Subgroups — C₂×C₃×#5593 #11901263

Order 1152.

3003 conjugacy classes of subgroups.

The subgroup lattice has 1028 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃²×#120	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×#953	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₃×#217	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃×#939	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₃×#939	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₃×#938	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₃×#936	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₃×#935	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₃×D₄×Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#5593	C₂	1	16	yes	maximal, direct product factor
11	C₂×C₃×#885	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₃×#883	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₃×#67⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₃×#879	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₃×#879	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₃×#878	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×C₃×#538	—	3	1	no	maximal
18	C₂×#5593	C₃	1	1	yes	maximal, characteristic, direct product factor
19	C₂⁵×C₃²	C₂²	1	1	yes	characteristic
20	C₂²×C₃²×D₄	C₂²	1	1	yes	characteristic
21	C₂²×C₃²×D₄	C₂²	1	1	yes	characteristic
22	C₂²×C₃²×D₄	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
26	C₂²×C₃×#67	C₂²	1	1	yes	characteristic, complemented
27	C₂³×C₃×Dic₃	C₂²	1	1	yes	characteristic
28	C₂³×C₃×Dic₃	C₂²	1	1	yes	characteristic
29	C₂³×C₃×Dic₃	C₂²	1	1	yes	characteristic, complemented
30	C₂²×C₃×C₄×D₃	C₂²	1	1	yes	characteristic, complemented
31	C₂²×C₃×Dic₆	C₂²	1	1	yes	characteristic, complemented
32	C₃²×#120	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
36	C₃×#953	C₂²	1	8	yes	complemented
37	C₂×C₃×#217	C₂²	1	1	yes	characteristic
38	C₂×C₃×#217	C₂²	1	1	yes	characteristic
39	C₂×C₃×#217	C₂²	1	1	yes	characteristic
40	C₂×C₃×#217	C₂²	1	1	yes	characteristic
41	C₂×C₃×#217	C₂²	1	1	yes	characteristic
42	C₂×C₃×#217	C₂²	1	1	yes	characteristic
43	C₂×C₃×#217	C₂²	1	1	yes	characteristic
44	C₂×C₃×#217	C₂²	1	8	yes	complemented
45	C₂×C₃×#217	C₂²	1	1	yes	characteristic, complemented
46	C₂×C₃×#217	C₂²	1	1	yes	characteristic, complemented
47	C₃×#939	C₂²	1	8	yes	complemented
48	C₃×#939	C₂²	1	8	yes	complemented
49	C₃×#938	C₂²	1	8	yes	complemented
50	C₃×#936	C₂²	1	8	yes	complemented
51	C₃×#935	C₂²	1	8	yes	complemented
52	C₃×D₄×Dic₃	C₂²	1	8	yes	complemented
53	C₂×C₃×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic, complemented
54	C₂×C₃×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic, complemented
55	C₂×C₃×C₄⋊Dic₃	C₂²	1	1	yes	characteristic, complemented
56	C₂×C₃×C₄⋊Dic₃	C₂²	1	1	yes	characteristic, complemented
57	C₂×C₃×Dic₃⋊C₄	C₂²	1	1	yes	characteristic, complemented
58	C₂×C₃×Dic₃⋊C₄	C₂²	1	1	yes	characteristic, complemented
59	C₂×C₃×Dic₃⋊C₄	C₂²	1	1	yes	characteristic, complemented
60	C₂×C₃×Dic₃⋊C₄	C₂²	1	1	yes	characteristic, complemented
61	C₂×C₃×C₄×Dic₃	C₂²	1	1	yes	characteristic, complemented
62	C₂×C₃×C₄×Dic₃	C₂²	1	1	yes	characteristic, complemented
63	C₃×#885	C₂²	1	8	yes	complemented
64	C₃×#883	C₂²	1	8	yes	complemented
65	C₃×#67⋊C₄	C₂²	1	8	yes	complemented
66	C₃×#879	C₂²	1	8	yes	complemented
67	C₃×#879	C₂²	1	8	yes	complemented
68	C₃×#878	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	—	3	1	no	—
73	C₂×C₃×#124	—	3	1	no	—
74	C₂×C₃×#123	—	3	1	no	—
75	C₂×C₃×#123	—	3	1	no	—
76	C₂×C₃×C₂²⋊Q₈	—	3	1	no	—
77	C₂×C₃×#121	—	3	1	no	—
78	C₂×C₃×#121	—	3	1	no	—
79	C₂×C₃×#121	—	3	1	no	—
80	C₂×C₃×#120	—	2	1	no	—
81	C₂×C₃×#120	—	3	1	no	—
82	C₂×C₃×#120	D₃	1	1	yes	characteristic, complemented
83	C₂×C₃×#120	C₂×C₃	1	1	yes	characteristic, complemented
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×#953	C₂×C₃	1	1	yes	characteristic, complemented
88	C₂²×#217	C₂×C₃	1	1	yes	characteristic, complemented
89	C₂×#939	C₂×C₃	1	1	yes	characteristic, complemented
90	C₂×#939	C₂×C₃	1	1	yes	characteristic, complemented
91	C₂×#938	C₂×C₃	1	1	yes	characteristic, complemented
92	C₂×#936	C₂×C₃	1	1	yes	characteristic, complemented
93	C₂×#935	C₂×C₃	1	1	yes	characteristic, complemented
