Subgroups — C₃×#63052 #10681659

Order 768.

7124 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	C₃×#3562	C₂	1	6	yes	maximal, complemented
2	C₃×#3561	C₂	1	3	yes	maximal, complemented
3	C₃×#3558	C₂	1	3	yes	maximal, complemented
4	C₃×#3548	C₂	1	3	yes	maximal, complemented
5	C₃×#3546	C₂	1	6	yes	maximal, complemented
6	C₃×#3546	C₂	1	6	yes	maximal, complemented
7	C₃×#3542	C₂	1	6	yes	maximal, complemented
8	C₃×#3541	C₂	1	6	yes	maximal, complemented
9	C₃×#3536	C₂	1	6	yes	maximal, complemented
10	C₃×#3529	C₂	1	3	yes	maximal, complemented
11	C₃×#3522	C₂	1	2	yes	maximal, complemented
12	C₃×#3518	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃×#3517	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃×#3516	C₂	1	2	yes	maximal, complemented
15	C₃×#3500	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃×#3497	C₂	1	2	yes	maximal, complemented
17	C₃×#3489	C₂	1	2	yes	maximal, complemented
18	C₃×#3488	C₂	1	2	yes	maximal, complemented
19	C₃×#3487	C₂	1	2	yes	maximal, complemented
20	#63052	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
21	C₂×C₃×2₋¹⁺⁴	C₂²	1	2	yes	complemented
22	C₂×C₃×2₋¹⁺⁴	C₂²	1	1	yes	characteristic, complemented
23	C₂×C₃×H(5,𝔽₂)	C₂²	1	1	yes	characteristic
24	C₂²×C₃×#41	C₂²	1	2	yes	complemented
25	C₃×#563	C₂²	1	6	yes	complemented
26	C₃×#563	C₂²	1	3	yes	complemented
27	C₃×#562	C₂²	1	1	yes	characteristic, complemented
28	C₃×#562	C₂²	1	6	yes	complemented
29	C₃×#562	C₂²	1	3	yes	complemented
30	C₃×#562	C₂²	1	6	yes	complemented
31	C₃×#562	C₂²	1	12	yes	complemented
32	C₃×#562	C₂²	1	6	yes	complemented
33	C₃×H(3,𝔽₄)	C₂²	1	3	yes	complemented
34	C₃×#560	C₂²	1	6	yes	complemented
35	C₃×#560	C₂²	1	6	yes	complemented
36	C₃×#560	C₂²	1	6	yes	complemented
37	C₃×#560	C₂²	1	12	yes	complemented
38	C₃×#559	C₂²	1	6	yes	complemented
39	C₃×Q₈²	C₂²	1	1	yes	characteristic, complemented
40	C₃×#557	C₂²	1	1	yes	characteristic, complemented
41	C₃×#556	C₂²	1	6	yes	complemented
42	C₃×#556	C₂²	1	6	yes	complemented
43	C₃×#556	C₂²	1	3	yes	complemented
44	C₃×#555	C₂²	1	3	yes	complemented
45	C₃×#554	C₂²	1	6	yes	complemented
46	C₃×#554	C₂²	1	6	yes	complemented
47	C₃×#554	C₂²	1	6	yes	complemented
48	C₃×#553	C₂²	1	6	yes	complemented
49	C₃×#553	C₂²	1	6	yes	complemented
50	C₃×#553	C₂²	1	12	yes	complemented
51	C₃×#552	C₂²	1	6	yes	complemented
52	C₃×#551	C₂²	1	12	yes	complemented
53	C₃×#550	C₂²	1	2	yes	—
54	C₃×#550	C₂²	1	1	yes	characteristic, complemented
55	C₃×#550	C₂²	1	6	yes	complemented
56	C₃×#550	C₂²	1	6	yes	complemented
57	C₃×#550	C₂²	1	2	yes	complemented
58	C₃×#550	C₂²	1	6	yes	complemented
59	C₃×#550	C₂²	1	3	yes	complemented
60	C₃×#550	C₂²	1	6	yes	complemented
61	C₃×D₄×Q₈	C₂²	1	1	yes	characteristic, complemented
62	C₃×D₄×Q₈	C₂²	1	2	yes	complemented
63	C₃×D₄×Q₈	C₂²	1	6	yes	complemented
64	C₃×#548	C₂²	1	2	yes	—
65	C₃×#548	C₂²	1	2	yes	complemented
66	C₃×#548	C₂²	1	2	yes	complemented
67	C₃×#548	C₂²	1	6	yes	complemented
68	C₃×#548	C₂²	1	6	yes	complemented
69	C₃×#548	C₂²	1	2	yes	complemented
70	C₃×#548	C₂²	1	2	yes	complemented
71	C₃×#548	C₂²	1	6	yes	complemented
72	C₃×#548	C₂²	1	6	yes	complemented
73	C₃×#547	C₂²	1	6	yes	complemented
74	C₃×#547	C₂²	1	6	yes	complemented
75	C₃×#547	C₂²	1	3	yes	complemented
76	C₃×#547	C₂²	1	6	yes	complemented
77	C₃×#547	C₂²	1	6	yes	complemented
78	C₃×#546	C₂²	1	6	yes	complemented
79	C₃×#546	C₂²	1	6	yes	complemented
80	C₃×#546	C₂²	1	6	yes	complemented
81	C₃×#546	C₂²	1	6	yes	complemented
82	C₃×#546	C₂²	1	6	yes	complemented
83	C₃×#546	C₂²	1	6	yes	complemented
84	C₃×#546	C₂²	1	12	yes	complemented
85	C₃×#546	C₂²	1	12	yes	complemented
86	C₃×D₄²	C₂²	1	6	yes	complemented
87	C₃×D₄²	C₂²	1	6	yes	complemented
88	C₃×#543	C₂²	1	6	yes	complemented
89	C₃×#542	C₂²	1	6	yes	complemented
90	C₃×#542	C₂²	1	6	yes	complemented
91	C₃×#542	C₂²	1	6	yes	complemented
92	C₃×#542	C₂²	1	6	yes	complemented
93	C₃×#542	C₂²	1	12	yes	complemented
94	C₃×#541	C₂²	1	6	yes	complemented
95	C₃×#540	C₂²	1	6	yes	complemented
96	C₃×#540	C₂²	1	12	yes	complemented
97	C₃×#539	C₂²	1	12	yes	complemented
98	C₃×#538	C₂²	1	12	yes	complemented
99	C₃×#538	C₂²	1	12	yes	complemented
100	C₃×#538	C₂²	1	12	yes	complemented
101	C₃×#538	C₂²	1	6	yes	complemented
102	C₃×#538	C₂²	1	6	yes	complemented
103	C₃×#537	C₂²	1	6	yes	complemented
104	C₃×#537	C₂²	1	6	yes	complemented
105	C₃×#537	C₂²	1	6	yes	complemented
106	C₃×#537	C₂²	1	6	yes	complemented
107	C₃×#537	C₂²	1	12	yes	complemented
108	C₃×#536	C₂²	1	6	yes	complemented
109	C₃×#536	C₂²	1	3	yes	complemented
110	C₃×#535	C₂²	1	6	yes	complemented
111	C₃×#535	C₂²	1	6	yes	complemented
112	C₃×#535	C₂²	1	6	yes	complemented
113	C₃×#535	C₂²	1	3	yes	complemented
114	C₃×#535	C₂²	1	12	yes	complemented
115	C₃×#534	C₂²	1	6	yes	complemented
116	C₃×#533	C₂²	1	3	yes	complemented
117	C₃×#532	C₂²	1	6	yes	complemented
118	C₃×#532	C₂²	1	6	yes	complemented
119	C₃×#532	C₂²	1	3	yes	complemented
120	C₃×#532	C₂²	1	3	yes	complemented
121	C₃×#532	C₂²	1	6	yes	complemented
122	C₃×#529	C₂²	1	6	yes	complemented
123	C₃×#529	C₂²	1	6	yes	complemented
124	C₃×#529	C₂²	1	3	yes	complemented
125	C₃×#529	C₂²	1	3	yes	complemented
126	C₃×#529	C₂²	1	6	yes	complemented
127	C₂×C₃×#124	C₂²	1	3	yes	complemented
128	C₃×#525	C₂²	1	6	yes	complemented
129	C₃×#525	C₂²	1	6	yes	complemented
130	C₃×#525	C₂²	1	6	yes	complemented
131	C₃×#525	C₂²	1	6	yes	complemented
132	C₂×C₃×C₂²⋊Q₈	C₂²	1	6	yes	complemented
133	C₂×C₃×#121	C₂²	1	6	yes	complemented
134	C₃×#520	C₂²	1	2	yes	complemented
135	C₃×#520	C₂²	1	2	yes	complemented
136	C₃×#519	C₂²	1	2	yes	complemented
137	C₃×C₄×#41	C₂²	1	1	yes	characteristic, complemented
