Subgroups — #14419176

Order 1920.

760 conjugacy classes of subgroups.

The subgroup lattice has 692 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#5538	C₂	1	1	yes	maximal, characteristic
2	D₄×C₃⋊#168	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#65300	C₂	1	1	yes	maximal, characteristic, complemented
4	#11748501	C₂	1	1	yes	maximal, characteristic, complemented
5	#11748500	C₂	1	1	yes	maximal, characteristic, complemented
6	#67⋊#168	C₂	1	1	yes	maximal, characteristic, complemented
7	#67⋊#168	C₂	1	1	yes	maximal, characteristic, complemented
8	#11748337	C₂	1	1	yes	maximal, characteristic, complemented
9	#11748330	C₂	1	1	yes	maximal, characteristic, complemented
10	#11748327	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×Dic₃×#168	C₂	1	1	yes	maximal, characteristic, complemented
12	#11746979	C₂	1	1	yes	maximal, characteristic, complemented
13	#11746857	C₂	1	1	yes	maximal, characteristic, complemented
14	#11746854	C₂	1	1	yes	maximal, characteristic, complemented
15	#11746850	C₂	1	1	yes	maximal, characteristic, complemented
16	#10614857	—	3	1	no	maximal, Hall
17	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
18	C₂²×C₃⋊#168	C₂²	1	1	yes	characteristic
19	C₂²×C₃⋊#168	C₂²	1	1	yes	characteristic
20	C₅×#939	C₄	1	1	yes	characteristic
21	C₅×#935	C₄	1	1	yes	characteristic
22	C₄×C₅×#67	C₂²	1	1	yes	characteristic
23	C₄×C₅×#67	C₂²	1	1	yes	characteristic
24	C₅×#926	C₂²	1	1	yes	characteristic
25	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
26	C₅×#898	C₄	1	1	yes	characteristic
27	C₅×#889	C₄	1	1	yes	characteristic
28	C₅×#886	C₄	1	1	yes	characteristic
29	C₅×#885	C₄	1	1	yes	characteristic
30	C₅×#879	C₄	1	1	yes	characteristic
31	C₅×#878	C₄	1	1	yes	characteristic
32	C₅×#872	C₂²	1	1	yes	characteristic
33	C₄×C₅×Dic₆	C₂²	1	1	yes	characteristic
34	C₂×C₃×#681	C₂²	1	1	yes	characteristic
35	C₂²×C₃×#168	C₂²	1	1	yes	characteristic
36	C₂×#6650	C₂²	1	1	yes	characteristic
37	C₂×D₃×#168	C₂²	1	1	yes	characteristic
38	#91114	C₂²	1	1	yes	characteristic
39	#91114	C₂²	1	1	yes	characteristic
40	C₄⋊(C₃⋊#168)	C₂²	1	1	yes	characteristic
41	C₄×C₃⋊#168	C₂²	1	1	yes	characteristic
42	C₃×C₂²⋊#168	C₂²	1	1	yes	characteristic
43	C₃×C₂²⋊#168	C₂²	1	1	yes	characteristic
44	C₃×C₄⋊#168	C₂²	1	1	yes	characteristic
45	C₃×#3935	C₂²	1	1	yes	characteristic
46	Dic₃⋊#168	C₂²	1	1	yes	characteristic
47	Dic₃⋊#168	C₂²	1	1	yes	characteristic
48	Dic₃⋊#168	C₂²	1	1	yes	characteristic
49	Dic₃⋊#168	C₂²	1	1	yes	characteristic
50	(C₂×D₃)⋊#168	C₂²	1	1	yes	characteristic
51	(C₂×D₃)⋊#168	C₂²	1	1	yes	characteristic
52	#90953	C₂²	1	1	yes	characteristic
53	#90953	C₂²	1	1	yes	characteristic
54	#90953	C₂²	1	1	yes	characteristic
55	Dic₃×#168	C₂²	1	1	yes	characteristic
56	Dic₃×#168	C₂²	1	1	yes	characteristic
57	Dic₃×#168	C₂²	1	1	yes	characteristic
58	Dic₃×#168	C₂²	1	1	yes	characteristic
59	Dic₃×#168	C₂²	1	1	yes	characteristic
