Subgroups — C₄×#91504 #14416716

Order 1920.

1096 conjugacy classes of subgroups.

The subgroup lattice has 768 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, complemented
2	C₂×#91504	C₂	1	1	yes	maximal, characteristic
3	C₄×D₃×D₂₀	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄×#6717	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×C₄×#688	C₂	1	1	yes	maximal, characteristic, complemented
6	#11749235	C₂	1	1	yes	maximal, characteristic, complemented
7	#11749234	C₂	1	1	yes	maximal, characteristic, complemented
8	#11749201	C₂	1	1	yes	maximal, characteristic, complemented
9	#11747477	C₂	1	1	yes	maximal, characteristic, complemented
10	#11747470	C₂	1	1	yes	maximal, characteristic, complemented
11	#11747220	C₂	1	1	yes	maximal, characteristic, complemented
12	#11747191	C₂	1	1	yes	maximal, characteristic, complemented
13	C₄×#6654	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄×#6652	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄×#6650	C₂	1	1	yes	maximal, characteristic, complemented
16	C₄×#4095	—	3	1	no	maximal, Hall
17	C₂×C₅×#239	C₂²	1	1	yes	characteristic
18	C₂×D₃×D₂₀	C₂²	1	1	yes	characteristic
19	C₂×C₄×D₃×D₅	—	2	1	no	—
20	C₃×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic, complemented
21	C₂×#6717	C₂²	1	1	yes	characteristic
22	C₄×D₆₀	C₂²	1	1	yes	characteristic
23	C₅×Q₈×Dic₃	C₂²	1	1	yes	characteristic, complemented
24	C₅×#893	—	2	1	no	—
25	C₅×#893	C₂²	1	1	yes	characteristic, complemented
26	C₅×#892	—	2	1	no	—
27	C₅×#892	C₂²	1	1	yes	characteristic
28	C₄×C₅×D₁₂	—	2	1	no	—
29	C₄×C₅×D₁₂	C₂²	1	1	yes	characteristic, complemented
30	C₄²×C₅×D₃	—	2	1	no	—
31	C₄²×C₅×D₃	C₂²	1	1	yes	characteristic
32	C₂×C₃×#688	C₂²	1	1	yes	characteristic
33	C₃×C₄×D₂₀	C₂²	1	1	yes	characteristic
34	#91504	C₄	1	8	yes	direct product factor
35	D₃×#685	—	2	1	no	—
36	C₄×#1202	—	2	1	no	—
37	#91428	C₂²	1	1	yes	characteristic
38	D₃×C₄⋊Dic₅	C₂²	1	1	yes	characteristic
39	Dic₃×D₂₀	C₂²	1	1	yes	characteristic
40	#91395	—	2	1	no	—
41	C₂×#6654	C₂²	1	1	yes	characteristic
42	C₂×#6652	C₂²	1	1	yes	characteristic
43	C₂×#6650	C₂²	1	1	yes	characteristic
44	C₂×#6650	C₂²	1	1	yes	characteristic
45	#91119	C₂²	1	1	yes	characteristic, complemented
46	#91093	C₂²	1	1	yes	characteristic
47	#91092	C₂²	1	1	yes	characteristic, complemented
48	C₄×C₃⋊#168	C₂²	1	1	yes	characteristic, complemented
49	C₃×#3967	C₂²	1	1	yes	characteristic, complemented
50	C₃×#3941	C₂²	1	1	yes	characteristic
51	C₃×#3940	C₂²	1	1	yes	characteristic, complemented
52	C₃×C₄×#168	C₂²	1	1	yes	characteristic, complemented
53	#90989	C₂²	1	1	yes	characteristic, complemented
54	#90988	C₂²	1	1	yes	characteristic, complemented
55	#90969	C₂²	1	1	yes	characteristic
56	#90967	C₂²	1	1	yes	characteristic, complemented
57	#90966	C₂²	1	1	yes	characteristic, complemented
58	#90964	C₂²	1	1	yes	characteristic
59	#90953	C₂²	1	1	yes	characteristic, complemented
60	#90953	C₂²	1	1	yes	characteristic, complemented
61	C₄×#914	—	5	1	no	maximal, Hall
62	C₄×C₅×#41	—	3	1	no	—
63	C₂×#4095	—	3	1	no	—
64	C₂×C₄×D₂₀	—	3	1	no	—
65	#65521	—	3	1	no	—
66	#65315	—	3	1	no	—
67	#65315	—	3	1	no	—
