Subgroups — C₄×#91305 #14416730

Order 1920.

1096 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×D₆₀	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄×C₅×#235	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#91305	C₂	1	1	yes	maximal, characteristic
4	C₃×C₄×#681	C₂	1	1	yes	maximal, characteristic, complemented
5	#11748460	C₂	1	1	yes	maximal, characteristic, complemented
6	#11748396	C₂	1	1	yes	maximal, characteristic, complemented
7	#11748390	C₂	1	1	yes	maximal, characteristic, complemented
8	#11747058	C₂	1	2	yes	maximal, complemented
9	C₄×#6660	C₂	1	2	yes	maximal, complemented
10	#11747025	C₂	1	2	yes	maximal, complemented
11	C₄×#6654	C₂	1	2	yes	maximal, complemented
12	C₄×#4095	—	3	1	no	maximal, Hall
13	C₂²×D₆₀	C₂²	1	1	yes	characteristic
14	C₂²×C₄×D₁₅	—	2	1	no	—
15	C₂×C₅×#235	C₂²	1	1	yes	characteristic
16	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
17	C₂×#6714	—	2	1	no	—
18	C₂×C₄⋊Dic₁₅	C₂²	1	1	yes	characteristic
19	C₄×D₆₀	—	2	1	no	—
20	C₄×D₆₀	—	2	1	no	—
21	C₄×D₆₀	C₂²	1	2	yes	—
22	C₄×D₆₀	C₂²	1	2	yes	—
23	C₄×C₅×#67	—	2	1	no	—
24	C₄×C₅×#67	—	2	1	no	—
25	C₅×#926	C₂²	1	1	yes	characteristic
26	C₄×C₅×D₁₂	C₂²	1	1	yes	characteristic, complemented
27	C₄×C₅×D₁₂	C₂²	1	1	yes	characteristic, complemented
28	C₅×#872	—	2	1	no	—
29	C₄²×C₅×D₃	—	2	1	no	—
30	C₄×C₅×Dic₆	C₂²	1	1	yes	characteristic, complemented
31	C₄×C₅×Dic₆	C₂²	1	1	yes	characteristic, complemented
32	C₂×C₃×#681	C₂²	1	1	yes	characteristic
33	C₂×C₃×#681	C₂²	1	1	yes	characteristic
34	C₂×#6660	C₂²	1	2	yes	—
35	#91305	C₄	1	8	yes	direct product factor
36	C₂×#6654	C₂²	1	2	yes	—
37	C₃×#3935	C₂²	1	2	yes	complemented
38	C₃×C₄×#168	C₂²	1	2	yes	complemented
39	#90988	C₂²	1	2	yes	complemented
40	#90985	C₂²	1	2	yes	complemented
41	#90973	C₂²	1	2	yes	complemented
42	#90969	C₂²	1	2	yes	—
43	#90969	C₂²	1	2	yes	—
44	#90967	C₂²	1	2	yes	complemented
45	C₄×#908	—	5	1	no	maximal, Hall
46	C₄×C₅×#41	—	3	1	no	—
47	C₂×#4095	—	3	1	no	—
48	C₂×C₄×D₂₀	—	3	1	no	—
49	#65521	—	3	1	no	—
50	#65315	—	3	2	no	—
51	C₄×#688	—	3	2	no	—
52	#65303	—	3	2	no	—
53	C₄×#686	—	3	2	no	—
54	#65290	—	3	1	no	—
55	#65284	—	3	1	no	—
56	C₄×#681	D₃	1	1	yes	characteristic, complemented
57	C₂³×D₁₅	—	2	1	no	—
58	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
59	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
60	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
61	C₂²×Dic₁₅	—	2	1	no	—
62	C₂×D₆₀	—	2	1	no	—
63	C₂×D₆₀	—	2	2	no	—
64	C₂×D₆₀	C₂×C₄	1	4	yes	complemented
65	C₂×D₆₀	C₂³	1	2	yes	—
