Subgroups — C₂×C₃×D₃×#135 #11918591

Order 1152.

3141 conjugacy classes of subgroups.

The subgroup lattice has 801 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×D₃×#41	C₂	1	2	yes	maximal, complemented
2	C₂×C₃²×#135	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×#950	C₂	1	2	yes	maximal, complemented
4	C₃×D₃×#135	C₂	1	16	yes	maximal, direct product factor
5	C₂×C₃×#919	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₃×D₃×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₃×#916	C₂	1	2	yes	maximal, complemented
8	C₂×C₃×D₃×SD₁₆	C₂	1	2	yes	maximal, complemented
9	C₂×C₃×#912	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₃×D₃×D₈	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₃×#904	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₃×D₃×C₈	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂²×C₃×#135	—	3	1	no	maximal
14	C₂×D₃×#135	C₃	1	1	yes	maximal, characteristic, direct product factor
15	C₂×C₃²×#41	C₂²	1	2	yes	complemented
16	C₃×D₃×#41	—	2	8	no	—
17	C₃×D₃×#41	C₂²	1	16	yes	complemented
18	C₂×C₃×#239	C₂²	1	2	yes	complemented
19	C₂×C₃×D₃×Q₈	C₂²	1	2	yes	—
20	C₂×C₃×#237	—	2	2	no	—
21	C₂×C₃×#237	C₂²	1	2	yes	complemented
22	C₂×C₃×D₃×D₄	—	2	2	no	—
23	C₂×C₃×D₃×D₄	C₂²	1	2	yes	—
24	C₂×C₃×#235	—	2	2	no	—
25	C₂×C₃×#235	C₂²	1	2	yes	complemented
26	C₂²×C₃×C₄×D₃	—	2	2	no	—
27	C₂²×C₃×C₄×D₃	C₂²	1	1	yes	characteristic
28	C₃²×#135	C₂²	1	8	yes	complemented
29	C₂×C₃²×Q₁₆	C₂²	1	1	yes	characteristic, complemented
30	C₂×C₃²×SD₁₆	C₂²	1	2	yes	complemented
31	C₂×C₃²×D₈	C₂²	1	1	yes	characteristic, complemented
32	C₂²×C₃²×C₈	C₂²	1	1	yes	characteristic, complemented
33	C₃×#950	C₂²	1	16	yes	complemented
34	C₂×C₃×#216	C₂²	1	2	yes	complemented
35	C₂×C₃×#215	C₂²	1	2	yes	complemented
36	C₂×C₃×#214	C₂²	1	2	yes	complemented
37	C₂×C₃×#213	C₂²	1	2	yes	complemented
38	C₂²×C₃×C₃⋊C₈	C₂²	1	1	yes	characteristic, complemented
39	C₃×#919	C₂²	1	8	yes	complemented
40	C₃×D₃×Q₁₆	C₂²	1	8	yes	complemented
41	C₃×#916	C₂²	1	16	yes	complemented
42	C₃×D₃×SD₁₆	C₂²	1	16	yes	complemented
43	C₃×#912	C₂²	1	8	yes	complemented
44	C₃×D₃×D₈	C₂²	1	8	yes	complemented
45	C₂×C₃×Dic₁₂	C₂²	1	1	yes	characteristic, complemented
46	C₃×#904	C₂²	1	8	yes	complemented
47	C₂×C₃×D₂₄	C₂²	1	1	yes	characteristic, complemented
48	C₂×C₃×#204	C₂²	1	2	yes	complemented
49	C₂×C₃×D₃×C₈	C₂²	1	1	yes	characteristic
50	C₂×C₃×D₃×C₈	C₂²	1	1	yes	characteristic
51	C₂×C₃×D₃×C₈	C₂²	1	8	yes	complemented
52	C₂×C₃×D₃×C₈	C₂²	1	1	yes	characteristic, complemented
53	C₂×C₃×D₃×C₈	C₂²	1	1	yes	characteristic, complemented
54	C₂²×C₃×#41	—	3	2	no	—
55	C₂×D₃×#41	C₂×C₃	1	2	yes	complemented
56	C₂×C₃×#135	—	2	1	no	—
57	C₂×C₃×#135	—	3	2	no	—
58	C₂×C₃×#135	—	3	16	no	—
59	C₂×C₃×#135	—	3	1	no	—
60	C₂×C₃×#135	—	3	2	no	—
61	C₂×C₃×#135	—	3	1	no	—
62	C₂×C₃×#135	—	3	1	no	—
63	C₂×C₃×#135	D₃	1	1	yes	characteristic, direct product factor
64	C₂×C₃×#135	C₂×C₃	1	1	yes	characteristic, complemented
65	C₂²×C₃×Q₁₆	—	3	1	no	—
66	C₂²×C₃×SD₁₆	—	3	2	no	—
67	C₂²×C₃×D₈	—	3	1	no	—
68	C₂³×C₃×C₈	—	3	1	no	—
69	C₂×#950	C₂×C₃	1	2	yes	complemented
70	D₃×#135	C₂×C₃	1	16	yes	direct product factor
71	C₂×#919	C₂×C₃	1	1	yes	characteristic, complemented
72	C₂×D₃×Q₁₆	C₂×C₃	1	1	yes	characteristic, complemented
73	C₂×#916	C₂×C₃	1	2	yes	complemented
74	C₂×D₃×SD₁₆	C₂×C₃	1	2	yes	complemented
75	C₂×#912	C₂×C₃	1	1	yes	characteristic, complemented
76	C₂×D₃×D₈	C₂×C₃	1	1	yes	characteristic, complemented
77	C₂×#904	C₂×C₃	1	1	yes	characteristic, complemented
78	C₂²×D₃×C₈	C₂×C₃	1	1	yes	characteristic, complemented
79	C₂³×C₃×D₃	—	2	2	no	—
80	C₂³×C₃×D₃	D₄	1	1	yes	characteristic
81	C₃²×#41	—	2	4	no	—
82	C₃²×#41	C₂³	1	8	yes	complemented
83	C₂×C₃²×Q₈	C₂³	1	2	yes	—
84	C₂×C₃²×D₄	—	2	2	no	—
