Subgroups — #14411415

Order 1920.

1128 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×D₃×#117	C₂	1	1	yes	maximal, characteristic
2	C₂²×#6650	C₂	1	1	yes	maximal, characteristic
3	C₂×D₃×#681	C₂	1	1	yes	maximal, characteristic
4	#11751098	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#65286	C₂	1	1	yes	maximal, characteristic, complemented
6	#11748327	C₂	1	1	yes	maximal, characteristic, complemented
7	#11748323	C₂	1	1	yes	maximal, characteristic, complemented
8	#11747005	C₂	1	2	yes	maximal, complemented
9	C₄×#6650	C₂	1	2	yes	maximal, complemented
10	#11746979	C₂	1	2	yes	maximal, complemented
11	#11746977	C₂	1	2	yes	maximal, complemented
12	#10613933	—	3	1	no	maximal, Hall
13	C₂²×C₄×C₅×D₃	C₂²	1	1	yes	characteristic
14	C₃×C₅×#117	C₂²	1	1	yes	characteristic
15	C₂×#6710	C₂²	1	1	yes	characteristic
16	C₂²×C₃⋊#168	C₂²	1	1	yes	characteristic
17	C₅×#926	C₂²	1	1	yes	characteristic
18	C₅×#892	C₄	1	2	yes	—
19	C₅×D₃×C₄⋊C₄	C₄	1	2	yes	—
20	C₅×D₃×C₂²⋊C₄	C₄	1	2	yes	—
21	C₅×#877	C₄	1	2	yes	—
22	C₅×#872	C₂²	1	2	yes	—
23	C₄²×C₅×D₃	C₂²	1	2	yes	—
24	C₂×C₃×#681	C₂²	1	1	yes	characteristic
25	C₂²×C₃×#168	C₂²	1	1	yes	characteristic
26	C₂×#6650	C₄	1	8	yes	complemented
27	C₂×#6650	C₂²	1	2	yes	—
28	C₂×#6650	C₂²	1	1	yes	characteristic
29	C₂×#6650	C₂²	1	1	yes	characteristic
30	C₂×#6650	C₂²	1	1	yes	characteristic
31	C₂×#6650	C₂²	1	1	yes	characteristic
32	D₃×#681	C₄	1	8	yes	complemented
33	C₂×D₃×#168	C₂²	1	2	yes	—
34	#91087	C₂²	1	2	yes	complemented
35	C₄×C₃⋊#168	C₂²	1	2	yes	complemented
36	C₃×#3935	C₂²	1	2	yes	complemented
37	C₃×C₄×#168	C₂²	1	2	yes	complemented
38	#90953	C₂²	1	2	yes	complemented
39	#90953	C₂²	1	2	yes	complemented
40	Dic₃×#168	C₂²	1	2	yes	complemented
41	Dic₃×#168	C₂²	1	2	yes	complemented
42	#78548	—	5	1	no	maximal, Hall
43	C₂×C₅×#117	—	3	1	no	—
44	C₂²×#681	—	3	1	no	—
45	C₂²×#681	—	3	1	no	—
46	#65286	—	3	1	no	—
47	#65286	—	3	1	no	—
48	#65286	—	3	2	no	—
49	#65286	—	3	2	no	—
50	#65286	—	3	1	no	—
51	#65286	D₃	1	1	yes	characteristic, complemented
52	C₄×#681	—	3	2	no	—
53	C₄×#681	—	3	2	no	—
