Subgroups — #14417014

Order 1920.

1012 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11756586	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#91838	C₂	1	1	yes	maximal, characteristic
3	#11756280	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₅×#416	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#91105	C₂	1	1	yes	maximal, characteristic, complemented
6	#11751202	C₂	1	1	yes	maximal, characteristic, complemented
7	#11751096	C₂	1	1	yes	maximal, characteristic, complemented
8	#11750918	C₂	1	2	yes	maximal, complemented
9	#11750889	C₂	1	2	yes	maximal, complemented
10	#11750886	C₂	1	2	yes	maximal, complemented
11	#11750857	C₂	1	2	yes	maximal, complemented
12	#10610551	—	3	1	no	maximal, Hall
13	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic
14	C₂²×D₆₀	C₂²	1	1	yes	characteristic
15	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
16	C₃×C₅×#117	C₂²	1	1	yes	characteristic
17	#91838	C₄	1	8	yes	complemented
18	Q₈×Dic₁₅	C₂²	1	2	yes	complemented
19	C₂×#6717	C₂²	1	2	yes	—
20	D₄×Dic₁₅	—	2	2	no	—
21	D₄×Dic₁₅	C₂²	1	2	yes	complemented
22	C₂×#6715	C₂²	1	2	yes	—
23	#91815	—	2	1	no	—
24	#91815	C₂²	1	1	yes	characteristic
25	C₂×C₄⋊Dic₁₅	—	2	1	no	—
26	C₂×C₄⋊Dic₁₅	C₂²	1	1	yes	characteristic
27	C₂×#6710	C₂²	1	1	yes	characteristic
28	#91782	C₂²	1	2	yes	—
29	#91782	C₂²	1	2	yes	—
30	C₂²⋊C₄×D₁₅	—	2	2	no	—
31	C₄×D₆₀	—	2	1	no	—
32	C₄×D₆₀	—	2	1	no	—
33	C₃×C₅×#103	C₂²	1	1	yes	characteristic, complemented
34	C₃×C₅×#103	C₂²	1	1	yes	characteristic, complemented
35	C₃×C₅×#102	C₂²	1	1	yes	characteristic, complemented
36	C₃×C₅×#102	C₂²	1	1	yes	characteristic, complemented
37	#91105	C₂²	1	2	yes	—
38	#91105	C₂²	1	2	yes	—
39	#91099	C₂²	1	2	yes	complemented
40	C₈×Dic₁₅	C₂²	1	2	yes	complemented
41	#91092	C₂²	1	2	yes	complemented
42	#91091	C₂²	1	2	yes	complemented
43	#78820	—	5	1	no	maximal, Hall
44	#66161	—	3	1	no	—
45	C₂×#4095	—	3	1	no	—
46	#65855	—	3	1	no	—
47	C₅×#416	D₃	1	1	yes	characteristic, complemented
48	C₂×#3953	—	3	1	no	—
49	#65390	—	3	1	no	—
50	#65284	—	3	1	no	—
51	#65106	—	3	2	no	—
52	#65077	—	3	2	no	—
53	#65074	—	3	2	no	—
54	#65045	—	3	2	no	—
55	C₂³×D₁₅	—	2	1	no	—
56	C₃×C₅×#41	—	2	2	no	—
57	C₃×C₅×#41	C₂×C₄	1	4	yes	complemented
58	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
59	C₂×C₃×C₅×D₄	—	2	1	no	—
