Subgroups — C₃×#60749 #10679356

Order 768.

2166 conjugacy classes of subgroups.

The subgroup lattice has 780 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#3449	C₂	1	2	yes	maximal, complemented
2	C₃×#3204	C₂	1	2	yes	maximal, complemented
3	C₃×#3203	C₂	1	2	yes	maximal, complemented
4	C₃×#3202	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#3201	C₂	1	4	yes	maximal, complemented
6	C₃×#3200	C₂	1	2	yes	maximal, complemented
7	C₃×#3199	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#3198	C₂	1	4	yes	maximal, complemented
9	C₃×#3091	C₂	1	4	yes	maximal, complemented
10	C₃×#3054	C₂	1	2	yes	maximal, complemented
11	C₃×#3050	C₂	1	2	yes	maximal, complemented
12	C₃×#3002	C₂	1	4	yes	maximal, complemented
13	C₂×C₃×#408	C₂	1	1	yes	maximal, characteristic, complemented
14	#60749	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
15	C₂²×C₃×#41	C₂²	1	1	yes	characteristic
16	C₂²×C₃×#41	C₂²	1	2	yes	complemented
17	C₂×C₃×#135	C₂²	1	2	yes	—
18	C₂×C₃×#135	C₂²	1	2	yes	—
19	C₂²×C₃×M₁₆	C₂²	1	1	yes	characteristic, complemented
20	C₂³×C₃×C₈	C₂²	1	1	yes	characteristic, complemented
21	C₃×#537	C₂²	1	4	yes	—
22	C₃×#537	C₂²	1	4	yes	complemented
23	C₃×#536	—	2	2	no	—
24	C₃×#536	C₂²	1	2	yes	—
25	C₃×#536	C₂²	1	2	yes	complemented
26	C₃×#535	—	2	2	no	—
27	C₃×#535	C₂²	1	2	yes	—
28	C₃×#535	C₂²	1	2	yes	complemented
29	C₃×#534	—	2	2	no	—
30	C₃×#534	—	2	2	no	—
31	C₃×#532	—	2	2	no	—
32	C₃×#532	—	2	2	no	—
33	C₃×#525	—	2	2	no	—
34	C₃×#525	—	2	2	no	—
35	C₃×#525	C₂²	1	4	yes	—
36	C₃×#525	C₂²	1	4	yes	complemented
37	C₂×C₃×#117	C₂²	1	2	yes	complemented
38	C₃×#485	C₂²	1	4	yes	complemented
39	C₃×#485	C₂²	1	4	yes	complemented
40	C₃×#484	C₂²	1	4	yes	complemented
41	C₃×#483	C₂²	1	4	yes	complemented
42	C₃×#482	C₂²	1	4	yes	complemented
43	C₃×#482	C₂²	1	4	yes	complemented
44	C₃×#481	C₂²	1	4	yes	complemented
45	C₃×#480	C₂²	1	4	yes	complemented
46	C₃×#470	C₂²	1	2	yes	complemented
47	C₃×#470	C₂²	1	2	yes	complemented
48	C₃×#469	C₂²	1	2	yes	complemented
49	C₃×#469	C₂²	1	2	yes	complemented
50	C₃×#468	C₂²	1	4	yes	complemented
51	C₃×#468	C₂²	1	4	yes	complemented
52	C₃×#467	C₂²	1	2	yes	complemented
53	C₃×#467	C₂²	1	2	yes	complemented
54	C₃×#466	C₂²	1	2	yes	complemented
55	C₃×#466	C₂²	1	2	yes	complemented
56	C₃×#465	C₂²	1	4	yes	complemented
57	C₃×#465	C₂²	1	4	yes	complemented
58	C₃×#452	C₂²	1	4	yes	complemented
59	C₃×#452	C₂²	1	4	yes	complemented
60	C₃×#451	C₂²	1	4	yes	complemented
61	C₃×#450	C₂²	1	4	yes	complemented
62	C₃×#449	C₂²	1	4	yes	complemented
63	C₃×#449	C₂²	1	4	yes	complemented
64	C₃×#448	C₂²	1	4	yes	complemented
65	C₃×#447	C₂²	1	4	yes	complemented
66	C₃×#427	C₂²	1	2	yes	complemented
67	C₃×#427	C₂²	1	2	yes	complemented
68	C₃×#416	C₂²	1	4	yes	complemented
69	C₃×#416	C₂²	1	4	yes	complemented
70	C₃×#408	C₂²	1	1	yes	characteristic
71	C₃×#408	C₂²	1	1	yes	characteristic
72	C₃×#408	C₂²	1	4	yes	complemented
73	C₃×#408	C₂²	1	1	yes	characteristic, complemented
74	C₃×#408	C₂²	1	1	yes	characteristic, complemented
75	C₂×C₃×C₂²⋊C₈	C₂²	1	4	yes	complemented
76	#3449	C₂×C₃	1	2	yes	complemented
77	#3204	C₂×C₃	1	2	yes	complemented
78	#3203	C₂×C₃	1	2	yes	complemented
79	#3202	C₂×C₃	1	1	yes	characteristic, complemented
80	#3201	C₂×C₃	1	4	yes	complemented
81	#3200	C₂×C₃	1	2	yes	complemented
82	#3199	C₂×C₃	1	1	yes	characteristic, complemented
