Subgroups — C₃×#63021 #10681628

Order 768.

7272 conjugacy classes of subgroups.

The subgroup lattice has 1040 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#3558	C₂	1	8	yes	maximal, complemented
2	C₃×#3554	C₂	1	4	yes	maximal, complemented
3	C₃×#3550	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#3543	C₂	1	2	yes	maximal, complemented
5	C₃×#3540	C₂	1	4	yes	maximal, complemented
6	C₃×#3533	C₂	1	8	yes	maximal, complemented
7	C₃×#3522	C₂	1	4	yes	maximal, complemented
8	C₃×#3514	C₂	1	4	yes	maximal, complemented
9	C₃×#3513	C₂	1	8	yes	maximal, complemented
10	C₃×#3508	C₂	1	2	yes	maximal, complemented
11	C₃×#3506	C₂	1	4	yes	maximal, complemented
12	C₃×#3498	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃×#3485	C₂	1	4	yes	maximal, complemented
14	C₃×#3482	C₂	1	2	yes	maximal, complemented
15	C₃×#3481	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₃×#559	C₂	1	2	yes	maximal, complemented
17	C₃×D₄×#41	C₂	1	4	yes	maximal, complemented
18	#63021	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
19	C₂×C₃×H(5,𝔽₂)	C₂²	1	2	yes	complemented
20	C₂²×C₃×#41	C₂²	1	4	yes	complemented
21	C₃×#563	C₂²	1	4	yes	complemented
22	C₃×#562	C₂²	1	16	yes	complemented
23	C₃×H(3,𝔽₄)	C₂²	1	8	yes	complemented
24	C₃×#560	C₂²	1	8	yes	complemented
25	C₃×#559	C₂²	1	1	yes	characteristic, complemented
26	C₃×#559	C₂²	1	8	yes	complemented
27	C₃×#559	C₂²	1	4	yes	complemented
28	C₃×#559	C₂²	1	8	yes	complemented
29	C₃×#559	C₂²	1	2	yes	complemented
30	C₃×#559	C₂²	1	8	yes	complemented
31	C₃×#559	C₂²	1	8	yes	complemented
32	C₃×#559	C₂²	1	4	yes	complemented
33	C₃×Q₈²	C₂²	1	2	yes	complemented
34	C₃×#557	C₂²	1	2	yes	complemented
35	C₃×#556	C₂²	1	2	yes	complemented
36	C₃×#556	C₂²	1	4	yes	complemented
37	C₃×#556	C₂²	1	4	yes	complemented
38	C₃×#555	C₂²	1	8	yes	complemented
39	C₃×#554	C₂²	1	2	yes	complemented
40	C₃×#554	C₂²	1	8	yes	complemented
41	C₃×#553	C₂²	1	4	yes	complemented
42	C₃×#553	C₂²	1	16	yes	complemented
43	C₃×#552	C₂²	1	4	yes	complemented
44	C₃×#552	C₂²	1	8	yes	complemented
45	C₃×#551	C₂²	1	4	yes	complemented
46	C₃×#551	C₂²	1	8	yes	complemented
47	C₃×#551	C₂²	1	16	yes	complemented
48	C₃×#550	C₂²	1	4	yes	complemented
49	C₃×#550	C₂²	1	4	yes	complemented
50	C₃×#550	C₂²	1	4	yes	complemented
51	C₃×D₄×Q₈	C₂²	1	4	yes	complemented
52	C₃×D₄×Q₈	C₂²	1	2	yes	complemented
53	C₃×#548	C₂²	1	8	yes	complemented
54	C₃×#548	C₂²	1	4	yes	complemented
55	C₃×#548	C₂²	1	8	yes	complemented
56	C₃×#547	C₂²	1	2	yes	complemented
57	C₃×#547	C₂²	1	8	yes	complemented
58	C₃×#547	C₂²	1	4	yes	complemented
59	C₃×#547	C₂²	1	8	yes	complemented
60	C₃×#547	C₂²	1	16	yes	complemented
61	C₃×#546	C₂²	1	8	yes	complemented
62	C₃×#546	C₂²	1	16	yes	complemented
63	C₃×#546	C₂²	1	4	yes	complemented
64	C₃×#546	C₂²	1	8	yes	complemented
65	C₃×#546	C₂²	1	16	yes	complemented
66	C₃×#546	C₂²	1	8	yes	complemented
67	C₃×#546	C₂²	1	8	yes	complemented
68	C₃×D₄²	C₂²	1	4	yes	complemented
69	C₃×D₄²	C₂²	1	8	yes	complemented
70	C₃×D₄²	C₂²	1	1	yes	characteristic, complemented
71	C₃×D₄²	C₂²	1	8	yes	complemented
72	C₃×#542	C₂²	1	8	yes	complemented
73	C₃×#542	C₂²	1	8	yes	complemented
74	C₃×#542	C₂²	1	16	yes	complemented
75	C₃×#542	C₂²	1	8	yes	complemented
76	C₃×#540	C₂²	1	8	yes	complemented
77	C₃×#540	C₂²	1	8	yes	complemented
78	C₃×#539	C₂²	1	16	yes	complemented
79	C₃×#538	C₂²	1	16	yes	complemented
80	C₃×#538	C₂²	1	16	yes	complemented
81	C₃×#538	C₂²	1	16	yes	complemented
82	C₃×#536	C₂²	1	4	yes	complemented
83	C₃×#536	C₂²	1	4	yes	complemented
84	C₃×#535	C₂²	1	4	yes	complemented
85	C₃×#535	C₂²	1	2	yes	complemented
86	C₃×#535	C₂²	1	8	yes	complemented
87	C₃×#535	C₂²	1	4	yes	complemented
88	C₃×#534	C₂²	1	8	yes	complemented
89	C₃×#534	C₂²	1	8	yes	complemented
90	C₃×#533	C₂²	1	4	yes	complemented
91	C₃×#533	C₂²	1	2	yes	complemented
92	C₃×#532	C₂²	1	1	yes	characteristic
93	C₃×#532	C₂²	1	4	yes	complemented
94	C₃×#532	C₂²	1	8	yes	complemented
95	C₃×#532	C₂²	1	2	yes	complemented
96	C₃×#532	C₂²	1	4	yes	complemented
97	C₂×C₃×#127	C₂²	1	2	yes	—
98	C₂×C₃×#127	C₂²	1	1	yes	characteristic, complemented
99	C₃×#529	C₂²	1	4	yes	complemented
100	C₃×#529	C₂²	1	8	yes	complemented
101	C₃×#529	C₂²	1	4	yes	complemented
102	C₃×#529	C₂²	1	8	yes	complemented
103	C₂×C₃×#124	C₂²	1	8	yes	complemented
104	C₃×#525	C₂²	1	8	yes	complemented
105	C₃×#525	C₂²	1	16	yes	complemented
106	C₃×#525	C₂²	1	4	yes	complemented
107	C₃×#525	C₂²	1	4	yes	complemented
108	C₂×C₃×#123	C₂²	1	8	yes	complemented
109	C₂×C₃×#123	C₂²	1	8	yes	complemented
110	C₃×#520	C₂²	1	8	yes	complemented
111	C₃×#518	C₂²	1	4	yes	complemented
112	C₃×#518	C₂²	1	4	yes	complemented
113	C₃×C₄×#41	C₂²	1	4	yes	complemented
114	C₃×C₄×#41	C₂²	1	2	yes	complemented
115	C₃×C₄×#41	C₂²	1	1	yes	characteristic, complemented
116	C₂×C₃×C₄×Q₈	C₂²	1	4	yes	complemented
117	C₂×C₃×C₄×D₄	C₂²	1	8	yes	complemented
118	C₂×C₃×C₄×D₄	C₂²	1	4	yes	complemented
