Subgroups — #14295060

Order 1920.

824 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×#1200	C₂	1	1	yes	maximal, characteristic
2	C₂×#91104	C₂	1	1	yes	maximal, characteristic
3	C₂×C₅×#815	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#90957	C₂	1	1	yes	maximal, characteristic
5	C₂×#90953	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#64770	C₂	1	1	yes	maximal, characteristic, complemented
7	#11745966	C₂	1	1	yes	maximal, characteristic, complemented
8	#10600600	—	3	1	no	maximal, Hall
9	C₂²×C₄×D₁₅	C₂²	1	1	yes	characteristic
10	C₂²×#1200	C₄	1	2	yes	—
11	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
12	C₂²×C₃⋊#168	C₂²	1	1	yes	characteristic
13	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
14	C₂²×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
15	C₂×C₃×C₄×Dic₅	C₂²	1	1	yes	characteristic
16	C₂²×C₃×#168	C₂²	1	1	yes	characteristic
17	C₂×Dic₃×Dic₅	C₄	1	2	yes	—
18	C₄×#1200	—	2	2	no	—
19	C₄×#1200	—	2	2	no	—
20	#91104	C₄	1	4	yes	complemented
21	C₅×#815	—	2	2	no	—
22	#90957	C₄	1	4	yes	complemented
23	#90953	—	2	2	no	—
24	#68600	—	5	1	no	maximal, Hall
25	C₂×C₄²×D₅	—	3	1	no	—
26	C₂×C₅×#97	—	3	1	no	—
27	C₂×#3952	—	3	1	no	—
28	C₂×#3952	—	3	1	no	—
29	C₂×#3935	—	3	1	no	—
30	#64770	—	3	1	no	—
31	#64770	D₃	1	1	yes	characteristic, complemented
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×#1200	—	2	4	no	—
44	C₂×#1200	—	2	4	no	—
45	C₂×#1200	—	2	4	no	—
46	C₂×C₃×C₅×C₈	—	2	1	no	—
47	C₂×C₃×C₅×C₈	—	2	1	no	—
48	C₂×C₃×C₅×C₈	C₂×C₄	1	2	yes	complemented
49	C₂×C₃⋊#168	—	2	1	no	—
50	C₂×C₃⋊#168	—	2	1	no	—
51	C₂×C₃⋊#168	C₂×C₄	1	2	yes	complemented
52	C₄×C₅×Dic₃	D₄	1	2	yes	—
53	C₄×C₅×Dic₃	D₄	1	2	yes	—
54	C₂×C₅×C₃⋊C₈	—	2	1	no	—
55	C₂×C₅×C₃⋊C₈	—	2	1	no	—
56	C₂×C₅×C₃⋊C₈	C₂×C₄	1	2	yes	complemented
57	C₃×C₄×Dic₅	—	2	1	no	—
58	C₃×C₄×Dic₅	—	2	1	no	—
59	C₂×C₃×#168	—	2	1	no	—
60	C₂×C₃×#168	—	2	1	no	—
61	C₂×C₃×#168	C₂×C₄	1	2	yes	complemented
62	Dic₃×Dic₅	—	2	4	no	—
63	C₂×C₄²×D₃	—	5	1	no	—
64	C₂×(C₂×D₃)⋊C₈	—	5	1	no	—
65	C₂×(C₂×D₃)⋊C₈	—	5	1	no	—
66	C₂×#815	—	5	1	no	—
67	C₂×#815	D₅	1	1	yes	characteristic, complemented
68	C₃×#336	—	5	1	no	—
69	#4524	—	5	1	no	—
70	C₂²×C₄×D₅	—	3	1	no	—
71	C₂²×C₄×D₅	—	3	2	no	—
72	C₂²×C₅×C₈	—	3	1	no	—