54	C₂³×C₅×D₃	C₂×C₄	1	1	yes	characteristic
55	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
56	C₂²×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
57	C₂×C₄×C₅×D₃	C₂×C₄	1	4	yes	—
58	C₂×C₄×C₅×D₃	C₂×C₄	1	1	yes	characteristic
59	C₂×C₄×C₅×D₃	C₂×C₄	1	1	yes	characteristic
60	C₂×C₄×C₅×D₃	C₂×C₄	1	4	yes	—
61	C₂×C₄×C₅×D₃	C₂×C₄	1	4	yes	—
62	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
63	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
64	C₃×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
65	C₃×C₅×C₂²⋊C₄	C₂×C₄	1	2	yes	—
66	C₃×C₄²×C₅	C₂³	1	2	yes	—
67	#6710	C₂×C₄	1	4	yes	complemented
68	C₂×C₃⋊#168	C₂×C₄	1	4	yes	complemented
69	C₂×C₃⋊#168	C₂³	1	1	yes	characteristic
70	C₂×C₃⋊#168	C₂³	1	2	yes	—
71	C₂×C₃⋊#168	C₂³	1	1	yes	characteristic
72	C₅×#217	C₂×C₄	1	2	yes	—
73	C₅×(C₂×D₃)⋊C₄	C₂×C₄	1	4	yes	—
74	C₅×C₄⋊Dic₃	C₂×C₄	1	2	yes	—
75	C₅×Dic₃⋊C₄	C₂×C₄	1	4	yes	—
76	C₄×C₅×Dic₃	C₂×C₄	1	4	yes	—
77	C₄×C₅×Dic₃	C₂³	1	2	yes	—
78	C₃×#681	C₂×C₄	1	4	yes	complemented
79	C₂×C₃×#168	C₂×C₄	1	4	yes	complemented
80	C₂×C₃×#168	C₂³	1	1	yes	characteristic
81	C₂×C₃×#168	C₂³	1	2	yes	—
82	C₂×C₃×#168	C₂³	1	1	yes	characteristic
83	#6650	C₂×C₄	1	8	yes	—
84	#6650	C₂×C₄	1	4	yes	—
85	#6650	C₂×C₄	1	4	yes	—
86	#6650	C₂×C₄	1	4	yes	complemented
87	#6650	C₂×C₄	1	4	yes	complemented
88	D₃×#168	C₂×C₄	1	8	yes	complemented
89	C₂×D₃×M₁₆	—	5	1	no	—
90	C₂²×ΓL(1,𝔽₂₅)	—	5	1	no	—
91	D₃×#117	D₅	1	1	yes	characteristic
92	C₃×#405	—	5	1	no	—
93	#5122	—	5	1	no	—
94	#5101	—	5	1	no	—
95	#4997	—	5	1	no	—
96	#4708	—	5	2	no	—
97	#4707	—	5	2	no	—
98	#4689	—	5	2	no	—
99	C₄×ΓL(1,𝔽₂₅)	—	5	2	no	—
100	C₂³×C₄×C₅	—	3	1	no	—
101	C₅×#117	—	3	1	no	—
102	C₅×#117	—	3	2	no	—
103	C₅×#117	—	3	2	no	—
104	C₅×#117	—	3	2	no	—
105	C₅×#117	C₂×D₃	1	1	yes	characteristic
106	C₂×C₅×C₄⋊C₄	—	3	2	no	—
107	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
108	C₂×C₄²×C₅	—	3	2	no	—
109	C₂×#681	—	3	1	no	—
110	C₂×#681	—	3	8	no	—
111	C₂×#681	—	3	8	no	—
112	C₂×#681	—	3	1	no	—
113	C₂×#681	—	3	1	no	—
114	C₂×#681	—	3	1	no	—
115	C₂×#681	—	3	2	no	—
116	C₂×#681	—	3	1	no	—
