Subgroups — C₂×C₃×#5531 #11902973

Order 1152.

2413 conjugacy classes of subgroups.

The subgroup lattice has 846 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃²×#117	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×#929	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₃×Dic₃⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#5531	C₂	1	16	yes	maximal, direct product factor
5	C₂×C₃×#898	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₃×#896	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₃×#889	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₃×#889	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₃×#886	C₂	1	1	yes	maximal, characteristic
10	C₂×C₃×#67⋊C₄	C₂	1	1	yes	maximal, characteristic
11	C₂×C₃×#878	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₃×#877	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₃×#876	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₃×#872	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₃×#870	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₃×C₄×Dic₆	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×C₃×#552	—	3	1	no	maximal
18	C₂×#5531	C₃	1	1	yes	maximal, characteristic, direct product factor
19	C₂³×C₃²×C₄	C₂²	1	1	yes	characteristic
20	C₂²×C₃×#67	C₂²	1	1	yes	characteristic
21	C₂³×C₃×Dic₃	C₂²	1	1	yes	characteristic
22	C₂³×C₃×Dic₃	C₂²	1	1	yes	characteristic
23	C₂²×C₃×C₄×D₃	C₂²	1	1	yes	characteristic
24	C₂²×C₃×Dic₆	C₂²	1	1	yes	characteristic
25	C₃²×#117	C₂²	1	8	yes	complemented
26	C₂×C₃²×C₄⋊C₄	C₂²	1	1	yes	characteristic
27	C₂×C₃²×C₄⋊C₄	C₂²	1	1	yes	characteristic
28	C₂×C₃²×C₂²⋊C₄	C₂²	1	1	yes	characteristic
29	C₂×C₃²×C₂²⋊C₄	C₂²	1	1	yes	characteristic
30	C₂×C₃²×C₄²	C₂²	1	1	yes	characteristic
31	C₂×C₃²×C₄²	C₂²	1	1	yes	characteristic
32	C₂×C₃×#217	C₂²	1	1	yes	characteristic
33	C₃×#929	C₂²	1	8	yes	—
34	C₂×C₃×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
35	C₂×C₃×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
36	C₂×C₃×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
37	C₂×C₃×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
38	C₂×C₃×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
39	C₂×C₃×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
40	C₂×C₃×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
41	C₂×C₃×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
42	C₂×C₃×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
43	C₂×C₃×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
44	C₂×C₃×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
45	C₂×C₃×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
46	C₂×C₃×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
47	C₂×C₃×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
48	C₂×C₃×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
49	C₂×C₃×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
50	C₂×C₃×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
51	C₂×C₃×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
52	C₂×C₃×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
53	C₂×C₃×Dic₃⋊C₄	C₂²	1	8	yes	complemented
54	C₂×C₃×C₄×Dic₃	C₂²	1	1	yes	characteristic
55	C₂×C₃×C₄×Dic₃	C₂²	1	1	yes	characteristic
56	C₂×C₃×C₄×Dic₃	C₂²	1	1	yes	characteristic
57	C₃×#898	C₂²	1	8	yes	complemented
58	C₃×#896	C₂²	1	8	yes	complemented
59	C₃×#889	C₂²	1	8	yes	complemented
60	C₃×#889	C₂²	1	8	yes	complemented
61	C₃×#886	C₂²	1	8	yes	—
62	C₃×#67⋊C₄	C₂²	1	8	yes	—
63	C₃×#878	C₂²	1	8	yes	complemented
64	C₃×#877	C₂²	1	8	yes	complemented
65	C₃×#876	C₂²	1	8	yes	complemented
66	C₃×#872	C₂²	1	8	yes	complemented
67	C₃×#870	C₂²	1	8	yes	complemented
68	C₃×C₄×Dic₆	C₂²	1	8	yes	complemented
69	C₃×#552	—	3	16	no	—
70	C₂×C₃×#126	—	3	1	no	—
