Subgroups — C₃×#10614270 #14430781

Order 1920.

796 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#518	C₂	1	1	yes	maximal, characteristic
2	C₃×#65853	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#65504	C₂	1	1	yes	maximal, characteristic
4	C₂×C₃×#3964	C₂	1	1	yes	maximal, characteristic
5	C₃×#65298	C₂	1	2	yes	maximal, complemented
6	C₃×#65298	C₂	1	2	yes	maximal, complemented
7	C₃×#65297	C₂	1	2	yes	maximal, complemented
8	C₃×#65296	C₂	1	2	yes	maximal, complemented
9	C₃×#65288	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#65287	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×#65284	C₂	1	1	yes	maximal, characteristic, complemented
12	#10614270	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
14	C₃×C₄×C₅×D₄	—	2	1	no	—
15	C₃×C₄×C₅×D₄	—	2	1	no	—
16	C₃×C₄×C₅×D₄	C₂²	1	2	yes	—
17	C₃×C₄×C₅×D₄	C₂²	1	2	yes	—
18	C₃×C₅×#117	C₂²	1	1	yes	characteristic
19	C₃×C₅×#117	C₂²	1	1	yes	characteristic
20	C₂×C₃×C₅×C₂²⋊C₄	—	2	2	no	—
21	C₃×#4072	C₂²	1	1	yes	characteristic
22	C₂×C₃×C₄⋊Dic₅	C₂²	1	1	yes	characteristic
23	C₂×C₃×#681	C₂²	1	1	yes	characteristic
24	C₂²×C₃×#168	C₂²	1	1	yes	characteristic
25	C₃×#4036	—	2	1	no	—
26	C₃×#4034	—	2	1	no	—
27	C₃×#4024	—	2	2	no	—
28	C₃×#4016	C₂²	1	2	yes	complemented
29	C₃×#4015	C₂²	1	2	yes	complemented
30	C₃×#3964	C₂²	1	2	yes	—
31	C₃×#3964	C₂²	1	2	yes	—
32	C₃×#3964	C₂²	1	2	yes	—
33	C₃×#3964	C₂²	1	2	yes	—
34	C₃×#3940	C₂²	1	2	yes	complemented
35	C₃×#3940	C₂²	1	1	yes	characteristic, complemented
36	C₃×#3940	C₂²	1	1	yes	characteristic, complemented
37	C₃×#3939	C₂²	1	2	yes	complemented
38	C₃×#3939	C₂²	1	1	yes	characteristic, complemented
39	C₃×#3939	C₂²	1	1	yes	characteristic, complemented
40	C₃×C₄⋊#168	C₂²	1	2	yes	complemented
41	C₃×C₄⋊#168	C₂²	1	2	yes	complemented
42	C₃×#3081	—	5	1	no	maximal, Hall
43	C₅×#518	C₂×C₃	1	1	yes	characteristic
44	#65853	C₂×C₃	1	1	yes	characteristic, complemented
45	#65504	C₂×C₃	1	1	yes	characteristic
46	C₂×#3964	C₂×C₃	1	1	yes	characteristic
47	#65298	C₂×C₃	1	2	yes	complemented
48	#65298	C₂×C₃	1	2	yes	complemented
49	#65297	C₂×C₃	1	2	yes	complemented
50	#65296	C₂×C₃	1	2	yes	complemented
51	#65288	C₂×C₃	1	1	yes	characteristic, complemented
52	#65287	C₂×C₃	1	1	yes	characteristic, complemented