83	#3198	C₂×C₃	1	4	yes	complemented
84	#3091	C₂×C₃	1	4	yes	complemented
85	#3054	C₂×C₃	1	2	yes	complemented
86	#3050	C₂×C₃	1	2	yes	complemented
87	#3002	C₂×C₃	1	4	yes	complemented
88	C₂×#408	C₂×C₃	1	1	yes	characteristic, complemented
89	C₂×C₃×#41	—	2	2	no	—
90	C₂×C₃×#41	—	2	2	no	—
91	C₂×C₃×#41	—	4	2	no	—
92	C₂×C₃×#41	—	4	2	no	—
93	C₂×C₃×#41	—	4	4	no	—
94	C₂×C₃×#41	—	4	4	no	—
95	C₂×C₃×#41	D₄	1	1	yes	characteristic
96	C₂×C₃×#41	D₄	1	2	yes	—
97	C₂×C₃×#41	D₄	1	1	yes	characteristic
98	C₂×C₃×#41	C₂³	1	4	yes	—
99	C₂×C₃×#41	C₂³	1	4	yes	—
100	C₂×C₃×#41	C₂³	1	1	yes	characteristic
101	C₂×C₃×#41	C₂³	1	2	yes	—
102	C₂×C₃×#41	C₂³	1	1	yes	characteristic
103	C₂²×C₃×Q₈	D₄	1	1	yes	characteristic
104	C₂²×C₃×Q₈	C₂³	1	2	yes	—
105	C₂²×C₃×D₄	—	2	2	no	—
106	C₂²×C₃×D₄	D₄	1	1	yes	characteristic
107	C₂²×C₃×D₄	D₄	1	2	yes	—
108	C₂²×C₃×D₄	C₂³	1	2	yes	—
109	C₂³×C₃×C₄	—	2	2	no	—
110	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
111	C₂³×C₃×C₄	C₂³	1	2	yes	—
112	C₃×#135	—	4	4	no	—
113	C₃×#135	—	4	4	no	—
114	C₂×C₃×Q₁₆	C₂³	1	2	yes	—
115	C₂×C₃×Q₁₆	C₂³	1	2	yes	—
116	C₂×C₃×SD₁₆	C₂³	1	4	yes	—
117	C₂×C₃×SD₁₆	C₂³	1	4	yes	—
118	C₂×C₃×D₈	C₂³	1	2	yes	—
119	C₂×C₃×D₈	C₂³	1	2	yes	—
120	C₂×C₃×M₁₆	—	4	2	no	—
121	C₂×C₃×M₁₆	C₂³	1	1	yes	characteristic
122	C₂×C₃×M₁₆	C₂³	1	1	yes	characteristic
123	C₂×C₃×M₁₆	C₂³	1	2	yes	—
124	C₂²×C₃×C₈	—	4	2	no	—
125	C₂²×C₃×C₈	C₂³	1	2	yes	—
126	C₂²×C₃×C₈	C₂³	1	2	yes	—
127	C₂²×C₃×C₈	C₂³	1	1	yes	characteristic
128	C₂²×C₃×C₈	C₂³	1	1	yes	characteristic
129	C₂²×C₃×C₈	C₂³	1	2	yes	—
130	C₃×C₄⋊Q₈	—	2	2	no	—
131	C₃×C₄⋊Q₈	—	2	2	no	—
132	C₃×#127	—	2	2	no	—
133	C₃×#127	—	2	2	no	—
134	C₃×#124	—	2	2	no	—
135	C₃×#124	—	2	2	no	—
136	C₃×#124	—	2	2	no	—
137	C₃×#124	—	2	2	no	—
138	C₃×#123	—	2	2	no	—
139	C₃×#123	—	2	2	no	—
140	C₃×#123	—	2	2	no	—
141	C₃×#123	—	2	2	no	—
142	C₃×#123	—	2	4	no	—
143	C₃×#123	—	2	4	no	—
144	C₃×C₂²⋊Q₈	—	2	4	no	—
145	C₃×C₂²⋊Q₈	—	2	4	no	—
146	C₃×C₂²⋊Q₈	C₂³	1	4	yes	—
147	C₃×C₂²⋊Q₈	C₂³	1	4	yes	—
148	C₃×C₂²⋊Q₈	C₂³	1	4	yes	—
149	C₃×C₂²⋊Q₈	C₂³	1	4	yes	—
150	C₃×#121	—	2	4	no	—
151	C₃×#121	—	2	4	no	—
152	C₃×#121	—	2	4	no	—
153	C₃×#121	—	2	4	no	—
154	C₃×#121	—	2	4	no	—
155	C₃×#121	—	2	4	no	—
156	C₃×#121	C₂³	1	4	yes	—
157	C₃×#121	C₂³	1	4	yes	—
158	C₃×#121	C₂³	1	4	yes	—
159	C₃×#121	C₂³	1	4	yes	—
160	C₃×#120	—	2	4	no	—
161	C₃×#120	—	2	4	no	—
162	C₃×#120	—	2	2	no	—
163	C₃×#120	—	2	2	no	—
164	C₃×#120	—	2	2	no	—
165	C₃×#120	—	2	2	no	—
166	C₃×C₄×D₄	—	2	4	no	—
167	C₃×C₄×D₄	—	2	4	no	—
168	C₃×C₄×D₄	—	2	4	no	—
169	C₃×C₄×D₄	—	2	4	no	—
170	C₃×#117	—	2	2	no	—
171	C₃×#117	—	2	2	no	—
172	C₃×#117	C₂³	1	4	yes	—
173	C₃×#117	C₂³	1	2	yes	—
174	C₃×#117	C₂³	1	2	yes	—
175	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
176	C₂×C₃×C₂²⋊C₄	—	2	2	no	—
177	C₂×C₃×C₄²	—	2	2	no	—
178	C₃×#107	C₂³	1	2	yes	—
179	C₃×#107	C₂³	1	2	yes	—
180	C₃×#107	C₂³	1	4	yes	—
181	C₃×#106	C₂³	1	4	yes	—
182	C₃×#106	C₂³	1	2	yes	—
183	C₃×#106	C₂³	1	2	yes	—
184	C₃×#103	C₂³	1	4	yes	—
185	C₃×#103	C₂³	1	4	yes	—
186	C₃×#103	C₂³	1	4	yes	—
187	C₃×#103	C₂³	1	4	yes	—
188	C₃×#102	C₂³	1	4	yes	—
189	C₃×#102	C₂³	1	4	yes	—
190	C₃×#102	C₂³	1	4	yes	—
191	C₃×#102	C₂³	1	4	yes	—
192	C₃×C₂²⋊C₈	C₂³	1	4	yes	—
193	C₃×C₂²⋊C₈	C₂³	1	4	yes	—
194	C₃×C₂²⋊C₈	C₂³	1	4	yes	—
195	C₃×C₂²⋊C₈	C₂³	1	4	yes	—
196	C₂²×#41	C₂²×C₃	1	1	yes	characteristic
