Subgroups — #14419622

Order 1920.

744 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	#11754226	C₂	1	1	yes	maximal, characteristic
2	C₈×#1220	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#5101	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#65400	C₂	1	1	yes	maximal, characteristic, complemented
5	#11748492	C₂	1	1	yes	maximal, characteristic, complemented
6	#11748488	C₂	1	1	yes	maximal, characteristic, complemented
7	#11748330	C₂	1	1	yes	maximal, characteristic, complemented
8	#11748051	C₂	1	1	yes	maximal, characteristic, complemented
9	#11748042	C₂	1	1	yes	maximal, characteristic, complemented
10	#11747824	C₂	1	1	yes	maximal, characteristic, complemented
11	#11747823	C₂	1	1	yes	maximal, characteristic, complemented
12	#11747725	C₂	1	1	yes	maximal, characteristic, complemented
13	#11747649	C₂	1	1	yes	maximal, characteristic, complemented
14	#11747603	C₂	1	1	yes	maximal, characteristic, complemented
15	#11747584	C₂	1	1	yes	maximal, characteristic, complemented
16	#10610289	—	3	1	no	maximal, Hall
17	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
18	C₄×#1220	C₂²	1	1	yes	characteristic
19	C₂×C₈×D₁₅	C₂²	1	1	yes	characteristic
20	C₅×#926	C₂²	1	1	yes	characteristic
21	C₂×C₅×#208	C₂²	1	1	yes	characteristic
22	C₃×C₄×C₂²⋊D₅	C₂²	1	1	yes	characteristic
23	C₂×C₃×#676	C₂²	1	1	yes	characteristic
24	#91562	C₄	1	1	yes	characteristic
25	#91534	C₄	1	1	yes	characteristic
26	#91533	C₄	1	1	yes	characteristic
27	#91531	C₄	1	1	yes	characteristic
28	C₄×#1204	C₂²	1	1	yes	characteristic
29	C₄×#1202	C₂²	1	1	yes	characteristic
30	#91419	C₄	1	1	yes	characteristic
31	C₄×#1200	C₂²	1	1	yes	characteristic
32	#91361	C₄	1	1	yes	characteristic
33	#91357	C₂²	1	1	yes	characteristic
34	#91356	C₄	1	1	yes	characteristic
35	#91335	C₄	1	1	yes	characteristic
36	C₂×#6648	C₂²	1	1	yes	characteristic
37	C₂×D₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
38	#91114	C₂²	1	1	yes	characteristic
39	#91104	C₂²	1	1	yes	characteristic
40	#91098	C₂²	1	1	yes	characteristic
41	C₈×Dic₁₅	C₂²	1	1	yes	characteristic
42	C₅×#815	C₂²	1	1	yes	characteristic
43	C₅×#815	C₂²	1	1	yes	characteristic
44	C₅×C₈×Dic₃	C₂²	1	1	yes	characteristic
45	C₅×C₈×Dic₃	C₂²	1	1	yes	characteristic
46	C₃×C₂²⋊#168	C₂²	1	1	yes	characteristic
47	C₃×#3952	C₂²	1	1	yes	characteristic
48	C₃×#3947	C₂²	1	1	yes	characteristic
49	C₃×#3946	C₂²	1	1	yes	characteristic
50	Dic₃⋊#168	C₂²	1	1	yes	characteristic
51	Dic₃⋊#168	C₂²	1	1	yes	characteristic
52	#90983	C₂²	1	1	yes	characteristic
53	#90982	C₂²	1	1	yes	characteristic
