	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
118	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
119	C₂×C₃×C₄×C₅	#41	1	2	yes	—
120	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
121	C₂×C₅×Dic₃	—	2	2	no	—
122	C₂×C₅×Dic₃	—	8	4	no	—
123	C₂×C₅×Dic₃	C₂×D₄	1	4	yes	—
124	C₅×D₁₂	—	2	4	no	—
125	C₅×D₁₂	—	2	2	no	—
126	C₅×D₁₂	C₂²×C₄	1	4	yes	—
127	C₄×C₅×D₃	—	8	4	no	—
128	C₃×C₅×C₈	—	2	2	no	—
129	C₅×C₃⋊C₈	C₂²×C₄	1	2	yes	—
130	C₅×C₃⋊C₈	C₂²×C₄	1	2	yes	—
131	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
132	C₂²×D₁₂	C₂²×C₅	1	1	yes	characteristic
133	C₂×C₃×M₁₆	C₂²×C₅	1	1	yes	characteristic
134	C₃×#117	C₂²×C₅	1	1	yes	characteristic
135	C₂×#217	—	2	2	no	—
136	D₄×Dic₃	—	2	2	no	—
137	D₄×Dic₃	C₂²×C₅	1	4	yes	complemented
138	C₂×#213	C₄×C₅	1	8	yes	complemented
139	C₂×#213	C₂²×C₅	1	2	yes	—
140	C₂×#213	C₂²×C₅	1	2	yes	—
141	#926	C₂²×C₅	1	1	yes	characteristic
142	#926	C₂²×C₅	1	1	yes	characteristic
143	C₂²×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic
144	#893	C₂²×C₅	1	4	yes	complemented
145	D₃×C₂²⋊C₄	—	2	2	no	—
146	C₄×D₁₂	—	2	2	no	—
147	C₃×#102	C₂²×C₅	1	4	yes	complemented
148	#821	C₂²×C₅	1	4	yes	complemented
149	#815	C₂²×C₅	1	2	yes	complemented
150	C₈×Dic₃	C₂²×C₅	1	2	yes	complemented
151	#808	C₂²×C₅	1	2	yes	complemented
152	#807	C₂²×C₅	1	2	yes	complemented
153	C₂⁴×C₅	—	2	1	no	—
154	C₂⁴×C₅	—	6	1	no	—
155	C₂×C₅×D₄	—	2	1	no	—
156	C₂×C₅×D₄	—	2	2	no	—
157	C₂×C₅×D₄	—	3	4	no	—
158	C₂×C₅×D₄	—	3	2	no	—
159	C₂×C₅×D₄	—	6	1	no	—
160	C₂×C₅×D₄	—	6	2	no	—
161	C₂×C₅×D₄	C₄×D₃	1	4	yes	complemented
162	C₂×C₅×D₄	C₂²×D₃	1	2	yes	—
163	C₂²×C₄×C₅	—	6	4	no	—
164	C₂²×C₄×C₅	—	6	4	no	—
165	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
166	C₅×D₈	—	3	8	no	—
167	C₅×D₈	—	3	8	no	—
168	C₅×M₁₆	—	2	2	no	—
169	C₂×C₅×C₈	—	3	4	no	—
170	C₂×C₅×C₈	—	3	1	no	—
171	C₂×C₅×C₈	—	3	1	no	—
172	C₂×C₅×C₈	C₂²×D₃	1	2	yes	—
173	C₅×C₄⋊C₄	—	3	2	no	—
174	C₅×C₄⋊C₄	—	3	2	no	—
175	C₅×C₄⋊C₄	C₂²×D₃	1	2	yes	—
176	C₅×C₂²⋊C₄	—	2	1	no	—
177	C₅×C₂²⋊C₄	—	3	2	no	—
178	C₅×C₂²⋊C₄	—	6	4	no	—
179	C₅×C₂²⋊C₄	—	6	4	no	—
180	C₅×C₂²⋊C₄	—	6	1	no	—
181	C₄²×C₅	—	2	1	no	—
182	C₄²×C₅	—	3	2	no	—
183	C₄²×C₅	—	6	1	no	—
184	C₂²×D₈	—	3	1	no	—
185	#518	—	3	1	no	—
186	#518	—	3	1	no	—
187	#442	—	3	4	no	—
188	C₄×D₈	—	3	4	no	—
189	#427	—	3	1	no	—
