Subgroups — C₅×#68229 #14281560

Order 1920.

552 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	C₄×C₅×#239	C₂	1	1	yes	maximal, characteristic
2	C₅×#4833	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×C₅×D₃×C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₅×Q₈⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#4535	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#4483	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#4459	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#1476	—	3	1	no	maximal, Hall
9	C₂×C₅×#239	C₄	1	1	yes	characteristic
10	C₃×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
11	C₅×Q₈×Dic₃	C₄	1	1	yes	characteristic
12	C₂×C₅×D₃×C₈	—	2	1	no	—
13	C₅×#893	—	2	1	no	—
14	C₅×#893	C₄	1	1	yes	characteristic
15	C₅×#892	—	2	1	no	—
16	C₅×#892	C₄	1	1	yes	characteristic
17	C₄×C₅×D₁₂	—	2	1	no	—
18	C₄×C₅×D₁₂	C₂²	1	1	yes	characteristic
19	C₄²×C₅×D₃	—	2	1	no	—
20	C₄²×C₅×D₃	C₂²	1	1	yes	characteristic
21	C₃×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
22	C₃×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
23	C₅×(C₂×D₃)⋊C₈	—	2	1	no	—
24	C₅×C₈×Dic₃	—	2	1	no	—
25	C₅×C₈×Dic₃	—	2	1	no	—
26	C₅×C₄⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic
27	C₄×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
28	#68229	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
29	C₄×C₅×#41	—	3	1	no	—
30	C₅×#431	—	3	1	no	—
31	C₂×C₄×C₅×C₈	—	3	1	no	—
32	C₅×Q₈⋊C₈	—	3	1	no	—
33	C₅×Q₈⋊C₈	D₃	1	1	yes	characteristic, complemented
34	C₅×D₄⋊C₈	—	3	1	no	—
35	C₅×D₄⋊C₈	—	3	1	no	—
36	C₂×C₃×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
37	C₅×#239	—	2	2	no	—
38	C₅×#239	C₈	1	4	yes	complemented
39	C₂×C₅×D₁₂	—	2	1	no	—
40	C₂×C₅×D₁₂	C₂×C₄	1	1	yes	characteristic
41	C₂×C₄×C₅×D₃	—	2	1	no	—
42	C₂×C₄×C₅×D₃	—	2	1	no	—
43	C₂×C₄×C₅×D₃	—	2	1	no	—
44	C₂×C₄×C₅×D₃	C₂×C₄	1	1	yes	characteristic
45	C₂×C₄×C₅×D₃	D₄	1	1	yes	characteristic
46	C₂×C₄×C₅×D₃	D₄	1	1	yes	characteristic
47	C₂×C₃×C₅×C₈	—	2	1	no	—
48	C₂×C₃×C₅×C₈	—	2	1	no	—
49	C₃×C₅×C₄⋊C₄	—	2	1	no	—
50	C₃×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
51	C₃×C₄²×C₅	—	2	1	no	—
52	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