85	C₂×C₃²×D₄	C₂³	1	2	yes	—
86	C₂²×C₃²×C₄	—	2	2	no	—
87	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
88	C₂×C₃×#67	—	2	2	no	—
89	C₂×C₃×#67	—	2	2	no	—
90	C₂×C₃×#67	—	2	2	no	—
91	C₂²×C₃×Dic₃	—	2	2	no	—
92	C₂²×C₃×Dic₃	D₄	1	1	yes	characteristic
93	C₃×#239	—	2	4	no	—
94	C₃×#239	C₂³	1	8	yes	complemented
95	C₃×D₃×Q₈	—	2	4	no	—
96	C₃×D₃×Q₈	C₂³	1	8	yes	—
97	C₃×#237	—	2	16	no	—
98	C₃×#237	—	2	4	no	—
99	C₃×#237	C₂³	1	8	yes	complemented
100	C₃×D₃×D₄	—	2	16	no	—
101	C₃×D₃×D₄	—	2	4	no	—
102	C₃×D₃×D₄	C₂³	1	8	yes	—
103	C₃×#235	—	2	4	no	—
104	C₃×#235	—	2	16	no	—
105	C₃×#235	C₂³	1	8	yes	complemented
106	C₂×C₃×D₁₂	—	2	2	no	—
107	C₂×C₃×D₁₂	C₂³	1	2	yes	—
108	C₂×C₃×C₄×D₃	—	2	2	no	—
109	C₂×C₃×C₄×D₃	—	2	2	no	—
110	C₂×C₃×C₄×D₃	—	2	2	no	—
111	C₂×C₃×C₄×D₃	—	2	16	no	—
112	C₂×C₃×C₄×D₃	D₄	1	1	yes	characteristic
113	C₂×C₃×C₄×D₃	D₄	1	1	yes	characteristic
114	C₂×C₃×C₄×D₃	D₄	1	4	yes	—
115	C₂×C₃×C₄×D₃	C₂³	1	1	yes	characteristic
116	C₂×C₃×C₄×D₃	C₂³	1	1	yes	characteristic
117	C₂×C₃×C₄×D₃	C₂³	1	4	yes	—
118	C₂×C₃×Dic₆	—	2	2	no	—
119	C₂×C₃×Dic₆	C₂³	1	2	yes	—
120	C₃²×Q₁₆	C₂³	1	4	yes	complemented
121	C₃²×SD₁₆	C₂³	1	8	yes	complemented
122	C₃²×D₈	C₂³	1	4	yes	complemented
123	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
124	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
125	C₂×C₃²×C₈	C₂³	1	4	yes	complemented
126	C₃×#216	C₂³	1	8	yes	complemented
127	C₃×#215	C₂³	1	8	yes	complemented
128	C₃×#214	C₂³	1	8	yes	complemented
129	C₃×#213	C₂³	1	8	yes	complemented
130	C₂×C₃×C₃⋊C₈	C₂³	1	1	yes	characteristic
131	C₂×C₃×C₃⋊C₈	C₂³	1	1	yes	characteristic
132	C₂×C₃×C₃⋊C₈	C₂³	1	4	yes	complemented
133	C₃×Dic₁₂	C₂³	1	4	yes	complemented
134	C₃×D₂₄	C₂³	1	4	yes	complemented
135	C₃×#204	C₂³	1	8	yes	complemented
136	C₃×D₃×C₈	C₂³	1	4	yes	—
137	C₃×D₃×C₈	C₂³	1	4	yes	—
138	C₃×D₃×C₈	C₂³	1	4	yes	complemented
139	C₃×D₃×C₈	C₂³	1	4	yes	complemented
140	C₂²×#135	—	3	1	no	Sylow
141	C₂×C₃×#41	—	2	2	no	—
142	C₂×C₃×#41	—	3	16	no	—
143	C₂×C₃×#41	—	3	2	no	—
144	C₂×C₃×#41	—	3	2	no	—
145	C₂×C₃×#41	—	3	2	no	—
146	C₂×C₃×#41	—	6	2	no	—
147	C₂×C₃×#41	—	6	2	no	—
148	C₂×C₃×#41	—	6	8	no	—
149	C₂×C₃×#41	C₂×D₃	1	2	yes	complemented
150	C₂×C₃×#41	C₂²×C₃	1	2	yes	complemented
151	C₂²×C₃×Q₈	—	3	2	no	—
152	C₂²×C₃×D₄	—	3	2	no	—
153	C₂²×C₃×D₄	—	6	2	no	—
154	C₂³×C₃×C₄	—	3	1	no	—
155	C₂³×C₃×C₄	—	6	2	no	—
156	D₃×#41	—	2	8	no	—
157	D₃×#41	C₂²×C₃	1	16	yes	complemented
158	C₂×#239	C₂²×C₃	1	2	yes	complemented
159	C₂×D₃×Q₈	C₂²×C₃	1	2	yes	—
160	C₂×#237	—	2	2	no	—
161	C₂×#237	C₂²×C₃	1	2	yes	complemented
162	C₂×D₃×D₄	—	2	2	no	—
163	C₂×D₃×D₄	C₂²×C₃	1	2	yes	—
164	C₂×#235	—	2	2	no	—
165	C₂×#235	C₂²×C₃	1	2	yes	complemented
166	C₂²×C₄×D₃	—	2	2	no	—
167	C₂²×C₄×D₃	C₂²×C₃	1	1	yes	characteristic
168	C₃×#135	—	2	8	no	—
169	C₃×#135	—	3	16	no	—
170	C₃×#135	—	3	8	no	—
171	C₃×#135	—	3	16	no	—
172	C₃×#135	—	3	8	no	—
173	C₃×#135	—	3	8	no	—
174	C₃×#135	C₂×D₃	1	8	yes	direct product factor
175	C₃×#135	C₂²×C₃	1	8	yes	complemented
176	C₂×C₃×Q₁₆	—	2	1	no	—
177	C₂×C₃×Q₁₆	—	3	2	no	—
178	C₂×C₃×Q₁₆	—	3	8	no	—
179	C₂×C₃×Q₁₆	—	3	1	no	—
180	C₂×C₃×Q₁₆	C₂×D₃	1	1	yes	characteristic, complemented
181	C₂×C₃×Q₁₆	C₂²×C₃	1	1	yes	characteristic, complemented
182	C₂×C₃×SD₁₆	—	2	2	no	—
183	C₂×C₃×SD₁₆	—	3	2	no	—
184	C₂×C₃×SD₁₆	—	3	2	no	—
185	C₂×C₃×SD₁₆	—	3	16	no	—
186	C₂×C₃×SD₁₆	—	3	2	no	—
187	C₂×C₃×SD₁₆	C₂×D₃	1	2	yes	complemented
188	C₂×C₃×SD₁₆	C₂²×C₃	1	2	yes	complemented
189	C₂×C₃×D₈	—	2	1	no	—
190	C₂×C₃×D₈	—	3	2	no	—
191	C₂×C₃×D₈	—	3	8	no	—
192	C₂×C₃×D₈	—	3	1	no	—
193	C₂×C₃×D₈	C₂×D₃	1	1	yes	characteristic, complemented
194	C₂×C₃×D₈	C₂²×C₃	1	1	yes	characteristic, complemented
195	C₂²×C₃×C₈	—	2	1	no	—
196	C₂²×C₃×C₈	—	3	1	no	—
197	C₂²×C₃×C₈	—	3	1	no	—
198	C₂²×C₃×C₈	—	3	1	no	—