94	C₂×D₄×Dic₃	C₂×C₃	1	1	yes	characteristic, complemented
95	#5593	C₂×C₃	1	16	yes	direct product factor
96	C₂×#885	C₂×C₃	1	1	yes	characteristic, complemented
97	C₂×#883	C₂×C₃	1	1	yes	characteristic, complemented
98	C₂×#67⋊C₄	C₂×C₃	1	1	yes	characteristic, complemented
99	C₂×#879	C₂×C₃	1	1	yes	characteristic, complemented
100	C₂×#879	C₂×C₃	1	1	yes	characteristic, complemented
101	C₂×#878	C₂×C₃	1	1	yes	characteristic, complemented
102	C₂⁴×C₃²	—	2	4	no	—
103	C₂⁴×C₃²	—	4	2	no	—
104	C₂⁴×C₃²	—	4	2	no	—
105	C₂⁴×C₃²	C₂³	1	1	yes	characteristic
106	C₂⁴×C₃²	C₂³	1	1	yes	characteristic
107	C₂⁴×C₃²	C₂³	1	1	yes	characteristic
108	C₂⁴×C₃²	C₂³	1	1	yes	characteristic
109	C₂⁴×C₃²	C₂³	1	4	yes	—
110	C₂³×C₃×D₃	C₂³	1	1	yes	characteristic
111	C₂×C₃²×D₄	—	2	4	no	—
112	C₂×C₃²×D₄	—	4	2	no	—
113	C₂×C₃²×D₄	—	4	2	no	—
114	C₂×C₃²×D₄	C₂³	1	4	yes	—
115	C₂×C₃²×D₄	C₂³	1	4	yes	—
116	C₂×C₃²×D₄	C₂³	1	4	yes	—
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	—	4	2	no	—
130	C₂²×C₃×Dic₃	—	4	2	no	—
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	1	yes	characteristic
135	C₂²×C₃×Dic₃	C₂³	1	1	yes	characteristic
136	C₂²×C₃×Dic₃	C₂³	1	1	yes	characteristic
137	C₂²×C₃×Dic₃	C₂³	1	1	yes	characteristic
138	C₂²×C₃×Dic₃	C₂³	1	4	yes	—
139	C₂²×C₃×Dic₃	C₂³	1	4	yes	—
140	C₂²×C₃×Dic₃	C₂³	1	4	yes	complemented
141	C₂×C₃×C₄×D₃	—	4	2	no	—
142	C₂×C₃×C₄×D₃	C₂³	1	4	yes	complemented
143	C₂×C₃×Dic₆	—	4	2	no	—
144	C₂×C₃×Dic₆	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	—
148	C₃×#217	C₂³	1	4	yes	—
149	C₃×#217	C₂³	1	4	yes	—
150	C₃×#217	C₂³	1	4	yes	—
151	C₃×#217	C₂³	1	4	yes	—
152	C₃×#217	C₂³	1	4	yes	—
153	C₃×#217	C₂³	1	4	yes	—
154	C₃×#217	C₂³	1	4	yes	—
155	C₃×#217	C₂³	1	4	yes	complemented
156	C₃×#217	C₂³	1	4	yes	complemented
157	C₃×(C₂×D₃)⋊C₄	C₂³	1	4	yes	complemented
158	C₃×(C₂×D₃)⋊C₄	C₂³	1	4	yes	complemented
159	C₃×C₄⋊Dic₃	C₂³	1	4	yes	complemented
160	C₃×C₄⋊Dic₃	C₂³	1	4	yes	complemented
161	C₃×Dic₃⋊C₄	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×C₄×Dic₃	C₂³	1	4	yes	complemented
166	C₃×C₄×Dic₃	C₂³	1	4	yes	complemented
167	C₂×#538	—	3	1	no	Sylow
168	C₂⁵×C₃	—	2	1	no	—
169	C₂⁵×C₃	C₂×D₃	1	1	yes	characteristic
170	C₂⁵×C₃	C₂²×C₃	1	1	yes	characteristic
171	C₂²×C₃×Q₈	—	3	1	no	—
172	C₂²×C₃×D₄	—	2	1	no	—
173	C₂²×C₃×D₄	—	2	1	no	—
174	C₂²×C₃×D₄	—	2	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	C₂×D₃	1	1	yes	characteristic
180	C₂²×C₃×D₄	C₂×D₃	1	1	yes	characteristic
181	C₂²×C₃×D₄	C₂×D₃	1	1	yes	characteristic
182	C₂²×C₃×D₄	C₂²×C₃	1	1	yes	characteristic
183	C₂²×C₃×D₄	C₂²×C₃	1	1	yes	characteristic
184	C₂²×C₃×D₄	C₂²×C₃	1	1	yes	characteristic
185	C₂³×C₃×C₄	—	3	1	no	—
186	C₂³×C₃×C₄	—	3	1	no	—
187	C₂³×C₃×C₄	—	3	1	no	—
188	C₂³×C₃×C₄	—	3	1	no	—
189	C₂²×#67	C₂²×C₃	1	1	yes	characteristic
190	C₂²×#67	C₂²×C₃	1	1	yes	characteristic
191	C₂²×#67	C₂²×C₃	1	1	yes	characteristic
192	C₂²×#67	C₂²×C₃	1	1	yes	characteristic, complemented
193	C₂³×Dic₃	C₂²×C₃	1	1	yes	characteristic
194	C₂³×Dic₃	C₂²×C₃	1	1	yes	characteristic
195	C₂³×Dic₃	C₂²×C₃	1	1	yes	characteristic, complemented
196	C₂²×C₄×D₃	C₂²×C₃	1	1	yes	characteristic, complemented
197	C₂²×Dic₆	C₂²×C₃	1	1	yes	characteristic, complemented
198	C₃×#126	—	3	8	no	—
199	C₃×#126	—	3	8	no	—
200	C₃×#124	—	3	8	no	—
201	C₃×#124	—	3	8	no	—
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	—	2	8	no	—
209	C₃×#120	—	3	8	no	—
210	C₃×#120	C₂×D₃	1	8	yes	complemented
211	C₃×#120	C₂²×C₃	1	8	yes	complemented
212	C₃×C₄×D₄	—	3	8	no	—
213	C₃×C₄×D₄	—	3	8	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×C₄⋊C₄	—	3	1	no	—
219	C₂×C₃×C₄⋊C₄	—	3	1	no	—
220	C₂×C₃×C₂²⋊C₄	—	2	1	no	—
221	C₂×C₃×C₂²⋊C₄	—	2	1	no	—
222	C₂×C₃×C₂²⋊C₄	—	2	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	8	no	—
231	C₂×C₃×C₂²⋊C₄	—	3	1	no	—
232	C₂×C₃×C₂²⋊C₄	—	3	1	no	—
233	C₂×C₃×C₂²⋊C₄	—	3	1	no	—
234	C₂×C₃×C₂²⋊C₄	—	3	1	no	—
235	C₂×C₃×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic
236	C₂×C₃×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic
237	C₂×C₃×C₂²⋊C₄	C₂×D₃	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
240	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
241	C₂×C₃×C₄²	—	3	1	no	—
242	C₂×C₃×C₄²	—	3	1	no	—
243	#953	C₂²×C₃	1	8	yes	complemented
244	C₂×#217	C₂²×C₃	1	1	yes	characteristic
245	C₂×#217	C₂²×C₃	1	1	yes	characteristic
