Subgroups — C₂×C₃×#5653 #11900940

Order 1152.

4139 conjugacy classes of subgroups.

The subgroup lattice has 820 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×D₃×D₄	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂³×C₃×D₁₂	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃²×#123	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃×#937	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₃×#929	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#5653	C₂	1	16	yes	maximal, direct product factor
7	C₂×C₃×#895	C₂	1	2	yes	maximal, complemented
8	C₂×C₃×#894	C₂	1	2	yes	maximal, complemented
9	C₂×C₃×#884	C₂	1	2	yes	maximal, complemented
10	C₂×C₃×#882	C₂	1	2	yes	maximal, complemented
11	C₂×C₃×#882	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₃×D₃×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₃×#534	—	3	1	no	maximal
14	C₂×#5653	C₃	1	1	yes	maximal, characteristic, direct product factor
15	C₂⁴×C₃×D₃	C₂²	1	1	yes	characteristic
16	C₂⁴×C₃×D₃	C₂²	1	1	yes	characteristic, complemented
17	C₂⁴×C₃×D₃	C₂²	1	1	yes	characteristic, complemented
18	C₂²×C₃²×D₄	C₂²	1	1	yes	characteristic
19	C₂³×C₃²×C₄	C₂²	1	1	yes	characteristic, complemented
20	C₂²×C₃×#67	C₂²	1	1	yes	characteristic
21	C₂²×C₃×#67	C₂²	1	1	yes	characteristic, complemented
22	C₂²×C₃×#67	C₂²	1	2	yes	complemented
23	C₂×C₃×D₃×D₄	—	2	8	no	—
24	C₂×C₃×D₃×D₄	C₂²	1	8	yes	complemented
25	C₂²×C₃×D₁₂	—	2	8	no	—
26	C₂²×C₃×D₁₂	C₂²	1	2	yes	—
27	C₂²×C₃×D₁₂	C₂²	1	2	yes	complemented
28	C₂²×C₃×D₁₂	C₂²	1	1	yes	characteristic, complemented
29	C₂²×C₃×D₁₂	C₂²	1	2	yes	complemented
30	C₂²×C₃×D₁₂	C₂²	1	8	yes	complemented
31	C₂²×C₃×C₄×D₃	C₂²	1	1	yes	characteristic, complemented
32	C₂²×C₃×C₄×D₃	C₂²	1	2	yes	complemented
33	C₃²×#123	C₂²	1	8	yes	complemented
34	C₂×C₃²×C₄⋊C₄	C₂²	1	2	yes	complemented
35	C₂×C₃²×C₂²⋊C₄	C₂²	1	2	yes	complemented
36	C₂×C₃²×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
37	C₂×C₃×#217	C₂²	1	1	yes	characteristic, complemented
38	C₃×#937	C₂²	1	8	yes	complemented
39	C₃×#929	C₂²	1	8	yes	complemented
40	C₂×C₃×(C₂×D₃)⋊C₄	C₂²	1	2	yes	complemented
41	C₂×C₃×(C₂×D₃)⋊C₄	C₂²	1	2	yes	complemented
42	C₂×C₃×(C₂×D₃)⋊C₄	C₂²	1	2	yes	complemented
43	C₂×C₃×(C₂×D₃)⋊C₄	C₂²	1	2	yes	complemented
44	C₂×C₃×Dic₃⋊C₄	C₂²	1	2	yes	complemented
45	C₃×#895	C₂²	1	16	yes	complemented
46	C₃×#894	C₂²	1	16	yes	complemented
47	C₃×#884	C₂²	1	16	yes	complemented
48	C₃×#882	C₂²	1	16	yes	complemented
49	C₃×#882	C₂²	1	8	yes	complemented
50	C₃×D₃×C₂²⋊C₄	C₂²	1	8	yes	complemented
51	C₂³×C₃×D₄	—	3	1	no	—
52	C₂³×C₃×D₄	—	3	1	no	—
53	C₂²×D₃×D₄	C₂×C₃	1	1	yes	characteristic, complemented
54	C₂³×D₁₂	C₂×C₃	1	1	yes	characteristic, complemented
55	C₃×#534	—	3	16	no	—
56	C₂×C₃×#123	—	2	1	no	—
57	C₂×C₃×#123	—	3	1	no	—
58	C₂×C₃×#123	—	3	2	no	—
59	C₂×C₃×#123	D₃	1	1	yes	characteristic, complemented
60	C₂×C₃×#123	C₂×C₃	1	1	yes	characteristic, complemented
61	C₂×C₃×#121	—	3	2	no	—
62	C₂×C₃×#121	—	3	2	no	—
63	C₂×C₃×#120	—	3	1	no	—
64	C₂×C₃×#120	—	3	2	no	—
65	C₂×C₃×#120	—	3	1	no	—
66	C₂²×C₃×C₂²⋊C₄	—	3	1	no	—
67	C₂×#937	C₂×C₃	1	1	yes	characteristic, complemented
68	C₂×#929	C₂×C₃	1	1	yes	characteristic, complemented
69	#5653	C₂×C₃	1	16	yes	direct product factor
70	C₂×#895	C₂×C₃	1	2	yes	complemented
71	C₂×#894	C₂×C₃	1	2	yes	complemented
72	C₂×#884	C₂×C₃	1	2	yes	complemented
73	C₂×#882	C₂×C₃	1	2	yes	complemented
74	C₂×#882	C₂×C₃	1	1	yes	characteristic, complemented
75	C₂×D₃×C₂²⋊C₄	C₂×C₃	1	1	yes	characteristic, complemented
76	C₂⁴×C₃²	C₂³	1	1	yes	characteristic
77	C₂⁴×C₃²	C₂³	1	1	yes	characteristic
78	C₂³×C₃×D₃	—	2	4	no	—
79	C₂³×C₃×D₃	—	2	4	no	—
80	C₂³×C₃×D₃	—	4	4	no	—
81	C₂³×C₃×D₃	—	4	4	no	—
82	C₂³×C₃×D₃	—	4	4	no	—
83	C₂³×C₃×D₃	D₄	1	8	yes	complemented
