Subgroups — C₃×#42975 #10661582

Order 768.

2066 conjugacy classes of subgroups.

The subgroup lattice has 690 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#2828	C₂	1	2	yes	maximal, complemented
2	C₃×#2736	C₂	1	2	yes	maximal, complemented
3	C₃×#2685	C₂	1	4	yes	maximal, complemented
4	C₃×#2670	C₂	1	2	yes	maximal, complemented
5	C₃×#2662	C₂	1	4	yes	maximal, complemented
6	C₃×#2628	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#2593	C₂	1	2	yes	maximal, complemented
8	C₃×#2512	C₂	1	2	yes	maximal, complemented
9	C₃×#2500	C₂	1	2	yes	maximal, complemented
10	C₃×#2491	C₂	1	2	yes	maximal, complemented
11	C₃×#2414	C₂	1	2	yes	maximal, complemented
12	C₃×#2408	C₂	1	2	yes	maximal, complemented
13	C₃×#2392	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃×#2354	C₂	1	2	yes	maximal, complemented
15	C₃×#2309	C₂	1	1	yes	maximal, characteristic, complemented
16	#42975	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
17	C₂³×C₃×D₄	C₂²	1	1	yes	characteristic
18	C₂×C₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
19	C₂×C₃×#126	C₂²	1	4	yes	complemented
20	C₂×C₃×#124	C₂²	1	4	yes	complemented
21	C₂×C₃×#121	C₂²	1	2	yes	—
22	C₂×C₃×#121	C₂²	1	2	yes	—
23	C₂×C₃×#120	C₂²	1	4	yes	—
24	C₂×C₃×C₄×D₄	C₂²	1	2	yes	—
25	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic, complemented
26	C₂×C₃×#117	C₂²	1	1	yes	characteristic
27	C₂×C₃×#117	C₂²	1	1	yes	characteristic
28	C₂×C₃×#117	C₂²	1	2	yes	complemented
29	C₃×#400	C₂²	1	2	yes	complemented
30	C₃×#399	C₂²	1	2	yes	—
31	C₃×#398	C₂²	1	1	yes	characteristic, complemented
32	C₃×#397	C₂²	1	1	yes	characteristic
33	C₃×#397	C₂²	1	4	yes	complemented
34	C₃×#396	C₂²	1	2	yes	complemented
35	C₃×#396	C₂²	1	4	yes	complemented
36	C₃×#395	C₂²	1	2	yes	complemented
37	C₃×#394	C₂²	1	2	yes	—
38	C₃×#394	C₂²	1	4	yes	—
39	C₃×#394	C₂²	1	1	yes	characteristic, complemented
40	C₃×#394	C₂²	1	4	yes	complemented
41	C₃×#394	C₂²	1	4	yes	complemented
42	C₃×#394	C₂²	1	4	yes	complemented
43	C₃×#394	C₂²	1	4	yes	complemented
44	C₃×#393	C₂²	1	2	yes	—
45	C₃×#393	C₂²	1	4	yes	complemented
46	C₃×#392	C₂²	1	1	yes	characteristic
47	C₃×#392	C₂²	1	4	yes	—
48	C₃×#392	C₂²	1	4	yes	complemented
49	C₃×#390	C₂²	1	2	yes	—
50	C₃×#390	C₂²	1	2	yes	—
51	C₃×#390	C₂²	1	2	yes	—
52	C₃×#390	C₂²	1	2	yes	—
53	C₃×#390	C₂²	1	4	yes	—
54	C₃×#390	C₂²	1	2	yes	—
55	C₃×#390	C₂²	1	2	yes	—
56	C₃×#390	C₂²	1	4	yes	complemented
57	C₃×#389	C₂²	1	2	yes	complemented
58	C₃×#388	C₂²	1	4	yes	—
59	C₃×#388	C₂²	1	4	yes	complemented
60	C₃×#388	C₂²	1	4	yes	complemented
61	C₃×#388	C₂²	1	4	yes	complemented
62	C₃×#388	C₂²	1	4	yes	complemented
63	C₃×#388	C₂²	1	4	yes	complemented
64	C₃×#388	C₂²	1	4	yes	complemented
65	C₃×#384	C₂²	1	2	yes	complemented
66	C₃×#382	C₂²	1	1	yes	characteristic, complemented
67	C₃×#380	C₂²	1	2	yes	—
68	C₃×#380	C₂²	1	2	yes	complemented
69	C₃×#379	C₂²	1	4	yes	—
70	C₃×#379	C₂²	1	2	yes	—
71	C₃×#379	C₂²	1	2	yes	—
72	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
73	C₃×C₄×C₄⋊C₄	C₂²	1	4	yes	complemented
74	C₃×C₄×C₄⋊C₄	C₂²	1	2	yes	complemented
75	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	complemented
76	#2828	C₂×C₃	1	2	yes	complemented
77	#2736	C₂×C₃	1	2	yes	complemented
