Subgroups — C₃×#86171 #11910358

Order 1152.

2233 conjugacy classes of subgroups.

The subgroup lattice has 1251 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×#529	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#5712	C₂	1	2	yes	maximal, complemented
3	C₃×#5711	C₂	1	2	yes	maximal, complemented
4	C₃×#5700	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#5699	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#5684	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#5683	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#5667	C₂	1	2	yes	maximal, complemented
9	C₃×#5666	C₂	1	2	yes	maximal, complemented
10	C₃×#5647	C₂	1	2	yes	maximal, complemented
11	C₃×#5620	C₂	1	2	yes	maximal, complemented
12	C₃×#5580	C₂	1	2	yes	maximal, complemented
13	C₃×#5548	C₂	1	2	yes	maximal, complemented
14	C₃×#5547	C₂	1	2	yes	maximal, complemented
15	C₃×#5547	C₂	1	2	yes	maximal, complemented
16	C₃×#5528	C₂	1	2	yes	maximal, complemented
17	C₃×#5524	C₂	1	2	yes	maximal, complemented
18	C₃×#5479	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃×#5477	C₂	1	1	yes	maximal, characteristic, complemented
20	C₃×#3529	—	3	1	no	maximal
21	#86171	C₃	1	1	yes	maximal, characteristic, direct product factor
22	C₂×C₃×#235	C₂²	1	2	yes	—
23	C₂×C₃×#235	C₂²	1	1	yes	characteristic
24	C₂×C₃×#235	C₂²	1	1	yes	characteristic, complemented
25	C₂²×C₃×C₄×D₃	C₂²	1	2	yes	complemented
26	C₃²×#126	C₂²	1	2	yes	complemented
27	C₃²×#125	C₂²	1	1	yes	characteristic, complemented
28	C₃²×#124	C₂²	1	1	yes	characteristic
29	C₃²×#123	C₂²	1	2	yes	complemented
30	C₃²×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
31	C₃²×#121	C₂²	1	1	yes	characteristic
32	C₃²×C₄×Q₈	C₂²	1	1	yes	characteristic, complemented
33	C₃²×C₄×D₄	C₂²	1	1	yes	characteristic
34	C₃²×C₄×D₄	C₂²	1	2	yes	complemented
35	C₃²×#117	C₂²	1	2	yes	complemented
36	C₂×C₃²×C₄²	C₂²	1	1	yes	characteristic, complemented
37	C₃×#947	C₂²	1	2	yes	—
38	C₃×#946	C₂²	1	2	yes	complemented
39	C₃×#940	C₂²	1	2	yes	—
40	C₃×#939	C₂²	1	2	yes	—
41	C₃×#939	C₂²	1	2	yes	—
42	C₃×#938	C₂²	1	2	yes	complemented
43	C₃×#937	C₂²	1	2	yes	—
44	C₃×#937	C₂²	1	2	yes	complemented
45	C₃×#930	C₂²	1	1	yes	characteristic
46	C₃×#930	C₂²	1	2	yes	complemented
47	C₃×#930	C₂²	1	2	yes	complemented
48	C₃×#929	C₂²	1	2	yes	complemented
49	C₃×C₄×#67	C₂²	1	2	yes	—
50	C₃×C₄×#67	C₂²	1	2	yes	complemented
51	C₃×C₄×#67	C₂²	1	2	yes	complemented
52	C₃×#924	C₂²	1	1	yes	characteristic, complemented
53	C₃×#898	C₂²	1	2	yes	complemented
54	C₃×#898	C₂²	1	2	yes	complemented
55	C₃×#898	C₂²	1	2	yes	complemented
56	C₃×#897	C₂²	1	2	yes	complemented
57	C₃×#897	C₂²	1	2	yes	complemented
58	C₃×#896	C₂²	1	2	yes	complemented
59	C₃×#896	C₂²	1	2	yes	complemented
60	C₃×#896	C₂²	1	2	yes	complemented
61	C₃×#895	C₂²	1	2	yes	—
62	C₃×#895	C₂²	1	2	yes	—
63	C₃×#895	C₂²	1	2	yes	—
64	C₃×#895	C₂²	1	2	yes	complemented
65	C₃×#894	C₂²	1	2	yes	—
66	C₃×#894	C₂²	1	2	yes	complemented
67	C₃×#894	C₂²	1	2	yes	complemented
68	C₃×#894	C₂²	1	2	yes	complemented
69	C₃×#894	C₂²	1	2	yes	complemented
70	C₃×#890	C₂²	1	2	yes	complemented
71	C₃×#889	C₂²	1	2	yes	complemented
72	C₃×#888	C₂²	1	2	yes	complemented
73	C₃×#886	C₂²	1	2	yes	—
74	C₃×#886	C₂²	1	2	yes	complemented
75	C₃×#885	C₂²	1	2	yes	—
76	C₃×#885	C₂²	1	2	yes	—
77	C₃×#885	C₂²	1	2	yes	complemented
78	C₃×#884	C₂²	1	2	yes	—
79	C₃×#884	C₂²	1	2	yes	—
80	C₃×#884	C₂²	1	2	yes	—
81	C₃×#884	C₂²	1	2	yes	complemented
82	C₃×#884	C₂²	1	2	yes	complemented
83	C₃×#883	C₂²	1	2	yes	—
84	C₃×#883	C₂²	1	2	yes	complemented
85	C₃×#883	C₂²	1	2	yes	complemented
86	C₃×#882	C₂²	1	2	yes	—
87	C₃×#882	C₂²	1	2	yes	—
88	C₃×#882	C₂²	1	2	yes	complemented
89	C₃×#882	C₂²	1	2	yes	complemented
90	C₃×#879	C₂²	1	2	yes	complemented
91	C₃×#878	C₂²	1	2	yes	complemented
92	C₃×#878	C₂²	1	2	yes	complemented
93	C₃×#876	C₂²	1	2	yes	complemented
94	C₃×#875	C₂²	1	1	yes	characteristic
95	C₃×#875	C₂²	1	1	yes	characteristic
96	C₃×#875	C₂²	1	1	yes	characteristic, complemented
97	C₃×#874	C₂²	1	1	yes	characteristic
98	C₃×C₄×D₁₂	C₂²	1	1	yes	characteristic
99	C₃×C₄×D₁₂	C₂²	1	2	yes	—
100	C₃×C₄×D₁₂	C₂²	1	2	yes	complemented
101	C₃×C₄×D₁₂	C₂²	1	2	yes	complemented
102	C₃×C₄×D₁₂	C₂²	1	2	yes	complemented
103	C₃×#872	C₂²	1	2	yes	complemented
104	C₃×#872	C₂²	1	2	yes	complemented
105	C₃×C₄²×D₃	C₂²	1	2	yes	complemented
106	C₃×#870	C₂²	1	1	yes	characteristic, complemented
107	C₃×#869	C₂²	1	1	yes	characteristic, complemented
108	C₃×C₄×Dic₆	C₂²	1	1	yes	characteristic, complemented
109	C₃×#563	—	3	2	no	—
110	C₃×#563	—	3	1	no	—
111	C₃×#562	—	3	1	no	—
112	C₃×#562	—	3	1	no	—
113	C₃×#562	—	3	2	no	—
114	C₃×#562	—	3	2	no	—
115	C₃×H(3,𝔽₄)	—	3	1	no	—
116	C₃×#560	—	3	2	no	—
117	C₃×#560	—	3	2	no	—
118	C₃×#560	—	3	2	no	—
119	C₃×#532	—	3	2	no	—
120	C₃×#532	—	3	1	no	—
121	C₃×#529	—	2	1	no	—
122	C₃×#529	—	3	2	no	—
123	C₃×#529	—	3	2	no	—
124	C₃×#529	—	3	1	no	—
125	C₃×#529	D₃	1	1	yes	characteristic, complemented
126	C₃×#529	C₂×C₃	1	1	yes	characteristic, complemented
127	C₃×#525	—	3	2	no	—
128	C₃×#525	—	3	2	no	—
129	C₃×#525	—	3	2	no	—
130	#5712	C₂×C₃	1	2	yes	complemented
131	#5711	C₂×C₃	1	2	yes	complemented
132	#5700	C₂×C₃	1	1	yes	characteristic, complemented
133	#5699	C₂×C₃	1	1	yes	characteristic, complemented
134	#5684	C₂×C₃	1	1	yes	characteristic, complemented
135	#5683	C₂×C₃	1	1	yes	characteristic, complemented
136	#5667	C₂×C₃	1	2	yes	complemented
137	#5666	C₂×C₃	1	2	yes	complemented
138	#5647	C₂×C₃	1	2	yes	complemented
139	#5620	C₂×C₃	1	2	yes	complemented
140	#5580	C₂×C₃	1	2	yes	complemented
141	#5548	C₂×C₃	1	2	yes	complemented
