Subgroups — #14418495

Order 1920.

728 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#5578	C₂	1	1	yes	maximal, characteristic
2	#11751125	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×Q₈×#168	C₂	1	1	yes	maximal, characteristic, complemented
4	#11747011	C₂	1	1	yes	maximal, characteristic
5	#11746993	C₂	1	2	yes	maximal
6	#11746977	C₂	1	2	yes	maximal
7	C₄×D₃×#168	C₂	1	1	yes	maximal, characteristic
8	#11746866	C₂	1	1	yes	maximal, characteristic, complemented
9	#11746858	C₂	1	2	yes	maximal, complemented
10	Dic₆×#168	C₂	1	2	yes	maximal, complemented
11	Dic₆×#168	C₂	1	1	yes	maximal, characteristic, complemented
12	#10615059	—	3	1	no	maximal, Hall
13	C₃×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
14	C₅×#946	C₄	1	1	yes	characteristic
15	C₅×#944	C₄	1	1	yes	characteristic
16	C₅×#897	C₄	1	1	yes	characteristic
17	C₅×#896	C₄	1	2	yes	—
18	C₅×#889	C₄	1	2	yes	—
19	C₅×#888	C₄	1	1	yes	characteristic
20	C₅×#872	C₂²	1	2	yes	—
21	C₄²×C₅×D₃	C₂²	1	1	yes	characteristic
22	C₄×C₅×Dic₆	C₂²	1	2	yes	—
23	C₄×C₅×Dic₆	C₂²	1	1	yes	characteristic
24	C₂×#6650	C₂²	1	2	yes	—
25	C₂×D₃×#168	C₂²	1	1	yes	characteristic
26	C₂×D₃×#168	C₂²	1	1	yes	characteristic
27	C₄⋊(C₃⋊#168)	C₂²	1	2	yes	—
28	C₄⋊(C₃⋊#168)	C₂²	1	1	yes	characteristic
29	#91087	C₂²	1	2	yes	—
30	C₄×C₃⋊#168	C₂²	1	1	yes	characteristic
31	C₃×C₄⋊#168	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	2	yes	—
35	Dic₃⋊#168	C₂²	1	2	yes	—
36	Dic₃⋊#168	C₂²	1	2	yes	—
37	Dic₃⋊#168	C₂²	1	2	yes	—
38	#90953	C₂²	1	2	yes	—
39	Dic₃×#168	C₂²	1	1	yes	characteristic
40	Dic₃×#168	C₂²	1	2	yes	—
41	Dic₃×#168	C₂²	1	1	yes	characteristic
42	#79917	—	5	1	no	maximal, Hall
43	C₅×#533	—	3	1	no	—
44	#65313	—	3	2	no	—
45	#65313	—	3	1	no	—
46	#65313	—	3	1	no	—
47	Q₈×#168	—	3	1	no	—
48	Q₈×#168	—	3	2	no	—
49	Q₈×#168	D₃	1	1	yes	characteristic, complemented
50	#65288	—	3	2	no	—
51	#65286	—	3	2	no	—
52	#65213	—	3	1	no	—
53	C₂×C₄×#168	—	3	1	no	—
54	C₂×C₃×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
55	C₂×C₄×C₅×D₃	C₂×C₄	1	1	yes	characteristic
56	C₂×C₄×C₅×D₃	C₂×C₄	1	1	yes	characteristic
57	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