138	C₂×C₃×C₄×Q₈	C₂²	1	2	yes	complemented
139	#3562	C₂×C₃	1	6	yes	complemented
140	#3561	C₂×C₃	1	3	yes	complemented
141	#3558	C₂×C₃	1	3	yes	complemented
142	#3548	C₂×C₃	1	3	yes	complemented
143	#3546	C₂×C₃	1	6	yes	complemented
144	#3546	C₂×C₃	1	6	yes	complemented
145	#3542	C₂×C₃	1	6	yes	complemented
146	#3541	C₂×C₃	1	6	yes	complemented
147	#3536	C₂×C₃	1	6	yes	complemented
148	#3529	C₂×C₃	1	3	yes	complemented
149	#3522	C₂×C₃	1	2	yes	complemented
150	#3518	C₂×C₃	1	1	yes	characteristic, complemented
151	#3517	C₂×C₃	1	1	yes	characteristic, complemented
152	#3516	C₂×C₃	1	2	yes	complemented
153	#3500	C₂×C₃	1	1	yes	characteristic, complemented
154	#3497	C₂×C₃	1	2	yes	complemented
155	#3489	C₂×C₃	1	2	yes	complemented
156	#3488	C₂×C₃	1	2	yes	complemented
157	#3487	C₂×C₃	1	2	yes	complemented
158	C₃×2₋¹⁺⁴	—	4	8	no	—
159	C₃×2₋¹⁺⁴	—	4	4	no	—
160	C₃×H(5,𝔽₂)	—	4	4	no	—
161	C₂×C₃×#41	—	4	8	no	—
162	C₂×C₃×#41	C₂³	1	2	yes	—
163	C₂×C₃×#41	C₂³	1	2	yes	—
164	C₂×C₃×#41	C₂³	1	1	yes	characteristic
165	C₂×C₃×#41	C₂³	1	6	yes	—
166	C₂×C₃×#41	C₂³	1	6	yes	—
167	C₂×C₃×#41	C₂³	1	3	yes	—
168	C₂×C₃×#41	C₂³	1	6	yes	—
169	C₂×C₃×#41	C₂³	1	6	yes	—
170	C₂×C₃×#41	C₂³	1	3	yes	—
171	C₂×C₃×#41	C₂³	1	6	yes	—
172	C₂×C₃×#41	C₂³	1	6	yes	—
173	C₂×C₃×#41	C₂³	1	12	yes	—
174	C₂×C₃×#41	C₂³	1	6	yes	—
175	C₂²×C₃×Q₈	C₂³	1	2	yes	—
176	C₂²×C₃×Q₈	C₂³	1	2	yes	—
177	C₂²×C₃×Q₈	C₂³	1	6	yes	—
178	C₂²×C₃×Q₈	C₂³	1	3	yes	—
179	C₂²×C₃×D₄	C₂³	1	6	yes	—
180	C₂²×C₃×D₄	C₂³	1	6	yes	—
181	C₂²×C₃×D₄	C₂³	1	3	yes	—
182	C₂²×C₃×D₄	C₂³	1	12	yes	—
183	C₂³×C₃×C₄	C₂³	1	6	yes	—
184	C₃×C₄⋊Q₈	C₂³	1	6	yes	—
185	C₃×C₄⋊Q₈	C₂³	1	3	yes	—
186	C₃×C₄⋊Q₈	C₂³	1	3	yes	—
187	C₃×C₄⋊Q₈	C₂³	1	6	yes	—
188	C₃×C₄⋊Q₈	C₂³	1	6	yes	—
189	C₃×C₄⋊Q₈	C₂³	1	3	yes	—
190	C₃×C₄⋊Q₈	C₂³	1	3	yes	—
191	C₃×#127	C₂³	1	6	yes	—
192	C₃×#127	C₂³	1	3	yes	—
193	C₃×#127	C₂³	1	6	yes	—
194	C₃×#127	C₂³	1	12	yes	—
195	C₃×#127	C₂³	1	3	yes	—
196	C₃×#127	C₂³	1	6	yes	—
197	C₃×#126	C₂³	1	6	yes	—
198	C₃×#126	C₂³	1	6	yes	—
199	C₃×#126	C₂³	1	6	yes	—
200	C₃×#126	C₂³	1	6	yes	—
201	C₃×#126	C₂³	1	6	yes	—
202	C₃×#126	C₂³	1	6	yes	—
203	C₃×#126	C₂³	1	12	yes	—
204	C₃×#126	C₂³	1	12	yes	—
205	C₃×#126	C₂³	1	12	yes	—
206	C₃×#125	C₂³	1	3	yes	—
207	C₃×#125	C₂³	1	1	yes	characteristic
208	C₃×#125	C₂³	1	6	yes	—
209	C₃×#125	C₂³	1	6	yes	—
210	C₃×#125	C₂³	1	12	yes	—
211	C₃×#125	C₂³	1	6	yes	—
212	C₃×#124	C₂³	1	6	yes	—
213	C₃×#124	C₂³	1	6	yes	—
214	C₃×#124	C₂³	1	6	yes	—
215	C₃×#124	C₂³	1	1	yes	characteristic
216	C₃×#124	C₂³	1	3	yes	—
217	C₃×#124	C₂³	1	3	yes	—
218	C₃×#124	C₂³	1	6	yes	—
219	C₃×#124	C₂³	1	6	yes	—
220	C₃×#124	C₂³	1	1	yes	characteristic
221	C₃×#124	C₂³	1	6	yes	—
222	C₃×#124	C₂³	1	12	yes	—
223	C₃×#124	C₂³	1	12	yes	—
224	C₃×#124	C₂³	1	6	yes	—
225	C₃×#124	C₂³	1	6	yes	—
226	C₃×#124	C₂³	1	6	yes	—
227	C₃×#124	C₂³	1	12	yes	—
228	C₃×#124	C₂³	1	6	yes	—
229	C₃×#123	C₂³	1	12	yes	—
230	C₃×#123	C₂³	1	12	yes	—
231	C₃×#123	C₂³	1	2	yes	—
232	C₃×#123	C₂³	1	6	yes	—
233	C₃×#123	C₂³	1	6	yes	—
234	C₃×#123	C₂³	1	6	yes	—
235	C₃×#123	C₂³	1	6	yes	—
236	C₃×#123	C₂³	1	6	yes	—
237	C₃×#123	C₂³	1	6	yes	—
238	C₃×#123	C₂³	1	6	yes	—
239	C₃×#123	C₂³	1	6	yes	—
240	C₃×#123	C₂³	1	12	yes	—
241	C₃×#123	C₂³	1	2	yes	—
242	C₃×#123	C₂³	1	6	yes	—
243	C₃×#123	C₂³	1	6	yes	—
244	C₃×#123	C₂³	1	12	yes	—
245	C₃×#123	C₂³	1	12	yes	—
246	C₃×#123	C₂³	1	12	yes	—
247	C₃×#123	C₂³	1	12	yes	—
248	C₃×C₂²⋊Q₈	C₂³	1	2	yes	—
249	C₃×C₂²⋊Q₈	C₂³	1	6	yes	—
250	C₃×C₂²⋊Q₈	C₂³	1	6	yes	—
251	C₃×C₂²⋊Q₈	C₂³	1	3	yes	—
252	C₃×C₂²⋊Q₈	C₂³	1	3	yes	—
253	C₃×C₂²⋊Q₈	C₂³	1	2	yes	—
254	C₃×C₂²⋊Q₈	C₂³	1	6	yes	—
255	C₃×C₂²⋊Q₈	C₂³	1	6	yes	—
256	C₃×C₂²⋊Q₈	C₂³	1	6	yes	—
257	C₃×C₂²⋊Q₈	C₂³	1	6	yes	—
258	C₃×C₂²⋊Q₈	C₂³	1	12	yes	—
259	C₃×C₂²⋊Q₈	C₂³	1	12	yes	—
260	C₃×C₂²⋊Q₈	C₂³	1	12	yes	—
261	C₃×C₂²⋊Q₈	C₂³	1	12	yes	—
262	C₃×C₂²⋊Q₈	C₂³	1	12	yes	—
263	C₃×C₂²⋊Q₈	C₂³	1	12	yes	—
264	C₃×C₂²⋊Q₈	C₂³	1	6	yes	—
265	C₃×C₂²⋊Q₈	C₂³	1	6	yes	—
266	C₃×C₂²⋊Q₈	C₂³	1	6	yes	—
267	C₃×C₂²⋊Q₈	C₂³	1	6	yes	—
268	C₃×C₂²⋊Q₈	C₂³	1	6	yes	—
269	C₃×C₂²⋊Q₈	C₂³	1	6	yes	—
270	C₃×C₂²⋊Q₈	C₂³	1	6	yes	—
271	C₃×C₂²⋊Q₈	C₂³	1	6	yes	—
272	C₃×C₂²⋊Q₈	C₂³	1	6	yes	—
273	C₃×#121	C₂³	1	6	yes	—
274	C₃×#121	C₂³	1	2	yes	—
275	C₃×#121	C₂³	1	2	yes	—
276	C₃×#121	C₂³	1	6	yes	—
277	C₃×#121	C₂³	1	3	yes	—
278	C₃×#121	C₂³	1	6	yes	—
279	C₃×#121	C₂³	1	3	yes	—
280	C₃×#121	C₂³	1	6	yes	—
281	C₃×#121	C₂³	1	6	yes	—
282	C₃×#121	C₂³	1	6	yes	—
283	C₃×#121	C₂³	1	6	yes	—
284	C₃×#121	C₂³	1	6	yes	—
285	C₃×#121	C₂³	1	6	yes	—
286	C₃×#121	C₂³	1	6	yes	—
287	C₃×#121	C₂³	1	6	yes	—
288	C₃×#121	C₂³	1	6	yes	—
289	C₃×#121	C₂³	1	12	yes	—
290	C₃×#121	C₂³	1	12	yes	—
291	C₃×#121	C₂³	1	12	yes	—
292	C₃×#121	C₂³	1	12	yes	—
293	C₃×#121	C₂³	1	12	yes	—
294	C₃×#121	C₂³	1	12	yes	—
295	C₃×#121	C₂³	1	12	yes	—
296	C₃×#121	C₂³	1	12	yes	—
297	C₃×#121	C₂³	1	12	yes	—
298	C₃×#121	C₂³	1	12	yes	—
299	C₃×#121	C₂³	1	6	yes	—
300	C₃×#121	C₂³	1	6	yes	—
301	C₃×#121	C₂³	1	6	yes	—
302	C₃×#121	C₂³	1	6	yes	—
303	C₃×#121	C₂³	1	6	yes	—
304	C₃×#121	C₂³	1	6	yes	—
305	C₃×#121	C₂³	1	6	yes	—
306	C₃×#121	C₂³	1	6	yes	—
307	C₃×#121	C₂³	1	12	yes	—
308	C₃×#121	C₂³	1	6	yes	—
309	C₃×#121	C₂³	1	6	yes	—
310	C₃×#121	C₂³	1	6	yes	—
311	C₃×#120	C₂³	1	6	yes	—
312	C₃×#120	C₂³	1	6	yes	—
313	C₃×#120	C₂³	1	6	yes	—
314	C₃×#120	C₂³	1	6	yes	—
315	C₃×#120	C₂³	1	6	yes	—
316	C₃×#120	C₂³	1	6	yes	—
317	C₃×#120	C₂³	1	12	yes	—
318	C₃×#120	C₂³	1	12	yes	—
319	C₃×#120	C₂³	1	12	yes	—
320	C₃×#120	C₂³	1	12	yes	—
321	C₃×C₄×Q₈	C₂³	1	3	yes	—
322	C₃×C₄×Q₈	C₂³	1	2	yes	—
323	C₃×C₄×Q₈	C₂³	1	1	yes	characteristic
324	C₃×C₄×Q₈	C₂³	1	6	yes	—
325	C₃×C₄×Q₈	C₂³	1	2	yes	—
326	C₃×C₄×Q₈	C₂³	1	6	yes	—
327	C₃×C₄×Q₈	C₂³	1	1	yes	characteristic
328	C₃×C₄×Q₈	C₂³	1	6	yes	—
329	C₃×C₄×Q₈	C₂³	1	6	yes	—
