Subgroups — C₃×Dic₅×#104 #14295578

Order 1920.

720 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#41×Dic₅	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×C₅×#104	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃×#3969	C₂	1	1	yes	maximal, characteristic
4	C₃×M₁₆×Dic₅	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×C₄²×Dic₅	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#64775	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#64743	C₂	1	1	yes	maximal, characteristic, complemented
8	Dic₅×#104	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic
10	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
11	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
12	C₃×Q₈×Dic₅	C₄	1	2	yes	complemented
13	C₃×D₄×Dic₅	—	2	2	no	—
14	C₃×D₄×Dic₅	C₄	1	2	yes	complemented
15	C₃×#4072	—	2	1	no	—
16	C₃×#4072	C₂²	1	1	yes	characteristic
17	C₂×C₃×C₄×Dic₅	—	2	2	no	—
18	C₂×C₃×C₄×Dic₅	—	2	1	no	—
19	C₂×C₃×C₄×Dic₅	C₂²	1	1	yes	characteristic
20	C₂×C₃×C₄×Dic₅	C₂²	1	1	yes	characteristic
21	C₂×C₃×#681	C₂²	1	1	yes	characteristic
22	C₃×C₅×#104	C₄	1	4	yes	complemented
23	C₃×#3969	C₄	1	4	yes	complemented
24	C₃×#3947	—	2	1	no	—
25	C₃×C₈×Dic₅	—	2	1	no	—
26	C₃×C₄×#104	—	5	1	no	maximal, Hall
27	#41×Dic₅	C₂×C₃	1	1	yes	characteristic
28	C₂×C₅×#104	C₂×C₃	1	1	yes	characteristic
29	C₂×#3969	C₂×C₃	1	1	yes	characteristic
30	M₁₆×Dic₅	C₂×C₃	1	1	yes	characteristic, complemented
31	C₄²×Dic₅	C₂×C₃	1	1	yes	characteristic, complemented
32	#64775	C₂×C₃	1	1	yes	characteristic, complemented
33	#64743	C₂×C₃	1	1	yes	characteristic, complemented
34	C₃×C₅×#41	—	2	1	no	—
35	C₃×C₅×#41	—	2	1	no	—
36	C₃×C₅×#41	C₂×C₄	1	2	yes	—
37	C₃×C₅×#41	C₂×C₄	1	2	yes	—
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	—	2	1	no	—
43	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
44	C₂²×C₃×Dic₅	—	2	1	no	—
45	C₂²×C₃×Dic₅	—	2	2	no	—
46	C₂²×C₃×Dic₅	D₄	1	2	yes	—
47	C₃×C₅×M₁₆	—	2	1	no	—
48	C₃×C₅×M₁₆	C₂×C₄	1	2	yes	complemented
49	C₂×C₃×C₅×C₈	—	2	1	no	—
50	C₃×C₄²×C₅	—	2	1	no	—
51	C₃×C₄²×C₅	C₂×C₄	1	2	yes	complemented
52	C₃×C₂²⋊Dic₅	—	2	1	no	—
53	C₃×C₂²⋊Dic₅	—	2	2	no	—
54	C₃×C₄⋊Dic₅	—	2	2	no	—
55	C₃×C₄⋊Dic₅	C₂×C₄	1	2	yes	—
56	C₃×C₄×Dic₅	—	2	8	no	—
57	C₃×C₄×Dic₅	—	2	1	no	—
58	C₃×C₄×Dic₅	—	2	1	no	—
