Subgroups — #14300232

Order 1920.

540 conjugacy classes of subgroups.

The subgroup lattice has 440 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#91790	C₂	1	1	yes	maximal, characteristic
2	#11751214	C₂	1	1	yes	maximal, characteristic
3	C₂×#91103	C₂	1	1	yes	maximal, characteristic, complemented
4	#11751203	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#91089	C₂	1	1	yes	maximal, characteristic
6	C₃×C₅×#336	C₂	1	1	yes	maximal, characteristic, complemented
7	#11746344	C₂	1	1	yes	maximal, characteristic, complemented
8	#10599487	—	3	1	no	maximal, Hall
9	C₂×#6817	C₂²	1	1	yes	characteristic
10	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
11	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
12	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
13	#91815	C₂²	1	1	yes	characteristic
14	C₂×#6710	C₂²	1	1	yes	characteristic
15	C₂×#6710	C₂²	1	1	yes	characteristic
16	#91790	—	2	2	no	—
17	#91790	—	2	2	no	—
18	C₂×#6705	—	2	1	no	—
19	C₂×C₈×D₁₅	—	2	1	no	—
20	#91105	C₄	1	1	yes	characteristic, complemented
21	#91105	C₄	1	1	yes	characteristic, complemented
22	#91103	—	2	2	no	—
23	#91100	C₄	1	1	yes	characteristic, complemented
24	#91100	C₄	1	1	yes	characteristic, complemented
25	#91098	—	2	1	no	—
26	#91098	—	2	1	no	—
27	#91089	—	2	2	no	—
28	#68694	—	5	1	no	maximal, Hall
29	C₂×#4047	—	3	1	no	—
30	#65402	—	3	1	no	—
31	C₂×#3951	—	3	1	no	—
32	#65391	—	3	1	no	—
33	C₂×#3937	—	3	1	no	—
34	C₅×#336	D₃	1	1	yes	characteristic, complemented
35	#64743	—	3	1	no	—
36	C₂²×C₃×C₄×C₅	—	2	1	no	—
37	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
38	C₂×#1220	—	2	1	no	—
39	#6817	—	2	1	no	—
40	#6817	—	2	1	no	—
41	#6817	D₄	1	2	yes	—
42	#6817	Q₈	1	2	yes	—
43	C₂×D₆₀	C₂×C₄	1	1	yes	characteristic
44	C₂×C₄×D₁₅	—	2	1	no	—
45	C₂×Dic₃₀	C₂×C₄	1	1	yes	characteristic
46	C₂×C₃×C₅×C₈	—	2	1	no	—
47	C₂×C₃×C₅×C₈	—	2	1	no	—
48	C₂×C₃×C₅×C₈	—	2	1	no	—
49	C₂×C₃×C₅×C₈	—	2	1	no	—
50	C₂×C₃×C₅×C₈	C₂×C₄	1	1	yes	characteristic
51	C₂×C₃×C₅×C₈	C₂×C₄	1	1	yes	characteristic
52	C₂×C₃×C₅×C₈	D₄	1	1	yes	characteristic
53	C₂×C₃×C₅×C₈	D₄	1	1	yes	characteristic
54	C₃×C₄²×C₅	—	2	1	no	—
55	C₃×C₄²×C₅	—	2	1	no	—
56	#6719	—	2	1	no	—
57	C₄⋊Dic₁₅	C₂×C₄	1	1	yes	characteristic
58	C₄⋊Dic₁₅	C₂×C₄	1	1	yes	characteristic
59	C₄×Dic₁₅	—	2	1	no	—
60	#6710	—	2	1	no	—
61	#6710	—	2	1	no	—