330	C₃×C₄×Q₈	C₂³	1	3	yes	—
331	C₃×C₄×Q₈	C₂³	1	6	yes	—
332	C₃×C₄×D₄	C₂³	1	6	yes	—
333	C₃×C₄×D₄	C₂³	1	6	yes	—
334	C₃×C₄×D₄	C₂³	1	12	yes	—
335	C₃×C₄×D₄	C₂³	1	3	yes	—
336	C₃×C₄×D₄	C₂³	1	3	yes	—
337	C₃×C₄×D₄	C₂³	1	6	yes	—
338	C₃×C₄×D₄	C₂³	1	6	yes	—
339	C₃×C₄×D₄	C₂³	1	6	yes	—
340	C₃×C₄×D₄	C₂³	1	3	yes	—
341	C₃×C₄×D₄	C₂³	1	6	yes	—
342	C₃×C₄×D₄	C₂³	1	3	yes	—
343	C₃×C₄×D₄	C₂³	1	6	yes	—
344	C₃×C₄×D₄	C₂³	1	6	yes	—
345	C₃×C₄×D₄	C₂³	1	6	yes	—
346	C₃×C₄×D₄	C₂³	1	6	yes	—
347	C₃×C₄×D₄	C₂³	1	6	yes	—
348	C₃×C₄×D₄	C₂³	1	6	yes	—
349	C₃×C₄×D₄	C₂³	1	12	yes	—
350	C₃×C₄×D₄	C₂³	1	12	yes	—
351	C₃×C₄×D₄	C₂³	1	12	yes	—
352	C₃×C₄×D₄	C₂³	1	12	yes	—
353	C₃×C₄×D₄	C₂³	1	6	yes	—
354	C₃×C₄×D₄	C₂³	1	12	yes	—
355	C₃×#117	C₂³	1	3	yes	—
356	C₃×#117	C₂³	1	6	yes	—
357	C₃×#117	C₂³	1	6	yes	—
358	C₃×#117	C₂³	1	6	yes	—
359	C₃×#117	C₂³	1	6	yes	—
360	C₃×#117	C₂³	1	12	yes	—
361	C₃×#117	C₂³	1	6	yes	—
362	C₂×C₃×C₄⋊C₄	C₂³	1	6	yes	—
363	C₂×C₃×C₄⋊C₄	C₂³	1	6	yes	—
364	C₂×C₃×C₄⋊C₄	C₂³	1	6	yes	—
365	C₂×C₃×C₄⋊C₄	C₂³	1	12	yes	—
366	C₂×C₃×C₂²⋊C₄	C₂³	1	12	yes	—
367	C₂×C₃×C₂²⋊C₄	C₂³	1	12	yes	—
368	C₂×C₃×C₂²⋊C₄	C₂³	1	6	yes	—
369	C₂×C₃×C₂²⋊C₄	C₂³	1	6	yes	—
370	C₂×C₃×C₄²	C₂³	1	6	yes	—
371	C₂×C₃×C₄²	C₂³	1	3	yes	—
372	C₂×2₋¹⁺⁴	C₂²×C₃	1	2	yes	complemented
373	C₂×2₋¹⁺⁴	C₂²×C₃	1	1	yes	characteristic, complemented
374	C₂×H(5,𝔽₂)	C₂²×C₃	1	1	yes	characteristic
375	C₂²×#41	C₂²×C₃	1	2	yes	complemented
376	#563	C₂²×C₃	1	6	yes	complemented
377	#563	C₂²×C₃	1	3	yes	complemented
378	#562	C₂²×C₃	1	1	yes	characteristic, complemented
379	#562	C₂²×C₃	1	6	yes	complemented
380	#562	C₂²×C₃	1	3	yes	complemented
381	#562	C₂²×C₃	1	6	yes	complemented
382	#562	C₂²×C₃	1	12	yes	complemented
383	#562	C₂²×C₃	1	6	yes	complemented
384	H(3,𝔽₄)	C₂²×C₃	1	3	yes	complemented
385	#560	C₂²×C₃	1	6	yes	complemented
386	#560	C₂²×C₃	1	6	yes	complemented
387	#560	C₂²×C₃	1	6	yes	complemented
388	#560	C₂²×C₃	1	12	yes	complemented
389	#559	C₂²×C₃	1	6	yes	complemented
390	Q₈²	C₂²×C₃	1	1	yes	characteristic, complemented
391	#557	C₂²×C₃	1	1	yes	characteristic, complemented
392	#556	C₂²×C₃	1	6	yes	complemented
393	#556	C₂²×C₃	1	6	yes	complemented
394	#556	C₂²×C₃	1	3	yes	complemented
395	#555	C₂²×C₃	1	3	yes	complemented
396	#554	C₂²×C₃	1	6	yes	complemented
397	#554	C₂²×C₃	1	6	yes	complemented
398	#554	C₂²×C₃	1	6	yes	complemented
399	#553	C₂²×C₃	1	6	yes	complemented
400	#553	C₂²×C₃	1	6	yes	complemented
401	#553	C₂²×C₃	1	12	yes	complemented
402	#552	C₂²×C₃	1	6	yes	complemented
403	#551	C₂²×C₃	1	12	yes	complemented
404	#550	C₂²×C₃	1	2	yes	—
405	#550	C₂²×C₃	1	1	yes	characteristic, complemented
406	#550	C₂²×C₃	1	6	yes	complemented
407	#550	C₂²×C₃	1	6	yes	complemented
408	#550	C₂²×C₃	1	2	yes	complemented
409	#550	C₂²×C₃	1	6	yes	complemented
410	#550	C₂²×C₃	1	3	yes	complemented
411	#550	C₂²×C₃	1	6	yes	complemented
412	D₄×Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
413	D₄×Q₈	C₂²×C₃	1	2	yes	complemented
414	D₄×Q₈	C₂²×C₃	1	6	yes	complemented
415	#548	C₂²×C₃	1	2	yes	—
416	#548	C₂²×C₃	1	2	yes	complemented
417	#548	C₂²×C₃	1	2	yes	complemented
418	#548	C₂²×C₃	1	6	yes	complemented
419	#548	C₂²×C₃	1	6	yes	complemented
420	#548	C₂²×C₃	1	2	yes	complemented
421	#548	C₂²×C₃	1	2	yes	complemented
422	#548	C₂²×C₃	1	6	yes	complemented
423	#548	C₂²×C₃	1	6	yes	complemented
424	#547	C₂²×C₃	1	6	yes	complemented
425	#547	C₂²×C₃	1	6	yes	complemented
426	#547	C₂²×C₃	1	3	yes	complemented
427	#547	C₂²×C₃	1	6	yes	complemented
428	#547	C₂²×C₃	1	6	yes	complemented
429	#546	C₂²×C₃	1	6	yes	complemented
430	#546	C₂²×C₃	1	6	yes	complemented
431	#546	C₂²×C₃	1	6	yes	complemented
432	#546	C₂²×C₃	1	6	yes	complemented
433	#546	C₂²×C₃	1	6	yes	complemented
434	#546	C₂²×C₃	1	6	yes	complemented
435	#546	C₂²×C₃	1	12	yes	complemented
436	#546	C₂²×C₃	1	12	yes	complemented
437	D₄²	C₂²×C₃	1	6	yes	complemented
438	D₄²	C₂²×C₃	1	6	yes	complemented
439	#543	C₂²×C₃	1	6	yes	complemented
440	#542	C₂²×C₃	1	6	yes	complemented
441	#542	C₂²×C₃	1	6	yes	complemented
442	#542	C₂²×C₃	1	6	yes	complemented
443	#542	C₂²×C₃	1	6	yes	complemented
444	#542	C₂²×C₃	1	12	yes	complemented
445	#541	C₂²×C₃	1	6	yes	complemented
446	#540	C₂²×C₃	1	6	yes	complemented
447	#540	C₂²×C₃	1	12	yes	complemented
448	#539	C₂²×C₃	1	12	yes	complemented
449	#538	C₂²×C₃	1	12	yes	complemented
450	#538	C₂²×C₃	1	12	yes	complemented
451	#538	C₂²×C₃	1	12	yes	complemented
452	#538	C₂²×C₃	1	6	yes	complemented
453	#538	C₂²×C₃	1	6	yes	complemented
454	#537	C₂²×C₃	1	6	yes	complemented
455	#537	C₂²×C₃	1	6	yes	complemented
456	#537	C₂²×C₃	1	6	yes	complemented
457	#537	C₂²×C₃	1	6	yes	complemented
458	#537	C₂²×C₃	1	12	yes	complemented
459	#536	C₂²×C₃	1	6	yes	complemented
460	#536	C₂²×C₃	1	3	yes	complemented
461	#535	C₂²×C₃	1	6	yes	complemented
462	#535	C₂²×C₃	1	6	yes	complemented
463	#535	C₂²×C₃	1	6	yes	complemented
464	#535	C₂²×C₃	1	3	yes	complemented
465	#535	C₂²×C₃	1	12	yes	complemented
466	#534	C₂²×C₃	1	6	yes	complemented
467	#533	C₂²×C₃	1	3	yes	complemented
468	#532	C₂²×C₃	1	6	yes	complemented
469	#532	C₂²×C₃	1	6	yes	complemented
470	#532	C₂²×C₃	1	3	yes	complemented
471	#532	C₂²×C₃	1	3	yes	complemented
472	#532	C₂²×C₃	1	6	yes	complemented
473	#529	C₂²×C₃	1	6	yes	complemented
474	#529	C₂²×C₃	1	6	yes	complemented
475	#529	C₂²×C₃	1	3	yes	complemented
476	#529	C₂²×C₃	1	3	yes	complemented
477	#529	C₂²×C₃	1	6	yes	complemented
478	C₂×#124	C₂²×C₃	1	3	yes	complemented
479	#525	C₂²×C₃	1	6	yes	complemented
480	#525	C₂²×C₃	1	6	yes	complemented
481	#525	C₂²×C₃	1	6	yes	complemented
482	#525	C₂²×C₃	1	6	yes	complemented
483	C₂×C₂²⋊Q₈	C₂²×C₃	1	6	yes	complemented
484	C₂×#121	C₂²×C₃	1	6	yes	complemented
