Subgroups — C₃×C₄×#4096 #14416210

Order 1920.

1000 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄×C₅×#41	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×#4096	C₂	1	1	yes	maximal, characteristic
3	C₃×C₄×#709	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#65522	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×C₄×#689	C₂	1	2	yes	maximal, complemented
6	C₃×C₄×#688	C₂	1	2	yes	maximal, complemented
7	C₃×C₄×#687	C₂	1	2	yes	maximal, complemented
8	C₃×C₄×#686	C₂	1	2	yes	maximal, complemented
9	C₃×#65291	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#65287	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₃×C₄×#168	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄×#4096	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic
14	C₂×C₃×#709	C₂²	1	1	yes	characteristic
15	C₃×C₄×C₅×Q₈	C₂²	1	2	yes	—
16	C₃×C₄×C₅×D₄	—	2	2	no	—
17	C₃×C₄×C₅×D₄	C₂²	1	2	yes	—
18	C₃×C₅×#117	—	2	1	no	—
19	C₃×C₅×#117	C₂²	1	1	yes	characteristic
20	C₂×C₃×C₄²×C₅	—	2	1	no	—
21	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
22	C₃×#4096	C₄	1	8	yes	direct product factor
23	C₂×C₃×#689	C₂²	1	1	yes	characteristic
24	C₂×C₃×#688	C₂²	1	1	yes	characteristic
25	C₂×C₃×#687	C₂²	1	1	yes	characteristic
26	C₂×C₃×#686	C₂²	1	1	yes	characteristic
27	C₃×C₄×C₂²⋊D₅	—	2	2	no	—
28	C₃×#4072	C₂²	1	1	yes	characteristic
29	C₂²×C₃×#168	C₂²	1	1	yes	characteristic
30	C₂²×C₃×#168	C₂²	1	1	yes	characteristic
31	C₃×C₄×D₂₀	C₂²	1	2	yes	—
32	C₃×#4018	—	2	1	no	—
33	C₃×C₄²×D₅	—	2	1	no	—
34	C₃×C₄×Dic₁₀	C₂²	1	2	yes	—
35	C₃×#3967	C₂²	1	2	yes	—
36	C₃×#3964	C₂²	1	2	yes	—
37	C₃×#3942	C₂²	1	2	yes	—
38	C₃×#3941	C₂²	1	2	yes	—
39	C₃×#3940	C₂²	1	2	yes	—
40	C₃×#3939	C₂²	1	2	yes	—
41	C₃×C₄×#168	C₂²	1	2	yes	—
42	C₃×C₄×#168	C₂²	1	2	yes	—
43	C₃×C₄×#135	—	5	1	no	maximal, Hall
44	C₄×C₅×#41	C₂×C₃	1	1	yes	characteristic, complemented
45	C₂×#4096	C₂×C₃	1	1	yes	characteristic
46	C₄×#709	C₂×C₃	1	1	yes	characteristic, complemented
47	#65522	C₂×C₃	1	1	yes	characteristic, complemented
48	C₄×#689	C₂×C₃	1	2	yes	complemented
49	C₄×#688	C₂×C₃	1	2	yes	complemented
50	C₄×#687	C₂×C₃	1	2	yes	complemented
51	C₄×#686	C₂×C₃	1	2	yes	complemented
52	#65291	C₂×C₃	1	1	yes	characteristic, complemented
53	#65287	C₂×C₃	1	1	yes	characteristic, complemented
54	C₂×C₄×#168	C₂×C₃	1	1	yes	characteristic, complemented
55	C₃×C₅×#41	—	2	2	no	—
56	C₃×C₅×#41	C₂×C₄	1	4	yes	complemented