54	#90957	C₂²	1	1	yes	characteristic
55	#90955	C₂²	1	1	yes	characteristic
56	#90954	C₂²	1	1	yes	characteristic
57	#90953	C₂²	1	1	yes	characteristic
58	#90952	C₂²	1	1	yes	characteristic
59	Dic₃×#168	C₂²	1	1	yes	characteristic
60	#79458	—	5	1	no	maximal, Hall
61	#65862	—	3	1	no	—
62	C₅×#405	—	3	1	no	—
63	#65416	—	3	1	no	—
64	#65416	—	3	1	no	—
65	#65400	D₃	1	1	yes	characteristic, complemented
66	C₈×C₂²⋊D₅	—	3	1	no	—
67	#65289	—	3	1	no	—
68	#64997	—	3	1	no	—
69	#64995	—	3	1	no	—
70	D₅×#97	—	3	1	no	—
71	#64990	—	3	1	no	—
72	#64979	—	3	1	no	—
73	C₈×D₂₀	—	3	1	no	—
74	#64974	—	3	1	no	—
75	#64968	—	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	C₂×C₃×C₂²⋊D₅	C₂×C₄	1	1	yes	characteristic
80	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
81	C₂×#1204	C₂×C₄	1	1	yes	characteristic
82	C₂×#1202	C₂×C₄	1	1	yes	characteristic
83	C₂×#1200	C₂×C₄	1	1	yes	characteristic
84	C₂×#1200	C₂×C₄	1	1	yes	characteristic
85	C₂×C₃×C₅×C₈	—	2	2	no	—
86	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
87	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
88	#6719	C₂×C₄	1	1	yes	characteristic
89	#6714	C₂×C₄	1	1	yes	characteristic
90	#6712	C₂×C₄	1	1	yes	characteristic
91	C₄×Dic₁₅	C₂³	1	1	yes	characteristic
92	C₂×C₃⋊#168	C₂³	1	1	yes	characteristic
93	C₂×C₃⋊#168	C₂³	1	1	yes	characteristic
94	C₈×D₁₅	—	2	2	no	—
95	C₅×#217	C₂×C₄	1	1	yes	characteristic
96	C₅×#217	C₂×C₄	1	1	yes	characteristic
97	C₅×C₄⋊Dic₃	C₂×C₄	1	1	yes	characteristic
98	C₅×C₄⋊Dic₃	C₂×C₄	1	1	yes	characteristic
99	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
100	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
101	C₅×#208	—	2	2	no	—
102	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
103	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
104	C₃×C₂²⋊Dic₅	C₂×C₄	1	1	yes	characteristic
105	C₃×#685	C₂×C₄	1	1	yes	characteristic
106	C₃×#683	C₂×C₄	1	1	yes	characteristic
107	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
108	C₂×C₃×#168	C₂³	1	1	yes	characteristic
109	C₂×C₃×#168	C₂³	1	1	yes	characteristic
110	C₃×#676	—	2	2	no	—
111	Dic₃⋊Dic₅	C₂×C₄	1	1	yes	characteristic
112	Dic₃⋊Dic₅	C₂×C₄	1	1	yes	characteristic
113	#6669	C₂×C₄	1	1	yes	characteristic
114	#6668	C₂×C₄	1	1	yes	characteristic
115	#6668	C₂×C₄	1	1	yes	characteristic
116	#6668	C₂×C₄	1	1	yes	characteristic
117	#6667	C₂×C₄	1	1	yes	characteristic
118	#6665	C₂×C₄	1	1	yes	characteristic
119	#6665	C₂×C₄	1	1	yes	characteristic
120	#6665	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	#6648	—	2	2	no	—
124	D₅×C₃⋊C₈	—	2	2	no	—
125	#5557	—	5	1	no	—
