Subgroups — C₂×C₃×#5592 #11900989

Order 1152.

4123 conjugacy classes of subgroups.

The subgroup lattice has 816 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₃×#67	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₃×#237	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃²×#120	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃×#953	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₃×#940	C₂	1	2	yes	maximal, complemented
6	C₂×C₃×#939	C₂	1	2	yes	maximal, complemented
7	C₂×C₃×#937	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#5592	C₂	1	16	yes	maximal, direct product factor
9	C₂×C₃×#885	C₂	1	2	yes	maximal, complemented
10	C₂×C₃×#884	C₂	1	2	yes	maximal, complemented
11	C₂×C₃×#882	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₃×#877	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₃×#535	—	3	1	no	maximal
14	C₂×#5592	C₃	1	1	yes	maximal, characteristic, direct product factor
15	C₂⁵×C₃²	C₂²	1	1	yes	characteristic
16	C₂⁴×C₃×D₃	C₂²	1	1	yes	characteristic
17	C₂²×C₃²×D₄	C₂²	1	1	yes	characteristic
18	C₂²×C₃²×D₄	C₂²	1	2	yes	complemented
19	C₂²×C₃×#67	—	2	8	no	—
20	C₂²×C₃×#67	C₂²	1	1	yes	characteristic
21	C₂²×C₃×#67	C₂²	1	2	yes	—
22	C₂²×C₃×#67	C₂²	1	2	yes	—
23	C₂²×C₃×#67	C₂²	1	8	yes	complemented
24	C₂²×C₃×#67	C₂²	1	1	yes	characteristic, complemented
25	C₂²×C₃×#67	C₂²	1	2	yes	complemented
26	C₂²×C₃×#67	C₂²	1	2	yes	complemented
27	C₂³×C₃×Dic₃	C₂²	1	1	yes	characteristic
28	C₂³×C₃×Dic₃	C₂²	1	1	yes	characteristic, complemented
29	C₂×C₃×#237	—	2	8	no	—
30	C₂×C₃×#237	C₂²	1	8	yes	complemented
31	C₂²×C₃×D₁₂	C₂²	1	2	yes	complemented
32	C₂²×C₃×C₄×D₃	C₂²	1	1	yes	characteristic, complemented
33	C₂²×C₃×Dic₆	C₂²	1	1	yes	characteristic, complemented
34	C₃²×#120	C₂²	1	8	yes	complemented
35	C₂×C₃²×C₂²⋊C₄	C₂²	1	1	yes	characteristic
36	C₂×C₃²×C₂²⋊C₄	C₂²	1	2	yes	complemented
37	C₃×#953	C₂²	1	8	yes	complemented
38	C₂×C₃×#217	C₂²	1	1	yes	characteristic
39	C₂×C₃×#217	C₂²	1	2	yes	complemented
40	C₃×#940	C₂²	1	16	yes	complemented
41	C₃×#939	C₂²	1	16	yes	complemented
42	C₃×#937	C₂²	1	8	yes	complemented
43	C₂×C₃×(C₂×D₃)⋊C₄	C₂²	1	2	yes	complemented
44	C₂×C₃×(C₂×D₃)⋊C₄	C₂²	1	2	yes	complemented
45	C₂×C₃×Dic₃⋊C₄	C₂²	1	2	yes	complemented
46	C₂×C₃×C₄×Dic₃	C₂²	1	2	yes	complemented
47	C₃×#885	C₂²	1	16	yes	complemented
48	C₃×#884	C₂²	1	16	yes	complemented
49	C₃×#882	C₂²	1	8	yes	complemented
50	C₃×#877	C₂²	1	8	yes	complemented
51	C₂²×C₃×#41	—	3	1	no	—
52	C₂³×C₃×D₄	—	3	1	no	—
53	C₂³×#67	C₂×C₃	1	1	yes	characteristic, complemented
54	C₂²×#237	C₂×C₃	1	1	yes	characteristic, complemented
55	C₃×#535	—	3	16	no	—
56	C₂×C₃×#127	—	3	2	no	—
57	C₂×C₃×#124	—	3	2	no	—
58	C₂×C₃×#121	—	3	2	no	—
59	C₂×C₃×#121	—	3	2	no	—
60	C₂×C₃×#120	—	2	1	no	—
61	C₂×C₃×#120	—	3	1	no	—
62	C₂×C₃×#120	—	3	1	no	—
63	C₂×C₃×#120	—	3	1	no	—
64	C₂×C₃×#120	D₃	1	1	yes	characteristic, complemented
65	C₂×C₃×#120	C₂×C₃	1	1	yes	characteristic, complemented
66	C₂×C₃×#117	—	3	1	no	—
67	C₂×#953	C₂×C₃	1	1	yes	characteristic, complemented
68	C₂×#940	C₂×C₃	1	2	yes	complemented
69	C₂×#939	C₂×C₃	1	2	yes	complemented
70	C₂×#937	C₂×C₃	1	1	yes	characteristic, complemented
71	#5592	C₂×C₃	1	16	yes	direct product factor
72	C₂×#885	C₂×C₃	1	2	yes	complemented
73	C₂×#884	C₂×C₃	1	2	yes	complemented
74	C₂×#882	C₂×C₃	1	1	yes	characteristic, complemented
75	C₂×#877	C₂×C₃	1	1	yes	characteristic, complemented
76	C₂⁴×C₃²	—	2	4	no	—
77	C₂⁴×C₃²	—	4	4	no	—
78	C₂⁴×C₃²	C₂³	1	2	yes	—
79	C₂⁴×C₃²	C₂³	1	1	yes	characteristic
80	C₂⁴×C₃²	C₂³	1	1	yes	characteristic