53	#65284	C₂×C₃	1	1	yes	characteristic, complemented
54	C₂⁴×C₃×C₅	—	2	1	no	—
55	C₂×C₃×C₅×D₄	—	2	1	no	—
56	C₂×C₃×C₅×D₄	—	2	2	no	—
57	C₂×C₃×C₅×D₄	Q₈	1	4	yes	complemented
58	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
59	C₂²×C₃×C₄×C₅	—	2	2	no	—
60	C₂²×C₃×C₄×C₅	—	2	2	no	—
61	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
62	C₂²×C₃×Dic₅	—	2	1	no	—
63	C₂×C₃×Dic₁₀	—	2	2	no	—
64	C₃×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
65	C₃×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
66	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
67	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
68	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
69	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
70	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
71	C₃×C₅×C₂²⋊C₄	D₄	1	2	yes	—
72	C₃×C₄²×C₅	—	2	1	no	—
73	C₃×C₄²×C₅	C₂³	1	2	yes	—
74	C₃×C₂²⋊Dic₅	—	2	1	no	—
75	C₃×C₄⋊Dic₅	—	2	2	no	—
76	C₃×C₄⋊Dic₅	—	2	1	no	—
77	C₃×C₄⋊Dic₅	C₂³	1	1	yes	characteristic
78	C₃×C₄⋊Dic₅	C₂³	1	2	yes	—
79	C₃×C₄⋊Dic₅	C₂³	1	1	yes	characteristic
80	C₃×#683	—	2	2	no	—
81	C₃×#683	—	2	2	no	—
82	C₃×C₄×Dic₅	—	2	1	no	—
83	C₃×#681	—	2	2	no	—
84	C₂×C₃×#168	—	2	2	no	—
85	C₂×C₃×#168	C₂³	1	1	yes	characteristic
86	C₂×C₃×#168	C₂³	1	2	yes	—
87	C₂×C₃×#168	C₂³	1	1	yes	characteristic
88	C₃×#544	—	5	1	no	—
89	C₃×#518	D₅	1	1	yes	characteristic
90	C₃×#478	—	5	2	no	—
91	C₃×#478	—	5	2	no	—
92	C₃×#476	—	5	2	no	—
93	C₃×#474	—	5	2	no	—
94	C₃×#428	—	5	1	no	—
95	C₃×#427	—	5	1	no	—
96	C₃×#424	—	5	1	no	—
97	C₃×#418	—	5	1	no	—
98	C₂×C₃×#102	—	5	1	no	—
99	C₂²×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
100	C₄×C₅×D₄	—	2	1	no	—
101	C₄×C₅×D₄	—	2	1	no	—
102	C₄×C₅×D₄	C₂²×C₃	1	2	yes	—
103	C₄×C₅×D₄	C₂²×C₃	1	2	yes	—
104	C₅×#117	C₂²×C₃	1	1	yes	characteristic
105	C₅×#117	C₂²×C₃	1	1	yes	characteristic
106	C₂×C₅×C₂²⋊C₄	—	2	2	no	—
107	#4072	C₂²×C₃	1	1	yes	characteristic
108	C₂×C₄⋊Dic₅	C₂²×C₃	1	1	yes	characteristic
109	C₂×#681	C₂²×C₃	1	1	yes	characteristic
110	C₂²×#168	C₂²×C₃	1	1	yes	characteristic
111	#4036	—	2	1	no	—
112	#4034	—	2	1	no	—
113	#4024	—	2	2	no	—
114	#4016	C₂²×C₃	1	2	yes	complemented
115	#4015	C₂²×C₃	1	2	yes	complemented
116	#3964	C₂²×C₃	1	2	yes	—