53	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
54	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
55	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
56	C₅×C₄⋊Dic₃	—	2	1	no	—
57	C₅×C₄⋊Dic₃	C₂×C₄	1	1	yes	characteristic
58	C₄×C₅×Dic₃	—	2	1	no	—
59	C₄×C₅×Dic₃	—	2	1	no	—
60	C₄×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
61	C₄×C₅×Dic₃	D₄	1	1	yes	characteristic
62	C₄×C₅×Dic₃	D₄	1	1	yes	characteristic
63	C₂×C₅×C₃⋊C₈	—	2	1	no	—
64	C₂×C₅×C₃⋊C₈	—	2	1	no	—
65	C₅×D₃×C₈	—	2	4	no	—
66	C₄×#239	C₂×C₅	1	1	yes	characteristic
67	#4833	C₂×C₅	1	1	yes	characteristic, complemented
68	C₄×D₃×C₈	C₂×C₅	1	1	yes	characteristic, complemented
69	C₃×Q₈⋊C₈	C₂×C₅	1	1	yes	characteristic, complemented
70	#4535	C₂×C₅	1	1	yes	characteristic, complemented
71	#4483	C₂×C₅	1	1	yes	characteristic, complemented
72	#4459	C₂×C₅	1	1	yes	characteristic, complemented
73	C₂×C₅×#41	—	3	1	no	—
74	C₂²×C₅×C₈	—	6	1	no	—
75	C₄×C₅×Q₈	—	3	1	no	—
76	C₄×C₅×Q₈	C₂×D₃	1	1	yes	characteristic
77	C₄×C₅×D₄	—	3	1	no	—
78	C₄×C₅×D₄	—	3	1	no	—
79	C₄×C₅×D₄	—	6	1	no	—
80	C₄×C₅×D₄	—	6	1	no	—
81	C₅×#117	—	3	1	no	—
82	C₅×#117	—	6	1	no	—
83	C₂×C₄²×C₅	—	3	1	no	—
84	C₂×C₄²×C₅	—	6	1	no	—
85	C₅×C₄⋊C₈	—	3	1	no	—
86	C₅×C₄⋊C₈	C₂×D₃	1	1	yes	characteristic
87	C₅×C₂²⋊C₈	—	6	1	no	—
88	C₄×C₅×C₈	—	3	1	no	—
89	C₄×C₅×C₈	—	6	1	no	—
90	C₄×C₅×C₈	—	6	1	no	—
91	C₄×C₅×C₈	C₂×D₃	1	1	yes	characteristic
92	#1476	—	3	1	no	Sylow
93	C₂²×C₅×D₃	—	2	1	no	—
94	C₂²×C₅×D₃	C₂²⋊C₄	1	1	yes	characteristic
95	C₃×C₅×Q₈	—	2	1	no	—
96	C₃×C₅×Q₈	C₂×C₈	1	2	yes	complemented
97	C₂×C₃×C₄×C₅	—	2	1	no	—
98	C₂×C₃×C₄×C₅	—	2	1	no	—
99	C₂×C₃×C₄×C₅	C₂²×C₄	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×C₅×Dic₃	—	2	1	no	—
103	C₂×C₅×Dic₃	C₂²⋊C₄	1	1	yes	characteristic
104	C₂×C₅×Dic₃	C₂²⋊C₄	1	1	yes	characteristic
105	C₂×C₅×Dic₃	C₂²⋊C₄	1	1	yes	characteristic
106	C₅×D₁₂	—	2	4	no	—
107	C₅×D₁₂	—	2	1	no	—
108	C₅×D₁₂	C₂×C₈	1	2	yes	complemented
109	C₄×C₅×D₃	—	2	1	no	—
110	C₄×C₅×D₃	—	2	1	no	—
111	C₄×C₅×D₃	—	2	4	no	—
112	C₄×C₅×D₃	—	2	2	no	—
113	C₄×C₅×D₃	—	4	1	no	—
114	C₄×C₅×D₃	—	4	1	no	—
115	C₄×C₅×D₃	—	4	2	no	—
116	C₄×C₅×D₃	C₂×C₈	1	2	yes	—