58	C₂×C₅×Dic₆	C₂×C₄	1	2	yes	—
59	C₂×C₅×Dic₆	C₂×C₄	1	1	yes	characteristic
60	C₃×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
61	C₃×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
62	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
63	C₃×C₄²×C₅	C₂³	1	2	yes	—
64	C₂×C₃⋊#168	C₂³	1	1	yes	characteristic
65	C₂×C₃⋊#168	C₂³	1	2	yes	—
66	C₂×C₃⋊#168	C₂³	1	1	yes	characteristic
67	C₅×(C₂×D₃)⋊C₄	C₂×C₄	1	2	yes	—
68	C₅×(C₂×D₃)⋊C₄	C₂×C₄	1	2	yes	—
69	C₅×C₄⋊Dic₃	C₂×C₄	1	1	yes	characteristic
70	C₅×C₄⋊Dic₃	C₂×C₄	1	2	yes	—
71	C₅×Dic₃⋊C₄	C₂×C₄	1	2	yes	—
72	C₅×Dic₃⋊C₄	C₂×C₄	1	2	yes	—
73	C₅×Dic₃⋊C₄	C₂×C₄	1	2	yes	—
74	C₅×Dic₃⋊C₄	C₂×C₄	1	2	yes	—
75	C₅×Dic₃⋊C₄	C₂×C₄	1	2	yes	—
76	C₄×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
77	C₄×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
78	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
79	C₄×C₅×Dic₃	C₂³	1	2	yes	—
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	—	2	4	no	—
84	D₃×#168	—	2	2	no	—
85	D₃×#168	Q₈	1	4	yes	complemented
86	#5578	D₅	1	1	yes	characteristic
87	C₃×C₈×Q₈	—	5	1	no	—
88	#5024	—	5	1	no	—
89	#4839	—	5	2	no	—
90	#4837	—	5	1	no	—
91	#4831	—	5	1	no	—
92	#4828	—	5	2	no	—
93	#4689	—	5	2	no	—
94	C₄×D₃×C₈	—	5	1	no	—
95	C₈×Dic₆	—	5	1	no	—
96	C₈×Dic₆	—	5	2	no	—
97	C₅×C₄⋊Q₈	—	3	1	no	—
98	C₅×C₄⋊Q₈	—	3	1	no	—
99	C₅×#125	—	3	2	no	—
100	C₅×C₂²⋊Q₈	—	3	1	no	—
101	C₅×C₂²⋊Q₈	—	3	2	no	—
102	C₅×C₂²⋊Q₈	—	3	1	no	—
103	C₄×C₅×Q₈	—	3	2	no	—
104	C₄×C₅×Q₈	—	3	1	no	—
105	C₄×C₅×Q₈	C₂×D₃	1	1	yes	characteristic
106	C₅×#117	—	3	2	no	—
107	C₂×C₄²×C₅	—	3	1	no	—
108	C₂×#681	—	3	2	no	—
109	C₂²×#168	—	3	1	no	—
110	C₂²×#168	—	3	1	no	—
111	C₄⋊#168	—	3	2	no	—
112	C₄⋊#168	—	3	1	no	—
113	C₄⋊#168	—	3	2	no	—
114	C₄⋊#168	—	3	2	no	—
115	C₄⋊#168	—	3	2	no	—
116	C₄⋊#168	C₂×D₃	1	2	yes	—
117	C₄⋊#168	C₂×D₃	1	1	yes	characteristic
118	#3935	—	3	2	no	—
119	#3935	—	3	2	no	—
120	C₄×#168	—	3	1	no	—
121	C₄×#168	—	3	2	no	—
122	C₄×#168	—	3	1	no	—
123	C₄×#168	—	3	1	no	—
124	C₄×#168	C₂×D₃	1	2	yes	—
125	C₄×#168	C₂×D₃	1	1	yes	characteristic
126	#2960	—	15	1	no	Sylow
127	C₂²×C₅×D₃	C₂²×C₄	1	1	yes	characteristic