73	C₂²×C₅×C₈	C₂×D₃	1	1	yes	characteristic
74	C₂×C₄²×C₅	—	3	1	no	—
75	C₂×C₄×Dic₅	—	3	2	no	—
76	C₂×C₄×Dic₅	C₂×D₃	1	1	yes	characteristic
77	C₂²×#168	—	3	1	no	—
78	C₂²×#168	C₂×D₃	1	1	yes	characteristic
79	C₄²×D₅	—	6	2	no	—
80	C₄²×D₅	—	6	2	no	—
81	C₅×#97	—	6	2	no	—
82	#3952	—	3	4	no	—
83	#3952	—	3	4	no	—
84	#3935	—	6	2	no	—
85	#1749	—	15	1	no	Sylow
86	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
87	C₂²×D₁₅	—	2	1	no	—
88	C₂²×D₁₅	—	2	1	no	—
89	C₂²×D₁₅	—	2	2	no	—
90	C₂²×D₁₅	C₄²	1	2	yes	—
91	C₂²×D₁₅	M₁₆	1	4	yes	—
92	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
93	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
94	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
95	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
96	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
97	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
98	C₂×Dic₁₅	—	2	1	no	—
99	C₂×Dic₁₅	—	2	1	no	—
100	C₂×Dic₁₅	C₄²	1	2	yes	—
101	C₄×D₁₅	—	2	2	no	—
102	C₄×D₁₅	—	2	2	no	—
103	C₄×D₁₅	—	2	2	no	—
104	C₄×D₁₅	—	2	2	no	—
105	C₂×C₅×Dic₃	—	2	2	no	—
106	C₂×C₅×Dic₃	—	2	2	no	—
107	C₂×C₅×Dic₃	C₂²⋊C₄	1	4	yes	—
108	C₂×C₃×Dic₅	—	2	2	no	—
109	C₂×C₃×Dic₅	—	2	2	no	—
110	C₂×C₃×Dic₅	M₁₆	1	4	yes	—
111	#1200	—	2	16	no	—
112	C₃×C₅×C₈	—	2	2	no	—
113	C₃⋊#168	—	2	2	no	—
114	C₃×#168	—	2	2	no	—
115	C₅×C₃⋊C₈	—	2	2	no	—
116	C₂²×C₄×D₃	—	5	1	no	—
117	C₂²×C₄×D₃	—	5	2	no	—
118	C₂²×C₃×C₈	—	5	1	no	—
119	C₂²×C₃×C₈	C₂×D₅	1	1	yes	characteristic
120	C₂×C₃×C₄²	—	5	1	no	—
121	C₂×C₄×Dic₃	—	5	2	no	—
122	C₂×C₄×Dic₃	C₂×D₅	1	1	yes	characteristic
123	C₂²×C₃⋊C₈	—	5	1	no	—
124	C₂²×C₃⋊C₈	C₂×D₅	1	1	yes	characteristic
125	C₄²×D₃	—	10	2	no	—
126	C₄²×D₃	—	10	2	no	—
127	(C₂×D₃)⋊C₈	—	5	4	no	—
128	(C₂×D₃)⋊C₈	—	5	4	no	—
129	#815	—	2	2	no	—
130	#815	—	10	2	no	—
131	C₂³×D₅	—	3	1	no	—
132	C₂²×C₄×C₅	—	3	2	no	—
133	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
134	C₂²×Dic₅	—	3	1	no	—
135	C₂²×Dic₅	C₄×D₃	1	2	yes	—
136	C₂×C₄×D₅	—	3	2	no	—
137	C₂×C₄×D₅	—	3	2	no	—
138	C₂×C₄×D₅	—	6	4	no	—
139	C₂×C₄×D₅	—	6	4	no	—
140	C₂×C₄×D₅	—	6	1	no	—
141	C₂×C₄×D₅	—	6	1	no	—
142	C₂×C₄×D₅	—	6	1	no	—
143	C₂×C₄×D₅	—	6	1	no	—
144	C₂×C₄×D₅	—	6	4	no	—
145	C₂×C₅×C₈	—	2	1	no	—
146	C₂×C₅×C₈	—	2	1	no	—
147	C₂×C₅×C₈	—	3	2	no	—
148	C₂×C₅×C₈	—	6	1	no	—
