Subgroups — #14418115

Order 1920.

916 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	#11756527	C₂	1	1	yes	maximal, characteristic
2	#11756509	C₂	1	2	yes	maximal, complemented
3	C₃×C₅×#444	C₂	1	1	yes	maximal, characteristic, complemented
4	#11751297	C₂	1	1	yes	maximal, characteristic, complemented
5	#11751245	C₂	1	2	yes	maximal, complemented
6	#11750996	C₂	1	1	yes	maximal, characteristic, complemented
7	#11750994	C₂	1	1	yes	maximal, characteristic, complemented
8	#11750924	C₂	1	2	yes	maximal, complemented
9	D₁₅×#104	C₂	1	2	yes	maximal, complemented
10	#11750818	C₂	1	1	yes	maximal, characteristic, complemented
11	#11750808	C₂	1	1	yes	maximal, characteristic, complemented
12	#10611629	—	3	1	no	maximal, Hall
13	#41×D₁₅	C₂²	1	2	yes	—
14	C₃×C₅×#135	C₂²	1	1	yes	characteristic
15	C₃×C₅×#131	C₂²	1	2	yes	complemented
16	#91839	C₂²	1	2	yes	—
17	#91837	C₂²	1	2	yes	complemented
18	#91807	C₄	1	2	yes	complemented
19	#91804	C₄	1	2	yes	complemented
20	#91803	C₄	1	2	yes	complemented
21	#91800	C₄	1	2	yes	complemented
22	#91796	—	2	2	no	—
23	#91796	C₂²	1	2	yes	complemented
24	M₁₆×D₁₅	—	2	2	no	—
25	M₁₆×D₁₅	C₂²	1	2	yes	—
26	#91793	C₂²	1	1	yes	characteristic
27	#91790	—	2	2	no	—
28	#91790	C₂²	1	2	yes	complemented
29	C₂×#6705	—	2	2	no	—
30	C₂×#6705	C₂²	1	1	yes	characteristic
31	C₂×#6705	C₂²	1	1	yes	characteristic
32	C₄²×D₁₅	C₂²	1	1	yes	characteristic
33	C₃×C₅×#108	C₂²	1	1	yes	characteristic, complemented
34	C₃×C₅×#104	C₂²	1	2	yes	complemented
35	C₃×C₅×#97	C₂²	1	1	yes	characteristic, complemented
36	#91121	C₂²	1	2	yes	complemented
37	#91109	C₂²	1	2	yes	complemented
38	#91106	C₂²	1	2	yes	complemented
39	#91103	C₂²	1	1	yes	characteristic, complemented
40	C₈×Dic₁₅	C₂²	1	1	yes	characteristic, complemented
41	C₈×Dic₁₅	C₂²	1	1	yes	characteristic, complemented
42	#91089	C₂²	1	2	yes	complemented
43	#91087	C₂²	1	1	yes	characteristic, complemented
44	#79898	—	5	1	no	maximal, Hall
45	#66102	—	3	1	no	—
46	#66084	—	3	2	no	—
47	C₅×#444	D₃	1	1	yes	characteristic, complemented
48	#65485	—	3	1	no	—
49	#65433	—	3	2	no	—
50	#65184	—	3	1	no	—
51	#65182	—	3	1	no	—
52	#65112	—	3	2	no	—
53	D₅×#104	—	3	2	no	—
54	#65006	—	3	1	no	—
55	#64996	—	3	1	no	—
56	C₃×C₅×#41	C₂³	1	2	yes	—
57	#6821	C₂×C₄	1	2	yes	—
58	Q₈×D₁₅	C₂×C₄	1	2	yes	—
