Subgroups — #14419211

Order 1920.

760 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#5479	C₂	1	1	yes	maximal, characteristic
2	#11751027	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×C₄×#168	C₂	1	1	yes	maximal, characteristic, complemented
4	#11748500	C₂	1	2	yes	maximal, complemented
5	#67×#168	C₂	1	2	yes	maximal, complemented
6	#11747008	C₂	1	1	yes	maximal, characteristic, complemented
7	D₁₂×#168	C₂	1	1	yes	maximal, characteristic, complemented
8	#11746977	C₂	1	2	yes	maximal, complemented
9	#11746877	C₂	1	2	yes	maximal, complemented
10	#11746863	C₂	1	1	yes	maximal, characteristic, complemented
11	Dic₆×#168	C₂	1	1	yes	maximal, characteristic, complemented
12	#10614857	—	3	1	no	maximal, Hall
13	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
14	C₅×#930	C₄	1	1	yes	characteristic
15	C₅×#929	C₄	1	2	yes	—
16	C₄×C₅×#67	C₂²	1	2	yes	—
17	C₅×#924	C₄	1	1	yes	characteristic
18	C₅×#876	C₄	1	2	yes	—
19	C₅×#875	C₄	1	1	yes	characteristic
20	C₄×C₅×D₁₂	C₂²	1	1	yes	characteristic
21	C₅×#872	C₂²	1	2	yes	—
22	C₅×#870	C₄	1	1	yes	characteristic
23	C₄×C₅×Dic₆	C₂²	1	1	yes	characteristic
24	C₂²×C₃×#168	C₂²	1	1	yes	characteristic
25	C₂²×C₃×#168	C₂²	1	1	yes	characteristic
26	C₂×#6650	C₂²	1	2	yes	—
27	C₂×D₃×#168	C₂²	1	2	yes	—
28	#91114	C₂²	1	2	yes	—
29	C₄⋊(C₃⋊#168)	C₂²	1	1	yes	characteristic
30	C₄⋊(C₃⋊#168)	C₂²	1	1	yes	characteristic
31	#91087	C₂²	1	2	yes	—
32	C₃×C₄×#168	C₂²	1	1	yes	characteristic
33	C₃×C₄×#168	C₂²	1	1	yes	characteristic
34	C₃×C₄×#168	C₂²	1	1	yes	characteristic
35	C₃×C₄×#168	C₂²	1	1	yes	characteristic
36	Dic₃⋊#168	C₂²	1	2	yes	—
37	Dic₃⋊#168	C₂²	1	2	yes	—
38	(C₂×D₃)⋊#168	C₂²	1	2	yes	—
39	(C₂×D₃)⋊#168	C₂²	1	2	yes	—
40	#90953	C₂²	1	2	yes	—
41	Dic₃×#168	C₂²	1	2	yes	—
42	#78448	—	5	1	no	maximal, Hall
43	C₅×#529	—	3	1	no	—
44	#65313	—	3	1	no	—
45	Q₈×#168	—	3	1	no	—
46	#65301	—	3	1	no	—
47	#65300	—	3	2	no	—
48	D₄×#168	—	3	2	no	—
49	D₄×#168	—	3	1	no	—
50	#65289	—	3	2	no	—
51	#65286	—	3	2	no	—
52	#65215	—	3	1	no	—
53	C₂×C₄×#168	D₃	1	1	yes	characteristic, complemented
54	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
55	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
56	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
57	C₂×C₅×#67	C₂×C₄	1	2	yes	—
58	C₂×C₅×D₁₂	C₂×C₄	1	1	yes	characteristic
