Subgroups — C₃×C₄×#4055 #14416839

Order 1920.

968 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#4055	C₂	1	1	yes	maximal, characteristic
2	C₃×C₄×#709	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃×C₄×Dic₁₀	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₄×C₅×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#65422	C₂	1	1	yes	maximal, characteristic
6	C₃×#65410	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#65409	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#65005	C₂	1	2	yes	maximal, complemented
9	C₃×#64999	C₂	1	2	yes	maximal, complemented
10	C₃×C₄×Dic₂₀	C₂	1	2	yes	maximal, complemented
11	C₃×C₄×#677	C₂	1	2	yes	maximal, complemented
12	C₄×#4055	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂×C₃×#709	C₂²	1	1	yes	characteristic
14	C₂²×C₃×Dic₁₀	C₂²	1	1	yes	characteristic
15	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
16	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
17	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
18	C₃×C₄×C₂²⋊D₅	—	2	1	no	—
19	C₃×C₄×C₂²⋊D₅	—	2	1	no	—
20	C₃×#4072	C₂²	1	1	yes	characteristic
21	C₂×C₃×C₄⋊Dic₅	C₂²	1	1	yes	characteristic
22	C₂×C₃×#683	—	2	1	no	—
23	C₂×C₃×C₄×Dic₅	—	2	1	no	—
24	C₃×#4055	C₄	1	8	yes	direct product factor
25	C₂×C₃×Dic₂₀	C₂²	1	2	yes	—
26	C₂×C₃×#677	C₂²	1	2	yes	—
27	C₃×C₄×D₂₀	C₂²	1	1	yes	characteristic
28	C₃×C₄×D₂₀	C₂²	1	1	yes	characteristic
29	C₃×#4018	—	2	1	no	—
30	C₃×C₄²×D₅	—	2	1	no	—
31	C₃×C₄×Dic₁₀	—	2	1	no	—
32	C₃×C₄×Dic₁₀	—	2	1	no	—
33	C₃×C₄×Dic₁₀	C₂²	1	2	yes	—
34	C₃×C₄×Dic₁₀	C₂²	1	2	yes	—
35	C₃×C₄×Dic₁₀	C₂²	1	1	yes	characteristic
36	C₃×C₄×Dic₁₀	C₂²	1	1	yes	characteristic
37	C₃×C₅×#97	C₂²	1	2	yes	—
38	C₃×C₄×C₅×C₈	C₂²	1	2	yes	—
39	C₃×#3953	C₂²	1	2	yes	—
40	C₃×#3950	C₂²	1	2	yes	—
41	C₃×#3949	C₂²	1	2	yes	—
42	C₃×#3948	C₂²	1	2	yes	—
43	C₃×#3948	C₂²	1	2	yes	—
44	C₃×#3948	C₂²	1	2	yes	—
45	C₃×C₄×#137	—	5	1	no	maximal, Hall
46	C₂×#4055	C₂×C₃	1	1	yes	characteristic
47	C₄×#709	C₂×C₃	1	1	yes	characteristic
48	C₂×C₄×Dic₁₀	C₂×C₃	1	1	yes	characteristic, complemented
49	C₄×C₅×M₁₆	C₂×C₃	1	1	yes	characteristic, complemented
50	#65422	C₂×C₃	1	1	yes	characteristic
51	#65410	C₂×C₃	1	1	yes	characteristic, complemented
52	#65409	C₂×C₃	1	1	yes	characteristic, complemented
53	#65005	C₂×C₃	1	2	yes	complemented
54	#64999	C₂×C₃	1	2	yes	complemented
55	C₄×Dic₂₀	C₂×C₃	1	2	yes	complemented
56	C₄×#677	C₂×C₃	1	2	yes	complemented
57	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
58	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
