Subgroups — C₃×#63066 #10681673

Order 768.

7352 conjugacy classes of subgroups.

The subgroup lattice has 784 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	6	yes	maximal, complemented
2	C₃×#3551	C₂	1	6	yes	maximal, complemented
3	C₃×#3549	C₂	1	3	yes	maximal, complemented
4	C₃×#3543	C₂	1	12	yes	maximal, complemented
5	C₃×#3542	C₂	1	12	yes	maximal, complemented
6	C₃×#3537	C₂	1	6	yes	maximal, complemented
7	C₃×#3529	C₂	1	3	yes	maximal, complemented
8	C₃×#3524	C₂	1	4	yes	maximal, complemented
9	C₃×#3517	C₂	1	2	yes	maximal, complemented
10	C₃×#3500	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×#3498	C₂	1	2	yes	maximal, complemented
12	C₃×#3488	C₂	1	4	yes	maximal, complemented
13	C₃×#3487	C₂	1	2	yes	maximal, complemented
14	#63066	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
15	C₂×C₃×2₋¹⁺⁴	C₂²	1	1	yes	characteristic, complemented
16	C₂×C₃×H(5,𝔽₂)	C₂²	1	2	yes	complemented
17	C₂×C₃×H(5,𝔽₂)	C₂²	1	1	yes	characteristic, complemented
18	C₂²×C₃×#41	C₂²	1	2	yes	complemented
19	C₃×#563	C₂²	1	1	yes	characteristic, complemented
20	C₃×#563	C₂²	1	6	yes	complemented
21	C₃×#562	C₂²	1	12	yes	complemented
22	C₃×#562	C₂²	1	6	yes	complemented
23	C₃×H(3,𝔽₄)	C₂²	1	3	yes	complemented
24	C₃×H(3,𝔽₄)	C₂²	1	6	yes	complemented
25	C₃×#560	C₂²	1	6	yes	complemented
26	C₃×#560	C₂²	1	12	yes	complemented
27	C₃×#560	C₂²	1	12	yes	complemented
28	C₃×#560	C₂²	1	12	yes	complemented
29	C₃×#559	C₂²	1	12	yes	complemented
30	C₃×#557	C₂²	1	2	yes	complemented
31	C₃×#555	C₂²	1	12	yes	complemented
32	C₃×#555	C₂²	1	6	yes	complemented
33	C₃×#553	C₂²	1	12	yes	complemented
34	C₃×#553	C₂²	1	12	yes	complemented
35	C₃×#552	C₂²	1	12	yes	complemented
36	C₃×#551	C₂²	1	12	yes	complemented
37	C₃×#550	C₂²	1	4	yes	complemented
38	C₃×#550	C₂²	1	12	yes	complemented
39	C₃×#550	C₂²	1	2	yes	complemented
40	C₃×#550	C₂²	1	4	yes	complemented
41	C₃×#550	C₂²	1	6	yes	complemented
42	C₃×#548	C₂²	1	4	yes	complemented
43	C₃×#548	C₂²	1	12	yes	complemented
44	C₃×#548	C₂²	1	4	yes	complemented
45	C₃×#547	C₂²	1	6	yes	complemented
46	C₃×#546	C₂²	1	12	yes	complemented
47	C₃×#546	C₂²	1	12	yes	complemented
48	C₃×#546	C₂²	1	12	yes	complemented
49	C₃×#546	C₂²	1	24	yes	complemented
50	C₃×D₄²	C₂²	1	12	yes	complemented
51	C₃×D₄²	C₂²	1	12	yes	complemented
52	C₃×D₄²	C₂²	1	12	yes	complemented
53	C₃×D₄²	C₂²	1	12	yes	complemented
54	C₃×D₄²	C₂²	1	6	yes	complemented
55	C₃×D₄²	C₂²	1	12	yes	complemented
56	C₃×#542	C₂²	1	12	yes	complemented
57	C₃×#540	C₂²	1	12	yes	complemented
58	C₃×#540	C₂²	1	12	yes	complemented
59	C₃×#540	C₂²	1	24	yes	complemented
60	C₃×#538	C₂²	1	24	yes	complemented
61	C₃×#538	C₂²	1	12	yes	complemented
62	C₃×#537	C₂²	1	12	yes	complemented
63	C₃×#536	C₂²	1	3	yes	complemented
64	C₃×#535	C₂²	1	6	yes	complemented
65	C₃×#535	C₂²	1	6	yes	complemented
66	C₃×#535	C₂²	1	12	yes	complemented
67	C₃×#535	C₂²	1	6	yes	complemented
68	C₃×#535	C₂²	1	6	yes	complemented
69	C₃×#535	C₂²	1	3	yes	complemented
70	C₃×#535	C₂²	1	24	yes	complemented
71	C₃×#534	C₂²	1	24	yes	complemented
72	C₃×#534	C₂²	1	12	yes	complemented
73	C₃×#532	C₂²	1	6	yes	complemented
74	C₃×#532	C₂²	1	3	yes	complemented
75	C₃×#532	C₂²	1	6	yes	complemented
76	C₂×C₃×#127	C₂²	1	6	yes	complemented
77	C₃×#529	C₂²	1	6	yes	complemented
78	C₃×#529	C₂²	1	12	yes	complemented
79	C₃×#529	C₂²	1	12	yes	complemented
80	C₂×C₃×#124	C₂²	1	3	yes	complemented
81	C₃×#525	C₂²	1	6	yes	complemented
82	C₃×#525	C₂²	1	6	yes	complemented
83	C₃×#525	C₂²	1	12	yes	complemented
84	C₂×C₃×#121	C₂²	1	12	yes	complemented
85	C₃×#520	C₂²	1	4	yes	complemented
86	C₃×#519	C₂²	1	2	yes	complemented