199	C₂²×C₃×C₈	—	3	1	no	—
200	C₂²×C₃×C₈	—	3	1	no	—
201	C₂²×C₃×C₈	—	3	8	no	—
202	C₂²×C₃×C₈	C₂×D₃	1	1	yes	characteristic, complemented
203	C₂²×C₃×C₈	C₂²×C₃	1	1	yes	characteristic, complemented
204	#950	C₂²×C₃	1	16	yes	complemented
205	C₂×#216	C₂²×C₃	1	2	yes	complemented
206	C₂×#215	C₂²×C₃	1	2	yes	complemented
207	C₂×#214	C₂²×C₃	1	2	yes	complemented
208	C₂×#213	C₂²×C₃	1	2	yes	complemented
209	C₂²×C₃⋊C₈	C₂²×C₃	1	1	yes	characteristic, complemented
210	#919	C₂²×C₃	1	8	yes	complemented
211	D₃×Q₁₆	C₂²×C₃	1	8	yes	complemented
212	#916	C₂²×C₃	1	16	yes	complemented
213	D₃×SD₁₆	C₂²×C₃	1	16	yes	complemented
214	#912	C₂²×C₃	1	8	yes	complemented
215	D₃×D₈	C₂²×C₃	1	8	yes	complemented
216	C₂×Dic₁₂	C₂²×C₃	1	1	yes	characteristic, complemented
217	#904	C₂²×C₃	1	8	yes	complemented
218	C₂×D₂₄	C₂²×C₃	1	1	yes	characteristic, complemented
219	C₂×#204	C₂²×C₃	1	2	yes	complemented
220	C₂×D₃×C₈	C₂²×C₃	1	1	yes	characteristic
221	C₂×D₃×C₈	C₂²×C₃	1	1	yes	characteristic
222	C₂×D₃×C₈	C₂²×C₃	1	8	yes	complemented
223	C₂×D₃×C₈	C₂²×C₃	1	1	yes	characteristic, complemented
224	C₂×D₃×C₈	C₂²×C₃	1	1	yes	characteristic, complemented
225	C₂³×C₃²	—	2	2	no	—
226	C₂³×C₃²	C₂×D₄	1	1	yes	characteristic
227	C₂²×C₃×D₃	—	2	4	no	—
228	C₂²×C₃×D₃	—	2	2	no	—
229	C₂²×C₃×D₃	—	2	8	no	—
230	C₂²×C₃×D₃	—	4	8	no	—
231	C₂²×C₃×D₃	C₂×D₄	1	1	yes	characteristic
232	C₂²×C₃×D₃	C₂×D₄	1	4	yes	—
233	C₂²×C₃×D₃	C₂×D₄	1	1	yes	characteristic
234	C₃²×Q₈	—	2	2	no	—
235	C₃²×Q₈	C₂⁴	1	4	yes	—
236	C₃²×D₄	—	2	8	no	—
237	C₃²×D₄	—	2	2	no	—
238	C₃²×D₄	C₂⁴	1	4	yes	—
239	C₂×C₃²×C₄	—	2	2	no	—
240	C₂×C₃²×C₄	—	2	8	no	—
241	C₂×C₃²×C₄	C₂×D₄	1	2	yes	—
242	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
243	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
244	C₂×C₃²×C₄	C₂⁴	1	2	yes	—
245	C₃×#67	—	2	8	no	—
246	C₃×#67	—	2	8	no	—
247	C₃×#67	—	2	8	no	—
248	C₂×C₃×Dic₃	—	2	2	no	—
249	C₂×C₃×Dic₃	—	2	8	no	—
250	C₂×C₃×Dic₃	C₂×D₄	1	1	yes	characteristic
251	C₂×C₃×Dic₃	C₂×D₄	1	1	yes	characteristic
252	C₂×C₃×Dic₃	C₂×D₄	1	4	yes	—
253	C₃×D₁₂	—	2	8	no	—
254	C₃×D₁₂	—	2	2	no	—
255	C₃×D₁₂	C₂⁴	1	4	yes	—
256	C₃×C₄×D₃	—	2	8	no	—
257	C₃×C₄×D₃	—	2	8	no	—
258	C₃×C₄×D₃	—	2	8	no	—
259	C₃×C₄×D₃	C₂×D₄	1	4	yes	—
260	C₃×C₄×D₃	C₂×D₄	1	4	yes	—
261	C₃×C₄×D₃	C₂×D₄	1	2	yes	—
262	C₃×C₄×D₃	C₂×D₄	1	2	yes	—
263	C₃×C₄×D₃	C₂⁴	1	2	yes	—
264	C₃×C₄×D₃	C₂⁴	1	2	yes	—
265	C₃×Dic₆	—	2	2	no	—
266	C₃×Dic₆	—	2	8	no	—
267	C₃×Dic₆	C₂⁴	1	4	yes	—
268	C₃²×C₈	C₂⁴	1	2	yes	—
269	C₃²×C₈	C₂⁴	1	2	yes	—
270	C₃×C₃⋊C₈	C₂⁴	1	2	yes	—
271	C₃×C₃⋊C₈	C₂⁴	1	2	yes	—
272	C₂²×#41	—	3	2	no	—
273	C₂×#135	—	3	2	no	—
274	C₂×#135	—	3	16	no	—
275	C₂×#135	—	3	1	no	—
276	C₂×#135	—	3	2	no	—
277	C₂×#135	—	3	1	no	—
278	C₂×#135	—	3	1	no	—
279	C₂×#135	C₃×D₃	1	1	yes	characteristic, direct product factor
280	C₂²×Q₁₆	—	3	1	no	—
281	C₂²×SD₁₆	—	3	2	no	—
282	C₂²×D₈	—	3	1	no	—
283	C₂³×C₈	—	3	1	no	—
284	C₂⁴×C₃	—	3	1	no	—
285	C₂⁴×C₃	—	6	2	no	—
286	C₂³×D₃	—	2	2	no	—
287	C₂³×D₃	C₃×D₄	1	1	yes	characteristic
288	C₃×#41	—	2	4	no	—
289	C₃×#41	—	2	4	no	—
290	C₃×#41	—	2	8	no	—
291	C₃×#41	—	3	8	no	—
292	C₃×#41	—	3	8	no	—
293	C₃×#41	—	3	8	no	—
294	C₃×#41	—	4	4	no	—
295	C₃×#41	—	6	16	no	—
296	C₃×#41	—	6	16	no	—
297	C₃×#41	—	6	4	no	—
298	C₃×#41	—	6	4	no	—
299	C₃×#41	—	6	4	no	—
300	C₃×#41	C₂²×D₃	1	8	yes	complemented
301	C₃×#41	C₂³×C₃	1	8	yes	complemented
302	C₂×C₃×Q₈	—	2	2	no	—
303	C₂×C₃×Q₈	—	3	8	no	—
304	C₂×C₃×Q₈	—	3	2	no	—
305	C₂×C₃×Q₈	—	6	2	no	—
306	C₂×C₃×Q₈	—	6	4	no	—
307	C₂×C₃×Q₈	C₂²×D₃	1	2	yes	—
308	C₂×C₃×Q₈	C₂³×C₃	1	2	yes	—
309	C₂×C₃×D₄	—	2	2	no	—
310	C₂×C₃×D₄	—	2	2	no	—
311	C₂×C₃×D₄	—	2	2	no	—
312	C₂×C₃×D₄	—	3	8	no	—
313	C₂×C₃×D₄	—	3	2	no	—
314	C₂×C₃×D₄	—	4	2	no	—
315	C₂×C₃×D₄	—	6	2	no	—
316	C₂×C₃×D₄	—	6	4	no	—
317	C₂×C₃×D₄	—	6	2	no	—
318	C₂×C₃×D₄	—	6	16	no	—