60	#79454	—	5	1	no	maximal, Hall
61	C₅×#529	—	3	1	no	—
62	#65313	—	3	1	no	—
63	Q₈×#168	—	3	1	no	—
64	#65301	—	3	1	no	—
65	#65300	—	3	1	no	—
66	#65300	D₃	1	1	yes	characteristic, complemented
67	D₄×#168	—	3	1	no	—
68	D₄×#168	—	3	1	no	—
69	D₄×#168	—	3	1	no	—
70	#65289	—	3	1	no	—
71	#65289	—	3	1	no	—
72	#65286	—	3	1	no	—
73	#65286	—	3	1	no	—
74	#65215	—	3	1	no	—
75	C₂×C₄×#168	—	3	1	no	—
76	C₂×C₃×C₅×D₄	C₂×C₄	1	1	yes	characteristic
77	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
78	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
79	C₂×C₅×#67	C₂×C₄	1	1	yes	characteristic
80	C₂×C₅×#67	C₂×C₄	1	1	yes	characteristic
81	C₂²×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
82	C₂²×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
83	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
84	C₂×C₅×Dic₆	C₂×C₄	1	1	yes	characteristic
85	C₃×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
86	C₃×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
87	C₃×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
88	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
89	C₂×C₃⋊#168	—	2	2	no	—
90	C₂×C₃⋊#168	—	2	2	no	—
91	C₂×C₃⋊#168	C₂³	1	1	yes	characteristic
92	C₂×C₃⋊#168	C₂³	1	1	yes	characteristic
93	C₂×C₃⋊#168	C₂³	1	1	yes	characteristic
94	C₂×C₃⋊#168	C₂³	1	1	yes	characteristic
95	C₅×#217	C₂×C₄	1	1	yes	characteristic
96	C₅×#217	C₂×C₄	1	1	yes	characteristic
97	C₅×#217	C₂×C₄	1	1	yes	characteristic
98	C₅×#217	C₂×C₄	1	1	yes	characteristic
99	C₅×(C₂×D₃)⋊C₄	C₂×C₄	1	1	yes	characteristic
100	C₅×(C₂×D₃)⋊C₄	C₂×C₄	1	1	yes	characteristic
101	C₅×(C₂×D₃)⋊C₄	C₂×C₄	1	1	yes	characteristic
102	C₅×(C₂×D₃)⋊C₄	C₂×C₄	1	1	yes	characteristic
103	C₅×C₄⋊Dic₃	C₂×C₄	1	1	yes	characteristic
104	C₅×C₄⋊Dic₃	C₂×C₄	1	1	yes	characteristic
105	C₅×C₄⋊Dic₃	C₂×C₄	1	1	yes	characteristic
106	C₅×Dic₃⋊C₄	C₂×C₄	1	1	yes	characteristic
107	C₅×Dic₃⋊C₄	C₂×C₄	1	1	yes	characteristic
108	C₅×Dic₃⋊C₄	C₂×C₄	1	1	yes	characteristic
109	C₅×Dic₃⋊C₄	C₂×C₄	1	1	yes	characteristic
110	C₅×Dic₃⋊C₄	C₂×C₄	1	1	yes	characteristic
111	C₅×Dic₃⋊C₄	C₂×C₄	1	1	yes	characteristic
112	C₄×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
113	C₄×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
114	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
115	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
116	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
117	C₃×#681	—	2	2	no	—
118	C₂×C₃×#168	—	2	2	no	—
119	C₂×C₃×#168	C₂³	1	1	yes	characteristic
120	C₂×C₃×#168	C₂³	1	1	yes	characteristic
121	C₂×C₃×#168	C₂³	1	1	yes	characteristic
122	C₂×C₃×#168	C₂³	1	1	yes	characteristic
123	#6650	—	2	2	no	—
124	D₃×#168	—	2	2	no	—
125	#5538	D₅	1	1	yes	characteristic
126	C₃×#435	—	5	1	no	—
127	#5128	—	5	1	no	—
128	#5122	—	5	1	no	—
129	#5111	—	5	1	no	—
130	C₂×C₈×Dic₃	—	5	1	no	—
131	D₄×C₃⋊C₈	—	5	1	no	—
132	#4840	—	5	1	no	—