87	C₃×C₄×#41	C₂²	1	2	yes	complemented
88	C₃×C₄×#41	C₂²	1	1	yes	characteristic, complemented
89	#3558	C₂×C₃	1	6	yes	complemented
90	#3551	C₂×C₃	1	6	yes	complemented
91	#3549	C₂×C₃	1	3	yes	complemented
92	#3543	C₂×C₃	1	12	yes	complemented
93	#3542	C₂×C₃	1	12	yes	complemented
94	#3537	C₂×C₃	1	6	yes	complemented
95	#3529	C₂×C₃	1	3	yes	complemented
96	#3524	C₂×C₃	1	4	yes	complemented
97	#3517	C₂×C₃	1	2	yes	complemented
98	#3500	C₂×C₃	1	1	yes	characteristic, complemented
99	#3498	C₂×C₃	1	2	yes	complemented
100	#3488	C₂×C₃	1	4	yes	complemented
101	#3487	C₂×C₃	1	2	yes	complemented
102	C₃×2₋¹⁺⁴	—	4	4	no	—
103	C₃×H(5,𝔽₂)	—	4	8	no	—
104	C₃×H(5,𝔽₂)	—	4	4	no	—
105	C₂×C₃×#41	—	4	8	no	—
106	C₂×C₃×#41	C₂³	1	4	yes	—
107	C₂×C₃×#41	C₂³	1	2	yes	—
108	C₂×C₃×#41	C₂³	1	1	yes	characteristic
109	C₂×C₃×#41	C₂³	1	12	yes	—
110	C₂×C₃×#41	C₂³	1	6	yes	—
111	C₂×C₃×#41	C₂³	1	3	yes	—
112	C₂×C₃×#41	C₂³	1	3	yes	—
113	C₂×C₃×#41	C₂³	1	6	yes	—
114	C₂×C₃×#41	C₂³	1	12	yes	—
115	C₂²×C₃×Q₈	C₂³	1	2	yes	—
116	C₂²×C₃×Q₈	C₂³	1	3	yes	—
117	C₂²×C₃×D₄	C₂³	1	6	yes	—
118	C₂²×C₃×D₄	C₂³	1	12	yes	—
119	C₂²×C₃×D₄	C₂³	1	3	yes	—
120	C₂²×C₃×D₄	C₂³	1	6	yes	—
121	C₂²×C₃×D₄	C₂³	1	6	yes	—
122	C₂²×C₃×D₄	C₂³	1	24	yes	—
123	C₂²×C₃×D₄	C₂³	1	24	yes	—
124	C₂³×C₃×C₄	C₂³	1	6	yes	—
125	C₃×C₄⋊Q₈	C₂³	1	2	yes	—
126	C₃×C₄⋊Q₈	C₂³	1	3	yes	—
127	C₃×C₄⋊Q₈	C₂³	1	6	yes	—
128	C₃×#127	C₂³	1	12	yes	—
129	C₃×#127	C₂³	1	6	yes	—
130	C₃×#127	C₂³	1	3	yes	—
131	C₃×#127	C₂³	1	12	yes	—
132	C₃×#127	C₂³	1	12	yes	—
133	C₃×#127	C₂³	1	12	yes	—
134	C₃×#127	C₂³	1	6	yes	—
135	C₃×#126	C₂³	1	4	yes	—
136	C₃×#126	C₂³	1	12	yes	—
137	C₃×#126	C₂³	1	12	yes	—
138	C₃×#126	C₂³	1	24	yes	—
139	C₃×#125	C₂³	1	2	yes	—
140	C₃×#125	C₂³	1	12	yes	—
141	C₃×#125	C₂³	1	12	yes	—
142	C₃×#124	C₂³	1	24	yes	—
143	C₃×#124	C₂³	1	12	yes	—
144	C₃×#124	C₂³	1	12	yes	—
145	C₃×#124	C₂³	1	6	yes	—
146	C₃×#124	C₂³	1	1	yes	characteristic
147	C₃×#124	C₂³	1	3	yes	—
148	C₃×#124	C₂³	1	12	yes	—
149	C₃×#124	C₂³	1	6	yes	—
150	C₃×#124	C₂³	1	12	yes	—
151	C₃×#124	C₂³	1	6	yes	—
152	C₃×#124	C₂³	1	6	yes	—
153	C₃×#123	C₂³	1	12	yes	—
154	C₃×#123	C₂³	1	24	yes	—
155	C₃×#123	C₂³	1	2	yes	—
156	C₃×#123	C₂³	1	6	yes	—
157	C₃×#123	C₂³	1	12	yes	—
158	C₃×#123	C₂³	1	12	yes	—
159	C₃×#123	C₂³	1	12	yes	—
160	C₃×#123	C₂³	1	24	yes	—
161	C₃×#123	C₂³	1	12	yes	—
162	C₃×#123	C₂³	1	12	yes	—
163	C₃×#123	C₂³	1	24	yes	—
164	C₃×C₂²⋊Q₈	C₂³	1	4	yes	—
165	C₃×C₂²⋊Q₈	C₂³	1	6	yes	—
166	C₃×C₂²⋊Q₈	C₂³	1	12	yes	—
167	C₃×C₂²⋊Q₈	C₂³	1	12	yes	—
168	C₃×C₂²⋊Q₈	C₂³	1	12	yes	—
169	C₃×C₂²⋊Q₈	C₂³	1	12	yes	—
170	C₃×C₂²⋊Q₈	C₂³	1	12	yes	—
171	C₃×#121	C₂³	1	12	yes	—
172	C₃×#121	C₂³	1	6	yes	—
173	C₃×#121	C₂³	1	12	yes	—
174	C₃×#121	C₂³	1	12	yes	—
175	C₃×#121	C₂³	1	12	yes	—
176	C₃×#121	C₂³	1	12	yes	—
177	C₃×#121	C₂³	1	12	yes	—
178	C₃×#121	C₂³	1	12	yes	—
179	C₃×#121	C₂³	1	24	yes	—
180	C₃×#121	C₂³	1	24	yes	—
181	C₃×#121	C₂³	1	24	yes	—
182	C₃×#121	C₂³	1	24	yes	—
183	C₃×#121	C₂³	1	24	yes	—
184	C₃×#121	C₂³	1	24	yes	—
185	C₃×#121	C₂³	1	12	yes	—
186	C₃×#121	C₂³	1	12	yes	—
187	C₃×#121	C₂³	1	12	yes	—
188	C₃×#121	C₂³	1	12	yes	—
189	C₃×#121	C₂³	1	12	yes	—
190	C₃×#121	C₂³	1	12	yes	—
191	C₃×#121	C₂³	1	12	yes	—
192	C₃×#121	C₂³	1	12	yes	—
193	C₃×#120	C₂³	1	12	yes	—
194	C₃×#120	C₂³	1	6	yes	—
195	C₃×#120	C₂³	1	6	yes	—
196	C₃×#120	C₂³	1	12	yes	—
197	C₃×#120	C₂³	1	12	yes	—
198	C₃×#120	C₂³	1	24	yes	—
199	C₃×#120	C₂³	1	24	yes	—
200	C₃×#120	C₂³	1	12	yes	—
201	C₃×#120	C₂³	1	24	yes	—
202	C₃×#120	C₂³	1	12	yes	—
203	C₃×#120	C₂³	1	12	yes	—
204	C₃×C₄×Q₈	C₂³	1	6	yes	—
205	C₃×C₄×Q₈	C₂³	1	12	yes	—
206	C₃×C₄×Q₈	C₂³	1	4	yes	—
207	C₃×C₄×Q₈	C₂³	1	2	yes	—
208	C₃×C₄×D₄	C₂³	1	12	yes	—