485	#520	C₂²×C₃	1	2	yes	complemented
486	#520	C₂²×C₃	1	2	yes	complemented
487	#519	C₂²×C₃	1	2	yes	complemented
488	C₄×#41	C₂²×C₃	1	1	yes	characteristic, complemented
489	C₂×C₄×Q₈	C₂²×C₃	1	2	yes	complemented
490	C₂⁴×C₃	C₂⁴	1	6	yes	—
491	C₂⁴×C₃	C₂⁴	1	6	yes	—
492	C₃×#41	—	2	8	no	—
493	C₃×#41	—	2	8	no	—
494	C₃×#41	—	2	4	no	—
495	C₃×#41	—	4	6	no	—
496	C₃×#41	—	4	12	no	—
497	C₃×#41	—	4	6	no	—
498	C₃×#41	—	4	12	no	—
499	C₃×#41	—	4	12	no	—
500	C₃×#41	—	4	12	no	—
501	C₃×#41	—	4	12	no	—
502	C₃×#41	—	4	12	no	—
503	C₃×#41	—	8	12	no	—
504	C₃×#41	—	8	6	no	—
505	C₂×C₃×Q₈	—	2	8	no	—
506	C₂×C₃×Q₈	—	2	8	no	—
507	C₂×C₃×Q₈	—	4	12	no	—
508	C₂×C₃×Q₈	—	4	6	no	—
509	C₂×C₃×Q₈	C₂⁴	1	6	yes	—
510	C₂×C₃×Q₈	C₂⁴	1	6	yes	—
511	C₂×C₃×Q₈	C₂⁴	1	1	yes	characteristic
512	C₂×C₃×Q₈	C₂⁴	1	3	yes	—
513	C₂×C₃×Q₈	C₂⁴	1	6	yes	—
514	C₂×C₃×Q₈	C₂⁴	1	6	yes	—
515	C₂×C₃×Q₈	C₂⁴	1	1	yes	characteristic
516	C₂×C₃×Q₈	C₂⁴	1	3	yes	—
517	C₂×C₃×Q₈	C₂⁴	1	1	yes	characteristic
518	C₂×C₃×D₄	—	4	12	no	—
519	C₂×C₃×D₄	—	4	12	no	—
520	C₂×C₃×D₄	—	4	6	no	—
521	C₂×C₃×D₄	—	8	12	no	—
522	C₂×C₃×D₄	C₂⁴	1	6	yes	—
523	C₂×C₃×D₄	C₂⁴	1	3	yes	—
524	C₂×C₃×D₄	C₂⁴	1	6	yes	—
525	C₂×C₃×D₄	C₂⁴	1	1	yes	characteristic
526	C₂×C₃×D₄	C₂⁴	1	6	yes	—
527	C₂×C₃×D₄	C₂⁴	1	6	yes	—
528	C₂×C₃×D₄	C₂⁴	1	2	yes	—
529	C₂×C₃×D₄	C₂⁴	1	6	yes	—
530	C₂×C₃×D₄	C₂⁴	1	6	yes	—
531	C₂×C₃×D₄	C₂⁴	1	6	yes	—
532	C₂×C₃×D₄	C₂⁴	1	6	yes	—
533	C₂×C₃×D₄	C₂⁴	1	3	yes	—
534	C₂×C₃×D₄	C₂⁴	1	12	yes	—
535	C₂×C₃×D₄	C₂⁴	1	12	yes	—
536	C₂×C₃×D₄	C₂⁴	1	6	yes	—
537	C₂×C₃×D₄	C₂⁴	1	6	yes	—
538	C₂×C₃×D₄	C₂⁴	1	6	yes	—
539	C₂×C₃×D₄	C₂⁴	1	2	yes	—
540	C₂×C₃×D₄	C₂⁴	1	6	yes	—
541	C₂×C₃×D₄	C₂⁴	1	12	yes	—
542	C₂×C₃×D₄	C₂⁴	1	3	yes	—
543	C₂×C₃×D₄	C₂⁴	1	6	yes	—
544	C₂×C₃×D₄	C₂⁴	1	6	yes	—
545	C₂×C₃×D₄	C₂⁴	1	1	yes	characteristic
546	C₂²×C₃×C₄	—	4	12	no	—
547	C₂²×C₃×C₄	C₂⁴	1	6	yes	—
548	C₂²×C₃×C₄	C₂⁴	1	3	yes	—
549	C₂²×C₃×C₄	C₂⁴	1	6	yes	—
550	C₂²×C₃×C₄	C₂⁴	1	6	yes	—
551	C₂²×C₃×C₄	C₂⁴	1	6	yes	—
552	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
553	C₂²×C₃×C₄	C₂⁴	1	3	yes	—
554	C₂²×C₃×C₄	C₂⁴	1	3	yes	—
555	C₂²×C₃×C₄	C₂⁴	1	6	yes	—
556	C₂²×C₃×C₄	C₂⁴	1	6	yes	—
557	C₂²×C₃×C₄	C₂⁴	1	6	yes	—
558	C₂²×C₃×C₄	C₂⁴	1	12	yes	—
559	C₂²×C₃×C₄	C₂⁴	1	12	yes	—
560	C₂²×C₃×C₄	C₂⁴	1	12	yes	—
561	C₂²×C₃×C₄	C₂⁴	1	6	yes	—
562	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
563	C₃×C₄⋊C₄	C₂⁴	1	6	yes	—
564	C₃×C₄⋊C₄	C₂⁴	1	3	yes	—
565	C₃×C₄⋊C₄	C₂⁴	1	6	yes	—
566	C₃×C₄⋊C₄	C₂⁴	1	6	yes	—
567	C₃×C₄⋊C₄	C₂⁴	1	6	yes	—
568	C₃×C₄⋊C₄	C₂⁴	1	6	yes	—
569	C₃×C₄⋊C₄	C₂⁴	1	6	yes	—
570	C₃×C₄⋊C₄	C₂⁴	1	6	yes	—
571	C₃×C₄⋊C₄	C₂⁴	1	12	yes	—
572	C₃×C₄⋊C₄	C₂⁴	1	12	yes	—
573	C₃×C₄⋊C₄	C₂⁴	1	3	yes	—
574	C₃×C₄⋊C₄	C₂⁴	1	2	yes	—
575	C₃×C₄⋊C₄	C₂⁴	1	2	yes	—
576	C₃×C₄⋊C₄	C₂⁴	1	3	yes	—
577	C₃×C₄⋊C₄	C₂⁴	1	6	yes	—
578	C₃×C₄⋊C₄	C₂⁴	1	3	yes	—
579	C₃×C₄⋊C₄	C₂⁴	1	6	yes	—
580	C₃×C₄⋊C₄	C₂⁴	1	6	yes	—
581	C₃×C₄⋊C₄	C₂⁴	1	6	yes	—
582	C₃×C₄⋊C₄	C₂⁴	1	6	yes	—
583	C₃×C₄⋊C₄	C₂⁴	1	2	yes	—
584	C₃×C₄⋊C₄	C₂⁴	1	6	yes	—
585	C₃×C₄⋊C₄	C₂⁴	1	6	yes	—
586	C₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
587	C₃×C₄⋊C₄	C₂⁴	1	2	yes	—
588	C₃×C₄⋊C₄	C₂⁴	1	6	yes	—
589	C₃×C₄⋊C₄	C₂⁴	1	6	yes	—
590	C₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
591	C₃×C₂²⋊C₄	C₂⁴	1	12	yes	—
592	C₃×C₂²⋊C₄	C₂⁴	1	6	yes	—
593	C₃×C₂²⋊C₄	C₂⁴	1	6	yes	—
594	C₃×C₂²⋊C₄	C₂⁴	1	6	yes	—
595	C₃×C₂²⋊C₄	C₂⁴	1	6	yes	—
596	C₃×C₂²⋊C₄	C₂⁴	1	12	yes	—
597	C₃×C₂²⋊C₄	C₂⁴	1	6	yes	—
598	C₃×C₂²⋊C₄	C₂⁴	1	6	yes	—
599	C₃×C₂²⋊C₄	C₂⁴	1	12	yes	—
600	C₃×C₂²⋊C₄	C₂⁴	1	12	yes	—
601	C₃×C₂²⋊C₄	C₂⁴	1	6	yes	—
602	C₃×C₂²⋊C₄	C₂⁴	1	2	yes	—
603	C₃×C₂²⋊C₄	C₂⁴	1	6	yes	—
604	C₃×C₂²⋊C₄	C₂⁴	1	6	yes	—
605	C₃×C₂²⋊C₄	C₂⁴	1	6	yes	—
606	C₃×C₂²⋊C₄	C₂⁴	1	6	yes	—
607	C₃×C₂²⋊C₄	C₂⁴	1	6	yes	—
608	C₃×C₂²⋊C₄	C₂⁴	1	6	yes	—
609	C₃×C₂²⋊C₄	C₂⁴	1	2	yes	—
610	C₃×C₂²⋊C₄	C₂⁴	1	2	yes	—
611	C₃×C₂²⋊C₄	C₂⁴	1	6	yes	—
612	C₃×C₂²⋊C₄	C₂⁴	1	6	yes	—
613	C₃×C₂²⋊C₄	C₂⁴	1	6	yes	—
614	C₃×C₂²⋊C₄	C₂⁴	1	12	yes	—
615	C₃×C₂²⋊C₄	C₂⁴	1	6	yes	—
616	C₃×C₂²⋊C₄	C₂⁴	1	6	yes	—
617	C₃×C₂²⋊C₄	C₂⁴	1	2	yes	—
618	C₃×C₂²⋊C₄	C₂⁴	1	6	yes	—
619	C₃×C₂²⋊C₄	C₂⁴	1	2	yes	—
620	C₃×C₂²⋊C₄	C₂⁴	1	2	yes	—
621	C₃×C₄²	C₂⁴	1	1	yes	characteristic
622	C₃×C₄²	C₂⁴	1	3	yes	—
623	C₃×C₄²	C₂⁴	1	6	yes	—
624	C₃×C₄²	C₂⁴	1	6	yes	—
625	C₃×C₄²	C₂⁴	1	3	yes	—
626	C₃×C₄²	C₂⁴	1	6	yes	—
627	C₃×C₄²	C₂⁴	1	3	yes	—
628	C₃×C₄²	C₂⁴	1	6	yes	—
629	C₃×C₄²	C₂⁴	1	12	yes	—
630	2₋¹⁺⁴	—	4	8	no	—
631	2₋¹⁺⁴	—	4	4	no	—
632	H(5,𝔽₂)	—	4	4	no	—
633	C₂×#41	—	4	8	no	—
634	C₂×#41	C₂³×C₃	1	1	yes	characteristic
635	C₂×#41	C₂³×C₃	1	2	yes	—
636	C₂×#41	C₂³×C₃	1	2	yes	—
637	C₂×#41	C₂³×C₃	1	6	yes	—
638	C₂×#41	C₂³×C₃	1	3	yes	—
639	C₂×#41	C₂³×C₃	1	6	yes	—
640	C₂×#41	C₂³×C₃	1	3	yes	—
641	C₂×#41	C₂³×C₃	1	6	yes	—
642	C₂×#41	C₂³×C₃	1	6	yes	—
643	C₂×#41	C₂³×C₃	1	6	yes	—
644	C₂×#41	C₂³×C₃	1	6	yes	—
645	C₂×#41	C₂³×C₃	1	12	yes	—
646	C₂×#41	C₂³×C₃	1	6	yes	—
647	C₂²×Q₈	C₂³×C₃	1	2	yes	—
648	C₂²×Q₈	C₂³×C₃	1	2	yes	—
649	C₂²×Q₈	C₂³×C₃	1	6	yes	—
650	C₂²×Q₈	C₂³×C₃	1	3	yes	—
651	C₂²×D₄	C₂³×C₃	1	6	yes	—
652	C₂²×D₄	C₂³×C₃	1	3	yes	—
653	C₂²×D₄	C₂³×C₃	1	6	yes	—
654	C₂²×D₄	C₂³×C₃	1	12	yes	—
655	C₂³×C₄	C₂³×C₃	1	6	yes	—
656	C₄⋊Q₈	C₂³×C₃	1	3	yes	—
657	C₄⋊Q₈	C₂³×C₃	1	6	yes	—
658	C₄⋊Q₈	C₂³×C₃	1	3	yes	—
659	C₄⋊Q₈	C₂³×C₃	1	6	yes	—
660	C₄⋊Q₈	C₂³×C₃	1	6	yes	—
661	C₄⋊Q₈	C₂³×C₃	1	3	yes	—
662	C₄⋊Q₈	C₂³×C₃	1	3	yes	—
663	#127	C₂³×C₃	1	6	yes	—
664	#127	C₂³×C₃	1	3	yes	—
665	#127	C₂³×C₃	1	3	yes	—
666	#127	C₂³×C₃	1	6	yes	—
667	#127	C₂³×C₃	1	6	yes	—
668	#127	C₂³×C₃	1	12	yes	—
669	#126	C₂³×C₃	1	12	yes	—
670	#126	C₂³×C₃	1	6	yes	—
671	#126	C₂³×C₃	1	6	yes	—
672	#126	C₂³×C₃	1	6	yes	—
673	#126	C₂³×C₃	1	6	yes	—
674	#126	C₂³×C₃	1	6	yes	—
675	#126	C₂³×C₃	1	6	yes	—
676	#126	C₂³×C₃	1	12	yes	—
677	#126	C₂³×C₃	1	12	yes	—
