Subgroups — C₄×#91808 #14416217

Order 1920.

1000 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	C₂×#91808	C₂	1	1	yes	maximal, characteristic
2	C₄×#6821	C₂	1	2	yes	maximal, complemented
3	C₃×C₄×C₅×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
4	Q₁₆×Dic₁₅	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄×#6717	C₂	1	2	yes	maximal, complemented
6	#11750981	C₂	1	1	yes	maximal, characteristic, complemented
7	#11750973	C₂	1	1	yes	maximal, characteristic, complemented
8	#11750905	C₂	1	2	yes	maximal, complemented
9	#11750889	C₂	1	2	yes	maximal, complemented
10	C₄×D₁₂₀	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×C₈×D₁₅	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄×#4065	—	3	1	no	maximal, Hall
13	C₂×#6821	C₂²	1	2	yes	—
14	C₂×C₃×C₅×Q₁₆	C₂²	1	1	yes	characteristic
15	C₃×C₄×C₅×Q₈	C₂²	1	2	yes	—
16	Q₈×Dic₁₅	C₂²	1	2	yes	—
17	C₂×#6717	C₂²	1	2	yes	—
18	#91808	C₄	1	8	yes	direct product factor
19	C₂×D₁₂₀	C₂²	1	1	yes	characteristic
20	C₂×C₈×D₁₅	C₂²	1	1	yes	characteristic
21	C₂×C₈×D₁₅	C₂²	1	1	yes	characteristic
22	#91782	—	2	2	no	—
23	#91782	C₂²	1	2	yes	—
24	#91781	—	2	2	no	—
25	#91781	C₂²	1	2	yes	—
26	C₄×D₆₀	—	2	2	no	—
27	C₄×D₆₀	C₂²	1	2	yes	—
28	C₄²×D₁₅	—	2	2	no	—
29	C₄²×D₁₅	C₂²	1	1	yes	characteristic
30	C₃×C₅×#107	C₂²	1	1	yes	characteristic
31	C₃×C₅×#103	C₂²	1	2	yes	—
32	C₃×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
33	#91119	C₂²	1	2	yes	—
34	#91105	C₂²	1	2	yes	—
35	#91102	C₂²	1	1	yes	characteristic
36	C₈×Dic₁₅	C₂²	1	1	yes	characteristic
37	C₈×Dic₁₅	C₂²	1	1	yes	characteristic
38	#91093	C₂²	1	2	yes	—
39	#91092	C₂²	1	2	yes	—
40	C₄×C₃⋊#168	C₂²	1	1	yes	characteristic
41	C₄×#919	—	5	1	no	maximal, Hall
42	C₂×#4065	—	3	1	no	—
43	C₄×#713	—	3	2	no	—
44	C₄×C₅×Q₁₆	D₃	1	1	yes	characteristic, complemented
45	Q₁₆×Dic₅	—	3	1	no	—
46	C₄×#688	—	3	2	no	—
47	#65169	—	3	1	no	—
48	#65161	—	3	1	no	—
49	#65093	—	3	2	no	—
50	#65077	—	3	2	no	—
51	C₄×D₄₀	—	3	1	no	—
52	C₄×C₈×D₅	—	3	1	no	—
53	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
54	#6821	—	2	4	no	—
55	#6821	C₂×C₄	1	8	yes	complemented
56	C₂×D₆₀	—	2	2	no	—
57	C₂×D₆₀	C₂³	1	2	yes	—
58	C₂×C₄×D₁₅	—	2	2	no	—
59	C₂×C₄×D₁₅	—	2	2	no	—
60	C₂×C₄×D₁₅	—	2	2	no	—
61	C₂×C₄×D₁₅	D₄	1	1	yes	characteristic