81	C₂⁴×C₃²	C₂³	1	4	yes	—
82	C₂³×C₃×D₃	—	2	4	no	—
83	C₂³×C₃×D₃	—	4	4	no	—
84	C₂³×C₃×D₃	C₂³	1	2	yes	—
85	C₂³×C₃×D₃	C₂³	1	1	yes	characteristic
86	C₂³×C₃×D₃	C₂³	1	4	yes	—
87	C₂×C₃²×D₄	—	2	4	no	—
88	C₂×C₃²×D₄	—	4	4	no	—
89	C₂×C₃²×D₄	C₂³	1	4	yes	—
90	C₂×C₃²×D₄	C₂³	1	8	yes	complemented
91	C₂²×C₃²×C₄	C₂³	1	2	yes	—
92	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
93	C₂×C₃×#67	—	2	4	no	—
94	C₂×C₃×#67	—	2	4	no	—
95	C₂×C₃×#67	—	2	8	no	—
96	C₂×C₃×#67	—	2	8	no	—
97	C₂×C₃×#67	—	2	32	no	—
98	C₂×C₃×#67	—	4	4	no	—
99	C₂×C₃×#67	—	4	4	no	—
100	C₂×C₃×#67	C₂³	1	4	yes	—
101	C₂×C₃×#67	C₂³	1	8	yes	—
102	C₂×C₃×#67	C₂³	1	8	yes	—
103	C₂×C₃×#67	C₂³	1	4	yes	complemented
104	C₂×C₃×#67	C₂³	1	8	yes	complemented
105	C₂×C₃×#67	C₂³	1	8	yes	complemented
106	C₂²×C₃×Dic₃	—	2	4	no	—
107	C₂²×C₃×Dic₃	D₄	1	8	yes	complemented
108	C₂²×C₃×Dic₃	C₂³	1	2	yes	—
109	C₂²×C₃×Dic₃	C₂³	1	1	yes	characteristic
110	C₂²×C₃×Dic₃	C₂³	1	1	yes	characteristic
111	C₂²×C₃×Dic₃	C₂³	1	1	yes	characteristic
112	C₂²×C₃×Dic₃	C₂³	1	4	yes	—
113	C₂²×C₃×Dic₃	C₂³	1	4	yes	complemented
114	C₃×#237	—	2	32	no	—
115	C₂×C₃×D₁₂	—	4	4	no	—
116	C₂×C₃×D₁₂	C₂³	1	8	yes	complemented
117	C₂×C₃×C₄×D₃	—	2	4	no	—
118	C₂×C₃×C₄×D₃	C₂³	1	4	yes	complemented
119	C₂×C₃×Dic₆	—	2	4	no	—
120	C₂×C₃×Dic₆	C₂³	1	4	yes	complemented
121	C₃²×C₂²⋊C₄	C₂³	1	4	yes	—
122	C₃²×C₂²⋊C₄	C₂³	1	8	yes	complemented
123	C₃×#217	C₂³	1	4	yes	—
124	C₃×#217	C₂³	1	8	yes	complemented
125	C₃×(C₂×D₃)⋊C₄	C₂³	1	8	yes	complemented
126	C₃×(C₂×D₃)⋊C₄	C₂³	1	8	yes	complemented
127	C₃×Dic₃⋊C₄	C₂³	1	8	yes	complemented
128	C₃×C₄×Dic₃	C₂³	1	8	yes	complemented
129	C₂×#535	—	3	1	no	Sylow
130	C₂⁵×C₃	—	2	1	no	—
131	C₂⁵×C₃	—	3	1	no	—
132	C₂⁵×C₃	C₂×D₃	1	1	yes	characteristic
133	C₂⁵×C₃	C₂²×C₃	1	1	yes	characteristic
134	C₂⁴×D₃	C₂²×C₃	1	1	yes	characteristic
135	C₂×C₃×#41	—	3	8	no	—
136	C₂×C₃×#41	—	6	8	no	—
137	C₂²×C₃×Q₈	—	3	1	no	—
138	C₂²×C₃×D₄	—	2	1	no	—
139	C₂²×C₃×D₄	—	2	2	no	—
140	C₂²×C₃×D₄	—	3	2	no	—
141	C₂²×C₃×D₄	—	3	2	no	—
142	C₂²×C₃×D₄	—	3	8	no	—
143	C₂²×C₃×D₄	—	3	1	no	—
144	C₂²×C₃×D₄	—	3	1	no	—
145	C₂²×C₃×D₄	—	3	2	no	—
146	C₂²×C₃×D₄	—	3	2	no	—
147	C₂²×C₃×D₄	—	3	2	no	—
148	C₂²×C₃×D₄	—	6	8	no	—
149	C₂²×C₃×D₄	C₂×D₃	1	1	yes	characteristic
150	C₂²×C₃×D₄	C₂×D₃	1	2	yes	complemented
151	C₂²×C₃×D₄	C₂²×C₃	1	1	yes	characteristic
152	C₂²×C₃×D₄	C₂²×C₃	1	2	yes	complemented
153	C₂³×C₃×C₄	—	3	1	no	—
154	C₂³×C₃×C₄	—	3	1	no	—
155	C₂³×C₃×C₄	—	3	1	no	—
156	C₂²×#67	—	2	8	no	—
157	C₂²×#67	C₂²×C₃	1	1	yes	characteristic
158	C₂²×#67	C₂²×C₃	1	2	yes	—
159	C₂²×#67	C₂²×C₃	1	2	yes	—
160	C₂²×#67	C₂²×C₃	1	8	yes	complemented
161	C₂²×#67	C₂²×C₃	1	1	yes	characteristic, complemented
162	C₂²×#67	C₂²×C₃	1	2	yes	complemented
163	C₂²×#67	C₂²×C₃	1	2	yes	complemented
164	C₂³×Dic₃	C₂²×C₃	1	1	yes	characteristic
165	C₂³×Dic₃	C₂²×C₃	1	1	yes	characteristic, complemented
166	C₂×#237	—	2	8	no	—
167	C₂×#237	C₂²×C₃	1	8	yes	complemented
168	C₂²×D₁₂	C₂²×C₃	1	2	yes	complemented
169	C₂²×C₄×D₃	C₂²×C₃	1	1	yes	characteristic, complemented
170	C₂²×Dic₆	C₂²×C₃	1	1	yes	characteristic, complemented
171	C₃×#127	—	3	16	no	—
172	C₃×#124	—	3	16	no	—
173	C₃×#121	—	3	16	no	—
174	C₃×#121	—	3	16	no	—
175	C₃×#120	—	2	8	no	—
176	C₃×#120	—	3	8	no	—
177	C₃×#120	—	3	8	no	—
178	C₃×#120	—	3	8	no	—
179	C₃×#120	C₂×D₃	1	8	yes	complemented
180	C₃×#120	C₂²×C₃	1	8	yes	complemented
181	C₃×#117	—	3	8	no	—
182	C₂×C₃×C₄⋊C₄	—	3	2	no	—
183	C₂×C₃×C₂²⋊C₄	—	2	1	no	—
184	C₂×C₃×C₂²⋊C₄	—	2	2	no	—
185	C₂×C₃×C₂²⋊C₄	—	3	1	no	—
186	C₂×C₃×C₂²⋊C₄	—	3	2	no	—
187	C₂×C₃×C₂²⋊C₄	—	3	2	no	—
188	C₂×C₃×C₂²⋊C₄	—	3	2	no	—