62	#6710	—	2	1	no	—
63	#6710	D₄	1	2	yes	—
64	C₂×C₃⋊#168	—	2	1	no	—
65	C₂×C₃⋊#168	—	2	1	no	—
66	#6705	—	2	4	no	—
67	C₈×D₁₅	—	2	4	no	—
68	C₂×#901	—	5	1	no	—
69	#5113	—	5	1	no	—
70	C₂×#819	—	5	1	no	—
71	#5102	—	5	1	no	—
72	C₂×#805	—	5	1	no	—
73	C₃×#336	D₅	1	1	yes	characteristic, complemented
74	#4523	—	5	1	no	—
75	C₂×#709	—	3	1	no	—
76	C₂²×C₅×C₈	C₂×D₃	1	1	yes	characteristic
77	C₂²×C₅×C₈	C₂×D₃	1	1	yes	characteristic
78	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
79	#4072	—	3	1	no	—
80	C₂×#681	—	3	1	no	—
81	C₂×#681	—	3	1	no	—
82	#4047	—	6	2	no	—
83	#4047	—	6	2	no	—
84	C₂×#676	—	6	1	no	—
85	C₂×C₈×D₅	—	6	1	no	—
86	#3953	—	3	1	no	—
87	#3953	—	3	1	no	—
88	#3951	—	6	2	no	—
89	#3948	—	3	1	no	—
90	#3948	—	3	1	no	—
91	#3946	—	6	1	no	—
92	#3946	—	6	1	no	—
93	#3937	—	6	2	no	—
94	#1866	—	15	1	no	Sylow
95	C₂³×C₃×C₅	#41	1	1	yes	characteristic
96	C₂²×D₁₅	—	2	1	no	—
97	C₂×C₃×C₄×C₅	—	2	2	no	—
98	C₂×C₃×C₄×C₅	—	4	1	no	—
99	C₂×C₃×C₄×C₅	—	4	1	no	—
100	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
101	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
102	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
103	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
104	C₂×C₃×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
105	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
106	#1220	—	2	2	no	—
107	#1220	—	2	2	no	—
108	C₂×Dic₁₅	—	2	1	no	—
109	C₂×Dic₁₅	—	2	1	no	—
110	C₂×Dic₁₅	—	2	1	no	—
111	D₆₀	—	2	1	no	—
112	D₆₀	C₄⋊C₄	1	2	yes	—
113	C₄×D₁₅	—	2	2	no	—
114	C₄×D₁₅	—	2	2	no	—
115	Dic₃₀	—	2	1	no	—
116	Dic₃₀	C₄⋊C₄	1	2	yes	—
117	C₃×C₅×C₈	—	2	1	no	—
118	C₃×C₅×C₈	—	2	1	no	—
119	C₃×C₅×C₈	—	2	1	no	—
120	C₃×C₅×C₈	—	2	1	no	—
121	C₃⋊#168	—	2	2	no	—
122	C₃⋊#168	—	4	1	no	—
123	C₂×#235	—	5	1	no	—
124	C₂²×C₃×C₈	C₂×D₅	1	1	yes	characteristic
125	C₂²×C₃×C₈	C₂×D₅	1	1	yes	characteristic
126	C₂×C₃×C₄²	C₂×D₅	1	1	yes	characteristic
127	#926	—	5	1	no	—
128	C₂×#208	—	5	1	no	—
129	C₂×#208	—	5	1	no	—
130	#901	—	10	2	no	—
131	#901	—	10	2	no	—
132	C₂×ΓL(1,𝔽₂₅)	—	10	1	no	—
133	C₂×D₃×C₈	—	10	1	no	—
134	#821	—	5	1	no	—
135	#821	—	5	1	no	—
136	#819	—	10	2	no	—
137	#816	—	5	1	no	—
138	#816	—	5	1	no	—
139	Dic₃⋊C₈	—	10	1	no	—
140	Dic₃⋊C₈	—	10	1	no	—
141	#805	—	10	2	no	—
142	C₂²×C₄×C₅	—	2	1	no	—
143	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