57	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
58	C₂×C₃×C₅×D₄	—	2	1	no	—
59	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
60	C₂²×C₃×C₄×C₅	—	2	1	no	—
61	C₂²×C₃×C₄×C₅	—	2	2	no	—
62	C₂²×C₃×C₄×C₅	D₄	1	2	yes	—
63	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
64	C₂×C₃×C₂²⋊D₅	—	2	1	no	—
65	C₃×#709	—	2	2	no	—
66	C₃×#709	C₂×C₄	1	4	yes	complemented
67	C₂×C₃×D₂₀	C₂³	1	1	yes	characteristic
68	C₂×C₃×C₄×D₅	—	2	1	no	—
69	C₂×C₃×C₄×D₅	—	2	2	no	—
70	C₂×C₃×Dic₁₀	C₂³	1	1	yes	characteristic
71	C₃×C₅×C₄⋊C₄	—	2	2	no	—
72	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
73	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
74	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
75	C₃×C₄²×C₅	—	2	1	no	—
76	C₃×C₄²×C₅	—	2	2	no	—
77	C₃×C₄²×C₅	D₄	1	1	yes	characteristic
78	C₃×C₄²×C₅	D₄	1	1	yes	characteristic
79	C₃×C₄²×C₅	C₂³	1	2	yes	—
80	C₃×C₂²⋊Dic₅	—	2	1	no	—
81	C₃×#689	C₂×C₄	1	4	yes	complemented
82	C₃×#688	C₂×C₄	1	4	yes	complemented
83	C₃×#687	C₂×C₄	1	4	yes	complemented
84	C₃×#686	C₂×C₄	1	4	yes	complemented
85	C₃×#685	—	2	2	no	—
86	C₃×C₄⋊Dic₅	C₂³	1	2	yes	—
87	C₃×#683	—	2	2	no	—
88	C₃×C₄×Dic₅	—	2	2	no	—
89	C₃×C₄×Dic₅	—	2	1	no	—
90	C₂×C₃×#168	—	2	2	no	—
91	C₂×C₃×#168	C₂×C₄	1	4	yes	complemented
92	C₂×C₃×#168	C₂³	1	2	yes	—
93	C₂×C₃×#168	C₂³	1	1	yes	characteristic
94	C₂×C₃×#168	C₂³	1	1	yes	characteristic
95	C₂×C₃×#135	—	5	1	no	—
96	C₃×C₄×#41	—	5	1	no	—
97	C₃×C₄×#41	D₅	1	1	yes	characteristic, complemented
98	C₃×C₄×Q₁₆	—	5	2	no	—
99	C₃×C₄×SD₁₆	—	5	2	no	—
100	C₃×C₄×SD₁₆	—	5	2	no	—
101	C₃×C₄×D₈	—	5	2	no	—
102	C₃×#427	—	5	1	no	—
103	C₃×#416	—	5	1	no	—
104	C₃×#416	—	5	1	no	—
105	C₂×C₃×C₄×C₈	—	5	1	no	—
106	C₂×C₅×#41	C₂²×C₃	1	1	yes	characteristic
107	C₂×#709	C₂²×C₃	1	1	yes	characteristic
108	C₄×C₅×Q₈	C₂²×C₃	1	2	yes	—
109	C₄×C₅×D₄	—	2	2	no	—
110	C₄×C₅×D₄	C₂²×C₃	1	2	yes	—
111	C₅×#117	—	2	1	no	—
112	C₅×#117	C₂²×C₃	1	1	yes	characteristic
113	C₂×C₄²×C₅	—	2	1	no	—
114	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
115	#4096	C₃×C₄	1	8	yes	direct product factor
116	C₂×#689	C₂²×C₃	1	1	yes	characteristic
117	C₂×#688	C₂²×C₃	1	1	yes	characteristic
118	C₂×#687	C₂²×C₃	1	1	yes	characteristic
119	C₂×#686	C₂²×C₃	1	1	yes	characteristic
120	C₄×C₂²⋊D₅	—	2	2	no	—
121	#4072	C₂²×C₃	1	1	yes	characteristic
122	C₂²×#168	C₂²×C₃	1	1	yes	characteristic
123	C₂²×#168	C₂²×C₃	1	1	yes	characteristic
124	C₄×D₂₀	C₂²×C₃	1	2	yes	—
