Subgroups — #14419059

Order 1920.

824 conjugacy classes of subgroups.

The subgroup lattice has 712 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#6779	C₂	1	1	yes	maximal, characteristic
2	#11750829	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#4718	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#65018	C₂	1	1	yes	maximal, characteristic, complemented
5	#11748486	C₂	1	1	yes	maximal, characteristic, complemented
6	#11748339	C₂	1	1	yes	maximal, characteristic, complemented
7	Dic₃×#681	C₂	1	1	yes	maximal, characteristic, complemented
8	#11747821	C₂	1	1	yes	maximal, characteristic, complemented
9	#11747820	C₂	1	1	yes	maximal, characteristic, complemented
10	#11747727	C₂	1	1	yes	maximal, characteristic, complemented
11	#11747726	C₂	1	1	yes	maximal, characteristic, complemented
12	Dic₃×#676	C₂	1	1	yes	maximal, characteristic, complemented
13	#11747584	C₂	1	1	yes	maximal, characteristic, complemented
14	C₈×#1200	C₂	1	1	yes	maximal, characteristic, complemented
15	#11747576	C₂	1	1	yes	maximal, characteristic, complemented
16	#10611009	—	3	1	no	maximal, Hall
17	C₂×#6779	C₄	1	1	yes	characteristic
18	C₄×#1220	C₂²	1	1	yes	characteristic
19	C₂×#6710	C₂²	1	1	yes	characteristic
20	C₂×C₈×D₁₅	C₂²	1	1	yes	characteristic
21	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
22	C₃×C₄×C₂²⋊D₅	C₂²	1	1	yes	characteristic
23	C₂×C₃×#681	C₂²	1	1	yes	characteristic
24	C₂×C₃×#676	C₂²	1	1	yes	characteristic
25	#91556	C₄	1	1	yes	characteristic
26	Dic₃×C₂²⋊D₅	C₄	1	1	yes	characteristic
27	#91529	C₄	1	1	yes	characteristic
28	C₄×#1204	C₂²	1	1	yes	characteristic
29	C₄×#1202	C₂²	1	1	yes	characteristic
30	#91403	C₄	1	1	yes	characteristic
31	C₄×#1200	C₂²	1	1	yes	characteristic
32	#91395	C₄	1	1	yes	characteristic
33	#91393	C₄	1	1	yes	characteristic
34	C₄×D₅×Dic₃	C₂²	1	1	yes	characteristic
35	#91324	C₄	1	1	yes	characteristic
36	C₂×#6649	C₂²	1	1	yes	characteristic
37	C₂×#6648	C₂²	1	1	yes	characteristic
38	C₃×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic
39	#91104	C₂²	1	1	yes	characteristic
40	#91099	C₂²	1	1	yes	characteristic
41	#91098	C₂²	1	1	yes	characteristic
42	C₅×#830	C₂²	1	1	yes	characteristic
43	C₅×Dic₃⋊C₈	C₂²	1	1	yes	characteristic
44	C₅×Dic₃⋊C₈	C₂²	1	1	yes	characteristic
45	C₅×C₈×Dic₃	C₂²	1	1	yes	characteristic
46	C₅×C₈×Dic₃	C₂²	1	1	yes	characteristic
47	C₃×#3952	C₂²	1	1	yes	characteristic
48	C₃×#3946	C₂²	1	1	yes	characteristic
49	C₃×C₈×Dic₅	C₂²	1	1	yes	characteristic
50	#90983	C₂²	1	1	yes	characteristic
51	#90982	C₂²	1	1	yes	characteristic
52	#90957	C₂²	1	1	yes	characteristic
53	#90955	C₂²	1	1	yes	characteristic
54	#90954	C₂²	1	1	yes	characteristic
55	#90953	C₂²	1	1	yes	characteristic
56	#90953	C₂²	1	1	yes	characteristic
57	Dic₃×#168	C₂²	1	1	yes	characteristic