59	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
60	C₂×C₃×C₂²⋊D₅	—	2	1	no	—
61	C₂²×C₃×Dic₅	—	2	1	no	—
62	C₂²×C₃×Dic₅	—	2	1	no	—
63	C₃×#709	—	2	2	no	—
64	C₃×#709	C₂×C₄	1	4	yes	—
65	C₂×C₃×D₂₀	C₂³	1	1	yes	characteristic
66	C₂×C₃×C₄×D₅	—	2	1	no	—
67	C₂×C₃×C₄×D₅	—	2	1	no	—
68	C₂×C₃×C₄×D₅	—	2	1	no	—
69	C₂×C₃×Dic₁₀	—	2	1	no	—
70	C₂×C₃×Dic₁₀	—	2	2	no	—
71	C₂×C₃×Dic₁₀	C₂×C₄	1	4	yes	complemented
72	C₂×C₃×Dic₁₀	C₂³	1	2	yes	—
73	C₂×C₃×Dic₁₀	C₂³	1	1	yes	characteristic
74	C₃×C₅×M₁₆	—	2	2	no	—
75	C₃×C₅×M₁₆	C₂×C₄	1	4	yes	complemented
76	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
77	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
78	C₃×C₄²×C₅	D₄	1	1	yes	characteristic
79	C₃×C₄²×C₅	D₄	1	1	yes	characteristic
80	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
81	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
82	C₃×C₂²⋊Dic₅	—	2	1	no	—
83	C₃×#685	—	2	1	no	—
84	C₃×#685	—	2	1	no	—
85	C₃×C₄⋊Dic₅	—	2	1	no	—
86	C₃×C₄⋊Dic₅	C₂³	1	1	yes	characteristic
87	C₃×C₄⋊Dic₅	C₂³	1	1	yes	characteristic
88	C₃×C₄⋊Dic₅	C₂³	1	2	yes	—
89	C₃×#683	—	2	2	no	—
90	C₃×#683	—	2	2	no	—
91	C₃×#683	—	2	1	no	—
92	C₃×#683	—	2	1	no	—
93	C₃×C₄×Dic₅	—	2	2	no	—
94	C₃×C₄×Dic₅	—	2	2	no	—
95	C₃×C₄×Dic₅	—	2	1	no	—
96	C₃×C₄×Dic₅	—	2	1	no	—
97	C₃×C₄×Dic₅	—	2	1	no	—
98	C₃×Dic₂₀	C₂×C₄	1	8	yes	complemented
99	C₃×#677	C₂×C₄	1	8	yes	complemented
100	C₂×C₃×#137	—	5	1	no	—
101	C₃×C₄×#41	—	5	1	no	—
102	C₂×C₃×C₄×Q₈	—	5	1	no	—
103	C₃×#441	—	5	2	no	—
104	C₃×#440	—	5	2	no	—
105	C₃×C₄×Q₁₆	—	5	2	no	—
106	C₃×C₄×SD₁₆	—	5	2	no	—
107	C₃×#428	—	5	1	no	—
108	C₃×#419	—	5	1	no	—
109	C₃×#417	—	5	1	no	—
110	C₃×C₄×M₁₆	D₅	1	1	yes	characteristic, complemented
111	C₂×#709	C₂²×C₃	1	1	yes	characteristic
112	C₂²×Dic₁₀	C₂²×C₃	1	1	yes	characteristic
113	C₂×C₅×M₁₆	C₂²×C₃	1	1	yes	characteristic
114	C₂×C₅×M₁₆	C₂²×C₃	1	1	yes	characteristic
115	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
116	C₄×C₂²⋊D₅	—	2	1	no	—
117	C₄×C₂²⋊D₅	—	2	1	no	—
118	#4072	C₂²×C₃	1	1	yes	characteristic
119	C₂×C₄⋊Dic₅	C₂²×C₃	1	1	yes	characteristic
120	C₂×#683	—	2	1	no	—
121	C₂×C₄×Dic₅	—	2	1	no	—
122	#4055	C₃×C₄	1	8	yes	direct product factor
123	C₂×Dic₂₀	C₂²×C₃	1	2	yes	—
124	C₂×#677	C₂²×C₃	1	2	yes	—
125	C₄×D₂₀	C₂²×C₃	1	1	yes	characteristic
126	C₄×D₂₀	C₂²×C₃	1	1	yes	characteristic
127	#4018	—	2	1	no	—
128	C₄²×D₅	—	2	1	no	—
129	C₄×Dic₁₀	—	2	1	no	—
130	C₄×Dic₁₀	—	2	1	no	—
131	C₄×Dic₁₀	C₂²×C₃	1	2	yes	—
132	C₄×Dic₁₀	C₂²×C₃	1	2	yes	—
133	C₄×Dic₁₀	C₂²×C₃	1	1	yes	characteristic