125	#4018	—	2	1	no	—
126	C₄²×D₅	—	2	1	no	—
127	C₄×Dic₁₀	C₂²×C₃	1	2	yes	—
128	#3967	C₂²×C₃	1	2	yes	—
129	#3964	C₂²×C₃	1	2	yes	—
130	#3942	C₂²×C₃	1	2	yes	—
131	#3941	C₂²×C₃	1	2	yes	—
132	#3940	C₂²×C₃	1	2	yes	—
133	#3939	C₂²×C₃	1	2	yes	—
134	C₄×#168	C₂²×C₃	1	2	yes	—
135	C₄×#168	C₂²×C₃	1	2	yes	—
136	C₄×#135	—	5	1	no	Sylow
137	C₂³×C₃×C₅	—	2	1	no	—
138	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
139	C₂²×C₃×D₅	—	2	1	no	—
140	C₃×C₅×Q₈	—	2	1	no	—
141	C₃×C₅×Q₈	C₂²×C₄	1	2	yes	—
142	C₃×C₅×D₄	—	2	4	no	—
143	C₃×C₅×D₄	—	2	1	no	—
144	C₃×C₅×D₄	C₂²×C₄	1	2	yes	—
145	C₂×C₃×C₄×C₅	—	2	1	no	—
146	C₂×C₃×C₄×C₅	—	2	4	no	—
147	C₂×C₃×C₄×C₅	—	2	4	no	—
148	C₂×C₃×C₄×C₅	—	2	2	no	—
149	C₂×C₃×C₄×C₅	—	4	4	no	—
150	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
151	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
152	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
153	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
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	1	no	—
158	C₂×C₃×Dic₅	—	2	2	no	—
159	C₃×D₂₀	—	2	1	no	—
160	C₃×D₂₀	C₂²×C₄	1	2	yes	—
161	C₃×C₄×D₅	—	2	4	no	—
162	C₃×C₄×D₅	—	4	4	no	—
163	C₃×Dic₁₀	—	2	1	no	—
164	C₃×Dic₁₀	C₂²×C₄	1	2	yes	—
165	C₃×#168	—	2	2	no	—
166	C₃×#168	C₂²×C₄	1	2	yes	—
167	C₃×#168	C₂²×C₄	1	2	yes	—
168	C₂×C₃×#41	—	5	1	no	—
169	C₂×C₃×#41	C₂×D₅	1	1	yes	characteristic
170	C₃×#135	—	5	8	no	—
171	C₂×C₃×Q₁₆	—	5	1	no	—
172	C₂×C₃×SD₁₆	—	5	1	no	—
173	C₂×C₃×SD₁₆	—	5	1	no	—
174	C₂×C₃×D₈	—	5	1	no	—
175	C₂²×C₃×C₈	—	5	1	no	—
176	C₂²×C₃×C₈	—	5	1	no	—
177	C₃×C₄×Q₈	—	5	2	no	—
178	C₃×C₄×Q₈	C₂×D₅	1	2	yes	—
179	C₃×C₄×D₄	—	2	2	no	—
180	C₃×C₄×D₄	—	5	2	no	—
181	C₃×C₄×D₄	—	10	2	no	—
182	C₃×C₄×D₄	C₂×D₅	1	2	yes	—
183	C₃×#117	—	2	1	no	—
184	C₃×#117	—	5	1	no	—
185	C₃×#117	—	10	1	no	—
186	C₃×#117	C₂×D₅	1	1	yes	characteristic
187	C₂×C₃×C₄²	—	2	1	no	—
188	C₂×C₃×C₄²	—	10	1	no	—
189	C₂×C₃×C₄²	C₂×D₅	1	1	yes	characteristic
190	C₃×#107	—	5	2	no	—
191	C₃×#106	—	5	2	no	—
192	C₃×#103	—	5	2	no	—
193	C₃×#103	—	5	2	no	—
194	C₃×#102	—	5	2	no	—
195	C₃×#102	—	5	2	no	—
196	C₃×C₄×C₈	—	5	2	no	—
197	C₃×C₄×C₈	—	5	2	no	—
198	C₅×#41	—	2	2	no	—
199	C₅×#41	C₂×C₃×C₄	1	4	yes	complemented
200	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
201	C₂×C₅×D₄	—	2	1	no	—
202	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
203	C₂²×C₄×C₅	—	2	1	no	—
204	C₂²×C₄×C₅	—	2	2	no	—
205	C₂²×C₄×C₅	C₃×D₄	1	2	yes	—