68	C₄×#688	—	3	1	no	—
69	C₄×#688	D₃	1	1	yes	characteristic, complemented
70	#65303	—	3	1	no	—
71	#65303	—	3	1	no	—
72	C₄×#686	—	3	1	no	—
73	C₄×#686	—	3	1	no	—
74	#65290	—	3	1	no	—
75	#65284	—	3	1	no	—
76	C₄×#681	—	3	1	no	—
77	C₂²×D₃×D₅	—	2	1	no	—
78	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
79	C₂×D₆₀	C₂³	1	1	yes	characteristic
80	C₂×C₄×D₁₅	—	2	1	no	—
81	C₅×#239	—	2	2	no	—
82	C₅×#239	C₂×C₄	1	4	yes	complemented
83	C₂×C₅×D₁₂	—	2	1	no	—
84	C₂×C₅×D₁₂	C₂³	1	1	yes	characteristic
85	C₂×C₄×C₅×D₃	—	2	1	no	—
86	C₂×C₄×C₅×D₃	—	2	1	no	—
87	C₂×C₄×C₅×D₃	—	2	1	no	—
88	C₂×C₄×C₅×D₃	D₄	1	1	yes	characteristic
89	C₂×C₄×C₅×D₃	D₄	1	1	yes	characteristic
90	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
91	C₂×C₃×D₂₀	C₂³	1	1	yes	characteristic
92	C₂×C₃×C₄×D₅	—	2	1	no	—
93	C₂×#1202	—	2	1	no	—
94	C₂×#1200	—	2	1	no	—
95	C₂×D₃×Dic₅	—	2	1	no	—
96	C₂×D₅×Dic₃	—	2	1	no	—
97	D₃×D₂₀	—	2	2	no	—
98	D₃×D₂₀	C₂×C₄	1	4	yes	complemented
99	C₄×D₃×D₅	—	4	4	no	—
100	C₃×C₅×C₄⋊C₄	—	2	1	no	—
101	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
102	C₃×C₄²×C₅	—	2	1	no	—
103	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
104	#6717	C₂×C₄	1	4	yes	complemented
105	#6714	—	2	1	no	—
106	C₄⋊Dic₁₅	C₂³	1	1	yes	characteristic
107	C₂×C₃⋊#168	C₂³	1	1	yes	characteristic
108	C₂×C₃⋊#168	C₂³	1	1	yes	characteristic
109	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
110	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
111	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
112	C₅×C₄⋊Dic₃	—	2	1	no	—
113	C₅×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
114	C₄×C₅×Dic₃	—	2	1	no	—
115	C₄×C₅×Dic₃	—	2	1	no	—
116	C₄×C₅×Dic₃	D₄	1	1	yes	characteristic
117	C₄×C₅×Dic₃	D₄	1	1	yes	characteristic
118	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
119	C₃×#688	C₂×C₄	1	4	yes	complemented
120	C₃×#685	—	2	1	no	—
121	C₃×C₄⋊Dic₅	C₂³	1	1	yes	characteristic
122	C₂×C₃×#168	C₂³	1	1	yes	characteristic
123	C₂×C₃×#168	C₂³	1	1	yes	characteristic
124	Dic₃⋊Dic₅	—	2	1	no	—
125	#6667	—	2	1	no	—
126	#6665	—	2	1	no	—
127	#6654	C₂×C₄	1	4	yes	complemented
128	#6652	C₂×C₄	1	4	yes	complemented
129	#6650	—	2	2	no	—
130	#6650	C₂×C₄	1	4	yes	complemented
131	C₂×#914	—	5	1	no	—
132	C₄×#239	D₅	1	1	yes	characteristic, complemented
133	C₄×D₃×D₄	—	5	1	no	—
134	C₃×C₄×SD₁₆	—	5	1	no	—
135	#5164	—	5	1	no	—
136	C₄×#215	—	5	1	no	—
137	C₄×#213	—	5	1	no	—
138	#4869	—	5	1	no	—
139	#4861	—	5	1	no	—
140	#4817	—	5	1	no	—
141	#4803	—	5	1	no	—
142	#4785	—	5	1	no	—
143	#4770	—	5	1	no	—
144	C₄×D₂₄	—	5	1	no	—
145	C₄×ΓL(1,𝔽₂₅)	—	5	1	no	—
146	C₂×C₅×#41	—	3	1	no	—
147	C₂²×D₂₀	—	3	1	no	—
148	C₂²×C₄×D₅	—	6	1	no	—
149	C₄×C₅×Q₈	—	3	1	no	—
150	C₄×C₅×Q₈	C₂×D₃	1	1	yes	characteristic, complemented
151	C₄×C₅×D₄	—	3	1	no	—
152	C₄×C₅×D₄	—	3	1	no	—
153	C₄×C₅×D₄	—	6	1	no	—
154	C₄×C₅×D₄	—	6	1	no	—
155	C₅×#117	—	3	1	no	—
156	C₅×#117	—	6	1	no	—
157	C₂×C₄²×C₅	—	3	1	no	—
158	C₂×C₄²×C₅	—	6	1	no	—
159	#4095	—	3	8	no	—
160	C₂×#688	—	3	1	no	—
161	C₂×#688	C₂×D₃	1	1	yes	characteristic
162	C₂×#686	—	3	1	no	—
163	C₂×#686	—	3	1	no	—
164	C₂×#685	—	6	1	no	—
165	C₂×C₄⋊Dic₅	—	3	1	no	—
166	C₂×#681	—	3	1	no	—