84	C₂³×C₃×D₃	C₂³	1	2	yes	—
85	C₂³×C₃×D₃	C₂³	1	1	yes	characteristic
86	C₂³×C₃×D₃	C₂³	1	1	yes	characteristic
87	C₂³×C₃×D₃	C₂³	1	1	yes	characteristic
88	C₂³×C₃×D₃	C₂³	1	4	yes	—
89	C₂³×C₃×D₃	C₂³	1	4	yes	complemented
90	C₂³×C₃×D₃	C₂³	1	4	yes	complemented
91	C₂×C₃²×D₄	—	2	4	no	—
92	C₂×C₃²×D₄	C₂³	1	4	yes	—
93	C₂²×C₃²×C₄	—	2	4	no	—
94	C₂²×C₃²×C₄	C₂³	1	2	yes	—
95	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
96	C₂²×C₃²×C₄	C₂³	1	2	yes	—
97	C₂²×C₃²×C₄	C₂³	1	4	yes	complemented
98	C₂×C₃×#67	—	2	4	no	—
99	C₂×C₃×#67	—	2	4	no	—
100	C₂×C₃×#67	—	4	4	no	—
101	C₂×C₃×#67	C₂³	1	4	yes	—
102	C₂×C₃×#67	C₂³	1	4	yes	complemented
103	C₂×C₃×#67	C₂³	1	8	yes	complemented
104	C₂²×C₃×Dic₃	C₂³	1	1	yes	characteristic
105	C₂²×C₃×Dic₃	C₂³	1	2	yes	—
106	C₃×D₃×D₄	—	2	32	no	—
107	C₂×C₃×D₁₂	—	2	8	no	—
108	C₂×C₃×D₁₂	—	2	8	no	—
109	C₂×C₃×D₁₂	—	2	4	no	—
110	C₂×C₃×D₁₂	—	2	32	no	—
111	C₂×C₃×D₁₂	—	4	4	no	—
112	C₂×C₃×D₁₂	C₂³	1	8	yes	—
113	C₂×C₃×D₁₂	C₂³	1	8	yes	complemented
114	C₂×C₃×D₁₂	C₂³	1	4	yes	complemented
115	C₂×C₃×D₁₂	C₂³	1	8	yes	complemented
116	C₂×C₃×C₄×D₃	—	2	4	no	—
117	C₂×C₃×C₄×D₃	—	4	4	no	—
118	C₂×C₃×C₄×D₃	C₂³	1	4	yes	complemented
119	C₂×C₃×C₄×D₃	C₂³	1	8	yes	complemented
120	C₃²×C₄⋊C₄	C₂³	1	8	yes	complemented
121	C₃²×C₂²⋊C₄	C₂³	1	4	yes	complemented
122	C₃²×C₂²⋊C₄	C₂³	1	8	yes	complemented
123	C₃×#217	C₂³	1	4	yes	complemented
124	C₃×(C₂×D₃)⋊C₄	C₂³	1	8	yes	complemented
125	C₃×(C₂×D₃)⋊C₄	C₂³	1	8	yes	complemented
126	C₃×(C₂×D₃)⋊C₄	C₂³	1	8	yes	complemented
127	C₃×(C₂×D₃)⋊C₄	C₂³	1	8	yes	complemented
128	C₃×Dic₃⋊C₄	C₂³	1	8	yes	complemented
129	C₂×#534	—	3	1	no	Sylow
130	C₂⁵×C₃	—	3	1	no	—
131	C₂⁵×C₃	—	3	1	no	—
132	C₂⁵×C₃	—	3	1	no	—
133	C₂⁴×D₃	C₂²×C₃	1	1	yes	characteristic
134	C₂⁴×D₃	C₂²×C₃	1	1	yes	characteristic, complemented
135	C₂⁴×D₃	C₂²×C₃	1	1	yes	characteristic, complemented
136	C₂²×C₃×D₄	—	2	1	no	—
137	C₂²×C₃×D₄	—	3	1	no	—
138	C₂²×C₃×D₄	—	3	1	no	—
139	C₂²×C₃×D₄	—	3	2	no	—
140	C₂²×C₃×D₄	—	3	8	no	—
141	C₂²×C₃×D₄	—	3	2	no	—
142	C₂²×C₃×D₄	—	3	1	no	—
143	C₂²×C₃×D₄	—	3	2	no	—
144	C₂²×C₃×D₄	—	3	2	no	—
145	C₂²×C₃×D₄	—	3	8	no	—
146	C₂²×C₃×D₄	—	6	8	no	—
147	C₂²×C₃×D₄	—	6	8	no	—
148	C₂²×C₃×D₄	C₂×D₃	1	1	yes	characteristic
149	C₂²×C₃×D₄	C₂²×C₃	1	1	yes	characteristic
150	C₂³×C₃×C₄	—	2	1	no	—
151	C₂³×C₃×C₄	—	3	1	no	—
152	C₂³×C₃×C₄	—	3	2	no	—
153	C₂³×C₃×C₄	C₂×D₃	1	1	yes	characteristic, complemented
154	C₂³×C₃×C₄	C₂²×C₃	1	1	yes	characteristic, complemented
155	C₂²×#67	C₂²×C₃	1	1	yes	characteristic
156	C₂²×#67	C₂²×C₃	1	1	yes	characteristic, complemented
157	C₂²×#67	C₂²×C₃	1	2	yes	complemented
158	C₂×D₃×D₄	—	2	8	no	—
159	C₂×D₃×D₄	C₂²×C₃	1	8	yes	complemented
160	C₂²×D₁₂	—	2	8	no	—
161	C₂²×D₁₂	C₂²×C₃	1	2	yes	—
162	C₂²×D₁₂	C₂²×C₃	1	8	yes	complemented
163	C₂²×D₁₂	C₂²×C₃	1	2	yes	complemented
164	C₂²×D₁₂	C₂²×C₃	1	1	yes	characteristic, complemented
165	C₂²×D₁₂	C₂²×C₃	1	2	yes	complemented
166	C₂²×C₄×D₃	C₂²×C₃	1	1	yes	characteristic, complemented
167	C₂²×C₄×D₃	C₂²×C₃	1	2	yes	complemented
168	C₃×#123	—	2	8	no	—
169	C₃×#123	—	3	8	no	—
170	C₃×#123	—	3	16	no	—
171	C₃×#123	C₂×D₃	1	8	yes	complemented
172	C₃×#123	C₂²×C₃	1	8	yes	complemented
173	C₃×#121	—	3	16	no	—
174	C₃×#121	—	3	16	no	—
175	C₃×#120	—	3	8	no	—
176	C₃×#120	—	3	16	no	—
177	C₃×#120	—	3	8	no	—
178	C₂×C₃×C₄⋊C₄	—	2	2	no	—
179	C₂×C₃×C₄⋊C₄	—	3	2	no	—
180	C₂×C₃×C₄⋊C₄	C₂×D₃	1	2	yes	complemented
181	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	2	yes	complemented
182	C₂×C₃×C₂²⋊C₄	—	2	1	no	—
183	C₂×C₃×C₂²⋊C₄	—	2	2	no	—
184	C₂×C₃×C₂²⋊C₄	—	3	1	no	—
185	C₂×C₃×C₂²⋊C₄	—	3	2	no	—
186	C₂×C₃×C₂²⋊C₄	—	3	2	no	—
187	C₂×C₃×C₂²⋊C₄	—	3	2	no	—
188	C₂×C₃×C₂²⋊C₄	—	3	2	no	—
189	C₂×C₃×C₂²⋊C₄	—	3	8	no	—
190	C₂×C₃×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic, complemented