209	C₃×C₄×D₄	C₂³	1	12	yes	—
210	C₃×C₄×D₄	C₂³	1	24	yes	—
211	C₃×C₄×D₄	C₂³	1	6	yes	—
212	C₃×C₄×D₄	C₂³	1	12	yes	—
213	C₃×C₄×D₄	C₂³	1	12	yes	—
214	C₃×C₄×D₄	C₂³	1	6	yes	—
215	C₃×C₄×D₄	C₂³	1	12	yes	—
216	C₃×C₄×D₄	C₂³	1	12	yes	—
217	C₃×C₄×D₄	C₂³	1	12	yes	—
218	C₃×C₄×D₄	C₂³	1	24	yes	—
219	C₃×C₄×D₄	C₂³	1	12	yes	—
220	C₃×#117	C₂³	1	6	yes	—
221	C₃×#117	C₂³	1	3	yes	—
222	C₃×#117	C₂³	1	6	yes	—
223	C₃×#117	C₂³	1	6	yes	—
224	C₃×#117	C₂³	1	12	yes	—
225	C₃×#117	C₂³	1	24	yes	—
226	C₂×C₃×C₄⋊C₄	C₂³	1	12	yes	—
227	C₂×C₃×C₂²⋊C₄	C₂³	1	24	yes	—
228	C₂×C₃×C₂²⋊C₄	C₂³	1	12	yes	—
229	C₂×C₃×C₄²	C₂³	1	3	yes	—
230	C₂×C₃×C₄²	C₂³	1	6	yes	—
231	C₂×2₋¹⁺⁴	C₂²×C₃	1	1	yes	characteristic, complemented
232	C₂×H(5,𝔽₂)	C₂²×C₃	1	2	yes	complemented
233	C₂×H(5,𝔽₂)	C₂²×C₃	1	1	yes	characteristic, complemented
234	C₂²×#41	C₂²×C₃	1	2	yes	complemented
235	#563	C₂²×C₃	1	1	yes	characteristic, complemented
236	#563	C₂²×C₃	1	6	yes	complemented
237	#562	C₂²×C₃	1	12	yes	complemented
238	#562	C₂²×C₃	1	6	yes	complemented
239	H(3,𝔽₄)	C₂²×C₃	1	3	yes	complemented
240	H(3,𝔽₄)	C₂²×C₃	1	6	yes	complemented
241	#560	C₂²×C₃	1	6	yes	complemented
242	#560	C₂²×C₃	1	12	yes	complemented
243	#560	C₂²×C₃	1	12	yes	complemented
244	#560	C₂²×C₃	1	12	yes	complemented
245	#559	C₂²×C₃	1	12	yes	complemented
246	#557	C₂²×C₃	1	2	yes	complemented
247	#555	C₂²×C₃	1	12	yes	complemented
248	#555	C₂²×C₃	1	6	yes	complemented
249	#553	C₂²×C₃	1	12	yes	complemented
250	#553	C₂²×C₃	1	12	yes	complemented
251	#552	C₂²×C₃	1	12	yes	complemented
252	#551	C₂²×C₃	1	12	yes	complemented
253	#550	C₂²×C₃	1	4	yes	complemented
254	#550	C₂²×C₃	1	12	yes	complemented
255	#550	C₂²×C₃	1	2	yes	complemented
256	#550	C₂²×C₃	1	4	yes	complemented
257	#550	C₂²×C₃	1	6	yes	complemented
258	#548	C₂²×C₃	1	4	yes	complemented
259	#548	C₂²×C₃	1	12	yes	complemented
260	#548	C₂²×C₃	1	4	yes	complemented
261	#547	C₂²×C₃	1	6	yes	complemented
262	#546	C₂²×C₃	1	12	yes	complemented
263	#546	C₂²×C₃	1	12	yes	complemented
264	#546	C₂²×C₃	1	12	yes	complemented
265	#546	C₂²×C₃	1	24	yes	complemented
266	D₄²	C₂²×C₃	1	12	yes	complemented
267	D₄²	C₂²×C₃	1	12	yes	complemented
268	D₄²	C₂²×C₃	1	12	yes	complemented
269	D₄²	C₂²×C₃	1	12	yes	complemented
270	D₄²	C₂²×C₃	1	6	yes	complemented
271	D₄²	C₂²×C₃	1	12	yes	complemented
272	#542	C₂²×C₃	1	12	yes	complemented
273	#540	C₂²×C₃	1	12	yes	complemented
274	#540	C₂²×C₃	1	12	yes	complemented
275	#540	C₂²×C₃	1	24	yes	complemented
276	#538	C₂²×C₃	1	24	yes	complemented
277	#538	C₂²×C₃	1	12	yes	complemented
278	#537	C₂²×C₃	1	12	yes	complemented
279	#536	C₂²×C₃	1	3	yes	complemented
280	#535	C₂²×C₃	1	6	yes	complemented
281	#535	C₂²×C₃	1	6	yes	complemented
282	#535	C₂²×C₃	1	12	yes	complemented
283	#535	C₂²×C₃	1	6	yes	complemented
284	#535	C₂²×C₃	1	6	yes	complemented
285	#535	C₂²×C₃	1	3	yes	complemented
286	#535	C₂²×C₃	1	24	yes	complemented
287	#534	C₂²×C₃	1	24	yes	complemented
288	#534	C₂²×C₃	1	12	yes	complemented
289	#532	C₂²×C₃	1	6	yes	complemented
290	#532	C₂²×C₃	1	3	yes	complemented
291	#532	C₂²×C₃	1	6	yes	complemented
292	C₂×#127	C₂²×C₃	1	6	yes	complemented
293	#529	C₂²×C₃	1	6	yes	complemented
294	#529	C₂²×C₃	1	12	yes	complemented
295	#529	C₂²×C₃	1	12	yes	complemented
296	C₂×#124	C₂²×C₃	1	3	yes	complemented
297	#525	C₂²×C₃	1	6	yes	complemented
298	#525	C₂²×C₃	1	6	yes	complemented
299	#525	C₂²×C₃	1	12	yes	complemented
300	C₂×#121	C₂²×C₃	1	12	yes	complemented
301	#520	C₂²×C₃	1	4	yes	complemented
302	#519	C₂²×C₃	1	2	yes	complemented
303	C₄×#41	C₂²×C₃	1	2	yes	complemented
304	C₄×#41	C₂²×C₃	1	1	yes	characteristic, complemented
305	C₂⁴×C₃	C₂⁴	1	6	yes	—
