Subgroups — C₄×#91322 #14416901

Order 1920.

968 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×Dic₃₀	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄×C₅×#235	C₂	1	1	yes	maximal, characteristic
3	C₂×#91322	C₂	1	1	yes	maximal, characteristic
4	C₃×C₄×#681	C₂	1	1	yes	maximal, characteristic, complemented
5	#11748460	C₂	1	1	yes	maximal, characteristic, complemented
6	#11748417	C₂	1	1	yes	maximal, characteristic, complemented
7	#11748390	C₂	1	1	yes	maximal, characteristic
8	#11747093	C₂	1	2	yes	maximal, complemented
9	C₄×#6663	C₂	1	2	yes	maximal, complemented
10	#11747056	C₂	1	2	yes	maximal, complemented
11	C₄×#6659	C₂	1	2	yes	maximal, complemented
12	C₄×#4097	—	3	1	no	maximal, Hall
13	C₂²×Dic₃₀	C₂²	1	1	yes	characteristic
14	C₂×C₅×#235	C₂²	1	1	yes	characteristic
15	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
16	C₂×C₄⋊Dic₁₅	C₂²	1	1	yes	characteristic
17	C₂×#6712	—	2	1	no	—
18	C₂×C₄×Dic₁₅	—	2	1	no	—
19	C₄×Dic₃₀	—	2	1	no	—
20	C₄×Dic₃₀	—	2	1	no	—
21	C₄×Dic₃₀	C₂²	1	2	yes	—
22	C₄×Dic₃₀	C₂²	1	2	yes	—
23	C₄×C₅×#67	—	2	1	no	—
24	C₄×C₅×#67	—	2	1	no	—
25	C₅×#926	C₂²	1	1	yes	characteristic
26	C₄×C₅×D₁₂	C₂²	1	1	yes	characteristic
27	C₄×C₅×D₁₂	C₂²	1	1	yes	characteristic
28	C₅×#872	—	2	1	no	—
29	C₄²×C₅×D₃	—	2	1	no	—
30	C₄×C₅×Dic₆	C₂²	1	1	yes	characteristic
31	C₄×C₅×Dic₆	C₂²	1	1	yes	characteristic
32	C₂×C₃×#681	C₂²	1	1	yes	characteristic
33	C₂×C₃×#681	C₂²	1	1	yes	characteristic
34	#91322	C₄	1	8	yes	direct product factor
35	C₂×#6663	C₂²	1	2	yes	—
36	C₂×#6659	C₂²	1	2	yes	—
37	C₃×#3935	C₂²	1	2	yes	—
38	C₃×C₄×#168	C₂²	1	2	yes	—
39	#90988	C₂²	1	2	yes	—
40	#90985	C₂²	1	2	yes	—
41	#90975	C₂²	1	2	yes	—
42	#90975	C₂²	1	2	yes	—
43	#90973	C₂²	1	2	yes	—
44	#90967	C₂²	1	2	yes	—
45	C₄×#909	—	5	1	no	maximal, Hall
46	C₄×C₅×#41	—	3	1	no	—
47	C₂×#4097	—	3	1	no	—
48	C₂×C₄×Dic₁₀	—	3	1	no	—
49	#65521	—	3	1	no	—
50	#65319	—	3	2	no	—
51	C₄×#689	—	3	2	no	—
52	#65307	—	3	2	no	—
53	C₄×#687	—	3	2	no	—
54	#65293	—	3	1	no	—
55	#65284	—	3	1	no	—
56	C₄×#681	D₃	1	1	yes	characteristic, complemented
57	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
58	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
59	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
60	C₂²×Dic₁₅	—	2	1	no	—
61	C₂²×Dic₁₅	—	2	1	no	—