59	C₃×C₄×Dic₅	—	2	2	no	—
60	C₃×C₄×Dic₅	C₂×C₄	1	2	yes	—
61	C₃×C₄×Dic₅	C₂×C₄	1	2	yes	complemented
62	C₃×C₄×Dic₅	D₄	1	1	yes	characteristic
63	C₃×C₄×Dic₅	D₄	1	1	yes	characteristic
64	C₃×#681	—	2	1	no	—
65	C₃×#681	C₂×C₄	1	2	yes	complemented
66	C₂×C₃×#168	—	2	1	no	—
67	C₃×C₄×#41	—	5	1	no	—
68	C₂×C₃×#104	—	5	1	no	—
69	C₂×C₃×#104	D₅	1	1	yes	characteristic
70	C₃×C₄×M₁₆	—	5	1	no	—
71	C₃×C₄³	—	5	1	no	—
72	C₃×#339	—	5	1	no	—
73	C₃×#339	—	5	1	no	—
74	C₂×C₅×#41	C₂²×C₃	1	1	yes	characteristic
75	C₂×C₅×M₁₆	C₂²×C₃	1	1	yes	characteristic
76	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
77	Q₈×Dic₅	C₃×C₄	1	2	yes	complemented
78	D₄×Dic₅	—	2	2	no	—
79	D₄×Dic₅	C₃×C₄	1	2	yes	complemented
80	#4072	—	2	1	no	—
81	#4072	C₂²×C₃	1	1	yes	characteristic
82	C₂×C₄×Dic₅	—	2	2	no	—
83	C₂×C₄×Dic₅	—	2	1	no	—
84	C₂×C₄×Dic₅	C₂²×C₃	1	1	yes	characteristic
85	C₂×C₄×Dic₅	C₂²×C₃	1	1	yes	characteristic
86	C₂×#681	C₂²×C₃	1	1	yes	characteristic
87	C₅×#104	C₃×C₄	1	4	yes	complemented
88	#3969	C₃×C₄	1	4	yes	complemented
89	#3947	—	2	1	no	—
90	C₈×Dic₅	—	2	1	no	—
91	C₄×#104	—	5	1	no	Sylow
92	C₂³×C₃×C₅	—	2	1	no	—
93	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
94	C₃×C₅×Q₈	—	2	1	no	—
95	C₃×C₅×Q₈	C₄²	1	2	yes	complemented
96	C₃×C₅×D₄	—	2	2	no	—
97	C₃×C₅×D₄	—	2	2	no	—
98	C₃×C₅×D₄	—	2	1	no	—
99	C₃×C₅×D₄	C₄²	1	2	yes	complemented
100	C₂×C₃×C₄×C₅	—	2	4	no	—
101	C₂×C₃×C₄×C₅	—	2	1	no	—
102	C₂×C₃×C₄×C₅	—	2	2	no	—
103	C₂×C₃×C₄×C₅	—	2	2	no	—
104	C₂×C₃×C₄×C₅	—	2	2	no	—
105	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
106	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
107	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
108	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
109	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
110	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
111	C₂×C₃×Dic₅	—	2	4	no	—
112	C₂×C₃×Dic₅	—	2	2	no	—
113	C₂×C₃×Dic₅	—	2	4	no	—
114	C₂×C₃×Dic₅	—	2	2	no	—
115	C₂×C₃×Dic₅	—	4	4	no	—
116	C₂×C₃×Dic₅	C₂²⋊C₄	1	2	yes	—
117	C₂×C₃×Dic₅	C₂²⋊C₄	1	2	yes	—
118	C₃×C₅×C₈	—	2	2	no	—
119	C₃×#168	—	2	2	no	—
120	C₂×C₃×#41	C₂×D₅	1	1	yes	characteristic
121	C₂×C₃×M₁₆	—	5	1	no	—
122	C₂×C₃×M₁₆	C₂×D₅	1	1	yes	characteristic
123	C₃×C₄×Q₈	—	5	2	no	—
124	C₃×C₄×D₄	—	5	2	no	—