190	#418	—	3	1	no	—
191	#418	C₅×D₃	1	1	yes	characteristic, complemented
192	#405	—	3	1	no	—
193	C₂²×C₃×C₅	—	2	2	no	—
194	C₂²×C₃×C₅	—	2	4	no	—
195	C₂²×C₃×C₅	—	4	4	no	—
196	C₂²×C₃×C₅	—	8	4	no	—
197	C₂²×C₃×C₅	C₄×D₄	1	2	yes	—
198	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
199	C₂×C₅×D₃	—	2	4	no	—
200	C₂×C₅×D₃	—	4	4	no	—
201	C₂×C₅×D₃	—	8	4	no	—
202	C₃×C₄×C₅	—	4	2	no	—
203	C₃×C₄×C₅	C₄×D₄	1	2	yes	—
204	C₃×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
205	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
206	C₅×Dic₃	—	2	4	no	—
207	C₅×Dic₃	—	4	2	no	—
208	C₂⁴×C₃	—	2	1	no	—
209	C₂³×D₃	—	2	1	no	—
210	C₂×C₃×D₄	—	2	1	no	—
211	C₂×C₃×D₄	—	2	2	no	—
212	C₂×C₃×D₄	C₂×C₄×C₅	1	4	yes	complemented
213	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
214	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
215	C₂²×Dic₃	—	2	4	no	—
216	C₂×D₁₂	—	2	1	no	—
217	C₂×D₁₂	—	2	2	no	—
218	C₂×D₁₂	C₂×C₄×C₅	1	4	yes	complemented
219	C₂×D₁₂	C₂³×C₅	1	2	yes	—
220	C₂×C₄×D₃	—	2	4	no	—
221	C₃×M₁₆	—	2	2	no	—
222	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
223	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
224	C₃×C₂²⋊C₄	—	2	1	no	—
225	C₃×C₄²	—	2	1	no	—
226	#217	—	2	1	no	—
227	#217	—	2	4	no	—
228	#217	C₅×D₄	1	2	yes	—
229	#213	C₂×C₄×C₅	1	8	yes	complemented
230	#213	C₂×C₄×C₅	1	8	yes	complemented
231	(C₂×D₃)⋊C₄	—	2	4	no	—
232	C₄⋊Dic₃	C₅×D₄	1	2	yes	—
233	C₄⋊Dic₃	C₂³×C₅	1	2	yes	—
234	C₄×Dic₃	—	2	1	no	—
235	C₄×Dic₃	C₂³×C₅	1	2	yes	—
236	C₂×C₃⋊C₈	C₂×C₄×C₅	1	4	yes	complemented
237	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
238	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
239	C₂³×C₅	—	2	2	no	—
240	C₂³×C₅	—	2	4	no	—
241	C₂³×C₅	—	6	2	no	—
242	C₂³×C₅	—	6	4	no	—
243	C₂³×C₅	—	8	2	no	—
244	C₂³×C₅	—	24	2	no	—
245	C₂³×C₅	D₃×D₄	1	1	yes	characteristic
246	C₅×D₄	—	2	4	no	—
247	C₅×D₄	—	2	2	no	—
248	C₅×D₄	—	3	4	no	—
249	C₅×D₄	—	6	4	no	—
250	C₅×D₄	—	6	2	no	—
251	C₅×D₄	C₂×C₄×D₃	1	4	yes	—
252	C₂×C₄×C₅	—	2	2	no	—
253	C₂×C₄×C₅	—	3	4	no	—
254	C₂×C₄×C₅	—	6	2	no	—
255	C₂×C₄×C₅	—	24	4	no	—
256	C₂×C₄×C₅	—	24	4	no	—
257	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
258	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
259	C₂×C₄×C₅	#237	1	2	yes	—
260	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
