Subgroups — C₃×#10613293 #14437774

Order 1920.

800 conjugacy classes of subgroups.

The subgroup lattice has 448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#66062	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#66050	C₂	1	1	yes	maximal, characteristic
3	C₃×C₅×#486	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#65382	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#65359	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#65061	C₂	1	4	yes	maximal, complemented
7	C₃×#65057	C₂	1	4	yes	maximal, complemented
8	C₃×C₄×C₈×D₅	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×#64970	C₂	1	1	yes	maximal, characteristic, complemented
10	#10613293	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₂×C₃×#711	C₂²	1	2	yes	—
12	C₃×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
13	C₃×C₅×#127	C₂²	1	1	yes	characteristic
14	C₃×#4092	—	2	1	no	—
15	C₃×Q₈×Dic₅	—	2	1	no	—
16	C₃×#4084	—	2	1	no	—
17	C₃×#4084	—	2	1	no	—
18	C₃×#4082	C₂²	1	2	yes	—
19	C₃×D₄×Dic₅	—	2	1	no	—
20	C₃×D₄×Dic₅	—	2	1	no	—
21	C₂×C₃×C₈×D₅	C₂²	1	2	yes	—
22	C₃×#4043	—	2	1	no	—
23	C₃×#4038	C₂²	1	2	yes	—
24	C₃×#4036	C₂²	1	2	yes	—
25	C₃×#4033	—	2	1	no	—
26	C₃×C₄²×D₅	C₂²	1	1	yes	characteristic
27	C₃×#4015	C₂²	1	1	yes	characteristic
28	C₃×#4015	C₂²	1	1	yes	characteristic
29	C₃×C₅×#102	C₂²	1	4	yes	—
30	C₃×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
31	C₃×#3964	C₂²	1	4	yes	—
32	C₃×#3948	C₂²	1	4	yes	—
33	C₃×C₈×Dic₅	C₂²	1	2	yes	—
34	C₃×#3942	C₂²	1	4	yes	—
35	C₃×C₄×#168	C₂²	1	1	yes	characteristic
36	C₃×#3131	—	5	1	no	maximal, Hall
37	#66062	C₂×C₃	1	1	yes	characteristic, complemented
38	#66050	C₂×C₃	1	1	yes	characteristic
39	C₅×#486	C₂×C₃	1	1	yes	characteristic, complemented
40	#65382	C₂×C₃	1	1	yes	characteristic, complemented
41	#65359	C₂×C₃	1	1	yes	characteristic, complemented
42	#65061	C₂×C₃	1	4	yes	complemented
43	#65057	C₂×C₃	1	4	yes	complemented
44	C₄×C₈×D₅	C₂×C₃	1	1	yes	characteristic, complemented
45	#64970	C₂×C₃	1	1	yes	characteristic, complemented
46	C₂×C₃×C₅×Q₈	—	2	1	no	—
47	C₂×C₃×C₅×D₄	—	2	1	no	—
48	C₂×C₃×C₅×D₄	—	2	1	no	—