126	C₃×#435	—	5	1	no	—
127	#5127	—	5	1	no	—
128	#5122	—	5	1	no	—
129	C₈×#67	—	5	1	no	—
130	#5101	D₅	1	1	yes	characteristic, complemented
131	#5011	—	5	1	no	—
132	#4833	—	5	1	no	—
133	#4828	—	5	1	no	—
134	#4728	—	5	1	no	—
135	#67⋊C₈	—	5	1	no	—
136	#4720	—	5	1	no	—
137	#4720	—	5	1	no	—
138	D₃×#97	—	5	1	no	—
139	#4701	—	5	1	no	—
140	C₂×C₅×M₁₆	—	3	1	no	—
141	C₂²×C₅×C₈	C₂×D₃	1	1	yes	characteristic
142	C₅×#117	—	3	1	no	—
143	C₄×C₂²⋊D₅	—	3	1	no	—
144	C₄×C₂²⋊D₅	C₂×D₃	1	1	yes	characteristic
145	C₂×#676	C₂×D₃	1	1	yes	characteristic
146	C₂×C₈×D₅	—	3	1	no	—
147	C₂×C₈×D₅	—	3	1	no	—
148	C₂×C₈×D₅	—	3	1	no	—
149	#4044	—	3	1	no	—
150	#4042	—	3	1	no	—
151	#4040	—	3	1	no	—
152	#4035	—	3	1	no	—
153	#4031	—	3	1	no	—
154	#4030	—	3	1	no	—
155	#4029	—	3	1	no	—
156	#4025	—	3	1	no	—
157	C₄×D₂₀	—	3	1	no	—
158	#4018	—	3	1	no	—
159	C₄²×D₅	—	3	1	no	—
160	C₄×Dic₁₀	—	3	1	no	—
161	C₅×#97	—	3	1	no	—
162	C₅×#97	—	3	1	no	—
163	C₄×C₅×C₈	—	3	1	no	—
164	C₄×C₅×C₈	—	3	1	no	—
165	C₂²⋊#168	—	3	1	no	—
166	C₂²⋊#168	C₂×D₃	1	1	yes	characteristic
167	#3952	—	3	1	no	—
168	#3952	—	3	1	no	—
169	#3952	—	3	1	no	—
170	#3952	C₂×D₃	1	1	yes	characteristic
171	#3947	—	3	1	no	—
172	#3947	—	3	1	no	—
173	#3947	C₂×D₃	1	1	yes	characteristic
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	C₄⋊#168	—	3	1	no	—
180	C₄⋊#168	—	3	1	no	—
181	#3935	—	3	1	no	—
182	C₄×#168	—	3	1	no	—
183	#2968	—	15	1	no	Sylow
184	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
185	C₂²×D₁₅	C₂²×C₄	1	1	yes	characteristic
186	C₂²×C₃×D₅	C₂²×C₄	1	1	yes	characteristic
187	C₂×C₃×C₄×C₅	—	2	1	no	—
188	C₂×C₃×C₄×C₅	—	2	1	no	—
189	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
190	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
191	#1220	—	2	2	no	—
192	C₂×Dic₁₅	C₂²×C₄	1	1	yes	characteristic
193	C₂×Dic₁₅	C₂²×C₄	1	1	yes	characteristic
194	C₂×Dic₁₅	C₂²×C₄	1	1	yes	characteristic
195	C₄×D₁₅	—	2	1	no	—
196	C₄×D₁₅	—	2	1	no	—
197	C₂×C₅×Dic₃	C₂²×C₄	1	1	yes	characteristic
198	C₂×C₅×Dic₃	C₂²×C₄	1	1	yes	characteristic
199	C₂×C₅×Dic₃	C₂²×C₄	1	1	yes	characteristic
200	C₂×C₅×Dic₃	C₂²×C₄	1	1	yes	characteristic
201	C₃×C₂²⋊D₅	—	4	1	no	—
202	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
203	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
204	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
205	C₃×C₄×D₅	—	2	1	no	—
206	C₃×C₄×D₅	—	2	1	no	—
207	#1204	—	4	1	no	—
208	#1202	—	2	2	no	—
209	#1200	—	2	2	no	—
210	#1200	—	4	1	no	—
211	C₃×C₅×C₈	—	2	1	no	—
212	C₃×C₅×C₈	#41	1	2	yes	—
213	C₃⋊#168	—	2	1	no	—
214	C₃⋊#168	—	2	1	no	—
215	C₃×#168	—	2	1	no	—