128	C₃×C₅×Q₈	—	2	2	no	—
129	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
130	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
131	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
132	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
133	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
134	C₂×C₅×Dic₃	C₂²×C₄	1	1	yes	characteristic
135	C₂×C₅×Dic₃	C₂²×C₄	1	2	yes	—
136	C₂×C₅×Dic₃	C₂²×C₄	1	2	yes	—
137	C₂×C₅×Dic₃	C₂²×C₄	1	1	yes	characteristic
138	C₂×C₅×Dic₃	C₂²×C₄	1	1	yes	characteristic
139	C₄×C₅×D₃	—	2	2	no	—
140	C₄×C₅×D₃	—	2	2	no	—
141	C₄×C₅×D₃	C₂×Q₈	1	2	yes	—
142	C₄×C₅×D₃	#41	1	2	yes	—
143	C₅×Dic₆	—	2	2	no	—
144	C₅×Dic₆	—	2	4	no	—
145	C₃⋊#168	—	2	1	no	—
146	C₃⋊#168	—	2	2	no	—
147	C₃⋊#168	C₂×Q₈	1	2	yes	—
148	C₃×#168	—	2	1	no	—
149	C₃×#168	—	2	2	no	—
150	C₃×#168	C₂×Q₈	1	2	yes	—
151	C₃×C₄×Q₈	C₂×D₅	1	1	yes	characteristic
152	#946	Dic₅	1	1	yes	characteristic
153	#944	Dic₅	1	1	yes	characteristic
154	C₂×ΓL(1,𝔽₂₅)	—	5	2	no	—
155	C₂×D₃×C₈	—	5	1	no	—
156	C₂×D₃×C₈	—	5	1	no	—
157	#897	Dic₅	1	1	yes	characteristic
158	#896	Dic₅	1	2	yes	—
159	#889	Dic₅	1	2	yes	—
160	#888	Dic₅	1	1	yes	characteristic
161	#872	C₂×D₅	1	2	yes	—
162	C₄²×D₃	C₂×D₅	1	1	yes	characteristic
163	C₄×Dic₆	C₂×D₅	1	2	yes	—
164	C₄×Dic₆	C₂×D₅	1	1	yes	characteristic
165	C₃×C₄⋊C₈	—	5	2	no	—
166	C₃×C₄⋊C₈	—	5	1	no	—
167	C₃×C₄×C₈	—	5	1	no	—
168	C₃×C₄×C₈	—	5	2	no	—
169	#815	—	5	2	no	—
170	Dic₃⋊C₈	—	5	2	no	—
171	Dic₃⋊C₈	—	5	2	no	—
172	Dic₃⋊C₈	—	5	2	no	—
173	C₈×Dic₃	—	5	1	no	—
174	C₈×Dic₃	—	5	2	no	—
175	C₈×Dic₃	—	5	1	no	—
176	C₄⋊(C₃⋊C₈)	—	5	1	no	—
177	C₄⋊(C₃⋊C₈)	—	5	2	no	—
178	#803	—	5	2	no	—
179	C₄×C₃⋊C₈	—	5	1	no	—
180	C₂×C₅×Q₈	—	3	2	no	—
181	C₂×C₅×Q₈	—	3	1	no	—
182	C₂×C₅×Q₈	C₄×D₃	1	1	yes	characteristic
183	C₂²×C₄×C₅	—	3	1	no	—
184	C₂²×C₄×C₅	—	3	1	no	—
185	C₂²×C₄×C₅	—	3	1	no	—
186	C₅×C₄⋊C₄	—	3	2	no	—
187	C₅×C₄⋊C₄	—	3	2	no	—
188	C₅×C₄⋊C₄	—	3	2	no	—
189	C₅×C₄⋊C₄	—	3	2	no	—
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	C₄×D₃	1	2	yes	—
194	C₅×C₄⋊C₄	C₄×D₃	1	1	yes	characteristic
195	C₅×C₂²⋊C₄	—	3	2	no	—
196	C₅×C₂²⋊C₄	—	3	2	no	—
197	C₄²×C₅	—	3	1	no	—
198	C₄²×C₅	—	3	1	no	—
199	C₄²×C₅	—	3	1	no	—