134	C₄×Dic₁₀	C₂²×C₃	1	1	yes	characteristic
135	C₅×#97	C₂²×C₃	1	2	yes	—
136	C₄×C₅×C₈	C₂²×C₃	1	2	yes	—
137	#3953	C₂²×C₃	1	2	yes	—
138	#3950	C₂²×C₃	1	2	yes	—
139	#3949	C₂²×C₃	1	2	yes	—
140	#3948	C₂²×C₃	1	2	yes	—
141	#3948	C₂²×C₃	1	2	yes	—
142	#3948	C₂²×C₃	1	2	yes	—
143	C₄×#137	—	5	1	no	Sylow
144	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
145	C₂²×C₃×D₅	—	2	1	no	—
146	C₂×C₃×C₄×C₅	—	2	2	no	—
147	C₂×C₃×C₄×C₅	—	4	1	no	—
148	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
149	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
150	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
151	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
152	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
153	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
154	C₂×C₃×C₄×C₅	#41	1	2	yes	—
155	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
156	C₃×C₂²⋊D₅	—	2	4	no	—
157	C₂×C₃×Dic₅	—	2	4	no	—
158	C₂×C₃×Dic₅	—	2	2	no	—
159	C₂×C₃×Dic₅	—	2	1	no	—
160	C₂×C₃×Dic₅	—	2	2	no	—
161	C₂×C₃×Dic₅	—	2	1	no	—
162	C₂×C₃×Dic₅	—	2	1	no	—
163	C₂×C₃×Dic₅	—	4	2	no	—
164	C₃×D₂₀	—	2	1	no	—
165	C₃×D₂₀	C₂²×C₄	1	2	yes	—
166	C₃×C₄×D₅	—	2	4	no	—
167	C₃×C₄×D₅	—	4	2	no	—
168	C₃×C₄×D₅	—	4	2	no	—
169	C₃×Dic₁₀	—	2	4	no	—
170	C₃×Dic₁₀	—	2	2	no	—
171	C₃×Dic₁₀	—	2	1	no	—
172	C₃×Dic₁₀	C₂²×C₄	1	4	yes	—
173	C₃×Dic₁₀	C₂²×C₄	1	2	yes	—
174	C₃×C₅×C₈	—	2	2	no	—
175	C₃×C₅×C₈	C₂²×C₄	1	4	yes	—
176	C₂×C₃×#41	—	5	1	no	—
177	C₂²×C₃×Q₈	—	5	1	no	—
178	C₃×#137	—	5	8	no	—
179	C₂×C₃×Q₁₆	—	5	2	no	—
180	C₂×C₃×SD₁₆	—	5	2	no	—
181	C₂×C₃×M₁₆	C₂×D₅	1	1	yes	characteristic
182	C₂×C₃×M₁₆	C₂×D₅	1	1	yes	characteristic
183	C₃×C₄×Q₈	—	5	2	no	—
184	C₃×C₄×Q₈	—	5	1	no	—
185	C₃×C₄×Q₈	—	5	2	no	—
186	C₃×C₄×Q₈	—	5	1	no	—
187	C₃×C₄×Q₈	—	10	1	no	—
188	C₃×C₄×Q₈	—	10	1	no	—
189	C₃×C₄×D₄	—	5	1	no	—
190	C₃×C₄×D₄	—	5	1	no	—
191	C₃×C₄×D₄	—	10	1	no	—
192	C₃×C₄×D₄	—	10	1	no	—
193	C₃×#117	—	5	1	no	—
194	C₃×#117	—	10	1	no	—
195	C₂×C₃×C₄⋊C₄	—	5	1	no	—
196	C₂×C₃×C₄⋊C₄	—	10	1	no	—
197	C₂×C₃×C₄²	—	10	1	no	—
198	C₂×C₃×C₄²	—	10	1	no	—
199	C₂×C₃×C₄²	C₂×D₅	1	1	yes	characteristic
200	C₃×#107	—	5	2	no	—
201	C₃×#106	—	5	2	no	—
202	C₃×#103	—	5	2	no	—
203	C₃×#103	—	5	2	no	—
204	C₃×#103	—	5	2	no	—
205	C₃×#102	—	5	2	no	—
206	C₃×#97	C₂×D₅	1	2	yes	—
207	C₃×C₄×C₈	C₂×D₅	1	2	yes	—
208	C₂²×C₄×C₅	C₃×D₄	1	1	yes	characteristic
209	C₂²×C₄×C₅	C₃×D₄	1	1	yes	characteristic
210	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
211	C₂×C₂²⋊D₅	—	2	1	no	—
212	C₂²×Dic₅	—	2	1	no	—
213	C₂²×Dic₅	—	2	1	no	—