71	C₂×C₃×#126	—	3	1	no	—
72	C₂×C₃×#125	—	3	1	no	—
73	C₂×C₃×#125	—	3	1	no	—
74	C₂×C₃×#125	—	3	1	no	—
75	C₂×C₃×#123	—	3	1	no	—
76	C₂×C₃×#123	—	3	1	no	—
77	C₂×C₃×C₂²⋊Q₈	—	3	1	no	—
78	C₂×C₃×C₂²⋊Q₈	—	3	1	no	—
79	C₂×C₃×C₄×Q₈	—	3	1	no	—
80	C₂×C₃×C₄×D₄	—	3	1	no	—
81	C₂×C₃×#117	—	2	1	no	—
82	C₂×C₃×#117	—	3	1	no	—
83	C₂×C₃×#117	—	3	1	no	—
84	C₂×C₃×#117	D₃	1	1	yes	characteristic, complemented
85	C₂×C₃×#117	C₂×C₃	1	1	yes	characteristic, complemented
86	C₂²×C₃×C₄⋊C₄	—	3	1	no	—
87	C₂×#929	C₂×C₃	1	1	yes	characteristic
88	C₂²×Dic₃⋊C₄	C₂×C₃	1	1	yes	characteristic, complemented
89	#5531	C₂×C₃	1	16	yes	direct product factor
90	C₂×#898	C₂×C₃	1	1	yes	characteristic, complemented
91	C₂×#896	C₂×C₃	1	1	yes	characteristic, complemented
92	C₂×#889	C₂×C₃	1	1	yes	characteristic, complemented
93	C₂×#889	C₂×C₃	1	1	yes	characteristic, complemented
94	C₂×#886	C₂×C₃	1	1	yes	characteristic
95	C₂×#67⋊C₄	C₂×C₃	1	1	yes	characteristic
96	C₂×#878	C₂×C₃	1	1	yes	characteristic, complemented
97	C₂×#877	C₂×C₃	1	1	yes	characteristic, complemented
98	C₂×#876	C₂×C₃	1	1	yes	characteristic, complemented
99	C₂×#872	C₂×C₃	1	1	yes	characteristic, complemented
100	C₂×#870	C₂×C₃	1	1	yes	characteristic, complemented
101	C₂×C₄×Dic₆	C₂×C₃	1	1	yes	characteristic, complemented
102	C₂⁴×C₃²	C₂³	1	1	yes	characteristic
103	C₂³×C₃×D₃	C₂³	1	1	yes	characteristic
104	C₂²×C₃²×C₄	—	2	4	no	—
105	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
106	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
107	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
108	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
109	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
110	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
111	C₂²×C₃²×C₄	C₂³	1	4	yes	—
112	C₂×C₃×#67	—	2	4	no	—
113	C₂×C₃×#67	C₂³	1	4	yes	—
114	C₂²×C₃×Dic₃	—	2	4	no	—
115	C₂²×C₃×Dic₃	—	2	4	no	—
116	C₂²×C₃×Dic₃	C₂³	1	4	yes	—
117	C₂²×C₃×Dic₃	C₂³	1	4	yes	—
118	C₂²×C₃×Dic₃	C₂³	1	1	yes	characteristic
119	C₂²×C₃×Dic₃	C₂³	1	1	yes	characteristic
120	C₂²×C₃×Dic₃	C₂³	1	1	yes	characteristic
121	C₂²×C₃×Dic₃	C₂³	1	1	yes	characteristic
122	C₂²×C₃×Dic₃	C₂³	1	1	yes	characteristic
123	C₂²×C₃×Dic₃	C₂³	1	1	yes	characteristic
124	C₂²×C₃×Dic₃	C₂³	1	1	yes	characteristic
125	C₂×C₃×C₄×D₃	—	2	4	no	—
126	C₂×C₃×C₄×D₃	C₂³	1	4	yes	—
127	C₂×C₃×Dic₆	—	2	4	no	—
128	C₂×C₃×Dic₆	C₂³	1	4	yes	—
129	C₃²×C₄⋊C₄	C₂³	1	4	yes	—
130	C₃²×C₄⋊C₄	C₂³	1	4	yes	—
131	C₃²×C₂²⋊C₄	C₂³	1	4	yes	—
132	C₃²×C₂²⋊C₄	C₂³	1	4	yes	—
133	C₃²×C₄²	C₂³	1	4	yes	—
134	C₃²×C₄²	C₂³	1	4	yes	—
135	C₃×#217	C₂³	1	4	yes	—
136	C₃×(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
137	C₃×(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
138	C₃×(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
139	C₃×(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
140	C₃×(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
141	C₃×C₄⋊Dic₃	C₂³	1	4	yes	—
142	C₃×C₄⋊Dic₃	C₂³	1	4	yes	—
143	C₃×C₄⋊Dic₃	C₂³	1	4	yes	—
144	C₃×Dic₃⋊C₄	C₂³	1	4	yes	—
145	C₃×Dic₃⋊C₄	C₂³	1	4	yes	—
146	C₃×Dic₃⋊C₄	C₂³	1	4	yes	—
147	C₃×Dic₃⋊C₄	C₂³	1	4	yes	—
148	C₃×Dic₃⋊C₄	C₂³	1	4	yes	—
149	C₃×Dic₃⋊C₄	C₂³	1	4	yes	—
150	C₃×Dic₃⋊C₄	C₂³	1	4	yes	—
151	C₃×Dic₃⋊C₄	C₂³	1	4	yes	—
152	C₃×Dic₃⋊C₄	C₂³	1	4	yes	—
153	C₃×Dic₃⋊C₄	C₂³	1	4	yes	—
154	C₃×Dic₃⋊C₄	C₂³	1	4	yes	—
155	C₃×C₄×Dic₃	C₂³	1	4	yes	—
156	C₃×C₄×Dic₃	C₂³	1	4	yes	—
157	C₃×C₄×Dic₃	C₂³	1	4	yes	—
158	C₂×#552	—	3	1	no	Sylow
159	C₂²×C₃×Q₈	—	3	1	no	—
160	C₂²×C₃×D₄	—	3	1	no	—
161	C₂³×C₃×C₄	—	2	1	no	—
162	C₂³×C₃×C₄	—	3	1	no	—
163	C₂³×C₃×C₄	—	3	1	no	—
164	C₂³×C₃×C₄	—	3	1	no	—
165	C₂³×C₃×C₄	C₂×D₃	1	1	yes	characteristic
166	C₂³×C₃×C₄	C₂²×C₃	1	1	yes	characteristic
167	C₂²×#67	C₂²×C₃	1	1	yes	characteristic
168	C₂³×Dic₃	C₂²×C₃	1	1	yes	characteristic