59	#6819	—	2	2	no	—
60	#6819	C₂×C₄	1	2	yes	—
61	D₄×D₁₅	—	2	2	no	—
62	D₄×D₁₅	C₂×C₄	1	2	yes	—
63	#6817	—	2	2	no	—
64	#6817	C₂³	1	2	yes	—
65	C₂×C₄×D₁₅	—	2	2	no	—
66	C₂×C₄×D₁₅	—	2	1	no	—
67	C₂×C₄×D₁₅	C₂³	1	1	yes	characteristic
68	C₃×C₅×Q₁₆	C₂×C₄	1	1	yes	characteristic, complemented
69	C₃×C₅×SD₁₆	C₂×C₄	1	2	yes	complemented
70	C₃×C₅×D₈	C₂×C₄	1	1	yes	characteristic, complemented
71	C₃×C₅×M₁₆	—	2	2	no	—
72	C₃×C₅×M₁₆	C₂³	1	2	yes	—
73	C₂×C₃×C₅×C₈	—	2	2	no	—
74	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
75	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
76	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
77	#6718	C₂×C₄	1	2	yes	complemented
78	#6717	C₂×C₄	1	2	yes	complemented
79	#6716	C₂×C₄	1	2	yes	complemented
80	#6715	C₂×C₄	1	2	yes	complemented
81	C₄×Dic₁₅	—	2	1	no	—
82	C₄×Dic₁₅	C₂³	1	1	yes	characteristic
83	#6710	—	2	2	no	—
84	#6710	C₂³	1	2	yes	—
85	C₂×C₃⋊#168	—	2	2	no	—
86	C₂×C₃⋊#168	C₂³	1	1	yes	characteristic
87	C₂×C₃⋊#168	C₂³	1	1	yes	characteristic
88	Dic₆₀	C₂×C₄	1	1	yes	characteristic, complemented
89	D₁₂₀	C₂×C₄	1	1	yes	characteristic, complemented
90	#6706	C₂×C₄	1	2	yes	complemented
91	#6705	—	2	2	no	—
92	#6705	—	2	2	no	—
93	#6705	—	2	2	no	—
94	#6705	C₂×C₄	1	2	yes	—
95	#6705	C₂×C₄	1	2	yes	—
96	#6705	D₄	1	2	yes	—
97	#6705	D₄	1	2	yes	—
98	C₈×D₁₅	—	2	2	no	—
99	C₈×D₁₅	—	2	2	no	—
100	C₈×D₁₅	—	2	2	no	—
101	#5768	—	5	1	no	—
102	#5750	—	5	2	no	—
103	C₃×#444	D₅	1	1	yes	characteristic, complemented
104	#5196	—	5	1	no	—
105	#5144	—	5	2	no	—
106	#4895	—	5	1	no	—
107	#4893	—	5	1	no	—
108	#4823	—	5	2	no	—
109	D₃×#104	—	5	2	no	—
110	#4717	—	5	1	no	—
111	#4707	—	5	1	no	—
112	D₅×#41	—	3	2	no	—
113	C₅×#135	C₂×D₃	1	1	yes	characteristic
114	C₅×#131	C₂×D₃	1	2	yes	complemented
115	#4096	—	3	2	no	—
116	#4094	—	3	2	no	—
117	#4064	—	3	2	no	—
118	#4061	—	3	2	no	—
119	#4060	—	3	2	no	—
120	#4057	—	3	2	no	—
121	#4053	—	3	2	no	—
122	#4053	—	6	2	no	—
123	D₅×M₁₆	—	3	2	no	—
124	D₅×M₁₆	—	6	2	no	—
125	#4050	—	3	1	no	—
126	#4047	—	3	2	no	—
127	#4047	—	6	2	no	—
128	C₂×#676	—	3	1	no	—
129	C₂×#676	—	3	1	no	—
130	C₂×#676	—	6	2	no	—
131	C₄²×D₅	—	3	1	no	—
132	C₅×#108	C₂×D₃	1	1	yes	characteristic, complemented
133	C₅×#104	C₂×D₃	1	2	yes	complemented
134	C₅×#97	C₂×D₃	1	1	yes	characteristic, complemented