62	C₂×C₄×D₁₅	D₄	1	1	yes	characteristic
63	C₂×C₄×D₁₅	C₂³	1	1	yes	characteristic
64	C₃×C₅×Q₁₆	C₂×C₄	1	4	yes	complemented
65	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
66	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
67	C₃×C₅×C₄⋊C₄	—	2	2	no	—
68	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
69	C₃×C₄²×C₅	—	2	2	no	—
70	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
71	#6717	C₂×C₄	1	8	yes	complemented
72	#6714	—	2	2	no	—
73	#6714	—	2	2	no	—
74	#6714	—	2	2	no	—
75	C₄⋊Dic₁₅	—	2	2	no	—
76	C₄⋊Dic₁₅	C₂³	1	2	yes	—
77	C₄×Dic₁₅	—	2	2	no	—
78	C₄×Dic₁₅	—	2	2	no	—
79	C₄×Dic₁₅	D₄	1	1	yes	characteristic
80	C₄×Dic₁₅	D₄	1	1	yes	characteristic
81	C₄×Dic₁₅	C₂³	1	1	yes	characteristic
82	C₂×C₃⋊#168	C₂³	1	1	yes	characteristic
83	C₂×C₃⋊#168	C₂³	1	1	yes	characteristic
84	D₁₂₀	C₂×C₄	1	4	yes	complemented
85	C₈×D₁₅	—	2	2	no	—
86	C₈×D₁₅	C₂×C₄	1	4	yes	complemented
87	C₂×#919	—	5	1	no	—
88	C₄×#239	—	5	2	no	—
89	C₃×C₄×Q₁₆	D₅	1	1	yes	characteristic, complemented
90	Dic₃×Q₁₆	—	5	1	no	—
91	C₄×#215	—	5	2	no	—
92	#4880	—	5	1	no	—
93	#4872	—	5	1	no	—
94	#4804	—	5	2	no	—
95	#4788	—	5	2	no	—
96	C₄×D₂₄	—	5	1	no	—
97	C₄×D₃×C₈	—	5	1	no	—
98	C₂×#713	—	3	2	no	—
99	C₂×C₅×Q₁₆	C₂×D₃	1	1	yes	characteristic
100	C₄×C₅×Q₈	C₂×D₃	1	2	yes	—
101	Q₈×Dic₅	—	3	2	no	—
102	C₂×#688	—	3	2	no	—
103	#4065	—	3	8	no	—
104	C₂×D₄₀	—	3	1	no	—
105	C₂×C₈×D₅	—	3	1	no	—
106	C₂×C₈×D₅	—	3	1	no	—
107	#4039	—	3	2	no	—
108	#4039	—	6	2	no	—
109	#4038	—	3	2	no	—
110	#4038	—	6	2	no	—
111	C₄×D₂₀	—	3	2	no	—
112	C₄×D₂₀	—	6	2	no	—
113	C₄²×D₅	—	3	1	no	—
114	C₄²×D₅	—	6	2	no	—
115	C₅×#107	C₂×D₃	1	1	yes	characteristic
116	C₅×#103	C₂×D₃	1	2	yes	—
117	C₄×C₅×C₈	C₂×D₃	1	1	yes	characteristic
118	#3967	—	3	2	no	—
119	#3953	—	3	2	no	—
120	#3950	—	3	1	no	—
121	C₈×Dic₅	—	3	1	no	—
122	C₈×Dic₅	—	3	1	no	—
123	#3941	—	3	2	no	—
124	#3940	—	3	2	no	—
125	C₄×#168	—	3	1	no	—
126	C₄×#135	—	15	1	no	Sylow
127	C₂²×D₁₅	—	2	2	no	—
128	C₂²×D₁₅	C₂×D₄	1	1	yes	characteristic
129	C₃×C₅×Q₈	—	2	2	no	—
130	C₃×C₅×Q₈	C₂²×C₄	1	4	yes	—
131	C₂×C₃×C₄×C₅	—	2	2	no	—
132	C₂×C₃×C₄×C₅	—	2	2	no	—
133	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
134	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
135	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
136	C₂×Dic₁₅	—	2	2	no	—