58	Dic₃×#168	C₂²	1	1	yes	characteristic
59	Dic₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
60	#79517	—	5	1	no	maximal, Hall
61	C₄×#709	—	3	1	no	—
62	C₅×#431	—	3	1	no	—
63	C₄×#681	—	3	1	no	—
64	#65125	—	3	1	no	—
65	#65125	—	3	1	no	—
66	#65117	—	3	1	no	—
67	#65117	—	3	1	no	—
68	#65018	—	3	1	no	—
69	#65018	D₃	1	1	yes	characteristic, complemented
70	#65017	—	3	1	no	—
71	#65017	—	3	1	no	—
72	C₄×#676	—	3	1	no	—
73	#64974	—	3	1	no	—
74	#64974	—	3	1	no	—
75	C₄×C₈×D₅	—	3	1	no	—
76	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
77	C₂×#1220	C₂×C₄	1	1	yes	characteristic
78	C₂×C₄×D₁₅	C₂³	1	1	yes	characteristic
79	C₂²×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
80	C₂²×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
81	C₂×C₃×C₂²⋊D₅	C₂×C₄	1	1	yes	characteristic
82	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
83	C₂×#1204	C₂×C₄	1	1	yes	characteristic
84	C₂×#1202	C₂×C₄	1	1	yes	characteristic
85	C₂×#1200	C₂×C₄	1	1	yes	characteristic
86	C₂×#1200	C₂×C₄	1	1	yes	characteristic
87	#6779	—	2	4	no	—
88	C₂×D₅×Dic₃	C₂×C₄	1	1	yes	characteristic
89	C₂×D₅×Dic₃	C₂×C₄	1	1	yes	characteristic
90	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
91	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
92	#6719	C₂×C₄	1	1	yes	characteristic
93	#6714	C₂×C₄	1	1	yes	characteristic
94	#6712	C₂×C₄	1	1	yes	characteristic
95	C₄×Dic₁₅	C₂³	1	1	yes	characteristic
96	#6710	—	2	2	no	—
97	C₂×C₃⋊#168	C₂³	1	1	yes	characteristic
98	C₂×C₃⋊#168	C₂³	1	1	yes	characteristic
99	C₈×D₁₅	—	2	2	no	—
100	C₄×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
101	C₄×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
102	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
103	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
104	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
105	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
106	C₃×C₂²⋊Dic₅	C₂×C₄	1	1	yes	characteristic
107	C₃×#685	C₂×C₄	1	1	yes	characteristic
108	C₃×#683	C₂×C₄	1	1	yes	characteristic
109	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
110	C₃×#681	—	2	2	no	—
111	C₂×C₃×#168	C₂³	1	1	yes	characteristic
112	C₂×C₃×#168	C₂³	1	1	yes	characteristic
113	C₃×#676	—	2	2	no	—
114	Dic₃⋊Dic₅	C₂×C₄	1	1	yes	characteristic
115	Dic₃⋊Dic₅	C₂×C₄	1	1	yes	characteristic
116	#6669	C₂×C₄	1	1	yes	characteristic
117	#6668	C₂×C₄	1	1	yes	characteristic
118	#6667	C₂×C₄	1	1	yes	characteristic
119	#6665	C₂×C₄	1	1	yes	characteristic
120	Dic₃×Dic₅	C₂×C₄	1	1	yes	characteristic
121	Dic₃×Dic₅	C₂×C₄	1	1	yes	characteristic
122	Dic₃×Dic₅	C₂×C₄	1	1	yes	characteristic
123	Dic₃×Dic₅	C₂×C₄	1	1	yes	characteristic
124	#6649	—	2	2	no	—
125	#6648	—	2	2	no	—
126	C₄×#237	—	5	1	no	—
127	C₃×#436	—	5	1	no	—
128	#5127	—	5	1	no	—
129	#5127	—	5	1	no	—