191	C₂×C₃×C₂²⋊C₄	C₂×D₃	1	2	yes	complemented
192	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
193	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	2	yes	complemented
194	C₂×#217	C₂²×C₃	1	1	yes	characteristic, complemented
195	#937	C₂²×C₃	1	8	yes	complemented
196	#929	C₂²×C₃	1	8	yes	complemented
197	C₂×(C₂×D₃)⋊C₄	C₂²×C₃	1	2	yes	complemented
198	C₂×(C₂×D₃)⋊C₄	C₂²×C₃	1	2	yes	complemented
199	C₂×(C₂×D₃)⋊C₄	C₂²×C₃	1	2	yes	complemented
200	C₂×(C₂×D₃)⋊C₄	C₂²×C₃	1	2	yes	complemented
201	C₂×Dic₃⋊C₄	C₂²×C₃	1	2	yes	complemented
202	#895	C₂²×C₃	1	16	yes	complemented
203	#894	C₂²×C₃	1	16	yes	complemented
204	#884	C₂²×C₃	1	16	yes	complemented
205	#882	C₂²×C₃	1	16	yes	complemented
206	#882	C₂²×C₃	1	8	yes	complemented
207	D₃×C₂²⋊C₄	C₂²×C₃	1	8	yes	complemented
208	C₂³×C₃²	—	2	4	no	—
209	C₂³×C₃²	—	2	2	no	—
210	C₂³×C₃²	—	2	4	no	—
211	C₂³×C₃²	C₂×D₄	1	4	yes	—
212	C₂³×C₃²	C₂⁴	1	2	yes	—
213	C₂³×C₃²	C₂⁴	1	2	yes	—
214	C₂³×C₃²	C₂⁴	1	1	yes	characteristic
215	C₂²×C₃×D₃	—	2	4	no	—
216	C₂²×C₃×D₃	—	2	4	no	—
217	C₂²×C₃×D₃	—	2	4	no	—
218	C₂²×C₃×D₃	—	2	2	no	—
219	C₂²×C₃×D₃	—	2	8	no	—
220	C₂²×C₃×D₃	—	2	4	no	—
221	C₂²×C₃×D₃	—	2	4	no	—
222	C₂²×C₃×D₃	—	2	4	no	—
223	C₂²×C₃×D₃	—	2	8	no	—
224	C₂²×C₃×D₃	—	4	16	no	—
225	C₂²×C₃×D₃	—	4	8	no	—
226	C₂²×C₃×D₃	—	4	8	no	—
227	C₂²×C₃×D₃	—	4	8	no	—
228	C₂²×C₃×D₃	—	4	16	no	—
229	C₂²×C₃×D₃	—	4	16	no	—
230	C₂²×C₃×D₃	C₂×D₄	1	4	yes	—
231	C₂²×C₃×D₃	C₂×D₄	1	4	yes	—
232	C₂²×C₃×D₃	C₂×D₄	1	16	yes	complemented
233	C₂²×C₃×D₃	C₂⁴	1	4	yes	—
234	C₂²×C₃×D₃	C₂⁴	1	2	yes	—
235	C₂²×C₃×D₃	C₂⁴	1	2	yes	—
236	C₂²×C₃×D₃	C₂⁴	1	2	yes	—
237	C₃²×D₄	—	2	8	no	—
238	C₂×C₃²×C₄	—	2	2	no	—
239	C₂×C₃²×C₄	—	2	4	no	—
240	C₂×C₃²×C₄	—	2	8	no	—
241	C₂×C₃²×C₄	—	2	4	no	—
242	C₂×C₃²×C₄	C₂⁴	1	4	yes	—
243	C₂×C₃²×C₄	C₂⁴	1	4	yes	—
244	C₂×C₃²×C₄	C₂⁴	1	2	yes	—
245	C₃×#67	—	2	8	no	—
246	C₃×#67	—	2	8	no	—
247	C₃×#67	—	4	8	no	—
248	C₂×C₃×Dic₃	—	2	2	no	—
249	C₂×C₃×Dic₃	—	2	4	no	—
250	C₂×C₃×Dic₃	C₂⁴	1	2	yes	—
251	C₂×C₃×Dic₃	C₂⁴	1	4	yes	—
252	C₃×D₁₂	—	2	16	no	—
253	C₃×D₁₂	—	2	16	no	—
254	C₃×D₁₂	—	2	8	no	—
255	C₃×D₁₂	—	4	8	no	—
256	C₃×C₄×D₃	—	2	8	no	—
257	C₃×C₄×D₃	—	4	8	no	—
258	C₂³×D₄	—	3	1	no	—
259	C₂³×D₄	—	3	1	no	—
260	#534	—	3	16	no	—
261	C₂×#123	—	3	1	no	—
262	C₂×#123	—	3	2	no	—
263	C₂×#123	C₃×D₃	1	1	yes	characteristic, complemented
264	C₂×#121	—	3	2	no	—
265	C₂×#121	—	3	2	no	—
266	C₂×#120	—	3	1	no	—
267	C₂×#120	—	3	2	no	—
268	C₂×#120	—	3	1	no	—
269	C₂²×C₂²⋊C₄	—	3	1	no	—
270	C₂⁴×C₃	—	2	1	no	—
271	C₂⁴×C₃	—	2	1	no	—
272	C₂⁴×C₃	—	3	1	no	—
273	C₂⁴×C₃	—	3	1	no	—
274	C₂⁴×C₃	—	3	8	no	—
275	C₂⁴×C₃	—	3	4	no	—
276	C₂⁴×C₃	—	3	2	no	—
277	C₂⁴×C₃	—	3	1	no	—
278	C₂⁴×C₃	—	3	4	no	—
279	C₂⁴×C₃	—	3	4	no	—
280	C₂⁴×C₃	—	6	4	no	—
281	C₂⁴×C₃	—	6	4	no	—
282	C₂⁴×C₃	—	12	4	no	—
283	C₂⁴×C₃	—	12	4	no	—
284	C₂⁴×C₃	—	12	4	no	—
285	C₂⁴×C₃	C₂²×D₃	1	1	yes	characteristic
286	C₂⁴×C₃	C₂²×D₃	1	1	yes	characteristic
287	C₂⁴×C₃	C₂³×C₃	1	1	yes	characteristic
288	C₂⁴×C₃	C₂³×C₃	1	1	yes	characteristic
289	C₂³×D₃	—	2	4	no	—
290	C₂³×D₃	—	2	4	no	—
291	C₂³×D₃	—	4	4	no	—
292	C₂³×D₃	—	4	4	no	—
293	C₂³×D₃	—	4	4	no	—
294	C₂³×D₃	C₃×D₄	1	8	yes	complemented
295	C₂³×D₃	C₂³×C₃	1	2	yes	—
296	C₂³×D₃	C₂³×C₃	1	1	yes	characteristic
297	C₂³×D₃	C₂³×C₃	1	1	yes	characteristic
298	C₂³×D₃	C₂³×C₃	1	1	yes	characteristic
299	C₂³×D₃	C₂³×C₃	1	4	yes	—
300	C₂³×D₃	C₂³×C₃	1	4	yes	complemented
301	C₂³×D₃	C₂³×C₃	1	4	yes	complemented
302	C₂×C₃×D₄	—	2	4	no	—
303	C₂×C₃×D₄	—	2	4	no	—
304	C₂×C₃×D₄	—	2	4	no	—
305	C₂×C₃×D₄	—	3	4	no	—
306	C₂×C₃×D₄	—	3	4	no	—
307	C₂×C₃×D₄	—	3	8	no	—
308	C₂×C₃×D₄	—	3	8	no	—
309	C₂×C₃×D₄	—	3	4	no	—
310	C₂×C₃×D₄	—	3	8	no	—
311	C₂×C₃×D₄	—	3	8	no	—
312	C₂×C₃×D₄	—	4	4	no	—
313	C₂×C₃×D₄	—	6	8	no	—
314	C₂×C₃×D₄	—	6	8	no	—
315	C₂×C₃×D₄	—	6	32	no	—