117	#3964	C₂²×C₃	1	2	yes	—
118	#3964	C₂²×C₃	1	2	yes	—
119	#3964	C₂²×C₃	1	2	yes	—
120	#3940	C₂²×C₃	1	2	yes	complemented
121	#3940	C₂²×C₃	1	1	yes	characteristic, complemented
122	#3940	C₂²×C₃	1	1	yes	characteristic, complemented
123	#3939	C₂²×C₃	1	2	yes	complemented
124	#3939	C₂²×C₃	1	1	yes	characteristic, complemented
125	#3939	C₂²×C₃	1	1	yes	characteristic, complemented
126	C₄⋊#168	C₂²×C₃	1	2	yes	complemented
127	C₄⋊#168	C₂²×C₃	1	2	yes	complemented
128	#3081	—	5	1	no	Sylow
129	C₂³×C₃×C₅	—	2	2	no	—
130	C₂³×C₃×C₅	—	2	4	no	—
131	C₂³×C₃×C₅	—	8	1	no	—
132	C₂³×C₃×C₅	—	8	1	no	—
133	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
134	C₃×C₅×D₄	—	2	4	no	—
135	C₃×C₅×D₄	—	2	2	no	—
136	C₃×C₅×D₄	C₂×Q₈	1	4	yes	—
137	C₂×C₃×C₄×C₅	—	2	1	no	—
138	C₂×C₃×C₄×C₅	—	2	1	no	—
139	C₂×C₃×C₄×C₅	—	8	2	no	—
140	C₂×C₃×C₄×C₅	—	8	2	no	—
141	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
142	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
143	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
144	C₂×C₃×C₄×C₅	C₂×Q₈	1	2	yes	—
145	C₂×C₃×C₄×C₅	#41	1	2	yes	—
146	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
147	C₂×C₃×Dic₅	—	2	1	no	—
148	C₂×C₃×Dic₅	—	2	1	no	—
149	C₂×C₃×Dic₅	—	2	2	no	—
150	C₂×C₃×Dic₅	—	8	1	no	—
151	C₃×Dic₁₀	—	8	2	no	—
152	C₃×#168	—	2	1	no	—
153	C₃×#168	—	2	1	no	—
154	C₃×#168	—	2	2	no	—
155	C₂²×C₃×D₄	C₂×D₅	1	1	yes	characteristic
156	C₂×C₃×M₁₆	—	5	1	no	—
157	C₂²×C₃×C₈	—	5	1	no	—
158	C₃×C₄⋊Q₈	—	5	2	no	—
159	C₃×C₄⋊Q₈	—	10	1	no	—
160	C₃×#125	—	5	2	no	—
161	C₃×#125	—	10	1	no	—
162	C₃×C₂²⋊Q₈	—	10	2	no	—
163	C₃×C₄×D₄	—	2	1	no	—
164	C₃×C₄×D₄	—	2	1	no	—
165	C₃×C₄×D₄	C₂×D₅	1	2	yes	—
166	C₃×C₄×D₄	C₂×D₅	1	2	yes	—
167	C₃×#117	—	5	1	no	—
168	C₃×#117	C₂×D₅	1	1	yes	characteristic
169	C₃×#117	C₂×D₅	1	1	yes	characteristic
170	C₂×C₃×C₄⋊C₄	—	5	1	no	—
171	C₂×C₃×C₂²⋊C₄	—	2	2	no	—
172	C₃×#107	—	5	1	no	—
173	C₃×#107	—	5	1	no	—
174	C₃×#107	—	5	2	no	—
175	C₃×#106	—	5	1	no	—
176	C₃×#106	—	5	1	no	—
177	C₃×#106	—	5	2	no	—
178	C₃×C₄⋊C₈	—	5	2	no	—
179	C₃×C₄⋊C₈	—	5	2	no	—
180	C₃×#102	—	5	2	no	—
181	C₃×#102	—	5	2	no	—
182	C₃×#102	—	5	2	no	—
183	C₃×#102	—	5	2	no	—
184	C₂⁴×C₅	—	2	1	no	—
185	C₂×C₅×D₄	—	2	1	no	—
186	C₂×C₅×D₄	—	2	2	no	—
187	C₂×C₅×D₄	C₃×Q₈	1	4	yes	complemented