246	C₂×#217	C₂²×C₃	1	1	yes	characteristic
247	C₂×#217	C₂²×C₃	1	1	yes	characteristic
248	C₂×#217	C₂²×C₃	1	1	yes	characteristic
249	C₂×#217	C₂²×C₃	1	1	yes	characteristic
250	C₂×#217	C₂²×C₃	1	1	yes	characteristic
251	C₂×#217	C₂²×C₃	1	8	yes	complemented
252	C₂×#217	C₂²×C₃	1	1	yes	characteristic, complemented
253	C₂×#217	C₂²×C₃	1	1	yes	characteristic, complemented
254	#939	C₂²×C₃	1	8	yes	complemented
255	#939	C₂²×C₃	1	8	yes	complemented
256	#938	C₂²×C₃	1	8	yes	complemented
257	#936	C₂²×C₃	1	8	yes	complemented
258	#935	C₂²×C₃	1	8	yes	complemented
259	D₄×Dic₃	C₂²×C₃	1	8	yes	complemented
260	C₂×(C₂×D₃)⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
261	C₂×(C₂×D₃)⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
262	C₂×C₄⋊Dic₃	C₂²×C₃	1	1	yes	characteristic, complemented
263	C₂×C₄⋊Dic₃	C₂²×C₃	1	1	yes	characteristic, complemented
264	C₂×Dic₃⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
265	C₂×Dic₃⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
266	C₂×Dic₃⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
267	C₂×Dic₃⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
268	C₂×C₄×Dic₃	C₂²×C₃	1	1	yes	characteristic, complemented
269	C₂×C₄×Dic₃	C₂²×C₃	1	1	yes	characteristic, complemented
270	#885	C₂²×C₃	1	8	yes	complemented
271	#883	C₂²×C₃	1	8	yes	complemented
272	#67⋊C₄	C₂²×C₃	1	8	yes	complemented
273	#879	C₂²×C₃	1	8	yes	complemented
274	#879	C₂²×C₃	1	8	yes	complemented
275	#878	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	8	no	—
281	C₂³×C₃²	—	2	2	no	—
282	C₂³×C₃²	—	2	2	no	—
283	C₂³×C₃²	—	2	2	no	—
284	C₂³×C₃²	—	2	2	no	—
285	C₂³×C₃²	—	2	2	no	—
286	C₂³×C₃²	—	2	2	no	—
287	C₂³×C₃²	—	2	2	no	—
288	C₂³×C₃²	—	4	4	no	—
289	C₂³×C₃²	—	4	4	no	—
290	C₂³×C₃²	—	4	16	no	—
291	C₂³×C₃²	#41	1	4	yes	—
292	C₂³×C₃²	C₂⁴	1	2	yes	—
293	C₂³×C₃²	C₂⁴	1	2	yes	—
294	C₂³×C₃²	C₂⁴	1	2	yes	—
295	C₂³×C₃²	C₂⁴	1	2	yes	—
296	C₂³×C₃²	C₂⁴	1	1	yes	characteristic
297	C₂²×C₃×D₃	—	2	2	no	—
298	C₂²×C₃×D₃	—	2	2	no	—
299	C₂²×C₃×D₃	—	2	2	no	—
300	C₂²×C₃×D₃	C₂⁴	1	2	yes	—
301	C₃²×D₄	—	2	8	no	—
302	C₃²×D₄	—	4	4	no	—
303	C₃²×D₄	—	4	4	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	C₂⁴	1	2	yes	—
308	C₂×C₃²×C₄	C₂⁴	1	2	yes	—
309	C₂×C₃²×C₄	C₂⁴	1	2	yes	—
310	C₃×#67	—	2	8	no	—
311	C₃×#67	—	4	4	no	—
312	C₃×#67	—	4	4	no	—
313	C₃×#67	—	4	4	no	—
314	C₂×C₃×Dic₃	—	2	2	no	—
315	C₂×C₃×Dic₃	—	2	2	no	—
316	C₂×C₃×Dic₃	—	2	2	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	—	4	4	no	—
322	C₂×C₃×Dic₃	—	4	4	no	—
323	C₂×C₃×Dic₃	—	4	4	no	—
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	C₂×C₃×Dic₃	C₂⁴	1	2	yes	—
329	C₂×C₃×Dic₃	C₂⁴	1	2	yes	—
330	C₂×C₃×Dic₃	C₂⁴	1	2	yes	—
331	C₃×C₄×D₃	—	4	4	no	—
332	C₃×Dic₆	—	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	—	3	1	no	—
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	C₃×D₃	1	1	yes	characteristic, complemented
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	4	no	—
350	C₂⁴×C₃	—	2	4	no	—
351	C₂⁴×C₃	—	2	1	no	—
352	C₂⁴×C₃	—	2	1	no	—
353	C₂⁴×C₃	—	2	1	no	—
354	C₂⁴×C₃	—	2	4	no	—
355	C₂⁴×C₃	—	2	1	no	—
356	C₂⁴×C₃	—	3	1	no	—
357	C₂⁴×C₃	—	4	4	no	—
358	C₂⁴×C₃	—	4	2	no	—
359	C₂⁴×C₃	—	4	2	no	—
360	C₂⁴×C₃	—	4	2	no	—
361	C₂⁴×C₃	—	4	2	no	—
362	C₂⁴×C₃	—	4	4	no	—
363	C₂⁴×C₃	—	4	4	no	—
364	C₂⁴×C₃	C₂²×D₃	1	1	yes	characteristic
365	C₂⁴×C₃	C₂²×D₃	1	1	yes	characteristic
366	C₂⁴×C₃	C₂²×D₃	1	1	yes	characteristic
367	C₂⁴×C₃	C₂²×D₃	1	1	yes	characteristic
368	C₂⁴×C₃	C₂²×D₃	1	4	yes	—
369	C₂⁴×C₃	C₂³×C₃	1	1	yes	characteristic
370	C₂⁴×C₃	C₂³×C₃	1	1	yes	characteristic
371	C₂⁴×C₃	C₂³×C₃	1	1	yes	characteristic
372	C₂⁴×C₃	C₂³×C₃	1	1	yes	characteristic
373	C₂⁴×C₃	C₂³×C₃	1	4	yes	—
374	C₂³×D₃	C₂³×C₃	1	1	yes	characteristic
375	C₂×C₃×Q₈	—	3	4	no	—
376	C₂×C₃×Q₈	—	12	2	no	—
377	C₂×C₃×D₄	—	2	4	no	—
378	C₂×C₃×D₄	—	2	4	no	—
379	C₂×C₃×D₄	—	2	4	no	—
380	C₂×C₃×D₄	—	2	4	no	—
381	C₂×C₃×D₄	—	2	4	no	—
382	C₂×C₃×D₄	—	3	4	no	—
383	C₂×C₃×D₄	—	3	4	no	—
384	C₂×C₃×D₄	—	3	4	no	—
385	C₂×C₃×D₄	—	3	4	no	—
386	C₂×C₃×D₄	—	4	4	no	—
387	C₂×C₃×D₄	—	4	2	no	—
388	C₂×C₃×D₄	—	4	2	no	—
389	C₂×C₃×D₄	—	4	2	no	—
390	C₂×C₃×D₄	—	4	2	no	—
391	C₂×C₃×D₄	—	4	4	no	—
392	C₂×C₃×D₄	—	4	4	no	—
393	C₂×C₃×D₄	—	6	4	no	—
394	C₂×C₃×D₄	—	12	2	no	—
395	C₂×C₃×D₄	—	12	2	no	—
396	C₂×C₃×D₄	—	12	2	no	—
397	C₂×C₃×D₄	C₂²×D₃	1	4	yes	—
