Subgroups — #14295326

Order 1920.

696 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#6651	C₂	1	1	yes	maximal, characteristic
2	C₂×#91104	C₂	1	1	yes	maximal, characteristic
3	C₂×C₅×C₈×Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄×#6667	C₂	1	1	yes	maximal, characteristic
5	C₂×#90952	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#64770	C₂	1	1	yes	maximal, characteristic, complemented
7	#11745967	C₂	1	1	yes	maximal, characteristic, complemented
8	#10600574	—	3	1	no	maximal, Hall
9	C₂²×C₄×D₁₅	C₂²	1	1	yes	characteristic
10	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
11	C₂²×C₃⋊#168	C₂²	1	1	yes	characteristic
12	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
13	C₂²×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
14	C₂×C₃×C₄×Dic₅	C₂²	1	1	yes	characteristic
15	C₂²×C₃×#168	C₂²	1	1	yes	characteristic
16	C₂×#6667	C₄	1	2	yes	—
17	C₂×#6651	—	2	2	no	—
18	C₂×#6651	—	2	2	no	—
19	C₂×#6651	C₄	1	4	yes	complemented
20	#91104	C₄	1	4	yes	complemented
21	C₅×C₈×Dic₃	—	2	2	no	—
22	#90994	C₄	1	2	yes	—
23	#90952	—	2	2	no	—
24	#68650	—	5	1	no	maximal, Hall
25	C₂²×#676	—	3	1	no	—
26	C₂×C₄×C₅×C₈	—	3	1	no	—
27	C₂×#3952	—	3	1	no	—
28	C₂×#3947	—	3	1	no	—
29	C₄×#685	—	3	1	no	—
30	#64770	D₃	1	1	yes	characteristic, complemented
31	#64744	—	3	1	no	—
32	C₂³×D₁₅	C₂×C₄	1	1	yes	characteristic
33	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
34	C₂²×Dic₁₅	C₂×C₄	1	1	yes	characteristic
35	C₂×C₄×D₁₅	—	2	1	no	—
36	C₂×C₄×D₁₅	—	2	1	no	—
37	C₂×C₄×D₁₅	—	2	1	no	—
38	C₂×C₄×D₁₅	—	2	1	no	—
39	C₂×C₄×D₁₅	C₂×C₄	1	2	yes	—
40	C₂×C₄×D₁₅	C₂×C₄	1	2	yes	—
41	C₂²×C₅×Dic₃	C₂×C₄	1	2	yes	—
42	C₂²×C₃×Dic₅	C₂×C₄	1	2	yes	—
43	C₂×C₃×C₅×C₈	—	2	1	no	—
44	C₂×C₃×C₅×C₈	—	2	1	no	—
45	C₂×C₃×C₅×C₈	C₂×C₄	1	2	yes	—
46	C₂×C₃⋊#168	—	2	1	no	—
47	C₂×C₃⋊#168	—	2	1	no	—
48	C₂×C₃⋊#168	C₂×C₄	1	2	yes	—
49	C₄×C₅×Dic₃	—	2	1	no	—
50	C₄×C₅×Dic₃	—	2	1	no	—
51	C₂×C₅×C₃⋊C₈	C₂×C₄	1	2	yes	—
52	C₂×C₅×C₃⋊C₈	D₄	1	2	yes	—
53	C₂×C₅×C₃⋊C₈	D₄	1	2	yes	—
54	C₃×C₄×Dic₅	—	2	1	no	—
55	C₃×C₄×Dic₅	—	2	1	no	—
56	C₂×C₃×#168	—	2	1	no	—
57	C₂×C₃×#168	—	2	1	no	—
58	C₂×C₃×#168	C₂×C₄	1	2	yes	—
59	#6667	—	2	4	no	—
60	#6651	—	2	8	no	—
61	C₂²×ΓL(1,𝔽₂₅)	—	5	1	no	—
62	C₂×(C₂×D₃)⋊C₈	—	5	1	no	—
63	C₂×C₈×Dic₃	D₅	1	1	yes	characteristic, complemented