142	#5547	C₂×C₃	1	2	yes	complemented
143	#5547	C₂×C₃	1	2	yes	complemented
144	#5528	C₂×C₃	1	2	yes	complemented
145	#5524	C₂×C₃	1	2	yes	complemented
146	#5479	C₂×C₃	1	1	yes	characteristic, complemented
147	#5477	C₂×C₃	1	1	yes	characteristic, complemented
148	C₂³×C₃×D₃	C₂³	1	2	yes	—
149	C₂×C₃²×Q₈	C₂³	1	1	yes	characteristic
150	C₂×C₃²×D₄	C₂³	1	1	yes	characteristic
151	C₂×C₃²×D₄	C₂³	1	2	yes	—
152	C₂²×C₃²×C₄	C₂³	1	2	yes	—
153	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
154	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
155	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
156	C₂×C₃×#67	C₂³	1	2	yes	—
157	C₂×C₃×#67	C₂³	1	2	yes	—
158	C₂×C₃×#67	C₂³	1	2	yes	—
159	C₂×C₃×#67	C₂³	1	2	yes	—
160	C₂×C₃×#67	C₂³	1	2	yes	—
161	C₂×C₃×#67	C₂³	1	2	yes	—
162	C₂×C₃×#67	C₂³	1	2	yes	—
163	C₂²×C₃×Dic₃	C₂³	1	2	yes	—
164	C₃×#235	—	4	2	no	—
165	C₃×#235	—	4	4	no	—
166	C₃×#235	—	4	2	no	—
167	C₂×C₃×D₁₂	C₂³	1	2	yes	—
168	C₂×C₃×D₁₂	C₂³	1	1	yes	characteristic
169	C₂×C₃×D₁₂	C₂³	1	1	yes	characteristic
170	C₂×C₃×D₁₂	C₂³	1	2	yes	—
171	C₂×C₃×D₁₂	C₂³	1	2	yes	—
172	C₂×C₃×D₁₂	C₂³	1	2	yes	—
173	C₂×C₃×D₁₂	C₂³	1	2	yes	—
174	C₂×C₃×D₁₂	C₂³	1	1	yes	characteristic
175	C₂×C₃×C₄×D₃	—	4	4	no	—
176	C₂×C₃×C₄×D₃	C₂³	1	2	yes	—
177	C₂×C₃×C₄×D₃	C₂³	1	2	yes	—
178	C₂×C₃×C₄×D₃	C₂³	1	2	yes	—
179	C₂×C₃×C₄×D₃	C₂³	1	2	yes	—
180	C₂×C₃×C₄×D₃	C₂³	1	2	yes	—
181	C₂×C₃×C₄×D₃	C₂³	1	2	yes	—
182	C₂×C₃×C₄×D₃	C₂³	1	2	yes	—
183	C₂×C₃×Dic₆	C₂³	1	1	yes	characteristic
184	C₂×C₃×Dic₆	C₂³	1	2	yes	—
185	C₂×C₃×Dic₆	C₂³	1	1	yes	characteristic
186	C₂×C₃×Dic₆	C₂³	1	1	yes	characteristic
187	C₃²×C₄⋊C₄	C₂³	1	2	yes	—
188	C₃²×C₄⋊C₄	C₂³	1	2	yes	—
189	C₃²×C₄⋊C₄	C₂³	1	2	yes	—
190	C₃²×C₄⋊C₄	C₂³	1	1	yes	characteristic
191	C₃²×C₄⋊C₄	C₂³	1	1	yes	characteristic
192	C₃²×C₄⋊C₄	C₂³	1	2	yes	—
193	C₃²×C₂²⋊C₄	C₂³	1	2	yes	—
194	C₃²×C₂²⋊C₄	C₂³	1	2	yes	—
195	C₃²×C₂²⋊C₄	C₂³	1	2	yes	—
196	C₃²×C₂²⋊C₄	C₂³	1	2	yes	—
197	C₃²×C₂²⋊C₄	C₂³	1	2	yes	—
198	C₃²×C₄²	C₂³	1	1	yes	characteristic
199	C₃²×C₄²	C₂³	1	1	yes	characteristic
200	C₃²×C₄²	C₂³	1	1	yes	characteristic
201	C₃²×C₄²	C₂³	1	1	yes	characteristic
202	C₃²×C₄²	C₂³	1	2	yes	—
203	C₃×#217	C₂³	1	2	yes	—
204	C₃×#217	C₂³	1	2	yes	—
205	C₃×#217	C₂³	1	2	yes	—
206	C₃×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
207	C₃×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
208	C₃×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
209	C₃×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
210	C₃×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
211	C₃×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
212	C₃×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
213	C₃×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
214	C₃×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
215	C₃×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
216	C₃×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
217	C₃×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
218	C₃×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
219	C₃×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
220	C₃×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
221	C₃×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
222	C₃×C₄⋊Dic₃	C₂³	1	2	yes	—
223	C₃×C₄⋊Dic₃	C₂³	1	2	yes	—
224	C₃×C₄⋊Dic₃	C₂³	1	2	yes	—
225	C₃×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
226	C₃×C₄⋊Dic₃	C₂³	1	2	yes	—
227	C₃×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
228	C₃×Dic₃⋊C₄	C₂³	1	2	yes	—
229	C₃×Dic₃⋊C₄	C₂³	1	2	yes	—
230	C₃×Dic₃⋊C₄	C₂³	1	2	yes	—
231	C₃×Dic₃⋊C₄	C₂³	1	2	yes	—
232	C₃×Dic₃⋊C₄	C₂³	1	2	yes	—
233	C₃×Dic₃⋊C₄	C₂³	1	2	yes	—
234	C₃×Dic₃⋊C₄	C₂³	1	2	yes	—
235	C₃×Dic₃⋊C₄	C₂³	1	2	yes	—
236	C₃×C₄×Dic₃	C₂³	1	2	yes	—
237	C₃×C₄×Dic₃	C₂³	1	2	yes	—
238	C₃×C₄×Dic₃	C₂³	1	2	yes	—
239	#3529	—	3	1	no	Sylow
240	C₂×C₃×#41	—	3	2	no	—
241	C₂×C₃×#41	—	3	1	no	—
242	C₂×C₃×#41	—	3	1	no	—
243	C₂³×C₃×C₄	—	3	2	no	—
244	C₂×#235	C₂²×C₃	1	1	yes	characteristic
245	C₂×#235	C₂²×C₃	1	2	yes	—
246	C₂×#235	C₂²×C₃	1	1	yes	characteristic, complemented
247	C₂²×C₄×D₃	C₂²×C₃	1	2	yes	complemented
248	C₃×C₄⋊Q₈	—	3	2	no	—
249	C₃×C₄⋊Q₈	—	3	1	no	—
250	C₃×#127	—	3	2	no	—
251	C₃×#127	—	3	1	no	—
252	C₃×#126	—	2	2	no	—
253	C₃×#126	—	3	2	no	—
254	C₃×#126	—	3	2	no	—
255	C₃×#126	—	3	2	no	—
256	C₃×#126	—	3	2	no	—
257	C₃×#126	—	3	2	no	—
258	C₃×#126	C₂×D₃	1	2	yes	complemented
259	C₃×#126	C₂²×C₃	1	2	yes	complemented
260	C₃×#125	—	2	1	no	—
261	C₃×#125	—	3	2	no	—
262	C₃×#125	—	3	2	no	—
263	C₃×#125	—	3	1	no	—
264	C₃×#125	C₂×D₃	1	1	yes	characteristic, complemented
265	C₃×#125	C₂²×C₃	1	1	yes	characteristic, complemented
266	C₃×#124	—	2	1	no	—
267	C₃×#124	—	3	2	no	—
268	C₃×#124	—	3	2	no	—
269	C₃×#124	—	3	2	no	—
270	C₃×#124	—	3	2	no	—
271	C₃×#124	—	3	1	no	—
272	C₃×#124	—	3	1	no	—
273	C₃×#124	—	3	1	no	—
274	C₃×#124	C₂×D₃	1	1	yes	characteristic
275	C₃×#124	C₂²×C₃	1	1	yes	characteristic
276	C₃×#123	—	2	2	no	—
277	C₃×#123	—	3	2	no	—
278	C₃×#123	—	3	2	no	—
279	C₃×#123	—	3	2	no	—
280	C₃×#123	—	3	2	no	—
281	C₃×#123	—	3	2	no	—
282	C₃×#123	—	3	2	no	—
283	C₃×#123	—	3	2	no	—
284	C₃×#123	—	3	2	no	—
285	C₃×#123	—	3	2	no	—
286	C₃×#123	—	3	2	no	—
287	C₃×#123	—	3	2	no	—
288	C₃×#123	C₂×D₃	1	2	yes	complemented
289	C₃×#123	C₂²×C₃	1	2	yes	complemented
290	C₃×C₂²⋊Q₈	—	2	1	no	—
291	C₃×C₂²⋊Q₈	—	3	2	no	—
292	C₃×C₂²⋊Q₈	—	3	1	no	—
293	C₃×C₂²⋊Q₈	—	3	2	no	—
294	C₃×C₂²⋊Q₈	—	3	2	no	—
295	C₃×C₂²⋊Q₈	—	3	2	no	—
296	C₃×C₂²⋊Q₈	—	3	2	no	—
297	C₃×C₂²⋊Q₈	—	3	2	no	—
298	C₃×C₂²⋊Q₈	—	3	2	no	—
299	C₃×C₂²⋊Q₈	—	3	2	no	—
300	C₃×C₂²⋊Q₈	C₂×D₃	1	1	yes	characteristic, complemented