206	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
207	C₂×C₂²⋊D₅	—	2	1	no	—
208	#709	—	2	2	no	—
209	#709	C₂×C₃×C₄	1	4	yes	complemented
210	C₂×D₂₀	C₂³×C₃	1	1	yes	characteristic
211	C₂×C₄×D₅	—	2	1	no	—
212	C₂×C₄×D₅	—	2	2	no	—
213	C₂×Dic₁₀	C₂³×C₃	1	1	yes	characteristic
214	C₅×C₄⋊C₄	—	2	2	no	—
215	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
216	C₅×C₂²⋊C₄	—	2	1	no	—
217	C₅×C₂²⋊C₄	—	2	2	no	—
218	C₄²×C₅	—	2	1	no	—
219	C₄²×C₅	—	2	2	no	—
220	C₄²×C₅	C₃×D₄	1	1	yes	characteristic
221	C₄²×C₅	C₃×D₄	1	1	yes	characteristic
222	C₄²×C₅	C₂³×C₃	1	2	yes	—
223	C₂²⋊Dic₅	—	2	1	no	—
224	#689	C₂×C₃×C₄	1	4	yes	complemented
225	#688	C₂×C₃×C₄	1	4	yes	complemented
226	#687	C₂×C₃×C₄	1	4	yes	complemented
227	#686	C₂×C₃×C₄	1	4	yes	complemented
228	#685	—	2	2	no	—
229	C₄⋊Dic₅	C₂³×C₃	1	2	yes	—
230	#683	—	2	2	no	—
231	C₄×Dic₅	—	2	2	no	—
232	C₄×Dic₅	—	2	1	no	—
233	C₂×#168	—	2	2	no	—
234	C₂×#168	C₂×C₃×C₄	1	4	yes	complemented
235	C₂×#168	C₂³×C₃	1	2	yes	—
236	C₂×#168	C₂³×C₃	1	1	yes	characteristic
237	C₂×#168	C₂³×C₃	1	1	yes	characteristic
238	C₂×#135	—	5	1	no	—
239	C₄×#41	—	5	1	no	—
240	C₄×#41	C₃×D₅	1	1	yes	characteristic, complemented
241	C₄×Q₁₆	—	5	2	no	—
242	C₄×SD₁₆	—	5	2	no	—
243	C₄×SD₁₆	—	5	2	no	—
244	C₄×D₈	—	5	2	no	—
245	#427	—	5	1	no	—
246	#416	—	5	1	no	—
247	#416	—	5	1	no	—
248	C₂×C₄×C₈	—	5	1	no	—
249	C₂²×C₃×C₅	—	2	2	no	—
250	C₂²×C₃×C₅	—	2	2	no	—
251	C₂²×C₃×C₅	—	4	2	no	—
252	C₂²×C₃×C₅	C₄×D₄	1	2	yes	—
253	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
254	C₂×C₃×D₅	—	2	2	no	—
255	C₂×C₃×D₅	—	4	2	no	—
256	C₃×C₄×C₅	—	2	2	no	—
257	C₃×C₄×C₅	—	2	2	no	—
258	C₃×C₄×C₅	—	4	2	no	—
259	C₃×C₄×C₅	C₄×D₄	1	2	yes	—
260	C₃×C₄×C₅	#135	1	4	yes	complemented
261	C₃×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
262	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
263	C₃×Dic₅	—	2	2	no	—
264	C₃×Dic₅	—	4	2	no	—
265	C₃×#41	—	2	2	no	—
266	C₃×#41	—	5	4	no	—
267	C₃×#41	—	10	2	no	—
268	C₃×#41	C₄×D₅	1	4	yes	complemented
269	C₂×C₃×Q₈	—	5	1	no	—
270	C₂×C₃×Q₈	C₂²×D₅	1	1	yes	characteristic
271	C₂×C₃×D₄	—	2	1	no	—
272	C₂×C₃×D₄	—	5	1	no	—
273	C₂×C₃×D₄	—	10	1	no	—
274	C₂×C₃×D₄	C₂²×D₅	1	1	yes	characteristic
275	C₂²×C₃×C₄	—	2	1	no	—
276	C₂²×C₃×C₄	—	2	2	no	—
277	C₂²×C₃×C₄	—	10	1	no	—
278	C₂²×C₃×C₄	—	10	2	no	—
279	C₂²×C₃×C₄	C₂²⋊D₅	1	2	yes	—
280	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
281	C₃×Q₁₆	—	5	4	no	—