133	#4830	—	5	1	no	—
134	#67⋊C₈	—	5	1	no	—
135	#67⋊C₈	—	5	1	no	—
136	#4720	—	5	1	no	—
137	#4719	—	5	1	no	—
138	#4708	—	5	1	no	—
139	#4701	—	5	1	no	—
140	C₅×#126	—	3	1	no	—
141	C₅×#126	—	3	1	no	—
142	C₅×#125	—	3	1	no	—
143	C₅×#124	—	3	1	no	—
144	C₅×#123	—	3	1	no	—
145	C₅×#123	—	3	1	no	—
146	C₅×C₂²⋊Q₈	—	3	1	no	—
147	C₅×#121	—	3	1	no	—
148	C₄×C₅×Q₈	—	3	1	no	—
149	C₄×C₅×D₄	—	3	1	no	—
150	C₄×C₅×D₄	—	3	1	no	—
151	C₄×C₅×D₄	C₂×D₃	1	1	yes	characteristic
152	C₅×#117	—	3	1	no	—
153	C₅×#117	—	3	1	no	—
154	C₂×C₄²×C₅	—	3	1	no	—
155	C₂×#681	—	3	1	no	—
156	C₂×#681	C₂×D₃	1	1	yes	characteristic
157	C₂²×#168	—	3	1	no	—
158	C₂²×#168	—	3	1	no	—
159	C₂²×#168	—	3	1	no	—
160	C₂²×#168	C₂×D₃	1	1	yes	characteristic
161	C₂²⋊#168	—	3	1	no	—
162	C₂²⋊#168	—	3	1	no	—
163	C₂²⋊#168	—	3	1	no	—
164	C₂²⋊#168	—	3	1	no	—
165	C₂²⋊#168	C₂×D₃	1	1	yes	characteristic
166	C₂²⋊#168	C₂×D₃	1	1	yes	characteristic
167	C₄⋊#168	—	3	1	no	—
168	C₄⋊#168	—	3	1	no	—
169	C₄⋊#168	—	3	1	no	—
170	C₄⋊#168	—	3	1	no	—
171	C₄⋊#168	—	3	1	no	—
172	C₄⋊#168	C₂×D₃	1	1	yes	characteristic
173	#3935	—	3	1	no	—
174	#3935	—	3	1	no	—
175	#3935	—	3	1	no	—
176	#3935	C₂×D₃	1	1	yes	characteristic
177	C₄×#168	—	3	1	no	—
178	C₄×#168	—	3	1	no	—
179	C₄×#168	—	3	1	no	—
180	C₄×#168	—	3	1	no	—
181	C₄×#168	—	3	1	no	—
182	C₄×#168	—	3	1	no	—
183	#2966	—	15	1	no	Sylow
184	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
185	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
186	C₂²×C₅×D₃	C₂²×C₄	1	1	yes	characteristic
187	C₃×C₅×D₄	—	2	2	no	—
188	C₂×C₃×C₄×C₅	—	2	1	no	—
189	C₂×C₃×C₄×C₅	—	2	1	no	—
190	C₂×C₃×C₄×C₅	—	2	1	no	—
191	C₂×C₃×C₄×C₅	—	2	1	no	—
192	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
193	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
194	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
195	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
196	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
197	C₅×#67	—	2	2	no	—
198	C₅×#67	—	2	2	no	—
199	C₂×C₅×Dic₃	—	2	2	no	—
200	C₂×C₅×Dic₃	—	2	2	no	—
201	C₂×C₅×Dic₃	C₂²×C₄	1	1	yes	characteristic
202	C₂×C₅×Dic₃	C₂²×C₄	1	1	yes	characteristic
203	C₂×C₅×Dic₃	C₂²×C₄	1	1	yes	characteristic
204	C₂×C₅×Dic₃	C₂²×C₄	1	1	yes	characteristic
205	C₂×C₅×Dic₃	C₂²×C₄	1	1	yes	characteristic
206	C₂×C₅×Dic₃	C₂²×C₄	1	1	yes	characteristic
207	C₂×C₅×Dic₃	C₂²×C₄	1	1	yes	characteristic
208	C₄×C₅×D₃	—	2	1	no	—
209	C₄×C₅×D₃	—	2	1	no	—
210	C₅×Dic₆	—	2	2	no	—
211	C₃⋊#168	—	2	1	no	—
212	C₃⋊#168	—	2	1	no	—
213	C₃⋊#168	—	2	1	no	—
214	C₃⋊#168	#41	1	2	yes	—
215	C₃×#168	—	2	1	no	—
216	C₃×#168	—	2	1	no	—
217	C₃×#168	—	2	1	no	—
218	C₃×#168	#41	1	2	yes	—
219	C₂×C₃×M₁₆	—	5	1	no	—
220	C₂²×C₃×C₈	—	5	1	no	—
221	C₃×C₄×D₄	C₂×D₅	1	1	yes	characteristic
222	#939	Dic₅	1	1	yes	characteristic
223	#935	Dic₅	1	1	yes	characteristic
224	C₄×#67	C₂×D₅	1	1	yes	characteristic
225	C₄×#67	C₂×D₅	1	1	yes	characteristic
