Subgroups — C₃×#35288 #10653895

Order 768.

1978 conjugacy classes of subgroups.

The subgroup lattice has 790 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#2859	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#2858	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#2857	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#2856	C₂	1	1	yes	maximal, characteristic
5	C₃×#2644	C₂	1	2	yes	maximal, complemented
6	C₃×#2624	C₂	1	2	yes	maximal, complemented
7	C₃×#2513	C₂	1	2	yes	maximal, complemented
8	C₃×#2490	C₂	1	2	yes	maximal, complemented
9	C₃×#2454	C₂	1	2	yes	maximal, complemented
10	C₃×#2448	C₂	1	2	yes	maximal, complemented
11	C₃×#2447	C₂	1	2	yes	maximal, complemented
12	C₃×#2427	C₂	1	2	yes	maximal, complemented
13	C₃×#2426	C₂	1	2	yes	maximal, complemented
14	C₃×#2420	C₂	1	2	yes	maximal, complemented
15	C₃×#2324	C₂	1	2	yes	maximal, complemented
16	C₃×#2319	C₂	1	2	yes	maximal, complemented
17	C₃×C₄×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
18	C₃×C₄×#127	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃×C₄×#117	C₂	1	1	yes	maximal, characteristic, complemented
20	#35288	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
21	C₂×C₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
22	C₂×C₃×#127	C₂²	1	1	yes	characteristic
23	C₂×C₃×#125	C₂²	1	2	yes	—
24	C₂×C₃×#124	C₂²	1	2	yes	—
25	C₂×C₃×#124	C₂²	1	2	yes	—
26	C₂×C₃×C₂²⋊Q₈	C₂²	1	2	yes	—
27	C₂×C₃×#121	C₂²	1	2	yes	—
28	C₂×C₃×#121	C₂²	1	2	yes	—
29	C₂×C₃×#121	C₂²	1	2	yes	—
30	C₂×C₃×C₄×Q₈	C₂²	1	2	yes	—
31	C₂×C₃×C₄×D₄	C₂²	1	2	yes	—
32	C₂×C₃×C₄×D₄	C₂²	1	2	yes	—
33	C₂×C₃×C₄×D₄	C₂²	1	2	yes	—
34	C₂×C₃×#117	C₂²	1	1	yes	characteristic
35	C₂×C₃×#117	C₂²	1	1	yes	characteristic
36	C₂²×C₃×C₄²	C₂²	1	1	yes	characteristic
37	C₃×#399	C₂²	1	4	yes	—
38	C₃×#397	C₂²	1	4	yes	—
39	C₃×#397	C₂²	1	4	yes	—
40	C₃×#397	C₂²	1	4	yes	—
41	C₃×#397	C₂²	1	4	yes	—
42	C₃×#396	C₂²	1	4	yes	—
43	C₃×#394	C₂²	1	4	yes	—
44	C₃×#394	C₂²	1	4	yes	—
45	C₃×#391	C₂²	1	2	yes	—
46	C₃×#391	C₂²	1	2	yes	—
47	C₃×#390	C₂²	1	2	yes	—
48	C₃×#390	C₂²	1	2	yes	—
49	C₃×#390	C₂²	1	2	yes	—
50	C₃×#390	C₂²	1	2	yes	—
51	C₃×#390	C₂²	1	2	yes	—
52	C₃×#390	C₂²	1	2	yes	—
53	C₃×#390	C₂²	1	4	yes	—
54	C₃×#390	C₂²	1	2	yes	—
55	C₃×#390	C₂²	1	2	yes	—
56	C₃×#390	C₂²	1	2	yes	—
57	C₃×#390	C₂²	1	2	yes	—
58	C₃×#389	C₂²	1	2	yes	—
59	C₃×#389	C₂²	1	2	yes	—
60	C₃×#389	C₂²	1	2	yes	—
61	C₃×#389	C₂²	1	2	yes	—
62	C₃×#389	C₂²	1	2	yes	—
63	C₃×#389	C₂²	1	2	yes	—
64	C₃×#389	C₂²	1	2	yes	—
65	C₃×#389	C₂²	1	2	yes	—
66	C₃×#388	C₂²	1	4	yes	—
67	C₃×#388	C₂²	1	4	yes	—
68	C₃×#388	C₂²	1	4	yes	—
69	C₃×#386	C₂²	1	4	yes	—
70	C₃×#385	C₂²	1	4	yes	—
71	C₃×#384	C₂²	1	1	yes	characteristic
72	C₃×#384	C₂²	1	1	yes	characteristic
73	C₃×#382	C₂²	1	2	yes	—
74	C₃×#381	C₂²	1	4	yes	—
75	C₃×#380	C₂²	1	2	yes	—
76	C₃×#380	C₂²	1	2	yes	—
77	C₃×#380	C₂²	1	4	yes	—
78	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
79	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
80	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
81	C₃×C₄×C₄⋊C₄	C₂²	1	2	yes	—
82	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
83	C₃×C₄×C₄⋊C₄	C₂²	1	2	yes	—
84	C₃×C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
85	C₃×C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
86	C₃×C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
87	C₃×C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
88	C₃×#376	C₂²	1	1	yes	characteristic
89	C₃×#376	C₂²	1	1	yes	characteristic
90	C₃×C₄³	C₂²	1	1	yes	characteristic
91	C₃×C₄³	C₂²	1	1	yes	characteristic