137	C₂×Dic₁₅	C₂×D₄	1	1	yes	characteristic
138	C₂×Dic₁₅	C₂×D₄	1	1	yes	characteristic
139	C₂×Dic₁₅	C₂×D₄	1	1	yes	characteristic
140	D₆₀	—	2	8	no	—
141	D₆₀	—	2	2	no	—
142	D₆₀	C₂²×C₄	1	4	yes	—
143	C₄×D₁₅	—	2	2	no	—
144	C₄×D₁₅	—	2	8	no	—
145	C₄×D₁₅	—	2	2	no	—
146	C₄×D₁₅	—	4	4	no	—
147	C₄×D₁₅	—	4	4	no	—
148	C₄×D₁₅	C₂²×C₄	1	2	yes	—
149	C₄×D₁₅	#41	1	2	yes	—
150	C₃×C₅×C₈	—	2	1	no	—
151	C₃×C₅×C₈	C₂²×C₄	1	2	yes	—
152	C₃⋊#168	—	2	1	no	—
153	C₃⋊#168	C₂²×C₄	1	2	yes	—
154	C₂×#239	—	5	2	no	—
155	C₂×C₃×Q₁₆	C₂×D₅	1	1	yes	characteristic
156	C₃×C₄×Q₈	C₂×D₅	1	2	yes	—
157	Q₈×Dic₃	—	5	2	no	—
158	C₂×#215	—	5	2	no	—
159	#919	—	5	8	no	—
160	C₂×D₂₄	—	5	1	no	—
161	C₂×D₃×C₈	—	5	1	no	—
162	C₂×D₃×C₈	—	5	1	no	—
163	#893	—	5	2	no	—
164	#893	—	10	2	no	—
165	#892	—	5	2	no	—
166	#892	—	10	2	no	—
167	C₄×D₁₂	—	5	2	no	—
168	C₄×D₁₂	—	10	2	no	—
169	C₄²×D₃	—	5	1	no	—
170	C₄²×D₃	—	10	2	no	—
171	C₃×#107	C₂×D₅	1	1	yes	characteristic
172	C₃×#103	C₂×D₅	1	2	yes	—
173	C₃×C₄×C₈	C₂×D₅	1	1	yes	characteristic
174	#835	—	5	2	no	—
175	#821	—	5	2	no	—
176	#818	—	5	1	no	—
177	C₈×Dic₃	—	5	1	no	—
178	C₈×Dic₃	—	5	1	no	—
179	#809	—	5	2	no	—
180	#808	—	5	2	no	—
181	C₄×C₃⋊C₈	—	5	1	no	—
182	C₂×C₅×Q₈	C₂²×D₃	1	2	yes	—
183	#713	—	3	8	no	—
184	#713	—	6	4	no	—
185	C₂×D₂₀	—	3	2	no	—
186	C₂×D₂₀	—	6	2	no	—
187	C₂×C₄×D₅	—	3	1	no	—
188	C₂×C₄×D₅	—	3	1	no	—
189	C₂×C₄×D₅	—	3	1	no	—
190	C₂×C₄×D₅	—	6	2	no	—
191	C₂×C₄×D₅	—	6	2	no	—
192	C₂×C₄×D₅	—	6	2	no	—
193	C₅×Q₁₆	C₄×D₃	1	4	yes	complemented
194	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
195	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
196	C₅×C₄⋊C₄	—	2	2	no	—
197	C₅×C₄⋊C₄	C₂²×D₃	1	2	yes	—
198	C₄²×C₅	—	2	2	no	—
199	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
200	#688	—	3	8	no	—
201	#685	—	6	2	no	—
202	#685	—	6	2	no	—
203	#685	—	6	2	no	—
204	C₄⋊Dic₅	—	3	2	no	—
205	C₄⋊Dic₅	—	6	2	no	—
206	C₄×Dic₅	—	3	1	no	—
207	C₄×Dic₅	—	3	1	no	—
208	C₄×Dic₅	—	3	1	no	—
209	C₄×Dic₅	—	6	2	no	—
210	C₄×Dic₅	—	6	2	no	—
211	C₂×#168	—	3	1	no	—
212	C₂×#168	—	3	1	no	—
213	D₄₀	—	3	4	no	—
214	C₈×D₅	—	3	4	no	—
215	C₈×D₅	—	6	2	no	—
216	C₂×#135	—	15	1	no	—
217	C₄×#41	—	15	2	no	—
218	C₄×Q₁₆	—	15	1	no	—
219	C₄×Q₁₆	D₁₅	1	1	yes	characteristic, complemented
220	C₄×SD₁₆	—	15	2	no	—
221	C₄×SD₁₆	—	15	2	no	—