189	C₂×C₃×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic
190	C₂×C₃×C₂²⋊C₄	C₂×D₃	1	2	yes	complemented
191	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
192	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	2	yes	complemented
193	C₂×C₃×C₄²	—	3	2	no	—
194	#953	C₂²×C₃	1	8	yes	complemented
195	C₂×#217	C₂²×C₃	1	1	yes	characteristic
196	C₂×#217	C₂²×C₃	1	2	yes	complemented
197	#940	C₂²×C₃	1	16	yes	complemented
198	#939	C₂²×C₃	1	16	yes	complemented
199	#937	C₂²×C₃	1	8	yes	complemented
200	C₂×(C₂×D₃)⋊C₄	C₂²×C₃	1	2	yes	complemented
201	C₂×(C₂×D₃)⋊C₄	C₂²×C₃	1	2	yes	complemented
202	C₂×Dic₃⋊C₄	C₂²×C₃	1	2	yes	complemented
203	C₂×C₄×Dic₃	C₂²×C₃	1	2	yes	complemented
204	#885	C₂²×C₃	1	16	yes	complemented
205	#884	C₂²×C₃	1	16	yes	complemented
206	#882	C₂²×C₃	1	8	yes	complemented
207	#877	C₂²×C₃	1	8	yes	complemented
208	C₂³×C₃²	—	2	4	no	—
209	C₂³×C₃²	—	2	4	no	—
210	C₂³×C₃²	—	2	8	no	—
211	C₂³×C₃²	—	2	4	no	—
212	C₂³×C₃²	—	2	2	no	—
213	C₂³×C₃²	—	2	4	no	—
214	C₂³×C₃²	—	2	4	no	—
215	C₂³×C₃²	—	4	8	no	—
216	C₂³×C₃²	—	4	16	no	—
217	C₂³×C₃²	C₂×D₄	1	4	yes	—
218	C₂³×C₃²	C₂⁴	1	4	yes	—
219	C₂³×C₃²	C₂⁴	1	2	yes	—
220	C₂³×C₃²	C₂⁴	1	2	yes	—
221	C₂³×C₃²	C₂⁴	1	1	yes	characteristic
222	C₂²×C₃×D₃	—	2	8	no	—
223	C₂²×C₃×D₃	—	2	4	no	—
224	C₂²×C₃×D₃	—	2	2	no	—
225	C₂²×C₃×D₃	—	2	4	no	—
226	C₂²×C₃×D₃	—	2	4	no	—
227	C₂²×C₃×D₃	—	2	4	no	—
228	C₂²×C₃×D₃	—	4	8	no	—
229	C₂²×C₃×D₃	—	4	16	no	—
230	C₂²×C₃×D₃	C₂⁴	1	4	yes	—
231	C₂²×C₃×D₃	C₂⁴	1	2	yes	—
232	C₃²×D₄	—	2	8	no	—
233	C₃²×D₄	—	4	8	no	—
234	C₂×C₃²×C₄	—	2	2	no	—
235	C₂×C₃²×C₄	—	2	4	no	—
236	C₂×C₃²×C₄	C₂⁴	1	4	yes	—
237	C₂×C₃²×C₄	C₂⁴	1	2	yes	—
238	C₃×#67	—	2	8	no	—
239	C₃×#67	—	2	8	no	—
240	C₃×#67	—	2	16	no	—
241	C₃×#67	—	2	16	no	—
242	C₃×#67	—	4	8	no	—
243	C₃×#67	—	4	8	no	—
244	C₂×C₃×Dic₃	—	2	2	no	—
245	C₂×C₃×Dic₃	—	2	4	no	—
246	C₂×C₃×Dic₃	—	2	8	no	—
247	C₂×C₃×Dic₃	C₂×D₄	1	4	yes	—
248	C₂×C₃×Dic₃	C₂×D₄	1	4	yes	—
249	C₂×C₃×Dic₃	C₂×D₄	1	16	yes	complemented
250	C₂×C₃×Dic₃	C₂⁴	1	4	yes	—
251	C₂×C₃×Dic₃	C₂⁴	1	2	yes	—
252	C₂×C₃×Dic₃	C₂⁴	1	2	yes	—
253	C₂×C₃×Dic₃	C₂⁴	1	2	yes	—
254	C₃×D₁₂	—	4	8	no	—
255	C₃×C₄×D₃	—	2	8	no	—
256	C₃×Dic₆	—	2	8	no	—
257	C₂²×#41	—	3	1	no	—
258	C₂³×D₄	—	3	1	no	—
259	#535	—	3	16	no	—
260	C₂×#127	—	3	2	no	—
261	C₂×#124	—	3	2	no	—
262	C₂×#121	—	3	2	no	—
263	C₂×#121	—	3	2	no	—
264	C₂×#120	—	3	1	no	—
265	C₂×#120	—	3	1	no	—
266	C₂×#120	—	3	1	no	—
267	C₂×#120	C₃×D₃	1	1	yes	characteristic, complemented
268	C₂×#117	—	3	1	no	—
269	C₂⁴×C₃	—	2	4	no	—
270	C₂⁴×C₃	—	2	4	no	—
271	C₂⁴×C₃	—	2	2	no	—
272	C₂⁴×C₃	—	2	1	no	—
273	C₂⁴×C₃	—	2	4	no	—
274	C₂⁴×C₃	—	2	1	no	—
275	C₂⁴×C₃	—	3	2	no	—
276	C₂⁴×C₃	—	3	1	no	—
277	C₂⁴×C₃	—	3	4	no	—
278	C₂⁴×C₃	—	4	4	no	—
279	C₂⁴×C₃	—	4	4	no	—
280	C₂⁴×C₃	—	4	4	no	—
281	C₂⁴×C₃	—	4	8	no	—
282	C₂⁴×C₃	—	6	4	no	—
283	C₂⁴×C₃	—	12	4	no	—
284	C₂⁴×C₃	C₂²×D₃	1	2	yes	—
285	C₂⁴×C₃	C₂²×D₃	1	1	yes	characteristic
286	C₂⁴×C₃	C₂²×D₃	1	1	yes	characteristic
287	C₂⁴×C₃	C₂²×D₃	1	4	yes	—
288	C₂⁴×C₃	C₂³×C₃	1	2	yes	—
289	C₂⁴×C₃	C₂³×C₃	1	1	yes	characteristic
290	C₂⁴×C₃	C₂³×C₃	1	1	yes	characteristic
291	C₂⁴×C₃	C₂³×C₃	1	4	yes	—
292	C₂³×D₃	—	2	4	no	—
293	C₂³×D₃	—	4	4	no	—
294	C₂³×D₃	C₂³×C₃	1	2	yes	—
295	C₂³×D₃	C₂³×C₃	1	1	yes	characteristic
296	C₂³×D₃	C₂³×C₃	1	4	yes	—
297	C₃×#41	—	6	32	no	—
298	C₂×C₃×Q₈	—	3	4	no	—
299	C₂×C₃×Q₈	—	6	4	no	—
300	C₂×C₃×D₄	—	2	4	no	—
301	C₂×C₃×D₄	—	2	4	no	—
302	C₂×C₃×D₄	—	2	4	no	—
303	C₂×C₃×D₄	—	2	8	no	—
304	C₂×C₃×D₄	—	3	4	no	—
305	C₂×C₃×D₄	—	3	8	no	—
306	C₂×C₃×D₄	—	3	8	no	—
307	C₂×C₃×D₄	—	3	4	no	—
308	C₂×C₃×D₄	—	3	8	no	—