169	C₂³×Dic₃	C₂²×C₃	1	1	yes	characteristic
170	C₂²×C₄×D₃	C₂²×C₃	1	1	yes	characteristic
171	C₂²×Dic₆	C₂²×C₃	1	1	yes	characteristic
172	C₃×#126	—	3	8	no	—
173	C₃×#126	—	3	8	no	—
174	C₃×#125	—	3	8	no	—
175	C₃×#125	—	3	8	no	—
176	C₃×#125	—	3	8	no	—
177	C₃×#123	—	3	8	no	—
178	C₃×#123	—	3	8	no	—
179	C₃×C₂²⋊Q₈	—	3	8	no	—
180	C₃×C₂²⋊Q₈	—	3	8	no	—
181	C₃×C₄×Q₈	—	3	8	no	—
182	C₃×C₄×D₄	—	3	8	no	—
183	C₃×#117	—	2	8	no	—
184	C₃×#117	—	3	8	no	—
185	C₃×#117	—	3	8	no	—
186	C₃×#117	C₂×D₃	1	8	yes	complemented
187	C₃×#117	C₂²×C₃	1	8	yes	complemented
188	C₂×C₃×C₄⋊C₄	—	2	1	no	—
189	C₂×C₃×C₄⋊C₄	—	2	1	no	—
190	C₂×C₃×C₄⋊C₄	—	3	1	no	—
191	C₂×C₃×C₄⋊C₄	—	3	1	no	—
192	C₂×C₃×C₄⋊C₄	—	3	1	no	—
193	C₂×C₃×C₄⋊C₄	—	3	1	no	—
194	C₂×C₃×C₄⋊C₄	—	3	1	no	—
195	C₂×C₃×C₄⋊C₄	—	3	1	no	—
196	C₂×C₃×C₄⋊C₄	—	3	1	no	—
197	C₂×C₃×C₄⋊C₄	—	3	1	no	—
198	C₂×C₃×C₄⋊C₄	—	3	1	no	—
199	C₂×C₃×C₄⋊C₄	—	3	1	no	—
200	C₂×C₃×C₄⋊C₄	—	3	1	no	—
201	C₂×C₃×C₄⋊C₄	—	3	8	no	—
202	C₂×C₃×C₄⋊C₄	—	3	1	no	—
203	C₂×C₃×C₄⋊C₄	—	3	1	no	—
204	C₂×C₃×C₄⋊C₄	—	3	1	no	—
205	C₂×C₃×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
206	C₂×C₃×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
207	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
208	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
209	C₂×C₃×C₂²⋊C₄	—	2	1	no	—
210	C₂×C₃×C₂²⋊C₄	—	2	1	no	—
211	C₂×C₃×C₂²⋊C₄	—	3	1	no	—
212	C₂×C₃×C₂²⋊C₄	—	3	1	no	—
213	C₂×C₃×C₂²⋊C₄	—	3	1	no	—
214	C₂×C₃×C₂²⋊C₄	—	3	1	no	—
215	C₂×C₃×C₂²⋊C₄	—	3	1	no	—
216	C₂×C₃×C₂²⋊C₄	—	3	1	no	—
217	C₂×C₃×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic
218	C₂×C₃×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic
219	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
220	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
221	C₂×C₃×C₄²	—	2	1	no	—
222	C₂×C₃×C₄²	—	2	1	no	—
223	C₂×C₃×C₄²	—	3	1	no	—
224	C₂×C₃×C₄²	—	3	1	no	—
225	C₂×C₃×C₄²	—	3	1	no	—
226	C₂×C₃×C₄²	C₂×D₃	1	1	yes	characteristic
227	C₂×C₃×C₄²	C₂×D₃	1	1	yes	characteristic
228	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
229	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
230	C₂×#217	C₂²×C₃	1	1	yes	characteristic
231	#929	C₂²×C₃	1	8	yes	—
232	C₂×(C₂×D₃)⋊C₄	C₂²×C₃	1	1	yes	characteristic
233	C₂×(C₂×D₃)⋊C₄	C₂²×C₃	1	1	yes	characteristic
234	C₂×(C₂×D₃)⋊C₄	C₂²×C₃	1	1	yes	characteristic
235	C₂×(C₂×D₃)⋊C₄	C₂²×C₃	1	1	yes	characteristic
236	C₂×(C₂×D₃)⋊C₄	C₂²×C₃	1	1	yes	characteristic
237	C₂×C₄⋊Dic₃	C₂²×C₃	1	1	yes	characteristic
238	C₂×C₄⋊Dic₃	C₂²×C₃	1	1	yes	characteristic
239	C₂×C₄⋊Dic₃	C₂²×C₃	1	1	yes	characteristic
240	C₂×Dic₃⋊C₄	C₂²×C₃	1	1	yes	characteristic
241	C₂×Dic₃⋊C₄	C₂²×C₃	1	1	yes	characteristic
242	C₂×Dic₃⋊C₄	C₂²×C₃	1	1	yes	characteristic
243	C₂×Dic₃⋊C₄	C₂²×C₃	1	1	yes	characteristic
244	C₂×Dic₃⋊C₄	C₂²×C₃	1	1	yes	characteristic
245	C₂×Dic₃⋊C₄	C₂²×C₃	1	1	yes	characteristic
246	C₂×Dic₃⋊C₄	C₂²×C₃	1	1	yes	characteristic
247	C₂×Dic₃⋊C₄	C₂²×C₃	1	1	yes	characteristic
248	C₂×Dic₃⋊C₄	C₂²×C₃	1	1	yes	characteristic
249	C₂×Dic₃⋊C₄	C₂²×C₃	1	1	yes	characteristic
250	C₂×Dic₃⋊C₄	C₂²×C₃	1	1	yes	characteristic
251	C₂×Dic₃⋊C₄	C₂²×C₃	1	8	yes	complemented
252	C₂×C₄×Dic₃	C₂²×C₃	1	1	yes	characteristic
253	C₂×C₄×Dic₃	C₂²×C₃	1	1	yes	characteristic
254	C₂×C₄×Dic₃	C₂²×C₃	1	1	yes	characteristic
255	#898	C₂²×C₃	1	8	yes	complemented
256	#896	C₂²×C₃	1	8	yes	complemented
257	#889	C₂²×C₃	1	8	yes	complemented
258	#889	C₂²×C₃	1	8	yes	complemented
259	#886	C₂²×C₃	1	8	yes	—
260	#67⋊C₄	C₂²×C₃	1	8	yes	—
261	#878	C₂²×C₃	1	8	yes	complemented
262	#877	C₂²×C₃	1	8	yes	complemented
263	#876	C₂²×C₃	1	8	yes	complemented
264	#872	C₂²×C₃	1	8	yes	complemented
265	#870	C₂²×C₃	1	8	yes	complemented
266	C₄×Dic₆	C₂²×C₃	1	8	yes	complemented
267	C₂³×C₃²	—	2	2	no	—
268	C₂³×C₃²	—	2	2	no	—