92	#2859	C₂×C₃	1	1	yes	characteristic, complemented
93	#2858	C₂×C₃	1	1	yes	characteristic, complemented
94	#2857	C₂×C₃	1	1	yes	characteristic, complemented
95	#2856	C₂×C₃	1	1	yes	characteristic
96	#2644	C₂×C₃	1	2	yes	complemented
97	#2624	C₂×C₃	1	2	yes	complemented
98	#2513	C₂×C₃	1	2	yes	complemented
99	#2490	C₂×C₃	1	2	yes	complemented
100	#2454	C₂×C₃	1	2	yes	complemented
101	#2448	C₂×C₃	1	2	yes	complemented
102	#2447	C₂×C₃	1	2	yes	complemented
103	#2427	C₂×C₃	1	2	yes	complemented
104	#2426	C₂×C₃	1	2	yes	complemented
105	#2420	C₂×C₃	1	2	yes	complemented
106	#2324	C₂×C₃	1	2	yes	complemented
107	#2319	C₂×C₃	1	2	yes	complemented
108	C₄×C₄⋊Q₈	C₂×C₃	1	1	yes	characteristic, complemented
109	C₄×#127	C₂×C₃	1	1	yes	characteristic, complemented
110	C₄×#117	C₂×C₃	1	1	yes	characteristic, complemented
111	C₂²×C₃×Q₈	C₂³	1	2	yes	—
112	C₂²×C₃×D₄	C₂³	1	2	yes	—
113	C₂²×C₃×D₄	C₂³	1	2	yes	—
114	C₂²×C₃×D₄	C₂³	1	2	yes	—
115	C₂²×C₃×D₄	C₂³	1	4	yes	—
116	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
117	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
118	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
119	C₂³×C₃×C₄	C₂³	1	4	yes	—
120	C₃×C₄⋊Q₈	—	2	4	no	—
121	C₃×#127	—	2	4	no	—
122	C₃×#125	—	4	4	no	—
123	C₃×#124	—	4	4	no	—
124	C₃×#124	—	4	4	no	—
125	C₃×C₂²⋊Q₈	—	4	4	no	—
126	C₃×#121	—	2	8	no	—
127	C₃×#121	—	4	4	no	—
128	C₃×#121	—	4	4	no	—
129	C₃×C₄×Q₈	—	4	4	no	—
130	C₃×C₄×D₄	—	2	8	no	—
131	C₃×C₄×D₄	—	4	4	no	—
132	C₃×C₄×D₄	—	4	4	no	—
133	C₃×#117	—	2	4	no	—
134	C₃×#117	—	2	4	no	—
135	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
136	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
137	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
138	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
139	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
140	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
141	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
142	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
143	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
144	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
145	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
146	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
147	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
148	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
149	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
150	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
151	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
152	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
153	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
154	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
155	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
156	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
157	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
158	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
159	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
160	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
161	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
162	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
163	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
164	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
165	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
166	C₂×C₃×C₄²	—	2	4	no	—
167	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
168	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
