Subgroups — C₄×#91264 #14416166

Order 1920.

976 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#91264	C₂	1	1	yes	maximal, characteristic
2	C₄×D₁₅⋊Q₈	C₂	1	2	yes	maximal
3	C₄×C₈×D₁₅	C₂	1	1	yes	maximal, characteristic
4	C₄×C₅×Dic₁₂	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×C₄×Dic₂₀	C₂	1	1	yes	maximal, characteristic, complemented
6	#11747886	C₂	1	1	yes	maximal, characteristic, complemented
7	#11747883	C₂	1	1	yes	maximal, characteristic, complemented
8	#11747828	C₂	1	2	yes	maximal, complemented
9	#11747636	C₂	1	1	yes	maximal, characteristic
10	#11747609	C₂	1	2	yes	maximal
11	C₄×#6661	C₂	1	2	yes	maximal, complemented
12	C₄×D₅×Q₁₆	—	3	1	no	maximal, Hall
13	C₂×D₁₅⋊Q₈	C₂²	1	2	yes	—
14	C₂×C₈×D₁₅	C₂²	1	1	yes	characteristic
15	C₂×C₈×D₁₅	C₂²	1	1	yes	characteristic
16	C₄²×D₁₅	C₂²	1	1	yes	characteristic
17	C₂×C₅×Dic₁₂	C₂²	1	1	yes	characteristic
18	C₄×C₅×Dic₆	C₂²	1	2	yes	—
19	C₂×C₃×Dic₂₀	C₂²	1	1	yes	characteristic
20	C₃×C₄×Dic₁₀	C₂²	1	2	yes	—
21	C₄×#1204	—	2	2	no	—
22	#91437	C₂²	1	2	yes	—
23	#91404	—	2	2	no	—
24	C₄×#1200	—	2	2	no	—
25	#91344	C₂²	1	2	yes	—
26	#91331	C₂²	1	2	yes	—
27	#91325	—	2	2	no	—
28	C₂×#6661	C₂²	1	2	yes	—
29	#91264	C₄	1	8	yes	direct product factor
30	C₃×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
31	C₈×Dic₁₅	C₂²	1	1	yes	characteristic
32	C₈×Dic₁₅	C₂²	1	1	yes	characteristic
33	C₄×C₃⋊#168	C₂²	1	1	yes	characteristic
34	C₅×#818	C₂²	1	1	yes	characteristic
35	C₅×#816	C₂²	1	2	yes	—
36	C₃×#3950	C₂²	1	1	yes	characteristic
37	C₃×#3948	C₂²	1	2	yes	—
38	#90989	C₂²	1	2	yes	—
39	#90972	C₂²	1	2	yes	—
40	#90970	C₂²	1	2	yes	—
41	C₄×D₃×Q₁₆	—	5	1	no	maximal, Hall
42	C₂×D₅×Q₁₆	—	3	1	no	—
43	C₄×Q₈×D₅	—	3	2	no	—
44	C₄×C₅×Q₁₆	—	3	1	no	—
45	Q₁₆×Dic₅	—	3	1	no	—
46	C₄×#689	—	3	2	no	—
47	D₅×#107	—	3	1	no	—
48	#65162	—	3	1	no	—
49	D₅×#103	—	3	2	no	—
50	#65079	—	3	2	no	—
51	C₄×Dic₂₀	D₃	1	1	yes	characteristic, complemented
52	C₄×C₈×D₅	—	3	1	no	—
53	C₂×C₄×D₁₅	D₄	1	1	yes	characteristic
54	C₂×C₄×D₁₅	D₄	1	1	yes	characteristic
55	C₂×C₄×D₁₅	C₂³	1	1	yes	characteristic
56	C₂×C₅×Dic₆	C₂³	1	2	yes	—
57	C₂×C₃×Dic₁₀	C₂³	1	2	yes	—
58	C₂×#1204	—	2	2	no	—
59	C₂×#1200	—	2	2	no	—
60	C₂×#1200	—	2	2	no	—