269	C₂³×C₃²	#41	1	4	yes	—
270	C₂³×C₃²	C₂⁴	1	2	yes	—
271	C₂³×C₃²	C₂⁴	1	1	yes	characteristic
272	C₂²×C₃×D₃	—	2	2	no	—
273	C₂²×C₃×D₃	—	2	2	no	—
274	C₂²×C₃×D₃	—	2	2	no	—
275	C₂²×C₃×D₃	C₂⁴	1	2	yes	—
276	C₂×C₃²×C₄	—	2	8	no	—
277	C₂×C₃²×C₄	—	2	2	no	—
278	C₂×C₃²×C₄	—	2	2	no	—
279	C₂×C₃²×C₄	—	2	2	no	—
280	C₂×C₃²×C₄	—	2	2	no	—
281	C₂×C₃²×C₄	—	2	2	no	—
282	C₂×C₃²×C₄	—	2	2	no	—
283	C₂×C₃²×C₄	C₂⁴	1	2	yes	—
284	C₂×C₃²×C₄	C₂⁴	1	2	yes	—
285	C₂×C₃²×C₄	C₂⁴	1	2	yes	—
286	C₂×C₃²×C₄	C₂⁴	1	2	yes	—
287	C₂×C₃²×C₄	C₂⁴	1	2	yes	—
288	C₂×C₃²×C₄	C₂⁴	1	2	yes	—
289	C₃×#67	—	2	8	no	—
290	C₂×C₃×Dic₃	—	2	2	no	—
291	C₂×C₃×Dic₃	—	2	8	no	—
292	C₂×C₃×Dic₃	—	2	2	no	—
293	C₂×C₃×Dic₃	—	2	2	no	—
294	C₂×C₃×Dic₃	—	2	2	no	—
295	C₂×C₃×Dic₃	—	2	2	no	—
296	C₂×C₃×Dic₃	—	2	2	no	—
297	C₂×C₃×Dic₃	—	2	8	no	—
298	C₂×C₃×Dic₃	#41	1	4	yes	—
299	C₂×C₃×Dic₃	C₂⁴	1	2	yes	—
300	C₂×C₃×Dic₃	C₂⁴	1	2	yes	—
301	C₂×C₃×Dic₃	C₂⁴	1	2	yes	—
302	C₂×C₃×Dic₃	C₂⁴	1	2	yes	—
303	C₂×C₃×Dic₃	C₂⁴	1	2	yes	—
304	C₂×C₃×Dic₃	C₂⁴	1	2	yes	—
305	C₂×C₃×Dic₃	C₂⁴	1	2	yes	—
306	C₃×C₄×D₃	—	2	8	no	—
307	C₃×Dic₆	—	2	8	no	—
308	#552	—	3	16	no	—
309	C₂×#126	—	3	1	no	—
310	C₂×#126	—	3	1	no	—
311	C₂×#125	—	3	1	no	—
312	C₂×#125	—	3	1	no	—
313	C₂×#125	—	3	1	no	—
314	C₂×#123	—	3	1	no	—
315	C₂×#123	—	3	1	no	—
316	C₂×C₂²⋊Q₈	—	3	1	no	—
317	C₂×C₂²⋊Q₈	—	3	1	no	—
318	C₂×C₄×Q₈	—	3	1	no	—
319	C₂×C₄×D₄	—	3	1	no	—
320	C₂×#117	—	3	1	no	—
321	C₂×#117	—	3	1	no	—
322	C₂×#117	C₃×D₃	1	1	yes	characteristic, complemented
323	C₂²×C₄⋊C₄	—	3	1	no	—
324	C₂⁴×C₃	—	2	1	no	—
325	C₂⁴×C₃	—	3	1	no	—
326	C₂⁴×C₃	C₂²×D₃	1	1	yes	characteristic
327	C₂⁴×C₃	C₂³×C₃	1	1	yes	characteristic
328	C₂³×D₃	C₂³×C₃	1	1	yes	characteristic
329	C₂×C₃×Q₈	—	3	4	no	—
330	C₂×C₃×Q₈	—	6	4	no	—
331	C₂×C₃×D₄	—	3	4	no	—
332	C₂×C₃×D₄	—	6	4	no	—
333	C₂²×C₃×C₄	—	2	8	no	—
334	C₂²×C₃×C₄	—	2	4	no	—
335	C₂²×C₃×C₄	—	2	4	no	—
336	C₂²×C₃×C₄	—	2	1	no	—
337	C₂²×C₃×C₄	—	2	1	no	—
338	C₂²×C₃×C₄	—	2	4	no	—
339	C₂²×C₃×C₄	—	2	1	no	—
340	C₂²×C₃×C₄	—	2	1	no	—
341	C₂²×C₃×C₄	—	2	1	no	—
342	C₂²×C₃×C₄	—	2	1	no	—
343	C₂²×C₃×C₄	—	3	1	no	—
344	C₂²×C₃×C₄	—	3	4	no	—
345	C₂²×C₃×C₄	—	3	4	no	—
346	C₂²×C₃×C₄	—	3	1	no	—
347	C₂²×C₃×C₄	—	3	1	no	—
348	C₂²×C₃×C₄	—	3	1	no	—
349	C₂²×C₃×C₄	—	3	1	no	—
350	C₂²×C₃×C₄	—	3	1	no	—
351	C₂²×C₃×C₄	—	3	1	no	—
352	C₂²×C₃×C₄	—	3	4	no	—
353	C₂²×C₃×C₄	—	6	4	no	—
354	C₂²×C₃×C₄	—	6	4	no	—
355	C₂²×C₃×C₄	—	6	4	no	—
356	C₂²×C₃×C₄	C₂²×D₃	1	4	yes	—
357	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
358	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
359	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
360	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
361	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
362	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
363	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
364	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
365	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
366	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
367	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
368	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
369	C₂²×C₃×C₄	C₂³×C₃	1	4	yes	—
370	C₂×#67	—	2	4	no	—
371	C₂×#67	C₂³×C₃	1	4	yes	—
372	C₂²×Dic₃	—	2	4	no	—
373	C₂²×Dic₃	—	2	4	no	—
374	C₂²×Dic₃	C₂³×C₃	1	4	yes	—
375	C₂²×Dic₃	C₂³×C₃	1	4	yes	—
376	C₂²×Dic₃	C₂³×C₃	1	1	yes	characteristic
377	C₂²×Dic₃	C₂³×C₃	1	1	yes	characteristic
378	C₂²×Dic₃	C₂³×C₃	1	1	yes	characteristic
379	C₂²×Dic₃	C₂³×C₃	1	1	yes	characteristic
380	C₂²×Dic₃	C₂³×C₃	1	1	yes	characteristic
381	C₂²×Dic₃	C₂³×C₃	1	1	yes	characteristic
382	C₂²×Dic₃	C₂³×C₃	1	1	yes	characteristic
383	C₂×C₄×D₃	—	2	4	no	—
384	C₂×C₄×D₃	C₂³×C₃	1	4	yes	—
385	C₂×Dic₆	—	2	4	no	—
386	C₂×Dic₆	C₂³×C₃	1	4	yes	—
387	C₃×C₄⋊C₄	—	2	4	no	—
