Subgroups — #14419042

Order 1920.

824 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₅×#235	C₂	1	1	yes	maximal, characteristic
2	C₄×#6710	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#65214	C₂	1	1	yes	maximal, characteristic, complemented
4	#11748496	C₂	1	2	yes	maximal, complemented
5	#11748314	C₂	1	2	yes	maximal, complemented
6	C₄×#6650	C₂	1	1	yes	maximal, characteristic, complemented
7	#11746999	C₂	1	2	yes	maximal, complemented
8	C₄×D₃×#168	C₂	1	1	yes	maximal, characteristic, complemented
9	#11746876	C₂	1	1	yes	maximal, characteristic, complemented
10	#11746876	C₂	1	1	yes	maximal, characteristic, complemented
11	#11746858	C₂	1	2	yes	maximal, complemented
12	#10614248	—	3	1	no	maximal, Hall
13	C₂×C₅×#235	C₄	1	1	yes	characteristic
14	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
15	C₂×#6710	C₂²	1	2	yes	—
16	C₄×C₅×#67	C₄	1	1	yes	characteristic
17	C₄×C₅×#67	C₄	1	1	yes	characteristic
18	C₄×C₅×#67	C₂²	1	1	yes	characteristic
19	C₄×C₅×#67	C₂²	1	1	yes	characteristic
20	C₅×#926	C₄	1	1	yes	characteristic
21	C₄×C₅×D₁₂	C₄	1	1	yes	characteristic
22	C₄×C₅×D₁₂	C₂²	1	1	yes	characteristic
23	C₅×#872	C₄	1	1	yes	characteristic
24	C₅×#872	C₄	1	1	yes	characteristic
25	C₄²×C₅×D₃	C₂²	1	1	yes	characteristic
26	C₄²×C₅×D₃	C₂²	1	1	yes	characteristic
27	C₄×C₅×Dic₆	C₄	1	1	yes	characteristic
28	C₄×C₅×Dic₆	C₂²	1	1	yes	characteristic
29	C₂×#6650	C₂²	1	2	yes	—
30	C₂×D₃×#168	C₂²	1	2	yes	—
31	#91087	C₂²	1	2	yes	—
32	C₄×C₃⋊#168	C₂²	1	1	yes	characteristic
33	C₄×C₃⋊#168	C₂²	1	1	yes	characteristic
34	C₃×C₂²⋊#168	C₂²	1	2	yes	—
35	C₃×C₄⋊#168	C₂²	1	2	yes	—
36	C₃×C₄×#168	C₂²	1	1	yes	characteristic
37	C₃×C₄×#168	C₂²	1	1	yes	characteristic
38	Dic₃⋊#168	C₂²	1	2	yes	—
39	Dic₃⋊#168	C₂²	1	2	yes	—
40	(C₂×D₃)⋊#168	C₂²	1	2	yes	—
41	(C₂×D₃)⋊#168	C₂²	1	2	yes	—
42	#90953	C₂²	1	2	yes	—
43	Dic₃×#168	C₂²	1	2	yes	—
44	#79278	—	5	1	no	maximal, Hall
45	C₄×C₅×#41	—	3	1	no	—
46	#65313	—	3	2	no	—
47	#65301	—	3	2	no	—
48	#65300	—	3	2	no	—
49	#65300	—	3	2	no	—
50	#65214	—	3	1	no	—
51	#65214	—	3	1	no	—
52	#65214	D₃	1	1	yes	characteristic, complemented
53	C₄×#681	—	3	1	no	—
54	C₄×#681	—	3	1	no	—
55	C₂×C₄×#168	—	3	1	no	—
56	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
57	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
58	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
59	C₂×C₅×#67	C₂×C₄	1	1	yes	characteristic
60	C₂×C₅×#67	C₂×C₄	1	1	yes	characteristic
61	C₅×#235	—	2	4	no	—
