Subgroups — #14415923

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	C₃×#65811	C₂	1	1	yes	maximal, characteristic
2	C₂×#91283	C₂	1	2	yes	maximal, complemented
3	C₄×#6710	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₅×C₄⋊(C₃⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
5	#11748342	C₂	1	2	yes	maximal, complemented
6	#11747013	C₂	1	2	yes	maximal, complemented
7	#11746997	C₂	1	4	yes	maximal, complemented
8	#11746996	C₂	1	2	yes	maximal, complemented
9	#10610735	—	3	1	no	maximal, Hall
10	C₂×C₃×#709	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	C₂²×C₅×C₃⋊C₈	C₂²	1	2	yes	—
15	C₃×#4076	C₄	1	2	yes	—
16	C₃×#4076	C₄	1	2	yes	—
17	C₃×#4021	C₄	1	2	yes	—
18	C₃×#4020	C₄	1	1	yes	characteristic
19	C₃×C₄×D₂₀	C₂²	1	2	yes	—
20	C₃×C₄×D₂₀	C₂²	1	2	yes	—
21	C₃×#4015	C₄	1	1	yes	characteristic
22	C₂×#6649	C₂²	1	4	yes	—
23	#91283	—	2	8	no	—
24	C₂×D₅×C₃⋊C₈	C₂²	1	4	yes	—
25	#91087	C₂²	1	2	yes	—
26	C₄×C₃⋊#168	C₂²	1	2	yes	—
27	C₅×C₄⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic
28	C₅×C₄⋊(C₃⋊C₈)	C₂²	1	2	yes	—
29	C₅×C₄⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic
30	#90955	C₂²	1	4	yes	—
31	#90955	C₂²	1	4	yes	—
32	#83277	—	5	1	no	maximal, Hall
33	C₂×#4047	—	3	2	no	—
34	#65811	D₃	1	1	yes	characteristic
35	C₂×C₅×C₄⋊C₈	—	3	1	no	—
36	#65399	—	3	2	no	—
37	C₄×#681	—	3	1	no	—
38	#65127	—	3	2	no	—
39	#65125	—	3	4	no	—
40	#65123	—	3	2	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×C₃×C₂²⋊D₅	C₂×C₄	1	4	yes	—
45	C₃×#709	—	2	4	no	—
46	C₃×#709	—	2	4	no	—
47	C₂×C₃×D₂₀	C₂×C₄	1	2	yes	—
48	C₂×C₃×D₂₀	C₂×C₄	1	2	yes	—
49	C₂×C₃×D₂₀	C₂×C₄	1	2	yes	—
50	C₂×C₃×C₄×D₅	C₂³	1	4	yes	—
51	C₂×C₃×Dic₁₀	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	C₂×C₅×C₃⋊C₈	—	2	4	no	—
61	C₂×C₅×C₃⋊C₈	C₂³	1	2	yes	—
62	C₂×C₅×C₃⋊C₈	C₂³	1	2	yes	—
63	C₃×#685	C₂×C₄	1	4	yes	—
64	C₃×#685	C₂×C₄	1	4	yes	—
65	C₃×C₄⋊Dic₅	C₂×C₄	1	2	yes	—
66	C₃×C₄⋊Dic₅	C₂×C₄	1	2	yes	—
67	#6649	—	2	8	no	—
68	D₅×C₃⋊C₈	—	2	8	no	—
69	C₃×#532	—	5	1	no	—
70	C₂×#948	—	5	2	no	—
71	#5234	—	5	2	no	—
72	#5012	—	5	2	no	—
73	#5011	—	5	4	no	—
74	D₄×C₃⋊C₈	—	5	2	no	—
75	C₂×C₄⋊(C₃⋊C₈)	D₅	1	1	yes	characteristic, complemented
76	C₄×#208	—	5	1	no	—
77	C₂×#709	C₂×D₃	1	2	yes	—
78	C₂²×C₅×C₈	—	3	2	no	—
79	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
80	#4076	Dic₃	1	2	yes	—