130	Dic₃×M₁₆	—	5	1	no	—
131	Dic₃×M₁₆	—	5	1	no	—
132	#5012	—	5	1	no	—
133	#4833	—	5	1	no	—
134	#4831	—	5	1	no	—
135	#4728	—	5	1	no	—
136	#4728	—	5	1	no	—
137	#4718	—	5	1	no	—
138	#4718	D₅	1	1	yes	characteristic, complemented
139	C₄×D₃×C₈	—	5	1	no	—
140	#4679	—	5	1	no	—
141	C₂×#709	—	3	1	no	—
142	C₂×C₄²×C₅	—	3	1	no	—
143	C₄×C₂²⋊D₅	—	3	1	no	—
144	C₄×C₂²⋊D₅	—	3	1	no	—
145	C₄×C₂²⋊D₅	—	3	1	no	—
146	C₄×C₂²⋊D₅	C₂×D₃	1	1	yes	characteristic
147	#4072	—	3	1	no	—
148	C₂×#681	—	3	1	no	—
149	C₂×#681	C₂×D₃	1	1	yes	characteristic
150	C₂×#676	—	3	1	no	—
151	C₂×#676	C₂×D₃	1	1	yes	characteristic
152	C₂×C₈×D₅	—	3	1	no	—
153	C₂×C₈×D₅	—	3	1	no	—
154	C₄×D₂₀	—	3	1	no	—
155	C₄×D₂₀	—	3	1	no	—
156	#4018	—	3	1	no	—
157	#4018	—	3	1	no	—
158	C₄²×D₅	—	3	1	no	—
159	C₄²×D₅	—	3	1	no	—
160	C₄×Dic₁₀	—	3	1	no	—
161	C₄×Dic₁₀	—	3	1	no	—
162	C₅×C₄⋊C₈	—	3	1	no	—
163	C₅×C₄⋊C₈	—	3	1	no	—
164	C₅×C₂²⋊C₈	—	3	1	no	—
165	C₅×C₂²⋊C₈	C₂×D₃	1	1	yes	characteristic
166	C₄×C₅×C₈	—	3	1	no	—
167	C₄×C₅×C₈	—	3	1	no	—
168	#3952	—	3	1	no	—
169	#3952	—	3	1	no	—
170	#3952	—	3	1	no	—
171	#3952	C₂×D₃	1	1	yes	characteristic
172	#3947	—	3	1	no	—
173	#3947	—	3	1	no	—
174	#3946	—	3	1	no	—
175	#3946	—	3	1	no	—
176	#3946	—	3	1	no	—
177	#3946	C₂×D₃	1	1	yes	characteristic
178	C₈×Dic₅	—	3	1	no	—
179	C₈×Dic₅	C₂×D₃	1	1	yes	characteristic
180	#3935	—	3	1	no	—
181	#3935	—	3	1	no	—
182	C₄×#168	—	3	1	no	—
183	C₄×#168	—	3	1	no	—
184	#2965	—	15	1	no	Sylow
185	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
186	C₂²×D₁₅	C₂²×C₄	1	1	yes	characteristic
187	C₂²×C₃×D₅	C₂²×C₄	1	1	yes	characteristic
188	C₂×C₃×C₄×C₅	—	2	1	no	—
189	C₂×C₃×C₄×C₅	—	2	1	no	—
190	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
191	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
192	#1220	—	2	2	no	—
193	C₂×Dic₁₅	C₂²×C₄	1	1	yes	characteristic
194	C₂×Dic₁₅	C₂²×C₄	1	1	yes	characteristic
195	C₂×Dic₁₅	C₂²×C₄	1	1	yes	characteristic
196	C₄×D₁₅	—	2	1	no	—
197	C₄×D₁₅	—	2	1	no	—
198	C₂×C₅×Dic₃	—	2	2	no	—
199	C₂×C₅×Dic₃	—	2	2	no	—
200	C₂×C₅×Dic₃	C₂²×C₄	1	1	yes	characteristic
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	C₃×C₂²⋊D₅	—	2	2	no	—
205	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
206	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
207	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
208	C₃×C₄×D₅	—	2	1	no	—
209	C₃×C₄×D₅	—	2	1	no	—
210	#1204	—	2	2	no	—
211	#1202	—	2	2	no	—
212	#1200	—	2	2	no	—
213	#1200	M₁₆	1	4	yes	complemented
214	D₅×Dic₃	—	2	2	no	—
215	D₅×Dic₃	—	2	2	no	—
216	C₃×C₅×C₈	—	2	1	no	—
217	C₃×C₅×C₈	—	2	1	no	—
218	C₃⋊#168	—	2	1	no	—
219	C₃⋊#168	#41	1	2	yes	complemented
220	C₃×#168	—	2	1	no	—
221	C₃×#168	#41	1	2	yes	complemented
222	C₅×C₃⋊C₈	—	2	1	no	—
223	C₅×C₃⋊C₈	—	2	1	no	—
224	C₂×#237	—	5	1	no	—
225	C₂×C₃×M₁₆	—	5	1	no	—