197	C₂²×#41	C₂²×C₃	1	2	yes	complemented
198	C₂×#135	C₂²×C₃	1	2	yes	—
199	C₂×#135	C₂²×C₃	1	2	yes	—
200	C₂²×M₁₆	C₂²×C₃	1	1	yes	characteristic, complemented
201	C₂³×C₈	C₂²×C₃	1	1	yes	characteristic, complemented
202	#537	C₂²×C₃	1	4	yes	—
203	#537	C₂²×C₃	1	4	yes	complemented
204	#536	—	2	2	no	—
205	#536	C₂²×C₃	1	2	yes	—
206	#536	C₂²×C₃	1	2	yes	complemented
207	#535	—	2	2	no	—
208	#535	C₂²×C₃	1	2	yes	—
209	#535	C₂²×C₃	1	2	yes	complemented
210	#534	—	2	2	no	—
211	#534	—	2	2	no	—
212	#532	—	2	2	no	—
213	#532	—	2	2	no	—
214	#525	—	2	2	no	—
215	#525	—	2	2	no	—
216	#525	C₂²×C₃	1	4	yes	—
217	#525	C₂²×C₃	1	4	yes	complemented
218	C₂×#117	C₂²×C₃	1	2	yes	complemented
219	#485	C₂²×C₃	1	4	yes	complemented
220	#485	C₂²×C₃	1	4	yes	complemented
221	#484	C₂²×C₃	1	4	yes	complemented
222	#483	C₂²×C₃	1	4	yes	complemented
223	#482	C₂²×C₃	1	4	yes	complemented
224	#482	C₂²×C₃	1	4	yes	complemented
225	#481	C₂²×C₃	1	4	yes	complemented
226	#480	C₂²×C₃	1	4	yes	complemented
227	#470	C₂²×C₃	1	2	yes	complemented
228	#470	C₂²×C₃	1	2	yes	complemented
229	#469	C₂²×C₃	1	2	yes	complemented
230	#469	C₂²×C₃	1	2	yes	complemented
231	#468	C₂²×C₃	1	4	yes	complemented
232	#468	C₂²×C₃	1	4	yes	complemented
233	#467	C₂²×C₃	1	2	yes	complemented
234	#467	C₂²×C₃	1	2	yes	complemented
235	#466	C₂²×C₃	1	2	yes	complemented
236	#466	C₂²×C₃	1	2	yes	complemented
237	#465	C₂²×C₃	1	4	yes	complemented
238	#465	C₂²×C₃	1	4	yes	complemented
239	#452	C₂²×C₃	1	4	yes	complemented
240	#452	C₂²×C₃	1	4	yes	complemented
241	#451	C₂²×C₃	1	4	yes	complemented
242	#450	C₂²×C₃	1	4	yes	complemented
243	#449	C₂²×C₃	1	4	yes	complemented
244	#449	C₂²×C₃	1	4	yes	complemented
245	#448	C₂²×C₃	1	4	yes	complemented
246	#447	C₂²×C₃	1	4	yes	complemented
247	#427	C₂²×C₃	1	2	yes	complemented
248	#427	C₂²×C₃	1	2	yes	complemented
249	#416	C₂²×C₃	1	4	yes	complemented
250	#416	C₂²×C₃	1	4	yes	complemented
251	#408	C₂²×C₃	1	1	yes	characteristic
252	#408	C₂²×C₃	1	1	yes	characteristic
253	#408	C₂²×C₃	1	4	yes	complemented
254	#408	C₂²×C₃	1	1	yes	characteristic, complemented
255	#408	C₂²×C₃	1	1	yes	characteristic, complemented
256	C₂×C₂²⋊C₈	C₂²×C₃	1	4	yes	complemented
257	C₂⁴×C₃	—	2	2	no	—
258	C₂⁴×C₃	C₂×D₄	1	2	yes	—
259	C₂⁴×C₃	C₂×D₄	1	1	yes	characteristic
260	C₃×#41	—	2	8	no	—
261	C₃×#41	—	2	8	no	—
262	C₃×#41	—	4	2	no	—
263	C₃×#41	—	4	4	no	—
264	C₃×#41	—	4	2	no	—
265	C₃×#41	—	4	1	no	—
266	C₃×#41	—	4	2	no	—
267	C₃×#41	—	4	1	no	—
268	C₃×#41	—	4	1	no	—
269	C₃×#41	—	4	2	no	—
270	C₃×#41	—	4	1	no	—
271	C₃×#41	—	4	4	no	—
272	C₃×#41	—	4	4	no	—
273	C₃×#41	—	4	8	no	—
274	C₃×#41	—	4	8	no	—
275	C₂×C₃×Q₈	—	2	2	no	—
276	C₂×C₃×Q₈	—	4	2	no	—
277	C₂×C₃×Q₈	—	4	2	no	—
278	C₂×C₃×Q₈	—	4	2	no	—
279	C₂×C₃×Q₈	C₂×D₄	1	1	yes	characteristic
280	C₂×C₃×Q₈	C₂×D₄	1	2	yes	—
281	C₂×C₃×Q₈	C₂×D₄	1	1	yes	characteristic
282	C₂×C₃×Q₈	C₂⁴	1	4	yes	—
283	C₂×C₃×D₄	—	2	4	no	—
284	C₂×C₃×D₄	—	2	4	no	—
285	C₂×C₃×D₄	—	2	4	no	—
286	C₂×C₃×D₄	—	2	4	no	—
287	C₂×C₃×D₄	—	2	4	no	—
288	C₂×C₃×D₄	—	2	4	no	—
289	C₂×C₃×D₄	—	2	2	no	—
290	C₂×C₃×D₄	—	4	2	no	—
291	C₂×C₃×D₄	—	4	2	no	—
292	C₂×C₃×D₄	—	4	2	no	—
293	C₂×C₃×D₄	—	4	4	no	—
294	C₂×C₃×D₄	—	4	8	no	—
295	C₂×C₃×D₄	C₂×D₄	1	1	yes	characteristic
296	C₂×C₃×D₄	C₂×D₄	1	2	yes	—
297	C₂×C₃×D₄	C₂×D₄	1	2	yes	—
298	C₂×C₃×D₄	C₂×D₄	1	2	yes	—
299	C₂×C₃×D₄	C₂×D₄	1	1	yes	characteristic
