Subgroups — #14417946

Order 1920.

928 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₁₅×#135	C₂	1	1	yes	maximal, characteristic
2	#11755299	C₂	1	2	yes	maximal, complemented
3	C₅×#5197	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#65486	C₂	1	1	yes	maximal, characteristic, complemented
5	#11749439	C₂	1	2	yes	maximal, complemented
6	#11749435	C₂	1	2	yes	maximal, complemented
7	#11749430	C₂	1	2	yes	maximal, complemented
8	#11748069	C₂	1	1	yes	maximal, characteristic, complemented
9	#11748065	C₂	1	1	yes	maximal, characteristic, complemented
10	#11748060	C₂	1	1	yes	maximal, characteristic, complemented
11	#11747603	C₂	1	1	yes	maximal, characteristic, complemented
12	D₅×#444	—	3	1	no	maximal, Hall
13	#41×D₁₅	C₂²	1	2	yes	—
14	C₃×C₅×#135	C₂²	1	1	yes	characteristic
15	#91839	C₂²	1	2	yes	—
16	#91808	C₄	1	1	yes	characteristic, complemented
17	Q₁₆×D₁₅	C₄	1	1	yes	characteristic, complemented
18	#91805	C₄	1	2	yes	complemented
19	SD₁₆×D₁₅	C₄	1	2	yes	complemented
20	#91801	C₄	1	1	yes	characteristic, complemented
21	D₈×D₁₅	C₄	1	1	yes	characteristic, complemented
22	#91793	C₂²	1	1	yes	characteristic
23	C₂×C₈×D₁₅	C₂²	1	1	yes	characteristic
24	C₅×#948	C₂²	1	2	yes	complemented
25	C₃×#4094	C₂²	1	2	yes	complemented
26	C₄×#1200	C₂²	1	1	yes	characteristic
27	#91292	—	2	2	no	—
28	#91292	C₂²	1	2	yes	—
29	#91291	—	2	2	no	—
30	#91291	C₂²	1	2	yes	complemented
31	#91290	—	2	2	no	—
32	#91290	C₂²	1	2	yes	complemented
33	C₂×#6648	—	2	2	no	—
34	C₂×#6648	C₂²	1	1	yes	characteristic
35	C₅×#837	C₂²	1	2	yes	complemented
36	C₅×#819	C₂²	1	1	yes	characteristic, complemented
37	C₅×#815	C₂²	1	1	yes	characteristic, complemented
38	C₃×#3969	C₂²	1	2	yes	complemented
39	C₃×#3951	C₂²	1	1	yes	characteristic, complemented
40	C₃×#3947	C₂²	1	1	yes	characteristic, complemented
41	#90992	C₂²	1	2	yes	complemented
42	#90981	C₂²	1	2	yes	complemented
43	#90980	C₂²	1	2	yes	complemented
44	#90953	C₂²	1	1	yes	characteristic, complemented
45	#90952	C₂²	1	1	yes	characteristic, complemented
46	D₃×#444	—	5	1	no	maximal, Hall
47	D₅×#135	—	3	1	no	—
48	D₅×#131	—	3	2	no	—
49	C₅×#444	—	3	1	no	—
50	#65486	D₃	1	1	yes	characteristic, complemented
51	#65434	—	3	2	no	—
52	#65183	—	3	1	no	—
53	D₅×#108	—	3	1	no	—
54	#65112	—	3	2	no	—
55	D₅×#104	—	3	2	no	—
56	#65006	—	3	1	no	—
57	D₅×#97	—	3	1	no	—
58	C₃×C₅×#41	C₂³	1	2	yes	—