125	C₃×C₄×D₄	—	10	2	no	—
126	C₃×#117	—	5	1	no	—
127	C₃×#117	—	10	1	no	—
128	C₂×C₃×C₄²	—	5	1	no	—
129	C₂×C₃×C₄²	—	5	1	no	—
130	C₂×C₃×C₄²	—	10	1	no	—
131	C₂×C₃×C₄²	—	10	2	no	—
132	C₂×C₃×C₄²	C₂×D₅	1	1	yes	characteristic
133	C₃×#104	—	5	4	no	—
134	C₃×#104	Dic₅	1	4	yes	direct product factor
135	C₃×#97	—	10	1	no	—
136	C₃×C₄×C₈	—	10	1	no	—
137	C₅×#41	—	2	1	no	—
138	C₅×#41	—	2	1	no	—
139	C₅×#41	C₂×C₃×C₄	1	2	yes	—
140	C₅×#41	C₂×C₃×C₄	1	2	yes	—
141	C₂×C₅×Q₈	C₂×C₃×C₄	1	1	yes	characteristic
142	C₂×C₅×D₄	—	2	1	no	—
143	C₂×C₅×D₄	C₂×C₃×C₄	1	1	yes	characteristic
144	C₂²×C₄×C₅	—	2	1	no	—
145	C₂²×C₄×C₅	—	2	1	no	—
146	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
147	C₂²×Dic₅	—	2	1	no	—
148	C₂²×Dic₅	—	2	2	no	—
149	C₂²×Dic₅	C₃×D₄	1	2	yes	—
150	C₅×M₁₆	—	2	1	no	—
151	C₅×M₁₆	C₂×C₃×C₄	1	2	yes	complemented
152	C₂×C₅×C₈	—	2	1	no	—
153	C₄²×C₅	—	2	1	no	—
154	C₄²×C₅	C₂×C₃×C₄	1	2	yes	complemented
155	C₂²⋊Dic₅	—	2	1	no	—
156	C₂²⋊Dic₅	—	2	2	no	—
157	C₄⋊Dic₅	—	2	2	no	—
158	C₄⋊Dic₅	C₂×C₃×C₄	1	2	yes	—
159	C₄×Dic₅	—	2	8	no	—
160	C₄×Dic₅	—	2	1	no	—
161	C₄×Dic₅	—	2	1	no	—
162	C₄×Dic₅	—	2	2	no	—
163	C₄×Dic₅	C₂×C₃×C₄	1	2	yes	—
164	C₄×Dic₅	C₂×C₃×C₄	1	2	yes	complemented
165	C₄×Dic₅	C₃×D₄	1	1	yes	characteristic
166	C₄×Dic₅	C₃×D₄	1	1	yes	characteristic
167	#681	—	2	1	no	—
168	#681	C₂×C₃×C₄	1	2	yes	complemented
169	C₂×#168	—	2	1	no	—
170	C₄×#41	—	5	1	no	—
171	C₂×#104	—	5	1	no	—
172	C₂×#104	C₃×D₅	1	1	yes	characteristic
173	C₄×M₁₆	—	5	1	no	—
174	C₄³	—	5	1	no	—
175	#339	—	5	1	no	—
176	#339	—	5	1	no	—
177	C₂²×C₃×C₅	—	2	2	no	—
178	C₂²×C₃×C₅	—	2	2	no	—
179	C₂²×C₃×C₅	—	4	2	no	—
180	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
181	C₂²×C₃×C₅	C₄×D₄	1	1	yes	characteristic
182	C₂²×C₃×C₅	C₄×D₄	1	1	yes	characteristic
183	C₃×C₄×C₅	—	2	4	no	—
184	C₃×C₄×C₅	—	2	2	no	—
185	C₃×C₄×C₅	C₂×C₄²	1	1	yes	characteristic
186	C₃×C₄×C₅	#117	1	1	yes	characteristic
187	C₃×C₄×C₅	C₄×D₄	1	1	yes	characteristic
188	C₃×C₄×C₅	C₄×D₄	1	1	yes	characteristic
189	C₃×Dic₅	—	2	4	no	—
190	C₃×Dic₅	—	2	2	no	—
191	C₃×Dic₅	—	4	2	no	—
192	C₃×Dic₅	#104	1	4	yes	direct product factor
193	C₃×#41	—	2	1	no	—
194	C₃×#41	—	2	1	no	—
195	C₃×#41	C₄×D₅	1	2	yes	—
196	C₃×#41	C₂×Dic₅	1	2	yes	—
197	C₂×C₃×Q₈	C₄×D₅	1	1	yes	characteristic
