Subgroups — C₃×#85919 #11904272

Order 1152.

4131 conjugacy classes of subgroups.

The subgroup lattice has 1214 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₃×#67	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×#1004	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃²×#120	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃×#953	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#5804	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×D₄×#67	C₂	1	4	yes	maximal, complemented
7	C₃×#5592	C₂	1	2	yes	maximal, complemented
8	C₃×#5591	C₂	1	4	yes	maximal, complemented
9	C₃×#5590	C₂	1	4	yes	maximal, complemented
10	C₃×#5589	C₂	1	2	yes	maximal, complemented
11	C₃×D₃×#120	C₂	1	2	yes	maximal, complemented
12	C₃×#5586	C₂	1	2	yes	maximal, complemented
13	C₃×#5493	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃×#5490	C₂	1	4	yes	maximal, complemented
15	C₃×#5486	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃×#3484	—	3	1	no	maximal
17	#85919	C₃	1	1	yes	maximal, characteristic, direct product factor
18	C₂⁵×C₃²	C₂²	1	1	yes	characteristic, complemented
19	C₂⁴×C₃×D₃	C₂²	1	1	yes	characteristic, complemented
20	C₂²×C₃²×D₄	C₂²	1	1	yes	characteristic, complemented
21	C₂²×C₃²×D₄	C₂²	1	2	yes	complemented
22	C₂²×C₃×#67	—	2	8	no	—
23	C₂²×C₃×#67	C₂²	1	1	yes	characteristic
24	C₂²×C₃×#67	C₂²	1	4	yes	complemented
25	C₂²×C₃×#67	C₂²	1	1	yes	characteristic, complemented
26	C₂²×C₃×#67	C₂²	1	1	yes	characteristic, complemented
27	C₂²×C₃×#67	C₂²	1	4	yes	complemented
28	C₂²×C₃×#67	C₂²	1	1	yes	characteristic, complemented
29	C₂²×C₃×#67	C₂²	1	1	yes	characteristic, complemented
30	C₂²×C₃×#67	C₂²	1	2	yes	complemented
31	C₂²×C₃×#67	C₂²	1	2	yes	complemented
32	C₂³×C₃×Dic₃	C₂²	1	1	yes	characteristic, complemented
33	C₃×#1004	—	2	8	no	—
34	C₂×C₃×#237	C₂²	1	2	yes	complemented
35	C₂×C₃×#237	C₂²	1	2	yes	complemented
36	C₂×C₃×D₃×D₄	C₂²	1	2	yes	complemented
37	C₂×C₃×D₃×D₄	C₂²	1	4	yes	complemented
38	C₂×C₃×D₃×D₄	C₂²	1	2	yes	complemented
39	C₂×C₃×#235	C₂²	1	2	yes	complemented
40	C₃²×#120	C₂²	1	2	yes	complemented
41	C₃²×#120	C₂²	1	2	yes	complemented
42	C₃²×#120	C₂²	1	4	yes	complemented
43	C₂×C₃²×C₂²⋊C₄	C₂²	1	2	yes	complemented
44	C₂×C₃²×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
45	C₃×#953	C₂²	1	2	yes	complemented
46	C₃×#953	C₂²	1	4	yes	complemented
47	C₃×#953	C₂²	1	2	yes	complemented
48	C₃×#953	C₂²	1	2	yes	complemented
49	C₂×C₃×#217	C₂²	1	1	yes	characteristic, complemented
50	C₂×C₃×#217	C₂²	1	2	yes	complemented
51	C₃×#940	C₂²	1	4	yes	complemented
52	C₃×#939	C₂²	1	4	yes	complemented
53	C₃×#939	C₂²	1	4	yes	complemented
54	C₃×#939	C₂²	1	4	yes	complemented
55	C₃×#938	C₂²	1	4	yes	complemented
56	C₃×#937	C₂²	1	4	yes	complemented
57	C₃×#937	C₂²	1	2	yes	complemented
58	C₃×#937	C₂²	1	4	yes	complemented
59	C₃×#935	C₂²	1	2	yes	complemented
60	C₃×D₄×Dic₃	C₂²	1	4	yes	complemented
61	C₃×#930	C₂²	1	4	yes	complemented
62	C₃×#929	C₂²	1	2	yes	complemented
63	C₃×C₄×#67	C₂²	1	4	yes	complemented
64	C₃×#886	C₂²	1	2	yes	complemented
65	C₃×#886	C₂²	1	2	yes	complemented
66	C₃×#885	C₂²	1	4	yes	complemented
67	C₃×#884	C₂²	1	4	yes	complemented
68	C₃×#884	C₂²	1	4	yes	complemented
69	C₃×#883	C₂²	1	4	yes	complemented
70	C₃×#882	C₂²	1	4	yes	complemented
71	C₃×#882	C₂²	1	2	yes	complemented
72	C₃×#882	C₂²	1	2	yes	complemented
73	C₃×#67⋊C₄	C₂²	1	4	yes	complemented
74	C₃×#67⋊C₄	C₂²	1	4	yes	complemented
75	C₃×D₃×C₂²⋊C₄	C₂²	1	4	yes	complemented
76	C₃×D₃×C₂²⋊C₄	C₂²	1	2	yes	complemented
77	C₃×#878	C₂²	1	4	yes	complemented
78	C₃×#877	C₂²	1	2	yes	complemented
79	C₂×C₃×H(5,𝔽₂)	—	3	1	no	—
80	C₂³×C₃×D₄	—	3	1	no	—
81	C₂³×#67	C₂×C₃	1	1	yes	characteristic, complemented
82	C₂×#1004	C₂×C₃	1	1	yes	characteristic, complemented
83	C₃×#546	—	3	4	no	—
84	C₃×#546	—	3	4	no	—
85	C₃×D₄²	—	3	4	no	—
86	C₃×D₄²	—	3	4	no	—
87	C₃×#535	—	3	2	no	—
88	C₃×#534	—	3	1	no	—
89	C₃×#534	—	3	2	no	—
90	C₃×#534	—	3	1	no	—
91	C₃×#525	—	3	2	no	—
92	C₂×C₃×#120	—	2	1	no	—
93	C₂×C₃×#120	—	3	2	no	—
94	C₂×C₃×#120	—	3	1	no	—
95	C₂×C₃×#120	D₃	1	1	yes	characteristic, complemented
96	C₂×C₃×#120	C₂×C₃	1	1	yes	characteristic, complemented
97	C₃×#518	—	3	1	no	—
98	C₂×#953	C₂×C₃	1	1	yes	characteristic, complemented
99	#5804	C₂×C₃	1	1	yes	characteristic, complemented
100	D₄×#67	C₂×C₃	1	4	yes	complemented
101	#5592	C₂×C₃	1	2	yes	complemented
102	#5591	C₂×C₃	1	4	yes	complemented
103	#5590	C₂×C₃	1	4	yes	complemented
104	#5589	C₂×C₃	1	2	yes	complemented
105	D₃×#120	C₂×C₃	1	2	yes	complemented
106	#5586	C₂×C₃	1	2	yes	complemented
107	#5493	C₂×C₃	1	1	yes	characteristic, complemented
108	#5490	C₂×C₃	1	4	yes	complemented
109	#5486	C₂×C₃	1	1	yes	characteristic, complemented
110	C₂⁴×C₃²	—	2	4	no	—
111	C₂⁴×C₃²	—	4	4	no	—
112	C₂⁴×C₃²	C₂³	1	1	yes	characteristic
113	C₂⁴×C₃²	C₂³	1	2	yes	—
114	C₂⁴×C₃²	C₂³	1	2	yes	—
115	C₂⁴×C₃²	C₂³	1	1	yes	characteristic
116	C₂⁴×C₃²	C₂³	1	1	yes	characteristic
117	C₂⁴×C₃²	C₂³	1	1	yes	characteristic, complemented
118	C₂³×C₃×D₃	—	2	4	no	—
119	C₂³×C₃×D₃	—	4	4	no	—
120	C₂³×C₃×D₃	C₂³	1	4	yes	—
121	C₂³×C₃×D₃	C₂³	1	1	yes	characteristic
122	C₂³×C₃×D₃	C₂³	1	1	yes	characteristic
123	C₂³×C₃×D₃	C₂³	1	1	yes	characteristic, complemented
124	C₂³×C₃×D₃	C₂³	1	2	yes	complemented
125	C₂×C₃²×D₄	—	2	4	no	—
126	C₂×C₃²×D₄	—	4	4	no	—
127	C₂×C₃²×D₄	C₂³	1	4	yes	—
128	C₂×C₃²×D₄	C₂³	1	2	yes	—
129	C₂×C₃²×D₄	C₂³	1	2	yes	complemented
130	C₂×C₃²×D₄	C₂³	1	4	yes	complemented
131	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic, complemented
132	C₂²×C₃²×C₄	C₂³	1	2	yes	complemented
133	C₂×C₃×#67	—	2	4	no	—