59	#6821	C₂×C₄	1	2	yes	—
60	Q₈×D₁₅	C₂×C₄	1	2	yes	—
61	#6819	—	2	2	no	—
62	#6819	C₂×C₄	1	2	yes	—
63	D₄×D₁₅	—	2	2	no	—
64	D₄×D₁₅	C₂×C₄	1	2	yes	—
65	#6817	—	2	2	no	—
66	#6817	C₂³	1	2	yes	—
67	C₂×C₄×D₁₅	—	2	2	no	—
68	C₂×C₄×D₁₅	C₂³	1	1	yes	characteristic
69	C₂×#1200	—	2	1	no	—
70	C₃×C₅×Q₁₆	C₂×C₄	1	1	yes	characteristic, complemented
71	C₃×C₅×SD₁₆	C₂×C₄	1	2	yes	complemented
72	C₃×C₅×D₈	C₂×C₄	1	1	yes	characteristic, complemented
73	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
74	#6718	C₂×C₄	1	2	yes	complemented
75	#6717	C₂×C₄	1	2	yes	complemented
76	#6716	C₂×C₄	1	2	yes	complemented
77	#6715	C₂×C₄	1	2	yes	complemented
78	C₂×C₃⋊#168	C₂³	1	1	yes	characteristic
79	Dic₆₀	C₂×C₄	1	1	yes	characteristic, complemented
80	D₁₂₀	C₂×C₄	1	1	yes	characteristic, complemented
81	#6706	C₂×C₄	1	2	yes	complemented
82	C₈×D₁₅	C₂×C₄	1	1	yes	characteristic
83	C₈×D₁₅	C₂×C₄	1	1	yes	characteristic
84	C₈×D₁₅	C₂×C₄	1	1	yes	characteristic
85	C₈×D₁₅	C₂×C₄	1	1	yes	characteristic
86	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
87	C₅×#208	—	2	2	no	—
88	C₅×#208	C₂³	1	2	yes	—
89	C₂×C₅×C₃⋊C₈	—	2	2	no	—
90	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
91	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
92	C₃×#681	—	2	2	no	—
93	C₃×#681	C₂³	1	2	yes	—
94	C₂×C₃×#168	—	2	2	no	—
95	C₂×C₃×#168	C₂³	1	1	yes	characteristic
96	Dic₃×Dic₅	—	2	1	no	—
97	#6651	—	2	2	no	—
98	#6651	—	2	2	no	—
99	#6651	—	2	2	no	—
100	#6648	—	2	2	no	—
101	#6648	—	2	2	no	—
102	#6648	—	2	2	no	—
103	#6648	D₄	1	2	yes	—
104	#6648	D₄	1	2	yes	—
105	D₃×#135	—	5	1	no	—
106	D₃×#131	—	5	2	no	—
107	C₃×#444	—	5	1	no	—
108	#5197	D₅	1	1	yes	characteristic, complemented
109	#5145	—	5	2	no	—
110	#4894	—	5	1	no	—
111	D₃×#108	—	5	1	no	—
112	#4823	—	5	2	no	—
113	D₃×#104	—	5	2	no	—
114	#4717	—	5	1	no	—
115	D₃×#97	—	5	1	no	—
116	D₅×#41	—	3	2	no	—
117	C₅×#135	C₂×D₃	1	1	yes	characteristic
118	C₅×#131	—	3	2	no	—
119	#4096	—	3	2	no	—
120	#4094	C₂×D₃	1	2	yes	complemented
121	#4065	—	3	1	no	—
122	D₅×Q₁₆	—	3	1	no	—
123	#4062	—	3	2	no	—
124	D₅×SD₁₆	—	3	2	no	—
125	#4058	—	3	1	no	—
126	D₅×D₈	—	3	1	no	—
127	#4053	—	3	2	no	—
128	#4053	—	6	2	no	—
129	D₅×M₁₆	—	3	2	no	—
130	D₅×M₁₆	—	6	2	no	—
131	#4050	—	3	1	no	—
132	#4047	—	3	2	no	—
133	#4047	—	6	2	no	—
134	C₂×C₈×D₅	—	3	1	no	—
135	C₂×C₈×D₅	—	3	1	no	—
136	C₂×C₈×D₅	—	6	2	no	—
137	C₄²×D₅	—	3	1	no	—