226	#926	C₂×D₅	1	1	yes	characteristic
227	C₂×C₄×Dic₃	C₂×D₅	1	1	yes	characteristic
228	C₂²×C₃⋊C₈	—	5	1	no	—
229	C₂²×C₃⋊C₈	—	5	1	no	—
230	C₂×ΓL(1,𝔽₂₅)	—	5	1	no	—
231	C₂×D₃×C₈	—	5	1	no	—
232	#898	Dic₅	1	1	yes	characteristic
233	#889	Dic₅	1	1	yes	characteristic
234	#886	Dic₅	1	1	yes	characteristic
235	#885	Dic₅	1	1	yes	characteristic
236	#879	Dic₅	1	1	yes	characteristic
237	#878	Dic₅	1	1	yes	characteristic
238	#872	C₂×D₅	1	1	yes	characteristic
239	C₄×Dic₆	C₂×D₅	1	1	yes	characteristic
240	C₃×C₄⋊C₈	—	5	1	no	—
241	C₃×C₂²⋊C₈	—	5	1	no	—
242	C₃×C₂²⋊C₈	—	5	1	no	—
243	C₃×#97	—	5	1	no	—
244	#830	—	5	1	no	—
245	#830	—	5	1	no	—
246	(C₂×D₃)⋊C₈	—	5	1	no	—
247	(C₂×D₃)⋊C₈	—	5	1	no	—
248	#815	—	5	1	no	—
249	#815	—	5	1	no	—
250	#815	—	5	1	no	—
251	Dic₃⋊C₈	—	5	1	no	—
252	Dic₃⋊C₈	—	5	1	no	—
253	Dic₃⋊C₈	—	5	1	no	—
254	Dic₃⋊C₈	—	5	1	no	—
255	C₈×Dic₃	—	5	1	no	—
256	C₈×Dic₃	—	5	1	no	—
257	C₈×Dic₃	—	5	1	no	—
258	C₈×Dic₃	—	5	1	no	—
259	C₈×Dic₃	—	5	1	no	—
260	C₄⋊(C₃⋊C₈)	—	5	1	no	—
261	C₄×C₃⋊C₈	—	5	1	no	—
262	C₂×C₅×Q₈	—	3	1	no	—
263	C₂×C₅×D₄	—	3	1	no	—
264	C₂×C₅×D₄	—	3	1	no	—
265	C₂×C₅×D₄	C₄×D₃	1	1	yes	characteristic
266	C₂²×C₄×C₅	—	3	1	no	—
267	C₂²×C₄×C₅	—	3	1	no	—
268	C₂²×C₄×C₅	—	3	1	no	—
269	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
270	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
271	C₅×C₄⋊C₄	—	3	1	no	—
272	C₅×C₄⋊C₄	—	3	1	no	—
273	C₅×C₄⋊C₄	—	3	1	no	—
274	C₅×C₄⋊C₄	—	3	1	no	—
275	C₅×C₄⋊C₄	—	3	1	no	—
276	C₅×C₄⋊C₄	—	3	1	no	—
277	C₅×C₄⋊C₄	—	3	1	no	—
278	C₅×C₄⋊C₄	—	3	1	no	—
279	C₅×C₄⋊C₄	—	3	1	no	—
280	C₅×C₄⋊C₄	C₄×D₃	1	1	yes	characteristic
281	C₅×C₂²⋊C₄	—	3	1	no	—
282	C₅×C₂²⋊C₄	—	3	1	no	—
283	C₅×C₂²⋊C₄	—	3	1	no	—
284	C₅×C₂²⋊C₄	—	3	1	no	—
285	C₅×C₂²⋊C₄	—	3	1	no	—
286	C₅×C₂²⋊C₄	—	3	1	no	—
287	C₅×C₂²⋊C₄	—	3	1	no	—
288	C₅×C₂²⋊C₄	—	3	1	no	—
289	C₅×C₂²⋊C₄	C₄×D₃	1	1	yes	characteristic
290	C₅×C₂²⋊C₄	C₄×D₃	1	1	yes	characteristic
291	C₄²×C₅	—	3	1	no	—
292	C₄²×C₅	—	3	1	no	—
293	C₄²×C₅	—	3	1	no	—
294	C₄²×C₅	—	3	1	no	—
295	C₄²×C₅	—	3	1	no	—
296	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
297	#681	—	2	2	no	—
298	#681	—	6	2	no	—
299	C₂×#168	—	2	2	no	—
300	C₂×#168	—	3	1	no	—
301	C₂×#168	—	3	1	no	—
302	C₂×#168	—	3	1	no	—
303	C₂×#168	—	3	1	no	—
304	C₂×#168	—	6	2	no	—
305	C₂×#168	—	6	2	no	—
306	C₂×#168	—	6	2	no	—
307	C₂×#168	C₂²×D₃	1	1	yes	characteristic
308	C₂×#168	C₂²×D₃	1	1	yes	characteristic
309	C₂×#168	C₂²×D₃	1	1	yes	characteristic
310	C₂×#168	C₂²×D₃	1	1	yes	characteristic
311	#529	—	3	1	no	—
312	#446	—	15	1	no	—
313	C₈×Q₈	—	15	1	no	—
314	#436	—	15	1	no	—
315	#435	—	5	1	no	—
316	#435	—	15	1	no	—
317	C₈×D₄	—	15	1	no	—
318	C₈×D₄	—	15	1	no	—
319	C₈×D₄	—	15	1	no	—
320	#433	—	15	1	no	—
321	#433	—	15	1	no	—
322	#432	—	15	1	no	—
323	#405	—	15	1	no	—
324	#405	—	15	1	no	—
325	C₂×C₄×C₈	—	15	1	no	—
326	C₂²×C₃×C₅	—	2	1	no	—
327	C₂²×C₃×C₅	—	2	1	no	—
328	C₂²×C₃×C₅	—	2	1	no	—
329	C₂²×C₃×C₅	—	2	1	no	—