64	C₄×(C₂×D₃)⋊C₄	—	5	1	no	—
65	C₂×#803	—	5	1	no	—
66	C₃×#336	—	5	1	no	—
67	#4550	—	5	1	no	—
68	C₂²×C₄×D₅	—	3	1	no	—
69	C₂²×C₅×C₈	—	3	1	no	—
70	C₂²×C₅×C₈	C₂×D₃	1	1	yes	characteristic
71	C₂×C₄²×C₅	—	3	1	no	—
72	C₂×#685	—	3	2	no	—
73	C₂×C₄×Dic₅	C₂×D₃	1	1	yes	characteristic
74	C₂²×#168	—	3	1	no	—
75	C₂²×#168	C₂×D₃	1	1	yes	characteristic
76	C₂×#676	—	3	4	no	—
77	C₂×#676	—	6	2	no	—
78	C₂×#676	—	6	2	no	—
79	C₄×C₅×C₈	—	6	2	no	—
80	#3963	—	3	2	no	—
81	#3952	—	3	4	no	—
82	#3947	—	6	2	no	—
83	#1753	—	15	1	no	Sylow
84	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
85	C₂²×D₁₅	—	2	1	no	—
86	C₂²×D₁₅	—	2	1	no	—
87	C₂²×D₁₅	—	2	2	no	—
88	C₂²×D₁₅	—	2	2	no	—
89	C₂²×D₁₅	C₄²	1	2	yes	—
90	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
91	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
92	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
93	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
94	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
95	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
96	C₂×Dic₁₅	—	2	1	no	—
97	C₂×Dic₁₅	—	2	1	no	—
98	C₂×Dic₁₅	C₄²	1	2	yes	—
99	C₄×D₁₅	—	2	2	no	—
100	C₄×D₁₅	—	2	2	no	—
101	C₄×D₁₅	—	2	2	no	—
102	C₄×D₁₅	—	2	2	no	—
103	C₂×C₅×Dic₃	—	2	2	no	—
104	C₂×C₅×Dic₃	—	2	2	no	—
105	C₂×C₅×Dic₃	M₁₆	1	4	yes	complemented
106	C₂×C₃×Dic₅	—	2	2	no	—
107	C₂×C₃×Dic₅	—	2	2	no	—
108	C₂×C₃×Dic₅	—	2	2	no	—
109	C₃×C₅×C₈	—	2	2	no	—
110	C₃⋊#168	—	2	2	no	—
111	C₃×#168	—	2	2	no	—
112	C₅×C₃⋊C₈	C₂²⋊C₄	1	4	yes	complemented
113	C₂²×C₄×D₃	—	5	1	no	—
114	C₂²×C₃×C₈	—	5	1	no	—
115	C₂²×C₃×C₈	C₂×D₅	1	1	yes	characteristic
116	C₂×C₃×C₄²	—	5	1	no	—
117	C₂×(C₂×D₃)⋊C₄	—	5	2	no	—
118	C₂×C₄×Dic₃	C₂×D₅	1	1	yes	characteristic
119	C₂²×C₃⋊C₈	—	5	1	no	—
120	C₂²×C₃⋊C₈	C₂×D₅	1	1	yes	characteristic
121	C₂×ΓL(1,𝔽₂₅)	—	5	4	no	—
122	C₂×ΓL(1,𝔽₂₅)	—	10	2	no	—
123	C₂×ΓL(1,𝔽₂₅)	—	10	2	no	—
124	C₃⋊#95	—	5	2	no	—
125	(C₂×D₃)⋊C₈	—	5	4	no	—
126	C₈×Dic₃	—	2	2	no	—
127	#803	—	10	2	no	—
128	C₂³×D₅	—	3	1	no	—
129	C₂²×C₄×C₅	—	3	2	no	—
130	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
131	C₂²×Dic₅	—	3	1	no	—
132	C₂²×Dic₅	C₄×D₃	1	2	yes	—
133	C₂×C₄×D₅	—	3	2	no	—
134	C₂×C₄×D₅	—	3	2	no	—
135	C₂×C₄×D₅	—	6	1	no	—
136	C₂×C₄×D₅	—	6	1	no	—
137	C₂×C₄×D₅	—	6	1	no	—