81	#4076	Dic₃	1	2	yes	—
82	C₂×#681	—	3	1	no	—
83	C₂×#681	—	3	1	no	—
84	#4047	—	6	8	no	—
85	C₂×#676	—	3	4	no	—
86	C₂×C₈×D₅	—	3	4	no	—
87	#4021	Dic₃	1	2	yes	—
88	#4020	Dic₃	1	1	yes	characteristic
89	C₄×D₂₀	C₂×D₃	1	2	yes	—
90	C₄×D₂₀	C₂×D₃	1	2	yes	—
91	#4015	Dic₃	1	1	yes	characteristic
92	C₅×C₄⋊C₈	—	3	1	no	—
93	C₅×C₄⋊C₈	—	3	2	no	—
94	C₅×C₄⋊C₈	—	3	1	no	—
95	#3952	—	3	4	no	—
96	#3952	—	3	4	no	—
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×C₃×D₅	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	C₃×C₂²⋊D₅	—	2	8	no	—
113	C₂×C₃×Dic₅	C₂²×C₄	1	4	yes	—
114	C₃×D₂₀	—	2	4	no	—
115	C₃×D₂₀	—	2	4	no	—
116	C₃×D₂₀	—	4	2	no	—
117	C₃×C₄×D₅	—	2	4	no	—
118	C₃×C₄×D₅	—	2	4	no	—
119	C₃×Dic₁₀	—	2	4	no	—
120	C₃⋊#168	—	2	2	no	—
121	C₃⋊#168	C₂×D₄	1	4	yes	—
122	C₅×C₃⋊C₈	—	2	2	no	—
123	C₅×C₃⋊C₈	—	2	2	no	—
124	C₂×C₃×#41	—	5	2	no	—
125	C₃×C₄⋊Q₈	—	5	1	no	—
126	C₃×#127	—	5	1	no	—
127	C₃×#124	—	5	2	no	—
128	C₃×#121	—	5	2	no	—
129	C₃×#121	—	5	2	no	—
130	C₃×C₄×D₄	—	5	2	no	—
131	C₃×C₄×D₄	—	5	2	no	—
132	C₂×C₃×C₄²	C₂×D₅	1	1	yes	characteristic
133	#948	—	10	8	no	—
134	C₂×#208	—	5	1	no	—
135	C₂×#208	—	5	1	no	—
136	C₂×#208	—	5	4	no	—
137	C₂²×C₃⋊C₈	—	5	4	no	—
138	C₂²×C₃⋊C₈	C₂×D₅	1	2	yes	—
139	#830	—	5	4	no	—
140	#830	—	5	4	no	—
141	C₄⋊(C₃⋊C₈)	C₂×D₅	1	1	yes	characteristic
142	C₄⋊(C₃⋊C₈)	C₂×D₅	1	2	yes	—
143	C₄⋊(C₃⋊C₈)	C₂×D₅	1	1	yes	characteristic
144	#803	—	5	2	no	—
145	C₄×C₃⋊C₈	—	5	2	no	—
146	C₂²×C₄×C₅	C₂×Dic₃	1	1	yes	characteristic
147	C₂²×C₄×C₅	C₂×Dic₃	1	1	yes	characteristic
148	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
149	C₂×C₂²⋊D₅	C₂×Dic₃	1	4	yes	—
150	#709	—	2	4	no	—
151	#709	—	2	4	no	—
152	C₂×D₂₀	C₂×Dic₃	1	2	yes	—
153	C₂×D₂₀	C₂×Dic₃	1	2	yes	—
154	C₂×D₂₀	C₂×Dic₃	1	2	yes	—
155	C₂×C₄×D₅	C₂²×D₃	1	4	yes	—
156	C₂×Dic₁₀	C₂×Dic₃	1	2	yes	—
157	C₂×C₅×C₈	—	3	2	no	—
158	C₂×C₅×C₈	—	3	2	no	—
159	C₂×C₅×C₈	—	6	4	no	—
160	C₄²×C₅	C₂×Dic₃	1	1	yes	characteristic
161	C₄²×C₅	C₂×Dic₃	1	1	yes	characteristic
162	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
163	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
164	#685	C₂×Dic₃	1	4	yes	—
165	#685	C₂×Dic₃	1	4	yes	—
166	C₄⋊Dic₅	C₂×Dic₃	1	2	yes	—
167	C₄⋊Dic₅	C₂×Dic₃	1	2	yes	—
168	#681	—	3	4	no	—
169	#681	—	6	2	no	—
170	C₂×#168	—	3	2	no	—
171	C₂×#168	—	3	2	no	—
172	#676	—	6	8	no	—
173	C₈×D₅	—	6	8	no	—