301	C₃×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
302	C₃×#121	—	2	1	no	—
303	C₃×#121	—	3	2	no	—
304	C₃×#121	—	3	2	no	—
305	C₃×#121	—	3	2	no	—
306	C₃×#121	—	3	1	no	—
307	C₃×#121	—	3	2	no	—
308	C₃×#121	—	3	2	no	—
309	C₃×#121	—	3	2	no	—
310	C₃×#121	—	3	2	no	—
311	C₃×#121	—	3	2	no	—
312	C₃×#121	—	3	2	no	—
313	C₃×#121	—	3	2	no	—
314	C₃×#121	—	3	2	no	—
315	C₃×#121	—	3	2	no	—
316	C₃×#121	—	3	2	no	—
317	C₃×#121	—	3	2	no	—
318	C₃×#121	C₂×D₃	1	1	yes	characteristic
319	C₃×#121	C₂²×C₃	1	1	yes	characteristic
320	C₃×#120	—	3	2	no	—
321	C₃×#120	—	3	2	no	—
322	C₃×#120	—	3	2	no	—
323	C₃×#120	—	3	2	no	—
324	C₃×#120	—	3	2	no	—
325	C₃×#120	—	3	2	no	—
326	C₃×C₄×Q₈	—	2	1	no	—
327	C₃×C₄×Q₈	—	3	1	no	—
328	C₃×C₄×Q₈	C₂×D₃	1	1	yes	characteristic, complemented
329	C₃×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
330	C₃×C₄×D₄	—	2	1	no	—
331	C₃×C₄×D₄	—	2	2	no	—
332	C₃×C₄×D₄	—	3	2	no	—
333	C₃×C₄×D₄	—	3	2	no	—
334	C₃×C₄×D₄	—	3	2	no	—
335	C₃×C₄×D₄	—	3	2	no	—
336	C₃×C₄×D₄	—	3	1	no	—
337	C₃×C₄×D₄	—	3	2	no	—
338	C₃×C₄×D₄	—	3	2	no	—
339	C₃×C₄×D₄	—	3	2	no	—
340	C₃×C₄×D₄	C₂×D₃	1	1	yes	characteristic
341	C₃×C₄×D₄	C₂×D₃	1	2	yes	complemented
342	C₃×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
343	C₃×C₄×D₄	C₂²×C₃	1	2	yes	complemented
344	C₃×#117	—	2	2	no	—
345	C₃×#117	—	3	2	no	—
346	C₃×#117	—	3	2	no	—
347	C₃×#117	C₂×D₃	1	2	yes	complemented
348	C₃×#117	C₂²×C₃	1	2	yes	complemented
349	C₂×C₃×C₄²	—	2	1	no	—
350	C₂×C₃×C₄²	—	3	2	no	—
351	C₂×C₃×C₄²	C₂×D₃	1	1	yes	characteristic, complemented
352	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic, complemented
353	#947	C₂²×C₃	1	2	yes	—
354	#946	C₂²×C₃	1	2	yes	complemented
355	#940	C₂²×C₃	1	2	yes	—
356	#939	C₂²×C₃	1	2	yes	—
357	#939	C₂²×C₃	1	2	yes	—
358	#938	C₂²×C₃	1	2	yes	complemented
359	#937	C₂²×C₃	1	2	yes	—
360	#937	C₂²×C₃	1	2	yes	complemented
361	#930	C₂²×C₃	1	1	yes	characteristic
362	#930	C₂²×C₃	1	2	yes	complemented
363	#930	C₂²×C₃	1	2	yes	complemented
364	#929	C₂²×C₃	1	2	yes	complemented
365	C₄×#67	C₂²×C₃	1	2	yes	—
366	C₄×#67	C₂²×C₃	1	2	yes	complemented
367	C₄×#67	C₂²×C₃	1	2	yes	complemented
368	#924	C₂²×C₃	1	1	yes	characteristic, complemented
369	#898	C₂²×C₃	1	2	yes	complemented
370	#898	C₂²×C₃	1	2	yes	complemented
371	#898	C₂²×C₃	1	2	yes	complemented
372	#897	C₂²×C₃	1	2	yes	complemented
373	#897	C₂²×C₃	1	2	yes	complemented
374	#896	C₂²×C₃	1	2	yes	complemented
375	#896	C₂²×C₃	1	2	yes	complemented
376	#896	C₂²×C₃	1	2	yes	complemented
377	#895	C₂²×C₃	1	2	yes	—
378	#895	C₂²×C₃	1	2	yes	—
379	#895	C₂²×C₃	1	2	yes	—
380	#895	C₂²×C₃	1	2	yes	complemented
381	#894	C₂²×C₃	1	2	yes	—
382	#894	C₂²×C₃	1	2	yes	complemented
383	#894	C₂²×C₃	1	2	yes	complemented
384	#894	C₂²×C₃	1	2	yes	complemented
385	#894	C₂²×C₃	1	2	yes	complemented
386	#890	C₂²×C₃	1	2	yes	complemented
387	#889	C₂²×C₃	1	2	yes	complemented
388	#888	C₂²×C₃	1	2	yes	complemented
389	#886	C₂²×C₃	1	2	yes	—
390	#886	C₂²×C₃	1	2	yes	complemented
391	#885	C₂²×C₃	1	2	yes	—
392	#885	C₂²×C₃	1	2	yes	—
393	#885	C₂²×C₃	1	2	yes	complemented
394	#884	C₂²×C₃	1	2	yes	—
395	#884	C₂²×C₃	1	2	yes	—
396	#884	C₂²×C₃	1	2	yes	—
397	#884	C₂²×C₃	1	2	yes	complemented
398	#884	C₂²×C₃	1	2	yes	complemented
399	#883	C₂²×C₃	1	2	yes	—
400	#883	C₂²×C₃	1	2	yes	complemented
401	#883	C₂²×C₃	1	2	yes	complemented
402	#882	C₂²×C₃	1	2	yes	—
403	#882	C₂²×C₃	1	2	yes	—
404	#882	C₂²×C₃	1	2	yes	complemented
405	#882	C₂²×C₃	1	2	yes	complemented
406	#879	C₂²×C₃	1	2	yes	complemented
407	#878	C₂²×C₃	1	2	yes	complemented
408	#878	C₂²×C₃	1	2	yes	complemented
409	#876	C₂²×C₃	1	2	yes	complemented
410	#875	C₂²×C₃	1	1	yes	characteristic
411	#875	C₂²×C₃	1	1	yes	characteristic
412	#875	C₂²×C₃	1	1	yes	characteristic, complemented
413	#874	C₂²×C₃	1	1	yes	characteristic
414	C₄×D₁₂	C₂²×C₃	1	1	yes	characteristic
415	C₄×D₁₂	C₂²×C₃	1	2	yes	—
416	C₄×D₁₂	C₂²×C₃	1	2	yes	complemented
417	C₄×D₁₂	C₂²×C₃	1	2	yes	complemented
418	C₄×D₁₂	C₂²×C₃	1	2	yes	complemented
419	#872	C₂²×C₃	1	2	yes	complemented
420	#872	C₂²×C₃	1	2	yes	complemented
421	C₄²×D₃	C₂²×C₃	1	2	yes	complemented
422	#870	C₂²×C₃	1	1	yes	characteristic, complemented
423	#869	C₂²×C₃	1	1	yes	characteristic, complemented
424	C₄×Dic₆	C₂²×C₃	1	1	yes	characteristic, complemented
425	C₂³×C₃²	C₂⁴	1	2	yes	—
426	C₂³×C₃²	C₂⁴	1	1	yes	characteristic
427	C₂²×C₃×D₃	—	4	2	no	—
428	C₂²×C₃×D₃	—	4	2	no	—
429	C₂²×C₃×D₃	—	4	2	no	—
430	C₂²×C₃×D₃	C₂⁴	1	2	yes	—
431	C₂²×C₃×D₃	C₂⁴	1	2	yes	—
432	C₂²×C₃×D₃	C₂⁴	1	2	yes	—
433	C₃²×Q₈	—	4	1	no	—
434	C₃²×D₄	—	4	1	no	—
435	C₃²×D₄	—	4	2	no	—
436	C₂×C₃²×C₄	—	2	4	no	—
437	C₂×C₃²×C₄	—	2	2	no	—
438	C₂×C₃²×C₄	—	4	1	no	—
439	C₂×C₃²×C₄	—	4	1	no	—
440	C₂×C₃²×C₄	C₂⁴	1	2	yes	—
441	C₂×C₃²×C₄	C₂⁴	1	2	yes	—
442	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
443	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
444	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
445	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
446	C₂×C₃²×C₄	C₂⁴	1	2	yes	—
447	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
448	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
449	C₃×#67	—	4	2	no	—
450	C₃×#67	—	4	2	no	—
451	C₃×#67	—	4	2	no	—
452	C₃×#67	—	4	2	no	—
453	C₃×#67	—	4	2	no	—
454	C₃×#67	—	4	2	no	—
455	C₃×#67	—	4	2	no	—
456	C₂×C₃×Dic₃	—	4	2	no	—
457	C₂×C₃×Dic₃	C₂⁴	1	2	yes	—
458	C₂×C₃×Dic₃	C₂⁴	1	2	yes	—
459	C₂×C₃×Dic₃	C₂⁴	1	2	yes	—
460	C₂×C₃×Dic₃	C₂⁴	1	2	yes	—
461	C₂×C₃×Dic₃	C₂⁴	1	2	yes	—
462	C₃×D₁₂	—	4	1	no	—
463	C₃×D₁₂	—	4	2	no	—
464	C₃×D₁₂	—	4	2	no	—
465	C₃×D₁₂	—	4	2	no	—
466	C₃×D₁₂	—	4	2	no	—
467	C₃×D₁₂	—	4	1	no	—