138	C₂×C₄×D₅	—	6	1	no	—
139	C₂×C₅×C₈	—	2	1	no	—
140	C₂×C₅×C₈	—	2	1	no	—
141	C₂×C₅×C₈	—	3	2	no	—
142	C₂×C₅×C₈	—	3	2	no	—
143	C₂×C₅×C₈	—	3	2	no	—
144	C₂×C₅×C₈	C₄×D₃	1	2	yes	—
145	C₄²×C₅	—	6	1	no	—
146	C₄²×C₅	—	6	1	no	—
147	#685	—	6	4	no	—
148	C₄×Dic₅	—	2	1	no	—
149	C₄×Dic₅	—	2	1	no	—
150	C₂×#168	—	2	1	no	—
151	C₂×#168	—	2	1	no	—
152	C₂×#168	—	3	2	no	—
153	C₂×#168	—	6	1	no	—
154	C₂×#168	—	6	1	no	—
155	C₂×#168	C₄×D₃	1	2	yes	—
156	#676	—	6	8	no	—
157	C₂²×M₁₆	—	15	1	no	—
158	C₂×C₂²⋊C₈	—	15	1	no	—
159	C₂×#97	—	15	1	no	—
160	C₂×C₄×C₈	—	3	1	no	—
161	C₄×C₂²⋊C₄	—	15	1	no	—
162	#336	—	5	1	no	—
163	#336	—	15	1	no	—
164	C₂²×C₃×C₅	C₂×C₄²	1	1	yes	characteristic
165	C₂²×C₃×C₅	C₄×D₄	1	1	yes	characteristic
166	C₂²×C₃×C₅	C₄×D₄	1	1	yes	characteristic
167	C₂²×C₃×C₅	C₂×M₁₆	1	2	yes	—
168	C₂²×C₃×C₅	#131	1	2	yes	—
169	C₂×D₁₅	—	2	2	no	—
170	C₂×D₁₅	—	2	2	no	—
171	C₂×D₁₅	—	2	2	no	—
172	C₂×D₁₅	—	4	2	no	—
173	C₂×D₁₅	—	4	2	no	—
174	C₃×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
175	C₃×C₄×C₅	#117	1	1	yes	characteristic
176	C₃×C₄×C₅	C₄×D₄	1	1	yes	characteristic
177	C₃×C₄×C₅	C₄×D₄	1	1	yes	characteristic
178	Dic₁₅	—	2	2	no	—
179	C₃×Dic₅	—	4	2	no	—
180	C₅×Dic₃	—	2	4	no	—
181	C₂³×D₃	—	5	1	no	—
182	C₂²×C₃×C₄	—	5	2	no	—
183	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
184	C₂²×Dic₃	—	5	1	no	—
185	C₂²×Dic₃	C₄×D₅	1	2	yes	—
186	C₂×C₄×D₃	—	5	2	no	—
187	C₂×C₄×D₃	—	5	2	no	—
188	C₂×C₄×D₃	—	10	1	no	—
189	C₂×C₄×D₃	—	10	1	no	—
190	C₂×C₄×D₃	—	10	1	no	—
191	C₂×C₄×D₃	—	10	1	no	—
192	C₂×C₃×C₈	—	2	1	no	—
193	C₂×C₃×C₈	—	2	1	no	—
194	C₂×C₃×C₈	—	5	2	no	—
195	C₂×C₃×C₈	—	10	1	no	—
196	C₂×C₃×C₈	—	10	1	no	—
197	C₂×C₃×C₈	C₄×D₅	1	2	yes	—
198	C₃×C₄²	—	10	1	no	—
199	C₃×C₄²	—	10	1	no	—
200	(C₂×D₃)⋊C₄	—	10	4	no	—
201	C₄×Dic₃	—	2	1	no	—
202	C₄×Dic₃	—	2	1	no	—
203	C₂×C₃⋊C₈	—	5	2	no	—
204	C₂×C₃⋊C₈	—	10	1	no	—
205	C₂×C₃⋊C₈	—	10	1	no	—
206	C₂×C₃⋊C₈	C₄×D₅	1	2	yes	—
207	C₂×C₃⋊C₈	D₂₀	1	2	yes	—
208	C₂×C₃⋊C₈	C₂²⋊D₅	1	2	yes	—
209	ΓL(1,𝔽₂₅)	—	10	8	no	—
210	C₂³×C₅	C₂×C₄×D₃	1	1	yes	characteristic
211	C₂²×D₅	—	3	2	no	—
212	C₂²×D₅	—	6	1	no	—
213	C₂²×D₅	—	6	1	no	—
214	C₂²×D₅	—	6	2	no	—
215	C₂²×D₅	—	6	2	no	—
216	C₂×C₄×C₅	—	3	4	no	—
217	C₂×C₄×C₅	—	6	2	no	—
218	C₂×C₄×C₅	—	6	2	no	—
219	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