134	C₂×C₃×#67	—	2	4	no	—
135	C₂×C₃×#67	—	2	4	no	—
136	C₂×C₃×#67	—	2	8	no	—
137	C₂×C₃×#67	—	2	16	no	—
138	C₂×C₃×#67	—	2	16	no	—
139	C₂×C₃×#67	—	2	4	no	—
140	C₂×C₃×#67	—	4	4	no	—
141	C₂×C₃×#67	D₄	1	8	yes	complemented
142	C₂×C₃×#67	C₂³	1	4	yes	—
143	C₂×C₃×#67	C₂³	1	2	yes	—
144	C₂×C₃×#67	C₂³	1	2	yes	—
145	C₂×C₃×#67	C₂³	1	4	yes	—
146	C₂×C₃×#67	C₂³	1	4	yes	—
147	C₂×C₃×#67	C₂³	1	2	yes	—
148	C₂×C₃×#67	C₂³	1	2	yes	—
149	C₂×C₃×#67	C₂³	1	2	yes	—
150	C₂×C₃×#67	C₂³	1	2	yes	complemented
151	C₂×C₃×#67	C₂³	1	2	yes	complemented
152	C₂×C₃×#67	C₂³	1	2	yes	complemented
153	C₂×C₃×#67	C₂³	1	4	yes	complemented
154	C₂×C₃×#67	C₂³	1	4	yes	complemented
155	C₂²×C₃×Dic₃	—	2	4	no	—
156	C₂²×C₃×Dic₃	C₂³	1	4	yes	—
157	C₂²×C₃×Dic₃	C₂³	1	1	yes	characteristic
158	C₂²×C₃×Dic₃	C₂³	1	1	yes	characteristic
159	C₂²×C₃×Dic₃	C₂³	1	1	yes	characteristic, complemented
160	C₂²×C₃×Dic₃	C₂³	1	2	yes	complemented
161	C₂²×C₃×Dic₃	C₂³	1	2	yes	complemented
162	C₃×#237	—	2	8	no	—
163	C₃×#237	—	2	8	no	—
164	C₃×D₃×D₄	—	2	8	no	—
165	C₃×D₃×D₄	—	2	8	no	—
166	C₃×D₃×D₄	—	4	8	no	—
167	C₃×#235	—	2	8	no	—
168	C₂×C₃×D₁₂	C₂³	1	2	yes	complemented
169	C₂×C₃×D₁₂	C₂³	1	4	yes	complemented
170	C₂×C₃×C₄×D₃	C₂³	1	2	yes	complemented
171	C₂×C₃×C₄×D₃	C₂³	1	2	yes	complemented
172	C₂×C₃×C₄×D₃	C₂³	1	4	yes	complemented
173	C₂×C₃×Dic₆	C₂³	1	2	yes	complemented
174	C₃²×C₂²⋊C₄	C₂³	1	2	yes	—
175	C₃²×C₂²⋊C₄	C₂³	1	4	yes	—
176	C₃²×C₂²⋊C₄	C₂³	1	2	yes	complemented
177	C₃²×C₂²⋊C₄	C₂³	1	4	yes	complemented
178	C₃×#217	C₂³	1	2	yes	—
179	C₃×#217	C₂³	1	4	yes	—
180	C₃×#217	C₂³	1	4	yes	complemented
181	C₃×#217	C₂³	1	2	yes	complemented
182	C₃×#217	C₂³	1	4	yes	complemented
183	C₃×(C₂×D₃)⋊C₄	C₂³	1	4	yes	complemented
184	C₃×(C₂×D₃)⋊C₄	C₂³	1	4	yes	complemented
185	C₃×(C₂×D₃)⋊C₄	C₂³	1	4	yes	complemented
186	C₃×(C₂×D₃)⋊C₄	C₂³	1	4	yes	complemented
187	C₃×C₄⋊Dic₃	C₂³	1	4	yes	complemented
188	C₃×Dic₃⋊C₄	C₂³	1	4	yes	complemented
189	C₃×Dic₃⋊C₄	C₂³	1	4	yes	complemented
190	C₃×C₄×Dic₃	C₂³	1	4	yes	complemented
191	#3484	—	3	1	no	Sylow
192	C₂⁵×C₃	—	2	1	no	—
193	C₂⁵×C₃	—	3	1	no	—
194	C₂⁵×C₃	C₂×D₃	1	1	yes	characteristic, complemented
195	C₂⁵×C₃	C₂²×C₃	1	1	yes	characteristic, complemented
196	C₂⁴×D₃	C₂²×C₃	1	1	yes	characteristic, complemented
197	C₃×H(5,𝔽₂)	—	6	8	no	—
198	C₂×C₃×#41	—	3	2	no	—
199	C₂×C₃×#41	—	3	2	no	—
200	C₂×C₃×#41	—	3	2	no	—
201	C₂²×C₃×D₄	—	2	1	no	—
202	C₂²×C₃×D₄	—	2	2	no	—
203	C₂²×C₃×D₄	—	3	1	no	—
204	C₂²×C₃×D₄	—	3	1	no	—
205	C₂²×C₃×D₄	—	3	1	no	—
206	C₂²×C₃×D₄	—	3	1	no	—
207	C₂²×C₃×D₄	—	3	4	no	—
208	C₂²×C₃×D₄	—	3	4	no	—
209	C₂²×C₃×D₄	—	3	1	no	—
210	C₂²×C₃×D₄	—	3	2	no	—
211	C₂²×C₃×D₄	—	3	2	no	—
212	C₂²×C₃×D₄	—	3	2	no	—
213	C₂²×C₃×D₄	—	3	2	no	—
214	C₂²×C₃×D₄	—	3	4	no	—
215	C₂²×C₃×D₄	—	6	8	no	—
216	C₂²×C₃×D₄	C₂×D₃	1	1	yes	characteristic, complemented
217	C₂²×C₃×D₄	C₂×D₃	1	2	yes	complemented
218	C₂²×C₃×D₄	C₂²×C₃	1	1	yes	characteristic, complemented
219	C₂²×C₃×D₄	C₂²×C₃	1	2	yes	complemented
220	C₂³×C₃×C₄	—	3	1	no	—
221	C₂²×#67	—	2	8	no	—
222	C₂²×#67	C₂²×C₃	1	1	yes	characteristic
223	C₂²×#67	C₂²×C₃	1	4	yes	complemented
224	C₂²×#67	C₂²×C₃	1	1	yes	characteristic, complemented
225	C₂²×#67	C₂²×C₃	1	1	yes	characteristic, complemented
226	C₂²×#67	C₂²×C₃	1	4	yes	complemented
227	C₂²×#67	C₂²×C₃	1	1	yes	characteristic, complemented
228	C₂²×#67	C₂²×C₃	1	1	yes	characteristic, complemented
229	C₂²×#67	C₂²×C₃	1	2	yes	complemented
230	C₂²×#67	C₂²×C₃	1	2	yes	complemented
231	C₂³×Dic₃	C₂²×C₃	1	1	yes	characteristic, complemented
232	#1004	—	2	8	no	—
233	C₂×#237	C₂²×C₃	1	2	yes	complemented
234	C₂×#237	C₂²×C₃	1	2	yes	complemented
235	C₂×D₃×D₄	C₂²×C₃	1	2	yes	complemented
236	C₂×D₃×D₄	C₂²×C₃	1	2	yes	complemented
237	C₂×D₃×D₄	C₂²×C₃	1	4	yes	complemented
238	C₂×#235	C₂²×C₃	1	2	yes	complemented
239	C₃×#127	—	3	4	no	—
240	C₃×#124	—	3	4	no	—
241	C₃×#123	—	3	2	no	—
242	C₃×#123	—	3	2	no	—
243	C₃×#123	—	3	2	no	—
244	C₃×#123	—	3	4	no	—
245	C₃×#123	—	3	2	no	—
246	C₃×C₂²⋊Q₈	—	3	4	no	—
247	C₃×#121	—	3	4	no	—
248	C₃×#121	—	3	4	no	—
249	C₃×#121	—	3	4	no	—
250	C₃×#121	—	3	4	no	—
251	C₃×#121	—	3	4	no	—
252	C₃×#121	—	3	4	no	—
253	C₃×#121	—	3	4	no	—
254	C₃×#120	—	2	2	no	—
255	C₃×#120	—	2	2	no	—
256	C₃×#120	—	2	4	no	—
257	C₃×#120	—	3	2	no	—
258	C₃×#120	—	3	2	no	—
259	C₃×#120	—	3	4	no	—
260	C₃×#120	—	3	2	no	—
261	C₃×#120	—	3	2	no	—
262	C₃×#120	—	3	4	no	—
263	C₃×#120	—	3	4	no	—
264	C₃×#120	—	3	2	no	—
265	C₃×#120	—	3	4	no	—
266	C₃×#120	—	3	2	no	—
267	C₃×#120	C₂×D₃	1	2	yes	complemented
268	C₃×#120	C₂×D₃	1	2	yes	complemented
269	C₃×#120	C₂×D₃	1	4	yes	complemented
270	C₃×#120	C₂²×C₃	1	2	yes	complemented
271	C₃×#120	C₂²×C₃	1	2	yes	complemented
272	C₃×#120	C₂²×C₃	1	4	yes	complemented
273	C₃×C₄×D₄	—	3	4	no	—
274	C₃×C₄×D₄	—	3	4	no	—
275	C₃×C₄×D₄	—	3	4	no	—
276	C₃×C₄×D₄	—	3	4	no	—
277	C₃×#117	—	3	2	no	—
278	C₂×C₃×C₂²⋊C₄	—	2	1	no	—
279	C₂×C₃×C₂²⋊C₄	—	2	2	no	—
280	C₂×C₃×C₂²⋊C₄	—	3	1	no	—
281	C₂×C₃×C₂²⋊C₄	—	3	2	no	—
282	C₂×C₃×C₂²⋊C₄	—	3	2	no	—
283	C₂×C₃×C₂²⋊C₄	—	3	4	no	—
284	C₂×C₃×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic, complemented
285	C₂×C₃×C₂²⋊C₄	C₂×D₃	1	2	yes	complemented
286	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
287	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	2	yes	complemented
288	#953	C₂²×C₃	1	2	yes	complemented
289	#953	C₂²×C₃	1	4	yes	complemented
290	#953	C₂²×C₃	1	2	yes	complemented
291	#953	C₂²×C₃	1	2	yes	complemented
292	C₂×#217	C₂²×C₃	1	1	yes	characteristic, complemented
293	C₂×#217	C₂²×C₃	1	2	yes	complemented
294	#940	C₂²×C₃	1	4	yes	complemented
295	#939	C₂²×C₃	1	4	yes	complemented