144	C₂×C₂²⋊D₅	—	6	1	no	—
145	#709	—	3	2	no	—
146	#709	—	3	2	no	—
147	#709	—	6	1	no	—
148	#709	—	6	1	no	—
149	C₂×D₂₀	—	3	1	no	—
150	C₂×C₄×D₅	—	6	1	no	—
151	C₂×Dic₁₀	—	3	1	no	—
152	C₂×C₅×C₈	—	2	1	no	—
153	C₂×C₅×C₈	—	2	1	no	—
154	C₂×C₅×C₈	—	2	1	no	—
155	C₂×C₅×C₈	—	2	1	no	—
156	C₂×C₅×C₈	C₄×D₃	1	1	yes	characteristic
157	C₂×C₅×C₈	C₄×D₃	1	1	yes	characteristic
158	C₂×C₅×C₈	D₁₂	1	1	yes	characteristic
159	C₂×C₅×C₈	D₁₂	1	1	yes	characteristic
160	C₄²×C₅	—	2	1	no	—
161	C₄²×C₅	—	2	1	no	—
162	C₂²⋊Dic₅	—	6	1	no	—
163	C₄⋊Dic₅	—	3	1	no	—
164	C₄⋊Dic₅	—	3	1	no	—
165	C₄×Dic₅	—	6	1	no	—
166	#681	—	3	2	no	—
167	#681	—	6	1	no	—
168	#681	—	6	1	no	—
169	#681	—	6	1	no	—
170	C₂×#168	—	6	1	no	—
171	C₂×#168	—	6	1	no	—
172	#676	—	6	4	no	—
173	C₈×D₅	—	6	4	no	—
174	C₂×#131	—	15	1	no	—
175	C₂×#108	—	15	1	no	—
176	#424	—	15	1	no	—
177	C₂×#104	—	15	1	no	—
178	#416	—	15	1	no	—
179	#339	—	15	1	no	—
180	#336	D₁₅	1	1	yes	characteristic, complemented
181	C₂²×C₃×C₅	—	2	1	no	—
182	C₂²×C₃×C₅	—	2	1	no	—
183	C₂²×C₃×C₅	C₄×D₄	1	1	yes	characteristic
184	C₂²×C₃×C₅	C₂²⋊Q₈	1	1	yes	characteristic
185	C₂²×C₃×C₅	#123	1	1	yes	characteristic
186	C₂×D₁₅	—	2	2	no	—
187	C₂×D₁₅	—	4	1	no	—
188	C₂×D₁₅	—	4	1	no	—
189	C₃×C₄×C₅	—	4	2	no	—
190	C₃×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
191	C₃×C₄×C₅	C₄×D₄	1	1	yes	characteristic
192	C₃×C₄×C₅	#120	1	1	yes	characteristic
193	C₃×C₄×C₅	C₂²⋊Q₈	1	1	yes	characteristic
194	Dic₁₅	—	2	2	no	—
195	Dic₁₅	—	4	1	no	—
196	Dic₁₅	—	4	1	no	—
197	C₂²×C₃×C₄	—	2	1	no	—
198	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
199	C₂×#67	—	10	1	no	—
200	#235	—	5	2	no	—
201	#235	—	5	2	no	—
202	#235	—	10	1	no	—
203	#235	—	10	1	no	—
204	C₂×D₁₂	—	5	1	no	—
205	C₂×C₄×D₃	—	10	1	no	—
206	C₂×Dic₆	—	5	1	no	—
207	C₂×C₃×C₈	—	2	1	no	—
208	C₂×C₃×C₈	—	2	1	no	—
209	C₂×C₃×C₈	—	2	1	no	—
210	C₂×C₃×C₈	—	2	1	no	—
211	C₂×C₃×C₈	C₄×D₅	1	1	yes	characteristic
212	C₂×C₃×C₈	C₄×D₅	1	1	yes	characteristic
213	C₂×C₃×C₈	D₂₀	1	1	yes	characteristic
214	C₂×C₃×C₈	D₂₀	1	1	yes	characteristic
215	C₃×C₄²	—	2	1	no	—
216	C₃×C₄²	—	2	1	no	—
217	#217	—	10	1	no	—
218	C₄⋊Dic₃	—	5	1	no	—
219	C₄⋊Dic₃	—	5	1	no	—
220	C₄×Dic₃	—	10	1	no	—
221	#208	—	5	2	no	—
222	#208	—	10	1	no	—
223	#208	—	10	1	no	—
224	#208	—	10	1	no	—
225	C₂×C₃⋊C₈	—	10	1	no	—
226	C₂×C₃⋊C₈	—	10	1	no	—
227	ΓL(1,𝔽₂₅)	—	10	4	no	—