78	#2685	C₂×C₃	1	4	yes	complemented
79	#2670	C₂×C₃	1	2	yes	complemented
80	#2662	C₂×C₃	1	4	yes	complemented
81	#2628	C₂×C₃	1	1	yes	characteristic, complemented
82	#2593	C₂×C₃	1	2	yes	complemented
83	#2512	C₂×C₃	1	2	yes	complemented
84	#2500	C₂×C₃	1	2	yes	complemented
85	#2491	C₂×C₃	1	2	yes	complemented
86	#2414	C₂×C₃	1	2	yes	complemented
87	#2408	C₂×C₃	1	2	yes	complemented
88	#2392	C₂×C₃	1	1	yes	characteristic, complemented
89	#2354	C₂×C₃	1	2	yes	complemented
90	#2309	C₂×C₃	1	1	yes	characteristic, complemented
91	C₂⁵×C₃	C₂³	1	2	yes	—
92	C₂²×C₃×Q₈	C₂³	1	2	yes	—
93	C₂²×C₃×D₄	—	2	4	no	—
94	C₂²×C₃×D₄	—	4	2	no	—
95	C₂²×C₃×D₄	—	4	2	no	—
96	C₂²×C₃×D₄	C₂³	1	2	yes	—
97	C₂²×C₃×D₄	C₂³	1	2	yes	—
98	C₂²×C₃×D₄	C₂³	1	2	yes	—
99	C₂²×C₃×D₄	C₂³	1	4	yes	—
100	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
101	C₂²×C₃×D₄	C₂³	1	4	yes	—
102	C₂³×C₃×C₄	C₂³	1	2	yes	—
103	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
104	C₃×C₄⋊Q₈	—	4	2	no	—
105	C₃×#126	—	4	8	no	—
106	C₃×#124	—	4	8	no	—
107	C₃×#121	—	4	4	no	—
108	C₃×#121	—	4	4	no	—
109	C₃×#120	—	4	8	no	—
110	C₃×C₄×D₄	—	2	8	no	—
111	C₃×C₄×D₄	—	4	2	no	—
112	C₃×#117	—	4	2	no	—
113	C₃×#117	—	4	2	no	—
114	C₃×#117	—	4	4	no	—
115	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
116	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
117	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
118	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
119	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
120	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
121	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
122	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
123	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
124	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
125	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
126	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
127	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
128	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
129	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
130	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
131	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
132	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
133	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
134	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
135	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
136	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
137	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
138	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
139	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
140	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
141	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
142	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
143	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
144	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
145	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
146	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
147	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
148	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