222	C₄×D₈	—	15	1	no	—
223	C₄×D₈	—	15	1	no	—
224	#427	—	15	1	no	—
225	#416	—	15	2	no	—
226	C₂×C₄×C₈	—	15	1	no	—
227	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
228	C₂×D₁₅	—	2	1	no	—
229	C₂×D₁₅	—	2	1	no	—
230	C₂×D₁₅	—	2	4	no	—
231	C₂×D₁₅	—	4	2	no	—
232	C₂×D₁₅	—	4	2	no	—
233	C₂×D₁₅	C₄×D₄	1	2	yes	—
234	C₃×C₄×C₅	—	2	4	no	—
235	C₃×C₄×C₅	—	2	1	no	—
236	C₃×C₄×C₅	—	4	2	no	—
237	C₃×C₄×C₅	#135	1	2	yes	complemented
238	C₃×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
239	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
240	Dic₁₅	—	2	1	no	—
241	Dic₁₅	—	4	2	no	—
242	Dic₁₅	C₄×D₄	1	2	yes	—
243	Dic₁₅	#135	1	2	yes	complemented
244	C₂×C₃×Q₈	C₂²×D₅	1	2	yes	—
245	#239	—	5	8	no	—
246	#239	—	10	4	no	—
247	C₂×D₁₂	—	5	2	no	—
248	C₂×D₁₂	—	10	2	no	—
249	C₂×C₄×D₃	—	5	1	no	—
250	C₂×C₄×D₃	—	5	1	no	—
251	C₂×C₄×D₃	—	5	1	no	—
252	C₂×C₄×D₃	—	10	2	no	—
253	C₂×C₄×D₃	—	10	2	no	—
254	C₂×C₄×D₃	—	10	2	no	—
255	C₃×Q₁₆	C₄×D₅	1	4	yes	complemented
256	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
257	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
258	C₃×C₄⋊C₄	—	2	2	no	—
259	C₃×C₄⋊C₄	C₂²×D₅	1	2	yes	—
260	C₃×C₄²	—	2	2	no	—
261	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
262	#215	—	5	8	no	—
263	(C₂×D₃)⋊C₄	—	10	2	no	—
264	(C₂×D₃)⋊C₄	—	10	2	no	—
265	(C₂×D₃)⋊C₄	—	10	2	no	—
266	C₄⋊Dic₃	—	5	2	no	—
267	C₄⋊Dic₃	—	10	2	no	—
268	C₄×Dic₃	—	5	1	no	—
269	C₄×Dic₃	—	5	1	no	—
270	C₄×Dic₃	—	5	1	no	—
271	C₄×Dic₃	—	10	2	no	—
272	C₄×Dic₃	—	10	2	no	—
273	C₂×C₃⋊C₈	—	5	1	no	—
274	C₂×C₃⋊C₈	—	5	1	no	—
275	D₂₄	—	5	4	no	—
276	D₃×C₈	—	5	4	no	—
277	D₃×C₈	—	10	2	no	—
278	C₂²×D₅	—	3	1	no	—
279	C₂²×D₅	—	6	2	no	—
280	C₅×Q₈	—	2	2	no	—
281	C₅×Q₈	C₂×C₄×D₃	1	4	yes	—
282	C₂×C₄×C₅	—	2	2	no	—
283	C₂×C₄×C₅	—	2	2	no	—
284	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
285	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
286	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
287	C₂×Dic₅	—	3	1	no	—
288	C₂×Dic₅	—	3	1	no	—
289	C₂×Dic₅	—	3	1	no	—
290	C₂×Dic₅	—	6	2	no	—
291	D₂₀	—	3	4	no	—
292	D₂₀	—	6	8	no	—
293	D₂₀	—	6	2	no	—
294	C₄×D₅	—	3	2	no	—
295	C₄×D₅	—	3	2	no	—
296	C₄×D₅	—	6	2	no	—
297	C₄×D₅	—	6	8	no	—
298	C₄×D₅	—	6	2	no	—
299	C₄×D₅	—	12	4	no	—
300	C₄×D₅	—	12	4	no	—
301	C₅×C₈	—	2	1	no	—
302	C₅×C₈	C₂×C₄×D₃	1	2	yes	—