228	D₃×C₈	—	10	4	no	—
229	C₂³×C₅	#235	1	1	yes	characteristic
230	C₂²×D₅	—	6	1	no	—
231	C₂×C₄×C₅	—	2	2	no	—
232	C₂×C₄×C₅	—	4	1	no	—
233	C₂×C₄×C₅	—	4	1	no	—
234	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
235	C₂×C₄×C₅	C₂×D₁₂	1	1	yes	characteristic
236	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
237	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
238	C₂×C₄×C₅	#237	1	1	yes	characteristic
239	C₂×C₄×C₅	D₃×Q₈	1	1	yes	characteristic
240	C₂²⋊D₅	—	6	2	no	—
241	C₂²⋊D₅	—	6	2	no	—
242	C₂×Dic₅	—	6	1	no	—
243	C₂×Dic₅	—	6	1	no	—
244	C₂×Dic₅	—	6	1	no	—
245	D₂₀	—	3	2	no	—
246	D₂₀	—	6	1	no	—
247	C₄×D₅	—	6	2	no	—
248	C₄×D₅	—	6	2	no	—
249	Dic₁₀	—	3	2	no	—
250	Dic₁₀	—	6	1	no	—
251	C₅×C₈	—	2	1	no	—
252	C₅×C₈	—	2	1	no	—
253	C₅×C₈	—	2	1	no	—
254	C₅×C₈	—	2	1	no	—
255	#168	—	6	2	no	—
256	#168	—	12	1	no	—
257	C₂×#41	—	15	1	no	—
258	#131	—	30	2	no	—
259	#131	—	30	2	no	—
260	C₂×M₁₆	—	15	1	no	—
261	C₂×M₁₆	—	15	1	no	—
262	C₂×M₁₆	—	30	1	no	—
263	C₂²×C₈	—	30	1	no	—
264	C₂²×C₈	C₂×D₁₅	1	1	yes	characteristic
265	C₂²×C₈	C₂×D₁₅	1	1	yes	characteristic
266	#117	—	15	1	no	—
267	C₂×C₄²	C₂×D₁₅	1	1	yes	characteristic
268	#108	—	30	2	no	—
269	C₄⋊C₈	—	30	1	no	—
270	C₄⋊C₈	—	30	1	no	—
271	#104	—	30	2	no	—
272	#103	—	15	1	no	—
273	#103	—	15	1	no	—
274	#102	—	15	1	no	—
275	#102	—	15	1	no	—
276	C₂×C₃×C₅	—	2	1	no	—
277	C₂×C₃×C₅	—	2	1	no	—
278	C₂×C₃×C₅	#385	1	1	yes	characteristic
279	C₂×C₃×C₅	#443	1	1	yes	characteristic
280	C₂×C₃×C₅	#444	1	1	yes	characteristic
281	D₁₅	—	4	2	no	—
282	C₂³×C₃	#709	1	1	yes	characteristic
283	C₂²×D₃	—	10	1	no	—
284	C₂×C₃×C₄	—	2	2	no	—
285	C₂×C₃×C₄	—	4	1	no	—
286	C₂×C₃×C₄	—	4	1	no	—
287	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
288	C₂×C₃×C₄	C₂×D₂₀	1	1	yes	characteristic
289	C₂×C₃×C₄	D₄×D₅	1	1	yes	characteristic
290	C₂×C₃×C₄	D₄×D₅	1	1	yes	characteristic
291	C₂×C₃×C₄	#711	1	1	yes	characteristic
292	C₂×C₃×C₄	Q₈×D₅	1	1	yes	characteristic
293	#67	—	10	2	no	—
294	#67	—	10	2	no	—
295	C₂×Dic₃	—	10	1	no	—
296	C₂×Dic₃	—	10	1	no	—
297	C₂×Dic₃	—	10	1	no	—
298	D₁₂	—	5	2	no	—
299	D₁₂	—	10	1	no	—
300	C₄×D₃	—	10	2	no	—
301	C₄×D₃	—	10	2	no	—
302	Dic₆	—	5	2	no	—
303	Dic₆	—	10	1	no	—
304	C₃×C₈	—	2	1	no	—
305	C₃×C₈	—	2	1	no	—
306	C₃×C₈	—	2	1	no	—
307	C₃×C₈	—	2	1	no	—
308	C₃⋊C₈	—	10	2	no	—
309	C₃⋊C₈	—	20	1	no	—
310	C₂²×C₅	—	2	1	no	—