169	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
170	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
171	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
172	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
173	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
174	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
175	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
176	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
177	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
178	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
179	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
180	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
181	C₂×C₃×C₄²	C₂³	1	4	yes	—
182	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
183	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
184	C₃×#95	C₂³	1	1	yes	characteristic
185	C₃×#95	C₂³	1	1	yes	characteristic
186	C₃×#95	C₂³	1	1	yes	characteristic
187	C₃×#95	C₂³	1	1	yes	characteristic
188	C₃×#95	C₂³	1	1	yes	characteristic
189	C₃×#95	C₂³	1	1	yes	characteristic
190	C₃×#95	C₂³	1	1	yes	characteristic
191	C₃×#95	C₂³	1	1	yes	characteristic
192	C₃×#95	C₂³	1	4	yes	—
193	C₃×#95	C₂³	1	4	yes	—
194	C₃×#95	C₂³	1	4	yes	—
195	C₃×#95	C₂³	1	4	yes	—
196	C₃×#95	C₂³	1	4	yes	—
197	C₃×#95	C₂³	1	4	yes	—
198	C₂×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
199	C₂×#127	C₂²×C₃	1	1	yes	characteristic
200	C₂×#125	C₂²×C₃	1	2	yes	—
201	C₂×#124	C₂²×C₃	1	2	yes	—
202	C₂×#124	C₂²×C₃	1	2	yes	—
203	C₂×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
204	C₂×#121	C₂²×C₃	1	2	yes	—
205	C₂×#121	C₂²×C₃	1	2	yes	—
206	C₂×#121	C₂²×C₃	1	2	yes	—
207	C₂×C₄×Q₈	C₂²×C₃	1	2	yes	—
208	C₂×C₄×D₄	C₂²×C₃	1	2	yes	—
209	C₂×C₄×D₄	C₂²×C₃	1	2	yes	—
210	C₂×C₄×D₄	C₂²×C₃	1	2	yes	—
211	C₂×#117	C₂²×C₃	1	1	yes	characteristic
212	C₂×#117	C₂²×C₃	1	1	yes	characteristic
213	C₂²×C₄²	C₂²×C₃	1	1	yes	characteristic
214	#399	C₂²×C₃	1	4	yes	—
215	#397	C₂²×C₃	1	4	yes	—
216	#397	C₂²×C₃	1	4	yes	—
217	#397	C₂²×C₃	1	4	yes	—
218	#397	C₂²×C₃	1	4	yes	—
219	#396	C₂²×C₃	1	4	yes	—
220	#394	C₂²×C₃	1	4	yes	—
221	#394	C₂²×C₃	1	4	yes	—
222	#391	C₂²×C₃	1	2	yes	—
223	#391	C₂²×C₃	1	2	yes	—
224	#390	C₂²×C₃	1	2	yes	—
225	#390	C₂²×C₃	1	2	yes	—
226	#390	C₂²×C₃	1	2	yes	—
227	#390	C₂²×C₃	1	2	yes	—
228	#390	C₂²×C₃	1	2	yes	—
229	#390	C₂²×C₃	1	2	yes	—
230	#390	C₂²×C₃	1	4	yes	—
231	#390	C₂²×C₃	1	2	yes	—
232	#390	C₂²×C₃	1	2	yes	—
233	#390	C₂²×C₃	1	2	yes	—
234	#390	C₂²×C₃	1	2	yes	—
235	#389	C₂²×C₃	1	2	yes	—
236	#389	C₂²×C₃	1	2	yes	—
237	#389	C₂²×C₃	1	2	yes	—
238	#389	C₂²×C₃	1	2	yes	—
239	#389	C₂²×C₃	1	2	yes	—
240	#389	C₂²×C₃	1	2	yes	—
241	#389	C₂²×C₃	1	2	yes	—
242	#389	C₂²×C₃	1	2	yes	—
243	#388	C₂²×C₃	1	4	yes	—
244	#388	C₂²×C₃	1	4	yes	—
245	#388	C₂²×C₃	1	4	yes	—
246	#386	C₂²×C₃	1	4	yes	—
247	#385	C₂²×C₃	1	4	yes	—
248	#384	C₂²×C₃	1	1	yes	characteristic
249	#384	C₂²×C₃	1	1	yes	characteristic
250	#382	C₂²×C₃	1	2	yes	—
251	#381	C₂²×C₃	1	4	yes	—
252	#380	C₂²×C₃	1	4	yes	—
253	#380	C₂²×C₃	1	2	yes	—
254	#380	C₂²×C₃	1	2	yes	—
255	C₄×C₄⋊C₄	C₂²×C₃	1	2	yes	—
256	C₄×C₄⋊C₄	C₂²×C₃	1	2	yes	—
257	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
258	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
259	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
260	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
261	C₄×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
262	C₄×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
263	C₄×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