62	C₂×C₅×D₁₂	C₂×C₄	1	1	yes	characteristic
63	C₂×C₄×C₅×D₃	C₂×C₄	1	1	yes	characteristic
64	C₂×C₄×C₅×D₃	C₂×C₄	1	1	yes	characteristic
65	C₂×C₄×C₅×D₃	C₂×C₄	1	1	yes	characteristic
66	C₂×C₄×C₅×D₃	C₂×C₄	1	1	yes	characteristic
67	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
68	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
69	C₂×C₅×Dic₆	C₂×C₄	1	1	yes	characteristic
70	C₃×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
71	C₃×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
72	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
73	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
74	#6710	—	2	4	no	—
75	C₂×C₃⋊#168	C₂³	1	2	yes	—
76	C₂×C₃⋊#168	C₂³	1	2	yes	—
77	C₅×#217	C₂×C₄	1	1	yes	characteristic
78	C₅×#217	C₂×C₄	1	1	yes	characteristic
79	C₅×(C₂×D₃)⋊C₄	C₂×C₄	1	1	yes	characteristic
80	C₅×(C₂×D₃)⋊C₄	C₂×C₄	1	1	yes	characteristic
81	C₅×(C₂×D₃)⋊C₄	C₂×C₄	1	1	yes	characteristic
82	C₅×(C₂×D₃)⋊C₄	C₂×C₄	1	1	yes	characteristic
83	C₅×C₄⋊Dic₃	C₂×C₄	1	1	yes	characteristic
84	C₅×C₄⋊Dic₃	C₂×C₄	1	1	yes	characteristic
85	C₅×Dic₃⋊C₄	C₂×C₄	1	1	yes	characteristic
86	C₅×Dic₃⋊C₄	C₂×C₄	1	1	yes	characteristic
87	C₅×Dic₃⋊C₄	C₂×C₄	1	1	yes	characteristic
88	C₅×Dic₃⋊C₄	C₂×C₄	1	1	yes	characteristic
89	C₄×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
90	C₄×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
91	C₄×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
92	C₄×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
93	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
94	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
95	C₂×C₃×#168	C₂³	1	2	yes	—
96	C₂×C₃×#168	C₂³	1	2	yes	—
97	#6650	—	2	4	no	—
98	D₃×#168	—	2	4	no	—
99	C₄×#235	D₅	1	1	yes	characteristic
100	C₃×#431	—	5	1	no	—
101	C₄×#208	—	5	1	no	—
102	#4836	—	5	2	no	—
103	#4828	—	5	2	no	—
104	#4729	—	5	2	no	—
105	#4728	—	5	2	no	—
106	C₄×ΓL(1,𝔽₂₅)	—	5	1	no	—
107	#4685	—	5	1	no	—
108	#4685	—	5	1	no	—
109	C₄×D₃×C₈	—	5	1	no	—
110	C₂×C₅×#41	—	3	1	no	—
111	C₄×C₅×Q₈	—	3	1	no	—
112	C₄×C₅×Q₈	—	3	1	no	—
113	C₄×C₅×D₄	—	3	1	no	—
114	C₄×C₅×D₄	—	3	1	no	—
115	C₄×C₅×D₄	—	3	1	no	—
116	C₄×C₅×D₄	—	3	1	no	—
117	C₄×C₅×D₄	—	3	1	no	—
118	C₄×C₅×D₄	—	3	1	no	—
119	C₅×#117	—	3	1	no	—
120	C₅×#117	—	3	1	no	—
121	C₅×#117	—	3	1	no	—
122	C₂×C₄²×C₅	—	3	1	no	—
123	C₂×C₄²×C₅	—	3	1	no	—
124	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
125	C₂×#681	—	3	2	no	—
126	C₂×#681	—	3	2	no	—
127	C₂²×#168	—	3	2	no	—