60	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
61	C₂²×C₃×C₄×C₅	—	2	1	no	—
62	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
63	C₂²×Dic₁₅	—	2	1	no	—
64	C₂²×Dic₁₅	—	2	2	no	—
65	C₂×D₆₀	—	2	1	no	—
66	C₂×D₆₀	—	2	2	no	—
67	C₂×D₆₀	C₂×C₄	1	4	yes	complemented
68	C₂×D₆₀	C₂³	1	2	yes	—
69	C₂×C₄×D₁₅	—	2	2	no	—
70	C₂×C₄×D₁₅	—	2	2	no	—
71	C₂×C₃×C₅×C₈	—	2	2	no	—
72	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
73	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
74	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
75	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
76	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
77	C₃×C₄²×C₅	—	2	1	no	—
78	#6719	—	2	2	no	—
79	#6719	D₄	1	2	yes	—
80	#6717	C₂×C₄	1	8	yes	complemented
81	#6715	C₂×C₄	1	8	yes	complemented
82	#6714	—	2	2	no	—
83	#6714	—	2	2	no	—
84	C₄⋊Dic₁₅	—	2	1	no	—
85	C₄⋊Dic₁₅	—	2	2	no	—
86	C₄⋊Dic₁₅	D₄	1	1	yes	characteristic
87	C₄⋊Dic₁₅	D₄	1	1	yes	characteristic
88	C₄⋊Dic₁₅	C₂³	1	2	yes	—
89	C₄×Dic₁₅	—	2	2	no	—
90	C₄×Dic₁₅	C₂³	1	2	yes	—
91	#6710	C₂×C₄	1	4	yes	complemented
92	C₂×C₃⋊#168	C₂³	1	2	yes	—
93	#5827	—	5	1	no	—
94	C₂×#949	—	5	1	no	—
95	#5521	—	5	1	no	—
96	C₃×#416	D₅	1	1	yes	characteristic, complemented
97	C₂×#821	—	5	1	no	—
98	#5101	—	5	1	no	—
99	#4995	—	5	1	no	—
100	#4817	—	5	2	no	—
101	#4788	—	5	2	no	—
102	#4785	—	5	2	no	—
103	#4756	—	5	2	no	—
104	C₂×C₅×#41	C₂×D₃	1	1	yes	characteristic
105	C₂²×D₂₀	—	3	1	no	—
106	C₂²×C₅×C₈	C₂×D₃	1	1	yes	characteristic
107	C₅×#117	C₂×D₃	1	1	yes	characteristic
108	#4095	—	3	8	no	—
109	Q₈×Dic₅	—	3	2	no	—
110	C₂×#688	—	3	2	no	—
111	D₄×Dic₅	—	3	2	no	—
112	D₄×Dic₅	—	6	2	no	—
113	C₂×#686	—	3	2	no	—
114	#4072	—	3	1	no	—
115	#4072	—	6	1	no	—
116	C₂×C₄⋊Dic₅	—	3	1	no	—
117	C₂×C₄⋊Dic₅	—	6	1	no	—
118	C₂×#681	—	3	1	no	—
119	#4039	—	3	2	no	—
120	#4039	—	3	2	no	—
121	D₅×C₂²⋊C₄	—	6	2	no	—
122	C₄×D₂₀	—	6	1	no	—
123	C₄×D₂₀	—	6	1	no	—
124	C₅×#103	C₂×D₃	1	1	yes	characteristic, complemented
125	C₅×#103	C₂×D₃	1	1	yes	characteristic, complemented
126	C₅×#102	C₂×D₃	1	1	yes	characteristic, complemented
127	C₅×#102	C₂×D₃	1	1	yes	characteristic, complemented
128	#3953	—	3	2	no	—
129	#3953	—	3	2	no	—
130	#3947	—	3	2	no	—
131	C₈×Dic₅	—	3	2	no	—
132	#3940	—	3	2	no	—
133	#3939	—	3	2	no	—
134	#2946	—	15	1	no	Sylow