117	C₄×C₅×D₃	M₁₆	1	2	yes	—
118	C₃×C₅×C₈	—	2	2	no	—
119	C₃×C₅×C₈	—	4	1	no	—
120	C₅×C₃⋊C₈	—	2	2	no	—
121	C₅×C₃⋊C₈	—	4	1	no	—
122	C₂×#239	C₄×C₅	1	1	yes	characteristic
123	C₃×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
124	Q₈×Dic₃	C₄×C₅	1	1	yes	characteristic
125	C₂×D₃×C₈	—	2	1	no	—
126	#893	—	2	1	no	—
127	#893	C₄×C₅	1	1	yes	characteristic
128	#892	—	2	1	no	—
129	#892	C₄×C₅	1	1	yes	characteristic
130	C₄×D₁₂	—	2	1	no	—
131	C₄×D₁₂	C₂²×C₅	1	1	yes	characteristic
132	C₄²×D₃	—	2	1	no	—
133	C₄²×D₃	C₂²×C₅	1	1	yes	characteristic
134	C₃×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
135	C₃×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
136	(C₂×D₃)⋊C₈	—	2	1	no	—
137	C₈×Dic₃	—	2	1	no	—
138	C₈×Dic₃	—	2	1	no	—
139	C₄⋊(C₃⋊C₈)	C₂²×C₅	1	1	yes	characteristic
140	C₄×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic
141	C₅×#41	—	3	4	no	—
142	C₅×#41	—	6	2	no	—
143	C₂×C₅×Q₈	C₄×D₃	1	1	yes	characteristic
144	C₂×C₅×D₄	—	3	1	no	—
145	C₂×C₅×D₄	—	6	1	no	—
146	C₂²×C₄×C₅	—	3	1	no	—
147	C₂²×C₄×C₅	—	3	1	no	—
148	C₂²×C₄×C₅	—	3	1	no	—
149	C₂²×C₄×C₅	—	6	1	no	—
150	C₂²×C₄×C₅	—	6	1	no	—
151	C₂²×C₄×C₅	—	6	1	no	—
152	C₂×C₅×C₈	—	2	1	no	—
153	C₂×C₅×C₈	—	2	1	no	—
154	C₂×C₅×C₈	—	6	4	no	—
155	C₂×C₅×C₈	—	6	1	no	—
156	C₂×C₅×C₈	—	6	1	no	—
157	C₅×C₄⋊C₄	—	2	1	no	—
158	C₅×C₄⋊C₄	—	3	1	no	—
159	C₅×C₄⋊C₄	—	6	1	no	—
160	C₅×C₄⋊C₄	C₄×D₃	1	1	yes	characteristic
161	C₅×C₂²⋊C₄	—	6	1	no	—
162	C₅×C₂²⋊C₄	—	6	1	no	—
163	C₅×C₂²⋊C₄	—	6	1	no	—
164	C₄²×C₅	—	2	1	no	—
165	C₄²×C₅	—	3	1	no	—
166	C₄²×C₅	—	3	1	no	—
167	C₄²×C₅	—	3	1	no	—
168	C₄²×C₅	—	6	1	no	—
169	C₄²×C₅	—	6	1	no	—
170	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
171	C₄×#41	—	3	1	no	—
172	#431	—	3	1	no	—
173	C₂×C₄×C₈	—	3	1	no	—
174	Q₈⋊C₈	—	3	1	no	—
175	Q₈⋊C₈	C₅×D₃	1	1	yes	characteristic, complemented
176	D₄⋊C₈	—	3	1	no	—
177	D₄⋊C₈	—	3	1	no	—
178	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
179	C₂×C₅×D₃	—	2	1	no	—
180	C₂×C₅×D₃	—	2	1	no	—
181	C₂×C₅×D₃	—	2	2	no	—
182	C₂×C₅×D₃	—	4	1	no	—
183	C₂×C₅×D₃	—	4	1	no	—
184	C₂×C₅×D₃	C₂²⋊C₈	1	2	yes	—
185	C₃×C₄×C₅	—	2	2	no	—
186	C₃×C₄×C₅	—	2	1	no	—
187	C₃×C₄×C₅	—	4	1	no	—
188	C₃×C₄×C₅	C₂²×C₈	1	1	yes	characteristic