119	#3558	C₂×C₃	1	8	yes	complemented
120	#3554	C₂×C₃	1	4	yes	complemented
121	#3550	C₂×C₃	1	1	yes	characteristic, complemented
122	#3543	C₂×C₃	1	2	yes	complemented
123	#3540	C₂×C₃	1	4	yes	complemented
124	#3533	C₂×C₃	1	8	yes	complemented
125	#3522	C₂×C₃	1	4	yes	complemented
126	#3514	C₂×C₃	1	4	yes	complemented
127	#3513	C₂×C₃	1	8	yes	complemented
128	#3508	C₂×C₃	1	2	yes	complemented
129	#3506	C₂×C₃	1	4	yes	complemented
130	#3498	C₂×C₃	1	1	yes	characteristic, complemented
131	#3485	C₂×C₃	1	4	yes	complemented
132	#3482	C₂×C₃	1	2	yes	complemented
133	#3481	C₂×C₃	1	1	yes	characteristic, complemented
134	C₂×#559	C₂×C₃	1	2	yes	complemented
135	D₄×#41	C₂×C₃	1	4	yes	complemented
136	C₃×H(5,𝔽₂)	—	4	8	no	—
137	C₂×C₃×#41	—	4	16	no	—
138	C₂×C₃×#41	C₂³	1	4	yes	—
139	C₂×C₃×#41	C₂³	1	1	yes	characteristic
140	C₂×C₃×#41	C₂³	1	16	yes	—
141	C₂×C₃×#41	C₂³	1	8	yes	—
142	C₂×C₃×#41	C₂³	1	2	yes	—
143	C₂×C₃×#41	C₂³	1	4	yes	—
144	C₂×C₃×#41	C₂³	1	4	yes	—
145	C₂×C₃×#41	C₂³	1	2	yes	—
146	C₂×C₃×#41	C₂³	1	8	yes	—
147	C₂²×C₃×Q₈	C₂³	1	4	yes	—
148	C₂²×C₃×Q₈	C₂³	1	4	yes	—
149	C₂²×C₃×D₄	C₂³	1	4	yes	—
150	C₂²×C₃×D₄	C₂³	1	8	yes	—
151	C₂²×C₃×D₄	C₂³	1	4	yes	—
152	C₂²×C₃×D₄	C₂³	1	8	yes	—
153	C₂²×C₃×D₄	C₂³	1	2	yes	—
154	C₂²×C₃×D₄	C₂³	1	8	yes	—
155	C₂²×C₃×D₄	C₂³	1	4	yes	—
156	C₂²×C₃×D₄	C₂³	1	4	yes	—
157	C₂³×C₃×C₄	C₂³	1	8	yes	—
158	C₂³×C₃×C₄	C₂³	1	4	yes	—
159	C₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
160	C₃×C₄⋊Q₈	C₂³	1	8	yes	—
161	C₃×C₄⋊Q₈	C₂³	1	8	yes	—
162	C₃×C₄⋊Q₈	C₂³	1	2	yes	—
163	C₃×C₄⋊Q₈	C₂³	1	2	yes	—
164	C₃×C₄⋊Q₈	C₂³	1	4	yes	—
165	C₃×C₄⋊Q₈	C₂³	1	4	yes	—
166	C₃×#127	C₂³	1	1	yes	characteristic
167	C₃×#127	C₂³	1	4	yes	—
168	C₃×#127	C₂³	1	2	yes	—
169	C₃×#127	C₂³	1	8	yes	—
170	C₃×#127	C₂³	1	4	yes	—
171	C₃×#127	C₂³	1	8	yes	—
172	C₃×#127	C₂³	1	2	yes	—
173	C₃×#126	C₂³	1	8	yes	—
174	C₃×#126	C₂³	1	16	yes	—
175	C₃×#126	C₂³	1	16	yes	—
176	C₃×#126	C₂³	1	8	yes	—
177	C₃×#126	C₂³	1	8	yes	—
178	C₃×#126	C₂³	1	8	yes	—
179	C₃×#125	C₂³	1	8	yes	—
180	C₃×#125	C₂³	1	4	yes	—
181	C₃×#125	C₂³	1	4	yes	—
182	C₃×#125	C₂³	1	4	yes	—
183	C₃×#125	C₂³	1	8	yes	—
184	C₃×#124	C₂³	1	4	yes	—
185	C₃×#124	C₂³	1	8	yes	—
186	C₃×#124	C₂³	1	8	yes	—
187	C₃×#124	C₂³	1	16	yes	—
188	C₃×#124	C₂³	1	8	yes	—
189	C₃×#124	C₂³	1	16	yes	—
190	C₃×#124	C₂³	1	4	yes	—
191	C₃×#124	C₂³	1	16	yes	—
192	C₃×#124	C₂³	1	8	yes	—
193	C₃×#124	C₂³	1	8	yes	—
194	C₃×#124	C₂³	1	16	yes	—
195	C₃×#124	C₂³	1	8	yes	—
196	C₃×#124	C₂³	1	2	yes	—
197	C₃×#124	C₂³	1	4	yes	—
198	C₃×#123	C₂³	1	4	yes	—
199	C₃×#123	C₂³	1	8	yes	—
200	C₃×#123	C₂³	1	8	yes	—
201	C₃×#123	C₂³	1	8	yes	—
202	C₃×#123	C₂³	1	16	yes	—
203	C₃×#123	C₂³	1	16	yes	—
204	C₃×#123	C₂³	1	16	yes	—
205	C₃×#123	C₂³	1	16	yes	—
206	C₃×#123	C₂³	1	16	yes	—
207	C₃×#123	C₂³	1	16	yes	—
208	C₃×#123	C₂³	1	8	yes	—
209	C₃×#123	C₂³	1	4	yes	—
210	C₃×#123	C₂³	1	8	yes	—
211	C₃×#123	C₂³	1	16	yes	—
212	C₃×#123	C₂³	1	8	yes	—
213	C₃×#123	C₂³	1	8	yes	—
214	C₃×#123	C₂³	1	8	yes	—
215	C₃×#123	C₂³	1	8	yes	—
216	C₃×C₂²⋊Q₈	C₂³	1	8	yes	—
217	C₃×C₂²⋊Q₈	C₂³	1	16	yes	—
218	C₃×C₂²⋊Q₈	C₂³	1	16	yes	—
219	C₃×C₂²⋊Q₈	C₂³	1	16	yes	—
220	C₃×C₂²⋊Q₈	C₂³	1	4	yes	—
221	C₃×C₂²⋊Q₈	C₂³	1	4	yes	—
222	C₃×C₂²⋊Q₈	C₂³	1	8	yes	—
223	C₃×C₂²⋊Q₈	C₂³	1	16	yes	—
224	C₃×C₂²⋊Q₈	C₂³	1	8	yes	—
225	C₃×C₂²⋊Q₈	C₂³	1	4	yes	—
226	C₃×C₂²⋊Q₈	C₂³	1	8	yes	—
227	C₃×C₂²⋊Q₈	C₂³	1	4	yes	—
228	C₃×C₂²⋊Q₈	C₂³	1	4	yes	—
229	C₃×C₂²⋊Q₈	C₂³	1	4	yes	—
230	C₃×#121	C₂³	1	16	yes	—
231	C₃×#121	C₂³	1	16	yes	—
232	C₃×#121	C₂³	1	16	yes	—
233	C₃×#121	C₂³	1	8	yes	—
234	C₃×#121	C₂³	1	16	yes	—
235	C₃×#121	C₂³	1	16	yes	—
236	C₃×#121	C₂³	1	8	yes	—
237	C₃×#121	C₂³	1	8	yes	—
238	C₃×#121	C₂³	1	8	yes	—
239	C₃×#121	C₂³	1	16	yes	—
240	C₃×#121	C₂³	1	4	yes	—
241	C₃×#121	C₂³	1	8	yes	—
242	C₃×#121	C₂³	1	8	yes	—
243	C₃×#121	C₂³	1	4	yes	—
244	C₃×#121	C₂³	1	4	yes	—
245	C₃×#121	C₂³	1	16	yes	—
246	C₃×#121	C₂³	1	8	yes	—
247	C₃×#121	C₂³	1	8	yes	—
248	C₃×#120	C₂³	1	4	yes	—
249	C₃×#120	C₂³	1	16	yes	—
250	C₃×#120	C₂³	1	4	yes	—
251	C₃×#120	C₂³	1	16	yes	—
252	C₃×#120	C₂³	1	8	yes	—
253	C₃×#120	C₂³	1	8	yes	—
254	C₃×#120	C₂³	1	16	yes	—
255	C₃×#120	C₂³	1	16	yes	—
256	C₃×C₄×Q₈	C₂³	1	4	yes	—
257	C₃×C₄×Q₈	C₂³	1	8	yes	—
258	C₃×C₄×Q₈	C₂³	1	2	yes	—
259	C₃×C₄×Q₈	C₂³	1	8	yes	—
260	C₃×C₄×Q₈	C₂³	1	4	yes	—
261	C₃×C₄×Q₈	C₂³	1	4	yes	—
262	C₃×C₄×Q₈	C₂³	1	8	yes	—
263	C₃×C₄×Q₈	C₂³	1	2	yes	—
264	C₃×C₄×Q₈	C₂³	1	4	yes	—
265	C₃×C₄×Q₈	C₂³	1	2	yes	—
266	C₃×C₄×Q₈	C₂³	1	4	yes	—
267	C₃×C₄×D₄	C₂³	1	4	yes	—
268	C₃×C₄×D₄	C₂³	1	8	yes	—
269	C₃×C₄×D₄	C₂³	1	16	yes	—
270	C₃×C₄×D₄	C₂³	1	8	yes	—
271	C₃×C₄×D₄	C₂³	1	4	yes	—
272	C₃×C₄×D₄	C₂³	1	16	yes	—
273	C₃×C₄×D₄	C₂³	1	8	yes	—
274	C₃×C₄×D₄	C₂³	1	8	yes	—
275	C₃×C₄×D₄	C₂³	1	8	yes	—
276	C₃×C₄×D₄	C₂³	1	16	yes	—
277	C₃×C₄×D₄	C₂³	1	8	yes	—
278	C₃×C₄×D₄	C₂³	1	2	yes	—
279	C₃×C₄×D₄	C₂³	1	8	yes	—
280	C₃×C₄×D₄	C₂³	1	8	yes	—
281	C₃×C₄×D₄	C₂³	1	4	yes	—
282	C₃×C₄×D₄	C₂³	1	2	yes	—
283	C₃×C₄×D₄	C₂³	1	4	yes	—
284	C₃×C₄×D₄	C₂³	1	4	yes	—