135	C₂³×C₃×C₅	—	2	1	no	—
136	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
137	C₂²×D₁₅	—	2	2	no	—
138	C₂²×D₁₅	—	2	4	no	—
139	C₂²×D₁₅	—	8	1	no	—
140	C₂²×D₁₅	—	8	1	no	—
141	C₃×C₅×Q₈	—	2	1	no	—
142	C₃×C₅×Q₈	C₂²×C₄	1	2	yes	—
143	C₃×C₅×D₄	—	2	4	no	—
144	C₃×C₅×D₄	—	2	1	no	—
145	C₃×C₅×D₄	C₂²×C₄	1	2	yes	—
146	C₂×C₃×C₄×C₅	—	2	1	no	—
147	C₂×C₃×C₄×C₅	—	2	4	no	—
148	C₂×C₃×C₄×C₅	—	2	1	no	—
149	C₂×C₃×C₄×C₅	—	2	1	no	—
150	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
151	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
152	C₂×C₃×C₄×C₅	#41	1	2	yes	—
153	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
154	C₂×Dic₁₅	—	2	2	no	—
155	C₂×Dic₁₅	—	8	2	no	—
156	C₂×Dic₁₅	—	8	1	no	—
157	C₂×Dic₁₅	C₂×D₄	1	2	yes	—
158	C₂×Dic₁₅	C₂×D₄	1	2	yes	—
159	D₆₀	—	2	4	no	—
160	D₆₀	—	2	2	no	—
161	D₆₀	C₂²×C₄	1	4	yes	—
162	C₄×D₁₅	—	8	2	no	—
163	C₄×D₁₅	—	8	2	no	—
164	C₃×C₅×C₈	—	2	1	no	—
165	C₃×C₅×C₈	—	2	1	no	—
166	C₃⋊#168	C₂²×C₄	1	4	yes	—
167	C₂×C₃×#41	C₂×D₅	1	1	yes	characteristic
168	C₂²×D₁₂	—	5	1	no	—
169	C₂²×C₃×C₈	C₂×D₅	1	1	yes	characteristic
170	C₃×#117	C₂×D₅	1	1	yes	characteristic
171	#949	—	5	8	no	—
172	Q₈×Dic₃	—	5	2	no	—
173	C₂×#215	—	5	2	no	—
174	D₄×Dic₃	—	5	2	no	—
175	D₄×Dic₃	—	10	2	no	—
176	C₂×#213	—	5	2	no	—
177	#926	—	5	1	no	—
178	#926	—	10	1	no	—
179	C₂×C₄⋊Dic₃	—	5	1	no	—
180	C₂×C₄⋊Dic₃	—	10	1	no	—
181	C₂×#208	—	5	1	no	—
182	#893	—	5	2	no	—
183	#893	—	5	2	no	—
184	D₃×C₂²⋊C₄	—	10	2	no	—
185	C₄×D₁₂	—	10	1	no	—
186	C₄×D₁₂	—	10	1	no	—
187	C₃×#103	C₂×D₅	1	1	yes	characteristic, complemented
188	C₃×#103	C₂×D₅	1	1	yes	characteristic, complemented
189	C₃×#102	C₂×D₅	1	1	yes	characteristic, complemented
190	C₃×#102	C₂×D₅	1	1	yes	characteristic, complemented
191	#821	—	5	2	no	—
192	#821	—	5	2	no	—
193	#815	—	5	2	no	—
194	C₈×Dic₃	—	5	2	no	—
195	#808	—	5	2	no	—
196	#807	—	5	2	no	—
197	C₂³×D₅	—	6	1	no	—
198	C₅×#41	—	2	2	no	—
199	C₅×#41	C₄×D₃	1	4	yes	complemented
200	C₂×C₅×Q₈	C₂²×D₃	1	1	yes	characteristic
201	C₂×C₅×D₄	—	2	1	no	—
202	C₂×C₅×D₄	C₂²×D₃	1	1	yes	characteristic
203	C₂²×C₄×C₅	—	2	1	no	—
204	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
205	C₂²×Dic₅	—	6	2	no	—
206	C₂²×Dic₅	—	6	1	no	—
207	C₂×D₂₀	—	3	4	no	—
208	C₂×D₂₀	—	3	2	no	—
209	C₂×D₂₀	—	6	1	no	—
210	C₂×D₂₀	—	6	2	no	—
211	C₂×C₄×D₅	—	6	2	no	—
212	C₂×C₄×D₅	—	6	2	no	—