188	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
189	C₂²×C₄×C₅	—	2	2	no	—
190	C₂²×C₄×C₅	—	2	2	no	—
191	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
192	C₂²×Dic₅	—	2	1	no	—
193	C₂×Dic₁₀	—	2	2	no	—
194	C₅×C₄⋊C₄	C₃×D₄	1	1	yes	characteristic
195	C₅×C₄⋊C₄	C₃×D₄	1	1	yes	characteristic
196	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
197	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
198	C₅×C₂²⋊C₄	—	2	1	no	—
199	C₅×C₂²⋊C₄	—	2	2	no	—
200	C₅×C₂²⋊C₄	—	2	2	no	—
201	C₅×C₂²⋊C₄	C₃×D₄	1	2	yes	—
202	C₄²×C₅	—	2	1	no	—
203	C₄²×C₅	C₂³×C₃	1	2	yes	—
204	C₂²⋊Dic₅	—	2	1	no	—
205	C₄⋊Dic₅	—	2	2	no	—
206	C₄⋊Dic₅	—	2	1	no	—
207	C₄⋊Dic₅	C₂³×C₃	1	1	yes	characteristic
208	C₄⋊Dic₅	C₂³×C₃	1	2	yes	—
209	C₄⋊Dic₅	C₂³×C₃	1	1	yes	characteristic
210	#683	—	2	2	no	—
211	#683	—	2	2	no	—
212	C₄×Dic₅	—	2	1	no	—
213	#681	—	2	2	no	—
214	C₂×#168	—	2	2	no	—
215	C₂×#168	C₂³×C₃	1	1	yes	characteristic
216	C₂×#168	C₂³×C₃	1	2	yes	—
217	C₂×#168	C₂³×C₃	1	1	yes	characteristic
218	#544	—	5	1	no	—
219	#518	C₃×D₅	1	1	yes	characteristic
220	#478	—	5	2	no	—
221	#478	—	5	2	no	—
222	#476	—	5	2	no	—
223	#474	—	5	2	no	—
224	#428	—	5	1	no	—
225	#427	—	5	1	no	—
226	#424	—	5	1	no	—
227	#418	—	5	1	no	—
228	C₂×#102	—	5	1	no	—
229	C₂²×C₃×C₅	—	2	1	no	—
230	C₂²×C₃×C₅	—	2	1	no	—
231	C₂²×C₃×C₅	—	2	4	no	—
232	C₂²×C₃×C₅	—	4	2	no	—
233	C₂²×C₃×C₅	—	4	2	no	—
234	C₂²×C₃×C₅	—	8	4	no	—
235	C₂²×C₃×C₅	C₂²⋊Q₈	1	2	yes	—
236	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
237	C₃×C₄×C₅	—	2	2	no	—
238	C₃×C₄×C₅	—	2	2	no	—
239	C₃×C₄×C₅	—	4	1	no	—
240	C₃×C₄×C₅	—	4	1	no	—
241	C₃×C₄×C₅	C₂²⋊Q₈	1	2	yes	—
242	C₃×C₄×C₅	C₂²×Q₈	1	1	yes	characteristic
243	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
244	C₃×Dic₅	—	4	1	no	—
245	C₃×Dic₅	—	4	2	no	—
246	C₃×Dic₅	—	4	1	no	—
247	C₂⁴×C₃	—	2	1	no	—
248	C₂×C₃×Q₈	—	10	2	no	—
249	C₂×C₃×D₄	—	2	2	no	—
250	C₂×C₃×D₄	—	2	1	no	—
251	C₂×C₃×D₄	Dic₁₀	1	4	yes	complemented
252	C₂×C₃×D₄	C₂²×D₅	1	2	yes	—
253	C₂²×C₃×C₄	—	2	2	no	—
254	C₂²×C₃×C₄	—	2	2	no	—
255	C₂²×C₃×C₄	—	10	1	no	—
256	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
257	C₃×M₁₆	—	10	2	no	—
258	C₂×C₃×C₈	—	5	1	no	—
259	C₂×C₃×C₈	—	5	2	no	—
260	C₂×C₃×C₈	—	5	1	no	—
261	C₂×C₃×C₈	—	10	2	no	—
