Subgroups — C₄×#91270 #14416244

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×#91270	C₂	1	1	yes	maximal, characteristic
2	C₄×#6772	C₂	1	2	yes	maximal, complemented
3	C₄×Dic₆₀	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄×C₅×D₂₄	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×C₄×C₈×D₅	C₂	1	1	yes	maximal, characteristic, complemented
6	#11748135	C₂	1	2	yes	maximal, complemented
7	#11747851	C₂	1	1	yes	maximal, characteristic, complemented
8	Dic₅×D₂₄	C₂	1	1	yes	maximal, characteristic, complemented
9	#11747744	C₂	1	2	yes	maximal, complemented
10	#11747672	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×#6659	C₂	1	2	yes	maximal, complemented
12	C₄×#4058	—	3	1	no	maximal, Hall
13	C₂×#6772	C₂²	1	2	yes	—
14	C₂×Dic₆₀	C₂²	1	1	yes	characteristic
15	C₄×Dic₃₀	C₂²	1	2	yes	—
16	C₂×C₅×D₂₄	C₂²	1	1	yes	characteristic
17	C₄×C₅×D₁₂	C₂²	1	2	yes	—
18	C₂×C₃×C₈×D₅	C₂²	1	1	yes	characteristic
19	C₂×C₃×C₈×D₅	C₂²	1	1	yes	characteristic
20	C₃×C₄²×D₅	C₂²	1	1	yes	characteristic
21	#91440	—	2	2	no	—
22	C₄×#1201	—	2	2	no	—
23	Dic₅×D₁₂	C₂²	1	2	yes	—
24	#91398	—	2	2	no	—
25	C₄×D₃×Dic₅	—	2	2	no	—
26	#91358	C₂²	1	2	yes	—
27	#91333	C₂²	1	2	yes	—
28	C₂×#6659	C₂²	1	2	yes	—
29	#91270	C₄	1	8	yes	direct product factor
30	C₃×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
31	#91102	C₂²	1	1	yes	characteristic
32	#91100	C₂²	1	2	yes	—
33	C₅×#821	C₂²	1	2	yes	—
34	C₅×#818	C₂²	1	1	yes	characteristic
35	C₃×C₈×Dic₅	C₂²	1	1	yes	characteristic
36	C₃×C₈×Dic₅	C₂²	1	1	yes	characteristic
37	C₃×C₄×#168	C₂²	1	1	yes	characteristic
38	#90985	C₂²	1	2	yes	—
39	#90975	C₂²	1	2	yes	—
40	#90967	C₂²	1	2	yes	—
41	C₄×#904	—	5	1	no	maximal, Hall
42	C₂×#4058	—	3	1	no	—
43	C₄×#711	—	3	2	no	—
44	C₄×C₅×D₈	—	3	1	no	—
45	D₈×Dic₅	—	3	1	no	—
46	C₄×#687	—	3	2	no	—
47	#65169	—	3	1	no	—
48	#65162	—	3	1	no	—
49	#65061	—	3	2	no	—
50	#65047	—	3	2	no	—
51	C₄×Dic₂₀	—	3	1	no	—
52	C₄×C₈×D₅	D₃	1	1	yes	characteristic, complemented
53	C₂×Dic₃₀	C₂³	1	2	yes	—
54	C₂×C₅×D₁₂	C₂³	1	2	yes	—
55	C₂×C₄×C₅×D₃	—	2	2	no	—
56	C₂×C₃×C₄×D₅	D₄	1	1	yes	characteristic
57	C₂×C₃×C₄×D₅	D₄	1	1	yes	characteristic
58	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
59	C₂×#1201	—	2	2	no	—
60	C₂×D₃×Dic₅	—	2	2	no	—