398	C₂×C₃×D₄	C₂²×D₃	1	4	yes	—
399	C₂×C₃×D₄	C₂²×D₃	1	4	yes	—
400	C₂×C₃×D₄	C₂³×C₃	1	4	yes	—
401	C₂×C₃×D₄	C₂³×C₃	1	4	yes	—
402	C₂×C₃×D₄	C₂³×C₃	1	4	yes	—
403	C₂²×C₃×C₄	—	2	1	no	—
404	C₂²×C₃×C₄	—	2	1	no	—
405	C₂²×C₃×C₄	—	2	1	no	—
406	C₂²×C₃×C₄	—	3	1	no	—
407	C₂²×C₃×C₄	—	3	1	no	—
408	C₂²×C₃×C₄	—	3	1	no	—
409	C₂²×C₃×C₄	—	3	1	no	—
410	C₂²×C₃×C₄	—	3	1	no	—
411	C₂²×C₃×C₄	—	3	1	no	—
412	C₂²×C₃×C₄	—	3	1	no	—
413	C₂²×C₃×C₄	—	3	4	no	—
414	C₂²×C₃×C₄	—	3	4	no	—
415	C₂²×C₃×C₄	—	3	4	no	—
416	C₂²×C₃×C₄	—	3	4	no	—
417	C₂²×C₃×C₄	—	12	2	no	—
418	C₂²×C₃×C₄	—	12	2	no	—
419	C₂²×C₃×C₄	—	12	2	no	—
420	C₂²×C₃×C₄	—	12	2	no	—
421	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
422	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
423	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
424	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
425	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
426	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
427	C₂×#67	—	2	4	no	—
428	C₂×#67	—	4	2	no	—
429	C₂×#67	—	4	2	no	—
430	C₂×#67	—	4	2	no	—
431	C₂×#67	C₂³×C₃	1	4	yes	—
432	C₂×#67	C₂³×C₃	1	4	yes	—
433	C₂×#67	C₂³×C₃	1	4	yes	—
434	C₂×#67	C₂³×C₃	1	4	yes	complemented
435	C₂²×Dic₃	—	4	2	no	—
436	C₂²×Dic₃	—	4	2	no	—
437	C₂²×Dic₃	—	4	2	no	—
438	C₂²×Dic₃	C₂³×C₃	1	1	yes	characteristic
439	C₂²×Dic₃	C₂³×C₃	1	1	yes	characteristic
440	C₂²×Dic₃	C₂³×C₃	1	1	yes	characteristic
441	C₂²×Dic₃	C₂³×C₃	1	1	yes	characteristic
442	C₂²×Dic₃	C₂³×C₃	1	1	yes	characteristic
443	C₂²×Dic₃	C₂³×C₃	1	1	yes	characteristic
444	C₂²×Dic₃	C₂³×C₃	1	1	yes	characteristic
445	C₂²×Dic₃	C₂³×C₃	1	4	yes	—
446	C₂²×Dic₃	C₂³×C₃	1	4	yes	—
447	C₂²×Dic₃	C₂³×C₃	1	4	yes	complemented
448	C₂×C₄×D₃	—	4	2	no	—
449	C₂×C₄×D₃	C₂³×C₃	1	4	yes	complemented
450	C₂×Dic₆	—	4	2	no	—
451	C₂×Dic₆	C₂³×C₃	1	4	yes	complemented
452	C₃×C₄⋊C₄	—	3	4	no	—
453	C₃×C₄⋊C₄	—	3	4	no	—
454	C₃×C₄⋊C₄	—	3	4	no	—
455	C₃×C₄⋊C₄	—	3	4	no	—
456	C₃×C₄⋊C₄	—	3	4	no	—
457	C₃×C₄⋊C₄	—	3	4	no	—
458	C₃×C₂²⋊C₄	—	2	4	no	—
459	C₃×C₂²⋊C₄	—	2	4	no	—
460	C₃×C₂²⋊C₄	—	2	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	—	3	4	no	—
467	C₃×C₂²⋊C₄	—	3	4	no	—
468	C₃×C₂²⋊C₄	—	3	4	no	—
469	C₃×C₂²⋊C₄	—	3	4	no	—
470	C₃×C₂²⋊C₄	—	3	4	no	—
471	C₃×C₂²⋊C₄	—	3	4	no	—
472	C₃×C₂²⋊C₄	C₂²×D₃	1	4	yes	—
473	C₃×C₂²⋊C₄	C₂²×D₃	1	4	yes	—
474	C₃×C₂²⋊C₄	C₂²×D₃	1	4	yes	—
475	C₃×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
476	C₃×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
477	C₃×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
478	C₃×C₄²	—	3	4	no	—
479	C₃×C₄²	—	3	4	no	—
480	#217	C₂³×C₃	1	4	yes	—
481	#217	C₂³×C₃	1	4	yes	—
482	#217	C₂³×C₃	1	4	yes	—
483	#217	C₂³×C₃	1	4	yes	—
484	#217	C₂³×C₃	1	4	yes	—
485	#217	C₂³×C₃	1	4	yes	—
486	#217	C₂³×C₃	1	4	yes	—
487	#217	C₂³×C₃	1	4	yes	complemented
488	#217	C₂³×C₃	1	4	yes	complemented
489	(C₂×D₃)⋊C₄	C₂³×C₃	1	4	yes	complemented
490	(C₂×D₃)⋊C₄	C₂³×C₃	1	4	yes	complemented
491	C₄⋊Dic₃	C₂³×C₃	1	4	yes	complemented
492	C₄⋊Dic₃	C₂³×C₃	1	4	yes	complemented
493	Dic₃⋊C₄	C₂³×C₃	1	4	yes	complemented
494	Dic₃⋊C₄	C₂³×C₃	1	4	yes	complemented
495	Dic₃⋊C₄	C₂³×C₃	1	4	yes	complemented
496	Dic₃⋊C₄	C₂³×C₃	1	4	yes	complemented
497	C₄×Dic₃	C₂³×C₃	1	4	yes	complemented
498	C₄×Dic₃	C₂³×C₃	1	4	yes	complemented
499	C₂²×C₃²	—	2	2	no	—
500	C₂²×C₃²	—	2	2	no	—
501	C₂²×C₃²	—	2	8	no	—
502	C₂²×C₃²	—	2	2	no	—
503	C₂²×C₃²	—	2	2	no	—
504	C₂²×C₃²	—	2	2	no	—
505	C₂²×C₃²	—	2	2	no	—
506	C₂²×C₃²	—	2	2	no	—
507	C₂²×C₃²	—	2	2	no	—
508	C₂²×C₃²	—	2	2	no	—
509	C₂²×C₃²	—	2	2	no	—
510	C₂²×C₃²	—	2	2	no	—
511	C₂²×C₃²	—	4	16	no	—
512	C₂²×C₃²	—	4	4	no	—
513	C₂²×C₃²	—	4	4	no	—
514	C₂²×C₃²	—	4	4	no	—
515	C₂²×C₃²	C₂×#41	1	4	yes	—
516	C₂²×C₃²	C₂×#41	1	2	yes	—
517	C₂²×C₃²	H(5,𝔽₂)	1	2	yes	—
518	C₂²×C₃²	H(5,𝔽₂)	1	2	yes	—
519	C₂²×C₃²	C₂⁵	1	1	yes	characteristic
520	C₂×C₃×D₃	—	2	2	no	—
521	C₂×C₃×D₃	—	2	2	no	—
522	C₂×C₃×D₃	—	2	2	no	—
523	C₂×C₃×D₃	—	4	4	no	—
524	C₃²×C₄	—	2	2	no	—
525	C₃²×C₄	—	2	2	no	—
526	C₃²×C₄	—	2	2	no	—
527	C₃×Dic₃	—	2	2	no	—
528	C₃×Dic₃	—	2	2	no	—
529	C₃×Dic₃	—	2	2	no	—
530	C₃×Dic₃	—	2	2	no	—
531	C₃×Dic₃	—	2	2	no	—
532	C₃×Dic₃	—	2	2	no	—
533	C₃×Dic₃	—	2	2	no	—
534	C₂⁵	C₂×C₃×D₃	1	1	yes	characteristic
535	C₂²×Q₈	—	3	1	no	—
536	C₂²×D₄	—	3	1	no	—
537	C₂²×D₄	—	3	1	no	—
538	C₂²×D₄	—	3	1	no	—
