Subgroups — C₃×#37265 #10655872

Order 768.

1552 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#2864	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#2861	C₂	1	1	yes	maximal, characteristic
3	C₃×#2808	C₂	1	1	yes	maximal, characteristic
4	C₃×#2806	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#2806	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#2773	C₂	1	2	yes	maximal, complemented
7	C₃×#2768	C₂	1	2	yes	maximal, complemented
8	C₃×#2732	C₂	1	1	yes	maximal, characteristic
9	C₃×#2729	C₂	1	2	yes	maximal, complemented
10	C₃×#2726	C₂	1	2	yes	maximal, complemented
11	C₃×#2721	C₂	1	2	yes	maximal, complemented
12	C₃×#2715	C₂	1	2	yes	maximal
13	C₃×#2637	C₂	1	2	yes	maximal, complemented
14	C₃×#2520	C₂	1	2	yes	maximal, complemented
15	C₃×#2519	C₂	1	2	yes	maximal, complemented
16	C₃×#2479	C₂	1	2	yes	maximal
17	C₃×#2478	C₂	1	2	yes	maximal, complemented
18	C₃×#2323	C₂	1	2	yes	maximal, complemented
19	C₃×C₄×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
20	#37265	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
21	C₂×C₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
22	C₂×C₃×#126	C₂²	1	2	yes	—
23	C₂×C₃×#126	C₂²	1	2	yes	—
24	C₂×C₃×#125	C₂²	1	2	yes	—
25	C₂×C₃×#125	C₂²	1	1	yes	characteristic
26	C₂×C₃×#124	C₂²	1	1	yes	characteristic
27	C₂×C₃×C₂²⋊Q₈	C₂²	1	2	yes	—
28	C₂×C₃×C₄×Q₈	C₂²	1	1	yes	characteristic
29	C₂×C₃×C₄×Q₈	C₂²	1	1	yes	characteristic
30	C₂×C₃×#117	C₂²	1	2	yes	—
31	C₃×#400	C₂²	1	2	yes	—
32	C₃×#399	C₂²	1	2	yes	—
33	C₃×#399	C₂²	1	2	yes	—
34	C₃×#399	C₂²	1	2	yes	—
35	C₃×#398	C₂²	1	2	yes	—
36	C₃×#398	C₂²	1	2	yes	—
37	C₃×#398	C₂²	1	2	yes	—
38	C₃×#398	C₂²	1	2	yes	—
39	C₃×#398	C₂²	1	2	yes	—
40	C₃×#398	C₂²	1	2	yes	—
41	C₃×#398	C₂²	1	2	yes	—
42	C₃×#398	C₂²	1	2	yes	—
43	C₃×#398	C₂²	1	2	yes	—
44	C₃×#398	C₂²	1	2	yes	—
45	C₃×#397	C₂²	1	2	yes	—
46	C₃×#397	C₂²	1	2	yes	—
47	C₃×#397	C₂²	1	2	yes	—
48	C₃×#396	C₂²	1	2	yes	—
49	C₃×#396	C₂²	1	2	yes	—
50	C₃×#396	C₂²	1	2	yes	—
51	C₃×#395	C₂²	1	2	yes	—
52	C₃×#395	C₂²	1	2	yes	—
53	C₃×#394	C₂²	1	2	yes	—
54	C₃×#393	C₂²	1	2	yes	—
55	C₃×#391	C₂²	1	2	yes	—
56	C₃×#391	C₂²	1	2	yes	—
57	C₃×#391	C₂²	1	1	yes	characteristic
58	C₃×#391	C₂²	1	1	yes	characteristic
59	C₃×#391	C₂²	1	1	yes	characteristic
60	C₃×#391	C₂²	1	1	yes	characteristic
61	C₃×#390	C₂²	1	1	yes	characteristic
62	C₃×#390	C₂²	1	1	yes	characteristic
63	C₃×#389	C₂²	1	2	yes	—
64	C₃×#389	C₂²	1	2	yes	—
65	C₃×#389	C₂²	1	2	yes	—
66	C₃×#389	C₂²	1	2	yes	—
67	C₃×#389	C₂²	1	2	yes	—
68	C₃×#389	C₂²	1	2	yes	—
69	C₃×#389	C₂²	1	1	yes	characteristic
70	C₃×#389	C₂²	1	1	yes	characteristic
71	C₃×#389	C₂²	1	2	yes	—
72	C₃×#389	C₂²	1	1	yes	characteristic
73	C₃×#389	C₂²	1	1	yes	characteristic
74	C₃×#388	C₂²	1	2	yes	—
75	C₃×#388	C₂²	1	2	yes	—
76	C₃×#388	C₂²	1	2	yes	—
77	C₃×#388	C₂²	1	2	yes	—
78	C₃×#388	C₂²	1	2	yes	—