300	C₂×C₃×D₄	C₂×D₄	1	2	yes	—
301	C₂×C₃×D₄	C₂×D₄	1	2	yes	—
302	C₂×C₃×D₄	C₂⁴	1	4	yes	—
303	C₂²×C₃×C₄	—	2	2	no	—
304	C₂²×C₃×C₄	—	2	2	no	—
305	C₂²×C₃×C₄	—	2	4	no	—
306	C₂²×C₃×C₄	—	2	4	no	—
307	C₂²×C₃×C₄	—	2	2	no	—
308	C₂²×C₃×C₄	—	2	4	no	—
309	C₂²×C₃×C₄	—	2	4	no	—
310	C₂²×C₃×C₄	—	2	4	no	—
311	C₂²×C₃×C₄	—	4	8	no	—
312	C₂²×C₃×C₄	C₂×D₄	1	2	yes	—
313	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
314	C₂²×C₃×C₄	C₂×D₄	1	2	yes	—
315	C₂²×C₃×C₄	C₂×D₄	1	2	yes	—
316	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
317	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
318	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
319	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
320	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
321	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
322	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
323	C₃×Q₁₆	—	4	2	no	—
324	C₃×Q₁₆	—	4	2	no	—
325	C₃×SD₁₆	—	4	4	no	—
326	C₃×SD₁₆	—	4	4	no	—
327	C₃×D₈	—	4	2	no	—
328	C₃×D₈	—	4	2	no	—
329	C₃×M₁₆	—	4	1	no	—
330	C₃×M₁₆	—	4	2	no	—
331	C₃×M₁₆	—	4	1	no	—
332	C₂×C₃×C₈	—	2	4	no	—
333	C₂×C₃×C₈	—	2	4	no	—
334	C₂×C₃×C₈	—	4	1	no	—
335	C₂×C₃×C₈	—	4	2	no	—
336	C₂×C₃×C₈	—	4	1	no	—
337	C₂×C₃×C₈	C₂⁴	1	2	yes	—
338	C₂×C₃×C₈	C₂⁴	1	2	yes	—
339	C₂×C₃×C₈	C₂⁴	1	2	yes	—
340	C₂×C₃×C₈	C₂⁴	1	2	yes	—
341	C₃×C₄⋊C₄	—	2	4	no	—
342	C₃×C₄⋊C₄	—	2	4	no	—
343	C₃×C₄⋊C₄	—	2	4	no	—
344	C₃×C₄⋊C₄	—	2	4	no	—
345	C₃×C₄⋊C₄	—	2	4	no	—
346	C₃×C₄⋊C₄	C₂⁴	1	4	yes	—
347	C₃×C₄⋊C₄	C₂⁴	1	4	yes	—
348	C₃×C₂²⋊C₄	—	2	2	no	—
349	C₃×C₂²⋊C₄	—	2	2	no	—
350	C₃×C₂²⋊C₄	—	2	4	no	—
351	C₃×C₂²⋊C₄	—	2	4	no	—
352	C₃×C₂²⋊C₄	—	2	4	no	—
353	C₃×C₂²⋊C₄	—	2	4	no	—
354	C₃×C₂²⋊C₄	—	2	4	no	—
355	C₃×C₂²⋊C₄	—	2	4	no	—
356	C₃×C₂²⋊C₄	—	2	4	no	—
357	C₃×C₂²⋊C₄	—	2	4	no	—
358	C₃×C₂²⋊C₄	—	2	4	no	—
359	C₃×C₄²	—	2	2	no	—
360	C₃×C₄²	—	2	2	no	—
361	C₃×C₄²	—	2	4	no	—
362	C₂×#41	—	2	2	no	—
363	C₂×#41	—	2	2	no	—
364	C₂×#41	—	4	2	no	—
365	C₂×#41	—	4	2	no	—
366	C₂×#41	—	4	4	no	—
367	C₂×#41	—	4	4	no	—
368	C₂×#41	C₃×D₄	1	1	yes	characteristic
369	C₂×#41	C₃×D₄	1	2	yes	—
370	C₂×#41	C₃×D₄	1	1	yes	characteristic
371	C₂×#41	C₂³×C₃	1	4	yes	—
372	C₂×#41	C₂³×C₃	1	4	yes	—
373	C₂×#41	C₂³×C₃	1	1	yes	characteristic
374	C₂×#41	C₂³×C₃	1	2	yes	—
375	C₂×#41	C₂³×C₃	1	1	yes	characteristic
376	C₂²×Q₈	C₃×D₄	1	1	yes	characteristic
377	C₂²×Q₈	C₂³×C₃	1	2	yes	—
378	C₂²×D₄	—	2	2	no	—
379	C₂²×D₄	C₃×D₄	1	1	yes	characteristic
380	C₂²×D₄	C₃×D₄	1	2	yes	—
381	C₂²×D₄	C₂³×C₃	1	2	yes	—
382	C₂³×C₄	—	2	2	no	—
383	C₂³×C₄	C₂³×C₃	1	2	yes	—
384	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
385	#135	—	4	4	no	—
386	#135	—	4	4	no	—
387	C₂×Q₁₆	C₂³×C₃	1	2	yes	—
388	C₂×Q₁₆	C₂³×C₃	1	2	yes	—
389	C₂×SD₁₆	C₂³×C₃	1	4	yes	—
390	C₂×SD₁₆	C₂³×C₃	1	4	yes	—
391	C₂×D₈	C₂³×C₃	1	2	yes	—
392	C₂×D₈	C₂³×C₃	1	2	yes	—
393	C₂×M₁₆	—	4	2	no	—
394	C₂×M₁₆	C₂³×C₃	1	1	yes	characteristic
395	C₂×M₁₆	C₂³×C₃	1	1	yes	characteristic
396	C₂×M₁₆	C₂³×C₃	1	2	yes	—
397	C₂²×C₈	—	4	2	no	—
398	C₂²×C₈	C₂³×C₃	1	2	yes	—
399	C₂²×C₈	C₂³×C₃	1	2	yes	—
400	C₂²×C₈	C₂³×C₃	1	1	yes	characteristic
401	C₂²×C₈	C₂³×C₃	1	1	yes	characteristic
402	C₂²×C₈	C₂³×C₃	1	2	yes	—
403	C₄⋊Q₈	—	2	2	no	—
404	C₄⋊Q₈	—	2	2	no	—
405	#127	—	2	2	no	—
406	#127	—	2	2	no	—
407	#124	—	2	2	no	—
408	#124	—	2	2	no	—
409	#124	—	2	2	no	—
410	#124	—	2	2	no	—
411	#123	—	2	2	no	—
412	#123	—	2	2	no	—