62	C₂×Dic₃₀	—	2	1	no	—
63	C₂×Dic₃₀	—	2	2	no	—
64	C₂×Dic₃₀	C₂×C₄	1	4	yes	complemented
65	C₂×Dic₃₀	C₂³	1	2	yes	—
66	C₂×C₅×#67	—	2	1	no	—
67	C₅×#235	—	2	2	no	—
68	C₅×#235	C₂×C₄	1	4	yes	—
69	C₂×C₅×D₁₂	C₂³	1	1	yes	characteristic
70	C₂×C₄×C₅×D₃	—	2	1	no	—
71	C₂×C₄×C₅×D₃	—	2	1	no	—
72	C₂×C₄×C₅×D₃	—	2	1	no	—
73	C₂×C₅×Dic₆	C₂³	1	1	yes	characteristic
74	C₃×C₄²×C₅	D₄	1	1	yes	characteristic
75	C₃×C₄²×C₅	D₄	1	1	yes	characteristic
76	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
77	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
78	C₄⋊Dic₁₅	—	2	1	no	—
79	C₄⋊Dic₁₅	C₂³	1	2	yes	—
80	#6712	—	2	2	no	—
81	#6712	—	2	2	no	—
82	C₄×Dic₁₅	—	2	2	no	—
83	C₄×Dic₁₅	—	2	2	no	—
84	C₅×#217	—	2	1	no	—
85	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
86	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
87	C₅×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
88	C₅×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
89	C₅×Dic₃⋊C₄	—	2	1	no	—
90	C₅×Dic₃⋊C₄	—	2	1	no	—
91	C₄×C₅×Dic₃	—	2	1	no	—
92	C₄×C₅×Dic₃	—	2	1	no	—
93	C₄×C₅×Dic₃	—	2	1	no	—
94	C₃×#681	—	2	2	no	—
95	C₃×#681	C₂×C₄	1	4	yes	complemented
96	C₂×C₃×#168	C₂³	1	2	yes	—
97	C₂×C₃×#168	C₂³	1	2	yes	—
98	#6663	C₂×C₄	1	8	yes	complemented
99	#6659	C₂×C₄	1	8	yes	complemented
100	C₂×#909	—	5	1	no	—
101	C₄×#235	D₅	1	1	yes	characteristic
102	C₂×C₄×Dic₆	—	5	1	no	—
103	C₃×C₄×M₁₆	—	5	1	no	—
104	#5133	—	5	1	no	—
105	#5121	—	5	1	no	—
106	#5120	—	5	1	no	—
107	#4716	—	5	2	no	—
108	#4710	—	5	2	no	—
109	C₄×Dic₁₂	—	5	2	no	—
110	C₄×#204	—	5	2	no	—
111	C₂×C₅×#41	—	3	1	no	—
112	C₂²×Dic₁₀	—	3	1	no	—
113	C₄×C₅×Q₈	—	3	1	no	—
114	C₄×C₅×Q₈	—	3	1	no	—
115	C₄×C₅×D₄	—	3	1	no	—
116	C₄×C₅×D₄	—	3	1	no	—
117	C₄×C₅×D₄	—	6	1	no	—
118	C₄×C₅×D₄	—	6	1	no	—
119	C₅×#117	—	3	1	no	—
120	C₅×#117	—	6	1	no	—
121	C₂×C₄²×C₅	—	6	1	no	—
122	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
123	#4097	—	3	8	no	—
124	C₂×#689	—	3	2	no	—
125	C₂×#687	—	3	2	no	—
126	C₂×C₄⋊Dic₅	—	3	1	no	—
127	C₂×#683	—	6	1	no	—
128	C₂×C₄×Dic₅	—	6	1	no	—
129	C₂×#681	C₂×D₃	1	1	yes	characteristic
130	C₂×#681	C₂×D₃	1	1	yes	characteristic
131	C₄×Dic₁₀	—	3	2	no	—
132	C₄×Dic₁₀	—	3	2	no	—
133	C₄×Dic₁₀	—	6	1	no	—
134	C₄×Dic₁₀	—	6	1	no	—
135	#3967	—	3	2	no	—
136	#3964	—	3	2	no	—
137	#3942	—	3	2	no	—
138	#3942	—	3	2	no	—