388	C₃×C₄⋊C₄	—	2	4	no	—
389	C₃×C₄⋊C₄	—	3	4	no	—
390	C₃×C₄⋊C₄	—	3	4	no	—
391	C₃×C₄⋊C₄	—	3	4	no	—
392	C₃×C₄⋊C₄	—	3	4	no	—
393	C₃×C₄⋊C₄	—	3	4	no	—
394	C₃×C₄⋊C₄	—	3	4	no	—
395	C₃×C₄⋊C₄	—	3	4	no	—
396	C₃×C₄⋊C₄	—	3	4	no	—
397	C₃×C₄⋊C₄	—	3	4	no	—
398	C₃×C₄⋊C₄	—	3	4	no	—
399	C₃×C₄⋊C₄	—	3	4	no	—
400	C₃×C₄⋊C₄	—	3	4	no	—
401	C₃×C₄⋊C₄	—	3	4	no	—
402	C₃×C₄⋊C₄	—	3	4	no	—
403	C₃×C₄⋊C₄	C₂²×D₃	1	4	yes	—
404	C₃×C₄⋊C₄	C₂²×D₃	1	4	yes	—
405	C₃×C₄⋊C₄	C₂³×C₃	1	4	yes	—
406	C₃×C₄⋊C₄	C₂³×C₃	1	4	yes	—
407	C₃×C₂²⋊C₄	—	2	4	no	—
408	C₃×C₂²⋊C₄	—	2	4	no	—
409	C₃×C₂²⋊C₄	—	3	4	no	—
410	C₃×C₂²⋊C₄	—	3	4	no	—
411	C₃×C₂²⋊C₄	—	3	4	no	—
412	C₃×C₂²⋊C₄	—	3	4	no	—
413	C₃×C₂²⋊C₄	—	3	4	no	—
414	C₃×C₂²⋊C₄	—	3	4	no	—
415	C₃×C₂²⋊C₄	C₂²×D₃	1	4	yes	—
416	C₃×C₂²⋊C₄	C₂²×D₃	1	4	yes	—
417	C₃×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
418	C₃×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
419	C₃×C₄²	—	2	4	no	—
420	C₃×C₄²	—	2	4	no	—
421	C₃×C₄²	—	3	4	no	—
422	C₃×C₄²	—	3	4	no	—
423	C₃×C₄²	—	3	4	no	—
424	C₃×C₄²	C₂²×D₃	1	4	yes	—
425	C₃×C₄²	C₂²×D₃	1	4	yes	—
426	C₃×C₄²	C₂³×C₃	1	4	yes	—
427	C₃×C₄²	C₂³×C₃	1	4	yes	—
428	#217	C₂³×C₃	1	4	yes	—
429	(C₂×D₃)⋊C₄	C₂³×C₃	1	4	yes	—
430	(C₂×D₃)⋊C₄	C₂³×C₃	1	4	yes	—
431	(C₂×D₃)⋊C₄	C₂³×C₃	1	4	yes	—
432	(C₂×D₃)⋊C₄	C₂³×C₃	1	4	yes	—
433	(C₂×D₃)⋊C₄	C₂³×C₃	1	4	yes	—
434	C₄⋊Dic₃	C₂³×C₃	1	4	yes	—
435	C₄⋊Dic₃	C₂³×C₃	1	4	yes	—
436	C₄⋊Dic₃	C₂³×C₃	1	4	yes	—
437	Dic₃⋊C₄	C₂³×C₃	1	4	yes	—
438	Dic₃⋊C₄	C₂³×C₃	1	4	yes	—
439	Dic₃⋊C₄	C₂³×C₃	1	4	yes	—
440	Dic₃⋊C₄	C₂³×C₃	1	4	yes	—
441	Dic₃⋊C₄	C₂³×C₃	1	4	yes	—
442	Dic₃⋊C₄	C₂³×C₃	1	4	yes	—
443	Dic₃⋊C₄	C₂³×C₃	1	4	yes	—
444	Dic₃⋊C₄	C₂³×C₃	1	4	yes	—
445	Dic₃⋊C₄	C₂³×C₃	1	4	yes	—
446	Dic₃⋊C₄	C₂³×C₃	1	4	yes	—
447	Dic₃⋊C₄	C₂³×C₃	1	4	yes	—
448	C₄×Dic₃	C₂³×C₃	1	4	yes	—
449	C₄×Dic₃	C₂³×C₃	1	4	yes	—
450	C₄×Dic₃	C₂³×C₃	1	4	yes	—
451	C₂²×C₃²	—	2	8	no	—
452	C₂²×C₃²	—	2	2	no	—
453	C₂²×C₃²	—	2	2	no	—
454	C₂²×C₃²	C₂×#41	1	4	yes	—
455	C₂²×C₃²	C₂×#41	1	2	yes	—
456	C₂²×C₃²	C₂×#41	1	2	yes	—
457	C₂²×C₃²	2₋¹⁺⁴	1	2	yes	—
458	C₂²×C₃²	C₂⁵	1	1	yes	characteristic
459	C₂×C₃×D₃	—	2	2	no	—
460	C₂×C₃×D₃	—	2	2	no	—
461	C₂×C₃×D₃	—	2	2	no	—
462	C₂×C₃×D₃	—	4	4	no	—
463	C₃²×C₄	—	2	2	no	—
464	C₃²×C₄	—	2	2	no	—
465	C₃²×C₄	—	2	2	no	—
466	C₃²×C₄	—	2	2	no	—
467	C₃²×C₄	—	2	2	no	—
468	C₃²×C₄	—	2	2	no	—
469	C₃×Dic₃	—	2	2	no	—
470	C₃×Dic₃	—	2	2	no	—
471	C₃×Dic₃	—	2	2	no	—
472	C₃×Dic₃	—	2	2	no	—
473	C₃×Dic₃	—	2	2	no	—
474	C₃×Dic₃	—	2	2	no	—
475	C₃×Dic₃	C₂×#41	1	4	yes	—
476	C₂²×Q₈	—	3	1	no	—
477	C₂²×D₄	—	3	1	no	—
478	C₂³×C₄	—	3	1	no	—
479	C₂³×C₄	—	3	1	no	—
480	C₂³×C₄	—	3	1	no	—
481	C₂³×C₄	C₂×C₃×D₃	1	1	yes	characteristic
482	#126	—	3	8	no	—
483	#126	—	3	8	no	—
484	#125	—	3	8	no	—
485	#125	—	3	8	no	—
486	#125	—	3	8	no	—
487	#123	—	3	8	no	—
488	#123	—	3	8	no	—
489	C₂²⋊Q₈	—	3	8	no	—
490	C₂²⋊Q₈	—	3	8	no	—
491	C₄×Q₈	—	3	8	no	—
492	C₄×D₄	—	3	8	no	—
493	#117	—	3	8	no	—
494	#117	—	3	8	no	—
495	#117	C₂×C₃×D₃	1	8	yes	complemented
496	C₂×C₄⋊C₄	—	3	1	no	—
497	C₂×C₄⋊C₄	—	3	1	no	—
498	C₂×C₄⋊C₄	—	3	1	no	—
499	C₂×C₄⋊C₄	—	3	1	no	—
500	C₂×C₄⋊C₄	—	3	8	no	—
501	C₂×C₄⋊C₄	—	3	1	no	—
502	C₂×C₄⋊C₄	—	3	1	no	—
503	C₂×C₄⋊C₄	—	3	1	no	—
504	C₂×C₄⋊C₄	—	3	1	no	—
505	C₂×C₄⋊C₄	—	3	1	no	—
506	C₂×C₄⋊C₄	—	3	1	no	—
507	C₂×C₄⋊C₄	—	3	1	no	—
508	C₂×C₄⋊C₄	—	3	1	no	—
509	C₂×C₄⋊C₄	—	3	1	no	—
510	C₂×C₄⋊C₄	—	3	1	no	—
511	C₂×C₄⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
512	C₂×C₄⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
513	C₂×C₂²⋊C₄	—	3	1	no	—
514	C₂×C₂²⋊C₄	—	3	1	no	—
515	C₂×C₂²⋊C₄	—	3	1	no	—
516	C₂×C₂²⋊C₄	—	3	1	no	—
517	C₂×C₂²⋊C₄	—	3	1	no	—
518	C₂×C₂²⋊C₄	—	3	1	no	—
519	C₂×C₂²⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
520	C₂×C₂²⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
521	C₂×C₄²	—	3	1	no	—
