Subgroups — C₂×C₃×#5678 #11901260

Order 1152.

2837 conjugacy classes of subgroups.

The subgroup lattice has 1006 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃²×#124	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×#947	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×#946	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃×#939	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₃×#937	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#5678	C₂	1	16	yes	maximal, direct product factor
7	C₂×C₃×#886	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₃×#884	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₃×#884	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₃×#883	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₃×#882	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₃×#67⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₃×D₃×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₃×#879	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₃×#876	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₃×C₄×D₁₂	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×C₃×#538	—	3	1	no	maximal
18	C₂×#5678	C₃	1	1	yes	maximal, characteristic, direct product factor
19	C₂⁴×C₃×D₃	C₂²	1	1	yes	characteristic
20	C₂²×C₃²×Q₈	C₂²	1	1	yes	characteristic, complemented
21	C₂²×C₃²×D₄	C₂²	1	1	yes	characteristic
22	C₂²×C₃×#67	C₂²	1	1	yes	characteristic
23	C₂²×C₃×#67	C₂²	1	1	yes	characteristic
24	C₂²×C₃×#67	C₂²	1	1	yes	characteristic
25	C₂²×C₃×#67	C₂²	1	1	yes	characteristic, complemented
26	C₂³×C₃×Dic₃	C₂²	1	1	yes	characteristic, complemented
27	C₂²×C₃×D₁₂	C₂²	1	1	yes	characteristic
28	C₂²×C₃×D₁₂	C₂²	1	1	yes	characteristic
29	C₂²×C₃×C₄×D₃	C₂²	1	1	yes	characteristic
30	C₂²×C₃×C₄×D₃	C₂²	1	1	yes	characteristic
31	C₂²×C₃×C₄×D₃	C₂²	1	1	yes	characteristic, complemented
32	C₃²×#124	C₂²	1	8	yes	complemented
33	C₂×C₃²×C₂²⋊C₄	C₂²	1	1	yes	characteristic
34	C₂×C₃²×C₂²⋊C₄	C₂²	1	1	yes	characteristic
35	C₂×C₃²×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
36	C₂×C₃²×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
37	C₂×C₃²×C₄²	C₂²	1	1	yes	characteristic, complemented
38	C₂×C₃×#217	C₂²	1	1	yes	characteristic
39	C₂×C₃×#217	C₂²	1	1	yes	characteristic
40	C₃×#947	C₂²	1	8	yes	complemented
41	C₃×#946	C₂²	1	8	yes	complemented
42	C₃×#939	C₂²	1	8	yes	complemented
43	C₃×#937	C₂²	1	8	yes	complemented
44	C₂×C₃×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
45	C₂×C₃×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
46	C₂×C₃×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
47	C₂×C₃×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
48	C₂×C₃×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
49	C₂×C₃×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
50	C₂×C₃×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic, complemented
51	C₂×C₃×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic, complemented
52	C₂×C₃×C₄⋊Dic₃	C₂²	1	1	yes	characteristic, complemented
53	C₂×C₃×C₄⋊Dic₃	C₂²	1	1	yes	characteristic, complemented
54	C₂×C₃×Dic₃⋊C₄	C₂²	1	1	yes	characteristic, complemented
55	C₂×C₃×Dic₃⋊C₄	C₂²	1	1	yes	characteristic, complemented
56	C₂×C₃×Dic₃⋊C₄	C₂²	1	1	yes	characteristic, complemented
57	C₂×C₃×Dic₃⋊C₄	C₂²	1	1	yes	characteristic, complemented
58	C₂×C₃×C₄×Dic₃	C₂²	1	1	yes	characteristic, complemented
59	C₃×#886	C₂²	1	8	yes	complemented
60	C₃×#884	C₂²	1	8	yes	complemented
61	C₃×#884	C₂²	1	8	yes	complemented
62	C₃×#883	C₂²	1	8	yes	complemented
63	C₃×#882	C₂²	1	8	yes	complemented
64	C₃×#67⋊C₄	C₂²	1	8	yes	complemented
65	C₃×D₃×C₂²⋊C₄	C₂²	1	8	yes	complemented
66	C₃×#879	C₂²	1	8	yes	complemented
67	C₃×#876	C₂²	1	8	yes	complemented
68	C₃×C₄×D₁₂	C₂²	1	8	yes	complemented
69	C₃×#538	—	3	16	no	—
70	C₂×C₃×#126	—	3	1	no	—
71	C₂×C₃×#126	—	3	1	no	—
72	C₂×C₃×#124	—	2	1	no	—
73	C₂×C₃×#124	—	3	1	no	—
74	C₂×C₃×#124	D₃	1	1	yes	characteristic, complemented
75	C₂×C₃×#124	C₂×C₃	1	1	yes	characteristic, complemented
76	C₂×C₃×#123	—	3	1	no	—
77	C₂×C₃×#123	—	3	1	no	—
78	C₂×C₃×C₂²⋊Q₈	—	3	1	no	—
79	C₂×C₃×#121	—	3	1	no	—
80	C₂×C₃×#121	—	3	1	no	—
81	C₂×C₃×#121	—	3	1	no	—
82	C₂×C₃×#120	—	3	1	no	—
83	C₂×C₃×#120	—	3	1	no	—
84	C₂×C₃×C₄×D₄	—	3	1	no	—
85	C₂×C₃×C₄×D₄	—	3	1	no	—
86	C₂²×C₃×C₂²⋊C₄	—	3	1	no	—
87	C₂×#947	C₂×C₃	1	1	yes	characteristic, complemented
88	C₂×#946	C₂×C₃	1	1	yes	characteristic, complemented
89	C₂×#939	C₂×C₃	1	1	yes	characteristic, complemented
90	C₂×#937	C₂×C₃	1	1	yes	characteristic, complemented
91	#5678	C₂×C₃	1	16	yes	direct product factor
92	C₂×#886	C₂×C₃	1	1	yes	characteristic, complemented
93	C₂×#884	C₂×C₃	1	1	yes	characteristic, complemented