226	C₂×C₃×M₁₆	—	5	1	no	—
227	C₃×C₄×D₄	—	5	1	no	—
228	D₄×Dic₃	—	5	1	no	—
229	C₄×#67	—	5	1	no	—
230	C₄×#67	—	5	1	no	—
231	C₂×C₄×Dic₃	—	5	1	no	—
232	C₂×C₄×Dic₃	C₂×D₅	1	1	yes	characteristic
233	C₂×#208	—	5	1	no	—
234	C₂×#208	—	5	1	no	—
235	C₂×D₃×C₈	—	5	1	no	—
236	C₂×D₃×C₈	—	5	1	no	—
237	#892	—	5	1	no	—
238	#887	—	5	1	no	—
239	#67⋊C₄	—	5	1	no	—
240	#67⋊C₄	—	5	1	no	—
241	#877	—	5	1	no	—
242	#877	—	5	1	no	—
243	C₄²×D₃	—	5	1	no	—
244	C₄×Dic₆	—	5	1	no	—
245	C₃×C₄⋊C₈	—	5	1	no	—
246	C₃×C₂²⋊C₈	—	5	1	no	—
247	C₃×C₂²⋊C₈	C₂×D₅	1	1	yes	characteristic
248	C₃×C₄×C₈	—	5	1	no	—
249	#830	—	5	1	no	—
250	#830	C₂×D₅	1	1	yes	characteristic
251	(C₂×D₃)⋊C₈	—	5	1	no	—
252	(C₂×D₃)⋊C₈	—	5	1	no	—
253	#815	—	5	1	no	—
254	#815	—	5	1	no	—
255	#815	—	5	1	no	—
256	#815	—	5	1	no	—
257	Dic₃⋊C₈	—	5	1	no	—
258	Dic₃⋊C₈	—	5	1	no	—
259	Dic₃⋊C₈	C₂×D₅	1	1	yes	characteristic
260	Dic₃⋊C₈	C₂×D₅	1	1	yes	characteristic
261	C₈×Dic₃	—	5	1	no	—
262	C₈×Dic₃	—	5	1	no	—
263	C₈×Dic₃	C₂×D₅	1	1	yes	characteristic
264	C₈×Dic₃	C₂×D₅	1	1	yes	characteristic
265	C₄⋊(C₃⋊C₈)	—	5	1	no	—
266	C₄×C₃⋊C₈	—	5	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	C₂×C₂²⋊D₅	—	3	1	no	—
271	C₂×C₂²⋊D₅	C₄×D₃	1	1	yes	characteristic
272	#709	—	6	4	no	—
273	C₂×D₂₀	—	3	1	no	—
274	C₂×C₄×D₅	—	3	1	no	—
275	C₂×C₄×D₅	—	3	1	no	—
276	C₂×C₄×D₅	—	3	1	no	—
277	C₂×C₄×D₅	—	3	1	no	—
278	C₂×C₄×D₅	—	3	1	no	—
279	C₂×C₄×D₅	C₂²×D₃	1	1	yes	characteristic
280	C₂×Dic₁₀	—	3	1	no	—
281	C₂×C₅×C₈	—	3	1	no	—
282	C₂×C₅×C₈	—	3	1	no	—
283	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
284	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
285	C₄²×C₅	—	3	1	no	—
286	C₄²×C₅	—	3	1	no	—
287	C₄²×C₅	—	3	1	no	—
288	C₄²×C₅	—	3	1	no	—
289	C₂²⋊Dic₅	—	3	1	no	—
290	C₂²⋊Dic₅	C₄×D₃	1	1	yes	characteristic
291	#685	—	3	1	no	—
292	#685	—	3	1	no	—
293	#685	—	3	1	no	—
294	#685	C₄×D₃	1	1	yes	characteristic
295	C₄⋊Dic₅	—	3	1	no	—
296	C₄⋊Dic₅	—	3	1	no	—
297	#683	—	3	1	no	—
298	#683	—	3	1	no	—
299	#683	—	3	1	no	—
300	#683	C₄×D₃	1	1	yes	characteristic
301	C₄×Dic₅	—	3	1	no	—
302	C₄×Dic₅	—	3	1	no	—
303	C₄×Dic₅	—	3	1	no	—
304	C₄×Dic₅	—	3	1	no	—
305	C₄×Dic₅	—	3	1	no	—
306	C₄×Dic₅	C₂²×D₃	1	1	yes	characteristic
307	#681	—	2	2	no	—
308	#681	—	6	2	no	—
309	C₂×#168	—	3	1	no	—
310	C₂×#168	—	3	1	no	—
311	C₂×#168	C₂²×D₃	1	1	yes	characteristic
312	C₂×#168	C₂²×D₃	1	1	yes	characteristic
313	#676	—	2	2	no	—
314	#676	—	6	2	no	—
315	C₈×D₅	—	6	2	no	—
316	C₈×D₅	—	6	2	no	—
317	C₄×#41	—	15	1	no	—
318	#446	—	15	1	no	—
319	#446	—	15	1	no	—
320	#436	—	5	1	no	—
321	#436	—	15	1	no	—
322	#435	—	15	1	no	—
323	#435	—	15	1	no	—
324	#435	—	15	1	no	—
325	#435	—	15	1	no	—
326	#431	—	3	1	no	—
327	#431	—	15	1	no	—
328	#431	—	15	1	no	—
329	C₄×M₁₆	—	15	1	no	—
330	C₄×M₁₆	—	15	1	no	—
331	C₂×C₄×C₈	—	15	1	no	—
332	C₂²×C₃×C₅	—	2	1	no	—