117	C₂×#681	C₂×D₃	1	1	yes	characteristic
118	C₂²×#168	—	3	1	no	—
119	C₂²×#168	—	3	2	no	—
120	C₂²×#168	C₂×D₃	1	1	yes	characteristic
121	#3935	—	3	2	no	—
122	#3935	—	3	2	no	—
123	#3935	—	3	2	no	—
124	#3935	C₂×D₃	1	2	yes	complemented
125	C₄×#168	—	3	2	no	—
126	C₄×#168	—	3	2	no	—
127	C₄×#168	—	3	2	no	—
128	C₄×#168	C₂×D₃	1	2	yes	complemented
129	#2873	—	15	1	no	Sylow
130	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
131	C₂²×C₅×D₃	—	4	2	no	—
132	C₂²×C₅×D₃	C₄²	1	4	yes	—
133	C₂²×C₅×D₃	C₂²×C₄	1	1	yes	characteristic
134	C₂²×C₅×D₃	C₂²×C₄	1	1	yes	characteristic
135	C₂×C₃×C₄×C₅	C₂²×C₄	1	4	yes	—
136	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
137	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
138	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
139	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
140	C₂×C₅×Dic₃	C₄²	1	4	yes	—
141	C₂×C₅×Dic₃	C₂²×C₄	1	4	yes	—
142	C₂×C₅×Dic₃	C₂²×C₄	1	1	yes	characteristic
143	C₂×C₅×Dic₃	C₂²×C₄	1	1	yes	characteristic
144	C₄×C₅×D₃	—	4	4	no	—
145	C₄×C₅×D₃	C₄²	1	4	yes	—
146	C₄×C₅×D₃	C₄²	1	4	yes	—
147	C₄×C₅×D₃	C₂²×C₄	1	2	yes	—
148	C₄×C₅×D₃	C₂²×C₄	1	2	yes	—
149	C₄×C₅×D₃	C₂²×C₄	1	2	yes	—
150	C₄×C₅×D₃	C₂²×C₄	1	2	yes	—
151	C₃⋊#168	C₂²×C₄	1	2	yes	—
152	C₃⋊#168	C₂²×C₄	1	2	yes	—
153	C₃⋊#168	C₂²×C₄	1	4	yes	—
154	C₃×#168	C₂²×C₄	1	2	yes	—
155	C₃×#168	C₂²×C₄	1	2	yes	—
156	C₃×#168	C₂²×C₄	1	4	yes	—
157	C₂²×C₄×D₃	C₂×D₅	1	1	yes	characteristic
158	C₂×C₃×M₁₆	—	5	1	no	—
159	C₂²×C₃×C₈	—	5	1	no	—
160	C₃×#117	C₂×D₅	1	1	yes	characteristic
161	#926	C₂×D₅	1	1	yes	characteristic
162	C₂×#208	—	5	1	no	—
163	C₂²×C₃⋊C₈	—	5	1	no	—
164	D₃×M₁₆	—	5	8	no	—
165	C₂×ΓL(1,𝔽₂₅)	—	5	8	no	—
166	C₂×ΓL(1,𝔽₂₅)	—	5	1	no	—
167	C₂×ΓL(1,𝔽₂₅)	—	5	2	no	—
168	C₂×ΓL(1,𝔽₂₅)	—	5	1	no	—
169	C₂×ΓL(1,𝔽₂₅)	—	5	1	no	—
170	C₂×ΓL(1,𝔽₂₅)	—	5	1	no	—
171	C₂×D₃×C₈	—	5	2	no	—
172	#892	Dic₅	1	2	yes	—
173	D₃×C₄⋊C₄	Dic₅	1	2	yes	—
174	D₃×C₂²⋊C₄	Dic₅	1	2	yes	—
175	#877	Dic₅	1	2	yes	—
176	#872	C₂×D₅	1	2	yes	—
177	C₄²×D₃	C₂×D₅	1	2	yes	—
178	C₃×#97	—	5	2	no	—
179	C₃×C₄×C₈	—	5	2	no	—
180	#815	—	5	2	no	—
181	#815	—	5	2	no	—