319	C₂×C₃×D₄	—	6	2	no	—
320	C₂×C₃×D₄	—	6	2	no	—
321	C₂×C₃×D₄	C₂²×D₃	1	2	yes	—
322	C₂×C₃×D₄	C₂³×C₃	1	2	yes	—
323	C₂²×C₃×C₄	—	2	2	no	—
324	C₂²×C₃×C₄	—	2	2	no	—
325	C₂²×C₃×C₄	—	2	1	no	—
326	C₂²×C₃×C₄	—	3	1	no	—
327	C₂²×C₃×C₄	—	3	4	no	—
328	C₂²×C₃×C₄	—	3	1	no	—
329	C₂²×C₃×C₄	—	3	1	no	—
330	C₂²×C₃×C₄	—	3	1	no	—
331	C₂²×C₃×C₄	—	3	1	no	—
332	C₂²×C₃×C₄	—	3	4	no	—
333	C₂²×C₃×C₄	—	4	2	no	—
334	C₂²×C₃×C₄	—	6	2	no	—
335	C₂²×C₃×C₄	—	6	16	no	—
336	C₂²×C₃×C₄	—	6	2	no	—
337	C₂²×C₃×C₄	—	6	2	no	—
338	C₂²×C₃×C₄	—	6	2	no	—
339	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
340	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
341	C₂×#67	—	2	2	no	—
342	C₂×#67	—	2	2	no	—
343	C₂×#67	—	2	2	no	—
344	C₂²×Dic₃	—	2	2	no	—
345	C₂²×Dic₃	C₃×D₄	1	1	yes	characteristic
346	#239	—	2	4	no	—
347	#239	C₂³×C₃	1	8	yes	complemented
348	D₃×Q₈	—	2	4	no	—
349	D₃×Q₈	C₂³×C₃	1	8	yes	—
350	#237	—	2	16	no	—
351	#237	—	2	4	no	—
352	#237	C₂³×C₃	1	8	yes	complemented
353	D₃×D₄	—	2	16	no	—
354	D₃×D₄	—	2	4	no	—
355	D₃×D₄	C₂³×C₃	1	8	yes	—
356	#235	—	2	4	no	—
357	#235	—	2	16	no	—
358	#235	C₂³×C₃	1	8	yes	complemented
359	C₂×D₁₂	—	2	2	no	—
360	C₂×D₁₂	C₂³×C₃	1	2	yes	—
361	C₂×C₄×D₃	—	2	2	no	—
362	C₂×C₄×D₃	—	2	2	no	—
363	C₂×C₄×D₃	—	2	2	no	—
364	C₂×C₄×D₃	—	2	16	no	—
365	C₂×C₄×D₃	C₃×D₄	1	1	yes	characteristic
366	C₂×C₄×D₃	C₃×D₄	1	1	yes	characteristic
367	C₂×C₄×D₃	C₃×D₄	1	4	yes	—
368	C₂×C₄×D₃	C₂³×C₃	1	1	yes	characteristic
369	C₂×C₄×D₃	C₂³×C₃	1	1	yes	characteristic
370	C₂×C₄×D₃	C₂³×C₃	1	4	yes	—
371	C₂×Dic₆	—	2	2	no	—
372	C₂×Dic₆	C₂³×C₃	1	2	yes	—
373	C₃×Q₁₆	—	2	4	no	—
374	C₃×Q₁₆	—	3	8	no	—
375	C₃×Q₁₆	—	3	4	no	—
376	C₃×Q₁₆	C₂²×D₃	1	4	yes	complemented
377	C₃×Q₁₆	C₂³×C₃	1	4	yes	complemented
378	C₃×SD₁₆	—	2	8	no	—
379	C₃×SD₁₆	—	3	8	no	—
380	C₃×SD₁₆	—	3	8	no	—
381	C₃×SD₁₆	—	3	8	no	—
382	C₃×SD₁₆	C₂²×D₃	1	8	yes	complemented
383	C₃×SD₁₆	C₂³×C₃	1	8	yes	complemented
384	C₃×D₈	—	2	4	no	—
385	C₃×D₈	—	3	8	no	—
386	C₃×D₈	—	3	4	no	—
387	C₃×D₈	C₂²×D₃	1	4	yes	complemented
388	C₃×D₈	C₂³×C₃	1	4	yes	complemented
389	C₂×C₃×C₈	—	2	1	no	—
390	C₂×C₃×C₈	—	2	1	no	—
391	C₂×C₃×C₈	—	2	4	no	—
392	C₂×C₃×C₈	—	3	1	no	—
393	C₂×C₃×C₈	—	3	1	no	—
394	C₂×C₃×C₈	—	3	4	no	—
395	C₂×C₃×C₈	—	3	4	no	—
396	C₂×C₃×C₈	—	3	4	no	—
397	C₂×C₃×C₈	—	3	4	no	—
398	C₂×C₃×C₈	—	3	4	no	—
399	C₂×C₃×C₈	C₂²×D₃	1	1	yes	characteristic
400	C₂×C₃×C₈	C₂²×D₃	1	1	yes	characteristic
401	C₂×C₃×C₈	C₂²×D₃	1	4	yes	complemented
402	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
403	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
404	C₂×C₃×C₈	C₂³×C₃	1	4	yes	complemented
405	#216	C₂³×C₃	1	8	yes	complemented
406	#215	C₂³×C₃	1	8	yes	complemented
407	#214	C₂³×C₃	1	8	yes	complemented
408	#213	C₂³×C₃	1	8	yes	complemented
409	C₂×C₃⋊C₈	C₂³×C₃	1	1	yes	characteristic
410	C₂×C₃⋊C₈	C₂³×C₃	1	1	yes	characteristic
411	C₂×C₃⋊C₈	C₂³×C₃	1	4	yes	complemented
412	Dic₁₂	C₂³×C₃	1	4	yes	complemented
413	D₂₄	C₂³×C₃	1	4	yes	complemented
414	#204	C₂³×C₃	1	8	yes	complemented
415	D₃×C₈	C₂³×C₃	1	4	yes	—
416	D₃×C₈	C₂³×C₃	1	4	yes	—
417	D₃×C₈	C₂³×C₃	1	4	yes	complemented
418	D₃×C₈	C₂³×C₃	1	4	yes	complemented
419	C₂²×C₃²	—	2	2	no	—
420	C₂²×C₃²	—	2	4	no	—
421	C₂²×C₃²	—	4	4	no	—
422	C₂²×C₃²	C₂²×D₄	1	2	yes	—
423	C₂²×C₃²	C₂²×D₄	1	1	yes	characteristic
424	C₂×C₃×D₃	—	2	2	no	—
425	C₂×C₃×D₃	—	2	8	no	—
426	C₂×C₃×D₃	—	2	4	no	—
427	C₂×C₃×D₃	—	4	4	no	—
428	C₂×C₃×D₃	—	4	16	no	—
429	C₂×C₃×D₃	#135	1	4	yes	direct product factor
430	C₂×C₃×D₃	C₂²×D₄	1	2	yes	—
431	C₂×C₃×D₃	C₂²×D₄	1	2	yes	—
432	C₃²×C₄	—	2	4	no	—
433	C₃²×C₄	C₂²×D₄	1	1	yes	characteristic
434	C₃²×C₄	C₂²×D₄	1	2	yes	—
435	C₃²×C₄	C₂⁵	1	1	yes	characteristic
436	C₃×Dic₃	—	2	4	no	—
437	C₃×Dic₃	C₂²×D₄	1	2	yes	—
438	C₃×Dic₃	C₂²×D₄	1	2	yes	—
439	C₂×#41	—	3	16	no	—