198	C₂×C₃×D₄	—	2	1	no	—
199	C₂×C₃×D₄	C₄×D₅	1	1	yes	characteristic
200	C₂²×C₃×C₄	—	2	1	no	—
201	C₂²×C₃×C₄	—	2	1	no	—
202	C₂²×C₃×C₄	—	5	2	no	—
203	C₂²×C₃×C₄	—	10	2	no	—
204	C₂²×C₃×C₄	—	10	1	no	—
205	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
206	C₃×M₁₆	—	2	1	no	—
207	C₃×M₁₆	—	5	2	no	—
208	C₃×M₁₆	—	10	1	no	—
209	C₃×M₁₆	C₂×Dic₅	1	2	yes	complemented
210	C₂×C₃×C₈	—	2	1	no	—
211	C₂×C₃×C₈	—	10	1	no	—
212	C₃×C₄⋊C₄	—	5	2	no	—
213	C₃×C₄⋊C₄	—	10	2	no	—
214	C₃×C₂²⋊C₄	—	10	2	no	—
215	C₃×C₂²⋊C₄	—	10	1	no	—
216	C₃×C₄²	—	2	1	no	—
217	C₃×C₄²	—	5	2	no	—
218	C₃×C₄²	—	5	1	no	—
219	C₃×C₄²	—	5	1	no	—
220	C₃×C₄²	—	5	2	no	—
221	C₃×C₄²	—	10	2	no	—
222	C₃×C₄²	—	10	8	no	—
223	C₃×C₄²	—	10	1	no	—
224	C₃×C₄²	—	10	1	no	—
225	C₃×C₄²	C₂×Dic₅	1	2	yes	complemented
226	C₂³×C₅	—	2	1	no	—
227	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
228	C₅×Q₈	—	2	1	no	—
229	C₅×Q₈	C₃×C₄²	1	2	yes	complemented
230	C₅×D₄	—	2	2	no	—
231	C₅×D₄	—	2	2	no	—
232	C₅×D₄	—	2	1	no	—
233	C₅×D₄	C₃×C₄²	1	2	yes	complemented
234	C₂×C₄×C₅	—	2	4	no	—
235	C₂×C₄×C₅	—	2	1	no	—
236	C₂×C₄×C₅	—	2	2	no	—
237	C₂×C₄×C₅	—	2	2	no	—
238	C₂×C₄×C₅	—	2	2	no	—
239	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
240	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
241	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
242	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
243	C₂×C₄×C₅	C₃×#41	1	1	yes	characteristic
244	C₂×C₄×C₅	C₃×#41	1	1	yes	characteristic
245	C₂×Dic₅	—	2	4	no	—
246	C₂×Dic₅	—	2	2	no	—
247	C₂×Dic₅	—	2	4	no	—
248	C₂×Dic₅	—	2	2	no	—
249	C₂×Dic₅	—	4	4	no	—
250	C₂×Dic₅	C₃×C₂²⋊C₄	1	2	yes	—
251	C₂×Dic₅	C₃×C₂²⋊C₄	1	2	yes	—
252	C₅×C₈	—	2	2	no	—
253	#168	—	2	2	no	—
254	C₂×#41	C₂×C₃×D₅	1	1	yes	characteristic
255	C₂×M₁₆	—	5	1	no	—
256	C₂×M₁₆	C₂×C₃×D₅	1	1	yes	characteristic
257	C₄×Q₈	—	5	2	no	—
258	C₄×D₄	—	5	2	no	—
259	C₄×D₄	—	10	2	no	—
260	#117	—	5	1	no	—
261	#117	—	10	1	no	—
262	C₂×C₄²	—	5	1	no	—
263	C₂×C₄²	—	5	1	no	—
264	C₂×C₄²	—	10	1	no	—
265	C₂×C₄²	—	10	2	no	—
266	C₂×C₄²	C₂×C₃×D₅	1	1	yes	characteristic
267	#104	—	5	4	no	—
268	#104	C₃×Dic₅	1	4	yes	direct product factor
269	#97	—	10	1	no	—
270	C₄×C₈	—	10	1	no	—
271	C₂×C₃×C₅	—	2	1	no	—
272	C₂×C₃×C₅	—	2	1	no	—
273	C₂×C₃×C₅	—	4	2	no	—