182	C₈×Dic₃	—	5	2	no	—
183	C₈×Dic₃	—	5	2	no	—
184	#803	—	5	2	no	—
185	C₄×C₃⋊C₈	—	5	2	no	—
186	C₂⁴×C₅	—	3	1	no	—
187	C₂²×C₄×C₅	—	3	1	no	—
188	C₂²×C₄×C₅	—	3	1	no	—
189	C₂²×C₄×C₅	—	3	1	no	—
190	C₂²×C₄×C₅	—	3	4	no	—
191	C₂²×C₄×C₅	—	3	4	no	—
192	C₂²×C₄×C₅	—	3	1	no	—
193	C₂²×C₄×C₅	—	3	1	no	—
194	C₂²×C₄×C₅	—	3	4	no	—
195	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
196	C₅×C₄⋊C₄	—	3	4	no	—
197	C₅×C₄⋊C₄	—	3	2	no	—
198	C₅×C₄⋊C₄	C₄×D₃	1	2	yes	—
199	C₅×C₂²⋊C₄	—	3	2	no	—
200	C₅×C₂²⋊C₄	—	3	4	no	—
201	C₅×C₂²⋊C₄	C₄×D₃	1	2	yes	—
202	C₄²×C₅	—	3	4	no	—
203	C₄²×C₅	—	3	2	no	—
204	C₄²×C₅	C₂²×D₃	1	2	yes	—
205	#681	—	3	4	no	—
206	#681	—	3	8	no	—
207	#681	—	3	4	no	—
208	#681	—	3	4	no	—
209	#681	—	3	4	no	—
210	#681	—	3	4	no	—
211	#681	C₄×D₃	1	4	yes	complemented
212	C₂×#168	—	3	4	no	—
213	C₂×#168	—	3	1	no	—
214	C₂×#168	—	3	2	no	—
215	C₂×#168	—	3	1	no	—
216	C₂×#168	—	3	8	no	—
217	C₂×#168	C₄×D₃	1	4	yes	complemented
218	C₂×#168	C₂²×D₃	1	1	yes	characteristic
219	C₂×#168	C₂²×D₃	1	2	yes	—
220	C₂×#168	C₂²×D₃	1	1	yes	characteristic
221	C₂²×M₁₆	—	15	1	no	—
222	C₂²×M₁₆	—	15	1	no	—
223	C₂×#117	—	3	1	no	—
224	#405	—	5	1	no	—
225	#405	—	15	2	no	—
226	#405	—	15	2	no	—
227	#405	—	15	1	no	—
228	#405	—	15	1	no	—
229	#405	—	15	1	no	—
230	C₄×M₁₆	—	15	2	no	—
231	C₄×M₁₆	—	15	2	no	—
232	C₂²×C₃×C₅	—	2	2	no	—
233	C₂²×C₃×C₅	C₂×C₄²	1	2	yes	—
234	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
235	C₂×C₅×D₃	—	2	2	no	—
236	C₂×C₅×D₃	—	2	2	no	—
237	C₂×C₅×D₃	—	4	4	no	—
238	C₂×C₅×D₃	C₂×C₄²	1	2	yes	—
239	C₂×C₅×D₃	C₂×C₄²	1	2	yes	—
240	C₃×C₄×C₅	—	2	4	no	—
241	C₃×C₄×C₅	C₂×C₄²	1	2	yes	—
242	C₃×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
243	C₃×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
244	C₅×Dic₃	—	2	4	no	—
245	C₅×Dic₃	C₂×C₄²	1	2	yes	—
246	C₅×Dic₃	C₂×C₄²	1	2	yes	—
247	C₂³×D₃	C₂×Dic₅	1	1	yes	characteristic
248	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
249	C₂²×Dic₃	C₂×Dic₅	1	1	yes	characteristic
250	C₂×C₄×D₃	C₄×D₅	1	4	yes	—
251	C₂×C₄×D₃	C₄×D₅	1	4	yes	—
252	C₂×C₄×D₃	C₂×Dic₅	1	4	yes	—