220	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
221	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
222	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
223	C₂×C₄×C₅	#237	1	1	yes	characteristic
224	C₂×C₄×C₅	#239	1	1	yes	characteristic
225	C₂×Dic₅	—	2	2	no	—
226	C₂×Dic₅	—	2	2	no	—
227	C₂×Dic₅	—	2	2	no	—
228	C₂×Dic₅	—	3	2	no	—
229	C₂×Dic₅	—	6	1	no	—
230	C₂×Dic₅	—	6	1	no	—
231	C₄×D₅	—	6	2	no	—
232	C₄×D₅	—	6	2	no	—
233	C₄×D₅	—	6	2	no	—
234	C₄×D₅	—	6	2	no	—
235	C₅×C₈	—	2	2	no	—
236	C₅×C₈	—	3	4	no	—
237	#168	—	2	2	no	—
238	#168	—	6	2	no	—
239	C₂³×C₄	—	15	1	no	—
240	C₂×M₁₆	—	15	4	no	—
241	C₂×M₁₆	—	30	2	no	—
242	C₂×M₁₆	—	30	2	no	—
243	C₂²×C₈	—	3	1	no	—
244	C₂²×C₈	—	5	1	no	—
245	C₂²×C₈	—	15	1	no	—
246	C₂²×C₈	D₃×D₅	1	1	yes	characteristic
247	C₂×C₂²⋊C₄	—	15	2	no	—
248	C₂×C₄²	—	3	1	no	—
249	C₂×C₄²	—	5	1	no	—
250	C₂²⋊C₈	—	15	4	no	—
251	#97	—	30	2	no	—
252	C₄×C₈	—	6	2	no	—
253	#95	—	15	2	no	—
254	C₂×C₃×C₅	C₄×C₂²⋊C₄	1	1	yes	characteristic
255	C₂×C₃×C₅	C₄×M₁₆	1	1	yes	characteristic
256	C₂×C₃×C₅	#405	1	1	yes	characteristic
257	C₂×C₃×C₅	#435	1	2	yes	—
258	C₂×C₃×C₅	#436	1	2	yes	—
259	D₁₅	—	4	2	no	—
260	C₂³×C₃	C₂×C₄×D₅	1	1	yes	characteristic
261	C₂²×D₃	—	5	2	no	—
262	C₂²×D₃	—	10	1	no	—
263	C₂²×D₃	—	10	2	no	—
264	C₂²×D₃	—	10	2	no	—
265	C₂²×D₃	—	10	1	no	—
266	C₂×C₃×C₄	—	10	2	no	—
267	C₂×C₃×C₄	—	10	2	no	—
268	C₂×C₃×C₄	—	10	2	no	—
269	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
270	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
271	C₂×C₃×C₄	C₂×D₂₀	1	1	yes	characteristic
272	C₂×C₃×C₄	#709	1	1	yes	characteristic
273	C₂×C₃×C₄	#709	1	1	yes	characteristic
274	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
275	C₂×Dic₃	—	2	2	no	—
276	C₂×Dic₃	—	2	2	no	—
277	C₂×Dic₃	—	5	2	no	—
278	C₂×Dic₃	—	10	1	no	—
279	C₂×Dic₃	—	10	1	no	—
280	C₂×Dic₃	#676	1	4	yes	complemented
281	C₄×D₃	—	10	2	no	—
282	C₄×D₃	—	10	2	no	—
283	C₄×D₃	—	10	2	no	—
284	C₄×D₃	—	10	2	no	—
285	C₃×C₈	—	2	2	no	—
286	C₃×C₈	—	10	2	no	—
287	C₃⋊C₈	—	10	2	no	—
288	C₃⋊C₈	#685	1	4	yes	complemented
289	C₂²×C₅	C₄²×D₃	1	1	yes	characteristic
290	C₂²×C₅	#67⋊C₄	1	1	yes	characteristic
291	C₂²×C₅	#893	1	1	yes	characteristic
292	C₂²×C₅	#901	1	2	yes	—
293	C₂²×C₅	D₃×M₁₆	1	2	yes	—
294	C₂×D₅	—	6	2	no	—