468	C₃×D₁₂	—	4	1	no	—
469	C₃×D₁₂	—	4	2	no	—
470	C₃×C₄×D₃	—	2	4	no	—
471	C₃×C₄×D₃	—	2	4	no	—
472	C₃×C₄×D₃	—	2	4	no	—
473	C₃×C₄×D₃	—	4	2	no	—
474	C₃×C₄×D₃	—	4	2	no	—
475	C₃×C₄×D₃	—	4	2	no	—
476	C₃×C₄×D₃	—	4	2	no	—
477	C₃×Dic₆	—	4	1	no	—
478	C₃×Dic₆	—	4	1	no	—
479	C₃×Dic₆	—	4	2	no	—
480	C₃×Dic₆	—	4	1	no	—
481	#563	—	3	2	no	—
482	#563	—	3	1	no	—
483	#562	—	3	1	no	—
484	#562	—	3	1	no	—
485	#562	—	3	2	no	—
486	#562	—	3	2	no	—
487	H(3,𝔽₄)	—	3	1	no	—
488	#560	—	3	2	no	—
489	#560	—	3	2	no	—
490	#560	—	3	2	no	—
491	#532	—	3	2	no	—
492	#532	—	3	1	no	—
493	#529	—	3	2	no	—
494	#529	—	3	2	no	—
495	#529	—	3	1	no	—
496	#529	C₃×D₃	1	1	yes	characteristic, complemented
497	#525	—	3	2	no	—
498	#525	—	3	2	no	—
499	#525	—	3	2	no	—
500	C₂⁴×C₃	—	3	2	no	—
501	C₂³×D₃	C₂³×C₃	1	2	yes	—
502	C₃×#41	—	12	4	no	—
503	C₃×#41	—	12	2	no	—
504	C₃×#41	—	12	2	no	—
505	C₂×C₃×Q₈	—	2	1	no	—
506	C₂×C₃×Q₈	—	3	1	no	—
507	C₂×C₃×Q₈	—	3	2	no	—
508	C₂×C₃×Q₈	—	3	1	no	—
509	C₂×C₃×Q₈	—	3	1	no	—
510	C₂×C₃×Q₈	C₂²×D₃	1	1	yes	characteristic
511	C₂×C₃×Q₈	C₂³×C₃	1	1	yes	characteristic
512	C₂×C₃×D₄	—	2	2	no	—
513	C₂×C₃×D₄	—	2	1	no	—
514	C₂×C₃×D₄	—	3	2	no	—
515	C₂×C₃×D₄	—	3	2	no	—
516	C₂×C₃×D₄	—	3	2	no	—
517	C₂×C₃×D₄	—	3	2	no	—
518	C₂×C₃×D₄	—	3	2	no	—
519	C₂×C₃×D₄	—	3	2	no	—
520	C₂×C₃×D₄	—	3	2	no	—
521	C₂×C₃×D₄	—	3	2	no	—
522	C₂×C₃×D₄	—	3	1	no	—
523	C₂×C₃×D₄	—	3	2	no	—
524	C₂×C₃×D₄	—	3	2	no	—
525	C₂×C₃×D₄	—	3	2	no	—
526	C₂×C₃×D₄	—	3	1	no	—
527	C₂×C₃×D₄	—	3	2	no	—
528	C₂×C₃×D₄	—	3	1	no	—
529	C₂×C₃×D₄	C₂²×D₃	1	1	yes	characteristic
530	C₂×C₃×D₄	C₂²×D₃	1	2	yes	—
531	C₂×C₃×D₄	C₂³×C₃	1	1	yes	characteristic
532	C₂×C₃×D₄	C₂³×C₃	1	2	yes	—
533	C₂²×C₃×C₄	—	2	1	no	—
534	C₂²×C₃×C₄	—	2	1	no	—
535	C₂²×C₃×C₄	—	2	1	no	—
536	C₂²×C₃×C₄	—	2	2	no	—
537	C₂²×C₃×C₄	—	3	2	no	—
538	C₂²×C₃×C₄	—	3	2	no	—
539	C₂²×C₃×C₄	—	3	2	no	—
540	C₂²×C₃×C₄	—	3	2	no	—
541	C₂²×C₃×C₄	—	3	2	no	—
542	C₂²×C₃×C₄	—	3	2	no	—
543	C₂²×C₃×C₄	—	3	2	no	—
544	C₂²×C₃×C₄	—	3	2	no	—
545	C₂²×C₃×C₄	—	12	4	no	—
546	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
547	C₂²×C₃×C₄	C₂²×D₃	1	2	yes	—
548	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
549	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
550	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
551	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
552	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
553	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
554	C₂×#67	C₂³×C₃	1	2	yes	—
555	C₂×#67	C₂³×C₃	1	2	yes	—
556	C₂×#67	C₂³×C₃	1	2	yes	—
557	C₂×#67	C₂³×C₃	1	2	yes	—
558	C₂×#67	C₂³×C₃	1	2	yes	—
559	C₂×#67	C₂³×C₃	1	2	yes	—
560	C₂×#67	C₂³×C₃	1	2	yes	—
561	C₂²×Dic₃	C₂³×C₃	1	2	yes	—
562	#235	—	4	2	no	—
563	#235	—	4	4	no	—
564	#235	—	4	2	no	—
565	C₂×D₁₂	C₂³×C₃	1	1	yes	characteristic
566	C₂×D₁₂	C₂³×C₃	1	2	yes	—
567	C₂×D₁₂	C₂³×C₃	1	2	yes	—
568	C₂×D₁₂	C₂³×C₃	1	2	yes	—
569	C₂×D₁₂	C₂³×C₃	1	2	yes	—
570	C₂×D₁₂	C₂³×C₃	1	1	yes	characteristic
571	C₂×D₁₂	C₂³×C₃	1	1	yes	characteristic
572	C₂×D₁₂	C₂³×C₃	1	2	yes	—
573	C₂×C₄×D₃	—	4	4	no	—
574	C₂×C₄×D₃	C₂³×C₃	1	2	yes	—
575	C₂×C₄×D₃	C₂³×C₃	1	2	yes	—
576	C₂×C₄×D₃	C₂³×C₃	1	2	yes	—
577	C₂×C₄×D₃	C₂³×C₃	1	2	yes	—
578	C₂×C₄×D₃	C₂³×C₃	1	2	yes	—
579	C₂×C₄×D₃	C₂³×C₃	1	2	yes	—
580	C₂×C₄×D₃	C₂³×C₃	1	2	yes	—
581	C₂×Dic₆	C₂³×C₃	1	1	yes	characteristic
582	C₂×Dic₆	C₂³×C₃	1	1	yes	characteristic
583	C₂×Dic₆	C₂³×C₃	1	1	yes	characteristic
584	C₂×Dic₆	C₂³×C₃	1	2	yes	—
585	C₃×C₄⋊C₄	—	2	2	no	—
586	C₃×C₄⋊C₄	—	2	2	no	—
587	C₃×C₄⋊C₄	—	2	1	no	—
588	C₃×C₄⋊C₄	—	2	2	no	—
589	C₃×C₄⋊C₄	—	2	1	no	—
590	C₃×C₄⋊C₄	—	2	2	no	—
591	C₃×C₄⋊C₄	—	3	2	no	—
592	C₃×C₄⋊C₄	—	3	2	no	—
593	C₃×C₄⋊C₄	—	3	2	no	—
594	C₃×C₄⋊C₄	—	3	2	no	—
595	C₃×C₄⋊C₄	—	3	2	no	—
596	C₃×C₄⋊C₄	—	3	2	no	—
597	C₃×C₄⋊C₄	—	3	2	no	—
598	C₃×C₄⋊C₄	—	3	2	no	—
599	C₃×C₄⋊C₄	—	3	2	no	—
600	C₃×C₄⋊C₄	—	3	2	no	—
601	C₃×C₄⋊C₄	—	3	2	no	—
602	C₃×C₄⋊C₄	—	3	2	no	—
603	C₃×C₄⋊C₄	—	3	1	no	—
604	C₃×C₄⋊C₄	—	3	1	no	—
605	C₃×C₄⋊C₄	C₂²×D₃	1	2	yes	—
606	C₃×C₄⋊C₄	C₂²×D₃	1	2	yes	—
607	C₃×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
608	C₃×C₄⋊C₄	C₂²×D₃	1	2	yes	—
609	C₃×C₄⋊C₄	C₂²×D₃	1	2	yes	—
610	C₃×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
611	C₃×C₄⋊C₄	C₂³×C₃	1	2	yes	—
612	C₃×C₄⋊C₄	C₂³×C₃	1	2	yes	—
613	C₃×C₄⋊C₄	C₂³×C₃	1	2	yes	—
614	C₃×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
615	C₃×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
616	C₃×C₄⋊C₄	C₂³×C₃	1	2	yes	—
617	C₃×C₂²⋊C₄	—	2	2	no	—
618	C₃×C₂²⋊C₄	—	2	2	no	—
619	C₃×C₂²⋊C₄	—	2	2	no	—
620	C₃×C₂²⋊C₄	—	2	2	no	—
621	C₃×C₂²⋊C₄	—	2	2	no	—
622	C₃×C₂²⋊C₄	—	3	2	no	—
623	C₃×C₂²⋊C₄	—	3	2	no	—
624	C₃×C₂²⋊C₄	—	3	2	no	—
625	C₃×C₂²⋊C₄	—	3	2	no	—
626	C₃×C₂²⋊C₄	—	3	2	no	—
627	C₃×C₂²⋊C₄	—	3	2	no	—
628	C₃×C₂²⋊C₄	—	3	2	no	—
629	C₃×C₂²⋊C₄	—	3	2	no	—
630	C₃×C₂²⋊C₄	—	3	2	no	—
631	C₃×C₂²⋊C₄	—	3	2	no	—
632	C₃×C₂²⋊C₄	—	3	2	no	—
633	C₃×C₂²⋊C₄	—	3	2	no	—
634	C₃×C₂²⋊C₄	—	3	2	no	—
635	C₃×C₂²⋊C₄	—	3	2	no	—
636	C₃×C₂²⋊C₄	—	3	2	no	—
637	C₃×C₂²⋊C₄	—	3	2	no	—
638	C₃×C₂²⋊C₄	—	3	2	no	—
639	C₃×C₂²⋊C₄	—	3	2	no	—
640	C₃×C₂²⋊C₄	—	3	2	no	—
641	C₃×C₂²⋊C₄	C₂²×D₃	1	2	yes	—
642	C₃×C₂²⋊C₄	C₂²×D₃	1	2	yes	—
643	C₃×C₂²⋊C₄	C₂²×D₃	1	2	yes	—
644	C₃×C₂²⋊C₄	C₂²×D₃	1	2	yes	—
645	C₃×C₂²⋊C₄	C₂²×D₃	1	2	yes	—
646	C₃×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
647	C₃×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
648	C₃×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
649	C₃×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
650	C₃×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
651	C₃×C₄²	—	2	1	no	—
652	C₃×C₄²	—	2	1	no	—
653	C₃×C₄²	—	2	1	no	—
654	C₃×C₄²	—	2	1	no	—