149	C₂×C₃×C₄²	C₂³	1	2	yes	—
150	C₂×C₃×C₄²	C₂³	1	4	yes	—
151	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
152	C₂×C₃×C₄²	C₂³	1	2	yes	—
153	C₂×C₃×C₄²	C₂³	1	4	yes	—
154	C₃×#95	C₂³	1	2	yes	—
155	C₃×#95	C₂³	1	2	yes	—
156	C₃×#95	C₂³	1	4	yes	—
157	C₃×#95	C₂³	1	4	yes	—
158	C₃×#95	C₂³	1	4	yes	—
159	C₃×#95	C₂³	1	1	yes	characteristic
160	C₃×#95	C₂³	1	1	yes	characteristic
161	C₃×#95	C₂³	1	2	yes	—
162	C₃×#95	C₂³	1	2	yes	—
163	C₃×#95	C₂³	1	4	yes	—
164	C₂³×D₄	C₂²×C₃	1	1	yes	characteristic
165	C₂×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
166	C₂×#126	C₂²×C₃	1	4	yes	complemented
167	C₂×#124	C₂²×C₃	1	4	yes	complemented
168	C₂×#121	C₂²×C₃	1	2	yes	—
169	C₂×#121	C₂²×C₃	1	2	yes	—
170	C₂×#120	C₂²×C₃	1	4	yes	—
171	C₂×C₄×D₄	C₂²×C₃	1	2	yes	—
172	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic, complemented
173	C₂×#117	C₂²×C₃	1	1	yes	characteristic
174	C₂×#117	C₂²×C₃	1	1	yes	characteristic
175	C₂×#117	C₂²×C₃	1	2	yes	complemented
176	#400	C₂²×C₃	1	2	yes	complemented
177	#399	C₂²×C₃	1	2	yes	—
178	#398	C₂²×C₃	1	1	yes	characteristic, complemented
179	#397	C₂²×C₃	1	1	yes	characteristic
180	#397	C₂²×C₃	1	4	yes	complemented
181	#396	C₂²×C₃	1	2	yes	complemented
182	#396	C₂²×C₃	1	4	yes	complemented
183	#395	C₂²×C₃	1	2	yes	complemented
184	#394	C₂²×C₃	1	4	yes	—
185	#394	C₂²×C₃	1	2	yes	—
186	#394	C₂²×C₃	1	1	yes	characteristic, complemented
187	#394	C₂²×C₃	1	4	yes	complemented
188	#394	C₂²×C₃	1	4	yes	complemented
189	#394	C₂²×C₃	1	4	yes	complemented
190	#394	C₂²×C₃	1	4	yes	complemented
191	#393	C₂²×C₃	1	2	yes	—
192	#393	C₂²×C₃	1	4	yes	complemented
193	#392	C₂²×C₃	1	4	yes	—
194	#392	C₂²×C₃	1	1	yes	characteristic
195	#392	C₂²×C₃	1	4	yes	complemented
196	#390	C₂²×C₃	1	2	yes	—
197	#390	C₂²×C₃	1	2	yes	—
198	#390	C₂²×C₃	1	2	yes	—
199	#390	C₂²×C₃	1	2	yes	—
200	#390	C₂²×C₃	1	4	yes	—
201	#390	C₂²×C₃	1	2	yes	—
202	#390	C₂²×C₃	1	2	yes	—
203	#390	C₂²×C₃	1	4	yes	complemented
204	#389	C₂²×C₃	1	2	yes	complemented
205	#388	C₂²×C₃	1	4	yes	—
206	#388	C₂²×C₃	1	4	yes	complemented
207	#388	C₂²×C₃	1	4	yes	complemented
208	#388	C₂²×C₃	1	4	yes	complemented
209	#388	C₂²×C₃	1	4	yes	complemented
210	#388	C₂²×C₃	1	4	yes	complemented
211	#388	C₂²×C₃	1	4	yes	complemented
212	#384	C₂²×C₃	1	2	yes	complemented
213	#382	C₂²×C₃	1	1	yes	characteristic, complemented
214	#380	C₂²×C₃	1	2	yes	—
215	#380	C₂²×C₃	1	2	yes	complemented
216	#379	C₂²×C₃	1	2	yes	—
217	#379	C₂²×C₃	1	2	yes	—
218	#379	C₂²×C₃	1	4	yes	—
219	C₄×C₄⋊C₄	C₂²×C₃	1	4	yes	complemented
220	C₄×C₄⋊C₄	C₂²×C₃	1	2	yes	complemented
221	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
222	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	complemented
223	C₂⁴×C₃	—	2	4	no	—
224	C₂⁴×C₃	—	4	2	no	—
225	C₂⁴×C₃	—	4	2	no	—
226	C₂⁴×C₃	—	4	4	no	—
227	C₂⁴×C₃	—	4	4	no	—
228	C₂⁴×C₃	C₂⁴	1	4	yes	—
229	C₂⁴×C₃	C₂⁴	1	2	yes	—
230	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
231	C₂×C₃×Q₈	—	4	4	no	—
232	C₂×C₃×Q₈	—	4	2	no	—
233	C₂×C₃×D₄	—	2	4	no	—
234	C₂×C₃×D₄	—	2	4	no	—
235	C₂×C₃×D₄	—	2	4	no	—
236	C₂×C₃×D₄	—	2	4	no	—
237	C₂×C₃×D₄	—	2	4	no	—
238	C₂×C₃×D₄	—	2	4	no	—
239	C₂×C₃×D₄	—	4	1	no	—
240	C₂×C₃×D₄	—	4	2	no	—
241	C₂×C₃×D₄	—	4	2	no	—