522	C₂×C₄²	—	3	1	no	—
523	C₂×C₄²	—	3	1	no	—
524	C₂×C₄²	C₂×C₃×D₃	1	1	yes	characteristic
525	C₂×C₄²	C₂×C₃×D₃	1	1	yes	characteristic
526	C₂³×C₃	—	2	2	no	—
527	C₂³×C₃	—	2	2	no	—
528	C₂³×C₃	—	2	2	no	—
529	C₂³×C₃	—	2	2	no	—
530	C₂³×C₃	—	2	1	no	—
531	C₂³×C₃	—	2	2	no	—
532	C₂³×C₃	—	2	4	no	—
533	C₂³×C₃	—	3	2	no	—
534	C₂³×C₃	—	4	2	no	—
535	C₂³×C₃	—	4	2	no	—
536	C₂³×C₃	—	6	2	no	—
537	C₂³×C₃	—	6	2	no	—
538	C₂³×C₃	—	6	2	no	—
539	C₂³×C₃	#235	1	4	yes	—
540	C₂³×C₃	C₃×#41	1	4	yes	—
541	C₂³×C₃	C₂³×D₃	1	2	yes	—
542	C₂³×C₃	C₂³×D₃	1	1	yes	characteristic
543	C₂³×C₃	C₂⁴×C₃	1	2	yes	—
544	C₂³×C₃	C₂⁴×C₃	1	1	yes	characteristic
545	C₂²×D₃	—	2	2	no	—
546	C₂²×D₃	—	2	2	no	—
547	C₂²×D₃	—	2	2	no	—
548	C₂²×D₃	C₂⁴×C₃	1	2	yes	—
549	C₃×Q₈	—	6	8	no	—
550	C₃×D₄	—	6	8	no	—
551	C₂×C₃×C₄	—	2	4	no	—
552	C₂×C₃×C₄	—	2	4	no	—
553	C₂×C₃×C₄	—	2	16	no	—
554	C₂×C₃×C₄	—	2	8	no	—
555	C₂×C₃×C₄	—	2	2	no	—
556	C₂×C₃×C₄	—	2	2	no	—
557	C₂×C₃×C₄	—	2	2	no	—
558	C₂×C₃×C₄	—	2	2	no	—
559	C₂×C₃×C₄	—	2	2	no	—
560	C₂×C₃×C₄	—	2	2	no	—
561	C₂×C₃×C₄	—	2	2	no	—
562	C₂×C₃×C₄	—	2	2	no	—
563	C₂×C₃×C₄	—	2	8	no	—
564	C₂×C₃×C₄	—	2	2	no	—
565	C₂×C₃×C₄	—	2	2	no	—
566	C₂×C₃×C₄	—	2	2	no	—
567	C₂×C₃×C₄	—	2	2	no	—
568	C₂×C₃×C₄	—	2	2	no	—
569	C₂×C₃×C₄	—	2	2	no	—
570	C₂×C₃×C₄	—	2	2	no	—
571	C₂×C₃×C₄	—	2	2	no	—
572	C₂×C₃×C₄	—	2	2	no	—
573	C₂×C₃×C₄	—	2	2	no	—
574	C₂×C₃×C₄	—	3	4	no	—
575	C₂×C₃×C₄	—	3	2	no	—
576	C₂×C₃×C₄	—	3	2	no	—
577	C₂×C₃×C₄	—	3	2	no	—
578	C₂×C₃×C₄	—	3	2	no	—
579	C₂×C₃×C₄	—	3	2	no	—
580	C₂×C₃×C₄	—	3	2	no	—
581	C₂×C₃×C₄	—	3	2	no	—
582	C₂×C₃×C₄	—	4	2	no	—
583	C₂×C₃×C₄	—	4	2	no	—
584	C₂×C₃×C₄	—	4	2	no	—
585	C₂×C₃×C₄	—	4	2	no	—
586	C₂×C₃×C₄	—	6	8	no	—
587	C₂×C₃×C₄	—	6	8	no	—
588	C₂×C₃×C₄	—	6	8	no	—
589	C₂×C₃×C₄	—	6	2	no	—
590	C₂×C₃×C₄	—	6	2	no	—
591	C₂×C₃×C₄	—	6	2	no	—
592	C₂×C₃×C₄	—	6	2	no	—
593	C₂×C₃×C₄	—	6	2	no	—
594	C₂×C₃×C₄	—	6	2	no	—
595	C₂×C₃×C₄	C₂³×D₃	1	2	yes	—
596	C₂×C₃×C₄	C₂³×D₃	1	2	yes	—
597	C₂×C₃×C₄	C₂³×D₃	1	2	yes	—
598	C₂×C₃×C₄	C₂³×D₃	1	2	yes	—
599	C₂×C₃×C₄	C₂³×D₃	1	2	yes	—
600	C₂×C₃×C₄	C₂³×D₃	1	2	yes	—
601	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
602	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
603	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
604	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
605	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
606	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
607	#67	—	2	8	no	—
608	C₂×Dic₃	—	2	2	no	—
609	C₂×Dic₃	—	2	8	no	—
610	C₂×Dic₃	—	2	2	no	—
611	C₂×Dic₃	—	2	2	no	—
612	C₂×Dic₃	—	2	2	no	—
613	C₂×Dic₃	—	2	2	no	—
614	C₂×Dic₃	—	2	2	no	—
615	C₂×Dic₃	—	2	8	no	—
616	C₂×Dic₃	C₃×#41	1	4	yes	—
617	C₂×Dic₃	C₂⁴×C₃	1	2	yes	—
618	C₂×Dic₃	C₂⁴×C₃	1	2	yes	—
619	C₂×Dic₃	C₂⁴×C₃	1	2	yes	—
620	C₂×Dic₃	C₂⁴×C₃	1	2	yes	—
621	C₂×Dic₃	C₂⁴×C₃	1	2	yes	—
622	C₂×Dic₃	C₂⁴×C₃	1	2	yes	—
623	C₂×Dic₃	C₂⁴×C₃	1	2	yes	—
624	C₄×D₃	—	2	8	no	—
625	Dic₆	—	2	8	no	—
626	C₂×C₃²	—	2	4	no	—
627	C₂×C₃²	#552	1	4	yes	complemented
628	C₂×C₃²	C₂²×#41	1	1	yes	characteristic
629	C₂×C₃²	C₂²×#41	1	1	yes	characteristic
630	C₂×C₃²	C₂×2₋¹⁺⁴	1	1	yes	characteristic
631	C₃×D₃	—	4	2	no	—
632	C₂⁴	—	3	1	no	—
633	C₂⁴	C₂²×C₃×D₃	1	1	yes	characteristic
634	C₂×Q₈	—	3	4	no	—
635	C₂×Q₈	—	6	4	no	—
636	C₂×D₄	—	3	4	no	—
637	C₂×D₄	—	6	4	no	—
638	C₂²×C₄	—	2	4	no	—
639	C₂²×C₄	—	3	1	no	—
640	C₂²×C₄	—	3	1	no	—
641	C₂²×C₄	—	3	1	no	—
642	C₂²×C₄	—	3	1	no	—
643	C₂²×C₄	—	3	1	no	—
644	C₂²×C₄	—	3	1	no	—
645	C₂²×C₄	—	3	1	no	—
646	C₂²×C₄	—	3	4	no	—
647	C₂²×C₄	—	3	4	no	—
648	C₂²×C₄	—	3	4	no	—
649	C₂²×C₄	—	6	4	no	—
650	C₂²×C₄	—	6	4	no	—
651	C₂²×C₄	—	6	4	no	—
652	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
653	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
654	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