200	C₄²×C₅	—	3	2	no	—
201	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
202	C₄²×C₅	C₂²×D₃	1	2	yes	—
203	#681	—	6	4	no	—
204	C₂×#168	—	3	1	no	—
205	C₂×#168	—	3	4	no	—
206	C₂×#168	—	3	1	no	—
207	C₂×#168	—	3	2	no	—
208	C₂×#168	—	6	2	no	—
209	C₂×#168	C₂²×D₃	1	1	yes	characteristic
210	C₂×#168	C₂²×D₃	1	2	yes	—
211	C₂×#168	C₂²×D₃	1	1	yes	characteristic
212	#533	—	3	1	no	—
213	#446	—	15	2	no	—
214	#446	—	15	1	no	—
215	#446	—	15	1	no	—
216	C₈×Q₈	—	5	1	no	—
217	C₈×Q₈	—	15	1	no	—
218	C₈×Q₈	—	15	2	no	—
219	#424	—	15	2	no	—
220	#423	—	15	1	no	—
221	#405	—	15	2	no	—
222	C₂×C₄×C₈	—	15	1	no	—
223	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
224	C₂×C₅×D₃	—	2	1	no	—
225	C₂×C₅×D₃	—	2	1	no	—
226	C₂×C₅×D₃	C₄×Q₈	1	2	yes	—
227	C₃×C₄×C₅	—	2	2	no	—
228	C₃×C₄×C₅	—	2	1	no	—
229	C₃×C₄×C₅	—	2	2	no	—
230	C₃×C₄×C₅	#131	1	2	yes	—
231	C₃×C₄×C₅	C₂²×Q₈	1	1	yes	characteristic
232	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
233	C₅×Dic₃	—	2	2	no	—
234	C₅×Dic₃	—	2	2	no	—
235	C₅×Dic₃	—	2	1	no	—
236	C₅×Dic₃	C₄×Q₈	1	2	yes	—
237	C₅×Dic₃	#131	1	2	yes	—
238	C₂×C₃×Q₈	C₂×Dic₅	1	1	yes	characteristic
239	C₂×C₄×D₃	C₂×Dic₅	1	1	yes	characteristic
240	C₂×C₄×D₃	C₂×Dic₅	1	1	yes	characteristic
241	C₂×C₄×D₃	C₂²×D₅	1	1	yes	characteristic
242	C₂×Dic₆	C₂×Dic₅	1	2	yes	—
243	C₂×Dic₆	C₂×Dic₅	1	1	yes	characteristic
244	C₂×C₃×C₈	—	5	1	no	—
245	C₂×C₃×C₈	—	5	1	no	—
246	C₂×C₃×C₈	—	5	2	no	—
247	C₃×C₄⋊C₄	C₂×Dic₅	1	1	yes	characteristic
248	C₃×C₄⋊C₄	C₂×Dic₅	1	2	yes	—
249	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
250	C₃×C₄²	C₂²×D₅	1	2	yes	—
251	(C₂×D₃)⋊C₄	C₂×Dic₅	1	2	yes	—
252	(C₂×D₃)⋊C₄	C₂×Dic₅	1	2	yes	—
253	C₄⋊Dic₃	C₂×Dic₅	1	1	yes	characteristic
254	C₄⋊Dic₃	C₂×Dic₅	1	2	yes	—
255	Dic₃⋊C₄	C₂×Dic₅	1	2	yes	—
256	Dic₃⋊C₄	C₂×Dic₅	1	2	yes	—
257	Dic₃⋊C₄	C₂×Dic₅	1	2	yes	—
258	Dic₃⋊C₄	C₂×Dic₅	1	2	yes	—
259	Dic₃⋊C₄	C₂×Dic₅	1	2	yes	—
260	C₄×Dic₃	C₂×Dic₅	1	1	yes	characteristic
261	C₄×Dic₃	C₂×Dic₅	1	1	yes	characteristic
262	C₄×Dic₃	C₂²×D₅	1	1	yes	characteristic
263	C₄×Dic₃	C₂²×D₅	1	2	yes	—
264	C₂×C₃⋊C₈	—	5	1	no	—
265	C₂×C₃⋊C₈	—	5	1	no	—
266	C₂×C₃⋊C₈	—	5	2	no	—
267	ΓL(1,𝔽₂₅)	—	10	4	no	—