66	C₂×C₄×D₁₅	—	2	2	no	—
67	C₂×C₄×D₁₅	—	2	2	no	—
68	C₂×C₄×D₁₅	—	4	4	no	—
69	C₂×C₅×#67	—	2	1	no	—
70	C₅×#235	—	2	2	no	—
71	C₅×#235	C₂×C₄	1	4	yes	complemented
72	C₂×C₅×D₁₂	C₂³	1	1	yes	characteristic
73	C₂×C₄×C₅×D₃	—	2	1	no	—
74	C₂×C₄×C₅×D₃	—	2	1	no	—
75	C₂×C₄×C₅×D₃	—	2	1	no	—
76	C₂×C₅×Dic₆	C₂³	1	1	yes	characteristic
77	C₃×C₄²×C₅	D₄	1	1	yes	characteristic
78	C₃×C₄²×C₅	D₄	1	1	yes	characteristic
79	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
80	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
81	#6714	—	2	2	no	—
82	#6714	—	2	2	no	—
83	C₄⋊Dic₁₅	—	2	1	no	—
84	C₄⋊Dic₁₅	C₂³	1	2	yes	—
85	C₅×#217	—	2	1	no	—
86	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
87	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
88	C₅×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
89	C₅×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
90	C₅×Dic₃⋊C₄	—	2	1	no	—
91	C₅×Dic₃⋊C₄	—	2	1	no	—
92	C₄×C₅×Dic₃	—	2	1	no	—
93	C₄×C₅×Dic₃	—	2	1	no	—
94	C₄×C₅×Dic₃	—	2	1	no	—
95	C₃×#681	—	2	2	no	—
96	C₃×#681	C₂×C₄	1	4	yes	complemented
97	C₂×C₃×#168	C₂³	1	2	yes	—
98	C₂×C₃×#168	C₂³	1	2	yes	—
99	#6660	C₂×C₄	1	8	yes	complemented
100	#6654	C₂×C₄	1	8	yes	complemented
101	C₂×#908	—	5	1	no	—
102	C₄×#235	D₅	1	1	yes	characteristic, complemented
103	C₂×C₄×D₁₂	—	5	1	no	—
104	C₃×C₄×M₁₆	—	5	1	no	—
105	#5133	—	5	1	no	—
106	#5131	—	5	1	no	—
107	#5121	—	5	1	no	—
108	#4711	—	5	2	no	—
109	#4710	—	5	2	no	—
110	C₄×D₂₄	—	5	2	no	—
111	C₄×#204	—	5	2	no	—
112	C₂×C₅×#41	—	3	1	no	—
113	C₂²×D₂₀	—	3	1	no	—
114	C₂²×C₄×D₅	—	6	1	no	—
115	C₄×C₅×Q₈	—	3	1	no	—
116	C₄×C₅×Q₈	—	3	1	no	—
117	C₄×C₅×D₄	—	3	1	no	—
118	C₄×C₅×D₄	—	3	1	no	—
119	C₄×C₅×D₄	—	6	1	no	—
120	C₄×C₅×D₄	—	6	1	no	—
121	C₅×#117	—	3	1	no	—
122	C₅×#117	—	6	1	no	—
123	C₂×C₄²×C₅	—	6	1	no	—
124	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
125	#4095	—	3	8	no	—
126	C₂×#688	—	3	2	no	—
127	C₂×#686	—	3	2	no	—
128	C₂×#685	—	6	1	no	—
129	C₂×C₄⋊Dic₅	—	3	1	no	—
130	C₂×#681	C₂×D₃	1	1	yes	characteristic
131	C₂×#681	C₂×D₃	1	1	yes	characteristic
132	C₄×D₂₀	—	3	2	no	—
133	C₄×D₂₀	—	3	2	no	—
134	C₄×D₂₀	—	6	1	no	—
135	C₄×D₂₀	—	6	1	no	—
136	#3967	—	3	2	no	—
137	#3964	—	3	2	no	—
138	#3941	—	3	2	no	—
139	#3941	—	3	2	no	—
140	#3940	—	3	2	no	—
141	#3939	—	3	2	no	—
142	#3935	C₂×D₃	1	2	yes	complemented
143	C₄×#168	C₂×D₃	1	2	yes	complemented
144	C₄×AGL(1,ℤ/8)	—	15	1	no	Sylow
145	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
146	C₂²×D₁₅	—	2	4	no	—
147	C₂²×D₁₅	—	2	2	no	—
148	C₂²×D₁₅	—	4	2	no	—
149	C₂²×D₁₅	—	4	2	no	—
150	C₂²×C₅×D₃	—	2	1	no	—