149	C₂×C₅×C₈	—	6	1	no	—
150	C₂×C₅×C₈	C₄×D₃	1	2	yes	complemented
151	C₄²×C₅	—	3	2	no	—
152	C₄²×C₅	—	3	2	no	—
153	C₄×Dic₅	—	2	1	no	—
154	C₄×Dic₅	—	2	1	no	—
155	C₄×Dic₅	—	6	4	no	—
156	C₂×#168	—	2	1	no	—
157	C₂×#168	—	2	1	no	—
158	C₂×#168	—	3	2	no	—
159	C₂×#168	—	6	1	no	—
160	C₂×#168	—	6	1	no	—
161	C₂×#168	C₄×D₃	1	2	yes	complemented
162	C₂²×C₄²	—	15	1	no	—
163	C₂×C₂²⋊C₈	—	15	1	no	—
164	C₂×C₂²⋊C₈	—	15	1	no	—
165	C₂×#97	—	3	1	no	—
166	C₂×#97	—	15	1	no	—
167	#336	—	5	1	no	—
168	#336	—	15	1	no	—
169	C₂²×C₃×C₅	C₂×C₄²	1	1	yes	characteristic
170	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
171	C₂²×C₃×C₅	#117	1	1	yes	characteristic
172	C₂²×C₃×C₅	C₂×M₁₆	1	2	yes	—
173	C₂²×C₃×C₅	C₂×M₁₆	1	2	yes	—
174	C₂×D₁₅	—	2	2	no	—
175	C₂×D₁₅	—	2	2	no	—
176	C₂×D₁₅	—	2	4	no	—
177	C₂×D₁₅	—	2	4	no	—
178	C₂×D₁₅	#97	1	4	yes	complemented
179	C₃×C₄×C₅	C₄×D₄	1	1	yes	characteristic
180	C₃×C₄×C₅	C₄×D₄	1	1	yes	characteristic
181	C₃×C₄×C₅	C₄×D₄	1	1	yes	characteristic
182	C₃×C₄×C₅	C₄×D₄	1	1	yes	characteristic
183	Dic₁₅	—	2	2	no	—
184	C₃×Dic₅	—	2	4	no	—
185	C₅×Dic₃	—	2	4	no	—
186	C₂³×D₃	—	5	1	no	—
187	C₂²×C₃×C₄	—	5	2	no	—
188	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
189	C₂²×Dic₃	—	5	1	no	—
190	C₂²×Dic₃	C₄×D₅	1	2	yes	—
191	C₂×C₄×D₃	—	5	2	no	—
192	C₂×C₄×D₃	—	5	2	no	—
193	C₂×C₄×D₃	—	10	4	no	—
194	C₂×C₄×D₃	—	10	4	no	—
195	C₂×C₄×D₃	—	10	1	no	—
196	C₂×C₄×D₃	—	10	1	no	—
197	C₂×C₄×D₃	—	10	1	no	—
198	C₂×C₄×D₃	—	10	1	no	—
199	C₂×C₄×D₃	—	10	4	no	—
200	C₂×C₃×C₈	—	2	1	no	—
201	C₂×C₃×C₈	—	2	1	no	—
202	C₂×C₃×C₈	—	5	2	no	—
203	C₂×C₃×C₈	—	10	1	no	—
204	C₂×C₃×C₈	—	10	1	no	—
205	C₂×C₃×C₈	C₄×D₅	1	2	yes	complemented
206	C₃×C₄²	—	10	1	no	—
207	C₃×C₄²	—	10	1	no	—
208	C₄×Dic₃	—	10	4	no	—
209	C₄×Dic₃	D₂₀	1	2	yes	—
210	C₄×Dic₃	C₂²⋊D₅	1	2	yes	—
211	C₂×C₃⋊C₈	—	2	1	no	—
212	C₂×C₃⋊C₈	—	2	1	no	—
213	C₂×C₃⋊C₈	—	5	2	no	—
214	C₂×C₃⋊C₈	—	10	1	no	—
215	C₂×C₃⋊C₈	—	10	1	no	—
216	C₂×C₃⋊C₈	C₄×D₅	1	2	yes	complemented
217	C₂³×C₅	C₂×C₄×D₃	1	1	yes	characteristic
218	C₂²×D₅	—	3	2	no	—
219	C₂²×D₅	—	3	4	no	—
220	C₂²×D₅	—	6	1	no	—
221	C₂²×D₅	—	6	1	no	—
222	C₂²×D₅	—	6	2	no	—
223	C₂×C₄×C₅	—	3	4	no	—
224	C₂×C₄×C₅	—	6	2	no	—
225	C₂×C₄×C₅	—	6	2	no	—
226	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