309	C₂×C₃×D₄	—	3	8	no	—
310	C₂×C₃×D₄	—	3	8	no	—
311	C₂×C₃×D₄	—	4	4	no	—
312	C₂×C₃×D₄	—	4	4	no	—
313	C₂×C₃×D₄	—	4	4	no	—
314	C₂×C₃×D₄	—	4	8	no	—
315	C₂×C₃×D₄	—	6	8	no	—
316	C₂×C₃×D₄	—	6	8	no	—
317	C₂×C₃×D₄	—	6	32	no	—
318	C₂×C₃×D₄	—	6	4	no	—
319	C₂×C₃×D₄	—	6	4	no	—
320	C₂×C₃×D₄	—	12	4	no	—
321	C₂×C₃×D₄	—	12	4	no	—
322	C₂×C₃×D₄	—	12	4	no	—
323	C₂×C₃×D₄	C₂²×D₃	1	4	yes	—
324	C₂×C₃×D₄	C₂²×D₃	1	8	yes	complemented
325	C₂×C₃×D₄	C₂³×C₃	1	4	yes	—
326	C₂×C₃×D₄	C₂³×C₃	1	8	yes	complemented
327	C₂²×C₃×C₄	—	2	2	no	—
328	C₂²×C₃×C₄	—	2	1	no	—
329	C₂²×C₃×C₄	—	3	8	no	—
330	C₂²×C₃×C₄	—	3	4	no	—
331	C₂²×C₃×C₄	—	3	1	no	—
332	C₂²×C₃×C₄	—	3	1	no	—
333	C₂²×C₃×C₄	—	3	4	no	—
334	C₂²×C₃×C₄	—	3	2	no	—
335	C₂²×C₃×C₄	—	3	1	no	—
336	C₂²×C₃×C₄	—	3	4	no	—
337	C₂²×C₃×C₄	—	6	4	no	—
338	C₂²×C₃×C₄	—	6	4	no	—
339	C₂²×C₃×C₄	C₂²×D₃	1	2	yes	—
340	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
341	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
342	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
343	C₂×#67	—	2	4	no	—
344	C₂×#67	—	2	4	no	—
345	C₂×#67	—	2	8	no	—
346	C₂×#67	—	2	8	no	—
347	C₂×#67	—	2	32	no	—
348	C₂×#67	—	4	4	no	—
349	C₂×#67	—	4	4	no	—
350	C₂×#67	C₂³×C₃	1	4	yes	—
351	C₂×#67	C₂³×C₃	1	8	yes	—
352	C₂×#67	C₂³×C₃	1	8	yes	—
353	C₂×#67	C₂³×C₃	1	4	yes	complemented
354	C₂×#67	C₂³×C₃	1	8	yes	complemented
355	C₂×#67	C₂³×C₃	1	8	yes	complemented
356	C₂²×Dic₃	—	2	4	no	—
357	C₂²×Dic₃	C₃×D₄	1	8	yes	complemented
358	C₂²×Dic₃	C₂³×C₃	1	2	yes	—
359	C₂²×Dic₃	C₂³×C₃	1	1	yes	characteristic
360	C₂²×Dic₃	C₂³×C₃	1	1	yes	characteristic
361	C₂²×Dic₃	C₂³×C₃	1	1	yes	characteristic
362	C₂²×Dic₃	C₂³×C₃	1	4	yes	—
363	C₂²×Dic₃	C₂³×C₃	1	4	yes	complemented
364	#237	—	2	32	no	—
365	C₂×D₁₂	—	4	4	no	—
366	C₂×D₁₂	C₂³×C₃	1	8	yes	complemented
367	C₂×C₄×D₃	—	2	4	no	—
368	C₂×C₄×D₃	C₂³×C₃	1	4	yes	complemented
369	C₂×Dic₆	—	2	4	no	—
370	C₂×Dic₆	C₂³×C₃	1	4	yes	complemented
371	C₃×C₄⋊C₄	—	3	8	no	—
372	C₃×C₂²⋊C₄	—	2	4	no	—
373	C₃×C₂²⋊C₄	—	2	8	no	—
374	C₃×C₂²⋊C₄	—	3	4	no	—
375	C₃×C₂²⋊C₄	—	3	8	no	—
376	C₃×C₂²⋊C₄	—	3	8	no	—
377	C₃×C₂²⋊C₄	—	3	8	no	—
378	C₃×C₂²⋊C₄	C₂²×D₃	1	4	yes	—
379	C₃×C₂²⋊C₄	C₂²×D₃	1	8	yes	complemented
380	C₃×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
381	C₃×C₂²⋊C₄	C₂³×C₃	1	8	yes	complemented
382	C₃×C₄²	—	3	8	no	—
383	#217	C₂³×C₃	1	4	yes	—
384	#217	C₂³×C₃	1	8	yes	complemented
385	(C₂×D₃)⋊C₄	C₂³×C₃	1	8	yes	complemented
386	(C₂×D₃)⋊C₄	C₂³×C₃	1	8	yes	complemented
387	Dic₃⋊C₄	C₂³×C₃	1	8	yes	complemented
388	C₄×Dic₃	C₂³×C₃	1	8	yes	complemented
389	C₂²×C₃²	—	2	4	no	—
390	C₂²×C₃²	—	2	8	no	—
391	C₂²×C₃²	—	2	4	no	—
392	C₂²×C₃²	—	2	2	no	—
393	C₂²×C₃²	—	2	4	no	—
394	C₂²×C₃²	—	2	4	no	—
395	C₂²×C₃²	—	2	4	no	—
396	C₂²×C₃²	—	4	16	no	—
397	C₂²×C₃²	—	4	8	no	—
398	C₂²×C₃²	—	4	4	no	—
399	C₂²×C₃²	C₂²×D₄	1	4	yes	—
400	C₂²×C₃²	C₂²×D₄	1	2	yes	—
401	C₂²×C₃²	H(5,𝔽₂)	1	4	yes	—
402	C₂²×C₃²	C₂⁵	1	1	yes	characteristic
403	C₂×C₃×D₃	—	2	2	no	—
404	C₂×C₃×D₃	—	2	4	no	—
405	C₂×C₃×D₃	—	2	4	no	—
406	C₂×C₃×D₃	—	2	4	no	—
407	C₂×C₃×D₃	—	2	4	no	—
408	C₂×C₃×D₃	—	4	16	no	—
409	C₂×C₃×D₃	—	4	4	no	—
410	C₂×C₃×D₃	—	4	8	no	—
411	C₃²×C₄	—	2	2	no	—
412	C₃²×C₄	—	2	4	no	—
413	C₃×Dic₃	—	2	2	no	—
414	C₃×Dic₃	—	2	4	no	—
415	C₃×Dic₃	C₂²×D₄	1	4	yes	—
416	C₃×Dic₃	C₂²×D₄	1	4	yes	—
417	C₂⁵	—	3	1	no	—
418	C₂⁵	C₂×C₃×D₃	1	1	yes	characteristic
419	C₂×#41	—	3	8	no	—
420	C₂×#41	—	6	8	no	—
421	C₂²×Q₈	—	3	1	no	—
422	C₂²×D₄	—	3	1	no	—
423	C₂²×D₄	—	3	2	no	—
424	C₂²×D₄	—	3	2	no	—
425	C₂²×D₄	—	3	1	no	—
426	C₂²×D₄	—	3	8	no	—
427	C₂²×D₄	—	3	2	no	—
428	C₂²×D₄	—	3	2	no	—
429	C₂²×D₄	—	3	2	no	—