274	C₂×C₃×C₅	C₄×C₂²⋊C₄	1	1	yes	characteristic
275	C₂×C₃×C₅	C₂×#104	1	2	yes	—
276	C₂³×C₃	—	2	1	no	—
277	C₂³×C₃	D₄×D₅	1	1	yes	characteristic
278	C₃×Q₈	—	2	1	no	—
279	C₃×Q₈	C₄×Dic₅	1	2	yes	complemented
280	C₃×D₄	—	2	2	no	—
281	C₃×D₄	—	2	2	no	—
282	C₃×D₄	—	2	1	no	—
283	C₃×D₄	C₄×Dic₅	1	2	yes	complemented
284	C₂×C₃×C₄	—	2	4	no	—
285	C₂×C₃×C₄	—	2	1	no	—
286	C₂×C₃×C₄	—	2	2	no	—
287	C₂×C₃×C₄	—	2	2	no	—
288	C₂×C₃×C₄	—	2	2	no	—
289	C₂×C₃×C₄	—	5	2	no	—
290	C₂×C₃×C₄	—	5	2	no	—
291	C₂×C₃×C₄	—	10	4	no	—
292	C₂×C₃×C₄	—	10	4	no	—
293	C₂×C₃×C₄	—	10	2	no	—
294	C₂×C₃×C₄	—	10	2	no	—
295	C₂×C₃×C₄	—	20	4	no	—
296	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
297	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
298	C₂×C₃×C₄	D₄×D₅	1	1	yes	characteristic
299	C₂×C₃×C₄	#711	1	1	yes	characteristic
300	C₂×C₃×C₄	#711	1	1	yes	characteristic
301	C₂×C₃×C₄	C₂²×Dic₅	1	1	yes	characteristic
302	C₃×C₈	—	2	2	no	—
303	C₃×C₈	—	10	2	no	—
304	C₂²×C₅	—	2	2	no	—
305	C₂²×C₅	—	2	2	no	—
306	C₂²×C₅	—	4	2	no	—
307	C₂²×C₅	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
308	C₂²×C₅	C₃×C₄×D₄	1	1	yes	characteristic
309	C₂²×C₅	C₃×C₄×D₄	1	1	yes	characteristic
310	C₄×C₅	—	2	4	no	—
311	C₄×C₅	—	2	2	no	—
312	C₄×C₅	C₂×C₃×C₄²	1	1	yes	characteristic
313	C₄×C₅	C₃×#117	1	1	yes	characteristic
314	C₄×C₅	C₃×C₄×D₄	1	1	yes	characteristic
315	C₄×C₅	C₃×C₄×D₄	1	1	yes	characteristic
316	Dic₅	—	2	4	no	—
317	Dic₅	—	2	2	no	—
318	Dic₅	—	4	2	no	—
319	Dic₅	C₃×#104	1	4	yes	direct product factor
320	#41	—	2	1	no	—
321	#41	—	2	1	no	—
322	#41	C₃×C₄×D₅	1	2	yes	—
323	#41	C₂×C₃×Dic₅	1	2	yes	—
324	C₂×Q₈	C₃×C₄×D₅	1	1	yes	characteristic
325	C₂×D₄	—	2	1	no	—
326	C₂×D₄	C₃×C₄×D₅	1	1	yes	characteristic
327	C₂²×C₄	—	2	1	no	—
328	C₂²×C₄	—	2	1	no	—
329	C₂²×C₄	—	5	2	no	—
330	C₂²×C₄	—	10	2	no	—
331	C₂²×C₄	—	10	1	no	—
332	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
333	M₁₆	—	2	1	no	—
334	M₁₆	—	5	2	no	—
335	M₁₆	—	10	1	no	—
336	M₁₆	C₂×C₃×Dic₅	1	2	yes	complemented
337	C₂×C₈	—	2	1	no	—
338	C₂×C₈	—	10	1	no	—
339	C₄⋊C₄	—	5	2	no	—
340	C₄⋊C₄	—	10	2	no	—
341	C₂²⋊C₄	—	10	2	no	—
342	C₂²⋊C₄	—	10	1	no	—
343	C₄²	—	2	1	no	—
344	C₄²	—	5	2	no	—
345	C₄²	—	5	1	no	—
346	C₄²	—	5	1	no	—
347	C₄²	—	5	2	no	—
348	C₄²	—	10	2	no	—
349	C₄²	—	10	8	no	—