61	C₂×D₃×Dic₅	—	2	2	no	—
62	#6772	—	2	4	no	—
63	#6772	C₂×C₄	1	8	yes	complemented
64	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
65	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
66	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
67	C₄⋊Dic₁₅	C₂³	1	2	yes	—
68	#6712	—	2	2	no	—
69	C₄×Dic₁₅	—	2	2	no	—
70	Dic₆₀	C₂×C₄	1	4	yes	complemented
71	C₅×(C₂×D₃)⋊C₄	—	2	2	no	—
72	C₅×C₄⋊Dic₃	C₂³	1	2	yes	—
73	C₅×D₂₄	C₂×C₄	1	4	yes	complemented
74	C₃×C₄×Dic₅	D₄	1	1	yes	characteristic
75	C₃×C₄×Dic₅	D₄	1	1	yes	characteristic
76	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
77	C₂×C₃×#168	C₂³	1	1	yes	characteristic
78	C₂×C₃×#168	C₂³	1	1	yes	characteristic
79	C₃×C₈×D₅	—	2	2	no	—
80	C₃×C₈×D₅	C₂×C₄	1	4	yes	complemented
81	#6669	—	2	2	no	—
82	(C₂×D₃)⋊Dic₅	—	2	2	no	—
83	#6665	—	2	2	no	—
84	Dic₃×Dic₅	—	2	2	no	—
85	Dic₃×Dic₅	—	2	2	no	—
86	#6659	C₂×C₄	1	8	yes	complemented
87	C₂×#904	—	5	1	no	—
88	C₄×#235	—	5	2	no	—
89	C₂×C₃×C₄×C₈	—	5	1	no	—
90	#5113	—	5	2	no	—
91	#5106	—	5	1	no	—
92	C₄×Dic₁₂	—	5	1	no	—
93	C₄×Dic₁₂	—	5	1	no	—
94	C₄×D₂₄	—	5	1	no	—
95	C₄×D₂₄	D₅	1	1	yes	characteristic, complemented
96	C₄×#204	—	5	2	no	—
97	C₄×#204	—	5	2	no	—
98	C₂×#711	—	3	2	no	—
99	C₂×C₅×D₈	—	3	1	no	—
100	C₄×C₅×D₄	—	3	2	no	—
101	D₄×Dic₅	—	3	2	no	—
102	C₂×#687	—	3	2	no	—
103	C₄×C₂²⋊D₅	—	6	2	no	—
104	C₂×C₄×Dic₅	—	6	2	no	—
105	#4058	—	3	8	no	—
106	C₂×Dic₂₀	—	3	1	no	—
107	C₂×C₈×D₅	C₂×D₃	1	1	yes	characteristic
108	C₂×C₈×D₅	C₂×D₃	1	1	yes	characteristic
109	#4038	—	3	2	no	—
110	#4033	—	3	2	no	—
111	#4027	—	6	2	no	—
112	#4023	—	6	2	no	—
113	C₄²×D₅	C₂×D₃	1	1	yes	characteristic
114	C₄×Dic₁₀	—	3	2	no	—
115	C₅×#107	—	3	1	no	—
116	C₅×#102	—	3	2	no	—
117	C₄×C₅×C₈	C₂×D₃	1	1	yes	characteristic
118	#3964	—	3	2	no	—
119	#3950	—	3	1	no	—
120	#3948	—	3	2	no	—
121	C₈×Dic₅	C₂×D₃	1	1	yes	characteristic
122	C₈×Dic₅	C₂×D₃	1	1	yes	characteristic
123	#3942	—	3	2	no	—
124	#3940	—	3	2	no	—
125	C₄×#168	C₂×D₃	1	1	yes	characteristic
126	C₄×#135	—	15	1	no	Sylow
127	C₂²×C₅×D₃	—	2	2	no	—
128	C₂²×C₃×D₅	C₂×D₄	1	1	yes	characteristic
129	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
130	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
131	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