135	#3969	—	3	2	no	—
136	#3957	—	3	2	no	—
137	#3954	—	3	2	no	—
138	#3951	—	3	1	no	—
139	C₈×Dic₅	—	3	1	no	—
140	C₈×Dic₅	—	3	1	no	—
141	#3937	—	3	2	no	—
142	#3935	—	3	1	no	—
143	#2956	—	15	1	no	Sylow
144	C₂²×D₁₅	—	2	2	no	—
145	C₂²×D₁₅	#41	1	1	yes	characteristic
146	C₃×C₅×Q₈	C₂²×C₄	1	2	yes	—
147	C₃×C₅×D₄	—	2	2	no	—
148	C₃×C₅×D₄	C₂²×C₄	1	2	yes	—
149	C₂×C₃×C₄×C₅	—	2	2	no	—
150	C₂×C₃×C₄×C₅	—	2	1	no	—
151	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
152	#1220	—	2	2	no	—
153	#1220	—	2	2	no	—
154	#1220	—	2	2	no	—
155	C₂×Dic₁₅	—	2	1	no	—
156	C₂×Dic₁₅	—	2	2	no	—
157	C₂×Dic₁₅	#41	1	1	yes	characteristic
158	D₆₀	—	2	2	no	—
159	D₆₀	C₂²×C₄	1	2	yes	—
160	C₄×D₁₅	—	2	2	no	—
161	C₄×D₁₅	—	2	2	no	—
162	C₄×D₁₅	—	2	2	no	—
163	C₄×D₁₅	—	4	2	no	—
164	C₄×D₁₅	C₂²×C₄	1	2	yes	—
165	C₄×D₁₅	C₂×D₄	1	2	yes	—
166	Dic₃₀	—	2	2	no	—
167	Dic₃₀	C₂²×C₄	1	2	yes	—
168	C₃×C₅×C₈	—	2	2	no	—
169	C₃×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
170	C₃×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
171	C₃×C₅×C₈	C₂×D₄	1	2	yes	—
172	C₃⋊#168	—	2	2	no	—
173	C₃⋊#168	C₂²×C₄	1	2	yes	—
174	C₃⋊#168	C₂×D₄	1	1	yes	characteristic
175	C₃⋊#168	C₂×D₄	1	1	yes	characteristic
176	D₃×#41	—	5	2	no	—
177	C₃×#135	C₂×D₅	1	1	yes	characteristic
178	C₃×#131	C₂×D₅	1	2	yes	complemented
179	#950	—	5	2	no	—
180	#948	—	5	2	no	—
181	#918	—	5	2	no	—
182	#915	—	5	2	no	—
183	#914	—	5	2	no	—
184	#911	—	5	2	no	—
185	#907	—	5	2	no	—
186	#907	—	10	2	no	—
187	D₃×M₁₆	—	5	2	no	—
188	D₃×M₁₆	—	10	2	no	—
189	#904	—	5	1	no	—
190	#901	—	5	2	no	—
191	#901	—	10	2	no	—
192	C₂×ΓL(1,𝔽₂₅)	—	5	1	no	—
193	C₂×ΓL(1,𝔽₂₅)	—	5	1	no	—
194	C₂×ΓL(1,𝔽₂₅)	—	10	2	no	—
195	C₄²×D₃	—	5	1	no	—
196	C₃×#108	C₂×D₅	1	1	yes	characteristic, complemented
197	C₃×#104	C₂×D₅	1	2	yes	complemented
198	C₃×#97	C₂×D₅	1	1	yes	characteristic, complemented
199	#837	—	5	2	no	—
200	#825	—	5	2	no	—
201	#822	—	5	2	no	—
202	#819	—	5	1	no	—
203	C₈×Dic₃	—	5	1	no	—
204	C₈×Dic₃	—	5	1	no	—
205	#805	—	5	2	no	—
206	#803	—	5	1	no	—
207	C₅×#41	C₂²×D₃	1	2	yes	—
208	#713	—	3	2	no	—
209	Q₈×D₅	—	3	2	no	—
210	#711	—	3	2	no	—
211	#711	—	6	2	no	—
212	D₄×D₅	—	3	2	no	—
213	D₄×D₅	—	6	2	no	—
214	#709	—	3	2	no	—
215	#709	—	6	2	no	—
216	C₂×C₄×D₅	—	3	1	no	—
217	C₂×C₄×D₅	—	6	2	no	—
218	C₂×C₄×D₅	—	6	1	no	—