227	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
228	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
229	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
230	C₂×C₄×C₅	#237	1	1	yes	characteristic
231	C₂×C₄×C₅	#239	1	1	yes	characteristic
232	C₂×Dic₅	—	2	2	no	—
233	C₂×Dic₅	—	2	2	no	—
234	C₂×Dic₅	—	3	2	no	—
235	C₂×Dic₅	—	6	1	no	—
236	C₂×Dic₅	—	6	1	no	—
237	C₂×Dic₅	ΓL(1,𝔽₂₅)	1	4	yes	—
238	C₄×D₅	—	6	16	no	—
239	C₄×D₅	—	6	2	no	—
240	C₄×D₅	—	6	2	no	—
241	C₄×D₅	—	6	2	no	—
242	C₄×D₅	—	6	2	no	—
243	C₅×C₈	—	2	2	no	—
244	C₅×C₈	—	6	2	no	—
245	#168	—	2	2	no	—
246	#168	—	6	2	no	—
247	C₂³×C₄	—	15	2	no	—
248	C₂³×C₄	—	15	1	no	—
249	C₂²×C₈	—	3	1	no	—
250	C₂²×C₈	—	5	1	no	—
251	C₂²×C₈	—	15	1	no	—
252	C₂²×C₈	D₃×D₅	1	1	yes	characteristic
253	C₂×C₄²	—	3	1	no	—
254	C₂×C₄²	—	5	1	no	—
255	C₂×C₄²	—	15	2	no	—
256	C₂×C₄²	—	30	2	no	—
257	C₂×C₄²	—	30	2	no	—
258	C₂²⋊C₈	—	15	4	no	—
259	C₂²⋊C₈	—	15	4	no	—
260	#97	—	6	2	no	—
261	#97	—	30	2	no	—
262	C₂×C₃×C₅	C₄×C₂²⋊C₄	1	1	yes	characteristic
263	C₂×C₃×C₅	C₂×#97	1	1	yes	characteristic
264	C₂×C₃×C₅	C₄×M₁₆	1	1	yes	characteristic
265	C₂×C₃×C₅	#407	1	2	yes	—
266	C₂×C₃×C₅	#432	1	2	yes	—
267	D₁₅	—	2	4	no	—
268	C₂³×C₃	C₂×C₄×D₅	1	1	yes	characteristic
269	C₂²×D₃	—	5	2	no	—
270	C₂²×D₃	—	5	4	no	—
271	C₂²×D₃	—	10	1	no	—
272	C₂²×D₃	—	10	2	no	—
273	C₂²×D₃	—	10	1	no	—
274	C₂×C₃×C₄	—	5	4	no	—
275	C₂×C₃×C₄	—	10	2	no	—
276	C₂×C₃×C₄	—	10	2	no	—
277	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
278	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
279	C₂×C₃×C₄	C₂×D₂₀	1	1	yes	characteristic
280	C₂×C₃×C₄	#709	1	1	yes	characteristic
281	C₂×C₃×C₄	#709	1	1	yes	characteristic
282	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
283	C₂×Dic₃	—	2	2	no	—
284	C₂×Dic₃	—	2	2	no	—
285	C₂×Dic₃	—	5	2	no	—
286	C₂×Dic₃	—	10	1	no	—
287	C₂×Dic₃	—	10	1	no	—
288	C₂×Dic₃	#685	1	4	yes	—
289	C₄×D₃	—	10	16	no	—
290	C₄×D₃	—	10	2	no	—
291	C₄×D₃	—	10	2	no	—
292	C₄×D₃	—	10	2	no	—
293	C₄×D₃	—	10	2	no	—
294	C₃×C₈	—	2	2	no	—
295	C₃×C₈	—	10	2	no	—
296	C₃⋊C₈	—	2	2	no	—
297	C₃⋊C₈	—	10	2	no	—
298	C₂²×C₅	C₄²×D₃	1	1	yes	characteristic
299	C₂²×C₅	D₃×C₂²⋊C₄	1	1	yes	characteristic
300	C₂²×C₅	#892	1	1	yes	characteristic
301	C₂²×C₅	C₂×ΓL(1,𝔽₂₅)	1	2	yes	—
302	C₂²×C₅	D₃×M₁₆	1	2	yes	—