330	C₂²×C₃×C₅	—	2	1	no	—
331	C₂²×C₃×C₅	#131	1	2	yes	—
332	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
333	C₂×C₅×D₃	—	2	1	no	—
334	C₂×C₅×D₃	—	2	1	no	—
335	C₂×C₅×D₃	—	2	1	no	—
336	C₃×C₄×C₅	—	2	1	no	—
337	C₃×C₄×C₅	—	2	1	no	—
338	C₃×C₄×C₅	—	2	1	no	—
339	C₃×C₄×C₅	—	2	1	no	—
340	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
341	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
342	C₅×Dic₃	—	2	1	no	—
343	C₅×Dic₃	—	2	1	no	—
344	C₅×Dic₃	—	2	1	no	—
345	C₅×Dic₃	—	2	1	no	—
346	C₅×Dic₃	—	2	1	no	—
347	C₅×Dic₃	—	2	1	no	—
348	C₅×Dic₃	#131	1	2	yes	—
349	C₂×C₃×D₄	C₂×Dic₅	1	1	yes	characteristic
350	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
351	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
352	C₂×#67	C₂×Dic₅	1	1	yes	characteristic
353	C₂×#67	C₂×Dic₅	1	1	yes	characteristic
354	C₂²×Dic₃	C₂×Dic₅	1	1	yes	characteristic
355	C₂²×Dic₃	C₂×Dic₅	1	1	yes	characteristic
356	C₂×C₄×D₃	C₂²×D₅	1	1	yes	characteristic
357	C₂×Dic₆	C₂×Dic₅	1	1	yes	characteristic
358	C₃×M₁₆	—	10	2	no	—
359	C₂×C₃×C₈	—	5	1	no	—
360	C₂×C₃×C₈	—	5	1	no	—
361	C₂×C₃×C₈	—	5	1	no	—
362	C₂×C₃×C₈	—	5	1	no	—
363	C₂×C₃×C₈	—	10	2	no	—
364	C₃×C₄⋊C₄	C₂×Dic₅	1	1	yes	characteristic
365	C₃×C₂²⋊C₄	C₂×Dic₅	1	1	yes	characteristic
366	C₃×C₂²⋊C₄	C₂×Dic₅	1	1	yes	characteristic
367	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
368	#217	C₂×Dic₅	1	1	yes	characteristic
369	#217	C₂×Dic₅	1	1	yes	characteristic
370	#217	C₂×Dic₅	1	1	yes	characteristic
371	#217	C₂×Dic₅	1	1	yes	characteristic
372	(C₂×D₃)⋊C₄	C₂×Dic₅	1	1	yes	characteristic
373	(C₂×D₃)⋊C₄	C₂×Dic₅	1	1	yes	characteristic
374	(C₂×D₃)⋊C₄	C₂×Dic₅	1	1	yes	characteristic
375	(C₂×D₃)⋊C₄	C₂×Dic₅	1	1	yes	characteristic
376	C₄⋊Dic₃	C₂×Dic₅	1	1	yes	characteristic
377	C₄⋊Dic₃	C₂×Dic₅	1	1	yes	characteristic
378	C₄⋊Dic₃	C₂×Dic₅	1	1	yes	characteristic
379	Dic₃⋊C₄	C₂×Dic₅	1	1	yes	characteristic
380	Dic₃⋊C₄	C₂×Dic₅	1	1	yes	characteristic
381	Dic₃⋊C₄	C₂×Dic₅	1	1	yes	characteristic
382	Dic₃⋊C₄	C₂×Dic₅	1	1	yes	characteristic
383	Dic₃⋊C₄	C₂×Dic₅	1	1	yes	characteristic
384	Dic₃⋊C₄	C₂×Dic₅	1	1	yes	characteristic
385	C₄×Dic₃	C₂×Dic₅	1	1	yes	characteristic
386	C₄×Dic₃	C₂×Dic₅	1	1	yes	characteristic
387	C₄×Dic₃	C₂²×D₅	1	1	yes	characteristic
388	C₄×Dic₃	C₂²×D₅	1	1	yes	characteristic
389	C₄×Dic₃	C₂²×D₅	1	1	yes	characteristic
390	C₂×C₃⋊C₈	—	5	1	no	—
391	C₂×C₃⋊C₈	—	5	1	no	—
392	C₂×C₃⋊C₈	—	5	1	no	—
393	C₂×C₃⋊C₈	—	5	1	no	—
394	C₂×C₃⋊C₈	—	10	2	no	—
395	C₂×C₃⋊C₈	—	10	2	no	—
396	ΓL(1,𝔽₂₅)	—	10	2	no	—
397	D₃×C₈	—	10	2	no	—
398	C₂³×C₅	—	3	1	no	—
399	C₂³×C₅	C₂×C₄×D₃	1	1	yes	characteristic
400	C₂³×C₅	C₂×C₄×D₃	1	1	yes	characteristic
401	C₅×Q₈	—	6	2	no	—
402	C₅×D₄	—	2	2	no	—
403	C₅×D₄	—	6	2	no	—
404	C₅×D₄	—	6	2	no	—
405	C₂×C₄×C₅	—	2	1	no	—
406	C₂×C₄×C₅	—	2	1	no	—
407	C₂×C₄×C₅	—	2	1	no	—
408	C₂×C₄×C₅	—	2	1	no	—
409	C₂×C₄×C₅	—	3	1	no	—
410	C₂×C₄×C₅	—	3	1	no	—
411	C₂×C₄×C₅	—	3	1	no	—