138	C₅×#108	—	3	1	no	—
139	C₅×#104	—	3	2	no	—
140	C₅×#97	—	3	1	no	—
141	#3969	C₂×D₃	1	2	yes	complemented
142	#3957	—	3	2	no	—
143	#3954	—	3	2	no	—
144	#3951	C₂×D₃	1	1	yes	characteristic, complemented
145	#3947	—	3	1	no	—
146	#3947	C₂×D₃	1	1	yes	characteristic, complemented
147	#3937	—	3	2	no	—
148	#3935	—	3	1	no	—
149	C₂×#444	—	15	1	no	Sylow
150	C₂²×D₁₅	—	2	2	no	—
151	C₂²×D₁₅	#41	1	1	yes	characteristic
152	C₃×C₅×Q₈	C₂²×C₄	1	2	yes	—
153	C₃×C₅×D₄	—	2	2	no	—
154	C₃×C₅×D₄	C₂²×C₄	1	2	yes	—
155	C₂×C₃×C₄×C₅	—	2	2	no	—
156	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
157	#1220	—	2	2	no	—
158	#1220	—	2	2	no	—
159	#1220	—	2	2	no	—
160	C₂×Dic₁₅	—	2	2	no	—
161	C₂×Dic₁₅	#41	1	1	yes	characteristic
162	D₆₀	—	2	2	no	—
163	D₆₀	C₂²×C₄	1	2	yes	—
164	C₄×D₁₅	—	2	2	no	—
165	C₄×D₁₅	—	2	2	no	—
166	C₄×D₁₅	—	2	2	no	—
167	C₄×D₁₅	C₂²×C₄	1	1	yes	characteristic
168	C₄×D₁₅	C₂²×C₄	1	1	yes	characteristic
169	C₄×D₁₅	C₂×D₄	1	1	yes	characteristic
170	C₄×D₁₅	C₂×D₄	1	1	yes	characteristic
171	Dic₃₀	—	2	2	no	—
172	Dic₃₀	C₂²×C₄	1	2	yes	—
173	C₂×C₅×Dic₃	—	2	1	no	—
174	C₂×C₃×Dic₅	—	2	1	no	—
175	#1200	—	4	2	no	—
176	C₃×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
177	C₃×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
178	C₃⋊#168	C₂²×C₄	1	1	yes	characteristic
179	C₃⋊#168	C₂²×C₄	1	1	yes	characteristic
180	C₃×#168	—	2	2	no	—
181	C₃×#168	C₂×D₄	1	2	yes	—
182	C₅×C₃⋊C₈	—	2	2	no	—
183	C₅×C₃⋊C₈	C₂×D₄	1	2	yes	—
184	D₃×#41	—	5	2	no	—
185	C₃×#135	C₂×D₅	1	1	yes	characteristic
186	C₃×#131	—	5	2	no	—
187	#950	—	5	2	no	—
188	#948	C₂×D₅	1	2	yes	complemented
189	#919	—	5	1	no	—
190	D₃×Q₁₆	—	5	1	no	—
191	#916	—	5	2	no	—
192	D₃×SD₁₆	—	5	2	no	—
193	#912	—	5	1	no	—
194	D₃×D₈	—	5	1	no	—
195	#907	—	5	2	no	—
196	#907	—	10	2	no	—
197	D₃×M₁₆	—	5	2	no	—
198	D₃×M₁₆	—	10	2	no	—
199	#904	—	5	1	no	—
200	#901	—	5	2	no	—
201	#901	—	10	2	no	—
202	C₂×D₃×C₈	—	5	1	no	—
203	C₂×D₃×C₈	—	5	1	no	—
204	C₂×D₃×C₈	—	10	2	no	—
205	C₄²×D₃	—	5	1	no	—
206	C₃×#108	—	5	1	no	—
207	C₃×#104	—	5	2	no	—
208	C₃×#97	—	5	1	no	—
209	#837	C₂×D₅	1	2	yes	complemented
210	#825	—	5	2	no	—
211	#822	—	5	2	no	—
212	#819	C₂×D₅	1	1	yes	characteristic, complemented
213	#815	—	5	1	no	—
214	#815	C₂×D₅	1	1	yes	characteristic, complemented
215	#805	—	5	2	no	—
216	#803	—	5	1	no	—
217	C₅×#41	C₂²×D₃	1	2	yes	—
218	#713	—	3	2	no	—
219	Q₈×D₅	—	3	2	no	—
220	#711	—	3	2	no	—