167	C₂×#681	—	3	1	no	—
168	C₄×D₂₀	—	3	1	no	—
169	C₄×D₂₀	—	3	1	no	—
170	C₄×D₂₀	—	3	1	no	—
171	C₄×D₂₀	—	6	1	no	—
172	C₄×D₂₀	—	6	1	no	—
173	C₄×D₂₀	C₂×D₃	1	1	yes	characteristic
174	#3967	—	3	1	no	—
175	#3967	C₂×D₃	1	1	yes	characteristic, complemented
176	#3964	—	3	1	no	—
177	#3964	—	3	1	no	—
178	#3941	—	3	1	no	—
179	#3941	—	3	1	no	—
180	#3941	—	3	1	no	—
181	#3941	C₂×D₃	1	1	yes	characteristic
182	#3940	—	3	1	no	—
183	#3940	C₂×D₃	1	1	yes	characteristic, complemented
184	#3939	—	3	1	no	—
185	#3939	—	3	1	no	—
186	#3935	—	3	1	no	—
187	#3935	—	3	1	no	—
188	C₄×#168	—	3	1	no	—
189	C₄×#168	C₂×D₃	1	1	yes	characteristic, complemented
190	C₄×AGL(1,ℤ/8)	—	15	1	no	Sylow
191	C₂²×D₁₅	—	2	1	no	—
192	C₂²×C₅×D₃	—	2	1	no	—
193	C₂²×C₅×D₃	C₂×D₄	1	1	yes	characteristic
194	C₂²×C₃×D₅	—	2	1	no	—
195	C₂×D₃×D₅	—	2	4	no	—
196	C₂×D₃×D₅	—	4	2	no	—
197	C₂×D₃×D₅	—	4	2	no	—
198	C₃×C₅×Q₈	—	2	1	no	—
199	C₃×C₅×Q₈	C₂²×C₄	1	2	yes	complemented
200	C₂×C₃×C₄×C₅	—	2	1	no	—
201	C₂×C₃×C₄×C₅	—	2	1	no	—
202	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
203	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
204	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
205	C₂×Dic₁₅	—	2	1	no	—
206	D₆₀	—	2	1	no	—
207	D₆₀	C₂²×C₄	1	2	yes	—
208	C₄×D₁₅	—	4	2	no	—
209	C₂×C₅×Dic₃	—	2	1	no	—
210	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
211	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
212	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
213	C₅×D₁₂	—	2	4	no	—
214	C₅×D₁₂	—	2	1	no	—
215	C₅×D₁₂	C₂²×C₄	1	2	yes	complemented
216	C₄×C₅×D₃	—	2	2	no	—
217	C₄×C₅×D₃	—	2	4	no	—
218	C₄×C₅×D₃	—	4	1	no	—
219	C₄×C₅×D₃	—	4	2	no	—
220	C₄×C₅×D₃	—	4	2	no	—
221	C₄×C₅×D₃	C₂²×C₄	1	2	yes	—
222	C₄×C₅×D₃	#41	1	2	yes	—
223	C₂×C₃×Dic₅	—	2	1	no	—
224	C₃×D₂₀	—	2	1	no	—
225	C₃×D₂₀	C₂²×C₄	1	2	yes	—
226	C₃×C₄×D₅	—	4	2	no	—
227	#1202	—	2	4	no	—
228	#1200	—	4	2	no	—
229	D₃×Dic₅	—	4	2	no	—
230	D₅×Dic₃	—	4	2	no	—
231	C₃⋊#168	—	2	1	no	—
232	C₃⋊#168	C₂²×C₄	1	2	yes	complemented
233	C₃×#168	—	2	1	no	—
234	C₃×#168	C₂²×C₄	1	2	yes	complemented
235	C₂×#239	C₂×D₅	1	1	yes	characteristic
236	C₂×D₃×D₄	—	5	1	no	—
237	C₂²×C₄×D₃	—	10	1	no	—
238	C₂×C₃×SD₁₆	—	5	1	no	—
239	C₃×C₄×Q₈	C₂×D₅	1	1	yes	characteristic, complemented
240	C₃×C₄×D₄	—	5	1	no	—
241	Q₈×Dic₃	C₂×D₅	1	1	yes	characteristic, complemented
242	C₂×#215	—	5	1	no	—
243	D₄×Dic₃	—	5	1	no	—
244	C₂×#213	—	5	1	no	—
245	C₄×#67	—	10	1	no	—
246	#914	—	5	8	no	—
247	C₂×D₂₄	—	5	1	no	—
248	C₂×ΓL(1,𝔽₂₅)	—	5	1	no	—
249	C₂×ΓL(1,𝔽₂₅)	—	5	1	no	—
250	#893	—	2	1	no	—
251	#893	—	5	1	no	—
252	#893	C₂×D₅	1	1	yes	characteristic, complemented
253	#892	—	2	1	no	—
254	#892	C₂×D₅	1	1	yes	characteristic
255	D₃×C₄⋊C₄	—	5	1	no	—
256	#67⋊C₄	—	10	1	no	—
257	D₃×C₂²⋊C₄	—	10	1	no	—
258	C₄×D₁₂	—	2	1	no	—
259	C₄×D₁₂	—	5	1	no	—
260	C₄×D₁₂	C₂×D₅	1	1	yes	characteristic, complemented
261	C₄²×D₃	—	2	1	no	—
262	C₄²×D₃	C₂×D₅	1	1	yes	characteristic
263	C₃×#106	—	5	1	no	—
264	C₃×#103	—	5	1	no	—
265	C₃×#102	—	5	1	no	—
266	C₃×C₄×C₈	—	5	1	no	—
267	#835	—	5	1	no	—
268	#832	—	5	1	no	—
269	#821	—	5	1	no	—
270	#821	—	5	1	no	—
271	#818	—	5	1	no	—
272	#815	—	5	1	no	—