655	C₃×C₄²	—	2	2	no	—
656	C₃×C₄²	—	3	2	no	—
657	C₃×C₄²	—	3	2	no	—
658	C₃×C₄²	—	3	2	no	—
659	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
660	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
661	C₃×C₄²	C₂²×D₃	1	2	yes	—
662	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
663	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
664	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
665	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
666	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
667	C₃×C₄²	C₂³×C₃	1	2	yes	—
668	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
669	#217	C₂³×C₃	1	2	yes	—
670	#217	C₂³×C₃	1	2	yes	—
671	#217	C₂³×C₃	1	2	yes	—
672	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
673	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
674	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
675	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
676	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
677	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
678	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
679	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
680	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
681	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
682	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
683	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
684	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
685	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
686	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
687	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
688	C₄⋊Dic₃	C₂³×C₃	1	1	yes	characteristic
689	C₄⋊Dic₃	C₂³×C₃	1	2	yes	—
690	C₄⋊Dic₃	C₂³×C₃	1	2	yes	—
691	C₄⋊Dic₃	C₂³×C₃	1	1	yes	characteristic
692	C₄⋊Dic₃	C₂³×C₃	1	2	yes	—
693	C₄⋊Dic₃	C₂³×C₃	1	2	yes	—
694	Dic₃⋊C₄	C₂³×C₃	1	2	yes	—
695	Dic₃⋊C₄	C₂³×C₃	1	2	yes	—
696	Dic₃⋊C₄	C₂³×C₃	1	2	yes	—
697	Dic₃⋊C₄	C₂³×C₃	1	2	yes	—
698	Dic₃⋊C₄	C₂³×C₃	1	2	yes	—
699	Dic₃⋊C₄	C₂³×C₃	1	2	yes	—
700	Dic₃⋊C₄	C₂³×C₃	1	2	yes	—
701	Dic₃⋊C₄	C₂³×C₃	1	2	yes	—
702	C₄×Dic₃	C₂³×C₃	1	2	yes	—
703	C₄×Dic₃	C₂³×C₃	1	2	yes	—
704	C₄×Dic₃	C₂³×C₃	1	2	yes	—
705	C₂²×C₃²	—	2	1	no	—
706	C₂²×C₃²	—	2	2	no	—
707	C₂²×C₃²	—	2	1	no	—
708	C₂²×C₃²	—	2	1	no	—
709	C₂²×C₃²	—	2	2	no	—
710	C₂²×C₃²	—	2	2	no	—
711	C₂²×C₃²	C₂⁵	1	1	yes	characteristic
712	C₂×C₃×D₃	—	2	2	no	—
713	C₂×C₃×D₃	—	2	2	no	—
714	C₂×C₃×D₃	—	2	2	no	—
715	C₂×C₃×D₃	—	2	2	no	—
716	C₂×C₃×D₃	—	2	2	no	—
717	C₂×C₃×D₃	—	2	2	no	—
718	C₂×C₃×D₃	—	2	2	no	—
719	C₂×C₃×D₃	—	2	2	no	—
720	C₂×C₃×D₃	—	2	2	no	—
721	C₂×C₃×D₃	—	4	8	no	—
722	C₃²×C₄	—	2	1	no	—
723	C₃²×C₄	—	2	1	no	—
724	C₃²×C₄	—	2	2	no	—
725	C₃²×C₄	—	2	1	no	—
726	C₃²×C₄	—	2	2	no	—
727	C₃²×C₄	—	2	2	no	—
728	C₃²×C₄	—	2	1	no	—
729	C₃²×C₄	—	2	1	no	—
730	C₃²×C₄	H(5,𝔽₂)	1	2	yes	—
731	C₃×Dic₃	—	2	2	no	—
732	C₃×Dic₃	—	2	2	no	—
733	C₃×Dic₃	—	2	2	no	—
734	C₃×Dic₃	—	2	2	no	—
735	C₃×Dic₃	—	2	2	no	—
736	C₂×#41	—	3	2	no	—
737	C₂×#41	—	3	1	no	—
738	C₂×#41	—	3	1	no	—
739	C₂³×C₄	—	3	2	no	—
740	C₄⋊Q₈	—	3	2	no	—
741	C₄⋊Q₈	—	3	1	no	—
742	#127	—	3	2	no	—
743	#127	—	3	1	no	—
744	#126	—	3	2	no	—
745	#126	—	3	2	no	—
746	#126	—	3	2	no	—
747	#126	—	3	2	no	—
748	#126	—	3	2	no	—
749	#126	C₂×C₃×D₃	1	2	yes	complemented
750	#125	—	3	2	no	—
751	#125	—	3	2	no	—
752	#125	—	3	1	no	—
753	#125	C₂×C₃×D₃	1	1	yes	characteristic, complemented
754	#124	—	3	2	no	—
755	#124	—	3	2	no	—
756	#124	—	3	2	no	—
757	#124	—	3	2	no	—
758	#124	—	3	1	no	—
759	#124	—	3	1	no	—
760	#124	—	3	1	no	—
761	#124	C₂×C₃×D₃	1	1	yes	characteristic
762	#123	—	3	2	no	—
763	#123	—	3	2	no	—
764	#123	—	3	2	no	—
765	#123	—	3	2	no	—
766	#123	—	3	2	no	—
767	#123	—	3	2	no	—
768	#123	—	3	2	no	—
769	#123	—	3	2	no	—
770	#123	—	3	2	no	—
771	#123	—	3	2	no	—
772	#123	—	3	2	no	—
773	#123	C₂×C₃×D₃	1	2	yes	complemented
774	C₂²⋊Q₈	—	3	2	no	—
775	C₂²⋊Q₈	—	3	1	no	—
776	C₂²⋊Q₈	—	3	2	no	—
777	C₂²⋊Q₈	—	3	2	no	—
778	C₂²⋊Q₈	—	3	2	no	—
779	C₂²⋊Q₈	—	3	2	no	—
780	C₂²⋊Q₈	—	3	2	no	—
781	C₂²⋊Q₈	—	3	2	no	—
782	C₂²⋊Q₈	—	3	2	no	—
783	C₂²⋊Q₈	C₂×C₃×D₃	1	1	yes	characteristic, complemented
784	#121	—	3	2	no	—
785	#121	—	3	2	no	—
786	#121	—	3	2	no	—
787	#121	—	3	1	no	—
788	#121	—	3	2	no	—
789	#121	—	3	2	no	—
790	#121	—	3	2	no	—
791	#121	—	3	2	no	—
792	#121	—	3	2	no	—
793	#121	—	3	2	no	—
794	#121	—	3	2	no	—
795	#121	—	3	2	no	—
796	#121	—	3	2	no	—
797	#121	—	3	2	no	—
798	#121	—	3	2	no	—
799	#121	C₂×C₃×D₃	1	1	yes	characteristic
800	#120	—	3	2	no	—
801	#120	—	3	2	no	—
802	#120	—	3	2	no	—
803	#120	—	3	2	no	—
804	#120	—	3	2	no	—
805	#120	—	3	2	no	—
806	C₄×Q₈	—	3	1	no	—
807	C₄×Q₈	C₂×C₃×D₃	1	1	yes	characteristic, complemented
808	C₄×D₄	—	3	2	no	—
809	C₄×D₄	—	3	2	no	—
810	C₄×D₄	—	3	2	no	—
811	C₄×D₄	—	3	2	no	—
812	C₄×D₄	—	3	1	no	—
813	C₄×D₄	—	3	2	no	—
814	C₄×D₄	—	3	2	no	—
815	C₄×D₄	—	3	2	no	—
816	C₄×D₄	C₂×C₃×D₃	1	1	yes	characteristic
817	C₄×D₄	C₂×C₃×D₃	1	2	yes	complemented
818	#117	—	3	2	no	—
819	#117	—	3	2	no	—
820	#117	C₂×C₃×D₃	1	2	yes	complemented
821	C₂×C₄²	—	3	2	no	—
822	C₂×C₄²	C₂×C₃×D₃	1	1	yes	characteristic, complemented
823	C₂³×C₃	—	2	1	no	—
824	C₂³×C₃	—	2	2	no	—
825	C₂³×C₃	—	3	2	no	—
826	C₂³×C₃	—	3	2	no	—
827	C₂³×C₃	—	3	2	no	—
828	C₂³×C₃	—	12	2	no	—
829	C₂³×C₃	—	12	2	no	—
830	C₂³×C₃	—	12	2	no	—
831	C₂³×C₃	C₂³×D₃	1	2	yes	—
832	C₂³×C₃	C₂³×D₃	1	1	yes	characteristic
833	C₂³×C₃	C₂⁴×C₃	1	2	yes	—
834	C₂³×C₃	C₂⁴×C₃	1	1	yes	characteristic
835	C₂²×D₃	—	4	2	no	—
836	C₂²×D₃	—	4	2	no	—
837	C₂²×D₃	—	4	2	no	—
838	C₂²×D₃	C₂⁴×C₃	1	2	yes	—
839	C₂²×D₃	C₂⁴×C₃	1	2	yes	—
840	C₂²×D₃	C₂⁴×C₃	1	2	yes	—