282	C₃×SD₁₆	—	5	4	no	—
283	C₃×SD₁₆	—	5	4	no	—
284	C₃×D₈	—	5	4	no	—
285	C₂×C₃×C₈	—	5	4	no	—
286	C₂×C₃×C₈	—	5	1	no	—
287	C₂×C₃×C₈	—	5	1	no	—
288	C₂×C₃×C₈	—	5	2	no	—
289	C₂×C₃×C₈	—	10	2	no	—
290	C₃×C₄⋊C₄	—	2	2	no	—
291	C₃×C₄⋊C₄	—	5	2	no	—
292	C₃×C₄⋊C₄	—	10	2	no	—
293	C₃×C₄⋊C₄	C₂²×D₅	1	2	yes	—
294	C₃×C₂²⋊C₄	—	2	1	no	—
295	C₃×C₂²⋊C₄	—	2	2	no	—
296	C₃×C₂²⋊C₄	—	10	1	no	—
297	C₃×C₂²⋊C₄	—	10	2	no	—
298	C₃×C₄²	—	2	1	no	—
299	C₃×C₄²	—	2	2	no	—
300	C₃×C₄²	—	10	1	no	—
301	C₃×C₄²	—	10	2	no	—
302	C₃×C₄²	C₂²⋊D₅	1	1	yes	characteristic
303	C₃×C₄²	C₂²⋊D₅	1	1	yes	characteristic
304	C₃×C₄²	C₂²×D₅	1	2	yes	—
305	C₂³×C₅	—	2	1	no	—
306	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
307	C₂²×D₅	—	2	1	no	—
308	C₅×Q₈	—	2	1	no	—
309	C₅×Q₈	C₂²×C₃×C₄	1	2	yes	—
310	C₅×D₄	—	2	4	no	—
311	C₅×D₄	—	2	1	no	—
312	C₅×D₄	C₂²×C₃×C₄	1	2	yes	—
313	C₂×C₄×C₅	—	2	1	no	—
314	C₂×C₄×C₅	—	2	4	no	—
315	C₂×C₄×C₅	—	2	4	no	—
316	C₂×C₄×C₅	—	2	2	no	—
317	C₂×C₄×C₅	—	4	4	no	—
318	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
319	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
320	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
321	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
322	C₂×C₄×C₅	C₃×#41	1	2	yes	—
323	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
324	C₂²⋊D₅	—	2	4	no	—
325	C₂×Dic₅	—	2	1	no	—
326	C₂×Dic₅	—	2	2	no	—
327	D₂₀	—	2	1	no	—
328	D₂₀	C₂²×C₃×C₄	1	2	yes	—
329	C₄×D₅	—	2	4	no	—
330	C₄×D₅	—	4	4	no	—
331	Dic₁₀	—	2	1	no	—
332	Dic₁₀	C₂²×C₃×C₄	1	2	yes	—
333	#168	—	2	2	no	—
334	#168	C₂²×C₃×C₄	1	2	yes	—
335	#168	C₂²×C₃×C₄	1	2	yes	—
336	C₂×#41	—	5	1	no	—
337	C₂×#41	C₂×C₃×D₅	1	1	yes	characteristic
338	#135	—	5	8	no	—
339	C₂×Q₁₆	—	5	1	no	—
340	C₂×SD₁₆	—	5	1	no	—
341	C₂×SD₁₆	—	5	1	no	—
342	C₂×D₈	—	5	1	no	—
343	C₂²×C₈	—	5	1	no	—
344	C₂²×C₈	—	5	1	no	—
345	C₄×Q₈	—	5	2	no	—
346	C₄×Q₈	C₂×C₃×D₅	1	2	yes	—
347	C₄×D₄	—	2	2	no	—
348	C₄×D₄	—	5	2	no	—
349	C₄×D₄	—	10	2	no	—
350	C₄×D₄	C₂×C₃×D₅	1	2	yes	—
351	#117	—	2	1	no	—
352	#117	—	5	1	no	—
353	#117	—	10	1	no	—
354	#117	C₂×C₃×D₅	1	1	yes	characteristic
355	C₂×C₄²	—	2	1	no	—
356	C₂×C₄²	—	10	1	no	—
357	C₂×C₄²	C₂×C₃×D₅	1	1	yes	characteristic
358	#107	—	5	2	no	—
359	#106	—	5	2	no	—
360	#103	—	5	2	no	—
361	#103	—	5	2	no	—
362	#102	—	5	2	no	—
363	#102	—	5	2	no	—
364	C₄×C₈	—	5	2	no	—
365	C₄×C₈	—	5	2	no	—
366	C₂×C₃×C₅	—	2	2	no	—
367	C₂×C₃×C₅	—	4	2	no	—
368	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