128	C₂²⋊#168	—	3	2	no	—
129	C₂²⋊#168	—	3	2	no	—
130	C₂²⋊#168	C₂×D₃	1	2	yes	—
131	C₄⋊#168	—	3	2	no	—
132	C₄⋊#168	—	3	2	no	—
133	C₄⋊#168	C₂×D₃	1	2	yes	—
134	#3935	—	3	2	no	—
135	#3935	—	3	2	no	—
136	C₄×#168	—	3	1	no	—
137	C₄×#168	—	3	1	no	—
138	C₄×#168	—	3	2	no	—
139	C₄×#168	C₂×D₃	1	1	yes	characteristic
140	C₄×#168	C₂×D₃	1	1	yes	characteristic
141	#2965	—	15	1	no	Sylow
142	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
143	C₂²×C₅×D₃	C₂²×C₄	1	1	yes	characteristic
144	C₂²×C₅×D₃	C₂²×C₄	1	1	yes	characteristic
145	C₂×C₃×C₄×C₅	—	2	2	no	—
146	C₂×C₃×C₄×C₅	—	2	2	no	—
147	C₂×C₃×C₄×C₅	—	2	2	no	—
148	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
149	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
150	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
151	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
152	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
153	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
154	C₅×#67	—	2	2	no	—
155	C₅×#67	—	2	2	no	—
156	C₂×C₅×Dic₃	C₂²×C₄	1	1	yes	characteristic
157	C₂×C₅×Dic₃	C₂²×C₄	1	1	yes	characteristic
158	C₂×C₅×Dic₃	C₂²×C₄	1	1	yes	characteristic
159	C₂×C₅×Dic₃	C₂²×C₄	1	1	yes	characteristic
160	C₂×C₅×Dic₃	C₂²×C₄	1	1	yes	characteristic
161	C₂×C₅×Dic₃	C₂²×C₄	1	1	yes	characteristic
162	C₅×D₁₂	—	2	2	no	—
163	C₄×C₅×D₃	—	2	2	no	—
164	C₄×C₅×D₃	—	2	2	no	—
165	C₄×C₅×D₃	—	2	2	no	—
166	C₄×C₅×D₃	—	2	2	no	—
167	C₄×C₅×D₃	—	2	2	no	—
168	C₄×C₅×D₃	M₁₆	1	4	yes	complemented
169	C₅×Dic₆	—	2	2	no	—
170	C₃⋊#168	—	2	2	no	—
171	C₃⋊#168	#41	1	4	yes	complemented
172	C₃×#168	—	2	2	no	—
173	C₃×#168	—	2	2	no	—
174	C₂×#235	Dic₅	1	1	yes	characteristic
175	C₂×C₃×C₄²	C₂×D₅	1	1	yes	characteristic
176	C₄×#67	Dic₅	1	1	yes	characteristic
177	C₄×#67	Dic₅	1	1	yes	characteristic
178	C₄×#67	C₂×D₅	1	1	yes	characteristic
179	C₄×#67	C₂×D₅	1	1	yes	characteristic
180	#926	Dic₅	1	1	yes	characteristic
181	C₂×#208	—	5	2	no	—
182	C₂×ΓL(1,𝔽₂₅)	—	5	2	no	—
183	C₂×D₃×C₈	—	5	2	no	—
184	C₄×D₁₂	Dic₅	1	1	yes	characteristic
185	C₄×D₁₂	C₂×D₅	1	1	yes	characteristic
186	#872	Dic₅	1	1	yes	characteristic
187	#872	Dic₅	1	1	yes	characteristic
188	C₄²×D₃	C₂×D₅	1	1	yes	characteristic
189	C₄²×D₃	C₂×D₅	1	1	yes	characteristic
190	C₄×Dic₆	Dic₅	1	1	yes	characteristic
191	C₄×Dic₆	C₂×D₅	1	1	yes	characteristic
192	C₃×C₄⋊C₈	—	5	2	no	—
193	C₃×C₂²⋊C₈	—	5	2	no	—
194	C₃×C₄×C₈	—	5	1	no	—
195	C₃×C₄×C₈	—	5	1	no	—
196	(C₂×D₃)⋊C₈	—	5	2	no	—
197	(C₂×D₃)⋊C₈	—	5	2	no	—