303	#168	—	3	2	no	—
304	#168	—	6	1	no	—
305	C₂×#41	—	15	2	no	—
306	#135	—	15	8	no	—
307	C₂×Q₁₆	C₂×D₁₅	1	1	yes	characteristic
308	C₂×SD₁₆	—	15	2	no	—
309	C₂×D₈	—	15	1	no	—
310	C₂²×C₈	—	15	1	no	—
311	C₂²×C₈	—	15	1	no	—
312	C₄×Q₈	—	15	2	no	—
313	C₄×Q₈	C₂×D₁₅	1	2	yes	—
314	C₄×D₄	—	15	2	no	—
315	C₄×D₄	—	15	2	no	—
316	C₄×D₄	—	30	2	no	—
317	C₄×D₄	—	30	2	no	—
318	#117	—	15	2	no	—
319	#117	—	30	2	no	—
320	C₂×C₄²	—	15	1	no	—
321	C₂×C₄²	—	30	2	no	—
322	#107	—	15	1	no	—
323	#107	C₂×D₁₅	1	1	yes	characteristic
324	#106	—	15	2	no	—
325	#103	—	15	2	no	—
326	#103	C₂×D₁₅	1	2	yes	—
327	#102	—	15	2	no	—
328	#102	—	15	2	no	—
329	C₄×C₈	—	15	1	no	—
330	C₄×C₈	—	15	1	no	—
331	C₄×C₈	—	15	1	no	—
332	C₄×C₈	C₂×D₁₅	1	1	yes	characteristic
333	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
334	C₂×C₃×C₅	C₂×#135	1	1	yes	characteristic
335	C₂×C₃×C₅	C₂×#135	1	1	yes	characteristic
336	D₁₅	—	2	2	no	—
337	D₁₅	—	4	4	no	—
338	C₂²×D₃	—	5	1	no	—
339	C₂²×D₃	—	10	2	no	—
340	C₃×Q₈	—	2	2	no	—
341	C₃×Q₈	C₂×C₄×D₅	1	4	yes	—
342	C₂×C₃×C₄	—	2	2	no	—
343	C₂×C₃×C₄	—	2	2	no	—
344	C₂×C₃×C₄	D₄×D₅	1	1	yes	characteristic
345	C₂×C₃×C₄	D₄×D₅	1	1	yes	characteristic
346	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
347	C₂×Dic₃	—	5	1	no	—
348	C₂×Dic₃	—	5	1	no	—
349	C₂×Dic₃	—	5	1	no	—
350	C₂×Dic₃	—	10	2	no	—
351	D₁₂	—	5	4	no	—
352	D₁₂	—	10	8	no	—
353	D₁₂	—	10	2	no	—
354	C₄×D₃	—	5	2	no	—
355	C₄×D₃	—	5	2	no	—
356	C₄×D₃	—	10	2	no	—
357	C₄×D₃	—	10	8	no	—
358	C₄×D₃	—	10	2	no	—
359	C₄×D₃	—	20	4	no	—
360	C₄×D₃	—	20	4	no	—
361	C₃×C₈	—	2	1	no	—
362	C₃×C₈	C₂×C₄×D₅	1	2	yes	—
363	C₃⋊C₈	—	5	2	no	—
364	C₃⋊C₈	—	10	1	no	—
365	C₂²×C₅	C₂×D₃×D₄	1	1	yes	characteristic
366	C₂×D₅	—	3	2	no	—
367	C₂×D₅	—	6	1	no	—
368	C₂×D₅	—	6	1	no	—
369	C₂×D₅	—	6	4	no	—
370	C₂×D₅	—	12	2	no	—
371	C₂×D₅	—	12	2	no	—
372	C₄×C₅	—	2	1	no	—
373	C₄×C₅	—	2	4	no	—
374	C₄×C₅	—	4	2	no	—
375	C₄×C₅	#919	1	2	yes	complemented
376	C₄×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
377	C₄×C₅	D₃×#41	1	1	yes	characteristic
378	Dic₅	—	3	2	no	—
379	Dic₅	—	3	2	no	—
380	Dic₅	—	6	1	no	—
381	Dic₅	—	12	2	no	—
382	#41	—	15	8	no	—
383	#41	—	30	4	no	—
384	C₂×Q₈	C₂²×D₁₅	1	2	yes	—
385	C₂×D₄	—	15	2	no	—
386	C₂×D₄	—	30	2	no	—
387	C₂²×C₄	—	15	1	no	—
388	C₂²×C₄	—	15	1	no	—