221	#711	—	6	2	no	—
222	D₄×D₅	—	3	2	no	—
223	D₄×D₅	—	6	2	no	—
224	#709	—	3	2	no	—
225	#709	—	6	2	no	—
226	C₂×C₄×D₅	—	3	1	no	—
227	C₂×C₄×D₅	—	6	2	no	—
228	C₂×C₄×D₅	—	6	1	no	—
229	C₅×Q₁₆	C₄×D₃	1	1	yes	characteristic, complemented
230	C₅×SD₁₆	C₄×D₃	1	2	yes	complemented
231	C₅×D₈	C₄×D₃	1	1	yes	characteristic, complemented
232	C₅×M₁₆	—	3	2	no	—
233	C₅×M₁₆	—	6	2	no	—
234	C₂×C₅×C₈	—	3	1	no	—
235	C₂×C₅×C₈	—	6	2	no	—
236	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
237	C₄²×C₅	—	3	1	no	—
238	#689	—	3	2	no	—
239	#688	—	3	2	no	—
240	#687	—	3	2	no	—
241	#686	—	3	2	no	—
242	C₄×Dic₅	—	6	1	no	—
243	C₄×Dic₅	C₂²×D₃	1	1	yes	characteristic
244	#681	—	2	2	no	—
245	#681	C₂²×D₃	1	2	yes	—
246	C₂×#168	—	2	2	no	—
247	C₂×#168	—	3	1	no	—
248	C₂×#168	C₂²×D₃	1	1	yes	characteristic
249	Dic₂₀	—	3	1	no	—
250	D₄₀	—	3	1	no	—
251	#677	—	3	2	no	—
252	#676	—	6	2	no	—
253	#676	—	6	2	no	—
254	#676	—	6	2	no	—
255	C₈×D₅	—	3	1	no	—
256	C₈×D₅	—	3	1	no	—
257	C₈×D₅	—	3	1	no	—
258	C₈×D₅	—	3	1	no	—
259	C₈×D₅	—	3	2	no	—
260	C₈×D₅	—	3	2	no	—
261	C₈×D₅	—	6	2	no	—
262	C₈×D₅	—	6	2	no	—
263	C₈×D₅	—	6	2	no	—
264	C₂×#135	—	15	1	no	—
265	C₂×#131	—	15	2	no	—
266	#444	—	3	1	no	—
267	#444	—	5	1	no	—
268	#444	—	15	1	no	—
269	#444	—	15	1	no	—
270	#444	—	15	2	no	—
271	#444	—	15	2	no	—
272	C₂×#108	—	15	1	no	—
273	C₂×#104	—	15	2	no	—
274	C₂×#97	—	15	1	no	—
275	C₂²×C₃×C₅	—	2	2	no	—
276	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
277	C₂×D₁₅	—	2	2	no	—
278	C₂×D₁₅	—	2	2	no	—
279	C₂×D₁₅	—	4	4	no	—
280	C₂×D₁₅	C₄×D₄	1	1	yes	characteristic
281	C₂×D₁₅	C₄×D₄	1	1	yes	characteristic
282	C₃×C₄×C₅	—	2	2	no	—
283	C₃×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
284	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
285	Dic₁₅	—	2	2	no	—
286	Dic₁₅	C₄×D₄	1	1	yes	characteristic
287	Dic₁₅	C₄×D₄	1	1	yes	characteristic
288	C₃×Dic₅	—	4	1	no	—
289	C₅×Dic₃	—	4	1	no	—
290	C₃×#41	C₂²×D₅	1	2	yes	—
291	#239	—	5	2	no	—
292	D₃×Q₈	—	5	2	no	—
293	#237	—	5	2	no	—
294	#237	—	10	2	no	—
295	D₃×D₄	—	5	2	no	—
296	D₃×D₄	—	10	2	no	—
297	#235	—	5	2	no	—
298	#235	—	10	2	no	—
299	C₂×C₄×D₃	—	5	1	no	—
300	C₂×C₄×D₃	—	10	2	no	—
301	C₂×C₄×D₃	—	10	1	no	—
302	C₃×Q₁₆	C₄×D₅	1	1	yes	characteristic, complemented
303	C₃×SD₁₆	C₄×D₅	1	2	yes	complemented
304	C₃×D₈	C₄×D₅	1	1	yes	characteristic, complemented
305	C₃×M₁₆	—	5	2	no	—
306	C₃×M₁₆	—	10	2	no	—