132	C₂×Dic₁₅	—	2	2	no	—
133	C₂×Dic₁₅	—	2	2	no	—
134	Dic₃₀	—	2	2	no	—
135	Dic₃₀	C₂²×C₄	1	4	yes	—
136	C₂×C₅×Dic₃	—	2	2	no	—
137	C₅×D₁₂	—	2	2	no	—
138	C₅×D₁₂	C₂²×C₄	1	4	yes	—
139	C₄×C₅×D₃	—	4	4	no	—
140	C₂×C₃×Dic₅	C₂×D₄	1	1	yes	characteristic
141	C₂×C₃×Dic₅	C₂×D₄	1	1	yes	characteristic
142	C₂×C₃×Dic₅	C₂×D₄	1	1	yes	characteristic
143	C₃×C₄×D₅	—	2	2	no	—
144	C₃×C₄×D₅	—	2	2	no	—
145	C₃×C₄×D₅	C₂²×C₄	1	2	yes	—
146	C₃×C₄×D₅	#41	1	2	yes	—
147	#1201	—	2	8	no	—
148	D₃×Dic₅	—	2	8	no	—
149	D₃×Dic₅	—	4	4	no	—
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×#235	—	5	2	no	—
155	C₂²×C₃×C₈	—	5	1	no	—
156	C₂²×C₃×C₈	—	5	1	no	—
157	C₂×C₃×C₄²	—	5	1	no	—
158	C₄×#67	—	10	2	no	—
159	C₄×#67	—	10	2	no	—
160	#926	—	5	2	no	—
161	C₂×Dic₁₂	—	5	1	no	—
162	#904	—	5	8	no	—
163	C₂×D₂₄	C₂×D₅	1	1	yes	characteristic
164	C₂×#204	—	5	2	no	—
165	C₄×D₁₂	—	5	2	no	—
166	C₄×D₁₂	C₂×D₅	1	2	yes	—
167	#872	—	10	2	no	—
168	C₄²×D₃	—	10	2	no	—
169	C₄×Dic₆	—	5	2	no	—
170	C₄×Dic₆	—	5	2	no	—
171	C₃×C₄×C₈	—	5	1	no	—
172	C₃×C₄×C₈	—	5	1	no	—
173	C₃×C₄×C₈	—	5	1	no	—
174	C₃×C₄×C₈	C₂×D₅	1	1	yes	characteristic
175	#821	—	5	2	no	—
176	#821	C₂×D₅	1	2	yes	—
177	#818	—	5	1	no	—
178	#818	C₂×D₅	1	1	yes	characteristic
179	#817	—	5	2	no	—
180	#816	—	5	2	no	—
181	#816	—	5	2	no	—
182	C₂×C₅×D₄	—	3	2	no	—
183	C₂²×C₄×C₅	—	6	2	no	—
184	C₂×C₂²⋊D₅	—	6	2	no	—
185	C₂²×Dic₅	—	6	2	no	—
186	C₂²×Dic₅	—	6	2	no	—
187	#711	—	3	8	no	—
188	#711	—	6	4	no	—
189	C₂×C₄×D₅	D₁₂	1	1	yes	characteristic
190	C₂×C₄×D₅	D₁₂	1	1	yes	characteristic
191	C₂×C₄×D₅	C₂²×D₃	1	1	yes	characteristic
192	C₂×Dic₁₀	—	3	2	no	—
193	C₅×D₈	—	3	4	no	—
194	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
195	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
196	C₅×C₄⋊C₄	—	3	2	no	—
197	C₅×C₂²⋊C₄	—	6	2	no	—
198	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
199	C₂²⋊Dic₅	—	6	2	no	—
200	#687	—	3	8	no	—
201	#685	—	6	2	no	—
202	C₄⋊Dic₅	—	3	2	no	—
203	#683	—	6	2	no	—
204	#683	—	6	2	no	—
205	C₄×Dic₅	—	6	2	no	—
206	C₄×Dic₅	—	6	2	no	—
207	C₄×Dic₅	—	6	2	no	—
208	C₄×Dic₅	D₁₂	1	1	yes	characteristic
209	C₄×Dic₅	D₁₂	1	1	yes	characteristic
210	C₄×Dic₅	C₂²×D₃	1	1	yes	characteristic
211	C₂×#168	C₂²×D₃	1	1	yes	characteristic