198	#815	—	5	2	no	—
199	Dic₃⋊C₈	—	5	2	no	—
200	Dic₃⋊C₈	—	5	2	no	—
201	C₈×Dic₃	—	5	2	no	—
202	#803	—	5	2	no	—
203	C₄×C₃⋊C₈	—	5	1	no	—
204	C₄×C₃⋊C₈	—	5	1	no	—
205	C₅×#41	—	6	4	no	—
206	C₂×C₅×Q₈	—	3	1	no	—
207	C₂×C₅×D₄	—	3	1	no	—
208	C₂×C₅×D₄	—	3	1	no	—
209	C₂×C₅×D₄	—	3	1	no	—
210	C₂²×C₄×C₅	—	3	1	no	—
211	C₂²×C₄×C₅	—	3	1	no	—
212	C₂²×C₄×C₅	—	3	1	no	—
213	C₂²×C₄×C₅	—	3	1	no	—
214	C₂²×C₄×C₅	—	3	1	no	—
215	C₂²×C₄×C₅	—	3	1	no	—
216	C₂²×C₄×C₅	C₄×D₃	1	1	yes	characteristic
217	C₂²×C₄×C₅	C₄×D₃	1	1	yes	characteristic
218	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
219	C₅×C₄⋊C₄	—	3	1	no	—
220	C₅×C₄⋊C₄	—	3	1	no	—
221	C₅×C₄⋊C₄	—	3	1	no	—
222	C₅×C₄⋊C₄	—	3	1	no	—
223	C₅×C₄⋊C₄	—	3	1	no	—
224	C₅×C₄⋊C₄	—	3	1	no	—
225	C₅×C₂²⋊C₄	—	3	1	no	—
226	C₅×C₂²⋊C₄	—	3	1	no	—
227	C₅×C₂²⋊C₄	—	3	1	no	—
228	C₅×C₂²⋊C₄	—	3	1	no	—
229	C₅×C₂²⋊C₄	—	3	1	no	—
230	C₅×C₂²⋊C₄	—	3	1	no	—
231	C₄²×C₅	—	3	1	no	—
232	C₄²×C₅	—	3	1	no	—
233	C₄²×C₅	—	3	1	no	—
234	C₄²×C₅	—	3	1	no	—
235	C₄²×C₅	—	3	1	no	—
236	C₄²×C₅	—	3	1	no	—
237	C₄²×C₅	C₄×D₃	1	1	yes	characteristic
238	C₄²×C₅	C₄×D₃	1	1	yes	characteristic
239	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
240	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
241	#681	—	6	4	no	—
242	#681	—	6	4	no	—
243	C₂×#168	—	3	2	no	—
244	C₂×#168	—	3	2	no	—
245	C₂×#168	—	6	4	no	—
246	C₂×#168	C₂²×D₃	1	2	yes	—
247	C₂×#168	C₂²×D₃	1	2	yes	—
248	C₄×#41	—	3	1	no	—
249	#446	—	15	2	no	—
250	#436	—	15	2	no	—
251	#435	—	15	2	no	—
252	#435	—	15	2	no	—
253	#431	—	5	1	no	—
254	#431	—	15	1	no	—
255	#431	—	15	1	no	—
256	C₄×M₁₆	—	15	1	no	—
257	C₄×M₁₆	—	15	1	no	—
258	C₂×C₄×C₈	—	15	1	no	—
259	C₂²×C₃×C₅	—	2	1	no	—
260	C₂²×C₃×C₅	—	2	1	no	—
261	C₂²×C₃×C₅	—	2	1	no	—
262	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
263	C₂×C₅×D₃	—	2	1	no	—
264	C₂×C₅×D₃	—	2	1	no	—
265	C₂×C₅×D₃	—	2	1	no	—
266	C₂×C₅×D₃	—	2	1	no	—
267	C₂×C₅×D₃	—	2	1	no	—
268	C₂×C₅×D₃	C₂×M₁₆	1	2	yes	—
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	C₂×M₁₆	1	2	yes	—
273	C₃×C₄×C₅	#131	1	2	yes	—
274	C₃×C₄×C₅	C₂×#41	1	2	yes	—
275	C₅×Dic₃	—	2	1	no	—
276	C₅×Dic₃	—	2	1	no	—
277	C₅×Dic₃	—	2	1	no	—
278	C₅×Dic₃	—	2	1	no	—
279	C₅×Dic₃	—	2	1	no	—
280	C₅×Dic₃	C₂×M₁₆	1	2	yes	—
281	C₂²×C₃×C₄	C₂×Dic₅	1	1	yes	characteristic
282	C₂²×C₃×C₄	C₂×Dic₅	1	1	yes	characteristic
283	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
284	C₂×#67	C₂×Dic₅	1	1	yes	characteristic
285	C₂×#67	C₂×Dic₅	1	1	yes	characteristic