316	C₂×C₃×D₄	—	6	4	no	—
317	C₂×C₃×D₄	—	6	32	no	—
318	C₂×C₃×D₄	—	6	4	no	—
319	C₂×C₃×D₄	—	6	4	no	—
320	C₂×C₃×D₄	—	12	4	no	—
321	C₂×C₃×D₄	—	12	4	no	—
322	C₂×C₃×D₄	C₂²×D₃	1	4	yes	—
323	C₂×C₃×D₄	C₂³×C₃	1	4	yes	—
324	C₂²×C₃×C₄	—	2	4	no	—
325	C₂²×C₃×C₄	—	2	4	no	—
326	C₂²×C₃×C₄	—	2	2	no	—
327	C₂²×C₃×C₄	—	2	2	no	—
328	C₂²×C₃×C₄	—	2	1	no	—
329	C₂²×C₃×C₄	—	2	4	no	—
330	C₂²×C₃×C₄	—	3	2	no	—
331	C₂²×C₃×C₄	—	3	1	no	—
332	C₂²×C₃×C₄	—	3	4	no	—
333	C₂²×C₃×C₄	—	3	8	no	—
334	C₂²×C₃×C₄	—	4	4	no	—
335	C₂²×C₃×C₄	—	6	4	no	—
336	C₂²×C₃×C₄	—	12	4	no	—
337	C₂²×C₃×C₄	C₂²×D₃	1	2	yes	—
338	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
339	C₂²×C₃×C₄	C₂²×D₃	1	2	yes	—
340	C₂²×C₃×C₄	C₂²×D₃	1	4	yes	complemented
341	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
342	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
343	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
344	C₂²×C₃×C₄	C₂³×C₃	1	4	yes	complemented
345	C₂×#67	—	2	4	no	—
346	C₂×#67	—	2	4	no	—
347	C₂×#67	—	4	4	no	—
348	C₂×#67	C₂³×C₃	1	4	yes	—
349	C₂×#67	C₂³×C₃	1	4	yes	complemented
350	C₂×#67	C₂³×C₃	1	8	yes	complemented
351	C₂²×Dic₃	C₂³×C₃	1	1	yes	characteristic
352	C₂²×Dic₃	C₂³×C₃	1	2	yes	—
353	D₃×D₄	—	2	32	no	—
354	C₂×D₁₂	—	2	8	no	—
355	C₂×D₁₂	—	2	8	no	—
356	C₂×D₁₂	—	2	4	no	—
357	C₂×D₁₂	—	2	32	no	—
358	C₂×D₁₂	—	4	4	no	—
359	C₂×D₁₂	C₂³×C₃	1	8	yes	—
360	C₂×D₁₂	C₂³×C₃	1	8	yes	complemented
361	C₂×D₁₂	C₂³×C₃	1	4	yes	complemented
362	C₂×D₁₂	C₂³×C₃	1	8	yes	complemented
363	C₂×C₄×D₃	—	2	4	no	—
364	C₂×C₄×D₃	—	4	4	no	—
365	C₂×C₄×D₃	C₂³×C₃	1	4	yes	complemented
366	C₂×C₄×D₃	C₂³×C₃	1	8	yes	complemented
367	C₃×C₄⋊C₄	—	2	8	no	—
368	C₃×C₄⋊C₄	—	3	8	no	—
369	C₃×C₄⋊C₄	C₂²×D₃	1	8	yes	complemented
370	C₃×C₄⋊C₄	C₂³×C₃	1	8	yes	complemented
371	C₃×C₂²⋊C₄	—	2	4	no	—
372	C₃×C₂²⋊C₄	—	2	8	no	—
373	C₃×C₂²⋊C₄	—	3	4	no	—
374	C₃×C₂²⋊C₄	—	3	8	no	—
375	C₃×C₂²⋊C₄	—	3	8	no	—
376	C₃×C₂²⋊C₄	—	3	8	no	—
377	C₃×C₂²⋊C₄	—	3	8	no	—
378	C₃×C₂²⋊C₄	C₂²×D₃	1	4	yes	complemented
379	C₃×C₂²⋊C₄	C₂²×D₃	1	8	yes	complemented
380	C₃×C₂²⋊C₄	C₂³×C₃	1	4	yes	complemented
381	C₃×C₂²⋊C₄	C₂³×C₃	1	8	yes	complemented
382	#217	C₂³×C₃	1	4	yes	complemented
383	(C₂×D₃)⋊C₄	C₂³×C₃	1	8	yes	complemented
384	(C₂×D₃)⋊C₄	C₂³×C₃	1	8	yes	complemented
385	(C₂×D₃)⋊C₄	C₂³×C₃	1	8	yes	complemented
386	(C₂×D₃)⋊C₄	C₂³×C₃	1	8	yes	complemented
387	Dic₃⋊C₄	C₂³×C₃	1	8	yes	complemented
388	C₂²×C₃²	—	2	8	no	—
389	C₂²×C₃²	—	2	4	no	—
390	C₂²×C₃²	—	2	2	no	—
391	C₂²×C₃²	—	2	4	no	—
392	C₂²×C₃²	—	4	4	no	—
393	C₂²×C₃²	C₂²×D₄	1	4	yes	—
394	C₂²×C₃²	C₂²×D₄	1	2	yes	—
395	C₂²×C₃²	H(5,𝔽₂)	1	4	yes	—
396	C₂²×C₃²	C₂⁵	1	1	yes	characteristic
397	C₂×C₃×D₃	—	2	8	no	—
398	C₂×C₃×D₃	—	2	8	no	—
399	C₂×C₃×D₃	—	2	4	no	—
400	C₂×C₃×D₃	—	2	4	no	—
401	C₂×C₃×D₃	—	2	4	no	—
402	C₂×C₃×D₃	—	2	2	no	—
403	C₂×C₃×D₃	—	2	4	no	—
404	C₂×C₃×D₃	—	2	4	no	—
405	C₂×C₃×D₃	—	2	4	no	—
406	C₂×C₃×D₃	—	4	16	no	—
407	C₂×C₃×D₃	—	4	16	no	—
408	C₂×C₃×D₃	—	4	16	no	—
409	C₂×C₃×D₃	—	4	8	no	—
410	C₂×C₃×D₃	—	4	4	no	—
411	C₂×C₃×D₃	C₂²×D₄	1	4	yes	—
412	C₂×C₃×D₃	C₂²×D₄	1	4	yes	—
413	C₃²×C₄	—	2	2	no	—
414	C₃²×C₄	—	2	4	no	—
415	C₃²×C₄	—	2	4	no	—
416	C₃×Dic₃	—	2	2	no	—
417	C₃×Dic₃	—	2	4	no	—
418	C₂⁵	—	3	1	no	—
419	C₂⁵	—	3	1	no	—
420	C₂⁵	—	3	1	no	—
421	C₂²×D₄	—	3	1	no	—
422	C₂²×D₄	—	3	1	no	—
423	C₂²×D₄	—	3	2	no	—
424	C₂²×D₄	—	3	8	no	—
425	C₂²×D₄	—	3	2	no	—
426	C₂²×D₄	—	3	1	no	—
427	C₂²×D₄	—	3	2	no	—
428	C₂²×D₄	—	3	2	no	—
429	C₂²×D₄	—	3	8	no	—
430	C₂²×D₄	—	6	8	no	—
431	C₂²×D₄	—	6	8	no	—
432	C₂²×D₄	C₂×C₃×D₃	1	1	yes	characteristic
433	C₂³×C₄	—	3	1	no	—
434	C₂³×C₄	—	3	2	no	—
435	C₂³×C₄	C₂×C₃×D₃	1	1	yes	characteristic, complemented
436	#123	—	3	8	no	—
437	#123	—	3	16	no	—
438	#123	C₂×C₃×D₃	1	8	yes	complemented
439	#121	—	3	16	no	—
440	#121	—	3	16	no	—
441	#120	—	3	8	no	—