350	C₄²	—	10	1	no	—
351	C₄²	—	10	1	no	—
352	C₄²	C₂×C₃×Dic₅	1	2	yes	complemented
353	C₃×C₅	C₄×#104	1	1	yes	characteristic, complemented, Hall
354	C₂²×C₃	—	2	2	no	—
355	C₂²×C₃	—	2	2	no	—
356	C₂²×C₃	—	4	2	no	—
357	C₂²×C₃	D₅×C₂²⋊C₄	1	1	yes	characteristic
358	C₂²×C₃	#4027	1	1	yes	characteristic
359	C₂²×C₃	D₄×Dic₅	1	1	yes	characteristic
360	C₃×C₄	—	2	4	no	—
361	C₃×C₄	—	2	2	no	—
362	C₃×C₄	—	5	4	no	—
363	C₃×C₄	—	10	4	no	—
364	C₃×C₄	—	10	2	no	—
365	C₃×C₄	—	20	2	no	—
366	C₃×C₄	#4023	1	1	yes	characteristic
367	C₃×C₄	#4027	1	1	yes	characteristic
368	C₃×C₄	C₂×C₄×Dic₅	1	1	yes	characteristic
369	C₃×C₄	D₄×Dic₅	1	1	yes	characteristic
370	C₂×C₅	—	2	1	no	—
371	C₂×C₅	—	2	1	no	—
372	C₂×C₅	—	4	2	no	—
373	C₂×C₅	C₃×C₄×C₂²⋊C₄	1	1	yes	characteristic
374	C₂×C₅	C₂×C₃×#104	1	2	yes	—
375	C₂³	—	2	1	no	—
376	C₂³	C₃×D₄×D₅	1	1	yes	characteristic
377	Q₈	—	2	1	no	—
378	Q₈	C₃×C₄×Dic₅	1	2	yes	complemented
379	D₄	—	2	2	no	—
380	D₄	—	2	2	no	—
381	D₄	—	2	1	no	—
382	D₄	C₃×C₄×Dic₅	1	2	yes	complemented
383	C₂×C₄	—	2	4	no	—
384	C₂×C₄	—	2	2	no	—
385	C₂×C₄	—	2	1	no	—
386	C₂×C₄	—	2	2	no	—
387	C₂×C₄	—	2	2	no	—
388	C₂×C₄	—	5	2	no	—
389	C₂×C₄	—	5	2	no	—
390	C₂×C₄	—	10	4	no	—
391	C₂×C₄	—	10	4	no	—
392	C₂×C₄	—	10	2	no	—
393	C₂×C₄	—	10	2	no	—
394	C₂×C₄	—	20	4	no	—
395	C₂×C₄	C₂×C₃×C₄×D₅	1	1	yes	characteristic
396	C₂×C₄	C₂×C₃×C₄×D₅	1	1	yes	characteristic
397	C₂×C₄	C₃×D₄×D₅	1	1	yes	characteristic
398	C₂×C₄	C₃×#711	1	1	yes	characteristic
399	C₂×C₄	C₃×#711	1	1	yes	characteristic
400	C₂×C₄	C₂²×C₃×Dic₅	1	1	yes	characteristic
401	C₈	—	2	2	no	—
402	C₈	—	10	2	no	—
403	C₂×C₃	—	2	1	no	—
404	C₂×C₃	—	2	1	no	—
405	C₂×C₃	—	4	2	no	—
406	C₂×C₃	D₅×#104	1	2	yes	—
407	C₂×C₃	C₂²⋊C₄×Dic₅	1	1	yes	characteristic
408	C₅	C₃×C₄×#104	1	1	yes	characteristic, complemented, Sylow
409	C₂²	—	2	2	no	—
410	C₂²	—	2	2	no	—
411	C₂²	—	4	2	no	—
412	C₂²	C₃×D₅×C₂²⋊C₄	1	1	yes	characteristic
413	C₂²	C₃×#4027	1	1	yes	characteristic
414	C₂²	C₃×D₄×Dic₅	1	1	yes	characteristic
415	C₄	—	2	4	no	—
416	C₄	—	2	2	no	—
417	C₄	—	5	4	no	—
418	C₄	—	10	4	no	—
419	C₄	—	10	2	no	—
420	C₄	—	20	2	no	—
421	C₄	C₃×#4023	1	1	yes	characteristic
422	C₄	C₃×#4027	1	1	yes	characteristic
423	C₄	C₂×C₃×C₄×Dic₅	1	1	yes	characteristic
424	C₄	C₃×D₄×Dic₅	1	1	yes	characteristic
