Subgroups — #14417979

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	#11754017	C₂	1	2	yes	maximal, complemented
2	#11753978	C₂	1	1	yes	maximal, characteristic
3	D₁₅×#108	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#4894	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#65183	C₂	1	1	yes	maximal, characteristic, complemented
6	#11748236	C₂	1	2	yes	maximal, complemented
7	#11748205	C₂	1	2	yes	maximal, complemented
8	#11748202	C₂	1	2	yes	maximal, complemented
9	#11748067	C₂	1	1	yes	maximal, characteristic, complemented
10	#11748063	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	#92016	C₂²	1	2	yes	—
14	M₁₆×D₁₅	C₂²	1	2	yes	—
15	C₂×C₈×D₁₅	C₂²	1	1	yes	characteristic
16	C₅×#907	C₂²	1	2	yes	complemented
17	C₅×#904	C₂²	1	1	yes	characteristic
18	C₃×#4053	C₂²	1	2	yes	complemented
19	C₃×#4050	C₂²	1	1	yes	characteristic
20	C₄×#1200	C₂²	1	1	yes	characteristic
21	#91297	C₂²	1	2	yes	—
22	C₂×#6648	C₂²	1	1	yes	characteristic
23	#91286	C₂²	1	2	yes	complemented
24	#91283	C₂²	1	2	yes	complemented
25	#91279	C₄	1	1	yes	characteristic, complemented
26	#91277	C₄	1	1	yes	characteristic, complemented
27	#91276	C₄	1	2	yes	complemented
28	#91267	—	2	2	no	—
29	#91266	—	2	2	no	—
30	#91264	C₄	1	1	yes	characteristic, complemented
31	#91256	C₄	1	1	yes	characteristic, complemented
32	#91255	C₄	1	2	yes	complemented
33	#91246	—	2	2	no	—
34	D₃×C₈×D₅	—	2	2	no	—
35	C₃×C₅×#108	C₂²	1	1	yes	characteristic, complemented
36	#91106	C₂²	1	2	yes	complemented
37	#91103	C₂²	1	1	yes	characteristic, complemented
38	C₅×#825	C₂²	1	2	yes	complemented
39	C₅×#815	C₂²	1	1	yes	characteristic, complemented
40	C₃×#3957	C₂²	1	2	yes	complemented
41	C₃×#3947	C₂²	1	1	yes	characteristic, complemented
42	#90979	C₂²	1	2	yes	complemented
43	#90977	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	—	3	1	no	—
51	#65434	—	3	2	no	—
52	#65183	D₃	1	1	yes	characteristic, complemented
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	C₂×C₄×D₁₅	C₂³	1	1	yes	characteristic
59	C₅×#235	C₂³	1	2	yes	—
60	C₃×#709	C₂³	1	2	yes	—
61	#6790	—	2	2	no	—
62	C₂×#1200	—	2	1	no	—
63	#6780	—	2	2	no	—
64	#6777	C₂×C₄	1	2	yes	—
65	C₄×D₃×D₅	—	2	2	no	—
66	#6771	—	2	2	no	—
67	D₁₅⋊Q₈	C₂×C₄	1	2	yes	—
68	#6768	C₂×C₄	1	2	yes	—
69	#6766	C₂×C₄	1	2	yes	—
70	C₃×C₅×M₁₆	C₂³	1	2	yes	—
71	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
72	#6710	C₂³	1	2	yes	—
73	C₂×C₃⋊#168	C₂³	1	1	yes	characteristic
74	#6705	—	2	2	no	—
75	C₈×D₁₅	—	2	2	no	—
76	C₈×D₁₅	C₂×C₄	1	1	yes	characteristic