216	C₃×#168	—	2	1	no	—
217	C₅×C₃⋊C₈	—	2	1	no	—
218	C₅×C₃⋊C₈	#41	1	2	yes	—
219	C₂×C₃×M₁₆	—	5	1	no	—
220	C₂²×C₃×C₈	C₂×D₅	1	1	yes	characteristic
221	C₃×C₄×D₄	—	5	1	no	—
222	#938	—	5	1	no	—
223	#936	—	5	1	no	—
224	C₄×#67	—	5	1	no	—
225	C₄×#67	—	5	1	no	—
226	#926	—	5	1	no	—
227	#926	C₂×D₅	1	1	yes	characteristic
228	C₂×#208	C₂×D₅	1	1	yes	characteristic
229	C₂²×C₃⋊C₈	—	5	1	no	—
230	C₂×D₃×C₈	—	5	1	no	—
231	C₂×D₃×C₈	—	5	1	no	—
232	#897	—	5	1	no	—
233	#890	—	5	1	no	—
234	#883	—	5	1	no	—
235	#883	—	5	1	no	—
236	#879	—	5	1	no	—
237	#879	—	5	1	no	—
238	C₄²×D₃	—	5	1	no	—
239	C₄×Dic₆	—	5	1	no	—
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	C₂×D₅	1	1	yes	characteristic
251	#815	C₂×D₅	1	1	yes	characteristic
252	Dic₃⋊C₈	—	5	1	no	—
253	Dic₃⋊C₈	—	5	1	no	—
254	Dic₃⋊C₈	—	5	1	no	—
255	Dic₃⋊C₈	—	5	1	no	—
256	C₈×Dic₃	—	5	1	no	—
257	C₈×Dic₃	—	5	1	no	—
258	C₈×Dic₃	C₂×D₅	1	1	yes	characteristic
259	C₈×Dic₃	C₂×D₅	1	1	yes	characteristic
260	C₄⋊(C₃⋊C₈)	—	5	1	no	—
261	#803	—	5	1	no	—
262	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
263	C₂×C₂²⋊D₅	—	3	1	no	—
264	C₂×C₂²⋊D₅	C₄×D₃	1	1	yes	characteristic
265	C₂×D₂₀	—	3	1	no	—
266	C₂×C₄×D₅	—	3	1	no	—
267	C₂×C₄×D₅	—	3	1	no	—
268	C₂×C₄×D₅	—	3	1	no	—
269	C₂×C₄×D₅	C₂²×D₃	1	1	yes	characteristic
270	C₂×Dic₁₀	—	3	1	no	—
271	C₅×M₁₆	—	6	2	no	—
272	C₂×C₅×C₈	—	2	2	no	—
273	C₂×C₅×C₈	—	3	1	no	—
274	C₂×C₅×C₈	—	3	1	no	—
275	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
276	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
277	C₅×C₄⋊C₄	—	3	1	no	—
278	C₅×C₄⋊C₄	—	3	1	no	—
279	C₅×C₂²⋊C₄	—	3	1	no	—
280	C₅×C₂²⋊C₄	—	3	1	no	—
281	C₄²×C₅	—	3	1	no	—
282	C₄²×C₅	—	3	1	no	—
283	C₂²⋊Dic₅	—	3	1	no	—
284	C₂²⋊Dic₅	C₄×D₃	1	1	yes	characteristic
285	#685	—	3	1	no	—
286	#685	—	3	1	no	—
287	#685	—	3	1	no	—
288	#685	—	3	1	no	—
289	#685	—	3	1	no	—
290	#685	C₄×D₃	1	1	yes	characteristic
291	C₄⋊Dic₅	—	3	1	no	—
292	C₄⋊Dic₅	—	3	1	no	—
293	#683	—	3	1	no	—
294	#683	—	3	1	no	—
295	#683	—	3	1	no	—
296	#683	—	3	1	no	—
297	#683	—	3	1	no	—
298	#683	C₄×D₃	1	1	yes	characteristic
299	C₄×Dic₅	—	3	1	no	—
300	C₄×Dic₅	—	3	1	no	—
301	C₄×Dic₅	—	3	1	no	—
302	C₄×Dic₅	C₂²×D₃	1	1	yes	characteristic
303	C₂×#168	—	3	1	no	—
304	C₂×#168	—	3	1	no	—
305	C₂×#168	C₂²×D₃	1	1	yes	characteristic
306	C₂×#168	C₂²×D₃	1	1	yes	characteristic
307	#676	—	2	2	no	—
308	C₈×D₅	—	6	2	no	—
309	C₈×D₅	—	6	2	no	—
310	C₈×D₅	—	6	2	no	—
311	#529	—	15	1	no	—
312	#446	—	15	1	no	—
313	#446	—	15	1	no	—
314	#435	—	5	1	no	—
315	#435	—	15	1	no	—
316	#435	—	15	1	no	—
317	#435	—	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	#431	—	15	1	no	—