268	D₃×C₈	—	5	4	no	—
269	D₃×C₈	—	10	2	no	—
270	C₂³×C₅	—	3	1	no	—
271	C₅×Q₈	—	2	2	no	—
272	C₅×Q₈	—	6	4	no	—
273	C₅×Q₈	—	6	2	no	—
274	C₂×C₄×C₅	—	3	1	no	—
275	C₂×C₄×C₅	—	3	1	no	—
276	C₂×C₄×C₅	—	3	2	no	—
277	C₂×C₄×C₅	—	3	2	no	—
278	C₂×C₄×C₅	—	3	1	no	—
279	C₂×C₄×C₅	—	3	2	no	—
280	C₂×C₄×C₅	—	3	2	no	—
281	C₂×C₄×C₅	—	6	2	no	—
282	C₂×C₄×C₅	—	6	2	no	—
283	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
284	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
285	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
286	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
287	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
288	#168	—	2	1	no	—
289	#168	—	2	2	no	—
290	#168	—	3	2	no	—
291	#168	—	6	1	no	—
292	#168	—	6	2	no	—
293	#168	D₃×Q₈	1	2	yes	—
294	C₂×M₁₆	—	15	2	no	—
295	C₂²×C₈	—	15	1	no	—
296	C₂²×C₈	—	15	1	no	—
297	C₄⋊Q₈	—	3	1	no	—
298	C₄⋊Q₈	—	3	1	no	—
299	#125	—	3	2	no	—
300	C₂²⋊Q₈	—	3	1	no	—
301	C₂²⋊Q₈	—	3	2	no	—
302	C₂²⋊Q₈	—	3	1	no	—
303	C₄×Q₈	—	3	2	no	—
304	C₄×Q₈	—	3	1	no	—
305	C₄×Q₈	D₃×D₅	1	1	yes	characteristic
306	#117	—	3	2	no	—
307	C₂×C₄²	—	3	1	no	—
308	C₄⋊C₈	—	5	1	no	—
309	C₄⋊C₈	—	5	2	no	—
310	C₄⋊C₈	—	15	2	no	—
311	C₄⋊C₈	—	15	2	no	—
312	C₄⋊C₈	—	15	2	no	—
313	C₄⋊C₈	—	15	1	no	—
314	C₄⋊C₈	—	15	2	no	—
315	#97	—	15	2	no	—
316	#97	—	15	2	no	—
317	C₄×C₈	—	5	1	no	—
318	C₄×C₈	—	5	2	no	—
319	C₄×C₈	—	15	1	no	—
320	C₄×C₈	—	15	1	no	—
321	C₄×C₈	—	15	2	no	—
322	C₄×C₈	—	15	1	no	—
323	C₂×C₃×C₅	C₂×C₄×Q₈	1	1	yes	characteristic
324	C₂×C₃×C₅	C₂×#131	1	1	yes	characteristic
325	C₂×C₃×C₅	C₂×#131	1	1	yes	characteristic
326	C₅×D₃	—	2	2	no	—
327	C₂²×D₃	C₂²×Dic₅	1	1	yes	characteristic
328	C₃×Q₈	—	2	2	no	—
329	C₂×C₃×C₄	C₂²×Dic₅	1	1	yes	characteristic
330	C₂×C₃×C₄	C₂²×Dic₅	1	2	yes	—
331	C₂×C₃×C₄	C₂²×Dic₅	1	2	yes	—
332	C₂×C₃×C₄	C₂²×Dic₅	1	1	yes	characteristic
333	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
334	C₂×Dic₃	C₂²×Dic₅	1	1	yes	characteristic
335	C₂×Dic₃	C₂²×Dic₅	1	2	yes	—
336	C₂×Dic₃	C₂²×Dic₅	1	2	yes	—
337	C₂×Dic₃	C₂²×Dic₅	1	1	yes	characteristic
338	C₂×Dic₃	C₂²×Dic₅	1	1	yes	characteristic
339	C₄×D₃	—	2	2	no	—
340	C₄×D₃	—	2	2	no	—
341	C₄×D₃	Q₈×D₅	1	2	yes	—