273	#815	—	5	1	no	—
274	#809	—	5	1	no	—
275	#809	—	5	1	no	—
276	#808	—	5	1	no	—
277	#807	—	5	1	no	—
278	C₄×C₃⋊C₈	—	5	1	no	—
279	C₂³×D₅	—	6	1	no	—
280	C₅×#41	—	3	4	no	—
281	C₅×#41	—	6	2	no	—
282	C₂×C₅×Q₈	C₂²×D₃	1	1	yes	characteristic
283	C₂×C₅×D₄	—	3	1	no	—
284	C₂×C₅×D₄	—	6	1	no	—
285	C₂²×C₄×C₅	—	3	1	no	—
286	C₂²×C₄×C₅	—	3	1	no	—
287	C₂²×C₄×C₅	—	3	1	no	—
288	C₂²×C₄×C₅	—	6	1	no	—
289	C₂²×C₄×C₅	—	6	1	no	—
290	C₂²×C₄×C₅	—	6	1	no	—
291	C₂²×Dic₅	—	6	1	no	—
292	C₂×D₂₀	—	3	1	no	—
293	C₂×D₂₀	—	3	4	no	—
294	C₂×D₂₀	—	6	2	no	—
295	C₂×D₂₀	—	6	1	no	—
296	C₂×D₂₀	C₂²×D₃	1	1	yes	characteristic
297	C₂×C₄×D₅	—	2	1	no	—
298	C₂×C₄×D₅	—	6	1	no	—
299	C₂×C₄×D₅	—	6	1	no	—
300	C₂×C₄×D₅	—	6	1	no	—
301	C₂×C₄×D₅	—	12	4	no	—
302	C₅×C₄⋊C₄	—	2	1	no	—
303	C₅×C₄⋊C₄	—	3	1	no	—
304	C₅×C₄⋊C₄	—	6	1	no	—
305	C₅×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
306	C₅×C₂²⋊C₄	—	6	1	no	—
307	C₅×C₂²⋊C₄	—	6	1	no	—
308	C₅×C₂²⋊C₄	—	6	1	no	—
309	C₄²×C₅	—	2	1	no	—
310	C₄²×C₅	—	3	1	no	—
311	C₄²×C₅	—	3	1	no	—
312	C₄²×C₅	—	3	1	no	—
313	C₄²×C₅	—	6	1	no	—
314	C₄²×C₅	—	6	1	no	—
315	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
316	#688	—	3	4	no	—
317	#688	C₄×D₃	1	4	yes	complemented
318	#686	—	3	4	no	—
319	#686	—	3	4	no	—
320	#685	—	2	1	no	—
321	#685	—	6	1	no	—
322	#685	—	6	1	no	—
323	#685	—	6	1	no	—
324	C₄⋊Dic₅	—	3	1	no	—
325	C₄⋊Dic₅	—	6	1	no	—
326	C₄⋊Dic₅	C₂²×D₃	1	1	yes	characteristic
327	#681	—	3	4	no	—
328	#681	—	6	2	no	—
329	C₂×#168	—	3	1	no	—
330	C₂×#168	—	3	1	no	—
331	C₂×#168	C₂²×D₃	1	1	yes	characteristic
332	C₂×#168	C₂²×D₃	1	1	yes	characteristic
333	C₂×AGL(1,ℤ/8)	—	15	1	no	—
334	C₄×#41	—	3	1	no	—
335	C₂×C₄×D₄	—	15	1	no	—
336	#442	—	15	1	no	—
337	#442	—	15	1	no	—
338	#440	—	15	1	no	—
339	#440	—	15	1	no	—
340	C₄×SD₁₆	—	5	1	no	—
341	C₄×SD₁₆	—	15	1	no	—
342	C₄×D₈	—	15	1	no	—
343	C₄×D₈	—	15	1	no	—
344	#428	—	15	1	no	—
345	#418	—	15	1	no	—
346	#417	—	15	1	no	—
347	C₄×M₁₆	—	15	1	no	—
348	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
349	C₂×D₁₅	—	2	2	no	—
350	C₂×D₁₅	—	4	1	no	—
351	C₂×D₁₅	—	4	1	no	—
352	C₂×C₅×D₃	—	2	1	no	—
353	C₂×C₅×D₃	—	2	1	no	—
354	C₂×C₅×D₃	—	2	2	no	—
355	C₂×C₅×D₃	—	4	1	no	—
356	C₂×C₅×D₃	—	4	1	no	—
357	C₂×C₅×D₃	C₄×D₄	1	2	yes	—
358	C₂×C₃×D₅	—	2	2	no	—
359	C₂×C₃×D₅	—	4	1	no	—
360	C₂×C₃×D₅	—	4	1	no	—
361	D₃×D₅	—	4	8	no	—
362	C₃×C₄×C₅	—	2	2	no	—
363	C₃×C₄×C₅	—	2	1	no	—
364	C₃×C₄×C₅	—	4	1	no	—
365	C₃×C₄×C₅	AGL(1,ℤ/8)	1	2	yes	complemented
366	C₃×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
367	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
368	Dic₁₅	—	4	1	no	—
369	C₃×Dic₅	—	4	1	no	—
370	C₅×Dic₃	—	2	1	no	—
371	C₅×Dic₃	—	2	1	no	—
372	C₅×Dic₃	—	4	1	no	—
373	C₅×Dic₃	C₄×D₄	1	2	yes	—
374	C₂³×D₃	—	10	1	no	—
375	C₂×C₃×Q₈	C₂²×D₅	1	1	yes	characteristic
376	C₂×C₃×D₄	—	5	1	no	—
377	C₂²×C₃×C₄	—	10	1	no	—
378	C₂×#67	—	10	1	no	—
379	C₂²×Dic₃	—	10	1	no	—
380	#239	—	2	2	no	—
381	#239	C₄×D₅	1	4	yes	complemented
382	D₃×D₄	—	5	4	no	—
383	D₃×D₄	—	10	2	no	—
384	C₂×D₁₂	—	2	1	no	—
385	C₂×D₁₂	—	5	1	no	—
386	C₂×D₁₂	C₂²×D₅	1	1	yes	characteristic
387	C₂×C₄×D₃	—	2	1	no	—
388	C₂×C₄×D₃	—	2	1	no	—
389	C₂×C₄×D₃	—	2	1	no	—
390	C₂×C₄×D₃	—	10	1	no	—