333	C₂²×C₃×C₅	—	2	1	no	—
334	C₂²×C₃×C₅	—	2	1	no	—
335	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
336	C₂×D₁₅	—	2	1	no	—
337	C₂×D₁₅	—	2	1	no	—
338	C₂×D₁₅	C₂×M₁₆	1	2	yes	—
339	C₂×C₃×D₅	—	2	1	no	—
340	C₂×C₃×D₅	—	2	1	no	—
341	C₂×C₃×D₅	—	2	1	no	—
342	C₃×C₄×C₅	—	2	1	no	—
343	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
344	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
345	Dic₁₅	—	2	1	no	—
346	Dic₁₅	—	2	1	no	—
347	Dic₁₅	—	2	1	no	—
348	C₃×Dic₅	—	2	1	no	—
349	C₃×Dic₅	—	2	1	no	—
350	C₃×Dic₅	C₂×M₁₆	1	2	yes	—
351	C₅×Dic₃	—	2	1	no	—
352	C₅×Dic₃	—	2	1	no	—
353	C₅×Dic₃	C₂×M₁₆	1	2	yes	—
354	C₅×Dic₃	#131	1	2	yes	—
355	C₂×C₃×D₄	—	5	1	no	—
356	C₂²×C₃×C₄	—	5	1	no	—
357	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
358	C₂×#67	—	5	1	no	—
359	C₂×#67	—	5	1	no	—
360	C₂²×Dic₃	—	5	1	no	—
361	C₂²×Dic₃	—	5	1	no	—
362	C₂²×Dic₃	C₄×D₅	1	1	yes	characteristic
363	C₂²×Dic₃	C₄×D₅	1	1	yes	characteristic
364	#237	—	10	4	no	—
365	C₂×C₄×D₃	—	5	1	no	—
366	C₂×C₄×D₃	—	5	1	no	—
367	C₂×C₄×D₃	—	5	1	no	—
368	C₂×Dic₆	—	5	1	no	—
369	C₃×M₁₆	—	10	2	no	—
370	C₃×M₁₆	—	10	2	no	—
371	C₂×C₃×C₈	—	5	1	no	—
372	C₂×C₃×C₈	—	5	1	no	—
373	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
374	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
375	C₃×C₄⋊C₄	—	5	1	no	—
376	C₃×C₂²⋊C₄	—	5	1	no	—
377	C₃×C₂²⋊C₄	—	5	1	no	—
378	C₃×C₄²	—	5	1	no	—
379	#217	—	5	1	no	—
380	#217	—	5	1	no	—
381	(C₂×D₃)⋊C₄	—	5	1	no	—
382	(C₂×D₃)⋊C₄	—	5	1	no	—
383	C₄⋊Dic₃	—	5	1	no	—
384	Dic₃⋊C₄	—	5	1	no	—
385	Dic₃⋊C₄	—	5	1	no	—
386	Dic₃⋊C₄	—	5	1	no	—
387	Dic₃⋊C₄	—	5	1	no	—
388	C₄×Dic₃	—	5	1	no	—
389	C₄×Dic₃	—	5	1	no	—
390	C₄×Dic₃	—	5	1	no	—
391	C₄×Dic₃	—	5	1	no	—
392	C₄×Dic₃	—	5	1	no	—
393	C₄×Dic₃	C₄×D₅	1	1	yes	characteristic
394	C₄×Dic₃	C₄×D₅	1	1	yes	characteristic
395	C₄×Dic₃	C₂²×D₅	1	1	yes	characteristic
396	C₄×Dic₃	C₂²×D₅	1	1	yes	characteristic
397	#208	—	10	2	no	—
398	#208	—	10	2	no	—
399	C₂×C₃⋊C₈	—	5	1	no	—
400	C₂×C₃⋊C₈	—	5	1	no	—
401	C₂×C₃⋊C₈	C₂²×D₅	1	1	yes	characteristic
402	C₂×C₃⋊C₈	C₂²×D₅	1	1	yes	characteristic
403	D₃×C₈	—	10	2	no	—
404	D₃×C₈	—	10	2	no	—
405	C₂³×C₅	C₂×C₄×D₃	1	1	yes	characteristic
406	C₂²×D₅	—	3	1	no	—
407	C₂²×D₅	C₂×C₄×D₃	1	1	yes	characteristic
408	C₂×C₄×C₅	—	2	1	no	—
409	C₂×C₄×C₅	—	2	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	—	6	2	no	—
415	C₂×C₄×C₅	—	6	2	no	—
416	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
417	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
418	C₂²⋊D₅	—	2	2	no	—
419	C₂²⋊D₅	—	6	2	no	—
420	C₂×Dic₅	—	3	1	no	—
421	C₂×Dic₅	—	3	1	no	—
422	C₂×Dic₅	—	3	1	no	—
423	C₂×Dic₅	C₂×C₄×D₃	1	1	yes	characteristic
424	C₂×Dic₅	C₂×C₄×D₃	1	1	yes	characteristic
425	C₂×Dic₅	C₂×C₄×D₃	1	1	yes	characteristic
426	D₂₀	—	6	2	no	—
427	C₄×D₅	—	2	1	no	—
428	C₄×D₅	—	2	1	no	—