369	C₂×C₃×C₅	C₂×#135	1	2	yes	—
370	C₃×D₅	—	4	2	no	—
371	C₂³×C₃	—	2	1	no	—
372	C₂³×C₃	—	10	1	no	—
373	C₂³×C₃	C₂×C₂²⋊D₅	1	1	yes	characteristic
374	C₃×Q₈	—	2	1	no	—
375	C₃×Q₈	—	5	2	no	—
376	C₃×Q₈	—	10	1	no	—
377	C₃×Q₈	C₂×C₄×D₅	1	2	yes	—
378	C₃×D₄	—	2	4	no	—
379	C₃×D₄	—	2	1	no	—
380	C₃×D₄	—	5	2	no	—
381	C₃×D₄	—	10	4	no	—
382	C₃×D₄	—	10	1	no	—
383	C₃×D₄	C₂×C₄×D₅	1	2	yes	—
384	C₂×C₃×C₄	—	2	1	no	—
385	C₂×C₃×C₄	—	2	4	no	—
386	C₂×C₃×C₄	—	2	4	no	—
387	C₂×C₃×C₄	—	2	2	no	—
388	C₂×C₃×C₄	—	4	4	no	—
389	C₂×C₃×C₄	—	10	1	no	—
390	C₂×C₃×C₄	—	10	4	no	—
391	C₂×C₃×C₄	—	10	2	no	—
392	C₂×C₃×C₄	—	20	4	no	—
393	C₂×C₃×C₄	C₂×C₄×D₅	1	2	yes	—
394	C₂×C₃×C₄	#709	1	2	yes	—
395	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	2	yes	—
396	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	2	yes	—
397	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
398	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
399	C₃×C₈	—	5	2	no	—
400	C₃×C₈	—	5	2	no	—
401	C₃×C₈	—	10	2	no	—
402	C₂²×C₅	—	2	2	no	—
403	C₂²×C₅	—	2	2	no	—
404	C₂²×C₅	—	4	2	no	—
405	C₂²×C₅	C₃×C₄×D₄	1	2	yes	—
406	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
407	C₂×D₅	—	2	2	no	—
408	C₂×D₅	—	4	2	no	—
409	C₄×C₅	—	2	2	no	—
410	C₄×C₅	—	2	2	no	—
411	C₄×C₅	—	4	2	no	—
412	C₄×C₅	C₃×C₄×D₄	1	2	yes	—
413	C₄×C₅	C₃×#135	1	4	yes	complemented
414	C₄×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
415	C₄×C₅	C₂×C₃×#41	1	1	yes	characteristic
416	Dic₅	—	2	2	no	—
417	Dic₅	—	4	2	no	—
418	#41	—	2	2	no	—
419	#41	—	5	4	no	—
420	#41	—	10	2	no	—
421	#41	C₃×C₄×D₅	1	4	yes	complemented
422	C₂×Q₈	—	5	1	no	—
423	C₂×Q₈	C₂²×C₃×D₅	1	1	yes	characteristic
424	C₂×D₄	—	2	1	no	—
425	C₂×D₄	—	5	1	no	—
426	C₂×D₄	—	10	1	no	—
427	C₂×D₄	C₂²×C₃×D₅	1	1	yes	characteristic
428	C₂²×C₄	—	2	1	no	—
429	C₂²×C₄	—	2	2	no	—
430	C₂²×C₄	—	10	1	no	—
431	C₂²×C₄	—	10	2	no	—
432	C₂²×C₄	C₃×C₂²⋊D₅	1	2	yes	—
433	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
434	Q₁₆	—	5	4	no	—
435	SD₁₆	—	5	4	no	—
436	SD₁₆	—	5	4	no	—
437	D₈	—	5	4	no	—
438	C₂×C₈	—	5	4	no	—
439	C₂×C₈	—	5	1	no	—
440	C₂×C₈	—	5	1	no	—
441	C₂×C₈	—	5	2	no	—
442	C₂×C₈	—	10	2	no	—
443	C₄⋊C₄	—	2	2	no	—
444	C₄⋊C₄	—	5	2	no	—
445	C₄⋊C₄	—	10	2	no	—
446	C₄⋊C₄	C₂²×C₃×D₅	1	2	yes	—
447	C₂²⋊C₄	—	2	1	no	—
448	C₂²⋊C₄	—	2	2	no	—
449	C₂²⋊C₄	—	10	1	no	—
450	C₂²⋊C₄	—	10	2	no	—
451	C₄²	—	2	1	no	—
452	C₄²	—	2	2	no	—
453	C₄²	—	10	1	no	—