391	C₂×C₄×D₃	—	10	1	no	—
392	C₂×C₄×D₃	—	10	1	no	—
393	C₂×C₄×D₃	—	20	4	no	—
394	C₂×C₄×D₃	C₂²⋊D₅	1	1	yes	characteristic
395	C₂×C₄×D₃	C₂²⋊D₅	1	1	yes	characteristic
396	C₂×C₄×D₃	C₂²×D₅	1	1	yes	characteristic
397	C₃×SD₁₆	—	5	4	no	—
398	C₂×C₃×C₈	—	5	1	no	—
399	C₂×C₃×C₈	—	5	1	no	—
400	C₃×C₄⋊C₄	—	2	1	no	—
401	C₃×C₄⋊C₄	—	5	1	no	—
402	C₃×C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
403	C₃×C₂²⋊C₄	—	10	1	no	—
404	C₃×C₄²	—	2	1	no	—
405	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
406	#217	—	10	1	no	—
407	#215	—	5	4	no	—
408	#213	—	5	4	no	—
409	(C₂×D₃)⋊C₄	—	2	1	no	—
410	(C₂×D₃)⋊C₄	—	2	1	no	—
411	(C₂×D₃)⋊C₄	—	2	1	no	—
412	(C₂×D₃)⋊C₄	—	10	1	no	—
413	(C₂×D₃)⋊C₄	—	10	1	no	—
414	C₄⋊Dic₃	—	2	1	no	—
415	C₄⋊Dic₃	—	5	1	no	—
416	C₄⋊Dic₃	C₂²×D₅	1	1	yes	characteristic
417	Dic₃⋊C₄	—	10	1	no	—
418	C₄×Dic₃	—	2	1	no	—
419	C₄×Dic₃	—	2	1	no	—
420	C₄×Dic₃	C₂²⋊D₅	1	1	yes	characteristic
421	C₄×Dic₃	C₂²⋊D₅	1	1	yes	characteristic
422	C₄×Dic₃	C₂²×D₅	1	1	yes	characteristic
423	C₂×C₃⋊C₈	—	5	1	no	—
424	C₂×C₃⋊C₈	—	5	1	no	—
425	D₂₄	—	5	4	no	—
426	ΓL(1,𝔽₂₅)	—	5	4	no	—
427	ΓL(1,𝔽₂₅)	—	10	2	no	—
428	C₂³×C₅	—	3	1	no	—
429	C₂³×C₅	—	6	1	no	—
430	C₂²×D₅	—	2	1	no	—
431	C₂²×D₅	—	6	4	no	—
432	C₂²×D₅	—	6	1	no	—
433	C₂²×D₅	—	12	2	no	—
434	C₂²×D₅	—	12	2	no	—
435	C₅×Q₈	—	2	1	no	—
436	C₅×Q₈	C₂×C₄×D₃	1	2	yes	complemented
437	C₅×D₄	—	3	2	no	—
438	C₅×D₄	—	6	4	no	—
439	C₅×D₄	—	6	1	no	—
440	C₂×C₄×C₅	—	2	1	no	—
441	C₂×C₄×C₅	—	2	1	no	—
442	C₂×C₄×C₅	—	3	1	no	—
443	C₂×C₄×C₅	—	3	2	no	—
444	C₂×C₄×C₅	—	3	2	no	—
445	C₂×C₄×C₅	—	3	1	no	—
446	C₂×C₄×C₅	—	3	1	no	—
447	C₂×C₄×C₅	—	6	4	no	—
448	C₂×C₄×C₅	—	6	2	no	—
449	C₂×C₄×C₅	—	6	1	no	—
450	C₂×C₄×C₅	—	12	1	no	—
451	C₂×C₄×C₅	—	12	2	no	—
452	C₂×C₄×C₅	—	12	2	no	—
453	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
454	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
455	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
456	C₂×Dic₅	—	2	1	no	—
457	C₂×Dic₅	—	6	1	no	—
458	C₂×Dic₅	—	12	2	no	—
459	D₂₀	—	2	1	no	—
460	D₂₀	—	3	2	no	—
461	D₂₀	—	6	4	no	—
462	D₂₀	—	6	1	no	—
463	D₂₀	C₂×C₄×D₃	1	2	yes	—
464	C₄×D₅	—	4	2	no	—
465	C₄×D₅	—	12	2	no	—
466	C₄×D₅	—	12	2	no	—
467	C₄×D₅	—	12	2	no	—
468	#168	—	2	1	no	—
469	#168	—	3	2	no	—
470	#168	—	6	1	no	—
471	#168	C₂×C₄×D₃	1	2	yes	complemented
472	C₂×#41	—	3	1	no	—
473	C₂²×D₄	—	15	1	no	—
474	C₂³×C₄	—	30	1	no	—
475	AGL(1,ℤ/8)	—	15	8	no	—
476	C₂×SD₁₆	—	5	1	no	—
477	C₂×SD₁₆	—	15	1	no	—
478	C₂×D₈	—	15	1	no	—
479	C₂×D₈	—	15	1	no	—
480	C₂×M₁₆	—	15	1	no	—
481	C₂×M₁₆	—	15	1	no	—
482	C₄×Q₈	—	3	1	no	—
483	C₄×Q₈	D₃×D₅	1	1	yes	characteristic, complemented
484	C₄×D₄	—	3	1	no	—
485	C₄×D₄	—	3	1	no	—
486	C₄×D₄	—	5	1	no	—
487	C₄×D₄	—	6	1	no	—
488	C₄×D₄	—	6	1	no	—
489	C₄×D₄	—	15	1	no	—
490	C₄×D₄	—	15	1	no	—
491	C₄×D₄	—	15	1	no	—
492	C₄×D₄	—	30	1	no	—
493	C₄×D₄	—	30	1	no	—
494	#117	—	3	1	no	—
495	#117	—	6	1	no	—
496	C₂×C₄⋊C₄	—	15	1	no	—
497	C₂×C₂²⋊C₄	—	30	1	no	—
498	C₂×C₄²	—	3	1	no	—
499	C₂×C₄²	—	6	1	no	—
500	#107	—	15	1	no	—
501	#107	—	15	1	no	—
502	#106	—	5	1	no	—
503	#106	—	15	1	no	—
504	#103	—	5	1	no	—
505	#103	—	15	1	no	—
506	#102	—	5	1	no	—
507	#102	—	15	1	no	—