151	C₂×C₃×C₄×C₅	—	2	2	no	—
152	C₂×C₃×C₄×C₅	—	4	1	no	—
153	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
154	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
155	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
156	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
157	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
158	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
159	C₂×C₃×C₄×C₅	#41	1	2	yes	—
160	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
161	C₂×Dic₁₅	—	2	2	no	—
162	C₂×Dic₁₅	—	4	2	no	—
163	D₆₀	—	2	4	no	—
164	D₆₀	—	2	2	no	—
165	D₆₀	C₂²×C₄	1	4	yes	—
166	C₄×D₁₅	—	4	4	no	—
167	C₄×D₁₅	—	4	4	no	—
168	C₅×#67	—	2	4	no	—
169	C₂×C₅×Dic₃	—	2	1	no	—
170	C₂×C₅×Dic₃	—	2	1	no	—
171	C₂×C₅×Dic₃	—	2	1	no	—
172	C₅×D₁₂	—	2	1	no	—
173	C₅×D₁₂	C₂²×C₄	1	2	yes	complemented
174	C₄×C₅×D₃	—	2	4	no	—
175	C₄×C₅×D₃	—	4	2	no	—
176	C₄×C₅×D₃	—	4	2	no	—
177	C₅×Dic₆	—	2	1	no	—
178	C₅×Dic₆	C₂²×C₄	1	2	yes	complemented
179	C₃×#168	—	2	2	no	—
180	C₃×#168	C₂²×C₄	1	4	yes	complemented
181	C₂×#235	C₂×D₅	1	1	yes	characteristic
182	C₂²×D₁₂	—	5	1	no	—
183	C₂²×C₄×D₃	—	10	1	no	—
184	C₂×C₃×M₁₆	—	5	1	no	—
185	C₂×C₃×M₁₆	—	5	1	no	—
186	C₂×C₃×C₄²	C₂×D₅	1	1	yes	characteristic
187	C₄×#67	—	2	1	no	—
188	C₄×#67	—	2	1	no	—
189	C₂×(C₂×D₃)⋊C₄	—	10	1	no	—
190	#926	C₂×D₅	1	1	yes	characteristic
191	C₂×C₄⋊Dic₃	—	5	1	no	—
192	#908	—	5	8	no	—
193	C₂×D₂₄	—	5	2	no	—
194	C₂×#204	—	5	2	no	—
195	C₄×D₁₂	—	5	2	no	—
196	C₄×D₁₂	—	5	2	no	—
197	C₄×D₁₂	—	10	1	no	—
198	C₄×D₁₂	—	10	1	no	—
199	C₄×D₁₂	C₂×D₅	1	1	yes	characteristic, complemented
200	C₄×D₁₂	C₂×D₅	1	1	yes	characteristic, complemented
201	#872	—	2	1	no	—
202	C₄²×D₃	—	2	1	no	—
203	C₄×Dic₆	C₂×D₅	1	1	yes	characteristic, complemented
204	C₄×Dic₆	C₂×D₅	1	1	yes	characteristic, complemented
205	C₃×#97	—	5	2	no	—
206	C₃×C₄×C₈	—	5	2	no	—
207	#821	—	5	2	no	—
208	#821	—	5	2	no	—
209	#821	—	5	2	no	—
210	#818	—	5	2	no	—
211	#817	—	5	2	no	—
212	#816	—	5	2	no	—
213	C₂³×D₅	—	6	1	no	—
214	C₅×#41	—	3	4	no	—
215	C₅×#41	—	6	2	no	—
216	C₂×C₅×Q₈	—	3	1	no	—
217	C₂×C₅×D₄	—	3	1	no	—
218	C₂×C₅×D₄	—	6	1	no	—
219	C₂²×C₄×C₅	—	6	1	no	—
220	C₂²×C₄×C₅	—	6	1	no	—
221	C₂²×C₄×C₅	—	6	1	no	—
222	C₂²×C₄×C₅	D₁₂	1	1	yes	characteristic
223	C₂²×C₄×C₅	D₁₂	1	1	yes	characteristic
224	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
225	C₂²×Dic₅	—	6	1	no	—
226	C₂×D₂₀	—	3	4	no	—
227	C₂×D₂₀	—	3	2	no	—
228	C₂×D₂₀	—	6	1	no	—
229	C₂×D₂₀	—	6	2	no	—
230	C₂×C₄×D₅	—	6	2	no	—
231	C₂×C₄×D₅	—	6	2	no	—
232	C₂×C₄×D₅	—	12	4	no	—
233	C₅×C₄⋊C₄	—	3	1	no	—