219	C₅×Q₁₆	C₄×D₃	1	1	yes	characteristic, complemented
220	C₅×SD₁₆	C₄×D₃	1	2	yes	complemented
221	C₅×D₈	C₄×D₃	1	1	yes	characteristic, complemented
222	C₅×M₁₆	—	2	2	no	—
223	C₅×M₁₆	C₂²×D₃	1	2	yes	—
224	C₂×C₅×C₈	—	2	2	no	—
225	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
226	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
227	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
228	#689	—	3	2	no	—
229	#688	—	3	2	no	—
230	#687	—	3	2	no	—
231	#686	—	3	2	no	—
232	C₄×Dic₅	—	3	1	no	—
233	C₄×Dic₅	—	6	1	no	—
234	#681	—	3	2	no	—
235	#681	—	6	2	no	—
236	C₂×#168	—	3	1	no	—
237	C₂×#168	—	3	1	no	—
238	C₂×#168	—	6	2	no	—
239	Dic₂₀	—	3	1	no	—
240	D₄₀	—	3	1	no	—
241	#677	—	3	2	no	—
242	#676	—	3	2	no	—
243	#676	—	3	2	no	—
244	#676	—	3	2	no	—
245	#676	—	3	2	no	—
246	#676	—	6	2	no	—
247	#676	—	6	2	no	—
248	#676	—	6	2	no	—
249	C₈×D₅	—	6	2	no	—
250	C₈×D₅	—	6	2	no	—
251	C₈×D₅	—	6	2	no	—
252	#575	—	15	1	no	—
253	#568	—	15	2	no	—
254	#444	—	15	2	no	—
255	#444	—	15	1	no	—
256	#444	D₁₅	1	1	yes	characteristic, complemented
257	#443	—	15	1	no	—
258	#443	—	15	2	no	—
259	#443	—	15	1	no	—
260	#430	—	15	1	no	—
261	C₂×#104	—	15	2	no	—
262	C₄×M₁₆	—	15	1	no	—
263	C₂²×C₃×C₅	—	2	2	no	—
264	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
265	C₂×D₁₅	—	2	2	no	—
266	C₂×D₁₅	—	4	1	no	—
267	C₂×D₁₅	—	8	2	no	—
268	C₂×D₁₅	C₄×D₄	1	2	yes	—
269	C₃×C₄×C₅	—	2	2	no	—
270	C₃×C₄×C₅	—	4	1	no	—
271	C₃×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
272	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
273	Dic₁₅	—	2	2	no	—
274	Dic₁₅	—	2	2	no	—
275	Dic₁₅	C₄×D₄	1	2	yes	—
276	C₃×#41	C₂²×D₅	1	2	yes	—
277	#239	—	5	2	no	—
278	D₃×Q₈	—	5	2	no	—
279	#237	—	5	2	no	—
280	#237	—	10	2	no	—
281	D₃×D₄	—	5	2	no	—
282	D₃×D₄	—	10	2	no	—
283	#235	—	5	2	no	—
284	#235	—	10	2	no	—
285	C₂×C₄×D₃	—	5	1	no	—
286	C₂×C₄×D₃	—	10	2	no	—
287	C₂×C₄×D₃	—	10	1	no	—
288	C₃×Q₁₆	C₄×D₅	1	1	yes	characteristic, complemented
289	C₃×SD₁₆	C₄×D₅	1	2	yes	complemented
290	C₃×D₈	C₄×D₅	1	1	yes	characteristic, complemented
291	C₃×M₁₆	—	2	2	no	—
292	C₃×M₁₆	C₂²×D₅	1	2	yes	—
293	C₂×C₃×C₈	—	2	2	no	—
294	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
295	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
296	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