678	#125	C₂³×C₃	1	1	yes	characteristic
679	#125	C₂³×C₃	1	3	yes	—
680	#125	C₂³×C₃	1	6	yes	—
681	#125	C₂³×C₃	1	6	yes	—
682	#125	C₂³×C₃	1	6	yes	—
683	#125	C₂³×C₃	1	12	yes	—
684	#124	C₂³×C₃	1	3	yes	—
685	#124	C₂³×C₃	1	6	yes	—
686	#124	C₂³×C₃	1	6	yes	—
687	#124	C₂³×C₃	1	6	yes	—
688	#124	C₂³×C₃	1	1	yes	characteristic
689	#124	C₂³×C₃	1	3	yes	—
690	#124	C₂³×C₃	1	6	yes	—
691	#124	C₂³×C₃	1	6	yes	—
692	#124	C₂³×C₃	1	6	yes	—
693	#124	C₂³×C₃	1	1	yes	characteristic
694	#124	C₂³×C₃	1	12	yes	—
695	#124	C₂³×C₃	1	6	yes	—
696	#124	C₂³×C₃	1	6	yes	—
697	#124	C₂³×C₃	1	6	yes	—
698	#124	C₂³×C₃	1	6	yes	—
699	#124	C₂³×C₃	1	12	yes	—
700	#124	C₂³×C₃	1	12	yes	—
701	#123	C₂³×C₃	1	6	yes	—
702	#123	C₂³×C₃	1	2	yes	—
703	#123	C₂³×C₃	1	6	yes	—
704	#123	C₂³×C₃	1	6	yes	—
705	#123	C₂³×C₃	1	6	yes	—
706	#123	C₂³×C₃	1	6	yes	—
707	#123	C₂³×C₃	1	2	yes	—
708	#123	C₂³×C₃	1	6	yes	—
709	#123	C₂³×C₃	1	6	yes	—
710	#123	C₂³×C₃	1	6	yes	—
711	#123	C₂³×C₃	1	6	yes	—
712	#123	C₂³×C₃	1	6	yes	—
713	#123	C₂³×C₃	1	12	yes	—
714	#123	C₂³×C₃	1	12	yes	—
715	#123	C₂³×C₃	1	12	yes	—
716	#123	C₂³×C₃	1	12	yes	—
717	#123	C₂³×C₃	1	12	yes	—
718	#123	C₂³×C₃	1	12	yes	—
719	#123	C₂³×C₃	1	12	yes	—
720	C₂²⋊Q₈	C₂³×C₃	1	6	yes	—
721	C₂²⋊Q₈	C₂³×C₃	1	12	yes	—
722	C₂²⋊Q₈	C₂³×C₃	1	6	yes	—
723	C₂²⋊Q₈	C₂³×C₃	1	6	yes	—
724	C₂²⋊Q₈	C₂³×C₃	1	6	yes	—
725	C₂²⋊Q₈	C₂³×C₃	1	6	yes	—
726	C₂²⋊Q₈	C₂³×C₃	1	2	yes	—
727	C₂²⋊Q₈	C₂³×C₃	1	6	yes	—
728	C₂²⋊Q₈	C₂³×C₃	1	6	yes	—
729	C₂²⋊Q₈	C₂³×C₃	1	6	yes	—
730	C₂²⋊Q₈	C₂³×C₃	1	6	yes	—
731	C₂²⋊Q₈	C₂³×C₃	1	6	yes	—
732	C₂²⋊Q₈	C₂³×C₃	1	6	yes	—
733	C₂²⋊Q₈	C₂³×C₃	1	2	yes	—
734	C₂²⋊Q₈	C₂³×C₃	1	6	yes	—
735	C₂²⋊Q₈	C₂³×C₃	1	6	yes	—
736	C₂²⋊Q₈	C₂³×C₃	1	3	yes	—
737	C₂²⋊Q₈	C₂³×C₃	1	3	yes	—
738	C₂²⋊Q₈	C₂³×C₃	1	6	yes	—
739	C₂²⋊Q₈	C₂³×C₃	1	6	yes	—
740	C₂²⋊Q₈	C₂³×C₃	1	12	yes	—
741	C₂²⋊Q₈	C₂³×C₃	1	12	yes	—
742	C₂²⋊Q₈	C₂³×C₃	1	12	yes	—
743	C₂²⋊Q₈	C₂³×C₃	1	12	yes	—
744	C₂²⋊Q₈	C₂³×C₃	1	12	yes	—
745	#121	C₂³×C₃	1	6	yes	—
746	#121	C₂³×C₃	1	12	yes	—
747	#121	C₂³×C₃	1	6	yes	—
748	#121	C₂³×C₃	1	6	yes	—
749	#121	C₂³×C₃	1	6	yes	—
750	#121	C₂³×C₃	1	6	yes	—
751	#121	C₂³×C₃	1	2	yes	—
752	#121	C₂³×C₃	1	6	yes	—
753	#121	C₂³×C₃	1	6	yes	—
754	#121	C₂³×C₃	1	6	yes	—
755	#121	C₂³×C₃	1	6	yes	—
756	#121	C₂³×C₃	1	6	yes	—
757	#121	C₂³×C₃	1	6	yes	—
758	#121	C₂³×C₃	1	6	yes	—
759	#121	C₂³×C₃	1	3	yes	—
760	#121	C₂³×C₃	1	6	yes	—
761	#121	C₂³×C₃	1	6	yes	—
762	#121	C₂³×C₃	1	3	yes	—
763	#121	C₂³×C₃	1	2	yes	—
764	#121	C₂³×C₃	1	6	yes	—
765	#121	C₂³×C₃	1	6	yes	—
766	#121	C₂³×C₃	1	12	yes	—
767	#121	C₂³×C₃	1	6	yes	—
768	#121	C₂³×C₃	1	6	yes	—
769	#121	C₂³×C₃	1	6	yes	—
770	#121	C₂³×C₃	1	6	yes	—
771	#121	C₂³×C₃	1	6	yes	—
772	#121	C₂³×C₃	1	6	yes	—
773	#121	C₂³×C₃	1	6	yes	—
774	#121	C₂³×C₃	1	12	yes	—
775	#121	C₂³×C₃	1	12	yes	—
776	#121	C₂³×C₃	1	12	yes	—
777	#121	C₂³×C₃	1	12	yes	—
778	#121	C₂³×C₃	1	12	yes	—
779	#121	C₂³×C₃	1	12	yes	—
780	#121	C₂³×C₃	1	12	yes	—
781	#121	C₂³×C₃	1	12	yes	—
782	#121	C₂³×C₃	1	12	yes	—
783	#120	C₂³×C₃	1	6	yes	—
784	#120	C₂³×C₃	1	12	yes	—
785	#120	C₂³×C₃	1	6	yes	—
786	#120	C₂³×C₃	1	6	yes	—
787	#120	C₂³×C₃	1	6	yes	—
788	#120	C₂³×C₃	1	6	yes	—
789	#120	C₂³×C₃	1	6	yes	—
790	#120	C₂³×C₃	1	12	yes	—
791	#120	C₂³×C₃	1	12	yes	—
792	#120	C₂³×C₃	1	12	yes	—
793	C₄×Q₈	C₂³×C₃	1	2	yes	—
794	C₄×Q₈	C₂³×C₃	1	2	yes	—
795	C₄×Q₈	C₂³×C₃	1	6	yes	—
796	C₄×Q₈	C₂³×C₃	1	6	yes	—
797	C₄×Q₈	C₂³×C₃	1	1	yes	characteristic
798	C₄×Q₈	C₂³×C₃	1	1	yes	characteristic
799	C₄×Q₈	C₂³×C₃	1	6	yes	—
800	C₄×Q₈	C₂³×C₃	1	6	yes	—
801	C₄×Q₈	C₂³×C₃	1	3	yes	—
802	C₄×Q₈	C₂³×C₃	1	3	yes	—
803	C₄×Q₈	C₂³×C₃	1	6	yes	—
804	C₄×D₄	C₂³×C₃	1	3	yes	—
805	C₄×D₄	C₂³×C₃	1	3	yes	—
806	C₄×D₄	C₂³×C₃	1	6	yes	—
807	C₄×D₄	C₂³×C₃	1	6	yes	—
808	C₄×D₄	C₂³×C₃	1	6	yes	—
809	C₄×D₄	C₂³×C₃	1	6	yes	—
810	C₄×D₄	C₂³×C₃	1	6	yes	—
811	C₄×D₄	C₂³×C₃	1	3	yes	—
812	C₄×D₄	C₂³×C₃	1	6	yes	—
813	C₄×D₄	C₂³×C₃	1	3	yes	—
814	C₄×D₄	C₂³×C₃	1	6	yes	—
815	C₄×D₄	C₂³×C₃	1	6	yes	—
816	C₄×D₄	C₂³×C₃	1	6	yes	—
817	C₄×D₄	C₂³×C₃	1	6	yes	—
818	C₄×D₄	C₂³×C₃	1	6	yes	—
819	C₄×D₄	C₂³×C₃	1	6	yes	—
820	C₄×D₄	C₂³×C₃	1	12	yes	—
821	C₄×D₄	C₂³×C₃	1	12	yes	—
822	C₄×D₄	C₂³×C₃	1	12	yes	—
823	C₄×D₄	C₂³×C₃	1	12	yes	—
824	C₄×D₄	C₂³×C₃	1	12	yes	—
825	C₄×D₄	C₂³×C₃	1	6	yes	—
826	C₄×D₄	C₂³×C₃	1	12	yes	—
827	#117	C₂³×C₃	1	3	yes	—
828	#117	C₂³×C₃	1	6	yes	—
829	#117	C₂³×C₃	1	6	yes	—
830	#117	C₂³×C₃	1	6	yes	—
831	#117	C₂³×C₃	1	6	yes	—
832	#117	C₂³×C₃	1	12	yes	—
833	#117	C₂³×C₃	1	6	yes	—
834	C₂×C₄⋊C₄	C₂³×C₃	1	6	yes	—
835	C₂×C₄⋊C₄	C₂³×C₃	1	6	yes	—
836	C₂×C₄⋊C₄	C₂³×C₃	1	6	yes	—
837	C₂×C₄⋊C₄	C₂³×C₃	1	12	yes	—
838	C₂×C₂²⋊C₄	C₂³×C₃	1	12	yes	—
839	C₂×C₂²⋊C₄	C₂³×C₃	1	12	yes	—
840	C₂×C₂²⋊C₄	C₂³×C₃	1	6	yes	—
841	C₂×C₂²⋊C₄	C₂³×C₃	1	6	yes	—
842	C₂×C₄²	C₂³×C₃	1	6	yes	—
843	C₂×C₄²	C₂³×C₃	1	3	yes	—
844	C₂³×C₃	—	4	6	no	—
845	C₂³×C₃	—	4	6	no	—
846	C₂³×C₃	—	4	6	no	—
847	C₂³×C₃	—	4	6	no	—
848	C₂³×C₃	—	4	6	no	—
849	C₂³×C₃	—	4	6	no	—
850	C₂³×C₃	C₂⁵	1	2	yes	—
851	C₂³×C₃	C₂⁵	1	6	yes	—
852	C₂³×C₃	C₂⁵	1	3	yes	—
853	C₂³×C₃	C₂⁵	1	6	yes	—
854	C₂³×C₃	C₂⁵	1	2	yes	—
855	C₃×Q₈	—	2	12	no	—
856	C₃×Q₈	—	2	12	no	—
857	C₃×Q₈	—	4	6	no	—
858	C₃×Q₈	—	4	3	no	—
859	C₃×Q₈	—	4	1	no	—
860	C₃×Q₈	—	4	1	no	—
861	C₃×Q₈	—	4	3	no	—
862	C₃×Q₈	—	4	6	no	—
863	C₃×Q₈	H(5,𝔽₂)	1	4	yes	—
864	C₃×D₄	—	2	12	no	—
865	C₃×D₄	—	2	6	no	—
866	C₃×D₄	—	2	12	no	—
867	C₃×D₄	—	4	6	no	—
868	C₃×D₄	—	4	3	no	—
869	C₃×D₄	—	4	12	no	—
870	C₃×D₄	—	4	6	no	—
871	C₃×D₄	—	4	6	no	—
872	C₃×D₄	—	4	12	no	—
873	C₃×D₄	—	4	12	no	—
874	C₃×D₄	—	4	1	no	—
875	C₃×D₄	—	4	2	no	—
876	C₃×D₄	—	4	6	no	—
877	C₃×D₄	—	4	6	no	—
878	C₃×D₄	—	4	6	no	—
879	C₃×D₄	—	4	6	no	—
880	C₃×D₄	—	4	2	no	—
881	C₃×D₄	—	4	1	no	—
882	C₃×D₄	—	4	6	no	—
883	C₃×D₄	—	4	6	no	—
884	C₃×D₄	—	4	6	no	—