296	#939	C₂²×C₃	1	4	yes	complemented
297	#939	C₂²×C₃	1	4	yes	complemented
298	#938	C₂²×C₃	1	4	yes	complemented
299	#937	C₂²×C₃	1	4	yes	complemented
300	#937	C₂²×C₃	1	2	yes	complemented
301	#937	C₂²×C₃	1	4	yes	complemented
302	#935	C₂²×C₃	1	2	yes	complemented
303	D₄×Dic₃	C₂²×C₃	1	4	yes	complemented
304	#930	C₂²×C₃	1	4	yes	complemented
305	#929	C₂²×C₃	1	2	yes	complemented
306	C₄×#67	C₂²×C₃	1	4	yes	complemented
307	#886	C₂²×C₃	1	2	yes	complemented
308	#886	C₂²×C₃	1	2	yes	complemented
309	#885	C₂²×C₃	1	4	yes	complemented
310	#884	C₂²×C₃	1	4	yes	complemented
311	#884	C₂²×C₃	1	4	yes	complemented
312	#883	C₂²×C₃	1	4	yes	complemented
313	#882	C₂²×C₃	1	4	yes	complemented
314	#882	C₂²×C₃	1	2	yes	complemented
315	#882	C₂²×C₃	1	2	yes	complemented
316	#67⋊C₄	C₂²×C₃	1	4	yes	complemented
317	#67⋊C₄	C₂²×C₃	1	4	yes	complemented
318	D₃×C₂²⋊C₄	C₂²×C₃	1	2	yes	complemented
319	D₃×C₂²⋊C₄	C₂²×C₃	1	4	yes	complemented
320	#878	C₂²×C₃	1	4	yes	complemented
321	#877	C₂²×C₃	1	2	yes	complemented
322	C₂³×C₃²	—	2	4	no	—
323	C₂³×C₃²	—	2	2	no	—
324	C₂³×C₃²	—	2	4	no	—
325	C₂³×C₃²	—	2	4	no	—
326	C₂³×C₃²	—	2	4	no	—
327	C₂³×C₃²	—	2	2	no	—
328	C₂³×C₃²	—	2	4	no	—
329	C₂³×C₃²	—	2	2	no	—
330	C₂³×C₃²	—	4	2	no	—
331	C₂³×C₃²	—	4	2	no	—
332	C₂³×C₃²	—	4	2	no	—
333	C₂³×C₃²	—	4	2	no	—
334	C₂³×C₃²	—	4	2	no	—
335	C₂³×C₃²	—	4	16	no	—
336	C₂³×C₃²	C₂×D₄	1	4	yes	complemented
337	C₂³×C₃²	C₂⁴	1	2	yes	—
338	C₂³×C₃²	C₂⁴	1	2	yes	—
339	C₂³×C₃²	C₂⁴	1	1	yes	characteristic
340	C₂³×C₃²	C₂⁴	1	1	yes	characteristic
341	C₂³×C₃²	C₂⁴	1	1	yes	characteristic
342	C₂³×C₃²	C₂⁴	1	2	yes	—
343	C₂²×C₃×D₃	—	2	2	no	—
344	C₂²×C₃×D₃	—	2	8	no	—
345	C₂²×C₃×D₃	—	2	2	no	—
346	C₂²×C₃×D₃	—	2	8	no	—
347	C₂²×C₃×D₃	—	2	4	no	—
348	C₂²×C₃×D₃	—	4	2	no	—
349	C₂²×C₃×D₃	—	4	4	no	—
350	C₂²×C₃×D₃	—	4	2	no	—
351	C₂²×C₃×D₃	—	4	4	no	—
352	C₂²×C₃×D₃	—	4	2	no	—
353	C₂²×C₃×D₃	—	4	16	no	—
354	C₂²×C₃×D₃	C₂×D₄	1	4	yes	complemented
355	C₂²×C₃×D₃	C₂⁴	1	2	yes	—
356	C₂²×C₃×D₃	C₂⁴	1	2	yes	—
357	C₂²×C₃×D₃	C₂⁴	1	2	yes	—
358	C₃²×D₄	—	2	4	no	—
359	C₃²×D₄	—	2	4	no	—
360	C₃²×D₄	—	2	8	no	—
361	C₃²×D₄	—	4	4	no	—
362	C₂×C₃²×C₄	—	2	2	no	—
363	C₂×C₃²×C₄	—	4	2	no	—
364	C₂×C₃²×C₄	C₂⁴	1	4	yes	—
365	C₂×C₃²×C₄	C₂⁴	1	2	yes	—
366	C₃×#67	—	2	4	no	—
367	C₃×#67	—	2	4	no	—
368	C₃×#67	—	2	4	no	—
369	C₃×#67	—	2	4	no	—
370	C₃×#67	—	2	8	no	—
371	C₃×#67	—	2	4	no	—
372	C₃×#67	—	2	8	no	—
373	C₃×#67	—	2	4	no	—
374	C₃×#67	—	2	8	no	—
375	C₃×#67	—	4	4	no	—
376	C₃×#67	—	4	4	no	—
377	C₃×#67	C₂×D₄	1	8	yes	complemented
378	C₃×#67	C₂×D₄	1	8	yes	complemented
379	C₂×C₃×Dic₃	—	2	2	no	—
380	C₂×C₃×Dic₃	—	2	2	no	—
381	C₂×C₃×Dic₃	—	2	4	no	—
382	C₂×C₃×Dic₃	—	2	8	no	—
383	C₂×C₃×Dic₃	—	4	2	no	—
384	C₂×C₃×Dic₃	C₂×D₄	1	4	yes	complemented
385	C₂×C₃×Dic₃	C₂⁴	1	4	yes	—
386	C₂×C₃×Dic₃	C₂⁴	1	2	yes	—
387	C₂×C₃×Dic₃	C₂⁴	1	2	yes	—
388	C₂×C₃×Dic₃	C₂⁴	1	2	yes	—
389	C₃×D₁₂	—	2	4	no	—
390	C₃×D₁₂	—	4	4	no	—
391	C₃×C₄×D₃	—	2	4	no	—
392	C₃×C₄×D₃	—	2	4	no	—
393	C₃×C₄×D₃	—	4	4	no	—
394	C₃×Dic₆	—	2	4	no	—
395	C₂×H(5,𝔽₂)	—	3	1	no	—
396	C₂³×D₄	—	3	1	no	—
397	#546	—	3	4	no	—
398	#546	—	3	4	no	—
399	D₄²	—	3	4	no	—
400	D₄²	—	3	4	no	—
401	#535	—	3	2	no	—
402	#534	—	3	1	no	—
403	#534	—	3	2	no	—
404	#534	—	3	1	no	—
405	#525	—	3	2	no	—
406	C₂×#120	—	3	1	no	—
407	C₂×#120	—	3	2	no	—
408	C₂×#120	C₃×D₃	1	1	yes	characteristic, complemented
409	#518	—	3	1	no	—
410	C₂⁴×C₃	—	2	4	no	—
411	C₂⁴×C₃	—	2	4	no	—
412	C₂⁴×C₃	—	2	2	no	—
413	C₂⁴×C₃	—	2	1	no	—
414	C₂⁴×C₃	—	2	1	no	—
415	C₂⁴×C₃	—	2	2	no	—
416	C₂⁴×C₃	—	2	1	no	—
417	C₂⁴×C₃	—	2	1	no	—
418	C₂⁴×C₃	—	3	1	no	—
419	C₂⁴×C₃	—	3	4	no	—
420	C₂⁴×C₃	—	3	1	no	—
421	C₂⁴×C₃	—	3	2	no	—
422	C₂⁴×C₃	—	3	1	no	—
423	C₂⁴×C₃	—	4	4	no	—
424	C₂⁴×C₃	—	4	4	no	—
425	C₂⁴×C₃	—	4	4	no	—
426	C₂⁴×C₃	—	4	8	no	—
427	C₂⁴×C₃	—	6	4	no	—
428	C₂⁴×C₃	—	12	4	no	—
429	C₂⁴×C₃	C₂²×D₃	1	1	yes	characteristic
430	C₂⁴×C₃	C₂²×D₃	1	2	yes	—
431	C₂⁴×C₃	C₂²×D₃	1	2	yes	—
432	C₂⁴×C₃	C₂²×D₃	1	1	yes	characteristic
433	C₂⁴×C₃	C₂²×D₃	1	1	yes	characteristic
434	C₂⁴×C₃	C₂²×D₃	1	1	yes	characteristic, complemented
435	C₂⁴×C₃	C₂³×C₃	1	1	yes	characteristic
436	C₂⁴×C₃	C₂³×C₃	1	2	yes	—
437	C₂⁴×C₃	C₂³×C₃	1	2	yes	—
438	C₂⁴×C₃	C₂³×C₃	1	1	yes	characteristic
439	C₂⁴×C₃	C₂³×C₃	1	1	yes	characteristic
440	C₂⁴×C₃	C₂³×C₃	1	1	yes	characteristic, complemented
441	C₂³×D₃	—	2	4	no	—
442	C₂³×D₃	—	4	4	no	—
443	C₂³×D₃	C₂³×C₃	1	4	yes	—
444	C₂³×D₃	C₂³×C₃	1	1	yes	characteristic
445	C₂³×D₃	C₂³×C₃	1	1	yes	characteristic
446	C₂³×D₃	C₂³×C₃	1	1	yes	characteristic, complemented
447	C₂³×D₃	C₂³×C₃	1	2	yes	complemented
448	C₃×#41	—	6	8	no	—
449	C₃×#41	—	6	8	no	—
450	C₃×#41	—	6	8	no	—
451	C₂×C₃×Q₈	—	3	2	no	—
452	C₂×C₃×D₄	—	2	4	no	—
453	C₂×C₃×D₄	—	2	4	no	—
454	C₂×C₃×D₄	—	2	4	no	—
455	C₂×C₃×D₄	—	2	2	no	—
456	C₂×C₃×D₄	—	2	2	no	—
457	C₂×C₃×D₄	—	2	4	no	—
458	C₂×C₃×D₄	—	3	8	no	—
459	C₂×C₃×D₄	—	3	2	no	—
460	C₂×C₃×D₄	—	3	2	no	—
461	C₂×C₃×D₄	—	3	4	no	—
462	C₂×C₃×D₄	—	3	2	no	—
463	C₂×C₃×D₄	—	3	2	no	—
464	C₂×C₃×D₄	—	3	2	no	—
465	C₂×C₃×D₄	—	3	4	no	—
466	C₂×C₃×D₄	—	3	2	no	—
467	C₂×C₃×D₄	—	3	2	no	—
468	C₂×C₃×D₄	—	3	4	no	—
469	C₂×C₃×D₄	—	3	2	no	—
470	C₂×C₃×D₄	—	3	4	no	—
471	C₂×C₃×D₄	—	3	4	no	—
472	C₂×C₃×D₄	—	3	2	no	—
473	C₂×C₃×D₄	—	3	4	no	—
474	C₂×C₃×D₄	—	4	4	no	—
475	C₂×C₃×D₄	—	4	4	no	—
476	C₂×C₃×D₄	—	4	4	no	—
477	C₂×C₃×D₄	—	4	8	no	—
478	C₂×C₃×D₄	—	6	4	no	—
479	C₂×C₃×D₄	—	6	8	no	—
480	C₂×C₃×D₄	—	6	8	no	—
481	C₂×C₃×D₄	—	6	16	no	—
482	C₂×C₃×D₄	—	6	16	no	—
483	C₂×C₃×D₄	—	6	8	no	—
484	C₂×C₃×D₄	—	6	4	no	—
485	C₂×C₃×D₄	—	6	4	no	—
486	C₂×C₃×D₄	—	6	4	no	—
487	C₂×C₃×D₄	—	12	8	no	—
488	C₂×C₃×D₄	—	12	4	no	—
489	C₂×C₃×D₄	C₂²×D₃	1	4	yes	—
490	C₂×C₃×D₄	C₂²×D₃	1	2	yes	—