253	C₂×C₄×D₃	C₂×Dic₅	1	1	yes	characteristic
254	C₂×C₄×D₃	C₂×Dic₅	1	1	yes	characteristic
255	C₂×C₄×D₃	C₂²×D₅	1	1	yes	characteristic
256	C₂×C₄×D₃	C₂²×D₅	1	1	yes	characteristic
257	C₃×M₁₆	—	5	4	no	—
258	C₂×C₃×C₈	—	5	4	no	—
259	C₂×C₃×C₈	—	5	1	no	—
260	C₂×C₃×C₈	—	5	2	no	—
261	C₂×C₃×C₈	—	5	1	no	—
262	C₃×C₄⋊C₄	C₂×Dic₅	1	2	yes	—
263	C₃×C₂²⋊C₄	C₂×Dic₅	1	2	yes	—
264	C₃×C₄²	C₂²×D₅	1	2	yes	—
265	#217	C₂×Dic₅	1	2	yes	—
266	(C₂×D₃)⋊C₄	C₂×Dic₅	1	4	yes	—
267	C₄⋊Dic₃	C₂×Dic₅	1	2	yes	—
268	Dic₃⋊C₄	C₂×Dic₅	1	4	yes	—
269	C₄×Dic₃	C₂×Dic₅	1	4	yes	—
270	C₄×Dic₃	C₂²×D₅	1	2	yes	—
271	#208	—	5	4	no	—
272	C₂×C₃⋊C₈	—	5	4	no	—
273	C₂×C₃⋊C₈	—	5	1	no	—
274	C₂×C₃⋊C₈	—	5	2	no	—
275	C₂×C₃⋊C₈	—	5	1	no	—
276	ΓL(1,𝔽₂₅)	—	5	4	no	—
277	ΓL(1,𝔽₂₅)	—	5	4	no	—
278	ΓL(1,𝔽₂₅)	—	5	4	no	—
279	ΓL(1,𝔽₂₅)	—	5	4	no	—
280	ΓL(1,𝔽₂₅)	—	5	8	no	—
281	D₃×C₈	—	5	8	no	—
282	C₂³×C₅	—	3	1	no	—
283	C₂³×C₅	—	3	1	no	—
284	C₂³×C₅	—	3	4	no	—
285	C₂³×C₅	—	12	2	no	—
286	C₂³×C₅	C₂×C₄×D₃	1	1	yes	characteristic
287	C₂×C₄×C₅	—	3	4	no	—
288	C₂×C₄×C₅	—	3	1	no	—
289	C₂×C₄×C₅	—	3	1	no	—
290	C₂×C₄×C₅	—	3	4	no	—
291	C₂×C₄×C₅	—	3	4	no	—
292	C₂×C₄×C₅	—	3	2	no	—
293	C₂×C₄×C₅	—	3	2	no	—
294	C₂×C₄×C₅	—	3	2	no	—
295	C₂×C₄×C₅	—	3	2	no	—
296	C₂×C₄×C₅	—	3	4	no	—
297	C₂×C₄×C₅	—	12	4	no	—
298	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
299	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
300	C₂×C₄×C₅	C₂×C₄×D₃	1	4	yes	—
301	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
302	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
303	#168	—	3	2	no	—
304	#168	—	3	2	no	—
305	#168	—	3	4	no	—
306	#168	C₂×C₄×D₃	1	4	yes	—
307	#168	C₂×C₄×D₃	1	2	yes	—
308	#168	C₂×C₄×D₃	1	2	yes	—
309	C₂³×C₄	—	3	1	no	—
310	C₂×M₁₆	—	5	1	no	—
311	C₂×M₁₆	—	15	1	no	—
312	C₂×M₁₆	—	15	2	no	—
313	C₂×M₁₆	—	15	1	no	—
314	C₂×M₁₆	—	15	1	no	—
315	C₂×M₁₆	—	15	1	no	—
316	C₂×M₁₆	—	15	8	no	—
317	C₂×M₁₆	—	15	8	no	—
318	C₂×M₁₆	—	15	1	no	—
319	C₂²×C₈	—	5	1	no	—
320	C₂²×C₈	—	15	2	no	—
321	C₂²×C₈	—	15	1	no	—
322	#117	—	3	1	no	—
323	#117	—	3	2	no	—
324	#117	—	3	2	no	—
325	#117	—	3	2	no	—
326	#117	D₃×D₅	1	1	yes	characteristic