655	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
656	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
657	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
658	C₂²×C₄	C₂²×C₃×D₃	1	4	yes	—
659	C₄⋊C₄	—	3	4	no	—
660	C₄⋊C₄	—	3	4	no	—
661	C₄⋊C₄	—	3	4	no	—
662	C₄⋊C₄	—	3	4	no	—
663	C₄⋊C₄	—	3	4	no	—
664	C₄⋊C₄	—	3	4	no	—
665	C₄⋊C₄	—	3	4	no	—
666	C₄⋊C₄	—	3	4	no	—
667	C₄⋊C₄	—	3	4	no	—
668	C₄⋊C₄	—	3	4	no	—
669	C₄⋊C₄	—	3	4	no	—
670	C₄⋊C₄	—	3	4	no	—
671	C₄⋊C₄	—	3	4	no	—
672	C₄⋊C₄	—	3	4	no	—
673	C₄⋊C₄	C₂²×C₃×D₃	1	4	yes	—
674	C₄⋊C₄	C₂²×C₃×D₃	1	4	yes	—
675	C₂²⋊C₄	—	3	4	no	—
676	C₂²⋊C₄	—	3	4	no	—
677	C₂²⋊C₄	—	3	4	no	—
678	C₂²⋊C₄	—	3	4	no	—
679	C₂²⋊C₄	—	3	4	no	—
680	C₂²⋊C₄	—	3	4	no	—
681	C₂²⋊C₄	C₂²×C₃×D₃	1	4	yes	—
682	C₂²⋊C₄	C₂²×C₃×D₃	1	4	yes	—
683	C₄²	—	3	4	no	—
684	C₄²	—	3	4	no	—
685	C₄²	—	3	4	no	—
686	C₄²	C₂²×C₃×D₃	1	4	yes	—
687	C₄²	C₂²×C₃×D₃	1	4	yes	—
688	C₂²×C₃	—	2	2	no	—
689	C₂²×C₃	—	2	2	no	—
690	C₂²×C₃	—	2	2	no	—
691	C₂²×C₃	—	2	2	no	—
692	C₂²×C₃	—	2	8	no	—
693	C₂²×C₃	—	2	8	no	—
694	C₂²×C₃	—	2	2	no	—
695	C₂²×C₃	—	2	4	no	—
696	C₂²×C₃	—	2	2	no	—
697	C₂²×C₃	—	2	2	no	—
698	C₂²×C₃	—	2	1	no	—
699	C₂²×C₃	—	4	8	no	—
700	C₂²×C₃	—	4	2	no	—
701	C₂²×C₃	—	4	2	no	—
702	C₂²×C₃	—	6	2	no	—
703	C₂²×C₃	—	6	2	no	—
704	C₂²×C₃	—	6	2	no	—
705	C₂²×C₃	—	12	4	no	—
706	C₂²×C₃	C₂×#235	1	4	yes	—
707	C₂²×C₃	C₂×#235	1	2	yes	—
708	C₂²×C₃	D₃×#41	1	2	yes	—
709	C₂²×C₃	#1010	1	2	yes	—
710	C₂²×C₃	C₂×C₃×#41	1	4	yes	—
711	C₂²×C₃	C₂×C₃×#41	1	2	yes	—
712	C₂²×C₃	C₂×C₃×#41	1	2	yes	—
713	C₂²×C₃	C₃×2₋¹⁺⁴	1	2	yes	—
714	C₂²×C₃	C₂⁴×D₃	1	1	yes	characteristic
715	C₂²×C₃	C₂⁵×C₃	1	1	yes	characteristic
716	C₂×D₃	—	2	2	no	—
717	C₂×D₃	—	2	2	no	—
718	C₂×D₃	—	2	2	no	—
719	C₂×D₃	—	4	4	no	—
720	C₃×C₄	—	2	4	no	—
721	C₃×C₄	—	2	4	no	—
722	C₃×C₄	—	2	2	no	—
723	C₃×C₄	—	2	2	no	—
724	C₃×C₄	—	2	2	no	—
725	C₃×C₄	—	2	2	no	—
726	C₃×C₄	—	2	2	no	—
727	C₃×C₄	—	2	2	no	—
728	C₃×C₄	—	2	2	no	—
729	C₃×C₄	—	2	2	no	—
730	C₃×C₄	—	2	2	no	—
731	C₃×C₄	—	2	2	no	—
732	C₃×C₄	—	2	2	no	—
733	C₃×C₄	—	2	2	no	—
734	C₃×C₄	—	3	4	no	—
735	C₃×C₄	—	4	2	no	—
736	C₃×C₄	—	4	2	no	—
737	C₃×C₄	—	4	2	no	—
738	C₃×C₄	—	4	2	no	—
739	C₃×C₄	—	6	2	no	—
740	C₃×C₄	—	6	2	no	—
741	C₃×C₄	—	6	2	no	—
742	C₃×C₄	—	6	2	no	—
743	C₃×C₄	—	6	2	no	—
744	C₃×C₄	—	6	2	no	—
745	Dic₃	—	2	2	no	—
746	Dic₃	—	2	2	no	—
747	Dic₃	—	2	2	no	—
748	Dic₃	—	2	2	no	—
749	Dic₃	—	2	2	no	—
750	Dic₃	—	2	2	no	—
751	Dic₃	C₂×C₃×#41	1	4	yes	—
752	C₃²	C₂×#552	1	1	yes	characteristic, complemented, Sylow
753	C₂³	—	2	2	no	—
754	C₂³	—	2	2	no	—
755	C₂³	—	3	2	no	—
756	C₂³	—	6	2	no	—
757	C₂³	—	6	2	no	—
758	C₂³	—	6	2	no	—
759	C₂³	C₃×#235	1	4	yes	—
760	C₂³	C₂³×C₃×D₃	1	2	yes	—
761	C₂³	C₂³×C₃×D₃	1	1	yes	characteristic
762	Q₈	—	6	8	no	—
763	D₄	—	6	8	no	—
764	C₂×C₄	—	2	8	no	—
765	C₂×C₄	—	2	2	no	—
766	C₂×C₄	—	2	2	no	—
767	C₂×C₄	—	2	2	no	—
768	C₂×C₄	—	2	2	no	—
769	C₂×C₄	—	2	2	no	—
770	C₂×C₄	—	2	2	no	—
771	C₂×C₄	—	3	4	no	—
772	C₂×C₄	—	3	2	no	—
773	C₂×C₄	—	3	2	no	—
774	C₂×C₄	—	3	2	no	—
775	C₂×C₄	—	3	2	no	—
776	C₂×C₄	—	3	2	no	—
777	C₂×C₄	—	3	2	no	—
778	C₂×C₄	—	3	2	no	—
779	C₂×C₄	—	6	8	no	—
780	C₂×C₄	—	6	8	no	—
781	C₂×C₄	—	6	8	no	—
782	C₂×C₄	—	6	2	no	—
783	C₂×C₄	—	6	2	no	—
784	C₂×C₄	—	6	2	no	—
785	C₂×C₄	—	6	2	no	—
786	C₂×C₄	—	6	2	no	—
787	C₂×C₄	—	6	2	no	—
788	C₂×C₄	C₂³×C₃×D₃	1	2	yes	—
789	C₂×C₄	C₂³×C₃×D₃	1	2	yes	—
790	C₂×C₄	C₂³×C₃×D₃	1	2	yes	—
791	C₂×C₄	C₂³×C₃×D₃	1	2	yes	—
792	C₂×C₄	C₂³×C₃×D₃	1	2	yes	—
793	C₂×C₄	C₂³×C₃×D₃	1	2	yes	—
794	C₂×C₃	—	2	4	no	—
795	C₂×C₃	—	2	4	no	—
796	C₂×C₃	—	2	4	no	—
797	C₂×C₃	—	2	1	no	—
798	C₂×C₃	—	2	1	no	—
799	C₂×C₃	—	2	1	no	—
800	C₂×C₃	—	4	4	no	—
801	C₂×C₃	—	12	2	no	—
802	C₂×C₃	#5531	1	4	yes	direct product factor
803	C₂×C₃	C₃×#552	1	4	yes	complemented
804	C₂×C₃	C₂²×#235	1	1	yes	characteristic