59	C₂×C₄×C₅×D₃	C₂³	1	2	yes	—
60	C₂×C₅×Dic₆	C₂×C₄	1	1	yes	characteristic
61	C₃×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
62	C₃×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
63	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
64	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
65	C₂×C₃⋊#168	C₂³	1	2	yes	—
66	C₂×C₃⋊#168	C₂³	1	2	yes	—
67	C₅×#217	C₂×C₄	1	2	yes	—
68	C₅×(C₂×D₃)⋊C₄	C₂×C₄	1	2	yes	—
69	C₅×(C₂×D₃)⋊C₄	C₂×C₄	1	2	yes	—
70	C₅×(C₂×D₃)⋊C₄	C₂×C₄	1	2	yes	—
71	C₅×(C₂×D₃)⋊C₄	C₂×C₄	1	2	yes	—
72	C₅×C₄⋊Dic₃	C₂×C₄	1	1	yes	characteristic
73	C₅×C₄⋊Dic₃	C₂×C₄	1	1	yes	characteristic
74	C₅×Dic₃⋊C₄	C₂×C₄	1	2	yes	—
75	C₅×Dic₃⋊C₄	C₂×C₄	1	2	yes	—
76	C₅×Dic₃⋊C₄	C₂×C₄	1	2	yes	—
77	C₅×Dic₃⋊C₄	C₂×C₄	1	2	yes	—
78	C₄×C₅×Dic₃	C₂³	1	2	yes	—
79	C₂×C₃×#168	—	2	2	no	—
80	C₂×C₃×#168	—	2	2	no	—
81	C₂×C₃×#168	C₂³	1	1	yes	characteristic
82	C₂×C₃×#168	C₂³	1	1	yes	characteristic
83	C₂×C₃×#168	C₂³	1	1	yes	characteristic
84	C₂×C₃×#168	C₂³	1	1	yes	characteristic
85	#6650	—	2	4	no	—
86	D₃×#168	—	2	4	no	—
87	#5479	D₅	1	1	yes	characteristic
88	C₂×C₃×C₄×C₈	—	5	1	no	—
89	#5111	—	5	2	no	—
90	C₈×#67	—	5	2	no	—
91	#4926	—	5	1	no	—
92	#4690	—	5	2	no	—
93	#4689	—	5	2	no	—
94	#4688	—	5	1	no	—
95	C₈×D₁₂	—	5	1	no	—
96	#4679	—	5	1	no	—
97	C₈×Dic₆	—	5	1	no	—
98	C₅×#126	—	3	2	no	—
99	C₅×#125	—	3	1	no	—
100	C₅×#124	—	3	1	no	—
101	C₅×#123	—	3	2	no	—
102	C₅×C₂²⋊Q₈	—	3	1	no	—
103	C₅×#121	—	3	1	no	—
104	C₄×C₅×Q₈	—	3	1	no	—
105	C₄×C₅×D₄	—	3	2	no	—
106	C₄×C₅×D₄	—	3	1	no	—
107	C₅×#117	—	3	2	no	—
108	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
109	C₂×#681	—	3	2	no	—
110	C₂²×#168	—	3	2	no	—
111	C₂²×#168	C₂×D₃	1	1	yes	characteristic
112	C₂²×#168	C₂×D₃	1	1	yes	characteristic
113	C₂²⋊#168	—	3	2	no	—
114	C₂²⋊#168	—	3	2	no	—
115	C₂²⋊#168	—	3	2	no	—
116	C₄⋊#168	—	3	1	no	—
117	C₄⋊#168	—	3	1	no	—
118	C₄⋊#168	—	3	2	no	—
119	C₄⋊#168	—	3	2	no	—
120	#3935	—	3	2	no	—
121	#3935	—	3	2	no	—
122	C₄×#168	—	3	2	no	—
123	C₄×#168	C₂×D₃	1	1	yes	characteristic
124	C₄×#168	C₂×D₃	1	1	yes	characteristic
125	C₄×#168	C₂×D₃	1	1	yes	characteristic
126	C₄×#168	C₂×D₃	1	1	yes	characteristic
127	#2966	—	15	1	no	Sylow
128	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
129	C₂²×C₅×D₃	C₂²×C₄	1	2	yes	—
130	C₂×C₃×C₄×C₅	—	2	2	no	—