442	#120	—	3	16	no	—
443	#120	—	3	8	no	—
444	C₂×C₄⋊C₄	—	3	2	no	—
445	C₂×C₄⋊C₄	C₂×C₃×D₃	1	2	yes	complemented
446	C₂×C₂²⋊C₄	—	3	1	no	—
447	C₂×C₂²⋊C₄	—	3	2	no	—
448	C₂×C₂²⋊C₄	—	3	2	no	—
449	C₂×C₂²⋊C₄	—	3	2	no	—
450	C₂×C₂²⋊C₄	—	3	2	no	—
451	C₂×C₂²⋊C₄	—	3	8	no	—
452	C₂×C₂²⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic, complemented
453	C₂×C₂²⋊C₄	C₂×C₃×D₃	1	2	yes	complemented
454	C₂³×C₃	—	2	4	no	—
455	C₂³×C₃	—	2	4	no	—
456	C₂³×C₃	—	2	2	no	—
457	C₂³×C₃	—	2	4	no	—
458	C₂³×C₃	—	2	2	no	—
459	C₂³×C₃	—	2	4	no	—
460	C₂³×C₃	—	2	1	no	—
461	C₂³×C₃	—	2	2	no	—
462	C₂³×C₃	—	2	2	no	—
463	C₂³×C₃	—	2	4	no	—
464	C₂³×C₃	—	3	4	no	—
465	C₂³×C₃	—	3	4	no	—
466	C₂³×C₃	—	3	2	no	—
467	C₂³×C₃	—	3	2	no	—
468	C₂³×C₃	—	3	16	no	—
469	C₂³×C₃	—	3	4	no	—
470	C₂³×C₃	—	3	2	no	—
471	C₂³×C₃	—	4	4	no	—
472	C₂³×C₃	—	4	2	no	—
473	C₂³×C₃	—	4	4	no	—
474	C₂³×C₃	—	6	8	no	—
475	C₂³×C₃	—	6	4	no	—
476	C₂³×C₃	—	6	4	no	—
477	C₂³×C₃	—	6	8	no	—
478	C₂³×C₃	—	6	4	no	—
479	C₂³×C₃	—	6	2	no	—
480	C₂³×C₃	—	6	4	no	—
481	C₂³×C₃	—	6	4	no	—
482	C₂³×C₃	—	6	4	no	—
483	C₂³×C₃	—	12	16	no	—
484	C₂³×C₃	—	12	8	no	—
485	C₂³×C₃	—	12	8	no	—
486	C₂³×C₃	—	12	8	no	—
487	C₂³×C₃	—	12	16	no	—
488	C₂³×C₃	—	12	16	no	—
489	C₂³×C₃	D₃×D₄	1	4	yes	—
490	C₂³×C₃	C₂×C₃×D₄	1	4	yes	—
491	C₂³×C₃	C₂³×D₃	1	2	yes	—
492	C₂³×C₃	C₂³×D₃	1	2	yes	—
493	C₂³×C₃	C₂³×D₃	1	1	yes	characteristic
494	C₂³×C₃	C₂⁴×C₃	1	2	yes	—
495	C₂³×C₃	C₂⁴×C₃	1	2	yes	—
496	C₂³×C₃	C₂⁴×C₃	1	1	yes	characteristic
497	C₂²×D₃	—	2	4	no	—
498	C₂²×D₃	—	2	4	no	—
499	C₂²×D₃	—	2	4	no	—
500	C₂²×D₃	—	2	8	no	—
501	C₂²×D₃	—	2	2	no	—
502	C₂²×D₃	—	2	4	no	—
503	C₂²×D₃	—	2	4	no	—
504	C₂²×D₃	—	2	4	no	—
505	C₂²×D₃	—	2	8	no	—
506	C₂²×D₃	—	4	16	no	—
507	C₂²×D₃	—	4	8	no	—
508	C₂²×D₃	—	4	8	no	—
509	C₂²×D₃	—	4	8	no	—
510	C₂²×D₃	—	4	16	no	—
511	C₂²×D₃	—	4	16	no	—
512	C₂²×D₃	C₂×C₃×D₄	1	4	yes	—
513	C₂²×D₃	C₂×C₃×D₄	1	4	yes	—
514	C₂²×D₃	C₂×C₃×D₄	1	16	yes	complemented
515	C₂²×D₃	C₂⁴×C₃	1	4	yes	—
516	C₂²×D₃	C₂⁴×C₃	1	2	yes	—
517	C₂²×D₃	C₂⁴×C₃	1	2	yes	—
518	C₂²×D₃	C₂⁴×C₃	1	2	yes	—
519	C₃×D₄	—	2	8	no	—
520	C₃×D₄	—	2	8	no	—
521	C₃×D₄	—	4	8	no	—
522	C₃×D₄	—	6	16	no	—
523	C₃×D₄	—	6	16	no	—
524	C₃×D₄	—	6	8	no	—
525	C₃×D₄	—	6	8	no	—
526	C₃×D₄	—	6	8	no	—
527	C₃×D₄	—	12	8	no	—
528	C₃×D₄	—	12	8	no	—
529	C₂×C₃×C₄	—	2	4	no	—
530	C₂×C₃×C₄	—	2	8	no	—
531	C₂×C₃×C₄	—	2	2	no	—
532	C₂×C₃×C₄	—	2	4	no	—
533	C₂×C₃×C₄	—	2	2	no	—
534	C₂×C₃×C₄	—	2	4	no	—
535	C₂×C₃×C₄	—	2	8	no	—
536	C₂×C₃×C₄	—	2	4	no	—
537	C₂×C₃×C₄	—	2	4	no	—
538	C₂×C₃×C₄	—	2	4	no	—
539	C₂×C₃×C₄	—	2	2	no	—
540	C₂×C₃×C₄	—	3	4	no	—
541	C₂×C₃×C₄	—	3	2	no	—
542	C₂×C₃×C₄	—	4	4	no	—
543	C₂×C₃×C₄	—	4	4	no	—
544	C₂×C₃×C₄	—	4	8	no	—
545	C₂×C₃×C₄	—	4	2	no	—
546	C₂×C₃×C₄	—	6	8	no	—
547	C₂×C₃×C₄	—	6	2	no	—
548	C₂×C₃×C₄	—	6	4	no	—
549	C₂×C₃×C₄	—	12	8	no	—
550	C₂×C₃×C₄	C₂³×D₃	1	4	yes	—
551	C₂×C₃×C₄	C₂³×D₃	1	2	yes	—
552	C₂×C₃×C₄	C₂³×D₃	1	4	yes	—
553	C₂×C₃×C₄	C₂⁴×C₃	1	4	yes	—
554	C₂×C₃×C₄	C₂⁴×C₃	1	4	yes	—
555	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
556	#67	—	2	8	no	—
557	#67	—	2	8	no	—
558	#67	—	4	8	no	—
559	C₂×Dic₃	—	2	2	no	—
560	C₂×Dic₃	—	2	4	no	—
561	C₂×Dic₃	C₂⁴×C₃	1	2	yes	—
562	C₂×Dic₃	C₂⁴×C₃	1	4	yes	—
563	D₁₂	—	2	16	no	—
564	D₁₂	—	2	16	no	—
565	D₁₂	—	2	8	no	—
566	D₁₂	—	4	8	no	—
567	C₄×D₃	—	2	8	no	—
568	C₄×D₃	—	4	8	no	—
569	C₂×C₃²	—	2	4	no	—
570	C₂×C₃²	—	4	2	no	—
571	C₂×C₃²	#534	1	4	yes	complemented
572	C₂×C₃²	C₂³×D₄	1	1	yes	characteristic
573	C₂×C₃²	C₂×H(5,𝔽₂)	1	2	yes	—
574	C₃×D₃	—	2	4	no	—
575	C₃×D₃	—	2	4	no	—
576	C₃×D₃	—	4	4	no	—
577	C₃×D₃	—	4	2	no	—
578	C₂⁴	—	3	1	no	—
579	C₂⁴	—	3	1	no	—
580	C₂⁴	—	3	4	no	—
581	C₂⁴	—	3	8	no	—
582	C₂⁴	—	3	1	no	—
583	C₂⁴	—	3	2	no	—
584	C₂⁴	—	3	4	no	—
585	C₂⁴	—	3	4	no	—
586	C₂⁴	—	6	4	no	—
587	C₂⁴	—	6	4	no	—
588	C₂⁴	—	12	4	no	—