262	C₃×C₄⋊C₄	—	5	2	no	—
263	C₃×C₄⋊C₄	—	5	1	no	—
264	C₃×C₄⋊C₄	—	5	1	no	—
265	C₃×C₄⋊C₄	—	10	2	no	—
266	C₃×C₄⋊C₄	—	10	2	no	—
267	C₃×C₄⋊C₄	—	10	1	no	—
268	C₃×C₄⋊C₄	—	10	2	no	—
269	C₃×C₄⋊C₄	C₂²⋊D₅	1	1	yes	characteristic
270	C₃×C₄⋊C₄	C₂²⋊D₅	1	1	yes	characteristic
271	C₃×C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
272	C₃×C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
273	C₃×C₂²⋊C₄	—	2	1	no	—
274	C₃×C₂²⋊C₄	—	2	2	no	—
275	C₃×C₂²⋊C₄	—	2	2	no	—
276	C₃×C₂²⋊C₄	—	10	1	no	—
277	C₃×C₂²⋊C₄	C₂²⋊D₅	1	2	yes	—
278	C₃×C₄²	—	2	1	no	—
279	C₃×C₄²	—	10	1	no	—
280	C₃×C₄²	C₂²×D₅	1	2	yes	—
281	C₂³×C₅	—	2	2	no	—
282	C₂³×C₅	—	2	4	no	—
283	C₂³×C₅	—	8	1	no	—
284	C₂³×C₅	—	8	1	no	—
285	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
286	C₅×D₄	—	2	4	no	—
287	C₅×D₄	—	2	2	no	—
288	C₅×D₄	C₂×C₃×Q₈	1	4	yes	—
289	C₂×C₄×C₅	—	2	1	no	—
290	C₂×C₄×C₅	—	2	1	no	—
291	C₂×C₄×C₅	—	8	2	no	—
292	C₂×C₄×C₅	—	8	2	no	—
293	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
294	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
295	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
296	C₂×C₄×C₅	C₂×C₃×Q₈	1	2	yes	—
297	C₂×C₄×C₅	C₃×#41	1	2	yes	—
298	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
299	C₂×Dic₅	—	2	1	no	—
300	C₂×Dic₅	—	2	1	no	—
301	C₂×Dic₅	—	2	2	no	—
302	C₂×Dic₅	—	8	1	no	—
303	Dic₁₀	—	8	2	no	—
304	#168	—	2	1	no	—
305	#168	—	2	1	no	—
306	#168	—	2	2	no	—
307	C₂²×D₄	C₂×C₃×D₅	1	1	yes	characteristic
308	C₂×M₁₆	—	5	1	no	—
309	C₂²×C₈	—	5	1	no	—
310	C₄⋊Q₈	—	5	2	no	—
311	C₄⋊Q₈	—	10	1	no	—
312	#125	—	5	2	no	—
313	#125	—	10	1	no	—
314	C₂²⋊Q₈	—	10	2	no	—
315	C₄×D₄	—	2	1	no	—
316	C₄×D₄	—	2	1	no	—
317	C₄×D₄	C₂×C₃×D₅	1	2	yes	—
318	C₄×D₄	C₂×C₃×D₅	1	2	yes	—
319	#117	—	5	1	no	—
320	#117	C₂×C₃×D₅	1	1	yes	characteristic
321	#117	C₂×C₃×D₅	1	1	yes	characteristic
322	C₂×C₄⋊C₄	—	5	1	no	—
323	C₂×C₂²⋊C₄	—	2	2	no	—
324	#107	—	5	1	no	—
325	#107	—	5	1	no	—
326	#107	—	5	2	no	—
327	#106	—	5	1	no	—
328	#106	—	5	1	no	—
329	#106	—	5	2	no	—
330	C₄⋊C₈	—	5	2	no	—
331	C₄⋊C₈	—	5	2	no	—
332	#102	—	5	2	no	—
333	#102	—	5	2	no	—
334	#102	—	5	2	no	—
335	#102	—	5	2	no	—
336	C₂×C₃×C₅	—	2	2	no	—
337	C₂×C₃×C₅	—	4	4	no	—
338	C₂×C₃×C₅	C₂×C₂²⋊Q₈	1	1	yes	characteristic
339	C₂×C₃×C₅	#576	1	1	yes	characteristic