286	#235	—	2	4	no	—
287	C₂×D₁₂	C₂×Dic₅	1	1	yes	characteristic
288	C₂×C₄×D₃	C₂×Dic₅	1	1	yes	characteristic
289	C₂×C₄×D₃	C₂×Dic₅	1	1	yes	characteristic
290	C₂×C₄×D₃	C₂×Dic₅	1	1	yes	characteristic
291	C₂×C₄×D₃	C₂×Dic₅	1	1	yes	characteristic
292	C₂×C₄×D₃	C₂²×D₅	1	1	yes	characteristic
293	C₂×C₄×D₃	C₂²×D₅	1	1	yes	characteristic
294	C₂×Dic₆	C₂×Dic₅	1	1	yes	characteristic
295	C₂×C₃×C₈	—	5	2	no	—
296	C₂×C₃×C₈	—	5	2	no	—
297	C₃×C₄²	C₂×Dic₅	1	1	yes	characteristic
298	C₃×C₄²	C₂×Dic₅	1	1	yes	characteristic
299	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
300	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
301	#217	C₂×Dic₅	1	1	yes	characteristic
302	#217	C₂×Dic₅	1	1	yes	characteristic
303	(C₂×D₃)⋊C₄	C₂×Dic₅	1	1	yes	characteristic
304	(C₂×D₃)⋊C₄	C₂×Dic₅	1	1	yes	characteristic
305	(C₂×D₃)⋊C₄	C₂×Dic₅	1	1	yes	characteristic
306	(C₂×D₃)⋊C₄	C₂×Dic₅	1	1	yes	characteristic
307	C₄⋊Dic₃	C₂×Dic₅	1	1	yes	characteristic
308	C₄⋊Dic₃	C₂×Dic₅	1	1	yes	characteristic
309	Dic₃⋊C₄	C₂×Dic₅	1	1	yes	characteristic
310	Dic₃⋊C₄	C₂×Dic₅	1	1	yes	characteristic
311	Dic₃⋊C₄	C₂×Dic₅	1	1	yes	characteristic
312	Dic₃⋊C₄	C₂×Dic₅	1	1	yes	characteristic
313	C₄×Dic₃	C₂×Dic₅	1	1	yes	characteristic
314	C₄×Dic₃	C₂×Dic₅	1	1	yes	characteristic
315	C₄×Dic₃	C₂×Dic₅	1	1	yes	characteristic
316	C₄×Dic₃	C₂×Dic₅	1	1	yes	characteristic
317	C₄×Dic₃	C₂²×D₅	1	1	yes	characteristic
318	C₄×Dic₃	C₂²×D₅	1	1	yes	characteristic
319	#208	—	10	4	no	—
320	C₂×C₃⋊C₈	—	5	2	no	—
321	C₂×C₃⋊C₈	—	5	2	no	—
322	ΓL(1,𝔽₂₅)	—	10	4	no	—
323	D₃×C₈	—	10	4	no	—
324	C₂³×C₅	—	3	1	no	—
325	C₂³×C₅	—	3	1	no	—
326	C₂³×C₅	C₂×C₄×D₃	1	1	yes	characteristic
327	C₅×Q₈	—	6	2	no	—
328	C₅×D₄	—	6	2	no	—
329	C₅×D₄	—	6	2	no	—
330	C₅×D₄	—	6	2	no	—
331	C₂×C₄×C₅	—	2	2	no	—
332	C₂×C₄×C₅	—	2	2	no	—
333	C₂×C₄×C₅	—	2	2	no	—
334	C₂×C₄×C₅	—	3	1	no	—
335	C₂×C₄×C₅	—	3	4	no	—
336	C₂×C₄×C₅	—	3	1	no	—
337	C₂×C₄×C₅	—	3	1	no	—
338	C₂×C₄×C₅	—	3	1	no	—
339	C₂×C₄×C₅	—	3	1	no	—
340	C₂×C₄×C₅	—	3	1	no	—
341	C₂×C₄×C₅	—	6	2	no	—
342	C₂×C₄×C₅	—	6	2	no	—
343	C₂×C₄×C₅	—	6	2	no	—
344	C₂×C₄×C₅	—	6	2	no	—
345	C₂×C₄×C₅	—	6	2	no	—
346	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
347	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
348	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
349	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
350	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
351	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