440	C₂×#41	—	3	2	no	—
441	C₂×#41	—	3	2	no	—
442	C₂×#41	—	3	2	no	—
443	C₂×#41	—	6	2	no	—
444	C₂×#41	—	6	2	no	—
445	C₂×#41	—	6	8	no	—
446	C₂×#41	C₂×C₃×D₃	1	2	yes	complemented
447	C₂²×Q₈	—	3	2	no	—
448	C₂²×D₄	—	3	2	no	—
449	C₂²×D₄	—	6	2	no	—
450	C₂³×C₄	—	3	1	no	—
451	C₂³×C₄	—	6	2	no	—
452	#135	—	3	16	no	—
453	#135	—	3	8	no	—
454	#135	—	3	16	no	—
455	#135	—	3	8	no	—
456	#135	—	3	8	no	—
457	#135	C₂×C₃×D₃	1	8	yes	direct product factor
458	C₂×Q₁₆	—	3	2	no	—
459	C₂×Q₁₆	—	3	8	no	—
460	C₂×Q₁₆	—	3	1	no	—
461	C₂×Q₁₆	C₂×C₃×D₃	1	1	yes	characteristic, complemented
462	C₂×SD₁₆	—	3	2	no	—
463	C₂×SD₁₆	—	3	2	no	—
464	C₂×SD₁₆	—	3	16	no	—
465	C₂×SD₁₆	—	3	2	no	—
466	C₂×SD₁₆	C₂×C₃×D₃	1	2	yes	complemented
467	C₂×D₈	—	3	2	no	—
468	C₂×D₈	—	3	8	no	—
469	C₂×D₈	—	3	1	no	—
470	C₂×D₈	C₂×C₃×D₃	1	1	yes	characteristic, complemented
471	C₂²×C₈	—	3	1	no	—
472	C₂²×C₈	—	3	1	no	—
473	C₂²×C₈	—	3	1	no	—
474	C₂²×C₈	—	3	1	no	—
475	C₂²×C₈	—	3	1	no	—
476	C₂²×C₈	—	3	8	no	—
477	C₂²×C₈	C₂×C₃×D₃	1	1	yes	characteristic, complemented
478	C₂³×C₃	—	2	2	no	—
479	C₂³×C₃	—	2	2	no	—
480	C₂³×C₃	—	2	1	no	—
481	C₂³×C₃	—	3	1	no	—
482	C₂³×C₃	—	3	4	no	—
483	C₂³×C₃	—	3	1	no	—
484	C₂³×C₃	—	4	2	no	—
485	C₂³×C₃	—	6	4	no	—
486	C₂³×C₃	—	6	8	no	—
487	C₂³×C₃	—	6	2	no	—
488	C₂³×C₃	—	12	8	no	—
489	C₂³×C₃	D₃×D₄	1	1	yes	characteristic
490	C₂³×C₃	C₂×C₃×D₄	1	1	yes	characteristic
491	C₂²×D₃	—	2	4	no	—
492	C₂²×D₃	—	2	2	no	—
493	C₂²×D₃	—	2	8	no	—
494	C₂²×D₃	—	4	8	no	—
495	C₂²×D₃	C₂×C₃×D₄	1	1	yes	characteristic
496	C₂²×D₃	C₂×C₃×D₄	1	4	yes	—
497	C₂²×D₃	C₂×C₃×D₄	1	1	yes	characteristic
498	C₃×Q₈	—	2	2	no	—
499	C₃×Q₈	—	2	2	no	—
500	C₃×Q₈	—	2	4	no	—
501	C₃×Q₈	—	3	4	no	—
502	C₃×Q₈	—	4	2	no	—
503	C₃×Q₈	—	6	8	no	—
504	C₃×Q₈	—	6	2	no	—
505	C₃×Q₈	C₂³×D₃	1	4	yes	—
506	C₃×Q₈	C₂⁴×C₃	1	4	yes	—
507	C₃×D₄	—	2	8	no	—
508	C₃×D₄	—	2	8	no	—
509	C₃×D₄	—	2	2	no	—
510	C₃×D₄	—	2	2	no	—
511	C₃×D₄	—	2	4	no	—
512	C₃×D₄	—	3	4	no	—
513	C₃×D₄	—	4	2	no	—
514	C₃×D₄	—	4	8	no	—
515	C₃×D₄	—	6	8	no	—
516	C₃×D₄	—	6	8	no	—
517	C₃×D₄	—	6	8	no	—
518	C₃×D₄	—	6	8	no	—
519	C₃×D₄	—	6	2	no	—
520	C₃×D₄	C₂³×D₃	1	4	yes	—
521	C₃×D₄	C₂⁴×C₃	1	4	yes	—
522	C₂×C₃×C₄	—	2	2	no	—
523	C₂×C₃×C₄	—	2	2	no	—
524	C₂×C₃×C₄	—	2	8	no	—
525	C₂×C₃×C₄	—	2	8	no	—
526	C₂×C₃×C₄	—	2	1	no	—
527	C₂×C₃×C₄	—	2	2	no	—
528	C₂×C₃×C₄	—	2	1	no	—
529	C₂×C₃×C₄	—	2	2	no	—
530	C₂×C₃×C₄	—	3	1	no	—
531	C₂×C₃×C₄	—	3	1	no	—
532	C₂×C₃×C₄	—	3	4	no	—
533	C₂×C₃×C₄	—	3	4	no	—
534	C₂×C₃×C₄	—	3	2	no	—
535	C₂×C₃×C₄	—	3	2	no	—
536	C₂×C₃×C₄	—	3	4	no	—
537	C₂×C₃×C₄	—	3	2	no	—
538	C₂×C₃×C₄	—	3	2	no	—
539	C₂×C₃×C₄	—	4	8	no	—
540	C₂×C₃×C₄	—	4	2	no	—
541	C₂×C₃×C₄	—	6	8	no	—
542	C₂×C₃×C₄	—	6	8	no	—
543	C₂×C₃×C₄	—	6	8	no	—
544	C₂×C₃×C₄	—	6	2	no	—
545	C₂×C₃×C₄	—	6	8	no	—
546	C₂×C₃×C₄	D₃×D₄	1	2	yes	—
547	C₂×C₃×C₄	D₃×D₄	1	1	yes	characteristic
548	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
549	C₂×C₃×C₄	C₂×C₃×D₄	1	2	yes	—
550	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
551	C₂×C₃×C₄	C₂³×D₃	1	2	yes	—
552	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
553	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
554	#67	—	2	8	no	—
555	#67	—	2	8	no	—
556	#67	—	2	8	no	—
557	C₂×Dic₃	—	2	2	no	—
558	C₂×Dic₃	—	2	8	no	—
559	C₂×Dic₃	C₂×C₃×D₄	1	1	yes	characteristic
560	C₂×Dic₃	C₂×C₃×D₄	1	1	yes	characteristic
561	C₂×Dic₃	C₂×C₃×D₄	1	4	yes	—
562	D₁₂	—	2	8	no	—
563	D₁₂	—	2	2	no	—
564	D₁₂	C₂⁴×C₃	1	4	yes	—
565	C₄×D₃	—	2	8	no	—
566	C₄×D₃	—	2	8	no	—
567	C₄×D₃	—	2	8	no	—
568	C₄×D₃	C₂×C₃×D₄	1	4	yes	—
569	C₄×D₃	C₂×C₃×D₄	1	4	yes	—
570	C₄×D₃	C₂×C₃×D₄	1	2	yes	—
571	C₄×D₃	C₂×C₃×D₄	1	2	yes	—
572	C₄×D₃	C₂⁴×C₃	1	2	yes	—
573	C₄×D₃	C₂⁴×C₃	1	2	yes	—
574	Dic₆	—	2	2	no	—
575	Dic₆	—	2	8	no	—
576	Dic₆	C₂⁴×C₃	1	4	yes	—
577	C₃×C₈	—	2	2	no	—
578	C₃×C₈	—	2	2	no	—