214	#709	—	2	2	no	—
215	#709	C₂×C₃×C₄	1	4	yes	—
216	C₂×D₂₀	C₂³×C₃	1	1	yes	characteristic
217	C₂×C₄×D₅	—	2	1	no	—
218	C₂×C₄×D₅	—	2	1	no	—
219	C₂×C₄×D₅	—	2	1	no	—
220	C₂×Dic₁₀	—	2	1	no	—
221	C₂×Dic₁₀	—	2	2	no	—
222	C₂×Dic₁₀	C₂×C₃×C₄	1	4	yes	complemented
223	C₂×Dic₁₀	C₂³×C₃	1	2	yes	—
224	C₂×Dic₁₀	C₂³×C₃	1	1	yes	characteristic
225	C₅×M₁₆	—	2	2	no	—
226	C₅×M₁₆	C₂×C₃×C₄	1	4	yes	complemented
227	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
228	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
229	C₄²×C₅	C₃×D₄	1	1	yes	characteristic
230	C₄²×C₅	C₃×D₄	1	1	yes	characteristic
231	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
232	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
233	C₂²⋊Dic₅	—	2	1	no	—
234	#685	—	2	1	no	—
235	#685	—	2	1	no	—
236	C₄⋊Dic₅	—	2	1	no	—
237	C₄⋊Dic₅	C₂³×C₃	1	1	yes	characteristic
238	C₄⋊Dic₅	C₂³×C₃	1	1	yes	characteristic
239	C₄⋊Dic₅	C₂³×C₃	1	2	yes	—
240	#683	—	2	2	no	—
241	#683	—	2	2	no	—
242	#683	—	2	1	no	—
243	#683	—	2	1	no	—
244	C₄×Dic₅	—	2	2	no	—
245	C₄×Dic₅	—	2	2	no	—
246	C₄×Dic₅	—	2	1	no	—
247	C₄×Dic₅	—	2	1	no	—
248	C₄×Dic₅	—	2	1	no	—
249	Dic₂₀	C₂×C₃×C₄	1	8	yes	complemented
250	#677	C₂×C₃×C₄	1	8	yes	complemented
251	C₂×#137	—	5	1	no	—
252	C₄×#41	—	5	1	no	—
253	C₂×C₄×Q₈	—	5	1	no	—
254	#441	—	5	2	no	—
255	#440	—	5	2	no	—
256	C₄×Q₁₆	—	5	2	no	—
257	C₄×SD₁₆	—	5	2	no	—
258	#428	—	5	1	no	—
259	#419	—	5	1	no	—
260	#417	—	5	1	no	—
261	C₄×M₁₆	C₃×D₅	1	1	yes	characteristic, complemented
262	C₂²×C₃×C₅	—	2	1	no	—
263	C₂²×C₃×C₅	—	2	1	no	—
264	C₂²×C₃×C₅	C₄×D₄	1	2	yes	—
265	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
266	C₂×C₃×D₅	—	2	2	no	—
267	C₂×C₃×D₅	—	4	1	no	—
268	C₂×C₃×D₅	—	4	1	no	—
269	C₃×C₄×C₅	—	2	1	no	—
270	C₃×C₄×C₅	—	2	1	no	—
271	C₃×C₄×C₅	—	2	1	no	—
272	C₃×C₄×C₅	C₄×D₄	1	2	yes	—
273	C₃×C₄×C₅	#137	1	2	yes	complemented
274	C₃×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
275	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
276	C₃×Dic₅	—	2	4	no	—
277	C₃×Dic₅	—	2	2	no	—
278	C₃×Dic₅	—	4	1	no	—
279	C₃×Dic₅	—	4	1	no	—
280	C₃×Dic₅	—	4	2	no	—
281	C₃×#41	—	5	4	no	—
282	C₃×#41	—	10	2	no	—
283	C₂×C₃×Q₈	—	5	4	no	—
284	C₂×C₃×Q₈	—	5	2	no	—
285	C₂×C₃×Q₈	—	5	1	no	—
286	C₂×C₃×Q₈	—	10	1	no	—
287	C₂×C₃×Q₈	—	10	2	no	—
288	C₂×C₃×D₄	—	5	1	no	—
289	C₂×C₃×D₄	—	10	1	no	—
290	C₂²×C₃×C₄	—	10	1	no	—
291	C₂²×C₃×C₄	—	10	1	no	—
292	C₂²×C₃×C₄	—	10	1	no	—
293	C₂²×C₃×C₄	—	10	1	no	—
294	C₂²×C₃×C₄	—	10	1	no	—
295	C₂²×C₃×C₄	D₂₀	1	1	yes	characteristic
296	C₂²×C₃×C₄	D₂₀	1	1	yes	characteristic