306	C₂⁴×C₃	C₂⁴	1	12	yes	—
307	C₂⁴×C₃	C₂⁴	1	6	yes	—
308	C₃×#41	—	2	16	no	—
309	C₃×#41	—	2	8	no	—
310	C₃×#41	—	2	4	no	—
311	C₃×#41	—	4	12	no	—
312	C₃×#41	—	4	6	no	—
313	C₃×#41	—	4	6	no	—
314	C₃×#41	—	4	24	no	—
315	C₃×#41	—	4	12	no	—
316	C₃×#41	—	8	12	no	—
317	C₂×C₃×Q₈	—	2	8	no	—
318	C₂×C₃×Q₈	—	4	6	no	—
319	C₂×C₃×Q₈	C₂⁴	1	6	yes	—
320	C₂×C₃×Q₈	C₂⁴	1	6	yes	—
321	C₂×C₃×Q₈	C₂⁴	1	2	yes	—
322	C₂×C₃×Q₈	C₂⁴	1	3	yes	—
323	C₂×C₃×Q₈	C₂⁴	1	1	yes	characteristic
324	C₂×C₃×Q₈	C₂⁴	1	1	yes	characteristic
325	C₂×C₃×D₄	—	4	12	no	—
326	C₂×C₃×D₄	—	4	24	no	—
327	C₂×C₃×D₄	—	4	12	no	—
328	C₂×C₃×D₄	—	4	12	no	—
329	C₂×C₃×D₄	—	4	6	no	—
330	C₂×C₃×D₄	—	8	24	no	—
331	C₂×C₃×D₄	—	8	24	no	—
332	C₂×C₃×D₄	C₂⁴	1	6	yes	—
333	C₂×C₃×D₄	C₂⁴	1	12	yes	—
334	C₂×C₃×D₄	C₂⁴	1	3	yes	—
335	C₂×C₃×D₄	C₂⁴	1	6	yes	—
336	C₂×C₃×D₄	C₂⁴	1	12	yes	—
337	C₂×C₃×D₄	C₂⁴	1	24	yes	—
338	C₂×C₃×D₄	C₂⁴	1	24	yes	—
339	C₂×C₃×D₄	C₂⁴	1	12	yes	—
340	C₂×C₃×D₄	C₂⁴	1	12	yes	—
341	C₂×C₃×D₄	C₂⁴	1	12	yes	—
342	C₂×C₃×D₄	C₂⁴	1	12	yes	—
343	C₂×C₃×D₄	C₂⁴	1	1	yes	characteristic
344	C₂×C₃×D₄	C₂⁴	1	6	yes	—
345	C₂×C₃×D₄	C₂⁴	1	12	yes	—
346	C₂×C₃×D₄	C₂⁴	1	3	yes	—
347	C₂×C₃×D₄	C₂⁴	1	12	yes	—
348	C₂×C₃×D₄	C₂⁴	1	6	yes	—
349	C₂×C₃×D₄	C₂⁴	1	6	yes	—
350	C₂²×C₃×C₄	—	4	12	no	—
351	C₂²×C₃×C₄	C₂⁴	1	3	yes	—
352	C₂²×C₃×C₄	C₂⁴	1	6	yes	—
353	C₂²×C₃×C₄	C₂⁴	1	12	yes	—
354	C₂²×C₃×C₄	C₂⁴	1	6	yes	—
355	C₂²×C₃×C₄	C₂⁴	1	6	yes	—
356	C₂²×C₃×C₄	C₂⁴	1	12	yes	—
357	C₂²×C₃×C₄	C₂⁴	1	6	yes	—
358	C₂²×C₃×C₄	C₂⁴	1	12	yes	—
359	C₂²×C₃×C₄	C₂⁴	1	24	yes	—
360	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
361	C₃×C₄⋊C₄	C₂⁴	1	6	yes	—
362	C₃×C₄⋊C₄	C₂⁴	1	12	yes	—
363	C₃×C₄⋊C₄	C₂⁴	1	12	yes	—
364	C₃×C₄⋊C₄	C₂⁴	1	4	yes	—
365	C₃×C₄⋊C₄	C₂⁴	1	12	yes	—
366	C₃×C₄⋊C₄	C₂⁴	1	12	yes	—
367	C₃×C₄⋊C₄	C₂⁴	1	12	yes	—
368	C₃×C₄⋊C₄	C₂⁴	1	4	yes	—
369	C₃×C₄⋊C₄	C₂⁴	1	4	yes	—
370	C₃×C₄⋊C₄	C₂⁴	1	12	yes	—
371	C₃×C₄⋊C₄	C₂⁴	1	2	yes	—
372	C₃×C₄⋊C₄	C₂⁴	1	12	yes	—
373	C₃×C₄⋊C₄	C₂⁴	1	2	yes	—
374	C₃×C₂²⋊C₄	C₂⁴	1	12	yes	—
375	C₃×C₂²⋊C₄	C₂⁴	1	24	yes	—
376	C₃×C₂²⋊C₄	C₂⁴	1	12	yes	—
377	C₃×C₂²⋊C₄	C₂⁴	1	12	yes	—
378	C₃×C₂²⋊C₄	C₂⁴	1	24	yes	—
379	C₃×C₂²⋊C₄	C₂⁴	1	2	yes	—
380	C₃×C₂²⋊C₄	C₂⁴	1	6	yes	—
381	C₃×C₂²⋊C₄	C₂⁴	1	12	yes	—
382	C₃×C₂²⋊C₄	C₂⁴	1	12	yes	—
383	C₃×C₂²⋊C₄	C₂⁴	1	12	yes	—
384	C₃×C₂²⋊C₄	C₂⁴	1	12	yes	—
385	C₃×C₂²⋊C₄	C₂⁴	1	6	yes	—
386	C₃×C₂²⋊C₄	C₂⁴	1	4	yes	—
387	C₃×C₂²⋊C₄	C₂⁴	1	12	yes	—
388	C₃×C₂²⋊C₄	C₂⁴	1	4	yes	—
389	C₃×C₂²⋊C₄	C₂⁴	1	12	yes	—
390	C₃×C₂²⋊C₄	C₂⁴	1	12	yes	—
391	C₃×C₄²	C₂⁴	1	1	yes	characteristic
392	C₃×C₄²	C₂⁴	1	2	yes	—
393	C₃×C₄²	C₂⁴	1	6	yes	—
394	C₃×C₄²	C₂⁴	1	6	yes	—
395	C₃×C₄²	C₂⁴	1	12	yes	—
396	C₃×C₄²	C₂⁴	1	3	yes	—
397	C₃×C₄²	C₂⁴	1	12	yes	—
398	2₋¹⁺⁴	—	4	4	no	—
399	H(5,𝔽₂)	—	4	8	no	—
400	H(5,𝔽₂)	—	4	4	no	—
401	C₂×#41	—	4	8	no	—
402	C₂×#41	C₂³×C₃	1	2	yes	—
403	C₂×#41	C₂³×C₃	1	1	yes	characteristic
404	C₂×#41	C₂³×C₃	1	4	yes	—
405	C₂×#41	C₂³×C₃	1	3	yes	—
406	C₂×#41	C₂³×C₃	1	6	yes	—
407	C₂×#41	C₂³×C₃	1	6	yes	—
408	C₂×#41	C₂³×C₃	1	3	yes	—
409	C₂×#41	C₂³×C₃	1	12	yes	—
410	C₂×#41	C₂³×C₃	1	12	yes	—
411	C₂²×Q₈	C₂³×C₃	1	2	yes	—
412	C₂²×Q₈	C₂³×C₃	1	3	yes	—
413	C₂²×D₄	C₂³×C₃	1	12	yes	—
414	C₂²×D₄	C₂³×C₃	1	3	yes	—
415	C₂²×D₄	C₂³×C₃	1	6	yes	—
416	C₂²×D₄	C₂³×C₃	1	6	yes	—
417	C₂²×D₄	C₂³×C₃	1	6	yes	—
418	C₂²×D₄	C₂³×C₃	1	24	yes	—
419	C₂²×D₄	C₂³×C₃	1	24	yes	—
420	C₂³×C₄	C₂³×C₃	1	6	yes	—
421	C₄⋊Q₈	C₂³×C₃	1	2	yes	—
422	C₄⋊Q₈	C₂³×C₃	1	3	yes	—
423	C₄⋊Q₈	C₂³×C₃	1	6	yes	—
424	#127	C₂³×C₃	1	6	yes	—
425	#127	C₂³×C₃	1	12	yes	—
426	#127	C₂³×C₃	1	12	yes	—
427	#127	C₂³×C₃	1	12	yes	—
428	#127	C₂³×C₃	1	6	yes	—
429	#127	C₂³×C₃	1	3	yes	—
430	#127	C₂³×C₃	1	12	yes	—
431	#126	C₂³×C₃	1	4	yes	—
432	#126	C₂³×C₃	1	12	yes	—