352	#168	—	2	2	no	—
353	#168	—	2	2	no	—
354	#168	—	3	4	no	—
355	#168	—	6	2	no	—
356	C₂×#41	—	3	1	no	—
357	C₂×M₁₆	—	15	2	no	—
358	C₂×M₁₆	—	15	2	no	—
359	C₂²×C₈	—	15	2	no	—
360	C₄×Q₈	—	3	1	no	—
361	C₄×Q₈	—	3	1	no	—
362	C₄×D₄	—	3	1	no	—
363	C₄×D₄	—	3	1	no	—
364	C₄×D₄	—	3	1	no	—
365	C₄×D₄	—	3	1	no	—
366	C₄×D₄	—	3	1	no	—
367	C₄×D₄	—	3	1	no	—
368	#117	—	3	1	no	—
369	#117	—	3	1	no	—
370	#117	—	3	1	no	—
371	C₂×C₄²	—	3	1	no	—
372	C₂×C₄²	—	3	1	no	—
373	C₂×C₄²	D₃×D₅	1	1	yes	characteristic
374	C₄⋊C₈	—	5	2	no	—
375	C₄⋊C₈	—	15	2	no	—
376	C₄⋊C₈	—	15	2	no	—
377	C₂²⋊C₈	—	5	2	no	—
378	C₂²⋊C₈	—	15	2	no	—
379	C₂²⋊C₈	—	15	2	no	—
380	#97	—	15	2	no	—
381	#97	—	15	2	no	—
382	C₄×C₈	—	5	1	no	—
383	C₄×C₈	—	5	1	no	—
384	C₄×C₈	—	15	2	no	—
385	C₄×C₈	—	15	1	no	—
386	C₄×C₈	—	15	1	no	—
387	C₂×C₃×C₅	—	4	1	no	—
388	C₂×C₃×C₅	C₄×#41	1	1	yes	characteristic
389	C₂×C₃×C₅	C₂²×M₁₆	1	1	yes	characteristic
390	C₂×C₃×C₅	C₂×#131	1	1	yes	characteristic
391	C₅×D₃	—	2	2	no	—
392	C₅×D₃	—	4	1	no	—
393	C₂³×C₃	C₂²×Dic₅	1	1	yes	characteristic
394	C₂²×D₃	C₂²×Dic₅	1	1	yes	characteristic
395	C₂²×D₃	C₂²×Dic₅	1	1	yes	characteristic
396	C₂×C₃×C₄	—	2	2	no	—
397	C₂×C₃×C₄	—	2	2	no	—
398	C₂×C₃×C₄	—	2	2	no	—
399	C₂×C₃×C₄	C₂²×Dic₅	1	1	yes	characteristic
400	C₂×C₃×C₄	C₂²×Dic₅	1	1	yes	characteristic
401	C₂×C₃×C₄	C₂²×Dic₅	1	1	yes	characteristic
402	C₂×C₃×C₄	C₂²×Dic₅	1	1	yes	characteristic
403	C₂×C₃×C₄	C₂²×Dic₅	1	1	yes	characteristic
404	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
405	#67	—	2	2	no	—
406	#67	—	2	2	no	—
407	C₂×Dic₃	C₂²×Dic₅	1	1	yes	characteristic
408	C₂×Dic₃	C₂²×Dic₅	1	1	yes	characteristic
409	C₂×Dic₃	C₂²×Dic₅	1	1	yes	characteristic
410	C₂×Dic₃	C₂²×Dic₅	1	1	yes	characteristic
411	C₂×Dic₃	C₂²×Dic₅	1	1	yes	characteristic
412	C₂×Dic₃	C₂²×Dic₅	1	1	yes	characteristic
413	D₁₂	—	2	2	no	—
414	C₄×D₃	—	2	2	no	—
415	C₄×D₃	—	2	2	no	—
416	C₄×D₃	—	2	2	no	—
417	C₄×D₃	—	2	2	no	—
418	C₄×D₃	—	2	2	no	—
419	C₄×D₃	#681	1	4	yes	complemented
420	Dic₆	—	2	2	no	—
421	C₃×C₈	—	10	2	no	—
422	C₃×C₈	—	10	2	no	—
423	C₃⋊C₈	—	5	4	no	—
424	C₃⋊C₈	—	10	2	no	—
425	C₂²×C₅	—	2	1	no	—
426	C₂²×C₅	—	2	1	no	—
427	C₂²×C₅	—	2	1	no	—
428	C₂²×C₅	—	3	2	no	—
429	C₂²×C₅	—	6	1	no	—
430	C₂²×C₅	—	6	1	no	—
431	C₂²×C₅	—	6	1	no	—
432	C₂²×C₅	—	6	1	no	—
433	C₂²×C₅	—	6	1	no	—
434	C₂²×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
435	C₄×C₅	—	2	1	no	—
436	C₄×C₅	—	2	1	no	—
437	C₄×C₅	—	2	1	no	—
438	C₄×C₅	—	3	2	no	—
439	C₄×C₅	—	6	1	no	—