297	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
298	C₃×Q₁₆	—	5	8	no	—
299	C₃×SD₁₆	—	5	8	no	—
300	C₃×M₁₆	—	2	2	no	—
301	C₃×M₁₆	C₄×D₅	1	4	yes	complemented
302	C₂×C₃×C₈	C₂²×D₅	1	2	yes	—
303	C₂×C₃×C₈	C₂²×D₅	1	2	yes	—
304	C₃×C₄⋊C₄	—	5	2	no	—
305	C₃×C₄⋊C₄	—	5	1	no	—
306	C₃×C₄⋊C₄	—	5	1	no	—
307	C₃×C₄⋊C₄	—	10	2	no	—
308	C₃×C₄⋊C₄	—	10	2	no	—
309	C₃×C₄⋊C₄	—	10	1	no	—
310	C₃×C₄⋊C₄	—	10	1	no	—
311	C₃×C₄⋊C₄	—	10	1	no	—
312	C₃×C₂²⋊C₄	—	10	1	no	—
313	C₃×C₂²⋊C₄	—	10	1	no	—
314	C₃×C₂²⋊C₄	—	10	1	no	—
315	C₃×C₄²	—	10	1	no	—
316	C₃×C₄²	—	10	1	no	—
317	C₃×C₄²	—	10	2	no	—
318	C₃×C₄²	—	10	1	no	—
319	C₃×C₄²	—	10	2	no	—
320	C₃×C₄²	D₂₀	1	1	yes	characteristic
321	C₃×C₄²	D₂₀	1	1	yes	characteristic
322	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
323	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
324	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
325	C₂²×D₅	—	2	1	no	—
326	C₂×C₄×C₅	—	2	2	no	—
327	C₂×C₄×C₅	—	4	1	no	—
328	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
329	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
330	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
331	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
332	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
333	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
334	C₂×C₄×C₅	C₃×#41	1	2	yes	—
335	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
336	C₂²⋊D₅	—	2	4	no	—
337	C₂×Dic₅	—	2	4	no	—
338	C₂×Dic₅	—	2	2	no	—
339	C₂×Dic₅	—	2	1	no	—
340	C₂×Dic₅	—	2	2	no	—
341	C₂×Dic₅	—	2	1	no	—
342	C₂×Dic₅	—	2	1	no	—
343	C₂×Dic₅	—	4	2	no	—
344	D₂₀	—	2	1	no	—
345	D₂₀	C₂²×C₃×C₄	1	2	yes	—
346	C₄×D₅	—	2	4	no	—
347	C₄×D₅	—	4	2	no	—
348	C₄×D₅	—	4	2	no	—
349	Dic₁₀	—	2	4	no	—
350	Dic₁₀	—	2	2	no	—
351	Dic₁₀	—	2	1	no	—
352	Dic₁₀	C₂²×C₃×C₄	1	4	yes	—
353	Dic₁₀	C₂²×C₃×C₄	1	2	yes	—
354	C₅×C₈	—	2	2	no	—
355	C₅×C₈	C₂²×C₃×C₄	1	4	yes	—
356	C₂×#41	—	5	1	no	—
357	C₂²×Q₈	—	5	1	no	—
358	#137	—	5	8	no	—
359	C₂×Q₁₆	—	5	2	no	—
360	C₂×SD₁₆	—	5	2	no	—
361	C₂×M₁₆	C₂×C₃×D₅	1	1	yes	characteristic
362	C₂×M₁₆	C₂×C₃×D₅	1	1	yes	characteristic
363	C₄×Q₈	—	5	2	no	—
364	C₄×Q₈	—	5	2	no	—
365	C₄×Q₈	—	5	1	no	—
366	C₄×Q₈	—	5	1	no	—
367	C₄×Q₈	—	10	1	no	—
368	C₄×Q₈	—	10	1	no	—
369	C₄×D₄	—	5	1	no	—
370	C₄×D₄	—	5	1	no	—
371	C₄×D₄	—	10	1	no	—
372	C₄×D₄	—	10	1	no	—
373	#117	—	5	1	no	—
374	#117	—	10	1	no	—
375	C₂×C₄⋊C₄	—	5	1	no	—
376	C₂×C₄⋊C₄	—	10	1	no	—
377	C₂×C₄²	—	10	1	no	—
378	C₂×C₄²	—	10	1	no	—
379	C₂×C₄²	C₂×C₃×D₅	1	1	yes	characteristic
380	#107	—	5	2	no	—