139	#3940	—	3	2	no	—
140	#3939	—	3	2	no	—
141	#3935	C₂×D₃	1	2	yes	—
142	C₄×#168	C₂×D₃	1	2	yes	—
143	C₄×#137	—	15	1	no	Sylow
144	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
145	C₂²×C₅×D₃	—	2	1	no	—
146	C₂×C₃×C₄×C₅	—	2	2	no	—
147	C₂×C₃×C₄×C₅	—	4	1	no	—
148	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
149	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
150	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
151	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
152	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
153	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
154	C₂×C₃×C₄×C₅	#41	1	2	yes	—
155	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
156	C₂×Dic₁₅	—	2	4	no	—
157	C₂×Dic₁₅	—	2	2	no	—
158	C₂×Dic₁₅	—	2	2	no	—
159	C₂×Dic₁₅	—	4	2	no	—
160	Dic₃₀	—	2	4	no	—
161	Dic₃₀	—	2	2	no	—
162	Dic₃₀	C₂²×C₄	1	4	yes	—
163	C₅×#67	—	2	4	no	—
164	C₂×C₅×Dic₃	—	2	1	no	—
165	C₂×C₅×Dic₃	—	2	1	no	—
166	C₂×C₅×Dic₃	—	2	1	no	—
167	C₅×D₁₂	—	2	1	no	—
168	C₅×D₁₂	C₂²×C₄	1	2	yes	—
169	C₄×C₅×D₃	—	2	4	no	—
170	C₄×C₅×D₃	—	4	2	no	—
171	C₄×C₅×D₃	—	4	2	no	—
172	C₅×Dic₆	—	2	1	no	—
173	C₅×Dic₆	C₂²×C₄	1	2	yes	—
174	C₃×#168	—	2	2	no	—
175	C₃×#168	C₂²×C₄	1	4	yes	—
176	C₂×#235	C₂×D₅	1	1	yes	characteristic
177	C₂²×Dic₆	—	5	1	no	—
178	C₂×C₃×M₁₆	—	5	1	no	—
179	C₂×C₃×M₁₆	—	5	1	no	—
180	C₂×C₃×C₄²	C₂×D₅	1	1	yes	characteristic
181	C₄×#67	—	2	1	no	—
182	C₄×#67	—	2	1	no	—
183	#926	C₂×D₅	1	1	yes	characteristic
184	C₂×C₄⋊Dic₃	—	5	1	no	—
185	C₂×Dic₃⋊C₄	—	10	1	no	—
186	C₂×C₄×Dic₃	—	10	1	no	—
187	#909	—	5	8	no	—
188	C₂×Dic₁₂	—	5	2	no	—
189	C₂×#204	—	5	2	no	—
190	C₄×D₁₂	C₂×D₅	1	1	yes	characteristic
191	C₄×D₁₂	C₂×D₅	1	1	yes	characteristic
192	#872	—	2	1	no	—
193	C₄²×D₃	—	2	1	no	—
194	C₄×Dic₆	—	5	2	no	—
195	C₄×Dic₆	—	5	2	no	—
196	C₄×Dic₆	—	10	1	no	—
197	C₄×Dic₆	—	10	1	no	—
198	C₄×Dic₆	C₂×D₅	1	1	yes	characteristic
199	C₄×Dic₆	C₂×D₅	1	1	yes	characteristic
200	C₃×#97	—	5	2	no	—
201	C₃×C₄×C₈	—	5	2	no	—
202	#821	—	5	2	no	—
203	#818	—	5	2	no	—
204	#817	—	5	2	no	—
205	#816	—	5	2	no	—
206	#816	—	5	2	no	—
207	#816	—	5	2	no	—
208	C₅×#41	—	3	4	no	—
209	C₅×#41	—	6	2	no	—
210	C₂×C₅×Q₈	—	3	1	no	—
211	C₂×C₅×D₄	—	3	1	no	—
212	C₂×C₅×D₄	—	6	1	no	—
213	C₂²×C₄×C₅	—	6	1	no	—
214	C₂²×C₄×C₅	—	6	1	no	—
215	C₂²×C₄×C₅	—	6	1	no	—
