Subgroups — #14415920

Order 1920.

984 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#5477	C₂	1	1	yes	maximal, characteristic
2	C₂×#91286	C₂	1	2	yes	maximal, complemented
3	C₄×#6710	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃×C₄⋊#168	C₂	1	1	yes	maximal, characteristic, complemented
5	#11748345	C₂	1	2	yes	maximal, complemented
6	#11747014	C₂	1	2	yes	maximal, complemented
7	#11746999	C₂	1	4	yes	maximal, complemented
8	#11746998	C₂	1	2	yes	maximal, complemented
9	#10615008	—	3	1	no	maximal, Hall
10	C₂×C₅×#235	C₂²	1	2	yes	—
11	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
12	C₂×#6710	C₂²	1	1	yes	characteristic
13	C₂×#6710	C₂²	1	1	yes	characteristic
14	C₅×#930	C₄	1	2	yes	—
15	C₅×#930	C₄	1	2	yes	—
16	C₅×#875	C₄	1	2	yes	—
17	C₅×#874	C₄	1	1	yes	characteristic
18	C₄×C₅×D₁₂	C₂²	1	2	yes	—
19	C₄×C₅×D₁₂	C₂²	1	2	yes	—
20	C₅×#869	C₄	1	1	yes	characteristic
21	C₂²×C₃×#168	C₂²	1	2	yes	—
22	C₂×#6650	C₂²	1	4	yes	—
23	#91286	—	2	8	no	—
24	C₂×D₃×#168	C₂²	1	4	yes	—
25	#91087	C₂²	1	2	yes	—
26	C₄×C₃⋊#168	C₂²	1	2	yes	—
27	C₃×C₄⋊#168	C₂²	1	1	yes	characteristic
28	C₃×C₄⋊#168	C₂²	1	2	yes	—
29	C₃×C₄⋊#168	C₂²	1	1	yes	characteristic
30	(C₂×D₃)⋊#168	C₂²	1	4	yes	—
31	(C₂×D₃)⋊#168	C₂²	1	4	yes	—
32	#79004	—	5	1	no	maximal, Hall
33	C₅×#532	—	3	1	no	—
34	C₂×#4094	—	3	2	no	—
35	#65523	—	3	2	no	—
36	#65301	—	3	2	no	—
37	#65300	—	3	4	no	—
38	D₄×#168	—	3	2	no	—
39	C₂×C₄⋊#168	D₃	1	1	yes	characteristic, complemented
40	C₄×#681	—	3	1	no	—
41	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
42	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
43	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
44	C₂×C₅×#67	C₂×C₄	1	4	yes	—
45	C₅×#235	—	2	4	no	—
46	C₅×#235	—	2	4	no	—
47	C₂×C₅×D₁₂	C₂×C₄	1	2	yes	—
48	C₂×C₅×D₁₂	C₂×C₄	1	2	yes	—
49	C₂×C₅×D₁₂	C₂×C₄	1	2	yes	—
50	C₂×C₄×C₅×D₃	C₂³	1	4	yes	—
51	C₂×C₅×Dic₆	C₂×C₄	1	2	yes	—
52	C₃×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
53	C₃×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
54	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
55	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
56	#6710	—	2	2	no	—
57	#6710	D₄	1	4	yes	complemented
58	C₂×C₃⋊#168	C₂³	1	2	yes	—
59	C₂×C₃⋊#168	C₂³	1	2	yes	—
60	C₅×(C₂×D₃)⋊C₄	C₂×C₄	1	4	yes	—
61	C₅×(C₂×D₃)⋊C₄	C₂×C₄	1	4	yes	—