430	C₂²×D₄	—	6	8	no	—
431	C₂²×D₄	C₂×C₃×D₃	1	1	yes	characteristic
432	C₂²×D₄	C₂×C₃×D₃	1	2	yes	complemented
433	C₂³×C₄	—	3	1	no	—
434	C₂³×C₄	—	3	1	no	—
435	C₂³×C₄	—	3	1	no	—
436	#127	—	3	16	no	—
437	#124	—	3	16	no	—
438	#121	—	3	16	no	—
439	#121	—	3	16	no	—
440	#120	—	3	8	no	—
441	#120	—	3	8	no	—
442	#120	—	3	8	no	—
443	#120	C₂×C₃×D₃	1	8	yes	complemented
444	#117	—	3	8	no	—
445	C₂×C₄⋊C₄	—	3	2	no	—
446	C₂×C₂²⋊C₄	—	3	1	no	—
447	C₂×C₂²⋊C₄	—	3	2	no	—
448	C₂×C₂²⋊C₄	—	3	2	no	—
449	C₂×C₂²⋊C₄	—	3	2	no	—
450	C₂×C₂²⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
451	C₂×C₂²⋊C₄	C₂×C₃×D₃	1	2	yes	complemented
452	C₂×C₄²	—	3	2	no	—
453	C₂³×C₃	—	2	4	no	—
454	C₂³×C₃	—	2	4	no	—
455	C₂³×C₃	—	2	8	no	—
456	C₂³×C₃	—	2	2	no	—
457	C₂³×C₃	—	2	8	no	—
458	C₂³×C₃	—	2	4	no	—
459	C₂³×C₃	—	2	4	no	—
460	C₂³×C₃	—	2	4	no	—
461	C₂³×C₃	—	2	4	no	—
462	C₂³×C₃	—	2	2	no	—
463	C₂³×C₃	—	2	8	no	—
464	C₂³×C₃	—	2	4	no	—
465	C₂³×C₃	—	2	4	no	—
466	C₂³×C₃	—	2	4	no	—
467	C₂³×C₃	—	2	4	no	—
468	C₂³×C₃	—	2	1	no	—
469	C₂³×C₃	—	2	4	no	—
470	C₂³×C₃	—	2	2	no	—
471	C₂³×C₃	—	2	2	no	—
472	C₂³×C₃	—	2	4	no	—
473	C₂³×C₃	—	3	4	no	—
474	C₂³×C₃	—	3	2	no	—
475	C₂³×C₃	—	4	4	no	—
476	C₂³×C₃	—	4	4	no	—
477	C₂³×C₃	—	4	8	no	—
478	C₂³×C₃	—	4	4	no	—
479	C₂³×C₃	—	4	2	no	—
480	C₂³×C₃	—	4	4	no	—
481	C₂³×C₃	—	4	8	no	—
482	C₂³×C₃	—	4	8	no	—
483	C₂³×C₃	—	4	16	no	—
484	C₂³×C₃	—	4	16	no	—
485	C₂³×C₃	—	4	16	no	—
486	C₂³×C₃	—	4	32	no	—
487	C₂³×C₃	—	6	2	no	—
488	C₂³×C₃	—	6	8	no	—
489	C₂³×C₃	—	6	4	no	—
490	C₂³×C₃	—	6	4	no	—
491	C₂³×C₃	—	6	4	no	—
492	C₂³×C₃	—	6	4	no	—
493	C₂³×C₃	—	12	8	no	—
494	C₂³×C₃	—	12	16	no	—
495	C₂³×C₃	D₃×D₄	1	4	yes	—
496	C₂³×C₃	C₂×C₃×D₄	1	4	yes	—
497	C₂³×C₃	C₂³×D₃	1	4	yes	—
498	C₂³×C₃	C₂³×D₃	1	2	yes	—
499	C₂³×C₃	C₂³×D₃	1	2	yes	—
500	C₂³×C₃	C₂³×D₃	1	1	yes	characteristic
501	C₂³×C₃	C₂⁴×C₃	1	4	yes	—
502	C₂³×C₃	C₂⁴×C₃	1	2	yes	—
503	C₂³×C₃	C₂⁴×C₃	1	2	yes	—
504	C₂³×C₃	C₂⁴×C₃	1	1	yes	characteristic
505	C₂²×D₃	—	2	2	no	—
506	C₂²×D₃	—	2	8	no	—
507	C₂²×D₃	—	2	4	no	—
508	C₂²×D₃	—	2	4	no	—
509	C₂²×D₃	—	2	4	no	—
510	C₂²×D₃	—	2	4	no	—
511	C₂²×D₃	—	4	8	no	—
512	C₂²×D₃	—	4	16	no	—
513	C₂²×D₃	C₂⁴×C₃	1	4	yes	—
514	C₂²×D₃	C₂⁴×C₃	1	2	yes	—
515	C₃×Q₈	—	6	8	no	—
516	C₃×D₄	—	2	8	no	—
517	C₃×D₄	—	2	8	no	—
518	C₃×D₄	—	4	8	no	—
519	C₃×D₄	—	4	8	no	—
520	C₃×D₄	—	4	8	no	—
521	C₃×D₄	—	4	16	no	—
522	C₃×D₄	—	6	16	no	—
523	C₃×D₄	—	6	16	no	—
524	C₃×D₄	—	6	8	no	—
525	C₃×D₄	—	6	8	no	—
526	C₃×D₄	—	12	8	no	—
527	C₃×D₄	—	12	8	no	—
528	C₃×D₄	—	12	8	no	—
529	C₂×C₃×C₄	—	2	2	no	—
530	C₂×C₃×C₄	—	2	4	no	—
531	C₂×C₃×C₄	—	2	2	no	—
532	C₂×C₃×C₄	—	2	4	no	—
533	C₂×C₃×C₄	—	2	4	no	—
534	C₂×C₃×C₄	—	2	2	no	—
535	C₂×C₃×C₄	—	3	4	no	—
536	C₂×C₃×C₄	—	3	4	no	—
537	C₂×C₃×C₄	—	3	16	no	—
538	C₂×C₃×C₄	—	3	2	no	—
539	C₂×C₃×C₄	—	3	2	no	—
540	C₂×C₃×C₄	—	3	4	no	—
541	C₂×C₃×C₄	—	3	2	no	—
542	C₂×C₃×C₄	—	4	2	no	—
543	C₂×C₃×C₄	—	4	4	no	—
544	C₂×C₃×C₄	—	6	8	no	—
545	C₂×C₃×C₄	—	6	8	no	—
546	C₂×C₃×C₄	—	6	2	no	—
547	C₂×C₃×C₄	—	6	4	no	—
548	C₂×C₃×C₄	C₂³×D₃	1	4	yes	—
549	C₂×C₃×C₄	C₂³×D₃	1	2	yes	—
550	C₂×C₃×C₄	C₂⁴×C₃	1	4	yes	—
551	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
552	#67	—	2	8	no	—
553	#67	—	2	8	no	—
554	#67	—	2	16	no	—
555	#67	—	2	16	no	—
556	#67	—	4	8	no	—
557	#67	—	4	8	no	—
558	C₂×Dic₃	—	2	2	no	—
559	C₂×Dic₃	—	2	4	no	—
560	C₂×Dic₃	—	2	8	no	—
561	C₂×Dic₃	C₂×C₃×D₄	1	4	yes	—
562	C₂×Dic₃	C₂×C₃×D₄	1	4	yes	—
563	C₂×Dic₃	C₂×C₃×D₄	1	16	yes	complemented
564	C₂×Dic₃	C₂⁴×C₃	1	4	yes	—
565	C₂×Dic₃	C₂⁴×C₃	1	2	yes	—
566	C₂×Dic₃	C₂⁴×C₃	1	2	yes	—
567	C₂×Dic₃	C₂⁴×C₃	1	2	yes	—
568	D₁₂	—	4	8	no	—