579	C₃×C₈	—	3	2	no	—
580	C₃×C₈	—	3	2	no	—
581	C₃×C₈	C₂³×D₃	1	2	yes	—
582	C₃×C₈	C₂³×D₃	1	2	yes	—
583	C₃×C₈	C₂⁴×C₃	1	2	yes	—
584	C₃×C₈	C₂⁴×C₃	1	2	yes	—
585	C₃⋊C₈	C₂⁴×C₃	1	2	yes	—
586	C₃⋊C₈	C₂⁴×C₃	1	2	yes	—
587	C₂×C₃²	—	2	2	no	—
588	C₂×C₃²	—	4	4	no	—
589	C₂×C₃²	C₂×#135	1	2	yes	complemented
590	C₂×C₃²	C₂³×D₄	1	1	yes	characteristic
591	C₃×D₃	—	2	2	no	—
592	C₃×D₃	—	4	4	no	—
593	C₃×D₃	C₂×#135	1	4	yes	direct product factor
594	C₂⁴	—	3	1	no	—
595	C₂⁴	—	6	2	no	—
596	#41	—	2	4	no	—
597	#41	—	3	8	no	—
598	#41	—	3	8	no	—
599	#41	—	3	8	no	—
600	#41	—	6	16	no	—
601	#41	—	6	16	no	—
602	#41	—	6	4	no	—
603	#41	—	6	4	no	—
604	#41	—	6	4	no	—
605	#41	C₂²×C₃×D₃	1	8	yes	complemented
606	C₂×Q₈	—	3	8	no	—
607	C₂×Q₈	—	3	2	no	—
608	C₂×Q₈	—	6	2	no	—
609	C₂×Q₈	—	6	4	no	—
610	C₂×Q₈	C₂²×C₃×D₃	1	2	yes	—
611	C₂×D₄	—	2	2	no	—
612	C₂×D₄	—	3	8	no	—
613	C₂×D₄	—	3	2	no	—
614	C₂×D₄	—	6	2	no	—
615	C₂×D₄	—	6	4	no	—
616	C₂×D₄	—	6	2	no	—
617	C₂×D₄	—	6	16	no	—
618	C₂×D₄	—	6	2	no	—
619	C₂×D₄	—	6	2	no	—
620	C₂×D₄	C₂²×C₃×D₃	1	2	yes	—
621	C₂²×C₄	—	2	2	no	—
622	C₂²×C₄	—	3	1	no	—
623	C₂²×C₄	—	3	1	no	—
624	C₂²×C₄	—	3	1	no	—
625	C₂²×C₄	—	3	4	no	—
626	C₂²×C₄	—	3	1	no	—
627	C₂²×C₄	—	3	1	no	—
628	C₂²×C₄	—	3	4	no	—
629	C₂²×C₄	—	6	2	no	—
630	C₂²×C₄	—	6	16	no	—
631	C₂²×C₄	—	6	2	no	—
632	C₂²×C₄	—	6	2	no	—
633	C₂²×C₄	—	6	2	no	—
634	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
635	Q₁₆	—	3	8	no	—
636	Q₁₆	—	3	4	no	—
637	Q₁₆	C₂²×C₃×D₃	1	4	yes	complemented
638	SD₁₆	—	3	8	no	—
639	SD₁₆	—	3	8	no	—
640	SD₁₆	—	3	8	no	—
641	SD₁₆	C₂²×C₃×D₃	1	8	yes	complemented
642	D₈	—	3	8	no	—
643	D₈	—	3	4	no	—
644	D₈	C₂²×C₃×D₃	1	4	yes	complemented
645	C₂×C₈	—	3	1	no	—
646	C₂×C₈	—	3	1	no	—
647	C₂×C₈	—	3	4	no	—
648	C₂×C₈	—	3	4	no	—
649	C₂×C₈	—	3	4	no	—
650	C₂×C₈	—	3	4	no	—
651	C₂×C₈	—	3	4	no	—
652	C₂×C₈	C₂²×C₃×D₃	1	1	yes	characteristic
653	C₂×C₈	C₂²×C₃×D₃	1	1	yes	characteristic
654	C₂×C₈	C₂²×C₃×D₃	1	4	yes	complemented
655	C₂²×C₃	—	2	2	no	—
656	C₂²×C₃	—	2	2	no	—
657	C₂²×C₃	—	2	4	no	—
658	C₂²×C₃	—	2	4	no	—
659	C₂²×C₃	—	2	1	no	—
660	C₂²×C₃	—	2	2	no	—
661	C₂²×C₃	—	3	2	no	—
662	C₂²×C₃	—	3	4	no	—
663	C₂²×C₃	—	3	2	no	—
664	C₂²×C₃	—	4	2	no	—
665	C₂²×C₃	—	4	4	no	—
666	C₂²×C₃	—	4	4	no	—
667	C₂²×C₃	—	4	4	no	—
668	C₂²×C₃	—	6	8	no	—
669	C₂²×C₃	—	6	2	no	—
670	C₂²×C₃	—	6	4	no	—
671	C₂²×C₃	—	8	4	no	—
672	C₂²×C₃	—	12	16	no	—
673	C₂²×C₃	—	12	4	no	—
674	C₂²×C₃	C₂×D₃×D₄	1	2	yes	—
675	C₂²×C₃	C₂×D₃×D₄	1	1	yes	characteristic
676	C₂²×C₃	C₂²×C₃×D₄	1	2	yes	—
677	C₂²×C₃	C₂²×C₃×D₄	1	1	yes	characteristic
678	C₂×D₃	—	2	2	no	—
679	C₂×D₃	—	2	8	no	—
680	C₂×D₃	—	2	4	no	—
681	C₂×D₃	—	4	4	no	—
682	C₂×D₃	—	4	16	no	—
683	C₂×D₃	C₃×#135	1	4	yes	direct product factor
684	C₂×D₃	C₂²×C₃×D₄	1	2	yes	—
685	C₂×D₃	C₂²×C₃×D₄	1	2	yes	—
686	C₃×C₄	—	2	4	no	—
687	C₃×C₄	—	2	4	no	—
688	C₃×C₄	—	2	2	no	—
689	C₃×C₄	—	2	1	no	—
690	C₃×C₄	—	2	1	no	—
691	C₃×C₄	—	3	2	no	—
692	C₃×C₄	—	3	2	no	—
693	C₃×C₄	—	4	4	no	—
694	C₃×C₄	—	6	4	no	—
695	C₃×C₄	C₂×D₃×D₄	1	2	yes	—
696	C₃×C₄	C₂×D₃×D₄	1	1	yes	characteristic
697	C₃×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
698	C₃×C₄	C₂²×C₃×D₄	1	2	yes	—
699	C₃×C₄	C₂⁴×D₃	1	1	yes	characteristic
700	C₃×C₄	C₂⁵×C₃	1	1	yes	characteristic
701	Dic₃	—	2	4	no	—
702	Dic₃	C₂²×C₃×D₄	1	2	yes	—
703	Dic₃	C₂²×C₃×D₄	1	2	yes	—
704	C₃²	C₂²×#135	1	1	yes	characteristic, complemented, Sylow
705	C₂³	—	2	2	no	—
706	C₂³	—	3	1	no	—
707	C₂³	—	3	4	no	—
708	C₂³	—	3	1	no	—
709	C₂³	—	6	4	no	—
710	C₂³	—	6	8	no	—
711	C₂³	—	6	2	no	—
712	C₂³	—	12	8	no	—
713	C₂³	C₃×D₃×D₄	1	1	yes	characteristic
714	Q₈	—	2	2	no	—
715	Q₈	—	3	4	no	—
716	Q₈	—	6	8	no	—
717	Q₈	—	6	2	no	—
718	Q₈	C₂³×C₃×D₃	1	4	yes	—
719	D₄	—	2	8	no	—
720	D₄	—	2	2	no	—
721	D₄	—	3	4	no	—
722	D₄	—	6	8	no	—
723	D₄	—	6	8	no	—