77	C₈×D₁₅	C₂×C₄	1	1	yes	characteristic
78	C₈×D₁₅	C₂×C₄	1	1	yes	characteristic
79	C₈×D₁₅	C₂×C₄	1	1	yes	characteristic
80	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
81	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
82	C₅×Dic₁₂	C₂×C₄	1	1	yes	characteristic, complemented
83	C₅×D₂₄	C₂×C₄	1	1	yes	characteristic, complemented
84	C₅×#204	C₂×C₄	1	2	yes	complemented
85	C₅×ΓL(1,𝔽₂₅)	—	2	2	no	—
86	C₅×D₃×C₈	—	2	2	no	—
87	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
88	C₂×C₃×#168	C₂³	1	1	yes	characteristic
89	C₃×Dic₂₀	C₂×C₄	1	1	yes	characteristic, complemented
90	C₃×D₄₀	C₂×C₄	1	1	yes	characteristic, complemented
91	C₃×#677	C₂×C₄	1	2	yes	complemented
92	C₃×#676	—	2	2	no	—
93	C₃×C₈×D₅	—	2	2	no	—
94	Dic₃×Dic₅	—	2	1	no	—
95	#6661	C₂×C₄	1	2	yes	complemented
96	#6656	C₂×C₄	1	2	yes	complemented
97	#6655	C₂×C₄	1	2	yes	complemented
98	#6652	C₂×C₄	1	2	yes	complemented
99	#6650	—	2	2	no	—
100	#6649	—	2	2	no	—
101	#6648	D₄	1	2	yes	—
102	#6648	D₄	1	2	yes	—
103	D₃×#168	—	2	2	no	—
104	D₅×C₃⋊C₈	—	2	2	no	—
105	D₃×#135	—	5	1	no	—
106	D₃×#131	—	5	2	no	—
107	C₃×#444	—	5	1	no	—
108	#5197	—	5	1	no	—
109	#5145	—	5	2	no	—
110	#4894	D₅	1	1	yes	characteristic, complemented
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	—	3	1	no	—
118	C₅×#131	—	3	2	no	—
119	#4096	—	3	2	no	—
120	#4094	—	3	2	no	—
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	—	6	2	no	—
128	#4053	C₂×D₃	1	2	yes	complemented
129	D₅×M₁₆	—	3	2	no	—
130	D₅×M₁₆	—	6	2	no	—
131	#4050	C₂×D₃	1	1	yes	characteristic
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	C₂×D₃	1	1	yes	characteristic, complemented
139	C₅×#104	—	3	2	no	—
140	C₅×#97	—	3	1	no	—
141	#3969	—	3	2	no	—
142	#3957	C₂×D₃	1	2	yes	complemented
143	#3954	—	3	2	no	—
144	#3951	—	3	1	no	—
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	#41	1	1	yes	characteristic
151	C₂×D₃×D₅	—	2	2	no	—
152	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
153	C₂×Dic₁₅	#41	1	1	yes	characteristic
154	C₄×D₁₅	C₂²×C₄	1	1	yes	characteristic
155	C₄×D₁₅	C₂²×C₄	1	1	yes	characteristic
156	C₄×D₁₅	C₂×D₄	1	1	yes	characteristic
157	C₄×D₁₅	C₂×D₄	1	1	yes	characteristic
158	C₅×#67	—	2	2	no	—
159	C₂×C₅×Dic₃	—	2	1	no	—
160	C₅×D₁₂	C₂²×C₄	1	2	yes	—
161	C₄×C₅×D₃	—	2	2	no	—
162	C₅×Dic₆	C₂²×C₄	1	2	yes	—
163	C₃×C₂²⋊D₅	—	2	2	no	—
164	C₂×C₃×Dic₅	—	2	1	no	—
165	C₃×D₂₀	C₂²×C₄	1	2	yes	—
166	C₃×C₄×D₅	—	2	2	no	—
167	C₃×Dic₁₀	C₂²×C₄	1	2	yes	—
168	#1204	—	2	2	no	—
169	#1203	—	2	2	no	—
170	#1202	—	2	2	no	—
171	#1201	—	2	2	no	—
172	#1200	—	2	2	no	—