569	C₄×D₃	—	2	8	no	—
570	Dic₆	—	2	8	no	—
571	C₂×C₃²	—	2	4	no	—
572	C₂×C₃²	—	4	4	no	—
573	C₂×C₃²	—	4	2	no	—
574	C₂×C₃²	#535	1	4	yes	complemented
575	C₂×C₃²	C₂³×D₄	1	1	yes	characteristic
576	C₂×C₃²	C₂×H(5,𝔽₂)	1	2	yes	—
577	C₃×D₃	—	4	2	no	—
578	C₃×D₃	—	4	4	no	—
579	C₂⁴	—	2	4	no	—
580	C₂⁴	—	3	2	no	—
581	C₂⁴	—	3	1	no	—
582	C₂⁴	—	3	4	no	—
583	C₂⁴	—	4	4	no	—
584	C₂⁴	—	6	4	no	—
585	C₂⁴	—	12	4	no	—
586	C₂⁴	C₂²×C₃×D₃	1	2	yes	—
587	C₂⁴	C₂²×C₃×D₃	1	1	yes	characteristic
588	C₂⁴	C₂²×C₃×D₃	1	1	yes	characteristic
589	C₂⁴	C₂²×C₃×D₃	1	4	yes	—
590	#41	—	6	32	no	—
591	C₂×Q₈	—	3	4	no	—
592	C₂×Q₈	—	6	4	no	—
593	C₂×D₄	—	2	4	no	—
594	C₂×D₄	—	3	4	no	—
595	C₂×D₄	—	3	8	no	—
596	C₂×D₄	—	3	8	no	—
597	C₂×D₄	—	3	4	no	—
598	C₂×D₄	—	3	8	no	—
599	C₂×D₄	—	3	8	no	—
600	C₂×D₄	—	3	8	no	—
601	C₂×D₄	—	4	4	no	—
602	C₂×D₄	—	6	8	no	—
603	C₂×D₄	—	6	8	no	—
604	C₂×D₄	—	6	32	no	—
605	C₂×D₄	—	6	4	no	—
606	C₂×D₄	—	6	4	no	—
607	C₂×D₄	—	12	4	no	—
608	C₂×D₄	—	12	4	no	—
609	C₂×D₄	—	12	4	no	—
610	C₂×D₄	C₂²×C₃×D₃	1	4	yes	—
611	C₂×D₄	C₂²×C₃×D₃	1	8	yes	complemented
612	C₂²×C₄	—	3	1	no	—
613	C₂²×C₄	—	3	1	no	—
614	C₂²×C₄	—	3	4	no	—
615	C₂²×C₄	—	3	8	no	—
616	C₂²×C₄	—	3	2	no	—
617	C₂²×C₄	—	3	1	no	—
618	C₂²×C₄	—	3	4	no	—
619	C₂²×C₄	—	3	4	no	—
620	C₂²×C₄	—	6	4	no	—
621	C₂²×C₄	—	6	4	no	—
622	C₂²×C₄	C₂²×C₃×D₃	1	2	yes	—
623	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
624	C₄⋊C₄	—	3	8	no	—
625	C₂²⋊C₄	—	3	4	no	—
626	C₂²⋊C₄	—	3	8	no	—
627	C₂²⋊C₄	—	3	8	no	—
628	C₂²⋊C₄	—	3	8	no	—
629	C₂²⋊C₄	C₂²×C₃×D₃	1	4	yes	—
630	C₂²⋊C₄	C₂²×C₃×D₃	1	8	yes	complemented
631	C₄²	—	3	8	no	—
632	C₂²×C₃	—	2	4	no	—
633	C₂²×C₃	—	2	4	no	—
634	C₂²×C₃	—	2	8	no	—
635	C₂²×C₃	—	2	8	no	—
636	C₂²×C₃	—	2	8	no	—
637	C₂²×C₃	—	2	2	no	—
638	C₂²×C₃	—	2	4	no	—
639	C₂²×C₃	—	2	4	no	—
640	C₂²×C₃	—	2	4	no	—
641	C₂²×C₃	—	2	4	no	—
642	C₂²×C₃	—	2	2	no	—
643	C₂²×C₃	—	2	4	no	—
644	C₂²×C₃	—	2	4	no	—
645	C₂²×C₃	—	2	4	no	—
646	C₂²×C₃	—	2	4	no	—
647	C₂²×C₃	—	2	2	no	—
648	C₂²×C₃	—	2	4	no	—
649	C₂²×C₃	—	2	4	no	—
650	C₂²×C₃	—	2	1	no	—
651	C₂²×C₃	—	4	8	no	—
652	C₂²×C₃	—	4	4	no	—
653	C₂²×C₃	—	4	4	no	—
654	C₂²×C₃	—	4	4	no	—
655	C₂²×C₃	—	4	2	no	—
656	C₂²×C₃	—	4	4	no	—
657	C₂²×C₃	—	4	16	no	—
658	C₂²×C₃	—	4	16	no	—
659	C₂²×C₃	—	4	16	no	—
660	C₂²×C₃	—	4	32	no	—
661	C₂²×C₃	—	4	8	no	—
662	C₂²×C₃	—	4	4	no	—
663	C₂²×C₃	—	4	8	no	—
664	C₂²×C₃	—	4	4	no	—
665	C₂²×C₃	—	6	2	no	—
666	C₂²×C₃	—	6	4	no	—
667	C₂²×C₃	—	6	4	no	—
668	C₂²×C₃	—	6	4	no	—
669	C₂²×C₃	—	6	4	no	—
670	C₂²×C₃	—	8	4	no	—
671	C₂²×C₃	—	12	16	no	—
672	C₂²×C₃	—	12	8	no	—
673	C₂²×C₃	—	12	4	no	—
674	C₂²×C₃	C₂×D₃×D₄	1	4	yes	—
675	C₂²×C₃	C₂×D₃×D₄	1	2	yes	—
676	C₂²×C₃	#1004	1	4	yes	—
677	C₂²×C₃	C₂²×C₃×D₄	1	4	yes	—
678	C₂²×C₃	C₂²×C₃×D₄	1	2	yes	—
679	C₂²×C₃	C₃×H(5,𝔽₂)	1	4	yes	—
680	C₂²×C₃	C₂⁴×D₃	1	1	yes	characteristic
681	C₂²×C₃	C₂⁵×C₃	1	1	yes	characteristic
682	C₂×D₃	—	2	2	no	—
683	C₂×D₃	—	2	4	no	—
684	C₂×D₃	—	2	4	no	—
685	C₂×D₃	—	2	4	no	—
686	C₂×D₃	—	2	4	no	—
687	C₂×D₃	—	4	16	no	—
688	C₂×D₃	—	4	8	no	—
689	C₂×D₃	—	4	4	no	—
690	C₃×C₄	—	2	2	no	—
691	C₃×C₄	—	2	4	no	—
692	C₃×C₄	—	2	2	no	—
693	C₃×C₄	—	2	4	no	—
694	C₃×C₄	—	3	4	no	—
695	C₃×C₄	—	3	4	no	—
696	C₃×C₄	—	4	2	no	—
697	C₃×C₄	—	4	4	no	—
698	C₃×C₄	—	6	2	no	—
699	C₃×C₄	—	6	4	no	—
700	Dic₃	—	2	2	no	—
701	Dic₃	—	2	4	no	—
702	Dic₃	C₂²×C₃×D₄	1	4	yes	—
703	Dic₃	C₂²×C₃×D₄	1	4	yes	—
704	C₃²	C₂×#535	1	1	yes	characteristic, complemented, Sylow
705	C₂³	—	2	4	no	—
706	C₂³	—	2	2	no	—
707	C₂³	—	2	8	no	—
708	C₂³	—	2	4	no	—
709	C₂³	—	2	4	no	—
710	C₂³	—	2	4	no	—
711	C₂³	—	2	4	no	—
712	C₂³	—	3	4	no	—
713	C₂³	—	3	2	no	—