61	D₁₅⋊Q₈	—	2	4	no	—
62	D₁₅⋊Q₈	C₂×C₄	1	8	yes	—
63	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
64	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
65	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
66	C₄×Dic₁₅	D₄	1	1	yes	characteristic
67	C₄×Dic₁₅	D₄	1	1	yes	characteristic
68	C₄×Dic₁₅	C₂³	1	1	yes	characteristic
69	C₂×C₃⋊#168	C₂³	1	1	yes	characteristic
70	C₂×C₃⋊#168	C₂³	1	1	yes	characteristic
71	C₈×D₁₅	—	2	2	no	—
72	C₈×D₁₅	C₂×C₄	1	4	yes	—
73	C₅×C₄⋊Dic₃	C₂³	1	2	yes	—
74	C₅×Dic₃⋊C₄	—	2	2	no	—
75	C₄×C₅×Dic₃	—	2	2	no	—
76	C₅×Dic₁₂	C₂×C₄	1	4	yes	complemented
77	C₃×C₄⋊Dic₅	C₂³	1	2	yes	—
78	C₃×#683	—	2	2	no	—
79	C₃×C₄×Dic₅	—	2	2	no	—
80	C₃×Dic₂₀	C₂×C₄	1	4	yes	complemented
81	Dic₃⋊Dic₅	—	2	2	no	—
82	#6669	—	2	2	no	—
83	#6668	—	2	2	no	—
84	Dic₃×Dic₅	—	2	2	no	—
85	Dic₃×Dic₅	—	2	2	no	—
86	#6661	C₂×C₄	1	8	yes	complemented
87	C₂×D₃×Q₁₆	—	5	1	no	—
88	C₄×D₃×Q₈	—	5	2	no	—
89	C₃×C₄×Q₁₆	—	5	1	no	—
90	Dic₃×Q₁₆	—	5	1	no	—
91	C₄×#216	—	5	2	no	—
92	D₃×#107	—	5	1	no	—
93	#4873	—	5	1	no	—
94	D₃×#103	—	5	2	no	—
95	#4790	—	5	2	no	—
96	C₄×Dic₁₂	D₅	1	1	yes	characteristic, complemented
97	C₄×D₃×C₈	—	5	1	no	—
98	C₂×Q₈×D₅	—	3	2	no	—
99	C₂×C₅×Q₁₆	—	3	1	no	—
100	C₄×C₅×Q₈	—	3	2	no	—
101	Q₈×Dic₅	—	3	2	no	—
102	C₂×#689	—	3	2	no	—
103	D₅×Q₁₆	—	3	8	no	—
104	C₂×Dic₂₀	C₂×D₃	1	1	yes	characteristic
105	C₂×C₈×D₅	—	3	1	no	—
106	C₂×C₈×D₅	—	3	1	no	—
107	D₅×C₄⋊C₄	—	3	2	no	—
108	D₅×C₄⋊C₄	—	6	2	no	—
109	#4033	—	3	2	no	—
110	#4033	—	6	2	no	—
111	C₄²×D₅	—	3	1	no	—
112	C₄²×D₅	—	6	2	no	—
113	C₄×Dic₁₀	—	6	2	no	—
114	C₄×Dic₁₀	C₂×D₃	1	2	yes	—
115	C₅×#107	—	3	1	no	—
116	C₅×#103	—	3	2	no	—
117	C₄×C₅×C₈	C₂×D₃	1	1	yes	characteristic
118	#3967	—	3	2	no	—
119	#3950	C₂×D₃	1	1	yes	characteristic
120	#3948	C₂×D₃	1	2	yes	—
121	C₈×Dic₅	—	3	1	no	—
122	C₈×Dic₅	—	3	1	no	—
123	#3942	—	3	2	no	—
124	#3939	—	3	2	no	—
125	C₄×#168	—	3	1	no	—
126	C₂×C₄×Q₁₆	—	15	1	no	Sylow
127	C₂²×D₁₅	C₂×D₄	1	1	yes	characteristic
128	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
129	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
130	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
131	C₂×Dic₁₅	C₂×D₄	1	1	yes	characteristic
132	C₂×Dic₁₅	C₂×D₄	1	1	yes	characteristic