885	C₃×D₄	—	4	6	no	—
886	C₃×D₄	—	4	6	no	—
887	C₃×D₄	—	4	3	no	—
888	C₂×C₃×C₄	—	2	12	no	—
889	C₂×C₃×C₄	—	2	12	no	—
890	C₂×C₃×C₄	—	2	12	no	—
891	C₂×C₃×C₄	—	2	6	no	—
892	C₂×C₃×C₄	—	2	12	no	—
893	C₂×C₃×C₄	—	4	2	no	—
894	C₂×C₃×C₄	—	4	6	no	—
895	C₂×C₃×C₄	—	4	6	no	—
896	C₂×C₃×C₄	—	4	3	no	—
897	C₂×C₃×C₄	—	4	2	no	—
898	C₂×C₃×C₄	—	4	12	no	—
899	C₂×C₃×C₄	—	4	12	no	—
900	C₂×C₃×C₄	—	4	6	no	—
901	C₂×C₃×C₄	—	4	12	no	—
902	C₂×C₃×C₄	—	4	6	no	—
903	C₂×C₃×C₄	—	4	3	no	—
904	C₂×C₃×C₄	C₂⁵	1	2	yes	—
905	C₂×C₃×C₄	C₂⁵	1	2	yes	—
906	C₂×C₃×C₄	C₂⁵	1	3	yes	—
907	C₂×C₃×C₄	C₂⁵	1	1	yes	characteristic
908	C₂×C₃×C₄	C₂⁵	1	1	yes	characteristic
909	C₂×C₃×C₄	C₂⁵	1	6	yes	—
910	C₂×C₃×C₄	C₂⁵	1	1	yes	characteristic
911	C₂×C₃×C₄	C₂⁵	1	3	yes	—
912	C₂×C₃×C₄	C₂⁵	1	6	yes	—
913	C₂×C₃×C₄	C₂⁵	1	6	yes	—
914	C₂×C₃×C₄	C₂⁵	1	6	yes	—
915	C₂×C₃×C₄	C₂⁵	1	2	yes	—
916	C₂×C₃×C₄	C₂⁵	1	2	yes	—
917	C₂×C₃×C₄	C₂⁵	1	3	yes	—
918	C₂⁴	C₂⁴×C₃	1	6	yes	—
919	C₂⁴	C₂⁴×C₃	1	6	yes	—
920	#41	—	2	8	no	—
921	#41	—	2	8	no	—
922	#41	—	2	4	no	—
923	#41	—	4	6	no	—
924	#41	—	4	12	no	—
925	#41	—	4	6	no	—
926	#41	—	4	12	no	—
927	#41	—	4	12	no	—
928	#41	—	4	12	no	—
929	#41	—	4	12	no	—
930	#41	—	4	12	no	—
931	#41	—	8	12	no	—
932	#41	—	8	6	no	—
933	C₂×Q₈	—	2	8	no	—
934	C₂×Q₈	—	2	8	no	—
935	C₂×Q₈	—	4	12	no	—
936	C₂×Q₈	—	4	6	no	—
937	C₂×Q₈	C₂⁴×C₃	1	6	yes	—
938	C₂×Q₈	C₂⁴×C₃	1	6	yes	—
939	C₂×Q₈	C₂⁴×C₃	1	1	yes	characteristic
940	C₂×Q₈	C₂⁴×C₃	1	3	yes	—
941	C₂×Q₈	C₂⁴×C₃	1	6	yes	—
942	C₂×Q₈	C₂⁴×C₃	1	6	yes	—
943	C₂×Q₈	C₂⁴×C₃	1	1	yes	characteristic
944	C₂×Q₈	C₂⁴×C₃	1	3	yes	—
945	C₂×Q₈	C₂⁴×C₃	1	1	yes	characteristic
946	C₂×D₄	—	4	12	no	—
947	C₂×D₄	—	4	12	no	—
948	C₂×D₄	—	4	6	no	—
949	C₂×D₄	—	8	12	no	—
950	C₂×D₄	C₂⁴×C₃	1	6	yes	—
951	C₂×D₄	C₂⁴×C₃	1	3	yes	—
952	C₂×D₄	C₂⁴×C₃	1	6	yes	—
953	C₂×D₄	C₂⁴×C₃	1	1	yes	characteristic
954	C₂×D₄	C₂⁴×C₃	1	6	yes	—
955	C₂×D₄	C₂⁴×C₃	1	6	yes	—
956	C₂×D₄	C₂⁴×C₃	1	2	yes	—
957	C₂×D₄	C₂⁴×C₃	1	6	yes	—
958	C₂×D₄	C₂⁴×C₃	1	6	yes	—
959	C₂×D₄	C₂⁴×C₃	1	6	yes	—
960	C₂×D₄	C₂⁴×C₃	1	6	yes	—
961	C₂×D₄	C₂⁴×C₃	1	3	yes	—
962	C₂×D₄	C₂⁴×C₃	1	12	yes	—
963	C₂×D₄	C₂⁴×C₃	1	12	yes	—
964	C₂×D₄	C₂⁴×C₃	1	6	yes	—
965	C₂×D₄	C₂⁴×C₃	1	6	yes	—
966	C₂×D₄	C₂⁴×C₃	1	6	yes	—
967	C₂×D₄	C₂⁴×C₃	1	2	yes	—
968	C₂×D₄	C₂⁴×C₃	1	6	yes	—
969	C₂×D₄	C₂⁴×C₃	1	12	yes	—
970	C₂×D₄	C₂⁴×C₃	1	3	yes	—
971	C₂×D₄	C₂⁴×C₃	1	6	yes	—
972	C₂×D₄	C₂⁴×C₃	1	6	yes	—
973	C₂×D₄	C₂⁴×C₃	1	1	yes	characteristic
974	C₂²×C₄	—	4	12	no	—
975	C₂²×C₄	C₂⁴×C₃	1	6	yes	—
976	C₂²×C₄	C₂⁴×C₃	1	3	yes	—
977	C₂²×C₄	C₂⁴×C₃	1	6	yes	—
978	C₂²×C₄	C₂⁴×C₃	1	6	yes	—
979	C₂²×C₄	C₂⁴×C₃	1	6	yes	—
980	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
981	C₂²×C₄	C₂⁴×C₃	1	3	yes	—
982	C₂²×C₄	C₂⁴×C₃	1	3	yes	—
983	C₂²×C₄	C₂⁴×C₃	1	6	yes	—
984	C₂²×C₄	C₂⁴×C₃	1	6	yes	—
985	C₂²×C₄	C₂⁴×C₃	1	6	yes	—
986	C₂²×C₄	C₂⁴×C₃	1	12	yes	—
987	C₂²×C₄	C₂⁴×C₃	1	12	yes	—
988	C₂²×C₄	C₂⁴×C₃	1	12	yes	—
989	C₂²×C₄	C₂⁴×C₃	1	6	yes	—
990	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
991	C₄⋊C₄	C₂⁴×C₃	1	6	yes	—
992	C₄⋊C₄	C₂⁴×C₃	1	3	yes	—
993	C₄⋊C₄	C₂⁴×C₃	1	6	yes	—
994	C₄⋊C₄	C₂⁴×C₃	1	6	yes	—
995	C₄⋊C₄	C₂⁴×C₃	1	6	yes	—
996	C₄⋊C₄	C₂⁴×C₃	1	6	yes	—
997	C₄⋊C₄	C₂⁴×C₃	1	6	yes	—
998	C₄⋊C₄	C₂⁴×C₃	1	6	yes	—
999	C₄⋊C₄	C₂⁴×C₃	1	12	yes	—
1000	C₄⋊C₄	C₂⁴×C₃	1	12	yes	—
1001	C₄⋊C₄	C₂⁴×C₃	1	3	yes	—
1002	C₄⋊C₄	C₂⁴×C₃	1	2	yes	—
1003	C₄⋊C₄	C₂⁴×C₃	1	2	yes	—
1004	C₄⋊C₄	C₂⁴×C₃	1	3	yes	—
1005	C₄⋊C₄	C₂⁴×C₃	1	6	yes	—
1006	C₄⋊C₄	C₂⁴×C₃	1	3	yes	—
1007	C₄⋊C₄	C₂⁴×C₃	1	6	yes	—
1008	C₄⋊C₄	C₂⁴×C₃	1	6	yes	—
1009	C₄⋊C₄	C₂⁴×C₃	1	6	yes	—
1010	C₄⋊C₄	C₂⁴×C₃	1	6	yes	—
1011	C₄⋊C₄	C₂⁴×C₃	1	2	yes	—
1012	C₄⋊C₄	C₂⁴×C₃	1	6	yes	—
1013	C₄⋊C₄	C₂⁴×C₃	1	6	yes	—
1014	C₄⋊C₄	C₂⁴×C₃	1	1	yes	characteristic
1015	C₄⋊C₄	C₂⁴×C₃	1	2	yes	—
1016	C₄⋊C₄	C₂⁴×C₃	1	6	yes	—
1017	C₄⋊C₄	C₂⁴×C₃	1	6	yes	—
1018	C₄⋊C₄	C₂⁴×C₃	1	1	yes	characteristic
1019	C₂²⋊C₄	C₂⁴×C₃	1	12	yes	—
1020	C₂²⋊C₄	C₂⁴×C₃	1	6	yes	—
1021	C₂²⋊C₄	C₂⁴×C₃	1	6	yes	—
1022	C₂²⋊C₄	C₂⁴×C₃	1	6	yes	—
1023	C₂²⋊C₄	C₂⁴×C₃	1	6	yes	—
1024	C₂²⋊C₄	C₂⁴×C₃	1	12	yes	—
1025	C₂²⋊C₄	C₂⁴×C₃	1	6	yes	—
1026	C₂²⋊C₄	C₂⁴×C₃	1	6	yes	—
1027	C₂²⋊C₄	C₂⁴×C₃	1	12	yes	—
1028	C₂²⋊C₄	C₂⁴×C₃	1	12	yes	—
1029	C₂²⋊C₄	C₂⁴×C₃	1	6	yes	—
1030	C₂²⋊C₄	C₂⁴×C₃	1	2	yes	—
1031	C₂²⋊C₄	C₂⁴×C₃	1	6	yes	—
1032	C₂²⋊C₄	C₂⁴×C₃	1	6	yes	—
1033	C₂²⋊C₄	C₂⁴×C₃	1	6	yes	—
1034	C₂²⋊C₄	C₂⁴×C₃	1	6	yes	—
1035	C₂²⋊C₄	C₂⁴×C₃	1	6	yes	—
1036	C₂²⋊C₄	C₂⁴×C₃	1	6	yes	—
1037	C₂²⋊C₄	C₂⁴×C₃	1	2	yes	—
1038	C₂²⋊C₄	C₂⁴×C₃	1	2	yes	—
1039	C₂²⋊C₄	C₂⁴×C₃	1	6	yes	—
1040	C₂²⋊C₄	C₂⁴×C₃	1	6	yes	—
1041	C₂²⋊C₄	C₂⁴×C₃	1	6	yes	—
1042	C₂²⋊C₄	C₂⁴×C₃	1	12	yes	—
1043	C₂²⋊C₄	C₂⁴×C₃	1	6	yes	—
1044	C₂²⋊C₄	C₂⁴×C₃	1	6	yes	—
1045	C₂²⋊C₄	C₂⁴×C₃	1	2	yes	—
1046	C₂²⋊C₄	C₂⁴×C₃	1	6	yes	—
1047	C₂²⋊C₄	C₂⁴×C₃	1	2	yes	—
1048	C₂²⋊C₄	C₂⁴×C₃	1	2	yes	—
1049	C₄²	C₂⁴×C₃	1	1	yes	characteristic
1050	C₄²	C₂⁴×C₃	1	3	yes	—
1051	C₄²	C₂⁴×C₃	1	6	yes	—
1052	C₄²	C₂⁴×C₃	1	6	yes	—
1053	C₄²	C₂⁴×C₃	1	3	yes	—
1054	C₄²	C₂⁴×C₃	1	6	yes	—
1055	C₄²	C₂⁴×C₃	1	3	yes	—
1056	C₄²	C₂⁴×C₃	1	6	yes	—
1057	C₄²	C₂⁴×C₃	1	12	yes	—
1058	C₂²×C₃	—	2	2	no	—
1059	C₂²×C₃	—	2	2	no	—
1060	C₂²×C₃	—	2	6	no	—
1061	C₂²×C₃	—	2	3	no	—
1062	C₂²×C₃	—	2	6	no	—
1063	C₂²×C₃	—	2	2	no	—
1064	C₂²×C₃	—	2	6	no	—
1065	C₂²×C₃	—	2	6	no	—
1066	C₂²×C₃	—	2	3	no	—
1067	C₂²×C₃	—	2	2	no	—
1068	C₂²×C₃	—	2	2	no	—
1069	C₂²×C₃	—	2	3	no	—
1070	C₂²×C₃	—	2	6	no	—
1071	C₂²×C₃	—	2	2	no	—
1072	C₂²×C₃	—	2	6	no	—
1073	C₂²×C₃	—	8	12	no	—
1074	C₂²×C₃	—	16	6	no	—
1075	C₂²×C₃	C₂⁶	1	1	yes	characteristic
1076	C₃×C₄	—	2	2	no	—
1077	C₃×C₄	—	2	2	no	—
1078	C₃×C₄	—	2	1	no	—
1079	C₃×C₄	—	2	6	no	—
1080	C₃×C₄	—	2	6	no	—
1081	C₃×C₄	—	2	6	no	—
1082	C₃×C₄	—	2	3	no	—
1083	C₃×C₄	—	2	6	no	—
1084	C₃×C₄	—	2	1	no	—
1085	C₃×C₄	—	2	1	no	—
1086	C₃×C₄	—	2	3	no	—
1087	C₃×C₄	—	2	2	no	—
1088	C₃×C₄	—	2	2	no	—