189	C₃×C₄×C₅	C₂×M₁₆	1	1	yes	characteristic
190	C₃×C₄×C₅	#135	1	1	yes	characteristic
191	C₃×C₄×C₅	#135	1	1	yes	characteristic
192	C₅×Dic₃	—	2	1	no	—
193	C₅×Dic₃	—	4	1	no	—
194	C₅×Dic₃	C₂²⋊C₈	1	2	yes	—
195	C₅×Dic₃	#104	1	2	yes	—
196	C₂×C₃×Q₈	C₂×C₄×C₅	1	1	yes	characteristic
197	#239	—	2	2	no	—
198	#239	C₅×C₈	1	4	yes	complemented
199	C₂×D₁₂	—	2	1	no	—
200	C₂×D₁₂	C₂×C₄×C₅	1	1	yes	characteristic
201	C₂×C₄×D₃	—	2	1	no	—
202	C₂×C₄×D₃	—	2	1	no	—
203	C₂×C₄×D₃	—	2	1	no	—
204	C₂×C₄×D₃	C₂×C₄×C₅	1	1	yes	characteristic
205	C₂×C₄×D₃	C₅×D₄	1	1	yes	characteristic
206	C₂×C₄×D₃	C₅×D₄	1	1	yes	characteristic
207	C₂×C₃×C₈	—	2	1	no	—
208	C₂×C₃×C₈	—	2	1	no	—
209	C₃×C₄⋊C₄	—	2	1	no	—
210	C₃×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
211	C₃×C₄²	—	2	1	no	—
212	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
213	(C₂×D₃)⋊C₄	—	2	1	no	—
214	(C₂×D₃)⋊C₄	—	2	1	no	—
215	(C₂×D₃)⋊C₄	—	2	1	no	—
216	C₄⋊Dic₃	—	2	1	no	—
217	C₄⋊Dic₃	C₂×C₄×C₅	1	1	yes	characteristic
218	C₄×Dic₃	—	2	1	no	—
219	C₄×Dic₃	—	2	1	no	—
220	C₄×Dic₃	C₂×C₄×C₅	1	1	yes	characteristic
221	C₄×Dic₃	C₅×D₄	1	1	yes	characteristic
222	C₄×Dic₃	C₅×D₄	1	1	yes	characteristic
223	C₂×C₃⋊C₈	—	2	1	no	—
224	C₂×C₃⋊C₈	—	2	1	no	—
225	D₃×C₈	—	2	4	no	—
226	C₂³×C₅	—	3	1	no	—
227	C₂³×C₅	—	6	1	no	—
228	C₅×Q₈	—	2	1	no	—
229	C₅×Q₈	D₃×C₈	1	2	yes	complemented
230	C₅×D₄	—	3	2	no	—
231	C₅×D₄	—	6	4	no	—
232	C₅×D₄	—	6	1	no	—
233	C₂×C₄×C₅	—	2	1	no	—
234	C₂×C₄×C₅	—	2	1	no	—
235	C₂×C₄×C₅	—	3	1	no	—
236	C₂×C₄×C₅	—	3	1	no	—
237	C₂×C₄×C₅	—	3	2	no	—
238	C₂×C₄×C₅	—	3	2	no	—
239	C₂×C₄×C₅	—	3	1	no	—
240	C₂×C₄×C₅	—	6	2	no	—
241	C₂×C₄×C₅	—	6	4	no	—
242	C₂×C₄×C₅	—	6	1	no	—
243	C₂×C₄×C₅	—	6	1	no	—
244	C₂×C₄×C₅	—	6	1	no	—
245	C₂×C₄×C₅	—	12	2	no	—
246	C₂×C₄×C₅	—	12	1	no	—
247	C₂×C₄×C₅	—	12	1	no	—
248	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
249	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
250	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
251	C₅×C₈	—	2	2	no	—
252	C₅×C₈	—	4	1	no	—
253	C₅×C₈	—	6	2	no	—
254	C₅×C₈	—	12	1	no	—
255	C₂×#41	—	3	1	no	—
256	C₂²×C₈	—	6	1	no	—
257	C₄×Q₈	—	3	1	no	—
258	C₄×Q₈	C₂×C₅×D₃	1	1	yes	characteristic
259	C₄×D₄	—	3	1	no	—