323	#405	—	3	1	no	—
324	#405	—	15	1	no	—
325	C₂×#97	—	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	C₂³×C₄	1	1	yes	characteristic
330	C₂×D₁₅	—	2	1	no	—
331	C₂×D₁₅	—	2	1	no	—
332	C₂×D₁₅	#131	1	2	yes	—
333	C₂×C₃×D₅	—	2	1	no	—
334	C₂×C₃×D₅	—	2	1	no	—
335	C₂×C₃×D₅	—	2	1	no	—
336	C₃×C₄×C₅	—	2	1	no	—
337	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
338	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
339	Dic₁₅	—	2	1	no	—
340	Dic₁₅	—	2	1	no	—
341	Dic₁₅	—	2	1	no	—
342	C₃×Dic₅	—	2	1	no	—
343	C₃×Dic₅	—	2	1	no	—
344	C₃×Dic₅	—	2	1	no	—
345	C₅×Dic₃	—	2	1	no	—
346	C₅×Dic₃	—	2	1	no	—
347	C₅×Dic₃	—	2	1	no	—
348	C₅×Dic₃	—	2	1	no	—
349	C₂×C₃×D₄	—	5	1	no	—
350	C₂²×C₃×C₄	—	5	1	no	—
351	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
352	C₂×#67	—	5	1	no	—
353	C₂×#67	—	5	1	no	—
354	C₂×C₄×D₃	—	5	1	no	—
355	C₂×C₄×D₃	—	5	1	no	—
356	C₂×C₄×D₃	—	5	1	no	—
357	C₂×Dic₆	—	5	1	no	—
358	C₃×M₁₆	—	10	2	no	—
359	C₂×C₃×C₈	—	2	2	no	—
360	C₂×C₃×C₈	—	5	1	no	—
361	C₂×C₃×C₈	—	5	1	no	—
362	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
363	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
364	C₃×C₄⋊C₄	—	5	1	no	—
365	C₃×C₂²⋊C₄	—	5	1	no	—
366	C₃×C₂²⋊C₄	—	5	1	no	—
367	C₃×C₄²	—	5	1	no	—
368	#217	—	5	1	no	—
369	#217	—	5	1	no	—
370	#217	—	5	1	no	—
371	#217	—	5	1	no	—
372	#217	C₄×D₅	1	1	yes	characteristic
373	#217	C₄×D₅	1	1	yes	characteristic
374	(C₂×D₃)⋊C₄	—	5	1	no	—
375	(C₂×D₃)⋊C₄	—	5	1	no	—
376	C₄⋊Dic₃	—	5	1	no	—
377	C₄⋊Dic₃	—	5	1	no	—
378	C₄⋊Dic₃	—	5	1	no	—
379	C₄⋊Dic₃	C₄×D₅	1	1	yes	characteristic
380	C₄⋊Dic₃	C₄×D₅	1	1	yes	characteristic
381	Dic₃⋊C₄	—	5	1	no	—
382	Dic₃⋊C₄	—	5	1	no	—
383	Dic₃⋊C₄	—	5	1	no	—
384	Dic₃⋊C₄	—	5	1	no	—
385	C₄×Dic₃	—	5	1	no	—
386	C₄×Dic₃	—	5	1	no	—
387	C₄×Dic₃	—	5	1	no	—
388	C₄×Dic₃	C₂²×D₅	1	1	yes	characteristic
389	C₄×Dic₃	C₂²×D₅	1	1	yes	characteristic
390	#208	—	2	2	no	—
391	C₂×C₃⋊C₈	—	5	1	no	—
392	C₂×C₃⋊C₈	—	5	1	no	—
393	C₂×C₃⋊C₈	—	10	2	no	—
394	C₂×C₃⋊C₈	C₂²×D₅	1	1	yes	characteristic
395	C₂×C₃⋊C₈	C₂²×D₅	1	1	yes	characteristic
396	D₃×C₈	—	10	2	no	—
397	D₃×C₈	—	10	2	no	—
398	C₂³×C₅	C₂×C₄×D₃	1	1	yes	characteristic
399	C₂²×D₅	—	3	1	no	—
400	C₂²×D₅	C₂×C₄×D₃	1	1	yes	characteristic
401	C₂×C₄×C₅	—	2	1	no	—
402	C₂×C₄×C₅	—	2	1	no	—
403	C₂×C₄×C₅	—	3	1	no	—
404	C₂×C₄×C₅	—	3	1	no	—
405	C₂×C₄×C₅	—	3	1	no	—
406	C₂×C₄×C₅	—	3	1	no	—
407	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
408	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
409	C₂²⋊D₅	—	4	1	no	—
410	C₂²⋊D₅	—	6	2	no	—
411	C₂×Dic₅	—	3	1	no	—
412	C₂×Dic₅	—	3	1	no	—