389	C₂²×C₄	—	15	1	no	—
390	C₂²×C₄	—	30	2	no	—
391	C₂²×C₄	—	30	2	no	—
392	C₂²×C₄	—	30	2	no	—
393	Q₁₆	C₄×D₁₅	1	4	yes	complemented
394	SD₁₆	—	15	8	no	—
395	D₈	—	15	4	no	—
396	C₂×C₈	—	15	1	no	—
397	C₂×C₈	—	15	4	no	—
398	C₂×C₈	—	15	1	no	—
399	C₂×C₈	—	30	2	no	—
400	C₂×C₈	C₂²×D₁₅	1	1	yes	characteristic
401	C₂×C₈	C₂²×D₁₅	1	1	yes	characteristic
402	C₄⋊C₄	—	2	2	no	—
403	C₄⋊C₄	—	15	2	no	—
404	C₄⋊C₄	—	30	2	no	—
405	C₄⋊C₄	C₂²×D₁₅	1	2	yes	—
406	C₂²⋊C₄	—	30	2	no	—
407	C₂²⋊C₄	—	30	2	no	—
408	C₂²⋊C₄	—	30	2	no	—
409	C₄²	—	2	2	no	—
410	C₄²	—	15	1	no	—
411	C₄²	—	15	1	no	—
412	C₄²	—	15	1	no	—
413	C₄²	—	30	2	no	—
414	C₄²	—	30	2	no	—
415	C₄²	C₂²×D₁₅	1	1	yes	characteristic
416	C₃×C₅	C₄×#135	1	1	yes	characteristic, complemented, Hall
417	C₂²×C₃	C₂×D₄×D₅	1	1	yes	characteristic
418	C₂×D₃	—	5	2	no	—
419	C₂×D₃	—	10	1	no	—
420	C₂×D₃	—	10	1	no	—
421	C₂×D₃	—	10	4	no	—
422	C₂×D₃	—	20	2	no	—
423	C₂×D₃	—	20	2	no	—
424	C₃×C₄	—	2	1	no	—
425	C₃×C₄	—	2	4	no	—
426	C₃×C₄	—	4	2	no	—
427	C₃×C₄	#4065	1	2	yes	complemented
428	C₃×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
429	C₃×C₄	D₅×#41	1	1	yes	characteristic
430	Dic₃	—	5	2	no	—
431	Dic₃	—	5	2	no	—
432	Dic₃	—	10	1	no	—
433	Dic₃	—	20	2	no	—
434	C₂×C₅	C₄×D₃×D₄	1	1	yes	characteristic
435	C₂×C₅	C₂×#919	1	1	yes	characteristic
436	C₂×C₅	D₃×#135	1	1	yes	characteristic
437	D₅	—	6	2	no	—
438	D₅	—	12	4	no	—
439	C₂³	—	15	1	no	—
440	C₂³	—	30	2	no	—
441	Q₈	—	2	2	no	—
442	Q₈	C₂×C₄×D₁₅	1	4	yes	—
443	D₄	—	15	4	no	—
444	D₄	—	30	8	no	—
445	D₄	—	30	2	no	—
446	C₂×C₄	—	2	2	no	—
447	C₂×C₄	—	2	2	no	—
448	C₂×C₄	—	15	1	no	—
449	C₂×C₄	—	15	1	no	—
450	C₂×C₄	—	15	2	no	—
451	C₂×C₄	—	15	2	no	—
452	C₂×C₄	—	15	1	no	—
453	C₂×C₄	—	30	2	no	—
454	C₂×C₄	—	30	8	no	—
455	C₂×C₄	—	30	2	no	—
456	C₂×C₄	—	30	2	no	—
457	C₂×C₄	—	60	4	no	—
458	C₂×C₄	—	60	4	no	—
459	C₂×C₄	D₄×D₁₅	1	1	yes	characteristic
460	C₂×C₄	D₄×D₁₅	1	1	yes	characteristic
461	C₂×C₄	C₂³×D₁₅	1	1	yes	characteristic
462	C₈	—	2	1	no	—
463	C₈	—	15	2	no	—
464	C₈	—	30	1	no	—
465	C₈	C₂×C₄×D₁₅	1	2	yes	—
466	C₂×C₃	C₄×D₄×D₅	1	1	yes	characteristic
467	C₂×C₃	C₂×#4065	1	1	yes	characteristic
468	C₂×C₃	D₅×#135	1	1	yes	characteristic
469	D₃	—	10	2	no	—
470	D₃	—	20	4	no	—
471	C₅	C₄×#919	1	1	yes	characteristic, complemented, Sylow
472	C₂²	—	15	2	no	—
473	C₂²	—	30	1	no	—