491	C₂×C₃×D₄	C₂²×D₃	1	2	yes	complemented
492	C₂×C₃×D₄	C₂²×D₃	1	4	yes	complemented
493	C₂×C₃×D₄	C₂³×C₃	1	4	yes	—
494	C₂×C₃×D₄	C₂³×C₃	1	2	yes	—
495	C₂×C₃×D₄	C₂³×C₃	1	2	yes	complemented
496	C₂×C₃×D₄	C₂³×C₃	1	4	yes	complemented
497	C₂²×C₃×C₄	—	2	1	no	—
498	C₂²×C₃×C₄	—	2	2	no	—
499	C₂²×C₃×C₄	—	3	1	no	—
500	C₂²×C₃×C₄	—	3	1	no	—
501	C₂²×C₃×C₄	—	3	2	no	—
502	C₂²×C₃×C₄	—	3	4	no	—
503	C₂²×C₃×C₄	—	3	1	no	—
504	C₂²×C₃×C₄	—	3	2	no	—
505	C₂²×C₃×C₄	—	3	2	no	—
506	C₂²×C₃×C₄	—	3	2	no	—
507	C₂²×C₃×C₄	—	3	4	no	—
508	C₂²×C₃×C₄	—	6	4	no	—
509	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic, complemented
510	C₂²×C₃×C₄	C₂²×D₃	1	2	yes	complemented
511	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic, complemented
512	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	complemented
513	C₂×#67	—	2	4	no	—
514	C₂×#67	—	2	4	no	—
515	C₂×#67	—	2	4	no	—
516	C₂×#67	—	2	8	no	—
517	C₂×#67	—	2	16	no	—
518	C₂×#67	—	2	16	no	—
519	C₂×#67	—	2	4	no	—
520	C₂×#67	—	4	4	no	—
521	C₂×#67	C₃×D₄	1	8	yes	complemented
522	C₂×#67	C₂³×C₃	1	4	yes	—
523	C₂×#67	C₂³×C₃	1	2	yes	—
524	C₂×#67	C₂³×C₃	1	2	yes	—
525	C₂×#67	C₂³×C₃	1	4	yes	—
526	C₂×#67	C₂³×C₃	1	4	yes	—
527	C₂×#67	C₂³×C₃	1	2	yes	—
528	C₂×#67	C₂³×C₃	1	2	yes	—
529	C₂×#67	C₂³×C₃	1	2	yes	—
530	C₂×#67	C₂³×C₃	1	2	yes	complemented
531	C₂×#67	C₂³×C₃	1	2	yes	complemented
532	C₂×#67	C₂³×C₃	1	2	yes	complemented
533	C₂×#67	C₂³×C₃	1	4	yes	complemented
534	C₂×#67	C₂³×C₃	1	4	yes	complemented
535	C₂²×Dic₃	—	2	4	no	—
536	C₂²×Dic₃	C₂³×C₃	1	4	yes	—
537	C₂²×Dic₃	C₂³×C₃	1	1	yes	characteristic
538	C₂²×Dic₃	C₂³×C₃	1	1	yes	characteristic
539	C₂²×Dic₃	C₂³×C₃	1	1	yes	characteristic, complemented
540	C₂²×Dic₃	C₂³×C₃	1	2	yes	complemented
541	C₂²×Dic₃	C₂³×C₃	1	2	yes	complemented
542	#237	—	2	8	no	—
543	#237	—	2	8	no	—
544	D₃×D₄	—	2	8	no	—
545	D₃×D₄	—	2	8	no	—
546	D₃×D₄	—	4	8	no	—
547	#235	—	2	8	no	—
548	C₂×D₁₂	C₂³×C₃	1	2	yes	complemented
549	C₂×D₁₂	C₂³×C₃	1	4	yes	complemented
550	C₂×C₄×D₃	C₂³×C₃	1	2	yes	complemented
551	C₂×C₄×D₃	C₂³×C₃	1	2	yes	complemented
552	C₂×C₄×D₃	C₂³×C₃	1	4	yes	complemented
553	C₂×Dic₆	C₂³×C₃	1	2	yes	complemented
554	C₃×C₄⋊C₄	—	3	4	no	—
555	C₃×C₄⋊C₄	—	3	4	no	—
556	C₃×C₄⋊C₄	—	3	4	no	—
557	C₃×C₂²⋊C₄	—	2	2	no	—
558	C₃×C₂²⋊C₄	—	2	4	no	—
559	C₃×C₂²⋊C₄	—	2	2	no	—
560	C₃×C₂²⋊C₄	—	2	4	no	—
561	C₃×C₂²⋊C₄	—	3	2	no	—
562	C₃×C₂²⋊C₄	—	3	4	no	—
563	C₃×C₂²⋊C₄	—	3	2	no	—
564	C₃×C₂²⋊C₄	—	3	4	no	—
565	C₃×C₂²⋊C₄	—	3	4	no	—
566	C₃×C₂²⋊C₄	—	3	4	no	—
567	C₃×C₂²⋊C₄	—	3	4	no	—
568	C₃×C₂²⋊C₄	—	3	4	no	—
569	C₃×C₂²⋊C₄	—	3	4	no	—
570	C₃×C₂²⋊C₄	C₂²×D₃	1	2	yes	—
571	C₃×C₂²⋊C₄	C₂²×D₃	1	4	yes	—
572	C₃×C₂²⋊C₄	C₂²×D₃	1	2	yes	complemented
573	C₃×C₂²⋊C₄	C₂²×D₃	1	4	yes	complemented
574	C₃×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
575	C₃×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
576	C₃×C₂²⋊C₄	C₂³×C₃	1	2	yes	complemented
577	C₃×C₂²⋊C₄	C₂³×C₃	1	4	yes	complemented
578	C₃×C₄²	—	3	4	no	—
579	#217	C₂³×C₃	1	2	yes	—
580	#217	C₂³×C₃	1	4	yes	—
581	#217	C₂³×C₃	1	4	yes	complemented
582	#217	C₂³×C₃	1	2	yes	complemented
583	#217	C₂³×C₃	1	4	yes	complemented
584	(C₂×D₃)⋊C₄	C₂³×C₃	1	4	yes	complemented
585	(C₂×D₃)⋊C₄	C₂³×C₃	1	4	yes	complemented
586	(C₂×D₃)⋊C₄	C₂³×C₃	1	4	yes	complemented
587	(C₂×D₃)⋊C₄	C₂³×C₃	1	4	yes	complemented
588	C₄⋊Dic₃	C₂³×C₃	1	4	yes	complemented
589	Dic₃⋊C₄	C₂³×C₃	1	4	yes	complemented
590	Dic₃⋊C₄	C₂³×C₃	1	4	yes	complemented
591	C₄×Dic₃	C₂³×C₃	1	4	yes	complemented
592	C₂²×C₃²	—	2	2	no	—
593	C₂²×C₃²	—	2	2	no	—
594	C₂²×C₃²	—	2	8	no	—
595	C₂²×C₃²	—	2	2	no	—
596	C₂²×C₃²	—	2	2	no	—
597	C₂²×C₃²	—	2	2	no	—
598	C₂²×C₃²	—	2	2	no	—
599	C₂²×C₃²	—	2	2	no	—
600	C₂²×C₃²	—	2	2	no	—
601	C₂²×C₃²	—	2	2	no	—
602	C₂²×C₃²	—	2	4	no	—
603	C₂²×C₃²	—	4	4	no	—
604	C₂²×C₃²	—	4	8	no	—
605	C₂²×C₃²	—	4	8	no	—
606	C₂²×C₃²	—	4	4	no	—
607	C₂²×C₃²	—	8	2	no	—
608	C₂²×C₃²	C₂²×D₄	1	2	yes	—
609	C₂²×C₃²	C₂²×D₄	1	2	yes	—
610	C₂²×C₃²	C₂²×D₄	1	2	yes	—
611	C₂²×C₃²	H(5,𝔽₂)	1	4	yes	complemented
612	C₂²×C₃²	C₂⁵	1	1	yes	characteristic
613	C₂×C₃×D₃	—	2	4	no	—
614	C₂×C₃×D₃	—	2	2	no	—
615	C₂×C₃×D₃	—	2	2	no	—
616	C₂×C₃×D₃	—	2	4	no	—
617	C₂×C₃×D₃	—	2	4	no	—
618	C₂×C₃×D₃	—	4	4	no	—
619	C₂×C₃×D₃	—	4	16	no	—
620	C₂×C₃×D₃	—	4	4	no	—
621	C₂×C₃×D₃	—	8	4	no	—
622	C₂×C₃×D₃	—	8	2	no	—
623	C₂×C₃×D₃	C₂²×D₄	1	4	yes	—
624	C₃²×C₄	—	2	2	no	—
625	C₃²×C₄	—	2	4	no	—
626	C₃×Dic₃	—	2	2	no	—
627	C₃×Dic₃	—	2	2	no	—
628	C₃×Dic₃	—	2	4	no	—
629	C₃×Dic₃	C₂²×D₄	1	4	yes	—
630	C₂⁵	—	3	1	no	—
631	C₂⁵	C₂×C₃×D₃	1	1	yes	characteristic, complemented
632	H(5,𝔽₂)	—	6	8	no	—
633	C₂×#41	—	3	2	no	—
634	C₂×#41	—	3	2	no	—
635	C₂×#41	—	3	2	no	—
636	C₂²×D₄	—	3	1	no	—
637	C₂²×D₄	—	3	1	no	—
638	C₂²×D₄	—	3	1	no	—
639	C₂²×D₄	—	3	1	no	—
640	C₂²×D₄	—	3	1	no	—
641	C₂²×D₄	—	3	4	no	—
642	C₂²×D₄	—	3	4	no	—
643	C₂²×D₄	—	3	2	no	—
644	C₂²×D₄	—	3	2	no	—
645	C₂²×D₄	—	3	2	no	—
646	C₂²×D₄	—	3	2	no	—
647	C₂²×D₄	—	3	4	no	—
648	C₂²×D₄	—	6	8	no	—
649	C₂²×D₄	C₂×C₃×D₃	1	1	yes	characteristic, complemented
650	C₂²×D₄	C₂×C₃×D₃	1	2	yes	complemented
651	C₂³×C₄	—	3	1	no	—
652	#127	—	3	4	no	—
653	#124	—	3	4	no	—
654	#123	—	3	2	no	—
655	#123	—	3	2	no	—
656	#123	—	3	2	no	—
657	#123	—	3	4	no	—
658	#123	—	3	2	no	—
659	C₂²⋊Q₈	—	3	4	no	—
660	#121	—	3	4	no	—
661	#121	—	3	4	no	—
662	#121	—	3	4	no	—
663	#121	—	3	4	no	—
664	#121	—	3	4	no	—
665	#121	—	3	4	no	—
666	#121	—	3	4	no	—
667	#120	—	3	2	no	—
668	#120	—	3	2	no	—
669	#120	—	3	4	no	—
670	#120	—	3	2	no	—
671	#120	—	3	2	no	—
672	#120	—	3	4	no	—
673	#120	—	3	4	no	—
674	#120	—	3	2	no	—
675	#120	—	3	4	no	—
676	#120	—	3	2	no	—
677	#120	C₂×C₃×D₃	1	2	yes	complemented
678	#120	C₂×C₃×D₃	1	2	yes	complemented