539	C₂²×D₄	—	3	1	no	—
540	C₂²×D₄	C₂×C₃×D₃	1	1	yes	characteristic
541	C₂²×D₄	C₂×C₃×D₃	1	1	yes	characteristic
542	C₂²×D₄	C₂×C₃×D₃	1	1	yes	characteristic
543	C₂³×C₄	—	3	1	no	—
544	C₂³×C₄	—	3	1	no	—
545	C₂³×C₄	—	3	1	no	—
546	C₂³×C₄	—	3	1	no	—
547	#126	—	3	8	no	—
548	#126	—	3	8	no	—
549	#124	—	3	8	no	—
550	#124	—	3	8	no	—
551	#123	—	3	8	no	—
552	#123	—	3	8	no	—
553	C₂²⋊Q₈	—	3	8	no	—
554	#121	—	3	8	no	—
555	#121	—	3	8	no	—
556	#121	—	3	8	no	—
557	#120	—	3	8	no	—
558	#120	C₂×C₃×D₃	1	8	yes	complemented
559	C₄×D₄	—	3	8	no	—
560	C₄×D₄	—	3	8	no	—
561	C₂×C₄⋊C₄	—	3	1	no	—
562	C₂×C₄⋊C₄	—	3	1	no	—
563	C₂×C₄⋊C₄	—	3	1	no	—
564	C₂×C₄⋊C₄	—	3	1	no	—
565	C₂×C₄⋊C₄	—	3	1	no	—
566	C₂×C₄⋊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	8	no	—
572	C₂×C₂²⋊C₄	—	3	1	no	—
573	C₂×C₂²⋊C₄	—	3	1	no	—
574	C₂×C₂²⋊C₄	—	3	1	no	—
575	C₂×C₂²⋊C₄	—	3	1	no	—
576	C₂×C₂²⋊C₄	—	3	1	no	—
577	C₂×C₂²⋊C₄	—	3	1	no	—
578	C₂×C₂²⋊C₄	—	3	1	no	—
579	C₂×C₂²⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
580	C₂×C₂²⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
581	C₂×C₂²⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
582	C₂×C₄²	—	3	1	no	—
583	C₂×C₄²	—	3	1	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	4	no	—
589	C₂³×C₃	—	2	4	no	—
590	C₂³×C₃	—	2	2	no	—
591	C₂³×C₃	—	2	8	no	—
592	C₂³×C₃	—	2	2	no	—
593	C₂³×C₃	—	2	2	no	—
594	C₂³×C₃	—	2	2	no	—
595	C₂³×C₃	—	2	2	no	—
596	C₂³×C₃	—	2	2	no	—
597	C₂³×C₃	—	2	2	no	—
598	C₂³×C₃	—	2	2	no	—
599	C₂³×C₃	—	2	2	no	—
600	C₂³×C₃	—	2	2	no	—
601	C₂³×C₃	—	2	8	no	—
602	C₂³×C₃	—	2	2	no	—
603	C₂³×C₃	—	2	2	no	—
604	C₂³×C₃	—	2	2	no	—
605	C₂³×C₃	—	2	2	no	—
606	C₂³×C₃	—	2	2	no	—
607	C₂³×C₃	—	2	2	no	—
608	C₂³×C₃	—	2	2	no	—
609	C₂³×C₃	—	2	2	no	—
610	C₂³×C₃	—	2	1	no	—
611	C₂³×C₃	—	2	2	no	—
612	C₂³×C₃	—	2	2	no	—
613	C₂³×C₃	—	2	2	no	—
614	C₂³×C₃	—	2	2	no	—
615	C₂³×C₃	—	2	4	no	—
616	C₂³×C₃	—	3	2	no	—
617	C₂³×C₃	—	4	2	no	—
618	C₂³×C₃	—	4	2	no	—
619	C₂³×C₃	—	4	2	no	—
620	C₂³×C₃	—	4	2	no	—
621	C₂³×C₃	—	4	8	no	—
622	C₂³×C₃	—	4	2	no	—
623	C₂³×C₃	—	4	2	no	—
624	C₂³×C₃	—	4	2	no	—
625	C₂³×C₃	—	4	2	no	—
626	C₂³×C₃	—	4	2	no	—
627	C₂³×C₃	—	4	4	no	—
628	C₂³×C₃	—	4	4	no	—
629	C₂³×C₃	—	4	4	no	—
630	C₂³×C₃	—	4	4	no	—
631	C₂³×C₃	—	4	8	no	—
632	C₂³×C₃	—	4	8	no	—
633	C₂³×C₃	—	4	16	no	—
634	C₂³×C₃	—	4	16	no	—
635	C₂³×C₃	—	4	32	no	—
636	C₂³×C₃	—	6	2	no	—
637	C₂³×C₃	—	6	2	no	—
638	C₂³×C₃	—	6	2	no	—
639	C₂³×C₃	#237	1	4	yes	—
640	C₂³×C₃	C₃×#41	1	4	yes	—
641	C₂³×C₃	C₂³×D₃	1	2	yes	—
642	C₂³×C₃	C₂³×D₃	1	2	yes	—
643	C₂³×C₃	C₂³×D₃	1	2	yes	—
644	C₂³×C₃	C₂³×D₃	1	2	yes	—
645	C₂³×C₃	C₂³×D₃	1	1	yes	characteristic
646	C₂³×C₃	C₂⁴×C₃	1	2	yes	—
647	C₂³×C₃	C₂⁴×C₃	1	2	yes	—
648	C₂³×C₃	C₂⁴×C₃	1	2	yes	—
649	C₂³×C₃	C₂⁴×C₃	1	2	yes	—
650	C₂³×C₃	C₂⁴×C₃	1	1	yes	characteristic
651	C₂²×D₃	—	2	2	no	—
652	C₂²×D₃	—	2	2	no	—
653	C₂²×D₃	—	2	2	no	—
654	C₂²×D₃	C₂⁴×C₃	1	2	yes	—
655	C₃×Q₈	—	12	4	no	—
656	C₃×D₄	—	2	8	no	—
657	C₃×D₄	—	2	8	no	—
658	C₃×D₄	—	4	8	no	—
659	C₃×D₄	—	4	4	no	—
660	C₃×D₄	—	4	4	no	—
661	C₃×D₄	—	4	4	no	—
662	C₃×D₄	—	4	4	no	—
663	C₃×D₄	—	4	8	no	—
664	C₃×D₄	—	4	8	no	—
665	C₃×D₄	—	6	8	no	—
666	C₃×D₄	—	12	4	no	—
667	C₃×D₄	—	12	4	no	—
668	C₃×D₄	—	12	4	no	—
669	C₂×C₃×C₄	—	2	2	no	—
670	C₂×C₃×C₄	—	2	2	no	—
671	C₂×C₃×C₄	—	2	2	no	—
672	C₂×C₃×C₄	—	2	2	no	—
673	C₂×C₃×C₄	—	2	2	no	—
674	C₂×C₃×C₄	—	2	2	no	—
675	C₂×C₃×C₄	—	2	2	no	—
676	C₂×C₃×C₄	—	2	2	no	—
677	C₂×C₃×C₄	—	2	2	no	—
678	C₂×C₃×C₄	—	3	2	no	—
679	C₂×C₃×C₄	—	3	2	no	—
680	C₂×C₃×C₄	—	3	2	no	—
681	C₂×C₃×C₄	—	3	2	no	—
682	C₂×C₃×C₄	—	3	2	no	—
683	C₂×C₃×C₄	—	3	2	no	—
684	C₂×C₃×C₄	—	3	2	no	—
685	C₂×C₃×C₄	—	4	2	no	—
686	C₂×C₃×C₄	—	4	2	no	—
687	C₂×C₃×C₄	—	4	2	no	—
688	C₂×C₃×C₄	—	6	2	no	—
689	C₂×C₃×C₄	—	6	2	no	—
690	C₂×C₃×C₄	—	6	2	no	—
691	C₂×C₃×C₄	—	6	2	no	—
692	C₂×C₃×C₄	—	6	2	no	—
693	C₂×C₃×C₄	—	6	2	no	—
694	C₂×C₃×C₄	—	6	2	no	—
695	C₂×C₃×C₄	—	12	4	no	—
696	C₂×C₃×C₄	—	12	4	no	—
697	C₂×C₃×C₄	—	12	4	no	—
698	C₂×C₃×C₄	—	12	4	no	—
699	C₂×C₃×C₄	C₂³×D₃	1	2	yes	—
700	C₂×C₃×C₄	C₂³×D₃	1	2	yes	—
701	C₂×C₃×C₄	C₂³×D₃	1	2	yes	—
702	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
703	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
704	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
705	#67	—	2	8	no	—
706	#67	—	4	4	no	—
707	#67	—	4	4	no	—
708	#67	—	4	4	no	—
709	C₂×Dic₃	—	2	2	no	—