260	C₄×D₄	—	3	1	no	—
261	C₄×D₄	—	6	1	no	—
262	C₄×D₄	—	6	1	no	—
263	#117	—	3	1	no	—
264	#117	—	6	1	no	—
265	C₂×C₄²	—	3	1	no	—
266	C₂×C₄²	—	6	1	no	—
267	C₄⋊C₈	—	3	1	no	—
268	C₄⋊C₈	C₂×C₅×D₃	1	1	yes	characteristic
269	C₂²⋊C₈	—	6	1	no	—
270	C₄×C₈	—	3	1	no	—
271	C₄×C₈	—	6	1	no	—
272	C₄×C₈	—	6	1	no	—
273	C₄×C₈	C₂×C₅×D₃	1	1	yes	characteristic
274	C₂×C₃×C₅	C₂×C₂²⋊C₈	1	1	yes	characteristic
275	C₂×C₃×C₅	#416	1	1	yes	characteristic
276	C₂×C₃×C₅	C₂×#104	1	1	yes	characteristic
277	C₅×D₃	—	2	2	no	—
278	C₅×D₃	—	4	2	no	—
279	C₂²×D₃	—	2	1	no	—
280	C₂²×D₃	C₅×C₂²⋊C₄	1	1	yes	characteristic
281	C₃×Q₈	—	2	1	no	—
282	C₃×Q₈	C₂×C₅×C₈	1	2	yes	complemented
283	C₂×C₃×C₄	—	2	1	no	—
284	C₂×C₃×C₄	—	2	1	no	—
285	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
286	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
287	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
288	C₂×Dic₃	—	2	1	no	—
289	C₂×Dic₃	C₅×C₂²⋊C₄	1	1	yes	characteristic
290	C₂×Dic₃	C₅×C₂²⋊C₄	1	1	yes	characteristic
291	C₂×Dic₃	C₅×C₂²⋊C₄	1	1	yes	characteristic
292	D₁₂	—	2	4	no	—
293	D₁₂	—	2	1	no	—
294	D₁₂	C₂×C₅×C₈	1	2	yes	complemented
295	C₄×D₃	—	2	1	no	—
296	C₄×D₃	—	2	1	no	—
297	C₄×D₃	—	2	4	no	—
298	C₄×D₃	—	2	2	no	—
299	C₄×D₃	—	4	1	no	—
300	C₄×D₃	—	4	1	no	—
301	C₄×D₃	—	4	2	no	—
302	C₄×D₃	C₂×C₅×C₈	1	2	yes	—
303	C₄×D₃	C₅×M₁₆	1	2	yes	—
304	C₃×C₈	—	2	2	no	—
305	C₃×C₈	—	4	1	no	—
306	C₃⋊C₈	—	2	2	no	—
307	C₃⋊C₈	—	4	1	no	—
308	C₂²×C₅	—	3	2	no	—
309	C₂²×C₅	—	6	1	no	—
310	C₂²×C₅	—	6	1	no	—
311	C₂²×C₅	—	6	2	no	—
312	C₂²×C₅	—	12	1	no	—
313	C₂²×C₅	—	12	1	no	—
314	C₂²×C₅	D₃×C₂²⋊C₄	1	1	yes	characteristic
315	C₄×C₅	—	2	2	no	—
316	C₄×C₅	—	2	1	no	—
317	C₄×C₅	—	3	2	no	—
318	C₄×C₅	—	3	2	no	—
319	C₄×C₅	—	4	1	no	—
320	C₄×C₅	—	6	1	no	—
321	C₄×C₅	—	12	1	no	—
322	C₄×C₅	C₂×D₃×C₈	1	1	yes	characteristic
323	C₄×C₅	D₃×M₁₆	1	1	yes	characteristic
324	C₄×C₅	#916	1	1	yes	characteristic
325	C₄×C₅	#919	1	1	yes	characteristic
326	#41	—	3	4	no	—
327	#41	—	6	2	no	—
328	C₂×Q₈	C₄×C₅×D₃	1	1	yes	characteristic
329	C₂×D₄	—	3	1	no	—
330	C₂×D₄	—	6	1	no	—
331	C₂²×C₄	—	3	1	no	—
332	C₂²×C₄	—	3	1	no	—
333	C₂²×C₄	—	3	1	no	—
334	C₂²×C₄	—	6	1	no	—
335	C₂²×C₄	—	6	1	no	—
336	C₂²×C₄	—	6	1	no	—