79	C₃×#388	C₂²	1	2	yes	—
80	C₃×#388	C₂²	1	2	yes	—
81	C₃×#388	C₂²	1	2	yes	—
82	C₃×#388	C₂²	1	2	yes	—
83	C₃×#388	C₂²	1	2	yes	—
84	C₃×#387	C₂²	1	2	yes	—
85	C₃×#387	C₂²	1	2	yes	—
86	C₃×#387	C₂²	1	2	yes	—
87	C₃×#387	C₂²	1	2	yes	—
88	C₃×#387	C₂²	1	2	yes	—
89	C₃×#387	C₂²	1	2	yes	—
90	C₃×#387	C₂²	1	2	yes	—
91	C₃×#387	C₂²	1	2	yes	—
92	C₃×#387	C₂²	1	2	yes	—
93	C₃×#387	C₂²	1	2	yes	—
94	C₃×#387	C₂²	1	2	yes	—
95	C₃×#386	C₂²	1	2	yes	—
96	C₃×#385	C₂²	1	2	yes	—
97	C₃×#385	C₂²	1	2	yes	—
98	C₃×#385	C₂²	1	2	yes	—
99	C₃×#384	C₂²	1	1	yes	characteristic
100	C₃×#382	C₂²	1	2	yes	—
101	C₃×#382	C₂²	1	1	yes	characteristic
102	C₃×#382	C₂²	1	1	yes	characteristic
103	C₃×#380	C₂²	1	2	yes	—
104	C₃×C₄×C₄⋊C₄	C₂²	1	2	yes	—
105	C₃×C₄×C₄⋊C₄	C₂²	1	2	yes	—
106	C₃×C₄×C₄⋊C₄	C₂²	1	2	yes	—
107	C₃×C₄³	C₂²	1	1	yes	characteristic
108	#2864	C₂×C₃	1	1	yes	characteristic, complemented
109	#2861	C₂×C₃	1	1	yes	characteristic
110	#2808	C₂×C₃	1	1	yes	characteristic
111	#2806	C₂×C₃	1	1	yes	characteristic, complemented
112	#2806	C₂×C₃	1	1	yes	characteristic, complemented
113	#2773	C₂×C₃	1	2	yes	complemented
114	#2768	C₂×C₃	1	2	yes	complemented
115	#2732	C₂×C₃	1	1	yes	characteristic
116	#2729	C₂×C₃	1	2	yes	complemented
117	#2726	C₂×C₃	1	2	yes	complemented
118	#2721	C₂×C₃	1	2	yes	complemented
119	#2715	C₂×C₃	1	2	yes	—
120	#2637	C₂×C₃	1	2	yes	complemented
121	#2520	C₂×C₃	1	2	yes	complemented
122	#2519	C₂×C₃	1	2	yes	complemented
123	#2479	C₂×C₃	1	2	yes	—
124	#2478	C₂×C₃	1	2	yes	complemented
125	#2323	C₂×C₃	1	2	yes	complemented
126	C₄×C₄⋊Q₈	C₂×C₃	1	1	yes	characteristic, complemented
127	C₂²×C₃×Q₈	C₂³	1	1	yes	characteristic
128	C₂²×C₃×Q₈	C₂³	1	1	yes	characteristic
129	C₂²×C₃×Q₈	C₂³	1	1	yes	characteristic
130	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
131	C₂³×C₃×C₄	C₂³	1	2	yes	—
132	C₃×C₄⋊Q₈	—	2	4	no	—
133	C₃×#126	—	4	4	no	—
134	C₃×#126	—	4	4	no	—
135	C₃×#125	—	4	2	no	—
136	C₃×#125	—	4	4	no	—
137	C₃×#124	—	4	2	no	—
138	C₃×C₂²⋊Q₈	—	2	8	no	—
139	C₃×C₄×Q₈	—	4	2	no	—
140	C₃×C₄×Q₈	—	4	2	no	—
141	C₃×#117	—	4	4	no	—
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	1	yes	characteristic
148	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
149	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
150	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
151	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
152	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
153	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
154	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
155	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
156	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
157	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
158	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
159	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