213	C₂×C₅×C₈	—	2	2	no	—
214	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
215	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
216	C₅×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
217	C₅×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
218	C₅×C₂²⋊C₄	—	2	1	no	—
219	C₄²×C₅	—	2	1	no	—
220	C₂²⋊Dic₅	—	3	2	no	—
221	C₂²⋊Dic₅	—	6	2	no	—
222	#688	—	3	8	no	—
223	#686	—	3	8	no	—
224	#685	—	6	2	no	—
225	#685	—	6	2	no	—
226	C₄⋊Dic₅	—	3	1	no	—
227	C₄⋊Dic₅	—	3	1	no	—
228	C₄⋊Dic₅	—	3	2	no	—
229	C₄⋊Dic₅	—	6	2	no	—
230	C₄⋊Dic₅	—	6	1	no	—
231	C₄×Dic₅	—	3	2	no	—
232	C₄×Dic₅	—	6	2	no	—
233	#681	—	3	4	no	—
234	C₂×#168	—	3	2	no	—
235	C₂×AGL(1,ℤ/8)	—	15	1	no	—
236	#520	—	15	1	no	—
237	#518	—	15	1	no	—
238	#442	—	15	2	no	—
239	#440	—	15	2	no	—
240	C₄×SD₁₆	—	15	2	no	—
241	C₄×D₈	—	15	2	no	—
242	#428	—	15	1	no	—
243	#416	D₁₅	1	1	yes	characteristic, complemented
244	C₂×#102	—	15	1	no	—
245	#405	—	15	1	no	—
246	C₂²×C₃×C₅	—	2	1	no	—
247	C₂²×C₃×C₅	—	2	1	no	—
248	C₂²×C₃×C₅	—	2	2	no	—
249	C₂²×C₃×C₅	—	4	1	no	—
250	C₂²×C₃×C₅	—	4	1	no	—
251	C₂²×C₃×C₅	C₄×D₄	1	2	yes	—
252	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
253	C₂×D₁₅	—	2	4	no	—
254	C₂×D₁₅	—	4	2	no	—
255	C₂×D₁₅	—	4	2	no	—
256	C₂×D₁₅	—	8	4	no	—
257	C₃×C₄×C₅	—	2	2	no	—
258	C₃×C₄×C₅	—	4	1	no	—
259	C₃×C₄×C₅	—	4	1	no	—
260	C₃×C₄×C₅	C₄×D₄	1	2	yes	—
261	C₃×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
262	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
263	Dic₁₅	—	2	2	no	—
264	Dic₁₅	—	2	2	no	—
265	Dic₁₅	—	4	2	no	—
266	C₂³×D₃	—	10	1	no	—
267	C₃×#41	—	2	2	no	—
268	C₃×#41	C₄×D₅	1	4	yes	complemented
269	C₂×C₃×Q₈	C₂²×D₅	1	1	yes	characteristic
270	C₂×C₃×D₄	—	2	1	no	—
271	C₂×C₃×D₄	C₂²×D₅	1	1	yes	characteristic
272	C₂²×C₃×C₄	—	2	1	no	—
273	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
274	C₂²×Dic₃	—	10	2	no	—
275	C₂²×Dic₃	—	10	1	no	—
276	C₂×D₁₂	—	5	4	no	—
277	C₂×D₁₂	—	5	2	no	—
278	C₂×D₁₂	—	10	1	no	—
279	C₂×D₁₂	—	10	2	no	—
280	C₂×C₄×D₃	—	10	2	no	—
281	C₂×C₄×D₃	—	10	2	no	—
282	C₂×C₃×C₈	—	2	2	no	—
283	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
284	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
285	C₃×C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
286	C₃×C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
287	C₃×C₂²⋊C₄	—	2	1	no	—