133	C₂×Dic₁₅	C₂×D₄	1	1	yes	characteristic
134	C₄×D₁₅	—	2	2	no	—
135	C₄×D₁₅	Q₁₆	1	4	yes	complemented
136	C₄×D₁₅	C₂²×C₄	1	2	yes	—
137	C₄×D₁₅	#41	1	2	yes	—
138	C₂×C₅×Dic₃	—	2	2	no	—
139	C₂×C₅×Dic₃	—	2	2	no	—
140	C₅×Dic₆	—	2	2	no	—
141	C₅×Dic₆	C₂²×C₄	1	4	yes	—
142	C₂×C₃×Dic₅	—	2	2	no	—
143	C₂×C₃×Dic₅	—	2	2	no	—
144	C₃×Dic₁₀	—	2	2	no	—
145	C₃×Dic₁₀	C₂²×C₄	1	4	yes	—
146	#1204	—	2	8	no	—
147	#1200	—	2	8	no	—
148	#1200	—	4	4	no	—
149	C₃×C₅×C₈	—	2	1	no	—
150	C₃×C₅×C₈	C₂²×C₄	1	2	yes	—
151	C₃⋊#168	—	2	1	no	—
152	C₃⋊#168	C₂²×C₄	1	2	yes	—
153	C₂×D₃×Q₈	—	5	2	no	—
154	C₂×C₃×Q₁₆	—	5	1	no	—
155	C₃×C₄×Q₈	—	5	2	no	—
156	Q₈×Dic₃	—	5	2	no	—
157	C₂×#216	—	5	2	no	—
158	D₃×Q₁₆	—	5	8	no	—
159	C₂×Dic₁₂	C₂×D₅	1	1	yes	characteristic
160	C₂×D₃×C₈	—	5	1	no	—
161	C₂×D₃×C₈	—	5	1	no	—
162	D₃×C₄⋊C₄	—	5	2	no	—
163	D₃×C₄⋊C₄	—	10	2	no	—
164	#887	—	5	2	no	—
165	#887	—	10	2	no	—
166	C₄²×D₃	—	5	1	no	—
167	C₄²×D₃	—	10	2	no	—
168	C₄×Dic₆	—	10	2	no	—
169	C₄×Dic₆	C₂×D₅	1	2	yes	—
170	C₃×#107	—	5	1	no	—
171	C₃×#103	—	5	2	no	—
172	C₃×C₄×C₈	C₂×D₅	1	1	yes	characteristic
173	#835	—	5	2	no	—
174	#818	C₂×D₅	1	1	yes	characteristic
175	#816	C₂×D₅	1	2	yes	—
176	C₈×Dic₃	—	5	1	no	—
177	C₈×Dic₃	—	5	1	no	—
178	#810	—	5	2	no	—
179	#807	—	5	2	no	—
180	C₄×C₃⋊C₈	—	5	1	no	—
181	C₂×C₅×Q₈	—	3	2	no	—
182	Q₈×D₅	—	3	8	no	—
183	Q₈×D₅	—	6	4	no	—
184	C₂×C₄×D₅	—	3	1	no	—
185	C₂×C₄×D₅	—	3	1	no	—
186	C₂×C₄×D₅	—	3	1	no	—
187	C₂×C₄×D₅	—	6	2	no	—
188	C₂×C₄×D₅	—	6	2	no	—
189	C₂×Dic₁₀	—	6	2	no	—
190	C₂×Dic₁₀	C₂²×D₃	1	2	yes	—
191	C₅×Q₁₆	—	3	4	no	—
192	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
193	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
194	C₅×C₄⋊C₄	—	3	2	no	—
195	C₅×C₄⋊C₄	—	6	2	no	—
196	C₄²×C₅	—	6	2	no	—
197	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
198	#689	—	3	8	no	—
199	C₄⋊Dic₅	—	6	2	no	—
200	C₄⋊Dic₅	C₂²×D₃	1	2	yes	—
201	#683	—	2	2	no	—
202	#683	—	6	2	no	—
203	#683	—	6	2	no	—
204	C₄×Dic₅	—	2	2	no	—
205	C₄×Dic₅	—	3	1	no	—
206	C₄×Dic₅	—	3	1	no	—
207	C₄×Dic₅	—	3	1	no	—
208	C₄×Dic₅	—	6	2	no	—
209	C₄×Dic₅	—	6	2	no	—
210	C₂×#168	—	3	1	no	—
211	C₂×#168	—	3	1	no	—
212	Dic₂₀	C₄×D₃	1	4	yes	complemented
213	C₈×D₅	—	3	4	no	—