454	C₄²	—	10	2	no	—
455	C₄²	C₃×C₂²⋊D₅	1	1	yes	characteristic
456	C₄²	C₃×C₂²⋊D₅	1	1	yes	characteristic
457	C₄²	C₂²×C₃×D₅	1	2	yes	—
458	C₃×C₅	C₄×#135	1	1	yes	characteristic, complemented, Hall
459	C₂²×C₃	—	2	2	no	—
460	C₂²×C₃	—	2	2	no	—
461	C₂²×C₃	—	4	2	no	—
462	C₂²×C₃	—	10	2	no	—
463	C₂²×C₃	—	20	2	no	—
464	C₂²×C₃	C₄×C₂²⋊D₅	1	2	yes	—
465	C₂²×C₃	C₂²×C₂²⋊D₅	1	1	yes	characteristic
466	C₃×C₄	—	2	2	no	—
467	C₃×C₄	—	2	2	no	—
468	C₃×C₄	—	4	2	no	—
469	C₃×C₄	—	10	2	no	—
470	C₃×C₄	—	20	2	no	—
471	C₃×C₄	C₄×C₂²⋊D₅	1	2	yes	—
472	C₃×C₄	#4096	1	4	yes	direct product factor
473	C₃×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
474	C₃×C₄	C₂×#709	1	1	yes	characteristic
475	C₂×C₅	—	2	2	no	—
476	C₂×C₅	—	4	2	no	—
477	C₂×C₅	C₂×C₃×C₄×D₄	1	1	yes	characteristic
478	C₂×C₅	C₂×C₃×#135	1	2	yes	—
479	D₅	—	4	2	no	—
480	C₂³	—	2	1	no	—
481	C₂³	—	10	1	no	—
482	C₂³	C₂×C₃×C₂²⋊D₅	1	1	yes	characteristic
483	Q₈	—	2	1	no	—
484	Q₈	—	5	2	no	—
485	Q₈	—	10	1	no	—
486	Q₈	C₂×C₃×C₄×D₅	1	2	yes	—
487	D₄	—	2	4	no	—
488	D₄	—	2	1	no	—
489	D₄	—	5	2	no	—
490	D₄	—	10	4	no	—
491	D₄	—	10	1	no	—
492	D₄	C₂×C₃×C₄×D₅	1	2	yes	—
493	C₂×C₄	—	2	1	no	—
494	C₂×C₄	—	2	4	no	—
495	C₂×C₄	—	2	4	no	—
496	C₂×C₄	—	2	2	no	—
497	C₂×C₄	—	4	4	no	—
498	C₂×C₄	—	10	1	no	—
499	C₂×C₄	—	10	4	no	—
500	C₂×C₄	—	10	2	no	—
501	C₂×C₄	—	20	4	no	—
502	C₂×C₄	C₂×C₃×C₄×D₅	1	2	yes	—
503	C₂×C₄	C₃×#709	1	2	yes	—
504	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	2	yes	—
505	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	2	yes	—
506	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	1	yes	characteristic
507	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
508	C₈	—	5	2	no	—
509	C₈	—	5	2	no	—
510	C₈	—	10	2	no	—
511	C₂×C₃	—	2	2	no	—
512	C₂×C₃	—	4	2	no	—
513	C₂×C₃	—	20	2	no	—
514	C₂×C₃	C₂×C₄×C₂²⋊D₅	1	1	yes	characteristic
515	C₂×C₃	C₂×#4096	1	2	yes	—
516	C₅	C₃×C₄×#135	1	1	yes	characteristic, complemented, Sylow
517	C₂²	—	2	2	no	—
518	C₂²	—	2	2	no	—
519	C₂²	—	4	2	no	—
520	C₂²	—	10	2	no	—
521	C₂²	—	20	2	no	—
522	C₂²	C₃×C₄×C₂²⋊D₅	1	2	yes	—
523	C₂²	C₂²×C₃×C₂²⋊D₅	1	1	yes	characteristic
524	C₄	—	2	2	no	—
525	C₄	—	2	2	no	—
526	C₄	—	4	2	no	—
527	C₄	—	10	2	no	—
528	C₄	—	20	2	no	—
529	C₄	C₃×C₄×C₂²⋊D₅	1	2	yes	—
530	C₄	C₃×#4096	1	4	yes	direct product factor
531	C₄	C₂²×C₃×C₄×D₅	1	1	yes	characteristic
532	C₄	C₂×C₃×#709	1	1	yes	characteristic
533	C₃	C₄×#4096	1	1	yes	characteristic, direct product factor, Sylow