234	C₅×C₄⋊C₄	—	3	1	no	—
235	C₅×C₄⋊C₄	—	6	1	no	—
236	C₅×C₄⋊C₄	—	6	1	no	—
237	C₅×C₂²⋊C₄	—	6	1	no	—
238	C₅×C₂²⋊C₄	—	6	1	no	—
239	C₅×C₂²⋊C₄	—	6	1	no	—
240	C₄²×C₅	—	6	1	no	—
241	C₄²×C₅	—	6	1	no	—
242	C₄²×C₅	—	6	1	no	—
243	C₄²×C₅	D₁₂	1	1	yes	characteristic
244	C₄²×C₅	D₁₂	1	1	yes	characteristic
245	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
246	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
247	#688	—	3	8	no	—
248	#686	—	3	8	no	—
249	#685	—	6	2	no	—
250	#685	—	6	2	no	—
251	C₄⋊Dic₅	—	3	2	no	—
252	C₄⋊Dic₅	—	6	1	no	—
253	#681	—	2	2	no	—
254	#681	C₄×D₃	1	4	yes	complemented
255	C₂×#168	C₂²×D₃	1	2	yes	—
256	C₂×#168	C₂²×D₃	1	2	yes	—
257	C₂×AGL(1,ℤ/8)	—	15	1	no	—
258	C₄×#41	—	3	1	no	—
259	C₂×C₄×D₄	—	15	1	no	—
260	#442	—	15	2	no	—
261	#440	—	15	2	no	—
262	C₄×SD₁₆	—	15	2	no	—
263	C₄×D₈	—	15	2	no	—
264	#428	—	15	1	no	—
265	#418	—	15	1	no	—
266	#417	—	15	1	no	—
267	C₄×M₁₆	—	5	1	no	—
268	C₂²×C₃×C₅	—	2	1	no	—
269	C₂²×C₃×C₅	—	2	1	no	—
270	C₂²×C₃×C₅	C₄×D₄	1	2	yes	—
271	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
272	C₂×D₁₅	—	2	4	no	—
273	C₂×D₁₅	—	4	8	no	—
274	C₂×D₁₅	—	4	2	no	—
275	C₂×D₁₅	—	4	2	no	—
276	C₂×C₅×D₃	—	2	2	no	—
277	C₂×C₅×D₃	—	4	1	no	—
278	C₂×C₅×D₃	—	4	1	no	—
279	C₃×C₄×C₅	—	2	1	no	—
280	C₃×C₄×C₅	—	2	1	no	—
281	C₃×C₄×C₅	—	2	1	no	—
282	C₃×C₄×C₅	C₄×D₄	1	2	yes	—
283	C₃×C₄×C₅	AGL(1,ℤ/8)	1	2	yes	complemented
284	C₃×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
285	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
286	Dic₁₅	—	4	2	no	—
287	C₅×Dic₃	—	2	2	no	—
288	C₅×Dic₃	—	4	1	no	—
289	C₅×Dic₃	—	4	1	no	—
290	C₂³×D₃	—	10	1	no	—
291	C₂²×C₃×C₄	C₂²⋊D₅	1	1	yes	characteristic
292	C₂²×C₃×C₄	C₂²⋊D₅	1	1	yes	characteristic
293	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
294	C₂×#67	—	2	1	no	—
295	C₂²×Dic₃	—	10	1	no	—
296	#235	—	2	2	no	—
297	#235	C₄×D₅	1	4	yes	complemented
298	C₂×D₁₂	—	5	4	no	—
299	C₂×D₁₂	—	5	2	no	—
300	C₂×D₁₂	—	10	2	no	—
301	C₂×D₁₂	—	10	1	no	—
302	C₂×D₁₂	C₂²×D₅	1	1	yes	characteristic
303	C₂×C₄×D₃	—	2	1	no	—
304	C₂×C₄×D₃	—	2	1	no	—
305	C₂×C₄×D₃	—	2	1	no	—
306	C₂×C₄×D₃	—	10	2	no	—
307	C₂×C₄×D₃	—	10	2	no	—
308	C₂×C₄×D₃	—	20	4	no	—
309	C₂×Dic₆	C₂²×D₅	1	1	yes	characteristic
310	C₃×M₁₆	—	5	4	no	—
311	C₃×M₁₆	—	10	2	no	—
312	C₂×C₃×C₈	—	5	2	no	—
313	C₂×C₃×C₈	—	5	2	no	—
314	C₃×C₄²	C₂²⋊D₅	1	1	yes	characteristic
315	C₃×C₄²	C₂²⋊D₅	1	1	yes	characteristic
316	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
317	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
318	#217	—	2	1	no	—
319	(C₂×D₃)⋊C₄	—	2	1	no	—