62	C₅×C₄⋊Dic₃	C₂×C₄	1	2	yes	—
63	C₅×C₄⋊Dic₃	C₂×C₄	1	2	yes	—
64	C₂×C₃×#168	—	2	4	no	—
65	C₂×C₃×#168	C₂³	1	2	yes	—
66	C₂×C₃×#168	C₂³	1	2	yes	—
67	#6650	—	2	8	no	—
68	D₃×#168	—	2	8	no	—
69	C₂×#901	—	5	2	no	—
70	#5477	D₅	1	1	yes	characteristic
71	C₂×C₃×C₄⋊C₈	—	5	1	no	—
72	#5110	—	5	2	no	—
73	C₄×#208	—	5	1	no	—
74	#4838	—	5	2	no	—
75	#4836	—	5	4	no	—
76	#4834	—	5	2	no	—
77	C₂×C₅×#41	—	3	2	no	—
78	C₅×C₄⋊Q₈	—	3	1	no	—
79	C₅×#127	—	3	1	no	—
80	C₅×#124	—	3	2	no	—
81	C₅×#121	—	3	2	no	—
82	C₅×#121	—	3	2	no	—
83	C₄×C₅×D₄	—	3	2	no	—
84	C₄×C₅×D₄	—	3	2	no	—
85	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
86	#4094	—	6	8	no	—
87	C₂×#681	—	3	1	no	—
88	C₂×#681	—	3	1	no	—
89	C₂×#681	—	3	4	no	—
90	C₂²×#168	—	3	4	no	—
91	C₂²×#168	C₂×D₃	1	2	yes	—
92	C₂²⋊#168	—	3	4	no	—
93	C₂²⋊#168	—	3	4	no	—
94	C₄⋊#168	C₂×D₃	1	1	yes	characteristic
95	C₄⋊#168	C₂×D₃	1	2	yes	—
96	C₄⋊#168	C₂×D₃	1	1	yes	characteristic
97	#3935	—	3	2	no	—
98	C₄×#168	—	3	2	no	—
99	#2935	—	15	1	no	Sylow
100	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
101	C₂²×C₅×D₃	C₂²×C₄	1	4	yes	—
102	C₂×C₃×C₄×C₅	—	2	2	no	—
103	C₂×C₃×C₄×C₅	—	4	1	no	—
104	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
105	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
106	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
107	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
108	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
109	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
110	C₂×C₃×C₄×C₅	#41	1	2	yes	—
111	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
112	C₅×#67	—	2	8	no	—
113	C₂×C₅×Dic₃	C₂²×C₄	1	4	yes	—
114	C₅×D₁₂	—	2	4	no	—
115	C₅×D₁₂	—	2	4	no	—
116	C₅×D₁₂	—	4	2	no	—
117	C₄×C₅×D₃	—	2	4	no	—
118	C₄×C₅×D₃	—	2	4	no	—
119	C₅×Dic₆	—	2	4	no	—
120	C₃⋊#168	—	2	2	no	—
121	C₃⋊#168	C₂×D₄	1	4	yes	—
122	C₃×#168	—	2	2	no	—
123	C₃×#168	—	2	2	no	—
124	C₂×#235	C₂×D₅	1	2	yes	—
125	C₂²×C₃×C₈	—	5	2	no	—
126	C₂×C₃×C₄²	C₂×D₅	1	1	yes	characteristic
127	#930	Dic₅	1	2	yes	—
128	#930	Dic₅	1	2	yes	—
129	C₂×#208	—	5	1	no	—
130	C₂×#208	—	5	1	no	—
131	#901	—	10	8	no	—
132	C₂×ΓL(1,𝔽₂₅)	—	5	4	no	—
133	C₂×D₃×C₈	—	5	4	no	—
134	#875	Dic₅	1	2	yes	—
135	#874	Dic₅	1	1	yes	characteristic
136	C₄×D₁₂	C₂×D₅	1	2	yes	—
137	C₄×D₁₂	C₂×D₅	1	2	yes	—
138	#869	Dic₅	1	1	yes	characteristic