160	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
161	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
162	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
163	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
164	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
165	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
166	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
167	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
168	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
169	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
170	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
171	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
172	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
173	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
174	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
175	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
176	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
177	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
178	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
179	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
180	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
181	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
182	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
183	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
184	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
185	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
186	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
187	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
188	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
189	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
190	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
191	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
192	C₂×C₃×C₄²	C₂³	1	2	yes	—
193	C₂×C₃×C₄²	C₂³	1	2	yes	—
194	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
195	C₂×C₃×C₄²	C₂³	1	2	yes	—
196	C₂×C₃×C₄²	C₂³	1	2	yes	—
197	C₂×C₃×C₄²	C₂³	1	2	yes	—
198	C₃×#95	C₂³	1	2	yes	—
199	C₃×#95	C₂³	1	2	yes	—
200	C₃×#95	C₂³	1	2	yes	—
201	C₃×#95	C₂³	1	2	yes	—
202	C₃×#95	C₂³	1	2	yes	—
203	C₃×#95	C₂³	1	2	yes	—
204	C₃×#95	C₂³	1	2	yes	—
205	C₃×#95	C₂³	1	2	yes	—
206	C₃×#95	C₂³	1	2	yes	—
207	C₃×#95	C₂³	1	2	yes	—
208	C₃×#95	C₂³	1	2	yes	—
209	C₃×#95	C₂³	1	2	yes	—
210	C₃×#95	C₂³	1	2	yes	—
211	C₃×#95	C₂³	1	2	yes	—
212	C₃×#95	C₂³	1	2	yes	—
213	C₃×#95	C₂³	1	2	yes	—
214	C₃×#95	C₂³	1	2	yes	—
215	C₃×#95	C₂³	1	2	yes	—
216	C₃×#95	C₂³	1	2	yes	—
217	C₃×#95	C₂³	1	2	yes	—
218	C₃×#95	C₂³	1	2	yes	—
219	C₃×#95	C₂³	1	2	yes	—
220	C₃×#95	C₂³	1	2	yes	—
221	C₃×#95	C₂³	1	2	yes	—
222	C₃×#95	C₂³	1	2	yes	—
223	C₃×#95	C₂³	1	2	yes	—
224	C₂×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