264	C₄×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
265	#376	C₂²×C₃	1	1	yes	characteristic
266	#376	C₂²×C₃	1	1	yes	characteristic
267	C₄³	C₂²×C₃	1	1	yes	characteristic
268	C₄³	C₂²×C₃	1	1	yes	characteristic
269	C₂⁴×C₃	C₂⁴	1	4	yes	—
270	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
271	C₂×C₃×Q₈	—	2	4	no	—
272	C₂×C₃×Q₈	—	2	4	no	—
273	C₂×C₃×Q₈	—	2	4	no	—
274	C₂×C₃×D₄	—	2	8	no	—
275	C₂×C₃×D₄	—	2	4	no	—
276	C₂×C₃×D₄	—	2	4	no	—
277	C₂×C₃×D₄	—	2	4	no	—
278	C₂×C₃×D₄	—	2	4	no	—
279	C₂×C₃×D₄	—	2	4	no	—
280	C₂×C₃×D₄	—	2	4	no	—
281	C₂×C₃×D₄	—	2	4	no	—
282	C₂×C₃×D₄	—	2	4	no	—
283	C₂×C₃×D₄	—	2	4	no	—
284	C₂×C₃×D₄	—	4	4	no	—
285	C₂×C₃×D₄	—	4	4	no	—
286	C₂²×C₃×C₄	—	2	2	no	—
287	C₂²×C₃×C₄	—	2	2	no	—
288	C₂²×C₃×C₄	—	2	2	no	—
289	C₂²×C₃×C₄	—	2	2	no	—
290	C₂²×C₃×C₄	—	2	2	no	—
291	C₂²×C₃×C₄	—	2	2	no	—
292	C₂²×C₃×C₄	—	2	2	no	—
293	C₂²×C₃×C₄	—	2	2	no	—
294	C₂²×C₃×C₄	—	2	8	no	—
295	C₂²×C₃×C₄	—	4	4	no	—
296	C₂²×C₃×C₄	—	4	4	no	—
297	C₂²×C₃×C₄	#41	1	4	yes	—
298	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
299	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
300	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
301	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
302	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
303	C₂²×C₃×C₄	C₂⁴	1	4	yes	—
304	C₂²×C₃×C₄	C₂⁴	1	4	yes	—
305	C₂²×C₃×C₄	C₂⁴	1	4	yes	—
306	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
307	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
308	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
309	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
310	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
311	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
312	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
313	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
314	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
315	C₃×C₄⋊C₄	—	2	2	no	—
316	C₃×C₄⋊C₄	—	2	2	no	—
317	C₃×C₄⋊C₄	—	2	2	no	—
318	C₃×C₄⋊C₄	—	2	2	no	—
319	C₃×C₄⋊C₄	—	2	4	no	—
320	C₃×C₄⋊C₄	—	2	4	no	—
321	C₃×C₄⋊C₄	—	2	4	no	—
322	C₃×C₄⋊C₄	—	2	4	no	—
323	C₃×C₄⋊C₄	—	2	4	no	—
324	C₃×C₄⋊C₄	—	2	4	no	—
325	C₃×C₄⋊C₄	—	2	4	no	—
326	C₃×C₄⋊C₄	—	2	4	no	—
327	C₃×C₄⋊C₄	—	4	4	no	—
328	C₃×C₄⋊C₄	—	4	4	no	—
329	C₃×C₄⋊C₄	—	4	4	no	—
330	C₃×C₄⋊C₄	—	4	4	no	—
331	C₃×C₂²⋊C₄	—	2	2	no	—
332	C₃×C₂²⋊C₄	—	2	2	no	—
333	C₃×C₂²⋊C₄	—	2	2	no	—
334	C₃×C₂²⋊C₄	—	2	2	no	—
335	C₃×C₂²⋊C₄	—	2	8	no	—
336	C₃×C₂²⋊C₄	—	2	8	no	—
337	C₃×C₂²⋊C₄	—	4	4	no	—
338	C₃×C₂²⋊C₄	—	4	4	no	—
339	C₃×C₂²⋊C₄	—	4	4	no	—
340	C₃×C₂²⋊C₄	—	4	4	no	—
341	C₃×C₂²⋊C₄	—	4	4	no	—
342	C₃×C₂²⋊C₄	—	4	4	no	—
343	C₃×C₂²⋊C₄	—	4	4	no	—
344	C₃×C₂²⋊C₄	—	4	4	no	—
345	C₃×C₂²⋊C₄	—	4	4	no	—
346	C₃×C₄²	—	2	2	no	—
347	C₃×C₄²	—	2	2	no	—
348	C₃×C₄²	—	2	2	no	—
349	C₃×C₄²	—	2	2	no	—
350	C₃×C₄²	—	2	2	no	—
351	C₃×C₄²	—	2	2	no	—
352	C₃×C₄²	—	2	2	no	—
353	C₃×C₄²	—	2	2	no	—
354	C₃×C₄²	—	2	2	no	—
355	C₃×C₄²	—	2	2	no	—
356	C₃×C₄²	—	2	2	no	—
357	C₃×C₄²	—	2	2	no	—
358	C₃×C₄²	—	2	2	no	—
359	C₃×C₄²	—	2	2	no	—
360	C₃×C₄²	—	4	4	no	—
361	C₃×C₄²	#41	1	4	yes	—
362	C₃×C₄²	#41	1	4	yes	—
363	C₂²×Q₈	C₂³×C₃	1	2	yes	—
364	C₂²×D₄	C₂³×C₃	1	2	yes	—
365	C₂²×D₄	C₂³×C₃	1	2	yes	—
366	C₂²×D₄	C₂³×C₃	1	2	yes	—
367	C₂²×D₄	C₂³×C₃	1	4	yes	—
368	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
369	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
370	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
371	C₂³×C₄	C₂³×C₃	1	4	yes	—
372	C₄⋊Q₈	—	2	4	no	—
373	#127	—	2	4	no	—
374	#125	—	4	4	no	—
375	#124	—	4	4	no	—
376	#124	—	4	4	no	—
377	C₂²⋊Q₈	—	4	4	no	—