242	C₂×C₃×D₄	—	4	2	no	—
243	C₂×C₃×D₄	—	4	2	no	—
244	C₂×C₃×D₄	—	4	16	no	—
245	C₂×C₃×D₄	—	4	4	no	—
246	C₂×C₃×D₄	—	4	4	no	—
247	C₂×C₃×D₄	—	4	4	no	—
248	C₂×C₃×D₄	—	4	4	no	—
249	C₂×C₃×D₄	—	4	4	no	—
250	C₂×C₃×D₄	—	4	4	no	—
251	C₂²×C₃×C₄	—	2	2	no	—
252	C₂²×C₃×C₄	—	2	2	no	—
253	C₂²×C₃×C₄	—	2	4	no	—
254	C₂²×C₃×C₄	—	2	4	no	—
255	C₂²×C₃×C₄	—	2	4	no	—
256	C₂²×C₃×C₄	#41	1	4	yes	—
257	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
258	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
259	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
260	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
261	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
262	C₂²×C₃×C₄	C₂⁴	1	4	yes	—
263	C₂²×C₃×C₄	C₂⁴	1	4	yes	—
264	C₂²×C₃×C₄	C₂⁴	1	4	yes	—
265	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
266	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
267	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
268	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
269	C₃×C₄⋊C₄	—	2	4	no	—
270	C₃×C₄⋊C₄	—	2	4	no	—
271	C₃×C₄⋊C₄	—	2	4	no	—
272	C₃×C₄⋊C₄	—	2	4	no	—
273	C₃×C₄⋊C₄	—	2	4	no	—
274	C₃×C₄⋊C₄	—	4	4	no	—
275	C₃×C₄⋊C₄	—	4	1	no	—
276	C₃×C₄⋊C₄	—	4	1	no	—
277	C₃×C₄⋊C₄	—	4	1	no	—
278	C₃×C₄⋊C₄	—	4	4	no	—
279	C₃×C₄⋊C₄	—	4	4	no	—
280	C₃×C₄⋊C₄	—	4	2	no	—
281	C₃×C₂²⋊C₄	—	2	4	no	—
282	C₃×C₂²⋊C₄	—	2	4	no	—
283	C₃×C₂²⋊C₄	—	2	8	no	—
284	C₃×C₂²⋊C₄	—	2	8	no	—
285	C₃×C₂²⋊C₄	—	2	4	no	—
286	C₃×C₂²⋊C₄	—	4	2	no	—
287	C₃×C₂²⋊C₄	—	4	4	no	—
288	C₃×C₂²⋊C₄	—	4	4	no	—
289	C₃×C₂²⋊C₄	—	4	4	no	—
290	C₃×C₂²⋊C₄	—	4	1	no	—
291	C₃×C₂²⋊C₄	—	4	1	no	—
292	C₃×C₂²⋊C₄	—	4	2	no	—
293	C₃×C₂²⋊C₄	—	4	4	no	—
294	C₃×C₂²⋊C₄	—	4	2	no	—
295	C₃×C₂²⋊C₄	—	4	4	no	—
296	C₃×C₂²⋊C₄	—	4	4	no	—
297	C₃×C₂²⋊C₄	—	4	4	no	—
298	C₃×C₂²⋊C₄	—	4	4	no	—
299	C₃×C₂²⋊C₄	—	4	4	no	—
300	C₃×C₂²⋊C₄	—	4	4	no	—
301	C₃×C₂²⋊C₄	—	4	4	no	—
302	C₃×C₄²	—	2	4	no	—
303	C₃×C₄²	—	2	2	no	—
304	C₃×C₄²	—	2	2	no	—
305	C₃×C₄²	—	2	8	no	—
306	C₃×C₄²	—	4	2	no	—
307	C₃×C₄²	—	4	4	no	—
308	C₂⁵	C₂³×C₃	1	2	yes	—
309	C₂²×Q₈	C₂³×C₃	1	2	yes	—
310	C₂²×D₄	—	2	4	no	—
311	C₂²×D₄	—	4	2	no	—
312	C₂²×D₄	—	4	2	no	—
313	C₂²×D₄	C₂³×C₃	1	2	yes	—
314	C₂²×D₄	C₂³×C₃	1	2	yes	—
315	C₂²×D₄	C₂³×C₃	1	2	yes	—
316	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
317	C₂²×D₄	C₂³×C₃	1	4	yes	—
318	C₂²×D₄	C₂³×C₃	1	4	yes	—
319	C₂³×C₄	C₂³×C₃	1	2	yes	—
320	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
321	C₄⋊Q₈	—	4	2	no	—
322	#126	—	4	8	no	—
323	#124	—	4	8	no	—
324	#121	—	4	4	no	—
325	#121	—	4	4	no	—
326	#120	—	4	8	no	—
327	C₄×D₄	—	2	8	no	—
328	C₄×D₄	—	4	2	no	—
329	#117	—	4	2	no	—
330	#117	—	4	2	no	—
331	#117	—	4	4	no	—
332	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
333	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
334	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
335	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
336	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
337	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
338	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
339	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
340	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
341	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