340	C₂×C₃×C₅	#577	1	1	yes	characteristic
341	C₂³×C₃	—	2	2	no	—
342	C₂³×C₃	—	2	4	no	—
343	C₂³×C₃	—	8	1	no	—
344	C₂³×C₃	—	8	1	no	—
345	C₂³×C₃	C₂×C₂²⋊D₅	1	1	yes	characteristic
346	C₃×Q₈	—	40	2	no	—
347	C₃×D₄	—	2	2	no	—
348	C₃×D₄	—	2	4	no	—
349	C₃×D₄	C₂×Dic₁₀	1	4	yes	—
350	C₂×C₃×C₄	—	2	1	no	—
351	C₂×C₃×C₄	—	2	1	no	—
352	C₂×C₃×C₄	—	8	2	no	—
353	C₂×C₃×C₄	—	8	2	no	—
354	C₂×C₃×C₄	—	10	1	no	—
355	C₂×C₃×C₄	—	10	1	no	—
356	C₂×C₃×C₄	—	10	2	no	—
357	C₂×C₃×C₄	—	40	1	no	—
358	C₂×C₃×C₄	C₂×Dic₁₀	1	2	yes	—
359	C₂×C₃×C₄	#709	1	2	yes	—
360	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	2	yes	—
361	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	2	yes	—
362	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
363	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
364	C₃×C₈	—	10	1	no	—
365	C₃×C₈	—	10	1	no	—
366	C₃×C₈	—	10	2	no	—
367	C₂²×C₅	—	2	1	no	—
368	C₂²×C₅	—	2	1	no	—
369	C₂²×C₅	—	2	4	no	—
370	C₂²×C₅	—	4	2	no	—
371	C₂²×C₅	—	4	2	no	—
372	C₂²×C₅	—	8	4	no	—
373	C₂²×C₅	C₃×C₂²⋊Q₈	1	2	yes	—
374	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
375	C₄×C₅	—	2	2	no	—
376	C₄×C₅	—	2	2	no	—
377	C₄×C₅	—	4	1	no	—
378	C₄×C₅	—	4	1	no	—
379	C₄×C₅	C₃×C₂²⋊Q₈	1	2	yes	—
380	C₄×C₅	C₂²×C₃×Q₈	1	1	yes	characteristic
381	C₄×C₅	C₂×C₃×#41	1	1	yes	characteristic
382	Dic₅	—	4	1	no	—
383	Dic₅	—	4	2	no	—
384	Dic₅	—	4	1	no	—
385	C₂⁴	—	2	1	no	—
386	C₂×Q₈	—	10	2	no	—
387	C₂×D₄	—	2	2	no	—
388	C₂×D₄	—	2	1	no	—
389	C₂×D₄	C₃×Dic₁₀	1	4	yes	complemented
390	C₂×D₄	C₂²×C₃×D₅	1	2	yes	—
391	C₂²×C₄	—	2	2	no	—
392	C₂²×C₄	—	2	2	no	—
393	C₂²×C₄	—	10	1	no	—
394	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
395	M₁₆	—	10	2	no	—
396	C₂×C₈	—	5	1	no	—
397	C₂×C₈	—	5	2	no	—
398	C₂×C₈	—	5	1	no	—
399	C₂×C₈	—	10	2	no	—
400	C₄⋊C₄	—	5	2	no	—
401	C₄⋊C₄	—	5	1	no	—
402	C₄⋊C₄	—	5	1	no	—
403	C₄⋊C₄	—	10	1	no	—
404	C₄⋊C₄	—	10	2	no	—
405	C₄⋊C₄	—	10	2	no	—
406	C₄⋊C₄	—	10	2	no	—
407	C₄⋊C₄	C₃×C₂²⋊D₅	1	1	yes	characteristic
408	C₄⋊C₄	C₃×C₂²⋊D₅	1	1	yes	characteristic
409	C₄⋊C₄	C₂²×C₃×D₅	1	1	yes	characteristic
410	C₄⋊C₄	C₂²×C₃×D₅	1	1	yes	characteristic
411	C₂²⋊C₄	—	2	1	no	—
412	C₂²⋊C₄	—	2	2	no	—
413	C₂²⋊C₄	—	2	2	no	—
414	C₂²⋊C₄	—	10	1	no	—
415	C₂²⋊C₄	C₃×C₂²⋊D₅	1	2	yes	—
416	C₄²	—	2	1	no	—