381	#106	—	5	2	no	—
382	#103	—	5	2	no	—
383	#103	—	5	2	no	—
384	#103	—	5	2	no	—
385	#102	—	5	2	no	—
386	#97	C₂×C₃×D₅	1	2	yes	—
387	C₄×C₈	C₂×C₃×D₅	1	2	yes	—
388	C₂×C₃×C₅	—	2	2	no	—
389	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
390	C₂×C₃×C₅	C₂×#137	1	1	yes	characteristic
391	C₂×C₃×C₅	#575	1	1	yes	characteristic
392	C₃×D₅	—	4	2	no	—
393	C₂³×C₃	—	10	1	no	—
394	C₂³×C₃	C₂×D₂₀	1	1	yes	characteristic
395	C₃×Q₈	—	5	4	no	—
396	C₃×Q₈	—	5	2	no	—
397	C₃×Q₈	—	10	2	no	—
398	C₃×Q₈	—	10	1	no	—
399	C₃×Q₈	—	10	4	no	—
400	C₃×D₄	—	5	2	no	—
401	C₃×D₄	—	10	4	no	—
402	C₃×D₄	—	10	1	no	—
403	C₂×C₃×C₄	—	2	2	no	—
404	C₂×C₃×C₄	—	4	1	no	—
405	C₂×C₃×C₄	—	10	1	no	—
406	C₂×C₃×C₄	—	10	2	no	—
407	C₂×C₃×C₄	—	10	4	no	—
408	C₂×C₃×C₄	—	10	4	no	—
409	C₂×C₃×C₄	—	10	1	no	—
410	C₂×C₃×C₄	—	10	1	no	—
411	C₂×C₃×C₄	—	10	2	no	—
412	C₂×C₃×C₄	—	20	2	no	—
413	C₂×C₃×C₄	—	20	2	no	—
414	C₂×C₃×C₄	—	20	2	no	—
415	C₂×C₃×C₄	C₂×C₄×D₅	1	2	yes	—
416	C₂×C₃×C₄	C₂×D₂₀	1	1	yes	characteristic
417	C₂×C₃×C₄	C₂×D₂₀	1	1	yes	characteristic
418	C₂×C₃×C₄	C₂×D₂₀	1	1	yes	characteristic
419	C₂×C₃×C₄	C₂×D₂₀	1	1	yes	characteristic
420	C₂×C₃×C₄	C₂×D₂₀	1	1	yes	characteristic
421	C₂×C₃×C₄	#709	1	2	yes	—
422	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
423	C₃×C₈	—	2	2	no	—
424	C₃×C₈	C₂×C₄×D₅	1	4	yes	—
425	C₂²×C₅	—	2	1	no	—
426	C₂²×C₅	—	2	1	no	—
427	C₂²×C₅	C₃×C₄×D₄	1	2	yes	—
428	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
429	C₂×D₅	—	2	2	no	—
430	C₂×D₅	—	4	1	no	—
431	C₂×D₅	—	4	1	no	—
432	C₄×C₅	—	2	1	no	—
433	C₄×C₅	—	2	1	no	—
434	C₄×C₅	—	2	1	no	—
435	C₄×C₅	C₃×C₄×D₄	1	2	yes	—
436	C₄×C₅	C₃×#137	1	2	yes	complemented
437	C₄×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
438	C₄×C₅	C₂×C₃×#41	1	1	yes	characteristic
439	Dic₅	—	2	4	no	—
440	Dic₅	—	2	2	no	—
441	Dic₅	—	4	1	no	—
442	Dic₅	—	4	1	no	—
443	Dic₅	—	4	2	no	—
444	#41	—	5	4	no	—
445	#41	—	10	2	no	—
446	C₂×Q₈	—	5	4	no	—
447	C₂×Q₈	—	5	2	no	—
448	C₂×Q₈	—	5	1	no	—
449	C₂×Q₈	—	10	1	no	—
450	C₂×Q₈	—	10	2	no	—
451	C₂×D₄	—	5	1	no	—
452	C₂×D₄	—	10	1	no	—
453	C₂²×C₄	—	10	1	no	—
454	C₂²×C₄	—	10	1	no	—
455	C₂²×C₄	—	10	1	no	—
456	C₂²×C₄	—	10	1	no	—
457	C₂²×C₄	—	10	1	no	—
458	C₂²×C₄	C₃×D₂₀	1	1	yes	characteristic
459	C₂²×C₄	C₃×D₂₀	1	1	yes	characteristic
460	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
461	Q₁₆	—	5	8	no	—
462	SD₁₆	—	5	8	no	—
463	M₁₆	—	2	2	no	—
464	M₁₆	C₃×C₄×D₅	1	4	yes	complemented
465	C₂×C₈	C₂²×C₃×D₅	1	2	yes	—
466	C₂×C₈	C₂²×C₃×D₅	1	2	yes	—
467	C₄⋊C₄	—	5	2	no	—
468	C₄⋊C₄	—	5	1	no	—