173	#1200	—	4	2	no	—
174	D₃×Dic₅	—	2	2	no	—
175	D₅×Dic₃	—	2	2	no	—
176	C₃×C₅×C₈	—	2	2	no	—
177	C₃×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
178	C₃×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
179	C₃⋊#168	—	2	2	no	—
180	C₃⋊#168	C₂²×C₄	1	1	yes	characteristic
181	C₃⋊#168	C₂²×C₄	1	1	yes	characteristic
182	C₃×#168	C₂×D₄	1	2	yes	—
183	C₅×C₃⋊C₈	C₂×D₄	1	2	yes	—
184	D₃×#41	—	5	2	no	—
185	C₃×#135	—	5	1	no	—
186	C₃×#131	—	5	2	no	—
187	#950	—	5	2	no	—
188	#948	—	5	2	no	—
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	—	10	2	no	—
196	#907	C₂×D₅	1	2	yes	complemented
197	D₃×M₁₆	—	5	2	no	—
198	D₃×M₁₆	—	10	2	no	—
199	#904	C₂×D₅	1	1	yes	characteristic
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	C₂×D₅	1	1	yes	characteristic, complemented
207	C₃×#104	—	5	2	no	—
208	C₃×#97	—	5	1	no	—
209	#837	—	5	2	no	—
210	#825	C₂×D₅	1	2	yes	complemented
211	#822	—	5	2	no	—
212	#819	—	5	1	no	—
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	—	3	2	no	—
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	—	6	2	no	—
225	#709	C₂²×D₃	1	2	yes	—
226	C₂×C₄×D₅	—	3	1	no	—
227	C₂×C₄×D₅	—	6	2	no	—
228	C₂×C₄×D₅	—	6	1	no	—
229	C₅×Q₁₆	—	3	1	no	—
230	C₅×SD₁₆	—	3	2	no	—
231	C₅×D₈	—	3	1	no	—
232	C₅×M₁₆	—	6	2	no	—
233	C₅×M₁₆	C₂²×D₃	1	2	yes	—
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	—	3	2	no	—
245	#681	—	6	2	no	—
246	C₂×#168	—	3	1	no	—
247	C₂×#168	—	6	2	no	—
248	C₂×#168	C₂²×D₃	1	1	yes	characteristic
249	Dic₂₀	C₄×D₃	1	1	yes	characteristic, complemented
250	D₄₀	C₄×D₃	1	1	yes	characteristic, complemented
251	#677	C₄×D₃	1	2	yes	complemented
252	#676	—	2	2	no	—
253	#676	—	6	2	no	—
254	#676	—	6	2	no	—
255	C₈×D₅	—	2	2	no	—
256	C₈×D₅	—	3	1	no	—
257	C₈×D₅	—	3	1	no	—
258	C₈×D₅	—	3	1	no	—
259	C₈×D₅	—	3	1	no	—
260	C₈×D₅	—	3	2	no	—
261	C₈×D₅	—	3	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	C₂×#41	1	1	yes	characteristic
276	C₂×D₁₅	—	2	2	no	—
277	C₂×D₁₅	C₄×D₄	1	1	yes	characteristic
278	C₂×D₁₅	C₄×D₄	1	1	yes	characteristic
279	C₂×C₅×D₃	—	2	2	no	—
280	C₂×C₃×D₅	—	2	2	no	—
281	D₃×D₅	—	4	4	no	—
282	C₃×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
283	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
284	Dic₁₅	C₄×D₄	1	1	yes	characteristic
285	Dic₁₅	C₄×D₄	1	1	yes	characteristic
286	C₃×Dic₅	—	2	2	no	—
287	C₃×Dic₅	—	4	1	no	—
288	C₅×Dic₃	—	2	2	no	—
289	C₅×Dic₃	—	4	1	no	—
290	C₃×#41	—	5	2	no	—
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	—	10	2	no	—
298	#235	C₂²×D₅	1	2	yes	—
299	C₂×C₄×D₃	—	5	1	no	—
300	C₂×C₄×D₃	—	10	2	no	—