417	C₄²	—	10	1	no	—
418	C₄²	C₂²×C₃×D₅	1	2	yes	—
419	C₃×C₅	#3081	1	1	yes	characteristic, complemented, Hall
420	C₂²×C₃	—	2	1	no	—
421	C₂²×C₃	—	2	1	no	—
422	C₂²×C₃	—	2	4	no	—
423	C₂²×C₃	—	4	2	no	—
424	C₂²×C₃	—	4	2	no	—
425	C₂²×C₃	—	8	4	no	—
426	C₂²×C₃	#4070	1	2	yes	—
427	C₂²×C₃	C₂²×C₂²⋊D₅	1	1	yes	characteristic
428	C₃×C₄	—	2	2	no	—
429	C₃×C₄	—	2	2	no	—
430	C₃×C₄	—	4	1	no	—
431	C₃×C₄	—	4	1	no	—
432	C₃×C₄	—	20	2	no	—
433	C₃×C₄	—	20	1	no	—
434	C₃×C₄	—	20	1	no	—
435	C₃×C₄	#4070	1	2	yes	—
436	C₃×C₄	C₂²×Dic₁₀	1	1	yes	characteristic
437	C₃×C₄	C₂×#709	1	1	yes	characteristic
438	C₂×C₅	—	2	2	no	—
439	C₂×C₅	—	4	4	no	—
440	C₂×C₅	C₂×C₃×C₂²⋊Q₈	1	1	yes	characteristic
441	C₂×C₅	C₃×#576	1	1	yes	characteristic
442	C₂×C₅	C₃×#577	1	1	yes	characteristic
443	C₂³	—	2	2	no	—
444	C₂³	—	2	4	no	—
445	C₂³	—	8	1	no	—
446	C₂³	—	8	1	no	—
447	C₂³	C₂×C₃×C₂²⋊D₅	1	1	yes	characteristic
448	Q₈	—	40	2	no	—
449	D₄	—	2	2	no	—
450	D₄	—	2	4	no	—
451	D₄	C₂×C₃×Dic₁₀	1	4	yes	—
452	C₂×C₄	—	2	1	no	—
453	C₂×C₄	—	2	1	no	—
454	C₂×C₄	—	8	2	no	—
455	C₂×C₄	—	8	2	no	—
456	C₂×C₄	—	10	1	no	—
457	C₂×C₄	—	10	1	no	—
458	C₂×C₄	—	10	2	no	—
459	C₂×C₄	—	40	1	no	—
460	C₂×C₄	C₂×C₃×Dic₁₀	1	2	yes	—
461	C₂×C₄	C₃×#709	1	2	yes	—
462	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	2	yes	—
463	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	2	yes	—
464	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	1	yes	characteristic
465	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
466	C₈	—	10	1	no	—
467	C₈	—	10	1	no	—
468	C₈	—	10	2	no	—
469	C₂×C₃	—	2	2	no	—
470	C₂×C₃	—	4	4	no	—
471	C₂×C₃	C₂×#4070	1	1	yes	characteristic
472	C₂×C₃	#66169	1	1	yes	characteristic
473	C₂×C₃	#66170	1	1	yes	characteristic
474	C₅	C₃×#3081	1	1	yes	characteristic, complemented, Sylow
475	C₂²	—	2	1	no	—
476	C₂²	—	2	1	no	—
477	C₂²	—	2	4	no	—
478	C₂²	—	4	2	no	—
479	C₂²	—	4	2	no	—
480	C₂²	—	8	4	no	—
481	C₂²	C₃×#4070	1	2	yes	—
482	C₂²	C₂²×C₃×C₂²⋊D₅	1	1	yes	characteristic
483	C₄	—	2	2	no	—
484	C₄	—	2	2	no	—
485	C₄	—	4	1	no	—
486	C₄	—	4	1	no	—
487	C₄	—	20	2	no	—
488	C₄	—	20	1	no	—
489	C₄	—	20	1	no	—
490	C₄	C₃×#4070	1	2	yes	—
491	C₄	C₂²×C₃×Dic₁₀	1	1	yes	characteristic
492	C₄	C₂×C₃×#709	1	1	yes	characteristic