225	C₂×#126	C₂²×C₃	1	2	yes	—
226	C₂×#126	C₂²×C₃	1	2	yes	—
227	C₂×#125	C₂²×C₃	1	1	yes	characteristic
228	C₂×#125	C₂²×C₃	1	2	yes	—
229	C₂×#124	C₂²×C₃	1	1	yes	characteristic
230	C₂×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
231	C₂×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic
232	C₂×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic
233	C₂×#117	C₂²×C₃	1	2	yes	—
234	#400	C₂²×C₃	1	2	yes	—
235	#399	C₂²×C₃	1	2	yes	—
236	#399	C₂²×C₃	1	2	yes	—
237	#399	C₂²×C₃	1	2	yes	—
238	#398	C₂²×C₃	1	2	yes	—
239	#398	C₂²×C₃	1	2	yes	—
240	#398	C₂²×C₃	1	2	yes	—
241	#398	C₂²×C₃	1	2	yes	—
242	#398	C₂²×C₃	1	2	yes	—
243	#398	C₂²×C₃	1	2	yes	—
244	#398	C₂²×C₃	1	2	yes	—
245	#398	C₂²×C₃	1	2	yes	—
246	#398	C₂²×C₃	1	2	yes	—
247	#398	C₂²×C₃	1	2	yes	—
248	#397	C₂²×C₃	1	2	yes	—
249	#397	C₂²×C₃	1	2	yes	—
250	#397	C₂²×C₃	1	2	yes	—
251	#396	C₂²×C₃	1	2	yes	—
252	#396	C₂²×C₃	1	2	yes	—
253	#396	C₂²×C₃	1	2	yes	—
254	#395	C₂²×C₃	1	2	yes	—
255	#395	C₂²×C₃	1	2	yes	—
256	#394	C₂²×C₃	1	2	yes	—
257	#393	C₂²×C₃	1	2	yes	—
258	#391	C₂²×C₃	1	1	yes	characteristic
259	#391	C₂²×C₃	1	1	yes	characteristic
260	#391	C₂²×C₃	1	2	yes	—
261	#391	C₂²×C₃	1	1	yes	characteristic
262	#391	C₂²×C₃	1	1	yes	characteristic
263	#391	C₂²×C₃	1	2	yes	—
264	#390	C₂²×C₃	1	1	yes	characteristic
265	#390	C₂²×C₃	1	1	yes	characteristic
266	#389	C₂²×C₃	1	2	yes	—
267	#389	C₂²×C₃	1	2	yes	—
268	#389	C₂²×C₃	1	2	yes	—
269	#389	C₂²×C₃	1	2	yes	—
270	#389	C₂²×C₃	1	2	yes	—
271	#389	C₂²×C₃	1	1	yes	characteristic
272	#389	C₂²×C₃	1	1	yes	characteristic
273	#389	C₂²×C₃	1	1	yes	characteristic
274	#389	C₂²×C₃	1	1	yes	characteristic
275	#389	C₂²×C₃	1	2	yes	—
276	#389	C₂²×C₃	1	2	yes	—
277	#388	C₂²×C₃	1	2	yes	—
278	#388	C₂²×C₃	1	2	yes	—
279	#388	C₂²×C₃	1	2	yes	—
280	#388	C₂²×C₃	1	2	yes	—
281	#388	C₂²×C₃	1	2	yes	—
282	#388	C₂²×C₃	1	2	yes	—
283	#388	C₂²×C₃	1	2	yes	—
284	#388	C₂²×C₃	1	2	yes	—
285	#388	C₂²×C₃	1	2	yes	—
286	#388	C₂²×C₃	1	2	yes	—
287	#387	C₂²×C₃	1	2	yes	—
288	#387	C₂²×C₃	1	2	yes	—
289	#387	C₂²×C₃	1	2	yes	—
290	#387	C₂²×C₃	1	2	yes	—
291	#387	C₂²×C₃	1	2	yes	—
292	#387	C₂²×C₃	1	2	yes	—
293	#387	C₂²×C₃	1	2	yes	—
294	#387	C₂²×C₃	1	2	yes	—
295	#387	C₂²×C₃	1	2	yes	—
296	#387	C₂²×C₃	1	2	yes	—
297	#387	C₂²×C₃	1	2	yes	—
298	#386	C₂²×C₃	1	2	yes	—
299	#385	C₂²×C₃	1	2	yes	—
300	#385	C₂²×C₃	1	2	yes	—
301	#385	C₂²×C₃	1	2	yes	—
302	#384	C₂²×C₃	1	1	yes	characteristic
303	#382	C₂²×C₃	1	1	yes	characteristic
304	#382	C₂²×C₃	1	1	yes	characteristic
305	#382	C₂²×C₃	1	2	yes	—
306	#380	C₂²×C₃	1	2	yes	—
307	C₄×C₄⋊C₄	C₂²×C₃	1	2	yes	—
308	C₄×C₄⋊C₄	C₂²×C₃	1	2	yes	—
309	C₄×C₄⋊C₄	C₂²×C₃	1	2	yes	—
310	C₄³	C₂²×C₃	1	1	yes	characteristic
311	C₂⁴×C₃	C₂⁴	1	2	yes	—
312	C₂×C₃×Q₈	—	2	2	no	—
313	C₂×C₃×Q₈	—	2	2	no	—
314	C₂×C₃×Q₈	—	4	1	no	—
315	C₂×C₃×Q₈	—	4	1	no	—
316	C₂×C₃×Q₈	—	4	1	no	—
317	C₂×C₃×Q₈	—	4	1	no	—