679	#120	C₂×C₃×D₃	1	4	yes	complemented
680	C₄×D₄	—	3	4	no	—
681	C₄×D₄	—	3	4	no	—
682	C₄×D₄	—	3	4	no	—
683	C₄×D₄	—	3	4	no	—
684	#117	—	3	2	no	—
685	C₂×C₂²⋊C₄	—	3	1	no	—
686	C₂×C₂²⋊C₄	—	3	2	no	—
687	C₂×C₂²⋊C₄	—	3	2	no	—
688	C₂×C₂²⋊C₄	—	3	4	no	—
689	C₂×C₂²⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic, complemented
690	C₂×C₂²⋊C₄	C₂×C₃×D₃	1	2	yes	complemented
691	C₂³×C₃	—	2	2	no	—
692	C₂³×C₃	—	2	4	no	—
693	C₂³×C₃	—	2	2	no	—
694	C₂³×C₃	—	2	4	no	—
695	C₂³×C₃	—	2	8	no	—
696	C₂³×C₃	—	2	4	no	—
697	C₂³×C₃	—	2	4	no	—
698	C₂³×C₃	—	2	2	no	—
699	C₂³×C₃	—	2	4	no	—
700	C₂³×C₃	—	2	4	no	—
701	C₂³×C₃	—	2	4	no	—
702	C₂³×C₃	—	2	4	no	—
703	C₂³×C₃	—	2	2	no	—
704	C₂³×C₃	—	2	4	no	—
705	C₂³×C₃	—	2	4	no	—
706	C₂³×C₃	—	2	2	no	—
707	C₂³×C₃	—	2	2	no	—
708	C₂³×C₃	—	2	1	no	—
709	C₂³×C₃	—	2	2	no	—
710	C₂³×C₃	—	2	1	no	—
711	C₂³×C₃	—	2	1	no	—
712	C₂³×C₃	—	2	2	no	—
713	C₂³×C₃	—	2	2	no	—
714	C₂³×C₃	—	2	4	no	—
715	C₂³×C₃	—	3	2	no	—
716	C₂³×C₃	—	3	4	no	—
717	C₂³×C₃	—	3	2	no	—
718	C₂³×C₃	—	3	2	no	—
719	C₂³×C₃	—	4	2	no	—
720	C₂³×C₃	—	4	4	no	—
721	C₂³×C₃	—	4	4	no	—
722	C₂³×C₃	—	4	4	no	—
723	C₂³×C₃	—	4	2	no	—
724	C₂³×C₃	—	4	4	no	—
725	C₂³×C₃	—	4	2	no	—
726	C₂³×C₃	—	4	2	no	—
727	C₂³×C₃	—	4	2	no	—
728	C₂³×C₃	—	4	2	no	—
729	C₂³×C₃	—	4	2	no	—
730	C₂³×C₃	—	4	2	no	—
731	C₂³×C₃	—	4	2	no	—
732	C₂³×C₃	—	4	2	no	—
733	C₂³×C₃	—	4	2	no	—
734	C₂³×C₃	—	4	2	no	—
735	C₂³×C₃	—	4	2	no	—
736	C₂³×C₃	—	4	4	no	—
737	C₂³×C₃	—	4	4	no	—
738	C₂³×C₃	—	4	4	no	—
739	C₂³×C₃	—	4	4	no	—
740	C₂³×C₃	—	4	16	no	—
741	C₂³×C₃	—	4	16	no	—
742	C₂³×C₃	—	4	4	no	—
743	C₂³×C₃	—	4	32	no	—
744	C₂³×C₃	—	6	8	no	—
745	C₂³×C₃	—	6	4	no	—
746	C₂³×C₃	—	6	2	no	—
747	C₂³×C₃	—	6	8	no	—
748	C₂³×C₃	—	6	2	no	—
749	C₂³×C₃	—	12	2	no	—
750	C₂³×C₃	—	12	4	no	—
751	C₂³×C₃	—	12	2	no	—
752	C₂³×C₃	—	12	2	no	—
753	C₂³×C₃	—	12	4	no	—
754	C₂³×C₃	—	12	16	no	—
755	C₂³×C₃	D₃×D₄	1	4	yes	complemented
756	C₂³×C₃	C₂×C₃×D₄	1	4	yes	complemented
757	C₂³×C₃	C₂³×D₃	1	2	yes	—
758	C₂³×C₃	C₂³×D₃	1	2	yes	—
759	C₂³×C₃	C₂³×D₃	1	1	yes	characteristic
760	C₂³×C₃	C₂³×D₃	1	1	yes	characteristic
761	C₂³×C₃	C₂³×D₃	1	1	yes	characteristic
762	C₂³×C₃	C₂³×D₃	1	2	yes	—
763	C₂³×C₃	C₂⁴×C₃	1	2	yes	—
764	C₂³×C₃	C₂⁴×C₃	1	2	yes	—
765	C₂³×C₃	C₂⁴×C₃	1	1	yes	characteristic
766	C₂³×C₃	C₂⁴×C₃	1	1	yes	characteristic
767	C₂³×C₃	C₂⁴×C₃	1	1	yes	characteristic
768	C₂³×C₃	C₂⁴×C₃	1	2	yes	—
769	C₂²×D₃	—	2	2	no	—
770	C₂²×D₃	—	2	8	no	—
771	C₂²×D₃	—	2	2	no	—
772	C₂²×D₃	—	2	8	no	—
773	C₂²×D₃	—	2	4	no	—
774	C₂²×D₃	—	4	2	no	—
775	C₂²×D₃	—	4	4	no	—
776	C₂²×D₃	—	4	2	no	—
777	C₂²×D₃	—	4	4	no	—
778	C₂²×D₃	—	4	2	no	—
779	C₂²×D₃	—	4	16	no	—
780	C₂²×D₃	C₂×C₃×D₄	1	4	yes	complemented
781	C₂²×D₃	C₂⁴×C₃	1	2	yes	—
782	C₂²×D₃	C₂⁴×C₃	1	2	yes	—
783	C₂²×D₃	C₂⁴×C₃	1	2	yes	—
784	C₃×Q₈	—	6	4	no	—
785	C₃×D₄	—	2	4	no	—
786	C₃×D₄	—	2	4	no	—
787	C₃×D₄	—	2	8	no	—
788	C₃×D₄	—	2	4	no	—
789	C₃×D₄	—	2	4	no	—
790	C₃×D₄	—	2	8	no	—
791	C₃×D₄	—	3	8	no	—
792	C₃×D₄	—	3	8	no	—
793	C₃×D₄	—	4	4	no	—
794	C₃×D₄	—	4	4	no	—
795	C₃×D₄	—	4	8	no	—
796	C₃×D₄	—	4	4	no	—
797	C₃×D₄	—	4	4	no	—
798	C₃×D₄	—	4	8	no	—
799	C₃×D₄	—	6	4	no	—
800	C₃×D₄	—	6	8	no	—
801	C₃×D₄	—	6	4	no	—
802	C₃×D₄	—	6	8	no	—
803	C₃×D₄	—	6	4	no	—
804	C₃×D₄	—	6	4	no	—
805	C₃×D₄	—	6	4	no	—
806	C₃×D₄	—	6	4	no	—
807	C₃×D₄	—	6	4	no	—
808	C₃×D₄	—	6	8	no	—
809	C₃×D₄	—	12	4	no	—
810	C₃×D₄	—	12	4	no	—
811	C₃×D₄	—	12	4	no	—
812	C₂×C₃×C₄	—	2	2	no	—
813	C₂×C₃×C₄	—	2	2	no	—
814	C₂×C₃×C₄	—	2	4	no	—
815	C₂×C₃×C₄	—	2	2	no	—
816	C₂×C₃×C₄	—	3	4	no	—
817	C₂×C₃×C₄	—	3	2	no	—
818	C₂×C₃×C₄	—	3	4	no	—
819	C₂×C₃×C₄	—	3	2	no	—
820	C₂×C₃×C₄	—	3	2	no	—
821	C₂×C₃×C₄	—	4	2	no	—
822	C₂×C₃×C₄	—	4	2	no	—
823	C₂×C₃×C₄	—	4	2	no	—
824	C₂×C₃×C₄	—	4	4	no	—
825	C₂×C₃×C₄	—	6	4	no	—
826	C₂×C₃×C₄	—	6	4	no	—
827	C₂×C₃×C₄	—	6	8	no	—
828	C₂×C₃×C₄	—	6	4	no	—
829	C₂×C₃×C₄	—	6	2	no	—
830	C₂×C₃×C₄	—	6	2	no	—
831	C₂×C₃×C₄	—	12	4	no	—
832	C₂×C₃×C₄	—	12	2	no	—
833	C₂×C₃×C₄	C₂³×D₃	1	4	yes	—
834	C₂×C₃×C₄	C₂³×D₃	1	2	yes	—
835	C₂×C₃×C₄	C₂⁴×C₃	1	4	yes	—
836	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
837	#67	—	2	4	no	—
838	#67	—	2	4	no	—
839	#67	—	2	4	no	—
840	#67	—	2	4	no	—
841	#67	—	2	8	no	—
842	#67	—	2	4	no	—
843	#67	—	2	8	no	—
844	#67	—	2	4	no	—
845	#67	—	2	8	no	—
846	#67	—	4	4	no	—
847	#67	—	4	4	no	—
848	#67	C₂×C₃×D₄	1	8	yes	complemented
849	#67	C₂×C₃×D₄	1	8	yes	complemented
850	C₂×Dic₃	—	2	2	no	—
851	C₂×Dic₃	—	2	2	no	—
852	C₂×Dic₃	—	2	4	no	—
853	C₂×Dic₃	—	2	8	no	—
854	C₂×Dic₃	—	4	2	no	—
855	C₂×Dic₃	C₂×C₃×D₄	1	4	yes	complemented
856	C₂×Dic₃	C₂⁴×C₃	1	4	yes	—
857	C₂×Dic₃	C₂⁴×C₃	1	2	yes	—
858	C₂×Dic₃	C₂⁴×C₃	1	2	yes	—
859	C₂×Dic₃	C₂⁴×C₃	1	2	yes	—
860	D₁₂	—	2	4	no	—
861	D₁₂	—	4	4	no	—
862	C₄×D₃	—	2	4	no	—
863	C₄×D₃	—	2	4	no	—
864	C₄×D₃	—	4	4	no	—
865	Dic₆	—	2	4	no	—
866	C₂×C₃²	—	2	2	no	—
867	C₂×C₃²	—	2	2	no	—
868	C₂×C₃²	—	2	4	no	—
869	C₂×C₃²	—	2	2	no	—
870	C₂×C₃²	—	4	2	no	—
871	C₂×C₃²	—	4	2	no	—
872	C₂×C₃²	C₂³×D₄	1	1	yes	characteristic
873	C₂×C₃²	C₂×H(5,𝔽₂)	1	2	yes	—
874	C₃×D₃	—	2	4	no	—
875	C₃×D₃	—	4	2	no	—
876	C₃×D₃	—	4	2	no	—
877	C₂⁴	—	2	4	no	—
878	C₂⁴	—	3	1	no	—
879	C₂⁴	—	3	4	no	—
880	C₂⁴	—	3	1	no	—
881	C₂⁴	—	3	2	no	—
882	C₂⁴	—	3	1	no	—
883	C₂⁴	—	4	4	no	—
884	C₂⁴	—	6	4	no	—
885	C₂⁴	—	12	4	no	—
886	C₂⁴	C₂²×C₃×D₃	1	1	yes	characteristic
887	C₂⁴	C₂²×C₃×D₃	1	2	yes	—
888	C₂⁴	C₂²×C₃×D₃	1	2	yes	—
889	C₂⁴	C₂²×C₃×D₃	1	1	yes	characteristic
890	C₂⁴	C₂²×C₃×D₃	1	1	yes	characteristic
891	C₂⁴	C₂²×C₃×D₃	1	1	yes	characteristic, complemented
892	#41	—	6	8	no	—
893	#41	—	6	8	no	—
894	#41	—	6	8	no	—
895	C₂×Q₈	—	3	2	no	—
896	C₂×D₄	—	2	4	no	—
897	C₂×D₄	—	3	2	no	—
898	C₂×D₄	—	3	2	no	—