49	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
50	C₂×C₃×C₂²⋊D₅	—	2	2	no	—
51	C₂²×C₃×Dic₅	—	2	2	no	—
52	C₃×#711	—	2	8	no	—
53	C₂×C₃×C₄×D₅	D₄	1	1	yes	characteristic
54	C₂×C₃×C₄×D₅	D₄	1	1	yes	characteristic
55	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
56	C₂×C₃×Dic₁₀	—	2	1	no	—
57	C₂×C₃×Dic₁₀	C₂³	1	2	yes	—
58	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
59	C₃×C₅×C₄⋊C₄	—	2	1	no	—
60	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
61	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
62	C₃×C₂²⋊Dic₅	—	2	2	no	—
63	C₃×C₂²⋊Dic₅	—	2	2	no	—
64	C₃×#685	—	2	2	no	—
65	C₃×C₄⋊Dic₅	—	2	1	no	—
66	C₃×C₄⋊Dic₅	—	2	1	no	—
67	C₃×C₄⋊Dic₅	—	2	1	no	—
68	C₃×C₄⋊Dic₅	—	2	2	no	—
69	C₃×C₄⋊Dic₅	C₂³	1	2	yes	—
70	C₃×#683	—	2	2	no	—
71	C₃×C₄×Dic₅	—	2	2	no	—
72	C₃×C₄×Dic₅	D₄	1	1	yes	characteristic
73	C₃×C₄×Dic₅	D₄	1	1	yes	characteristic
74	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
75	C₂×C₃×#168	C₂³	1	2	yes	—
76	C₃×C₈×D₅	—	2	4	no	—
77	C₃×#533	—	5	1	no	—
78	C₃×#532	—	5	1	no	—
79	C₃×#488	—	5	4	no	—
80	C₃×#487	—	5	1	no	—
81	C₃×#487	—	5	1	no	—
82	C₃×#486	—	5	1	no	—
83	C₃×#486	D₅	1	1	yes	characteristic, complemented
84	C₃×#416	—	5	4	no	—
85	C₂×C₃×C₄×C₈	—	5	1	no	—
86	C₂×#711	C₂²×C₃	1	2	yes	—
87	C₅×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
88	C₅×#127	C₂²×C₃	1	1	yes	characteristic
89	#4092	—	2	1	no	—
90	Q₈×Dic₅	—	2	1	no	—
91	#4084	—	2	1	no	—
92	#4084	—	2	1	no	—
93	#4082	C₂²×C₃	1	2	yes	—
94	D₄×Dic₅	—	2	1	no	—
95	D₄×Dic₅	—	2	1	no	—
96	C₂×C₈×D₅	C₂²×C₃	1	2	yes	—
97	#4043	—	2	1	no	—
98	#4038	C₂²×C₃	1	2	yes	—
99	#4036	C₂²×C₃	1	2	yes	—
100	#4033	—	2	1	no	—
101	C₄²×D₅	C₂²×C₃	1	1	yes	characteristic
102	#4015	C₂²×C₃	1	1	yes	characteristic
103	#4015	C₂²×C₃	1	1	yes	characteristic
104	C₅×#102	C₂²×C₃	1	4	yes	—
105	C₄×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
106	#3964	C₂²×C₃	1	4	yes	—
107	#3948	C₂²×C₃	1	4	yes	—
108	C₈×Dic₅	C₂²×C₃	1	2	yes	—
109	#3942	C₂²×C₃	1	4	yes	—
110	C₄×#168	C₂²×C₃	1	1	yes	characteristic
111	#3131	—	5	1	no	Sylow
112	C₂³×C₃×C₅	—	2	2	no	—
113	C₂²×C₃×D₅	C₂×D₄	1	1	yes	characteristic
114	C₃×C₅×Q₈	—	4	2	no	—