318	C₂×C₃×Q₈	—	4	1	no	—
319	C₂×C₃×Q₈	—	4	1	no	—
320	C₂×C₃×Q₈	#41	1	4	yes	—
321	C₂×C₃×D₄	—	2	2	no	—
322	C₂×C₃×D₄	—	4	1	no	—
323	C₂×C₃×D₄	—	4	1	no	—
324	C₂²×C₃×C₄	—	2	4	no	—
325	C₂²×C₃×C₄	—	4	2	no	—
326	C₂²×C₃×C₄	—	4	2	no	—
327	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
328	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
329	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
330	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
331	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
332	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
333	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
334	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
335	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
336	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
337	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
338	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
339	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
340	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
341	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
342	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
343	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
344	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
345	C₃×C₄⋊C₄	—	2	4	no	—
346	C₃×C₄⋊C₄	—	2	4	no	—
347	C₃×C₄⋊C₄	—	2	4	no	—
348	C₃×C₄⋊C₄	—	2	4	no	—
349	C₃×C₄⋊C₄	—	2	4	no	—
350	C₃×C₄⋊C₄	—	2	4	no	—
351	C₃×C₄⋊C₄	—	2	4	no	—
352	C₃×C₄⋊C₄	—	2	4	no	—
353	C₃×C₄⋊C₄	—	2	4	no	—
354	C₃×C₄⋊C₄	—	2	4	no	—
355	C₃×C₄⋊C₄	—	2	2	no	—
356	C₃×C₄⋊C₄	—	2	2	no	—
357	C₃×C₄⋊C₄	—	2	4	no	—
358	C₃×C₄⋊C₄	—	4	1	no	—
359	C₃×C₄⋊C₄	—	4	1	no	—
360	C₃×C₄⋊C₄	—	4	2	no	—
361	C₃×C₄⋊C₄	—	4	2	no	—
362	C₃×C₄⋊C₄	—	4	2	no	—
363	C₃×C₄⋊C₄	—	4	2	no	—
364	C₃×C₄⋊C₄	—	4	1	no	—
365	C₃×C₄⋊C₄	—	4	1	no	—
366	C₃×C₄⋊C₄	—	4	2	no	—
367	C₃×C₄⋊C₄	—	4	1	no	—
368	C₃×C₄⋊C₄	—	4	1	no	—
369	C₃×C₄⋊C₄	—	4	2	no	—
370	C₃×C₄⋊C₄	—	4	2	no	—
371	C₃×C₄⋊C₄	—	4	2	no	—
372	C₃×C₄⋊C₄	—	4	2	no	—
373	C₃×C₄⋊C₄	—	4	2	no	—
374	C₃×C₄⋊C₄	—	4	2	no	—
375	C₃×C₄⋊C₄	—	4	2	no	—
376	C₃×C₂²⋊C₄	—	2	4	no	—
377	C₃×C₂²⋊C₄	—	2	4	no	—
378	C₃×C₂²⋊C₄	—	2	4	no	—
379	C₃×C₂²⋊C₄	—	2	4	no	—
380	C₃×C₂²⋊C₄	—	2	4	no	—
381	C₃×C₂²⋊C₄	—	2	4	no	—
382	C₃×C₂²⋊C₄	—	4	2	no	—
383	C₃×C₂²⋊C₄	—	4	2	no	—
384	C₃×C₂²⋊C₄	—	4	2	no	—
385	C₃×C₂²⋊C₄	—	4	2	no	—
386	C₃×C₂²⋊C₄	—	4	2	no	—
387	C₃×C₂²⋊C₄	—	4	2	no	—
388	C₃×C₂²⋊C₄	—	4	2	no	—
389	C₃×C₄²	—	2	2	no	—
390	C₃×C₄²	—	2	4	no	—
391	C₃×C₄²	—	2	2	no	—
392	C₃×C₄²	—	2	4	no	—
393	C₃×C₄²	—	2	2	no	—
394	C₃×C₄²	—	2	2	no	—
395	C₃×C₄²	—	2	2	no	—
396	C₃×C₄²	—	2	2	no	—
397	C₃×C₄²	—	4	1	no	—
398	C₃×C₄²	—	4	2	no	—
399	C₃×C₄²	—	4	2	no	—
400	C₃×C₄²	—	4	2	no	—
401	C₂²×Q₈	C₂³×C₃	1	1	yes	characteristic
402	C₂²×Q₈	C₂³×C₃	1	1	yes	characteristic
403	C₂²×Q₈	C₂³×C₃	1	1	yes	characteristic