131	C₂×C₃×C₄×C₅	—	2	2	no	—
132	C₂×C₃×C₄×C₅	—	2	1	no	—
133	C₂×C₃×C₄×C₅	—	2	1	no	—
134	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
135	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
136	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
137	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
138	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
139	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
140	C₅×#67	—	2	4	no	—
141	C₂×C₅×Dic₃	C₂²×C₄	1	2	yes	—
142	C₂×C₅×Dic₃	C₂²×C₄	1	2	yes	—
143	C₂×C₅×Dic₃	C₂²×C₄	1	2	yes	—
144	C₅×D₁₂	—	2	2	no	—
145	C₄×C₅×D₃	—	2	2	no	—
146	C₄×C₅×D₃	—	2	2	no	—
147	C₅×Dic₆	—	2	2	no	—
148	C₃⋊#168	—	2	2	no	—
149	C₃⋊#168	—	2	2	no	—
150	C₃×#168	—	2	1	no	—
151	C₃×#168	—	2	1	no	—
152	C₃×#168	#41	1	2	yes	—
153	C₃×#168	#41	1	2	yes	—
154	C₂²×C₃×C₈	—	5	1	no	—
155	C₂²×C₃×C₈	—	5	1	no	—
156	C₂×C₃×C₄²	C₂×D₅	1	1	yes	characteristic
157	#930	Dic₅	1	1	yes	characteristic
158	#929	Dic₅	1	2	yes	—
159	C₄×#67	C₂×D₅	1	2	yes	—
160	#924	Dic₅	1	1	yes	characteristic
161	C₂×ΓL(1,𝔽₂₅)	—	5	2	no	—
162	C₂×D₃×C₈	—	5	2	no	—
163	#876	Dic₅	1	2	yes	—
164	#875	Dic₅	1	1	yes	characteristic
165	C₄×D₁₂	C₂×D₅	1	1	yes	characteristic
166	#872	C₂×D₅	1	2	yes	—
167	#870	Dic₅	1	1	yes	characteristic
168	C₄×Dic₆	C₂×D₅	1	1	yes	characteristic
169	C₃×C₄×C₈	—	5	1	no	—
170	C₃×C₄×C₈	—	5	1	no	—
171	C₃×C₄×C₈	—	5	1	no	—
172	C₃×C₄×C₈	—	5	1	no	—
173	#830	—	5	2	no	—
174	(C₂×D₃)⋊C₈	—	5	2	no	—
175	(C₂×D₃)⋊C₈	—	5	2	no	—
176	#815	—	5	2	no	—
177	Dic₃⋊C₈	—	5	2	no	—
178	Dic₃⋊C₈	—	5	2	no	—
179	C₈×Dic₃	—	5	2	no	—
180	C₄⋊(C₃⋊C₈)	—	5	1	no	—
181	C₄⋊(C₃⋊C₈)	—	5	1	no	—
182	#803	—	5	2	no	—
183	C₂×C₅×Q₈	—	3	1	no	—
184	C₂×C₅×D₄	—	3	2	no	—
185	C₂×C₅×D₄	—	3	1	no	—
186	C₂²×C₄×C₅	—	3	2	no	—
187	C₂²×C₄×C₅	C₄×D₃	1	1	yes	characteristic
188	C₂²×C₄×C₅	C₄×D₃	1	1	yes	characteristic
189	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
190	C₅×C₄⋊C₄	—	3	2	no	—
191	C₅×C₄⋊C₄	—	3	2	no	—
192	C₅×C₄⋊C₄	—	3	1	no	—
193	C₅×C₄⋊C₄	—	3	2	no	—
194	C₅×C₄⋊C₄	—	3	1	no	—
195	C₅×C₄⋊C₄	—	3	2	no	—
196	C₅×C₂²⋊C₄	—	3	2	no	—
197	C₅×C₂²⋊C₄	—	3	2	no	—
198	C₅×C₂²⋊C₄	—	3	2	no	—
199	C₅×C₂²⋊C₄	—	3	2	no	—
200	C₅×C₂²⋊C₄	—	3	2	no	—
201	C₄²×C₅	—	3	2	no	—
202	C₄²×C₅	C₄×D₃	1	1	yes	characteristic
203	C₄²×C₅	C₄×D₃	1	1	yes	characteristic
204	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