413	#123	—	2	2	no	—
414	#123	—	2	2	no	—
415	#123	—	2	4	no	—
416	#123	—	2	4	no	—
417	C₂²⋊Q₈	—	2	4	no	—
418	C₂²⋊Q₈	—	2	4	no	—
419	C₂²⋊Q₈	C₂³×C₃	1	4	yes	—
420	C₂²⋊Q₈	C₂³×C₃	1	4	yes	—
421	C₂²⋊Q₈	C₂³×C₃	1	4	yes	—
422	C₂²⋊Q₈	C₂³×C₃	1	4	yes	—
423	#121	—	2	4	no	—
424	#121	—	2	4	no	—
425	#121	—	2	4	no	—
426	#121	—	2	4	no	—
427	#121	—	2	4	no	—
428	#121	—	2	4	no	—
429	#121	C₂³×C₃	1	4	yes	—
430	#121	C₂³×C₃	1	4	yes	—
431	#121	C₂³×C₃	1	4	yes	—
432	#121	C₂³×C₃	1	4	yes	—
433	#120	—	2	4	no	—
434	#120	—	2	4	no	—
435	#120	—	2	2	no	—
436	#120	—	2	2	no	—
437	#120	—	2	2	no	—
438	#120	—	2	2	no	—
439	C₄×D₄	—	2	4	no	—
440	C₄×D₄	—	2	4	no	—
441	C₄×D₄	—	2	4	no	—
442	C₄×D₄	—	2	4	no	—
443	#117	—	2	2	no	—
444	#117	—	2	2	no	—
445	#117	C₂³×C₃	1	4	yes	—
446	#117	C₂³×C₃	1	2	yes	—
447	#117	C₂³×C₃	1	2	yes	—
448	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
449	C₂×C₂²⋊C₄	—	2	2	no	—
450	C₂×C₄²	—	2	2	no	—
451	#107	C₂³×C₃	1	2	yes	—
452	#107	C₂³×C₃	1	2	yes	—
453	#107	C₂³×C₃	1	4	yes	—
454	#106	C₂³×C₃	1	4	yes	—
455	#106	C₂³×C₃	1	2	yes	—
456	#106	C₂³×C₃	1	2	yes	—
457	#103	C₂³×C₃	1	4	yes	—
458	#103	C₂³×C₃	1	4	yes	—
459	#103	C₂³×C₃	1	4	yes	—
460	#103	C₂³×C₃	1	4	yes	—
461	#102	C₂³×C₃	1	4	yes	—
462	#102	C₂³×C₃	1	4	yes	—
463	#102	C₂³×C₃	1	4	yes	—
464	#102	C₂³×C₃	1	4	yes	—
465	C₂²⋊C₈	C₂³×C₃	1	4	yes	—
466	C₂²⋊C₈	C₂³×C₃	1	4	yes	—
467	C₂²⋊C₈	C₂³×C₃	1	4	yes	—
468	C₂²⋊C₈	C₂³×C₃	1	4	yes	—
469	C₂³×C₃	—	2	2	no	—
470	C₂³×C₃	—	2	4	no	—
471	C₂³×C₃	—	2	4	no	—
472	C₂³×C₃	—	4	2	no	—
473	C₂³×C₃	—	4	4	no	—
474	C₂³×C₃	—	4	4	no	—
475	C₂³×C₃	—	8	4	no	—
476	C₂³×C₃	C₂²×D₄	1	2	yes	—
477	C₂³×C₃	C₂²×D₄	1	1	yes	characteristic
478	C₂³×C₃	C₂²×D₄	1	1	yes	characteristic
479	C₂³×C₃	C₂²×D₄	1	2	yes	—
480	C₂³×C₃	C₂²×D₄	1	1	yes	characteristic
481	C₃×Q₈	—	2	4	no	—
482	C₃×Q₈	—	2	4	no	—
483	C₃×Q₈	—	4	1	no	—
484	C₃×Q₈	—	4	2	no	—
485	C₃×Q₈	—	4	1	no	—
486	C₃×Q₈	—	4	4	no	—
487	C₃×D₄	—	2	4	no	—
488	C₃×D₄	—	2	4	no	—
489	C₃×D₄	—	4	2	no	—
490	C₃×D₄	—	4	2	no	—
491	C₃×D₄	—	4	2	no	—
492	C₃×D₄	—	4	2	no	—
493	C₃×D₄	—	4	1	no	—
494	C₃×D₄	—	4	2	no	—
495	C₃×D₄	—	4	1	no	—
496	C₃×D₄	—	4	4	no	—
497	C₃×D₄	—	4	8	no	—
498	C₃×D₄	—	4	8	no	—
499	C₃×D₄	—	8	4	no	—
500	C₃×D₄	—	8	4	no	—
501	C₃×D₄	—	8	4	no	—
502	C₃×D₄	—	8	4	no	—
503	C₂×C₃×C₄	—	2	2	no	—
504	C₂×C₃×C₄	—	2	4	no	—
505	C₂×C₃×C₄	—	2	4	no	—
506	C₂×C₃×C₄	—	2	2	no	—
507	C₂×C₃×C₄	—	2	2	no	—
508	C₂×C₃×C₄	—	2	4	no	—
509	C₂×C₃×C₄	—	2	1	no	—
510	C₂×C₃×C₄	—	2	1	no	—
511	C₂×C₃×C₄	—	2	1	no	—
512	C₂×C₃×C₄	—	2	1	no	—
513	C₂×C₃×C₄	—	2	2	no	—
514	C₂×C₃×C₄	—	2	2	no	—
515	C₂×C₃×C₄	—	2	2	no	—
516	C₂×C₃×C₄	—	2	2	no	—
517	C₂×C₃×C₄	—	2	4	no	—
518	C₂×C₃×C₄	—	2	4	no	—
519	C₂×C₃×C₄	—	2	4	no	—
520	C₂×C₃×C₄	—	4	8	no	—
521	C₂×C₃×C₄	—	4	4	no	—
522	C₂×C₃×C₄	—	4	8	no	—
523	C₂×C₃×C₄	—	8	4	no	—
524	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
525	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
526	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
527	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
528	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
529	C₂×C₃×C₄	H(5,𝔽₂)	1	2	yes	—
530	C₂×C₃×C₄	H(5,𝔽₂)	1	2	yes	—
531	C₂×C₃×C₄	C₂⁵	1	1	yes	characteristic
532	C₃×C₈	—	2	2	no	—
533	C₃×C₈	—	2	2	no	—
534	C₃×C₈	—	2	2	no	—
535	C₃×C₈	—	2	2	no	—
536	C₂⁴	—	2	2	no	—
537	C₂⁴	C₂×C₃×D₄	1	2	yes	—
538	C₂⁴	C₂×C₃×D₄	1	1	yes	characteristic
539	#41	—	2	8	no	—