378	#121	—	2	8	no	—
379	#121	—	4	4	no	—
380	#121	—	4	4	no	—
381	C₄×Q₈	—	4	4	no	—
382	C₄×D₄	—	2	8	no	—
383	C₄×D₄	—	4	4	no	—
384	C₄×D₄	—	4	4	no	—
385	#117	—	2	4	no	—
386	#117	—	2	4	no	—
387	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
388	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
389	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
390	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
391	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
392	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
393	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
394	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
395	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
396	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
397	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
398	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
399	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
400	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
401	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
402	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
403	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
404	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
405	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
406	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
407	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
408	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
409	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
410	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
411	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
412	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
413	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
414	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
415	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
416	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
417	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
418	C₂×C₄²	—	2	4	no	—
419	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
420	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
421	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
422	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
423	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
424	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
425	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
426	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
427	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
428	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
429	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
430	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
431	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
432	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
433	C₂×C₄²	C₂³×C₃	1	4	yes	—
434	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
435	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
436	#95	C₂³×C₃	1	1	yes	characteristic
437	#95	C₂³×C₃	1	1	yes	characteristic
438	#95	C₂³×C₃	1	1	yes	characteristic
439	#95	C₂³×C₃	1	1	yes	characteristic
440	#95	C₂³×C₃	1	1	yes	characteristic
441	#95	C₂³×C₃	1	1	yes	characteristic
442	#95	C₂³×C₃	1	1	yes	characteristic
443	#95	C₂³×C₃	1	1	yes	characteristic
444	#95	C₂³×C₃	1	4	yes	—
445	#95	C₂³×C₃	1	4	yes	—
446	#95	C₂³×C₃	1	4	yes	—
447	#95	C₂³×C₃	1	4	yes	—
448	#95	C₂³×C₃	1	4	yes	—
449	#95	C₂³×C₃	1	4	yes	—
450	C₂³×C₃	—	2	1	no	—