285	C₃×C₄×D₄	C₂³	1	4	yes	—
286	C₃×C₄×D₄	C₂³	1	8	yes	—
287	C₃×C₄×D₄	C₂³	1	2	yes	—
288	C₃×C₄×D₄	C₂³	1	4	yes	—
289	C₃×C₄×D₄	C₂³	1	8	yes	—
290	C₃×C₄×D₄	C₂³	1	8	yes	—
291	C₃×C₄×D₄	C₂³	1	16	yes	—
292	C₃×C₄×D₄	C₂³	1	8	yes	—
293	C₃×C₄×D₄	C₂³	1	16	yes	—
294	C₃×#117	C₂³	1	2	yes	—
295	C₃×#117	C₂³	1	8	yes	—
296	C₃×#117	C₂³	1	4	yes	—
297	C₃×#117	C₂³	1	2	yes	—
298	C₃×#117	C₂³	1	1	yes	characteristic
299	C₃×#117	C₂³	1	4	yes	—
300	C₃×#117	C₂³	1	4	yes	—
301	C₃×#117	C₂³	1	4	yes	—
302	C₃×#117	C₂³	1	4	yes	—
303	C₃×#117	C₂³	1	8	yes	—
304	C₃×#117	C₂³	1	16	yes	—
305	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
306	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
307	C₂×C₃×C₄⋊C₄	C₂³	1	8	yes	—
308	C₂×C₃×C₄⋊C₄	C₂³	1	16	yes	—
309	C₂×C₃×C₂²⋊C₄	C₂³	1	16	yes	—
310	C₂×C₃×C₂²⋊C₄	C₂³	1	8	yes	—
311	C₂×C₃×C₂²⋊C₄	C₂³	1	8	yes	—
312	C₂×C₃×C₂²⋊C₄	C₂³	1	8	yes	—
313	C₂×C₃×C₂²⋊C₄	C₂³	1	16	yes	—
314	C₂×C₃×C₄²	C₂³	1	8	yes	—
315	C₂×C₃×C₄²	C₂³	1	4	yes	—
316	C₂×C₃×C₄²	C₂³	1	2	yes	—
317	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
318	C₂×H(5,𝔽₂)	C₂²×C₃	1	2	yes	complemented
319	C₂²×#41	C₂²×C₃	1	4	yes	complemented
320	#563	C₂²×C₃	1	4	yes	complemented
321	#562	C₂²×C₃	1	16	yes	complemented
322	H(3,𝔽₄)	C₂²×C₃	1	8	yes	complemented
323	#560	C₂²×C₃	1	8	yes	complemented
324	#559	C₂²×C₃	1	1	yes	characteristic, complemented
325	#559	C₂²×C₃	1	8	yes	complemented
326	#559	C₂²×C₃	1	4	yes	complemented
327	#559	C₂²×C₃	1	8	yes	complemented
328	#559	C₂²×C₃	1	2	yes	complemented
329	#559	C₂²×C₃	1	8	yes	complemented
330	#559	C₂²×C₃	1	8	yes	complemented
331	#559	C₂²×C₃	1	4	yes	complemented
332	Q₈²	C₂²×C₃	1	2	yes	complemented
333	#557	C₂²×C₃	1	2	yes	complemented
334	#556	C₂²×C₃	1	2	yes	complemented
335	#556	C₂²×C₃	1	4	yes	complemented
336	#556	C₂²×C₃	1	4	yes	complemented
337	#555	C₂²×C₃	1	8	yes	complemented
338	#554	C₂²×C₃	1	2	yes	complemented
339	#554	C₂²×C₃	1	8	yes	complemented
340	#553	C₂²×C₃	1	4	yes	complemented
341	#553	C₂²×C₃	1	16	yes	complemented
342	#552	C₂²×C₃	1	4	yes	complemented
343	#552	C₂²×C₃	1	8	yes	complemented
344	#551	C₂²×C₃	1	4	yes	complemented
345	#551	C₂²×C₃	1	8	yes	complemented
346	#551	C₂²×C₃	1	16	yes	complemented
347	#550	C₂²×C₃	1	4	yes	complemented
348	#550	C₂²×C₃	1	4	yes	complemented
349	#550	C₂²×C₃	1	4	yes	complemented
350	D₄×Q₈	C₂²×C₃	1	4	yes	complemented
351	D₄×Q₈	C₂²×C₃	1	2	yes	complemented
352	#548	C₂²×C₃	1	8	yes	complemented
353	#548	C₂²×C₃	1	4	yes	complemented
354	#548	C₂²×C₃	1	8	yes	complemented
355	#547	C₂²×C₃	1	2	yes	complemented
356	#547	C₂²×C₃	1	8	yes	complemented
357	#547	C₂²×C₃	1	4	yes	complemented
358	#547	C₂²×C₃	1	8	yes	complemented
359	#547	C₂²×C₃	1	16	yes	complemented
360	#546	C₂²×C₃	1	8	yes	complemented
361	#546	C₂²×C₃	1	16	yes	complemented
362	#546	C₂²×C₃	1	4	yes	complemented
363	#546	C₂²×C₃	1	8	yes	complemented
364	#546	C₂²×C₃	1	16	yes	complemented
365	#546	C₂²×C₃	1	8	yes	complemented
366	#546	C₂²×C₃	1	8	yes	complemented
367	D₄²	C₂²×C₃	1	4	yes	complemented
368	D₄²	C₂²×C₃	1	8	yes	complemented
369	D₄²	C₂²×C₃	1	1	yes	characteristic, complemented
370	D₄²	C₂²×C₃	1	8	yes	complemented
371	#542	C₂²×C₃	1	8	yes	complemented
372	#542	C₂²×C₃	1	8	yes	complemented
373	#542	C₂²×C₃	1	16	yes	complemented
374	#542	C₂²×C₃	1	8	yes	complemented
375	#540	C₂²×C₃	1	8	yes	complemented
376	#540	C₂²×C₃	1	8	yes	complemented
377	#539	C₂²×C₃	1	16	yes	complemented
378	#538	C₂²×C₃	1	16	yes	complemented
379	#538	C₂²×C₃	1	16	yes	complemented
380	#538	C₂²×C₃	1	16	yes	complemented
381	#536	C₂²×C₃	1	4	yes	complemented
382	#536	C₂²×C₃	1	4	yes	complemented
383	#535	C₂²×C₃	1	4	yes	complemented
384	#535	C₂²×C₃	1	2	yes	complemented
385	#535	C₂²×C₃	1	8	yes	complemented
386	#535	C₂²×C₃	1	4	yes	complemented
387	#534	C₂²×C₃	1	8	yes	complemented
388	#534	C₂²×C₃	1	8	yes	complemented
389	#533	C₂²×C₃	1	4	yes	complemented
390	#533	C₂²×C₃	1	2	yes	complemented
391	#532	C₂²×C₃	1	1	yes	characteristic
392	#532	C₂²×C₃	1	4	yes	complemented
393	#532	C₂²×C₃	1	8	yes	complemented
394	#532	C₂²×C₃	1	2	yes	complemented
395	#532	C₂²×C₃	1	4	yes	complemented
396	C₂×#127	C₂²×C₃	1	2	yes	—
397	C₂×#127	C₂²×C₃	1	1	yes	characteristic, complemented
398	#529	C₂²×C₃	1	4	yes	complemented
399	#529	C₂²×C₃	1	8	yes	complemented
400	#529	C₂²×C₃	1	4	yes	complemented
401	#529	C₂²×C₃	1	8	yes	complemented
402	C₂×#124	C₂²×C₃	1	8	yes	complemented
403	#525	C₂²×C₃	1	8	yes	complemented
404	#525	C₂²×C₃	1	16	yes	complemented
405	#525	C₂²×C₃	1	4	yes	complemented
406	#525	C₂²×C₃	1	4	yes	complemented
407	C₂×#123	C₂²×C₃	1	8	yes	complemented
408	C₂×#123	C₂²×C₃	1	8	yes	complemented
409	#520	C₂²×C₃	1	8	yes	complemented
410	#518	C₂²×C₃	1	4	yes	complemented
411	#518	C₂²×C₃	1	4	yes	complemented
412	C₄×#41	C₂²×C₃	1	4	yes	complemented
413	C₄×#41	C₂²×C₃	1	2	yes	complemented
414	C₄×#41	C₂²×C₃	1	1	yes	characteristic, complemented
415	C₂×C₄×Q₈	C₂²×C₃	1	4	yes	complemented