139	C₃×C₄⋊C₈	—	5	1	no	—
140	C₃×C₄⋊C₈	—	5	2	no	—
141	C₃×C₄⋊C₈	—	5	1	no	—
142	(C₂×D₃)⋊C₈	—	5	4	no	—
143	(C₂×D₃)⋊C₈	—	5	4	no	—
144	#803	—	5	2	no	—
145	C₄×C₃⋊C₈	—	5	2	no	—
146	C₅×#41	—	6	4	no	—
147	C₅×#41	—	6	4	no	—
148	C₂×C₅×Q₈	—	3	2	no	—
149	C₂×C₅×D₄	—	3	4	no	—
150	C₂×C₅×D₄	—	3	2	no	—
151	C₂×C₅×D₄	—	3	2	no	—
152	C₂×C₅×D₄	—	3	2	no	—
153	C₂²×C₄×C₅	—	3	4	no	—
154	C₂²×C₄×C₅	C₄×D₃	1	1	yes	characteristic
155	C₂²×C₄×C₅	C₄×D₃	1	1	yes	characteristic
156	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
157	C₅×C₄⋊C₄	—	3	2	no	—
158	C₅×C₄⋊C₄	—	3	2	no	—
159	C₅×C₂²⋊C₄	—	3	4	no	—
160	C₅×C₂²⋊C₄	—	3	4	no	—
161	C₄²×C₅	C₄×D₃	1	1	yes	characteristic
162	C₄²×C₅	C₄×D₃	1	1	yes	characteristic
163	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
164	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
165	#681	—	3	4	no	—
166	#681	—	6	8	no	—
167	#681	—	6	2	no	—
168	C₂×#168	—	2	4	no	—
169	C₂×#168	—	3	2	no	—
170	C₂×#168	—	3	2	no	—
171	C₂×#168	—	6	8	no	—
172	C₂×#168	C₂²×D₃	1	2	yes	—
173	C₂×#168	C₂²×D₃	1	2	yes	—
174	C₂×#131	—	15	2	no	—
175	#532	—	3	1	no	—
176	#436	—	15	2	no	—
177	#435	—	15	4	no	—
178	C₈×D₄	—	15	2	no	—
179	C₂×C₄⋊C₈	—	5	1	no	—
180	#408	—	15	2	no	—
181	C₄×M₁₆	—	15	1	no	—
182	C₂²×C₃×C₅	—	2	1	no	—
183	C₂²×C₃×C₅	—	2	1	no	—
184	C₂²×C₃×C₅	C₄×D₄	1	2	yes	—
185	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
186	C₂×C₅×D₃	—	2	4	no	—
187	C₂×C₅×D₃	—	2	4	no	—
188	C₂×C₅×D₃	—	2	4	no	—
189	C₃×C₄×C₅	—	2	1	no	—
190	C₃×C₄×C₅	—	2	1	no	—
191	C₃×C₄×C₅	—	2	1	no	—
192	C₃×C₄×C₅	C₄×D₄	1	2	yes	—
193	C₃×C₄×C₅	#131	1	2	yes	complemented
194	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
195	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
196	C₅×Dic₃	—	2	4	no	—
197	C₂²×C₃×C₄	C₂×Dic₅	1	1	yes	characteristic
198	C₂²×C₃×C₄	C₂×Dic₅	1	1	yes	characteristic
199	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
200	C₂×#67	C₂×Dic₅	1	4	yes	—
201	#235	—	2	4	no	—
202	#235	—	2	4	no	—
203	C₂×D₁₂	C₂×Dic₅	1	2	yes	—
204	C₂×D₁₂	C₂×Dic₅	1	2	yes	—
205	C₂×D₁₂	C₂×Dic₅	1	2	yes	—
206	C₂×C₄×D₃	C₂²×D₅	1	4	yes	—
207	C₂×Dic₆	C₂×Dic₅	1	2	yes	—
208	C₂×C₃×C₈	—	5	2	no	—
209	C₂×C₃×C₈	—	5	2	no	—
210	C₂×C₃×C₈	—	10	4	no	—
211	C₃×C₄²	C₂×Dic₅	1	1	yes	characteristic
212	C₃×C₄²	C₂×Dic₅	1	1	yes	characteristic
213	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