534	C₂	—	2	2	no	—
535	C₂	—	4	2	no	—
536	C₂	—	20	2	no	—
537	C₂	C₂×C₃×C₄×C₂²⋊D₅	1	1	yes	characteristic
538	C₂	C₂×C₃×#4096	1	2	yes	—

	subgroup	G/H
center	C₃×C₄²	C₂²⋊D₅
commutator	C₄×C₅	C₂³×C₃×C₄
Frattini	C₂×C₄	C₂³×C₃×D₅
Fitting	C₃×C₄×C₅×#41	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
prime radical	C₂×C₃×#4096	C₂
cosocle	C₂×C₄×C₅	C₂⁴×C₃
hypercenter	C₃×C₄×#41	D₅
hypocenter	C₅	C₃×C₄×#135
LCS	G ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₃×C₄² ◁ C₂×C₃×C₄² ◁ C₃×C₄×#41

Complements

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

N	H ≅ G/N	type
1. C₃×C₄×C₅×#41	C₂	semidirect
3. C₃×C₄×#709	C₂	semidirect
4. C₃×#65522	C₂	semidirect
5. C₃×C₄×#689	C₂	semidirect
6. C₃×C₄×#688	C₂	semidirect
7. C₃×C₄×#687	C₂	semidirect
8. C₃×C₄×#686	C₂	semidirect
9. C₃×#65291	C₂	semidirect
10. C₃×#65287	C₂	semidirect
11. C₂×C₃×C₄×#168	C₂	semidirect
12. C₄×#4096	C₃	direct (N × H)
22. C₃×#4096	C₄	direct (N × H)
44. C₄×C₅×#41	C₂×C₃	semidirect
46. C₄×#709	C₂×C₃	semidirect
47. #65522	C₂×C₃	semidirect
48. C₄×#689	C₂×C₃	semidirect
49. C₄×#688	C₂×C₃	semidirect
50. C₄×#687	C₂×C₃	semidirect
51. C₄×#686	C₂×C₃	semidirect
52. #65291	C₂×C₃	semidirect
53. #65287	C₂×C₃	semidirect
54. C₂×C₄×#168	C₂×C₃	semidirect
56. C₃×C₅×#41	C₂×C₄	semidirect
66. C₃×#709	C₂×C₄	semidirect
81. C₃×#689	C₂×C₄	semidirect
82. C₃×#688	C₂×C₄	semidirect
83. C₃×#687	C₂×C₄	semidirect
84. C₃×#686	C₂×C₄	semidirect
91. C₂×C₃×#168	C₂×C₄	semidirect
97. C₃×C₄×#41	D₅	semidirect
115. #4096	C₃×C₄	direct (N × H)
199. C₅×#41	C₂×C₃×C₄	semidirect
209. #709	C₂×C₃×C₄	semidirect
224. #689	C₂×C₃×C₄	semidirect
225. #688	C₂×C₃×C₄	semidirect
226. #687	C₂×C₃×C₄	semidirect
227. #686	C₂×C₃×C₄	semidirect
234. C₂×#168	C₂×C₃×C₄	semidirect
240. C₄×#41	C₃×D₅	semidirect
260. C₃×C₄×C₅	#135	semidirect
268. C₃×#41	C₄×D₅	semidirect
413. C₄×C₅	C₃×#135	semidirect
421. #41	C₃×C₄×D₅	semidirect
458. C₃×C₅	C₄×#135	semidirect
472. C₃×C₄	#4096	direct (N × H)
516. C₅	C₃×C₄×#135	semidirect
530. C₄	C₃×#4096	direct (N × H)
533. C₃	C₄×#4096	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×C₄×C₅×#41	2
C₂×C₃×#4096	2
C₃×C₄×#709	2
C₃×#65522	2
C₃×C₄×#689	2
C₃×C₄×#688	2
C₃×C₄×#687	2
C₃×C₄×#686	2
C₃×#65291	2
C₃×#65287	2
C₂×C₃×C₄×#168	2
C₄×#4096	3
C₃×C₄×#135	5

Subgroups — C3×C4×#4096 #14416210

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₄×#4096 #14416210