295	C₂×D₅	—	6	2	no	—
296	C₂×D₅	—	6	2	no	—
297	C₂×D₅	—	12	2	no	—
298	C₂×D₅	—	12	2	no	—
299	C₄×C₅	—	6	4	no	—
300	C₄×C₅	D₃×C₂²⋊C₄	1	1	yes	characteristic
301	C₄×C₅	#67⋊C₄	1	1	yes	characteristic
302	C₄×C₅	#892	1	1	yes	characteristic
303	C₄×C₅	#893	1	1	yes	characteristic
304	Dic₅	—	4	2	no	—
305	Dic₅	—	6	2	no	—
306	C₂⁴	—	15	1	no	—
307	C₂²×C₄	—	3	2	no	—
308	C₂²×C₄	—	5	2	no	—
309	C₂²×C₄	—	15	1	no	—
310	C₂²×C₄	—	15	2	no	—
311	C₂²×C₄	—	15	2	no	—
312	C₂²×C₄	—	30	1	no	—
313	C₂²×C₄	—	30	1	no	—
314	C₂²×C₄	—	30	1	no	—
315	C₂²×C₄	—	30	1	no	—
316	C₂²×C₄	C₂×D₃×D₅	1	1	yes	characteristic
317	M₁₆	—	30	8	no	—
318	C₂×C₈	—	2	1	no	—
319	C₂×C₈	—	2	1	no	—
320	C₂×C₈	—	3	2	no	—
321	C₂×C₈	—	3	2	no	—
322	C₂×C₈	—	3	2	no	—
323	C₂×C₈	—	5	2	no	—
324	C₂×C₈	—	10	1	no	—
325	C₂×C₈	—	10	1	no	—
326	C₂×C₈	—	15	2	no	—
327	C₂×C₈	—	30	1	no	—
328	C₂×C₈	—	30	1	no	—
329	C₂×C₈	#1200	1	2	yes	—
330	C₂²⋊C₄	—	30	4	no	—
331	C₄²	—	6	1	no	—
332	C₄²	—	6	1	no	—
333	C₄²	—	10	1	no	—
334	C₄²	—	10	1	no	—
335	C₃×C₅	#1753	1	1	yes	characteristic, complemented, Hall
336	C₂²×C₃	C₄²×D₅	1	1	yes	characteristic
337	C₂²×C₃	C₄×D₂₀	1	1	yes	characteristic
338	C₂²×C₃	C₂×#676	1	2	yes	—
339	C₂²×C₃	#4047	1	2	yes	—
340	C₂²×C₃	C₄×C₂²⋊D₅	1	1	yes	characteristic
341	C₂×D₃	—	10	2	no	—
342	C₂×D₃	—	10	2	no	—
343	C₂×D₃	—	10	2	no	—
344	C₂×D₃	—	20	2	no	—
345	C₂×D₃	—	20	2	no	—
346	C₃×C₄	—	20	2	no	—
347	C₃×C₄	#4018	1	1	yes	characteristic
348	C₃×C₄	C₄×D₂₀	1	1	yes	characteristic
349	C₃×C₄	C₂×#685	1	1	yes	characteristic
350	C₃×C₄	C₄×C₂²⋊D₅	1	1	yes	characteristic
351	Dic₃	—	2	4	no	—
352	Dic₃	—	10	2	no	—
353	C₂×C₅	#4666	1	1	yes	characteristic
354	C₂×C₅	#4689	1	1	yes	characteristic
355	C₂×C₅	#4707	1	1	yes	characteristic
356	C₂×C₅	#4729	1	2	yes	—
357	C₂×C₅	#4836	1	2	yes	—
358	D₅	—	12	2	no	—
359	C₂³	—	15	2	no	—
360	C₂³	—	30	1	no	—
361	C₂³	—	30	1	no	—
362	C₂³	—	30	2	no	—
363	C₂³	—	30	2	no	—
364	C₂³	C₄×D₃×D₅	1	1	yes	characteristic
365	C₂×C₄	—	3	4	no	—
366	C₂×C₄	—	6	2	no	—
367	C₂×C₄	—	6	2	no	—
368	C₂×C₄	—	10	2	no	—
369	C₂×C₄	—	10	2	no	—
370	C₂×C₄	—	10	2	no	—
371	C₂×C₄	—	15	2	no	—
372	C₂×C₄	—	30	1	no	—
373	C₂×C₄	—	30	1	no	—
374	C₂×C₄	—	30	2	no	—
375	C₂×C₄	—	30	2	no	—
376	C₂×C₄	—	30	2	no	—
377	C₂×C₄	—	30	2	no	—
378	C₂×C₄	#6769	1	1	yes	characteristic