115	C₃×C₅×D₄	—	2	4	no	—
116	C₃×C₅×D₄	—	4	2	no	—
117	C₃×C₅×D₄	—	4	2	no	—
118	C₂×C₃×C₄×C₅	—	2	2	no	—
119	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
120	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
121	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
122	C₃×C₂²⋊D₅	—	4	4	no	—
123	C₂×C₃×Dic₅	—	2	2	no	—
124	C₂×C₃×Dic₅	—	2	2	no	—
125	C₂×C₃×Dic₅	—	4	4	no	—
126	C₂×C₃×Dic₅	C₂×D₄	1	1	yes	characteristic
127	C₂×C₃×Dic₅	C₂×D₄	1	1	yes	characteristic
128	C₂×C₃×Dic₅	C₂×D₄	1	1	yes	characteristic
129	C₃×C₄×D₅	—	2	2	no	—
130	C₃×C₄×D₅	—	2	2	no	—
131	C₃×C₄×D₅	#41	1	4	yes	—
132	C₃×Dic₁₀	—	2	4	no	—
133	C₃×Dic₁₀	—	4	2	no	—
134	C₃×C₅×C₈	—	2	2	no	—
135	C₃×#168	—	2	2	no	—
136	C₂×C₃×#41	—	5	2	no	—
137	C₂²×C₃×C₈	—	5	2	no	—
138	C₃×C₄⋊Q₈	—	5	1	no	—
139	C₃×C₄⋊Q₈	—	5	1	no	—
140	C₃×C₄⋊Q₈	C₂×D₅	1	1	yes	characteristic
141	C₃×#127	C₂×D₅	1	1	yes	characteristic
142	C₃×#125	—	5	2	no	—
143	C₃×#124	—	5	2	no	—
144	C₃×C₂²⋊Q₈	—	10	1	no	—
145	C₃×C₂²⋊Q₈	—	10	1	no	—
146	C₃×#121	—	10	1	no	—
147	C₃×#121	—	10	1	no	—
148	C₃×C₄×Q₈	—	10	1	no	—
149	C₃×C₄×Q₈	—	10	1	no	—
150	C₃×C₄×D₄	—	10	1	no	—
151	C₃×C₄×D₄	—	10	1	no	—
152	C₃×#117	—	5	2	no	—
153	C₂×C₃×C₄²	—	5	1	no	—
154	C₃×#103	—	5	4	no	—
155	C₃×#103	—	5	4	no	—
156	C₃×#102	—	5	4	no	—
157	C₃×#102	C₂×D₅	1	4	yes	—
158	C₃×C₄×C₈	—	5	2	no	—
159	C₃×C₄×C₈	—	5	1	no	—
160	C₃×C₄×C₈	C₂×D₅	1	1	yes	characteristic
161	C₂×C₅×Q₈	—	2	1	no	—
162	C₂×C₅×D₄	—	2	1	no	—
163	C₂×C₅×D₄	—	2	1	no	—
164	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
165	C₂×C₂²⋊D₅	—	2	2	no	—
166	C₂²×Dic₅	—	2	2	no	—
167	#711	—	2	8	no	—
168	C₂×C₄×D₅	C₃×D₄	1	1	yes	characteristic
169	C₂×C₄×D₅	C₃×D₄	1	1	yes	characteristic
170	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
171	C₂×Dic₁₀	—	2	1	no	—
172	C₂×Dic₁₀	C₂³×C₃	1	2	yes	—
173	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
174	C₅×C₄⋊C₄	—	2	1	no	—
175	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
176	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
177	C₂²⋊Dic₅	—	2	2	no	—
178	C₂²⋊Dic₅	—	2	2	no	—
179	#685	—	2	2	no	—
180	C₄⋊Dic₅	—	2	1	no	—
181	C₄⋊Dic₅	—	2	1	no	—
182	C₄⋊Dic₅	—	2	1	no	—