724	D₄	—	6	8	no	—
725	D₄	—	6	8	no	—
726	D₄	—	6	2	no	—
727	D₄	C₂³×C₃×D₃	1	4	yes	—
728	C₂×C₄	—	2	2	no	—
729	C₂×C₄	—	2	8	no	—
730	C₂×C₄	—	3	1	no	—
731	C₂×C₄	—	3	1	no	—
732	C₂×C₄	—	3	4	no	—
733	C₂×C₄	—	3	4	no	—
734	C₂×C₄	—	3	2	no	—
735	C₂×C₄	—	3	2	no	—
736	C₂×C₄	—	3	4	no	—
737	C₂×C₄	—	3	2	no	—
738	C₂×C₄	—	3	2	no	—
739	C₂×C₄	—	6	8	no	—
740	C₂×C₄	—	6	8	no	—
741	C₂×C₄	—	6	8	no	—
742	C₂×C₄	—	6	2	no	—
743	C₂×C₄	—	6	8	no	—
744	C₂×C₄	C₃×D₃×D₄	1	1	yes	characteristic
745	C₂×C₄	C₃×D₃×D₄	1	2	yes	—
746	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
747	C₂×C₄	C₂³×C₃×D₃	1	2	yes	—
748	C₈	—	3	2	no	—
749	C₈	—	3	2	no	—
750	C₈	C₂³×C₃×D₃	1	2	yes	—
751	C₈	C₂³×C₃×D₃	1	2	yes	—
752	C₂×C₃	—	2	2	no	—
753	C₂×C₃	—	2	2	no	—
754	C₂×C₃	—	2	2	no	—
755	C₂×C₃	—	2	1	no	—
756	C₂×C₃	—	3	4	no	—
757	C₂×C₃	—	4	2	no	—
758	C₂×C₃	—	4	4	no	—
759	C₂×C₃	—	4	4	no	—
760	C₂×C₃	—	6	2	no	—
761	C₂×C₃	—	8	4	no	—
762	C₂×C₃	—	12	4	no	—
763	C₂×C₃	D₃×#135	1	2	yes	direct product factor
764	C₂×C₃	C₂×C₃×#135	1	2	yes	complemented
765	C₂×C₃	C₂²×D₃×D₄	1	1	yes	characteristic
766	C₂×C₃	C₂³×C₃×D₄	1	1	yes	characteristic
767	D₃	—	2	2	no	—
768	D₃	—	4	4	no	—
769	D₃	C₂×C₃×#135	1	4	yes	direct product factor
770	C₂²	—	2	2	no	—
771	C₂²	—	2	4	no	—
772	C₂²	—	3	4	no	—
773	C₂²	—	3	2	no	—
774	C₂²	—	3	2	no	—
775	C₂²	—	4	4	no	—
776	C₂²	—	6	8	no	—
777	C₂²	—	6	2	no	—
778	C₂²	—	6	4	no	—
779	C₂²	—	12	16	no	—
780	C₂²	—	12	4	no	—
781	C₂²	C₂×C₃×D₃×D₄	1	2	yes	—
782	C₂²	C₂×C₃×D₃×D₄	1	1	yes	characteristic
783	C₄	—	2	4	no	—
784	C₄	—	3	2	no	—
785	C₄	—	3	2	no	—
786	C₄	—	6	4	no	—
787	C₄	C₂×C₃×D₃×D₄	1	2	yes	—
788	C₄	C₂×C₃×D₃×D₄	1	1	yes	characteristic
789	C₄	C₂⁴×C₃×D₃	1	1	yes	characteristic
790	C₃	—	2	1	no	—
791	C₃	C₂×D₃×#135	1	1	yes	characteristic, direct product factor
792	C₃	C₂²×C₃×#135	1	1	yes	characteristic, complemented
793	C₂	—	2	2	no	—
794	C₂	—	3	4	no	—
795	C₂	—	4	4	no	—
796	C₂	—	6	2	no	—
797	C₂	—	12	4	no	—
798	C₂	C₃×D₃×#135	1	2	yes	direct product factor
799	C₂	C₂²×C₃×D₃×D₄	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃×C₄	D₃×D₄
commutator, cosocle	C₃×C₄	C₂⁵×C₃
Frattini	C₄	C₂⁴×C₃×D₃
Fitting	C₂×C₃²×#135	C₂
socle	C₂²×C₃²	C₂²×D₄
hypercenter	C₂×C₃×#135	D₃
hypocenter	C₃	C₂²×C₃×#135
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₂²×C₃×C₄ ◁ C₂×C₃×#135

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×D₃×#41	C₂	semidirect
2. C₂×C₃²×#135	C₂	semidirect
3. C₂×C₃×#950	C₂	semidirect
4. C₃×D₃×#135	C₂	direct (N × H)
5. C₂×C₃×#919	C₂	semidirect
6. C₂×C₃×D₃×Q₁₆	C₂	semidirect
7. C₂×C₃×#916	C₂	semidirect
8. C₂×C₃×D₃×SD₁₆	C₂	semidirect
9. C₂×C₃×#912	C₂	semidirect
10. C₂×C₃×D₃×D₈	C₂	semidirect
11. C₂×C₃×#904	C₂	semidirect
12. C₂²×C₃×D₃×C₈	C₂	semidirect
14. C₂×D₃×#135	C₃	direct (N × H)
15. C₂×C₃²×#41	C₂²	semidirect
17. C₃×D₃×#41	C₂²	semidirect
18. C₂×C₃×#239	C₂²	semidirect
21. C₂×C₃×#237	C₂²	semidirect
25. C₂×C₃×#235	C₂²	semidirect
28. C₃²×#135	C₂²	semidirect
29. C₂×C₃²×Q₁₆	C₂²	semidirect
30. C₂×C₃²×SD₁₆	C₂²	semidirect
31. C₂×C₃²×D₈	C₂²	semidirect
32. C₂²×C₃²×C₈	C₂²	semidirect
33. C₃×#950	C₂²	semidirect
34. C₂×C₃×#216	C₂²	semidirect
35. C₂×C₃×#215	C₂²	semidirect
36. C₂×C₃×#214	C₂²	semidirect
37. C₂×C₃×#213	C₂²	semidirect
38. C₂²×C₃×C₃⋊C₈	C₂²	semidirect
39. C₃×#919	C₂²	semidirect
40. C₃×D₃×Q₁₆	C₂²	semidirect
41. C₃×#916	C₂²	semidirect
42. C₃×D₃×SD₁₆	C₂²	semidirect
43. C₃×#912	C₂²	semidirect
44. C₃×D₃×D₈	C₂²	semidirect
45. C₂×C₃×Dic₁₂	C₂²	semidirect
46. C₃×#904	C₂²	semidirect
47. C₂×C₃×D₂₄	C₂²	semidirect
48. C₂×C₃×#204	C₂²	semidirect
51. C₂×C₃×D₃×C₈	C₂²	semidirect
52. C₂×C₃×D₃×C₈	C₂²	semidirect
53. C₂×C₃×D₃×C₈	C₂²	semidirect
55. C₂×D₃×#41	C₂×C₃	semidirect
63. C₂×C₃×#135	D₃	direct (N × H)
64. C₂×C₃×#135	C₂×C₃	semidirect
69. C₂×#950	C₂×C₃	semidirect