337	C₂×C₈	—	2	1	no	—
338	C₂×C₈	—	2	1	no	—
339	C₂×C₈	—	6	4	no	—
340	C₂×C₈	—	6	1	no	—
341	C₂×C₈	—	6	1	no	—
342	C₄⋊C₄	—	2	1	no	—
343	C₄⋊C₄	—	3	1	no	—
344	C₄⋊C₄	—	6	1	no	—
345	C₄⋊C₄	C₄×C₅×D₃	1	1	yes	characteristic
346	C₂²⋊C₄	—	6	1	no	—
347	C₂²⋊C₄	—	6	1	no	—
348	C₂²⋊C₄	—	6	1	no	—
349	C₄²	—	2	1	no	—
350	C₄²	—	3	1	no	—
351	C₄²	—	3	1	no	—
352	C₄²	—	3	1	no	—
353	C₄²	—	6	1	no	—
354	C₄²	—	6	1	no	—
355	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
356	C₃×C₅	#1476	1	1	yes	characteristic, complemented, Hall
357	C₂²×C₃	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
358	C₂×D₃	—	2	1	no	—
359	C₂×D₃	—	2	1	no	—
360	C₂×D₃	—	2	2	no	—
361	C₂×D₃	—	4	1	no	—
362	C₂×D₃	—	4	1	no	—
363	C₂×D₃	C₅×C₂²⋊C₈	1	2	yes	—
364	C₃×C₄	—	2	2	no	—
365	C₃×C₄	—	2	1	no	—
366	C₃×C₄	—	4	1	no	—
367	C₃×C₄	C₂²×C₅×C₈	1	1	yes	characteristic
368	C₃×C₄	C₂×C₅×M₁₆	1	1	yes	characteristic
369	C₃×C₄	C₅×#135	1	1	yes	characteristic
370	C₃×C₄	C₅×#135	1	1	yes	characteristic
371	Dic₃	—	2	1	no	—
372	Dic₃	—	4	1	no	—
373	Dic₃	C₅×C₂²⋊C₈	1	2	yes	—
374	Dic₃	C₅×#104	1	2	yes	—
375	C₂×C₅	—	6	2	no	—
376	C₂×C₅	—	12	2	no	—
377	C₂×C₅	D₃×C₂²⋊C₈	1	1	yes	characteristic
378	C₂×C₅	#4804	1	1	yes	characteristic
379	C₂×C₅	D₃×#104	1	1	yes	characteristic
380	C₂³	—	3	1	no	—
381	C₂³	—	6	1	no	—
382	Q₈	—	2	1	no	—
383	Q₈	C₅×D₃×C₈	1	2	yes	complemented
384	D₄	—	3	2	no	—
385	D₄	—	6	4	no	—
386	D₄	—	6	1	no	—
387	C₂×C₄	—	2	1	no	—
388	C₂×C₄	—	2	1	no	—
389	C₂×C₄	—	3	1	no	—
390	C₂×C₄	—	3	1	no	—
391	C₂×C₄	—	3	2	no	—
392	C₂×C₄	—	3	2	no	—
393	C₂×C₄	—	3	1	no	—
394	C₂×C₄	—	6	2	no	—
395	C₂×C₄	—	6	4	no	—
396	C₂×C₄	—	6	1	no	—
397	C₂×C₄	—	6	1	no	—
398	C₂×C₄	—	6	1	no	—
399	C₂×C₄	—	12	2	no	—
400	C₂×C₄	—	12	1	no	—
401	C₂×C₄	—	12	1	no	—
402	C₂×C₄	C₂×C₄×C₅×D₃	1	1	yes	characteristic
403	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
404	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
405	C₈	—	2	2	no	—
406	C₈	—	4	1	no	—
407	C₈	—	6	2	no	—
408	C₈	—	12	1	no	—
409	C₂×C₃	C₂×C₅×C₂²⋊C₈	1	1	yes	characteristic
410	C₂×C₃	C₅×#416	1	1	yes	characteristic
411	C₂×C₃	C₂×C₅×#104	1	1	yes	characteristic
412	D₃	—	2	2	no	—
413	D₃	—	4	2	no	—
414	C₅	#68229	1	1	yes	characteristic, direct product factor, Sylow