183	C₄⋊Dic₅	—	2	2	no	—
184	C₄⋊Dic₅	C₂³×C₃	1	2	yes	—
185	#683	—	2	2	no	—
186	C₄×Dic₅	—	2	2	no	—
187	C₄×Dic₅	C₃×D₄	1	1	yes	characteristic
188	C₄×Dic₅	C₃×D₄	1	1	yes	characteristic
189	C₄×Dic₅	C₂³×C₃	1	1	yes	characteristic
190	C₂×#168	C₂³×C₃	1	2	yes	—
191	C₈×D₅	—	2	4	no	—
192	#533	—	5	1	no	—
193	#532	—	5	1	no	—
194	#488	—	5	4	no	—
195	#487	—	5	1	no	—
196	#487	—	5	1	no	—
197	#486	—	5	1	no	—
198	#486	C₃×D₅	1	1	yes	characteristic, complemented
199	#416	—	5	4	no	—
200	C₂×C₄×C₈	—	5	1	no	—
201	C₂²×C₃×C₅	—	4	2	no	—
202	C₂²×C₃×C₅	—	4	2	no	—
203	C₂²×C₃×C₅	—	4	2	no	—
204	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
205	C₂×C₃×D₅	—	2	1	no	—
206	C₂×C₃×D₅	—	2	1	no	—
207	C₂×C₃×D₅	#124	1	2	yes	—
208	C₃×C₄×C₅	—	4	2	no	—
209	C₃×C₄×C₅	#135	1	2	yes	—
210	C₃×C₄×C₅	#135	1	2	yes	—
211	C₃×C₄×C₅	C₂×#41	1	2	yes	—
212	C₃×Dic₅	—	2	1	no	—
213	C₃×Dic₅	—	2	1	no	—
214	C₃×Dic₅	—	4	2	no	—
215	C₃×Dic₅	—	4	2	no	—
216	C₃×Dic₅	#124	1	2	yes	—
217	C₃×#41	—	10	8	no	—
218	C₂×C₃×Q₈	—	2	1	no	—
219	C₂×C₃×Q₈	—	5	2	no	—
220	C₂×C₃×Q₈	—	10	1	no	—
221	C₂×C₃×D₄	—	2	1	no	—
222	C₂×C₃×D₄	—	2	1	no	—
223	C₂×C₃×D₄	—	10	2	no	—
224	C₂×C₃×D₄	C₂²×D₅	1	2	yes	—
225	C₂²×C₃×C₄	—	5	1	no	—
226	C₂²×C₃×C₄	—	5	1	no	—
227	C₂²×C₃×C₄	—	5	1	no	—
228	C₂²×C₃×C₄	—	10	2	no	—
229	C₂×C₃×C₈	—	5	2	no	—
230	C₂×C₃×C₈	—	10	4	no	—
231	C₂×C₃×C₈	C₂²×D₅	1	2	yes	—
232	C₃×C₄⋊C₄	—	2	1	no	—
233	C₃×C₄⋊C₄	—	5	2	no	—
234	C₃×C₄⋊C₄	—	10	2	no	—
235	C₃×C₄⋊C₄	—	10	2	no	—
236	C₃×C₄⋊C₄	—	10	1	no	—
237	C₃×C₄⋊C₄	—	10	1	no	—
238	C₃×C₄⋊C₄	—	10	1	no	—
239	C₃×C₄⋊C₄	C₂²×D₅	1	2	yes	—
240	C₃×C₂²⋊C₄	—	10	2	no	—
241	C₃×C₂²⋊C₄	—	10	2	no	—
242	C₃×C₂²⋊C₄	—	10	2	no	—
243	C₃×C₄²	—	5	1	no	—
244	C₃×C₄²	—	5	1	no	—
245	C₃×C₄²	—	5	1	no	—
246	C₃×C₄²	—	10	2	no	—
247	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
248	C₂³×C₅	—	2	2	no	—
249	C₂²×D₅	C₂×C₃×D₄	1	1	yes	characteristic
250	C₅×Q₈	—	4	2	no	—
251	C₅×D₄	—	2	4	no	—
252	C₅×D₄	—	4	2	no	—
253	C₅×D₄	—	4	2	no	—
254	C₂×C₄×C₅	—	2	2	no	—
255	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
256	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
257	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