94	C₂×#884	C₂×C₃	1	1	yes	characteristic, complemented
95	C₂×#883	C₂×C₃	1	1	yes	characteristic, complemented
96	C₂×#882	C₂×C₃	1	1	yes	characteristic, complemented
97	C₂×#67⋊C₄	C₂×C₃	1	1	yes	characteristic, complemented
98	C₂×D₃×C₂²⋊C₄	C₂×C₃	1	1	yes	characteristic, complemented
99	C₂×#879	C₂×C₃	1	1	yes	characteristic, complemented
100	C₂×#876	C₂×C₃	1	1	yes	characteristic, complemented
101	C₂×C₄×D₁₂	C₂×C₃	1	1	yes	characteristic, complemented
102	C₂⁴×C₃²	C₂³	1	1	yes	characteristic
103	C₂⁴×C₃²	C₂³	1	1	yes	characteristic
104	C₂³×C₃×D₃	—	2	4	no	—
105	C₂³×C₃×D₃	—	4	2	no	—
106	C₂³×C₃×D₃	—	4	2	no	—
107	C₂³×C₃×D₃	C₂³	1	1	yes	characteristic
108	C₂³×C₃×D₃	C₂³	1	1	yes	characteristic
109	C₂³×C₃×D₃	C₂³	1	1	yes	characteristic
110	C₂³×C₃×D₃	C₂³	1	4	yes	—
111	C₂×C₃²×Q₈	—	4	2	no	—
112	C₂×C₃²×Q₈	C₂³	1	4	yes	complemented
113	C₂×C₃²×D₄	—	4	2	no	—
114	C₂×C₃²×D₄	C₂³	1	4	yes	—
115	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
116	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
117	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
118	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
119	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
120	C₂×C₃×#67	—	2	4	no	—
121	C₂×C₃×#67	—	4	2	no	—
122	C₂×C₃×#67	—	4	2	no	—
123	C₂×C₃×#67	—	4	2	no	—
124	C₂×C₃×#67	C₂³	1	4	yes	—
125	C₂×C₃×#67	C₂³	1	4	yes	—
126	C₂×C₃×#67	C₂³	1	4	yes	—
127	C₂×C₃×#67	C₂³	1	4	yes	complemented
128	C₂²×C₃×Dic₃	—	4	2	no	—
129	C₂²×C₃×Dic₃	C₂³	1	1	yes	characteristic
130	C₂²×C₃×Dic₃	C₂³	1	1	yes	characteristic
131	C₂²×C₃×Dic₃	C₂³	1	1	yes	characteristic
132	C₂²×C₃×Dic₃	C₂³	1	1	yes	characteristic
133	C₂²×C₃×Dic₃	C₂³	1	1	yes	characteristic
134	C₂²×C₃×Dic₃	C₂³	1	4	yes	complemented
135	C₂×C₃×D₁₂	—	2	4	no	—
136	C₂×C₃×D₁₂	—	4	2	no	—
137	C₂×C₃×D₁₂	C₂³	1	4	yes	—
138	C₂×C₃×D₁₂	C₂³	1	4	yes	—
139	C₂×C₃×C₄×D₃	—	4	2	no	—
140	C₂×C₃×C₄×D₃	—	4	2	no	—
141	C₂×C₃×C₄×D₃	—	4	2	no	—
142	C₂×C₃×C₄×D₃	C₂³	1	4	yes	—
143	C₂×C₃×C₄×D₃	C₂³	1	4	yes	—
144	C₂×C₃×C₄×D₃	C₂³	1	4	yes	complemented
145	C₃²×C₂²⋊C₄	C₂³	1	4	yes	—
146	C₃²×C₂²⋊C₄	C₂³	1	4	yes	—
147	C₃²×C₂²⋊C₄	C₂³	1	4	yes	complemented
148	C₃²×C₂²⋊C₄	C₂³	1	4	yes	complemented
149	C₃²×C₄²	C₂³	1	4	yes	complemented
150	C₃×#217	C₂³	1	4	yes	—
151	C₃×#217	C₂³	1	4	yes	—
152	C₃×(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
153	C₃×(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
154	C₃×(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
155	C₃×(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
156	C₃×(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
157	C₃×(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
158	C₃×(C₂×D₃)⋊C₄	C₂³	1	4	yes	complemented
159	C₃×(C₂×D₃)⋊C₄	C₂³	1	4	yes	complemented
160	C₃×C₄⋊Dic₃	C₂³	1	4	yes	complemented
161	C₃×C₄⋊Dic₃	C₂³	1	4	yes	complemented
162	C₃×Dic₃⋊C₄	C₂³	1	4	yes	complemented
163	C₃×Dic₃⋊C₄	C₂³	1	4	yes	complemented
164	C₃×Dic₃⋊C₄	C₂³	1	4	yes	complemented
165	C₃×Dic₃⋊C₄	C₂³	1	4	yes	complemented
166	C₃×C₄×Dic₃	C₂³	1	4	yes	complemented
167	C₂×#538	—	3	1	no	Sylow
168	C₂⁵×C₃	—	3	1	no	—
169	C₂⁴×D₃	C₂²×C₃	1	1	yes	characteristic
170	C₂²×C₃×Q₈	—	2	1	no	—
171	C₂²×C₃×Q₈	C₂×D₃	1	1	yes	characteristic, complemented
172	C₂²×C₃×Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
173	C₂²×C₃×D₄	—	2	1	no	—
174	C₂²×C₃×D₄	—	3	1	no	—
175	C₂²×C₃×D₄	—	3	1	no	—
176	C₂²×C₃×D₄	—	3	1	no	—
177	C₂²×C₃×D₄	—	3	1	no	—
178	C₂²×C₃×D₄	—	3	1	no	—
179	C₂²×C₃×D₄	—	3	1	no	—
180	C₂²×C₃×D₄	C₂×D₃	1	1	yes	characteristic
181	C₂²×C₃×D₄	C₂²×C₃	1	1	yes	characteristic
182	C₂³×C₃×C₄	—	3	1	no	—
183	C₂³×C₃×C₄	—	3	1	no	—
184	C₂³×C₃×C₄	—	3	1	no	—
185	C₂³×C₃×C₄	—	3	1	no	—
186	C₂²×#67	C₂²×C₃	1	1	yes	characteristic
187	C₂²×#67	C₂²×C₃	1	1	yes	characteristic
188	C₂²×#67	C₂²×C₃	1	1	yes	characteristic
189	C₂²×#67	C₂²×C₃	1	1	yes	characteristic, complemented
190	C₂³×Dic₃	C₂²×C₃	1	1	yes	characteristic, complemented
191	C₂²×D₁₂	C₂²×C₃	1	1	yes	characteristic
192	C₂²×D₁₂	C₂²×C₃	1	1	yes	characteristic
193	C₂²×C₄×D₃	C₂²×C₃	1	1	yes	characteristic
194	C₂²×C₄×D₃	C₂²×C₃	1	1	yes	characteristic
195	C₂²×C₄×D₃	C₂²×C₃	1	1	yes	characteristic, complemented
196	C₃×#126	—	3	8	no	—
197	C₃×#126	—	3	8	no	—
198	C₃×#124	—	2	8	no	—
199	C₃×#124	—	3	8	no	—
200	C₃×#124	C₂×D₃	1	8	yes	complemented
201	C₃×#124	C₂²×C₃	1	8	yes	complemented
202	C₃×#123	—	3	8	no	—
203	C₃×#123	—	3	8	no	—
204	C₃×C₂²⋊Q₈	—	3	8	no	—
205	C₃×#121	—	3	8	no	—
206	C₃×#121	—	3	8	no	—
207	C₃×#121	—	3	8	no	—
208	C₃×#120	—	3	8	no	—
209	C₃×#120	—	3	8	no	—
210	C₃×C₄×D₄	—	3	8	no	—
211	C₃×C₄×D₄	—	3	8	no	—
212	C₂×C₃×C₄⋊C₄	—	3	1	no	—
213	C₂×C₃×C₄⋊C₄	—	3	1	no	—
214	C₂×C₃×C₄⋊C₄	—	3	1	no	—
215	C₂×C₃×C₄⋊C₄	—	3	1	no	—
216	C₂×C₃×C₄⋊C₄	—	3	1	no	—