320	(C₂×D₃)⋊C₄	—	2	1	no	—
321	(C₂×D₃)⋊C₄	—	10	2	no	—
322	(C₂×D₃)⋊C₄	—	10	2	no	—
323	C₄⋊Dic₃	—	5	2	no	—
324	C₄⋊Dic₃	—	10	1	no	—
325	C₄⋊Dic₃	C₂²×D₅	1	1	yes	characteristic
326	C₄⋊Dic₃	C₂²×D₅	1	1	yes	characteristic
327	Dic₃⋊C₄	—	2	1	no	—
328	Dic₃⋊C₄	—	2	1	no	—
329	C₄×Dic₃	—	2	1	no	—
330	C₄×Dic₃	—	2	1	no	—
331	C₄×Dic₃	—	2	1	no	—
332	D₂₄	—	5	8	no	—
333	#204	—	5	8	no	—
334	C₂³×C₅	—	6	1	no	—
335	C₂³×C₅	C₂×D₁₂	1	1	yes	characteristic
336	C₂²×D₅	—	6	4	no	—
337	C₂²×D₅	—	6	2	no	—
338	C₂²×D₅	—	12	2	no	—
339	C₂²×D₅	—	12	2	no	—
340	C₅×Q₈	—	3	2	no	—
341	C₅×Q₈	—	6	1	no	—
342	C₅×D₄	—	3	2	no	—
343	C₅×D₄	—	6	4	no	—
344	C₅×D₄	—	6	1	no	—
345	C₂×C₄×C₅	—	2	2	no	—
346	C₂×C₄×C₅	—	4	1	no	—
347	C₂×C₄×C₅	—	6	1	no	—
348	C₂×C₄×C₅	—	6	4	no	—
349	C₂×C₄×C₅	—	6	1	no	—
350	C₂×C₄×C₅	—	6	1	no	—
351	C₂×C₄×C₅	—	12	2	no	—
352	C₂×C₄×C₅	—	12	2	no	—
353	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
354	C₂×C₄×C₅	C₂×D₁₂	1	1	yes	characteristic
355	C₂×C₄×C₅	C₂×D₁₂	1	1	yes	characteristic
356	C₂×C₄×C₅	C₂×D₁₂	1	1	yes	characteristic
357	C₂×C₄×C₅	C₂×D₁₂	1	1	yes	characteristic
358	C₂×C₄×C₅	C₂×D₁₂	1	1	yes	characteristic
359	C₂×C₄×C₅	#235	1	2	yes	—
360	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
361	C₂×Dic₅	—	6	2	no	—
362	C₂×Dic₅	—	12	2	no	—
363	D₂₀	—	3	4	no	—
364	D₂₀	—	6	4	no	—
365	D₂₀	—	6	2	no	—
366	C₄×D₅	—	12	4	no	—
367	C₄×D₅	—	12	4	no	—
368	#168	—	2	2	no	—
369	#168	C₂×C₄×D₃	1	4	yes	complemented
370	C₂×#41	—	3	1	no	—
371	C₂²×D₄	—	15	1	no	—
372	C₂³×C₄	—	30	1	no	—
373	AGL(1,ℤ/8)	—	15	8	no	—
374	C₂×SD₁₆	—	15	2	no	—
375	C₂×D₈	—	15	2	no	—
376	C₂×M₁₆	—	5	1	no	—
377	C₂×M₁₆	—	5	1	no	—
378	C₄×Q₈	—	3	1	no	—
379	C₄×Q₈	—	3	1	no	—
380	C₄×D₄	—	3	1	no	—
381	C₄×D₄	—	3	1	no	—
382	C₄×D₄	—	6	1	no	—
383	C₄×D₄	—	6	1	no	—
384	C₄×D₄	—	15	2	no	—
385	C₄×D₄	—	15	2	no	—
386	C₄×D₄	—	30	1	no	—
387	C₄×D₄	—	30	1	no	—
388	#117	—	3	1	no	—
389	#117	—	6	1	no	—
390	C₂×C₄⋊C₄	—	15	1	no	—
391	C₂×C₂²⋊C₄	—	30	1	no	—
392	C₂×C₄²	—	6	1	no	—
393	C₂×C₄²	D₃×D₅	1	1	yes	characteristic
394	#107	—	15	2	no	—
395	#106	—	15	2	no	—
396	#103	—	15	2	no	—
397	#102	—	15	2	no	—
398	#102	—	15	2	no	—
399	#102	—	15	2	no	—
400	#97	—	5	2	no	—
401	C₄×C₈	—	5	2	no	—
402	C₂×C₃×C₅	—	2	2	no	—
403	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
404	C₂×C₃×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
405	C₂×C₃×C₅	#575	1	1	yes	characteristic
406	D₁₅	—	4	4	no	—
407	C₅×D₃	—	4	2	no	—
408	C₂³×C₃	C₂×C₂²⋊D₅	1	1	yes	characteristic
409	C₂²×D₃	—	2	1	no	—
410	C₂²×D₃	—	10	2	no	—
411	C₂²×D₃	—	10	4	no	—
412	C₂²×D₃	—	20	2	no	—