303	C₂×D₅	—	3	4	no	—
304	C₂×D₅	—	6	2	no	—
305	C₂×D₅	—	6	2	no	—
306	C₂×D₅	—	6	4	no	—
307	C₂×D₅	—	6	4	no	—
308	C₄×C₅	—	6	4	no	—
309	C₄×C₅	#67⋊C₄	1	1	yes	characteristic
310	C₄×C₅	#67⋊C₄	1	1	yes	characteristic
311	C₄×C₅	#893	1	1	yes	characteristic
312	C₄×C₅	#893	1	1	yes	characteristic
313	Dic₅	—	2	4	no	—
314	Dic₅	—	6	2	no	—
315	C₂⁴	—	15	1	no	—
316	C₂²×C₄	—	3	2	no	—
317	C₂²×C₄	—	5	2	no	—
318	C₂²×C₄	—	15	1	no	—
319	C₂²×C₄	—	15	2	no	—
320	C₂²×C₄	—	15	2	no	—
321	C₂²×C₄	—	30	4	no	—
322	C₂²×C₄	—	30	4	no	—
323	C₂²×C₄	—	30	4	no	—
324	C₂²×C₄	—	30	1	no	—
325	C₂²×C₄	—	30	1	no	—
326	C₂²×C₄	—	30	1	no	—
327	C₂²×C₄	—	30	1	no	—
328	C₂²×C₄	C₂×D₃×D₅	1	1	yes	characteristic
329	C₂×C₈	—	2	1	no	—
330	C₂×C₈	—	2	1	no	—
331	C₂×C₈	—	3	2	no	—
332	C₂×C₈	—	5	2	no	—
333	C₂×C₈	—	6	1	no	—
334	C₂×C₈	—	6	1	no	—
335	C₂×C₈	—	10	1	no	—
336	C₂×C₈	—	10	1	no	—
337	C₂×C₈	—	15	2	no	—
338	C₂×C₈	—	30	1	no	—
339	C₂×C₈	—	30	1	no	—
340	C₂×C₈	#1200	1	2	yes	complemented
341	C₄²	—	3	2	no	—
342	C₄²	—	3	2	no	—
343	C₄²	—	10	1	no	—
344	C₄²	—	10	1	no	—
345	C₄²	—	30	4	no	—
346	C₃×C₅	#1749	1	1	yes	characteristic, complemented, Hall
347	C₂²×C₃	C₄²×D₅	1	1	yes	characteristic
348	C₂²×C₃	#4018	1	1	yes	characteristic
349	C₂²×C₃	D₅×M₁₆	1	2	yes	—
350	C₂²×C₃	D₅×M₁₆	1	2	yes	—
351	C₂²×C₃	C₂×#685	1	1	yes	characteristic
352	C₂×D₃	—	5	4	no	—
353	C₂×D₃	—	10	4	no	—
354	C₂×D₃	—	10	2	no	—
355	C₂×D₃	—	10	4	no	—
356	C₂×D₃	—	10	2	no	—
357	C₃×C₄	—	10	4	no	—
358	C₃×C₄	C₄×D₂₀	1	1	yes	characteristic
359	C₃×C₄	C₄×D₂₀	1	1	yes	characteristic
360	C₃×C₄	C₄×C₂²⋊D₅	1	1	yes	characteristic
361	C₃×C₄	C₄×C₂²⋊D₅	1	1	yes	characteristic
362	Dic₃	—	2	4	no	—
363	Dic₃	—	10	2	no	—
364	C₂×C₅	#4666	1	1	yes	characteristic
365	C₂×C₅	C₄×ΓL(1,𝔽₂₅)	1	1	yes	characteristic
366	C₂×C₅	D₃×#97	1	1	yes	characteristic
367	C₂×C₅	#4726	1	2	yes	—
368	C₂×C₅	#4835	1	2	yes	—
369	D₅	—	6	4	no	—
370	C₂³	—	15	2	no	—
371	C₂³	—	15	4	no	—
372	C₂³	—	30	1	no	—
373	C₂³	—	30	1	no	—
374	C₂³	—	30	2	no	—
375	C₂³	C₄×D₃×D₅	1	1	yes	characteristic
376	C₂×C₄	—	3	4	no	—
377	C₂×C₄	—	5	4	no	—
378	C₂×C₄	—	6	2	no	—
379	C₂×C₄	—	6	2	no	—
380	C₂×C₄	—	10	2	no	—
381	C₂×C₄	—	10	2	no	—
382	C₂×C₄	—	15	2	no	—
383	C₂×C₄	—	30	16	no	—
384	C₂×C₄	—	30	1	no	—
385	C₂×C₄	—	30	1	no	—
386	C₂×C₄	—	30	2	no	—