469	C₄⋊C₄	—	5	1	no	—
470	C₄⋊C₄	—	10	1	no	—
471	C₄⋊C₄	—	10	2	no	—
472	C₄⋊C₄	—	10	2	no	—
473	C₄⋊C₄	—	10	1	no	—
474	C₄⋊C₄	—	10	1	no	—
475	C₂²⋊C₄	—	10	1	no	—
476	C₂²⋊C₄	—	10	1	no	—
477	C₂²⋊C₄	—	10	1	no	—
478	C₄²	—	10	1	no	—
479	C₄²	—	10	1	no	—
480	C₄²	—	10	1	no	—
481	C₄²	—	10	2	no	—
482	C₄²	—	10	2	no	—
483	C₄²	C₃×D₂₀	1	1	yes	characteristic
484	C₄²	C₃×D₂₀	1	1	yes	characteristic
485	C₄²	C₂²×C₃×D₅	1	1	yes	characteristic
486	C₄²	C₂²×C₃×D₅	1	1	yes	characteristic
487	C₃×C₅	C₄×#137	1	1	yes	characteristic, complemented, Hall
488	C₂²×C₃	—	2	1	no	—
489	C₂²×C₃	—	2	1	no	—
490	C₂²×C₃	—	10	2	no	—
491	C₂²×C₃	—	20	1	no	—
492	C₂²×C₃	—	20	1	no	—
493	C₂²×C₃	C₄×D₂₀	1	2	yes	—
494	C₂²×C₃	C₂²×D₂₀	1	1	yes	characteristic
495	C₃×C₄	—	2	1	no	—
496	C₃×C₄	—	2	1	no	—
497	C₃×C₄	—	2	1	no	—
498	C₃×C₄	—	10	2	no	—
499	C₃×C₄	—	10	4	no	—
500	C₃×C₄	—	20	1	no	—
501	C₃×C₄	—	20	1	no	—
502	C₃×C₄	—	20	2	no	—
503	C₃×C₄	C₄×D₂₀	1	2	yes	—
504	C₃×C₄	#4055	1	2	yes	direct product factor
505	C₃×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
506	C₃×C₄	C₂×#709	1	1	yes	characteristic
507	C₂×C₅	—	2	2	no	—
508	C₂×C₅	C₂×C₃×C₄×D₄	1	1	yes	characteristic
509	C₂×C₅	C₂×C₃×#137	1	1	yes	characteristic
510	C₂×C₅	C₃×#575	1	1	yes	characteristic
511	D₅	—	4	2	no	—
512	C₂³	—	10	1	no	—
513	C₂³	C₂×C₃×D₂₀	1	1	yes	characteristic
514	Q₈	—	5	4	no	—
515	Q₈	—	5	2	no	—
516	Q₈	—	10	2	no	—
517	Q₈	—	10	1	no	—
518	Q₈	—	10	4	no	—
519	D₄	—	5	2	no	—
520	D₄	—	10	4	no	—
521	D₄	—	10	1	no	—
522	C₂×C₄	—	2	2	no	—
523	C₂×C₄	—	4	1	no	—
524	C₂×C₄	—	10	1	no	—
525	C₂×C₄	—	10	2	no	—
526	C₂×C₄	—	10	4	no	—
527	C₂×C₄	—	10	4	no	—
528	C₂×C₄	—	10	1	no	—
529	C₂×C₄	—	10	1	no	—
530	C₂×C₄	—	10	2	no	—
531	C₂×C₄	—	20	2	no	—
532	C₂×C₄	—	20	2	no	—
533	C₂×C₄	—	20	2	no	—
534	C₂×C₄	C₂×C₃×C₄×D₅	1	2	yes	—
535	C₂×C₄	C₂×C₃×D₂₀	1	1	yes	characteristic
536	C₂×C₄	C₂×C₃×D₂₀	1	1	yes	characteristic
537	C₂×C₄	C₂×C₃×D₂₀	1	1	yes	characteristic
538	C₂×C₄	C₂×C₃×D₂₀	1	1	yes	characteristic
539	C₂×C₄	C₂×C₃×D₂₀	1	1	yes	characteristic
540	C₂×C₄	C₃×#709	1	2	yes	—
541	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
542	C₈	—	2	2	no	—
543	C₈	C₂×C₃×C₄×D₅	1	4	yes	—
544	C₂×C₃	—	2	2	no	—
545	C₂×C₃	—	20	2	no	—
546	C₂×C₃	C₂×C₄×D₂₀	1	1	yes	characteristic
547	C₂×C₃	C₂×#4055	1	1	yes	characteristic
548	C₂×C₃	#66082	1	1	yes	characteristic
549	C₅	C₃×C₄×#137	1	1	yes	characteristic, complemented, Sylow
550	C₂²	—	2	1	no	—
551	C₂²	—	2	1	no	—
552	C₂²	—	10	2	no	—
553	C₂²	—	20	1	no	—
554	C₂²	—	20	1	no	—
555	C₂²	C₃×C₄×D₂₀	1	2	yes	—