288	C₃×C₄²	—	2	1	no	—
289	#217	—	5	2	no	—
290	#217	—	10	2	no	—
291	#215	—	5	8	no	—
292	#213	—	5	8	no	—
293	(C₂×D₃)⋊C₄	—	10	2	no	—
294	(C₂×D₃)⋊C₄	—	10	2	no	—
295	C₄⋊Dic₃	—	5	1	no	—
296	C₄⋊Dic₃	—	5	1	no	—
297	C₄⋊Dic₃	—	5	2	no	—
298	C₄⋊Dic₃	—	10	2	no	—
299	C₄⋊Dic₃	—	10	1	no	—
300	C₄×Dic₃	—	5	2	no	—
301	C₄×Dic₃	—	10	2	no	—
302	#208	—	5	4	no	—
303	C₂×C₃⋊C₈	—	5	2	no	—
304	C₂³×C₅	—	2	1	no	—
305	C₂³×C₅	D₃×D₄	1	1	yes	characteristic
306	C₂²×D₅	—	6	2	no	—
307	C₂²×D₅	—	6	4	no	—
308	C₂²×D₅	—	24	1	no	—
309	C₂²×D₅	—	24	1	no	—
310	C₅×Q₈	—	2	1	no	—
311	C₅×Q₈	C₂×C₄×D₃	1	2	yes	—
312	C₅×D₄	—	2	4	no	—
313	C₅×D₄	—	2	1	no	—
314	C₅×D₄	C₂×C₄×D₃	1	2	yes	—
315	C₂×C₄×C₅	—	2	1	no	—
316	C₂×C₄×C₅	—	2	4	no	—
317	C₂×C₄×C₅	—	2	1	no	—
318	C₂×C₄×C₅	—	2	1	no	—
319	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
320	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
321	C₂×C₄×C₅	#237	1	2	yes	—
322	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
323	C₂×Dic₅	—	3	2	no	—
324	C₂×Dic₅	—	3	2	no	—
325	C₂×Dic₅	—	6	2	no	—
326	C₂×Dic₅	—	24	2	no	—
327	C₂×Dic₅	—	24	1	no	—
328	D₂₀	—	3	4	no	—
329	D₂₀	—	6	4	no	—
330	D₂₀	—	6	2	no	—
331	C₄×D₅	—	24	2	no	—
332	C₄×D₅	—	24	2	no	—
333	C₅×C₈	—	2	1	no	—
334	C₅×C₈	—	2	1	no	—
335	#168	—	3	4	no	—
336	C₂×#41	C₂×D₁₅	1	1	yes	characteristic
337	C₂²×D₄	—	15	1	no	—
338	AGL(1,ℤ/8)	—	15	8	no	—
339	C₂×SD₁₆	—	15	2	no	—
340	C₂×D₈	—	15	2	no	—
341	C₂×M₁₆	—	15	1	no	—
342	C₂²×C₈	C₂×D₁₅	1	1	yes	characteristic
343	C₄×Q₈	—	15	2	no	—
344	C₄×D₄	—	15	2	no	—
345	C₄×D₄	—	15	2	no	—
346	C₄×D₄	—	15	2	no	—
347	C₄×D₄	—	30	1	no	—
348	C₄×D₄	—	30	1	no	—
349	C₄×D₄	—	30	2	no	—
350	#117	—	15	1	no	—
351	#117	—	30	1	no	—
352	#117	C₂×D₁₅	1	1	yes	characteristic
353	C₂×C₄⋊C₄	—	15	1	no	—
354	C₂×C₄⋊C₄	—	30	1	no	—
355	C₂×C₂²⋊C₄	—	30	2	no	—
356	#107	—	15	2	no	—
357	#106	—	15	2	no	—
358	#103	C₂×D₁₅	1	1	yes	characteristic, complemented
359	#103	C₂×D₁₅	1	1	yes	characteristic, complemented
360	#102	—	15	2	no	—
361	#102	—	15	2	no	—
362	#102	C₂×D₁₅	1	1	yes	characteristic, complemented
363	#102	C₂×D₁₅	1	1	yes	characteristic, complemented
364	#97	—	15	2	no	—
365	C₄×C₈	—	15	2	no	—
366	C₂×C₃×C₅	—	2	2	no	—
367	C₂×C₃×C₅	—	4	2	no	—
368	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
369	C₂×C₃×C₅	#576	1	1	yes	characteristic
370	C₂×C₃×C₅	#577	1	1	yes	characteristic