387	C₂×C₄	—	30	2	no	—
388	C₂×C₄	—	30	2	no	—
389	C₂×C₄	—	30	2	no	—
390	C₂×C₄	#6769	1	1	yes	characteristic
391	C₂×C₄	C₄×D₃×D₅	1	1	yes	characteristic
392	C₂×C₄	D₃×D₂₀	1	1	yes	characteristic
393	C₂×C₄	#6779	1	1	yes	characteristic
394	C₂×C₄	C₂×#1200	1	1	yes	characteristic
395	C₂×C₄	D₃×C₂²⋊D₅	1	1	yes	characteristic
396	C₈	—	2	2	no	—
397	C₈	—	6	2	no	—
398	C₈	—	10	2	no	—
399	C₈	—	30	2	no	—
400	C₂×C₃	D₅×#97	1	1	yes	characteristic
401	C₂×C₃	#64994	1	2	yes	—
402	C₂×C₃	#64996	1	1	yes	characteristic
403	C₂×C₃	C₄×#685	1	1	yes	characteristic
404	C₂×C₃	#65415	1	2	yes	—
405	D₃	—	10	4	no	—
406	C₅	#68600	1	1	yes	characteristic, complemented, Sylow
407	C₂²	—	15	4	no	—
408	C₂²	—	30	4	no	—
409	C₂²	—	30	2	no	—
410	C₂²	—	30	4	no	—
411	C₂²	—	30	2	no	—
412	C₂²	D₅×ΓL(1,𝔽₂₅)	1	2	yes	—
413	C₂²	#91246	1	2	yes	—
414	C₂²	C₄×#1200	1	1	yes	characteristic
415	C₂²	#91403	1	1	yes	characteristic
416	C₂²	D₃×#685	1	1	yes	characteristic
417	C₄	—	6	4	no	—
418	C₄	—	10	4	no	—
419	C₄	—	30	2	no	—
420	C₄	#91395	1	1	yes	characteristic
421	C₄	#91428	1	1	yes	characteristic
422	C₄	#91446	1	1	yes	characteristic
423	C₄	#91556	1	1	yes	characteristic
424	C₃	#10600600	1	1	yes	characteristic, complemented, Sylow
425	C₂	—	30	4	no	—
426	C₂	#11747592	1	1	yes	characteristic
427	C₂	#11747593	1	2	yes	—
428	C₂	#11747603	1	1	yes	characteristic
429	C₂	#11748102	1	2	yes	—
430	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	#1749
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×#815	C₂	semidirect
5. C₂×#90953	C₂	semidirect
6. C₃×#64770	C₂	semidirect
7. #11745966	C₂	semidirect
20. #91104	C₄	semidirect
22. #90957	C₄	semidirect
31. #64770	D₃	semidirect
48. C₂×C₃×C₅×C₈	C₂×C₄	semidirect
51. C₂×C₃⋊#168	C₂×C₄	semidirect
56. C₂×C₅×C₃⋊C₈	C₂×C₄	semidirect
61. C₂×C₃×#168	C₂×C₄	semidirect
67. C₂×#815	D₅	semidirect
150. C₂×C₅×C₈	C₄×D₃	semidirect
161. C₂×#168	C₄×D₃	semidirect
178. C₂×D₁₅	#97	semidirect
205. C₂×C₃×C₈	C₄×D₅	semidirect
216. C₂×C₃⋊C₈	C₄×D₅	semidirect
340. C₂×C₈	#1200	semidirect
346. C₃×C₅	#1749	semidirect
406. C₅	#68600	semidirect
424. C₃	#10600600	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄×#1200	2
C₂×#91104	2
C₂×C₅×#815	2
C₂×#90957	2
C₂×#90953	2
C₃×#64770	2
#11745966	2
#10600600	3
#68600	5