556	C₂²	C₂²×C₃×D₂₀	1	1	yes	characteristic
557	C₄	—	2	1	no	—
558	C₄	—	2	1	no	—
559	C₄	—	2	1	no	—
560	C₄	—	10	2	no	—
561	C₄	—	10	4	no	—
562	C₄	—	20	1	no	—
563	C₄	—	20	1	no	—
564	C₄	—	20	2	no	—
565	C₄	C₃×C₄×D₂₀	1	2	yes	—
566	C₄	C₃×#4055	1	2	yes	direct product factor
567	C₄	C₂²×C₃×C₄×D₅	1	1	yes	characteristic
568	C₄	C₂×C₃×#709	1	1	yes	characteristic
569	C₃	C₄×#4055	1	1	yes	characteristic, direct product factor, Sylow
570	C₂	—	2	2	no	—
571	C₂	—	20	2	no	—
572	C₂	C₂×C₃×C₄×D₂₀	1	1	yes	characteristic
573	C₂	C₂×C₃×#4055	1	1	yes	characteristic
574	C₂	C₃×#66082	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃×C₄	C₂×D₂₀
commutator	C₄×C₅	C₂³×C₃×C₄
Frattini	C₂×C₄	C₂³×C₃×D₅
Fitting	C₃×C₄×C₅×M₁₆	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
prime radical	C₂×C₃×#709	C₂²
cosocle	C₂×C₄×C₅	C₂⁴×C₃
hypercenter	C₃×C₄×M₁₆	D₅
hypocenter	C₅	C₃×C₄×#137
LCS	G ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₂×C₃×C₄² ◁ C₃×C₄×M₁₆

Complements

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

N	H ≅ G/N	type
3. C₂×C₃×C₄×Dic₁₀	C₂	semidirect
4. C₃×C₄×C₅×M₁₆	C₂	semidirect
6. C₃×#65410	C₂	semidirect
7. C₃×#65409	C₂	semidirect
8. C₃×#65005	C₂	semidirect
9. C₃×#64999	C₂	semidirect
10. C₃×C₄×Dic₂₀	C₂	semidirect
11. C₃×C₄×#677	C₂	semidirect
12. C₄×#4055	C₃	direct (N × H)
24. C₃×#4055	C₄	direct (N × H)
48. C₂×C₄×Dic₁₀	C₂×C₃	semidirect
49. C₄×C₅×M₁₆	C₂×C₃	semidirect
51. #65410	C₂×C₃	semidirect
52. #65409	C₂×C₃	semidirect
53. #65005	C₂×C₃	semidirect
54. #64999	C₂×C₃	semidirect
55. C₄×Dic₂₀	C₂×C₃	semidirect
56. C₄×#677	C₂×C₃	semidirect
71. C₂×C₃×Dic₁₀	C₂×C₄	semidirect
75. C₃×C₅×M₁₆	C₂×C₄	semidirect
98. C₃×Dic₂₀	C₂×C₄	semidirect
99. C₃×#677	C₂×C₄	semidirect
110. C₃×C₄×M₁₆	D₅	semidirect
122. #4055	C₃×C₄	direct (N × H)
222. C₂×Dic₁₀	C₂×C₃×C₄	semidirect
226. C₅×M₁₆	C₂×C₃×C₄	semidirect
249. Dic₂₀	C₂×C₃×C₄	semidirect
250. #677	C₂×C₃×C₄	semidirect
261. C₄×M₁₆	C₃×D₅	semidirect
273. C₃×C₄×C₅	#137	semidirect
301. C₃×M₁₆	C₄×D₅	semidirect
436. C₄×C₅	C₃×#137	semidirect
464. M₁₆	C₃×C₄×D₅	semidirect
487. C₃×C₅	C₄×#137	semidirect
504. C₃×C₄	#4055	direct (N × H)
549. C₅	C₃×C₄×#137	semidirect
566. C₄	C₃×#4055	direct (N × H)
569. C₃	C₄×#4055	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃×#4055	2
C₃×C₄×#709	2
C₂×C₃×C₄×Dic₁₀	2
C₃×C₄×C₅×M₁₆	2
C₃×#65422	2
C₃×#65410	2
C₃×#65409	2
C₃×#65005	2
C₃×#64999	2
C₃×C₄×Dic₂₀	2
C₃×C₄×#677	2
C₄×#4055	3
C₃×C₄×#137	5

Subgroups — C3×C4×#4055 #14416839

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₄×#4055 #14416839