433	#126	C₂³×C₃	1	12	yes	—
434	#126	C₂³×C₃	1	24	yes	—
435	#125	C₂³×C₃	1	2	yes	—
436	#125	C₂³×C₃	1	12	yes	—
437	#125	C₂³×C₃	1	12	yes	—
438	#124	C₂³×C₃	1	3	yes	—
439	#124	C₂³×C₃	1	6	yes	—
440	#124	C₂³×C₃	1	12	yes	—
441	#124	C₂³×C₃	1	6	yes	—
442	#124	C₂³×C₃	1	12	yes	—
443	#124	C₂³×C₃	1	12	yes	—
444	#124	C₂³×C₃	1	1	yes	characteristic
445	#124	C₂³×C₃	1	6	yes	—
446	#124	C₂³×C₃	1	6	yes	—
447	#124	C₂³×C₃	1	12	yes	—
448	#124	C₂³×C₃	1	24	yes	—
449	#123	C₂³×C₃	1	2	yes	—
450	#123	C₂³×C₃	1	6	yes	—
451	#123	C₂³×C₃	1	12	yes	—
452	#123	C₂³×C₃	1	12	yes	—
453	#123	C₂³×C₃	1	24	yes	—
454	#123	C₂³×C₃	1	12	yes	—
455	#123	C₂³×C₃	1	12	yes	—
456	#123	C₂³×C₃	1	12	yes	—
457	#123	C₂³×C₃	1	24	yes	—
458	#123	C₂³×C₃	1	24	yes	—
459	#123	C₂³×C₃	1	12	yes	—
460	C₂²⋊Q₈	C₂³×C₃	1	4	yes	—
461	C₂²⋊Q₈	C₂³×C₃	1	12	yes	—
462	C₂²⋊Q₈	C₂³×C₃	1	12	yes	—
463	C₂²⋊Q₈	C₂³×C₃	1	12	yes	—
464	C₂²⋊Q₈	C₂³×C₃	1	12	yes	—
465	C₂²⋊Q₈	C₂³×C₃	1	6	yes	—
466	C₂²⋊Q₈	C₂³×C₃	1	12	yes	—
467	#121	C₂³×C₃	1	12	yes	—
468	#121	C₂³×C₃	1	24	yes	—
469	#121	C₂³×C₃	1	12	yes	—
470	#121	C₂³×C₃	1	12	yes	—
471	#121	C₂³×C₃	1	12	yes	—
472	#121	C₂³×C₃	1	12	yes	—
473	#121	C₂³×C₃	1	12	yes	—
474	#121	C₂³×C₃	1	12	yes	—
475	#121	C₂³×C₃	1	12	yes	—
476	#121	C₂³×C₃	1	6	yes	—
477	#121	C₂³×C₃	1	12	yes	—
478	#121	C₂³×C₃	1	12	yes	—
479	#121	C₂³×C₃	1	12	yes	—
480	#121	C₂³×C₃	1	12	yes	—
481	#121	C₂³×C₃	1	12	yes	—
482	#121	C₂³×C₃	1	12	yes	—
483	#121	C₂³×C₃	1	12	yes	—
484	#121	C₂³×C₃	1	24	yes	—
485	#121	C₂³×C₃	1	24	yes	—
486	#121	C₂³×C₃	1	24	yes	—
487	#121	C₂³×C₃	1	24	yes	—
488	#121	C₂³×C₃	1	24	yes	—
489	#120	C₂³×C₃	1	12	yes	—
490	#120	C₂³×C₃	1	12	yes	—
491	#120	C₂³×C₃	1	6	yes	—
492	#120	C₂³×C₃	1	6	yes	—
493	#120	C₂³×C₃	1	12	yes	—
494	#120	C₂³×C₃	1	12	yes	—
495	#120	C₂³×C₃	1	24	yes	—
496	#120	C₂³×C₃	1	24	yes	—
497	#120	C₂³×C₃	1	24	yes	—
498	#120	C₂³×C₃	1	12	yes	—
499	#120	C₂³×C₃	1	12	yes	—
500	C₄×Q₈	C₂³×C₃	1	4	yes	—
501	C₄×Q₈	C₂³×C₃	1	2	yes	—
502	C₄×Q₈	C₂³×C₃	1	12	yes	—
503	C₄×Q₈	C₂³×C₃	1	6	yes	—
504	C₄×D₄	C₂³×C₃	1	6	yes	—
505	C₄×D₄	C₂³×C₃	1	12	yes	—
506	C₄×D₄	C₂³×C₃	1	12	yes	—
507	C₄×D₄	C₂³×C₃	1	12	yes	—
508	C₄×D₄	C₂³×C₃	1	12	yes	—
509	C₄×D₄	C₂³×C₃	1	6	yes	—
510	C₄×D₄	C₂³×C₃	1	12	yes	—
511	C₄×D₄	C₂³×C₃	1	12	yes	—
512	C₄×D₄	C₂³×C₃	1	12	yes	—
513	C₄×D₄	C₂³×C₃	1	24	yes	—
514	C₄×D₄	C₂³×C₃	1	24	yes	—
515	C₄×D₄	C₂³×C₃	1	12	yes	—
516	#117	C₂³×C₃	1	6	yes	—
517	#117	C₂³×C₃	1	3	yes	—
518	#117	C₂³×C₃	1	6	yes	—
519	#117	C₂³×C₃	1	6	yes	—
520	#117	C₂³×C₃	1	12	yes	—
521	#117	C₂³×C₃	1	24	yes	—
522	C₂×C₄⋊C₄	C₂³×C₃	1	12	yes	—
523	C₂×C₂²⋊C₄	C₂³×C₃	1	24	yes	—
524	C₂×C₂²⋊C₄	C₂³×C₃	1	12	yes	—
525	C₂×C₄²	C₂³×C₃	1	3	yes	—
526	C₂×C₄²	C₂³×C₃	1	6	yes	—
527	C₂³×C₃	—	4	6	no	—
528	C₂³×C₃	—	4	12	no	—
529	C₂³×C₃	—	4	6	no	—
530	C₂³×C₃	—	4	12	no	—
531	C₂³×C₃	—	4	24	no	—
532	C₂³×C₃	—	4	12	no	—
533	C₂³×C₃	C₂⁵	1	6	yes	—
534	C₂³×C₃	C₂⁵	1	2	yes	—
535	C₂³×C₃	C₂⁵	1	12	yes	—
536	C₂³×C₃	C₂⁵	1	3	yes	—
537	C₃×Q₈	—	2	12	no	—
538	C₃×Q₈	—	4	3	no	—
539	C₃×Q₈	—	4	2	no	—
540	C₃×Q₈	—	4	1	no	—
541	C₃×Q₈	—	4	6	no	—
542	C₃×Q₈	H(5,𝔽₂)	1	4	yes	—
543	C₃×D₄	—	2	12	no	—
544	C₃×D₄	—	2	24	no	—
545	C₃×D₄	—	2	6	no	—
546	C₃×D₄	—	4	12	no	—
547	C₃×D₄	—	4	6	no	—
548	C₃×D₄	—	4	6	no	—
549	C₃×D₄	—	4	3	no	—
550	C₃×D₄	—	4	12	no	—
551	C₃×D₄	—	4	12	no	—
552	C₃×D₄	—	4	12	no	—
553	C₃×D₄	—	4	12	no	—
554	C₃×D₄	—	4	12	no	—
555	C₃×D₄	—	4	24	no	—
556	C₃×D₄	—	4	12	no	—
557	C₃×D₄	—	4	24	no	—
558	C₃×D₄	—	4	1	no	—
559	C₃×D₄	—	4	6	no	—
560	C₃×D₄	—	4	6	no	—
561	C₂×C₃×C₄	—	2	12	no	—
562	C₂×C₃×C₄	—	2	24	no	—
563	C₂×C₃×C₄	—	2	12	no	—
564	C₂×C₃×C₄	—	2	6	no	—
565	C₂×C₃×C₄	—	4	2	no	—
566	C₂×C₃×C₄	—	4	12	no	—
567	C₂×C₃×C₄	—	4	12	no	—