297	#216	—	5	2	no	—
298	#215	—	5	2	no	—
299	#214	—	5	2	no	—
300	#213	—	5	2	no	—
301	C₄×Dic₃	—	5	1	no	—
302	C₄×Dic₃	—	10	1	no	—
303	#208	—	5	2	no	—
304	#208	—	10	2	no	—
305	C₂×C₃⋊C₈	—	5	1	no	—
306	C₂×C₃⋊C₈	—	5	1	no	—
307	C₂×C₃⋊C₈	—	10	2	no	—
308	Dic₁₂	—	5	1	no	—
309	D₂₄	—	5	1	no	—
310	#204	—	5	2	no	—
311	ΓL(1,𝔽₂₅)	—	5	2	no	—
312	ΓL(1,𝔽₂₅)	—	5	2	no	—
313	ΓL(1,𝔽₂₅)	—	5	2	no	—
314	ΓL(1,𝔽₂₅)	—	5	2	no	—
315	ΓL(1,𝔽₂₅)	—	10	2	no	—
316	ΓL(1,𝔽₂₅)	—	10	2	no	—
317	ΓL(1,𝔽₂₅)	—	10	2	no	—
318	D₃×C₈	—	10	2	no	—
319	D₃×C₈	—	10	2	no	—
320	D₃×C₈	—	10	2	no	—
321	C₂²×D₅	—	3	1	no	—
322	C₂²×D₅	—	6	2	no	—
323	C₅×Q₈	C₂×C₄×D₃	1	2	yes	—
324	C₅×D₄	—	2	2	no	—
325	C₅×D₄	C₂×C₄×D₃	1	2	yes	—
326	C₂×C₄×C₅	—	2	2	no	—
327	C₂×C₄×C₅	—	2	1	no	—
328	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
329	C₂²⋊D₅	—	6	2	no	—
330	C₂²⋊D₅	—	6	2	no	—
331	C₂²⋊D₅	—	6	2	no	—
332	C₂×Dic₅	—	3	1	no	—
333	C₂×Dic₅	—	6	2	no	—
334	C₂×Dic₅	—	6	1	no	—
335	D₂₀	—	3	2	no	—
336	D₂₀	—	6	2	no	—
337	C₄×D₅	—	3	2	no	—
338	C₄×D₅	—	3	2	no	—
339	C₄×D₅	—	6	2	no	—
340	C₄×D₅	—	6	2	no	—
341	C₄×D₅	—	6	2	no	—
342	C₄×D₅	—	12	2	no	—
343	Dic₁₀	—	3	2	no	—
344	Dic₁₀	—	6	2	no	—
345	C₅×C₈	—	2	2	no	—
346	C₅×C₈	C₂×C₄×D₃	1	1	yes	characteristic
347	C₅×C₈	C₂×C₄×D₃	1	1	yes	characteristic
348	C₅×C₈	D₃×D₄	1	2	yes	—
349	#168	—	3	2	no	—
350	#168	—	3	1	no	—
351	#168	—	3	1	no	—
352	#168	—	6	2	no	—
353	C₂×#41	—	15	2	no	—
354	#137	—	15	2	no	—
355	#137	—	15	2	no	—
356	AGL(1,ℤ/8)	—	15	2	no	—
357	AGL(1,ℤ/8)	—	15	2	no	—
358	#135	—	15	2	no	—
359	#135	—	15	1	no	—
360	#135	C₂×D₁₅	1	1	yes	characteristic
361	#131	—	15	2	no	—
362	#131	—	15	2	no	—
363	#131	—	15	2	no	—
364	#131	—	30	2	no	—
365	#131	—	30	2	no	—
366	#131	C₂×D₁₅	1	2	yes	complemented
367	C₂×M₁₆	—	15	1	no	—
368	C₂×M₁₆	—	15	1	no	—
369	C₂×M₁₆	—	15	2	no	—
370	C₂×M₁₆	—	30	2	no	—
371	C₂×M₁₆	—	30	2	no	—
372	C₂×C₄²	—	15	1	no	—
373	#108	—	15	2	no	—
374	#108	—	15	1	no	—
375	#108	C₂×D₁₅	1	1	yes	characteristic, complemented
376	#104	—	15	2	no	—
377	#104	—	15	2	no	—
378	#104	—	15	2	no	—
379	#104	C₂×D₁₅	1	2	yes	complemented
380	#97	—	15	1	no	—
381	#97	C₂×D₁₅	1	1	yes	characteristic, complemented
382	C₄×C₈	—	15	1	no	—
383	C₄×C₈	—	15	1	no	—
384	C₂×C₃×C₅	—	2	1	no	—
385	C₂×C₃×C₅	—	4	2	no	—
386	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