307	C₂×C₃×C₈	—	5	1	no	—
308	C₂×C₃×C₈	—	10	2	no	—
309	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
310	C₃×C₄²	—	5	1	no	—
311	#216	—	5	2	no	—
312	#215	—	5	2	no	—
313	#214	—	5	2	no	—
314	#213	—	5	2	no	—
315	C₄×Dic₃	—	10	1	no	—
316	C₄×Dic₃	C₂²×D₅	1	1	yes	characteristic
317	#208	—	2	2	no	—
318	#208	C₂²×D₅	1	2	yes	—
319	C₂×C₃⋊C₈	—	2	2	no	—
320	C₂×C₃⋊C₈	—	5	1	no	—
321	C₂×C₃⋊C₈	C₂²×D₅	1	1	yes	characteristic
322	Dic₁₂	—	5	1	no	—
323	D₂₄	—	5	1	no	—
324	#204	—	5	2	no	—
325	ΓL(1,𝔽₂₅)	—	10	2	no	—
326	ΓL(1,𝔽₂₅)	—	10	2	no	—
327	ΓL(1,𝔽₂₅)	—	10	2	no	—
328	D₃×C₈	—	5	1	no	—
329	D₃×C₈	—	5	1	no	—
330	D₃×C₈	—	5	1	no	—
331	D₃×C₈	—	5	1	no	—
332	D₃×C₈	—	5	2	no	—
333	D₃×C₈	—	5	2	no	—
334	D₃×C₈	—	10	2	no	—
335	D₃×C₈	—	10	2	no	—
336	D₃×C₈	—	10	2	no	—
337	C₂²×D₅	—	3	1	no	—
338	C₂²×D₅	—	6	2	no	—
339	C₅×Q₈	C₂×C₄×D₃	1	2	yes	—
340	C₅×D₄	—	2	2	no	—
341	C₅×D₄	C₂×C₄×D₃	1	2	yes	—
342	C₂×C₄×C₅	—	2	2	no	—
343	C₂×C₄×C₅	—	6	1	no	—
344	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
345	C₂²⋊D₅	—	6	2	no	—
346	C₂²⋊D₅	—	6	2	no	—
347	C₂²⋊D₅	—	6	2	no	—
348	C₂×Dic₅	—	2	1	no	—
349	C₂×Dic₅	—	3	1	no	—
350	C₂×Dic₅	—	6	2	no	—
351	D₂₀	—	3	2	no	—
352	D₂₀	—	6	2	no	—
353	C₄×D₅	—	3	1	no	—
354	C₄×D₅	—	3	1	no	—
355	C₄×D₅	—	3	1	no	—
356	C₄×D₅	—	3	1	no	—
357	C₄×D₅	—	6	2	no	—
358	C₄×D₅	—	6	2	no	—
359	C₄×D₅	—	6	2	no	—
360	C₄×D₅	—	12	2	no	—
361	Dic₁₀	—	3	2	no	—
362	Dic₁₀	—	6	2	no	—
363	C₅×C₈	—	3	2	no	—
364	C₅×C₈	—	6	2	no	—
365	C₅×C₈	C₂×C₄×D₃	1	1	yes	characteristic
366	C₅×C₈	C₂×C₄×D₃	1	1	yes	characteristic
367	#168	—	2	2	no	—
368	#168	—	3	1	no	—
369	#168	—	3	1	no	—
370	#168	D₃×D₄	1	2	yes	—
371	C₂×#41	—	15	2	no	—
372	#135	—	15	2	no	—
373	#135	—	15	1	no	—
374	#135	—	15	2	no	—
375	#135	—	15	1	no	—
376	#135	—	15	1	no	—
377	#135	D₃×D₅	1	1	yes	characteristic
378	C₂×Q₁₆	—	15	1	no	—
379	C₂×SD₁₆	—	15	2	no	—
380	C₂×D₈	—	15	1	no	—
381	#131	—	3	2	no	—
382	#131	—	5	2	no	—
383	#131	—	15	2	no	—
384	#131	—	15	2	no	—
385	#131	—	30	2	no	—
386	#131	—	30	2	no	—
387	C₂×M₁₆	—	15	2	no	—
388	C₂×M₁₆	—	30	2	no	—
389	C₂²×C₈	—	15	1	no	—
390	C₂²×C₈	—	15	1	no	—
391	C₂²×C₈	—	30	2	no	—
392	C₂×C₄²	—	15	1	no	—
393	#108	—	3	1	no	—
394	#108	—	5	1	no	—
395	#108	—	15	2	no	—
396	#104	—	3	2	no	—
397	#104	—	5	2	no	—
398	#104	—	15	2	no	—
399	#104	—	15	2	no	—
400	#97	—	3	1	no	—
401	#97	—	5	1	no	—
402	#97	—	15	1	no	—
403	#97	—	15	1	no	—
404	C₂×C₃×C₅	—	2	1	no	—