214	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
215	(C₂×D₃)⋊C₄	C₂×Dic₅	1	4	yes	—
216	(C₂×D₃)⋊C₄	C₂×Dic₅	1	4	yes	—
217	C₄⋊Dic₃	C₂×Dic₅	1	2	yes	—
218	C₄⋊Dic₃	C₂×Dic₅	1	2	yes	—
219	#208	—	5	4	no	—
220	#208	—	10	2	no	—
221	C₂×C₃⋊C₈	—	5	2	no	—
222	C₂×C₃⋊C₈	—	5	2	no	—
223	ΓL(1,𝔽₂₅)	—	10	8	no	—
224	D₃×C₈	—	10	8	no	—
225	C₂³×C₅	—	3	4	no	—
226	C₂³×C₅	C₂×C₄×D₃	1	1	yes	characteristic
227	C₅×Q₈	—	6	4	no	—
228	C₅×D₄	—	6	8	no	—
229	C₅×D₄	—	6	4	no	—
230	C₅×D₄	—	6	4	no	—
231	C₅×D₄	—	12	2	no	—
232	C₂×C₄×C₅	—	2	2	no	—
233	C₂×C₄×C₅	—	3	4	no	—
234	C₂×C₄×C₅	—	4	1	no	—
235	C₂×C₄×C₅	—	6	4	no	—
236	C₂×C₄×C₅	—	6	4	no	—
237	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
238	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
239	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
240	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
241	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
242	C₂×C₄×C₅	D₃×D₄	1	2	yes	—
243	C₂×C₄×C₅	#239	1	2	yes	—
244	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
245	#168	—	2	2	no	—
246	#168	—	2	2	no	—
247	#168	—	3	4	no	—
248	#168	—	6	2	no	—
249	C₂×#41	—	3	2	no	—
250	#131	—	30	8	no	—
251	C₂×M₁₆	—	15	4	no	—
252	C₂×M₁₆	—	15	1	no	—
253	C₂×M₁₆	—	15	1	no	—
254	C₂²×C₈	—	5	2	no	—
255	C₂²×C₈	—	15	4	no	—
256	C₄⋊Q₈	—	3	1	no	—
257	#127	—	3	1	no	—
258	#124	—	3	2	no	—
259	#121	—	3	2	no	—
260	#121	—	3	2	no	—
261	C₄×D₄	—	3	2	no	—
262	C₄×D₄	—	3	2	no	—
263	C₂×C₄²	D₃×D₅	1	1	yes	characteristic
264	C₄⋊C₈	—	5	1	no	—
265	C₄⋊C₈	—	5	2	no	—
266	C₄⋊C₈	—	5	1	no	—
267	C₂²⋊C₈	—	15	4	no	—
268	C₂²⋊C₈	—	15	4	no	—
269	#97	—	15	2	no	—
270	C₄×C₈	—	15	2	no	—
271	C₂×C₃×C₅	—	2	2	no	—
272	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
273	C₂×C₃×C₅	C₂×#131	1	1	yes	characteristic
274	C₂×C₃×C₅	#568	1	1	yes	characteristic
275	C₅×D₃	—	4	4	no	—
276	C₂³×C₃	C₂²×Dic₅	1	1	yes	characteristic
277	C₂²×D₃	C₂²×Dic₅	1	4	yes	—
278	C₂×C₃×C₄	—	2	2	no	—
279	C₂×C₃×C₄	—	4	1	no	—
280	C₂×C₃×C₄	D₄×D₅	1	2	yes	—
281	C₂×C₃×C₄	#711	1	2	yes	—
282	C₂×C₃×C₄	C₂²×Dic₅	1	1	yes	characteristic
283	C₂×C₃×C₄	C₂²×Dic₅	1	1	yes	characteristic
284	C₂×C₃×C₄	C₂²×Dic₅	1	1	yes	characteristic
285	C₂×C₃×C₄	C₂²×Dic₅	1	1	yes	characteristic
286	C₂×C₃×C₄	C₂²×Dic₅	1	1	yes	characteristic
287	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