174	C₂×#131	—	15	2	no	—
175	#532	—	5	1	no	—
176	#436	—	15	2	no	—
177	#435	—	15	4	no	—
178	C₈×D₄	—	15	2	no	—
179	C₂×C₄⋊C₈	—	3	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×C₃×D₅	—	2	4	no	—
187	C₂×C₃×D₅	—	2	4	no	—
188	C₂×C₃×D₅	—	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	C₃×Dic₅	—	2	4	no	—
197	C₃×#41	—	10	4	no	—
198	C₃×#41	—	10	4	no	—
199	C₂×C₃×Q₈	—	5	2	no	—
200	C₂×C₃×D₄	—	5	4	no	—
201	C₂×C₃×D₄	—	5	2	no	—
202	C₂×C₃×D₄	—	5	2	no	—
203	C₂×C₃×D₄	—	5	2	no	—
204	C₂²×C₃×C₄	—	5	4	no	—
205	C₂²×C₃×C₄	C₄×D₅	1	1	yes	characteristic
206	C₂²×C₃×C₄	C₄×D₅	1	1	yes	characteristic
207	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
208	C₃×C₄⋊C₄	—	5	2	no	—
209	C₃×C₄⋊C₄	—	5	2	no	—
210	C₃×C₂²⋊C₄	—	5	4	no	—
211	C₃×C₂²⋊C₄	—	5	4	no	—
212	C₃×C₄²	C₄×D₅	1	1	yes	characteristic
213	C₃×C₄²	C₄×D₅	1	1	yes	characteristic
214	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
215	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
216	#208	—	5	4	no	—
217	#208	—	10	8	no	—
218	#208	—	10	2	no	—
219	C₂×C₃⋊C₈	—	2	4	no	—
220	C₂×C₃⋊C₈	—	5	2	no	—
221	C₂×C₃⋊C₈	—	5	2	no	—
222	C₂×C₃⋊C₈	—	10	8	no	—
223	C₂×C₃⋊C₈	C₂²×D₅	1	2	yes	—
224	C₂×C₃⋊C₈	C₂²×D₅	1	2	yes	—
225	C₂³×C₅	C₂²×Dic₃	1	1	yes	characteristic
226	C₂²×D₅	C₂²×Dic₃	1	4	yes	—
227	C₂×C₄×C₅	—	2	2	no	—
228	C₂×C₄×C₅	—	4	1	no	—
229	C₂×C₄×C₅	D₃×D₄	1	2	yes	—
230	C₂×C₄×C₅	#237	1	2	yes	—
231	C₂×C₄×C₅	C₂²×Dic₃	1	1	yes	characteristic
232	C₂×C₄×C₅	C₂²×Dic₃	1	1	yes	characteristic
233	C₂×C₄×C₅	C₂²×Dic₃	1	1	yes	characteristic
234	C₂×C₄×C₅	C₂²×Dic₃	1	1	yes	characteristic
235	C₂×C₄×C₅	C₂²×Dic₃	1	1	yes	characteristic
236	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
237	C₂²⋊D₅	—	2	8	no	—
238	C₂×Dic₅	C₂²×Dic₃	1	4	yes	—
239	D₂₀	—	2	4	no	—
240	D₂₀	—	2	4	no	—
241	D₂₀	—	4	2	no	—
242	C₄×D₅	—	2	4	no	—
243	C₄×D₅	—	2	4	no	—
244	Dic₁₀	—	2	4	no	—
245	C₅×C₈	—	6	2	no	—
246	C₅×C₈	—	6	2	no	—
247	#168	—	3	4	no	—
248	#168	—	6	2	no	—
249	C₂×#41	—	5	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	—	3	2	no	—
255	C₂²×C₈	—	15	4	no	—
256	C₄⋊Q₈	—	5	1	no	—
257	#127	—	5	1	no	—
258	#124	—	5	2	no	—
259	#121	—	5	2	no	—
260	#121	—	5	2	no	—
261	C₄×D₄	—	5	2	no	—
262	C₄×D₄	—	5	2	no	—
263	C₂×C₄²	D₃×D₅	1	1	yes	characteristic
264	C₄⋊C₈	—	3	1	no	—
265	C₄⋊C₈	—	3	2	no	—
266	C₄⋊C₈	—	3	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	C₃×D₅	—	4	4	no	—