508	#102	—	15	1	no	—
509	#102	—	15	1	no	—
510	#102	—	15	1	no	—
511	#102	—	15	1	no	—
512	#97	—	15	1	no	—
513	#97	—	15	1	no	—
514	C₄×C₈	—	5	1	no	—
515	C₄×C₈	—	15	1	no	—
516	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
517	C₂×C₃×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
518	C₂×C₃×C₅	#575	1	1	yes	characteristic
519	D₁₅	—	4	2	no	—
520	C₃×D₅	—	4	2	no	—
521	C₅×D₃	—	2	2	no	—
522	C₅×D₃	—	4	2	no	—
523	C₂³×C₃	—	10	1	no	—
524	C₂²×D₃	—	2	1	no	—
525	C₂²×D₃	—	10	1	no	—
526	C₂²×D₃	—	10	4	no	—
527	C₂²×D₃	—	20	2	no	—
528	C₂²×D₃	—	20	2	no	—
529	C₂²×D₃	C₂×C₂²⋊D₅	1	1	yes	characteristic
530	C₃×Q₈	—	2	1	no	—
531	C₃×Q₈	C₂×C₄×D₅	1	2	yes	complemented
532	C₃×D₄	—	5	2	no	—
533	C₃×D₄	—	10	1	no	—
534	C₂×C₃×C₄	—	2	1	no	—
535	C₂×C₃×C₄	—	2	1	no	—
536	C₂×C₃×C₄	—	10	1	no	—
537	C₂×C₃×C₄	—	20	2	no	—
538	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
539	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
540	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
541	#67	—	10	4	no	—
542	C₂×Dic₃	—	2	1	no	—
543	C₂×Dic₃	—	10	1	no	—
544	C₂×Dic₃	—	20	2	no	—
545	C₂×Dic₃	C₂×C₂²⋊D₅	1	1	yes	characteristic
546	C₂×Dic₃	C₂×C₂²⋊D₅	1	1	yes	characteristic
547	C₂×Dic₃	C₂×C₂²⋊D₅	1	1	yes	characteristic
548	D₁₂	—	2	4	no	—
549	D₁₂	—	2	1	no	—
550	D₁₂	—	5	2	no	—
551	D₁₂	—	10	1	no	—
552	D₁₂	C₂×C₄×D₅	1	2	yes	complemented
553	C₄×D₃	—	2	2	no	—
554	C₄×D₃	—	2	4	no	—
555	C₄×D₃	—	4	1	no	—
556	C₄×D₃	—	4	2	no	—
557	C₄×D₃	—	4	2	no	—
558	C₄×D₃	—	20	2	no	—
559	C₄×D₃	—	20	2	no	—
560	C₄×D₃	—	20	2	no	—
561	C₄×D₃	C₂×C₄×D₅	1	2	yes	—
562	C₄×D₃	#709	1	2	yes	—
563	C₃×C₈	—	5	2	no	—
564	C₃×C₈	—	10	1	no	—
565	C₃⋊C₈	—	5	2	no	—
566	C₃⋊C₈	—	10	1	no	—
567	C₂²×C₅	—	3	2	no	—
568	C₂²×C₅	—	6	1	no	—
569	C₂²×C₅	—	6	1	no	—
570	C₂²×C₅	—	6	2	no	—
571	C₂²×C₅	—	12	1	no	—
572	C₂²×C₅	—	12	1	no	—
573	C₂²×C₅	C₂×D₃×D₄	1	1	yes	characteristic
574	C₂×D₅	—	2	2	no	—
575	C₂×D₅	—	4	1	no	—
576	C₂×D₅	—	4	1	no	—
577	C₂×D₅	—	6	2	no	—
578	C₂×D₅	—	12	8	no	—
579	C₂×D₅	—	12	1	no	—
580	C₂×D₅	—	12	1	no	—
581	C₄×C₅	—	2	1	no	—
582	C₄×C₅	—	2	2	no	—
583	C₄×C₅	—	3	2	no	—
584	C₄×C₅	—	4	1	no	—
585	C₄×C₅	—	6	1	no	—
586	C₄×C₅	—	6	1	no	—
587	C₄×C₅	—	12	1	no	—
588	C₄×C₅	#914	1	2	yes	complemented
589	C₄×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
590	C₄×C₅	D₃×#41	1	1	yes	characteristic
591	Dic₅	—	4	1	no	—
592	Dic₅	—	12	1	no	—
593	C₂⁴	—	30	1	no	—
594	#41	—	3	4	no	—
595	#41	—	6	2	no	—
596	C₂×Q₈	C₂×D₃×D₅	1	1	yes	characteristic
597	C₂×D₄	—	3	1	no	—
598	C₂×D₄	—	5	1	no	—
599	C₂×D₄	—	6	1	no	—
600	C₂×D₄	—	15	4	no	—
601	C₂×D₄	—	15	1	no	—
602	C₂×D₄	—	30	2	no	—
603	C₂×D₄	—	30	1	no	—
604	C₂²×C₄	—	3	1	no	—
605	C₂²×C₄	—	3	1	no	—
606	C₂²×C₄	—	3	1	no	—
607	C₂²×C₄	—	6	1	no	—
608	C₂²×C₄	—	6	1	no	—
609	C₂²×C₄	—	6	1	no	—
610	C₂²×C₄	—	10	1	no	—
611	C₂²×C₄	—	30	1	no	—
612	C₂²×C₄	—	30	1	no	—
613	C₂²×C₄	—	30	1	no	—
614	C₂²×C₄	—	30	1	no	—
615	C₂²×C₄	—	60	4	no	—
616	SD₁₆	—	5	4	no	—
617	SD₁₆	—	15	4	no	—
618	D₈	—	15	4	no	—
619	D₈	—	15	4	no	—
620	M₁₆	—	15	4	no	—
621	M₁₆	—	30	2	no	—
622	C₂×C₈	—	5	1	no	—
623	C₂×C₈	—	5	1	no	—
624	C₂×C₈	—	15	1	no	—
625	C₂×C₈	—	15	1	no	—
626	C₄⋊C₄	—	2	1	no	—
627	C₄⋊C₄	—	3	1	no	—
628	C₄⋊C₄	—	5	1	no	—