568	C₂×C₃×C₄	—	4	24	no	—
569	C₂×C₃×C₄	—	4	6	no	—
570	C₂×C₃×C₄	—	4	6	no	—
571	C₂×C₃×C₄	C₂⁵	1	2	yes	—
572	C₂×C₃×C₄	C₂⁵	1	1	yes	characteristic
573	C₂×C₃×C₄	C₂⁵	1	12	yes	—
574	C₂×C₃×C₄	C₂⁵	1	4	yes	—
575	C₂×C₃×C₄	C₂⁵	1	2	yes	—
576	C₂×C₃×C₄	C₂⁵	1	6	yes	—
577	C₂×C₃×C₄	C₂⁵	1	6	yes	—
578	C₂×C₃×C₄	C₂⁵	1	4	yes	—
579	C₂×C₃×C₄	C₂⁵	1	3	yes	—
580	C₂⁴	C₂⁴×C₃	1	6	yes	—
581	C₂⁴	C₂⁴×C₃	1	12	yes	—
582	C₂⁴	C₂⁴×C₃	1	6	yes	—
583	#41	—	2	16	no	—
584	#41	—	2	8	no	—
585	#41	—	2	4	no	—
586	#41	—	4	12	no	—
587	#41	—	4	6	no	—
588	#41	—	4	6	no	—
589	#41	—	4	24	no	—
590	#41	—	4	12	no	—
591	#41	—	8	12	no	—
592	C₂×Q₈	—	2	8	no	—
593	C₂×Q₈	—	4	6	no	—
594	C₂×Q₈	C₂⁴×C₃	1	6	yes	—
595	C₂×Q₈	C₂⁴×C₃	1	6	yes	—
596	C₂×Q₈	C₂⁴×C₃	1	2	yes	—
597	C₂×Q₈	C₂⁴×C₃	1	3	yes	—
598	C₂×Q₈	C₂⁴×C₃	1	1	yes	characteristic
599	C₂×Q₈	C₂⁴×C₃	1	1	yes	characteristic
600	C₂×D₄	—	4	12	no	—
601	C₂×D₄	—	4	24	no	—
602	C₂×D₄	—	4	12	no	—
603	C₂×D₄	—	4	12	no	—
604	C₂×D₄	—	4	6	no	—
605	C₂×D₄	—	8	24	no	—
606	C₂×D₄	—	8	24	no	—
607	C₂×D₄	C₂⁴×C₃	1	6	yes	—
608	C₂×D₄	C₂⁴×C₃	1	12	yes	—
609	C₂×D₄	C₂⁴×C₃	1	3	yes	—
610	C₂×D₄	C₂⁴×C₃	1	6	yes	—
611	C₂×D₄	C₂⁴×C₃	1	12	yes	—
612	C₂×D₄	C₂⁴×C₃	1	24	yes	—
613	C₂×D₄	C₂⁴×C₃	1	24	yes	—
614	C₂×D₄	C₂⁴×C₃	1	12	yes	—
615	C₂×D₄	C₂⁴×C₃	1	12	yes	—
616	C₂×D₄	C₂⁴×C₃	1	12	yes	—
617	C₂×D₄	C₂⁴×C₃	1	12	yes	—
618	C₂×D₄	C₂⁴×C₃	1	1	yes	characteristic
619	C₂×D₄	C₂⁴×C₃	1	6	yes	—
620	C₂×D₄	C₂⁴×C₃	1	12	yes	—
621	C₂×D₄	C₂⁴×C₃	1	3	yes	—
622	C₂×D₄	C₂⁴×C₃	1	12	yes	—
623	C₂×D₄	C₂⁴×C₃	1	6	yes	—
624	C₂×D₄	C₂⁴×C₃	1	6	yes	—
625	C₂²×C₄	—	4	12	no	—
626	C₂²×C₄	C₂⁴×C₃	1	3	yes	—
627	C₂²×C₄	C₂⁴×C₃	1	6	yes	—
628	C₂²×C₄	C₂⁴×C₃	1	12	yes	—
629	C₂²×C₄	C₂⁴×C₃	1	6	yes	—
630	C₂²×C₄	C₂⁴×C₃	1	6	yes	—
631	C₂²×C₄	C₂⁴×C₃	1	12	yes	—
632	C₂²×C₄	C₂⁴×C₃	1	6	yes	—
633	C₂²×C₄	C₂⁴×C₃	1	12	yes	—
634	C₂²×C₄	C₂⁴×C₃	1	24	yes	—
635	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
636	C₄⋊C₄	C₂⁴×C₃	1	6	yes	—
637	C₄⋊C₄	C₂⁴×C₃	1	12	yes	—
638	C₄⋊C₄	C₂⁴×C₃	1	12	yes	—
639	C₄⋊C₄	C₂⁴×C₃	1	4	yes	—
640	C₄⋊C₄	C₂⁴×C₃	1	12	yes	—
641	C₄⋊C₄	C₂⁴×C₃	1	12	yes	—
642	C₄⋊C₄	C₂⁴×C₃	1	12	yes	—
643	C₄⋊C₄	C₂⁴×C₃	1	4	yes	—
644	C₄⋊C₄	C₂⁴×C₃	1	4	yes	—
645	C₄⋊C₄	C₂⁴×C₃	1	12	yes	—
646	C₄⋊C₄	C₂⁴×C₃	1	2	yes	—
647	C₄⋊C₄	C₂⁴×C₃	1	12	yes	—
648	C₄⋊C₄	C₂⁴×C₃	1	2	yes	—
649	C₂²⋊C₄	C₂⁴×C₃	1	12	yes	—
650	C₂²⋊C₄	C₂⁴×C₃	1	24	yes	—
651	C₂²⋊C₄	C₂⁴×C₃	1	12	yes	—
652	C₂²⋊C₄	C₂⁴×C₃	1	12	yes	—
653	C₂²⋊C₄	C₂⁴×C₃	1	24	yes	—
654	C₂²⋊C₄	C₂⁴×C₃	1	2	yes	—
655	C₂²⋊C₄	C₂⁴×C₃	1	6	yes	—
656	C₂²⋊C₄	C₂⁴×C₃	1	12	yes	—
657	C₂²⋊C₄	C₂⁴×C₃	1	12	yes	—
658	C₂²⋊C₄	C₂⁴×C₃	1	12	yes	—
659	C₂²⋊C₄	C₂⁴×C₃	1	12	yes	—
660	C₂²⋊C₄	C₂⁴×C₃	1	6	yes	—
661	C₂²⋊C₄	C₂⁴×C₃	1	4	yes	—
662	C₂²⋊C₄	C₂⁴×C₃	1	12	yes	—
663	C₂²⋊C₄	C₂⁴×C₃	1	4	yes	—
664	C₂²⋊C₄	C₂⁴×C₃	1	12	yes	—
665	C₂²⋊C₄	C₂⁴×C₃	1	12	yes	—
666	C₄²	C₂⁴×C₃	1	1	yes	characteristic
667	C₄²	C₂⁴×C₃	1	2	yes	—
668	C₄²	C₂⁴×C₃	1	6	yes	—
669	C₄²	C₂⁴×C₃	1	6	yes	—
670	C₄²	C₂⁴×C₃	1	12	yes	—
671	C₄²	C₂⁴×C₃	1	3	yes	—
672	C₄²	C₂⁴×C₃	1	12	yes	—
673	C₂²×C₃	—	2	2	no	—
674	C₂²×C₃	—	2	3	no	—
675	C₂²×C₃	—	2	12	no	—
676	C₂²×C₃	—	2	6	no	—
677	C₂²×C₃	—	2	12	no	—
678	C₂²×C₃	—	2	6	no	—
679	C₂²×C₃	—	2	12	no	—
680	C₂²×C₃	—	2	4	no	—
681	C₂²×C₃	—	2	12	no	—
682	C₂²×C₃	—	8	12	no	—
683	C₂²×C₃	—	16	12	no	—
684	C₂²×C₃	—	16	6	no	—
685	C₂²×C₃	C₂⁶	1	1	yes	characteristic
686	C₃×C₄	—	2	4	no	—
687	C₃×C₄	—	2	2	no	—
688	C₃×C₄	—	2	1	no	—
689	C₃×C₄	—	2	6	no	—
690	C₃×C₄	—	2	6	no	—
691	C₃×C₄	—	2	4	no	—
692	C₃×C₄	—	2	12	no	—
693	C₃×C₄	—	2	2	no	—
694	C₃×C₄	C₂×H(5,𝔽₂)	1	6	yes	—
695	C₂³	—	4	6	no	—
696	C₂³	—	4	12	no	—
697	C₂³	—	4	6	no	—
698	C₂³	—	4	12	no	—
699	C₂³	—	4	24	no	—
700	C₂³	—	4	12	no	—
701	C₂³	C₂⁵×C₃	1	6	yes	—