261	C₅×C₈	—	2	2	no	—
262	C₅×C₈	—	3	2	no	—
263	C₅×C₈	—	3	2	no	—
264	C₂²×D₄	—	3	1	no	—
265	C₂²×D₄	C₂×C₅×D₃	1	1	yes	characteristic
266	C₂×D₈	—	3	8	no	—
267	C₂×D₈	—	3	2	no	—
268	C₂×D₈	—	3	2	no	—
269	C₂×M₁₆	C₂×C₅×D₃	1	1	yes	characteristic
270	C₂²×C₈	—	3	1	no	—
271	C₄×D₄	—	3	4	no	—
272	C₄×D₄	—	3	4	no	—
273	C₄×D₄	—	6	2	no	—
274	C₄×D₄	—	6	2	no	—
275	#117	—	3	1	no	—
276	#117	—	3	1	no	—
277	#117	C₂×C₅×D₃	1	1	yes	characteristic
278	C₂×C₂²⋊C₄	—	6	2	no	—
279	C₂×C₂²⋊C₄	—	6	2	no	—
280	#107	—	3	2	no	—
281	#106	—	3	2	no	—
282	#102	—	3	4	no	—
283	#102	C₂×C₅×D₃	1	4	yes	complemented
284	#97	—	3	2	no	—
285	C₄×C₈	—	3	2	no	—
286	C₂×C₃×C₅	—	2	2	no	—
287	C₂×C₃×C₅	—	4	4	no	—
288	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
289	C₂×C₃×C₅	#576	1	2	yes	—
290	C₅×D₃	—	4	4	no	—
291	C₂³×C₃	—	2	2	no	—
292	C₂³×C₃	—	2	4	no	—
293	C₂³×C₃	—	8	2	no	—
294	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
295	C₂²×D₃	—	2	2	no	—
296	C₂²×D₃	—	2	4	no	—
297	C₂²×D₃	—	8	2	no	—
298	C₃×D₄	—	2	4	no	—
299	C₃×D₄	—	2	2	no	—
300	C₃×D₄	C₂²×C₄×C₅	1	4	yes	—
301	C₂×C₃×C₄	—	2	2	no	—
302	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
303	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
304	C₂×C₃×C₄	C₅×#41	1	2	yes	—
305	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
306	C₂×Dic₃	—	2	2	no	—
307	C₂×Dic₃	—	8	4	no	—
308	C₂×Dic₃	C₂×C₅×D₄	1	4	yes	—
309	D₁₂	—	2	4	no	—
310	D₁₂	—	2	2	no	—
311	D₁₂	C₂²×C₄×C₅	1	4	yes	—
312	C₄×D₃	—	8	4	no	—
313	C₃×C₈	—	2	2	no	—
314	C₃⋊C₈	C₂²×C₄×C₅	1	2	yes	—
315	C₃⋊C₈	C₂²×C₄×C₅	1	2	yes	—
316	C₂²×C₅	—	2	2	no	—
317	C₂²×C₅	—	2	4	no	—
318	C₂²×C₅	—	4	4	no	—
319	C₂²×C₅	—	6	4	no	—
320	C₂²×C₅	—	8	4	no	—
321	C₂²×C₅	—	12	4	no	—
322	C₂²×C₅	—	24	4	no	—
323	C₂²×C₅	#67⋊C₄	1	2	yes	—
324	C₂²×C₅	C₂×D₃×D₄	1	1	yes	characteristic
325	C₄×C₅	—	4	2	no	—
326	C₄×C₅	—	6	4	no	—
327	C₄×C₅	—	12	2	no	—
328	C₄×C₅	#67⋊C₄	1	2	yes	—
329	C₄×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
330	C₄×C₅	C₂×#237	1	1	yes	characteristic
331	C₂⁴	—	2	1	no	—
332	C₂⁴	—	6	1	no	—
333	C₂×D₄	—	2	1	no	—
334	C₂×D₄	—	2	2	no	—
335	C₂×D₄	—	3	4	no	—
336	C₂×D₄	—	3	2	no	—
337	C₂×D₄	—	6	1	no	—
338	C₂×D₄	—	6	2	no	—
339	C₂×D₄	C₄×C₅×D₃	1	4	yes	complemented
340	C₂×D₄	C₂²×C₅×D₃	1	2	yes	—
341	C₂²×C₄	—	6	4	no	—
342	C₂²×C₄	—	6	4	no	—