214	C₈×D₅	—	6	2	no	—
215	C₂²×Q₁₆	—	15	1	no	—
216	C₂×C₄×Q₈	—	15	2	no	—
217	C₄×Q₁₆	—	3	1	no	—
218	C₄×Q₁₆	—	5	1	no	—
219	C₄×Q₁₆	—	15	2	no	—
220	C₄×Q₁₆	—	15	1	no	—
221	C₄×Q₁₆	—	15	1	no	—
222	C₄×Q₁₆	—	15	2	no	—
223	C₂×#107	—	15	1	no	—
224	C₂×#103	—	15	2	no	—
225	C₂×C₄×C₈	—	15	1	no	—
226	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
227	C₂×D₁₅	C₄×D₄	1	2	yes	—
228	C₂×D₁₅	C₂×Q₁₆	1	2	yes	—
229	C₂×D₁₅	#135	1	2	yes	—
230	C₃×C₄×C₅	—	2	1	no	—
231	C₃×C₄×C₅	C₂×Q₁₆	1	2	yes	complemented
232	C₃×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
233	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
234	Dic₁₅	—	2	1	no	—
235	Dic₁₅	C₄×D₄	1	2	yes	—
236	Dic₁₅	C₂×Q₁₆	1	2	yes	complemented
237	C₃×Dic₅	—	2	4	no	—
238	C₃×Dic₅	—	4	2	no	—
239	C₅×Dic₃	—	2	4	no	—
240	C₅×Dic₃	—	4	2	no	—
241	C₂×C₃×Q₈	—	5	2	no	—
242	D₃×Q₈	—	5	8	no	—
243	D₃×Q₈	—	10	4	no	—
244	C₂×C₄×D₃	—	5	1	no	—
245	C₂×C₄×D₃	—	5	1	no	—
246	C₂×C₄×D₃	—	5	1	no	—
247	C₂×C₄×D₃	—	10	2	no	—
248	C₂×C₄×D₃	—	10	2	no	—
249	C₂×Dic₆	—	10	2	no	—
250	C₂×Dic₆	C₂²×D₅	1	2	yes	—
251	C₃×Q₁₆	—	5	4	no	—
252	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
253	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
254	C₃×C₄⋊C₄	—	5	2	no	—
255	C₃×C₄⋊C₄	—	10	2	no	—
256	C₃×C₄²	—	10	2	no	—
257	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
258	#216	—	5	8	no	—
259	C₄⋊Dic₃	—	10	2	no	—
260	C₄⋊Dic₃	C₂²×D₅	1	2	yes	—
261	Dic₃⋊C₄	—	2	2	no	—
262	Dic₃⋊C₄	—	10	2	no	—
263	Dic₃⋊C₄	—	10	2	no	—
264	C₄×Dic₃	—	2	2	no	—
265	C₄×Dic₃	—	5	1	no	—
266	C₄×Dic₃	—	5	1	no	—
267	C₄×Dic₃	—	5	1	no	—
268	C₄×Dic₃	—	10	2	no	—
269	C₄×Dic₃	—	10	2	no	—
270	C₂×C₃⋊C₈	—	5	1	no	—
271	C₂×C₃⋊C₈	—	5	1	no	—
272	Dic₁₂	C₄×D₅	1	4	yes	complemented
273	D₃×C₈	—	5	4	no	—
274	D₃×C₈	—	10	2	no	—
275	C₂²×D₅	—	3	1	no	—
276	C₅×Q₈	—	3	4	no	—
277	C₅×Q₈	—	6	2	no	—
278	C₂×C₄×C₅	—	6	2	no	—
279	C₂×C₄×C₅	—	6	2	no	—
280	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
281	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
282	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
283	C₂×Dic₅	—	2	2	no	—
284	C₂×Dic₅	—	2	2	no	—
285	C₂×Dic₅	—	3	1	no	—
286	C₂×Dic₅	—	3	1	no	—
287	C₂×Dic₅	—	3	1	no	—
288	C₄×D₅	—	3	4	no	—