405	C₂×C₃×C₅	—	4	2	no	—
406	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
407	D₁₅	—	2	1	no	—
408	D₁₅	—	4	2	no	—
409	D₁₅	#444	1	2	yes	complemented
410	C₂²×D₃	—	5	1	no	—
411	C₂²×D₃	—	10	2	no	—
412	C₃×Q₈	C₂×C₄×D₅	1	2	yes	—
413	C₃×D₄	—	2	2	no	—
414	C₃×D₄	C₂×C₄×D₅	1	2	yes	—
415	C₂×C₃×C₄	—	2	2	no	—
416	C₂×C₃×C₄	—	10	1	no	—
417	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
418	#67	—	10	2	no	—
419	#67	—	10	2	no	—
420	#67	—	10	2	no	—
421	C₂×Dic₃	—	2	1	no	—
422	C₂×Dic₃	—	5	1	no	—
423	C₂×Dic₃	—	10	2	no	—
424	D₁₂	—	5	2	no	—
425	D₁₂	—	10	2	no	—
426	C₄×D₃	—	5	1	no	—
427	C₄×D₃	—	5	1	no	—
428	C₄×D₃	—	5	1	no	—
429	C₄×D₃	—	5	1	no	—
430	C₄×D₃	—	10	2	no	—
431	C₄×D₃	—	10	2	no	—
432	C₄×D₃	—	10	2	no	—
433	C₄×D₃	—	20	2	no	—
434	Dic₆	—	5	2	no	—
435	Dic₆	—	10	2	no	—
436	C₃×C₈	—	5	2	no	—
437	C₃×C₈	—	10	2	no	—
438	C₃×C₈	C₂×C₄×D₅	1	1	yes	characteristic
439	C₃×C₈	C₂×C₄×D₅	1	1	yes	characteristic
440	C₃⋊C₈	—	2	2	no	—
441	C₃⋊C₈	—	5	1	no	—
442	C₃⋊C₈	—	5	1	no	—
443	C₃⋊C₈	D₄×D₅	1	2	yes	—
444	C₂²×C₅	—	2	2	no	—
445	C₂²×C₅	D₃×#41	1	1	yes	characteristic
446	C₂×D₅	—	3	1	no	—
447	C₂×D₅	—	3	1	no	—
448	C₂×D₅	—	6	2	no	—
449	C₂×D₅	—	6	2	no	—
450	C₂×D₅	—	12	4	no	—
451	C₄×C₅	—	2	2	no	—
452	C₄×C₅	—	12	1	no	—
453	C₄×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
454	C₄×C₅	C₂×D₃×D₄	1	1	yes	characteristic
455	Dic₅	—	3	1	no	—
456	Dic₅	—	3	1	no	—
457	Dic₅	—	4	1	no	—
458	Dic₅	—	6	2	no	—
459	#41	—	15	2	no	—
460	#41	—	15	2	no	—
461	#41	—	15	2	no	—
462	#41	—	30	2	no	—
463	#41	—	30	2	no	—
464	#41	C₂×D₃×D₅	1	2	yes	—
465	C₂×Q₈	—	15	2	no	—
466	C₂×D₄	—	15	2	no	—
467	C₂×D₄	—	30	2	no	—
468	C₂²×C₄	—	15	1	no	—
469	C₂²×C₄	—	30	2	no	—
470	C₂²×C₄	—	30	1	no	—
471	Q₁₆	—	15	2	no	—
472	Q₁₆	—	15	1	no	—
473	Q₁₆	#1200	1	1	yes	characteristic, complemented
474	SD₁₆	—	15	2	no	—
475	SD₁₆	—	15	2	no	—
476	SD₁₆	—	15	2	no	—
477	SD₁₆	#1200	1	2	yes	complemented
478	D₈	—	15	2	no	—
479	D₈	—	15	1	no	—
480	D₈	#1200	1	1	yes	characteristic, complemented
481	M₁₆	—	3	2	no	—
482	M₁₆	—	5	2	no	—
483	M₁₆	—	6	2	no	—
484	M₁₆	—	10	2	no	—
485	M₁₆	—	30	2	no	—
486	M₁₆	—	30	2	no	—
487	M₁₆	—	30	2	no	—
488	C₂×C₈	—	3	1	no	—
489	C₂×C₈	—	5	1	no	—
490	C₂×C₈	—	6	2	no	—
491	C₂×C₈	—	10	2	no	—
492	C₂×C₈	—	15	2	no	—
493	C₂×C₈	—	15	2	no	—
494	C₂×C₈	—	15	1	no	—
495	C₂×C₈	—	15	1	no	—
496	C₂×C₈	—	15	1	no	—
497	C₂×C₈	—	15	1	no	—
498	C₂×C₈	—	15	1	no	—
499	C₂×C₈	—	30	2	no	—