416	C₂×C₄×D₄	C₂²×C₃	1	8	yes	complemented
417	C₂×C₄×D₄	C₂²×C₃	1	4	yes	complemented
418	C₂⁴×C₃	C₂⁴	1	8	yes	—
419	C₂⁴×C₃	C₂⁴	1	4	yes	—
420	C₂⁴×C₃	C₂⁴	1	4	yes	—
421	C₃×#41	—	2	16	no	—
422	C₃×#41	—	2	4	no	—
423	C₃×#41	—	4	4	no	—
424	C₃×#41	—	4	32	no	—
425	C₃×#41	—	4	8	no	—
426	C₃×#41	—	4	16	no	—
427	C₃×#41	—	4	4	no	—
428	C₃×#41	—	4	16	no	—
429	C₃×#41	—	4	8	no	—
430	C₂×C₃×Q₈	—	4	8	no	—
431	C₂×C₃×Q₈	—	4	8	no	—
432	C₂×C₃×Q₈	C₂⁴	1	2	yes	—
433	C₂×C₃×Q₈	C₂⁴	1	4	yes	—
434	C₂×C₃×Q₈	C₂⁴	1	4	yes	—
435	C₂×C₃×Q₈	C₂⁴	1	1	yes	characteristic
436	C₂×C₃×Q₈	C₂⁴	1	8	yes	—
437	C₂×C₃×Q₈	C₂⁴	1	8	yes	—
438	C₂×C₃×Q₈	C₂⁴	1	2	yes	—
439	C₂×C₃×D₄	—	2	16	no	—
440	C₂×C₃×D₄	—	4	16	no	—
441	C₂×C₃×D₄	—	4	8	no	—
442	C₂×C₃×D₄	—	4	8	no	—
443	C₂×C₃×D₄	—	4	4	no	—
444	C₂×C₃×D₄	—	4	8	no	—
445	C₂×C₃×D₄	—	4	16	no	—
446	C₂×C₃×D₄	—	4	16	no	—
447	C₂×C₃×D₄	C₂⁴	1	4	yes	—
448	C₂×C₃×D₄	C₂⁴	1	8	yes	—
449	C₂×C₃×D₄	C₂⁴	1	2	yes	—
450	C₂×C₃×D₄	C₂⁴	1	8	yes	—
451	C₂×C₃×D₄	C₂⁴	1	8	yes	—
452	C₂×C₃×D₄	C₂⁴	1	2	yes	—
453	C₂×C₃×D₄	C₂⁴	1	4	yes	—
454	C₂×C₃×D₄	C₂⁴	1	4	yes	—
455	C₂×C₃×D₄	C₂⁴	1	16	yes	—
456	C₂×C₃×D₄	C₂⁴	1	8	yes	—
457	C₂×C₃×D₄	C₂⁴	1	16	yes	—
458	C₂×C₃×D₄	C₂⁴	1	8	yes	—
459	C₂×C₃×D₄	C₂⁴	1	4	yes	—
460	C₂×C₃×D₄	C₂⁴	1	16	yes	—
461	C₂×C₃×D₄	C₂⁴	1	2	yes	—
462	C₂×C₃×D₄	C₂⁴	1	8	yes	—
463	C₂×C₃×D₄	C₂⁴	1	4	yes	—
464	C₂×C₃×D₄	C₂⁴	1	1	yes	characteristic
465	C₂²×C₃×C₄	—	4	8	no	—
466	C₂²×C₃×C₄	—	4	16	no	—
467	C₂²×C₃×C₄	C₂⁴	1	4	yes	—
468	C₂²×C₃×C₄	C₂⁴	1	8	yes	—
469	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
470	C₂²×C₃×C₄	C₂⁴	1	4	yes	—
471	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
472	C₂²×C₃×C₄	C₂⁴	1	4	yes	—
473	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
474	C₂²×C₃×C₄	C₂⁴	1	4	yes	—
475	C₂²×C₃×C₄	C₂⁴	1	8	yes	—
476	C₂²×C₃×C₄	C₂⁴	1	4	yes	—
477	C₂²×C₃×C₄	C₂⁴	1	16	yes	—
478	C₂²×C₃×C₄	C₂⁴	1	8	yes	—
479	C₂²×C₃×C₄	C₂⁴	1	16	yes	—
480	C₂²×C₃×C₄	C₂⁴	1	8	yes	—
481	C₂²×C₃×C₄	C₂⁴	1	4	yes	—
482	C₂²×C₃×C₄	C₂⁴	1	8	yes	—
483	C₃×C₄⋊C₄	C₂⁴	1	2	yes	—
484	C₃×C₄⋊C₄	C₂⁴	1	8	yes	—
485	C₃×C₄⋊C₄	C₂⁴	1	8	yes	—
486	C₃×C₄⋊C₄	C₂⁴	1	4	yes	—
487	C₃×C₄⋊C₄	C₂⁴	1	8	yes	—
488	C₃×C₄⋊C₄	C₂⁴	1	4	yes	—
489	C₃×C₄⋊C₄	C₂⁴	1	4	yes	—
490	C₃×C₄⋊C₄	C₂⁴	1	8	yes	—
491	C₃×C₄⋊C₄	C₂⁴	1	16	yes	—
492	C₃×C₄⋊C₄	C₂⁴	1	8	yes	—
493	C₃×C₄⋊C₄	C₂⁴	1	8	yes	—
494	C₃×C₄⋊C₄	C₂⁴	1	4	yes	—
495	C₃×C₄⋊C₄	C₂⁴	1	2	yes	—
496	C₃×C₄⋊C₄	C₂⁴	1	8	yes	—
497	C₃×C₄⋊C₄	C₂⁴	1	2	yes	—
498	C₃×C₄⋊C₄	C₂⁴	1	4	yes	—
499	C₃×C₄⋊C₄	C₂⁴	1	4	yes	—
500	C₃×C₄⋊C₄	C₂⁴	1	8	yes	—
501	C₃×C₄⋊C₄	C₂⁴	1	4	yes	—
502	C₃×C₄⋊C₄	C₂⁴	1	8	yes	—
503	C₃×C₄⋊C₄	C₂⁴	1	8	yes	—
504	C₃×C₄⋊C₄	C₂⁴	1	4	yes	—
505	C₃×C₂²⋊C₄	C₂⁴	1	4	yes	—
506	C₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
507	C₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
508	C₃×C₂²⋊C₄	C₂⁴	1	4	yes	—
509	C₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
510	C₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
511	C₃×C₂²⋊C₄	C₂⁴	1	4	yes	—
512	C₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
513	C₃×C₂²⋊C₄	C₂⁴	1	4	yes	—
514	C₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
515	C₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
516	C₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
517	C₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
518	C₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
519	C₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
520	C₃×C₂²⋊C₄	C₂⁴	1	4	yes	—
521	C₃×C₂²⋊C₄	C₂⁴	1	2	yes	—
522	C₃×C₂²⋊C₄	C₂⁴	1	4	yes	—
523	C₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
524	C₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
525	C₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
526	C₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
527	C₃×C₄²	C₂⁴	1	4	yes	—
528	C₃×C₄²	C₂⁴	1	2	yes	—
529	C₃×C₄²	C₂⁴	1	1	yes	characteristic
530	C₃×C₄²	C₂⁴	1	1	yes	characteristic
531	C₃×C₄²	C₂⁴	1	4	yes	—
532	C₃×C₄²	C₂⁴	1	8	yes	—
533	C₃×C₄²	C₂⁴	1	4	yes	—
534	C₃×C₄²	C₂⁴	1	8	yes	—
535	C₃×C₄²	C₂⁴	1	4	yes	—
536	C₃×C₄²	C₂⁴	1	2	yes	—
537	C₃×C₄²	C₂⁴	1	8	yes	—
538	C₃×C₄²	C₂⁴	1	8	yes	—
539	H(5,𝔽₂)	—	4	8	no	—
540	C₂×#41	—	4	16	no	—
541	C₂×#41	C₂³×C₃	1	4	yes	—
542	C₂×#41	C₂³×C₃	1	1	yes	characteristic
543	C₂×#41	C₂³×C₃	1	2	yes	—
544	C₂×#41	C₂³×C₃	1	8	yes	—
545	C₂×#41	C₂³×C₃	1	2	yes	—
546	C₂×#41	C₂³×C₃	1	16	yes	—
547	C₂×#41	C₂³×C₃	1	8	yes	—
548	C₂×#41	C₂³×C₃	1	4	yes	—
549	C₂×#41	C₂³×C₃	1	4	yes	—
550	C₂²×Q₈	C₂³×C₃	1	4	yes	—
551	C₂²×Q₈	C₂³×C₃	1	4	yes	—
552	C₂²×D₄	C₂³×C₃	1	4	yes	—
553	C₂²×D₄	C₂³×C₃	1	8	yes	—
554	C₂²×D₄	C₂³×C₃	1	4	yes	—
555	C₂²×D₄	C₂³×C₃	1	4	yes	—
556	C₂²×D₄	C₂³×C₃	1	4	yes	—
557	C₂²×D₄	C₂³×C₃	1	8	yes	—
558	C₂²×D₄	C₂³×C₃	1	2	yes	—
559	C₂²×D₄	C₂³×C₃	1	8	yes	—
560	C₂³×C₄	C₂³×C₃	1	8	yes	—
561	C₂³×C₄	C₂³×C₃	1	4	yes	—
562	C₄⋊Q₈	C₂³×C₃	1	1	yes	characteristic
563	C₄⋊Q₈	C₂³×C₃	1	2	yes	—
564	C₄⋊Q₈	C₂³×C₃	1	2	yes	—
565	C₄⋊Q₈	C₂³×C₃	1	8	yes	—
566	C₄⋊Q₈	C₂³×C₃	1	4	yes	—
567	C₄⋊Q₈	C₂³×C₃	1	4	yes	—