451	C₂³×C₃	—	2	1	no	—
452	C₂³×C₃	—	2	1	no	—
453	C₂³×C₃	—	2	1	no	—
454	C₂³×C₃	—	2	1	no	—
455	C₂³×C₃	—	2	1	no	—
456	C₂³×C₃	—	2	4	no	—
457	C₂³×C₃	—	2	4	no	—
458	C₂³×C₃	—	2	4	no	—
459	C₂³×C₃	—	2	4	no	—
460	C₂³×C₃	—	2	4	no	—
461	C₂³×C₃	—	2	4	no	—
462	C₂³×C₃	—	2	4	no	—
463	C₂³×C₃	C₂×#41	1	2	yes	—
464	C₂³×C₃	C₂⁵	1	1	yes	characteristic
465	C₃×Q₈	—	4	8	no	—
466	C₃×D₄	—	4	8	no	—
467	C₃×D₄	—	4	8	no	—
468	C₃×D₄	—	4	8	no	—
469	C₃×D₄	—	8	8	no	—
470	C₂×C₃×C₄	—	2	1	no	—
471	C₂×C₃×C₄	—	2	1	no	—
472	C₂×C₃×C₄	—	2	1	no	—
473	C₂×C₃×C₄	—	2	1	no	—
474	C₂×C₃×C₄	—	2	1	no	—
475	C₂×C₃×C₄	—	2	1	no	—
476	C₂×C₃×C₄	—	2	8	no	—
477	C₂×C₃×C₄	—	2	1	no	—
478	C₂×C₃×C₄	—	2	1	no	—
479	C₂×C₃×C₄	—	2	1	no	—
480	C₂×C₃×C₄	—	2	1	no	—
481	C₂×C₃×C₄	—	2	1	no	—
482	C₂×C₃×C₄	—	2	1	no	—
483	C₂×C₃×C₄	—	2	1	no	—
484	C₂×C₃×C₄	—	2	1	no	—
485	C₂×C₃×C₄	—	2	4	no	—
486	C₂×C₃×C₄	—	2	4	no	—
487	C₂×C₃×C₄	—	2	4	no	—
488	C₂×C₃×C₄	—	2	1	no	—
489	C₂×C₃×C₄	—	2	1	no	—
490	C₂×C₃×C₄	—	2	1	no	—
491	C₂×C₃×C₄	—	2	1	no	—
492	C₂×C₃×C₄	—	2	1	no	—
493	C₂×C₃×C₄	—	2	1	no	—
494	C₂×C₃×C₄	—	2	1	no	—
495	C₂×C₃×C₄	—	2	1	no	—
496	C₂×C₃×C₄	—	2	1	no	—
497	C₂×C₃×C₄	—	2	4	no	—
498	C₂×C₃×C₄	—	2	4	no	—
499	C₂×C₃×C₄	—	2	1	no	—
500	C₂×C₃×C₄	—	2	1	no	—
501	C₂×C₃×C₄	—	2	4	no	—
502	C₂×C₃×C₄	—	2	4	no	—
503	C₂×C₃×C₄	—	2	4	no	—
504	C₂×C₃×C₄	—	2	4	no	—
505	C₂×C₃×C₄	—	2	1	no	—
506	C₂×C₃×C₄	—	2	1	no	—
507	C₂×C₃×C₄	—	2	1	no	—
508	C₂×C₃×C₄	—	2	1	no	—
509	C₂×C₃×C₄	—	2	1	no	—
510	C₂×C₃×C₄	—	4	4	no	—
511	C₂×C₃×C₄	—	4	4	no	—
512	C₂×C₃×C₄	—	8	8	no	—
513	C₂×C₃×C₄	C₂×#41	1	2	yes	—
514	C₂×C₃×C₄	C₂×#41	1	2	yes	—
515	C₂×C₃×C₄	C₂×#41	1	2	yes	—
516	C₂×C₃×C₄	C₂×#41	1	2	yes	—
517	C₂×C₃×C₄	C₂×#41	1	2	yes	—
518	C₂×C₃×C₄	C₂×#41	1	2	yes	—
519	C₂×C₃×C₄	C₂×#41	1	2	yes	—
520	C₂×C₃×C₄	C₂×#41	1	2	yes	—
521	C₂×C₃×C₄	H(5,𝔽₂)	1	2	yes	—
522	C₂×C₃×C₄	H(5,𝔽₂)	1	2	yes	—
523	C₂×C₃×C₄	H(5,𝔽₂)	1	2	yes	—
524	C₂×C₃×C₄	2₋¹⁺⁴	1	2	yes	—
525	C₂⁴	C₂⁴×C₃	1	4	yes	—
526	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
527	C₂×Q₈	—	2	4	no	—
528	C₂×Q₈	—	2	4	no	—
529	C₂×Q₈	—	2	4	no	—
530	C₂×D₄	—	2	8	no	—
531	C₂×D₄	—	2	4	no	—
532	C₂×D₄	—	2	4	no	—
533	C₂×D₄	—	2	4	no	—
534	C₂×D₄	—	2	4	no	—
535	C₂×D₄	—	2	4	no	—
536	C₂×D₄	—	2	4	no	—
537	C₂×D₄	—	2	4	no	—
538	C₂×D₄	—	2	4	no	—
539	C₂×D₄	—	2	4	no	—
540	C₂×D₄	—	4	4	no	—
541	C₂×D₄	—	4	4	no	—
542	C₂²×C₄	—	2	2	no	—
543	C₂²×C₄	—	2	2	no	—
544	C₂²×C₄	—	2	2	no	—
545	C₂²×C₄	—	2	2	no	—
546	C₂²×C₄	—	2	2	no	—
547	C₂²×C₄	—	2	2	no	—
548	C₂²×C₄	—	2	2	no	—
549	C₂²×C₄	—	2	2	no	—
550	C₂²×C₄	—	2	8	no	—
551	C₂²×C₄	—	4	4	no	—
552	C₂²×C₄	—	4	4	no	—
553	C₂²×C₄	C₃×#41	1	4	yes	—
554	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
555	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
556	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
557	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
558	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
559	C₂²×C₄	C₂⁴×C₃	1	4	yes	—
560	C₂²×C₄	C₂⁴×C₃	1	4	yes	—
561	C₂²×C₄	C₂⁴×C₃	1	4	yes	—
562	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
563	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
564	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
565	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
566	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
567	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
568	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
569	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
570	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
571	C₄⋊C₄	—	2	2	no	—
572	C₄⋊C₄	—	2	2	no	—
573	C₄⋊C₄	—	2	2	no	—