714	C₂³	—	4	8	no	—
715	C₂³	—	4	16	no	—
716	C₂³	—	6	2	no	—
717	C₂³	—	6	8	no	—
718	C₂³	—	6	4	no	—
719	C₂³	—	6	4	no	—
720	C₂³	—	6	4	no	—
721	C₂³	—	6	4	no	—
722	C₂³	—	12	8	no	—
723	C₂³	—	12	16	no	—
724	C₂³	C₃×D₃×D₄	1	4	yes	—
725	C₂³	C₂³×C₃×D₃	1	4	yes	—
726	C₂³	C₂³×C₃×D₃	1	2	yes	—
727	C₂³	C₂³×C₃×D₃	1	2	yes	—
728	C₂³	C₂³×C₃×D₃	1	1	yes	characteristic
729	Q₈	—	6	8	no	—
730	D₄	—	2	8	no	—
731	D₄	—	4	8	no	—
732	D₄	—	6	16	no	—
733	D₄	—	6	16	no	—
734	D₄	—	6	8	no	—
735	D₄	—	6	8	no	—
736	D₄	—	12	8	no	—
737	D₄	—	12	8	no	—
738	D₄	—	12	8	no	—
739	C₂×C₄	—	2	2	no	—
740	C₂×C₄	—	2	4	no	—
741	C₂×C₄	—	3	4	no	—
742	C₂×C₄	—	3	4	no	—
743	C₂×C₄	—	3	16	no	—
744	C₂×C₄	—	3	2	no	—
745	C₂×C₄	—	3	2	no	—
746	C₂×C₄	—	3	4	no	—
747	C₂×C₄	—	3	2	no	—
748	C₂×C₄	—	6	8	no	—
749	C₂×C₄	—	6	8	no	—
750	C₂×C₄	—	6	2	no	—
751	C₂×C₄	—	6	4	no	—
752	C₂×C₄	C₂³×C₃×D₃	1	4	yes	—
753	C₂×C₄	C₂³×C₃×D₃	1	2	yes	—
754	C₂×C₃	—	2	4	no	—
755	C₂×C₃	—	2	4	no	—
756	C₂×C₃	—	2	4	no	—
757	C₂×C₃	—	2	1	no	—
758	C₂×C₃	—	2	2	no	—
759	C₂×C₃	—	4	4	no	—
760	C₂×C₃	—	4	8	no	—
761	C₂×C₃	—	4	4	no	—
762	C₂×C₃	—	4	2	no	—
763	C₂×C₃	—	4	4	no	—
764	C₂×C₃	—	4	2	no	—
765	C₂×C₃	—	8	2	no	—
766	C₂×C₃	—	12	4	no	—
767	C₂×C₃	—	12	2	no	—
768	C₂×C₃	#5592	1	4	yes	direct product factor
769	C₂×C₃	C₃×#535	1	4	yes	complemented
770	C₂×C₃	C₂²×D₃×D₄	1	1	yes	characteristic
771	C₂×C₃	C₂×#1004	1	2	yes	—
772	C₂×C₃	C₂³×C₃×D₄	1	1	yes	characteristic
773	C₂×C₃	C₂×C₃×H(5,𝔽₂)	1	2	yes	—
774	D₃	—	4	4	no	—
775	D₃	—	4	2	no	—
776	C₂²	—	2	8	no	—
777	C₂²	—	2	4	no	—
778	C₂²	—	2	2	no	—
779	C₂²	—	2	4	no	—
780	C₂²	—	2	4	no	—
781	C₂²	—	2	4	no	—
782	C₂²	—	2	4	no	—
783	C₂²	—	4	16	no	—
784	C₂²	—	4	8	no	—
785	C₂²	—	4	4	no	—
786	C₂²	—	6	2	no	—
787	C₂²	—	6	4	no	—
788	C₂²	—	6	4	no	—
789	C₂²	—	6	4	no	—
790	C₂²	—	6	4	no	—
791	C₂²	—	12	16	no	—
792	C₂²	—	12	8	no	—
793	C₂²	—	12	4	no	—
794	C₂²	C₂×C₃×D₃×D₄	1	4	yes	—
795	C₂²	C₂×C₃×D₃×D₄	1	2	yes	—
796	C₂²	C₃×#1004	1	4	yes	—
797	C₂²	C₂⁴×C₃×D₃	1	1	yes	characteristic
798	C₄	—	2	2	no	—
799	C₄	—	2	4	no	—
800	C₄	—	3	4	no	—
801	C₄	—	3	4	no	—
802	C₄	—	6	2	no	—
803	C₄	—	6	4	no	—
804	C₃	—	2	1	no	—
805	C₃	C₂×#5592	1	1	yes	characteristic, direct product factor
806	C₃	C₂×C₃×#535	1	1	yes	characteristic, complemented
807	C₂	—	2	4	no	—
808	C₂	—	4	4	no	—
809	C₂	—	4	2	no	—
810	C₂	—	12	4	no	—
811	C₂	—	12	2	no	—
812	C₂	C₃×#5592	1	4	yes	direct product factor
813	C₂	C₂²×C₃×D₃×D₄	1	1	yes	characteristic
814	C₂	C₂×C₃×#1004	1	2	yes	—

	subgroup	G/H
center	C₂³×C₃	C₂³×D₃
commutator, cosocle	C₂²×C₃	C₂⁵×C₃
Frattini	C₂²	C₂⁴×C₃×D₃
Fitting	C₂×C₃²×#120	C₂
socle	C₂³×C₃²	C₂⁴
hypercenter	C₂×C₃×#120	D₃
hypocenter	C₃	C₂×C₃×#535
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₃ ◁ C₂×C₃×#120

Complements

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

N	H ≅ G/N	type
1. C₂³×C₃×#67	C₂	semidirect
2. C₂²×C₃×#237	C₂	semidirect
3. C₂×C₃²×#120	C₂	semidirect
4. C₂×C₃×#953	C₂	semidirect
5. C₂×C₃×#940	C₂	semidirect
6. C₂×C₃×#939	C₂	semidirect
7. C₂×C₃×#937	C₂	semidirect
8. C₃×#5592	C₂	direct (N × H)
9. C₂×C₃×#885	C₂	semidirect
10. C₂×C₃×#884	C₂	semidirect
11. C₂×C₃×#882	C₂	semidirect
12. C₂×C₃×#877	C₂	semidirect
14. C₂×#5592	C₃	direct (N × H)
18. C₂²×C₃²×D₄	C₂²	semidirect
23. C₂²×C₃×#67	C₂²	semidirect
24. C₂²×C₃×#67	C₂²	semidirect
25. C₂²×C₃×#67	C₂²	semidirect
26. C₂²×C₃×#67	C₂²	semidirect
28. C₂³×C₃×Dic₃	C₂²	semidirect
30. C₂×C₃×#237	C₂²	semidirect
31. C₂²×C₃×D₁₂	C₂²	semidirect
32. C₂²×C₃×C₄×D₃	C₂²	semidirect
33. C₂²×C₃×Dic₆	C₂²	semidirect
34. C₃²×#120	C₂²	semidirect
36. C₂×C₃²×C₂²⋊C₄	C₂²	semidirect