217	C₂×C₃×C₄⋊C₄	—	3	1	no	—
218	C₂×C₃×C₂²⋊C₄	—	2	1	no	—
219	C₂×C₃×C₂²⋊C₄	—	2	1	no	—
220	C₂×C₃×C₂²⋊C₄	—	2	1	no	—
221	C₂×C₃×C₂²⋊C₄	—	2	1	no	—
222	C₂×C₃×C₂²⋊C₄	—	3	1	no	—
223	C₂×C₃×C₂²⋊C₄	—	3	1	no	—
224	C₂×C₃×C₂²⋊C₄	—	3	1	no	—
225	C₂×C₃×C₂²⋊C₄	—	3	1	no	—
226	C₂×C₃×C₂²⋊C₄	—	3	1	no	—
227	C₂×C₃×C₂²⋊C₄	—	3	1	no	—
228	C₂×C₃×C₂²⋊C₄	—	3	1	no	—
229	C₂×C₃×C₂²⋊C₄	—	3	1	no	—
230	C₂×C₃×C₂²⋊C₄	—	3	1	no	—
231	C₂×C₃×C₂²⋊C₄	—	3	1	no	—
232	C₂×C₃×C₂²⋊C₄	—	3	8	no	—
233	C₂×C₃×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic
234	C₂×C₃×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic
235	C₂×C₃×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic, complemented
236	C₂×C₃×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic, complemented
237	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
238	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
239	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
240	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
241	C₂×C₃×C₄²	—	2	1	no	—
242	C₂×C₃×C₄²	—	3	1	no	—
243	C₂×C₃×C₄²	C₂×D₃	1	1	yes	characteristic, complemented
244	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic, complemented
245	C₂×#217	C₂²×C₃	1	1	yes	characteristic
246	C₂×#217	C₂²×C₃	1	1	yes	characteristic
247	#947	C₂²×C₃	1	8	yes	complemented
248	#946	C₂²×C₃	1	8	yes	complemented
249	#939	C₂²×C₃	1	8	yes	complemented
250	#937	C₂²×C₃	1	8	yes	complemented
251	C₂×(C₂×D₃)⋊C₄	C₂²×C₃	1	1	yes	characteristic
252	C₂×(C₂×D₃)⋊C₄	C₂²×C₃	1	1	yes	characteristic
253	C₂×(C₂×D₃)⋊C₄	C₂²×C₃	1	1	yes	characteristic
254	C₂×(C₂×D₃)⋊C₄	C₂²×C₃	1	1	yes	characteristic
255	C₂×(C₂×D₃)⋊C₄	C₂²×C₃	1	1	yes	characteristic
256	C₂×(C₂×D₃)⋊C₄	C₂²×C₃	1	1	yes	characteristic
257	C₂×(C₂×D₃)⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
258	C₂×(C₂×D₃)⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
259	C₂×C₄⋊Dic₃	C₂²×C₃	1	1	yes	characteristic, complemented
260	C₂×C₄⋊Dic₃	C₂²×C₃	1	1	yes	characteristic, complemented
261	C₂×Dic₃⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
262	C₂×Dic₃⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
263	C₂×Dic₃⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
264	C₂×Dic₃⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
265	C₂×C₄×Dic₃	C₂²×C₃	1	1	yes	characteristic, complemented
266	#886	C₂²×C₃	1	8	yes	complemented
267	#884	C₂²×C₃	1	8	yes	complemented
268	#884	C₂²×C₃	1	8	yes	complemented
269	#883	C₂²×C₃	1	8	yes	complemented
270	#882	C₂²×C₃	1	8	yes	complemented
271	#67⋊C₄	C₂²×C₃	1	8	yes	complemented
272	D₃×C₂²⋊C₄	C₂²×C₃	1	8	yes	complemented
273	#879	C₂²×C₃	1	8	yes	complemented
274	#876	C₂²×C₃	1	8	yes	complemented
275	C₄×D₁₂	C₂²×C₃	1	8	yes	complemented
276	C₂³×C₃²	—	2	2	no	—
277	C₂³×C₃²	—	2	2	no	—
278	C₂³×C₃²	—	2	2	no	—
279	C₂³×C₃²	—	2	2	no	—
280	C₂³×C₃²	—	2	2	no	—
281	C₂³×C₃²	—	2	2	no	—
282	C₂³×C₃²	C₂⁴	1	2	yes	—
283	C₂³×C₃²	C₂⁴	1	2	yes	—
284	C₂³×C₃²	C₂⁴	1	1	yes	characteristic
285	C₂²×C₃×D₃	—	2	2	no	—
286	C₂²×C₃×D₃	—	2	2	no	—
287	C₂²×C₃×D₃	—	2	2	no	—
288	C₂²×C₃×D₃	—	2	2	no	—
289	C₂²×C₃×D₃	—	2	2	no	—
290	C₂²×C₃×D₃	—	2	2	no	—
291	C₂²×C₃×D₃	—	2	2	no	—
292	C₂²×C₃×D₃	—	2	2	no	—
293	C₂²×C₃×D₃	—	2	8	no	—
294	C₂²×C₃×D₃	—	4	4	no	—
295	C₂²×C₃×D₃	—	4	4	no	—
296	C₂²×C₃×D₃	—	4	16	no	—
297	C₂²×C₃×D₃	#41	1	4	yes	—
298	C₂²×C₃×D₃	C₂⁴	1	2	yes	—
299	C₂²×C₃×D₃	C₂⁴	1	2	yes	—
300	C₂²×C₃×D₃	C₂⁴	1	2	yes	—
301	C₃²×Q₈	—	4	4	no	—
302	C₃²×D₄	—	4	4	no	—
303	C₂×C₃²×C₄	—	2	2	no	—
304	C₂×C₃²×C₄	—	2	2	no	—
305	C₂×C₃²×C₄	—	2	2	no	—
306	C₂×C₃²×C₄	—	2	2	no	—
307	C₂×C₃²×C₄	—	2	2	no	—
308	C₂×C₃²×C₄	C₂⁴	1	2	yes	—
309	C₂×C₃²×C₄	C₂⁴	1	2	yes	—
310	C₂×C₃²×C₄	C₂⁴	1	2	yes	—
311	C₂×C₃²×C₄	C₂⁴	1	2	yes	—
312	C₂×C₃²×C₄	C₂⁴	1	2	yes	—
313	C₃×#67	—	2	8	no	—
314	C₃×#67	—	4	4	no	—
315	C₃×#67	—	4	4	no	—
316	C₃×#67	—	4	4	no	—
317	C₂×C₃×Dic₃	—	2	2	no	—
318	C₂×C₃×Dic₃	—	2	2	no	—
319	C₂×C₃×Dic₃	—	2	2	no	—
320	C₂×C₃×Dic₃	—	2	2	no	—
321	C₂×C₃×Dic₃	—	2	2	no	—
322	C₂×C₃×Dic₃	—	4	4	no	—
323	C₂×C₃×Dic₃	C₂⁴	1	2	yes	—
324	C₂×C₃×Dic₃	C₂⁴	1	2	yes	—
325	C₂×C₃×Dic₃	C₂⁴	1	2	yes	—
326	C₂×C₃×Dic₃	C₂⁴	1	2	yes	—
327	C₂×C₃×Dic₃	C₂⁴	1	2	yes	—
328	C₃×D₁₂	—	2	8	no	—
329	C₃×D₁₂	—	4	4	no	—
330	C₃×C₄×D₃	—	4	4	no	—
331	C₃×C₄×D₃	—	4	4	no	—
332	C₃×C₄×D₃	—	4	4	no	—
333	#538	—	3	16	no	—
334	C₂×#126	—	3	1	no	—
335	C₂×#126	—	3	1	no	—
336	C₂×#124	—	3	1	no	—
337	C₂×#124	C₃×D₃	1	1	yes	characteristic, complemented
338	C₂×#123	—	3	1	no	—
339	C₂×#123	—	3	1	no	—
340	C₂×C₂²⋊Q₈	—	3	1	no	—
341	C₂×#121	—	3	1	no	—
342	C₂×#121	—	3	1	no	—
343	C₂×#121	—	3	1	no	—
344	C₂×#120	—	3	1	no	—
345	C₂×#120	—	3	1	no	—
346	C₂×C₄×D₄	—	3	1	no	—
347	C₂×C₄×D₄	—	3	1	no	—
348	C₂²×C₂²⋊C₄	—	3	1	no	—
349	C₂⁴×C₃	—	2	1	no	—