212	C₂×#168	C₂²×D₃	1	1	yes	characteristic
213	Dic₂₀	—	3	4	no	—
214	C₈×D₅	—	2	2	no	—
215	C₈×D₅	C₄×D₃	1	4	yes	complemented
216	C₂×#135	—	15	1	no	—
217	C₄×#41	—	15	2	no	—
218	C₄×Q₁₆	—	15	1	no	—
219	C₄×Q₁₆	—	15	1	no	—
220	C₄×SD₁₆	—	15	2	no	—
221	C₄×SD₁₆	—	15	2	no	—
222	C₄×D₈	—	3	1	no	—
223	C₄×D₈	—	15	1	no	—
224	#427	—	15	1	no	—
225	#416	—	15	2	no	—
226	C₂×C₄×C₈	—	5	1	no	—
227	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
228	C₂×C₅×D₃	—	2	4	no	—
229	C₂×C₅×D₃	—	4	2	no	—
230	C₂×C₅×D₃	—	4	2	no	—
231	C₂×C₃×D₅	—	2	1	no	—
232	C₂×C₃×D₅	—	2	1	no	—
233	C₂×C₃×D₅	C₄×D₄	1	2	yes	—
234	C₃×C₄×C₅	—	2	1	no	—
235	C₃×C₄×C₅	#135	1	2	yes	complemented
236	C₃×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
237	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
238	Dic₁₅	—	2	4	no	—
239	Dic₁₅	—	4	2	no	—
240	C₃×Dic₅	—	2	1	no	—
241	C₃×Dic₅	C₄×D₄	1	2	yes	—
242	C₃×Dic₅	#135	1	2	yes	complemented
243	C₅×Dic₃	—	4	2	no	—
244	C₂²×C₃×C₄	—	5	1	no	—
245	C₂²×C₃×C₄	—	5	1	no	—
246	C₂²×C₃×C₄	—	5	1	no	—
247	C₂×#67	—	10	2	no	—
248	#235	—	5	8	no	—
249	#235	—	10	4	no	—
250	C₂×D₁₂	C₂²×D₅	1	2	yes	—
251	C₂×C₄×D₃	—	2	2	no	—
252	C₂×C₄×D₃	—	10	2	no	—
253	C₂×C₄×D₃	—	10	2	no	—
254	C₂×Dic₆	—	5	2	no	—
255	C₂×C₃×C₈	—	5	1	no	—
256	C₂×C₃×C₈	—	5	4	no	—
257	C₂×C₃×C₈	—	5	1	no	—
258	C₂×C₃×C₈	—	10	2	no	—
259	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
260	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
261	C₃×C₄²	—	5	1	no	—
262	C₃×C₄²	—	5	1	no	—
263	C₃×C₄²	—	5	1	no	—
264	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
265	#217	—	10	2	no	—
266	(C₂×D₃)⋊C₄	—	2	2	no	—
267	(C₂×D₃)⋊C₄	—	10	2	no	—
268	C₄⋊Dic₃	—	5	2	no	—
269	C₄⋊Dic₃	C₂²×D₅	1	2	yes	—
270	Dic₃⋊C₄	—	10	2	no	—
271	Dic₃⋊C₄	—	10	2	no	—
272	C₄×Dic₃	—	10	2	no	—
273	C₄×Dic₃	—	10	2	no	—
274	C₄×Dic₃	—	10	2	no	—
275	Dic₁₂	—	5	4	no	—
276	D₂₄	C₄×D₅	1	4	yes	complemented
277	#204	—	5	8	no	—
278	C₂³×C₅	—	6	2	no	—
279	C₂²×D₅	C₂×D₁₂	1	1	yes	characteristic
280	C₅×D₄	—	3	4	no	—
281	C₅×D₄	—	6	2	no	—
282	C₂×C₄×C₅	—	6	2	no	—
283	C₂×C₄×C₅	—	12	4	no	—
284	C₂×C₄×C₅	C₂×D₁₂	1	1	yes	characteristic
285	C₂×C₄×C₅	C₂×D₁₂	1	1	yes	characteristic
286	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
287	C₂²⋊D₅	—	6	8	no	—
288	C₂×Dic₅	—	6	2	no	—