276	C₂³×C₃	—	5	4	no	—
277	C₂³×C₃	C₂×C₄×D₅	1	1	yes	characteristic
278	C₃×Q₈	—	10	4	no	—
279	C₃×D₄	—	10	8	no	—
280	C₃×D₄	—	10	4	no	—
281	C₃×D₄	—	10	4	no	—
282	C₃×D₄	—	20	2	no	—
283	C₂×C₃×C₄	—	2	2	no	—
284	C₂×C₃×C₄	—	4	1	no	—
285	C₂×C₃×C₄	—	5	4	no	—
286	C₂×C₃×C₄	—	10	4	no	—
287	C₂×C₃×C₄	—	10	4	no	—
288	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
289	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
290	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
291	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
292	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
293	C₂×C₃×C₄	D₄×D₅	1	2	yes	—
294	C₂×C₃×C₄	#713	1	2	yes	—
295	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
296	C₃⋊C₈	—	2	2	no	—
297	C₃⋊C₈	—	2	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	D₄×Dic₃	1	2	yes	—
303	C₂²×C₅	C₂³×Dic₃	1	1	yes	characteristic
304	C₂×D₅	—	2	4	no	—
305	C₂×D₅	—	2	4	no	—
306	C₂×D₅	—	2	4	no	—
307	C₄×C₅	—	2	1	no	—
308	C₄×C₅	—	2	1	no	—
309	C₄×C₅	—	2	1	no	—
310	C₄×C₅	D₄×Dic₃	1	2	yes	—
311	C₄×C₅	#948	1	2	yes	complemented
312	C₄×C₅	C₂×D₃×D₄	1	1	yes	characteristic
313	C₄×C₅	C₂×#237	1	1	yes	characteristic
314	Dic₅	—	2	4	no	—
315	#41	—	10	4	no	—
316	#41	—	10	4	no	—
317	C₂×Q₈	—	5	2	no	—
318	C₂×D₄	—	5	4	no	—
319	C₂×D₄	—	5	2	no	—
320	C₂×D₄	—	5	2	no	—
321	C₂×D₄	—	5	2	no	—
322	C₂²×C₄	—	5	4	no	—
323	C₂²×C₄	D₅×Dic₃	1	1	yes	characteristic
324	C₂²×C₄	D₅×Dic₃	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	—	3	2	no	—
330	C₂×C₈	—	3	2	no	—
331	C₂×C₈	—	6	4	no	—
332	C₂×C₈	—	15	2	no	—
333	C₂×C₈	—	15	2	no	—
334	C₂×C₈	—	30	8	no	—
335	C₄⋊C₄	—	5	2	no	—
336	C₄⋊C₄	—	5	2	no	—
337	C₂²⋊C₄	—	5	4	no	—
338	C₂²⋊C₄	—	5	4	no	—
339	C₄²	D₅×Dic₃	1	1	yes	characteristic
340	C₄²	D₅×Dic₃	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	—	10	4	no	—
347	C₂²×C₃	—	10	4	no	—
348	C₂²×C₃	—	10	4	no	—
349	C₂²×C₃	#4039	1	2	yes	—
350	C₂²×C₃	C₂²×C₄×D₅	1	1	yes	characteristic
351	C₃×C₄	—	2	1	no	—
352	C₃×C₄	—	2	1	no	—
353	C₃×C₄	—	2	1	no	—
354	C₃×C₄	—	10	4	no	—
355	C₃×C₄	#4039	1	2	yes	—
356	C₃×C₄	#4047	1	2	yes	complemented
357	C₃×C₄	C₂×D₄×D₅	1	1	yes	characteristic
358	C₃×C₄	C₂×#713	1	1	yes	characteristic
359	C₂×C₅	—	2	2	no	—
360	C₂×C₅	C₂×D₄×Dic₃	1	1	yes	characteristic
361	C₂×C₅	C₂×#948	1	1	yes	characteristic