288	#67	—	2	8	no	—
289	C₂×Dic₃	C₂²×Dic₅	1	4	yes	—
290	D₁₂	—	2	4	no	—
291	D₁₂	—	2	4	no	—
292	D₁₂	—	4	2	no	—
293	C₄×D₃	—	2	4	no	—
294	C₄×D₃	—	2	4	no	—
295	Dic₆	—	2	4	no	—
296	C₃×C₈	—	10	2	no	—
297	C₃×C₈	—	10	2	no	—
298	C₃⋊C₈	—	5	4	no	—
299	C₃⋊C₈	—	10	2	no	—
300	C₂²×C₅	—	2	1	no	—
301	C₂²×C₅	—	2	1	no	—
302	C₂²×C₅	—	6	4	no	—
303	C₂²×C₅	—	6	4	no	—
304	C₂²×C₅	—	6	4	no	—
305	C₂²×C₅	#893	1	2	yes	—
306	C₂²×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
307	C₄×C₅	—	2	1	no	—
308	C₄×C₅	—	2	1	no	—
309	C₄×C₅	—	2	1	no	—
310	C₄×C₅	—	6	4	no	—
311	C₄×C₅	#893	1	2	yes	—
312	C₄×C₅	#901	1	2	yes	complemented
313	C₄×C₅	C₂×D₃×D₄	1	1	yes	characteristic
314	C₄×C₅	C₂×#239	1	1	yes	characteristic
315	#41	—	6	4	no	—
316	#41	—	6	4	no	—
317	C₂×Q₈	—	3	2	no	—
318	C₂×D₄	—	3	4	no	—
319	C₂×D₄	—	3	2	no	—
320	C₂×D₄	—	3	2	no	—
321	C₂×D₄	—	3	2	no	—
322	C₂²×C₄	—	3	4	no	—
323	C₂²×C₄	D₃×Dic₅	1	1	yes	characteristic
324	C₂²×C₄	D₃×Dic₅	1	1	yes	characteristic
325	C₂²×C₄	C₂×D₃×D₅	1	1	yes	characteristic
326	M₁₆	—	15	4	no	—
327	M₁₆	—	30	8	no	—
328	M₁₆	—	30	2	no	—
329	C₂×C₈	—	5	2	no	—
330	C₂×C₈	—	5	2	no	—
331	C₂×C₈	—	10	4	no	—
332	C₂×C₈	—	15	2	no	—
333	C₂×C₈	—	15	2	no	—
334	C₂×C₈	—	30	8	no	—
335	C₄⋊C₄	—	3	2	no	—
336	C₄⋊C₄	—	3	2	no	—
337	C₂²⋊C₄	—	3	4	no	—
338	C₂²⋊C₄	—	3	4	no	—
339	C₄²	D₃×Dic₅	1	1	yes	characteristic
340	C₄²	D₃×Dic₅	1	1	yes	characteristic
341	C₄²	C₂×D₃×D₅	1	1	yes	characteristic
342	C₄²	C₂×D₃×D₅	1	1	yes	characteristic
343	C₃×C₅	#2935	1	1	yes	characteristic, complemented, Hall
344	C₂²×C₃	—	2	1	no	—
345	C₂²×C₃	—	2	1	no	—
346	C₂²×C₃	D₄×Dic₅	1	2	yes	—
347	C₂²×C₃	C₂³×Dic₅	1	1	yes	characteristic
348	C₂×D₃	—	2	4	no	—
349	C₂×D₃	—	2	4	no	—
350	C₂×D₃	—	2	4	no	—
351	C₃×C₄	—	2	1	no	—
352	C₃×C₄	—	2	1	no	—
353	C₃×C₄	—	2	1	no	—
354	C₃×C₄	D₄×Dic₅	1	2	yes	—
355	C₃×C₄	#4094	1	2	yes	complemented
356	C₃×C₄	C₂×D₄×D₅	1	1	yes	characteristic
357	C₃×C₄	C₂×#711	1	1	yes	characteristic
358	Dic₃	—	2	4	no	—
359	C₂×C₅	—	2	2	no	—
360	C₂×C₅	—	12	4	no	—
361	C₂×C₅	C₂×#893	1	1	yes	characteristic
362	C₂×C₅	C₂×#901	1	1	yes	characteristic
363	C₂×C₅	#5745	1	1	yes	characteristic
364	C₂³	—	3	4	no	—
365	C₂³	C₂×D₃×Dic₅	1	1	yes	characteristic
366	Q₈	—	6	4	no	—
367	D₄	—	6	8	no	—
368	D₄	—	6	4	no	—
369	D₄	—	6	4	no	—
370	D₄	—	12	2	no	—
371	C₂×C₄	—	2	2	no	—
372	C₂×C₄	—	3	4	no	—
373	C₂×C₄	—	4	1	no	—