412	C₂×C₄×C₅	—	3	1	no	—
413	C₂×C₄×C₅	—	3	1	no	—
414	C₂×C₄×C₅	—	3	1	no	—
415	C₂×C₄×C₅	—	3	1	no	—
416	C₂×C₄×C₅	—	6	2	no	—
417	C₂×C₄×C₅	—	6	2	no	—
418	C₂×C₄×C₅	—	6	1	no	—
419	C₂×C₄×C₅	—	6	1	no	—
420	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
421	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
422	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
423	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
424	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
425	#168	—	2	1	no	—
426	#168	—	2	1	no	—
427	#168	—	2	1	no	—
428	#168	—	3	2	no	—
429	#168	—	6	1	no	—
430	#168	—	6	1	no	—
431	#168	—	6	1	no	—
432	#168	#237	1	2	yes	—
433	C₂×M₁₆	—	5	1	no	—
434	C₂×M₁₆	—	15	1	no	—
435	C₂²×C₈	—	5	1	no	—
436	C₂²×C₈	—	15	1	no	—
437	C₂²×C₈	—	15	1	no	—
438	C₂²×C₈	—	15	1	no	—
439	#126	—	3	1	no	—
440	#126	—	3	1	no	—
441	#125	—	3	1	no	—
442	#124	—	3	1	no	—
443	#123	—	3	1	no	—
444	#123	—	3	1	no	—
445	C₂²⋊Q₈	—	3	1	no	—
446	#121	—	3	1	no	—
447	C₄×Q₈	—	3	1	no	—
448	C₄×D₄	—	3	1	no	—
449	C₄×D₄	—	3	1	no	—
450	C₄×D₄	D₃×D₅	1	1	yes	characteristic
451	#117	—	3	1	no	—
452	#117	—	3	1	no	—
453	C₂×C₄²	—	3	1	no	—
454	C₄⋊C₈	—	5	1	no	—
455	C₄⋊C₈	—	15	1	no	—
456	C₄⋊C₈	—	15	1	no	—
457	C₄⋊C₈	—	15	1	no	—
458	C₄⋊C₈	—	15	1	no	—
459	C₄⋊C₈	—	15	1	no	—
460	C₂²⋊C₈	—	5	1	no	—
461	C₂²⋊C₈	—	5	1	no	—
462	C₂²⋊C₈	—	15	1	no	—
463	C₂²⋊C₈	—	15	1	no	—
464	C₂²⋊C₈	—	15	1	no	—
465	C₂²⋊C₈	—	15	1	no	—
466	#97	—	5	1	no	—
467	#97	—	15	1	no	—
468	#97	—	15	1	no	—
469	#97	—	15	1	no	—
470	C₄×C₈	—	15	1	no	—
471	C₄×C₈	—	15	1	no	—
472	C₄×C₈	—	15	1	no	—
473	C₄×C₈	—	15	1	no	—
474	C₄×C₈	—	15	1	no	—
475	C₄×C₈	—	15	1	no	—
476	C₂×C₃×C₅	—	2	2	no	—
477	C₂×C₃×C₅	—	4	1	no	—
478	C₂×C₃×C₅	C₄×#41	1	1	yes	characteristic
479	C₂×C₃×C₅	C₂×#131	1	1	yes	characteristic
480	C₂×C₃×C₅	C₂×#131	1	1	yes	characteristic
481	C₅×D₃	—	4	1	no	—
482	C₂³×C₃	C₂²×Dic₅	1	1	yes	characteristic
483	C₂³×C₃	C₂²×Dic₅	1	1	yes	characteristic
484	C₂²×D₃	C₂²×Dic₅	1	1	yes	characteristic
485	C₃×D₄	—	2	2	no	—
486	C₂×C₃×C₄	—	2	1	no	—
487	C₂×C₃×C₄	—	2	1	no	—
488	C₂×C₃×C₄	—	2	1	no	—
489	C₂×C₃×C₄	—	2	1	no	—
490	C₂×C₃×C₄	C₂²×Dic₅	1	1	yes	characteristic
491	C₂×C₃×C₄	C₂²×Dic₅	1	1	yes	characteristic
492	C₂×C₃×C₄	C₂²×Dic₅	1	1	yes	characteristic
493	C₂×C₃×C₄	C₂²×Dic₅	1	1	yes	characteristic
494	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
495	#67	—	2	2	no	—
496	#67	—	2	2	no	—
497	C₂×Dic₃	—	2	2	no	—
498	C₂×Dic₃	—	2	2	no	—
499	C₂×Dic₃	C₂²×Dic₅	1	1	yes	characteristic
500	C₂×Dic₃	C₂²×Dic₅	1	1	yes	characteristic
501	C₂×Dic₃	C₂²×Dic₅	1	1	yes	characteristic
502	C₂×Dic₃	C₂²×Dic₅	1	1	yes	characteristic
503	C₂×Dic₃	C₂²×Dic₅	1	1	yes	characteristic
504	C₂×Dic₃	C₂²×Dic₅	1	1	yes	characteristic
505	C₂×Dic₃	C₂²×Dic₅	1	1	yes	characteristic
506	C₄×D₃	—	2	1	no	—
507	C₄×D₃	—	2	1	no	—
508	Dic₆	—	2	2	no	—
509	C₃×C₈	—	5	2	no	—
510	C₃×C₈	—	10	1	no	—
511	C₃×C₈	—	10	1	no	—