216	C₂²×C₄×C₅	D₁₂	1	1	yes	characteristic
217	C₂²×C₄×C₅	D₁₂	1	1	yes	characteristic
218	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
219	C₂²×Dic₅	—	6	1	no	—
220	C₂²×Dic₅	—	6	1	no	—
221	C₂×Dic₁₀	—	3	4	no	—
222	C₂×Dic₁₀	—	3	2	no	—
223	C₂×Dic₁₀	—	6	1	no	—
224	C₂×Dic₁₀	—	6	2	no	—
225	C₅×C₄⋊C₄	—	3	1	no	—
226	C₅×C₄⋊C₄	—	3	1	no	—
227	C₅×C₄⋊C₄	—	6	1	no	—
228	C₅×C₄⋊C₄	—	6	1	no	—
229	C₅×C₂²⋊C₄	—	6	1	no	—
230	C₅×C₂²⋊C₄	—	6	1	no	—
231	C₅×C₂²⋊C₄	—	6	1	no	—
232	C₄²×C₅	—	6	1	no	—
233	C₄²×C₅	—	6	1	no	—
234	C₄²×C₅	—	6	1	no	—
235	C₄²×C₅	D₁₂	1	1	yes	characteristic
236	C₄²×C₅	D₁₂	1	1	yes	characteristic
237	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
238	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
239	#689	—	3	8	no	—
240	#687	—	3	8	no	—
241	C₄⋊Dic₅	—	3	2	no	—
242	C₄⋊Dic₅	—	6	1	no	—
243	#683	—	6	2	no	—
244	#683	—	6	2	no	—
245	C₄×Dic₅	—	6	2	no	—
246	C₄×Dic₅	—	6	2	no	—
247	#681	—	2	2	no	—
248	#681	C₄×D₃	1	4	yes	complemented
249	C₂×#168	C₂²×D₃	1	2	yes	—
250	C₂×#168	C₂²×D₃	1	2	yes	—
251	C₂×#137	—	15	1	no	—
252	C₄×#41	—	3	1	no	—
253	C₂×C₄×Q₈	—	15	1	no	—
254	#441	—	15	2	no	—
255	#440	—	15	2	no	—
256	C₄×Q₁₆	—	15	2	no	—
257	C₄×SD₁₆	—	15	2	no	—
258	#428	—	15	1	no	—
259	#419	—	15	1	no	—
260	#417	—	15	1	no	—
261	C₄×M₁₆	—	5	1	no	—
262	C₂²×C₃×C₅	—	2	1	no	—
263	C₂²×C₃×C₅	—	2	1	no	—
264	C₂²×C₃×C₅	C₄×D₄	1	2	yes	—
265	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
266	C₂×C₅×D₃	—	2	2	no	—
267	C₂×C₅×D₃	—	4	1	no	—
268	C₂×C₅×D₃	—	4	1	no	—
269	C₃×C₄×C₅	—	2	1	no	—
270	C₃×C₄×C₅	—	2	1	no	—
271	C₃×C₄×C₅	—	2	1	no	—
272	C₃×C₄×C₅	C₄×D₄	1	2	yes	—
273	C₃×C₄×C₅	#137	1	2	yes	complemented
274	C₃×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
275	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
276	Dic₁₅	—	2	4	no	—
277	Dic₁₅	—	4	2	no	—
278	C₅×Dic₃	—	2	2	no	—
279	C₅×Dic₃	—	4	1	no	—
280	C₅×Dic₃	—	4	1	no	—
281	C₂²×C₃×C₄	C₂²⋊D₅	1	1	yes	characteristic
282	C₂²×C₃×C₄	C₂²⋊D₅	1	1	yes	characteristic
283	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
284	C₂×#67	—	2	1	no	—
285	C₂²×Dic₃	—	10	1	no	—
286	C₂²×Dic₃	—	10	1	no	—
287	#235	—	2	2	no	—
288	#235	C₄×D₅	1	4	yes	—
289	C₂×D₁₂	C₂²×D₅	1	1	yes	characteristic
290	C₂×C₄×D₃	—	2	1	no	—
291	C₂×C₄×D₃	—	2	1	no	—
292	C₂×C₄×D₃	—	2	1	no	—
293	C₂×Dic₆	—	5	4	no	—