342	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
343	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
344	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
345	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
346	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
347	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
348	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
349	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
350	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
351	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
352	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
353	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
354	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
355	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
356	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
357	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
358	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
359	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
360	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
361	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
362	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
363	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
364	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
365	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
366	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
367	C₂×C₄²	C₂³×C₃	1	2	yes	—
368	C₂×C₄²	C₂³×C₃	1	4	yes	—
369	C₂×C₄²	C₂³×C₃	1	2	yes	—
370	C₂×C₄²	C₂³×C₃	1	4	yes	—
371	#95	C₂³×C₃	1	2	yes	—
372	#95	C₂³×C₃	1	2	yes	—
373	#95	C₂³×C₃	1	4	yes	—
374	#95	C₂³×C₃	1	4	yes	—
375	#95	C₂³×C₃	1	4	yes	—
376	#95	C₂³×C₃	1	1	yes	characteristic
377	#95	C₂³×C₃	1	1	yes	characteristic
378	#95	C₂³×C₃	1	2	yes	—
379	#95	C₂³×C₃	1	2	yes	—
380	#95	C₂³×C₃	1	4	yes	—
381	C₂³×C₃	—	2	1	no	—
382	C₂³×C₃	—	2	1	no	—
383	C₂³×C₃	—	2	2	no	—
384	C₂³×C₃	—	2	2	no	—
385	C₂³×C₃	—	2	2	no	—
386	C₂³×C₃	—	2	4	no	—
387	C₂³×C₃	—	2	2	no	—
388	C₂³×C₃	—	2	4	no	—
389	C₂³×C₃	—	2	4	no	—
390	C₂³×C₃	—	2	2	no	—
391	C₂³×C₃	—	2	2	no	—
392	C₂³×C₃	—	2	4	no	—
393	C₂³×C₃	—	2	4	no	—
394	C₂³×C₃	—	2	2	no	—
395	C₂³×C₃	—	2	4	no	—
396	C₂³×C₃	—	2	2	no	—
397	C₂³×C₃	—	2	4	no	—
398	C₂³×C₃	—	2	2	no	—
399	C₂³×C₃	—	4	8	no	—
400	C₂³×C₃	—	8	8	no	—
401	C₂³×C₃	—	8	4	no	—
402	C₂³×C₃	—	8	8	no	—
403	C₂³×C₃	—	8	4	no	—
404	C₂³×C₃	C₂×#41	1	2	yes	—
405	C₂³×C₃	C₂⁵	1	1	yes	characteristic
406	C₃×Q₈	—	8	4	no	—
407	C₃×D₄	—	4	8	no	—
408	C₃×D₄	—	4	8	no	—
409	C₃×D₄	—	4	4	no	—
410	C₃×D₄	—	4	8	no	—
411	C₃×D₄	—	8	8	no	—
412	C₃×D₄	—	8	8	no	—
413	C₂×C₃×C₄	—	2	2	no	—
414	C₂×C₃×C₄	—	2	1	no	—
415	C₂×C₃×C₄	—	2	1	no	—
416	C₂×C₃×C₄	—	2	2	no	—
417	C₂×C₃×C₄	—	2	8	no	—
418	C₂×C₃×C₄	—	2	2	no	—
419	C₂×C₃×C₄	—	2	2	no	—
420	C₂×C₃×C₄	—	2	4	no	—
421	C₂×C₃×C₄	—	2	1	no	—
422	C₂×C₃×C₄	—	2	1	no	—
423	C₂×C₃×C₄	—	2	1	no	—
424	C₂×C₃×C₄	—	2	4	no	—
425	C₂×C₃×C₄	—	2	1	no	—
426	C₂×C₃×C₄	—	2	4	no	—
427	C₂×C₃×C₄	—	2	2	no	—
428	C₂×C₃×C₄	—	2	4	no	—
429	C₂×C₃×C₄	—	2	4	no	—
430	C₂×C₃×C₄	—	2	2	no	—
431	C₂×C₃×C₄	—	2	4	no	—
432	C₂×C₃×C₄	—	2	2	no	—
433	C₂×C₃×C₄	—	2	2	no	—
434	C₂×C₃×C₄	—	2	2	no	—
435	C₂×C₃×C₄	—	2	4	no	—