415	C₂²	—	3	2	no	—
416	C₂²	—	6	1	no	—
417	C₂²	—	6	1	no	—
418	C₂²	—	6	2	no	—
419	C₂²	—	12	1	no	—
420	C₂²	—	12	1	no	—
421	C₂²	C₅×D₃×C₂²⋊C₄	1	1	yes	characteristic
422	C₄	—	2	2	no	—
423	C₄	—	2	1	no	—
424	C₄	—	3	2	no	—
425	C₄	—	3	2	no	—
426	C₄	—	4	1	no	—
427	C₄	—	6	1	no	—
428	C₄	—	12	1	no	—
429	C₄	C₂×C₅×D₃×C₈	1	1	yes	characteristic
430	C₄	C₅×D₃×M₁₆	1	1	yes	characteristic
431	C₄	C₅×#916	1	1	yes	characteristic
432	C₄	C₅×#919	1	1	yes	characteristic
433	C₃	C₅×#1476	1	1	yes	characteristic, complemented, Sylow
434	C₂	—	6	2	no	—
435	C₂	—	12	2	no	—
436	C₂	C₅×D₃×C₂²⋊C₈	1	1	yes	characteristic
437	C₂	C₅×#4804	1	1	yes	characteristic
438	C₂	C₅×D₃×#104	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₅	D₃×D₄
commutator	C₃×C₄	C₂²×C₅×C₈
Frattini	C₄²	C₂²×C₅×D₃
Fitting	C₃×C₅×Q₈⋊C₈	C₂
socle	C₂²×C₃×C₅	C₂×C₂²⋊C₄
prime radical	C₂×C₅×#239	C₄
cosocle	C₃×C₄²	C₂³×C₅
hypercenter	C₅×Q₈⋊C₈	D₃
hypocenter	C₃	C₅×#1476
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₄×C₅ ◁ C₄²×C₅ ◁ C₅×Q₈⋊C₈

Complements

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

N	H ≅ G/N	type
2. C₅×#4833	C₂	semidirect
3. C₄×C₅×D₃×C₈	C₂	semidirect
4. C₃×C₅×Q₈⋊C₈	C₂	semidirect
5. C₅×#4535	C₂	semidirect
6. C₅×#4483	C₂	semidirect
7. C₅×#4459	C₂	semidirect
28. #68229	C₅	direct (N × H)
33. C₅×Q₈⋊C₈	D₃	semidirect
38. C₅×#239	C₈	semidirect
67. #4833	C₂×C₅	semidirect
68. C₄×D₃×C₈	C₂×C₅	semidirect
69. C₃×Q₈⋊C₈	C₂×C₅	semidirect
70. #4535	C₂×C₅	semidirect
71. #4483	C₂×C₅	semidirect
72. #4459	C₂×C₅	semidirect
96. C₃×C₅×Q₈	C₂×C₈	semidirect
108. C₅×D₁₂	C₂×C₈	semidirect
175. Q₈⋊C₈	C₅×D₃	semidirect
198. #239	C₅×C₈	semidirect
229. C₅×Q₈	D₃×C₈	semidirect
282. C₃×Q₈	C₂×C₅×C₈	semidirect
294. D₁₂	C₂×C₅×C₈	semidirect
356. C₃×C₅	#1476	semidirect
383. Q₈	C₅×D₃×C₈	semidirect
414. C₅	#68229	direct (N × H)
433. C₃	C₅×#1476	semidirect

Maximal subgroups

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

subgroup	index
C₄×C₅×#239	2
C₅×#4833	2
C₄×C₅×D₃×C₈	2
C₃×C₅×Q₈⋊C₈	2
C₅×#4535	2
C₅×#4483	2
C₅×#4459	2
C₅×#1476	3
#68229	5

Subgroups — C5×#68229 #14281560

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#68229 #14281560