294	C₂×Dic₆	—	5	2	no	—
295	C₂×Dic₆	—	10	2	no	—
296	C₂×Dic₆	—	10	1	no	—
297	C₂×Dic₆	C₂²×D₅	1	1	yes	characteristic
298	C₃×M₁₆	—	5	4	no	—
299	C₃×M₁₆	—	10	2	no	—
300	C₂×C₃×C₈	—	5	2	no	—
301	C₂×C₃×C₈	—	5	2	no	—
302	C₃×C₄²	C₂²⋊D₅	1	1	yes	characteristic
303	C₃×C₄²	C₂²⋊D₅	1	1	yes	characteristic
304	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
305	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
306	#217	—	2	1	no	—
307	(C₂×D₃)⋊C₄	—	2	1	no	—
308	(C₂×D₃)⋊C₄	—	2	1	no	—
309	C₄⋊Dic₃	—	5	2	no	—
310	C₄⋊Dic₃	—	10	1	no	—
311	C₄⋊Dic₃	C₂²×D₅	1	1	yes	characteristic
312	C₄⋊Dic₃	C₂²×D₅	1	1	yes	characteristic
313	Dic₃⋊C₄	—	2	1	no	—
314	Dic₃⋊C₄	—	2	1	no	—
315	Dic₃⋊C₄	—	10	2	no	—
316	Dic₃⋊C₄	—	10	2	no	—
317	C₄×Dic₃	—	2	1	no	—
318	C₄×Dic₃	—	2	1	no	—
319	C₄×Dic₃	—	2	1	no	—
320	C₄×Dic₃	—	10	2	no	—
321	C₄×Dic₃	—	10	2	no	—
322	Dic₁₂	—	5	8	no	—
323	#204	—	5	8	no	—
324	C₂³×C₅	—	6	1	no	—
325	C₂³×C₅	C₂×D₁₂	1	1	yes	characteristic
326	C₅×Q₈	—	3	2	no	—
327	C₅×Q₈	—	6	1	no	—
328	C₅×D₄	—	3	2	no	—
329	C₅×D₄	—	6	4	no	—
330	C₅×D₄	—	6	1	no	—
331	C₂×C₄×C₅	—	2	2	no	—
332	C₂×C₄×C₅	—	4	1	no	—
333	C₂×C₄×C₅	—	6	1	no	—
334	C₂×C₄×C₅	—	6	4	no	—
335	C₂×C₄×C₅	—	6	1	no	—
336	C₂×C₄×C₅	—	6	1	no	—
337	C₂×C₄×C₅	—	12	2	no	—
338	C₂×C₄×C₅	—	12	2	no	—
339	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
340	C₂×C₄×C₅	C₂×D₁₂	1	1	yes	characteristic
341	C₂×C₄×C₅	C₂×D₁₂	1	1	yes	characteristic
342	C₂×C₄×C₅	C₂×D₁₂	1	1	yes	characteristic
343	C₂×C₄×C₅	C₂×D₁₂	1	1	yes	characteristic
344	C₂×C₄×C₅	C₂×D₁₂	1	1	yes	characteristic
345	C₂×C₄×C₅	#235	1	2	yes	—
346	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
347	C₂×Dic₅	—	6	4	no	—
348	C₂×Dic₅	—	6	2	no	—
349	C₂×Dic₅	—	6	2	no	—
350	C₂×Dic₅	—	12	2	no	—
351	Dic₁₀	—	3	4	no	—
352	Dic₁₀	—	6	4	no	—
353	Dic₁₀	—	6	2	no	—
354	#168	—	2	2	no	—
355	#168	C₂×C₄×D₃	1	4	yes	—
356	C₂×#41	—	3	1	no	—
357	C₂²×Q₈	—	15	1	no	—
358	#137	—	15	8	no	—
359	C₂×Q₁₆	—	15	2	no	—
360	C₂×SD₁₆	—	15	2	no	—
361	C₂×M₁₆	—	5	1	no	—
362	C₂×M₁₆	—	5	1	no	—
363	C₄×Q₈	—	3	1	no	—
364	C₄×Q₈	—	3	1	no	—
365	C₄×Q₈	—	15	2	no	—
366	C₄×Q₈	—	15	2	no	—
367	C₄×Q₈	—	30	1	no	—
368	C₄×Q₈	—	30	1	no	—
369	C₄×D₄	—	3	1	no	—
370	C₄×D₄	—	3	1	no	—
371	C₄×D₄	—	6	1	no	—
372	C₄×D₄	—	6	1	no	—
373	#117	—	3	1	no	—
374	#117	—	6	1	no	—
375	C₂×C₄⋊C₄	—	15	1	no	—