589	C₂⁴	—	12	4	no	—
590	C₂⁴	—	12	4	no	—
591	C₂⁴	C₂²×C₃×D₃	1	1	yes	characteristic
592	C₂⁴	C₂²×C₃×D₃	1	1	yes	characteristic
593	C₂×D₄	—	2	4	no	—
594	C₂×D₄	—	3	4	no	—
595	C₂×D₄	—	3	4	no	—
596	C₂×D₄	—	3	8	no	—
597	C₂×D₄	—	3	8	no	—
598	C₂×D₄	—	3	4	no	—
599	C₂×D₄	—	3	8	no	—
600	C₂×D₄	—	3	8	no	—
601	C₂×D₄	—	6	8	no	—
602	C₂×D₄	—	6	8	no	—
603	C₂×D₄	—	6	32	no	—
604	C₂×D₄	—	6	4	no	—
605	C₂×D₄	—	6	32	no	—
606	C₂×D₄	—	6	4	no	—
607	C₂×D₄	—	6	4	no	—
608	C₂×D₄	—	12	4	no	—
609	C₂×D₄	—	12	4	no	—
610	C₂×D₄	C₂²×C₃×D₃	1	4	yes	—
611	C₂²×C₄	—	2	4	no	—
612	C₂²×C₄	—	3	2	no	—
613	C₂²×C₄	—	3	1	no	—
614	C₂²×C₄	—	3	4	no	—
615	C₂²×C₄	—	3	8	no	—
616	C₂²×C₄	—	6	4	no	—
617	C₂²×C₄	—	12	4	no	—
618	C₂²×C₄	C₂²×C₃×D₃	1	2	yes	—
619	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
620	C₂²×C₄	C₂²×C₃×D₃	1	2	yes	—
621	C₂²×C₄	C₂²×C₃×D₃	1	4	yes	complemented
622	C₄⋊C₄	—	3	8	no	—
623	C₄⋊C₄	C₂²×C₃×D₃	1	8	yes	complemented
624	C₂²⋊C₄	—	3	4	no	—
625	C₂²⋊C₄	—	3	8	no	—
626	C₂²⋊C₄	—	3	8	no	—
627	C₂²⋊C₄	—	3	8	no	—
628	C₂²⋊C₄	—	3	8	no	—
629	C₂²⋊C₄	C₂²×C₃×D₃	1	4	yes	complemented
630	C₂²⋊C₄	C₂²×C₃×D₃	1	8	yes	complemented
631	C₂²×C₃	—	2	8	no	—
632	C₂²×C₃	—	2	4	no	—
633	C₂²×C₃	—	2	4	no	—
634	C₂²×C₃	—	2	8	no	—
635	C₂²×C₃	—	2	2	no	—
636	C₂²×C₃	—	2	4	no	—
637	C₂²×C₃	—	2	2	no	—
638	C₂²×C₃	—	2	4	no	—
639	C₂²×C₃	—	2	2	no	—
640	C₂²×C₃	—	2	4	no	—
641	C₂²×C₃	—	2	4	no	—
642	C₂²×C₃	—	2	1	no	—
643	C₂²×C₃	—	3	4	no	—
644	C₂²×C₃	—	3	4	no	—
645	C₂²×C₃	—	4	4	no	—
646	C₂²×C₃	—	4	8	no	—
647	C₂²×C₃	—	4	2	no	—
648	C₂²×C₃	—	4	4	no	—
649	C₂²×C₃	—	4	4	no	—
650	C₂²×C₃	—	4	4	no	—
651	C₂²×C₃	—	6	8	no	—
652	C₂²×C₃	—	6	8	no	—
653	C₂²×C₃	—	6	4	no	—
654	C₂²×C₃	—	6	4	no	—
655	C₂²×C₃	—	6	4	no	—
656	C₂²×C₃	—	6	2	no	—
657	C₂²×C₃	—	6	4	no	—
658	C₂²×C₃	—	6	4	no	—
659	C₂²×C₃	—	6	4	no	—
660	C₂²×C₃	—	8	4	no	—
661	C₂²×C₃	—	12	16	no	—
662	C₂²×C₃	—	12	16	no	—
663	C₂²×C₃	—	12	16	no	—
664	C₂²×C₃	—	12	8	no	—
665	C₂²×C₃	—	12	4	no	—
666	C₂²×C₃	C₂×D₃×D₄	1	4	yes	—
667	C₂²×C₃	C₂×D₃×D₄	1	2	yes	—
668	C₂²×C₃	#1009	1	4	yes	—
669	C₂²×C₃	C₂²×C₃×D₄	1	4	yes	—
670	C₂²×C₃	C₂²×C₃×D₄	1	2	yes	—
671	C₂²×C₃	C₃×H(5,𝔽₂)	1	4	yes	—
672	C₂²×C₃	C₂⁴×D₃	1	1	yes	characteristic
673	C₂²×C₃	C₂⁵×C₃	1	1	yes	characteristic
674	C₂×D₃	—	2	4	no	—
675	C₂×D₃	—	2	4	no	—
676	C₂×D₃	—	2	8	no	—
677	C₂×D₃	—	2	8	no	—
678	C₂×D₃	—	2	4	no	—
679	C₂×D₃	—	2	2	no	—
680	C₂×D₃	—	2	4	no	—
681	C₂×D₃	—	2	4	no	—
682	C₂×D₃	—	2	4	no	—
683	C₂×D₃	—	4	16	no	—
684	C₂×D₃	—	4	16	no	—
685	C₂×D₃	—	4	16	no	—
686	C₂×D₃	—	4	8	no	—
687	C₂×D₃	—	4	4	no	—
688	C₂×D₃	C₂²×C₃×D₄	1	4	yes	—
689	C₂×D₃	C₂²×C₃×D₄	1	4	yes	—
690	C₃×C₄	—	2	4	no	—
691	C₃×C₄	—	2	2	no	—
692	C₃×C₄	—	2	4	no	—
693	C₃×C₄	—	2	2	no	—
694	C₃×C₄	—	2	4	no	—
695	C₃×C₄	—	2	4	no	—
696	C₃×C₄	—	4	4	no	—
697	C₃×C₄	—	4	2	no	—
698	C₃×C₄	—	4	4	no	—
699	C₃×C₄	—	6	2	no	—
700	C₃×C₄	—	6	4	no	—
701	Dic₃	—	2	2	no	—
702	Dic₃	—	2	4	no	—
703	C₃²	C₂×#534	1	1	yes	characteristic, complemented, Sylow
704	C₂³	—	2	4	no	—
705	C₂³	—	2	2	no	—
706	C₂³	—	2	4	no	—
707	C₂³	—	3	4	no	—
708	C₂³	—	3	4	no	—
709	C₂³	—	3	2	no	—
710	C₂³	—	3	2	no	—
711	C₂³	—	3	16	no	—
712	C₂³	—	3	2	no	—
713	C₂³	—	3	4	no	—
714	C₂³	—	6	8	no	—
715	C₂³	—	6	4	no	—
716	C₂³	—	6	4	no	—
717	C₂³	—	6	8	no	—
718	C₂³	—	6	4	no	—
719	C₂³	—	6	2	no	—
720	C₂³	—	6	4	no	—
721	C₂³	—	6	4	no	—
722	C₂³	—	6	4	no	—
723	C₂³	—	12	8	no	—
724	C₂³	—	12	8	no	—
725	C₂³	—	12	16	no	—
726	C₂³	—	12	8	no	—
727	C₂³	—	12	16	no	—
728	C₂³	—	12	16	no	—
729	C₂³	C₃×D₃×D₄	1	4	yes	—
730	C₂³	C₂³×C₃×D₃	1	2	yes	—
731	C₂³	C₂³×C₃×D₃	1	2	yes	—
732	C₂³	C₂³×C₃×D₃	1	1	yes	characteristic
733	D₄	—	2	8	no	—
734	D₄	—	6	16	no	—
735	D₄	—	6	16	no	—
736	D₄	—	6	8	no	—
737	D₄	—	6	8	no	—
738	D₄	—	6	8	no	—
739	D₄	—	12	8	no	—
740	D₄	—	12	8	no	—
741	C₂×C₄	—	2	4	no	—
742	C₂×C₄	—	2	8	no	—
743	C₂×C₄	—	2	2	no	—