343	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
344	D₈	—	3	8	no	—
345	D₈	—	3	8	no	—
346	M₁₆	—	2	2	no	—
347	C₂×C₈	—	3	4	no	—
348	C₂×C₈	—	3	1	no	—
349	C₂×C₈	—	3	1	no	—
350	C₂×C₈	C₂²×C₅×D₃	1	2	yes	—
351	C₄⋊C₄	—	3	2	no	—
352	C₄⋊C₄	—	3	2	no	—
353	C₄⋊C₄	C₂²×C₅×D₃	1	2	yes	—
354	C₂²⋊C₄	—	2	1	no	—
355	C₂²⋊C₄	—	3	2	no	—
356	C₂²⋊C₄	—	6	4	no	—
357	C₂²⋊C₄	—	6	4	no	—
358	C₂²⋊C₄	—	6	1	no	—
359	C₄²	—	2	1	no	—
360	C₄²	—	3	2	no	—
361	C₄²	—	6	1	no	—
362	C₃×C₅	#2948	1	1	yes	characteristic, complemented, Hall
363	C₂²×C₃	—	2	2	no	—
364	C₂²×C₃	—	2	4	no	—
365	C₂²×C₃	—	4	4	no	—
366	C₂²×C₃	—	8	4	no	—
367	C₂²×C₃	C₄×C₅×D₄	1	2	yes	—
368	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
369	C₂×D₃	—	2	4	no	—
370	C₂×D₃	—	4	4	no	—
371	C₂×D₃	—	8	4	no	—
372	C₃×C₄	—	4	2	no	—
373	C₃×C₄	C₄×C₅×D₄	1	2	yes	—
374	C₃×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
375	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
376	Dic₃	—	2	4	no	—
377	Dic₃	—	4	2	no	—
378	C₂×C₅	—	2	2	no	—
379	C₂×C₅	—	4	4	no	—
380	C₂×C₅	—	12	4	no	—
381	C₂×C₅	C₂×#67⋊C₄	1	1	yes	characteristic
382	C₂×C₅	#5774	1	2	yes	—
383	C₂³	—	2	2	no	—
384	C₂³	—	2	4	no	—
385	C₂³	—	6	2	no	—
386	C₂³	—	6	4	no	—
387	C₂³	—	8	2	no	—
388	C₂³	—	24	2	no	—
389	C₂³	C₅×D₃×D₄	1	1	yes	characteristic
390	D₄	—	2	4	no	—
391	D₄	—	2	2	no	—
392	D₄	—	3	4	no	—
393	D₄	—	6	4	no	—
394	D₄	—	6	2	no	—
395	D₄	C₂×C₄×C₅×D₃	1	4	yes	—
396	C₂×C₄	—	2	2	no	—
397	C₂×C₄	—	3	4	no	—
398	C₂×C₄	—	6	2	no	—
399	C₂×C₄	—	24	4	no	—
400	C₂×C₄	—	24	4	no	—
401	C₂×C₄	C₂×C₄×C₅×D₃	1	2	yes	—
402	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
403	C₂×C₄	C₅×#237	1	2	yes	—
404	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
405	C₈	—	2	2	no	—
406	C₈	—	3	2	no	—
407	C₈	—	3	2	no	—
408	C₂×C₃	—	2	2	no	—
409	C₂×C₃	—	4	4	no	—
410	C₂×C₃	C₂×C₄×C₅×D₄	1	1	yes	characteristic
411	C₂×C₃	C₅×#576	1	2	yes	—
412	D₃	—	4	4	no	—
413	C₅	#78915	1	1	yes	characteristic, direct product factor, Sylow
414	C₂²	—	2	2	no	—
415	C₂²	—	2	4	no	—
416	C₂²	—	4	4	no	—
417	C₂²	—	6	4	no	—
418	C₂²	—	8	4	no	—
419	C₂²	—	12	4	no	—
420	C₂²	—	24	4	no	—
421	C₂²	C₅×#67⋊C₄	1	2	yes	—
422	C₂²	C₂×C₅×D₃×D₄	1	1	yes	characteristic
423	C₄	—	4	2	no	—
424	C₄	—	6	4	no	—
425	C₄	—	12	2	no	—
426	C₄	C₅×#67⋊C₄	1	2	yes	—
427	C₄	C₂²×C₄×C₅×D₃	1	1	yes	characteristic