574	C₄⋊C₄	—	2	2	no	—
575	C₄⋊C₄	—	2	4	no	—
576	C₄⋊C₄	—	2	4	no	—
577	C₄⋊C₄	—	2	4	no	—
578	C₄⋊C₄	—	2	4	no	—
579	C₄⋊C₄	—	2	4	no	—
580	C₄⋊C₄	—	2	4	no	—
581	C₄⋊C₄	—	2	4	no	—
582	C₄⋊C₄	—	2	4	no	—
583	C₄⋊C₄	—	4	4	no	—
584	C₄⋊C₄	—	4	4	no	—
585	C₄⋊C₄	—	4	4	no	—
586	C₄⋊C₄	—	4	4	no	—
587	C₂²⋊C₄	—	2	2	no	—
588	C₂²⋊C₄	—	2	2	no	—
589	C₂²⋊C₄	—	2	2	no	—
590	C₂²⋊C₄	—	2	2	no	—
591	C₂²⋊C₄	—	2	8	no	—
592	C₂²⋊C₄	—	2	8	no	—
593	C₂²⋊C₄	—	4	4	no	—
594	C₂²⋊C₄	—	4	4	no	—
595	C₂²⋊C₄	—	4	4	no	—
596	C₂²⋊C₄	—	4	4	no	—
597	C₂²⋊C₄	—	4	4	no	—
598	C₂²⋊C₄	—	4	4	no	—
599	C₂²⋊C₄	—	4	4	no	—
600	C₂²⋊C₄	—	4	4	no	—
601	C₂²⋊C₄	—	4	4	no	—
602	C₄²	—	2	2	no	—
603	C₄²	—	2	2	no	—
604	C₄²	—	2	2	no	—
605	C₄²	—	2	2	no	—
606	C₄²	—	2	2	no	—
607	C₄²	—	2	2	no	—
608	C₄²	—	2	2	no	—
609	C₄²	—	2	2	no	—
610	C₄²	—	2	2	no	—
611	C₄²	—	2	2	no	—
612	C₄²	—	2	2	no	—
613	C₄²	—	2	2	no	—
614	C₄²	—	2	2	no	—
615	C₄²	—	2	2	no	—
616	C₄²	—	4	4	no	—
617	C₄²	C₃×#41	1	4	yes	—
618	C₄²	C₃×#41	1	4	yes	—
619	C₂²×C₃	—	2	2	no	—
620	C₂²×C₃	—	2	2	no	—
621	C₂²×C₃	—	2	2	no	—
622	C₂²×C₃	—	4	1	no	—
623	C₂²×C₃	—	4	1	no	—
624	C₂²×C₃	—	4	1	no	—
625	C₂²×C₃	—	4	1	no	—
626	C₂²×C₃	—	4	4	no	—
627	C₂²×C₃	—	4	4	no	—
628	C₂²×C₃	—	4	4	no	—
629	C₂²×C₃	—	4	4	no	—
630	C₂²×C₃	—	4	4	no	—
631	C₂²×C₃	—	4	4	no	—
632	C₂²×C₃	—	4	4	no	—
633	C₂²×C₃	C₂²×#41	1	1	yes	characteristic
634	C₂²×C₃	C₂²×#41	1	1	yes	characteristic
635	C₂²×C₃	C₂²×#41	1	1	yes	characteristic
636	C₂²×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
637	C₂²×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
638	C₂²×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
639	C₂²×C₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
640	C₃×C₄	—	2	2	no	—
641	C₃×C₄	—	2	2	no	—
642	C₃×C₄	—	2	2	no	—
643	C₃×C₄	—	4	1	no	—
644	C₃×C₄	—	4	4	no	—
645	C₃×C₄	—	4	1	no	—
646	C₃×C₄	—	4	1	no	—
647	C₃×C₄	—	4	1	no	—
648	C₃×C₄	—	4	1	no	—
649	C₃×C₄	—	4	4	no	—
650	C₃×C₄	—	4	4	no	—
651	C₃×C₄	—	4	1	no	—
652	C₃×C₄	—	4	1	no	—
653	C₃×C₄	—	4	1	no	—
654	C₃×C₄	#529	1	4	yes	—
655	C₃×C₄	#540	1	4	yes	—
656	C₃×C₄	#542	1	4	yes	—
657	C₂³	—	2	1	no	—
658	C₂³	—	2	1	no	—
659	C₂³	—	2	1	no	—
660	C₂³	—	2	1	no	—
661	C₂³	—	2	1	no	—
662	C₂³	—	2	1	no	—
663	C₂³	—	2	4	no	—
664	C₂³	—	2	4	no	—
665	C₂³	—	2	4	no	—
666	C₂³	—	2	4	no	—
667	C₂³	—	2	4	no	—
668	C₂³	—	2	4	no	—
669	C₂³	—	2	4	no	—
670	C₂³	C₂×C₃×#41	1	2	yes	—
671	C₂³	C₂⁵×C₃	1	1	yes	characteristic
672	Q₈	—	4	8	no	—
673	D₄	—	4	8	no	—
674	D₄	—	4	8	no	—
675	D₄	—	4	8	no	—
676	D₄	—	8	8	no	—
677	C₂×C₄	—	2	1	no	—
678	C₂×C₄	—	2	1	no	—
679	C₂×C₄	—	2	1	no	—
680	C₂×C₄	—	2	1	no	—
681	C₂×C₄	—	2	1	no	—
682	C₂×C₄	—	2	1	no	—
683	C₂×C₄	—	2	8	no	—
684	C₂×C₄	—	2	1	no	—
685	C₂×C₄	—	2	1	no	—
686	C₂×C₄	—	2	1	no	—
687	C₂×C₄	—	2	1	no	—
688	C₂×C₄	—	2	1	no	—
689	C₂×C₄	—	2	1	no	—
690	C₂×C₄	—	2	1	no	—
691	C₂×C₄	—	2	1	no	—
692	C₂×C₄	—	2	4	no	—
693	C₂×C₄	—	2	4	no	—
694	C₂×C₄	—	2	4	no	—
695	C₂×C₄	—	2	1	no	—
696	C₂×C₄	—	2	1	no	—
697	C₂×C₄	—	2	1	no	—
698	C₂×C₄	—	2	1	no	—
699	C₂×C₄	—	2	1	no	—
700	C₂×C₄	—	2	1	no	—
701	C₂×C₄	—	2	1	no	—
702	C₂×C₄	—	2	1	no	—
703	C₂×C₄	—	2	1	no	—
704	C₂×C₄	—	2	4	no	—
705	C₂×C₄	—	2	4	no	—
706	C₂×C₄	—	2	1	no	—
707	C₂×C₄	—	2	1	no	—
708	C₂×C₄	—	2	4	no	—
709	C₂×C₄	—	2	4	no	—
710	C₂×C₄	—	2	4	no	—
711	C₂×C₄	—	2	4	no	—
712	C₂×C₄	—	2	1	no	—
713	C₂×C₄	—	2	1	no	—
714	C₂×C₄	—	2	1	no	—
715	C₂×C₄	—	2	1	no	—
716	C₂×C₄	—	2	1	no	—
717	C₂×C₄	—	4	4	no	—
718	C₂×C₄	—	4	4	no	—
719	C₂×C₄	—	8	8	no	—
720	C₂×C₄	C₂×C₃×#41	1	2	yes	—
721	C₂×C₄	C₂×C₃×#41	1	2	yes	—
722	C₂×C₄	C₂×C₃×#41	1	2	yes	—
723	C₂×C₄	C₂×C₃×#41	1	2	yes	—
724	C₂×C₄	C₂×C₃×#41	1	2	yes	—