205	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
206	#681	—	6	4	no	—
207	C₂×#168	—	2	2	no	—
208	C₂×#168	—	2	2	no	—
209	C₂×#168	—	3	2	no	—
210	C₂×#168	—	3	2	no	—
211	C₂×#168	—	6	4	no	—
212	C₂×#168	C₂²×D₃	1	1	yes	characteristic
213	C₂×#168	C₂²×D₃	1	1	yes	characteristic
214	C₂×#168	C₂²×D₃	1	1	yes	characteristic
215	C₂×#168	C₂²×D₃	1	1	yes	characteristic
216	#529	—	3	1	no	—
217	#446	—	15	1	no	—
218	C₈×Q₈	—	15	1	no	—
219	#436	—	15	1	no	—
220	#435	—	15	2	no	—
221	C₈×D₄	—	15	1	no	—
222	C₈×D₄	—	15	2	no	—
223	#433	—	15	2	no	—
224	#432	—	15	1	no	—
225	#405	—	15	2	no	—
226	C₂×C₄×C₈	—	5	1	no	—
227	C₂²×C₃×C₅	—	2	1	no	—
228	C₂²×C₃×C₅	—	2	1	no	—
229	C₂²×C₃×C₅	#131	1	2	yes	—
230	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
231	C₂×C₅×D₃	—	2	2	no	—
232	C₂×C₅×D₃	—	2	2	no	—
233	C₂×C₅×D₃	—	2	2	no	—
234	C₃×C₄×C₅	—	2	1	no	—
235	C₃×C₄×C₅	—	2	1	no	—
236	C₃×C₄×C₅	—	2	1	no	—
237	C₃×C₄×C₅	—	2	1	no	—
238	C₃×C₄×C₅	#131	1	2	yes	—
239	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
240	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
241	C₅×Dic₃	—	2	2	no	—
242	C₅×Dic₃	—	2	2	no	—
243	C₅×Dic₃	—	2	2	no	—
244	C₂²×C₃×C₄	C₂×Dic₅	1	1	yes	characteristic
245	C₂²×C₃×C₄	C₂×Dic₅	1	1	yes	characteristic
246	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
247	C₂×#67	C₂×Dic₅	1	2	yes	—
248	C₂×D₁₂	C₂×Dic₅	1	1	yes	characteristic
249	C₂×C₄×D₃	C₂²×D₅	1	2	yes	—
250	C₂×Dic₆	C₂×Dic₅	1	1	yes	characteristic
251	C₂×C₃×C₈	—	5	1	no	—
252	C₂×C₃×C₈	—	5	1	no	—
253	C₂×C₃×C₈	—	5	1	no	—
254	C₂×C₃×C₈	—	5	1	no	—
255	C₂×C₃×C₈	—	10	2	no	—
256	C₂×C₃×C₈	—	10	2	no	—
257	C₃×C₄²	C₂×Dic₅	1	1	yes	characteristic
258	C₃×C₄²	C₂×Dic₅	1	1	yes	characteristic
259	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
260	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
261	#217	C₂×Dic₅	1	2	yes	—
262	(C₂×D₃)⋊C₄	C₂×Dic₅	1	2	yes	—
263	(C₂×D₃)⋊C₄	C₂×Dic₅	1	2	yes	—
264	(C₂×D₃)⋊C₄	C₂×Dic₅	1	2	yes	—
265	(C₂×D₃)⋊C₄	C₂×Dic₅	1	2	yes	—
266	C₄⋊Dic₃	C₂×Dic₅	1	1	yes	characteristic
267	C₄⋊Dic₃	C₂×Dic₅	1	1	yes	characteristic
268	Dic₃⋊C₄	C₂×Dic₅	1	2	yes	—
269	Dic₃⋊C₄	C₂×Dic₅	1	2	yes	—
270	Dic₃⋊C₄	C₂×Dic₅	1	2	yes	—
271	Dic₃⋊C₄	C₂×Dic₅	1	2	yes	—
272	C₄×Dic₃	C₂²×D₅	1	2	yes	—
273	C₂×C₃⋊C₈	—	5	2	no	—
274	C₂×C₃⋊C₈	—	5	2	no	—