37. C₃×#953	C₂²	semidirect
39. C₂×C₃×#217	C₂²	semidirect
40. C₃×#940	C₂²	semidirect
41. C₃×#939	C₂²	semidirect
42. C₃×#937	C₂²	semidirect
43. C₂×C₃×(C₂×D₃)⋊C₄	C₂²	semidirect
44. C₂×C₃×(C₂×D₃)⋊C₄	C₂²	semidirect
45. C₂×C₃×Dic₃⋊C₄	C₂²	semidirect
46. C₂×C₃×C₄×Dic₃	C₂²	semidirect
47. C₃×#885	C₂²	semidirect
48. C₃×#884	C₂²	semidirect
49. C₃×#882	C₂²	semidirect
50. C₃×#877	C₂²	semidirect
53. C₂³×#67	C₂×C₃	semidirect
54. C₂²×#237	C₂×C₃	semidirect
64. C₂×C₃×#120	D₃	semidirect
65. C₂×C₃×#120	C₂×C₃	semidirect
67. C₂×#953	C₂×C₃	semidirect
68. C₂×#940	C₂×C₃	semidirect
69. C₂×#939	C₂×C₃	semidirect
70. C₂×#937	C₂×C₃	semidirect
71. #5592	C₂×C₃	direct (N × H)
72. C₂×#885	C₂×C₃	semidirect
73. C₂×#884	C₂×C₃	semidirect
74. C₂×#882	C₂×C₃	semidirect
75. C₂×#877	C₂×C₃	semidirect
90. C₂×C₃²×D₄	C₂³	semidirect
103. C₂×C₃×#67	C₂³	semidirect
104. C₂×C₃×#67	C₂³	semidirect
105. C₂×C₃×#67	C₂³	semidirect
107. C₂²×C₃×Dic₃	D₄	semidirect
113. C₂²×C₃×Dic₃	C₂³	semidirect
116. C₂×C₃×D₁₂	C₂³	semidirect
118. C₂×C₃×C₄×D₃	C₂³	semidirect
120. C₂×C₃×Dic₆	C₂³	semidirect
122. C₃²×C₂²⋊C₄	C₂³	semidirect
124. C₃×#217	C₂³	semidirect
125. C₃×(C₂×D₃)⋊C₄	C₂³	semidirect
126. C₃×(C₂×D₃)⋊C₄	C₂³	semidirect
127. C₃×Dic₃⋊C₄	C₂³	semidirect
128. C₃×C₄×Dic₃	C₂³	semidirect
150. C₂²×C₃×D₄	C₂×D₃	semidirect
152. C₂²×C₃×D₄	C₂²×C₃	semidirect
160. C₂²×#67	C₂²×C₃	semidirect
161. C₂²×#67	C₂²×C₃	semidirect
162. C₂²×#67	C₂²×C₃	semidirect
163. C₂²×#67	C₂²×C₃	semidirect
165. C₂³×Dic₃	C₂²×C₃	semidirect
167. C₂×#237	C₂²×C₃	semidirect
168. C₂²×D₁₂	C₂²×C₃	semidirect
169. C₂²×C₄×D₃	C₂²×C₃	semidirect
170. C₂²×Dic₆	C₂²×C₃	semidirect
179. C₃×#120	C₂×D₃	semidirect
180. C₃×#120	C₂²×C₃	semidirect
190. C₂×C₃×C₂²⋊C₄	C₂×D₃	semidirect
192. C₂×C₃×C₂²⋊C₄	C₂²×C₃	semidirect
194. #953	C₂²×C₃	semidirect
196. C₂×#217	C₂²×C₃	semidirect
197. #940	C₂²×C₃	semidirect
198. #939	C₂²×C₃	semidirect
199. #937	C₂²×C₃	semidirect
200. C₂×(C₂×D₃)⋊C₄	C₂²×C₃	semidirect
201. C₂×(C₂×D₃)⋊C₄	C₂²×C₃	semidirect
202. C₂×Dic₃⋊C₄	C₂²×C₃	semidirect
203. C₂×C₄×Dic₃	C₂²×C₃	semidirect
204. #885	C₂²×C₃	semidirect
205. #884	C₂²×C₃	semidirect
206. #882	C₂²×C₃	semidirect
207. #877	C₂²×C₃	semidirect
249. C₂×C₃×Dic₃	C₂×D₄	semidirect
267. C₂×#120	C₃×D₃	semidirect
324. C₂×C₃×D₄	C₂²×D₃	semidirect
326. C₂×C₃×D₄	C₂³×C₃	semidirect
353. C₂×#67	C₂³×C₃	semidirect
354. C₂×#67	C₂³×C₃	semidirect
355. C₂×#67	C₂³×C₃	semidirect
357. C₂²×Dic₃	C₃×D₄	semidirect
363. C₂²×Dic₃	C₂³×C₃	semidirect
366. C₂×D₁₂	C₂³×C₃	semidirect
368. C₂×C₄×D₃	C₂³×C₃	semidirect
370. C₂×Dic₆	C₂³×C₃	semidirect
379. C₃×C₂²⋊C₄	C₂²×D₃	semidirect
381. C₃×C₂²⋊C₄	C₂³×C₃	semidirect
384. #217	C₂³×C₃	semidirect
385. (C₂×D₃)⋊C₄	C₂³×C₃	semidirect
386. (C₂×D₃)⋊C₄	C₂³×C₃	semidirect
387. Dic₃⋊C₄	C₂³×C₃	semidirect
388. C₄×Dic₃	C₂³×C₃	semidirect
432. C₂²×D₄	C₂×C₃×D₃	semidirect
443. #120	C₂×C₃×D₃	semidirect
451. C₂×C₂²⋊C₄	C₂×C₃×D₃	semidirect
563. C₂×Dic₃	C₂×C₃×D₄	semidirect
574. C₂×C₃²	#535	semidirect
611. C₂×D₄	C₂²×C₃×D₃	semidirect
630. C₂²⋊C₄	C₂²×C₃×D₃	semidirect
704. C₃²	C₂×#535	semidirect
768. C₂×C₃	#5592	direct (N × H)
769. C₂×C₃	C₃×#535	semidirect
805. C₃	C₂×#5592	direct (N × H)
806. C₃	C₂×C₃×#535	semidirect
812. C₂	C₃×#5592	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×C₃×#67	2
C₂²×C₃×#237	2
C₂×C₃²×#120	2
C₂×C₃×#953	2
C₂×C₃×#940	2
C₂×C₃×#939	2
C₂×C₃×#937	2
C₃×#5592	2
C₂×C₃×#885	2
C₂×C₃×#884	2
C₂×C₃×#882	2
C₂×C₃×#877	2
C₂×C₃×#535	3
C₂×#5592	3

Subgroups — C2×C3×#5592 #11900989

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#5592 #11900989