710	C₂×Dic₃	—	2	2	no	—
711	C₂×Dic₃	—	2	2	no	—
712	C₂×Dic₃	—	2	2	no	—
713	C₂×Dic₃	—	2	2	no	—
714	C₂×Dic₃	—	2	2	no	—
715	C₂×Dic₃	—	2	2	no	—
716	C₂×Dic₃	—	4	4	no	—
717	C₂×Dic₃	—	4	4	no	—
718	C₂×Dic₃	—	4	4	no	—
719	C₂×Dic₃	C₂⁴×C₃	1	2	yes	—
720	C₂×Dic₃	C₂⁴×C₃	1	2	yes	—
721	C₂×Dic₃	C₂⁴×C₃	1	2	yes	—
722	C₂×Dic₃	C₂⁴×C₃	1	2	yes	—
723	C₂×Dic₃	C₂⁴×C₃	1	2	yes	—
724	C₂×Dic₃	C₂⁴×C₃	1	2	yes	—
725	C₂×Dic₃	C₂⁴×C₃	1	2	yes	—
726	C₄×D₃	—	4	4	no	—
727	Dic₆	—	4	4	no	—
728	C₂×C₃²	—	2	4	no	—
729	C₂×C₃²	—	4	2	no	—
730	C₂×C₃²	—	4	2	no	—
731	C₂×C₃²	—	4	2	no	—
732	C₂×C₃²	#538	1	4	yes	complemented
733	C₂×C₃²	C₂²×#41	1	1	yes	characteristic
734	C₂×C₃²	C₂×H(5,𝔽₂)	1	1	yes	characteristic
735	C₂×C₃²	C₂×H(5,𝔽₂)	1	1	yes	characteristic
736	C₃×D₃	—	4	2	no	—
737	C₂⁴	—	2	4	no	—
738	C₂⁴	—	3	1	no	—
739	C₂⁴	—	4	2	no	—
740	C₂⁴	—	4	2	no	—
741	C₂⁴	C₂²×C₃×D₃	1	1	yes	characteristic
742	C₂⁴	C₂²×C₃×D₃	1	1	yes	characteristic
743	C₂⁴	C₂²×C₃×D₃	1	1	yes	characteristic
744	C₂⁴	C₂²×C₃×D₃	1	1	yes	characteristic
745	C₂⁴	C₂²×C₃×D₃	1	4	yes	—
746	C₂×Q₈	—	3	4	no	—
747	C₂×Q₈	—	12	2	no	—
748	C₂×D₄	—	2	4	no	—
749	C₂×D₄	—	3	4	no	—
750	C₂×D₄	—	3	4	no	—
751	C₂×D₄	—	3	4	no	—
752	C₂×D₄	—	3	4	no	—
753	C₂×D₄	—	4	2	no	—
754	C₂×D₄	—	4	2	no	—
755	C₂×D₄	—	6	4	no	—
756	C₂×D₄	—	12	2	no	—
757	C₂×D₄	—	12	2	no	—
758	C₂×D₄	—	12	2	no	—
759	C₂×D₄	C₂²×C₃×D₃	1	4	yes	—
760	C₂×D₄	C₂²×C₃×D₃	1	4	yes	—
761	C₂×D₄	C₂²×C₃×D₃	1	4	yes	—
762	C₂²×C₄	—	3	1	no	—
763	C₂²×C₄	—	3	1	no	—
764	C₂²×C₄	—	3	1	no	—
765	C₂²×C₄	—	3	1	no	—
766	C₂²×C₄	—	3	1	no	—
767	C₂²×C₄	—	3	1	no	—
768	C₂²×C₄	—	3	1	no	—
769	C₂²×C₄	—	3	4	no	—
770	C₂²×C₄	—	3	4	no	—
771	C₂²×C₄	—	3	4	no	—
772	C₂²×C₄	—	3	4	no	—
773	C₂²×C₄	—	12	2	no	—
774	C₂²×C₄	—	12	2	no	—
775	C₂²×C₄	—	12	2	no	—
776	C₂²×C₄	—	12	2	no	—
777	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
778	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
779	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
780	C₄⋊C₄	—	3	4	no	—
781	C₄⋊C₄	—	3	4	no	—
782	C₄⋊C₄	—	3	4	no	—
783	C₄⋊C₄	—	3	4	no	—
784	C₄⋊C₄	—	3	4	no	—
785	C₄⋊C₄	—	3	4	no	—
786	C₂²⋊C₄	—	3	4	no	—
787	C₂²⋊C₄	—	3	4	no	—
788	C₂²⋊C₄	—	3	4	no	—
789	C₂²⋊C₄	—	3	4	no	—
790	C₂²⋊C₄	—	3	4	no	—
791	C₂²⋊C₄	—	3	4	no	—
792	C₂²⋊C₄	—	3	4	no	—
793	C₂²⋊C₄	—	3	4	no	—
794	C₂²⋊C₄	—	3	4	no	—
795	C₂²⋊C₄	—	3	4	no	—
796	C₂²⋊C₄	—	3	4	no	—
797	C₂²⋊C₄	C₂²×C₃×D₃	1	4	yes	—
798	C₂²⋊C₄	C₂²×C₃×D₃	1	4	yes	—
799	C₂²⋊C₄	C₂²×C₃×D₃	1	4	yes	—
800	C₄²	—	3	4	no	—
801	C₄²	—	3	4	no	—
802	C₂²×C₃	—	2	2	no	—
803	C₂²×C₃	—	2	2	no	—
804	C₂²×C₃	—	2	2	no	—
805	C₂²×C₃	—	2	2	no	—
806	C₂²×C₃	—	2	8	no	—
807	C₂²×C₃	—	2	8	no	—
808	C₂²×C₃	—	2	4	no	—
809	C₂²×C₃	—	2	4	no	—
810	C₂²×C₃	—	2	2	no	—
811	C₂²×C₃	—	2	2	no	—
812	C₂²×C₃	—	2	2	no	—
813	C₂²×C₃	—	2	2	no	—
814	C₂²×C₃	—	2	2	no	—
815	C₂²×C₃	—	2	2	no	—
816	C₂²×C₃	—	2	2	no	—
817	C₂²×C₃	—	2	2	no	—
818	C₂²×C₃	—	2	2	no	—
819	C₂²×C₃	—	2	2	no	—
820	C₂²×C₃	—	2	2	no	—
821	C₂²×C₃	—	2	2	no	—
822	C₂²×C₃	—	2	2	no	—
823	C₂²×C₃	—	2	2	no	—
824	C₂²×C₃	—	2	2	no	—
825	C₂²×C₃	—	2	2	no	—
826	C₂²×C₃	—	2	2	no	—
827	C₂²×C₃	—	2	2	no	—
828	C₂²×C₃	—	2	2	no	—
829	C₂²×C₃	—	2	4	no	—
830	C₂²×C₃	—	2	2	no	—
831	C₂²×C₃	—	2	2	no	—
832	C₂²×C₃	—	2	1	no	—
833	C₂²×C₃	—	4	8	no	—
834	C₂²×C₃	—	4	2	no	—
835	C₂²×C₃	—	4	2	no	—
836	C₂²×C₃	—	4	2	no	—
837	C₂²×C₃	—	4	2	no	—
838	C₂²×C₃	—	4	2	no	—
839	C₂²×C₃	—	4	2	no	—
840	C₂²×C₃	—	4	2	no	—
841	C₂²×C₃	—	4	2	no	—
842	C₂²×C₃	—	4	2	no	—
843	C₂²×C₃	—	4	16	no	—
844	C₂²×C₃	—	4	16	no	—
845	C₂²×C₃	—	4	8	no	—
846	C₂²×C₃	—	4	8	no	—
847	C₂²×C₃	—	4	32	no	—
848	C₂²×C₃	—	4	4	no	—
849	C₂²×C₃	—	4	4	no	—
850	C₂²×C₃	—	4	4	no	—
851	C₂²×C₃	—	4	4	no	—
852	C₂²×C₃	—	4	4	no	—
853	C₂²×C₃	—	4	4	no	—
854	C₂²×C₃	—	6	2	no	—
855	C₂²×C₃	—	6	2	no	—
856	C₂²×C₃	—	6	2	no	—
857	C₂²×C₃	—	8	4	no	—
858	C₂²×C₃	—	12	4	no	—
859	C₂²×C₃	C₂×#237	1	4	yes	—
860	C₂²×C₃	C₂×#237	1	2	yes	—
861	C₂²×C₃	#1004	1	2	yes	—
862	C₂²×C₃	#1004	1	2	yes	—
863	C₂²×C₃	C₂×C₃×#41	1	4	yes	—
864	C₂²×C₃	C₂×C₃×#41	1	2	yes	—
865	C₂²×C₃	C₃×H(5,𝔽₂)	1	2	yes	—
866	C₂²×C₃	C₃×H(5,𝔽₂)	1	2	yes	—
867	C₂²×C₃	C₂⁴×D₃	1	1	yes	characteristic
868	C₂²×C₃	C₂⁵×C₃	1	1	yes	characteristic
869	C₂×D₃	—	2	2	no	—
870	C₂×D₃	—	2	2	no	—
871	C₂×D₃	—	2	2	no	—
872	C₂×D₃	—	4	4	no	—
873	C₃×C₄	—	2	2	no	—
874	C₃×C₄	—	2	2	no	—
875	C₃×C₄	—	2	2	no	—
876	C₃×C₄	—	2	2	no	—
877	C₃×C₄	—	2	2	no	—