275	ΓL(1,𝔽₂₅)	—	10	4	no	—
276	D₃×C₈	—	10	4	no	—
277	C₂³×C₅	—	3	2	no	—
278	C₂³×C₅	C₂×C₄×D₃	1	1	yes	characteristic
279	C₅×Q₈	—	6	2	no	—
280	C₅×D₄	—	6	4	no	—
281	C₅×D₄	—	6	2	no	—
282	C₂×C₄×C₅	—	2	2	no	—
283	C₂×C₄×C₅	—	2	2	no	—
284	C₂×C₄×C₅	—	2	1	no	—
285	C₂×C₄×C₅	—	2	1	no	—
286	C₂×C₄×C₅	—	3	2	no	—
287	C₂×C₄×C₅	—	3	2	no	—
288	C₂×C₄×C₅	—	3	2	no	—
289	C₂×C₄×C₅	—	6	2	no	—
290	C₂×C₄×C₅	—	6	2	no	—
291	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
292	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
293	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
294	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
295	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
296	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
297	#168	—	2	1	no	—
298	#168	—	2	1	no	—
299	#168	—	6	2	no	—
300	#168	—	6	2	no	—
301	#168	#235	1	2	yes	—
302	#168	#235	1	2	yes	—
303	C₂×M₁₆	—	15	2	no	—
304	C₂²×C₈	—	5	1	no	—
305	C₂²×C₈	—	5	1	no	—
306	C₂²×C₈	—	15	2	no	—
307	#126	—	3	2	no	—
308	#125	—	3	1	no	—
309	#124	—	3	1	no	—
310	#123	—	3	2	no	—
311	C₂²⋊Q₈	—	3	1	no	—
312	#121	—	3	1	no	—
313	C₄×Q₈	—	3	1	no	—
314	C₄×D₄	—	3	2	no	—
315	C₄×D₄	—	3	1	no	—
316	#117	—	3	2	no	—
317	C₂×C₄²	D₃×D₅	1	1	yes	characteristic
318	C₄⋊C₈	—	15	2	no	—
319	C₄⋊C₈	—	15	2	no	—
320	C₄⋊C₈	—	15	1	no	—
321	C₄⋊C₈	—	15	1	no	—
322	C₂²⋊C₈	—	15	2	no	—
323	C₂²⋊C₈	—	15	2	no	—
324	C₂²⋊C₈	—	15	2	no	—
325	#97	—	15	2	no	—
326	#97	—	15	2	no	—
327	C₄×C₈	—	5	1	no	—
328	C₄×C₈	—	5	1	no	—
329	C₄×C₈	—	5	1	no	—
330	C₄×C₈	—	5	1	no	—
331	C₄×C₈	—	15	2	no	—
332	C₂×C₃×C₅	—	2	2	no	—
333	C₂×C₃×C₅	C₄×#41	1	1	yes	characteristic
334	C₂×C₃×C₅	C₂×#131	1	1	yes	characteristic
335	C₂×C₃×C₅	C₂×#131	1	1	yes	characteristic
336	C₅×D₃	—	4	2	no	—
337	C₂³×C₃	C₂²×Dic₅	1	1	yes	characteristic
338	C₂²×D₃	C₂²×Dic₅	1	2	yes	—
339	C₂×C₃×C₄	—	2	2	no	—
340	C₂×C₃×C₄	—	2	1	no	—
341	C₂×C₃×C₄	—	2	1	no	—
342	C₂×C₃×C₄	—	2	2	no	—
343	C₂×C₃×C₄	C₂²×Dic₅	1	1	yes	characteristic
344	C₂×C₃×C₄	C₂²×Dic₅	1	1	yes	characteristic
345	C₂×C₃×C₄	C₂²×Dic₅	1	1	yes	characteristic
346	C₂×C₃×C₄	C₂²×Dic₅	1	1	yes	characteristic
347	C₂×C₃×C₄	C₂²×Dic₅	1	1	yes	characteristic
348	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
349	#67	—	2	4	no	—
350	C₂×Dic₃	C₂²×Dic₅	1	2	yes	—
351	C₂×Dic₃	C₂²×Dic₅	1	2	yes	—
352	C₂×Dic₃	C₂²×Dic₅	1	2	yes	—