258	C₂²⋊D₅	—	4	4	no	—
259	C₂×Dic₅	—	2	2	no	—
260	C₂×Dic₅	—	2	2	no	—
261	C₂×Dic₅	—	4	4	no	—
262	C₂×Dic₅	C₂×C₃×D₄	1	1	yes	characteristic
263	C₂×Dic₅	C₂×C₃×D₄	1	1	yes	characteristic
264	C₂×Dic₅	C₂×C₃×D₄	1	1	yes	characteristic
265	C₄×D₅	—	2	2	no	—
266	C₄×D₅	—	2	2	no	—
267	C₄×D₅	C₃×#41	1	4	yes	—
268	Dic₁₀	—	2	4	no	—
269	Dic₁₀	—	4	2	no	—
270	C₅×C₈	—	2	2	no	—
271	#168	—	2	2	no	—
272	C₂×#41	—	5	2	no	—
273	C₂²×C₈	—	5	2	no	—
274	C₄⋊Q₈	—	5	1	no	—
275	C₄⋊Q₈	—	5	1	no	—
276	C₄⋊Q₈	C₂×C₃×D₅	1	1	yes	characteristic
277	#127	C₂×C₃×D₅	1	1	yes	characteristic
278	#125	—	5	2	no	—
279	#124	—	5	2	no	—
280	C₂²⋊Q₈	—	10	1	no	—
281	C₂²⋊Q₈	—	10	1	no	—
282	#121	—	10	1	no	—
283	#121	—	10	1	no	—
284	C₄×Q₈	—	10	1	no	—
285	C₄×Q₈	—	10	1	no	—
286	C₄×D₄	—	10	1	no	—
287	C₄×D₄	—	10	1	no	—
288	#117	—	5	2	no	—
289	C₂×C₄²	—	5	1	no	—
290	#103	—	5	4	no	—
291	#103	—	5	4	no	—
292	#102	—	5	4	no	—
293	#102	C₂×C₃×D₅	1	4	yes	—
294	C₄×C₈	—	5	2	no	—
295	C₄×C₈	—	5	1	no	—
296	C₄×C₈	C₂×C₃×D₅	1	1	yes	characteristic
297	C₂×C₃×C₅	—	8	2	no	—
298	C₂×C₃×C₅	C₂×#124	1	1	yes	characteristic
299	C₂×C₃×C₅	C₂×#135	1	1	yes	characteristic
300	C₂×C₃×C₅	C₂×#135	1	1	yes	characteristic
301	C₃×D₅	—	2	2	no	—
302	C₂³×C₃	—	2	2	no	—
303	C₂³×C₃	—	5	1	no	—
304	C₃×Q₈	—	4	2	no	—
305	C₃×Q₈	—	10	4	no	—
306	C₃×Q₈	—	20	2	no	—
307	C₃×D₄	—	2	4	no	—
308	C₃×D₄	—	4	2	no	—
309	C₃×D₄	—	4	2	no	—
310	C₃×D₄	—	20	4	no	—
311	C₂×C₃×C₄	—	2	2	no	—
312	C₂×C₃×C₄	—	5	1	no	—
313	C₂×C₃×C₄	—	5	4	no	—
314	C₂×C₃×C₄	—	5	1	no	—
315	C₂×C₃×C₄	—	5	1	no	—
316	C₂×C₃×C₄	—	10	2	no	—
317	C₂×C₃×C₄	—	10	2	no	—
318	C₂×C₃×C₄	—	10	2	no	—
319	C₂×C₃×C₄	—	10	2	no	—
320	C₂×C₃×C₄	—	20	4	no	—
321	C₂×C₃×C₄	D₄×D₅	1	1	yes	characteristic
322	C₂×C₃×C₄	D₄×D₅	1	1	yes	characteristic
323	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
324	C₃×C₈	—	2	2	no	—
325	C₃×C₈	—	10	2	no	—
326	C₂²×C₅	—	4	2	no	—
327	C₂²×C₅	—	4	2	no	—
328	C₂²×C₅	—	4	2	no	—
329	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
330	C₂×D₅	—	2	1	no	—
331	C₂×D₅	—	2	1	no	—
332	C₂×D₅	C₃×#124	1	2	yes	—
333	C₄×C₅	—	4	2	no	—
334	C₄×C₅	C₃×#135	1	2	yes	—
335	C₄×C₅	C₃×#135	1	2	yes	—