428	C₄	C₂×C₅×#237	1	1	yes	characteristic
429	C₃	C₅×#2948	1	1	yes	characteristic, complemented, Sylow
430	C₂	—	2	2	no	—
431	C₂	—	4	4	no	—
432	C₂	—	12	4	no	—
433	C₂	C₂×C₅×#67⋊C₄	1	1	yes	characteristic
434	C₂	C₅×#5774	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×C₅×#213	C₂
cosocle	C₂×C₃×C₄	C₂⁴×C₅
hypercenter	C₅×#418	D₃
hypocenter	C₃	C₅×#2948
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
1. C₅×#5798	C₂	semidirect
3. C₅×#5521	C₂	semidirect
4. C₃×C₅×#418	C₂	semidirect
5. C₅×#5131	C₂	semidirect
6. C₅×#5122	C₂	semidirect
7. C₅×#4998	C₂	semidirect
8. C₅×#4785	C₂	semidirect
9. C₅×#4756	C₂	semidirect
17. C₅×D₄×Dic₃	C₂²	semidirect
18. C₂×C₅×#213	C₄	semidirect
24. C₅×#893	C₂²	semidirect
27. C₃×C₅×#102	C₂²	semidirect
28. C₅×#821	C₂²	semidirect
29. C₅×#815	C₂²	semidirect
30. C₅×C₈×Dic₃	C₂²	semidirect
31. C₅×#808	C₂²	semidirect
32. C₅×#807	C₂²	semidirect
33. #78915	C₅	direct (N × H)
41. C₅×#418	D₃	semidirect
47. C₂×C₃×C₅×D₄	C₂×C₄	semidirect
53. C₂×C₅×D₁₂	C₂×C₄	semidirect
64. C₅×#213	C₂×C₄	semidirect
65. C₅×#213	C₂×C₄	semidirect
71. C₂×C₅×C₃⋊C₈	C₂×C₄	semidirect
74. #5798	C₂×C₅	semidirect
76. #5521	C₂×C₅	semidirect
77. C₃×#418	C₂×C₅	semidirect
78. #5131	C₂×C₅	semidirect
79. #5122	C₂×C₅	semidirect
80. #4998	C₂×C₅	semidirect
81. #4785	C₂×C₅	semidirect
82. #4756	C₂×C₅	semidirect
102. C₅×#102	C₂×D₃	semidirect
137. D₄×Dic₃	C₂²×C₅	semidirect
138. C₂×#213	C₄×C₅	semidirect
144. #893	C₂²×C₅	semidirect
147. C₃×#102	C₂²×C₅	semidirect
148. #821	C₂²×C₅	semidirect
149. #815	C₂²×C₅	semidirect
150. C₈×Dic₃	C₂²×C₅	semidirect
151. #808	C₂²×C₅	semidirect
152. #807	C₂²×C₅	semidirect
161. C₂×C₅×D₄	C₄×D₃	semidirect
191. #418	C₅×D₃	semidirect
212. C₂×C₃×D₄	C₂×C₄×C₅	semidirect
218. C₂×D₁₂	C₂×C₄×C₅	semidirect
229. #213	C₂×C₄×C₅	semidirect
230. #213	C₂×C₄×C₅	semidirect
236. C₂×C₃⋊C₈	C₂×C₄×C₅	semidirect
283. #102	C₂×C₅×D₃	semidirect
339. C₂×D₄	C₄×C₅×D₃	semidirect
362. C₃×C₅	#2948	semidirect
413. C₅	#78915	direct (N × H)
429. C₃	C₅×#2948	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×#213	2
C₅×#5521	2
C₃×C₅×#418	2
C₅×#5131	2
C₅×#5122	2
C₅×#4998	2
C₅×#4785	2
C₅×#4756	2
C₅×#2948	3
#78915	5

Subgroups — C5×#78915 #14417327

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#78915 #14417327