629	C₄⋊C₄	—	6	1	no	—
630	C₄⋊C₄	—	15	1	no	—
631	C₄⋊C₄	—	30	1	no	—
632	C₄⋊C₄	C₂×D₃×D₅	1	1	yes	characteristic
633	C₂²⋊C₄	—	6	1	no	—
634	C₂²⋊C₄	—	6	1	no	—
635	C₂²⋊C₄	—	6	1	no	—
636	C₂²⋊C₄	—	10	1	no	—
637	C₂²⋊C₄	—	30	1	no	—
638	C₂²⋊C₄	—	30	1	no	—
639	C₂²⋊C₄	—	30	1	no	—
640	C₄²	—	2	1	no	—
641	C₄²	—	3	1	no	—
642	C₄²	—	3	1	no	—
643	C₄²	—	3	1	no	—
644	C₄²	—	6	1	no	—
645	C₄²	—	6	1	no	—
646	C₄²	C₂×D₃×D₅	1	1	yes	characteristic
647	C₃×C₅	C₄×AGL(1,ℤ/8)	1	1	yes	characteristic, complemented, Hall
648	C₂²×C₃	—	10	2	no	—
649	C₂²×C₃	—	20	1	no	—
650	C₂²×C₃	—	20	1	no	—
651	C₂²×C₃	C₂²×C₂²⋊D₅	1	1	yes	characteristic
652	C₂×D₃	—	2	1	no	—
653	C₂×D₃	—	2	1	no	—
654	C₂×D₃	—	2	2	no	—
655	C₂×D₃	—	4	1	no	—
656	C₂×D₃	—	4	1	no	—
657	C₂×D₃	—	10	2	no	—
658	C₂×D₃	—	20	8	no	—
659	C₂×D₃	—	20	1	no	—
660	C₂×D₃	—	20	1	no	—
661	C₂×D₃	C₄×C₂²⋊D₅	1	2	yes	—
662	C₃×C₄	—	2	2	no	—
663	C₃×C₄	—	2	1	no	—
664	C₃×C₄	—	4	1	no	—
665	C₃×C₄	—	20	1	no	—
666	C₃×C₄	#4095	1	2	yes	complemented
667	C₃×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
668	C₃×C₄	C₂×#709	1	1	yes	characteristic
669	Dic₃	—	2	1	no	—
670	Dic₃	—	2	1	no	—
671	Dic₃	—	4	1	no	—
672	Dic₃	—	20	1	no	—
673	Dic₃	C₄×C₂²⋊D₅	1	2	yes	—
674	C₂×C₅	—	6	2	no	—
675	C₂×C₅	—	12	2	no	—
676	C₂×C₅	C₄×D₃×D₄	1	1	yes	characteristic
677	C₂×C₅	C₂×#914	1	1	yes	characteristic
678	C₂×C₅	#5768	1	1	yes	characteristic
679	D₅	—	4	2	no	—
680	D₅	—	12	2	no	—
681	C₂³	—	3	1	no	—
682	C₂³	—	6	1	no	—
683	C₂³	—	10	1	no	—
684	C₂³	—	30	4	no	—
685	C₂³	—	30	1	no	—
686	C₂³	—	60	2	no	—
687	C₂³	—	60	2	no	—
688	Q₈	—	2	1	no	—
689	Q₈	C₄×D₃×D₅	1	2	yes	complemented
690	D₄	—	3	2	no	—
691	D₄	—	5	2	no	—
692	D₄	—	6	4	no	—
693	D₄	—	6	1	no	—
694	D₄	—	10	1	no	—
695	D₄	—	15	2	no	—
696	D₄	—	30	4	no	—
697	D₄	—	30	1	no	—
698	C₂×C₄	—	2	1	no	—
699	C₂×C₄	—	2	1	no	—
700	C₂×C₄	—	3	1	no	—
701	C₂×C₄	—	3	2	no	—
702	C₂×C₄	—	3	2	no	—
703	C₂×C₄	—	3	1	no	—
704	C₂×C₄	—	3	1	no	—
705	C₂×C₄	—	6	4	no	—
706	C₂×C₄	—	6	2	no	—
707	C₂×C₄	—	6	1	no	—
708	C₂×C₄	—	10	1	no	—
709	C₂×C₄	—	12	1	no	—
710	C₂×C₄	—	12	2	no	—
711	C₂×C₄	—	12	2	no	—
712	C₂×C₄	—	20	2	no	—
713	C₂×C₄	—	30	1	no	—
714	C₂×C₄	—	60	2	no	—
715	C₂×C₄	—	60	2	no	—
716	C₂×C₄	—	60	2	no	—
717	C₂×C₄	—	60	2	no	—
718	C₂×C₄	D₃×C₂²⋊D₅	1	1	yes	characteristic
719	C₂×C₄	D₃×C₂²⋊D₅	1	1	yes	characteristic
720	C₂×C₄	C₂²×D₃×D₅	1	1	yes	characteristic
721	C₈	—	5	2	no	—
722	C₈	—	10	1	no	—
723	C₈	—	15	2	no	—
724	C₈	—	30	1	no	—
725	C₂×C₃	—	20	2	no	—
726	C₂×C₃	C₂×C₄×C₂²⋊D₅	1	1	yes	characteristic
727	C₂×C₃	C₂×#4095	1	1	yes	characteristic
728	C₂×C₃	#66156	1	1	yes	characteristic
729	D₃	—	2	2	no	—
730	D₃	—	4	2	no	—
731	D₃	—	20	2	no	—
732	C₅	C₄×#914	1	1	yes	characteristic, complemented, Sylow
733	C₂²	—	3	2	no	—
734	C₂²	—	6	1	no	—
735	C₂²	—	6	1	no	—
736	C₂²	—	6	2	no	—
737	C₂²	—	10	2	no	—
738	C₂²	—	12	1	no	—
739	C₂²	—	12	1	no	—
740	C₂²	—	20	1	no	—
741	C₂²	—	20	1	no	—
742	C₂²	—	30	2	no	—
743	C₂²	—	60	8	no	—
744	C₂²	—	60	1	no	—
745	C₂²	—	60	1	no	—
746	C₂²	C₂×D₃×C₂²⋊D₅	1	1	yes	characteristic
747	C₄	—	2	1	no	—
748	C₄	—	2	2	no	—
749	C₄	—	3	2	no	—
750	C₄	—	4	1	no	—
751	C₄	—	6	1	no	—
752	C₄	—	6	1	no	—
753	C₄	—	12	1	no	—
754	C₄	—	20	1	no	—