568	C₄⋊Q₈	C₂³×C₃	1	8	yes	—
569	#127	C₂³×C₃	1	1	yes	characteristic
570	#127	C₂³×C₃	1	2	yes	—
571	#127	C₂³×C₃	1	4	yes	—
572	#127	C₂³×C₃	1	8	yes	—
573	#127	C₂³×C₃	1	4	yes	—
574	#127	C₂³×C₃	1	2	yes	—
575	#127	C₂³×C₃	1	8	yes	—
576	#126	C₂³×C₃	1	16	yes	—
577	#126	C₂³×C₃	1	8	yes	—
578	#126	C₂³×C₃	1	8	yes	—
579	#126	C₂³×C₃	1	8	yes	—
580	#126	C₂³×C₃	1	8	yes	—
581	#126	C₂³×C₃	1	16	yes	—
582	#125	C₂³×C₃	1	4	yes	—
583	#125	C₂³×C₃	1	8	yes	—
584	#125	C₂³×C₃	1	4	yes	—
585	#125	C₂³×C₃	1	8	yes	—
586	#125	C₂³×C₃	1	4	yes	—
587	#124	C₂³×C₃	1	4	yes	—
588	#124	C₂³×C₃	1	8	yes	—
589	#124	C₂³×C₃	1	8	yes	—
590	#124	C₂³×C₃	1	8	yes	—
591	#124	C₂³×C₃	1	16	yes	—
592	#124	C₂³×C₃	1	16	yes	—
593	#124	C₂³×C₃	1	4	yes	—
594	#124	C₂³×C₃	1	8	yes	—
595	#124	C₂³×C₃	1	2	yes	—
596	#124	C₂³×C₃	1	4	yes	—
597	#124	C₂³×C₃	1	8	yes	—
598	#124	C₂³×C₃	1	16	yes	—
599	#124	C₂³×C₃	1	8	yes	—
600	#124	C₂³×C₃	1	16	yes	—
601	#123	C₂³×C₃	1	4	yes	—
602	#123	C₂³×C₃	1	4	yes	—
603	#123	C₂³×C₃	1	8	yes	—
604	#123	C₂³×C₃	1	8	yes	—
605	#123	C₂³×C₃	1	16	yes	—
606	#123	C₂³×C₃	1	8	yes	—
607	#123	C₂³×C₃	1	8	yes	—
608	#123	C₂³×C₃	1	8	yes	—
609	#123	C₂³×C₃	1	8	yes	—
610	#123	C₂³×C₃	1	16	yes	—
611	#123	C₂³×C₃	1	16	yes	—
612	#123	C₂³×C₃	1	8	yes	—
613	#123	C₂³×C₃	1	16	yes	—
614	#123	C₂³×C₃	1	8	yes	—
615	#123	C₂³×C₃	1	8	yes	—
616	#123	C₂³×C₃	1	16	yes	—
617	#123	C₂³×C₃	1	16	yes	—
618	#123	C₂³×C₃	1	16	yes	—
619	C₂²⋊Q₈	C₂³×C₃	1	4	yes	—
620	C₂²⋊Q₈	C₂³×C₃	1	4	yes	—
621	C₂²⋊Q₈	C₂³×C₃	1	8	yes	—
622	C₂²⋊Q₈	C₂³×C₃	1	16	yes	—
623	C₂²⋊Q₈	C₂³×C₃	1	16	yes	—
624	C₂²⋊Q₈	C₂³×C₃	1	8	yes	—
625	C₂²⋊Q₈	C₂³×C₃	1	4	yes	—
626	C₂²⋊Q₈	C₂³×C₃	1	8	yes	—
627	C₂²⋊Q₈	C₂³×C₃	1	4	yes	—
628	C₂²⋊Q₈	C₂³×C₃	1	4	yes	—
629	C₂²⋊Q₈	C₂³×C₃	1	8	yes	—
630	C₂²⋊Q₈	C₂³×C₃	1	4	yes	—
631	C₂²⋊Q₈	C₂³×C₃	1	16	yes	—
632	C₂²⋊Q₈	C₂³×C₃	1	16	yes	—
633	#121	C₂³×C₃	1	8	yes	—
634	#121	C₂³×C₃	1	8	yes	—
635	#121	C₂³×C₃	1	8	yes	—
636	#121	C₂³×C₃	1	16	yes	—
637	#121	C₂³×C₃	1	16	yes	—
638	#121	C₂³×C₃	1	4	yes	—
639	#121	C₂³×C₃	1	8	yes	—
640	#121	C₂³×C₃	1	8	yes	—
641	#121	C₂³×C₃	1	4	yes	—
642	#121	C₂³×C₃	1	4	yes	—
643	#121	C₂³×C₃	1	16	yes	—
644	#121	C₂³×C₃	1	8	yes	—
645	#121	C₂³×C₃	1	8	yes	—
646	#121	C₂³×C₃	1	8	yes	—
647	#121	C₂³×C₃	1	16	yes	—
648	#121	C₂³×C₃	1	16	yes	—
649	#121	C₂³×C₃	1	16	yes	—
650	#121	C₂³×C₃	1	16	yes	—
651	#120	C₂³×C₃	1	8	yes	—
652	#120	C₂³×C₃	1	4	yes	—
653	#120	C₂³×C₃	1	4	yes	—
654	#120	C₂³×C₃	1	16	yes	—
655	#120	C₂³×C₃	1	16	yes	—
656	#120	C₂³×C₃	1	16	yes	—
657	#120	C₂³×C₃	1	16	yes	—
658	#120	C₂³×C₃	1	8	yes	—
659	C₄×Q₈	C₂³×C₃	1	2	yes	—
660	C₄×Q₈	C₂³×C₃	1	4	yes	—
661	C₄×Q₈	C₂³×C₃	1	4	yes	—
662	C₄×Q₈	C₂³×C₃	1	8	yes	—
663	C₄×Q₈	C₂³×C₃	1	4	yes	—
664	C₄×Q₈	C₂³×C₃	1	8	yes	—
665	C₄×Q₈	C₂³×C₃	1	2	yes	—
666	C₄×Q₈	C₂³×C₃	1	4	yes	—
667	C₄×Q₈	C₂³×C₃	1	2	yes	—
668	C₄×Q₈	C₂³×C₃	1	4	yes	—
669	C₄×Q₈	C₂³×C₃	1	8	yes	—
670	C₄×D₄	C₂³×C₃	1	4	yes	—
671	C₄×D₄	C₂³×C₃	1	2	yes	—
672	C₄×D₄	C₂³×C₃	1	8	yes	—
673	C₄×D₄	C₂³×C₃	1	8	yes	—
674	C₄×D₄	C₂³×C₃	1	16	yes	—
675	C₄×D₄	C₂³×C₃	1	8	yes	—
676	C₄×D₄	C₂³×C₃	1	4	yes	—
677	C₄×D₄	C₂³×C₃	1	8	yes	—
678	C₄×D₄	C₂³×C₃	1	4	yes	—
679	C₄×D₄	C₂³×C₃	1	16	yes	—
680	C₄×D₄	C₂³×C₃	1	8	yes	—
681	C₄×D₄	C₂³×C₃	1	2	yes	—
682	C₄×D₄	C₂³×C₃	1	4	yes	—
683	C₄×D₄	C₂³×C₃	1	4	yes	—
684	C₄×D₄	C₂³×C₃	1	4	yes	—
685	C₄×D₄	C₂³×C₃	1	8	yes	—
686	C₄×D₄	C₂³×C₃	1	2	yes	—
687	C₄×D₄	C₂³×C₃	1	4	yes	—
688	C₄×D₄	C₂³×C₃	1	8	yes	—
689	C₄×D₄	C₂³×C₃	1	8	yes	—
690	C₄×D₄	C₂³×C₃	1	16	yes	—
691	C₄×D₄	C₂³×C₃	1	8	yes	—
692	C₄×D₄	C₂³×C₃	1	8	yes	—
693	C₄×D₄	C₂³×C₃	1	8	yes	—
694	C₄×D₄	C₂³×C₃	1	16	yes	—
695	C₄×D₄	C₂³×C₃	1	16	yes	—
696	C₄×D₄	C₂³×C₃	1	8	yes	—
697	#117	C₂³×C₃	1	2	yes	—
698	#117	C₂³×C₃	1	8	yes	—
699	#117	C₂³×C₃	1	4	yes	—
700	#117	C₂³×C₃	1	2	yes	—
701	#117	C₂³×C₃	1	1	yes	characteristic
702	#117	C₂³×C₃	1	4	yes	—
703	#117	C₂³×C₃	1	4	yes	—
704	#117	C₂³×C₃	1	4	yes	—
705	#117	C₂³×C₃	1	4	yes	—
706	#117	C₂³×C₃	1	8	yes	—
707	#117	C₂³×C₃	1	16	yes	—
708	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
709	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
710	C₂×C₄⋊C₄	C₂³×C₃	1	8	yes	—
711	C₂×C₄⋊C₄	C₂³×C₃	1	16	yes	—
712	C₂×C₂²⋊C₄	C₂³×C₃	1	16	yes	—
713	C₂×C₂²⋊C₄	C₂³×C₃	1	8	yes	—
714	C₂×C₂²⋊C₄	C₂³×C₃	1	8	yes	—
715	C₂×C₂²⋊C₄	C₂³×C₃	1	8	yes	—
716	C₂×C₂²⋊C₄	C₂³×C₃	1	16	yes	—
717	C₂×C₄²	C₂³×C₃	1	8	yes	—
718	C₂×C₄²	C₂³×C₃	1	4	yes	—
719	C₂×C₄²	C₂³×C₃	1	2	yes	—
720	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
721	C₂³×C₃	—	2	16	no	—
722	C₂³×C₃	—	4	4	no	—
723	C₂³×C₃	—	4	16	no	—
724	C₂³×C₃	—	4	8	no	—
725	C₂³×C₃	—	4	4	no	—
726	C₂³×C₃	—	4	8	no	—
727	C₂³×C₃	C₂⁵	1	1	yes	characteristic
728	C₂³×C₃	C₂⁵	1	4	yes	—
729	C₂³×C₃	C₂⁵	1	4	yes	—
730	C₂³×C₃	C₂⁵	1	8	yes	—
731	C₂³×C₃	C₂⁵	1	2	yes	—
732	C₃×Q₈	—	2	8	no	—
733	C₃×Q₈	—	2	2	no	—
734	C₃×Q₈	—	2	4	no	—
735	C₃×Q₈	—	2	8	no	—
736	C₃×Q₈	—	4	8	no	—
737	C₃×Q₈	—	4	8	no	—
738	C₃×Q₈	—	4	2	no	—
739	C₃×D₄	—	2	16	no	—
740	C₃×D₄	—	2	4	no	—
741	C₃×D₄	—	2	16	no	—
742	C₃×D₄	—	2	8	no	—