371	D₁₅	—	4	4	no	—
372	C₂³×C₃	—	2	1	no	—
373	C₂³×C₃	D₄×D₅	1	1	yes	characteristic
374	C₂²×D₃	—	10	2	no	—
375	C₂²×D₃	—	10	4	no	—
376	C₂²×D₃	—	40	1	no	—
377	C₂²×D₃	—	40	1	no	—
378	C₃×Q₈	—	2	1	no	—
379	C₃×Q₈	C₂×C₄×D₅	1	2	yes	—
380	C₃×D₄	—	2	4	no	—
381	C₃×D₄	—	2	1	no	—
382	C₃×D₄	C₂×C₄×D₅	1	2	yes	—
383	C₂×C₃×C₄	—	2	1	no	—
384	C₂×C₃×C₄	—	2	4	no	—
385	C₂×C₃×C₄	—	2	1	no	—
386	C₂×C₃×C₄	—	2	1	no	—
387	C₂×C₃×C₄	C₂×C₄×D₅	1	2	yes	—
388	C₂×C₃×C₄	D₄×D₅	1	1	yes	characteristic
389	C₂×C₃×C₄	#711	1	2	yes	—
390	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
391	C₂×Dic₃	—	5	2	no	—
392	C₂×Dic₃	—	5	2	no	—
393	C₂×Dic₃	—	10	2	no	—
394	C₂×Dic₃	—	40	2	no	—
395	C₂×Dic₃	—	40	1	no	—
396	D₁₂	—	5	4	no	—
397	D₁₂	—	10	2	no	—
398	D₁₂	—	10	4	no	—
399	C₄×D₃	—	40	2	no	—
400	C₄×D₃	—	40	2	no	—
401	C₃×C₈	—	2	1	no	—
402	C₃×C₈	—	2	1	no	—
403	C₃⋊C₈	—	5	4	no	—
404	C₂²×C₅	—	2	1	no	—
405	C₂²×C₅	—	2	1	no	—
406	C₂²×C₅	—	2	2	no	—
407	C₂²×C₅	—	4	1	no	—
408	C₂²×C₅	—	4	1	no	—
409	C₂²×C₅	#67⋊C₄	1	2	yes	—
410	C₂²×C₅	C₂×D₃×D₄	1	1	yes	characteristic
411	C₂×D₅	—	6	4	no	—
412	C₂×D₅	—	12	2	no	—
413	C₂×D₅	—	12	2	no	—
414	C₂×D₅	—	24	4	no	—
415	C₄×C₅	—	2	2	no	—
416	C₄×C₅	—	4	1	no	—
417	C₄×C₅	—	4	1	no	—
418	C₄×C₅	#67⋊C₄	1	2	yes	—
419	C₄×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
420	C₄×C₅	C₂×#237	1	1	yes	characteristic
421	Dic₅	—	6	2	no	—
422	Dic₅	—	6	2	no	—
423	Dic₅	—	12	2	no	—
424	C₂⁴	—	30	1	no	—
425	#41	—	2	2	no	—
426	#41	C₄×D₁₅	1	4	yes	complemented
427	C₂×Q₈	C₂²×D₁₅	1	1	yes	characteristic
428	C₂×D₄	—	2	1	no	—
429	C₂×D₄	—	15	4	no	—
430	C₂×D₄	—	15	2	no	—
431	C₂×D₄	—	30	1	no	—
432	C₂×D₄	—	30	2	no	—
433	C₂×D₄	C₂²×D₁₅	1	1	yes	characteristic
434	C₂²×C₄	—	2	1	no	—
435	C₂²×C₄	—	30	2	no	—
436	C₂²×C₄	—	30	2	no	—
437	C₂²×C₄	—	30	2	no	—
438	C₂²×C₄	—	30	1	no	—
439	C₂²×C₄	C₂²×D₁₅	1	1	yes	characteristic
440	SD₁₆	—	15	8	no	—
441	D₈	—	15	8	no	—
442	M₁₆	—	15	4	no	—
443	C₂×C₈	—	2	2	no	—
444	C₂×C₈	—	15	2	no	—
445	C₂×C₈	C₂²×D₁₅	1	1	yes	characteristic
446	C₂×C₈	C₂²×D₁₅	1	1	yes	characteristic
447	C₄⋊C₄	—	15	1	no	—
448	C₄⋊C₄	—	15	1	no	—
449	C₄⋊C₄	—	15	2	no	—
450	C₄⋊C₄	—	30	2	no	—
451	C₄⋊C₄	—	30	1	no	—
452	C₄⋊C₄	C₂²×D₁₅	1	1	yes	characteristic
453	C₄⋊C₄	C₂²×D₁₅	1	1	yes	characteristic
454	C₂²⋊C₄	—	2	1	no	—
455	C₂²⋊C₄	—	15	2	no	—
456	C₂²⋊C₄	—	30	2	no	—
457	C₂²⋊C₄	—	30	2	no	—