725	C₂×C₄	C₂×C₃×#41	1	2	yes	—
726	C₂×C₄	C₂×C₃×#41	1	2	yes	—
727	C₂×C₄	C₂×C₃×#41	1	2	yes	—
728	C₂×C₄	C₃×H(5,𝔽₂)	1	2	yes	—
729	C₂×C₄	C₃×H(5,𝔽₂)	1	2	yes	—
730	C₂×C₄	C₃×H(5,𝔽₂)	1	2	yes	—
731	C₂×C₄	C₃×2₋¹⁺⁴	1	2	yes	—
732	C₂×C₃	—	4	2	no	—
733	C₂×C₃	—	8	4	no	—
734	C₂×C₃	C₂×#529	1	1	yes	characteristic
735	C₂×C₃	C₂×#540	1	1	yes	characteristic
736	C₂×C₃	C₂×#542	1	1	yes	characteristic
737	C₂×C₃	#3508	1	1	yes	characteristic
738	C₂×C₃	#3508	1	1	yes	characteristic
739	C₂×C₃	#3511	1	1	yes	characteristic
740	C₂×C₃	#3511	1	1	yes	characteristic
741	C₂²	—	2	2	no	—
742	C₂²	—	2	2	no	—
743	C₂²	—	2	2	no	—
744	C₂²	—	4	1	no	—
745	C₂²	—	4	1	no	—
746	C₂²	—	4	1	no	—
747	C₂²	—	4	1	no	—
748	C₂²	—	4	4	no	—
749	C₂²	—	4	4	no	—
750	C₂²	—	4	4	no	—
751	C₂²	—	4	4	no	—
752	C₂²	—	4	4	no	—
753	C₂²	—	4	4	no	—
754	C₂²	—	4	4	no	—
755	C₂²	C₂²×C₃×#41	1	1	yes	characteristic
756	C₂²	C₂²×C₃×#41	1	1	yes	characteristic
757	C₂²	C₂²×C₃×#41	1	1	yes	characteristic
758	C₂²	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
759	C₂²	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
760	C₂²	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
761	C₂²	C₂×C₃×2₋¹⁺⁴	1	1	yes	characteristic
762	C₄	—	2	2	no	—
763	C₄	—	2	2	no	—
764	C₄	—	2	2	no	—
765	C₄	—	4	1	no	—
766	C₄	—	4	4	no	—
767	C₄	—	4	1	no	—
768	C₄	—	4	4	no	—
769	C₄	—	4	4	no	—
770	C₄	—	4	1	no	—
771	C₄	—	4	1	no	—
772	C₄	—	4	1	no	—
773	C₄	—	4	1	no	—
774	C₄	—	4	1	no	—
775	C₄	—	4	1	no	—
776	C₄	C₃×#529	1	4	yes	—
777	C₄	C₃×#540	1	4	yes	—
778	C₄	C₃×#542	1	4	yes	—
779	C₃	#35288	1	1	yes	characteristic, direct product factor, Sylow
780	C₂	—	4	2	no	—
781	C₂	—	8	4	no	—
782	C₂	C₂×C₃×#529	1	1	yes	characteristic
783	C₂	C₂×C₃×#540	1	1	yes	characteristic
784	C₂	C₂×C₃×#542	1	1	yes	characteristic
785	C₂	C₃×#3508	1	1	yes	characteristic
786	C₂	C₃×#3508	1	1	yes	characteristic
787	C₂	C₃×#3511	1	1	yes	characteristic
788	C₂	C₃×#3511	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₃	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₃
prime radical	C₃×#2856	C₂
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃×#2859	C₂	semidirect
2. C₃×#2858	C₂	semidirect
3. C₃×#2857	C₂	semidirect
5. C₃×#2644	C₂	semidirect
6. C₃×#2624	C₂	semidirect
7. C₃×#2513	C₂	semidirect
8. C₃×#2490	C₂	semidirect
9. C₃×#2454	C₂	semidirect
10. C₃×#2448	C₂	semidirect
11. C₃×#2447	C₂	semidirect
12. C₃×#2427	C₂	semidirect
13. C₃×#2426	C₂	semidirect
14. C₃×#2420	C₂	semidirect
15. C₃×#2324	C₂	semidirect
16. C₃×#2319	C₂	semidirect
17. C₃×C₄×C₄⋊Q₈	C₂	semidirect
18. C₃×C₄×#127	C₂	semidirect
19. C₃×C₄×#117	C₂	semidirect
20. #35288	C₃	direct (N × H)
92. #2859	C₂×C₃	semidirect
93. #2858	C₂×C₃	semidirect
94. #2857	C₂×C₃	semidirect
96. #2644	C₂×C₃	semidirect
97. #2624	C₂×C₃	semidirect
98. #2513	C₂×C₃	semidirect
99. #2490	C₂×C₃	semidirect
100. #2454	C₂×C₃	semidirect
101. #2448	C₂×C₃	semidirect
102. #2447	C₂×C₃	semidirect
103. #2427	C₂×C₃	semidirect
104. #2426	C₂×C₃	semidirect
105. #2420	C₂×C₃	semidirect
106. #2324	C₂×C₃	semidirect
107. #2319	C₂×C₃	semidirect
108. C₄×C₄⋊Q₈	C₂×C₃	semidirect
109. C₄×#127	C₂×C₃	semidirect
110. C₄×#117	C₂×C₃	semidirect
779. C₃	#35288	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×#2859	2
C₃×#2858	2
C₃×#2857	2
C₃×#2856	2
C₃×#2644	2
C₃×#2624	2
C₃×#2513	2
C₃×#2490	2
C₃×#2454	2
C₃×#2448	2
C₃×#2447	2
C₃×#2427	2
C₃×#2426	2
C₃×#2420	2
C₃×#2324	2
C₃×#2319	2
C₃×C₄×C₄⋊Q₈	2
C₃×C₄×#127	2
C₃×C₄×#117	2
#35288	3

Subgroups — C3×#35288 #10653895

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#35288 #10653895