289	C₂×Dic₅	—	6	8	no	—
290	C₂×Dic₅	—	6	2	no	—
291	C₂×Dic₅	—	12	4	no	—
292	C₂×Dic₅	C₂×D₁₂	1	1	yes	characteristic
293	C₂×Dic₅	C₂×D₁₂	1	1	yes	characteristic
294	C₂×Dic₅	C₂×D₁₂	1	1	yes	characteristic
295	C₄×D₅	—	2	2	no	—
296	C₄×D₅	—	2	2	no	—
297	C₄×D₅	C₂×C₄×D₃	1	2	yes	—
298	C₄×D₅	#235	1	2	yes	—
299	Dic₁₀	—	3	4	no	—
300	Dic₁₀	—	6	2	no	—
301	C₅×C₈	—	2	1	no	—
302	C₅×C₈	C₂×C₄×D₃	1	2	yes	—
303	#168	—	2	1	no	—
304	#168	C₂×C₄×D₃	1	2	yes	—
305	C₂×#41	—	15	2	no	—
306	#135	—	15	8	no	—
307	C₂×Q₁₆	—	15	1	no	—
308	C₂×SD₁₆	—	15	2	no	—
309	C₂×D₈	—	3	1	no	—
310	C₂²×C₈	—	5	1	no	—
311	C₂²×C₈	—	5	1	no	—
312	C₄×Q₈	—	15	2	no	—
313	C₄×Q₈	—	15	2	no	—
314	C₄×D₄	—	3	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	—	5	1	no	—
321	C₂×C₄²	—	30	2	no	—
322	#107	—	3	1	no	—
323	#107	—	15	1	no	—
324	#106	—	15	2	no	—
325	#103	—	15	2	no	—
326	#103	—	15	2	no	—
327	#102	—	3	2	no	—
328	#102	—	15	2	no	—
329	C₄×C₈	—	5	1	no	—
330	C₄×C₈	—	5	1	no	—
331	C₄×C₈	—	5	1	no	—
332	C₄×C₈	D₃×D₅	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	C₃×D₅	—	2	2	no	—
337	C₅×D₃	—	4	4	no	—
338	C₂³×C₃	—	5	1	no	—
339	C₂²×D₃	—	2	2	no	—
340	C₂×C₃×C₄	—	5	1	no	—
341	C₂×C₃×C₄	—	5	1	no	—
342	C₂×C₃×C₄	—	5	2	no	—
343	C₂×C₃×C₄	—	5	2	no	—
344	C₂×C₃×C₄	—	5	1	no	—
345	C₂×C₃×C₄	—	10	2	no	—
346	C₂×C₃×C₄	—	10	2	no	—
347	C₂×C₃×C₄	D₄×D₅	1	1	yes	characteristic
348	C₂×C₃×C₄	D₄×D₅	1	1	yes	characteristic
349	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
350	#67	—	10	8	no	—
351	C₂×Dic₃	—	2	2	no	—
352	C₂×Dic₃	—	10	2	no	—
353	C₂×Dic₃	—	10	2	no	—
354	D₁₂	—	2	2	no	—
355	D₁₂	C₂×C₄×D₅	1	4	yes	—
356	C₄×D₃	—	4	4	no	—
357	C₄×D₃	—	10	8	no	—
358	C₄×D₃	—	20	4	no	—
359	Dic₆	—	5	4	no	—
360	Dic₆	—	10	2	no	—
361	C₃×C₈	—	2	1	no	—
362	C₃×C₈	—	5	2	no	—
363	C₃×C₈	—	10	1	no	—
364	C₃×C₈	C₂×C₄×D₅	1	2	yes	—
365	C₂²×C₅	—	6	4	no	—
366	C₂²×C₅	—	12	2	no	—
367	C₂²×C₅	—	12	2	no	—
368	C₂²×C₅	C₂²×D₁₂	1	1	yes	characteristic
369	C₂×D₅	—	2	1	no	—
370	C₂×D₅	—	2	1	no	—
371	C₂×D₅	C₄×D₁₂	1	2	yes	—
372	C₄×C₅	—	2	1	no	—
373	C₄×C₅	—	12	2	no	—
374	C₄×C₅	#904	1	2	yes	complemented
375	C₄×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
376	C₄×C₅	C₂×#235	1	1	yes	characteristic
377	Dic₅	—	2	1	no	—
378	Dic₅	—	6	4	no	—
379	Dic₅	—	12	2	no	—
380	Dic₅	C₄×D₁₂	1	2	yes	—