755	C₄	—	60	1	no	—
756	C₄	#91504	1	2	yes	direct product factor
757	C₄	C₂×C₄×D₃×D₅	1	1	yes	characteristic
758	C₄	D₃×#709	1	1	yes	characteristic
759	C₃	C₄×#4095	1	1	yes	characteristic, complemented, Sylow
760	C₂	—	6	2	no	—
761	C₂	—	12	2	no	—
762	C₂	—	20	2	no	—
763	C₂	—	60	2	no	—
764	C₂	C₄×D₃×C₂²⋊D₅	1	1	yes	characteristic
765	C₂	C₂×#91504	1	1	yes	characteristic
766	C₂	#11755322	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	D₃×C₂²⋊D₅
commutator	C₃×C₄×C₅	C₂³×C₄
Frattini	C₂×C₄	C₂²×D₃×D₅
Fitting	C₃×C₄×C₅×Q₈	C₂²
socle	C₂²×C₃×C₅	C₂²×D₄
prime radical	C₂×#91504	C₂
cosocle	C₂×C₃×C₄×C₅	C₂⁴
hypercenter	C₄×Q₈	D₃×D₅
hypocenter	C₃×C₅	C₄×AGL(1,ℤ/8)
LCS	G ▷ C₃×C₄×C₅ ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂×C₄ ◁ C₄² ◁ C₄×Q₈

Complements

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

N	H ≅ G/N	type
1. C₄×C₅×#239	C₂	semidirect
3. C₄×D₃×D₂₀	C₂	semidirect
4. C₄×#6717	C₂	semidirect
5. C₃×C₄×#688	C₂	semidirect
6. #11749235	C₂	semidirect
7. #11749234	C₂	semidirect
8. #11749201	C₂	semidirect
9. #11747477	C₂	semidirect
10. #11747470	C₂	semidirect
11. #11747220	C₂	semidirect
12. #11747191	C₂	semidirect
13. C₄×#6654	C₂	semidirect
14. C₄×#6652	C₂	semidirect
15. C₄×#6650	C₂	semidirect
20. C₃×C₄×C₅×Q₈	C₂²	semidirect
23. C₅×Q₈×Dic₃	C₂²	semidirect
25. C₅×#893	C₂²	semidirect
29. C₄×C₅×D₁₂	C₂²	semidirect
34. #91504	C₄	direct (N × H)
45. #91119	C₂²	semidirect
47. #91092	C₂²	semidirect
48. C₄×C₃⋊#168	C₂²	semidirect
49. C₃×#3967	C₂²	semidirect
51. C₃×#3940	C₂²	semidirect
52. C₃×C₄×#168	C₂²	semidirect
53. #90989	C₂²	semidirect
54. #90988	C₂²	semidirect
56. #90967	C₂²	semidirect
57. #90966	C₂²	semidirect
59. #90953	C₂²	semidirect
60. #90953	C₂²	semidirect
69. C₄×#688	D₃	semidirect
82. C₅×#239	C₂×C₄	semidirect
98. D₃×D₂₀	C₂×C₄	semidirect
104. #6717	C₂×C₄	semidirect
119. C₃×#688	C₂×C₄	semidirect
127. #6654	C₂×C₄	semidirect
128. #6652	C₂×C₄	semidirect
130. #6650	C₂×C₄	semidirect
132. C₄×#239	D₅	semidirect
150. C₄×C₅×Q₈	C₂×D₃	semidirect
175. #3967	C₂×D₃	semidirect
183. #3940	C₂×D₃	semidirect
189. C₄×#168	C₂×D₃	semidirect
199. C₃×C₅×Q₈	C₂²×C₄	semidirect
215. C₅×D₁₂	C₂²×C₄	semidirect
232. C₃⋊#168	C₂²×C₄	semidirect
234. C₃×#168	C₂²×C₄	semidirect
239. C₃×C₄×Q₈	C₂×D₅	semidirect
241. Q₈×Dic₃	C₂×D₅	semidirect
252. #893	C₂×D₅	semidirect
260. C₄×D₁₂	C₂×D₅	semidirect
317. #688	C₄×D₃	semidirect
365. C₃×C₄×C₅	AGL(1,ℤ/8)	semidirect
381. #239	C₄×D₅	semidirect
436. C₅×Q₈	C₂×C₄×D₃	semidirect
471. #168	C₂×C₄×D₃	semidirect
483. C₄×Q₈	D₃×D₅	semidirect
531. C₃×Q₈	C₂×C₄×D₅	semidirect
552. D₁₂	C₂×C₄×D₅	semidirect
588. C₄×C₅	#914	semidirect
647. C₃×C₅	C₄×AGL(1,ℤ/8)	semidirect
666. C₃×C₄	#4095	semidirect
689. Q₈	C₄×D₃×D₅	semidirect
732. C₅	C₄×#914	semidirect
756. C₄	#91504	direct (N × H)
759. C₃	C₄×#4095	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
C₂×#91504	2
C₄×D₃×D₂₀	2
C₄×#6717	2
C₃×C₄×#688	2
#11749235	2
#11749234	2
#11749201	2
#11747477	2
#11747470	2
#11747220	2
#11747191	2
C₄×#6654	2
C₄×#6652	2
C₄×#6650	2
C₄×#4095	3
C₄×#914	5

Subgroups — C4×#91504 #14416716

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#91504 #14416716