289	C₄×D₅	—	3	2	no	—
290	C₄×D₅	—	3	2	no	—
291	C₄×D₅	—	6	8	no	—
292	C₄×D₅	—	6	2	no	—
293	C₄×D₅	—	12	4	no	—
294	Dic₁₀	—	2	2	no	—
295	Dic₁₀	—	6	8	no	—
296	Dic₁₀	C₂×C₄×D₃	1	4	yes	—
297	C₅×C₈	—	2	1	no	—
298	C₅×C₈	C₂×C₄×D₃	1	2	yes	—
299	#168	—	3	2	no	—
300	#168	—	6	1	no	—
301	C₂²×Q₈	—	15	2	no	—
302	C₂×Q₁₆	—	3	1	no	—
303	C₂×Q₁₆	—	5	1	no	—
304	C₂×Q₁₆	—	15	8	no	—
305	C₂×Q₁₆	—	15	2	no	—
306	C₂²×C₈	—	15	1	no	—
307	C₂²×C₈	—	15	1	no	—
308	C₄×Q₈	—	3	2	no	—
309	C₄×Q₈	—	5	2	no	—
310	C₄×Q₈	—	15	2	no	—
311	C₄×Q₈	—	15	2	no	—
312	C₄×Q₈	—	30	2	no	—
313	C₄×Q₈	—	30	2	no	—
314	C₂×C₄⋊C₄	—	15	2	no	—
315	C₂×C₄⋊C₄	—	30	2	no	—
316	C₂×C₄²	—	15	1	no	—
317	C₂×C₄²	—	30	2	no	—
318	#107	—	3	1	no	—
319	#107	—	5	1	no	—
320	#107	—	15	2	no	—
321	#103	—	3	2	no	—
322	#103	—	5	2	no	—
323	#103	—	15	2	no	—
324	#103	—	15	2	no	—
325	C₄×C₈	—	15	1	no	—
326	C₄×C₈	—	15	1	no	—
327	C₄×C₈	—	15	1	no	—
328	C₄×C₈	D₃×D₅	1	1	yes	characteristic
329	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
330	C₂×C₃×C₅	C₂²×Q₁₆	1	1	yes	characteristic
331	C₂×C₃×C₅	C₂×#135	1	1	yes	characteristic
332	D₁₅	C₄×Q₁₆	1	4	yes	complemented
333	C₂²×D₃	—	5	1	no	—
334	C₃×Q₈	—	5	4	no	—
335	C₃×Q₈	—	10	2	no	—
336	C₂×C₃×C₄	—	10	2	no	—
337	C₂×C₃×C₄	—	10	2	no	—
338	C₂×C₃×C₄	D₄×D₅	1	1	yes	characteristic
339	C₂×C₃×C₄	D₄×D₅	1	1	yes	characteristic
340	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
341	C₂×Dic₃	—	2	2	no	—
342	C₂×Dic₃	—	2	2	no	—
343	C₂×Dic₃	—	5	1	no	—
344	C₂×Dic₃	—	5	1	no	—
345	C₂×Dic₃	—	5	1	no	—
346	C₄×D₃	—	5	2	no	—
347	C₄×D₃	—	5	2	no	—
348	C₄×D₃	—	5	4	no	—
349	C₄×D₃	—	10	8	no	—
350	C₄×D₃	—	10	2	no	—
351	C₄×D₃	—	20	4	no	—
352	Dic₆	—	2	2	no	—
353	Dic₆	—	10	8	no	—
354	Dic₆	C₂×C₄×D₅	1	4	yes	—
355	C₃×C₈	—	2	1	no	—
356	C₃×C₈	C₂×C₄×D₅	1	2	yes	—
357	C₃⋊C₈	—	5	2	no	—
358	C₃⋊C₈	—	10	1	no	—
359	C₂²×C₅	C₂×D₃×D₄	1	1	yes	characteristic
360	C₂×D₅	—	3	2	no	—
361	C₂×D₅	—	3	2	no	—
362	C₂×D₅	—	3	2	no	—
363	C₄×C₅	—	2	1	no	—
364	C₄×C₅	—	6	4	no	—
365	C₄×C₅	—	12	2	no	—
366	C₄×C₅	D₃×Q₁₆	1	2	yes	complemented
367	C₄×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
368	C₄×C₅	D₃×#41	1	1	yes	characteristic
369	Dic₅	—	2	4	no	—
370	Dic₅	—	3	2	no	—
371	Dic₅	—	3	2	no	—
372	Dic₅	—	4	2	no	—