336	C₄×C₅	C₂×C₃×#41	1	2	yes	—
337	Dic₅	—	2	1	no	—
338	Dic₅	—	2	1	no	—
339	Dic₅	—	4	2	no	—
340	Dic₅	—	4	2	no	—
341	Dic₅	C₃×#124	1	2	yes	—
342	#41	—	10	8	no	—
343	C₂×Q₈	—	2	1	no	—
344	C₂×Q₈	—	5	2	no	—
345	C₂×Q₈	—	10	1	no	—
346	C₂×D₄	—	2	1	no	—
347	C₂×D₄	—	2	1	no	—
348	C₂×D₄	—	10	2	no	—
349	C₂×D₄	C₂²×C₃×D₅	1	2	yes	—
350	C₂²×C₄	—	5	1	no	—
351	C₂²×C₄	—	5	1	no	—
352	C₂²×C₄	—	5	1	no	—
353	C₂²×C₄	—	10	2	no	—
354	C₂×C₈	—	5	2	no	—
355	C₂×C₈	—	10	4	no	—
356	C₂×C₈	C₂²×C₃×D₅	1	2	yes	—
357	C₄⋊C₄	—	2	1	no	—
358	C₄⋊C₄	—	5	2	no	—
359	C₄⋊C₄	—	10	2	no	—
360	C₄⋊C₄	—	10	2	no	—
361	C₄⋊C₄	—	10	1	no	—
362	C₄⋊C₄	—	10	1	no	—
363	C₄⋊C₄	—	10	1	no	—
364	C₄⋊C₄	C₂²×C₃×D₅	1	2	yes	—
365	C₂²⋊C₄	—	10	2	no	—
366	C₂²⋊C₄	—	10	2	no	—
367	C₂²⋊C₄	—	10	2	no	—
368	C₄²	—	5	1	no	—
369	C₄²	—	5	1	no	—
370	C₄²	—	5	1	no	—
371	C₄²	—	10	2	no	—
372	C₄²	C₂²×C₃×D₅	1	1	yes	characteristic
373	C₃×C₅	#3131	1	1	yes	characteristic, complemented, Hall
374	C₂²×C₃	—	4	2	no	—
375	C₂²×C₃	—	4	2	no	—
376	C₂²×C₃	—	4	2	no	—
377	C₂²×C₃	—	5	2	no	—
378	C₂²×C₃	—	10	1	no	—
379	C₂²×C₃	—	10	1	no	—
380	C₂²×C₃	C₂×D₄×D₅	1	1	yes	characteristic
381	C₃×C₄	—	4	2	no	—
382	C₃×C₄	—	5	2	no	—
383	C₃×C₄	—	10	1	no	—
384	C₃×C₄	—	10	1	no	—
385	C₃×C₄	—	20	2	no	—
386	C₃×C₄	—	20	2	no	—
387	C₃×C₄	#4058	1	2	yes	—
388	C₃×C₄	#4062	1	2	yes	—
389	C₃×C₄	D₅×#41	1	2	yes	—
390	C₂×C₅	—	8	2	no	—
391	C₂×C₅	C₂×C₃×#124	1	1	yes	characteristic
392	C₂×C₅	C₂×C₃×#135	1	1	yes	characteristic
393	C₂×C₅	C₂×C₃×#135	1	1	yes	characteristic
394	D₅	—	2	2	no	—
395	C₂³	—	2	2	no	—
396	C₂³	—	5	1	no	—
397	Q₈	—	4	2	no	—
398	Q₈	—	10	4	no	—
399	Q₈	—	20	2	no	—
400	D₄	—	2	4	no	—
401	D₄	—	4	2	no	—
402	D₄	—	4	2	no	—
403	D₄	—	20	4	no	—
404	C₂×C₄	—	2	2	no	—
405	C₂×C₄	—	5	1	no	—
406	C₂×C₄	—	5	4	no	—
407	C₂×C₄	—	5	1	no	—
408	C₂×C₄	—	5	1	no	—
409	C₂×C₄	—	10	2	no	—
410	C₂×C₄	—	10	2	no	—
411	C₂×C₄	—	10	2	no	—
412	C₂×C₄	—	10	2	no	—
413	C₂×C₄	—	20	4	no	—
414	C₂×C₄	C₃×D₄×D₅	1	1	yes	characteristic
415	C₂×C₄	C₃×D₄×D₅	1	1	yes	characteristic
416	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
417	C₈	—	2	2	no	—
418	C₈	—	10	2	no	—
419	C₂×C₃	—	8	2	no	—
420	C₂×C₃	—	10	2	no	—