702	C₂³	C₂⁵×C₃	1	2	yes	—
703	C₂³	C₂⁵×C₃	1	12	yes	—
704	C₂³	C₂⁵×C₃	1	3	yes	—
705	Q₈	—	2	12	no	—
706	Q₈	—	4	3	no	—
707	Q₈	—	4	2	no	—
708	Q₈	—	4	1	no	—
709	Q₈	—	4	6	no	—
710	Q₈	C₃×H(5,𝔽₂)	1	4	yes	—
711	D₄	—	2	12	no	—
712	D₄	—	2	24	no	—
713	D₄	—	2	6	no	—
714	D₄	—	4	12	no	—
715	D₄	—	4	6	no	—
716	D₄	—	4	6	no	—
717	D₄	—	4	3	no	—
718	D₄	—	4	12	no	—
719	D₄	—	4	12	no	—
720	D₄	—	4	12	no	—
721	D₄	—	4	12	no	—
722	D₄	—	4	12	no	—
723	D₄	—	4	24	no	—
724	D₄	—	4	12	no	—
725	D₄	—	4	24	no	—
726	D₄	—	4	1	no	—
727	D₄	—	4	6	no	—
728	D₄	—	4	6	no	—
729	C₂×C₄	—	2	12	no	—
730	C₂×C₄	—	2	24	no	—
731	C₂×C₄	—	2	12	no	—
732	C₂×C₄	—	2	6	no	—
733	C₂×C₄	—	4	2	no	—
734	C₂×C₄	—	4	12	no	—
735	C₂×C₄	—	4	12	no	—
736	C₂×C₄	—	4	24	no	—
737	C₂×C₄	—	4	6	no	—
738	C₂×C₄	—	4	6	no	—
739	C₂×C₄	C₂⁵×C₃	1	2	yes	—
740	C₂×C₄	C₂⁵×C₃	1	1	yes	characteristic
741	C₂×C₄	C₂⁵×C₃	1	12	yes	—
742	C₂×C₄	C₂⁵×C₃	1	4	yes	—
743	C₂×C₄	C₂⁵×C₃	1	2	yes	—
744	C₂×C₄	C₂⁵×C₃	1	6	yes	—
745	C₂×C₄	C₂⁵×C₃	1	6	yes	—
746	C₂×C₄	C₂⁵×C₃	1	4	yes	—
747	C₂×C₄	C₂⁵×C₃	1	3	yes	—
748	C₂×C₃	—	4	2	no	—
749	C₂×C₃	—	4	12	no	—
750	C₂×C₃	—	4	3	no	—
751	C₂×C₃	—	4	6	no	—
752	C₂×C₃	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
753	C₂×C₃	H(7,𝔽₂)	1	2	yes	—
754	C₂²	—	2	2	no	—
755	C₂²	—	2	3	no	—
756	C₂²	—	2	12	no	—
757	C₂²	—	2	6	no	—
758	C₂²	—	2	12	no	—
759	C₂²	—	2	6	no	—
760	C₂²	—	2	12	no	—
761	C₂²	—	2	4	no	—
762	C₂²	—	2	12	no	—
763	C₂²	—	8	12	no	—
764	C₂²	—	16	12	no	—
765	C₂²	—	16	6	no	—
766	C₂²	C₂⁶×C₃	1	1	yes	characteristic
767	C₄	—	2	4	no	—
768	C₄	—	2	2	no	—
769	C₄	—	2	1	no	—
770	C₄	—	2	6	no	—
771	C₄	—	2	6	no	—
772	C₄	—	2	4	no	—
773	C₄	—	2	12	no	—
774	C₄	—	2	2	no	—
775	C₄	C₂×C₃×H(5,𝔽₂)	1	6	yes	—
776	C₃	#63066	1	1	yes	characteristic, direct product factor, Sylow
777	C₂	—	4	2	no	—
778	C₂	—	4	12	no	—
779	C₂	—	4	6	no	—
780	C₂	—	4	3	no	—
781	C₂	C₂²×C₃×H(5,𝔽₂)	1	1	yes	characteristic
782	C₂	C₃×H(7,𝔽₂)	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×#3551	C₂	semidirect
3. C₃×#3549	C₂	semidirect
4. C₃×#3543	C₂	semidirect
5. C₃×#3542	C₂	semidirect
6. C₃×#3537	C₂	semidirect
7. C₃×#3529	C₂	semidirect
8. C₃×#3524	C₂	semidirect
9. C₃×#3517	C₂	semidirect
10. C₃×#3500	C₂	semidirect
11. C₃×#3498	C₂	semidirect
12. C₃×#3488	C₂	semidirect
13. C₃×#3487	C₂	semidirect
14. #63066	C₃	direct (N × H)
15. C₂×C₃×2₋¹⁺⁴	C₂²	semidirect
16. C₂×C₃×H(5,𝔽₂)	C₂²	semidirect
17. C₂×C₃×H(5,𝔽₂)	C₂²	semidirect
18. C₂²×C₃×#41	C₂²	semidirect
19. C₃×#563	C₂²	semidirect
20. C₃×#563	C₂²	semidirect
21. C₃×#562	C₂²	semidirect
22. C₃×#562	C₂²	semidirect
23. C₃×H(3,𝔽₄)	C₂²	semidirect
24. C₃×H(3,𝔽₄)	C₂²	semidirect
25. C₃×#560	C₂²	semidirect
26. C₃×#560	C₂²	semidirect
27. C₃×#560	C₂²	semidirect
28. C₃×#560	C₂²	semidirect
29. C₃×#559	C₂²	semidirect
30. C₃×#557	C₂²	semidirect
31. C₃×#555	C₂²	semidirect
32. C₃×#555	C₂²	semidirect
33. C₃×#553	C₂²	semidirect
34. C₃×#553	C₂²	semidirect
35. C₃×#552	C₂²	semidirect
36. C₃×#551	C₂²	semidirect
37. C₃×#550	C₂²	semidirect
38. C₃×#550	C₂²	semidirect
39. C₃×#550	C₂²	semidirect
40. C₃×#550	C₂²	semidirect
41. C₃×#550	C₂²	semidirect
42. C₃×#548	C₂²	semidirect
43. C₃×#548	C₂²	semidirect
44. C₃×#548	C₂²	semidirect
45. C₃×#547	C₂²	semidirect
46. C₃×#546	C₂²	semidirect
47. C₃×#546	C₂²	semidirect
48. C₃×#546	C₂²	semidirect
49. C₃×#546	C₂²	semidirect
50. C₃×D₄²	C₂²	semidirect
51. C₃×D₄²	C₂²	semidirect
52. C₃×D₄²	C₂²	semidirect
53. C₃×D₄²	C₂²	semidirect
54. C₃×D₄²	C₂²	semidirect
55. C₃×D₄²	C₂²	semidirect
56. C₃×#542	C₂²	semidirect
57. C₃×#540	C₂²	semidirect
58. C₃×#540	C₂²	semidirect
59. C₃×#540	C₂²	semidirect
60. C₃×#538	C₂²	semidirect
61. C₃×#538	C₂²	semidirect