413	C₂²×D₃	—	20	2	no	—
414	C₂×C₃×C₄	—	2	2	no	—
415	C₂×C₃×C₄	—	4	1	no	—
416	C₂×C₃×C₄	C₂×C₄×D₅	1	2	yes	—
417	C₂×C₃×C₄	#709	1	2	yes	—
418	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
419	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
420	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
421	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
422	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
423	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
424	#67	—	2	4	no	—
425	C₂×Dic₃	—	2	1	no	—
426	C₂×Dic₃	—	2	1	no	—
427	C₂×Dic₃	—	2	1	no	—
428	C₂×Dic₃	—	10	2	no	—
429	C₂×Dic₃	—	20	2	no	—
430	D₁₂	—	2	1	no	—
431	D₁₂	—	5	4	no	—
432	D₁₂	—	10	2	no	—
433	D₁₂	—	10	4	no	—
434	D₁₂	C₂×C₄×D₅	1	2	yes	complemented
435	C₄×D₃	—	2	4	no	—
436	C₄×D₃	—	4	2	no	—
437	C₄×D₃	—	4	2	no	—
438	C₄×D₃	—	20	4	no	—
439	C₄×D₃	—	20	4	no	—
440	Dic₆	—	2	1	no	—
441	Dic₆	C₂×C₄×D₅	1	2	yes	complemented
442	C₃×C₈	—	5	4	no	—
443	C₃×C₈	—	10	2	no	—
444	C₂²×C₅	—	2	1	no	—
445	C₂²×C₅	—	2	1	no	—
446	C₂²×C₅	—	6	2	no	—
447	C₂²×C₅	—	12	1	no	—
448	C₂²×C₅	—	12	1	no	—
449	C₂²×C₅	C₄×D₁₂	1	2	yes	—
450	C₂²×C₅	C₂²×D₁₂	1	1	yes	characteristic
451	C₂×D₅	—	6	4	no	—
452	C₂×D₅	—	12	8	no	—
453	C₂×D₅	—	12	2	no	—
454	C₂×D₅	—	12	2	no	—
455	C₄×C₅	—	2	1	no	—
456	C₄×C₅	—	2	1	no	—
457	C₄×C₅	—	2	1	no	—
458	C₄×C₅	—	6	2	no	—
459	C₄×C₅	—	12	1	no	—
460	C₄×C₅	—	12	1	no	—
461	C₄×C₅	C₄×D₁₂	1	2	yes	—
462	C₄×C₅	#908	1	2	yes	complemented
463	C₄×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
464	C₄×C₅	C₂×#235	1	1	yes	characteristic
465	Dic₅	—	12	2	no	—
466	C₂⁴	—	30	1	no	—
467	#41	—	3	4	no	—
468	#41	—	6	2	no	—
469	C₂×Q₈	—	3	1	no	—
470	C₂×D₄	—	3	1	no	—
471	C₂×D₄	—	6	1	no	—
472	C₂×D₄	—	15	4	no	—
473	C₂×D₄	—	15	2	no	—
474	C₂×D₄	—	30	2	no	—
475	C₂×D₄	—	30	1	no	—
476	C₂²×C₄	—	6	1	no	—
477	C₂²×C₄	—	6	1	no	—
478	C₂²×C₄	—	6	1	no	—
479	C₂²×C₄	—	30	1	no	—
480	C₂²×C₄	—	30	2	no	—
481	C₂²×C₄	—	30	2	no	—
482	C₂²×C₄	—	60	4	no	—
483	C₂²×C₄	#1203	1	1	yes	characteristic
484	C₂²×C₄	#1203	1	1	yes	characteristic
485	C₂²×C₄	C₂×D₃×D₅	1	1	yes	characteristic
486	SD₁₆	—	15	8	no	—
487	D₈	—	15	8	no	—
488	M₁₆	—	5	4	no	—
489	M₁₆	—	10	2	no	—
490	C₂×C₈	—	5	2	no	—
491	C₂×C₈	—	5	2	no	—
492	C₄⋊C₄	—	3	1	no	—
493	C₄⋊C₄	—	3	1	no	—
494	C₄⋊C₄	—	6	1	no	—
495	C₄⋊C₄	—	6	1	no	—
496	C₄⋊C₄	—	15	2	no	—
497	C₄⋊C₄	—	30	1	no	—
498	C₂²⋊C₄	—	6	1	no	—
499	C₂²⋊C₄	—	6	1	no	—
500	C₂²⋊C₄	—	6	1	no	—
501	C₂²⋊C₄	—	30	2	no	—
502	C₂²⋊C₄	—	30	2	no	—
503	C₄²	—	6	1	no	—
504	C₄²	—	6	1	no	—
505	C₄²	—	6	1	no	—
506	C₄²	#1203	1	1	yes	characteristic