421	C₂×C₃	D₅×#124	1	1	yes	characteristic
422	C₂×C₃	C₂×#4058	1	1	yes	characteristic
423	C₂×C₃	C₂×#4062	1	1	yes	characteristic
424	C₅	C₃×#3131	1	1	yes	characteristic, complemented, Sylow
425	C₂²	—	4	2	no	—
426	C₂²	—	4	2	no	—
427	C₂²	—	4	2	no	—
428	C₂²	—	5	2	no	—
429	C₂²	—	10	1	no	—
430	C₂²	—	10	1	no	—
431	C₂²	C₂×C₃×D₄×D₅	1	1	yes	characteristic
432	C₄	—	4	2	no	—
433	C₄	—	5	2	no	—
434	C₄	—	10	1	no	—
435	C₄	—	10	1	no	—
436	C₄	—	20	2	no	—
437	C₄	—	20	2	no	—
438	C₄	C₃×#4058	1	2	yes	—
439	C₄	C₃×#4062	1	2	yes	—
440	C₄	C₃×D₅×#41	1	2	yes	—
441	C₃	#10613293	1	1	yes	characteristic, direct product factor, Sylow
442	C₂	—	8	2	no	—
443	C₂	—	10	2	no	—
444	C₂	C₃×D₅×#124	1	1	yes	characteristic
445	C₂	C₂×C₃×#4058	1	1	yes	characteristic
446	C₂	C₂×C₃×#4062	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	C₂×D₄×D₅
commutator, cosocle	C₂×C₄×C₅	C₂⁴×C₃
Frattini	C₂×C₄	C₂³×C₃×D₅
Fitting	C₃×C₅×#486	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
prime radical	C₃×#66050	C₂
hypercenter	C₃×#486	D₅
hypocenter	C₅	C₃×#3131
LCS	G ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×C₄² ◁ C₃×#486

Complements

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

N	H ≅ G/N	type
1. C₃×#66062	C₂	semidirect
3. C₃×C₅×#486	C₂	semidirect
4. C₃×#65382	C₂	semidirect
5. C₃×#65359	C₂	semidirect
6. C₃×#65061	C₂	semidirect
7. C₃×#65057	C₂	semidirect
8. C₃×C₄×C₈×D₅	C₂	semidirect
9. C₃×#64970	C₂	semidirect
10. #10613293	C₃	direct (N × H)
37. #66062	C₂×C₃	semidirect
39. C₅×#486	C₂×C₃	semidirect
40. #65382	C₂×C₃	semidirect
41. #65359	C₂×C₃	semidirect
42. #65061	C₂×C₃	semidirect
43. #65057	C₂×C₃	semidirect
44. C₄×C₈×D₅	C₂×C₃	semidirect
45. #64970	C₂×C₃	semidirect
83. C₃×#486	D₅	semidirect
198. #486	C₃×D₅	semidirect
373. C₃×C₅	#3131	semidirect
424. C₅	C₃×#3131	semidirect
441. C₃	#10613293	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×#66062	2
C₃×#66050	2
C₃×C₅×#486	2
C₃×#65382	2
C₃×#65359	2
C₃×#65061	2
C₃×#65057	2
C₃×C₄×C₈×D₅	2
C₃×#64970	2
#10613293	3
C₃×#3131	5

Subgroups — C3×#10613293 #14437774

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10613293 #14437774