878	C₃×C₄	—	2	2	no	—
879	C₃×C₄	—	4	2	no	—
880	C₃×C₄	—	4	2	no	—
881	C₃×C₄	—	4	2	no	—
882	C₃×C₄	—	6	2	no	—
883	C₃×C₄	—	6	2	no	—
884	C₃×C₄	—	6	2	no	—
885	C₃×C₄	—	6	2	no	—
886	C₃×C₄	—	6	2	no	—
887	C₃×C₄	—	6	2	no	—
888	C₃×C₄	—	6	2	no	—
889	Dic₃	—	2	2	no	—
890	Dic₃	—	2	2	no	—
891	Dic₃	—	2	2	no	—
892	Dic₃	—	2	2	no	—
893	Dic₃	—	2	2	no	—
894	Dic₃	—	2	2	no	—
895	Dic₃	—	2	2	no	—
896	C₃²	C₂×#538	1	1	yes	characteristic, complemented, Sylow
897	C₂³	—	2	2	no	—
898	C₂³	—	2	2	no	—
899	C₂³	—	2	2	no	—
900	C₂³	—	2	8	no	—
901	C₂³	—	2	2	no	—
902	C₂³	—	2	2	no	—
903	C₂³	—	2	2	no	—
904	C₂³	—	2	2	no	—
905	C₂³	—	2	2	no	—
906	C₂³	—	2	2	no	—
907	C₂³	—	2	2	no	—
908	C₂³	—	2	2	no	—
909	C₂³	—	3	2	no	—
910	C₂³	—	4	4	no	—
911	C₂³	—	4	4	no	—
912	C₂³	—	4	16	no	—
913	C₂³	—	6	2	no	—
914	C₂³	—	6	2	no	—
915	C₂³	—	6	2	no	—
916	C₂³	C₃×#237	1	4	yes	—
917	C₂³	C₂³×C₃×D₃	1	2	yes	—
918	C₂³	C₂³×C₃×D₃	1	2	yes	—
919	C₂³	C₂³×C₃×D₃	1	2	yes	—
920	C₂³	C₂³×C₃×D₃	1	2	yes	—
921	C₂³	C₂³×C₃×D₃	1	1	yes	characteristic
922	Q₈	—	12	4	no	—
923	D₄	—	2	8	no	—
924	D₄	—	4	4	no	—
925	D₄	—	4	4	no	—
926	D₄	—	6	8	no	—
927	D₄	—	12	4	no	—
928	D₄	—	12	4	no	—
929	D₄	—	12	4	no	—
930	C₂×C₄	—	2	2	no	—
931	C₂×C₄	—	2	2	no	—
932	C₂×C₄	—	2	2	no	—
933	C₂×C₄	—	3	2	no	—
934	C₂×C₄	—	3	2	no	—
935	C₂×C₄	—	3	2	no	—
936	C₂×C₄	—	3	2	no	—
937	C₂×C₄	—	3	2	no	—
938	C₂×C₄	—	3	2	no	—
939	C₂×C₄	—	3	2	no	—
940	C₂×C₄	—	6	2	no	—
941	C₂×C₄	—	6	2	no	—
942	C₂×C₄	—	6	2	no	—
943	C₂×C₄	—	6	2	no	—
944	C₂×C₄	—	6	2	no	—
945	C₂×C₄	—	6	2	no	—
946	C₂×C₄	—	6	2	no	—
947	C₂×C₄	—	12	4	no	—
948	C₂×C₄	—	12	4	no	—
949	C₂×C₄	—	12	4	no	—
950	C₂×C₄	—	12	4	no	—
951	C₂×C₄	C₂³×C₃×D₃	1	2	yes	—
952	C₂×C₄	C₂³×C₃×D₃	1	2	yes	—
953	C₂×C₄	C₂³×C₃×D₃	1	2	yes	—
954	C₂×C₃	—	2	4	no	—
955	C₂×C₃	—	2	4	no	—
956	C₂×C₃	—	2	4	no	—
957	C₂×C₃	—	2	1	no	—
958	C₂×C₃	—	2	1	no	—
959	C₂×C₃	—	2	1	no	—
960	C₂×C₃	—	4	4	no	—
961	C₂×C₃	—	4	4	no	—
962	C₂×C₃	—	4	4	no	—
963	C₂×C₃	—	4	2	no	—
964	C₂×C₃	—	4	2	no	—
965	C₂×C₃	—	4	2	no	—
966	C₂×C₃	—	4	2	no	—
967	C₂×C₃	—	4	2	no	—
968	C₂×C₃	—	4	2	no	—
969	C₂×C₃	—	8	2	no	—
970	C₂×C₃	—	12	2	no	—
971	C₂×C₃	#5593	1	4	yes	direct product factor
972	C₂×C₃	C₃×#538	1	4	yes	complemented
973	C₂×C₃	C₂²×#237	1	1	yes	characteristic
974	C₂×C₃	C₂×#1004	1	1	yes	characteristic
975	C₂×C₃	C₂×#1004	1	1	yes	characteristic
976	C₂×C₃	C₂²×C₃×#41	1	1	yes	characteristic
977	C₂×C₃	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
978	C₂×C₃	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
979	D₃	—	4	2	no	—
980	C₂²	—	2	8	no	—
981	C₂²	—	2	2	no	—
982	C₂²	—	2	2	no	—
983	C₂²	—	2	2	no	—
984	C₂²	—	2	2	no	—
985	C₂²	—	2	2	no	—
986	C₂²	—	2	2	no	—
987	C₂²	—	2	2	no	—
988	C₂²	—	2	2	no	—
989	C₂²	—	2	2	no	—
990	C₂²	—	2	2	no	—
991	C₂²	—	2	2	no	—
992	C₂²	—	4	16	no	—
993	C₂²	—	4	4	no	—
994	C₂²	—	4	4	no	—
995	C₂²	—	4	4	no	—
996	C₂²	—	6	2	no	—
997	C₂²	—	6	2	no	—
998	C₂²	—	6	2	no	—
999	C₂²	—	12	4	no	—
1000	C₂²	C₂×C₃×#237	1	4	yes	—
1001	C₂²	C₂×C₃×#237	1	2	yes	—
1002	C₂²	C₃×#1004	1	2	yes	—
1003	C₂²	C₃×#1004	1	2	yes	—
1004	C₂²	C₂⁴×C₃×D₃	1	1	yes	characteristic
1005	C₄	—	2	2	no	—
1006	C₄	—	2	2	no	—
1007	C₄	—	2	2	no	—
1008	C₄	—	6	2	no	—
1009	C₄	—	6	2	no	—
1010	C₄	—	6	2	no	—
1011	C₄	—	6	2	no	—
1012	C₄	—	6	2	no	—
1013	C₄	—	6	2	no	—
1014	C₄	—	6	2	no	—
1015	C₃	—	2	1	no	—
1016	C₃	C₂×#5593	1	1	yes	characteristic, direct product factor
1017	C₃	C₂×C₃×#538	1	1	yes	characteristic, complemented
1018	C₂	—	2	4	no	—
1019	C₂	—	4	2	no	—
1020	C₂	—	4	2	no	—
1021	C₂	—	4	2	no	—
1022	C₂	—	12	2	no	—
1023	C₂	C₃×#5593	1	4	yes	direct product factor
1024	C₂	C₂²×C₃×#237	1	1	yes	characteristic
1025	C₂	C₂×C₃×#1004	1	1	yes	characteristic
1026	C₂	C₂×C₃×#1004	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×#120	C₂
socle	C₂³×C₃²	C₂⁴
hypercenter	C₂×C₃×#120	D₃
hypocenter	C₃	C₂×C₃×#538
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. C₂×C₃²×#120	C₂	semidirect
2. C₂×C₃×#953	C₂	semidirect
3. C₂²×C₃×#217	C₂	semidirect
4. C₂×C₃×#939	C₂	semidirect
5. C₂×C₃×#939	C₂	semidirect
6. C₂×C₃×#938	C₂	semidirect
7. C₂×C₃×#936	C₂	semidirect
8. C₂×C₃×#935	C₂	semidirect
9. C₂×C₃×D₄×Dic₃	C₂	semidirect
10. C₃×#5593	C₂	direct (N × H)
11. C₂×C₃×#885	C₂	semidirect
12. C₂×C₃×#883	C₂	semidirect
13. C₂×C₃×#67⋊C₄	C₂	semidirect
14. C₂×C₃×#879	C₂	semidirect