425	C₃	Dic₅×#104	1	1	yes	characteristic, direct product factor, Sylow
426	C₂	—	2	1	no	—
427	C₂	—	2	1	no	—
428	C₂	—	4	2	no	—
429	C₂	C₃×D₅×#104	1	2	yes	—
430	C₂	C₃×C₂²⋊C₄×Dic₅	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃×C₄	D₄×D₅
commutator	C₄×C₅	C₂×C₃×C₄²
Frattini	C₂²×C₄	C₂²×C₃×D₅
Fitting	C₂×C₃×C₅×#104	C₂
socle	C₂²×C₃×C₅	C₂×C₂²⋊C₄
prime radical	C₂×C₃×C₅×#41	C₂²
cosocle	C₂²×C₄×C₅	C₂³×C₃
hypercenter	C₂×C₃×#104	D₅
hypocenter	C₅	C₃×C₄×#104
LCS	G ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₂²×C₃×C₄ ◁ C₂×C₃×#104

Complements

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

N	H ≅ G/N	type
4. C₃×M₁₆×Dic₅	C₂	semidirect
5. C₃×C₄²×Dic₅	C₂	semidirect
6. C₃×#64775	C₂	semidirect
7. C₃×#64743	C₂	semidirect
8. Dic₅×#104	C₃	direct (N × H)
12. C₃×Q₈×Dic₅	C₄	semidirect
14. C₃×D₄×Dic₅	C₄	semidirect
22. C₃×C₅×#104	C₄	semidirect
23. C₃×#3969	C₄	semidirect
30. M₁₆×Dic₅	C₂×C₃	semidirect
31. C₄²×Dic₅	C₂×C₃	semidirect
32. #64775	C₂×C₃	semidirect
33. #64743	C₂×C₃	semidirect
48. C₃×C₅×M₁₆	C₂×C₄	semidirect
51. C₃×C₄²×C₅	C₂×C₄	semidirect
61. C₃×C₄×Dic₅	C₂×C₄	semidirect
65. C₃×#681	C₂×C₄	semidirect
77. Q₈×Dic₅	C₃×C₄	semidirect
79. D₄×Dic₅	C₃×C₄	semidirect
87. C₅×#104	C₃×C₄	semidirect
88. #3969	C₃×C₄	semidirect
95. C₃×C₅×Q₈	C₄²	semidirect
99. C₃×C₅×D₄	C₄²	semidirect
134. C₃×#104	Dic₅	direct (N × H)
151. C₅×M₁₆	C₂×C₃×C₄	semidirect
154. C₄²×C₅	C₂×C₃×C₄	semidirect
164. C₄×Dic₅	C₂×C₃×C₄	semidirect
168. #681	C₂×C₃×C₄	semidirect
192. C₃×Dic₅	#104	direct (N × H)
209. C₃×M₁₆	C₂×Dic₅	semidirect
225. C₃×C₄²	C₂×Dic₅	semidirect
229. C₅×Q₈	C₃×C₄²	semidirect
233. C₅×D₄	C₃×C₄²	semidirect
268. #104	C₃×Dic₅	direct (N × H)
279. C₃×Q₈	C₄×Dic₅	semidirect
283. C₃×D₄	C₄×Dic₅	semidirect
319. Dic₅	C₃×#104	direct (N × H)
336. M₁₆	C₂×C₃×Dic₅	semidirect
352. C₄²	C₂×C₃×Dic₅	semidirect
353. C₃×C₅	C₄×#104	semidirect
378. Q₈	C₃×C₄×Dic₅	semidirect
382. D₄	C₃×C₄×Dic₅	semidirect
408. C₅	C₃×C₄×#104	semidirect
425. C₃	Dic₅×#104	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×#41×Dic₅	2
C₂×C₃×C₅×#104	2
C₂×C₃×#3969	2
C₃×M₁₆×Dic₅	2
C₃×C₄²×Dic₅	2
C₃×#64775	2
C₃×#64743	2
Dic₅×#104	3
C₃×C₄×#104	5

Subgroups — C3×Dic5×#104 #14295578

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×Dic₅×#104 #14295578