70. D₃×#135	C₂×C₃	direct (N × H)
71. C₂×#919	C₂×C₃	semidirect
72. C₂×D₃×Q₁₆	C₂×C₃	semidirect
73. C₂×#916	C₂×C₃	semidirect
74. C₂×D₃×SD₁₆	C₂×C₃	semidirect
75. C₂×#912	C₂×C₃	semidirect
76. C₂×D₃×D₈	C₂×C₃	semidirect
77. C₂×#904	C₂×C₃	semidirect
78. C₂²×D₃×C₈	C₂×C₃	semidirect
82. C₃²×#41	C₂³	semidirect
94. C₃×#239	C₂³	semidirect
99. C₃×#237	C₂³	semidirect
105. C₃×#235	C₂³	semidirect
120. C₃²×Q₁₆	C₂³	semidirect
121. C₃²×SD₁₆	C₂³	semidirect
122. C₃²×D₈	C₂³	semidirect
125. C₂×C₃²×C₈	C₂³	semidirect
126. C₃×#216	C₂³	semidirect
127. C₃×#215	C₂³	semidirect
128. C₃×#214	C₂³	semidirect
129. C₃×#213	C₂³	semidirect
132. C₂×C₃×C₃⋊C₈	C₂³	semidirect
133. C₃×Dic₁₂	C₂³	semidirect
134. C₃×D₂₄	C₂³	semidirect
135. C₃×#204	C₂³	semidirect
138. C₃×D₃×C₈	C₂³	semidirect
139. C₃×D₃×C₈	C₂³	semidirect
149. C₂×C₃×#41	C₂×D₃	semidirect
150. C₂×C₃×#41	C₂²×C₃	semidirect
157. D₃×#41	C₂²×C₃	semidirect
158. C₂×#239	C₂²×C₃	semidirect
161. C₂×#237	C₂²×C₃	semidirect
165. C₂×#235	C₂²×C₃	semidirect
174. C₃×#135	C₂×D₃	direct (N × H)
175. C₃×#135	C₂²×C₃	semidirect
180. C₂×C₃×Q₁₆	C₂×D₃	semidirect
181. C₂×C₃×Q₁₆	C₂²×C₃	semidirect
187. C₂×C₃×SD₁₆	C₂×D₃	semidirect
188. C₂×C₃×SD₁₆	C₂²×C₃	semidirect
193. C₂×C₃×D₈	C₂×D₃	semidirect
194. C₂×C₃×D₈	C₂²×C₃	semidirect
202. C₂²×C₃×C₈	C₂×D₃	semidirect
203. C₂²×C₃×C₈	C₂²×C₃	semidirect
204. #950	C₂²×C₃	semidirect
205. C₂×#216	C₂²×C₃	semidirect
206. C₂×#215	C₂²×C₃	semidirect
207. C₂×#214	C₂²×C₃	semidirect
208. C₂×#213	C₂²×C₃	semidirect
209. C₂²×C₃⋊C₈	C₂²×C₃	semidirect
210. #919	C₂²×C₃	semidirect
211. D₃×Q₁₆	C₂²×C₃	semidirect
212. #916	C₂²×C₃	semidirect
213. D₃×SD₁₆	C₂²×C₃	semidirect
214. #912	C₂²×C₃	semidirect
215. D₃×D₈	C₂²×C₃	semidirect
216. C₂×Dic₁₂	C₂²×C₃	semidirect
217. #904	C₂²×C₃	semidirect
218. C₂×D₂₄	C₂²×C₃	semidirect
219. C₂×#204	C₂²×C₃	semidirect
222. C₂×D₃×C₈	C₂²×C₃	semidirect
223. C₂×D₃×C₈	C₂²×C₃	semidirect
224. C₂×D₃×C₈	C₂²×C₃	semidirect
279. C₂×#135	C₃×D₃	direct (N × H)
300. C₃×#41	C₂²×D₃	semidirect
301. C₃×#41	C₂³×C₃	semidirect
347. #239	C₂³×C₃	semidirect
352. #237	C₂³×C₃	semidirect
358. #235	C₂³×C₃	semidirect
376. C₃×Q₁₆	C₂²×D₃	semidirect
377. C₃×Q₁₆	C₂³×C₃	semidirect
382. C₃×SD₁₆	C₂²×D₃	semidirect
383. C₃×SD₁₆	C₂³×C₃	semidirect
387. C₃×D₈	C₂²×D₃	semidirect
388. C₃×D₈	C₂³×C₃	semidirect
401. C₂×C₃×C₈	C₂²×D₃	semidirect
404. C₂×C₃×C₈	C₂³×C₃	semidirect
405. #216	C₂³×C₃	semidirect
406. #215	C₂³×C₃	semidirect
407. #214	C₂³×C₃	semidirect
408. #213	C₂³×C₃	semidirect
411. C₂×C₃⋊C₈	C₂³×C₃	semidirect
412. Dic₁₂	C₂³×C₃	semidirect
413. D₂₄	C₂³×C₃	semidirect
414. #204	C₂³×C₃	semidirect
417. D₃×C₈	C₂³×C₃	semidirect
418. D₃×C₈	C₂³×C₃	semidirect
429. C₂×C₃×D₃	#135	direct (N × H)
446. C₂×#41	C₂×C₃×D₃	semidirect
457. #135	C₂×C₃×D₃	direct (N × H)
461. C₂×Q₁₆	C₂×C₃×D₃	semidirect
466. C₂×SD₁₆	C₂×C₃×D₃	semidirect
470. C₂×D₈	C₂×C₃×D₃	semidirect
477. C₂²×C₈	C₂×C₃×D₃	semidirect
589. C₂×C₃²	C₂×#135	semidirect
593. C₃×D₃	C₂×#135	direct (N × H)
605. #41	C₂²×C₃×D₃	semidirect
637. Q₁₆	C₂²×C₃×D₃	semidirect
641. SD₁₆	C₂²×C₃×D₃	semidirect
644. D₈	C₂²×C₃×D₃	semidirect
654. C₂×C₈	C₂²×C₃×D₃	semidirect
683. C₂×D₃	C₃×#135	direct (N × H)
704. C₃²	C₂²×#135	semidirect
763. C₂×C₃	D₃×#135	direct (N × H)
764. C₂×C₃	C₂×C₃×#135	semidirect
769. D₃	C₂×C₃×#135	direct (N × H)
791. C₃	C₂×D₃×#135	direct (N × H)
792. C₃	C₂²×C₃×#135	semidirect
798. C₂	C₃×D₃×#135	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃×D₃×#41	2
C₂×C₃²×#135	2
C₂×C₃×#950	2
C₃×D₃×#135	2
C₂×C₃×#919	2
C₂×C₃×D₃×Q₁₆	2
C₂×C₃×#916	2
C₂×C₃×D₃×SD₁₆	2
C₂×C₃×#912	2
C₂×C₃×D₃×D₈	2
C₂×C₃×#904	2
C₂²×C₃×D₃×C₈	2
C₂²×C₃×#135	3
C₂×D₃×#135	3

Subgroups — C2×C3×D3×#135 #11918591

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×D₃×#135 #11918591