350	C₂⁴×C₃	—	2	1	no	—
351	C₂⁴×C₃	—	3	1	no	—
352	C₂⁴×C₃	—	3	1	no	—
353	C₂⁴×C₃	—	3	1	no	—
354	C₂⁴×C₃	—	3	4	no	—
355	C₂⁴×C₃	—	6	4	no	—
356	C₂⁴×C₃	—	12	2	no	—
357	C₂⁴×C₃	—	12	2	no	—
358	C₂⁴×C₃	C₂²×D₃	1	1	yes	characteristic
359	C₂⁴×C₃	C₂²×D₃	1	1	yes	characteristic
360	C₂⁴×C₃	C₂³×C₃	1	1	yes	characteristic
361	C₂⁴×C₃	C₂³×C₃	1	1	yes	characteristic
362	C₂³×D₃	—	2	4	no	—
363	C₂³×D₃	—	4	2	no	—
364	C₂³×D₃	—	4	2	no	—
365	C₂³×D₃	C₂³×C₃	1	1	yes	characteristic
366	C₂³×D₃	C₂³×C₃	1	1	yes	characteristic
367	C₂³×D₃	C₂³×C₃	1	1	yes	characteristic
368	C₂³×D₃	C₂³×C₃	1	4	yes	—
369	C₂×C₃×Q₈	—	2	4	no	—
370	C₂×C₃×Q₈	—	4	2	no	—
371	C₂×C₃×Q₈	—	4	2	no	—
372	C₂×C₃×Q₈	—	4	4	no	—
373	C₂×C₃×Q₈	C₂²×D₃	1	4	yes	complemented
374	C₂×C₃×Q₈	C₂³×C₃	1	4	yes	complemented
375	C₂×C₃×D₄	—	2	4	no	—
376	C₂×C₃×D₄	—	3	4	no	—
377	C₂×C₃×D₄	—	3	4	no	—
378	C₂×C₃×D₄	—	3	4	no	—
379	C₂×C₃×D₄	—	3	4	no	—
380	C₂×C₃×D₄	—	3	4	no	—
381	C₂×C₃×D₄	—	3	4	no	—
382	C₂×C₃×D₄	—	4	2	no	—
383	C₂×C₃×D₄	—	4	2	no	—
384	C₂×C₃×D₄	—	4	4	no	—
385	C₂×C₃×D₄	—	6	4	no	—
386	C₂×C₃×D₄	—	6	4	no	—
387	C₂×C₃×D₄	—	12	2	no	—
388	C₂×C₃×D₄	—	12	2	no	—
389	C₂×C₃×D₄	—	12	2	no	—
390	C₂×C₃×D₄	—	12	2	no	—
391	C₂×C₃×D₄	C₂²×D₃	1	4	yes	—
392	C₂×C₃×D₄	C₂³×C₃	1	4	yes	—
393	C₂²×C₃×C₄	—	2	1	no	—
394	C₂²×C₃×C₄	—	2	1	no	—
395	C₂²×C₃×C₄	—	2	1	no	—
396	C₂²×C₃×C₄	—	2	1	no	—
397	C₂²×C₃×C₄	—	2	1	no	—
398	C₂²×C₃×C₄	—	3	1	no	—
399	C₂²×C₃×C₄	—	3	1	no	—
400	C₂²×C₃×C₄	—	3	1	no	—
401	C₂²×C₃×C₄	—	3	1	no	—
402	C₂²×C₃×C₄	—	3	1	no	—
403	C₂²×C₃×C₄	—	3	4	no	—
404	C₂²×C₃×C₄	—	3	4	no	—
405	C₂²×C₃×C₄	—	3	4	no	—
406	C₂²×C₃×C₄	—	3	4	no	—
407	C₂²×C₃×C₄	—	12	2	no	—
408	C₂²×C₃×C₄	—	12	2	no	—
409	C₂²×C₃×C₄	—	12	2	no	—
410	C₂²×C₃×C₄	—	12	2	no	—
411	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
412	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
413	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
414	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
415	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
416	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
417	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
418	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
419	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
420	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
421	C₂×#67	—	2	4	no	—
422	C₂×#67	—	4	2	no	—
423	C₂×#67	—	4	2	no	—
424	C₂×#67	—	4	2	no	—
425	C₂×#67	C₂³×C₃	1	4	yes	—
426	C₂×#67	C₂³×C₃	1	4	yes	—
427	C₂×#67	C₂³×C₃	1	4	yes	—
428	C₂×#67	C₂³×C₃	1	4	yes	complemented
429	C₂²×Dic₃	—	4	2	no	—
430	C₂²×Dic₃	C₂³×C₃	1	1	yes	characteristic
431	C₂²×Dic₃	C₂³×C₃	1	1	yes	characteristic
432	C₂²×Dic₃	C₂³×C₃	1	1	yes	characteristic
433	C₂²×Dic₃	C₂³×C₃	1	1	yes	characteristic
434	C₂²×Dic₃	C₂³×C₃	1	1	yes	characteristic
435	C₂²×Dic₃	C₂³×C₃	1	4	yes	complemented
436	C₂×D₁₂	—	2	4	no	—
437	C₂×D₁₂	—	4	2	no	—
438	C₂×D₁₂	C₂³×C₃	1	4	yes	—
439	C₂×D₁₂	C₂³×C₃	1	4	yes	—
440	C₂×C₄×D₃	—	4	2	no	—
441	C₂×C₄×D₃	—	4	2	no	—
442	C₂×C₄×D₃	—	4	2	no	—
443	C₂×C₄×D₃	C₂³×C₃	1	4	yes	—
444	C₂×C₄×D₃	C₂³×C₃	1	4	yes	—
445	C₂×C₄×D₃	C₂³×C₃	1	4	yes	complemented
446	C₃×C₄⋊C₄	—	3	4	no	—
447	C₃×C₄⋊C₄	—	3	4	no	—
448	C₃×C₄⋊C₄	—	3	4	no	—
449	C₃×C₄⋊C₄	—	3	4	no	—
450	C₃×C₄⋊C₄	—	3	4	no	—
451	C₃×C₄⋊C₄	—	3	4	no	—
452	C₃×C₂²⋊C₄	—	2	4	no	—
453	C₃×C₂²⋊C₄	—	2	4	no	—
454	C₃×C₂²⋊C₄	—	2	4	no	—
455	C₃×C₂²⋊C₄	—	2	4	no	—
456	C₃×C₂²⋊C₄	—	3	4	no	—
457	C₃×C₂²⋊C₄	—	3	4	no	—
458	C₃×C₂²⋊C₄	—	3	4	no	—
459	C₃×C₂²⋊C₄	—	3	4	no	—
460	C₃×C₂²⋊C₄	—	3	4	no	—
461	C₃×C₂²⋊C₄	—	3	4	no	—
462	C₃×C₂²⋊C₄	—	3	4	no	—
463	C₃×C₂²⋊C₄	—	3	4	no	—
464	C₃×C₂²⋊C₄	—	3	4	no	—
465	C₃×C₂²⋊C₄	—	3	4	no	—
466	C₃×C₂²⋊C₄	C₂²×D₃	1	4	yes	—
467	C₃×C₂²⋊C₄	C₂²×D₃	1	4	yes	—
468	C₃×C₂²⋊C₄	C₂²×D₃	1	4	yes	complemented
469	C₃×C₂²⋊C₄	C₂²×D₃	1	4	yes	complemented
470	C₃×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
471	C₃×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
472	C₃×C₂²⋊C₄	C₂³×C₃	1	4	yes	complemented
473	C₃×C₂²⋊C₄	C₂³×C₃	1	4	yes	complemented
474	C₃×C₄²	—	2	4	no	—
475	C₃×C₄²	—	3	4	no	—
476	C₃×C₄²	C₂²×D₃	1	4	yes	complemented
477	C₃×C₄²	C₂³×C₃	1	4	yes	complemented
478	#217	C₂³×C₃	1	4	yes	—
479	#217	C₂³×C₃	1	4	yes	—
480	(C₂×D₃)⋊C₄	C₂³×C₃	1	4	yes	—
481	(C₂×D₃)⋊C₄	C₂³×C₃	1	4	yes	—
482	(C₂×D₃)⋊C₄	C₂³×C₃	1	4	yes	—
483	(C₂×D₃)⋊C₄	C₂³×C₃	1	4	yes	—
484	(C₂×D₃)⋊C₄	C₂³×C₃	1	4	yes	—
485	(C₂×D₃)⋊C₄	C₂³×C₃	1	4	yes	—
486	(C₂×D₃)⋊C₄	C₂³×C₃	1	4	yes	complemented
487	(C₂×D₃)⋊C₄	C₂³×C₃	1	4	yes	complemented
488	C₄⋊Dic₃	C₂³×C₃	1	4	yes	complemented
489	C₄⋊Dic₃	C₂³×C₃	1	4	yes	complemented
490	Dic₃⋊C₄	C₂³×C₃	1	4	yes	complemented
491	Dic₃⋊C₄	C₂³×C₃	1	4	yes	complemented
492	Dic₃⋊C₄	C₂³×C₃	1	4	yes	complemented
493	Dic₃⋊C₄	C₂³×C₃	1	4	yes	complemented