841	C₃×Q₈	—	4	1	no	—
842	C₃×Q₈	—	4	1	no	—
843	C₃×Q₈	—	4	2	no	—
844	C₃×Q₈	—	12	1	no	—
845	C₃×Q₈	—	12	2	no	—
846	C₃×Q₈	—	12	1	no	—
847	C₃×Q₈	—	12	1	no	—
848	C₃×D₄	—	4	1	no	—
849	C₃×D₄	—	4	2	no	—
850	C₃×D₄	—	4	2	no	—
851	C₃×D₄	—	4	1	no	—
852	C₃×D₄	—	4	2	no	—
853	C₃×D₄	—	4	4	no	—
854	C₃×D₄	—	12	2	no	—
855	C₃×D₄	—	12	2	no	—
856	C₃×D₄	—	12	1	no	—
857	C₃×D₄	—	12	2	no	—
858	C₃×D₄	—	12	2	no	—
859	C₃×D₄	—	12	2	no	—
860	C₃×D₄	—	12	1	no	—
861	C₃×D₄	—	12	1	no	—
862	C₃×D₄	—	12	2	no	—
863	C₃×D₄	—	12	2	no	—
864	C₃×D₄	—	12	2	no	—
865	C₃×D₄	—	12	2	no	—
866	C₃×D₄	—	12	2	no	—
867	C₃×D₄	—	12	2	no	—
868	C₃×D₄	—	12	2	no	—
869	C₂×C₃×C₄	—	2	4	no	—
870	C₂×C₃×C₄	—	2	2	no	—
871	C₂×C₃×C₄	—	2	4	no	—
872	C₂×C₃×C₄	—	2	2	no	—
873	C₂×C₃×C₄	—	2	1	no	—
874	C₂×C₃×C₄	—	2	1	no	—
875	C₂×C₃×C₄	—	2	1	no	—
876	C₂×C₃×C₄	—	2	1	no	—
877	C₂×C₃×C₄	—	2	1	no	—
878	C₂×C₃×C₄	—	2	1	no	—
879	C₂×C₃×C₄	—	2	2	no	—
880	C₂×C₃×C₄	—	2	2	no	—
881	C₂×C₃×C₄	—	2	2	no	—
882	C₂×C₃×C₄	—	3	2	no	—
883	C₂×C₃×C₄	—	3	2	no	—
884	C₂×C₃×C₄	—	3	2	no	—
885	C₂×C₃×C₄	—	3	2	no	—
886	C₂×C₃×C₄	—	3	2	no	—
887	C₂×C₃×C₄	—	4	4	no	—
888	C₂×C₃×C₄	—	4	2	no	—
889	C₂×C₃×C₄	—	4	1	no	—
890	C₂×C₃×C₄	—	4	1	no	—
891	C₂×C₃×C₄	—	4	1	no	—
892	C₂×C₃×C₄	—	4	1	no	—
893	C₂×C₃×C₄	—	4	2	no	—
894	C₂×C₃×C₄	—	4	2	no	—
895	C₂×C₃×C₄	—	6	4	no	—
896	C₂×C₃×C₄	—	6	4	no	—
897	C₂×C₃×C₄	—	6	4	no	—
898	C₂×C₃×C₄	—	12	2	no	—
899	C₂×C₃×C₄	—	12	2	no	—
900	C₂×C₃×C₄	—	12	2	no	—
901	C₂×C₃×C₄	—	12	2	no	—
902	C₂×C₃×C₄	—	12	2	no	—
903	C₂×C₃×C₄	C₂³×D₃	1	2	yes	—
904	C₂×C₃×C₄	C₂³×D₃	1	2	yes	—
905	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
906	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
907	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
908	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
909	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
910	C₂×C₃×C₄	C₂³×D₃	1	2	yes	—
911	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
912	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
913	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
914	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
915	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
916	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
917	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
918	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
919	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
920	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
921	#67	—	4	2	no	—
922	#67	—	4	2	no	—
923	#67	—	4	2	no	—
924	#67	—	4	2	no	—
925	#67	—	4	2	no	—
926	#67	—	4	2	no	—
927	#67	—	4	2	no	—
928	C₂×Dic₃	—	4	2	no	—
929	C₂×Dic₃	C₂⁴×C₃	1	2	yes	—
930	C₂×Dic₃	C₂⁴×C₃	1	2	yes	—
931	C₂×Dic₃	C₂⁴×C₃	1	2	yes	—
932	C₂×Dic₃	C₂⁴×C₃	1	2	yes	—
933	C₂×Dic₃	C₂⁴×C₃	1	2	yes	—
934	D₁₂	—	4	1	no	—
935	D₁₂	—	4	2	no	—
936	D₁₂	—	4	2	no	—
937	D₁₂	—	4	2	no	—
938	D₁₂	—	4	2	no	—
939	D₁₂	—	4	1	no	—
940	D₁₂	—	4	1	no	—
941	D₁₂	—	4	2	no	—
942	C₄×D₃	—	2	4	no	—
943	C₄×D₃	—	2	4	no	—
944	C₄×D₃	—	2	4	no	—
945	C₄×D₃	—	4	2	no	—
946	C₄×D₃	—	4	2	no	—
947	C₄×D₃	—	4	2	no	—
948	C₄×D₃	—	4	2	no	—
949	Dic₆	—	4	1	no	—
950	Dic₆	—	4	1	no	—
951	Dic₆	—	4	2	no	—
952	Dic₆	—	4	1	no	—
953	C₂×C₃²	—	4	1	no	—
954	C₂×C₃²	—	4	2	no	—
955	C₂×C₃²	C₂×H(5,𝔽₂)	1	1	yes	characteristic
956	C₂×C₃²	#585	1	1	yes	characteristic
957	C₂×C₃²	#585	1	1	yes	characteristic
958	C₃×D₃	—	4	2	no	—
959	C₃×D₃	—	4	2	no	—
960	C₃×D₃	—	4	2	no	—
961	C₂⁴	—	3	2	no	—
962	#41	—	12	4	no	—
963	#41	—	12	2	no	—
964	#41	—	12	2	no	—
965	C₂×Q₈	—	3	1	no	—
966	C₂×Q₈	—	3	2	no	—
967	C₂×Q₈	—	3	1	no	—
968	C₂×Q₈	—	3	1	no	—
969	C₂×Q₈	C₂²×C₃×D₃	1	1	yes	characteristic
970	C₂×D₄	—	3	2	no	—
971	C₂×D₄	—	3	2	no	—
972	C₂×D₄	—	3	2	no	—
973	C₂×D₄	—	3	2	no	—
974	C₂×D₄	—	3	2	no	—
975	C₂×D₄	—	3	2	no	—
976	C₂×D₄	—	3	2	no	—
977	C₂×D₄	—	3	2	no	—
978	C₂×D₄	—	3	1	no	—
979	C₂×D₄	—	3	2	no	—
980	C₂×D₄	—	3	2	no	—
981	C₂×D₄	—	3	2	no	—
982	C₂×D₄	—	3	1	no	—
983	C₂×D₄	—	3	2	no	—
984	C₂×D₄	—	3	1	no	—
985	C₂×D₄	C₂²×C₃×D₃	1	1	yes	characteristic
986	C₂×D₄	C₂²×C₃×D₃	1	2	yes	—
987	C₂²×C₄	—	3	2	no	—
988	C₂²×C₄	—	3	2	no	—
989	C₂²×C₄	—	3	2	no	—
990	C₂²×C₄	—	3	2	no	—
991	C₂²×C₄	—	3	2	no	—
992	C₂²×C₄	—	3	2	no	—
993	C₂²×C₄	—	3	2	no	—
994	C₂²×C₄	—	3	2	no	—
995	C₂²×C₄	—	12	4	no	—
996	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
997	C₂²×C₄	C₂²×C₃×D₃	1	2	yes	—
998	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
999	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
1000	C₄⋊C₄	—	3	2	no	—
1001	C₄⋊C₄	—	3	2	no	—
1002	C₄⋊C₄	—	3	2	no	—
1003	C₄⋊C₄	—	3	2	no	—
1004	C₄⋊C₄	—	3	2	no	—
1005	C₄⋊C₄	—	3	2	no	—
1006	C₄⋊C₄	—	3	2	no	—
1007	C₄⋊C₄	—	3	2	no	—
1008	C₄⋊C₄	—	3	2	no	—
1009	C₄⋊C₄	—	3	2	no	—
1010	C₄⋊C₄	—	3	2	no	—
1011	C₄⋊C₄	—	3	1	no	—
1012	C₄⋊C₄	—	3	2	no	—
1013	C₄⋊C₄	—	3	1	no	—
1014	C₄⋊C₄	C₂²×C₃×D₃	1	2	yes	—
1015	C₄⋊C₄	C₂²×C₃×D₃	1	2	yes	—
1016	C₄⋊C₄	C₂²×C₃×D₃	1	1	yes	characteristic
1017	C₄⋊C₄	C₂²×C₃×D₃	1	2	yes	—
1018	C₄⋊C₄	C₂²×C₃×D₃	1	2	yes	—
1019	C₄⋊C₄	C₂²×C₃×D₃	1	1	yes	characteristic
1020	C₂²⋊C₄	—	3	2	no	—
1021	C₂²⋊C₄	—	3	2	no	—
1022	C₂²⋊C₄	—	3	2	no	—
1023	C₂²⋊C₄	—	3	2	no	—
1024	C₂²⋊C₄	—	3	2	no	—
1025	C₂²⋊C₄	—	3	2	no	—
1026	C₂²⋊C₄	—	3	2	no	—
1027	C₂²⋊C₄	—	3	2	no	—
1028	C₂²⋊C₄	—	3	2	no	—
1029	C₂²⋊C₄	—	3	2	no	—
1030	C₂²⋊C₄	—	3	2	no	—
1031	C₂²⋊C₄	—	3	2	no	—
1032	C₂²⋊C₄	—	3	2	no	—
1033	C₂²⋊C₄	—	3	2	no	—
1034	C₂²⋊C₄	—	3	2	no	—
1035	C₂²⋊C₄	—	3	2	no	—
1036	C₂²⋊C₄	—	3	2	no	—
1037	C₂²⋊C₄	—	3	2	no	—
1038	C₂²⋊C₄	—	3	2	no	—
1039	C₂²⋊C₄	C₂²×C₃×D₃	1	2	yes	—
1040	C₂²⋊C₄	C₂²×C₃×D₃	1	2	yes	—
1041	C₂²⋊C₄	C₂²×C₃×D₃	1	2	yes	—
1042	C₂²⋊C₄	C₂²×C₃×D₃	1	2	yes	—
1043	C₂²⋊C₄	C₂²×C₃×D₃	1	2	yes	—