540	#41	—	2	8	no	—
541	#41	—	4	2	no	—
542	#41	—	4	4	no	—
543	#41	—	4	2	no	—
544	#41	—	4	1	no	—
545	#41	—	4	2	no	—
546	#41	—	4	1	no	—
547	#41	—	4	1	no	—
548	#41	—	4	2	no	—
549	#41	—	4	1	no	—
550	#41	—	4	4	no	—
551	#41	—	4	4	no	—
552	#41	—	4	8	no	—
553	#41	—	4	8	no	—
554	C₂×Q₈	—	2	2	no	—
555	C₂×Q₈	—	4	2	no	—
556	C₂×Q₈	—	4	2	no	—
557	C₂×Q₈	—	4	2	no	—
558	C₂×Q₈	C₂×C₃×D₄	1	1	yes	characteristic
559	C₂×Q₈	C₂×C₃×D₄	1	2	yes	—
560	C₂×Q₈	C₂×C₃×D₄	1	1	yes	characteristic
561	C₂×Q₈	C₂⁴×C₃	1	4	yes	—
562	C₂×D₄	—	2	4	no	—
563	C₂×D₄	—	2	4	no	—
564	C₂×D₄	—	2	4	no	—
565	C₂×D₄	—	2	4	no	—
566	C₂×D₄	—	2	4	no	—
567	C₂×D₄	—	2	4	no	—
568	C₂×D₄	—	2	2	no	—
569	C₂×D₄	—	4	2	no	—
570	C₂×D₄	—	4	2	no	—
571	C₂×D₄	—	4	4	no	—
572	C₂×D₄	—	4	2	no	—
573	C₂×D₄	—	4	8	no	—
574	C₂×D₄	C₂×C₃×D₄	1	1	yes	characteristic
575	C₂×D₄	C₂×C₃×D₄	1	2	yes	—
576	C₂×D₄	C₂×C₃×D₄	1	2	yes	—
577	C₂×D₄	C₂×C₃×D₄	1	2	yes	—
578	C₂×D₄	C₂×C₃×D₄	1	1	yes	characteristic
579	C₂×D₄	C₂×C₃×D₄	1	2	yes	—
580	C₂×D₄	C₂×C₃×D₄	1	2	yes	—
581	C₂×D₄	C₂⁴×C₃	1	4	yes	—
582	C₂²×C₄	—	2	2	no	—
583	C₂²×C₄	—	2	2	no	—
584	C₂²×C₄	—	2	4	no	—
585	C₂²×C₄	—	2	4	no	—
586	C₂²×C₄	—	2	2	no	—
587	C₂²×C₄	—	2	4	no	—
588	C₂²×C₄	—	2	4	no	—
589	C₂²×C₄	—	2	4	no	—
590	C₂²×C₄	—	4	8	no	—
591	C₂²×C₄	C₂×C₃×D₄	1	2	yes	—
592	C₂²×C₄	C₂×C₃×D₄	1	2	yes	—
593	C₂²×C₄	C₂×C₃×D₄	1	2	yes	—
594	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
595	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
596	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
597	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
598	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
599	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
600	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
601	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
602	Q₁₆	—	4	2	no	—
603	Q₁₆	—	4	2	no	—
604	SD₁₆	—	4	4	no	—
605	SD₁₆	—	4	4	no	—
606	D₈	—	4	2	no	—
607	D₈	—	4	2	no	—
608	M₁₆	—	4	1	no	—
609	M₁₆	—	4	2	no	—
610	M₁₆	—	4	1	no	—
611	C₂×C₈	—	2	4	no	—
612	C₂×C₈	—	2	4	no	—
613	C₂×C₈	—	4	1	no	—
614	C₂×C₈	—	4	2	no	—
615	C₂×C₈	—	4	1	no	—
616	C₂×C₈	C₂⁴×C₃	1	2	yes	—
617	C₂×C₈	C₂⁴×C₃	1	2	yes	—
618	C₂×C₈	C₂⁴×C₃	1	2	yes	—
619	C₂×C₈	C₂⁴×C₃	1	2	yes	—
620	C₄⋊C₄	—	2	4	no	—
621	C₄⋊C₄	—	2	4	no	—
622	C₄⋊C₄	—	2	4	no	—
623	C₄⋊C₄	—	2	4	no	—
624	C₄⋊C₄	—	2	4	no	—
625	C₄⋊C₄	C₂⁴×C₃	1	4	yes	—
626	C₄⋊C₄	C₂⁴×C₃	1	4	yes	—
627	C₂²⋊C₄	—	2	2	no	—
628	C₂²⋊C₄	—	2	2	no	—
629	C₂²⋊C₄	—	2	4	no	—
630	C₂²⋊C₄	—	2	4	no	—
631	C₂²⋊C₄	—	2	4	no	—
632	C₂²⋊C₄	—	2	4	no	—
633	C₂²⋊C₄	—	2	4	no	—
634	C₂²⋊C₄	—	2	4	no	—
635	C₂²⋊C₄	—	2	4	no	—
636	C₂²⋊C₄	—	2	4	no	—
637	C₂²⋊C₄	—	2	4	no	—
638	C₄²	—	2	4	no	—
639	C₄²	—	2	2	no	—
640	C₄²	—	2	2	no	—
641	C₂²×C₃	—	2	2	no	—
642	C₂²×C₃	—	2	4	no	—
643	C₂²×C₃	—	2	2	no	—
644	C₂²×C₃	—	2	2	no	—
645	C₂²×C₃	—	2	4	no	—
646	C₂²×C₃	—	2	2	no	—
647	C₂²×C₃	—	2	2	no	—
648	C₂²×C₃	—	2	1	no	—
649	C₂²×C₃	—	2	1	no	—
650	C₂²×C₃	—	4	4	no	—
651	C₂²×C₃	—	4	4	no	—
652	C₂²×C₃	—	4	4	no	—
653	C₂²×C₃	—	4	4	no	—
654	C₂²×C₃	—	8	4	no	—
655	C₂²×C₃	—	8	8	no	—
656	C₂²×C₃	#534	1	2	yes	—
657	C₂²×C₃	C₂³×D₄	1	1	yes	characteristic
658	C₃×C₄	—	2	2	no	—
659	C₃×C₄	—	2	2	no	—
660	C₃×C₄	—	2	1	no	—
661	C₃×C₄	—	2	1	no	—
662	C₃×C₄	—	4	4	no	—
663	C₃×C₄	—	4	4	no	—
664	C₃×C₄	—	4	4	no	—
665	C₃×C₄	#534	1	2	yes	—
666	C₃×C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