494	C₄×Dic₃	C₂³×C₃	1	4	yes	complemented
495	C₂²×C₃²	—	2	2	no	—
496	C₂²×C₃²	—	2	2	no	—
497	C₂²×C₃²	—	2	2	no	—
498	C₂²×C₃²	—	2	2	no	—
499	C₂²×C₃²	—	2	2	no	—
500	C₂²×C₃²	—	2	2	no	—
501	C₂²×C₃²	—	4	4	no	—
502	C₂²×C₃²	—	4	4	no	—
503	C₂²×C₃²	C₂×#41	1	2	yes	—
504	C₂²×C₃²	H(5,𝔽₂)	1	2	yes	—
505	C₂²×C₃²	H(5,𝔽₂)	1	2	yes	—
506	C₂²×C₃²	C₂⁵	1	1	yes	characteristic
507	C₂×C₃×D₃	—	2	8	no	—
508	C₂×C₃×D₃	—	2	2	no	—
509	C₂×C₃×D₃	—	2	2	no	—
510	C₂×C₃×D₃	—	2	2	no	—
511	C₂×C₃×D₃	—	2	2	no	—
512	C₂×C₃×D₃	—	2	2	no	—
513	C₂×C₃×D₃	—	2	2	no	—
514	C₂×C₃×D₃	—	2	2	no	—
515	C₂×C₃×D₃	—	2	2	no	—
516	C₂×C₃×D₃	—	4	16	no	—
517	C₂×C₃×D₃	—	4	4	no	—
518	C₂×C₃×D₃	—	4	4	no	—
519	C₂×C₃×D₃	C₂×#41	1	4	yes	—
520	C₃²×C₄	—	2	2	no	—
521	C₃²×C₄	—	2	2	no	—
522	C₃²×C₄	—	2	2	no	—
523	C₃²×C₄	—	2	2	no	—
524	C₃²×C₄	—	2	2	no	—
525	C₃×Dic₃	—	2	2	no	—
526	C₃×Dic₃	—	2	2	no	—
527	C₃×Dic₃	—	2	2	no	—
528	C₃×Dic₃	—	2	2	no	—
529	C₃×Dic₃	—	2	2	no	—
530	C₂⁵	—	3	1	no	—
531	C₂²×Q₈	C₂×C₃×D₃	1	1	yes	characteristic, complemented
532	C₂²×D₄	—	3	1	no	—
533	C₂²×D₄	—	3	1	no	—
534	C₂²×D₄	—	3	1	no	—
535	C₂²×D₄	—	3	1	no	—
536	C₂²×D₄	—	3	1	no	—
537	C₂²×D₄	—	3	1	no	—
538	C₂²×D₄	C₂×C₃×D₃	1	1	yes	characteristic
539	C₂³×C₄	—	3	1	no	—
540	C₂³×C₄	—	3	1	no	—
541	C₂³×C₄	—	3	1	no	—
542	C₂³×C₄	—	3	1	no	—
543	#126	—	3	8	no	—
544	#126	—	3	8	no	—
545	#124	—	3	8	no	—
546	#124	C₂×C₃×D₃	1	8	yes	complemented
547	#123	—	3	8	no	—
548	#123	—	3	8	no	—
549	C₂²⋊Q₈	—	3	8	no	—
550	#121	—	3	8	no	—
551	#121	—	3	8	no	—
552	#121	—	3	8	no	—
553	#120	—	3	8	no	—
554	#120	—	3	8	no	—
555	C₄×D₄	—	3	8	no	—
556	C₄×D₄	—	3	8	no	—
557	C₂×C₄⋊C₄	—	3	1	no	—
558	C₂×C₄⋊C₄	—	3	1	no	—
559	C₂×C₄⋊C₄	—	3	1	no	—
560	C₂×C₄⋊C₄	—	3	1	no	—
561	C₂×C₄⋊C₄	—	3	1	no	—
562	C₂×C₄⋊C₄	—	3	1	no	—
563	C₂×C₂²⋊C₄	—	3	1	no	—
564	C₂×C₂²⋊C₄	—	3	1	no	—
565	C₂×C₂²⋊C₄	—	3	1	no	—
566	C₂×C₂²⋊C₄	—	3	1	no	—
567	C₂×C₂²⋊C₄	—	3	1	no	—
568	C₂×C₂²⋊C₄	—	3	1	no	—
569	C₂×C₂²⋊C₄	—	3	1	no	—
570	C₂×C₂²⋊C₄	—	3	1	no	—
571	C₂×C₂²⋊C₄	—	3	1	no	—
572	C₂×C₂²⋊C₄	—	3	1	no	—
573	C₂×C₂²⋊C₄	—	3	8	no	—
574	C₂×C₂²⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
575	C₂×C₂²⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
576	C₂×C₂²⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic, complemented
577	C₂×C₂²⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic, complemented
578	C₂×C₄²	—	3	1	no	—
579	C₂×C₄²	C₂×C₃×D₃	1	1	yes	characteristic, complemented
580	C₂³×C₃	—	2	2	no	—
581	C₂³×C₃	—	2	2	no	—
582	C₂³×C₃	—	2	2	no	—
583	C₂³×C₃	—	2	2	no	—
584	C₂³×C₃	—	2	2	no	—
585	C₂³×C₃	—	2	2	no	—
586	C₂³×C₃	—	2	2	no	—
587	C₂³×C₃	—	2	2	no	—
588	C₂³×C₃	—	2	2	no	—
589	C₂³×C₃	—	2	2	no	—
590	C₂³×C₃	—	2	2	no	—
591	C₂³×C₃	—	2	2	no	—
592	C₂³×C₃	—	2	1	no	—
593	C₂³×C₃	—	2	2	no	—
594	C₂³×C₃	—	2	2	no	—
595	C₂³×C₃	—	3	4	no	—
596	C₂³×C₃	—	3	2	no	—
597	C₂³×C₃	—	3	2	no	—
598	C₂³×C₃	—	3	2	no	—
599	C₂³×C₃	—	4	2	no	—
600	C₂³×C₃	—	4	2	no	—
601	C₂³×C₃	—	4	2	no	—
602	C₂³×C₃	—	4	2	no	—
603	C₂³×C₃	—	4	2	no	—
604	C₂³×C₃	—	4	2	no	—
605	C₂³×C₃	—	6	8	no	—
606	C₂³×C₃	—	6	2	no	—
607	C₂³×C₃	—	6	2	no	—
608	C₂³×C₃	—	6	2	no	—
609	C₂³×C₃	—	6	2	no	—
610	C₂³×C₃	—	6	2	no	—
611	C₂³×C₃	—	6	2	no	—
612	C₂³×C₃	—	6	2	no	—
613	C₂³×C₃	—	6	2	no	—
614	C₂³×C₃	—	12	4	no	—
615	C₂³×C₃	—	12	4	no	—
616	C₂³×C₃	—	12	16	no	—
617	C₂³×C₃	C₂³×D₃	1	2	yes	—
618	C₂³×C₃	C₂³×D₃	1	2	yes	—
619	C₂³×C₃	C₂³×D₃	1	1	yes	characteristic
620	C₂³×C₃	C₂⁴×C₃	1	2	yes	—
621	C₂³×C₃	C₂⁴×C₃	1	2	yes	—
622	C₂³×C₃	C₂⁴×C₃	1	1	yes	characteristic
623	C₂²×D₃	—	2	2	no	—
624	C₂²×D₃	—	2	2	no	—
625	C₂²×D₃	—	2	2	no	—
626	C₂²×D₃	—	2	2	no	—
627	C₂²×D₃	—	2	2	no	—
628	C₂²×D₃	—	2	2	no	—
629	C₂²×D₃	—	2	2	no	—
630	C₂²×D₃	—	2	2	no	—
631	C₂²×D₃	—	2	8	no	—
632	C₂²×D₃	—	4	4	no	—
633	C₂²×D₃	—	4	4	no	—
634	C₂²×D₃	—	4	16	no	—
635	C₂²×D₃	C₃×#41	1	4	yes	—
636	C₂²×D₃	C₂⁴×C₃	1	2	yes	—
637	C₂²×D₃	C₂⁴×C₃	1	2	yes	—
638	C₂²×D₃	C₂⁴×C₃	1	2	yes	—
639	C₃×Q₈	—	4	4	no	—
640	C₃×Q₈	—	4	4	no	—
641	C₃×Q₈	—	4	8	no	—
642	C₃×D₄	—	4	4	no	—
643	C₃×D₄	—	4	4	no	—
644	C₃×D₄	—	4	8	no	—
645	C₃×D₄	—	6	8	no	—
646	C₃×D₄	—	6	8	no	—
647	C₃×D₄	—	12	4	no	—
648	C₃×D₄	—	12	4	no	—
649	C₃×D₄	—	12	4	no	—
650	C₃×D₄	—	12	4	no	—
651	C₂×C₃×C₄	—	2	4	no	—
652	C₂×C₃×C₄	—	2	2	no	—
653	C₂×C₃×C₄	—	2	2	no	—
654	C₂×C₃×C₄	—	2	2	no	—
655	C₂×C₃×C₄	—	2	2	no	—
656	C₂×C₃×C₄	—	2	2	no	—
657	C₂×C₃×C₄	—	2	2	no	—
658	C₂×C₃×C₄	—	2	2	no	—
659	C₂×C₃×C₄	—	2	2	no	—
660	C₂×C₃×C₄	—	2	2	no	—
661	C₂×C₃×C₄	—	2	2	no	—
662	C₂×C₃×C₄	—	2	2	no	—
663	C₂×C₃×C₄	—	2	2	no	—
664	C₂×C₃×C₄	—	2	2	no	—
665	C₂×C₃×C₄	—	2	2	no	—
666	C₂×C₃×C₄	—	2	2	no	—
667	C₂×C₃×C₄	—	3	2	no	—
668	C₂×C₃×C₄	—	3	2	no	—
669	C₂×C₃×C₄	—	3	2	no	—
670	C₂×C₃×C₄	—	3	2	no	—
671	C₂×C₃×C₄	—	3	2	no	—
672	C₂×C₃×C₄	—	4	2	no	—
673	C₂×C₃×C₄	—	4	2	no	—
674	C₂×C₃×C₄	—	4	2	no	—