512	C₃×C₈	—	10	1	no	—
513	C₃⋊C₈	—	5	2	no	—
514	C₃⋊C₈	—	10	1	no	—
515	C₃⋊C₈	—	10	1	no	—
516	C₃⋊C₈	—	10	1	no	—
517	C₂²×C₅	—	2	1	no	—
518	C₂²×C₅	—	2	1	no	—
519	C₂²×C₅	—	2	1	no	—
520	C₂²×C₅	—	2	1	no	—
521	C₂²×C₅	—	2	1	no	—
522	C₂²×C₅	—	6	1	no	—
523	C₂²×C₅	—	6	1	no	—
524	C₂²×C₅	—	6	1	no	—
525	C₂²×C₅	#907	1	2	yes	—
526	C₂²×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
527	C₄×C₅	—	2	1	no	—
528	C₄×C₅	—	2	1	no	—
529	C₄×C₅	—	2	1	no	—
530	C₄×C₅	—	2	1	no	—
531	C₄×C₅	—	3	2	no	—
532	C₄×C₅	—	6	1	no	—
533	C₄×C₅	—	6	1	no	—
534	C₄×C₅	—	6	1	no	—
535	C₄×C₅	—	6	1	no	—
536	C₄×C₅	—	6	1	no	—
537	C₄×C₅	—	6	1	no	—
538	C₄×C₅	C₂×#237	1	1	yes	characteristic
539	C₄×C₅	D₃×#41	1	1	yes	characteristic
540	C₂×Q₈	—	3	1	no	—
541	C₂×D₄	—	3	1	no	—
542	C₂×D₄	—	3	1	no	—
543	C₂×D₄	D₃×Dic₅	1	1	yes	characteristic
544	C₂²×C₄	—	3	1	no	—
545	C₂²×C₄	—	3	1	no	—
546	C₂²×C₄	—	3	1	no	—
547	C₂²×C₄	C₂×D₃×D₅	1	1	yes	characteristic
548	C₂²×C₄	C₂×D₃×D₅	1	1	yes	characteristic
549	M₁₆	—	10	2	no	—
550	M₁₆	—	30	2	no	—
551	C₂×C₈	—	5	1	no	—
552	C₂×C₈	—	5	1	no	—
553	C₂×C₈	—	5	1	no	—
554	C₂×C₈	—	5	1	no	—
555	C₂×C₈	—	10	2	no	—
556	C₂×C₈	—	15	1	no	—
557	C₂×C₈	—	15	1	no	—
558	C₂×C₈	—	15	1	no	—
559	C₂×C₈	—	15	1	no	—
560	C₂×C₈	—	30	2	no	—
561	C₂×C₈	—	30	2	no	—
562	C₂×C₈	—	30	2	no	—
563	C₄⋊C₄	—	3	1	no	—
564	C₄⋊C₄	—	3	1	no	—
565	C₄⋊C₄	—	3	1	no	—
566	C₄⋊C₄	—	3	1	no	—
567	C₄⋊C₄	—	3	1	no	—
568	C₄⋊C₄	—	3	1	no	—
569	C₄⋊C₄	—	3	1	no	—
570	C₄⋊C₄	—	3	1	no	—
571	C₄⋊C₄	—	3	1	no	—
572	C₄⋊C₄	D₃×Dic₅	1	1	yes	characteristic
573	C₂²⋊C₄	—	3	1	no	—
574	C₂²⋊C₄	—	3	1	no	—
575	C₂²⋊C₄	—	3	1	no	—
576	C₂²⋊C₄	—	3	1	no	—
577	C₂²⋊C₄	—	3	1	no	—
578	C₂²⋊C₄	—	3	1	no	—
579	C₂²⋊C₄	—	3	1	no	—
580	C₂²⋊C₄	—	3	1	no	—
581	C₂²⋊C₄	D₃×Dic₅	1	1	yes	characteristic
582	C₂²⋊C₄	D₃×Dic₅	1	1	yes	characteristic
583	C₄²	—	3	1	no	—
584	C₄²	—	3	1	no	—
585	C₄²	—	3	1	no	—
586	C₄²	—	3	1	no	—
587	C₄²	—	3	1	no	—
588	C₄²	C₂×D₃×D₅	1	1	yes	characteristic
589	C₃×C₅	#2966	1	1	yes	characteristic, complemented, Hall
590	C₂²×C₃	—	2	1	no	—
591	C₂²×C₃	—	2	1	no	—
592	C₂²×C₃	—	2	1	no	—
593	C₂²×C₃	—	2	1	no	—
594	C₂²×C₃	—	2	1	no	—
595	C₂²×C₃	#4094	1	2	yes	—
596	C₂²×C₃	C₂³×Dic₅	1	1	yes	characteristic
597	C₂×D₃	—	2	1	no	—
598	C₂×D₃	—	2	1	no	—
599	C₂×D₃	—	2	1	no	—
600	C₃×C₄	—	2	1	no	—
601	C₃×C₄	—	2	1	no	—
602	C₃×C₄	—	2	1	no	—
603	C₃×C₄	—	2	1	no	—
604	C₃×C₄	D₅×#41	1	1	yes	characteristic
605	C₃×C₄	D₅×#41	1	1	yes	characteristic
606	Dic₃	—	2	1	no	—
607	Dic₃	—	2	1	no	—
608	Dic₃	—	2	1	no	—
609	Dic₃	—	2	1	no	—
610	Dic₃	—	2	1	no	—
611	Dic₃	—	2	1	no	—
612	Dic₃	#4094	1	2	yes	—
613	C₂×C₅	—	2	2	no	—
614	C₂×C₅	—	4	1	no	—
615	C₂×C₅	—	12	1	no	—
616	C₂×C₅	C₄×#237	1	1	yes	characteristic
617	C₂×C₅	C₂×#907	1	1	yes	characteristic
618	C₂×C₅	D₃×#131	1	1	yes	characteristic
619	C₂³	—	3	1	no	—
620	C₂³	C₂×D₃×Dic₅	1	1	yes	characteristic
621	C₂³	C₂×D₃×Dic₅	1	1	yes	characteristic
622	Q₈	—	6	2	no	—
623	D₄	—	2	2	no	—
624	D₄	—	6	2	no	—