436	C₂×C₃×C₄	—	2	2	no	—
437	C₂×C₃×C₄	—	2	2	no	—
438	C₂×C₃×C₄	—	2	4	no	—
439	C₂×C₃×C₄	—	2	2	no	—
440	C₂×C₃×C₄	—	2	4	no	—
441	C₂×C₃×C₄	—	4	8	no	—
442	C₂×C₃×C₄	C₂×#41	1	2	yes	—
443	C₂×C₃×C₄	C₂×#41	1	2	yes	—
444	C₂×C₃×C₄	H(5,𝔽₂)	1	4	yes	—
445	C₂×C₃×C₄	H(5,𝔽₂)	1	2	yes	—
446	C₂×C₃×C₄	H(5,𝔽₂)	1	2	yes	—
447	C₂⁴	—	2	4	no	—
448	C₂⁴	—	4	2	no	—
449	C₂⁴	—	4	2	no	—
450	C₂⁴	—	4	4	no	—
451	C₂⁴	—	4	4	no	—
452	C₂⁴	C₂⁴×C₃	1	4	yes	—
453	C₂⁴	C₂⁴×C₃	1	2	yes	—
454	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
455	C₂×Q₈	—	4	4	no	—
456	C₂×Q₈	—	4	2	no	—
457	C₂×D₄	—	2	4	no	—
458	C₂×D₄	—	2	4	no	—
459	C₂×D₄	—	2	4	no	—
460	C₂×D₄	—	2	4	no	—
461	C₂×D₄	—	2	4	no	—
462	C₂×D₄	—	2	4	no	—
463	C₂×D₄	—	4	1	no	—
464	C₂×D₄	—	4	2	no	—
465	C₂×D₄	—	4	2	no	—
466	C₂×D₄	—	4	2	no	—
467	C₂×D₄	—	4	2	no	—
468	C₂×D₄	—	4	16	no	—
469	C₂×D₄	—	4	4	no	—
470	C₂×D₄	—	4	4	no	—
471	C₂×D₄	—	4	4	no	—
472	C₂×D₄	—	4	4	no	—
473	C₂×D₄	—	4	4	no	—
474	C₂×D₄	—	4	4	no	—
475	C₂²×C₄	—	2	2	no	—
476	C₂²×C₄	—	2	2	no	—
477	C₂²×C₄	—	2	4	no	—
478	C₂²×C₄	—	2	4	no	—
479	C₂²×C₄	—	2	4	no	—
480	C₂²×C₄	C₃×#41	1	4	yes	—
481	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
482	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
483	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
484	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
485	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
486	C₂²×C₄	C₂⁴×C₃	1	4	yes	—
487	C₂²×C₄	C₂⁴×C₃	1	4	yes	—
488	C₂²×C₄	C₂⁴×C₃	1	4	yes	—
489	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
490	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
491	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
492	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
493	C₄⋊C₄	—	2	4	no	—
494	C₄⋊C₄	—	2	4	no	—
495	C₄⋊C₄	—	2	4	no	—
496	C₄⋊C₄	—	2	4	no	—
497	C₄⋊C₄	—	2	4	no	—
498	C₄⋊C₄	—	4	1	no	—
499	C₄⋊C₄	—	4	1	no	—
500	C₄⋊C₄	—	4	1	no	—
501	C₄⋊C₄	—	4	4	no	—
502	C₄⋊C₄	—	4	4	no	—
503	C₄⋊C₄	—	4	2	no	—
504	C₄⋊C₄	—	4	4	no	—
505	C₂²⋊C₄	—	2	4	no	—
506	C₂²⋊C₄	—	2	4	no	—
507	C₂²⋊C₄	—	2	8	no	—
508	C₂²⋊C₄	—	2	8	no	—
509	C₂²⋊C₄	—	2	4	no	—
510	C₂²⋊C₄	—	4	1	no	—
511	C₂²⋊C₄	—	4	1	no	—
512	C₂²⋊C₄	—	4	2	no	—
513	C₂²⋊C₄	—	4	4	no	—
514	C₂²⋊C₄	—	4	2	no	—
515	C₂²⋊C₄	—	4	4	no	—
516	C₂²⋊C₄	—	4	4	no	—
517	C₂²⋊C₄	—	4	4	no	—
518	C₂²⋊C₄	—	4	4	no	—
519	C₂²⋊C₄	—	4	4	no	—
520	C₂²⋊C₄	—	4	4	no	—
521	C₂²⋊C₄	—	4	4	no	—
522	C₂²⋊C₄	—	4	2	no	—
523	C₂²⋊C₄	—	4	4	no	—
524	C₂²⋊C₄	—	4	4	no	—
525	C₂²⋊C₄	—	4	4	no	—
526	C₄²	—	2	4	no	—
527	C₄²	—	2	2	no	—
528	C₄²	—	2	2	no	—
529	C₄²	—	2	8	no	—
530	C₄²	—	4	2	no	—
531	C₄²	—	4	4	no	—
532	C₂²×C₃	—	2	2	no	—
533	C₂²×C₃	—	2	4	no	—
534	C₂²×C₃	—	4	1	no	—
535	C₂²×C₃	—	4	2	no	—
536	C₂²×C₃	—	4	1	no	—
537	C₂²×C₃	—	4	2	no	—
538	C₂²×C₃	—	4	4	no	—
539	C₂²×C₃	—	4	2	no	—
540	C₂²×C₃	—	4	2	no	—
541	C₂²×C₃	—	4	4	no	—
542	C₂²×C₃	—	4	4	no	—
543	C₂²×C₃	—	4	2	no	—
544	C₂²×C₃	—	4	4	no	—
545	C₂²×C₃	—	4	2	no	—
546	C₂²×C₃	—	4	4	no	—
547	C₂²×C₃	—	4	2	no	—
548	C₂²×C₃	—	4	4	no	—
549	C₂²×C₃	—	4	2	no	—
550	C₂²×C₃	—	4	4	no	—
551	C₂²×C₃	—	8	16	no	—
552	C₂²×C₃	C₂²×#41	1	1	yes	characteristic
553	C₂²×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
554	C₂²×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