744	C₂×C₄	—	2	4	no	—
745	C₂×C₄	—	3	4	no	—
746	C₂×C₄	—	3	2	no	—
747	C₂×C₄	—	6	8	no	—
748	C₂×C₄	—	6	2	no	—
749	C₂×C₄	—	6	4	no	—
750	C₂×C₄	—	12	8	no	—
751	C₂×C₄	C₂³×C₃×D₃	1	4	yes	—
752	C₂×C₄	C₂³×C₃×D₃	1	2	yes	—
753	C₂×C₄	C₂³×C₃×D₃	1	4	yes	—
754	C₂×C₃	—	2	4	no	—
755	C₂×C₃	—	2	4	no	—
756	C₂×C₃	—	2	1	no	—
757	C₂×C₃	—	2	2	no	—
758	C₂×C₃	—	2	4	no	—
759	C₂×C₃	—	4	4	no	—
760	C₂×C₃	—	4	2	no	—
761	C₂×C₃	—	4	2	no	—
762	C₂×C₃	—	6	4	no	—
763	C₂×C₃	—	6	4	no	—
764	C₂×C₃	—	8	2	no	—
765	C₂×C₃	—	12	4	no	—
766	C₂×C₃	—	12	2	no	—
767	C₂×C₃	#5653	1	4	yes	direct product factor
768	C₂×C₃	C₃×#534	1	4	yes	complemented
769	C₂×C₃	C₂²×D₃×D₄	1	1	yes	characteristic
770	C₂×C₃	C₂×#1009	1	2	yes	—
771	C₂×C₃	C₂³×C₃×D₄	1	1	yes	characteristic
772	C₂×C₃	C₂×C₃×H(5,𝔽₂)	1	2	yes	—
773	D₃	—	2	4	no	—
774	D₃	—	2	4	no	—
775	D₃	—	4	4	no	—
776	D₃	—	4	2	no	—
777	C₂²	—	2	4	no	—
778	C₂²	—	2	8	no	—
779	C₂²	—	2	2	no	—
780	C₂²	—	2	4	no	—
781	C₂²	—	3	4	no	—
782	C₂²	—	3	4	no	—
783	C₂²	—	4	4	no	—
784	C₂²	—	6	4	no	—
785	C₂²	—	6	4	no	—
786	C₂²	—	6	8	no	—
787	C₂²	—	6	8	no	—
788	C₂²	—	6	4	no	—
789	C₂²	—	6	2	no	—
790	C₂²	—	6	4	no	—
791	C₂²	—	6	4	no	—
792	C₂²	—	6	4	no	—
793	C₂²	—	12	16	no	—
794	C₂²	—	12	16	no	—
795	C₂²	—	12	16	no	—
796	C₂²	—	12	8	no	—
797	C₂²	—	12	4	no	—
798	C₂²	C₂×C₃×D₃×D₄	1	4	yes	—
799	C₂²	C₂×C₃×D₃×D₄	1	2	yes	—
800	C₂²	C₃×#1009	1	4	yes	—
801	C₂²	C₂⁴×C₃×D₃	1	1	yes	characteristic
802	C₄	—	2	4	no	—
803	C₄	—	2	2	no	—
804	C₄	—	2	4	no	—
805	C₄	—	6	2	no	—
806	C₄	—	6	4	no	—
807	C₃	—	2	1	no	—
808	C₃	C₂×#5653	1	1	yes	characteristic, direct product factor
809	C₃	C₂×C₃×#534	1	1	yes	characteristic, complemented
810	C₂	—	2	4	no	—
811	C₂	—	4	2	no	—
812	C₂	—	6	4	no	—
813	C₂	—	6	4	no	—
814	C₂	—	12	4	no	—
815	C₂	—	12	2	no	—
816	C₂	C₃×#5653	1	4	yes	direct product factor
817	C₂	C₂²×C₃×D₃×D₄	1	1	yes	characteristic
818	C₂	C₂×C₃×#1009	1	2	yes	—

	subgroup	G/H
center	C₂³×C₃	C₂³×D₃
commutator, cosocle	C₂²×C₃	C₂⁵×C₃
Frattini	C₂²	C₂⁴×C₃×D₃
Fitting	C₂×C₃²×#123	C₂
socle	C₂³×C₃²	C₂⁴
hypercenter	C₂×C₃×#123	D₃
hypocenter	C₃	C₂×C₃×#534
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₃ ◁ C₂×C₃×#123

Complements

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

N	H ≅ G/N	type
1. C₂²×C₃×D₃×D₄	C₂	semidirect
2. C₂³×C₃×D₁₂	C₂	semidirect
3. C₂×C₃²×#123	C₂	semidirect
4. C₂×C₃×#937	C₂	semidirect
5. C₂×C₃×#929	C₂	semidirect
6. C₃×#5653	C₂	direct (N × H)
7. C₂×C₃×#895	C₂	semidirect
8. C₂×C₃×#894	C₂	semidirect
9. C₂×C₃×#884	C₂	semidirect
10. C₂×C₃×#882	C₂	semidirect
11. C₂×C₃×#882	C₂	semidirect
12. C₂×C₃×D₃×C₂²⋊C₄	C₂	semidirect
14. C₂×#5653	C₃	direct (N × H)
16. C₂⁴×C₃×D₃	C₂²	semidirect
17. C₂⁴×C₃×D₃	C₂²	semidirect
19. C₂³×C₃²×C₄	C₂²	semidirect
21. C₂²×C₃×#67	C₂²	semidirect
22. C₂²×C₃×#67	C₂²	semidirect
24. C₂×C₃×D₃×D₄	C₂²	semidirect
27. C₂²×C₃×D₁₂	C₂²	semidirect
28. C₂²×C₃×D₁₂	C₂²	semidirect
29. C₂²×C₃×D₁₂	C₂²	semidirect
30. C₂²×C₃×D₁₂	C₂²	semidirect
31. C₂²×C₃×C₄×D₃	C₂²	semidirect
32. C₂²×C₃×C₄×D₃	C₂²	semidirect
33. C₃²×#123	C₂²	semidirect
34. C₂×C₃²×C₄⋊C₄	C₂²	semidirect
35. C₂×C₃²×C₂²⋊C₄	C₂²	semidirect
36. C₂×C₃²×C₂²⋊C₄	C₂²	semidirect
37. C₂×C₃×#217	C₂²	semidirect
38. C₃×#937	C₂²	semidirect
39. C₃×#929	C₂²	semidirect
40. C₂×C₃×(C₂×D₃)⋊C₄	C₂²	semidirect
41. C₂×C₃×(C₂×D₃)⋊C₄	C₂²	semidirect
42. C₂×C₃×(C₂×D₃)⋊C₄	C₂²	semidirect
43. C₂×C₃×(C₂×D₃)⋊C₄	C₂²	semidirect
44. C₂×C₃×Dic₃⋊C₄	C₂²	semidirect
45. C₃×#895	C₂²	semidirect
46. C₃×#894	C₂²	semidirect
47. C₃×#884	C₂²	semidirect
48. C₃×#882	C₂²	semidirect
49. C₃×#882	C₂²	semidirect
50. C₃×D₃×C₂²⋊C₄	C₂²	semidirect
53. C₂²×D₃×D₄	C₂×C₃	semidirect
54. C₂³×D₁₂	C₂×C₃	semidirect
59. C₂×C₃×#123	D₃	semidirect
60. C₂×C₃×#123	C₂×C₃	semidirect
67. C₂×#937	C₂×C₃	semidirect
68. C₂×#929	C₂×C₃	semidirect