507	C₄²	#1203	1	1	yes	characteristic
508	C₄²	C₂×D₃×D₅	1	1	yes	characteristic
509	C₄²	C₂×D₃×D₅	1	1	yes	characteristic
510	C₃×C₅	C₄×AGL(1,ℤ/8)	1	1	yes	characteristic, complemented, Hall
511	C₂²×C₃	—	2	1	no	—
512	C₂²×C₃	—	2	1	no	—
513	C₂²×C₃	C₄×C₂²⋊D₅	1	2	yes	—
514	C₂²×C₃	C₂²×C₂²⋊D₅	1	1	yes	characteristic
515	C₂×D₃	—	2	2	no	—
516	C₂×D₃	—	4	1	no	—
517	C₂×D₃	—	4	1	no	—
518	C₂×D₃	—	10	4	no	—
519	C₂×D₃	—	20	8	no	—
520	C₂×D₃	—	20	2	no	—
521	C₂×D₃	—	20	2	no	—
522	C₃×C₄	—	2	1	no	—
523	C₃×C₄	—	2	1	no	—
524	C₃×C₄	—	2	1	no	—
525	C₃×C₄	C₄×C₂²⋊D₅	1	2	yes	—
526	C₃×C₄	#4095	1	2	yes	complemented
527	C₃×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
528	C₃×C₄	C₂×#709	1	1	yes	characteristic
529	Dic₃	—	2	2	no	—
530	Dic₃	—	4	1	no	—
531	Dic₃	—	4	1	no	—
532	Dic₃	—	20	2	no	—
533	C₂×C₅	—	2	2	no	—
534	C₂×C₅	—	12	2	no	—
535	C₂×C₅	C₂×C₄×D₁₂	1	1	yes	characteristic
536	C₂×C₅	C₂×#908	1	1	yes	characteristic
537	C₂×C₅	#5748	1	1	yes	characteristic
538	D₅	—	12	4	no	—
539	C₂³	—	6	1	no	—
540	C₂³	—	30	4	no	—
541	C₂³	—	30	2	no	—
542	C₂³	—	60	2	no	—
543	C₂³	—	60	2	no	—
544	C₂³	C₂×#1203	1	1	yes	characteristic
545	Q₈	—	3	2	no	—
546	Q₈	—	6	1	no	—
547	D₄	—	3	2	no	—
548	D₄	—	6	4	no	—
549	D₄	—	6	1	no	—
550	D₄	—	15	4	no	—
551	D₄	—	30	4	no	—
552	D₄	—	30	2	no	—
553	C₂×C₄	—	2	2	no	—
554	C₂×C₄	—	4	1	no	—
555	C₂×C₄	—	6	1	no	—
556	C₂×C₄	—	6	4	no	—
557	C₂×C₄	—	6	1	no	—
558	C₂×C₄	—	6	1	no	—
559	C₂×C₄	—	12	2	no	—
560	C₂×C₄	—	12	2	no	—
561	C₂×C₄	—	30	2	no	—
562	C₂×C₄	—	60	4	no	—
563	C₂×C₄	—	60	2	no	—
564	C₂×C₄	—	60	4	no	—
565	C₂×C₄	#6771	1	2	yes	—
566	C₂×C₄	C₄×D₃×D₅	1	2	yes	—
567	C₂×C₄	C₂×#1203	1	1	yes	characteristic
568	C₂×C₄	C₂×#1203	1	1	yes	characteristic
569	C₂×C₄	C₂×#1203	1	1	yes	characteristic
570	C₂×C₄	C₂×#1203	1	1	yes	characteristic
571	C₂×C₄	C₂×#1203	1	1	yes	characteristic
572	C₂×C₄	C₂²×D₃×D₅	1	1	yes	characteristic
573	C₈	—	5	4	no	—
574	C₈	—	10	2	no	—
575	C₂×C₃	—	2	2	no	—
576	C₂×C₃	C₂×C₄×C₂²⋊D₅	1	1	yes	characteristic
577	C₂×C₃	C₂×#4095	1	1	yes	characteristic
578	C₂×C₃	#66156	1	1	yes	characteristic
579	D₃	—	4	2	no	—
580	D₃	—	20	4	no	—
581	C₅	C₄×#908	1	1	yes	characteristic, complemented, Sylow
582	C₂²	—	2	1	no	—
583	C₂²	—	2	1	no	—
584	C₂²	—	6	2	no	—
585	C₂²	—	12	1	no	—
586	C₂²	—	12	1	no	—
587	C₂²	—	30	4	no	—
588	C₂²	—	60	8	no	—
589	C₂²	—	60	2	no	—
590	C₂²	—	60	2	no	—
591	C₂²	C₄×#1203	1	2	yes	—
592	C₂²	C₂²×#1203	1	1	yes	characteristic
593	C₄	—	2	1	no	—
594	C₄	—	2	1	no	—
595	C₄	—	2	1	no	—
596	C₄	—	6	2	no	—
597	C₄	—	12	1	no	—
598	C₄	—	12	1	no	—
599	C₄	—	60	2	no	—