353	D₁₂	—	2	2	no	—
354	C₄×D₃	—	2	2	no	—
355	C₄×D₃	—	2	2	no	—
356	Dic₆	—	2	2	no	—
357	C₃×C₈	—	5	2	no	—
358	C₃×C₈	—	5	2	no	—
359	C₃×C₈	—	10	1	no	—
360	C₃×C₈	—	10	1	no	—
361	C₃⋊C₈	—	10	2	no	—
362	C₃⋊C₈	—	10	2	no	—
363	C₂²×C₅	—	2	1	no	—
364	C₂²×C₅	—	2	1	no	—
365	C₂²×C₅	—	6	2	no	—
366	C₂²×C₅	—	6	2	no	—
367	C₂²×C₅	—	6	2	no	—
368	C₂²×C₅	#901	1	2	yes	—
369	C₂²×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
370	C₄×C₅	—	2	1	no	—
371	C₄×C₅	—	2	1	no	—
372	C₄×C₅	—	2	1	no	—
373	C₄×C₅	—	2	1	no	—
374	C₄×C₅	—	6	2	no	—
375	C₄×C₅	—	6	2	no	—
376	C₄×C₅	—	6	2	no	—
377	C₄×C₅	#901	1	2	yes	—
378	C₄×C₅	C₂×#235	1	1	yes	characteristic
379	C₄×C₅	C₂×#235	1	1	yes	characteristic
380	C₂×Q₈	—	3	1	no	—
381	C₂×D₄	—	3	2	no	—
382	C₂×D₄	—	3	1	no	—
383	C₂²×C₄	—	3	2	no	—
384	C₂²×C₄	D₃×Dic₅	1	1	yes	characteristic
385	C₂²×C₄	D₃×Dic₅	1	1	yes	characteristic
386	C₂²×C₄	C₂×D₃×D₅	1	1	yes	characteristic
387	M₁₆	—	30	4	no	—
388	C₂×C₈	—	5	1	no	—
389	C₂×C₈	—	5	1	no	—
390	C₂×C₈	—	5	1	no	—
391	C₂×C₈	—	5	1	no	—
392	C₂×C₈	—	10	2	no	—
393	C₂×C₈	—	10	2	no	—
394	C₂×C₈	—	15	2	no	—
395	C₂×C₈	—	15	2	no	—
396	C₂×C₈	—	30	4	no	—
397	C₄⋊C₄	—	3	2	no	—
398	C₄⋊C₄	—	3	2	no	—
399	C₄⋊C₄	—	3	1	no	—
400	C₄⋊C₄	—	3	2	no	—
401	C₄⋊C₄	—	3	1	no	—
402	C₄⋊C₄	—	3	2	no	—
403	C₂²⋊C₄	—	3	2	no	—
404	C₂²⋊C₄	—	3	2	no	—
405	C₂²⋊C₄	—	3	2	no	—
406	C₂²⋊C₄	—	3	2	no	—
407	C₂²⋊C₄	—	3	2	no	—
408	C₄²	—	3	2	no	—
409	C₄²	D₃×Dic₅	1	1	yes	characteristic
410	C₄²	D₃×Dic₅	1	1	yes	characteristic
411	C₄²	C₂×D₃×D₅	1	1	yes	characteristic
412	C₄²	C₂×D₃×D₅	1	1	yes	characteristic
413	C₃×C₅	#2966	1	1	yes	characteristic, complemented, Hall
414	C₂²×C₃	—	2	1	no	—
415	C₂²×C₃	—	2	1	no	—
416	C₂²×C₃	#4094	1	2	yes	—
417	C₂²×C₃	C₂³×Dic₅	1	1	yes	characteristic
418	C₂×D₃	—	2	2	no	—
419	C₂×D₃	—	2	2	no	—
420	C₂×D₃	—	2	2	no	—
421	C₃×C₄	—	2	1	no	—
422	C₃×C₄	—	2	1	no	—
423	C₃×C₄	—	2	1	no	—
424	C₃×C₄	—	2	1	no	—
425	C₃×C₄	#4094	1	2	yes	—
426	C₃×C₄	D₅×#41	1	1	yes	characteristic
427	C₃×C₄	D₅×#41	1	1	yes	characteristic
428	Dic₃	—	2	2	no	—
429	Dic₃	—	2	2	no	—
430	Dic₃	—	2	2	no	—
431	C₂×C₅	—	2	2	no	—
432	C₂×C₅	—	12	2	no	—
433	C₂×C₅	C₄×#235	1	1	yes	characteristic
434	C₂×C₅	C₂×#901	1	1	yes	characteristic
435	C₂×C₅	C₂×#901	1	1	yes	characteristic
436	C₂³	—	3	2	no	—
437	C₂³	C₂×D₃×Dic₅	1	1	yes	characteristic
438	Q₈	—	6	2	no	—