373	Dic₅	—	6	1	no	—
374	C₂×Q₈	—	3	2	no	—
375	C₂×Q₈	—	5	2	no	—
376	C₂×Q₈	—	15	8	no	—
377	C₂×Q₈	—	30	2	no	—
378	C₂×Q₈	—	30	4	no	—
379	C₂²×C₄	—	15	1	no	—
380	C₂²×C₄	—	15	1	no	—
381	C₂²×C₄	—	15	1	no	—
382	C₂²×C₄	—	30	2	no	—
383	C₂²×C₄	—	30	2	no	—
384	Q₁₆	—	3	4	no	—
385	Q₁₆	—	5	4	no	—
386	Q₁₆	—	15	8	no	—
387	C₂×C₈	—	15	1	no	—
388	C₂×C₈	—	15	4	no	—
389	C₂×C₈	—	15	1	no	—
390	C₂×C₈	—	30	2	no	—
391	C₂×C₈	C₂×D₃×D₅	1	1	yes	characteristic
392	C₂×C₈	C₂×D₃×D₅	1	1	yes	characteristic
393	C₄⋊C₄	—	3	2	no	—
394	C₄⋊C₄	—	5	2	no	—
395	C₄⋊C₄	—	6	2	no	—
396	C₄⋊C₄	—	10	2	no	—
397	C₄⋊C₄	—	30	2	no	—
398	C₄⋊C₄	—	30	2	no	—
399	C₄⋊C₄	—	30	2	no	—
400	C₄²	—	6	2	no	—
401	C₄²	—	10	2	no	—
402	C₄²	—	15	1	no	—
403	C₄²	—	15	1	no	—
404	C₄²	—	15	1	no	—
405	C₄²	—	30	2	no	—
406	C₄²	—	30	2	no	—
407	C₄²	C₂×D₃×D₅	1	1	yes	characteristic
408	C₃×C₅	C₂×C₄×Q₁₆	1	1	yes	characteristic, complemented, Hall
409	C₂²×C₃	C₂×D₄×D₅	1	1	yes	characteristic
410	C₂×D₃	—	5	2	no	—
411	C₂×D₃	—	5	2	no	—
412	C₂×D₃	—	5	2	no	—
413	C₃×C₄	—	2	1	no	—
414	C₃×C₄	—	10	4	no	—
415	C₃×C₄	—	20	2	no	—
416	C₃×C₄	D₅×Q₁₆	1	2	yes	complemented
417	C₃×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
418	C₃×C₄	D₅×#41	1	1	yes	characteristic
419	Dic₃	—	2	4	no	—
420	Dic₃	—	4	2	no	—
421	Dic₃	—	5	2	no	—
422	Dic₃	—	5	2	no	—
423	Dic₃	—	10	1	no	—
424	C₂×C₅	C₄×D₃×D₄	1	1	yes	characteristic
425	C₂×C₅	C₂×D₃×Q₁₆	1	1	yes	characteristic
426	C₂×C₅	D₃×#135	1	1	yes	characteristic
427	D₅	—	3	4	no	—
428	C₂³	—	15	1	no	—
429	Q₈	—	3	4	no	—
430	Q₈	—	5	4	no	—
431	Q₈	—	6	2	no	—
432	Q₈	—	10	2	no	—
433	Q₈	—	30	8	no	—
434	C₂×C₄	—	6	2	no	—
435	C₂×C₄	—	6	2	no	—
436	C₂×C₄	—	10	2	no	—
437	C₂×C₄	—	10	2	no	—
438	C₂×C₄	—	15	1	no	—
439	C₂×C₄	—	15	1	no	—
440	C₂×C₄	—	15	2	no	—
441	C₂×C₄	—	15	2	no	—
442	C₂×C₄	—	15	4	no	—
443	C₂×C₄	—	15	1	no	—
444	C₂×C₄	—	30	2	no	—
445	C₂×C₄	—	30	8	no	—
446	C₂×C₄	—	60	4	no	—
447	C₂×C₄	#6777	1	1	yes	characteristic
448	C₂×C₄	#6777	1	1	yes	characteristic
449	C₂×C₄	C₂²×D₃×D₅	1	1	yes	characteristic
450	C₈	—	2	1	no	—
451	C₈	—	15	2	no	—
452	C₈	—	30	1	no	—
453	C₈	C₄×D₃×D₅	1	2	yes	—
454	C₂×C₃	C₄×D₄×D₅	1	1	yes	characteristic
455	C₂×C₃	C₂×D₅×Q₁₆	1	1	yes	characteristic