600	C₄	#91305	1	2	yes	direct product factor
601	C₄	C₄×#1203	1	2	yes	—
602	C₄	C₂×#6771	1	1	yes	characteristic
603	C₄	C₂×C₄×D₃×D₅	1	1	yes	characteristic
604	C₃	C₄×#4095	1	1	yes	characteristic, complemented, Sylow
605	C₂	—	2	2	no	—
606	C₂	—	12	2	no	—
607	C₂	—	60	4	no	—
608	C₂	C₂×#91305	1	1	yes	characteristic
609	C₂	#11754145	1	1	yes	characteristic
610	C₂	C₂×C₄×#1203	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×#1203
commutator	C₃×C₄×C₅	C₂³×C₄
Frattini	C₂×C₄	C₂²×D₃×D₅
Fitting	C₂×C₃×C₄²×C₅	C₂²
socle	C₂²×C₃×C₅	C₂²×D₄
prime radical	C₂×#91305	C₂
cosocle	C₂×C₃×C₄×C₅	C₂⁴
hypercenter	C₂×C₄²	D₃×D₅
hypocenter	C₃×C₅	C₄×AGL(1,ℤ/8)
LCS	G ▷ C₃×C₄×C₅ ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄²

Complements

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

N	H ≅ G/N	type
1. C₂×C₄×D₆₀	C₂	semidirect
2. C₄×C₅×#235	C₂	semidirect
4. C₃×C₄×#681	C₂	semidirect
5. #11748460	C₂	semidirect
6. #11748396	C₂	semidirect
7. #11748390	C₂	semidirect
8. #11747058	C₂	semidirect
9. C₄×#6660	C₂	semidirect
10. #11747025	C₂	semidirect
11. C₄×#6654	C₂	semidirect
26. C₄×C₅×D₁₂	C₂²	semidirect
27. C₄×C₅×D₁₂	C₂²	semidirect
30. C₄×C₅×Dic₆	C₂²	semidirect
31. C₄×C₅×Dic₆	C₂²	semidirect
35. #91305	C₄	direct (N × H)
37. C₃×#3935	C₂²	semidirect
38. C₃×C₄×#168	C₂²	semidirect
39. #90988	C₂²	semidirect
40. #90985	C₂²	semidirect
41. #90973	C₂²	semidirect
44. #90967	C₂²	semidirect
56. C₄×#681	D₃	semidirect
64. C₂×D₆₀	C₂×C₄	semidirect
71. C₅×#235	C₂×C₄	semidirect
96. C₃×#681	C₂×C₄	semidirect
99. #6660	C₂×C₄	semidirect
100. #6654	C₂×C₄	semidirect
102. C₄×#235	D₅	semidirect
142. #3935	C₂×D₃	semidirect
143. C₄×#168	C₂×D₃	semidirect
173. C₅×D₁₂	C₂²×C₄	semidirect
178. C₅×Dic₆	C₂²×C₄	semidirect
180. C₃×#168	C₂²×C₄	semidirect
199. C₄×D₁₂	C₂×D₅	semidirect
200. C₄×D₁₂	C₂×D₅	semidirect
203. C₄×Dic₆	C₂×D₅	semidirect
204. C₄×Dic₆	C₂×D₅	semidirect
254. #681	C₄×D₃	semidirect
283. C₃×C₄×C₅	AGL(1,ℤ/8)	semidirect
297. #235	C₄×D₅	semidirect
369. #168	C₂×C₄×D₃	semidirect
434. D₁₂	C₂×C₄×D₅	semidirect
441. Dic₆	C₂×C₄×D₅	semidirect
462. C₄×C₅	#908	semidirect
510. C₃×C₅	C₄×AGL(1,ℤ/8)	semidirect
526. C₃×C₄	#4095	semidirect
581. C₅	C₄×#908	semidirect
600. C₄	#91305	direct (N × H)
604. 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
C₂×C₄×D₆₀	2
C₄×C₅×#235	2
C₂×#91305	2
C₃×C₄×#681	2
#11748460	2
#11748396	2
#11748390	2
#11747058	2
C₄×#6660	2
#11747025	2
C₄×#6654	2
C₄×#4095	3
C₄×#908	5

Subgroups — C4×#91305 #14416730

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#91305 #14416730