342	C₄×D₃	#713	1	2	yes	—
343	Dic₆	—	2	2	no	—
344	Dic₆	—	2	4	no	—
345	C₃×C₈	—	5	2	no	—
346	C₃×C₈	—	10	1	no	—
347	C₃×C₈	—	10	2	no	—
348	C₃⋊C₈	—	5	2	no	—
349	C₃⋊C₈	—	10	1	no	—
350	C₃⋊C₈	—	10	2	no	—
351	C₂²×C₅	—	3	2	no	—
352	C₂²×C₅	—	6	1	no	—
353	C₂²×C₅	—	6	1	no	—
354	C₂²×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
355	C₄×C₅	—	2	2	no	—
356	C₄×C₅	—	2	1	no	—
357	C₄×C₅	—	2	2	no	—
358	C₄×C₅	—	3	2	no	—
359	C₄×C₅	—	3	2	no	—
360	C₄×C₅	—	6	1	no	—
361	C₄×C₅	—	6	2	no	—
362	C₄×C₅	—	6	2	no	—
363	C₄×C₅	#901	1	2	yes	—
364	C₄×C₅	C₂×D₃×Q₈	1	1	yes	characteristic
365	C₄×C₅	D₃×#41	1	1	yes	characteristic
366	C₂×Q₈	—	3	2	no	—
367	C₂×Q₈	—	3	1	no	—
368	C₂×Q₈	D₃×Dic₅	1	1	yes	characteristic
369	C₂²×C₄	—	3	1	no	—
370	C₂²×C₄	—	3	1	no	—
371	C₂²×C₄	—	3	1	no	—
372	M₁₆	—	30	4	no	—
373	C₂×C₈	—	5	1	no	—
374	C₂×C₈	—	5	1	no	—
375	C₂×C₈	—	5	2	no	—
376	C₂×C₈	—	15	4	no	—
377	C₂×C₈	—	15	1	no	—
378	C₂×C₈	—	15	1	no	—
379	C₂×C₈	—	15	2	no	—
380	C₂×C₈	—	30	2	no	—
381	C₄⋊C₄	—	3	2	no	—
382	C₄⋊C₄	—	3	2	no	—
383	C₄⋊C₄	—	3	2	no	—
384	C₄⋊C₄	—	3	2	no	—
385	C₄⋊C₄	—	3	2	no	—
386	C₄⋊C₄	—	3	2	no	—
387	C₄⋊C₄	—	3	1	no	—
388	C₄⋊C₄	D₃×Dic₅	1	2	yes	—
389	C₄⋊C₄	D₃×Dic₅	1	1	yes	characteristic
390	C₂²⋊C₄	—	3	2	no	—
391	C₂²⋊C₄	—	3	2	no	—
392	C₄²	—	3	1	no	—
393	C₄²	—	3	1	no	—
394	C₄²	—	3	1	no	—
395	C₄²	—	3	2	no	—
396	C₄²	C₂×D₃×D₅	1	1	yes	characteristic
397	C₄²	C₂×D₃×D₅	1	2	yes	—
398	C₃×C₅	#2960	1	1	yes	characteristic, complemented, Hall
399	C₂²×C₃	C₂³×Dic₅	1	1	yes	characteristic
400	C₂×D₃	—	2	1	no	—
401	C₂×D₃	—	2	1	no	—
402	C₂×D₃	Q₈×Dic₅	1	2	yes	—
403	C₃×C₄	—	2	2	no	—
404	C₃×C₄	—	2	1	no	—
405	C₃×C₄	—	2	2	no	—
406	C₃×C₄	#4094	1	2	yes	—
407	C₃×C₄	C₂×Q₈×D₅	1	1	yes	characteristic
408	C₃×C₄	C₂×#713	1	1	yes	characteristic
409	Dic₃	—	2	2	no	—
410	Dic₃	—	2	2	no	—
411	Dic₃	—	2	1	no	—
412	Dic₃	Q₈×Dic₅	1	2	yes	—
413	Dic₃	#4094	1	2	yes	—
414	C₂×C₅	—	6	2	no	—
415	C₂×C₅	C₄×D₃×Q₈	1	1	yes	characteristic
416	C₂×C₅	C₂×#901	1	1	yes	characteristic
417	C₂×C₅	D₃×#131	1	1	yes	characteristic
418	C₂³	—	3	1	no	—
419	Q₈	—	2	2	no	—
420	Q₈	—	6	4	no	—
421	Q₈	—	6	2	no	—
422	C₂×C₄	—	3	1	no	—
423	C₂×C₄	—	3	1	no	—