376	C₂×C₄⋊C₄	—	30	1	no	—
377	C₂×C₄²	—	6	1	no	—
378	C₂×C₄²	—	30	1	no	—
379	C₂×C₄²	D₃×D₅	1	1	yes	characteristic
380	#107	—	15	2	no	—
381	#106	—	15	2	no	—
382	#103	—	15	2	no	—
383	#103	—	15	2	no	—
384	#103	—	15	2	no	—
385	#102	—	15	2	no	—
386	#97	—	5	2	no	—
387	C₄×C₈	—	5	2	no	—
388	C₂×C₃×C₅	—	2	2	no	—
389	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
390	C₂×C₃×C₅	C₂×#137	1	1	yes	characteristic
391	C₂×C₃×C₅	#575	1	1	yes	characteristic
392	C₅×D₃	—	4	2	no	—
393	C₂³×C₃	C₂×C₂²⋊D₅	1	1	yes	characteristic
394	C₂²×D₃	—	2	1	no	—
395	C₂×C₃×C₄	—	2	2	no	—
396	C₂×C₃×C₄	—	4	1	no	—
397	C₂×C₃×C₄	C₂×C₄×D₅	1	2	yes	—
398	C₂×C₃×C₄	#709	1	2	yes	—
399	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
400	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
401	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
402	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
403	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
404	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
405	#67	—	2	4	no	—
406	C₂×Dic₃	—	2	1	no	—
407	C₂×Dic₃	—	2	1	no	—
408	C₂×Dic₃	—	2	1	no	—
409	C₂×Dic₃	—	10	2	no	—
410	C₂×Dic₃	—	10	4	no	—
411	C₂×Dic₃	—	10	2	no	—
412	C₂×Dic₃	—	20	2	no	—
413	D₁₂	—	2	1	no	—
414	D₁₂	C₂×C₄×D₅	1	2	yes	—
415	C₄×D₃	—	2	4	no	—
416	C₄×D₃	—	4	2	no	—
417	C₄×D₃	—	4	2	no	—
418	Dic₆	—	2	1	no	—
419	Dic₆	—	5	4	no	—
420	Dic₆	—	10	2	no	—
421	Dic₆	—	10	4	no	—
422	Dic₆	C₂×C₄×D₅	1	2	yes	—
423	C₃×C₈	—	5	4	no	—
424	C₃×C₈	—	10	2	no	—
425	C₂²×C₅	—	2	1	no	—
426	C₂²×C₅	—	2	1	no	—
427	C₂²×C₅	—	6	2	no	—
428	C₂²×C₅	—	12	1	no	—
429	C₂²×C₅	—	12	1	no	—
430	C₂²×C₅	C₄×D₁₂	1	2	yes	—
431	C₂²×C₅	C₂²×D₁₂	1	1	yes	characteristic
432	C₄×C₅	—	2	1	no	—
433	C₄×C₅	—	2	1	no	—
434	C₄×C₅	—	2	1	no	—
435	C₄×C₅	—	6	2	no	—
436	C₄×C₅	—	12	1	no	—
437	C₄×C₅	—	12	1	no	—
438	C₄×C₅	C₄×D₁₂	1	2	yes	—
439	C₄×C₅	#909	1	2	yes	complemented
440	C₄×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
441	C₄×C₅	C₂×#235	1	1	yes	characteristic
442	Dic₅	—	6	4	no	—
443	Dic₅	—	12	2	no	—
444	#41	—	3	4	no	—
445	#41	—	6	2	no	—
446	C₂×Q₈	—	3	1	no	—
447	C₂×Q₈	—	15	4	no	—
448	C₂×Q₈	—	15	2	no	—
449	C₂×Q₈	—	30	2	no	—
450	C₂×Q₈	—	30	1	no	—
451	C₂×D₄	—	3	1	no	—
452	C₂×D₄	—	6	1	no	—
453	C₂²×C₄	—	6	1	no	—
454	C₂²×C₄	—	6	1	no	—
455	C₂²×C₄	—	6	1	no	—
456	C₂²×C₄	—	30	1	no	—