311	C₂²×C₅	—	2	1	no	—
312	C₂²×C₅	C₄×D₁₂	1	1	yes	characteristic
313	C₂²×C₅	#883	1	1	yes	characteristic
314	C₂²×C₅	#896	1	1	yes	characteristic
315	C₂×D₅	—	6	2	no	—
316	C₂×D₅	—	12	1	no	—
317	C₂×D₅	—	12	1	no	—
318	C₄×C₅	—	4	2	no	—
319	C₄×C₅	#67⋊C₄	1	1	yes	characteristic
320	C₄×C₅	#882	1	1	yes	characteristic
321	C₄×C₅	D₃×C₄⋊C₄	1	1	yes	characteristic
322	C₄×C₅	#897	1	1	yes	characteristic
323	Dic₅	—	6	2	no	—
324	Dic₅	—	12	1	no	—
325	Dic₅	—	12	1	no	—
326	#41	—	15	2	no	—
327	#41	—	15	2	no	—
328	#41	—	30	1	no	—
329	#41	—	30	1	no	—
330	C₂×Q₈	—	15	1	no	—
331	C₂×D₄	—	15	1	no	—
332	C₂×D₄	—	30	1	no	—
333	C₂²×C₄	—	2	1	no	—
334	C₂²×C₄	—	30	1	no	—
335	C₂²×C₄	C₂²×D₁₅	1	1	yes	characteristic
336	M₁₆	—	15	2	no	—
337	M₁₆	—	30	4	no	—
338	M₁₆	—	30	1	no	—
339	M₁₆	—	30	1	no	—
340	M₁₆	—	30	1	no	—
341	C₂×C₈	—	2	1	no	—
342	C₂×C₈	—	2	1	no	—
343	C₂×C₈	—	2	1	no	—
344	C₂×C₈	—	2	1	no	—
345	C₂×C₈	—	30	4	no	—
346	C₂×C₈	—	30	1	no	—
347	C₂×C₈	—	30	1	no	—
348	C₂×C₈	C₄×D₁₅	1	1	yes	characteristic
349	C₂×C₈	C₄×D₁₅	1	1	yes	characteristic
350	C₂×C₈	D₆₀	1	1	yes	characteristic
351	C₂×C₈	D₆₀	1	1	yes	characteristic
352	C₄⋊C₄	—	15	1	no	—
353	C₄⋊C₄	—	15	1	no	—
354	C₂²⋊C₄	—	30	1	no	—
355	C₄²	—	2	1	no	—
356	C₄²	—	2	1	no	—
357	C₄²	—	30	1	no	—
358	C₃×C₅	#1866	1	1	yes	characteristic, complemented, Hall
359	C₂²×C₃	—	2	1	no	—
360	C₂²×C₃	—	2	1	no	—
361	C₂²×C₃	C₄×D₂₀	1	1	yes	characteristic
362	C₂²×C₃	#4029	1	1	yes	characteristic
363	C₂²×C₃	#4042	1	1	yes	characteristic
364	C₂×D₃	—	10	2	no	—
365	C₂×D₃	—	20	1	no	—
366	C₂×D₃	—	20	1	no	—
367	C₃×C₄	—	4	2	no	—
368	C₃×C₄	#4027	1	1	yes	characteristic
369	C₃×C₄	#4028	1	1	yes	characteristic
370	C₃×C₄	D₅×C₄⋊C₄	1	1	yes	characteristic
371	C₃×C₄	#4043	1	1	yes	characteristic
372	Dic₃	—	10	2	no	—
373	Dic₃	—	20	1	no	—
374	Dic₃	—	20	1	no	—
375	C₂×C₅	—	2	1	no	—
376	C₂×C₅	—	2	1	no	—
377	C₂×C₅	#4668	1	1	yes	characteristic
378	C₂×C₅	#4700	1	1	yes	characteristic
379	C₂×C₅	#4717	1	1	yes	characteristic
380	D₅	—	12	2	no	—
381	C₂³	—	30	1	no	—
382	C₂³	#6817	1	1	yes	characteristic
383	Q₈	—	15	2	no	—
384	Q₈	—	30	1	no	—
385	D₄	—	15	2	no	—
386	D₄	—	30	2	no	—
387	D₄	—	30	2	no	—
388	D₄	—	30	1	no	—
389	C₂×C₄	—	2	2	no	—
390	C₂×C₄	—	4	1	no	—
391	C₂×C₄	—	4	1	no	—
392	C₂×C₄	—	30	1	no	—
393	C₂×C₄	—	30	2	no	—
394	C₂×C₄	—	30	2	no	—
395	C₂×C₄	—	30	1	no	—