456	C₂×C₃	D₅×#135	1	1	yes	characteristic
457	D₃	—	5	4	no	—
458	C₅	C₄×D₃×Q₁₆	1	1	yes	characteristic, complemented, Sylow
459	C₂²	—	15	2	no	—
460	C₂²	—	15	2	no	—
461	C₂²	—	15	2	no	—
462	C₂²	C₂×#6777	1	1	yes	characteristic
463	C₄	—	2	1	no	—
464	C₄	—	6	4	no	—
465	C₄	—	10	4	no	—
466	C₄	—	12	2	no	—
467	C₄	—	15	2	no	—
468	C₄	—	15	2	no	—
469	C₄	—	20	2	no	—
470	C₄	—	30	1	no	—
471	C₄	#91264	1	2	yes	direct product factor
472	C₄	C₂×C₄×D₃×D₅	1	1	yes	characteristic
473	C₄	#92016	1	1	yes	characteristic
474	C₃	C₄×D₅×Q₁₆	1	1	yes	characteristic, complemented, Sylow
475	C₂	—	15	4	no	—
476	C₂	C₄×#6777	1	1	yes	characteristic
477	C₂	#11753978	1	1	yes	characteristic
478	C₂	C₂×#91264	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#6777
commutator	C₃×C₄×C₅	C₂³×C₄
Frattini	C₂×C₄	C₂²×D₃×D₅
Fitting	C₃×C₄×C₅×C₈	C₂²
socle	C₂²×C₃×C₅	C₂²×D₄
prime radical	C₂²×D₁₅	C₂×D₄
cosocle	C₂×C₃×C₄×C₅	C₂⁴
hypercenter	C₄×C₈	D₃×D₅
hypocenter	C₃×C₅	C₂×C₄×Q₁₆
LCS	G ▷ C₃×C₄×C₅ ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂×C₄ ◁ C₄² ◁ C₄×C₈

Complements

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

N	H ≅ G/N	type
4. C₄×C₅×Dic₁₂	C₂	semidirect
5. C₃×C₄×Dic₂₀	C₂	semidirect
6. #11747886	C₂	semidirect
7. #11747883	C₂	semidirect
8. #11747828	C₂	semidirect
11. C₄×#6661	C₂	semidirect
29. #91264	C₄	direct (N × H)
51. C₄×Dic₂₀	D₃	semidirect
76. C₅×Dic₁₂	C₂×C₄	semidirect
80. C₃×Dic₂₀	C₂×C₄	semidirect
86. #6661	C₂×C₄	semidirect
96. C₄×Dic₁₂	D₅	semidirect
135. C₄×D₁₅	Q₁₆	semidirect
212. Dic₂₀	C₄×D₃	semidirect
231. C₃×C₄×C₅	C₂×Q₁₆	semidirect
236. Dic₁₅	C₂×Q₁₆	semidirect
272. Dic₁₂	C₄×D₅	semidirect
332. D₁₅	C₄×Q₁₆	semidirect
366. C₄×C₅	D₃×Q₁₆	semidirect
408. C₃×C₅	C₂×C₄×Q₁₆	semidirect
416. C₃×C₄	D₅×Q₁₆	semidirect
458. C₅	C₄×D₃×Q₁₆	semidirect
471. C₄	#91264	direct (N × H)
474. C₃	C₄×D₅×Q₁₆	semidirect

Maximal subgroups

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

subgroup	index
C₂×#91264	2
C₄×D₁₅⋊Q₈	2
C₄×C₈×D₁₅	2
C₄×C₅×Dic₁₂	2
C₃×C₄×Dic₂₀	2
#11747886	2
#11747883	2
#11747828	2
#11747636	2
#11747609	2
C₄×#6661	2
C₄×D₅×Q₁₆	3
C₄×D₃×Q₁₆	5

Subgroups — C4×#91264 #14416166

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#91264 #14416166