667	C₃×C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
668	C₂³	—	2	2	no	—
669	C₂³	—	2	4	no	—
670	C₂³	—	2	4	no	—
671	C₂³	—	4	2	no	—
672	C₂³	—	4	4	no	—
673	C₂³	—	4	4	no	—
674	C₂³	—	8	4	no	—
675	C₂³	C₂²×C₃×D₄	1	2	yes	—
676	C₂³	C₂²×C₃×D₄	1	1	yes	characteristic
677	C₂³	C₂²×C₃×D₄	1	1	yes	characteristic
678	C₂³	C₂²×C₃×D₄	1	2	yes	—
679	C₂³	C₂²×C₃×D₄	1	1	yes	characteristic
680	Q₈	—	2	4	no	—
681	Q₈	—	2	4	no	—
682	Q₈	—	4	1	no	—
683	Q₈	—	4	2	no	—
684	Q₈	—	4	1	no	—
685	Q₈	—	4	4	no	—
686	D₄	—	2	4	no	—
687	D₄	—	2	4	no	—
688	D₄	—	4	2	no	—
689	D₄	—	4	2	no	—
690	D₄	—	4	2	no	—
691	D₄	—	4	2	no	—
692	D₄	—	4	1	no	—
693	D₄	—	4	2	no	—
694	D₄	—	4	1	no	—
695	D₄	—	4	4	no	—
696	D₄	—	4	8	no	—
697	D₄	—	4	8	no	—
698	D₄	—	8	4	no	—
699	D₄	—	8	4	no	—
700	D₄	—	8	4	no	—
701	D₄	—	8	4	no	—
702	C₂×C₄	—	2	4	no	—
703	C₂×C₄	—	2	2	no	—
704	C₂×C₄	—	2	1	no	—
705	C₂×C₄	—	2	1	no	—
706	C₂×C₄	—	2	1	no	—
707	C₂×C₄	—	2	1	no	—
708	C₂×C₄	—	2	2	no	—
709	C₂×C₄	—	2	2	no	—
710	C₂×C₄	—	2	2	no	—
711	C₂×C₄	—	2	2	no	—
712	C₂×C₄	—	2	4	no	—
713	C₂×C₄	—	2	4	no	—
714	C₂×C₄	—	2	2	no	—
715	C₂×C₄	—	2	2	no	—
716	C₂×C₄	—	2	4	no	—
717	C₂×C₄	—	2	4	no	—
718	C₂×C₄	—	2	4	no	—
719	C₂×C₄	—	4	8	no	—
720	C₂×C₄	—	4	4	no	—
721	C₂×C₄	—	4	8	no	—
722	C₂×C₄	—	8	4	no	—
723	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
724	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
725	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
726	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
727	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
728	C₂×C₄	C₃×H(5,𝔽₂)	1	2	yes	—
729	C₂×C₄	C₃×H(5,𝔽₂)	1	2	yes	—
730	C₂×C₄	C₂⁵×C₃	1	1	yes	characteristic
731	C₈	—	2	2	no	—
732	C₈	—	2	2	no	—
733	C₈	—	2	2	no	—
734	C₈	—	2	2	no	—
735	C₂×C₃	—	2	2	no	—
736	C₂×C₃	—	4	1	no	—
737	C₂×C₃	—	4	1	no	—
738	C₂×C₃	—	4	2	no	—
739	C₂×C₃	—	4	2	no	—
740	C₂×C₃	—	8	4	no	—
741	C₂×C₃	C₂×#534	1	1	yes	characteristic
742	C₂×C₃	#3584	1	2	yes	—
743	C₂²	—	2	2	no	—
744	C₂²	—	2	2	no	—
745	C₂²	—	2	2	no	—
746	C₂²	—	2	1	no	—
747	C₂²	—	2	1	no	—
748	C₂²	—	2	4	no	—
749	C₂²	—	2	2	no	—
750	C₂²	—	2	2	no	—
751	C₂²	—	2	4	no	—
752	C₂²	—	4	4	no	—
753	C₂²	—	4	4	no	—
754	C₂²	—	4	4	no	—
755	C₂²	—	4	4	no	—
756	C₂²	—	8	4	no	—
757	C₂²	—	8	8	no	—
758	C₂²	C₃×#534	1	2	yes	—
759	C₂²	C₂³×C₃×D₄	1	1	yes	characteristic
760	C₄	—	2	2	no	—
761	C₄	—	2	2	no	—
762	C₄	—	2	1	no	—
763	C₄	—	2	1	no	—
764	C₄	—	4	4	no	—
765	C₄	—	4	4	no	—
766	C₄	—	4	4	no	—
767	C₄	C₃×#534	1	2	yes	—
768	C₄	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
769	C₄	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
770	C₃	#60749	1	1	yes	characteristic, direct product factor, Sylow
771	C₂	—	2	2	no	—
772	C₂	—	4	1	no	—
773	C₂	—	4	1	no	—
774	C₂	—	4	2	no	—
775	C₂	—	4	2	no	—
776	C₂	—	8	4	no	—
777	C₂	C₂×C₃×#534	1	1	yes	characteristic
778	C₂	C₃×#3584	1	2	yes	—

	subgroup	G/H
center	C₂×C₃×C₄	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₃
socle	C₂²×C₃	C₂³×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₂²×C₃×#41 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃×#3449	C₂	semidirect
2. C₃×#3204	C₂	semidirect
3. C₃×#3203	C₂	semidirect
4. C₃×#3202	C₂	semidirect
5. C₃×#3201	C₂	semidirect
6. C₃×#3200	C₂	semidirect
7. C₃×#3199	C₂	semidirect
8. C₃×#3198	C₂	semidirect
9. C₃×#3091	C₂	semidirect
10. C₃×#3054	C₂	semidirect