675	C₂×C₃×C₄	—	4	2	no	—
676	C₂×C₃×C₄	—	6	2	no	—
677	C₂×C₃×C₄	—	6	2	no	—
678	C₂×C₃×C₄	—	6	2	no	—
679	C₂×C₃×C₄	—	6	2	no	—
680	C₂×C₃×C₄	—	6	2	no	—
681	C₂×C₃×C₄	—	12	4	no	—
682	C₂×C₃×C₄	—	12	4	no	—
683	C₂×C₃×C₄	—	12	4	no	—
684	C₂×C₃×C₄	—	12	4	no	—
685	C₂×C₃×C₄	C₂³×D₃	1	2	yes	—
686	C₂×C₃×C₄	C₂³×D₃	1	2	yes	—
687	C₂×C₃×C₄	C₂³×D₃	1	2	yes	—
688	C₂×C₃×C₄	C₂³×D₃	1	2	yes	—
689	C₂×C₃×C₄	C₂³×D₃	1	2	yes	—
690	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
691	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
692	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
693	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
694	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
695	#67	—	2	8	no	—
696	#67	—	4	4	no	—
697	#67	—	4	4	no	—
698	#67	—	4	4	no	—
699	C₂×Dic₃	—	2	2	no	—
700	C₂×Dic₃	—	2	2	no	—
701	C₂×Dic₃	—	2	2	no	—
702	C₂×Dic₃	—	2	2	no	—
703	C₂×Dic₃	—	2	2	no	—
704	C₂×Dic₃	—	4	4	no	—
705	C₂×Dic₃	C₂⁴×C₃	1	2	yes	—
706	C₂×Dic₃	C₂⁴×C₃	1	2	yes	—
707	C₂×Dic₃	C₂⁴×C₃	1	2	yes	—
708	C₂×Dic₃	C₂⁴×C₃	1	2	yes	—
709	C₂×Dic₃	C₂⁴×C₃	1	2	yes	—
710	D₁₂	—	2	8	no	—
711	D₁₂	—	4	4	no	—
712	C₄×D₃	—	4	4	no	—
713	C₄×D₃	—	4	4	no	—
714	C₄×D₃	—	4	4	no	—
715	C₂×C₃²	—	4	2	no	—
716	C₂×C₃²	—	4	2	no	—
717	C₂×C₃²	#538	1	4	yes	complemented
718	C₂×C₃²	C₂²×#41	1	1	yes	characteristic
719	C₂×C₃²	C₂×H(5,𝔽₂)	1	1	yes	characteristic
720	C₂×C₃²	C₂×H(5,𝔽₂)	1	1	yes	characteristic
721	C₃×D₃	—	2	4	no	—
722	C₃×D₃	—	4	2	no	—
723	C₃×D₃	—	4	2	no	—
724	C₂⁴	—	3	1	no	—
725	C₂⁴	—	3	1	no	—
726	C₂⁴	—	3	1	no	—
727	C₂⁴	—	3	4	no	—
728	C₂⁴	—	6	4	no	—
729	C₂⁴	—	12	2	no	—
730	C₂⁴	—	12	2	no	—
731	C₂⁴	C₂²×C₃×D₃	1	1	yes	characteristic
732	C₂⁴	C₂²×C₃×D₃	1	1	yes	characteristic
733	C₂×Q₈	—	4	2	no	—
734	C₂×Q₈	C₂²×C₃×D₃	1	4	yes	complemented
735	C₂×D₄	—	3	4	no	—
736	C₂×D₄	—	3	4	no	—
737	C₂×D₄	—	3	4	no	—
738	C₂×D₄	—	3	4	no	—
739	C₂×D₄	—	3	4	no	—
740	C₂×D₄	—	3	4	no	—
741	C₂×D₄	—	4	2	no	—
742	C₂×D₄	—	6	4	no	—
743	C₂×D₄	—	6	4	no	—
744	C₂×D₄	—	12	2	no	—
745	C₂×D₄	—	12	2	no	—
746	C₂×D₄	—	12	2	no	—
747	C₂×D₄	—	12	2	no	—
748	C₂×D₄	C₂²×C₃×D₃	1	4	yes	—
749	C₂²×C₄	—	3	1	no	—
750	C₂²×C₄	—	3	1	no	—
751	C₂²×C₄	—	3	1	no	—
752	C₂²×C₄	—	3	1	no	—
753	C₂²×C₄	—	3	1	no	—
754	C₂²×C₄	—	3	4	no	—
755	C₂²×C₄	—	3	4	no	—
756	C₂²×C₄	—	3	4	no	—
757	C₂²×C₄	—	3	4	no	—
758	C₂²×C₄	—	12	2	no	—
759	C₂²×C₄	—	12	2	no	—
760	C₂²×C₄	—	12	2	no	—
761	C₂²×C₄	—	12	2	no	—
762	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
763	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
764	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
765	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
766	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
767	C₄⋊C₄	—	3	4	no	—
768	C₄⋊C₄	—	3	4	no	—
769	C₄⋊C₄	—	3	4	no	—
770	C₄⋊C₄	—	3	4	no	—
771	C₄⋊C₄	—	3	4	no	—
772	C₄⋊C₄	—	3	4	no	—
773	C₂²⋊C₄	—	3	4	no	—
774	C₂²⋊C₄	—	3	4	no	—
775	C₂²⋊C₄	—	3	4	no	—
776	C₂²⋊C₄	—	3	4	no	—
777	C₂²⋊C₄	—	3	4	no	—
778	C₂²⋊C₄	—	3	4	no	—
779	C₂²⋊C₄	—	3	4	no	—
780	C₂²⋊C₄	—	3	4	no	—
781	C₂²⋊C₄	—	3	4	no	—
782	C₂²⋊C₄	—	3	4	no	—
783	C₂²⋊C₄	C₂²×C₃×D₃	1	4	yes	—
784	C₂²⋊C₄	C₂²×C₃×D₃	1	4	yes	—
785	C₂²⋊C₄	C₂²×C₃×D₃	1	4	yes	complemented
786	C₂²⋊C₄	C₂²×C₃×D₃	1	4	yes	complemented
787	C₄²	—	3	4	no	—
788	C₄²	C₂²×C₃×D₃	1	4	yes	complemented
789	C₂²×C₃	—	2	2	no	—
790	C₂²×C₃	—	2	2	no	—
791	C₂²×C₃	—	2	2	no	—
792	C₂²×C₃	—	2	2	no	—
793	C₂²×C₃	—	2	2	no	—
794	C₂²×C₃	—	2	2	no	—
795	C₂²×C₃	—	2	2	no	—
796	C₂²×C₃	—	2	2	no	—
797	C₂²×C₃	—	2	2	no	—
798	C₂²×C₃	—	2	2	no	—
799	C₂²×C₃	—	2	2	no	—
800	C₂²×C₃	—	2	2	no	—
801	C₂²×C₃	—	2	2	no	—
802	C₂²×C₃	—	2	2	no	—
803	C₂²×C₃	—	2	2	no	—
804	C₂²×C₃	—	2	1	no	—
805	C₂²×C₃	—	3	4	no	—
806	C₂²×C₃	—	4	2	no	—
807	C₂²×C₃	—	4	2	no	—
808	C₂²×C₃	—	4	2	no	—
809	C₂²×C₃	—	4	2	no	—
810	C₂²×C₃	—	4	2	no	—
811	C₂²×C₃	—	4	2	no	—
812	C₂²×C₃	—	4	4	no	—
813	C₂²×C₃	—	4	4	no	—
814	C₂²×C₃	—	4	4	no	—
815	C₂²×C₃	—	4	4	no	—
816	C₂²×C₃	—	6	8	no	—
817	C₂²×C₃	—	6	2	no	—
818	C₂²×C₃	—	6	2	no	—
819	C₂²×C₃	—	6	2	no	—
820	C₂²×C₃	—	6	2	no	—
821	C₂²×C₃	—	6	2	no	—
822	C₂²×C₃	—	6	2	no	—
823	C₂²×C₃	—	6	2	no	—
824	C₂²×C₃	—	6	2	no	—
825	C₂²×C₃	—	8	4	no	—
826	C₂²×C₃	—	8	4	no	—
827	C₂²×C₃	—	12	16	no	—
828	C₂²×C₃	—	12	4	no	—
829	C₂²×C₃	—	12	4	no	—
830	C₂²×C₃	#1004	1	2	yes	—
831	C₂²×C₃	D₃×#41	1	2	yes	—
832	C₂²×C₃	#1009	1	2	yes	—
833	C₂²×C₃	C₂×C₃×#41	1	2	yes	—
834	C₂²×C₃	C₃×H(5,𝔽₂)	1	2	yes	—
835	C₂²×C₃	C₃×H(5,𝔽₂)	1	2	yes	—
836	C₂²×C₃	C₂⁴×D₃	1	1	yes	characteristic
837	C₂²×C₃	C₂⁵×C₃	1	1	yes	characteristic
838	C₂×D₃	—	2	2	no	—
839	C₂×D₃	—	2	2	no	—
840	C₂×D₃	—	2	8	no	—
841	C₂×D₃	—	2	2	no	—
842	C₂×D₃	—	2	2	no	—
843	C₂×D₃	—	2	2	no	—
844	C₂×D₃	—	2	2	no	—
845	C₂×D₃	—	2	2	no	—
846	C₂×D₃	—	2	2	no	—
847	C₂×D₃	—	4	16	no	—
848	C₂×D₃	—	4	4	no	—