429	C₄×D₅	—	3	4	no	—
430	C₄×D₅	—	6	2	no	—
431	C₄×D₅	—	6	2	no	—
432	C₄×D₅	—	6	2	no	—
433	C₄×D₅	—	6	1	no	—
434	C₄×D₅	—	6	1	no	—
435	Dic₁₀	—	6	2	no	—
436	C₅×C₈	—	2	1	no	—
437	C₅×C₈	—	2	1	no	—
438	C₅×C₈	—	6	1	no	—
439	C₅×C₈	—	6	1	no	—
440	#168	—	2	1	no	—
441	#168	—	3	2	no	—
442	#168	—	6	1	no	—
443	#168	#237	1	2	yes	complemented
444	C₂×#41	—	15	1	no	—
445	C₂×M₁₆	—	5	1	no	—
446	C₂×M₁₆	—	5	1	no	—
447	C₂×M₁₆	—	15	1	no	—
448	C₂×M₁₆	—	15	1	no	—
449	C₂²×C₈	—	15	1	no	—
450	C₂²×C₈	—	15	1	no	—
451	C₄×Q₈	—	15	1	no	—
452	C₄×Q₈	—	15	1	no	—
453	C₄×D₄	—	5	1	no	—
454	C₄×D₄	—	15	1	no	—
455	C₄×D₄	—	15	1	no	—
456	C₄×D₄	—	15	1	no	—
457	C₄×D₄	—	15	1	no	—
458	C₄×D₄	—	15	1	no	—
459	#117	—	15	1	no	—
460	#117	—	15	1	no	—
461	#117	—	15	1	no	—
462	C₂×C₄²	—	3	1	no	—
463	C₂×C₄²	—	15	1	no	—
464	C₂×C₄²	—	15	1	no	—
465	C₄⋊C₈	—	3	1	no	—
466	C₄⋊C₈	—	3	1	no	—
467	C₄⋊C₈	—	5	1	no	—
468	C₄⋊C₈	—	15	1	no	—
469	C₄⋊C₈	—	15	1	no	—
470	C₄⋊C₈	—	15	1	no	—
471	C₂²⋊C₈	—	3	1	no	—
472	C₂²⋊C₈	—	5	1	no	—
473	C₂²⋊C₈	—	15	1	no	—
474	C₂²⋊C₈	—	15	1	no	—
475	C₂²⋊C₈	—	15	1	no	—
476	C₂²⋊C₈	D₃×D₅	1	1	yes	characteristic
477	#97	—	15	1	no	—
478	#97	—	15	1	no	—
479	#97	—	15	1	no	—
480	#97	—	15	1	no	—
481	C₄×C₈	—	3	1	no	—
482	C₄×C₈	—	3	1	no	—
483	C₄×C₈	—	5	1	no	—
484	C₄×C₈	—	15	1	no	—
485	C₄×C₈	—	15	1	no	—
486	C₄×C₈	—	15	1	no	—
487	C₂×C₃×C₅	—	4	1	no	—
488	C₂×C₃×C₅	C₄×#41	1	1	yes	characteristic
489	C₂×C₃×C₅	C₂²×M₁₆	1	1	yes	characteristic
490	C₂×C₃×C₅	C₂×#131	1	1	yes	characteristic
491	D₁₅	—	2	2	no	—
492	C₃×D₅	—	4	1	no	—
493	C₂³×C₃	—	5	1	no	—
494	C₂³×C₃	C₂×C₄×D₅	1	1	yes	characteristic
495	C₂²×D₃	—	5	1	no	—
496	C₃×D₄	—	10	2	no	—
497	C₂×C₃×C₄	—	2	1	no	—
498	C₂×C₃×C₄	—	2	1	no	—
499	C₂×C₃×C₄	—	5	1	no	—
500	C₂×C₃×C₄	—	5	1	no	—
501	C₂×C₃×C₄	—	5	1	no	—
502	C₂×C₃×C₄	—	10	1	no	—
503	C₂×C₃×C₄	—	10	1	no	—
504	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
505	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
506	#67	—	10	2	no	—
507	#67	—	10	2	no	—
508	C₂×Dic₃	—	2	2	no	—
509	C₂×Dic₃	—	2	2	no	—
510	C₂×Dic₃	—	5	1	no	—
511	C₂×Dic₃	—	5	1	no	—
512	C₂×Dic₃	—	5	1	no	—
513	C₂×Dic₃	—	10	2	no	—
514	C₂×Dic₃	—	10	2	no	—
515	C₂×Dic₃	C₂×C₄×D₅	1	1	yes	characteristic
516	C₂×Dic₃	C₂×C₄×D₅	1	1	yes	characteristic
517	C₂×Dic₃	C₂×C₄×D₅	1	1	yes	characteristic
518	C₂×Dic₃	C₂×C₄×D₅	1	1	yes	characteristic
519	C₄×D₃	—	5	4	no	—
520	C₄×D₃	—	10	1	no	—
521	C₄×D₃	—	10	1	no	—
522	C₄×D₃	—	10	2	no	—
523	Dic₆	—	10	2	no	—
524	C₃×C₈	—	2	1	no	—
525	C₃×C₈	—	2	1	no	—
526	C₃×C₈	—	5	2	no	—
527	C₃×C₈	—	10	1	no	—
528	C₃⋊C₈	—	2	1	no	—
529	C₃⋊C₈	—	2	1	no	—
530	C₃⋊C₈	—	5	2	no	—
531	C₃⋊C₈	—	10	1	no	—
532	C₂²×C₅	—	2	1	no	—
533	C₂²×C₅	—	2	1	no	—
534	C₂²×C₅	—	2	1	no	—
535	C₂²×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
536	C₂×D₅	—	2	1	no	—
537	C₂×D₅	—	2	1	no	—
538	C₂×D₅	—	2	1	no	—