11. C₃×#3050	C₂	semidirect
12. C₃×#3002	C₂	semidirect
13. C₂×C₃×#408	C₂	semidirect
14. #60749	C₃	direct (N × H)
16. C₂²×C₃×#41	C₂²	semidirect
19. C₂²×C₃×M₁₆	C₂²	semidirect
20. C₂³×C₃×C₈	C₂²	semidirect
22. C₃×#537	C₂²	semidirect
25. C₃×#536	C₂²	semidirect
28. C₃×#535	C₂²	semidirect
36. C₃×#525	C₂²	semidirect
37. C₂×C₃×#117	C₂²	semidirect
38. C₃×#485	C₂²	semidirect
39. C₃×#485	C₂²	semidirect
40. C₃×#484	C₂²	semidirect
41. C₃×#483	C₂²	semidirect
42. C₃×#482	C₂²	semidirect
43. C₃×#482	C₂²	semidirect
44. C₃×#481	C₂²	semidirect
45. C₃×#480	C₂²	semidirect
46. C₃×#470	C₂²	semidirect
47. C₃×#470	C₂²	semidirect
48. C₃×#469	C₂²	semidirect
49. C₃×#469	C₂²	semidirect
50. C₃×#468	C₂²	semidirect
51. C₃×#468	C₂²	semidirect
52. C₃×#467	C₂²	semidirect
53. C₃×#467	C₂²	semidirect
54. C₃×#466	C₂²	semidirect
55. C₃×#466	C₂²	semidirect
56. C₃×#465	C₂²	semidirect
57. C₃×#465	C₂²	semidirect
58. C₃×#452	C₂²	semidirect
59. C₃×#452	C₂²	semidirect
60. C₃×#451	C₂²	semidirect
61. C₃×#450	C₂²	semidirect
62. C₃×#449	C₂²	semidirect
63. C₃×#449	C₂²	semidirect
64. C₃×#448	C₂²	semidirect
65. C₃×#447	C₂²	semidirect
66. C₃×#427	C₂²	semidirect
67. C₃×#427	C₂²	semidirect
68. C₃×#416	C₂²	semidirect
69. C₃×#416	C₂²	semidirect
72. C₃×#408	C₂²	semidirect
73. C₃×#408	C₂²	semidirect
74. C₃×#408	C₂²	semidirect
75. C₂×C₃×C₂²⋊C₈	C₂²	semidirect
76. #3449	C₂×C₃	semidirect
77. #3204	C₂×C₃	semidirect
78. #3203	C₂×C₃	semidirect
79. #3202	C₂×C₃	semidirect
80. #3201	C₂×C₃	semidirect
81. #3200	C₂×C₃	semidirect
82. #3199	C₂×C₃	semidirect
83. #3198	C₂×C₃	semidirect
84. #3091	C₂×C₃	semidirect
85. #3054	C₂×C₃	semidirect
86. #3050	C₂×C₃	semidirect
87. #3002	C₂×C₃	semidirect
88. C₂×#408	C₂×C₃	semidirect
197. C₂²×#41	C₂²×C₃	semidirect
200. C₂²×M₁₆	C₂²×C₃	semidirect
201. C₂³×C₈	C₂²×C₃	semidirect
203. #537	C₂²×C₃	semidirect
206. #536	C₂²×C₃	semidirect
209. #535	C₂²×C₃	semidirect
217. #525	C₂²×C₃	semidirect
218. C₂×#117	C₂²×C₃	semidirect
219. #485	C₂²×C₃	semidirect
220. #485	C₂²×C₃	semidirect
221. #484	C₂²×C₃	semidirect
222. #483	C₂²×C₃	semidirect
223. #482	C₂²×C₃	semidirect
224. #482	C₂²×C₃	semidirect
225. #481	C₂²×C₃	semidirect
226. #480	C₂²×C₃	semidirect
227. #470	C₂²×C₃	semidirect
228. #470	C₂²×C₃	semidirect
229. #469	C₂²×C₃	semidirect
230. #469	C₂²×C₃	semidirect
231. #468	C₂²×C₃	semidirect
232. #468	C₂²×C₃	semidirect
233. #467	C₂²×C₃	semidirect
234. #467	C₂²×C₃	semidirect
235. #466	C₂²×C₃	semidirect
236. #466	C₂²×C₃	semidirect
237. #465	C₂²×C₃	semidirect
238. #465	C₂²×C₃	semidirect
239. #452	C₂²×C₃	semidirect
240. #452	C₂²×C₃	semidirect
241. #451	C₂²×C₃	semidirect
242. #450	C₂²×C₃	semidirect
243. #449	C₂²×C₃	semidirect
244. #449	C₂²×C₃	semidirect
245. #448	C₂²×C₃	semidirect
246. #447	C₂²×C₃	semidirect
247. #427	C₂²×C₃	semidirect
248. #427	C₂²×C₃	semidirect
249. #416	C₂²×C₃	semidirect
250. #416	C₂²×C₃	semidirect
253. #408	C₂²×C₃	semidirect
254. #408	C₂²×C₃	semidirect
255. #408	C₂²×C₃	semidirect
256. C₂×C₂²⋊C₈	C₂²×C₃	semidirect
770. C₃	#60749	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×#3449	2
C₃×#3204	2
C₃×#3203	2
C₃×#3202	2
C₃×#3201	2
C₃×#3200	2
C₃×#3199	2
C₃×#3198	2
C₃×#3091	2
C₃×#3054	2
C₃×#3050	2
C₃×#3002	2
C₂×C₃×#408	2
#60749	3

Subgroups — C3×#60749 #10679356

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#60749 #10679356