327	C₂×C₄⋊C₄	—	3	2	no	—
328	C₂×C₂²⋊C₄	—	3	2	no	—
329	C₂×C₄²	—	3	2	no	—
330	#97	—	5	2	no	—
331	#97	—	15	2	no	—
332	#97	—	15	2	no	—
333	#97	—	15	2	no	—
334	C₄×C₈	—	5	2	no	—
335	C₄×C₈	—	15	2	no	—
336	C₄×C₈	—	15	2	no	—
337	C₄×C₈	—	15	2	no	—
338	C₂×C₃×C₅	—	2	2	no	—
339	C₂×C₃×C₅	C₂²×C₄²	1	1	yes	characteristic
340	C₂×C₃×C₅	#568	1	2	yes	—
341	C₅×D₃	—	2	2	no	—
342	C₅×D₃	—	2	2	no	—
343	C₂³×C₃	C₂²×Dic₅	1	1	yes	characteristic
344	C₂²×D₃	—	4	2	no	—
345	C₂²×D₃	C₄×Dic₅	1	4	yes	—
346	C₂²×D₃	C₂²×Dic₅	1	1	yes	characteristic
347	C₂²×D₃	C₂²×Dic₅	1	1	yes	characteristic
348	C₂×C₃×C₄	C₂×C₄×D₅	1	2	yes	—
349	C₂×C₃×C₄	C₂×C₄×D₅	1	2	yes	—
350	C₂×C₃×C₄	C₂²×Dic₅	1	4	yes	—
351	C₂×C₃×C₄	C₂²×Dic₅	1	1	yes	characteristic
352	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
353	C₂×Dic₃	C₄×Dic₅	1	4	yes	—
354	C₂×Dic₃	C₂²×Dic₅	1	4	yes	—
355	C₂×Dic₃	C₂²×Dic₅	1	1	yes	characteristic
356	C₂×Dic₃	C₂²×Dic₅	1	1	yes	characteristic
357	C₄×D₃	—	4	4	no	—
358	C₄×D₃	C₄×Dic₅	1	4	yes	—
359	C₄×D₃	C₄×Dic₅	1	4	yes	—
360	C₄×D₃	C₂×C₄×D₅	1	2	yes	—
361	C₄×D₃	C₂×C₄×D₅	1	2	yes	—
362	C₄×D₃	C₂×C₄×D₅	1	2	yes	—
363	C₄×D₃	C₂×C₄×D₅	1	2	yes	—
364	C₃×C₈	—	5	4	no	—
365	C₃×C₈	—	5	2	no	—
366	C₃×C₈	—	5	2	no	—
367	C₃⋊C₈	—	5	4	no	—
368	C₃⋊C₈	—	5	2	no	—
369	C₃⋊C₈	—	5	2	no	—
370	C₂²×C₅	—	2	2	no	—
371	C₂²×C₅	—	3	2	no	—
372	C₂²×C₅	—	3	2	no	—
373	C₂²×C₅	—	6	2	no	—
374	C₂²×C₅	—	6	2	no	—
375	C₂²×C₅	—	12	4	no	—
376	C₂²×C₅	C₄²×D₃	1	2	yes	—
377	C₂²×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
378	C₄×C₅	—	2	4	no	—
379	C₄×C₅	—	3	2	no	—
380	C₄×C₅	—	3	2	no	—
381	C₄×C₅	—	6	4	no	—
382	C₄×C₅	C₄²×D₃	1	2	yes	—
383	C₄×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
384	C₄×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
385	C₂⁴	—	3	1	no	—
386	C₂²×C₄	—	3	1	no	—
387	C₂²×C₄	—	3	4	no	—
388	C₂²×C₄	—	3	4	no	—
389	C₂²×C₄	—	3	1	no	—
390	C₂²×C₄	—	3	1	no	—
391	C₂²×C₄	—	3	1	no	—
392	C₂²×C₄	—	3	1	no	—
393	C₂²×C₄	—	3	4	no	—
394	C₂²×C₄	C₂×D₃×D₅	1	1	yes	characteristic
395	M₁₆	—	5	4	no	—
396	M₁₆	—	15	4	no	—
397	M₁₆	—	15	4	no	—
398	M₁₆	—	15	4	no	—
399	M₁₆	—	15	4	no	—