1044	C₄²	—	3	2	no	—
1045	C₄²	—	3	2	no	—
1046	C₄²	—	3	2	no	—
1047	C₄²	C₂²×C₃×D₃	1	2	yes	—
1048	C₄²	C₂²×C₃×D₃	1	1	yes	characteristic
1049	C₄²	C₂²×C₃×D₃	1	1	yes	characteristic
1050	C₄²	C₂²×C₃×D₃	1	1	yes	characteristic
1051	C₄²	C₂²×C₃×D₃	1	1	yes	characteristic
1052	C₂²×C₃	—	2	2	no	—
1053	C₂²×C₃	—	2	2	no	—
1054	C₂²×C₃	—	2	1	no	—
1055	C₂²×C₃	—	2	1	no	—
1056	C₂²×C₃	—	2	1	no	—
1057	C₂²×C₃	—	2	2	no	—
1058	C₂²×C₃	—	2	2	no	—
1059	C₂²×C₃	—	2	2	no	—
1060	C₂²×C₃	—	2	1	no	—
1061	C₂²×C₃	—	2	1	no	—
1062	C₂²×C₃	—	2	2	no	—
1063	C₂²×C₃	—	2	2	no	—
1064	C₂²×C₃	—	2	1	no	—
1065	C₂²×C₃	—	2	1	no	—
1066	C₂²×C₃	—	4	1	no	—
1067	C₂²×C₃	—	4	1	no	—
1068	C₂²×C₃	—	4	2	no	—
1069	C₂²×C₃	—	4	2	no	—
1070	C₂²×C₃	—	4	2	no	—
1071	C₂²×C₃	—	6	2	no	—
1072	C₂²×C₃	—	6	2	no	—
1073	C₂²×C₃	—	6	2	no	—
1074	C₂²×C₃	—	6	2	no	—
1075	C₂²×C₃	—	6	2	no	—
1076	C₂²×C₃	—	6	2	no	—
1077	C₂²×C₃	—	6	2	no	—
1078	C₂²×C₃	—	6	2	no	—
1079	C₂²×C₃	—	6	2	no	—
1080	C₂²×C₃	—	12	8	no	—
1081	C₂²×C₃	C₂⁴×D₃	1	1	yes	characteristic
1082	C₂²×C₃	C₂⁵×C₃	1	1	yes	characteristic
1083	C₂×D₃	—	2	2	no	—
1084	C₂×D₃	—	2	2	no	—
1085	C₂×D₃	—	2	2	no	—
1086	C₂×D₃	—	2	2	no	—
1087	C₂×D₃	—	2	2	no	—
1088	C₂×D₃	—	2	2	no	—
1089	C₂×D₃	—	2	2	no	—
1090	C₂×D₃	—	2	2	no	—
1091	C₂×D₃	—	2	2	no	—
1092	C₂×D₃	—	4	8	no	—
1093	C₃×C₄	—	2	2	no	—
1094	C₃×C₄	—	2	2	no	—
1095	C₃×C₄	—	2	1	no	—
1096	C₃×C₄	—	2	1	no	—
1097	C₃×C₄	—	2	1	no	—
1098	C₃×C₄	—	2	1	no	—
1099	C₃×C₄	—	2	1	no	—
1100	C₃×C₄	—	2	2	no	—
1101	C₃×C₄	—	2	2	no	—
1102	C₃×C₄	—	2	1	no	—
1103	C₃×C₄	—	2	2	no	—
1104	C₃×C₄	—	2	1	no	—
1105	C₃×C₄	—	2	2	no	—
1106	C₃×C₄	—	2	2	no	—
1107	C₃×C₄	—	2	1	no	—
1108	C₃×C₄	—	2	1	no	—
1109	C₃×C₄	—	2	1	no	—
1110	C₃×C₄	—	2	2	no	—
1111	C₃×C₄	—	4	2	no	—
1112	C₃×C₄	—	4	1	no	—
1113	C₃×C₄	—	4	1	no	—
1114	C₃×C₄	—	4	1	no	—
1115	C₃×C₄	—	4	1	no	—
1116	C₃×C₄	—	4	2	no	—
1117	C₃×C₄	—	4	2	no	—
1118	C₃×C₄	—	6	2	no	—
1119	C₃×C₄	—	6	2	no	—
1120	C₃×C₄	—	6	2	no	—
1121	C₃×C₄	—	6	2	no	—
1122	C₃×C₄	—	6	2	no	—
1123	C₃×C₄	#1009	1	2	yes	—
1124	C₃×C₄	C₃×H(5,𝔽₂)	1	2	yes	—
1125	Dic₃	—	2	2	no	—
1126	Dic₃	—	2	2	no	—
1127	Dic₃	—	2	2	no	—
1128	Dic₃	—	2	2	no	—
1129	Dic₃	—	2	2	no	—
1130	C₃²	#3529	1	1	yes	characteristic, complemented, Sylow
1131	C₂³	—	3	2	no	—
1132	C₂³	—	3	2	no	—
1133	C₂³	—	3	2	no	—
1134	C₂³	—	12	2	no	—
1135	C₂³	—	12	2	no	—
1136	C₂³	—	12	2	no	—
1137	C₂³	C₂³×C₃×D₃	1	2	yes	—
1138	C₂³	C₂³×C₃×D₃	1	1	yes	characteristic
1139	Q₈	—	4	1	no	—
1140	Q₈	—	12	2	no	—
1141	Q₈	—	12	1	no	—
1142	Q₈	—	12	1	no	—
1143	Q₈	—	12	1	no	—
1144	D₄	—	4	1	no	—
1145	D₄	—	4	2	no	—
1146	D₄	—	12	2	no	—
1147	D₄	—	12	1	no	—
1148	D₄	—	12	1	no	—
1149	D₄	—	12	2	no	—
1150	D₄	—	12	2	no	—
1151	D₄	—	12	1	no	—
1152	D₄	—	12	2	no	—
1153	D₄	—	12	2	no	—
1154	D₄	—	12	2	no	—
1155	D₄	—	12	2	no	—
1156	D₄	—	12	2	no	—
1157	D₄	—	12	2	no	—
1158	D₄	—	12	2	no	—
1159	D₄	—	12	2	no	—
1160	D₄	—	12	2	no	—
1161	C₂×C₄	—	2	4	no	—
1162	C₂×C₄	—	2	2	no	—
1163	C₂×C₄	—	3	2	no	—
1164	C₂×C₄	—	3	2	no	—
1165	C₂×C₄	—	3	2	no	—
1166	C₂×C₄	—	3	2	no	—
1167	C₂×C₄	—	3	2	no	—
1168	C₂×C₄	—	4	1	no	—
1169	C₂×C₄	—	4	1	no	—
1170	C₂×C₄	—	6	4	no	—
1171	C₂×C₄	—	6	4	no	—
1172	C₂×C₄	—	6	4	no	—
1173	C₂×C₄	—	12	2	no	—
1174	C₂×C₄	—	12	2	no	—
1175	C₂×C₄	—	12	2	no	—
1176	C₂×C₄	—	12	2	no	—
1177	C₂×C₄	—	12	2	no	—
1178	C₂×C₄	C₂³×C₃×D₃	1	2	yes	—
1179	C₂×C₄	C₂³×C₃×D₃	1	2	yes	—
1180	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
1181	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
1182	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
1183	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
1184	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
1185	C₂×C₄	C₂³×C₃×D₃	1	2	yes	—
1186	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
1187	C₂×C₃	—	2	1	no	—
1188	C₂×C₃	—	2	1	no	—
1189	C₂×C₃	—	2	1	no	—
1190	C₂×C₃	—	4	2	no	—
1191	C₂×C₃	—	4	2	no	—
1192	C₂×C₃	—	4	1	no	—
1193	C₂×C₃	—	4	2	no	—
1194	C₂×C₃	—	4	1	no	—
1195	C₂×C₃	—	8	2	no	—
1196	C₂×C₃	—	12	2	no	—
1197	C₂×C₃	—	12	2	no	—
1198	C₂×C₃	—	12	2	no	—
1199	C₂×C₃	C₂×#1009	1	1	yes	characteristic
1200	C₂×C₃	#5964	1	1	yes	characteristic
1201	C₂×C₃	#5964	1	1	yes	characteristic
1202	C₂×C₃	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
1203	C₂×C₃	C₃×#585	1	1	yes	characteristic
1204	C₂×C₃	C₃×#585	1	1	yes	characteristic
1205	D₃	—	4	2	no	—
1206	D₃	—	4	2	no	—
1207	D₃	—	4	2	no	—
1208	C₂²	—	2	2	no	—
1209	C₂²	—	2	1	no	—
1210	C₂²	—	2	1	no	—
1211	C₂²	—	2	1	no	—
1212	C₂²	—	2	2	no	—
1213	C₂²	—	2	2	no	—
1214	C₂²	—	6	2	no	—
1215	C₂²	—	6	2	no	—
1216	C₂²	—	6	2	no	—
1217	C₂²	—	6	2	no	—
1218	C₂²	—	6	2	no	—
1219	C₂²	—	6	2	no	—
1220	C₂²	—	6	2	no	—
1221	C₂²	—	6	2	no	—
1222	C₂²	—	6	2	no	—
1223	C₂²	—	12	8	no	—
1224	C₂²	C₂⁴×C₃×D₃	1	1	yes	characteristic
1225	C₄	—	2	2	no	—
1226	C₄	—	2	1	no	—
1227	C₄	—	2	1	no	—
1228	C₄	—	2	1	no	—
1229	C₄	—	2	1	no	—
1230	C₄	—	2	1	no	—
1231	C₄	—	2	2	no	—
1232	C₄	—	2	2	no	—
1233	C₄	—	6	2	no	—
1234	C₄	—	6	2	no	—
1235	C₄	—	6	2	no	—
1236	C₄	—	6	2	no	—
1237	C₄	—	6	2	no	—
1238	C₄	C₃×#1009	1	2	yes	—
1239	C₃	—	2	1	no	—
1240	C₃	#86171	1	1	yes	characteristic, direct product factor
1241	C₃	C₃×#3529	1	1	yes	characteristic, complemented
1242	C₂	—	4	2	no	—
1243	C₂	—	4	1	no	—
1244	C₂	—	12	2	no	—
1245	C₂	—	12	2	no	—
1246	C₂	—	12	2	no	—
1247	C₂	C₂×C₃×#1009	1	1	yes	characteristic
1248	C₂	C₃×#5964	1	1	yes	characteristic
1249	C₂	C₃×#5964	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃×C₄	C₂³×D₃
commutator, cosocle	C₂²×C₃	C₂⁵×C₃
Frattini	C₂²	C₂⁴×C₃×D₃
Fitting	C₃²×#529	C₂
socle	C₂²×C₃²	C₂⁵
hypercenter	C₃×#529	D₃
hypocenter	C₃	C₃×#3529
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₃×#529

Complements