362	C₂×C₅	#5819	1	1	yes	characteristic
363	D₅	—	4	4	no	—
364	C₂³	—	5	4	no	—
365	C₂³	C₂×D₅×Dic₃	1	1	yes	characteristic
366	Q₈	—	10	4	no	—
367	D₄	—	10	8	no	—
368	D₄	—	10	4	no	—
369	D₄	—	10	4	no	—
370	D₄	—	20	2	no	—
371	C₂×C₄	—	2	2	no	—
372	C₂×C₄	—	4	1	no	—
373	C₂×C₄	—	5	4	no	—
374	C₂×C₄	—	10	4	no	—
375	C₂×C₄	—	10	4	no	—
376	C₂×C₄	#6766	1	2	yes	—
377	C₂×C₄	#6777	1	2	yes	—
378	C₂×C₄	C₂×D₅×Dic₃	1	1	yes	characteristic
379	C₂×C₄	C₂×D₅×Dic₃	1	1	yes	characteristic
380	C₂×C₄	C₂×D₅×Dic₃	1	1	yes	characteristic
381	C₂×C₄	C₂×D₅×Dic₃	1	1	yes	characteristic
382	C₂×C₄	C₂×D₅×Dic₃	1	1	yes	characteristic
383	C₂×C₄	C₂²×D₃×D₅	1	1	yes	characteristic
384	C₈	—	6	2	no	—
385	C₈	—	6	2	no	—
386	C₈	—	15	4	no	—
387	C₈	—	30	2	no	—
388	C₂×C₃	—	2	2	no	—
389	C₂×C₃	—	20	4	no	—
390	C₂×C₃	C₂×#4039	1	1	yes	characteristic
391	C₂×C₃	C₂×#4047	1	1	yes	characteristic
392	C₂×C₃	#66079	1	1	yes	characteristic
393	C₅	#83277	1	1	yes	characteristic, complemented, Sylow
394	C₂²	—	2	1	no	—
395	C₂²	—	2	1	no	—
396	C₂²	—	10	4	no	—
397	C₂²	—	10	4	no	—
398	C₂²	—	10	4	no	—
399	C₂²	#91434	1	2	yes	—
400	C₂²	C₂²×D₅×Dic₃	1	1	yes	characteristic
401	C₄	—	2	1	no	—
402	C₄	—	2	1	no	—
403	C₄	—	2	1	no	—
404	C₄	—	10	4	no	—
405	C₄	#91283	1	2	yes	complemented
406	C₄	#91434	1	2	yes	—
407	C₄	C₂×#6766	1	1	yes	characteristic
408	C₄	C₂×#6777	1	1	yes	characteristic
409	C₃	#10610735	1	1	yes	characteristic, complemented, Sylow
410	C₂	—	2	2	no	—
411	C₂	—	20	4	no	—
412	C₂	C₂×#91283	1	1	yes	characteristic
413	C₂	#11754120	1	1	yes	characteristic
414	C₂	C₂×#91434	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	C₃×#65811	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×#91283	C₂	semidirect
3. C₄×#6710	C₂	semidirect
4. C₂×C₅×C₄⋊(C₃⋊C₈)	C₂	semidirect
5. #11748342	C₂	semidirect
6. #11747013	C₂	semidirect
7. #11746997	C₂	semidirect
8. #11746996	C₂	semidirect
57. #6710	D₄	semidirect
75. C₂×C₄⋊(C₃⋊C₈)	D₅	semidirect
193. C₃×C₄×C₅	#131	semidirect
311. C₄×C₅	#948	semidirect
343. C₃×C₅	#2935	semidirect
356. C₃×C₄	#4047	semidirect
393. C₅	#83277	semidirect
405. C₄	#91283	semidirect
409. C₃	#10610735	semidirect

Maximal subgroups

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

subgroup	index
C₃×#65811	2
C₂×#91283	2
C₄×#6710	2
C₂×C₅×C₄⋊(C₃⋊C₈)	2
#11748342	2
#11747013	2
#11746997	2
#11746996	2
#10610735	3
#83277	5