440	C₄×C₅	—	6	1	no	—
441	C₄×C₅	—	6	1	no	—
442	C₄×C₅	—	6	1	no	—
443	C₄×C₅	—	6	1	no	—
444	C₄×C₅	#901	1	2	yes	—
445	C₄×C₅	D₃×M₁₆	1	2	yes	—
446	C₄×C₅	D₃×#41	1	2	yes	—
447	#41	—	6	4	no	—
448	C₂×Q₈	—	3	1	no	—
449	C₂×D₄	—	3	1	no	—
450	C₂×D₄	—	3	1	no	—
451	C₂×D₄	—	3	1	no	—
452	C₂²×C₄	—	3	1	no	—
453	C₂²×C₄	—	3	1	no	—
454	C₂²×C₄	—	3	1	no	—
455	C₂²×C₄	—	3	1	no	—
456	C₂²×C₄	—	3	1	no	—
457	C₂²×C₄	—	3	1	no	—
458	C₂²×C₄	D₃×Dic₅	1	1	yes	characteristic
459	C₂²×C₄	D₃×Dic₅	1	1	yes	characteristic
460	C₂²×C₄	C₂×D₃×D₅	1	1	yes	characteristic
461	M₁₆	—	30	4	no	—
462	M₁₆	—	30	4	no	—
463	C₂×C₈	—	5	2	no	—
464	C₂×C₈	—	5	2	no	—
465	C₂×C₈	—	15	2	no	—
466	C₂×C₈	—	15	2	no	—
467	C₂×C₈	—	30	4	no	—
468	C₄⋊C₄	—	3	1	no	—
469	C₄⋊C₄	—	3	1	no	—
470	C₄⋊C₄	—	3	1	no	—
471	C₄⋊C₄	—	3	1	no	—
472	C₄⋊C₄	—	3	1	no	—
473	C₄⋊C₄	—	3	1	no	—
474	C₂²⋊C₄	—	3	1	no	—
475	C₂²⋊C₄	—	3	1	no	—
476	C₂²⋊C₄	—	3	1	no	—
477	C₂²⋊C₄	—	3	1	no	—
478	C₂²⋊C₄	—	3	1	no	—
479	C₂²⋊C₄	—	3	1	no	—
480	C₄²	—	3	1	no	—
481	C₄²	—	3	1	no	—
482	C₄²	—	3	1	no	—
483	C₄²	—	3	1	no	—
484	C₄²	—	3	1	no	—
485	C₄²	—	3	1	no	—
486	C₄²	D₃×Dic₅	1	1	yes	characteristic
487	C₄²	D₃×Dic₅	1	1	yes	characteristic
488	C₄²	C₂×D₃×D₅	1	1	yes	characteristic
489	C₄²	C₂×D₃×D₅	1	1	yes	characteristic
490	C₃×C₅	#2965	1	1	yes	characteristic, complemented, Hall
491	C₂²×C₃	—	2	1	no	—
492	C₂²×C₃	—	2	1	no	—
493	C₂²×C₃	—	2	1	no	—
494	C₂²×C₃	C₂³×Dic₅	1	1	yes	characteristic
495	C₂×D₃	—	2	1	no	—
496	C₂×D₃	—	2	1	no	—
497	C₂×D₃	—	2	1	no	—
498	C₂×D₃	—	2	1	no	—
499	C₂×D₃	—	2	1	no	—
500	C₂×D₃	C₂×#681	1	2	yes	—
501	C₃×C₄	—	2	1	no	—
502	C₃×C₄	—	2	1	no	—
503	C₃×C₄	—	2	1	no	—
504	C₃×C₄	C₂×#681	1	2	yes	—
505	C₃×C₄	#4094	1	2	yes	—
506	C₃×C₄	D₅×#41	1	2	yes	—
507	Dic₃	—	2	1	no	—
508	Dic₃	—	2	1	no	—
509	Dic₃	—	2	1	no	—
510	Dic₃	—	2	1	no	—
511	Dic₃	—	2	1	no	—
512	Dic₃	C₂×#681	1	2	yes	—
513	C₂×C₅	—	4	1	no	—
514	C₂×C₅	—	6	2	no	—
515	C₂×C₅	—	12	1	no	—
516	C₂×C₅	#5522	1	1	yes	characteristic
517	C₂×C₅	C₂×#901	1	1	yes	characteristic
518	C₂×C₅	C₂×D₃×M₁₆	1	1	yes	characteristic
519	C₂³	—	3	1	no	—
520	C₂³	—	3	1	no	—
521	C₂³	C₂×D₃×Dic₅	1	1	yes	characteristic
522	Q₈	—	6	2	no	—
523	D₄	—	6	2	no	—
524	D₄	—	6	2	no	—
525	D₄	—	6	2	no	—
526	C₂×C₄	—	2	2	no	—
527	C₂×C₄	—	2	2	no	—
528	C₂×C₄	—	2	2	no	—
529	C₂×C₄	—	3	1	no	—
530	C₂×C₄	—	3	4	no	—
531	C₂×C₄	—	3	1	no	—
532	C₂×C₄	—	3	1	no	—
533	C₂×C₄	—	3	1	no	—
534	C₂×C₄	—	3	1	no	—
535	C₂×C₄	—	3	1	no	—
536	C₂×C₄	—	6	2	no	—
537	C₂×C₄	—	6	2	no	—
538	C₂×C₄	—	6	2	no	—