555	C₂²×C₃	C₂×H(5,𝔽₂)	1	2	yes	—
556	C₂²×C₃	#585	1	2	yes	—
557	C₃×C₄	—	2	2	no	—
558	C₃×C₄	—	2	4	no	—
559	C₃×C₄	—	4	2	no	—
560	C₃×C₄	—	4	2	no	—
561	C₃×C₄	—	4	1	no	—
562	C₃×C₄	—	4	1	no	—
563	C₃×C₄	—	4	4	no	—
564	C₃×C₄	—	4	4	no	—
565	C₃×C₄	—	4	1	no	—
566	C₃×C₄	—	4	4	no	—
567	C₃×C₄	—	4	1	no	—
568	C₃×C₄	#538	1	4	yes	—
569	C₂³	—	2	1	no	—
570	C₂³	—	2	1	no	—
571	C₂³	—	2	2	no	—
572	C₂³	—	2	2	no	—
573	C₂³	—	2	2	no	—
574	C₂³	—	2	4	no	—
575	C₂³	—	2	2	no	—
576	C₂³	—	2	4	no	—
577	C₂³	—	2	4	no	—
578	C₂³	—	2	2	no	—
579	C₂³	—	2	2	no	—
580	C₂³	—	2	4	no	—
581	C₂³	—	2	4	no	—
582	C₂³	—	2	2	no	—
583	C₂³	—	2	4	no	—
584	C₂³	—	2	2	no	—
585	C₂³	—	2	4	no	—
586	C₂³	—	2	2	no	—
587	C₂³	—	4	8	no	—
588	C₂³	—	8	8	no	—
589	C₂³	—	8	4	no	—
590	C₂³	—	8	8	no	—
591	C₂³	—	8	4	no	—
592	C₂³	C₂×C₃×#41	1	2	yes	—
593	C₂³	C₂⁵×C₃	1	1	yes	characteristic
594	Q₈	—	8	4	no	—
595	D₄	—	4	8	no	—
596	D₄	—	4	8	no	—
597	D₄	—	4	4	no	—
598	D₄	—	4	8	no	—
599	D₄	—	8	8	no	—
600	D₄	—	8	8	no	—
601	C₂×C₄	—	2	2	no	—
602	C₂×C₄	—	2	1	no	—
603	C₂×C₄	—	2	1	no	—
604	C₂×C₄	—	2	2	no	—
605	C₂×C₄	—	2	8	no	—
606	C₂×C₄	—	2	2	no	—
607	C₂×C₄	—	2	2	no	—
608	C₂×C₄	—	2	4	no	—
609	C₂×C₄	—	2	1	no	—
610	C₂×C₄	—	2	1	no	—
611	C₂×C₄	—	2	1	no	—
612	C₂×C₄	—	2	4	no	—
613	C₂×C₄	—	2	1	no	—
614	C₂×C₄	—	2	4	no	—
615	C₂×C₄	—	2	2	no	—
616	C₂×C₄	—	2	4	no	—
617	C₂×C₄	—	2	4	no	—
618	C₂×C₄	—	2	2	no	—
619	C₂×C₄	—	2	4	no	—
620	C₂×C₄	—	2	2	no	—
621	C₂×C₄	—	2	2	no	—
622	C₂×C₄	—	2	2	no	—
623	C₂×C₄	—	2	4	no	—
624	C₂×C₄	—	2	2	no	—
625	C₂×C₄	—	2	2	no	—
626	C₂×C₄	—	2	4	no	—
627	C₂×C₄	—	2	2	no	—
628	C₂×C₄	—	2	4	no	—
629	C₂×C₄	—	4	8	no	—
630	C₂×C₄	C₂×C₃×#41	1	2	yes	—
631	C₂×C₄	C₂×C₃×#41	1	2	yes	—
632	C₂×C₄	C₃×H(5,𝔽₂)	1	4	yes	—
633	C₂×C₄	C₃×H(5,𝔽₂)	1	2	yes	—
634	C₂×C₄	C₃×H(5,𝔽₂)	1	2	yes	—
635	C₂×C₃	—	4	2	no	—
636	C₂×C₃	—	8	2	no	—
637	C₂×C₃	—	8	4	no	—
638	C₂×C₃	C₂×#538	1	1	yes	characteristic
639	C₂×C₃	#3494	1	2	yes	—
640	C₂×C₃	#3540	1	1	yes	characteristic
641	C₂×C₃	#3546	1	2	yes	—
642	C₂×C₃	#3549	1	1	yes	characteristic
643	C₂²	—	2	2	no	—
644	C₂²	—	2	4	no	—
645	C₂²	—	4	1	no	—
646	C₂²	—	4	2	no	—
647	C₂²	—	4	1	no	—
648	C₂²	—	4	2	no	—
649	C₂²	—	4	4	no	—
650	C₂²	—	4	2	no	—
651	C₂²	—	4	4	no	—
652	C₂²	—	4	4	no	—
653	C₂²	—	4	2	no	—
654	C₂²	—	4	2	no	—
655	C₂²	—	4	4	no	—
656	C₂²	—	4	2	no	—
657	C₂²	—	4	4	no	—
658	C₂²	—	4	4	no	—
659	C₂²	—	4	2	no	—
660	C₂²	—	4	2	no	—
661	C₂²	—	4	4	no	—
662	C₂²	—	8	16	no	—
663	C₂²	C₂²×C₃×#41	1	1	yes	characteristic
664	C₂²	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
665	C₂²	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
666	C₂²	C₂×C₃×H(5,𝔽₂)	1	2	yes	—
667	C₂²	C₃×#585	1	2	yes	—
668	C₄	—	2	2	no	—
669	C₄	—	2	4	no	—
670	C₄	—	4	2	no	—
671	C₄	—	4	2	no	—
672	C₄	—	4	1	no	—
673	C₄	—	4	1	no	—
674	C₄	—	4	4	no	—
675	C₄	—	4	4	no	—
676	C₄	—	4	4	no	—
677	C₄	—	4	1	no	—
678	C₄	—	4	1	no	—
679	C₄	C₃×#538	1	4	yes	—
680	C₃	#42975	1	1	yes	characteristic, direct product factor, Sylow
681	C₂	—	4	2	no	—
682	C₂	—	8	4	no	—
683	C₂	—	8	2	no	—
684	C₂	C₂×C₃×#538	1	1	yes	characteristic
685	C₂	C₃×#3494	1	2	yes	—
686	C₂	C₃×#3540	1	1	yes	characteristic
687	C₂	C₃×#3546	1	2	yes	—
688	C₂	C₃×#3549	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₃	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₃