301	C₂×C₄×D₃	—	10	1	no	—
302	C₃×Q₁₆	—	5	1	no	—
303	C₃×SD₁₆	—	5	2	no	—
304	C₃×D₈	—	5	1	no	—
305	C₃×M₁₆	—	10	2	no	—
306	C₃×M₁₆	C₂²×D₅	1	2	yes	—
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	—	5	2	no	—
318	#208	—	10	2	no	—
319	C₂×C₃⋊C₈	—	5	1	no	—
320	C₂×C₃⋊C₈	—	10	2	no	—
321	C₂×C₃⋊C₈	C₂²×D₅	1	1	yes	characteristic
322	Dic₁₂	C₄×D₅	1	1	yes	characteristic, complemented
323	D₂₄	C₄×D₅	1	1	yes	characteristic, complemented
324	#204	C₄×D₅	1	2	yes	complemented
325	ΓL(1,𝔽₂₅)	—	2	2	no	—
326	ΓL(1,𝔽₂₅)	—	10	2	no	—
327	ΓL(1,𝔽₂₅)	—	10	2	no	—
328	D₃×C₈	—	2	2	no	—
329	D₃×C₈	—	5	1	no	—
330	D₃×C₈	—	5	1	no	—
331	D₃×C₈	—	5	1	no	—
332	D₃×C₈	—	5	1	no	—
333	D₃×C₈	—	5	2	no	—
334	D₃×C₈	—	5	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	—	3	2	no	—
340	C₅×D₄	—	3	2	no	—
341	C₅×D₄	—	6	2	no	—
342	C₂×C₄×C₅	—	6	2	no	—
343	C₂×C₄×C₅	—	6	1	no	—
344	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
345	C₂²⋊D₅	—	2	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	—	6	2	no	—
352	D₂₀	C₂×C₄×D₃	1	2	yes	—
353	C₄×D₅	—	2	2	no	—
354	C₄×D₅	—	3	1	no	—
355	C₄×D₅	—	3	1	no	—
356	C₄×D₅	—	3	1	no	—
357	C₄×D₅	—	3	1	no	—
358	C₄×D₅	—	6	2	no	—
359	C₄×D₅	—	6	2	no	—
360	C₄×D₅	—	12	2	no	—
361	Dic₁₀	—	6	2	no	—
362	Dic₁₀	C₂×C₄×D₃	1	2	yes	—
363	C₅×C₈	—	2	2	no	—
364	C₅×C₈	—	3	2	no	—
365	C₅×C₈	C₂×C₄×D₃	1	1	yes	characteristic
366	C₅×C₈	C₂×C₄×D₃	1	1	yes	characteristic
367	#168	—	3	1	no	—
368	#168	—	3	1	no	—
369	#168	—	6	2	no	—
370	#168	D₃×D₄	1	2	yes	—
371	C₂×#41	—	15	2	no	—
372	#135	—	3	1	no	—
373	#135	—	5	1	no	—
374	#135	—	15	1	no	—
375	#135	—	15	1	no	—
376	#135	—	15	2	no	—
377	#135	—	15	2	no	—
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	—	15	2	no	—
394	#108	—	15	1	no	—
395	#108	D₃×D₅	1	1	yes	characteristic, complemented
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	C₂×C₄×D₄	1	1	yes	characteristic
406	D₁₅	—	2	1	no	—
407	D₁₅	#444	1	2	yes	complemented
408	C₃×D₅	—	4	2	no	—
409	C₅×D₃	—	4	2	no	—
410	C₂²×D₃	—	5	1	no	—
411	C₂²×D₃	—	10	2	no	—
412	C₃×Q₈	—	5	2	no	—
413	C₃×D₄	—	5	2	no	—
414	C₃×D₄	—	10	2	no	—
415	C₂×C₃×C₄	—	10	2	no	—
416	C₂×C₃×C₄	—	10	1	no	—
417	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
418	#67	—	2	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	—	10	2	no	—
425	D₁₂	C₂×C₄×D₅	1	2	yes	—
426	C₄×D₃	—	2	2	no	—
427	C₄×D₃	—	5	1	no	—
428	C₄×D₃	—	5	1	no	—
429	C₄×D₃	—	5	1	no	—
430	C₄×D₃	—	5	1	no	—
431	C₄×D₃	—	10	2	no	—
432	C₄×D₃	—	10	2	no	—
433	C₄×D₃	—	20	2	no	—
434	Dic₆	—	10	2	no	—
435	Dic₆	C₂×C₄×D₅	1	2	yes	—
436	C₃×C₈	—	2	2	no	—