899	C₂×D₄	—	3	8	no	—
900	C₂×D₄	—	3	4	no	—
901	C₂×D₄	—	3	2	no	—
902	C₂×D₄	—	3	2	no	—
903	C₂×D₄	—	3	2	no	—
904	C₂×D₄	—	3	4	no	—
905	C₂×D₄	—	3	2	no	—
906	C₂×D₄	—	3	2	no	—
907	C₂×D₄	—	3	4	no	—
908	C₂×D₄	—	3	2	no	—
909	C₂×D₄	—	3	4	no	—
910	C₂×D₄	—	3	4	no	—
911	C₂×D₄	—	3	2	no	—
912	C₂×D₄	—	3	4	no	—
913	C₂×D₄	—	4	4	no	—
914	C₂×D₄	—	6	4	no	—
915	C₂×D₄	—	6	8	no	—
916	C₂×D₄	—	6	8	no	—
917	C₂×D₄	—	6	16	no	—
918	C₂×D₄	—	6	16	no	—
919	C₂×D₄	—	6	8	no	—
920	C₂×D₄	—	6	4	no	—
921	C₂×D₄	—	6	4	no	—
922	C₂×D₄	—	6	4	no	—
923	C₂×D₄	—	12	8	no	—
924	C₂×D₄	—	12	4	no	—
925	C₂×D₄	C₂²×C₃×D₃	1	4	yes	—
926	C₂×D₄	C₂²×C₃×D₃	1	2	yes	—
927	C₂×D₄	C₂²×C₃×D₃	1	2	yes	complemented
928	C₂×D₄	C₂²×C₃×D₃	1	4	yes	complemented
929	C₂²×C₄	—	3	1	no	—
930	C₂²×C₄	—	3	1	no	—
931	C₂²×C₄	—	3	2	no	—
932	C₂²×C₄	—	3	4	no	—
933	C₂²×C₄	—	3	1	no	—
934	C₂²×C₄	—	3	2	no	—
935	C₂²×C₄	—	3	2	no	—
936	C₂²×C₄	—	3	2	no	—
937	C₂²×C₄	—	3	4	no	—
938	C₂²×C₄	—	6	4	no	—
939	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic, complemented
940	C₂²×C₄	C₂²×C₃×D₃	1	2	yes	complemented
941	C₄⋊C₄	—	3	4	no	—
942	C₄⋊C₄	—	3	4	no	—
943	C₄⋊C₄	—	3	4	no	—
944	C₂²⋊C₄	—	3	2	no	—
945	C₂²⋊C₄	—	3	4	no	—
946	C₂²⋊C₄	—	3	2	no	—
947	C₂²⋊C₄	—	3	4	no	—
948	C₂²⋊C₄	—	3	4	no	—
949	C₂²⋊C₄	—	3	4	no	—
950	C₂²⋊C₄	—	3	4	no	—
951	C₂²⋊C₄	—	3	4	no	—
952	C₂²⋊C₄	—	3	4	no	—
953	C₂²⋊C₄	C₂²×C₃×D₃	1	2	yes	—
954	C₂²⋊C₄	C₂²×C₃×D₃	1	4	yes	—
955	C₂²⋊C₄	C₂²×C₃×D₃	1	2	yes	complemented
956	C₂²⋊C₄	C₂²×C₃×D₃	1	4	yes	complemented
957	C₄²	—	3	4	no	—
958	C₂²×C₃	—	2	4	no	—
959	C₂²×C₃	—	2	8	no	—
960	C₂²×C₃	—	2	8	no	—
961	C₂²×C₃	—	2	2	no	—
962	C₂²×C₃	—	2	2	no	—
963	C₂²×C₃	—	2	2	no	—
964	C₂²×C₃	—	2	2	no	—
965	C₂²×C₃	—	2	2	no	—
966	C₂²×C₃	—	2	2	no	—
967	C₂²×C₃	—	2	2	no	—
968	C₂²×C₃	—	2	2	no	—
969	C₂²×C₃	—	2	2	no	—
970	C₂²×C₃	—	2	2	no	—
971	C₂²×C₃	—	2	4	no	—
972	C₂²×C₃	—	2	2	no	—
973	C₂²×C₃	—	2	2	no	—
974	C₂²×C₃	—	2	4	no	—
975	C₂²×C₃	—	2	2	no	—
976	C₂²×C₃	—	2	2	no	—
977	C₂²×C₃	—	2	2	no	—
978	C₂²×C₃	—	2	2	no	—
979	C₂²×C₃	—	2	2	no	—
980	C₂²×C₃	—	2	4	no	—
981	C₂²×C₃	—	2	2	no	—
982	C₂²×C₃	—	2	2	no	—
983	C₂²×C₃	—	2	2	no	—
984	C₂²×C₃	—	2	2	no	—
985	C₂²×C₃	—	2	4	no	—
986	C₂²×C₃	—	2	1	no	—
987	C₂²×C₃	—	3	4	no	—
988	C₂²×C₃	—	4	2	no	—
989	C₂²×C₃	—	4	2	no	—
990	C₂²×C₃	—	4	2	no	—
991	C₂²×C₃	—	4	2	no	—
992	C₂²×C₃	—	4	2	no	—
993	C₂²×C₃	—	4	2	no	—
994	C₂²×C₃	—	4	2	no	—
995	C₂²×C₃	—	4	4	no	—
996	C₂²×C₃	—	4	8	no	—
997	C₂²×C₃	—	4	4	no	—
998	C₂²×C₃	—	4	4	no	—
999	C₂²×C₃	—	4	8	no	—
1000	C₂²×C₃	—	4	8	no	—
1001	C₂²×C₃	—	4	8	no	—
1002	C₂²×C₃	—	4	8	no	—
1003	C₂²×C₃	—	4	8	no	—
1004	C₂²×C₃	—	4	16	no	—
1005	C₂²×C₃	—	4	4	no	—
1006	C₂²×C₃	—	4	4	no	—
1007	C₂²×C₃	—	4	16	no	—
1008	C₂²×C₃	—	4	8	no	—
1009	C₂²×C₃	—	6	4	no	—
1010	C₂²×C₃	—	6	2	no	—
1011	C₂²×C₃	—	6	2	no	—
1012	C₂²×C₃	—	6	4	no	—
1013	C₂²×C₃	—	6	4	no	—
1014	C₂²×C₃	—	8	2	no	—
1015	C₂²×C₃	—	8	2	no	—
1016	C₂²×C₃	—	8	4	no	—
1017	C₂²×C₃	—	12	4	no	—
1018	C₂²×C₃	—	12	16	no	—
1019	C₂²×C₃	—	12	4	no	—
1020	C₂²×C₃	—	24	2	no	—
1021	C₂²×C₃	—	24	4	no	—
1022	C₂²×C₃	C₂×D₃×D₄	1	2	yes	—
1023	C₂²×C₃	C₂×D₃×D₄	1	2	yes	—
1024	C₂²×C₃	C₂×D₃×D₄	1	2	yes	—
1025	C₂²×C₃	#1004	1	4	yes	complemented
1026	C₂²×C₃	C₂²×C₃×D₄	1	2	yes	—
1027	C₂²×C₃	C₂²×C₃×D₄	1	2	yes	—
1028	C₂²×C₃	C₂²×C₃×D₄	1	2	yes	—
1029	C₂²×C₃	C₃×H(5,𝔽₂)	1	4	yes	complemented
1030	C₂²×C₃	C₂⁴×D₃	1	1	yes	characteristic
1031	C₂²×C₃	C₂⁵×C₃	1	1	yes	characteristic
1032	C₂×D₃	—	2	4	no	—
1033	C₂×D₃	—	2	2	no	—
1034	C₂×D₃	—	2	2	no	—
1035	C₂×D₃	—	2	4	no	—
1036	C₂×D₃	—	2	4	no	—
1037	C₂×D₃	—	4	4	no	—
1038	C₂×D₃	—	4	16	no	—
1039	C₂×D₃	—	4	4	no	—
1040	C₂×D₃	—	8	4	no	—
1041	C₂×D₃	—	8	2	no	—
1042	C₂×D₃	C₂²×C₃×D₄	1	4	yes	—
1043	C₃×C₄	—	2	2	no	—
1044	C₃×C₄	—	2	4	no	—
1045	C₃×C₄	—	2	2	no	—
1046	C₃×C₄	—	2	4	no	—
1047	C₃×C₄	—	3	4	no	—
1048	C₃×C₄	—	4	2	no	—
1049	C₃×C₄	—	4	4	no	—
1050	C₃×C₄	—	6	2	no	—
1051	C₃×C₄	—	6	2	no	—
1052	C₃×C₄	—	6	4	no	—
1053	Dic₃	—	2	2	no	—
1054	Dic₃	—	2	2	no	—
1055	Dic₃	—	2	4	no	—
1056	Dic₃	C₂²×C₃×D₄	1	4	yes	—
1057	C₃²	#3484	1	1	yes	characteristic, complemented, Sylow
1058	C₂³	—	2	2	no	—
1059	C₂³	—	2	4	no	—
1060	C₂³	—	2	4	no	—
1061	C₂³	—	2	4	no	—
1062	C₂³	—	2	2	no	—
1063	C₂³	—	2	4	no	—
1064	C₂³	—	2	4	no	—
1065	C₂³	—	2	2	no	—
1066	C₂³	—	3	2	no	—
1067	C₂³	—	3	4	no	—
1068	C₂³	—	3	2	no	—
1069	C₂³	—	3	2	no	—
1070	C₂³	—	4	2	no	—
1071	C₂³	—	4	2	no	—
1072	C₂³	—	4	2	no	—
1073	C₂³	—	4	2	no	—
1074	C₂³	—	4	2	no	—
1075	C₂³	—	4	16	no	—
1076	C₂³	—	6	8	no	—
1077	C₂³	—	6	4	no	—
1078	C₂³	—	6	2	no	—
1079	C₂³	—	6	8	no	—
1080	C₂³	—	6	2	no	—
1081	C₂³	—	12	2	no	—
1082	C₂³	—	12	4	no	—
1083	C₂³	—	12	2	no	—
1084	C₂³	—	12	2	no	—
1085	C₂³	—	12	4	no	—
1086	C₂³	—	12	16	no	—
1087	C₂³	C₃×D₃×D₄	1	4	yes	complemented
1088	C₂³	C₂³×C₃×D₃	1	2	yes	—
1089	C₂³	C₂³×C₃×D₃	1	2	yes	—
1090	C₂³	C₂³×C₃×D₃	1	1	yes	characteristic
1091	C₂³	C₂³×C₃×D₃	1	1	yes	characteristic
1092	C₂³	C₂³×C₃×D₃	1	1	yes	characteristic
1093	C₂³	C₂³×C₃×D₃	1	2	yes	—
1094	Q₈	—	6	4	no	—
1095	D₄	—	2	4	no	—
1096	D₄	—	2	4	no	—
1097	D₄	—	2	8	no	—
1098	D₄	—	3	8	no	—
1099	D₄	—	3	8	no	—
1100	D₄	—	4	4	no	—
1101	D₄	—	6	4	no	—
1102	D₄	—	6	8	no	—
1103	D₄	—	6	4	no	—
1104	D₄	—	6	8	no	—
1105	D₄	—	6	4	no	—
1106	D₄	—	6	4	no	—
1107	D₄	—	6	4	no	—
1108	D₄	—	6	4	no	—
1109	D₄	—	6	4	no	—
1110	D₄	—	6	8	no	—
1111	D₄	—	12	4	no	—
1112	D₄	—	12	4	no	—
1113	D₄	—	12	4	no	—
1114	C₂×C₄	—	2	2	no	—
1115	C₂×C₄	—	3	4	no	—
1116	C₂×C₄	—	3	2	no	—
1117	C₂×C₄	—	3	4	no	—
1118	C₂×C₄	—	3	2	no	—
1119	C₂×C₄	—	3	2	no	—
1120	C₂×C₄	—	4	2	no	—
1121	C₂×C₄	—	6	4	no	—
1122	C₂×C₄	—	6	4	no	—
1123	C₂×C₄	—	6	8	no	—
1124	C₂×C₄	—	6	4	no	—
1125	C₂×C₄	—	6	2	no	—
1126	C₂×C₄	—	6	2	no	—