387	D₁₅	—	2	2	no	—
388	D₁₅	—	4	2	no	—
389	C₂²×D₃	—	5	1	no	—
390	C₂²×D₃	—	10	2	no	—
391	C₃×Q₈	C₂×C₄×D₅	1	2	yes	—
392	C₃×D₄	—	2	2	no	—
393	C₃×D₄	C₂×C₄×D₅	1	2	yes	—
394	C₂×C₃×C₄	—	2	2	no	—
395	C₂×C₃×C₄	—	2	1	no	—
396	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
397	#67	—	10	2	no	—
398	#67	—	10	2	no	—
399	#67	—	10	2	no	—
400	C₂×Dic₃	—	5	1	no	—
401	C₂×Dic₃	—	10	2	no	—
402	C₂×Dic₃	—	10	1	no	—
403	D₁₂	—	5	2	no	—
404	D₁₂	—	10	2	no	—
405	C₄×D₃	—	5	2	no	—
406	C₄×D₃	—	5	2	no	—
407	C₄×D₃	—	10	2	no	—
408	C₄×D₃	—	10	2	no	—
409	C₄×D₃	—	10	2	no	—
410	C₄×D₃	—	20	2	no	—
411	Dic₆	—	5	2	no	—
412	Dic₆	—	10	2	no	—
413	C₃×C₈	—	2	2	no	—
414	C₃×C₈	C₂×C₄×D₅	1	1	yes	characteristic
415	C₃×C₈	C₂×C₄×D₅	1	1	yes	characteristic
416	C₃×C₈	D₄×D₅	1	2	yes	—
417	C₃⋊C₈	—	5	2	no	—
418	C₃⋊C₈	—	5	1	no	—
419	C₃⋊C₈	—	5	1	no	—
420	C₃⋊C₈	—	10	2	no	—
421	C₂²×C₅	—	2	2	no	—
422	C₂²×C₅	D₃×#41	1	1	yes	characteristic
423	C₂×D₅	—	3	2	no	—
424	C₂×D₅	—	6	2	no	—
425	C₂×D₅	—	12	1	no	—
426	C₂×D₅	—	24	2	no	—
427	C₄×C₅	—	2	2	no	—
428	C₄×C₅	—	4	1	no	—
429	C₄×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
430	C₄×C₅	C₂×D₃×D₄	1	1	yes	characteristic
431	Dic₅	—	3	2	no	—
432	Dic₅	—	6	2	no	—
433	Dic₅	—	6	2	no	—
434	#41	—	15	2	no	—
435	#41	—	15	2	no	—
436	#41	—	15	2	no	—
437	#41	—	30	2	no	—
438	#41	—	30	2	no	—
439	#41	C₂²×D₁₅	1	2	yes	—
440	C₂×Q₈	—	15	2	no	—
441	C₂×D₄	—	15	2	no	—
442	C₂×D₄	—	30	2	no	—
443	C₂²×C₄	—	15	1	no	—
444	C₂²×C₄	—	30	2	no	—
445	C₂²×C₄	—	30	1	no	—
446	Q₁₆	—	15	2	no	—
447	Q₁₆	—	15	1	no	—
448	Q₁₆	C₄×D₁₅	1	1	yes	characteristic, complemented
449	SD₁₆	—	15	2	no	—
450	SD₁₆	—	15	2	no	—
451	SD₁₆	—	15	2	no	—
452	SD₁₆	C₄×D₁₅	1	2	yes	complemented
453	D₈	—	15	2	no	—
454	D₈	—	15	1	no	—
455	D₈	C₄×D₁₅	1	1	yes	characteristic, complemented
456	M₁₆	—	2	2	no	—
457	M₁₆	—	15	2	no	—
458	M₁₆	—	15	2	no	—
459	M₁₆	—	15	2	no	—
460	M₁₆	—	15	2	no	—
461	M₁₆	—	15	2	no	—
462	M₁₆	—	30	2	no	—
463	M₁₆	—	30	2	no	—
464	M₁₆	—	30	2	no	—
465	M₁₆	—	30	2	no	—
466	M₁₆	C₂²×D₁₅	1	2	yes	—
467	C₂×C₈	—	2	2	no	—
468	C₂×C₈	—	15	1	no	—
469	C₂×C₈	—	15	1	no	—
470	C₂×C₈	—	30	2	no	—
471	C₂×C₈	—	30	2	no	—
472	C₂×C₈	—	30	2	no	—
473	C₂×C₈	—	30	2	no	—
474	C₂×C₈	C₂²×D₁₅	1	1	yes	characteristic
475	C₂×C₈	C₂²×D₁₅	1	1	yes	characteristic
476	C₄²	—	15	1	no	—
477	C₄²	—	30	1	no	—