457	C₂²×C₄	—	30	1	no	—
458	C₂²×C₄	#1203	1	1	yes	characteristic
459	C₂²×C₄	#1203	1	1	yes	characteristic
460	C₂²×C₄	C₂×D₃×D₅	1	1	yes	characteristic
461	Q₁₆	—	15	8	no	—
462	SD₁₆	—	15	8	no	—
463	M₁₆	—	5	4	no	—
464	M₁₆	—	10	2	no	—
465	C₂×C₈	—	5	2	no	—
466	C₂×C₈	—	5	2	no	—
467	C₄⋊C₄	—	3	1	no	—
468	C₄⋊C₄	—	3	1	no	—
469	C₄⋊C₄	—	6	1	no	—
470	C₄⋊C₄	—	6	1	no	—
471	C₄⋊C₄	—	15	2	no	—
472	C₄⋊C₄	—	30	1	no	—
473	C₄⋊C₄	—	30	2	no	—
474	C₄⋊C₄	—	30	2	no	—
475	C₂²⋊C₄	—	6	1	no	—
476	C₂²⋊C₄	—	6	1	no	—
477	C₂²⋊C₄	—	6	1	no	—
478	C₄²	—	6	1	no	—
479	C₄²	—	6	1	no	—
480	C₄²	—	6	1	no	—
481	C₄²	—	30	2	no	—
482	C₄²	—	30	2	no	—
483	C₄²	#1203	1	1	yes	characteristic
484	C₄²	#1203	1	1	yes	characteristic
485	C₄²	C₂×D₃×D₅	1	1	yes	characteristic
486	C₄²	C₂×D₃×D₅	1	1	yes	characteristic
487	C₃×C₅	C₄×#137	1	1	yes	characteristic, complemented, Hall
488	C₂²×C₃	—	2	1	no	—
489	C₂²×C₃	—	2	1	no	—
490	C₂²×C₃	C₄×C₂²⋊D₅	1	2	yes	—
491	C₂²×C₃	C₂²×C₂²⋊D₅	1	1	yes	characteristic
492	C₂×D₃	—	2	2	no	—
493	C₂×D₃	—	4	1	no	—
494	C₂×D₃	—	4	1	no	—
495	C₃×C₄	—	2	1	no	—
496	C₃×C₄	—	2	1	no	—
497	C₃×C₄	—	2	1	no	—
498	C₃×C₄	C₄×C₂²⋊D₅	1	2	yes	—
499	C₃×C₄	#4097	1	2	yes	complemented
500	C₃×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
501	C₃×C₄	C₂×#709	1	1	yes	characteristic
502	Dic₃	—	2	2	no	—
503	Dic₃	—	4	1	no	—
504	Dic₃	—	4	1	no	—
505	Dic₃	—	10	4	no	—
506	Dic₃	—	20	2	no	—
507	C₂×C₅	—	2	2	no	—
508	C₂×C₅	—	12	2	no	—
509	C₂×C₅	C₂×C₄×D₁₂	1	1	yes	characteristic
510	C₂×C₅	C₂×#909	1	1	yes	characteristic
511	C₂×C₅	#5748	1	1	yes	characteristic
512	C₂³	—	6	1	no	—
513	C₂³	C₂×#1203	1	1	yes	characteristic
514	Q₈	—	3	2	no	—
515	Q₈	—	6	1	no	—
516	Q₈	—	15	4	no	—
517	Q₈	—	30	4	no	—
518	Q₈	—	30	2	no	—
519	D₄	—	3	2	no	—
520	D₄	—	6	4	no	—
521	D₄	—	6	1	no	—
522	C₂×C₄	—	2	2	no	—
523	C₂×C₄	—	4	1	no	—
524	C₂×C₄	—	6	1	no	—
525	C₂×C₄	—	6	4	no	—
526	C₂×C₄	—	6	1	no	—
527	C₂×C₄	—	6	1	no	—
528	C₂×C₄	—	12	2	no	—
529	C₂×C₄	—	12	2	no	—
530	C₂×C₄	—	30	4	no	—
531	C₂×C₄	—	30	2	no	—
532	C₂×C₄	—	30	2	no	—
533	C₂×C₄	—	60	2	no	—
534	C₂×C₄	#6771	1	2	yes	—
535	C₂×C₄	C₄×D₃×D₅	1	2	yes	—
536	C₂×C₄	C₂×#1203	1	1	yes	characteristic
537	C₂×C₄	C₂×#1203	1	1	yes	characteristic
538	C₂×C₄	C₂×#1203	1	1	yes	characteristic
539	C₂×C₄	C₂×#1203	1	1	yes	characteristic
540	C₂×C₄	C₂×#1203	1	1	yes	characteristic