374	C₂×C₄	—	6	4	no	—
375	C₂×C₄	—	6	4	no	—
376	C₂×C₄	#6768	1	2	yes	—
377	C₂×C₄	#6777	1	2	yes	—
378	C₂×C₄	C₂×D₃×Dic₅	1	1	yes	characteristic
379	C₂×C₄	C₂×D₃×Dic₅	1	1	yes	characteristic
380	C₂×C₄	C₂×D₃×Dic₅	1	1	yes	characteristic
381	C₂×C₄	C₂×D₃×Dic₅	1	1	yes	characteristic
382	C₂×C₄	C₂×D₃×Dic₅	1	1	yes	characteristic
383	C₂×C₄	C₂²×D₃×D₅	1	1	yes	characteristic
384	C₈	—	10	2	no	—
385	C₈	—	10	2	no	—
386	C₈	—	15	4	no	—
387	C₈	—	30	2	no	—
388	C₂×C₃	—	2	2	no	—
389	C₂×C₃	C₂×D₄×Dic₅	1	1	yes	characteristic
390	C₂×C₃	C₂×#4094	1	1	yes	characteristic
391	C₂×C₃	#66153	1	1	yes	characteristic
392	D₃	—	4	4	no	—
393	C₅	#79004	1	1	yes	characteristic, complemented, Sylow
394	C₂²	—	2	1	no	—
395	C₂²	—	2	1	no	—
396	C₂²	—	6	4	no	—
397	C₂²	—	6	4	no	—
398	C₂²	—	6	4	no	—
399	C₂²	#91435	1	2	yes	—
400	C₂²	C₂²×D₃×Dic₅	1	1	yes	characteristic
401	C₄	—	2	1	no	—
402	C₄	—	2	1	no	—
403	C₄	—	2	1	no	—
404	C₄	—	6	4	no	—
405	C₄	#91286	1	2	yes	complemented
406	C₄	#91435	1	2	yes	—
407	C₄	C₂×#6768	1	1	yes	characteristic
408	C₄	C₂×#6777	1	1	yes	characteristic
409	C₃	#10615008	1	1	yes	characteristic, complemented, Sylow
410	C₂	—	2	2	no	—
411	C₂	—	12	4	no	—
412	C₂	C₂×#91286	1	1	yes	characteristic
413	C₂	#11754125	1	1	yes	characteristic
414	C₂	C₂×#91435	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×D₃×D₅
commutator, socle	C₂²×C₃×C₅	C₂³×C₄
Fitting	C₂×C₃×C₄²×C₅	C₂²
prime radical	C₅×#5477	C₂
cosocle	C₂×C₃×C₄×C₅	C₂⁴
hypercenter	C₂×C₄²	D₃×D₅
hypocenter	C₃×C₅	#2935
LCS	G ▷ C₂²×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄²

Complements

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

N	H ≅ G/N	type
2. C₂×#91286	C₂	semidirect
3. C₄×#6710	C₂	semidirect
4. C₂×C₃×C₄⋊#168	C₂	semidirect
5. #11748345	C₂	semidirect
6. #11747014	C₂	semidirect
7. #11746999	C₂	semidirect
8. #11746998	C₂	semidirect
39. C₂×C₄⋊#168	D₃	semidirect
57. #6710	D₄	semidirect
193. C₃×C₄×C₅	#131	semidirect
312. C₄×C₅	#901	semidirect
343. C₃×C₅	#2935	semidirect
355. C₃×C₄	#4094	semidirect
393. C₅	#79004	semidirect
405. C₄	#91286	semidirect
409. C₃	#10615008	semidirect

Maximal subgroups

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

subgroup	index
C₅×#5477	2
C₂×#91286	2
C₄×#6710	2
C₂×C₃×C₄⋊#168	2
#11748345	2
#11747014	2
#11746999	2
#11746998	2
#10615008	3
#79004	5