413	C₂×Dic₅	—	3	1	no	—
414	C₂×Dic₅	C₂×C₄×D₃	1	1	yes	characteristic
415	C₂×Dic₅	C₂×C₄×D₃	1	1	yes	characteristic
416	C₂×Dic₅	C₂×C₄×D₃	1	1	yes	characteristic
417	D₂₀	—	6	2	no	—
418	C₄×D₅	—	2	1	no	—
419	C₄×D₅	—	2	1	no	—
420	C₄×D₅	—	6	2	no	—
421	C₄×D₅	—	6	1	no	—
422	C₄×D₅	—	6	1	no	—
423	C₄×D₅	—	12	1	no	—
424	Dic₁₀	—	12	1	no	—
425	C₅×C₈	—	2	1	no	—
426	C₅×C₈	—	3	2	no	—
427	C₅×C₈	—	6	1	no	—
428	C₅×C₈	#237	1	2	yes	—
429	#168	—	2	1	no	—
430	#168	—	2	1	no	—
431	#168	—	6	1	no	—
432	#168	—	6	1	no	—
433	C₂×M₁₆	—	3	1	no	—
434	C₂×M₁₆	—	5	1	no	—
435	C₂²×C₈	—	15	1	no	—
436	C₂²×C₈	—	15	1	no	—
437	C₂²×C₈	—	15	1	no	—
438	C₂²×C₈	D₃×D₅	1	1	yes	characteristic
439	#126	—	15	1	no	—
440	#126	—	15	1	no	—
441	#125	—	15	1	no	—
442	#124	—	15	1	no	—
443	#123	—	15	1	no	—
444	#123	—	15	1	no	—
445	C₂²⋊Q₈	—	15	1	no	—
446	#121	—	15	1	no	—
447	C₄×Q₈	—	15	1	no	—
448	C₄×D₄	—	5	1	no	—
449	C₄×D₄	—	15	1	no	—
450	C₄×D₄	—	15	1	no	—
451	#117	—	3	1	no	—
452	#117	—	15	1	no	—
453	C₂×C₄²	—	15	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	—	3	1	no	—
467	#97	—	3	1	no	—
468	#97	—	5	1	no	—
469	#97	—	15	1	no	—
470	#97	—	15	1	no	—
471	#97	—	15	1	no	—
472	C₄×C₈	—	3	1	no	—
473	C₄×C₈	—	3	1	no	—
474	C₄×C₈	—	15	1	no	—
475	C₄×C₈	—	15	1	no	—
476	C₂×C₃×C₅	—	4	1	no	—
477	C₂×C₃×C₅	C₄×#41	1	1	yes	characteristic
478	C₂×C₃×C₅	C₂×#131	1	1	yes	characteristic
479	C₂×C₃×C₅	#568	1	1	yes	characteristic
480	D₁₅	—	2	2	no	—
481	C₃×D₅	—	4	1	no	—
482	C₂³×C₃	—	5	1	no	—
483	C₂³×C₃	C₂×C₄×D₅	1	1	yes	characteristic
484	C₂²×D₃	—	5	1	no	—
485	C₃×D₄	—	20	1	no	—
486	C₂×C₃×C₄	—	2	1	no	—
487	C₂×C₃×C₄	—	2	1	no	—
488	C₂×C₃×C₄	—	5	1	no	—
489	C₂×C₃×C₄	—	5	1	no	—
490	C₂×C₃×C₄	—	5	1	no	—
491	C₂×C₃×C₄	—	10	1	no	—
492	C₂×C₃×C₄	—	10	1	no	—
493	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
494	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
495	#67	—	10	2	no	—
496	#67	—	10	2	no	—
497	C₂×Dic₃	—	5	1	no	—
498	C₂×Dic₃	—	5	1	no	—
499	C₂×Dic₃	—	5	1	no	—
500	C₂×Dic₃	C₂×C₄×D₅	1	1	yes	characteristic
501	C₂×Dic₃	C₂×C₄×D₅	1	1	yes	characteristic
502	C₂×Dic₃	C₂×C₄×D₅	1	1	yes	characteristic
503	C₂×Dic₃	C₂×C₄×D₅	1	1	yes	characteristic
504	C₄×D₃	—	10	2	no	—
505	C₄×D₃	—	10	1	no	—
506	C₄×D₃	—	10	1	no	—
507	C₄×D₃	—	20	1	no	—
508	Dic₆	—	20	1	no	—
509	C₃×C₈	—	2	1	no	—
510	C₃×C₈	—	10	1	no	—
511	C₃×C₈	—	10	1	no	—
512	C₃×C₈	#709	1	2	yes	—
513	C₃⋊C₈	—	2	1	no	—
514	C₃⋊C₈	—	10	1	no	—
515	C₃⋊C₈	—	10	1	no	—
516	C₃⋊C₈	#709	1	2	yes	—
517	C₂²×C₅	—	2	1	no	—
518	C₂²×C₅	—	2	1	no	—
519	C₂²×C₅	—	2	1	no	—
520	C₂²×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
521	C₂×D₅	—	2	1	no	—