849	C₂×D₃	—	4	4	no	—
850	C₂×D₃	C₂×C₃×#41	1	4	yes	—
851	C₃×C₄	—	2	4	no	—
852	C₃×C₄	—	2	2	no	—
853	C₃×C₄	—	2	2	no	—
854	C₃×C₄	—	2	2	no	—
855	C₃×C₄	—	2	2	no	—
856	C₃×C₄	—	2	2	no	—
857	C₃×C₄	—	2	2	no	—
858	C₃×C₄	—	2	2	no	—
859	C₃×C₄	—	2	2	no	—
860	C₃×C₄	—	2	2	no	—
861	C₃×C₄	—	2	2	no	—
862	C₃×C₄	—	4	2	no	—
863	C₃×C₄	—	4	2	no	—
864	C₃×C₄	—	4	2	no	—
865	C₃×C₄	—	4	2	no	—
866	C₃×C₄	—	6	2	no	—
867	C₃×C₄	—	6	2	no	—
868	C₃×C₄	—	6	2	no	—
869	C₃×C₄	—	6	2	no	—
870	C₃×C₄	—	6	2	no	—
871	Dic₃	—	2	2	no	—
872	Dic₃	—	2	2	no	—
873	Dic₃	—	2	2	no	—
874	Dic₃	—	2	2	no	—
875	Dic₃	—	2	2	no	—
876	C₃²	C₂×#538	1	1	yes	characteristic, complemented, Sylow
877	C₂³	—	2	2	no	—
878	C₂³	—	2	2	no	—
879	C₂³	—	2	2	no	—
880	C₂³	—	2	2	no	—
881	C₂³	—	2	2	no	—
882	C₂³	—	2	2	no	—
883	C₂³	—	3	4	no	—
884	C₂³	—	3	2	no	—
885	C₂³	—	3	2	no	—
886	C₂³	—	3	2	no	—
887	C₂³	—	6	8	no	—
888	C₂³	—	6	2	no	—
889	C₂³	—	6	2	no	—
890	C₂³	—	6	2	no	—
891	C₂³	—	6	2	no	—
892	C₂³	—	6	2	no	—
893	C₂³	—	6	2	no	—
894	C₂³	—	6	2	no	—
895	C₂³	—	6	2	no	—
896	C₂³	—	12	4	no	—
897	C₂³	—	12	4	no	—
898	C₂³	—	12	16	no	—
899	C₂³	C₂³×C₃×D₃	1	2	yes	—
900	C₂³	C₂³×C₃×D₃	1	2	yes	—
901	C₂³	C₂³×C₃×D₃	1	1	yes	characteristic
902	Q₈	—	4	4	no	—
903	D₄	—	4	4	no	—
904	D₄	—	6	8	no	—
905	D₄	—	6	8	no	—
906	D₄	—	12	4	no	—
907	D₄	—	12	4	no	—
908	D₄	—	12	4	no	—
909	D₄	—	12	4	no	—
910	C₂×C₄	—	2	2	no	—
911	C₂×C₄	—	2	2	no	—
912	C₂×C₄	—	2	2	no	—
913	C₂×C₄	—	2	2	no	—
914	C₂×C₄	—	2	2	no	—
915	C₂×C₄	—	3	2	no	—
916	C₂×C₄	—	3	2	no	—
917	C₂×C₄	—	3	2	no	—
918	C₂×C₄	—	3	2	no	—
919	C₂×C₄	—	3	2	no	—
920	C₂×C₄	—	6	2	no	—
921	C₂×C₄	—	6	2	no	—
922	C₂×C₄	—	6	2	no	—
923	C₂×C₄	—	6	2	no	—
924	C₂×C₄	—	6	2	no	—
925	C₂×C₄	—	12	4	no	—
926	C₂×C₄	—	12	4	no	—
927	C₂×C₄	—	12	4	no	—
928	C₂×C₄	—	12	4	no	—
929	C₂×C₄	C₂³×C₃×D₃	1	2	yes	—
930	C₂×C₄	C₂³×C₃×D₃	1	2	yes	—
931	C₂×C₄	C₂³×C₃×D₃	1	2	yes	—
932	C₂×C₄	C₂³×C₃×D₃	1	2	yes	—
933	C₂×C₄	C₂³×C₃×D₃	1	2	yes	—
934	C₂×C₃	—	2	1	no	—
935	C₂×C₃	—	2	1	no	—
936	C₂×C₃	—	2	1	no	—
937	C₂×C₃	—	2	4	no	—
938	C₂×C₃	—	4	2	no	—
939	C₂×C₃	—	4	2	no	—
940	C₂×C₃	—	4	2	no	—
941	C₂×C₃	—	4	2	no	—
942	C₂×C₃	—	6	4	no	—
943	C₂×C₃	—	8	2	no	—
944	C₂×C₃	—	8	2	no	—
945	C₂×C₃	—	12	2	no	—
946	C₂×C₃	—	12	2	no	—
947	C₂×C₃	#5678	1	4	yes	direct product factor
948	C₂×C₃	C₃×#538	1	4	yes	complemented
949	C₂×C₃	C₂×#1004	1	1	yes	characteristic
950	C₂×C₃	C₂×D₃×#41	1	1	yes	characteristic
951	C₂×C₃	C₂×#1009	1	1	yes	characteristic
952	C₂×C₃	C₂²×C₃×#41	1	1	yes	characteristic
953	C₂×C₃	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
954	C₂×C₃	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
955	D₃	—	2	4	no	—
956	D₃	—	4	2	no	—
957	D₃	—	4	2	no	—
958	C₂²	—	2	2	no	—
959	C₂²	—	2	2	no	—
960	C₂²	—	2	2	no	—
961	C₂²	—	2	2	no	—
962	C₂²	—	2	2	no	—
963	C₂²	—	2	2	no	—
964	C₂²	—	3	4	no	—
965	C₂²	—	4	4	no	—
966	C₂²	—	4	4	no	—
967	C₂²	—	6	2	no	—
968	C₂²	—	6	2	no	—
969	C₂²	—	6	8	no	—
970	C₂²	—	6	2	no	—
971	C₂²	—	6	2	no	—
972	C₂²	—	6	2	no	—
973	C₂²	—	6	2	no	—
974	C₂²	—	6	2	no	—
975	C₂²	—	6	2	no	—
976	C₂²	—	12	16	no	—
977	C₂²	—	12	4	no	—
978	C₂²	—	12	4	no	—
979	C₂²	C₃×#1004	1	2	yes	—
980	C₂²	C₃×D₃×#41	1	2	yes	—
981	C₂²	C₃×#1009	1	2	yes	—
982	C₂²	C₂⁴×C₃×D₃	1	1	yes	characteristic
983	C₄	—	2	2	no	—
984	C₄	—	2	2	no	—
985	C₄	—	2	2	no	—
986	C₄	—	2	2	no	—
987	C₄	—	2	2	no	—
988	C₄	—	6	2	no	—
989	C₄	—	6	2	no	—
990	C₄	—	6	2	no	—
991	C₄	—	6	2	no	—
992	C₄	—	6	2	no	—
993	C₃	—	2	1	no	—
994	C₃	C₂×#5678	1	1	yes	characteristic, direct product factor
995	C₃	C₂×C₃×#538	1	1	yes	characteristic, complemented
996	C₂	—	4	2	no	—
997	C₂	—	4	2	no	—
998	C₂	—	6	4	no	—
999	C₂	—	12	2	no	—
1000	C₂	—	12	2	no	—
1001	C₂	C₃×#5678	1	4	yes	direct product factor
1002	C₂	C₂×C₃×#1004	1	1	yes	characteristic
1003	C₂	C₂×C₃×D₃×#41	1	1	yes	characteristic
1004	C₂	C₂×C₃×#1009	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×#124	C₂
socle	C₂³×C₃²	C₂⁴
hypercenter	C₂×C₃×#124	D₃
hypocenter	C₃	C₂×C₃×#538
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₃ ◁ C₂×C₃×#124

Complements

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

N	H ≅ G/N	type
1. C₂×C₃²×#124	C₂	semidirect
2. C₂×C₃×#947	C₂	semidirect
3. C₂×C₃×#946	C₂	semidirect
4. C₂×C₃×#939	C₂	semidirect
5. C₂×C₃×#937	C₂	semidirect
6. C₃×#5678	C₂	direct (N × H)
7. C₂×C₃×#886	C₂	semidirect
8. C₂×C₃×#884	C₂	semidirect
9. C₂×C₃×#884	C₂	semidirect
10. C₂×C₃×#883	C₂	semidirect
11. C₂×C₃×#882	C₂	semidirect
12. C₂×C₃×#67⋊C₄	C₂	semidirect
13. C₂×C₃×D₃×C₂²⋊C₄	C₂	semidirect
14. C₂×C₃×#879	C₂	semidirect
15. C₂×C₃×#876	C₂	semidirect
16. C₂×C₃×C₄×D₁₂	C₂	semidirect
18. C₂×#5678	C₃	direct (N × H)
20. C₂²×C₃²×Q₈	C₂²	semidirect
25. C₂²×C₃×#67	C₂²	semidirect
26. C₂³×C₃×Dic₃	C₂²	semidirect