69. #5653	C₂×C₃	direct (N × H)
70. C₂×#895	C₂×C₃	semidirect
71. C₂×#894	C₂×C₃	semidirect
72. C₂×#884	C₂×C₃	semidirect
73. C₂×#882	C₂×C₃	semidirect
74. C₂×#882	C₂×C₃	semidirect
75. C₂×D₃×C₂²⋊C₄	C₂×C₃	semidirect
83. C₂³×C₃×D₃	D₄	semidirect
89. C₂³×C₃×D₃	C₂³	semidirect
90. C₂³×C₃×D₃	C₂³	semidirect
97. C₂²×C₃²×C₄	C₂³	semidirect
102. C₂×C₃×#67	C₂³	semidirect
103. C₂×C₃×#67	C₂³	semidirect
113. C₂×C₃×D₁₂	C₂³	semidirect
114. C₂×C₃×D₁₂	C₂³	semidirect
115. C₂×C₃×D₁₂	C₂³	semidirect
118. C₂×C₃×C₄×D₃	C₂³	semidirect
119. C₂×C₃×C₄×D₃	C₂³	semidirect
120. C₃²×C₄⋊C₄	C₂³	semidirect
121. C₃²×C₂²⋊C₄	C₂³	semidirect
122. C₃²×C₂²⋊C₄	C₂³	semidirect
123. C₃×#217	C₂³	semidirect
124. C₃×(C₂×D₃)⋊C₄	C₂³	semidirect
125. C₃×(C₂×D₃)⋊C₄	C₂³	semidirect
126. C₃×(C₂×D₃)⋊C₄	C₂³	semidirect
127. C₃×(C₂×D₃)⋊C₄	C₂³	semidirect
128. C₃×Dic₃⋊C₄	C₂³	semidirect
134. C₂⁴×D₃	C₂²×C₃	semidirect
135. C₂⁴×D₃	C₂²×C₃	semidirect
153. C₂³×C₃×C₄	C₂×D₃	semidirect
154. C₂³×C₃×C₄	C₂²×C₃	semidirect
156. C₂²×#67	C₂²×C₃	semidirect
157. C₂²×#67	C₂²×C₃	semidirect
159. C₂×D₃×D₄	C₂²×C₃	semidirect
162. C₂²×D₁₂	C₂²×C₃	semidirect
163. C₂²×D₁₂	C₂²×C₃	semidirect
164. C₂²×D₁₂	C₂²×C₃	semidirect
165. C₂²×D₁₂	C₂²×C₃	semidirect
166. C₂²×C₄×D₃	C₂²×C₃	semidirect
167. C₂²×C₄×D₃	C₂²×C₃	semidirect
171. C₃×#123	C₂×D₃	semidirect
172. C₃×#123	C₂²×C₃	semidirect
180. C₂×C₃×C₄⋊C₄	C₂×D₃	semidirect
181. C₂×C₃×C₄⋊C₄	C₂²×C₃	semidirect
190. C₂×C₃×C₂²⋊C₄	C₂×D₃	semidirect
191. C₂×C₃×C₂²⋊C₄	C₂×D₃	semidirect
192. C₂×C₃×C₂²⋊C₄	C₂²×C₃	semidirect
193. C₂×C₃×C₂²⋊C₄	C₂²×C₃	semidirect
194. C₂×#217	C₂²×C₃	semidirect
195. #937	C₂²×C₃	semidirect
196. #929	C₂²×C₃	semidirect
197. C₂×(C₂×D₃)⋊C₄	C₂²×C₃	semidirect
198. C₂×(C₂×D₃)⋊C₄	C₂²×C₃	semidirect
199. C₂×(C₂×D₃)⋊C₄	C₂²×C₃	semidirect
200. C₂×(C₂×D₃)⋊C₄	C₂²×C₃	semidirect
201. C₂×Dic₃⋊C₄	C₂²×C₃	semidirect
202. #895	C₂²×C₃	semidirect
203. #894	C₂²×C₃	semidirect
204. #884	C₂²×C₃	semidirect
205. #882	C₂²×C₃	semidirect
206. #882	C₂²×C₃	semidirect
207. D₃×C₂²⋊C₄	C₂²×C₃	semidirect
232. C₂²×C₃×D₃	C₂×D₄	semidirect
263. C₂×#123	C₃×D₃	semidirect
294. C₂³×D₃	C₃×D₄	semidirect
300. C₂³×D₃	C₂³×C₃	semidirect
301. C₂³×D₃	C₂³×C₃	semidirect
340. C₂²×C₃×C₄	C₂²×D₃	semidirect
344. C₂²×C₃×C₄	C₂³×C₃	semidirect
349. C₂×#67	C₂³×C₃	semidirect
350. C₂×#67	C₂³×C₃	semidirect
360. C₂×D₁₂	C₂³×C₃	semidirect
361. C₂×D₁₂	C₂³×C₃	semidirect
362. C₂×D₁₂	C₂³×C₃	semidirect
365. C₂×C₄×D₃	C₂³×C₃	semidirect
366. C₂×C₄×D₃	C₂³×C₃	semidirect
369. C₃×C₄⋊C₄	C₂²×D₃	semidirect
370. C₃×C₄⋊C₄	C₂³×C₃	semidirect
378. C₃×C₂²⋊C₄	C₂²×D₃	semidirect
379. C₃×C₂²⋊C₄	C₂²×D₃	semidirect
380. C₃×C₂²⋊C₄	C₂³×C₃	semidirect
381. C₃×C₂²⋊C₄	C₂³×C₃	semidirect
382. #217	C₂³×C₃	semidirect
383. (C₂×D₃)⋊C₄	C₂³×C₃	semidirect
384. (C₂×D₃)⋊C₄	C₂³×C₃	semidirect
385. (C₂×D₃)⋊C₄	C₂³×C₃	semidirect
386. (C₂×D₃)⋊C₄	C₂³×C₃	semidirect
387. Dic₃⋊C₄	C₂³×C₃	semidirect
435. C₂³×C₄	C₂×C₃×D₃	semidirect
438. #123	C₂×C₃×D₃	semidirect
445. C₂×C₄⋊C₄	C₂×C₃×D₃	semidirect
452. C₂×C₂²⋊C₄	C₂×C₃×D₃	semidirect
453. C₂×C₂²⋊C₄	C₂×C₃×D₃	semidirect
514. C₂²×D₃	C₂×C₃×D₄	semidirect
571. C₂×C₃²	#534	semidirect
621. C₂²×C₄	C₂²×C₃×D₃	semidirect
623. C₄⋊C₄	C₂²×C₃×D₃	semidirect
629. C₂²⋊C₄	C₂²×C₃×D₃	semidirect
630. C₂²⋊C₄	C₂²×C₃×D₃	semidirect
703. C₃²	C₂×#534	semidirect
767. C₂×C₃	#5653	direct (N × H)
768. C₂×C₃	C₃×#534	semidirect
808. C₃	C₂×#5653	direct (N × H)
809. C₃	C₂×C₃×#534	semidirect
816. C₂	C₃×#5653	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₃×D₃×D₄	2
C₂³×C₃×D₁₂	2
C₂×C₃²×#123	2
C₂×C₃×#937	2
C₂×C₃×#929	2
C₃×#5653	2
C₂×C₃×#895	2
C₂×C₃×#894	2
C₂×C₃×#884	2
C₂×C₃×#882	2
C₂×C₃×D₃×C₂²⋊C₄	2
C₂×C₃×#534	3
C₂×#5653	3

Subgroups — C2×C3×#5653 #11900940

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#5653 #11900940