805	C₂×C₃	C₂×D₃×#41	1	1	yes	characteristic
806	C₂×C₃	C₂×#1010	1	1	yes	characteristic
807	C₂×C₃	C₂²×C₃×#41	1	1	yes	characteristic
808	C₂×C₃	C₂²×C₃×#41	1	1	yes	characteristic
809	C₂×C₃	C₂×C₃×2₋¹⁺⁴	1	1	yes	characteristic
810	D₃	—	4	2	no	—
811	C₂²	—	2	8	no	—
812	C₂²	—	2	2	no	—
813	C₂²	—	2	2	no	—
814	C₂²	—	6	2	no	—
815	C₂²	—	6	2	no	—
816	C₂²	—	6	2	no	—
817	C₂²	—	12	4	no	—
818	C₂²	C₂×C₃×#235	1	4	yes	—
819	C₂²	C₂×C₃×#235	1	2	yes	—
820	C₂²	C₃×D₃×#41	1	2	yes	—
821	C₂²	C₃×#1010	1	2	yes	—
822	C₂²	C₂⁴×C₃×D₃	1	1	yes	characteristic
823	C₄	—	2	2	no	—
824	C₄	—	2	2	no	—
825	C₄	—	2	2	no	—
826	C₄	—	2	2	no	—
827	C₄	—	2	2	no	—
828	C₄	—	2	2	no	—
829	C₄	—	3	4	no	—
830	C₄	—	6	2	no	—
831	C₄	—	6	2	no	—
832	C₄	—	6	2	no	—
833	C₄	—	6	2	no	—
834	C₄	—	6	2	no	—
835	C₄	—	6	2	no	—
836	C₃	—	2	1	no	—
837	C₃	C₂×#5531	1	1	yes	characteristic, direct product factor
838	C₃	C₂×C₃×#552	1	1	yes	characteristic, complemented
839	C₂	—	2	4	no	—
840	C₂	—	12	2	no	—
841	C₂	C₃×#5531	1	4	yes	direct product factor
842	C₂	C₂²×C₃×#235	1	1	yes	characteristic
843	C₂	C₂×C₃×D₃×#41	1	1	yes	characteristic
844	C₂	C₂×C₃×#1010	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₃	C₂³×D₃
commutator, cosocle	C₂²×C₃	C₂⁵×C₃
Frattini	C₂²	C₂⁴×C₃×D₃
Fitting	C₂×C₃²×#117	C₂
socle	C₂³×C₃²	C₂⁴
prime radical	C₂²×C₃×#67	C₂²
hypercenter	C₂×C₃×#117	D₃
hypocenter	C₃	C₂×C₃×#552
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₃ ◁ C₂×C₃×#117

Complements

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

N	H ≅ G/N	type
1. C₂×C₃²×#117	C₂	semidirect
3. C₂²×C₃×Dic₃⋊C₄	C₂	semidirect
4. C₃×#5531	C₂	direct (N × H)
5. C₂×C₃×#898	C₂	semidirect
6. C₂×C₃×#896	C₂	semidirect
7. C₂×C₃×#889	C₂	semidirect
8. C₂×C₃×#889	C₂	semidirect
11. C₂×C₃×#878	C₂	semidirect
12. C₂×C₃×#877	C₂	semidirect
13. C₂×C₃×#876	C₂	semidirect
14. C₂×C₃×#872	C₂	semidirect
15. C₂×C₃×#870	C₂	semidirect
16. C₂×C₃×C₄×Dic₆	C₂	semidirect
18. C₂×#5531	C₃	direct (N × H)
25. C₃²×#117	C₂²	semidirect
53. C₂×C₃×Dic₃⋊C₄	C₂²	semidirect
57. C₃×#898	C₂²	semidirect
58. C₃×#896	C₂²	semidirect
59. C₃×#889	C₂²	semidirect
60. C₃×#889	C₂²	semidirect
63. C₃×#878	C₂²	semidirect
64. C₃×#877	C₂²	semidirect
65. C₃×#876	C₂²	semidirect
66. C₃×#872	C₂²	semidirect
67. C₃×#870	C₂²	semidirect
68. C₃×C₄×Dic₆	C₂²	semidirect
84. C₂×C₃×#117	D₃	semidirect
85. C₂×C₃×#117	C₂×C₃	semidirect
88. C₂²×Dic₃⋊C₄	C₂×C₃	semidirect
89. #5531	C₂×C₃	direct (N × H)
90. C₂×#898	C₂×C₃	semidirect
91. C₂×#896	C₂×C₃	semidirect
92. C₂×#889	C₂×C₃	semidirect
93. C₂×#889	C₂×C₃	semidirect
96. C₂×#878	C₂×C₃	semidirect
97. C₂×#877	C₂×C₃	semidirect
98. C₂×#876	C₂×C₃	semidirect
99. C₂×#872	C₂×C₃	semidirect
100. C₂×#870	C₂×C₃	semidirect
101. C₂×C₄×Dic₆	C₂×C₃	semidirect
186. C₃×#117	C₂×D₃	semidirect
187. C₃×#117	C₂²×C₃	semidirect
251. C₂×Dic₃⋊C₄	C₂²×C₃	semidirect
255. #898	C₂²×C₃	semidirect
256. #896	C₂²×C₃	semidirect
257. #889	C₂²×C₃	semidirect
258. #889	C₂²×C₃	semidirect
261. #878	C₂²×C₃	semidirect
262. #877	C₂²×C₃	semidirect
263. #876	C₂²×C₃	semidirect
264. #872	C₂²×C₃	semidirect
265. #870	C₂²×C₃	semidirect
266. C₄×Dic₆	C₂²×C₃	semidirect
322. C₂×#117	C₃×D₃	semidirect
495. #117	C₂×C₃×D₃	semidirect
627. C₂×C₃²	#552	semidirect
752. C₃²	C₂×#552	semidirect
802. C₂×C₃	#5531	direct (N × H)
803. C₂×C₃	C₃×#552	semidirect
837. C₃	C₂×#5531	direct (N × H)
838. C₃	C₂×C₃×#552	semidirect
841. C₂	C₃×#5531	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×C₃²×#117	2
C₂×C₃×#929	2
C₂²×C₃×Dic₃⋊C₄	2
C₃×#5531	2
C₂×C₃×#898	2
C₂×C₃×#896	2
C₂×C₃×#889	2
C₂×C₃×#886	2
C₂×C₃×#67⋊C₄	2
C₂×C₃×#878	2
C₂×C₃×#877	2
C₂×C₃×#876	2
C₂×C₃×#872	2
C₂×C₃×#870	2
C₂×C₃×C₄×Dic₆	2
C₂×C₃×#552	3
C₂×#5531	3

Subgroups — C2×C3×#5531 #11902973

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#5531 #11902973