379	C₂×C₄	C₄×D₃×D₅	1	1	yes	characteristic
380	C₂×C₄	D₃×D₂₀	1	1	yes	characteristic
381	C₂×C₄	#6779	1	1	yes	characteristic
382	C₂×C₄	C₂×#1200	1	1	yes	characteristic
383	C₂×C₄	D₃×C₂²⋊D₅	1	1	yes	characteristic
384	C₈	—	2	2	no	—
385	C₈	—	3	4	no	—
386	C₈	—	10	2	no	—
387	C₈	—	30	2	no	—
388	C₂×C₃	C₄×#676	1	1	yes	characteristic
389	C₂×C₃	#64977	1	2	yes	—
390	C₂×C₃	#64978	1	1	yes	characteristic
391	C₂×C₃	C₄×#685	1	1	yes	characteristic
392	C₂×C₃	#65400	1	2	yes	—
393	D₃	—	20	2	no	—
394	C₅	#68650	1	1	yes	characteristic, complemented, Sylow
395	C₂²	—	30	2	no	—
396	C₂²	—	30	2	no	—
397	C₂²	—	30	2	no	—
398	C₂²	—	60	2	no	—
399	C₂²	—	60	2	no	—
400	C₂²	D₃×#676	1	2	yes	—
401	C₂²	#91265	1	2	yes	—
402	C₂²	#91395	1	1	yes	characteristic
403	C₂²	C₄×#1200	1	1	yes	characteristic
404	C₂²	#91446	1	1	yes	characteristic
405	C₄	—	6	4	no	—
406	C₄	—	20	2	no	—
407	C₄	—	30	2	no	—
408	C₄	#91403	1	1	yes	characteristic
409	C₄	#91428	1	1	yes	characteristic
410	C₄	D₃×#685	1	1	yes	characteristic
411	C₄	#91556	1	1	yes	characteristic
412	C₃	#10600574	1	1	yes	characteristic, complemented, Sylow
413	C₂	—	60	2	no	—
414	C₂	#11747599	1	1	yes	characteristic
415	C₂	#11747657	1	1	yes	characteristic
416	C₂	#11747716	1	2	yes	—
417	C₂	#11747720	1	2	yes	—
418	C₂	#11748881	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂×D₃×D₅
commutator	C₂²×C₃×C₅	C₂×C₄²
Fitting	C₂²×C₃×C₅×C₈	C₂²
socle	C₂³×C₃×C₅	C₂²×C₄
prime radical	C₂³×D₁₅	C₂×C₄
cosocle	C₂²×C₃×C₄×C₅	C₂³
hypercenter	C₂²×C₈	D₃×D₅
hypocenter	C₃×C₅	#1753
LCS	G ▷ C₂²×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂²×C₄ ◁ C₂²×C₈

Complements

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

N	H ≅ G/N	type
3. C₂×C₅×C₈×Dic₃	C₂	semidirect
5. C₂×#90952	C₂	semidirect
6. C₃×#64770	C₂	semidirect
7. #11745967	C₂	semidirect
19. C₂×#6651	C₄	semidirect
20. #91104	C₄	semidirect
30. #64770	D₃	semidirect
63. C₂×C₈×Dic₃	D₅	semidirect
105. C₂×C₅×Dic₃	M₁₆	semidirect
112. C₅×C₃⋊C₈	C₂²⋊C₄	semidirect
280. C₂×Dic₃	#676	semidirect
288. C₃⋊C₈	#685	semidirect
335. C₃×C₅	#1753	semidirect
394. C₅	#68650	semidirect
412. C₃	#10600574	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#6651	2
C₂×#91104	2
C₂×C₅×C₈×Dic₃	2
C₄×#6667	2
C₂×#90952	2
C₃×#64770	2
#11745967	2
#10600574	3
#68650	5