424	C₂×C₄	—	3	2	no	—
425	C₂×C₄	—	3	2	no	—
426	C₂×C₄	—	3	1	no	—
427	C₂×C₄	—	3	2	no	—
428	C₂×C₄	—	3	2	no	—
429	C₂×C₄	—	6	2	no	—
430	C₂×C₄	—	6	2	no	—
431	C₂×C₄	C₂×D₃×Dic₅	1	1	yes	characteristic
432	C₂×C₄	C₂×D₃×Dic₅	1	2	yes	—
433	C₂×C₄	C₂×D₃×Dic₅	1	2	yes	—
434	C₂×C₄	C₂×D₃×Dic₅	1	1	yes	characteristic
435	C₂×C₄	C₂²×D₃×D₅	1	1	yes	characteristic
436	C₈	—	5	2	no	—
437	C₈	—	10	1	no	—
438	C₈	—	10	2	no	—
439	C₈	—	15	2	no	—
440	C₈	—	30	1	no	—
441	C₈	—	30	2	no	—
442	C₂×C₃	C₂×Q₈×Dic₅	1	1	yes	characteristic
443	C₂×C₃	C₂×#4094	1	1	yes	characteristic
444	C₂×C₃	C₂×#4094	1	1	yes	characteristic
445	D₃	—	2	2	no	—
446	C₅	#79917	1	1	yes	characteristic, complemented, Sylow
447	C₂²	—	3	2	no	—
448	C₂²	—	6	1	no	—
449	C₂²	—	6	1	no	—
450	C₂²	C₂²×D₃×Dic₅	1	1	yes	characteristic
451	C₄	—	2	1	no	—
452	C₄	—	2	2	no	—
453	C₄	—	2	2	no	—
454	C₄	—	3	2	no	—
455	C₄	—	3	2	no	—
456	C₄	—	6	2	no	—
457	C₄	—	6	1	no	—
458	C₄	—	6	2	no	—
459	C₄	#91286	1	2	yes	—
460	C₄	D₃×Q₈×D₅	1	1	yes	characteristic
461	C₄	D₃×#713	1	1	yes	characteristic
462	C₃	#10615059	1	1	yes	characteristic, complemented, Sylow
463	C₂	—	6	2	no	—
464	C₂	C₂×#91286	1	1	yes	characteristic
465	C₂	D₃×Q₈×Dic₅	1	1	yes	characteristic
466	C₂	D₃×#4094	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×D₃×D₅
commutator, socle	C₂²×C₃×C₅	C₂³×C₄
Fitting	C₃×C₄×C₅×Q₈	C₂²
prime radical	C₂²×C₅×D₃	C₂²×C₄
cosocle	C₂×C₃×C₄×C₅	C₂⁴
hypercenter	C₄×Q₈	D₃×D₅
hypocenter	C₃×C₅	#2960
LCS	G ▷ C₂²×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂×C₄ ◁ C₄×Q₈

Complements

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

N	H ≅ G/N	type
2. #11751125	C₂	semidirect
3. C₃×Q₈×#168	C₂	semidirect
8. #11746866	C₂	semidirect
9. #11746858	C₂	semidirect
10. Dic₆×#168	C₂	semidirect
11. Dic₆×#168	C₂	semidirect
49. Q₈×#168	D₃	semidirect
85. D₃×#168	Q₈	semidirect
398. C₃×C₅	#2960	semidirect
446. C₅	#79917	semidirect
462. C₃	#10615059	semidirect

Maximal subgroups

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

subgroup	index
C₅×#5578	2
#11751125	2
C₃×Q₈×#168	2
#11747011	2
#11746993	2
#11746977	2
C₄×D₃×#168	2
#11746866	2
#11746858	2
Dic₆×#168	2
#10615059	3
#79917	5