522	C₂×D₅	—	2	1	no	—
523	C₂×D₅	—	2	1	no	—
524	C₂×D₅	—	3	2	no	—
525	C₂×D₅	—	6	1	no	—
526	C₂×D₅	—	6	1	no	—
527	C₄×C₅	—	2	1	no	—
528	C₄×C₅	—	6	1	no	—
529	C₄×C₅	—	6	1	no	—
530	C₄×C₅	—	6	1	no	—
531	C₄×C₅	—	6	1	no	—
532	C₄×C₅	C₂×#237	1	1	yes	characteristic
533	C₄×C₅	D₃×#41	1	1	yes	characteristic
534	Dic₅	—	2	1	no	—
535	Dic₅	—	2	1	no	—
536	Dic₅	—	2	1	no	—
537	Dic₅	—	6	1	no	—
538	Dic₅	—	6	1	no	—
539	Dic₅	—	6	1	no	—
540	C₂×Q₈	—	15	1	no	—
541	C₂×D₄	—	5	1	no	—
542	C₂×D₄	—	15	1	no	—
543	C₂×D₄	—	15	1	no	—
544	C₂²×C₄	—	5	1	no	—
545	C₂²×C₄	—	15	1	no	—
546	C₂²×C₄	—	15	1	no	—
547	C₂²×C₄	—	15	1	no	—
548	C₂²×C₄	C₂×D₃×D₅	1	1	yes	characteristic
549	M₁₆	—	6	2	no	—
550	M₁₆	—	10	2	no	—
551	C₂×C₈	—	2	2	no	—
552	C₂×C₈	—	3	1	no	—
553	C₂×C₈	—	3	1	no	—
554	C₂×C₈	—	5	1	no	—
555	C₂×C₈	—	5	1	no	—
556	C₂×C₈	—	15	1	no	—
557	C₂×C₈	—	15	1	no	—
558	C₂×C₈	—	30	2	no	—
559	C₂×C₈	—	30	2	no	—
560	C₂×C₈	—	30	2	no	—
561	C₂×C₈	C₂×D₃×D₅	1	1	yes	characteristic
562	C₂×C₈	C₂×D₃×D₅	1	1	yes	characteristic
563	C₄⋊C₄	—	3	1	no	—
564	C₄⋊C₄	—	3	1	no	—
565	C₄⋊C₄	—	5	1	no	—
566	C₄⋊C₄	—	15	1	no	—
567	C₄⋊C₄	—	15	1	no	—
568	C₄⋊C₄	—	15	1	no	—
569	C₄⋊C₄	—	15	1	no	—
570	C₄⋊C₄	—	15	1	no	—
571	C₄⋊C₄	—	15	1	no	—
572	C₄⋊C₄	—	15	1	no	—
573	C₂²⋊C₄	—	3	1	no	—
574	C₂²⋊C₄	—	3	1	no	—
575	C₂²⋊C₄	—	5	1	no	—
576	C₂²⋊C₄	—	5	1	no	—
577	C₂²⋊C₄	—	15	1	no	—
578	C₂²⋊C₄	—	15	1	no	—
579	C₂²⋊C₄	—	15	1	no	—
580	C₂²⋊C₄	—	15	1	no	—
581	C₂²⋊C₄	—	15	1	no	—
582	C₂²⋊C₄	—	15	1	no	—
583	C₄²	—	3	1	no	—
584	C₄²	—	3	1	no	—
585	C₄²	—	5	1	no	—
586	C₄²	—	15	1	no	—
587	C₄²	—	15	1	no	—
588	C₄²	—	15	1	no	—
589	C₃×C₅	#2968	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	—	10	1	no	—
594	C₂²×C₃	—	10	1	no	—
595	C₂²×C₃	—	10	1	no	—
596	C₂²×C₃	C₂²×C₄×D₅	1	1	yes	characteristic
597	C₂×D₃	—	5	2	no	—
598	C₂×D₃	—	10	1	no	—
599	C₂×D₃	—	10	1	no	—
600	C₃×C₄	—	2	1	no	—
601	C₃×C₄	—	10	1	no	—
602	C₃×C₄	—	10	1	no	—
603	C₃×C₄	—	10	1	no	—
604	C₃×C₄	C₂×#709	1	1	yes	characteristic
605	C₃×C₄	C₂×#709	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	—	10	1	no	—
611	Dic₃	—	10	1	no	—
612	Dic₃	—	10	1	no	—
613	C₂×C₅	—	4	1	no	—
614	C₂×C₅	C₄×#237	1	1	yes	characteristic
615	C₂×C₅	#5745	1	1	yes	characteristic
616	C₂×C₅	D₃×#131	1	1	yes	characteristic
617	D₅	—	4	1	no	—
618	D₅	—	6	2	no	—
619	C₂³	—	5	1	no	—
620	C₂³	—	15	1	no	—
621	C₂³	C₄×D₃×D₅	1	1	yes	characteristic
622	Q₈	—	60	1	no	—
623	D₄	—	20	1	no	—
624	D₄	—	30	2	no	—
625	D₄	—	30	2	no	—
626	C₂×C₄	—	2	1	no	—
627	C₂×C₄	—	2	1	no	—
628	C₂×C₄	—	3	1	no	—
629	C₂×C₄	—	3	1	no	—
630	C₂×C₄	—	3	1	no	—
631	C₂×C₄	—	3	1	no	—
632	C₂×C₄	—	5	1	no	—