743	C₃×D₄	—	2	8	no	—
744	C₃×D₄	—	2	4	no	—
745	C₃×D₄	—	2	16	no	—
746	C₃×D₄	—	4	2	no	—
747	C₃×D₄	—	4	4	no	—
748	C₃×D₄	—	4	4	no	—
749	C₃×D₄	—	4	8	no	—
750	C₃×D₄	—	4	8	no	—
751	C₃×D₄	—	4	8	no	—
752	C₃×D₄	—	4	16	no	—
753	C₃×D₄	—	4	16	no	—
754	C₃×D₄	—	4	16	no	—
755	C₃×D₄	—	4	4	no	—
756	C₃×D₄	H(5,𝔽₂)	1	4	yes	—
757	C₂×C₃×C₄	—	2	16	no	—
758	C₂×C₃×C₄	—	2	4	no	—
759	C₂×C₃×C₄	—	2	8	no	—
760	C₂×C₃×C₄	—	2	8	no	—
761	C₂×C₃×C₄	—	2	2	no	—
762	C₂×C₃×C₄	—	2	8	no	—
763	C₂×C₃×C₄	—	2	4	no	—
764	C₂×C₃×C₄	—	2	8	no	—
765	C₂×C₃×C₄	—	4	4	no	—
766	C₂×C₃×C₄	—	4	8	no	—
767	C₂×C₃×C₄	—	4	8	no	—
768	C₂×C₃×C₄	—	4	16	no	—
769	C₂×C₃×C₄	—	4	8	no	—
770	C₂×C₃×C₄	—	4	8	no	—
771	C₂×C₃×C₄	—	4	16	no	—
772	C₂×C₃×C₄	—	4	4	no	—
773	C₂×C₃×C₄	C₂⁵	1	4	yes	—
774	C₂×C₃×C₄	C₂⁵	1	4	yes	—
775	C₂×C₃×C₄	C₂⁵	1	8	yes	—
776	C₂×C₃×C₄	C₂⁵	1	2	yes	—
777	C₂×C₃×C₄	C₂⁵	1	4	yes	—
778	C₂×C₃×C₄	C₂⁵	1	1	yes	characteristic
779	C₂×C₃×C₄	C₂⁵	1	4	yes	—
780	C₂×C₃×C₄	C₂⁵	1	4	yes	—
781	C₂×C₃×C₄	C₂⁵	1	8	yes	—
782	C₂×C₃×C₄	C₂⁵	1	2	yes	—
783	C₂×C₃×C₄	C₂⁵	1	1	yes	characteristic
784	C₂×C₃×C₄	C₂⁵	1	2	yes	—
785	C₂⁴	C₂⁴×C₃	1	8	yes	—
786	C₂⁴	C₂⁴×C₃	1	4	yes	—
787	C₂⁴	C₂⁴×C₃	1	4	yes	—
788	#41	—	2	16	no	—
789	#41	—	2	4	no	—
790	#41	—	4	4	no	—
791	#41	—	4	32	no	—
792	#41	—	4	8	no	—
793	#41	—	4	16	no	—
794	#41	—	4	8	no	—
795	#41	—	4	4	no	—
796	#41	—	4	16	no	—
797	C₂×Q₈	—	4	8	no	—
798	C₂×Q₈	—	4	8	no	—
799	C₂×Q₈	C₂⁴×C₃	1	2	yes	—
800	C₂×Q₈	C₂⁴×C₃	1	4	yes	—
801	C₂×Q₈	C₂⁴×C₃	1	4	yes	—
802	C₂×Q₈	C₂⁴×C₃	1	1	yes	characteristic
803	C₂×Q₈	C₂⁴×C₃	1	8	yes	—
804	C₂×Q₈	C₂⁴×C₃	1	8	yes	—
805	C₂×Q₈	C₂⁴×C₃	1	2	yes	—
806	C₂×D₄	—	2	16	no	—
807	C₂×D₄	—	4	4	no	—
808	C₂×D₄	—	4	16	no	—
809	C₂×D₄	—	4	8	no	—
810	C₂×D₄	—	4	8	no	—
811	C₂×D₄	—	4	8	no	—
812	C₂×D₄	—	4	16	no	—
813	C₂×D₄	—	4	16	no	—
814	C₂×D₄	C₂⁴×C₃	1	4	yes	—
815	C₂×D₄	C₂⁴×C₃	1	2	yes	—
816	C₂×D₄	C₂⁴×C₃	1	8	yes	—
817	C₂×D₄	C₂⁴×C₃	1	8	yes	—
818	C₂×D₄	C₂⁴×C₃	1	8	yes	—
819	C₂×D₄	C₂⁴×C₃	1	2	yes	—
820	C₂×D₄	C₂⁴×C₃	1	4	yes	—
821	C₂×D₄	C₂⁴×C₃	1	4	yes	—
822	C₂×D₄	C₂⁴×C₃	1	16	yes	—
823	C₂×D₄	C₂⁴×C₃	1	8	yes	—
824	C₂×D₄	C₂⁴×C₃	1	16	yes	—
825	C₂×D₄	C₂⁴×C₃	1	8	yes	—
826	C₂×D₄	C₂⁴×C₃	1	4	yes	—
827	C₂×D₄	C₂⁴×C₃	1	16	yes	—
828	C₂×D₄	C₂⁴×C₃	1	2	yes	—
829	C₂×D₄	C₂⁴×C₃	1	8	yes	—
830	C₂×D₄	C₂⁴×C₃	1	4	yes	—
831	C₂×D₄	C₂⁴×C₃	1	1	yes	characteristic
832	C₂²×C₄	—	4	8	no	—
833	C₂²×C₄	—	4	16	no	—
834	C₂²×C₄	C₂⁴×C₃	1	4	yes	—
835	C₂²×C₄	C₂⁴×C₃	1	8	yes	—
836	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
837	C₂²×C₄	C₂⁴×C₃	1	4	yes	—
838	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
839	C₂²×C₄	C₂⁴×C₃	1	4	yes	—
840	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
841	C₂²×C₄	C₂⁴×C₃	1	4	yes	—
842	C₂²×C₄	C₂⁴×C₃	1	8	yes	—
843	C₂²×C₄	C₂⁴×C₃	1	4	yes	—
844	C₂²×C₄	C₂⁴×C₃	1	16	yes	—
845	C₂²×C₄	C₂⁴×C₃	1	8	yes	—
846	C₂²×C₄	C₂⁴×C₃	1	16	yes	—
847	C₂²×C₄	C₂⁴×C₃	1	8	yes	—
848	C₂²×C₄	C₂⁴×C₃	1	4	yes	—
849	C₂²×C₄	C₂⁴×C₃	1	8	yes	—
850	C₄⋊C₄	C₂⁴×C₃	1	2	yes	—
851	C₄⋊C₄	C₂⁴×C₃	1	8	yes	—
852	C₄⋊C₄	C₂⁴×C₃	1	8	yes	—
853	C₄⋊C₄	C₂⁴×C₃	1	4	yes	—
854	C₄⋊C₄	C₂⁴×C₃	1	8	yes	—
855	C₄⋊C₄	C₂⁴×C₃	1	4	yes	—
856	C₄⋊C₄	C₂⁴×C₃	1	4	yes	—
857	C₄⋊C₄	C₂⁴×C₃	1	8	yes	—
858	C₄⋊C₄	C₂⁴×C₃	1	16	yes	—
859	C₄⋊C₄	C₂⁴×C₃	1	8	yes	—
860	C₄⋊C₄	C₂⁴×C₃	1	8	yes	—
861	C₄⋊C₄	C₂⁴×C₃	1	4	yes	—
862	C₄⋊C₄	C₂⁴×C₃	1	2	yes	—
863	C₄⋊C₄	C₂⁴×C₃	1	8	yes	—
864	C₄⋊C₄	C₂⁴×C₃	1	2	yes	—
865	C₄⋊C₄	C₂⁴×C₃	1	4	yes	—
866	C₄⋊C₄	C₂⁴×C₃	1	4	yes	—
867	C₄⋊C₄	C₂⁴×C₃	1	8	yes	—
868	C₄⋊C₄	C₂⁴×C₃	1	4	yes	—
869	C₄⋊C₄	C₂⁴×C₃	1	8	yes	—
870	C₄⋊C₄	C₂⁴×C₃	1	8	yes	—
871	C₄⋊C₄	C₂⁴×C₃	1	4	yes	—
872	C₂²⋊C₄	C₂⁴×C₃	1	4	yes	—
873	C₂²⋊C₄	C₂⁴×C₃	1	8	yes	—
874	C₂²⋊C₄	C₂⁴×C₃	1	8	yes	—
875	C₂²⋊C₄	C₂⁴×C₃	1	4	yes	—
876	C₂²⋊C₄	C₂⁴×C₃	1	16	yes	—
877	C₂²⋊C₄	C₂⁴×C₃	1	8	yes	—
878	C₂²⋊C₄	C₂⁴×C₃	1	4	yes	—
879	C₂²⋊C₄	C₂⁴×C₃	1	8	yes	—
880	C₂²⋊C₄	C₂⁴×C₃	1	4	yes	—
881	C₂²⋊C₄	C₂⁴×C₃	1	8	yes	—
882	C₂²⋊C₄	C₂⁴×C₃	1	16	yes	—
883	C₂²⋊C₄	C₂⁴×C₃	1	16	yes	—
884	C₂²⋊C₄	C₂⁴×C₃	1	16	yes	—
885	C₂²⋊C₄	C₂⁴×C₃	1	8	yes	—
886	C₂²⋊C₄	C₂⁴×C₃	1	16	yes	—
887	C₂²⋊C₄	C₂⁴×C₃	1	4	yes	—
888	C₂²⋊C₄	C₂⁴×C₃	1	2	yes	—
889	C₂²⋊C₄	C₂⁴×C₃	1	4	yes	—
890	C₂²⋊C₄	C₂⁴×C₃	1	8	yes	—
891	C₂²⋊C₄	C₂⁴×C₃	1	8	yes	—
892	C₂²⋊C₄	C₂⁴×C₃	1	16	yes	—
893	C₂²⋊C₄	C₂⁴×C₃	1	8	yes	—
894	C₄²	C₂⁴×C₃	1	4	yes	—
895	C₄²	C₂⁴×C₃	1	2	yes	—
896	C₄²	C₂⁴×C₃	1	1	yes	characteristic
897	C₄²	C₂⁴×C₃	1	1	yes	characteristic
898	C₄²	C₂⁴×C₃	1	4	yes	—
899	C₄²	C₂⁴×C₃	1	8	yes	—
900	C₄²	C₂⁴×C₃	1	4	yes	—
901	C₄²	C₂⁴×C₃	1	8	yes	—
902	C₄²	C₂⁴×C₃	1	4	yes	—
903	C₄²	C₂⁴×C₃	1	2	yes	—
904	C₄²	C₂⁴×C₃	1	8	yes	—
905	C₄²	C₂⁴×C₃	1	8	yes	—
906	C₂²×C₃	—	2	4	no	—
907	C₂²×C₃	—	2	4	no	—
908	C₂²×C₃	—	2	4	no	—
909	C₂²×C₃	—	2	1	no	—
910	C₂²×C₃	—	2	8	no	—
911	C₂²×C₃	—	2	4	no	—
912	C₂²×C₃	—	2	2	no	—
913	C₂²×C₃	—	2	4	no	—
914	C₂²×C₃	—	2	16	no	—
915	C₂²×C₃	—	2	8	no	—
916	C₂²×C₃	—	8	16	no	—
917	C₂²×C₃	—	8	8	no	—
918	C₂²×C₃	—	16	4	no	—
919	C₂²×C₃	C₂×H(5,𝔽₂)	1	4	yes	—
920	C₂²×C₃	C₂⁶	1	1	yes	characteristic
921	C₃×C₄	—	2	4	no	—
922	C₃×C₄	—	2	1	no	—
923	C₃×C₄	—	2	4	no	—