400	M₁₆	—	15	8	no	—
401	M₁₆	—	15	4	no	—
402	C₂×C₈	—	5	4	no	—
403	C₂×C₈	—	5	1	no	—
404	C₂×C₈	—	5	2	no	—
405	C₂×C₈	—	5	1	no	—
406	C₂×C₈	—	15	8	no	—
407	C₂×C₈	—	15	4	no	—
408	C₂×C₈	—	15	1	no	—
409	C₂×C₈	—	15	2	no	—
410	C₂×C₈	—	15	1	no	—
411	C₄⋊C₄	—	3	4	no	—
412	C₄⋊C₄	—	3	2	no	—
413	C₄⋊C₄	D₃×Dic₅	1	2	yes	—
414	C₂²⋊C₄	—	3	2	no	—
415	C₂²⋊C₄	—	3	4	no	—
416	C₂²⋊C₄	D₃×Dic₅	1	2	yes	—
417	C₄²	—	3	4	no	—
418	C₄²	—	3	2	no	—
419	C₄²	C₂×D₃×D₅	1	2	yes	—
420	C₃×C₅	#2873	1	1	yes	characteristic, complemented, Hall
421	C₂²×C₃	—	2	2	no	—
422	C₂²×C₃	C₂×C₄×Dic₅	1	2	yes	—
423	C₂²×C₃	C₂³×Dic₅	1	1	yes	characteristic
424	C₂×D₃	—	2	2	no	—
425	C₂×D₃	—	2	2	no	—
426	C₂×D₃	—	4	4	no	—
427	C₂×D₃	C₂×C₄×Dic₅	1	2	yes	—
428	C₂×D₃	C₂×C₄×Dic₅	1	2	yes	—
429	C₃×C₄	—	2	4	no	—
430	C₃×C₄	C₂×C₄×Dic₅	1	2	yes	—
431	C₃×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
432	C₃×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
433	Dic₃	—	2	4	no	—
434	Dic₃	C₂×C₄×Dic₅	1	2	yes	—
435	Dic₃	C₂×C₄×Dic₅	1	2	yes	—
436	C₂×C₅	—	2	2	no	—
437	C₂×C₅	—	6	2	no	—
438	C₂×C₅	—	6	2	no	—
439	C₂×C₅	C₂×C₄²×D₃	1	1	yes	characteristic
440	C₂×C₅	#5750	1	2	yes	—
441	C₂³	—	3	1	no	—
442	C₂³	—	3	1	no	—
443	C₂³	—	3	4	no	—
444	C₂³	—	12	2	no	—
445	C₂³	C₂×D₃×Dic₅	1	1	yes	characteristic
446	C₂×C₄	—	3	4	no	—
447	C₂×C₄	—	3	1	no	—
448	C₂×C₄	—	3	1	no	—
449	C₂×C₄	—	3	4	no	—
450	C₂×C₄	—	3	4	no	—
451	C₂×C₄	—	3	2	no	—
452	C₂×C₄	—	3	2	no	—
453	C₂×C₄	—	3	2	no	—
454	C₂×C₄	—	3	2	no	—
455	C₂×C₄	—	3	4	no	—
456	C₂×C₄	—	12	4	no	—
457	C₂×C₄	C₄×D₃×D₅	1	2	yes	—
458	C₂×C₄	C₄×D₃×D₅	1	2	yes	—
459	C₂×C₄	C₂×D₃×Dic₅	1	4	yes	—
460	C₂×C₄	C₂×D₃×Dic₅	1	1	yes	characteristic
461	C₂×C₄	C₂²×D₃×D₅	1	1	yes	characteristic
462	C₈	—	5	2	no	—
463	C₈	—	5	2	no	—
464	C₈	—	5	4	no	—
465	C₈	—	15	4	no	—
466	C₈	—	15	2	no	—
467	C₈	—	15	2	no	—
468	C₂×C₃	—	2	2	no	—
469	C₂×C₃	C₂²×C₄×Dic₅	1	1	yes	characteristic
470	C₂×C₃	#66153	1	2	yes	—
471	D₃	—	2	2	no	—
472	D₃	—	2	2	no	—
473	C₅	#78548	1	1	yes	characteristic, complemented, Sylow
474	C₂²	—	2	2	no	—
475	C₂²	—	3	2	no	—
476	C₂²	—	3	2	no	—
477	C₂²	—	6	2	no	—