437	C₃×C₈	—	5	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	—	5	1	no	—
441	C₃⋊C₈	—	5	1	no	—
442	C₃⋊C₈	—	10	2	no	—
443	C₃⋊C₈	D₄×D₅	1	2	yes	—
444	C₂²×C₅	—	6	2	no	—
445	C₂²×C₅	D₃×#41	1	1	yes	characteristic
446	C₂×D₅	—	2	2	no	—
447	C₂×D₅	—	3	1	no	—
448	C₂×D₅	—	3	1	no	—
449	C₂×D₅	—	6	2	no	—
450	C₂×D₅	—	12	4	no	—
451	C₄×C₅	—	6	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	—	2	2	no	—
456	Dic₅	—	3	1	no	—
457	Dic₅	—	3	1	no	—
458	Dic₅	—	4	1	no	—
459	#41	—	3	2	no	—
460	#41	—	5	2	no	—
461	#41	—	15	2	no	—
462	#41	—	15	2	no	—
463	#41	—	30	2	no	—
464	#41	—	30	2	no	—
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	—	3	1	no	—
472	Q₁₆	—	5	1	no	—
473	Q₁₆	—	15	2	no	—
474	SD₁₆	—	3	2	no	—
475	SD₁₆	—	5	2	no	—
476	SD₁₆	—	15	2	no	—
477	SD₁₆	—	15	2	no	—
478	D₈	—	3	1	no	—
479	D₈	—	5	1	no	—
480	D₈	—	15	2	no	—
481	M₁₆	—	6	2	no	—
482	M₁₆	—	10	2	no	—
483	M₁₆	—	15	2	no	—
484	M₁₆	—	30	2	no	—
485	M₁₆	—	30	2	no	—
486	M₁₆	—	30	2	no	—
487	M₁₆	C₂×D₃×D₅	1	2	yes	—
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	—	10	2	no	—
508	C₂²×C₃	D₅×#41	1	1	yes	characteristic
509	C₂×D₃	—	2	2	no	—
510	C₂×D₃	—	5	1	no	—
511	C₂×D₃	—	5	1	no	—
512	C₂×D₃	—	10	2	no	—
513	C₂×D₃	—	20	4	no	—
514	C₃×C₄	—	10	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	—	2	2	no	—
519	Dic₃	—	4	1	no	—
520	Dic₃	—	5	1	no	—
521	Dic₃	—	5	1	no	—
522	C₂×C₅	—	2	1	no	—
523	C₂×C₅	—	12	2	no	—
524	C₂×C₅	C₄×D₃×D₄	1	1	yes	characteristic
525	D₅	—	3	2	no	—
526	D₅	—	4	2	no	—
527	D₅	—	6	1	no	—
528	C₂³	—	15	1	no	—
529	C₂³	—	30	2	no	—
530	Q₈	—	3	2	no	—
531	Q₈	—	5	2	no	—
532	Q₈	—	30	2	no	—
533	D₄	—	3	2	no	—
534	D₄	—	5	2	no	—
535	D₄	—	6	2	no	—
536	D₄	—	10	2	no	—
537	D₄	—	30	2	no	—
538	D₄	—	30	2	no	—
539	D₄	—	30	2	no	—
540	C₂×C₄	—	6	2	no	—
541	C₂×C₄	—	6	1	no	—
542	C₂×C₄	—	10	2	no	—
543	C₂×C₄	—	10	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	—	15	1	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	—	2	2	no	—
555	C₈	—	3	2	no	—
556	C₈	—	5	2	no	—
557	C₈	—	15	1	no	—
558	C₈	—	15	1	no	—
559	C₈	—	30	2	no	—
560	C₈	C₄×D₃×D₅	1	1	yes	characteristic
561	C₈	C₄×D₃×D₅	1	1	yes	characteristic
562	C₂×C₃	—	2	1	no	—
563	C₂×C₃	—	20	2	no	—
564	C₂×C₃	C₄×D₄×D₅	1	1	yes	characteristic
565	D₃	—	4	2	no	—
566	D₃	—	5	2	no	—
567	D₃	—	10	1	no	—
568	C₅	D₃×#444	1	1	yes	characteristic, complemented, Sylow
569	C₂²	—	6	2	no	—
570	C₂²	—	10	2	no	—
571	C₂²	—	15	1	no	—
572	C₂²	—	15	1	no	—
573	C₂²	—	30	2	no	—
574	C₂²	—	60	4	no	—
575	C₂²	#92034	1	1	yes	characteristic
576	C₄	—	6	2	no	—
577	C₄	—	10	2	no	—