1089	C₃×C₄	C₂×H(5,𝔽₂)	1	6	yes	—
1090	C₂³	—	4	6	no	—
1091	C₂³	—	4	6	no	—
1092	C₂³	—	4	6	no	—
1093	C₂³	—	4	6	no	—
1094	C₂³	—	4	6	no	—
1095	C₂³	—	4	6	no	—
1096	C₂³	C₂⁵×C₃	1	2	yes	—
1097	C₂³	C₂⁵×C₃	1	6	yes	—
1098	C₂³	C₂⁵×C₃	1	3	yes	—
1099	C₂³	C₂⁵×C₃	1	6	yes	—
1100	C₂³	C₂⁵×C₃	1	2	yes	—
1101	Q₈	—	2	12	no	—
1102	Q₈	—	2	12	no	—
1103	Q₈	—	4	6	no	—
1104	Q₈	—	4	3	no	—
1105	Q₈	—	4	1	no	—
1106	Q₈	—	4	3	no	—
1107	Q₈	—	4	6	no	—
1108	Q₈	—	4	1	no	—
1109	Q₈	C₃×H(5,𝔽₂)	1	4	yes	—
1110	D₄	—	2	12	no	—
1111	D₄	—	2	6	no	—
1112	D₄	—	2	12	no	—
1113	D₄	—	4	6	no	—
1114	D₄	—	4	3	no	—
1115	D₄	—	4	12	no	—
1116	D₄	—	4	6	no	—
1117	D₄	—	4	6	no	—
1118	D₄	—	4	12	no	—
1119	D₄	—	4	12	no	—
1120	D₄	—	4	2	no	—
1121	D₄	—	4	1	no	—
1122	D₄	—	4	6	no	—
1123	D₄	—	4	6	no	—
1124	D₄	—	4	6	no	—
1125	D₄	—	4	6	no	—
1126	D₄	—	4	6	no	—
1127	D₄	—	4	3	no	—
1128	D₄	—	4	1	no	—
1129	D₄	—	4	2	no	—
1130	D₄	—	4	6	no	—
1131	D₄	—	4	6	no	—
1132	D₄	—	4	6	no	—
1133	D₄	—	4	6	no	—
1134	C₂×C₄	—	2	12	no	—
1135	C₂×C₄	—	2	12	no	—
1136	C₂×C₄	—	2	12	no	—
1137	C₂×C₄	—	2	6	no	—
1138	C₂×C₄	—	2	12	no	—
1139	C₂×C₄	—	4	2	no	—
1140	C₂×C₄	—	4	6	no	—
1141	C₂×C₄	—	4	6	no	—
1142	C₂×C₄	—	4	12	no	—
1143	C₂×C₄	—	4	12	no	—
1144	C₂×C₄	—	4	6	no	—
1145	C₂×C₄	—	4	12	no	—
1146	C₂×C₄	—	4	6	no	—
1147	C₂×C₄	—	4	3	no	—
1148	C₂×C₄	—	4	3	no	—
1149	C₂×C₄	—	4	2	no	—
1150	C₂×C₄	C₂⁵×C₃	1	2	yes	—
1151	C₂×C₄	C₂⁵×C₃	1	2	yes	—
1152	C₂×C₄	C₂⁵×C₃	1	3	yes	—
1153	C₂×C₄	C₂⁵×C₃	1	1	yes	characteristic
1154	C₂×C₄	C₂⁵×C₃	1	1	yes	characteristic
1155	C₂×C₄	C₂⁵×C₃	1	6	yes	—
1156	C₂×C₄	C₂⁵×C₃	1	1	yes	characteristic
1157	C₂×C₄	C₂⁵×C₃	1	3	yes	—
1158	C₂×C₄	C₂⁵×C₃	1	6	yes	—
1159	C₂×C₄	C₂⁵×C₃	1	6	yes	—
1160	C₂×C₄	C₂⁵×C₃	1	6	yes	—
1161	C₂×C₄	C₂⁵×C₃	1	2	yes	—
1162	C₂×C₄	C₂⁵×C₃	1	2	yes	—
1163	C₂×C₄	C₂⁵×C₃	1	3	yes	—
1164	C₂×C₃	—	4	2	no	—
1165	C₂×C₃	—	4	6	no	—
1166	C₂×C₃	—	4	2	no	—
1167	C₂×C₃	—	4	6	no	—
1168	C₂×C₃	—	4	3	no	—
1169	C₂×C₃	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
1170	C₂×C₃	H(7,𝔽₂)	1	1	yes	characteristic
1171	C₂×C₃	2₋¹⁺⁶	1	1	yes	characteristic
1172	C₂²	—	2	2	no	—
1173	C₂²	—	2	2	no	—
1174	C₂²	—	2	6	no	—
1175	C₂²	—	2	3	no	—
1176	C₂²	—	2	6	no	—
1177	C₂²	—	2	2	no	—
1178	C₂²	—	2	6	no	—
1179	C₂²	—	2	6	no	—
1180	C₂²	—	2	3	no	—
1181	C₂²	—	2	2	no	—
1182	C₂²	—	2	2	no	—
1183	C₂²	—	2	3	no	—
1184	C₂²	—	2	6	no	—
1185	C₂²	—	2	2	no	—
1186	C₂²	—	2	6	no	—
1187	C₂²	—	8	12	no	—
1188	C₂²	—	16	6	no	—
1189	C₂²	C₂⁶×C₃	1	1	yes	characteristic
1190	C₄	—	2	2	no	—
1191	C₄	—	2	2	no	—
1192	C₄	—	2	1	no	—
1193	C₄	—	2	6	no	—
1194	C₄	—	2	6	no	—
1195	C₄	—	2	6	no	—
1196	C₄	—	2	3	no	—
1197	C₄	—	2	6	no	—
1198	C₄	—	2	1	no	—
1199	C₄	—	2	1	no	—
1200	C₄	—	2	3	no	—
1201	C₄	—	2	2	no	—
1202	C₄	—	2	2	no	—
1203	C₄	C₂×C₃×H(5,𝔽₂)	1	6	yes	—
1204	C₃	#63052	1	1	yes	characteristic, direct product factor, Sylow
1205	C₂	—	4	2	no	—
1206	C₂	—	4	6	no	—
1207	C₂	—	4	6	no	—
1208	C₂	—	4	3	no	—
1209	C₂	—	4	2	no	—
1210	C₂	C₂²×C₃×H(5,𝔽₂)	1	1	yes	characteristic
1211	C₂	C₃×H(7,𝔽₂)	1	1	yes	characteristic
1212	C₂	C₃×2₋¹⁺⁶	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃	C₂⁶
commutator, Frattini, cosocle	C₂²	C₂⁶×C₃
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃×#3562	C₂	semidirect
2. C₃×#3561	C₂	semidirect
3. C₃×#3558	C₂	semidirect
4. C₃×#3548	C₂	semidirect
5. C₃×#3546	C₂	semidirect
6. C₃×#3546	C₂	semidirect
7. C₃×#3542	C₂	semidirect
8. C₃×#3541	C₂	semidirect
9. C₃×#3536	C₂	semidirect
10. C₃×#3529	C₂	semidirect
11. C₃×#3522	C₂	semidirect
12. C₃×#3518	C₂	semidirect
13. C₃×#3517	C₂	semidirect
14. C₃×#3516	C₂	semidirect
15. C₃×#3500	C₂	semidirect
16. C₃×#3497	C₂	semidirect
17. C₃×#3489	C₂	semidirect
18. C₃×#3488	C₂	semidirect
19. C₃×#3487	C₂	semidirect
20. #63052	C₃	direct (N × H)
21. C₂×C₃×2₋¹⁺⁴	C₂²	semidirect
22. C₂×C₃×2₋¹⁺⁴	C₂²	semidirect
24. C₂²×C₃×#41	C₂²	semidirect
25. C₃×#563	C₂²	semidirect
26. C₃×#563	C₂²	semidirect
27. C₃×#562	C₂²	semidirect
28. C₃×#562	C₂²	semidirect
29. C₃×#562	C₂²	semidirect
30. C₃×#562	C₂²	semidirect
31. C₃×#562	C₂²	semidirect
32. C₃×#562	C₂²	semidirect
33. C₃×H(3,𝔽₄)	C₂²	semidirect
34. C₃×#560	C₂²	semidirect
35. C₃×#560	C₂²	semidirect
36. C₃×#560	C₂²	semidirect
37. C₃×#560	C₂²	semidirect
38. C₃×#559	C₂²	semidirect
39. C₃×Q₈²	C₂²	semidirect
40. C₃×#557	C₂²	semidirect
41. C₃×#556	C₂²	semidirect
42. C₃×#556	C₂²	semidirect
43. C₃×#556	C₂²	semidirect
44. C₃×#555	C₂²	semidirect
45. C₃×#554	C₂²	semidirect
46. C₃×#554	C₂²	semidirect
47. C₃×#554	C₂²	semidirect
48. C₃×#553	C₂²	semidirect
49. C₃×#553	C₂²	semidirect
50. C₃×#553	C₂²	semidirect
51. C₃×#552	C₂²	semidirect
52. C₃×#551	C₂²	semidirect
54. C₃×#550	C₂²	semidirect
55. C₃×#550	C₂²	semidirect
56. C₃×#550	C₂²	semidirect
57. C₃×#550	C₂²	semidirect
58. C₃×#550	C₂²	semidirect
59. C₃×#550	C₂²	semidirect
60. C₃×#550	C₂²	semidirect
61. C₃×D₄×Q₈	C₂²	semidirect
62. C₃×D₄×Q₈	C₂²	semidirect
63. C₃×D₄×Q₈	C₂²	semidirect
65. C₃×#548	C₂²	semidirect
66. C₃×#548	C₂²	semidirect
67. C₃×#548	C₂²	semidirect
68. C₃×#548	C₂²	semidirect
69. C₃×#548	C₂²	semidirect
70. C₃×#548	C₂²	semidirect
71. C₃×#548	C₂²	semidirect
72. C₃×#548	C₂²	semidirect
73. C₃×#547	C₂²	semidirect
74. C₃×#547	C₂²	semidirect
75. C₃×#547	C₂²	semidirect
76. C₃×#547	C₂²	semidirect
77. C₃×#547	C₂²	semidirect
78. C₃×#546	C₂²	semidirect
79. C₃×#546	C₂²	semidirect
80. C₃×#546	C₂²	semidirect
81. C₃×#546	C₂²	semidirect
82. C₃×#546	C₂²	semidirect
83. C₃×#546	C₂²	semidirect
84. C₃×#546	C₂²	semidirect
85. C₃×#546	C₂²	semidirect
86. C₃×D₄²	C₂²	semidirect
87. C₃×D₄²	C₂²	semidirect
88. C₃×#543	C₂²	semidirect
89. C₃×#542	C₂²	semidirect
90. C₃×#542	C₂²	semidirect
91. C₃×#542	C₂²	semidirect
92. C₃×#542	C₂²	semidirect