458	C₂²⋊C₄	—	30	2	no	—
459	C₄²	—	2	1	no	—
460	C₄²	—	15	2	no	—
461	C₄²	—	30	2	no	—
462	C₃×C₅	#2946	1	1	yes	characteristic, complemented, Hall
463	C₂²×C₃	—	2	1	no	—
464	C₂²×C₃	—	2	1	no	—
465	C₂²×C₃	—	2	2	no	—
466	C₂²×C₃	—	4	1	no	—
467	C₂²×C₃	—	4	1	no	—
468	C₂²×C₃	#4027	1	2	yes	—
469	C₂²×C₃	C₂×D₄×D₅	1	1	yes	characteristic
470	C₂×D₃	—	10	4	no	—
471	C₂×D₃	—	20	2	no	—
472	C₂×D₃	—	20	2	no	—
473	C₂×D₃	—	40	4	no	—
474	C₃×C₄	—	2	2	no	—
475	C₃×C₄	—	4	1	no	—
476	C₃×C₄	—	4	1	no	—
477	C₃×C₄	#4027	1	2	yes	—
478	C₃×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
479	C₃×C₄	C₂×#711	1	1	yes	characteristic
480	Dic₃	—	10	2	no	—
481	Dic₃	—	10	2	no	—
482	Dic₃	—	20	2	no	—
483	C₂×C₅	—	2	2	no	—
484	C₂×C₅	—	4	2	no	—
485	C₂×C₅	C₂×#67⋊C₄	1	1	yes	characteristic
486	C₂×C₅	#5769	1	1	yes	characteristic
487	C₂×C₅	#5770	1	1	yes	characteristic
488	D₅	—	12	4	no	—
489	C₂³	—	2	1	no	—
490	C₂³	—	30	2	no	—
491	C₂³	—	30	4	no	—
492	C₂³	—	120	1	no	—
493	C₂³	—	120	1	no	—
494	C₂³	D₄×D₁₅	1	1	yes	characteristic
495	Q₈	—	2	1	no	—
496	Q₈	C₂×C₄×D₁₅	1	2	yes	—
497	D₄	—	2	4	no	—
498	D₄	—	2	1	no	—
499	D₄	—	15	4	no	—
500	D₄	—	30	4	no	—
501	D₄	—	30	2	no	—
502	D₄	C₂×C₄×D₁₅	1	2	yes	—
503	C₂×C₄	—	2	1	no	—
504	C₂×C₄	—	2	4	no	—
505	C₂×C₄	—	2	1	no	—
506	C₂×C₄	—	2	1	no	—
507	C₂×C₄	—	15	2	no	—
508	C₂×C₄	—	15	2	no	—
509	C₂×C₄	—	30	2	no	—
510	C₂×C₄	—	120	2	no	—
511	C₂×C₄	—	120	2	no	—
512	C₂×C₄	—	120	2	no	—
513	C₂×C₄	—	120	1	no	—
514	C₂×C₄	C₂×C₄×D₁₅	1	2	yes	—
515	C₂×C₄	D₄×D₁₅	1	1	yes	characteristic
516	C₂×C₄	#6819	1	2	yes	—
517	C₂×C₄	C₂³×D₁₅	1	1	yes	characteristic
518	C₈	—	2	1	no	—
519	C₈	—	2	1	no	—
520	C₈	—	15	4	no	—
521	C₂×C₃	—	2	2	no	—
522	C₂×C₃	—	4	2	no	—
523	C₂×C₃	C₂×#4027	1	1	yes	characteristic
524	C₂×C₃	#66103	1	1	yes	characteristic
525	C₂×C₃	#66104	1	1	yes	characteristic
526	D₃	—	20	4	no	—
527	C₅	#78820	1	1	yes	characteristic, complemented, Sylow
528	C₂²	—	2	1	no	—
529	C₂²	—	2	1	no	—
530	C₂²	—	2	2	no	—
531	C₂²	—	4	1	no	—
532	C₂²	—	4	1	no	—
533	C₂²	—	30	4	no	—
534	C₂²	—	60	2	no	—
535	C₂²	—	60	2	no	—
536	C₂²	—	120	4	no	—
537	C₂²	#91770	1	2	yes	—
538	C₂²	C₂×D₄×D₁₅	1	1	yes	characteristic
539	C₄	—	2	2	no	—
540	C₄	—	4	1	no	—
541	C₄	—	4	1	no	—
542	C₄	—	30	2	no	—
543	C₄	—	30	2	no	—
544	C₄	—	60	2	no	—
545	C₄	#91770	1	2	yes	—
546	C₄	C₂²×C₄×D₁₅	1	1	yes	characteristic