31. C₂²×C₃×C₄×D₃	C₂²	semidirect
32. C₃²×#124	C₂²	semidirect
35. C₂×C₃²×C₂²⋊C₄	C₂²	semidirect
36. C₂×C₃²×C₂²⋊C₄	C₂²	semidirect
37. C₂×C₃²×C₄²	C₂²	semidirect
40. C₃×#947	C₂²	semidirect
41. C₃×#946	C₂²	semidirect
42. C₃×#939	C₂²	semidirect
43. C₃×#937	C₂²	semidirect
50. C₂×C₃×(C₂×D₃)⋊C₄	C₂²	semidirect
51. C₂×C₃×(C₂×D₃)⋊C₄	C₂²	semidirect
52. C₂×C₃×C₄⋊Dic₃	C₂²	semidirect
53. C₂×C₃×C₄⋊Dic₃	C₂²	semidirect
54. C₂×C₃×Dic₃⋊C₄	C₂²	semidirect
55. C₂×C₃×Dic₃⋊C₄	C₂²	semidirect
56. C₂×C₃×Dic₃⋊C₄	C₂²	semidirect
57. C₂×C₃×Dic₃⋊C₄	C₂²	semidirect
58. C₂×C₃×C₄×Dic₃	C₂²	semidirect
59. C₃×#886	C₂²	semidirect
60. C₃×#884	C₂²	semidirect
61. C₃×#884	C₂²	semidirect
62. C₃×#883	C₂²	semidirect
63. C₃×#882	C₂²	semidirect
64. C₃×#67⋊C₄	C₂²	semidirect
65. C₃×D₃×C₂²⋊C₄	C₂²	semidirect
66. C₃×#879	C₂²	semidirect
67. C₃×#876	C₂²	semidirect
68. C₃×C₄×D₁₂	C₂²	semidirect
74. C₂×C₃×#124	D₃	semidirect
75. C₂×C₃×#124	C₂×C₃	semidirect
87. C₂×#947	C₂×C₃	semidirect
88. C₂×#946	C₂×C₃	semidirect
89. C₂×#939	C₂×C₃	semidirect
90. C₂×#937	C₂×C₃	semidirect
91. #5678	C₂×C₃	direct (N × H)
92. C₂×#886	C₂×C₃	semidirect
93. C₂×#884	C₂×C₃	semidirect
94. C₂×#884	C₂×C₃	semidirect
95. C₂×#883	C₂×C₃	semidirect
96. C₂×#882	C₂×C₃	semidirect
97. C₂×#67⋊C₄	C₂×C₃	semidirect
98. C₂×D₃×C₂²⋊C₄	C₂×C₃	semidirect
99. C₂×#879	C₂×C₃	semidirect
100. C₂×#876	C₂×C₃	semidirect
101. C₂×C₄×D₁₂	C₂×C₃	semidirect
112. C₂×C₃²×Q₈	C₂³	semidirect
127. C₂×C₃×#67	C₂³	semidirect
134. C₂²×C₃×Dic₃	C₂³	semidirect
144. C₂×C₃×C₄×D₃	C₂³	semidirect
147. C₃²×C₂²⋊C₄	C₂³	semidirect
148. C₃²×C₂²⋊C₄	C₂³	semidirect
149. C₃²×C₄²	C₂³	semidirect
158. C₃×(C₂×D₃)⋊C₄	C₂³	semidirect
159. C₃×(C₂×D₃)⋊C₄	C₂³	semidirect
160. C₃×C₄⋊Dic₃	C₂³	semidirect
161. C₃×C₄⋊Dic₃	C₂³	semidirect
162. C₃×Dic₃⋊C₄	C₂³	semidirect
163. C₃×Dic₃⋊C₄	C₂³	semidirect
164. C₃×Dic₃⋊C₄	C₂³	semidirect
165. C₃×Dic₃⋊C₄	C₂³	semidirect
166. C₃×C₄×Dic₃	C₂³	semidirect
171. C₂²×C₃×Q₈	C₂×D₃	semidirect
172. C₂²×C₃×Q₈	C₂²×C₃	semidirect
189. C₂²×#67	C₂²×C₃	semidirect
190. C₂³×Dic₃	C₂²×C₃	semidirect
195. C₂²×C₄×D₃	C₂²×C₃	semidirect
200. C₃×#124	C₂×D₃	semidirect
201. C₃×#124	C₂²×C₃	semidirect
235. C₂×C₃×C₂²⋊C₄	C₂×D₃	semidirect
236. C₂×C₃×C₂²⋊C₄	C₂×D₃	semidirect
239. C₂×C₃×C₂²⋊C₄	C₂²×C₃	semidirect
240. C₂×C₃×C₂²⋊C₄	C₂²×C₃	semidirect
243. C₂×C₃×C₄²	C₂×D₃	semidirect
244. C₂×C₃×C₄²	C₂²×C₃	semidirect
247. #947	C₂²×C₃	semidirect
248. #946	C₂²×C₃	semidirect
249. #939	C₂²×C₃	semidirect
250. #937	C₂²×C₃	semidirect
257. C₂×(C₂×D₃)⋊C₄	C₂²×C₃	semidirect
258. C₂×(C₂×D₃)⋊C₄	C₂²×C₃	semidirect
259. C₂×C₄⋊Dic₃	C₂²×C₃	semidirect
260. C₂×C₄⋊Dic₃	C₂²×C₃	semidirect
261. C₂×Dic₃⋊C₄	C₂²×C₃	semidirect
262. C₂×Dic₃⋊C₄	C₂²×C₃	semidirect
263. C₂×Dic₃⋊C₄	C₂²×C₃	semidirect
264. C₂×Dic₃⋊C₄	C₂²×C₃	semidirect
265. C₂×C₄×Dic₃	C₂²×C₃	semidirect
266. #886	C₂²×C₃	semidirect
267. #884	C₂²×C₃	semidirect
268. #884	C₂²×C₃	semidirect
269. #883	C₂²×C₃	semidirect
270. #882	C₂²×C₃	semidirect
271. #67⋊C₄	C₂²×C₃	semidirect
272. D₃×C₂²⋊C₄	C₂²×C₃	semidirect
273. #879	C₂²×C₃	semidirect
274. #876	C₂²×C₃	semidirect
275. C₄×D₁₂	C₂²×C₃	semidirect
337. C₂×#124	C₃×D₃	semidirect
373. C₂×C₃×Q₈	C₂²×D₃	semidirect
374. C₂×C₃×Q₈	C₂³×C₃	semidirect
428. C₂×#67	C₂³×C₃	semidirect
435. C₂²×Dic₃	C₂³×C₃	semidirect
445. C₂×C₄×D₃	C₂³×C₃	semidirect
468. C₃×C₂²⋊C₄	C₂²×D₃	semidirect
469. C₃×C₂²⋊C₄	C₂²×D₃	semidirect
472. C₃×C₂²⋊C₄	C₂³×C₃	semidirect
473. C₃×C₂²⋊C₄	C₂³×C₃	semidirect
476. C₃×C₄²	C₂²×D₃	semidirect
477. C₃×C₄²	C₂³×C₃	semidirect
486. (C₂×D₃)⋊C₄	C₂³×C₃	semidirect
487. (C₂×D₃)⋊C₄	C₂³×C₃	semidirect
488. C₄⋊Dic₃	C₂³×C₃	semidirect
489. C₄⋊Dic₃	C₂³×C₃	semidirect
490. Dic₃⋊C₄	C₂³×C₃	semidirect
491. Dic₃⋊C₄	C₂³×C₃	semidirect
492. Dic₃⋊C₄	C₂³×C₃	semidirect
493. Dic₃⋊C₄	C₂³×C₃	semidirect
494. C₄×Dic₃	C₂³×C₃	semidirect
531. C₂²×Q₈	C₂×C₃×D₃	semidirect
546. #124	C₂×C₃×D₃	semidirect
576. C₂×C₂²⋊C₄	C₂×C₃×D₃	semidirect
577. C₂×C₂²⋊C₄	C₂×C₃×D₃	semidirect
579. C₂×C₄²	C₂×C₃×D₃	semidirect
717. C₂×C₃²	#538	semidirect
734. C₂×Q₈	C₂²×C₃×D₃	semidirect
785. C₂²⋊C₄	C₂²×C₃×D₃	semidirect
786. C₂²⋊C₄	C₂²×C₃×D₃	semidirect
788. C₄²	C₂²×C₃×D₃	semidirect
876. C₃²	C₂×#538	semidirect
947. C₂×C₃	#5678	direct (N × H)
948. C₂×C₃	C₃×#538	semidirect
994. C₃	C₂×#5678	direct (N × H)
995. C₃	C₂×C₃×#538	semidirect
1001. C₂	C₃×#5678	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×#124	2
C₂×C₃×#947	2
C₂×C₃×#946	2
C₂×C₃×#939	2
C₂×C₃×#937	2
C₃×#5678	2
C₂×C₃×#886	2
C₂×C₃×#884	2
C₂×C₃×#883	2
C₂×C₃×#882	2
C₂×C₃×#67⋊C₄	2
C₂×C₃×D₃×C₂²⋊C₄	2
C₂×C₃×#879	2
C₂×C₃×#876	2
C₂×C₃×C₄×D₁₂	2
C₂×C₃×#538	3
C₂×#5678	3

Subgroups — C2×C3×#5678 #11901260

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#5678 #11901260