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃×#2828	C₂	semidirect
2. C₃×#2736	C₂	semidirect
3. C₃×#2685	C₂	semidirect
4. C₃×#2670	C₂	semidirect
5. C₃×#2662	C₂	semidirect
6. C₃×#2628	C₂	semidirect
7. C₃×#2593	C₂	semidirect
8. C₃×#2512	C₂	semidirect
9. C₃×#2500	C₂	semidirect
10. C₃×#2491	C₂	semidirect
11. C₃×#2414	C₂	semidirect
12. C₃×#2408	C₂	semidirect
13. C₃×#2392	C₂	semidirect
14. C₃×#2354	C₂	semidirect
15. C₃×#2309	C₂	semidirect
16. #42975	C₃	direct (N × H)
18. C₂×C₃×C₄⋊Q₈	C₂²	semidirect
19. C₂×C₃×#126	C₂²	semidirect
20. C₂×C₃×#124	C₂²	semidirect
25. C₂×C₃×C₄×D₄	C₂²	semidirect
28. C₂×C₃×#117	C₂²	semidirect
29. C₃×#400	C₂²	semidirect
31. C₃×#398	C₂²	semidirect
33. C₃×#397	C₂²	semidirect
34. C₃×#396	C₂²	semidirect
35. C₃×#396	C₂²	semidirect
36. C₃×#395	C₂²	semidirect
39. C₃×#394	C₂²	semidirect
40. C₃×#394	C₂²	semidirect
41. C₃×#394	C₂²	semidirect
42. C₃×#394	C₂²	semidirect
43. C₃×#394	C₂²	semidirect
45. C₃×#393	C₂²	semidirect
48. C₃×#392	C₂²	semidirect
56. C₃×#390	C₂²	semidirect
57. C₃×#389	C₂²	semidirect
59. C₃×#388	C₂²	semidirect
60. C₃×#388	C₂²	semidirect
61. C₃×#388	C₂²	semidirect
62. C₃×#388	C₂²	semidirect
63. C₃×#388	C₂²	semidirect
64. C₃×#388	C₂²	semidirect
65. C₃×#384	C₂²	semidirect
66. C₃×#382	C₂²	semidirect
68. C₃×#380	C₂²	semidirect
72. C₃×C₄×C₄⋊C₄	C₂²	semidirect
73. C₃×C₄×C₄⋊C₄	C₂²	semidirect
74. C₃×C₄×C₄⋊C₄	C₂²	semidirect
75. C₃×C₄×C₂²⋊C₄	C₂²	semidirect
76. #2828	C₂×C₃	semidirect
77. #2736	C₂×C₃	semidirect
78. #2685	C₂×C₃	semidirect
79. #2670	C₂×C₃	semidirect
80. #2662	C₂×C₃	semidirect
81. #2628	C₂×C₃	semidirect
82. #2593	C₂×C₃	semidirect
83. #2512	C₂×C₃	semidirect
84. #2500	C₂×C₃	semidirect
85. #2491	C₂×C₃	semidirect
86. #2414	C₂×C₃	semidirect
87. #2408	C₂×C₃	semidirect
88. #2392	C₂×C₃	semidirect
89. #2354	C₂×C₃	semidirect
90. #2309	C₂×C₃	semidirect
165. C₂×C₄⋊Q₈	C₂²×C₃	semidirect
166. C₂×#126	C₂²×C₃	semidirect
167. C₂×#124	C₂²×C₃	semidirect
172. C₂×C₄×D₄	C₂²×C₃	semidirect
175. C₂×#117	C₂²×C₃	semidirect
176. #400	C₂²×C₃	semidirect
178. #398	C₂²×C₃	semidirect
180. #397	C₂²×C₃	semidirect
181. #396	C₂²×C₃	semidirect
182. #396	C₂²×C₃	semidirect
183. #395	C₂²×C₃	semidirect
186. #394	C₂²×C₃	semidirect
187. #394	C₂²×C₃	semidirect
188. #394	C₂²×C₃	semidirect
189. #394	C₂²×C₃	semidirect
190. #394	C₂²×C₃	semidirect
192. #393	C₂²×C₃	semidirect
195. #392	C₂²×C₃	semidirect
203. #390	C₂²×C₃	semidirect
204. #389	C₂²×C₃	semidirect
206. #388	C₂²×C₃	semidirect
207. #388	C₂²×C₃	semidirect
208. #388	C₂²×C₃	semidirect
209. #388	C₂²×C₃	semidirect
210. #388	C₂²×C₃	semidirect
211. #388	C₂²×C₃	semidirect
212. #384	C₂²×C₃	semidirect
213. #382	C₂²×C₃	semidirect
215. #380	C₂²×C₃	semidirect
219. C₄×C₄⋊C₄	C₂²×C₃	semidirect
220. C₄×C₄⋊C₄	C₂²×C₃	semidirect
221. C₄×C₄⋊C₄	C₂²×C₃	semidirect
222. C₄×C₂²⋊C₄	C₂²×C₃	semidirect
680. C₃	#42975	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×#2828	2
C₃×#2736	2
C₃×#2685	2
C₃×#2670	2
C₃×#2662	2
C₃×#2628	2
C₃×#2593	2
C₃×#2512	2
C₃×#2500	2
C₃×#2491	2
C₃×#2414	2
C₃×#2408	2
C₃×#2392	2
C₃×#2354	2
C₃×#2309	2
#42975	3

Subgroups — C3×#42975 #10661582

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#42975 #10661582