547	C₄	C₂×#6819	1	1	yes	characteristic
548	C₃	#10610551	1	1	yes	characteristic, complemented, Sylow
549	C₂	—	2	2	no	—
550	C₂	—	4	2	no	—
551	C₂	—	60	4	no	—
552	C₂	C₂×#91770	1	1	yes	characteristic
553	C₂	#11756528	1	1	yes	characteristic
554	C₂	#11756529	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₄×D₁₅
commutator	C₃×C₄×C₅	C₂³×C₄
Frattini	C₂×C₄	C₂³×D₁₅
Fitting	C₃×C₅×#416	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
prime radical	C₂×#91838	C₂
cosocle	C₂×C₃×C₄×C₅	C₂⁴
hypercenter	#416	D₁₅
hypocenter	C₃×C₅	#2946
LCS	G ▷ C₃×C₄×C₅ ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #416

Complements

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

N	H ≅ G/N	type
1. #11756586	C₂	semidirect
3. #11756280	C₂	semidirect
4. C₃×C₅×#416	C₂	semidirect
5. C₂×#91105	C₂	semidirect
6. #11751202	C₂	semidirect
7. #11751096	C₂	semidirect
8. #11750918	C₂	semidirect
9. #11750889	C₂	semidirect
10. #11750886	C₂	semidirect
11. #11750857	C₂	semidirect
17. #91838	C₄	semidirect
18. Q₈×Dic₁₅	C₂²	semidirect
21. D₄×Dic₁₅	C₂²	semidirect
33. C₃×C₅×#103	C₂²	semidirect
34. C₃×C₅×#103	C₂²	semidirect
35. C₃×C₅×#102	C₂²	semidirect
36. C₃×C₅×#102	C₂²	semidirect
39. #91099	C₂²	semidirect
40. C₈×Dic₁₅	C₂²	semidirect
41. #91092	C₂²	semidirect
42. #91091	C₂²	semidirect
47. C₅×#416	D₃	semidirect
57. C₃×C₅×#41	C₂×C₄	semidirect
67. C₂×D₆₀	C₂×C₄	semidirect
80. #6717	C₂×C₄	semidirect
81. #6715	C₂×C₄	semidirect
91. #6710	C₂×C₄	semidirect
96. C₃×#416	D₅	semidirect
124. C₅×#103	C₂×D₃	semidirect
125. C₅×#103	C₂×D₃	semidirect
126. C₅×#102	C₂×D₃	semidirect
127. C₅×#102	C₂×D₃	semidirect
187. C₃×#103	C₂×D₅	semidirect
188. C₃×#103	C₂×D₅	semidirect
189. C₃×#102	C₂×D₅	semidirect
190. C₃×#102	C₂×D₅	semidirect
199. C₅×#41	C₄×D₃	semidirect
243. #416	D₁₅	semidirect
268. C₃×#41	C₄×D₅	semidirect
358. #103	C₂×D₁₅	semidirect
359. #103	C₂×D₁₅	semidirect
362. #102	C₂×D₁₅	semidirect
363. #102	C₂×D₁₅	semidirect
426. #41	C₄×D₁₅	semidirect
462. C₃×C₅	#2946	semidirect
527. C₅	#78820	semidirect
548. C₃	#10610551	semidirect

Maximal subgroups

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

subgroup	index
#11756586	2
C₂×#91838	2
#11756280	2
C₃×C₅×#416	2
C₂×#91105	2
#11751202	2
#11751096	2
#11750918	2
#11750889	2
#11750886	2
#11750857	2
#10610551	3
#78820	5