924	C₃×C₄	—	2	2	no	—
925	C₃×C₄	—	2	8	no	—
926	C₃×C₄	—	2	4	no	—
927	C₃×C₄	—	2	2	no	—
928	C₃×C₄	—	2	4	no	—
929	C₃×C₄	—	2	8	no	—
930	C₃×C₄	—	2	4	no	—
931	C₃×C₄	C₂×H(5,𝔽₂)	1	2	yes	—
932	C₃×C₄	#585	1	4	yes	—
933	C₂³	—	2	16	no	—
934	C₂³	—	4	4	no	—
935	C₂³	—	4	16	no	—
936	C₂³	—	4	8	no	—
937	C₂³	—	4	4	no	—
938	C₂³	—	4	8	no	—
939	C₂³	C₂⁵×C₃	1	1	yes	characteristic
940	C₂³	C₂⁵×C₃	1	4	yes	—
941	C₂³	C₂⁵×C₃	1	4	yes	—
942	C₂³	C₂⁵×C₃	1	8	yes	—
943	C₂³	C₂⁵×C₃	1	2	yes	—
944	Q₈	—	2	8	no	—
945	Q₈	—	2	2	no	—
946	Q₈	—	2	4	no	—
947	Q₈	—	2	8	no	—
948	Q₈	—	4	8	no	—
949	Q₈	—	4	8	no	—
950	Q₈	—	4	2	no	—
951	D₄	—	2	16	no	—
952	D₄	—	2	4	no	—
953	D₄	—	2	16	no	—
954	D₄	—	2	8	no	—
955	D₄	—	2	8	no	—
956	D₄	—	2	4	no	—
957	D₄	—	2	16	no	—
958	D₄	—	4	2	no	—
959	D₄	—	4	4	no	—
960	D₄	—	4	4	no	—
961	D₄	—	4	8	no	—
962	D₄	—	4	16	no	—
963	D₄	—	4	8	no	—
964	D₄	—	4	8	no	—
965	D₄	—	4	16	no	—
966	D₄	—	4	16	no	—
967	D₄	—	4	4	no	—
968	D₄	C₃×H(5,𝔽₂)	1	4	yes	—
969	C₂×C₄	—	2	16	no	—
970	C₂×C₄	—	2	4	no	—
971	C₂×C₄	—	2	8	no	—
972	C₂×C₄	—	2	8	no	—
973	C₂×C₄	—	2	2	no	—
974	C₂×C₄	—	2	8	no	—
975	C₂×C₄	—	2	4	no	—
976	C₂×C₄	—	2	8	no	—
977	C₂×C₄	—	4	4	no	—
978	C₂×C₄	—	4	8	no	—
979	C₂×C₄	—	4	8	no	—
980	C₂×C₄	—	4	16	no	—
981	C₂×C₄	—	4	8	no	—
982	C₂×C₄	—	4	8	no	—
983	C₂×C₄	—	4	16	no	—
984	C₂×C₄	—	4	4	no	—
985	C₂×C₄	C₂⁵×C₃	1	4	yes	—
986	C₂×C₄	C₂⁵×C₃	1	4	yes	—
987	C₂×C₄	C₂⁵×C₃	1	8	yes	—
988	C₂×C₄	C₂⁵×C₃	1	2	yes	—
989	C₂×C₄	C₂⁵×C₃	1	4	yes	—
990	C₂×C₄	C₂⁵×C₃	1	1	yes	characteristic
991	C₂×C₄	C₂⁵×C₃	1	4	yes	—
992	C₂×C₄	C₂⁵×C₃	1	4	yes	—
993	C₂×C₄	C₂⁵×C₃	1	8	yes	—
994	C₂×C₄	C₂⁵×C₃	1	2	yes	—
995	C₂×C₄	C₂⁵×C₃	1	1	yes	characteristic
996	C₂×C₄	C₂⁵×C₃	1	2	yes	—
997	C₂×C₃	—	2	4	no	—
998	C₂×C₃	—	4	4	no	—
999	C₂×C₃	—	4	4	no	—
1000	C₂×C₃	—	4	8	no	—
1001	C₂×C₃	—	4	1	no	—
1002	C₂×C₃	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
1003	C₂×C₃	C₂×#585	1	2	yes	—
1004	C₂²	—	2	4	no	—
1005	C₂²	—	2	4	no	—
1006	C₂²	—	2	4	no	—
1007	C₂²	—	2	1	no	—
1008	C₂²	—	2	8	no	—
1009	C₂²	—	2	4	no	—
1010	C₂²	—	2	2	no	—
1011	C₂²	—	2	4	no	—
1012	C₂²	—	2	16	no	—
1013	C₂²	—	2	8	no	—
1014	C₂²	—	8	16	no	—
1015	C₂²	—	8	8	no	—
1016	C₂²	—	16	4	no	—
1017	C₂²	C₂×C₃×H(5,𝔽₂)	1	4	yes	—
1018	C₂²	C₂⁶×C₃	1	1	yes	characteristic
1019	C₄	—	2	4	no	—
1020	C₄	—	2	1	no	—
1021	C₄	—	2	4	no	—
1022	C₄	—	2	2	no	—
1023	C₄	—	2	8	no	—
1024	C₄	—	2	4	no	—
1025	C₄	—	2	2	no	—
1026	C₄	—	2	4	no	—
1027	C₄	—	2	8	no	—
1028	C₄	—	2	4	no	—
1029	C₄	C₂×C₃×H(5,𝔽₂)	1	2	yes	—
1030	C₄	C₃×#585	1	4	yes	—
1031	C₃	#63021	1	1	yes	characteristic, direct product factor, Sylow
1032	C₂	—	2	4	no	—
1033	C₂	—	4	4	no	—
1034	C₂	—	4	4	no	—
1035	C₂	—	4	8	no	—
1036	C₂	—	4	1	no	—
1037	C₂	C₂²×C₃×H(5,𝔽₂)	1	1	yes	characteristic
1038	C₂	C₂×C₃×#585	1	2	yes	—

	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×#3558	C₂	semidirect
2. C₃×#3554	C₂	semidirect
3. C₃×#3550	C₂	semidirect
4. C₃×#3543	C₂	semidirect
5. C₃×#3540	C₂	semidirect
6. C₃×#3533	C₂	semidirect
7. C₃×#3522	C₂	semidirect
8. C₃×#3514	C₂	semidirect
9. C₃×#3513	C₂	semidirect
10. C₃×#3508	C₂	semidirect
11. C₃×#3506	C₂	semidirect
12. C₃×#3498	C₂	semidirect
13. C₃×#3485	C₂	semidirect
14. C₃×#3482	C₂	semidirect
15. C₃×#3481	C₂	semidirect
16. C₂×C₃×#559	C₂	semidirect
17. C₃×D₄×#41	C₂	semidirect
18. #63021	C₃	direct (N × H)
19. C₂×C₃×H(5,𝔽₂)	C₂²	semidirect
20. C₂²×C₃×#41	C₂²	semidirect
21. C₃×#563	C₂²	semidirect
22. C₃×#562	C₂²	semidirect
23. C₃×H(3,𝔽₄)	C₂²	semidirect
24. C₃×#560	C₂²	semidirect
25. C₃×#559	C₂²	semidirect
26. C₃×#559	C₂²	semidirect
27. C₃×#559	C₂²	semidirect
28. C₃×#559	C₂²	semidirect
29. C₃×#559	C₂²	semidirect
30. C₃×#559	C₂²	semidirect
31. C₃×#559	C₂²	semidirect
32. C₃×#559	C₂²	semidirect
33. C₃×Q₈²	C₂²	semidirect
34. C₃×#557	C₂²	semidirect
35. C₃×#556	C₂²	semidirect
36. C₃×#556	C₂²	semidirect
37. C₃×#556	C₂²	semidirect
38. C₃×#555	C₂²	semidirect
39. C₃×#554	C₂²	semidirect
40. C₃×#554	C₂²	semidirect
41. C₃×#553	C₂²	semidirect
42. C₃×#553	C₂²	semidirect
43. C₃×#552	C₂²	semidirect
44. C₃×#552	C₂²	semidirect
45. C₃×#551	C₂²	semidirect
46. C₃×#551	C₂²	semidirect
47. C₃×#551	C₂²	semidirect
48. C₃×#550	C₂²	semidirect
49. C₃×#550	C₂²	semidirect
50. C₃×#550	C₂²	semidirect
51. C₃×D₄×Q₈	C₂²	semidirect
52. C₃×D₄×Q₈	C₂²	semidirect
53. C₃×#548	C₂²	semidirect
54. C₃×#548	C₂²	semidirect
55. C₃×#548	C₂²	semidirect
56. C₃×#547	C₂²	semidirect
57. C₃×#547	C₂²	semidirect
58. C₃×#547	C₂²	semidirect
59. C₃×#547	C₂²	semidirect
60. C₃×#547	C₂²	semidirect
61. C₃×#546	C₂²	semidirect
62. C₃×#546	C₂²	semidirect
63. C₃×#546	C₂²	semidirect
64. C₃×#546	C₂²	semidirect
65. C₃×#546	C₂²	semidirect
66. C₃×#546	C₂²	semidirect
67. C₃×#546	C₂²	semidirect
68. C₃×D₄²	C₂²	semidirect
69. C₃×D₄²	C₂²	semidirect
70. C₃×D₄²	C₂²	semidirect
71. C₃×D₄²	C₂²	semidirect
72. C₃×#542	C₂²	semidirect
73. C₃×#542	C₂²	semidirect
74. C₃×#542	C₂²	semidirect
75. C₃×#542	C₂²	semidirect
76. C₃×#540	C₂²	semidirect