439	D₄	—	6	4	no	—
440	D₄	—	6	2	no	—
441	C₂×C₄	—	2	2	no	—
442	C₂×C₄	—	2	1	no	—
443	C₂×C₄	—	2	1	no	—
444	C₂×C₄	—	2	2	no	—
445	C₂×C₄	—	3	2	no	—
446	C₂×C₄	—	3	2	no	—
447	C₂×C₄	—	3	2	no	—
448	C₂×C₄	—	6	2	no	—
449	C₂×C₄	—	6	2	no	—
450	C₂×C₄	C₂×D₃×Dic₅	1	1	yes	characteristic
451	C₂×C₄	C₂×D₃×Dic₅	1	1	yes	characteristic
452	C₂×C₄	C₂×D₃×Dic₅	1	1	yes	characteristic
453	C₂×C₄	C₂×D₃×Dic₅	1	1	yes	characteristic
454	C₂×C₄	C₂×D₃×Dic₅	1	1	yes	characteristic
455	C₂×C₄	C₂²×D₃×D₅	1	1	yes	characteristic
456	C₈	—	5	2	no	—
457	C₈	—	5	2	no	—
458	C₈	—	10	1	no	—
459	C₈	—	10	1	no	—
460	C₈	—	30	2	no	—
461	C₈	—	30	2	no	—
462	C₂×C₃	—	2	2	no	—
463	C₂×C₃	C₂×#4094	1	1	yes	characteristic
464	C₂×C₃	C₂×#4094	1	1	yes	characteristic
465	C₂×C₃	#41×Dic₅	1	1	yes	characteristic
466	D₃	—	4	2	no	—
467	C₅	#78448	1	1	yes	characteristic, complemented, Sylow
468	C₂²	—	2	1	no	—
469	C₂²	—	2	1	no	—
470	C₂²	—	6	2	no	—
471	C₂²	—	6	2	no	—
472	C₂²	—	6	2	no	—
473	C₂²	#91286	1	2	yes	—
474	C₂²	C₂²×D₃×Dic₅	1	1	yes	characteristic
475	C₄	—	2	1	no	—
476	C₄	—	2	1	no	—
477	C₄	—	2	1	no	—
478	C₄	—	2	1	no	—
479	C₄	—	6	2	no	—
480	C₄	—	6	2	no	—
481	C₄	—	6	2	no	—
482	C₄	#91286	1	2	yes	—
483	C₄	D₅×#235	1	1	yes	characteristic
484	C₄	D₅×#235	1	1	yes	characteristic
485	C₃	#10614857	1	1	yes	characteristic, complemented, Sylow
486	C₂	—	2	2	no	—
487	C₂	—	12	2	no	—
488	C₂	C₂×#91286	1	1	yes	characteristic
489	C₂	C₂×#91286	1	1	yes	characteristic
490	C₂	Dic₅×#235	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×#930	C₄
cosocle	C₂×C₃×C₄×C₅	C₂⁴
hypercenter	C₂×C₄²	D₃×D₅
hypocenter	C₃×C₅	#2966
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. #11751027	C₂	semidirect
3. C₂×C₃×C₄×#168	C₂	semidirect
4. #11748500	C₂	semidirect
5. #67×#168	C₂	semidirect
6. #11747008	C₂	semidirect
7. D₁₂×#168	C₂	semidirect
8. #11746977	C₂	semidirect
9. #11746877	C₂	semidirect
10. #11746863	C₂	semidirect
11. Dic₆×#168	C₂	semidirect
53. C₂×C₄×#168	D₃	semidirect
413. C₃×C₅	#2966	semidirect
467. C₅	#78448	semidirect
485. C₃	#10614857	semidirect

Maximal subgroups

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

subgroup	index
C₅×#5479	2
#11751027	2
C₂×C₃×C₄×#168	2
#11748500	2
#67×#168	2
#11747008	2
D₁₂×#168	2
#11746977	2
#11746877	2
#11746863	2
Dic₆×#168	2
#10614857	3
#78448	5