478	C₂²	—	6	2	no	—
479	C₂²	—	12	4	no	—
480	C₂²	C₄×D₃×Dic₅	1	2	yes	—
481	C₂²	C₂²×D₃×Dic₅	1	1	yes	characteristic
482	C₄	—	2	4	no	—
483	C₄	—	3	2	no	—
484	C₄	—	3	2	no	—
485	C₄	—	6	4	no	—
486	C₄	C₄×D₃×Dic₅	1	2	yes	—
487	C₄	C₂×C₄×D₃×D₅	1	1	yes	characteristic
488	C₄	C₂×C₄×D₃×D₅	1	1	yes	characteristic
489	C₃	#10613933	1	1	yes	characteristic, complemented, Sylow
490	C₂	—	2	2	no	—
491	C₂	—	6	2	no	—
492	C₂	—	6	2	no	—
493	C₂	C₂×C₄×D₃×Dic₅	1	1	yes	characteristic
494	C₂	#11755298	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×D₃×D₅
commutator	C₂×C₃×C₅	C₂²×C₄²
Fitting	C₃×C₅×#117	C₂²
socle	C₂²×C₃×C₅	C₂³×C₄
prime radical	C₂³×C₅×D₃	C₂×C₄
cosocle	C₂×C₃×C₄×C₅	C₂⁴
hypercenter	#117	D₃×D₅
hypocenter	C₃×C₅	#2873
LCS	G ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂×C₄ ◁ #117

Complements

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

N	H ≅ G/N	type
4. #11751098	C₂	semidirect
5. C₃×#65286	C₂	semidirect
6. #11748327	C₂	semidirect
7. #11748323	C₂	semidirect
8. #11747005	C₂	semidirect
9. C₄×#6650	C₂	semidirect
10. #11746979	C₂	semidirect
11. #11746977	C₂	semidirect
26. C₂×#6650	C₄	semidirect
32. D₃×#681	C₄	semidirect
34. #91087	C₂²	semidirect
35. C₄×C₃⋊#168	C₂²	semidirect
36. C₃×#3935	C₂²	semidirect
37. C₃×C₄×#168	C₂²	semidirect
38. #90953	C₂²	semidirect
39. #90953	C₂²	semidirect
40. Dic₃×#168	C₂²	semidirect
41. Dic₃×#168	C₂²	semidirect
51. #65286	D₃	semidirect
67. #6710	C₂×C₄	semidirect
68. C₂×C₃⋊#168	C₂×C₄	semidirect
78. C₃×#681	C₂×C₄	semidirect
79. C₂×C₃×#168	C₂×C₄	semidirect
86. #6650	C₂×C₄	semidirect
87. #6650	C₂×C₄	semidirect
88. D₃×#168	C₂×C₄	semidirect
124. #3935	C₂×D₃	semidirect
128. C₄×#168	C₂×D₃	semidirect
211. #681	C₄×D₃	semidirect
217. C₂×#168	C₄×D₃	semidirect
420. C₃×C₅	#2873	semidirect
473. C₅	#78548	semidirect
489. C₃	#10613933	semidirect

Maximal subgroups

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

subgroup	index
C₅×D₃×#117	2
C₂²×#6650	2
C₂×D₃×#681	2
#11751098	2
C₃×#65286	2
#11748327	2
#11748323	2
#11747005	2
C₄×#6650	2
#11746979	2
#11746977	2
#10613933	3
#78548	5