633	C₂×C₄	—	5	1	no	—
634	C₂×C₄	—	5	1	no	—
635	C₂×C₄	—	10	1	no	—
636	C₂×C₄	—	10	1	no	—
637	C₂×C₄	—	15	1	no	—
638	C₂×C₄	—	15	1	no	—
639	C₂×C₄	—	15	1	no	—
640	C₂×C₄	—	30	2	no	—
641	C₂×C₄	—	30	1	no	—
642	C₂×C₄	—	30	1	no	—
643	C₂×C₄	—	60	1	no	—
644	C₂×C₄	C₄×D₃×D₅	1	1	yes	characteristic
645	C₂×C₄	C₂²×D₃×D₅	1	1	yes	characteristic
646	C₈	—	2	1	no	—
647	C₈	—	3	2	no	—
648	C₈	—	6	1	no	—
649	C₈	—	10	1	no	—
650	C₈	—	10	1	no	—
651	C₈	—	30	1	no	—
652	C₈	—	30	1	no	—
653	C₈	#6779	1	2	yes	—
654	C₂×C₃	—	4	1	no	—
655	C₂×C₃	—	20	1	no	—
656	C₂×C₃	C₄×#709	1	1	yes	characteristic
657	C₂×C₃	D₅×#131	1	1	yes	characteristic
658	C₂×C₃	#66084	1	1	yes	characteristic
659	D₃	—	10	2	no	—
660	C₅	#79458	1	1	yes	characteristic, complemented, Sylow
661	C₂²	—	2	1	no	—
662	C₂²	—	2	1	no	—
663	C₂²	—	2	1	no	—
664	C₂²	—	10	1	no	—
665	C₂²	—	10	1	no	—
666	C₂²	—	10	1	no	—
667	C₂²	—	15	2	no	—
668	C₂²	—	30	1	no	—
669	C₂²	—	30	1	no	—
670	C₂²	C₂×C₄×D₃×D₅	1	1	yes	characteristic
671	C₄	—	2	1	no	—
672	C₄	—	6	1	no	—
673	C₄	—	6	1	no	—
674	C₄	—	6	1	no	—
675	C₄	—	6	1	no	—
676	C₄	—	10	1	no	—
677	C₄	—	10	1	no	—
678	C₄	—	10	1	no	—
679	C₄	—	30	1	no	—
680	C₄	—	30	1	no	—
681	C₄	—	30	1	no	—
682	C₄	D₃×#709	1	1	yes	characteristic
683	C₄	C₂×#6779	1	1	yes	characteristic
684	C₃	#10610289	1	1	yes	characteristic, complemented, Sylow
685	C₂	—	4	1	no	—
686	C₂	—	20	1	no	—
687	C₂	—	30	2	no	—
688	C₂	#11753949	1	1	yes	characteristic
689	C₂	#11753952	1	1	yes	characteristic
690	C₂	C₄×#6779	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×D₃×D₅
commutator, socle	C₂²×C₃×C₅	C₂³×C₄
Fitting	C₂²×C₃×C₅×C₈	C₂²
prime radical	#91533	C₄
cosocle	C₂×C₃×C₄×C₅	C₂⁴
hypercenter	C₂²×C₈	D₃×D₅
hypocenter	C₃×C₅	#2968
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. C₈×#1220	C₂	semidirect
3. C₅×#5101	C₂	semidirect
4. C₃×#65400	C₂	semidirect
5. #11748492	C₂	semidirect
6. #11748488	C₂	semidirect
7. #11748330	C₂	semidirect
8. #11748051	C₂	semidirect
9. #11748042	C₂	semidirect
10. #11747824	C₂	semidirect
11. #11747823	C₂	semidirect
12. #11747725	C₂	semidirect
13. #11747649	C₂	semidirect
14. #11747603	C₂	semidirect
15. #11747584	C₂	semidirect
65. #65400	D₃	semidirect
130. #5101	D₅	semidirect
589. C₃×C₅	#2968	semidirect
660. C₅	#79458	semidirect
684. C₃	#10610289	semidirect

Maximal subgroups

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

subgroup	index
#11754226	2
C₈×#1220	2
C₅×#5101	2
C₃×#65400	2
#11748492	2
#11748488	2
#11748330	2
#11748051	2
#11748042	2
#11747824	2
#11747823	2
#11747725	2
#11747649	2
#11747603	2
#11747584	2
#10610289	3
#79458	5