500	C₂×C₈	—	30	2	no	—
501	C₂×C₈	—	30	2	no	—
502	C₂×C₈	C₂×D₃×D₅	1	1	yes	characteristic
503	C₄²	—	3	1	no	—
504	C₄²	—	5	1	no	—
505	C₄²	—	30	1	no	—
506	C₃×C₅	C₂×#444	1	1	yes	characteristic, complemented, Hall
507	C₂²×C₃	—	2	2	no	—
508	C₂²×C₃	D₅×#41	1	1	yes	characteristic
509	C₂×D₃	—	5	1	no	—
510	C₂×D₃	—	5	1	no	—
511	C₂×D₃	—	10	2	no	—
512	C₂×D₃	—	10	2	no	—
513	C₂×D₃	—	20	4	no	—
514	C₃×C₄	—	2	2	no	—
515	C₃×C₄	—	20	1	no	—
516	C₃×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
517	C₃×C₄	C₂×D₄×D₅	1	1	yes	characteristic
518	Dic₃	—	4	1	no	—
519	Dic₃	—	5	1	no	—
520	Dic₃	—	5	1	no	—
521	Dic₃	—	10	2	no	—
522	C₂×C₅	—	2	1	no	—
523	C₂×C₅	—	4	2	no	—
524	C₂×C₅	C₄×D₃×D₄	1	1	yes	characteristic
525	D₅	—	3	2	no	—
526	D₅	—	6	1	no	—
527	D₅	—	12	2	no	—
528	C₂³	—	15	1	no	—
529	C₂³	—	30	2	no	—
530	Q₈	—	15	2	no	—
531	Q₈	—	30	2	no	—
532	Q₈	C₂×#1200	1	2	yes	—
533	D₄	—	2	2	no	—
534	D₄	—	15	2	no	—
535	D₄	—	30	2	no	—
536	D₄	—	30	2	no	—
537	D₄	—	30	2	no	—
538	D₄	—	30	2	no	—
539	D₄	C₂×#1200	1	2	yes	—
540	C₂×C₄	—	2	2	no	—
541	C₂×C₄	—	6	1	no	—
542	C₂×C₄	—	10	1	no	—
543	C₂×C₄	—	15	1	no	—
544	C₂×C₄	—	15	1	no	—
545	C₂×C₄	—	15	1	no	—
546	C₂×C₄	—	15	1	no	—
547	C₂×C₄	—	15	1	no	—
548	C₂×C₄	—	30	2	no	—
549	C₂×C₄	—	30	2	no	—
550	C₂×C₄	—	30	2	no	—
551	C₂×C₄	—	30	2	no	—
552	C₂×C₄	—	60	2	no	—
553	C₂×C₄	C₂²×D₃×D₅	1	1	yes	characteristic
554	C₈	—	3	2	no	—
555	C₈	—	5	2	no	—
556	C₈	—	6	2	no	—
557	C₈	—	10	2	no	—
558	C₈	—	15	1	no	—
559	C₈	—	15	1	no	—
560	C₈	C₂×#1200	1	1	yes	characteristic
561	C₈	C₂×#1200	1	1	yes	characteristic
562	C₂×C₃	—	2	1	no	—
563	C₂×C₃	—	4	2	no	—
564	C₂×C₃	C₄×D₄×D₅	1	1	yes	characteristic
565	D₃	—	5	2	no	—
566	D₃	—	10	1	no	—
567	D₃	—	20	2	no	—
568	C₅	D₃×#444	1	1	yes	characteristic, complemented, Sylow
569	C₂²	—	2	2	no	—
570	C₂²	—	15	1	no	—
571	C₂²	—	15	1	no	—
572	C₂²	—	30	2	no	—
573	C₂²	—	30	2	no	—
574	C₂²	—	60	4	no	—
575	C₂²	#92024	1	1	yes	characteristic
576	C₄	—	2	2	no	—
577	C₄	—	12	1	no	—
578	C₄	—	15	1	no	—
579	C₄	—	15	1	no	—
580	C₄	—	20	1	no	—
581	C₄	—	30	2	no	—
582	C₄	D₃×D₄×D₅	1	1	yes	characteristic
583	C₄	C₂²×#1200	1	1	yes	characteristic
584	C₃	D₅×#444	1	1	yes	characteristic, complemented, Sylow
585	C₂	—	2	1	no	—
586	C₂	—	4	2	no	—
587	C₂	—	15	2	no	—
588	C₂	—	30	1	no	—
589	C₂	—	60	2	no	—
590	C₂	D₄×#1200	1	1	yes	characteristic

	subgroup	G/H
center	C₄	D₃×D₄×D₅
commutator	C₃×C₄×C₅	C₂³×C₄