539	C₂×D₅	—	3	2	no	—
540	C₂×D₅	—	6	1	no	—
541	C₂×D₅	—	6	1	no	—
542	C₄×C₅	—	2	1	no	—
543	C₄×C₅	—	3	2	no	—
544	C₄×C₅	—	3	2	no	—
545	C₄×C₅	—	6	1	no	—
546	C₄×C₅	—	6	1	no	—
547	C₄×C₅	C₂×#237	1	1	yes	characteristic
548	C₄×C₅	D₃×#41	1	1	yes	characteristic
549	Dic₅	—	2	1	no	—
550	Dic₅	—	2	1	no	—
551	Dic₅	—	6	1	no	—
552	Dic₅	—	6	1	no	—
553	Dic₅	—	6	1	no	—
554	Dic₅	D₃×M₁₆	1	2	yes	—
555	#41	—	30	4	no	—
556	C₂×Q₈	—	15	1	no	—
557	C₂×D₄	—	5	1	no	—
558	C₂×D₄	—	15	1	no	—
559	C₂×D₄	—	15	1	no	—
560	C₂²×C₄	—	3	1	no	—
561	C₂²×C₄	—	3	1	no	—
562	C₂²×C₄	—	5	1	no	—
563	C₂²×C₄	—	15	1	no	—
564	C₂²×C₄	—	15	1	no	—
565	C₂²×C₄	—	15	1	no	—
566	C₂²×C₄	—	15	1	no	—
567	C₂²×C₄	—	15	1	no	—
568	C₂²×C₄	C₂×D₃×D₅	1	1	yes	characteristic
569	M₁₆	—	10	2	no	—
570	M₁₆	—	10	2	no	—
571	M₁₆	—	30	2	no	—
572	M₁₆	—	30	2	no	—
573	C₂×C₈	—	3	1	no	—
574	C₂×C₈	—	3	1	no	—
575	C₂×C₈	—	5	1	no	—
576	C₂×C₈	—	5	1	no	—
577	C₂×C₈	—	15	1	no	—
578	C₂×C₈	—	15	1	no	—
579	C₂×C₈	—	30	2	no	—
580	C₂×C₈	—	30	2	no	—
581	C₂×C₈	C₂×D₃×D₅	1	1	yes	characteristic
582	C₂×C₈	C₂×D₃×D₅	1	1	yes	characteristic
583	C₄⋊C₄	—	5	1	no	—
584	C₄⋊C₄	—	15	1	no	—
585	C₄⋊C₄	—	15	1	no	—
586	C₄⋊C₄	—	15	1	no	—
587	C₄⋊C₄	—	15	1	no	—
588	C₄⋊C₄	—	15	1	no	—
589	C₂²⋊C₄	—	5	1	no	—
590	C₂²⋊C₄	—	5	1	no	—
591	C₂²⋊C₄	—	15	1	no	—
592	C₂²⋊C₄	—	15	1	no	—
593	C₂²⋊C₄	—	15	1	no	—
594	C₂²⋊C₄	—	15	1	no	—
595	C₄²	—	3	1	no	—
596	C₄²	—	3	1	no	—
597	C₄²	—	3	1	no	—
598	C₄²	—	3	1	no	—
599	C₄²	—	5	1	no	—
600	C₄²	—	15	1	no	—
601	C₄²	—	15	1	no	—
602	C₄²	—	15	1	no	—
603	C₄²	—	15	1	no	—
604	C₄²	—	15	1	no	—
605	C₃×C₅	#2965	1	1	yes	characteristic, complemented, Hall
606	C₂²×C₃	—	2	1	no	—
607	C₂²×C₃	—	2	1	no	—
608	C₂²×C₃	—	2	1	no	—
609	C₂²×C₃	—	10	1	no	—
610	C₂²×C₃	—	10	1	no	—
611	C₂²×C₃	—	10	1	no	—
612	C₂²×C₃	C₂²×C₄×D₅	1	1	yes	characteristic
613	C₂×D₃	—	5	2	no	—
614	C₂×D₃	—	10	1	no	—
615	C₂×D₃	—	10	1	no	—
616	C₃×C₄	—	2	1	no	—
617	C₃×C₄	—	5	2	no	—
618	C₃×C₄	—	10	1	no	—
619	C₃×C₄	—	10	1	no	—
620	C₃×C₄	D₅×#41	1	1	yes	characteristic
621	C₃×C₄	D₅×#41	1	1	yes	characteristic
622	Dic₃	—	2	1	no	—
623	Dic₃	—	2	1	no	—
624	Dic₃	—	10	1	no	—
625	Dic₃	—	10	1	no	—
626	Dic₃	—	10	1	no	—
627	Dic₃	#4047	1	2	yes	—
628	Dic₃	D₅×M₁₆	1	2	yes	—
629	C₂×C₅	—	4	1	no	—
630	C₂×C₅	C₄×#237	1	1	yes	characteristic
631	C₂×C₅	C₂×D₃×M₁₆	1	1	yes	characteristic
632	C₂×C₅	D₃×#131	1	1	yes	characteristic
633	D₅	—	4	1	no	—
634	D₅	—	6	2	no	—
635	C₂³	—	5	1	no	—
636	C₂³	—	15	1	no	—
637	C₂³	C₄×D₃×D₅	1	1	yes	characteristic
638	Q₈	—	30	2	no	—
639	D₄	—	10	2	no	—
640	D₄	—	30	2	no	—
641	D₄	—	30	2	no	—
642	C₂×C₄	—	2	1	no	—
643	C₂×C₄	—	2	1	no	—
644	C₂×C₄	—	3	1	no	—
645	C₂×C₄	—	3	1	no	—
646	C₂×C₄	—	3	1	no	—
647	C₂×C₄	—	3	1	no	—
648	C₂×C₄	—	5	1	no	—
649	C₂×C₄	—	5	1	no	—
650	C₂×C₄	—	5	1	no	—
651	C₂×C₄	—	6	2	no	—
652	C₂×C₄	—	6	2	no	—