15. C₂×C₃×#879	C₂	semidirect
16. C₂×C₃×#878	C₂	semidirect
18. C₂×#5593	C₃	direct (N × H)
26. C₂²×C₃×#67	C₂²	semidirect
29. C₂³×C₃×Dic₃	C₂²	semidirect
30. C₂²×C₃×C₄×D₃	C₂²	semidirect
31. C₂²×C₃×Dic₆	C₂²	semidirect
32. C₃²×#120	C₂²	semidirect
36. C₃×#953	C₂²	semidirect
44. C₂×C₃×#217	C₂²	semidirect
45. C₂×C₃×#217	C₂²	semidirect
46. C₂×C₃×#217	C₂²	semidirect
47. C₃×#939	C₂²	semidirect
48. C₃×#939	C₂²	semidirect
49. C₃×#938	C₂²	semidirect
50. C₃×#936	C₂²	semidirect
51. C₃×#935	C₂²	semidirect
52. C₃×D₄×Dic₃	C₂²	semidirect
53. C₂×C₃×(C₂×D₃)⋊C₄	C₂²	semidirect
54. C₂×C₃×(C₂×D₃)⋊C₄	C₂²	semidirect
55. C₂×C₃×C₄⋊Dic₃	C₂²	semidirect
56. C₂×C₃×C₄⋊Dic₃	C₂²	semidirect
57. C₂×C₃×Dic₃⋊C₄	C₂²	semidirect
58. C₂×C₃×Dic₃⋊C₄	C₂²	semidirect
59. C₂×C₃×Dic₃⋊C₄	C₂²	semidirect
60. C₂×C₃×Dic₃⋊C₄	C₂²	semidirect
61. C₂×C₃×C₄×Dic₃	C₂²	semidirect
62. C₂×C₃×C₄×Dic₃	C₂²	semidirect
63. C₃×#885	C₂²	semidirect
64. C₃×#883	C₂²	semidirect
65. C₃×#67⋊C₄	C₂²	semidirect
66. C₃×#879	C₂²	semidirect
67. C₃×#879	C₂²	semidirect
68. C₃×#878	C₂²	semidirect
82. C₂×C₃×#120	D₃	semidirect
83. C₂×C₃×#120	C₂×C₃	semidirect
87. C₂×#953	C₂×C₃	semidirect
88. C₂²×#217	C₂×C₃	semidirect
89. C₂×#939	C₂×C₃	semidirect
90. C₂×#939	C₂×C₃	semidirect
91. C₂×#938	C₂×C₃	semidirect
92. C₂×#936	C₂×C₃	semidirect
93. C₂×#935	C₂×C₃	semidirect
94. C₂×D₄×Dic₃	C₂×C₃	semidirect
95. #5593	C₂×C₃	direct (N × H)
96. C₂×#885	C₂×C₃	semidirect
97. C₂×#883	C₂×C₃	semidirect
98. C₂×#67⋊C₄	C₂×C₃	semidirect
99. C₂×#879	C₂×C₃	semidirect
100. C₂×#879	C₂×C₃	semidirect
101. C₂×#878	C₂×C₃	semidirect
127. C₂×C₃×#67	C₂³	semidirect
140. C₂²×C₃×Dic₃	C₂³	semidirect
142. C₂×C₃×C₄×D₃	C₂³	semidirect
144. C₂×C₃×Dic₆	C₂³	semidirect
155. C₃×#217	C₂³	semidirect
156. C₃×#217	C₂³	semidirect
157. C₃×(C₂×D₃)⋊C₄	C₂³	semidirect
158. C₃×(C₂×D₃)⋊C₄	C₂³	semidirect
159. C₃×C₄⋊Dic₃	C₂³	semidirect
160. C₃×C₄⋊Dic₃	C₂³	semidirect
161. C₃×Dic₃⋊C₄	C₂³	semidirect
162. C₃×Dic₃⋊C₄	C₂³	semidirect
163. C₃×Dic₃⋊C₄	C₂³	semidirect
164. C₃×Dic₃⋊C₄	C₂³	semidirect
165. C₃×C₄×Dic₃	C₂³	semidirect
166. C₃×C₄×Dic₃	C₂³	semidirect
192. C₂²×#67	C₂²×C₃	semidirect
195. C₂³×Dic₃	C₂²×C₃	semidirect
196. C₂²×C₄×D₃	C₂²×C₃	semidirect
197. C₂²×Dic₆	C₂²×C₃	semidirect
210. C₃×#120	C₂×D₃	semidirect
211. C₃×#120	C₂²×C₃	semidirect
243. #953	C₂²×C₃	semidirect
251. C₂×#217	C₂²×C₃	semidirect
252. C₂×#217	C₂²×C₃	semidirect
253. C₂×#217	C₂²×C₃	semidirect
254. #939	C₂²×C₃	semidirect
255. #939	C₂²×C₃	semidirect
256. #938	C₂²×C₃	semidirect
257. #936	C₂²×C₃	semidirect
258. #935	C₂²×C₃	semidirect
259. D₄×Dic₃	C₂²×C₃	semidirect
260. C₂×(C₂×D₃)⋊C₄	C₂²×C₃	semidirect
261. C₂×(C₂×D₃)⋊C₄	C₂²×C₃	semidirect
262. C₂×C₄⋊Dic₃	C₂²×C₃	semidirect
263. C₂×C₄⋊Dic₃	C₂²×C₃	semidirect
264. C₂×Dic₃⋊C₄	C₂²×C₃	semidirect
265. C₂×Dic₃⋊C₄	C₂²×C₃	semidirect
266. C₂×Dic₃⋊C₄	C₂²×C₃	semidirect
267. C₂×Dic₃⋊C₄	C₂²×C₃	semidirect
268. C₂×C₄×Dic₃	C₂²×C₃	semidirect
269. C₂×C₄×Dic₃	C₂²×C₃	semidirect
270. #885	C₂²×C₃	semidirect
271. #883	C₂²×C₃	semidirect
272. #67⋊C₄	C₂²×C₃	semidirect
273. #879	C₂²×C₃	semidirect
274. #879	C₂²×C₃	semidirect
275. #878	C₂²×C₃	semidirect
345. C₂×#120	C₃×D₃	semidirect
434. C₂×#67	C₂³×C₃	semidirect
447. C₂²×Dic₃	C₂³×C₃	semidirect
449. C₂×C₄×D₃	C₂³×C₃	semidirect
451. C₂×Dic₆	C₂³×C₃	semidirect
487. #217	C₂³×C₃	semidirect
488. #217	C₂³×C₃	semidirect
489. (C₂×D₃)⋊C₄	C₂³×C₃	semidirect
490. (C₂×D₃)⋊C₄	C₂³×C₃	semidirect
491. C₄⋊Dic₃	C₂³×C₃	semidirect
492. C₄⋊Dic₃	C₂³×C₃	semidirect
493. Dic₃⋊C₄	C₂³×C₃	semidirect
494. Dic₃⋊C₄	C₂³×C₃	semidirect
495. Dic₃⋊C₄	C₂³×C₃	semidirect
496. Dic₃⋊C₄	C₂³×C₃	semidirect
497. C₄×Dic₃	C₂³×C₃	semidirect
498. C₄×Dic₃	C₂³×C₃	semidirect
558. #120	C₂×C₃×D₃	semidirect
732. C₂×C₃²	#538	semidirect
896. C₃²	C₂×#538	semidirect
971. C₂×C₃	#5593	direct (N × H)
972. C₂×C₃	C₃×#538	semidirect
1016. C₃	C₂×#5593	direct (N × H)
1017. C₃	C₂×C₃×#538	semidirect
1023. C₂	C₃×#5593	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×#120	2
C₂×C₃×#953	2
C₂²×C₃×#217	2
C₂×C₃×#939	2
C₂×C₃×#938	2
C₂×C₃×#936	2
C₂×C₃×#935	2
C₂×C₃×D₄×Dic₃	2
C₃×#5593	2
C₂×C₃×#885	2
C₂×C₃×#883	2
C₂×C₃×#67⋊C₄	2
C₂×C₃×#879	2
C₂×C₃×#878	2
C₂×C₃×#538	3
C₂×#5593	3

Subgroups — C2×C3×#5593 #11901263

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#5593 #11901263