1127	C₂×C₄	—	12	4	no	—
1128	C₂×C₄	—	12	2	no	—
1129	C₂×C₄	C₂³×C₃×D₃	1	4	yes	—
1130	C₂×C₄	C₂³×C₃×D₃	1	2	yes	—
1131	C₂×C₃	—	2	4	no	—
1132	C₂×C₃	—	2	2	no	—
1133	C₂×C₃	—	2	4	no	—
1134	C₂×C₃	—	2	2	no	—
1135	C₂×C₃	—	2	2	no	—
1136	C₂×C₃	—	2	2	no	—
1137	C₂×C₃	—	2	4	no	—
1138	C₂×C₃	—	2	2	no	—
1139	C₂×C₃	—	2	2	no	—
1140	C₂×C₃	—	2	1	no	—
1141	C₂×C₃	—	2	2	no	—
1142	C₂×C₃	—	4	2	no	—
1143	C₂×C₃	—	4	4	no	—
1144	C₂×C₃	—	4	2	no	—
1145	C₂×C₃	—	4	4	no	—
1146	C₂×C₃	—	4	2	no	—
1147	C₂×C₃	—	4	2	no	—
1148	C₂×C₃	—	4	2	no	—
1149	C₂×C₃	—	4	2	no	—
1150	C₂×C₃	—	6	4	no	—
1151	C₂×C₃	—	8	2	no	—
1152	C₂×C₃	—	12	2	no	—
1153	C₂×C₃	—	12	2	no	—
1154	C₂×C₃	C₂²×D₃×D₄	1	1	yes	characteristic
1155	C₂×C₃	C₂×#1004	1	2	yes	—
1156	C₂×C₃	C₂³×C₃×D₄	1	1	yes	characteristic
1157	C₂×C₃	C₂×C₃×H(5,𝔽₂)	1	2	yes	—
1158	D₃	—	2	4	no	—
1159	D₃	—	4	2	no	—
1160	D₃	—	4	2	no	—
1161	C₂²	—	2	8	no	—
1162	C₂²	—	2	2	no	—
1163	C₂²	—	2	2	no	—
1164	C₂²	—	2	2	no	—
1165	C₂²	—	2	2	no	—
1166	C₂²	—	2	2	no	—
1167	C₂²	—	2	2	no	—
1168	C₂²	—	2	2	no	—
1169	C₂²	—	2	4	no	—
1170	C₂²	—	2	2	no	—
1171	C₂²	—	2	2	no	—
1172	C₂²	—	3	4	no	—
1173	C₂²	—	4	4	no	—
1174	C₂²	—	4	8	no	—
1175	C₂²	—	4	8	no	—
1176	C₂²	—	4	4	no	—
1177	C₂²	—	6	4	no	—
1178	C₂²	—	6	2	no	—
1179	C₂²	—	6	2	no	—
1180	C₂²	—	6	4	no	—
1181	C₂²	—	6	4	no	—
1182	C₂²	—	8	2	no	—
1183	C₂²	—	12	4	no	—
1184	C₂²	—	12	16	no	—
1185	C₂²	—	12	4	no	—
1186	C₂²	—	24	2	no	—
1187	C₂²	—	24	4	no	—
1188	C₂²	C₂×C₃×D₃×D₄	1	2	yes	—
1189	C₂²	C₂×C₃×D₃×D₄	1	2	yes	—
1190	C₂²	C₂×C₃×D₃×D₄	1	2	yes	—
1191	C₂²	C₃×#1004	1	4	yes	complemented
1192	C₂²	C₂⁴×C₃×D₃	1	1	yes	characteristic
1193	C₄	—	2	2	no	—
1194	C₄	—	2	4	no	—
1195	C₄	—	3	4	no	—
1196	C₄	—	6	2	no	—
1197	C₄	—	6	2	no	—
1198	C₄	—	6	4	no	—
1199	C₃	—	2	1	no	—
1200	C₃	#85919	1	1	yes	characteristic, direct product factor
1201	C₃	C₃×#3484	1	1	yes	characteristic, complemented
1202	C₂	—	2	2	no	—
1203	C₂	—	2	4	no	—
1204	C₂	—	2	2	no	—
1205	C₂	—	2	2	no	—
1206	C₂	—	4	2	no	—
1207	C₂	—	4	2	no	—
1208	C₂	—	6	4	no	—
1209	C₂	—	12	2	no	—
1210	C₂	—	12	2	no	—
1211	C₂	C₂²×C₃×D₃×D₄	1	1	yes	characteristic
1212	C₂	C₂×C₃×#1004	1	2	yes	—

	subgroup	G/H
center	C₂²×C₃	C₂⁴×D₃
commutator, cosocle	C₂²×C₃	C₂⁵×C₃
Frattini	C₂²	C₂⁴×C₃×D₃
Fitting	C₂×C₃²×#120	C₂
socle	C₂²×C₃²	C₂⁵
hypercenter	C₂×C₃×#120	D₃
hypocenter	C₃	C₃×#3484
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₃ ◁ C₂×C₃×#120

Complements

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

N	H ≅ G/N	type
1. C₂³×C₃×#67	C₂	semidirect
2. C₂×C₃×#1004	C₂	semidirect
3. C₂×C₃²×#120	C₂	semidirect
4. C₂×C₃×#953	C₂	semidirect
5. C₃×#5804	C₂	semidirect
6. C₃×D₄×#67	C₂	semidirect
7. C₃×#5592	C₂	semidirect
8. C₃×#5591	C₂	semidirect
9. C₃×#5590	C₂	semidirect
10. C₃×#5589	C₂	semidirect
11. C₃×D₃×#120	C₂	semidirect
12. C₃×#5586	C₂	semidirect
13. C₃×#5493	C₂	semidirect
14. C₃×#5490	C₂	semidirect
15. C₃×#5486	C₂	semidirect
17. #85919	C₃	direct (N × H)
18. C₂⁵×C₃²	C₂²	semidirect
19. C₂⁴×C₃×D₃	C₂²	semidirect
20. C₂²×C₃²×D₄	C₂²	semidirect
21. C₂²×C₃²×D₄	C₂²	semidirect
24. C₂²×C₃×#67	C₂²	semidirect
25. C₂²×C₃×#67	C₂²	semidirect
26. C₂²×C₃×#67	C₂²	semidirect
27. C₂²×C₃×#67	C₂²	semidirect
28. C₂²×C₃×#67	C₂²	semidirect
29. C₂²×C₃×#67	C₂²	semidirect
30. C₂²×C₃×#67	C₂²	semidirect
31. C₂²×C₃×#67	C₂²	semidirect
32. C₂³×C₃×Dic₃	C₂²	semidirect
34. C₂×C₃×#237	C₂²	semidirect
35. C₂×C₃×#237	C₂²	semidirect
36. C₂×C₃×D₃×D₄	C₂²	semidirect
37. C₂×C₃×D₃×D₄	C₂²	semidirect
38. C₂×C₃×D₃×D₄	C₂²	semidirect
39. C₂×C₃×#235	C₂²	semidirect
40. C₃²×#120	C₂²	semidirect
41. C₃²×#120	C₂²	semidirect
42. C₃²×#120	C₂²	semidirect
43. C₂×C₃²×C₂²⋊C₄	C₂²	semidirect
44. C₂×C₃²×C₂²⋊C₄	C₂²	semidirect
45. C₃×#953	C₂²	semidirect
46. C₃×#953	C₂²	semidirect
47. C₃×#953	C₂²	semidirect
48. C₃×#953	C₂²	semidirect
49. C₂×C₃×#217	C₂²	semidirect
50. C₂×C₃×#217	C₂²	semidirect
51. C₃×#940	C₂²	semidirect
52. C₃×#939	C₂²	semidirect
53. C₃×#939	C₂²	semidirect
54. C₃×#939	C₂²	semidirect
55. C₃×#938	C₂²	semidirect
56. C₃×#937	C₂²	semidirect
57. C₃×#937	C₂²	semidirect
58. C₃×#937	C₂²	semidirect
59. C₃×#935	C₂²	semidirect
60. C₃×D₄×Dic₃	C₂²	semidirect
61. C₃×#930	C₂²	semidirect
62. C₃×#929	C₂²	semidirect
63. C₃×C₄×#67	C₂²	semidirect
64. C₃×#886	C₂²	semidirect
65. C₃×#886	C₂²	semidirect
66. C₃×#885	C₂²	semidirect
67. C₃×#884	C₂²	semidirect
68. C₃×#884	C₂²	semidirect
69. C₃×#883	C₂²	semidirect
70. C₃×#882	C₂²	semidirect
71. C₃×#882	C₂²	semidirect
72. C₃×#882	C₂²	semidirect
73. C₃×#67⋊C₄	C₂²	semidirect
74. C₃×#67⋊C₄	C₂²	semidirect
75. C₃×D₃×C₂²⋊C₄	C₂²	semidirect
76. C₃×D₃×C₂²⋊C₄	C₂²	semidirect
77. C₃×#878	C₂²	semidirect
78. C₃×#877	C₂²	semidirect
81. C₂³×#67	C₂×C₃	semidirect
82. C₂×#1004	C₂×C₃	semidirect
95. C₂×C₃×#120	D₃	semidirect
96. C₂×C₃×#120	C₂×C₃	semidirect
98. C₂×#953	C₂×C₃	semidirect
99. #5804	C₂×C₃	semidirect
100. D₄×#67	C₂×C₃	semidirect
101. #5592	C₂×C₃	semidirect
102. #5591	C₂×C₃	semidirect
103. #5590	C₂×C₃	semidirect
104. #5589	C₂×C₃	semidirect
105. D₃×#120	C₂×C₃	semidirect
106. #5586	C₂×C₃	semidirect
107. #5493	C₂×C₃	semidirect
108. #5490	C₂×C₃	semidirect
109. #5486	C₂×C₃	semidirect
117. C₂⁴×C₃²	C₂³	semidirect
123. C₂³×C₃×D₃	C₂³	semidirect
124. C₂³×C₃×D₃	C₂³	semidirect
129. C₂×C₃²×D₄	C₂³	semidirect
130. C₂×C₃²×D₄	C₂³	semidirect
131. C₂²×C₃²×C₄	C₂³	semidirect
132. C₂²×C₃²×C₄	C₂³	semidirect
141. C₂×C₃×#67	D₄	semidirect
150. C₂×C₃×#67	C₂³	semidirect
151. C₂×C₃×#67	C₂³	semidirect
152. C₂×C₃×#67	C₂³	semidirect
153. C₂×C₃×#67	C₂³	semidirect
154. C₂×C₃×#67	C₂³	semidirect
159. C₂²×C₃×Dic₃	C₂³	semidirect
160. C₂²×C₃×Dic₃	C₂³	semidirect
161. C₂²×C₃×Dic₃	C₂³	semidirect