381	Dic₅	#904	1	2	yes	complemented
382	#41	—	15	8	no	—
383	#41	—	30	4	no	—
384	C₂×Q₈	—	15	2	no	—
385	C₂×D₄	—	3	2	no	—
386	C₂×D₄	—	30	2	no	—
387	C₂²×C₄	—	5	1	no	—
388	C₂²×C₄	—	5	1	no	—
389	C₂²×C₄	—	5	1	no	—
390	C₂²×C₄	—	6	2	no	—
391	C₂²×C₄	—	30	2	no	—
392	C₂²×C₄	—	30	2	no	—
393	Q₁₆	—	15	4	no	—
394	SD₁₆	—	15	8	no	—
395	D₈	—	3	4	no	—
396	C₂×C₈	—	5	1	no	—
397	C₂×C₈	—	5	4	no	—
398	C₂×C₈	—	5	1	no	—
399	C₂×C₈	—	10	2	no	—
400	C₂×C₈	C₂×D₃×D₅	1	1	yes	characteristic
401	C₂×C₈	C₂×D₃×D₅	1	1	yes	characteristic
402	C₄⋊C₄	—	3	2	no	—
403	C₄⋊C₄	—	15	2	no	—
404	C₄⋊C₄	—	30	2	no	—
405	C₄⋊C₄	—	30	2	no	—
406	C₂²⋊C₄	—	6	2	no	—
407	C₂²⋊C₄	—	30	2	no	—
408	C₂²⋊C₄	—	30	2	no	—
409	C₄²	—	5	1	no	—
410	C₄²	—	5	1	no	—
411	C₄²	—	5	1	no	—
412	C₄²	—	30	2	no	—
413	C₄²	—	30	2	no	—
414	C₄²	—	30	2	no	—
415	C₄²	C₂×D₃×D₅	1	1	yes	characteristic
416	C₃×C₅	C₄×#135	1	1	yes	characteristic, complemented, Hall
417	C₂²×C₃	—	5	2	no	—
418	C₂²×C₃	—	10	1	no	—
419	C₂²×C₃	—	10	1	no	—
420	C₂²×C₃	C₂×D₄×D₅	1	1	yes	characteristic
421	C₂×D₃	—	2	4	no	—
422	C₂×D₃	—	4	2	no	—
423	C₂×D₃	—	4	2	no	—
424	C₃×C₄	—	2	1	no	—
425	C₃×C₄	—	5	2	no	—
426	C₃×C₄	—	5	2	no	—
427	C₃×C₄	—	10	1	no	—
428	C₃×C₄	#4058	1	2	yes	complemented
429	C₃×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
430	C₃×C₄	D₅×#41	1	1	yes	characteristic
431	Dic₃	—	4	2	no	—
432	Dic₃	—	10	4	no	—
433	Dic₃	—	20	2	no	—
434	C₂×C₅	—	12	4	no	—
435	C₂×C₅	C₂×C₄×D₁₂	1	1	yes	characteristic
436	C₂×C₅	C₂×#904	1	1	yes	characteristic
437	C₂×C₅	C₂×#904	1	1	yes	characteristic
438	D₅	—	2	2	no	—
439	C₂³	—	5	1	no	—
440	C₂³	—	6	2	no	—
441	Q₈	—	15	4	no	—
442	Q₈	—	30	2	no	—
443	D₄	—	3	4	no	—
444	D₄	—	6	2	no	—
445	D₄	—	30	8	no	—
446	C₂×C₄	—	5	1	no	—
447	C₂×C₄	—	5	1	no	—
448	C₂×C₄	—	5	2	no	—
449	C₂×C₄	—	5	2	no	—
450	C₂×C₄	—	5	1	no	—
451	C₂×C₄	—	6	2	no	—
452	C₂×C₄	—	10	2	no	—
453	C₂×C₄	—	10	2	no	—
454	C₂×C₄	—	12	4	no	—
455	C₂×C₄	—	30	8	no	—
456	C₂×C₄	—	30	2	no	—
457	C₂×C₄	—	30	2	no	—
458	C₂×C₄	—	60	4	no	—
459	C₂×C₄	D₅×D₁₂	1	1	yes	characteristic
460	C₂×C₄	D₅×D₁₂	1	1	yes	characteristic
461	C₂×C₄	C₂²×D₃×D₅	1	1	yes	characteristic
462	C₈	—	2	1	no	—
463	C₈	—	5	2	no	—
464	C₈	—	10	1	no	—
465	C₈	C₄×D₃×D₅	1	2	yes	—
466	C₂×C₃	—	10	2	no	—
467	C₂×C₃	C₄×D₄×D₅	1	1	yes	characteristic