653	C₂×C₄	—	10	1	no	—
654	C₂×C₄	—	10	1	no	—
655	C₂×C₄	—	15	4	no	—
656	C₂×C₄	—	15	1	no	—
657	C₂×C₄	—	15	1	no	—
658	C₂×C₄	—	15	1	no	—
659	C₂×C₄	—	30	2	no	—
660	C₂×C₄	—	30	2	no	—
661	C₂×C₄	—	30	2	no	—
662	C₂×C₄	—	30	1	no	—
663	C₂×C₄	—	30	1	no	—
664	C₂×C₄	C₄×D₃×D₅	1	1	yes	characteristic
665	C₂×C₄	C₂²×D₃×D₅	1	1	yes	characteristic
666	C₈	—	2	1	no	—
667	C₈	—	2	1	no	—
668	C₈	—	5	2	no	—
669	C₈	—	6	1	no	—
670	C₈	—	6	1	no	—
671	C₈	—	10	1	no	—
672	C₈	—	15	2	no	—
673	C₈	—	30	1	no	—
674	C₂×C₃	—	4	1	no	—
675	C₂×C₃	—	20	1	no	—
676	C₂×C₃	#65856	1	1	yes	characteristic
677	C₂×C₃	C₂×#4047	1	1	yes	characteristic
678	C₂×C₃	C₂×D₅×M₁₆	1	1	yes	characteristic
679	D₃	—	10	2	no	—
680	C₅	#79517	1	1	yes	characteristic, complemented, Sylow
681	C₂²	—	2	1	no	—
682	C₂²	—	2	1	no	—
683	C₂²	—	2	1	no	—
684	C₂²	—	10	1	no	—
685	C₂²	—	10	1	no	—
686	C₂²	—	10	1	no	—
687	C₂²	—	15	2	no	—
688	C₂²	—	30	1	no	—
689	C₂²	—	30	1	no	—
690	C₂²	C₂×C₄×D₃×D₅	1	1	yes	characteristic
691	C₄	—	2	1	no	—
692	C₄	—	3	2	no	—
693	C₄	—	3	2	no	—
694	C₄	—	5	2	no	—
695	C₄	—	6	1	no	—
696	C₄	—	6	1	no	—
697	C₄	—	10	1	no	—
698	C₄	—	10	1	no	—
699	C₄	—	30	1	no	—
700	C₄	—	30	1	no	—
701	C₄	—	30	1	no	—
702	C₄	D₅×#237	1	1	yes	characteristic
703	C₄	#92024	1	1	yes	characteristic
704	C₃	#10611009	1	1	yes	characteristic, complemented, Sylow
705	C₂	—	4	1	no	—
706	C₂	—	20	1	no	—
707	C₂	—	30	2	no	—
708	C₂	#11752818	1	1	yes	characteristic
709	C₂	D₃×#4047	1	1	yes	characteristic
710	C₂	D₃×D₅×M₁₆	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×D₃×D₅
commutator, socle	C₂²×C₃×C₅	C₂³×C₄
Fitting	C₃×C₅×C₂²⋊C₈	C₂²
prime radical	C₂×#6779	C₄
cosocle	C₂×C₃×C₄×C₅	C₂⁴
hypercenter	C₂²⋊C₈	D₃×D₅
hypocenter	C₃×C₅	#2965
LCS	G ▷ C₂²×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂×C₄ ◁ C₂²⋊C₈

Complements

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

N	H ≅ G/N	type
2. #11750829	C₂	semidirect
3. C₅×#4718	C₂	semidirect
4. C₃×#65018	C₂	semidirect
5. #11748486	C₂	semidirect
6. #11748339	C₂	semidirect
7. Dic₃×#681	C₂	semidirect
8. #11747821	C₂	semidirect
9. #11747820	C₂	semidirect
10. #11747727	C₂	semidirect
11. #11747726	C₂	semidirect
12. Dic₃×#676	C₂	semidirect
13. #11747584	C₂	semidirect
14. C₈×#1200	C₂	semidirect
15. #11747576	C₂	semidirect
69. #65018	D₃	semidirect
138. #4718	D₅	semidirect
213. #1200	M₁₆	semidirect
219. C₃⋊#168	#41	semidirect
221. C₃×#168	#41	semidirect
443. #168	#237	semidirect
605. C₃×C₅	#2965	semidirect
680. C₅	#79517	semidirect
704. C₃	#10611009	semidirect

Maximal subgroups

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

subgroup	index
C₄×#6779	2
#11750829	2
C₅×#4718	2
C₃×#65018	2
#11748486	2
#11748339	2
Dic₃×#681	2
#11747821	2
#11747820	2
#11747727	2
#11747726	2
Dic₃×#676	2
#11747584	2
C₈×#1200	2
#11747576	2
#10611009	3
#79517	5