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

N	H ≅ G/N	type
1. C₃²×#529	C₂	semidirect
2. C₃×#5712	C₂	semidirect
3. C₃×#5711	C₂	semidirect
4. C₃×#5700	C₂	semidirect
5. C₃×#5699	C₂	semidirect
6. C₃×#5684	C₂	semidirect
7. C₃×#5683	C₂	semidirect
8. C₃×#5667	C₂	semidirect
9. C₃×#5666	C₂	semidirect
10. C₃×#5647	C₂	semidirect
11. C₃×#5620	C₂	semidirect
12. C₃×#5580	C₂	semidirect
13. C₃×#5548	C₂	semidirect
14. C₃×#5547	C₂	semidirect
15. C₃×#5547	C₂	semidirect
16. C₃×#5528	C₂	semidirect
17. C₃×#5524	C₂	semidirect
18. C₃×#5479	C₂	semidirect
19. C₃×#5477	C₂	semidirect
21. #86171	C₃	direct (N × H)
24. C₂×C₃×#235	C₂²	semidirect
25. C₂²×C₃×C₄×D₃	C₂²	semidirect
26. C₃²×#126	C₂²	semidirect
27. C₃²×#125	C₂²	semidirect
29. C₃²×#123	C₂²	semidirect
30. C₃²×C₂²⋊Q₈	C₂²	semidirect
32. C₃²×C₄×Q₈	C₂²	semidirect
34. C₃²×C₄×D₄	C₂²	semidirect
35. C₃²×#117	C₂²	semidirect
36. C₂×C₃²×C₄²	C₂²	semidirect
38. C₃×#946	C₂²	semidirect
42. C₃×#938	C₂²	semidirect
44. C₃×#937	C₂²	semidirect
46. C₃×#930	C₂²	semidirect
47. C₃×#930	C₂²	semidirect
48. C₃×#929	C₂²	semidirect
50. C₃×C₄×#67	C₂²	semidirect
51. C₃×C₄×#67	C₂²	semidirect
52. C₃×#924	C₂²	semidirect
53. C₃×#898	C₂²	semidirect
54. C₃×#898	C₂²	semidirect
55. C₃×#898	C₂²	semidirect
56. C₃×#897	C₂²	semidirect
57. C₃×#897	C₂²	semidirect
58. C₃×#896	C₂²	semidirect
59. C₃×#896	C₂²	semidirect
60. C₃×#896	C₂²	semidirect
64. C₃×#895	C₂²	semidirect
66. C₃×#894	C₂²	semidirect
67. C₃×#894	C₂²	semidirect
68. C₃×#894	C₂²	semidirect
69. C₃×#894	C₂²	semidirect
70. C₃×#890	C₂²	semidirect
71. C₃×#889	C₂²	semidirect
72. C₃×#888	C₂²	semidirect
74. C₃×#886	C₂²	semidirect
77. C₃×#885	C₂²	semidirect
81. C₃×#884	C₂²	semidirect
82. C₃×#884	C₂²	semidirect
84. C₃×#883	C₂²	semidirect
85. C₃×#883	C₂²	semidirect
88. C₃×#882	C₂²	semidirect
89. C₃×#882	C₂²	semidirect
90. C₃×#879	C₂²	semidirect
91. C₃×#878	C₂²	semidirect
92. C₃×#878	C₂²	semidirect
93. C₃×#876	C₂²	semidirect
96. C₃×#875	C₂²	semidirect
100. C₃×C₄×D₁₂	C₂²	semidirect
101. C₃×C₄×D₁₂	C₂²	semidirect
102. C₃×C₄×D₁₂	C₂²	semidirect
103. C₃×#872	C₂²	semidirect
104. C₃×#872	C₂²	semidirect
105. C₃×C₄²×D₃	C₂²	semidirect
106. C₃×#870	C₂²	semidirect
107. C₃×#869	C₂²	semidirect
108. C₃×C₄×Dic₆	C₂²	semidirect
125. C₃×#529	D₃	semidirect
126. C₃×#529	C₂×C₃	semidirect
130. #5712	C₂×C₃	semidirect
131. #5711	C₂×C₃	semidirect
132. #5700	C₂×C₃	semidirect
133. #5699	C₂×C₃	semidirect
134. #5684	C₂×C₃	semidirect
135. #5683	C₂×C₃	semidirect
136. #5667	C₂×C₃	semidirect
137. #5666	C₂×C₃	semidirect
138. #5647	C₂×C₃	semidirect
139. #5620	C₂×C₃	semidirect
140. #5580	C₂×C₃	semidirect
141. #5548	C₂×C₃	semidirect
142. #5547	C₂×C₃	semidirect
143. #5547	C₂×C₃	semidirect
144. #5528	C₂×C₃	semidirect
145. #5524	C₂×C₃	semidirect
146. #5479	C₂×C₃	semidirect
147. #5477	C₂×C₃	semidirect
246. C₂×#235	C₂²×C₃	semidirect
247. C₂²×C₄×D₃	C₂²×C₃	semidirect
258. C₃×#126	C₂×D₃	semidirect
259. C₃×#126	C₂²×C₃	semidirect
264. C₃×#125	C₂×D₃	semidirect
265. C₃×#125	C₂²×C₃	semidirect
288. C₃×#123	C₂×D₃	semidirect
289. C₃×#123	C₂²×C₃	semidirect
300. C₃×C₂²⋊Q₈	C₂×D₃	semidirect
301. C₃×C₂²⋊Q₈	C₂²×C₃	semidirect
328. C₃×C₄×Q₈	C₂×D₃	semidirect
329. C₃×C₄×Q₈	C₂²×C₃	semidirect
341. C₃×C₄×D₄	C₂×D₃	semidirect
343. C₃×C₄×D₄	C₂²×C₃	semidirect
347. C₃×#117	C₂×D₃	semidirect
348. C₃×#117	C₂²×C₃	semidirect
351. C₂×C₃×C₄²	C₂×D₃	semidirect
352. C₂×C₃×C₄²	C₂²×C₃	semidirect
354. #946	C₂²×C₃	semidirect
358. #938	C₂²×C₃	semidirect
360. #937	C₂²×C₃	semidirect
362. #930	C₂²×C₃	semidirect
363. #930	C₂²×C₃	semidirect
364. #929	C₂²×C₃	semidirect
366. C₄×#67	C₂²×C₃	semidirect
367. C₄×#67	C₂²×C₃	semidirect
368. #924	C₂²×C₃	semidirect
369. #898	C₂²×C₃	semidirect
370. #898	C₂²×C₃	semidirect
371. #898	C₂²×C₃	semidirect
372. #897	C₂²×C₃	semidirect
373. #897	C₂²×C₃	semidirect
374. #896	C₂²×C₃	semidirect
375. #896	C₂²×C₃	semidirect
376. #896	C₂²×C₃	semidirect
380. #895	C₂²×C₃	semidirect
382. #894	C₂²×C₃	semidirect
383. #894	C₂²×C₃	semidirect
384. #894	C₂²×C₃	semidirect
385. #894	C₂²×C₃	semidirect
386. #890	C₂²×C₃	semidirect
387. #889	C₂²×C₃	semidirect
388. #888	C₂²×C₃	semidirect
390. #886	C₂²×C₃	semidirect
393. #885	C₂²×C₃	semidirect
397. #884	C₂²×C₃	semidirect
398. #884	C₂²×C₃	semidirect
400. #883	C₂²×C₃	semidirect
401. #883	C₂²×C₃	semidirect
404. #882	C₂²×C₃	semidirect
405. #882	C₂²×C₃	semidirect
406. #879	C₂²×C₃	semidirect
407. #878	C₂²×C₃	semidirect
408. #878	C₂²×C₃	semidirect
409. #876	C₂²×C₃	semidirect
412. #875	C₂²×C₃	semidirect
416. C₄×D₁₂	C₂²×C₃	semidirect
417. C₄×D₁₂	C₂²×C₃	semidirect
418. C₄×D₁₂	C₂²×C₃	semidirect
419. #872	C₂²×C₃	semidirect
420. #872	C₂²×C₃	semidirect
421. C₄²×D₃	C₂²×C₃	semidirect
422. #870	C₂²×C₃	semidirect
423. #869	C₂²×C₃	semidirect
424. C₄×Dic₆	C₂²×C₃	semidirect
496. #529	C₃×D₃	semidirect
749. #126	C₂×C₃×D₃	semidirect
753. #125	C₂×C₃×D₃	semidirect
773. #123	C₂×C₃×D₃	semidirect
783. C₂²⋊Q₈	C₂×C₃×D₃	semidirect
807. C₄×Q₈	C₂×C₃×D₃	semidirect
817. C₄×D₄	C₂×C₃×D₃	semidirect
820. #117	C₂×C₃×D₃	semidirect
822. C₂×C₄²	C₂×C₃×D₃	semidirect
1130. C₃²	#3529	semidirect
1240. C₃	#86171	direct (N × H)
1241. C₃	C₃×#3529	semidirect

Maximal subgroups

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

subgroup	index
C₃²×#529	2
C₃×#5712	2
C₃×#5711	2
C₃×#5700	2
C₃×#5699	2
C₃×#5684	2
C₃×#5683	2
C₃×#5667	2
C₃×#5666	2
C₃×#5647	2
C₃×#5620	2
C₃×#5580	2
C₃×#5548	2
C₃×#5547	2
C₃×#5528	2
C₃×#5524	2
C₃×#5479	2
C₃×#5477	2
C₃×#3529	3
#86171	3

Subgroups — C3×#86171 #11910358

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#86171 #11910358