474	C₂²	—	30	1	no	—
475	C₂²	—	30	4	no	—
476	C₂²	—	60	2	no	—
477	C₂²	—	60	2	no	—
478	C₂²	C₂×D₄×D₁₅	1	1	yes	characteristic
479	C₄	—	2	4	no	—
480	C₄	—	2	1	no	—
481	C₄	—	4	2	no	—
482	C₄	—	15	2	no	—
483	C₄	—	15	2	no	—
484	C₄	—	30	1	no	—
485	C₄	—	60	2	no	—
486	C₄	#91808	1	2	yes	direct product factor
487	C₄	C₂²×C₄×D₁₅	1	1	yes	characteristic
488	C₄	#41×D₁₅	1	1	yes	characteristic
489	C₃	C₄×#4065	1	1	yes	characteristic, complemented, Sylow
490	C₂	—	30	2	no	—
491	C₂	—	60	4	no	—
492	C₂	C₄×D₄×D₁₅	1	1	yes	characteristic
493	C₂	C₂×#91808	1	1	yes	characteristic
494	C₂	D₁₅×#135	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	D₄×D₁₅
commutator	C₃×C₄×C₅	C₂³×C₄
Frattini	C₂×C₄	C₂³×D₁₅
Fitting	C₃×C₄×C₅×Q₁₆	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
prime radical	C₂×#91808	C₂
cosocle	C₂×C₃×C₄×C₅	C₂⁴
hypercenter	C₄×Q₁₆	D₁₅
hypocenter	C₃×C₅	C₄×#135
LCS	G ▷ C₃×C₄×C₅ ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂×C₄ ◁ C₄² ◁ C₄×Q₁₆

Complements

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

N	H ≅ G/N	type
2. C₄×#6821	C₂	semidirect
3. C₃×C₄×C₅×Q₁₆	C₂	semidirect
4. Q₁₆×Dic₁₅	C₂	semidirect
5. C₄×#6717	C₂	semidirect
6. #11750981	C₂	semidirect
7. #11750973	C₂	semidirect
8. #11750905	C₂	semidirect
9. #11750889	C₂	semidirect
10. C₄×D₁₂₀	C₂	semidirect
11. C₄×C₈×D₁₅	C₂	semidirect
18. #91808	C₄	direct (N × H)
44. C₄×C₅×Q₁₆	D₃	semidirect
55. #6821	C₂×C₄	semidirect
64. C₃×C₅×Q₁₆	C₂×C₄	semidirect
71. #6717	C₂×C₄	semidirect
84. D₁₂₀	C₂×C₄	semidirect
86. C₈×D₁₅	C₂×C₄	semidirect
89. C₃×C₄×Q₁₆	D₅	semidirect
193. C₅×Q₁₆	C₄×D₃	semidirect
219. C₄×Q₁₆	D₁₅	semidirect
237. C₃×C₄×C₅	#135	semidirect
243. Dic₁₅	#135	semidirect
255. C₃×Q₁₆	C₄×D₅	semidirect
375. C₄×C₅	#919	semidirect
393. Q₁₆	C₄×D₁₅	semidirect
416. C₃×C₅	C₄×#135	semidirect
427. C₃×C₄	#4065	semidirect
471. C₅	C₄×#919	semidirect
486. C₄	#91808	direct (N × H)
489. C₃	C₄×#4065	semidirect

Maximal subgroups

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

subgroup	index
C₂×#91808	2
C₄×#6821	2
C₃×C₄×C₅×Q₁₆	2
Q₁₆×Dic₁₅	2
C₄×#6717	2
#11750981	2
#11750973	2
#11750905	2
#11750889	2
C₄×D₁₂₀	2
C₄×C₈×D₁₅	2
C₄×#4065	3
C₄×#919	5

Subgroups — C4×#91808 #14416217

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#91808 #14416217