625	D₄	—	6	2	no	—
626	C₂×C₄	—	2	1	no	—
627	C₂×C₄	—	2	1	no	—
628	C₂×C₄	—	2	1	no	—
629	C₂×C₄	—	2	1	no	—
630	C₂×C₄	—	3	1	no	—
631	C₂×C₄	—	3	1	no	—
632	C₂×C₄	—	3	1	no	—
633	C₂×C₄	—	3	1	no	—
634	C₂×C₄	—	3	1	no	—
635	C₂×C₄	—	3	1	no	—
636	C₂×C₄	—	3	1	no	—
637	C₂×C₄	—	6	2	no	—
638	C₂×C₄	—	6	2	no	—
639	C₂×C₄	—	6	1	no	—
640	C₂×C₄	—	6	1	no	—
641	C₂×C₄	C₂×D₃×Dic₅	1	1	yes	characteristic
642	C₂×C₄	C₂×D₃×Dic₅	1	1	yes	characteristic
643	C₂×C₄	C₂×D₃×Dic₅	1	1	yes	characteristic
644	C₂×C₄	C₂×D₃×Dic₅	1	1	yes	characteristic
645	C₂×C₄	C₂²×D₃×D₅	1	1	yes	characteristic
646	C₈	—	5	2	no	—
647	C₈	—	10	1	no	—
648	C₈	—	10	1	no	—
649	C₈	—	10	1	no	—
650	C₈	—	15	2	no	—
651	C₈	—	30	1	no	—
652	C₈	—	30	1	no	—
653	C₈	—	30	1	no	—
654	C₂×C₃	—	2	2	no	—
655	C₂×C₃	—	4	1	no	—
656	C₂×C₃	C₂×#4094	1	1	yes	characteristic
657	C₂×C₃	C₂×#4094	1	1	yes	characteristic
658	C₂×C₃	#41×Dic₅	1	1	yes	characteristic
659	D₃	—	4	1	no	—
660	C₅	#79454	1	1	yes	characteristic, complemented, Sylow
661	C₂²	—	2	1	no	—
662	C₂²	—	2	1	no	—
663	C₂²	—	2	1	no	—
664	C₂²	—	2	1	no	—
665	C₂²	—	2	1	no	—
666	C₂²	—	6	1	no	—
667	C₂²	—	6	1	no	—
668	C₂²	—	6	1	no	—
669	C₂²	#91288	1	2	yes	—
670	C₂²	C₂²×D₃×Dic₅	1	1	yes	characteristic
671	C₄	—	2	1	no	—
672	C₄	—	2	1	no	—
673	C₄	—	2	1	no	—
674	C₄	—	2	1	no	—
675	C₄	—	3	2	no	—
676	C₄	—	6	1	no	—
677	C₄	—	6	1	no	—
678	C₄	—	6	1	no	—
679	C₄	—	6	1	no	—
680	C₄	—	6	1	no	—
681	C₄	—	6	1	no	—
682	C₄	D₅×#237	1	1	yes	characteristic
683	C₄	#92024	1	1	yes	characteristic
684	C₃	#10614857	1	1	yes	characteristic, complemented, Sylow
685	C₂	—	2	2	no	—
686	C₂	—	4	1	no	—
687	C₂	—	12	1	no	—
688	C₂	C₂×#91288	1	1	yes	characteristic
689	C₂	Dic₅×#237	1	1	yes	characteristic
690	C₂	D₃×#4094	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×D₃×D₅
commutator, socle	C₂²×C₃×C₅	C₂³×C₄
Fitting	C₃×C₄×C₅×D₄	C₂²
prime radical	C₅×#939	C₄
cosocle	C₂×C₃×C₄×C₅	C₂⁴
hypercenter	C₄×D₄	D₃×D₅
hypocenter	C₃×C₅	#2966
LCS	G ▷ C₂²×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂×C₄ ◁ C₄×D₄

Complements

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

N	H ≅ G/N	type
2. D₄×C₃⋊#168	C₂	semidirect
3. C₃×#65300	C₂	semidirect
4. #11748501	C₂	semidirect
5. #11748500	C₂	semidirect
6. #67⋊#168	C₂	semidirect
7. #67⋊#168	C₂	semidirect
8. #11748337	C₂	semidirect
9. #11748330	C₂	semidirect
10. #11748327	C₂	semidirect
11. C₂×Dic₃×#168	C₂	semidirect
12. #11746979	C₂	semidirect
13. #11746857	C₂	semidirect
14. #11746854	C₂	semidirect
15. #11746850	C₂	semidirect
66. #65300	D₃	semidirect
589. C₃×C₅	#2966	semidirect
660. C₅	#79454	semidirect
684. C₃	#10614857	semidirect

Maximal subgroups

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

subgroup	index
C₅×#5538	2
D₄×C₃⋊#168	2
C₃×#65300	2
#11748501	2
#11748500	2
#67⋊#168	2
#11748337	2
#11748330	2
#11748327	2
C₂×Dic₃×#168	2
#11746979	2
#11746857	2
#11746854	2
#11746850	2
#10614857	3
#79454	5