539	C₂×C₄	—	6	2	no	—
540	C₂×C₄	—	6	2	no	—
541	C₂×C₄	C₂×D₃×Dic₅	1	1	yes	characteristic
542	C₂×C₄	C₂×D₃×Dic₅	1	1	yes	characteristic
543	C₂×C₄	C₂×D₃×Dic₅	1	1	yes	characteristic
544	C₂×C₄	C₂×D₃×Dic₅	1	1	yes	characteristic
545	C₂×C₄	C₂×D₃×Dic₅	1	1	yes	characteristic
546	C₂×C₄	C₂²×D₃×D₅	1	1	yes	characteristic
547	C₈	—	10	2	no	—
548	C₈	—	10	2	no	—
549	C₈	—	15	4	no	—
550	C₈	—	30	2	no	—
551	C₂×C₃	—	4	1	no	—
552	C₂×C₃	C₂²×#681	1	1	yes	characteristic
553	C₂×C₃	C₂×#4094	1	1	yes	characteristic
554	C₂×C₃	#41×Dic₅	1	1	yes	characteristic
555	D₃	—	2	2	no	—
556	D₃	—	4	1	no	—
557	C₅	#79278	1	1	yes	characteristic, complemented, Sylow
558	C₂²	—	2	1	no	—
559	C₂²	—	2	1	no	—
560	C₂²	—	2	1	no	—
561	C₂²	—	3	2	no	—
562	C₂²	—	6	1	no	—
563	C₂²	—	6	1	no	—
564	C₂²	—	6	1	no	—
565	C₂²	—	6	1	no	—
566	C₂²	—	6	1	no	—
567	C₂²	C₂²×D₃×Dic₅	1	1	yes	characteristic
568	C₄	—	2	1	no	—
569	C₄	—	2	1	no	—
570	C₄	—	2	1	no	—
571	C₄	—	3	2	no	—
572	C₄	—	6	1	no	—
573	C₄	—	6	1	no	—
574	C₄	—	6	1	no	—
575	C₄	—	6	1	no	—
576	C₄	—	6	1	no	—
577	C₄	#91286	1	2	yes	—
578	C₄	D₃×#681	1	2	yes	—
579	C₄	#92016	1	2	yes	—
580	C₃	#10614248	1	1	yes	characteristic, complemented, Sylow
581	C₂	—	4	1	no	—
582	C₂	—	6	2	no	—
583	C₂	—	12	1	no	—
584	C₂	C₂×#91286	1	1	yes	characteristic
585	C₂	C₂×D₃×#681	1	1	yes	characteristic
586	C₂	#11754455	1	1	yes	characteristic

	subgroup	G/H
center	C₄²	C₂×D₃×D₅
commutator, socle	C₂²×C₃×C₅	C₂³×C₄
Frattini	C₂×C₄	C₂²×D₃×D₅
Fitting	C₂×C₃×C₄²×C₅	C₂²
prime radical	C₂×C₅×#235	C₄
cosocle	C₂×C₃×C₄×C₅	C₂⁴
hypercenter	C₂×C₄²	D₃×D₅
hypocenter	C₃×C₅	#2965
LCS	G ▷ C₂²×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₄² ◁ C₂×C₄²

Complements

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

N	H ≅ G/N	type
2. C₄×#6710	C₂	semidirect
3. C₃×#65214	C₂	semidirect
4. #11748496	C₂	semidirect
5. #11748314	C₂	semidirect
6. C₄×#6650	C₂	semidirect
7. #11746999	C₂	semidirect
8. C₄×D₃×#168	C₂	semidirect
9. #11746876	C₂	semidirect
10. #11746876	C₂	semidirect
11. #11746858	C₂	semidirect
52. #65214	D₃	semidirect
168. C₄×C₅×D₃	M₁₆	semidirect
171. C₃⋊#168	#41	semidirect
419. C₄×D₃	#681	semidirect
490. C₃×C₅	#2965	semidirect
557. C₅	#79278	semidirect
580. C₃	#10614248	semidirect

Maximal subgroups

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

subgroup	index
C₄×C₅×#235	2
C₄×#6710	2
C₃×#65214	2
#11748496	2
#11748314	2
C₄×#6650	2
#11746999	2
C₄×D₃×#168	2
#11746876	2
#11746858	2
#10614248	3
#79278	5