62. C₃×#537	C₂²	semidirect
63. C₃×#536	C₂²	semidirect
64. C₃×#535	C₂²	semidirect
65. C₃×#535	C₂²	semidirect
66. C₃×#535	C₂²	semidirect
67. C₃×#535	C₂²	semidirect
68. C₃×#535	C₂²	semidirect
69. C₃×#535	C₂²	semidirect
70. C₃×#535	C₂²	semidirect
71. C₃×#534	C₂²	semidirect
72. C₃×#534	C₂²	semidirect
73. C₃×#532	C₂²	semidirect
74. C₃×#532	C₂²	semidirect
75. C₃×#532	C₂²	semidirect
76. C₂×C₃×#127	C₂²	semidirect
77. C₃×#529	C₂²	semidirect
78. C₃×#529	C₂²	semidirect
79. C₃×#529	C₂²	semidirect
80. C₂×C₃×#124	C₂²	semidirect
81. C₃×#525	C₂²	semidirect
82. C₃×#525	C₂²	semidirect
83. C₃×#525	C₂²	semidirect
84. C₂×C₃×#121	C₂²	semidirect
85. C₃×#520	C₂²	semidirect
86. C₃×#519	C₂²	semidirect
87. C₃×C₄×#41	C₂²	semidirect
88. C₃×C₄×#41	C₂²	semidirect
89. #3558	C₂×C₃	semidirect
90. #3551	C₂×C₃	semidirect
91. #3549	C₂×C₃	semidirect
92. #3543	C₂×C₃	semidirect
93. #3542	C₂×C₃	semidirect
94. #3537	C₂×C₃	semidirect
95. #3529	C₂×C₃	semidirect
96. #3524	C₂×C₃	semidirect
97. #3517	C₂×C₃	semidirect
98. #3500	C₂×C₃	semidirect
99. #3498	C₂×C₃	semidirect
100. #3488	C₂×C₃	semidirect
101. #3487	C₂×C₃	semidirect
231. C₂×2₋¹⁺⁴	C₂²×C₃	semidirect
232. C₂×H(5,𝔽₂)	C₂²×C₃	semidirect
233. C₂×H(5,𝔽₂)	C₂²×C₃	semidirect
234. C₂²×#41	C₂²×C₃	semidirect
235. #563	C₂²×C₃	semidirect
236. #563	C₂²×C₃	semidirect
237. #562	C₂²×C₃	semidirect
238. #562	C₂²×C₃	semidirect
239. H(3,𝔽₄)	C₂²×C₃	semidirect
240. H(3,𝔽₄)	C₂²×C₃	semidirect
241. #560	C₂²×C₃	semidirect
242. #560	C₂²×C₃	semidirect
243. #560	C₂²×C₃	semidirect
244. #560	C₂²×C₃	semidirect
245. #559	C₂²×C₃	semidirect
246. #557	C₂²×C₃	semidirect
247. #555	C₂²×C₃	semidirect
248. #555	C₂²×C₃	semidirect
249. #553	C₂²×C₃	semidirect
250. #553	C₂²×C₃	semidirect
251. #552	C₂²×C₃	semidirect
252. #551	C₂²×C₃	semidirect
253. #550	C₂²×C₃	semidirect
254. #550	C₂²×C₃	semidirect
255. #550	C₂²×C₃	semidirect
256. #550	C₂²×C₃	semidirect
257. #550	C₂²×C₃	semidirect
258. #548	C₂²×C₃	semidirect
259. #548	C₂²×C₃	semidirect
260. #548	C₂²×C₃	semidirect
261. #547	C₂²×C₃	semidirect
262. #546	C₂²×C₃	semidirect
263. #546	C₂²×C₃	semidirect
264. #546	C₂²×C₃	semidirect
265. #546	C₂²×C₃	semidirect
266. D₄²	C₂²×C₃	semidirect
267. D₄²	C₂²×C₃	semidirect
268. D₄²	C₂²×C₃	semidirect
269. D₄²	C₂²×C₃	semidirect
270. D₄²	C₂²×C₃	semidirect
271. D₄²	C₂²×C₃	semidirect
272. #542	C₂²×C₃	semidirect
273. #540	C₂²×C₃	semidirect
274. #540	C₂²×C₃	semidirect
275. #540	C₂²×C₃	semidirect
276. #538	C₂²×C₃	semidirect
277. #538	C₂²×C₃	semidirect
278. #537	C₂²×C₃	semidirect
279. #536	C₂²×C₃	semidirect
280. #535	C₂²×C₃	semidirect
281. #535	C₂²×C₃	semidirect
282. #535	C₂²×C₃	semidirect
283. #535	C₂²×C₃	semidirect
284. #535	C₂²×C₃	semidirect
285. #535	C₂²×C₃	semidirect
286. #535	C₂²×C₃	semidirect
287. #534	C₂²×C₃	semidirect
288. #534	C₂²×C₃	semidirect
289. #532	C₂²×C₃	semidirect
290. #532	C₂²×C₃	semidirect
291. #532	C₂²×C₃	semidirect
292. C₂×#127	C₂²×C₃	semidirect
293. #529	C₂²×C₃	semidirect
294. #529	C₂²×C₃	semidirect
295. #529	C₂²×C₃	semidirect
296. C₂×#124	C₂²×C₃	semidirect
297. #525	C₂²×C₃	semidirect
298. #525	C₂²×C₃	semidirect
299. #525	C₂²×C₃	semidirect
300. C₂×#121	C₂²×C₃	semidirect
301. #520	C₂²×C₃	semidirect
302. #519	C₂²×C₃	semidirect
303. C₄×#41	C₂²×C₃	semidirect
304. C₄×#41	C₂²×C₃	semidirect
776. C₃	#63066	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×#3551	2
C₃×#3549	2
C₃×#3543	2
C₃×#3542	2
C₃×#3537	2
C₃×#3529	2
C₃×#3524	2
C₃×#3517	2
C₃×#3500	2
C₃×#3498	2
C₃×#3488	2
C₃×#3487	2
#63066	3

Subgroups — C3×#63066 #10681673

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#63066 #10681673