168. C₂×C₃×D₁₂	C₂³	semidirect
169. C₂×C₃×D₁₂	C₂³	semidirect
170. C₂×C₃×C₄×D₃	C₂³	semidirect
171. C₂×C₃×C₄×D₃	C₂³	semidirect
172. C₂×C₃×C₄×D₃	C₂³	semidirect
173. C₂×C₃×Dic₆	C₂³	semidirect
176. C₃²×C₂²⋊C₄	C₂³	semidirect
177. C₃²×C₂²⋊C₄	C₂³	semidirect
180. C₃×#217	C₂³	semidirect
181. C₃×#217	C₂³	semidirect
182. C₃×#217	C₂³	semidirect
183. C₃×(C₂×D₃)⋊C₄	C₂³	semidirect
184. C₃×(C₂×D₃)⋊C₄	C₂³	semidirect
185. C₃×(C₂×D₃)⋊C₄	C₂³	semidirect
186. C₃×(C₂×D₃)⋊C₄	C₂³	semidirect
187. C₃×C₄⋊Dic₃	C₂³	semidirect
188. C₃×Dic₃⋊C₄	C₂³	semidirect
189. C₃×Dic₃⋊C₄	C₂³	semidirect
190. C₃×C₄×Dic₃	C₂³	semidirect
194. C₂⁵×C₃	C₂×D₃	semidirect
195. C₂⁵×C₃	C₂²×C₃	semidirect
196. C₂⁴×D₃	C₂²×C₃	semidirect
216. C₂²×C₃×D₄	C₂×D₃	semidirect
217. C₂²×C₃×D₄	C₂×D₃	semidirect
218. C₂²×C₃×D₄	C₂²×C₃	semidirect
219. C₂²×C₃×D₄	C₂²×C₃	semidirect
223. C₂²×#67	C₂²×C₃	semidirect
224. C₂²×#67	C₂²×C₃	semidirect
225. C₂²×#67	C₂²×C₃	semidirect
226. C₂²×#67	C₂²×C₃	semidirect
227. C₂²×#67	C₂²×C₃	semidirect
228. C₂²×#67	C₂²×C₃	semidirect
229. C₂²×#67	C₂²×C₃	semidirect
230. C₂²×#67	C₂²×C₃	semidirect
231. C₂³×Dic₃	C₂²×C₃	semidirect
233. C₂×#237	C₂²×C₃	semidirect
234. C₂×#237	C₂²×C₃	semidirect
235. C₂×D₃×D₄	C₂²×C₃	semidirect
236. C₂×D₃×D₄	C₂²×C₃	semidirect
237. C₂×D₃×D₄	C₂²×C₃	semidirect
238. C₂×#235	C₂²×C₃	semidirect
267. C₃×#120	C₂×D₃	semidirect
268. C₃×#120	C₂×D₃	semidirect
269. C₃×#120	C₂×D₃	semidirect
270. C₃×#120	C₂²×C₃	semidirect
271. C₃×#120	C₂²×C₃	semidirect
272. C₃×#120	C₂²×C₃	semidirect
284. C₂×C₃×C₂²⋊C₄	C₂×D₃	semidirect
285. C₂×C₃×C₂²⋊C₄	C₂×D₃	semidirect
286. C₂×C₃×C₂²⋊C₄	C₂²×C₃	semidirect
287. C₂×C₃×C₂²⋊C₄	C₂²×C₃	semidirect
288. #953	C₂²×C₃	semidirect
289. #953	C₂²×C₃	semidirect
290. #953	C₂²×C₃	semidirect
291. #953	C₂²×C₃	semidirect
292. C₂×#217	C₂²×C₃	semidirect
293. C₂×#217	C₂²×C₃	semidirect
294. #940	C₂²×C₃	semidirect
295. #939	C₂²×C₃	semidirect
296. #939	C₂²×C₃	semidirect
297. #939	C₂²×C₃	semidirect
298. #938	C₂²×C₃	semidirect
299. #937	C₂²×C₃	semidirect
300. #937	C₂²×C₃	semidirect
301. #937	C₂²×C₃	semidirect
302. #935	C₂²×C₃	semidirect
303. D₄×Dic₃	C₂²×C₃	semidirect
304. #930	C₂²×C₃	semidirect
305. #929	C₂²×C₃	semidirect
306. C₄×#67	C₂²×C₃	semidirect
307. #886	C₂²×C₃	semidirect
308. #886	C₂²×C₃	semidirect
309. #885	C₂²×C₃	semidirect
310. #884	C₂²×C₃	semidirect
311. #884	C₂²×C₃	semidirect
312. #883	C₂²×C₃	semidirect
313. #882	C₂²×C₃	semidirect
314. #882	C₂²×C₃	semidirect
315. #882	C₂²×C₃	semidirect
316. #67⋊C₄	C₂²×C₃	semidirect
317. #67⋊C₄	C₂²×C₃	semidirect
318. D₃×C₂²⋊C₄	C₂²×C₃	semidirect
319. D₃×C₂²⋊C₄	C₂²×C₃	semidirect
320. #878	C₂²×C₃	semidirect
321. #877	C₂²×C₃	semidirect
336. C₂³×C₃²	C₂×D₄	semidirect
354. C₂²×C₃×D₃	C₂×D₄	semidirect
377. C₃×#67	C₂×D₄	semidirect
378. C₃×#67	C₂×D₄	semidirect
384. C₂×C₃×Dic₃	C₂×D₄	semidirect
408. C₂×#120	C₃×D₃	semidirect
434. C₂⁴×C₃	C₂²×D₃	semidirect
440. C₂⁴×C₃	C₂³×C₃	semidirect
446. C₂³×D₃	C₂³×C₃	semidirect
447. C₂³×D₃	C₂³×C₃	semidirect
491. C₂×C₃×D₄	C₂²×D₃	semidirect
492. C₂×C₃×D₄	C₂²×D₃	semidirect
495. C₂×C₃×D₄	C₂³×C₃	semidirect
496. C₂×C₃×D₄	C₂³×C₃	semidirect
509. C₂²×C₃×C₄	C₂²×D₃	semidirect
510. C₂²×C₃×C₄	C₂²×D₃	semidirect
511. C₂²×C₃×C₄	C₂³×C₃	semidirect
512. C₂²×C₃×C₄	C₂³×C₃	semidirect
521. C₂×#67	C₃×D₄	semidirect
530. C₂×#67	C₂³×C₃	semidirect
531. C₂×#67	C₂³×C₃	semidirect
532. C₂×#67	C₂³×C₃	semidirect
533. C₂×#67	C₂³×C₃	semidirect
534. C₂×#67	C₂³×C₃	semidirect
539. C₂²×Dic₃	C₂³×C₃	semidirect
540. C₂²×Dic₃	C₂³×C₃	semidirect
541. C₂²×Dic₃	C₂³×C₃	semidirect
548. C₂×D₁₂	C₂³×C₃	semidirect
549. C₂×D₁₂	C₂³×C₃	semidirect
550. C₂×C₄×D₃	C₂³×C₃	semidirect
551. C₂×C₄×D₃	C₂³×C₃	semidirect
552. C₂×C₄×D₃	C₂³×C₃	semidirect
553. C₂×Dic₆	C₂³×C₃	semidirect
572. C₃×C₂²⋊C₄	C₂²×D₃	semidirect
573. C₃×C₂²⋊C₄	C₂²×D₃	semidirect
576. C₃×C₂²⋊C₄	C₂³×C₃	semidirect
577. C₃×C₂²⋊C₄	C₂³×C₃	semidirect
581. #217	C₂³×C₃	semidirect
582. #217	C₂³×C₃	semidirect
583. #217	C₂³×C₃	semidirect
584. (C₂×D₃)⋊C₄	C₂³×C₃	semidirect
585. (C₂×D₃)⋊C₄	C₂³×C₃	semidirect
586. (C₂×D₃)⋊C₄	C₂³×C₃	semidirect
587. (C₂×D₃)⋊C₄	C₂³×C₃	semidirect
588. C₄⋊Dic₃	C₂³×C₃	semidirect
589. Dic₃⋊C₄	C₂³×C₃	semidirect
590. Dic₃⋊C₄	C₂³×C₃	semidirect
591. C₄×Dic₃	C₂³×C₃	semidirect
611. C₂²×C₃²	H(5,𝔽₂)	semidirect
631. C₂⁵	C₂×C₃×D₃	semidirect
649. C₂²×D₄	C₂×C₃×D₃	semidirect
650. C₂²×D₄	C₂×C₃×D₃	semidirect
677. #120	C₂×C₃×D₃	semidirect
678. #120	C₂×C₃×D₃	semidirect
679. #120	C₂×C₃×D₃	semidirect
689. C₂×C₂²⋊C₄	C₂×C₃×D₃	semidirect
690. C₂×C₂²⋊C₄	C₂×C₃×D₃	semidirect
755. C₂³×C₃	D₃×D₄	semidirect
756. C₂³×C₃	C₂×C₃×D₄	semidirect
780. C₂²×D₃	C₂×C₃×D₄	semidirect
848. #67	C₂×C₃×D₄	semidirect
849. #67	C₂×C₃×D₄	semidirect
855. C₂×Dic₃	C₂×C₃×D₄	semidirect
891. C₂⁴	C₂²×C₃×D₃	semidirect
927. C₂×D₄	C₂²×C₃×D₃	semidirect
928. C₂×D₄	C₂²×C₃×D₃	semidirect
939. C₂²×C₄	C₂²×C₃×D₃	semidirect
940. C₂²×C₄	C₂²×C₃×D₃	semidirect
955. C₂²⋊C₄	C₂²×C₃×D₃	semidirect
956. C₂²⋊C₄	C₂²×C₃×D₃	semidirect
1025. C₂²×C₃	#1004	semidirect
1029. C₂²×C₃	C₃×H(5,𝔽₂)	semidirect
1057. C₃²	#3484	semidirect
1087. C₂³	C₃×D₃×D₄	semidirect
1191. C₂²	C₃×#1004	semidirect
1200. C₃	#85919	direct (N × H)
1201. C₃	C₃×#3484	semidirect

Maximal subgroups

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

subgroup	index
C₂³×C₃×#67	2
C₂×C₃×#1004	2
C₂×C₃²×#120	2
C₂×C₃×#953	2
C₃×#5804	2
C₃×D₄×#67	2
C₃×#5592	2
C₃×#5591	2
C₃×#5590	2
C₃×#5589	2
C₃×D₃×#120	2
C₃×#5586	2
C₃×#5493	2
C₃×#5490	2
C₃×#5486	2
C₃×#3484	3
#85919	3

Subgroups — C3×#85919 #11904272

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#85919 #11904272