396	C₂×C₄	—	30	1	no	—
397	C₂×C₄	C₂×C₄×D₁₅	1	1	yes	characteristic
398	C₂×C₄	C₂×D₆₀	1	1	yes	characteristic
399	C₂×C₄	D₄×D₁₅	1	1	yes	characteristic
400	C₂×C₄	D₄×D₁₅	1	1	yes	characteristic
401	C₂×C₄	#6819	1	1	yes	characteristic
402	C₂×C₄	Q₈×D₁₅	1	1	yes	characteristic
403	C₈	—	2	1	no	—
404	C₈	—	2	1	no	—
405	C₈	—	2	1	no	—
406	C₈	—	2	1	no	—
407	C₈	—	30	2	no	—
408	C₈	—	60	1	no	—
409	C₂×C₃	—	2	1	no	—
410	C₂×C₃	—	2	1	no	—
411	C₂×C₃	#64957	1	1	yes	characteristic
412	C₂×C₃	#64989	1	1	yes	characteristic
413	C₂×C₃	#65006	1	1	yes	characteristic
414	D₃	—	20	2	no	—
415	C₅	#68694	1	1	yes	characteristic, complemented, Sylow
416	C₂²	—	2	1	no	—
417	C₂²	—	2	1	no	—
418	C₂²	—	30	2	no	—
419	C₂²	—	60	1	no	—
420	C₂²	—	60	1	no	—
421	C₂²	C₄×D₆₀	1	1	yes	characteristic
422	C₂²	#91772	1	1	yes	characteristic
423	C₂²	#91785	1	1	yes	characteristic
424	C₄	—	4	2	no	—
425	C₄	—	30	2	no	—
426	C₄	—	60	1	no	—
427	C₄	—	60	1	no	—
428	C₄	#91770	1	1	yes	characteristic
429	C₄	#91771	1	1	yes	characteristic
430	C₄	C₄⋊C₄×D₁₅	1	1	yes	characteristic
431	C₄	#91786	1	1	yes	characteristic
432	C₃	#10599487	1	1	yes	characteristic, complemented, Sylow
433	C₂	—	2	1	no	—
434	C₂	—	2	1	no	—
435	C₂	—	60	2	no	—
436	C₂	#11750769	1	1	yes	characteristic
437	C₂	#11750801	1	1	yes	characteristic
438	C₂	#11750818	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₆₀
commutator	C₂×C₃×C₄×C₅	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₁₅
Fitting	C₃×C₅×#336	C₂
socle	C₂²×C₃×C₅	C₄×D₄
prime radical	C₂×#6817	C₂²
cosocle	C₂²×C₃×C₄×C₅	C₂³
hypercenter	#336	D₁₅
hypocenter	C₃×C₅	#1866
LCS	G ▷ C₂×C₃×C₄×C₅ ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₈ ◁ #336

Complements

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

N	H ≅ G/N	type
3. C₂×#91103	C₂	semidirect
4. #11751203	C₂	semidirect
6. C₃×C₅×#336	C₂	semidirect
7. #11746344	C₂	semidirect
20. #91105	C₄	semidirect
21. #91105	C₄	semidirect
23. #91100	C₄	semidirect
24. #91100	C₄	semidirect
34. C₅×#336	D₃	semidirect
73. C₃×#336	D₅	semidirect
180. #336	D₁₅	semidirect
358. C₃×C₅	#1866	semidirect
415. C₅	#68694	semidirect
432. C₃	#10599487	semidirect

Maximal subgroups

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

subgroup	index
C₂×#91790	2
#11751214	2
C₂×#91103	2
#11751203	2
C₂×#91089	2
C₃×C₅×#336	2
#11746344	2
#10599487	3
#68694	5