578	C₄	—	12	1	no	—
579	C₄	—	15	1	no	—
580	C₄	—	15	1	no	—
581	C₄	—	20	1	no	—
582	C₄	C₂×C₄×D₃×D₅	1	1	yes	characteristic
583	C₄	D₃×D₄×D₅	1	1	yes	characteristic
584	C₃	D₅×#444	1	1	yes	characteristic, complemented, Sylow
585	C₂	—	2	1	no	—
586	C₂	—	12	2	no	—
587	C₂	—	15	2	no	—
588	C₂	—	20	2	no	—
589	C₂	—	30	1	no	—
590	C₂	#11753840	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×#108	C₂²
socle	C₂×C₃×C₅	C₂×C₄×D₄
prime radical	#11753978	C₂
cosocle	C₂×C₃×C₄×C₅	C₂⁴
hypercenter	#108	D₃×D₅
hypocenter	C₃×C₅	C₂×#444
LCS	G ▷ C₃×C₄×C₅ ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ #108

Complements

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

N	H ≅ G/N	type
1. #11754017	C₂	semidirect
3. D₁₅×#108	C₂	semidirect
4. C₅×#4894	C₂	semidirect
5. C₃×#65183	C₂	semidirect
6. #11748236	C₂	semidirect
7. #11748205	C₂	semidirect
8. #11748202	C₂	semidirect
9. #11748067	C₂	semidirect
10. #11748063	C₂	semidirect
11. #11747603	C₂	semidirect
16. C₅×#907	C₂²	semidirect
18. C₃×#4053	C₂²	semidirect
23. #91286	C₂²	semidirect
24. #91283	C₂²	semidirect
25. #91279	C₄	semidirect
26. #91277	C₄	semidirect
27. #91276	C₄	semidirect
30. #91264	C₄	semidirect
31. #91256	C₄	semidirect
32. #91255	C₄	semidirect
35. C₃×C₅×#108	C₂²	semidirect
36. #91106	C₂²	semidirect
37. #91103	C₂²	semidirect
38. C₅×#825	C₂²	semidirect
39. C₅×#815	C₂²	semidirect
40. C₃×#3957	C₂²	semidirect
41. C₃×#3947	C₂²	semidirect
42. #90979	C₂²	semidirect
43. #90977	C₂²	semidirect
44. #90953	C₂²	semidirect
45. #90952	C₂²	semidirect
52. #65183	D₃	semidirect
82. C₅×Dic₁₂	C₂×C₄	semidirect
83. C₅×D₂₄	C₂×C₄	semidirect
84. C₅×#204	C₂×C₄	semidirect
89. C₃×Dic₂₀	C₂×C₄	semidirect
90. C₃×D₄₀	C₂×C₄	semidirect
91. C₃×#677	C₂×C₄	semidirect
95. #6661	C₂×C₄	semidirect
96. #6656	C₂×C₄	semidirect
97. #6655	C₂×C₄	semidirect
98. #6652	C₂×C₄	semidirect
110. #4894	D₅	semidirect
128. #4053	C₂×D₃	semidirect
138. C₅×#108	C₂×D₃	semidirect
142. #3957	C₂×D₃	semidirect
146. #3947	C₂×D₃	semidirect
196. #907	C₂×D₅	semidirect
206. C₃×#108	C₂×D₅	semidirect
210. #825	C₂×D₅	semidirect
214. #815	C₂×D₅	semidirect
249. Dic₂₀	C₄×D₃	semidirect
250. D₄₀	C₄×D₃	semidirect
251. #677	C₄×D₃	semidirect
322. Dic₁₂	C₄×D₅	semidirect
323. D₂₄	C₄×D₅	semidirect
324. #204	C₄×D₅	semidirect
395. #108	D₃×D₅	semidirect
407. D₁₅	#444	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
#11754017	2
#11753978	2
D₁₅×#108	2
C₅×#4894	2
C₃×#65183	2
#11748236	2
#11748205	2
#11748202	2
#11748067	2
#11748063	2
#11747603	2
D₅×#444	3
D₃×#444	5