Frattini	C₂×C₄	C₂²×D₃×D₅
Fitting	C₃×C₅×#135	C₂²
socle	C₂×C₃×C₅	C₂×C₄×D₄
prime radical	D₁₅×#135	C₂
cosocle	C₂×C₃×C₄×C₅	C₂⁴
hypercenter	#135	D₃×D₅
hypocenter	C₃×C₅	C₂×#444
LCS	G ▷ C₃×C₄×C₅ ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ #135

Complements

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

N	H ≅ G/N	type
2. #11755299	C₂	semidirect
3. C₅×#5197	C₂	semidirect
4. C₃×#65486	C₂	semidirect
5. #11749439	C₂	semidirect
6. #11749435	C₂	semidirect
7. #11749430	C₂	semidirect
8. #11748069	C₂	semidirect
9. #11748065	C₂	semidirect
10. #11748060	C₂	semidirect
11. #11747603	C₂	semidirect
16. #91808	C₄	semidirect
17. Q₁₆×D₁₅	C₄	semidirect
18. #91805	C₄	semidirect
19. SD₁₆×D₁₅	C₄	semidirect
20. #91801	C₄	semidirect
21. D₈×D₁₅	C₄	semidirect
24. C₅×#948	C₂²	semidirect
25. C₃×#4094	C₂²	semidirect
30. #91291	C₂²	semidirect
32. #91290	C₂²	semidirect
35. C₅×#837	C₂²	semidirect
36. C₅×#819	C₂²	semidirect
37. C₅×#815	C₂²	semidirect
38. C₃×#3969	C₂²	semidirect
39. C₃×#3951	C₂²	semidirect
40. C₃×#3947	C₂²	semidirect
41. #90992	C₂²	semidirect
42. #90981	C₂²	semidirect
43. #90980	C₂²	semidirect
44. #90953	C₂²	semidirect
45. #90952	C₂²	semidirect
50. #65486	D₃	semidirect
70. C₃×C₅×Q₁₆	C₂×C₄	semidirect
71. C₃×C₅×SD₁₆	C₂×C₄	semidirect
72. C₃×C₅×D₈	C₂×C₄	semidirect
74. #6718	C₂×C₄	semidirect
75. #6717	C₂×C₄	semidirect
76. #6716	C₂×C₄	semidirect
77. #6715	C₂×C₄	semidirect
79. Dic₆₀	C₂×C₄	semidirect
80. D₁₂₀	C₂×C₄	semidirect
81. #6706	C₂×C₄	semidirect
108. #5197	D₅	semidirect
120. #4094	C₂×D₃	semidirect
141. #3969	C₂×D₃	semidirect
144. #3951	C₂×D₃	semidirect
146. #3947	C₂×D₃	semidirect
188. #948	C₂×D₅	semidirect
209. #837	C₂×D₅	semidirect
212. #819	C₂×D₅	semidirect
214. #815	C₂×D₅	semidirect
229. C₅×Q₁₆	C₄×D₃	semidirect
230. C₅×SD₁₆	C₄×D₃	semidirect
231. C₅×D₈	C₄×D₃	semidirect
302. C₃×Q₁₆	C₄×D₅	semidirect
303. C₃×SD₁₆	C₄×D₅	semidirect
304. C₃×D₈	C₄×D₅	semidirect
409. D₁₅	#444	semidirect
473. Q₁₆	#1200	semidirect
477. SD₁₆	#1200	semidirect
480. D₈	#1200	semidirect
506. C₃×C₅	C₂×#444	semidirect
568. C₅	D₃×#444	semidirect
584. C₃	D₅×#444	semidirect

Maximal subgroups

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

subgroup	index
D₁₅×#135	2
#11755299	2
C₅×#5197	2
C₃×#65486	2
#11749439	2
#11749435	2
#11749430	2
#11748069	2
#11748065	2
#11748060	2
#11747603	2
D₅×#444	3
D₃×#444	5