468	C₂×C₃	C₂×#4058	1	1	yes	characteristic
469	C₂×C₃	D₅×#135	1	1	yes	characteristic
470	D₃	—	4	4	no	—
471	C₅	C₄×#904	1	1	yes	characteristic, complemented, Sylow
472	C₂²	—	5	2	no	—
473	C₂²	—	6	4	no	—
474	C₂²	—	10	1	no	—
475	C₂²	—	10	1	no	—
476	C₂²	—	12	2	no	—
477	C₂²	—	12	2	no	—
478	C₂²	C₂×D₅×D₁₂	1	1	yes	characteristic
479	C₄	—	2	1	no	—
480	C₄	—	5	2	no	—
481	C₄	—	5	2	no	—
482	C₄	—	10	1	no	—
483	C₄	—	12	2	no	—
484	C₄	—	30	4	no	—
485	C₄	—	60	2	no	—
486	C₄	#91270	1	2	yes	direct product factor
487	C₄	C₂×C₄×D₃×D₅	1	1	yes	characteristic
488	C₄	D₅×#235	1	1	yes	characteristic
489	C₃	C₄×#4058	1	1	yes	characteristic, complemented, Sylow
490	C₂	—	10	2	no	—
491	C₂	—	12	4	no	—
492	C₂	C₄×D₅×D₁₂	1	1	yes	characteristic
493	C₂	D₅×#904	1	1	yes	characteristic
494	C₂	C₂×#91270	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	D₅×D₁₂
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	C₂×#91270	C₂
cosocle	C₂×C₃×C₄×C₅	C₂⁴
hypercenter	C₄×C₈	D₃×D₅
hypocenter	C₃×C₅	C₄×#135
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
2. C₄×#6772	C₂	semidirect
3. C₄×Dic₆₀	C₂	semidirect
4. C₄×C₅×D₂₄	C₂	semidirect
5. C₃×C₄×C₈×D₅	C₂	semidirect
6. #11748135	C₂	semidirect
7. #11747851	C₂	semidirect
8. Dic₅×D₂₄	C₂	semidirect
9. #11747744	C₂	semidirect
10. #11747672	C₂	semidirect
11. C₄×#6659	C₂	semidirect
29. #91270	C₄	direct (N × H)
52. C₄×C₈×D₅	D₃	semidirect
63. #6772	C₂×C₄	semidirect
70. Dic₆₀	C₂×C₄	semidirect
73. C₅×D₂₄	C₂×C₄	semidirect
80. C₃×C₈×D₅	C₂×C₄	semidirect
86. #6659	C₂×C₄	semidirect
95. C₄×D₂₄	D₅	semidirect
215. C₈×D₅	C₄×D₃	semidirect
235. C₃×C₄×C₅	#135	semidirect
242. C₃×Dic₅	#135	semidirect
276. D₂₄	C₄×D₅	semidirect
374. C₄×C₅	#904	semidirect
381. Dic₅	#904	semidirect
416. C₃×C₅	C₄×#135	semidirect
428. C₃×C₄	#4058	semidirect
471. C₅	C₄×#904	semidirect
486. C₄	#91270	direct (N × H)
489. C₃	C₄×#4058	semidirect

Maximal subgroups

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

subgroup	index
C₂×#91270	2
C₄×#6772	2
C₄×Dic₆₀	2
C₄×C₅×D₂₄	2
C₃×C₄×C₈×D₅	2
#11748135	2
#11747851	2
Dic₅×D₂₄	2
#11747744	2
#11747672	2
C₄×#6659	2
C₄×#4058	3
C₄×#904	5

Subgroups — C4×#91270 #14416244

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#91270 #14416244