541	C₂×C₄	C₂²×D₃×D₅	1	1	yes	characteristic
542	C₈	—	5	4	no	—
543	C₈	—	10	2	no	—
544	C₂×C₃	—	2	2	no	—
545	C₂×C₃	C₂×C₄×C₂²⋊D₅	1	1	yes	characteristic
546	C₂×C₃	#66156	1	1	yes	characteristic
547	C₂×C₃	C₂×#4097	1	1	yes	characteristic
548	D₃	—	4	2	no	—
549	C₅	C₄×#909	1	1	yes	characteristic, complemented, Sylow
550	C₂²	—	2	1	no	—
551	C₂²	—	2	1	no	—
552	C₂²	—	6	2	no	—
553	C₂²	—	12	1	no	—
554	C₂²	—	12	1	no	—
555	C₂²	C₄×#1203	1	2	yes	—
556	C₂²	C₂²×#1203	1	1	yes	characteristic
557	C₄	—	2	1	no	—
558	C₄	—	2	1	no	—
559	C₄	—	2	1	no	—
560	C₄	—	6	2	no	—
561	C₄	—	12	1	no	—
562	C₄	—	12	1	no	—
563	C₄	—	30	4	no	—
564	C₄	—	60	2	no	—
565	C₄	#91322	1	2	yes	direct product factor
566	C₄	C₄×#1203	1	2	yes	—
567	C₄	C₂×#6771	1	1	yes	characteristic
568	C₄	C₂×C₄×D₃×D₅	1	1	yes	characteristic
569	C₃	C₄×#4097	1	1	yes	characteristic, complemented, Sylow
570	C₂	—	2	2	no	—
571	C₂	—	12	2	no	—
572	C₂	#11754145	1	1	yes	characteristic
573	C₂	C₂×#91322	1	1	yes	characteristic
574	C₂	C₂×C₄×#1203	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×#1203
commutator	C₃×C₄×C₅	C₂³×C₄
Frattini	C₂×C₄	C₂²×D₃×D₅
Fitting	C₂×C₃×C₄²×C₅	C₂²
socle	C₂²×C₃×C₅	C₂²×D₄
prime radical	C₂×C₅×#235	C₂²
cosocle	C₂×C₃×C₄×C₅	C₂⁴
hypercenter	C₂×C₄²	D₃×D₅
hypocenter	C₃×C₅	C₄×#137
LCS	G ▷ C₃×C₄×C₅ ▷ C₂×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
1. C₂×C₄×Dic₃₀	C₂	semidirect
4. C₃×C₄×#681	C₂	semidirect
5. #11748460	C₂	semidirect
6. #11748417	C₂	semidirect
8. #11747093	C₂	semidirect
9. C₄×#6663	C₂	semidirect
10. #11747056	C₂	semidirect
11. C₄×#6659	C₂	semidirect
34. #91322	C₄	direct (N × H)
56. C₄×#681	D₃	semidirect
64. C₂×Dic₃₀	C₂×C₄	semidirect
95. C₃×#681	C₂×C₄	semidirect
98. #6663	C₂×C₄	semidirect
99. #6659	C₂×C₄	semidirect
248. #681	C₄×D₃	semidirect
273. C₃×C₄×C₅	#137	semidirect
439. C₄×C₅	#909	semidirect
487. C₃×C₅	C₄×#137	semidirect
499. C₃×C₄	#4097	semidirect
549. C₅	C₄×#909	semidirect
565. C₄	#91322	direct (N × H)
569. C₃	C₄×#4097	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄×Dic₃₀	2
C₄×C₅×#235	2
C₂×#91322	2
C₃×C₄×#681	2
#11748460	2
#11748417	2
#11748390	2
#11747093	2
C₄×#6663	2
#11747056	2
C₄×#6659	2
C₄×#4097	3
C₄×#909	5

Subgroups — C4×#91322 #14416901

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#91322 #14416901