77. C₃×#540	C₂²	semidirect
78. C₃×#539	C₂²	semidirect
79. C₃×#538	C₂²	semidirect
80. C₃×#538	C₂²	semidirect
81. C₃×#538	C₂²	semidirect
82. C₃×#536	C₂²	semidirect
83. C₃×#536	C₂²	semidirect
84. C₃×#535	C₂²	semidirect
85. C₃×#535	C₂²	semidirect
86. C₃×#535	C₂²	semidirect
87. C₃×#535	C₂²	semidirect
88. C₃×#534	C₂²	semidirect
89. C₃×#534	C₂²	semidirect
90. C₃×#533	C₂²	semidirect
91. C₃×#533	C₂²	semidirect
93. C₃×#532	C₂²	semidirect
94. C₃×#532	C₂²	semidirect
95. C₃×#532	C₂²	semidirect
96. C₃×#532	C₂²	semidirect
98. C₂×C₃×#127	C₂²	semidirect
99. C₃×#529	C₂²	semidirect
100. C₃×#529	C₂²	semidirect
101. C₃×#529	C₂²	semidirect
102. C₃×#529	C₂²	semidirect
103. C₂×C₃×#124	C₂²	semidirect
104. C₃×#525	C₂²	semidirect
105. C₃×#525	C₂²	semidirect
106. C₃×#525	C₂²	semidirect
107. C₃×#525	C₂²	semidirect
108. C₂×C₃×#123	C₂²	semidirect
109. C₂×C₃×#123	C₂²	semidirect
110. C₃×#520	C₂²	semidirect
111. C₃×#518	C₂²	semidirect
112. C₃×#518	C₂²	semidirect
113. C₃×C₄×#41	C₂²	semidirect
114. C₃×C₄×#41	C₂²	semidirect
115. C₃×C₄×#41	C₂²	semidirect
116. C₂×C₃×C₄×Q₈	C₂²	semidirect
117. C₂×C₃×C₄×D₄	C₂²	semidirect
118. C₂×C₃×C₄×D₄	C₂²	semidirect
119. #3558	C₂×C₃	semidirect
120. #3554	C₂×C₃	semidirect
121. #3550	C₂×C₃	semidirect
122. #3543	C₂×C₃	semidirect
123. #3540	C₂×C₃	semidirect
124. #3533	C₂×C₃	semidirect
125. #3522	C₂×C₃	semidirect
126. #3514	C₂×C₃	semidirect
127. #3513	C₂×C₃	semidirect
128. #3508	C₂×C₃	semidirect
129. #3506	C₂×C₃	semidirect
130. #3498	C₂×C₃	semidirect
131. #3485	C₂×C₃	semidirect
132. #3482	C₂×C₃	semidirect
133. #3481	C₂×C₃	semidirect
134. C₂×#559	C₂×C₃	semidirect
135. D₄×#41	C₂×C₃	semidirect
318. C₂×H(5,𝔽₂)	C₂²×C₃	semidirect
319. C₂²×#41	C₂²×C₃	semidirect
320. #563	C₂²×C₃	semidirect
321. #562	C₂²×C₃	semidirect
322. H(3,𝔽₄)	C₂²×C₃	semidirect
323. #560	C₂²×C₃	semidirect
324. #559	C₂²×C₃	semidirect
325. #559	C₂²×C₃	semidirect
326. #559	C₂²×C₃	semidirect
327. #559	C₂²×C₃	semidirect
328. #559	C₂²×C₃	semidirect
329. #559	C₂²×C₃	semidirect
330. #559	C₂²×C₃	semidirect
331. #559	C₂²×C₃	semidirect
332. Q₈²	C₂²×C₃	semidirect
333. #557	C₂²×C₃	semidirect
334. #556	C₂²×C₃	semidirect
335. #556	C₂²×C₃	semidirect
336. #556	C₂²×C₃	semidirect
337. #555	C₂²×C₃	semidirect
338. #554	C₂²×C₃	semidirect
339. #554	C₂²×C₃	semidirect
340. #553	C₂²×C₃	semidirect
341. #553	C₂²×C₃	semidirect
342. #552	C₂²×C₃	semidirect
343. #552	C₂²×C₃	semidirect
344. #551	C₂²×C₃	semidirect
345. #551	C₂²×C₃	semidirect
346. #551	C₂²×C₃	semidirect
347. #550	C₂²×C₃	semidirect
348. #550	C₂²×C₃	semidirect
349. #550	C₂²×C₃	semidirect
350. D₄×Q₈	C₂²×C₃	semidirect
351. D₄×Q₈	C₂²×C₃	semidirect
352. #548	C₂²×C₃	semidirect
353. #548	C₂²×C₃	semidirect
354. #548	C₂²×C₃	semidirect
355. #547	C₂²×C₃	semidirect
356. #547	C₂²×C₃	semidirect
357. #547	C₂²×C₃	semidirect
358. #547	C₂²×C₃	semidirect
359. #547	C₂²×C₃	semidirect
360. #546	C₂²×C₃	semidirect
361. #546	C₂²×C₃	semidirect
362. #546	C₂²×C₃	semidirect
363. #546	C₂²×C₃	semidirect
364. #546	C₂²×C₃	semidirect
365. #546	C₂²×C₃	semidirect
366. #546	C₂²×C₃	semidirect
367. D₄²	C₂²×C₃	semidirect
368. D₄²	C₂²×C₃	semidirect
369. D₄²	C₂²×C₃	semidirect
370. D₄²	C₂²×C₃	semidirect
371. #542	C₂²×C₃	semidirect
372. #542	C₂²×C₃	semidirect
373. #542	C₂²×C₃	semidirect
374. #542	C₂²×C₃	semidirect
375. #540	C₂²×C₃	semidirect
376. #540	C₂²×C₃	semidirect
377. #539	C₂²×C₃	semidirect
378. #538	C₂²×C₃	semidirect
379. #538	C₂²×C₃	semidirect
380. #538	C₂²×C₃	semidirect
381. #536	C₂²×C₃	semidirect
382. #536	C₂²×C₃	semidirect
383. #535	C₂²×C₃	semidirect
384. #535	C₂²×C₃	semidirect
385. #535	C₂²×C₃	semidirect
386. #535	C₂²×C₃	semidirect
387. #534	C₂²×C₃	semidirect
388. #534	C₂²×C₃	semidirect
389. #533	C₂²×C₃	semidirect
390. #533	C₂²×C₃	semidirect
392. #532	C₂²×C₃	semidirect
393. #532	C₂²×C₃	semidirect
394. #532	C₂²×C₃	semidirect
395. #532	C₂²×C₃	semidirect
397. C₂×#127	C₂²×C₃	semidirect
398. #529	C₂²×C₃	semidirect
399. #529	C₂²×C₃	semidirect
400. #529	C₂²×C₃	semidirect
401. #529	C₂²×C₃	semidirect
402. C₂×#124	C₂²×C₃	semidirect
403. #525	C₂²×C₃	semidirect
404. #525	C₂²×C₃	semidirect
405. #525	C₂²×C₃	semidirect
406. #525	C₂²×C₃	semidirect
407. C₂×#123	C₂²×C₃	semidirect
408. C₂×#123	C₂²×C₃	semidirect
409. #520	C₂²×C₃	semidirect
410. #518	C₂²×C₃	semidirect
411. #518	C₂²×C₃	semidirect
412. C₄×#41	C₂²×C₃	semidirect
413. C₄×#41	C₂²×C₃	semidirect
414. C₄×#41	C₂²×C₃	semidirect
415. C₂×C₄×Q₈	C₂²×C₃	semidirect
416. C₂×C₄×D₄	C₂²×C₃	semidirect
417. C₂×C₄×D₄	C₂²×C₃	semidirect
1031. C₃	#63021	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×#3558	2
C₃×#3554	2
C₃×#3550	2
C₃×#3543	2
C₃×#3540	2
C₃×#3533	2
C₃×#3522	2
C₃×#3514	2
C₃×#3513	2
C₃×#3508	2
C₃×#3506	2
C₃×#3498	2
C₃×#3485	2
C₃×#3482	2
C₃×#3481	2
C₂×C₃×#559	2
C₃×D₄×#41	2
#63021	3

Subgroups — C3×#63021 #10681628

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#63021 #10681628