93. C₃×#542	C₂²	semidirect
94. C₃×#541	C₂²	semidirect
95. C₃×#540	C₂²	semidirect
96. C₃×#540	C₂²	semidirect
97. C₃×#539	C₂²	semidirect
98. C₃×#538	C₂²	semidirect
99. C₃×#538	C₂²	semidirect
100. C₃×#538	C₂²	semidirect
101. C₃×#538	C₂²	semidirect
102. C₃×#538	C₂²	semidirect
103. C₃×#537	C₂²	semidirect
104. C₃×#537	C₂²	semidirect
105. C₃×#537	C₂²	semidirect
106. C₃×#537	C₂²	semidirect
107. C₃×#537	C₂²	semidirect
108. C₃×#536	C₂²	semidirect
109. C₃×#536	C₂²	semidirect
110. C₃×#535	C₂²	semidirect
111. C₃×#535	C₂²	semidirect
112. C₃×#535	C₂²	semidirect
113. C₃×#535	C₂²	semidirect
114. C₃×#535	C₂²	semidirect
115. C₃×#534	C₂²	semidirect
116. C₃×#533	C₂²	semidirect
117. C₃×#532	C₂²	semidirect
118. C₃×#532	C₂²	semidirect
119. C₃×#532	C₂²	semidirect
120. C₃×#532	C₂²	semidirect
121. C₃×#532	C₂²	semidirect
122. C₃×#529	C₂²	semidirect
123. C₃×#529	C₂²	semidirect
124. C₃×#529	C₂²	semidirect
125. C₃×#529	C₂²	semidirect
126. C₃×#529	C₂²	semidirect
127. C₂×C₃×#124	C₂²	semidirect
128. C₃×#525	C₂²	semidirect
129. C₃×#525	C₂²	semidirect
130. C₃×#525	C₂²	semidirect
131. C₃×#525	C₂²	semidirect
132. C₂×C₃×C₂²⋊Q₈	C₂²	semidirect
133. C₂×C₃×#121	C₂²	semidirect
134. C₃×#520	C₂²	semidirect
135. C₃×#520	C₂²	semidirect
136. C₃×#519	C₂²	semidirect
137. C₃×C₄×#41	C₂²	semidirect
138. C₂×C₃×C₄×Q₈	C₂²	semidirect
139. #3562	C₂×C₃	semidirect
140. #3561	C₂×C₃	semidirect
141. #3558	C₂×C₃	semidirect
142. #3548	C₂×C₃	semidirect
143. #3546	C₂×C₃	semidirect
144. #3546	C₂×C₃	semidirect
145. #3542	C₂×C₃	semidirect
146. #3541	C₂×C₃	semidirect
147. #3536	C₂×C₃	semidirect
148. #3529	C₂×C₃	semidirect
149. #3522	C₂×C₃	semidirect
150. #3518	C₂×C₃	semidirect
151. #3517	C₂×C₃	semidirect
152. #3516	C₂×C₃	semidirect
153. #3500	C₂×C₃	semidirect
154. #3497	C₂×C₃	semidirect
155. #3489	C₂×C₃	semidirect
156. #3488	C₂×C₃	semidirect
157. #3487	C₂×C₃	semidirect
372. C₂×2₋¹⁺⁴	C₂²×C₃	semidirect
373. C₂×2₋¹⁺⁴	C₂²×C₃	semidirect
375. C₂²×#41	C₂²×C₃	semidirect
376. #563	C₂²×C₃	semidirect
377. #563	C₂²×C₃	semidirect
378. #562	C₂²×C₃	semidirect
379. #562	C₂²×C₃	semidirect
380. #562	C₂²×C₃	semidirect
381. #562	C₂²×C₃	semidirect
382. #562	C₂²×C₃	semidirect
383. #562	C₂²×C₃	semidirect
384. H(3,𝔽₄)	C₂²×C₃	semidirect
385. #560	C₂²×C₃	semidirect
386. #560	C₂²×C₃	semidirect
387. #560	C₂²×C₃	semidirect
388. #560	C₂²×C₃	semidirect
389. #559	C₂²×C₃	semidirect
390. Q₈²	C₂²×C₃	semidirect
391. #557	C₂²×C₃	semidirect
392. #556	C₂²×C₃	semidirect
393. #556	C₂²×C₃	semidirect
394. #556	C₂²×C₃	semidirect
395. #555	C₂²×C₃	semidirect
396. #554	C₂²×C₃	semidirect
397. #554	C₂²×C₃	semidirect
398. #554	C₂²×C₃	semidirect
399. #553	C₂²×C₃	semidirect
400. #553	C₂²×C₃	semidirect
401. #553	C₂²×C₃	semidirect
402. #552	C₂²×C₃	semidirect
403. #551	C₂²×C₃	semidirect
405. #550	C₂²×C₃	semidirect
406. #550	C₂²×C₃	semidirect
407. #550	C₂²×C₃	semidirect
408. #550	C₂²×C₃	semidirect
409. #550	C₂²×C₃	semidirect
410. #550	C₂²×C₃	semidirect
411. #550	C₂²×C₃	semidirect
412. D₄×Q₈	C₂²×C₃	semidirect
413. D₄×Q₈	C₂²×C₃	semidirect
414. D₄×Q₈	C₂²×C₃	semidirect
416. #548	C₂²×C₃	semidirect
417. #548	C₂²×C₃	semidirect
418. #548	C₂²×C₃	semidirect
419. #548	C₂²×C₃	semidirect
420. #548	C₂²×C₃	semidirect
421. #548	C₂²×C₃	semidirect
422. #548	C₂²×C₃	semidirect
423. #548	C₂²×C₃	semidirect
424. #547	C₂²×C₃	semidirect
425. #547	C₂²×C₃	semidirect
426. #547	C₂²×C₃	semidirect
427. #547	C₂²×C₃	semidirect
428. #547	C₂²×C₃	semidirect
429. #546	C₂²×C₃	semidirect
430. #546	C₂²×C₃	semidirect
431. #546	C₂²×C₃	semidirect
432. #546	C₂²×C₃	semidirect
433. #546	C₂²×C₃	semidirect
434. #546	C₂²×C₃	semidirect
435. #546	C₂²×C₃	semidirect
436. #546	C₂²×C₃	semidirect
437. D₄²	C₂²×C₃	semidirect
438. D₄²	C₂²×C₃	semidirect
439. #543	C₂²×C₃	semidirect
440. #542	C₂²×C₃	semidirect
441. #542	C₂²×C₃	semidirect
442. #542	C₂²×C₃	semidirect
443. #542	C₂²×C₃	semidirect
444. #542	C₂²×C₃	semidirect
445. #541	C₂²×C₃	semidirect
446. #540	C₂²×C₃	semidirect
447. #540	C₂²×C₃	semidirect
448. #539	C₂²×C₃	semidirect
449. #538	C₂²×C₃	semidirect
450. #538	C₂²×C₃	semidirect
451. #538	C₂²×C₃	semidirect
452. #538	C₂²×C₃	semidirect
453. #538	C₂²×C₃	semidirect
454. #537	C₂²×C₃	semidirect
455. #537	C₂²×C₃	semidirect
456. #537	C₂²×C₃	semidirect
457. #537	C₂²×C₃	semidirect
458. #537	C₂²×C₃	semidirect
459. #536	C₂²×C₃	semidirect
460. #536	C₂²×C₃	semidirect
461. #535	C₂²×C₃	semidirect
462. #535	C₂²×C₃	semidirect
463. #535	C₂²×C₃	semidirect
464. #535	C₂²×C₃	semidirect
465. #535	C₂²×C₃	semidirect
466. #534	C₂²×C₃	semidirect
467. #533	C₂²×C₃	semidirect
468. #532	C₂²×C₃	semidirect
469. #532	C₂²×C₃	semidirect
470. #532	C₂²×C₃	semidirect
471. #532	C₂²×C₃	semidirect
472. #532	C₂²×C₃	semidirect
473. #529	C₂²×C₃	semidirect
474. #529	C₂²×C₃	semidirect
475. #529	C₂²×C₃	semidirect
476. #529	C₂²×C₃	semidirect
477. #529	C₂²×C₃	semidirect
478. C₂×#124	C₂²×C₃	semidirect
479. #525	C₂²×C₃	semidirect
480. #525	C₂²×C₃	semidirect
481. #525	C₂²×C₃	semidirect
482. #525	C₂²×C₃	semidirect
483. C₂×C₂²⋊Q₈	C₂²×C₃	semidirect
484. C₂×#121	C₂²×C₃	semidirect
485. #520	C₂²×C₃	semidirect
486. #520	C₂²×C₃	semidirect
487. #519	C₂²×C₃	semidirect
488. C₄×#41	C₂²×C₃	semidirect
489. C₂×C₄×Q₈	C₂²×C₃	semidirect
1204. C₃	#63052	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×#3562	2
C₃×#3561	2
C₃×#3558	2
C₃×#3548	2
C₃×#3546	2
C₃×#3542	2
C₃×#3541	2
C₃×#3536	2
C₃×#3529	2
C₃×#3522	2
C₃×#3518	2
C₃×#3517	2
C₃×#3516	2
C₃×#3500	2
C₃×#3497	2
C₃×#3489	2
C₃×#3488	2
C₃×#3487	2
#63052	3

Subgroups — C3×#63052 #10681659

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#63052 #10681659