478	C₄²	C₂²×D₁₅	1	1	yes	characteristic
479	C₃×C₅	#2956	1	1	yes	characteristic, complemented, Hall
480	C₂²×C₃	—	2	2	no	—
481	C₂²×C₃	D₅×#41	1	1	yes	characteristic
482	C₂×D₃	—	5	2	no	—
483	C₂×D₃	—	10	2	no	—
484	C₂×D₃	—	20	1	no	—
485	C₂×D₃	—	40	2	no	—
486	C₃×C₄	—	2	2	no	—
487	C₃×C₄	—	4	1	no	—
488	C₃×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
489	C₃×C₄	C₂×D₄×D₅	1	1	yes	characteristic
490	Dic₃	—	5	2	no	—
491	Dic₃	—	10	2	no	—
492	Dic₃	—	10	2	no	—
493	C₂×C₅	—	2	1	no	—
494	C₂×C₅	—	4	2	no	—
495	C₂×C₅	C₄×D₃×D₄	1	1	yes	characteristic
496	D₅	—	6	2	no	—
497	D₅	—	12	2	no	—
498	C₂³	—	15	1	no	—
499	C₂³	—	30	2	no	—
500	Q₈	—	15	2	no	—
501	Q₈	—	30	2	no	—
502	Q₈	C₂×C₄×D₁₅	1	2	yes	—
503	D₄	—	2	2	no	—
504	D₄	—	15	2	no	—
505	D₄	—	30	2	no	—
506	D₄	—	30	2	no	—
507	D₄	—	30	2	no	—
508	D₄	—	30	2	no	—
509	D₄	C₂×C₄×D₁₅	1	2	yes	—
510	C₂×C₄	—	2	2	no	—
511	C₂×C₄	—	2	1	no	—
512	C₂×C₄	—	15	1	no	—
513	C₂×C₄	—	15	2	no	—
514	C₂×C₄	—	15	2	no	—
515	C₂×C₄	—	30	2	no	—
516	C₂×C₄	—	30	2	no	—
517	C₂×C₄	—	30	2	no	—
518	C₂×C₄	—	30	1	no	—
519	C₂×C₄	—	30	2	no	—
520	C₂×C₄	—	60	2	no	—
521	C₂×C₄	C₂³×D₁₅	1	1	yes	characteristic
522	C₈	—	2	2	no	—
523	C₈	—	15	2	no	—
524	C₈	—	15	1	no	—
525	C₈	—	15	1	no	—
526	C₈	—	30	2	no	—
527	C₈	C₂×C₄×D₁₅	1	1	yes	characteristic
528	C₈	C₂×C₄×D₁₅	1	1	yes	characteristic
529	C₈	D₄×D₁₅	1	2	yes	—
530	C₂×C₃	—	2	1	no	—
531	C₂×C₃	—	4	2	no	—
532	C₂×C₃	C₄×D₄×D₅	1	1	yes	characteristic
533	D₃	—	10	2	no	—
534	D₃	—	20	2	no	—
535	C₅	#79898	1	1	yes	characteristic, complemented, Sylow
536	C₂²	—	2	2	no	—
537	C₂²	—	15	2	no	—
538	C₂²	—	30	2	no	—
539	C₂²	—	60	1	no	—
540	C₂²	—	120	2	no	—
541	C₂²	#41×D₁₅	1	1	yes	characteristic
542	C₄	—	2	2	no	—
543	C₄	—	4	1	no	—
544	C₄	—	15	2	no	—
545	C₄	—	30	2	no	—
546	C₄	—	30	2	no	—
547	C₄	C₂²×C₄×D₁₅	1	1	yes	characteristic
548	C₄	C₂×D₄×D₁₅	1	1	yes	characteristic
549	C₃	#10611629	1	1	yes	characteristic, complemented, Sylow
550	C₂	—	2	1	no	—
551	C₂	—	4	2	no	—
552	C₂	—	30	2	no	—
553	C₂	—	60	2	no	—
554	C₂	C₄×D₄×D₁₅	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂×D₄×D₁₅
commutator	C₃×C₄×C₅	C₂³×C₄
Frattini	C₂×C₄	C₂³×D₁₅
Fitting	C₃×C₅×#444	C₂
socle	C₂×C₃×C₅	C₂×C₄×D₄
prime radical	#11756527	C₂
cosocle	C₂×C₃×C₄×C₅	C₂⁴
hypercenter	#444	D₁₅
hypocenter	C₃×C₅	#2956