493	C₃	#10614270	1	1	yes	characteristic, direct product factor, Sylow
494	C₂	—	2	2	no	—
495	C₂	—	4	4	no	—
496	C₂	C₂×C₃×#4070	1	1	yes	characteristic
497	C₂	C₃×#66169	1	1	yes	characteristic
498	C₂	C₃×#66170	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	C₂²×C₂²⋊D₅
commutator, cosocle	C₂×C₄×C₅	C₂⁴×C₃
Frattini	C₂×C₄	C₂³×C₃×D₅
Fitting	C₃×C₅×#518	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
prime radical	C₂²×C₃×C₅×D₄	C₂²
hypercenter	C₃×#518	D₅
hypocenter	C₅	C₃×#3081
LCS	G ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×#117 ◁ C₃×#518

Complements

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

N	H ≅ G/N	type
2. C₃×#65853	C₂	semidirect
5. C₃×#65298	C₂	semidirect
6. C₃×#65298	C₂	semidirect
7. C₃×#65297	C₂	semidirect
8. C₃×#65296	C₂	semidirect
9. C₃×#65288	C₂	semidirect
10. C₃×#65287	C₂	semidirect
11. C₃×#65284	C₂	semidirect
12. #10614270	C₃	direct (N × H)
28. C₃×#4016	C₂²	semidirect
29. C₃×#4015	C₂²	semidirect
34. C₃×#3940	C₂²	semidirect
35. C₃×#3940	C₂²	semidirect
36. C₃×#3940	C₂²	semidirect
37. C₃×#3939	C₂²	semidirect
38. C₃×#3939	C₂²	semidirect
39. C₃×#3939	C₂²	semidirect
40. C₃×C₄⋊#168	C₂²	semidirect
41. C₃×C₄⋊#168	C₂²	semidirect
44. #65853	C₂×C₃	semidirect
47. #65298	C₂×C₃	semidirect
48. #65298	C₂×C₃	semidirect
49. #65297	C₂×C₃	semidirect
50. #65296	C₂×C₃	semidirect
51. #65288	C₂×C₃	semidirect
52. #65287	C₂×C₃	semidirect
53. #65284	C₂×C₃	semidirect
57. C₂×C₃×C₅×D₄	Q₈	semidirect
114. #4016	C₂²×C₃	semidirect
115. #4015	C₂²×C₃	semidirect
120. #3940	C₂²×C₃	semidirect
121. #3940	C₂²×C₃	semidirect
122. #3940	C₂²×C₃	semidirect
123. #3939	C₂²×C₃	semidirect
124. #3939	C₂²×C₃	semidirect
125. #3939	C₂²×C₃	semidirect
126. C₄⋊#168	C₂²×C₃	semidirect
127. C₄⋊#168	C₂²×C₃	semidirect
187. C₂×C₅×D₄	C₃×Q₈	semidirect
251. C₂×C₃×D₄	Dic₁₀	semidirect
389. C₂×D₄	C₃×Dic₁₀	semidirect
419. C₃×C₅	#3081	semidirect
474. C₅	C₃×#3081	semidirect
493. C₃	#10614270	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×C₅×#518	2
C₃×#65853	2
C₃×#65504	2
C₂×C₃×#3964	2
C₃×#65298	2
C₃×#65297	2
C₃×#65296	2
C₃×#65288	2
C₃×#65287	2
C₃×#65284	2
#10614270	3
C₃×#3081	5

Subgroups — C3×#10614270 #14430781

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10614270 #14430781