LCS	G ▷ C₃×C₄×C₅ ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₄ ◁ C₂×C₈ ◁ #444

Complements

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

N	H ≅ G/N	type
2. #11756509	C₂	semidirect
3. C₃×C₅×#444	C₂	semidirect
4. #11751297	C₂	semidirect
5. #11751245	C₂	semidirect
6. #11750996	C₂	semidirect
7. #11750994	C₂	semidirect
8. #11750924	C₂	semidirect
9. D₁₅×#104	C₂	semidirect
10. #11750818	C₂	semidirect
11. #11750808	C₂	semidirect
15. C₃×C₅×#131	C₂²	semidirect
17. #91837	C₂²	semidirect
18. #91807	C₄	semidirect
19. #91804	C₄	semidirect
20. #91803	C₄	semidirect
21. #91800	C₄	semidirect
23. #91796	C₂²	semidirect
28. #91790	C₂²	semidirect
33. C₃×C₅×#108	C₂²	semidirect
34. C₃×C₅×#104	C₂²	semidirect
35. C₃×C₅×#97	C₂²	semidirect
36. #91121	C₂²	semidirect
37. #91109	C₂²	semidirect
38. #91106	C₂²	semidirect
39. #91103	C₂²	semidirect
40. C₈×Dic₁₅	C₂²	semidirect
41. C₈×Dic₁₅	C₂²	semidirect
42. #91089	C₂²	semidirect
43. #91087	C₂²	semidirect
47. C₅×#444	D₃	semidirect
68. C₃×C₅×Q₁₆	C₂×C₄	semidirect
69. C₃×C₅×SD₁₆	C₂×C₄	semidirect
70. C₃×C₅×D₈	C₂×C₄	semidirect
77. #6718	C₂×C₄	semidirect
78. #6717	C₂×C₄	semidirect
79. #6716	C₂×C₄	semidirect
80. #6715	C₂×C₄	semidirect
88. Dic₆₀	C₂×C₄	semidirect
89. D₁₂₀	C₂×C₄	semidirect
90. #6706	C₂×C₄	semidirect
103. C₃×#444	D₅	semidirect
114. C₅×#131	C₂×D₃	semidirect
132. C₅×#108	C₂×D₃	semidirect
133. C₅×#104	C₂×D₃	semidirect
134. C₅×#97	C₂×D₃	semidirect
178. C₃×#131	C₂×D₅	semidirect
196. C₃×#108	C₂×D₅	semidirect
197. C₃×#104	C₂×D₅	semidirect
198. C₃×#97	C₂×D₅	semidirect
219. C₅×Q₁₆	C₄×D₃	semidirect
220. C₅×SD₁₆	C₄×D₃	semidirect
221. C₅×D₈	C₄×D₃	semidirect
256. #444	D₁₅	semidirect
288. C₃×Q₁₆	C₄×D₅	semidirect
289. C₃×SD₁₆	C₄×D₅	semidirect
290. C₃×D₈	C₄×D₅	semidirect
366. #131	C₂×D₁₅	semidirect
375. #108	C₂×D₁₅	semidirect
379. #104	C₂×D₁₅	semidirect
381. #97	C₂×D₁₅	semidirect
448. Q₁₆	C₄×D₁₅	semidirect
452. SD₁₆	C₄×D₁₅	semidirect
455. D₈	C₄×D₁₅	semidirect
479. C₃×C₅	#2956	semidirect
535. C₅	#79898	semidirect
549. C₃	#10611629	semidirect

Maximal subgroups

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

subgroup	index
#11756527	2
#11756509	2
C₃×C₅×#444	2
#11751297	2
#11751245	2
#11750996	2
#11750994	2
#11750924	2
D₁₅×#104	2
#11750818	2
#11750808	2
#10611629	3
#79898	5