404	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
405	C₂³×C₄	C₂³×C₃	1	2	yes	—
406	C₄⋊Q₈	—	2	4	no	—
407	#126	—	4	4	no	—
408	#126	—	4	4	no	—
409	#125	—	4	2	no	—
410	#125	—	4	4	no	—
411	#124	—	4	2	no	—
412	C₂²⋊Q₈	—	2	8	no	—
413	C₄×Q₈	—	4	2	no	—
414	C₄×Q₈	—	4	2	no	—
415	#117	—	4	4	no	—
416	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
417	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
418	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
419	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
420	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
421	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
422	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
423	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
424	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
425	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
426	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
427	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
428	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
429	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
430	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
431	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
432	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
433	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
434	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
435	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
436	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
437	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
438	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
439	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
440	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
441	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
442	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
443	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
444	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
445	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
446	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
447	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
448	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
449	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
450	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
451	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
452	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
453	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
454	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
455	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
456	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
457	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
458	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
459	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
460	C₂×C₄²	C₂³×C₃	1	2	yes	—
461	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
462	C₂×C₄²	C₂³×C₃	1	2	yes	—
463	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
464	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
465	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
466	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
467	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
468	C₂×C₄²	C₂³×C₃	1	2	yes	—
469	C₂×C₄²	C₂³×C₃	1	2	yes	—
470	C₂×C₄²	C₂³×C₃	1	2	yes	—
471	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
472	#95	C₂³×C₃	1	2	yes	—
473	#95	C₂³×C₃	1	2	yes	—
474	#95	C₂³×C₃	1	2	yes	—
475	#95	C₂³×C₃	1	2	yes	—
476	#95	C₂³×C₃	1	2	yes	—
477	#95	C₂³×C₃	1	2	yes	—
478	#95	C₂³×C₃	1	2	yes	—
479	#95	C₂³×C₃	1	2	yes	—
480	#95	C₂³×C₃	1	2	yes	—
481	#95	C₂³×C₃	1	2	yes	—
482	#95	C₂³×C₃	1	2	yes	—
483	#95	C₂³×C₃	1	2	yes	—
484	#95	C₂³×C₃	1	2	yes	—
485	#95	C₂³×C₃	1	2	yes	—
486	#95	C₂³×C₃	1	2	yes	—
487	#95	C₂³×C₃	1	2	yes	—
488	#95	C₂³×C₃	1	2	yes	—
489	#95	C₂³×C₃	1	2	yes	—
490	#95	C₂³×C₃	1	2	yes	—
491	#95	C₂³×C₃	1	2	yes	—
492	#95	C₂³×C₃	1	2	yes	—
493	#95	C₂³×C₃	1	2	yes	—
494	#95	C₂³×C₃	1	2	yes	—
495	#95	C₂³×C₃	1	2	yes	—
496	#95	C₂³×C₃	1	2	yes	—
497	#95	C₂³×C₃	1	2	yes	—
498	C₂³×C₃	—	2	2	no	—
499	C₂³×C₃	—	2	2	no	—
500	C₂³×C₃	—	2	2	no	—
501	C₂³×C₃	—	2	2	no	—
502	C₂³×C₃	—	2	2	no	—
503	C₂³×C₃	—	2	2	no	—
504	C₂³×C₃	—	2	2	no	—
505	C₂³×C₃	C₂⁵	1	1	yes	characteristic
506	C₃×Q₈	—	4	4	no	—
507	C₃×Q₈	—	4	4	no	—
508	C₃×Q₈	—	8	2	no	—
509	C₃×D₄	—	8	2	no	—
510	C₂×C₃×C₄	—	2	1	no	—
511	C₂×C₃×C₄	—	2	1	no	—
512	C₂×C₃×C₄	—	2	2	no	—
513	C₂×C₃×C₄	—	2	1	no	—
514	C₂×C₃×C₄	—	2	1	no	—
515	C₂×C₃×C₄	—	2	1	no	—
516	C₂×C₃×C₄	—	2	1	no	—
517	C₂×C₃×C₄	—	2	1	no	—
518	C₂×C₃×C₄	—	2	1	no	—
519	C₂×C₃×C₄	—	2	1	no	—
520	C₂×C₃×C₄	—	2	1	no	—
521	C₂×C₃×C₄	—	2	1	no	—
522	C₂×C₃×C₄	—	2	1	no	—
523	C₂×C₃×C₄	—	2	2	no	—
524	C₂×C₃×C₄	—	2	2	no	—
525	C₂×C₃×C₄	—	2	2	no	—
526	C₂×C₃×C₄	—	2	2	no	—
527	C₂×C₃×C₄	—	2	2	no	—
528	C₂×C₃×C₄	—	2	1	no	—
529	C₂×C₃×C₄	—	2	2	no	—
530	C₂×C₃×C₄	—	2	2	no	—
531	C₂×C₃×C₄	—	2	2	no	—
532	C₂×C₃×C₄	—	2	1	no	—
533	C₂×C₃×C₄	—	2	2	no	—
534	C₂×C₃×C₄	—	2	2	no	—
535	C₂×C₃×C₄	—	2	2	no	—
536	C₂×C₃×C₄	—	2	2	no	—
537	C₂×C₃×C₄	—	2	2	no	—
538	C₂×C₃×C₄	—	2	2	no	—
539	C₂×C₃×C₄	—	2	2	no	—
540	C₂×C₃×C₄	—	2	2	no	—
541	C₂×C₃×C₄	—	2	2	no	—
542	C₂×C₃×C₄	—	2	2	no	—
543	C₂×C₃×C₄	—	2	1	no	—
544	C₂×C₃×C₄	—	2	2	no	—
545	C₂×C₃×C₄	—	2	2	no	—
546	C₂×C₃×C₄	—	2	2	no	—
547	C₂×C₃×C₄	—	2	2	no	—
548	C₂×C₃×C₄	—	2	2	no	—
549	C₂×C₃×C₄	—	2	2	no	—
550	C₂×C₃×C₄	—	2	2	no	—
551	C₂×C₃×C₄	—	2	2	no	—
552	C₂×C₃×C₄	—	2	2	no	—
553	C₂×C₃×C₄	—	2	2	no	—
554	C₂×C₃×C₄	—	2	2	no	—
555	C₂×C₃×C₄	—	2	2	no	—
556	C₂×C₃×C₄	—	2	2	no	—
557	C₂×C₃×C₄	—	4	8	no	—
558	C₂×C₃×C₄	C₂×#41	1	2	yes	—
559	C₂×C₃×C₄	C₂×#41	1	4	yes	—
560	C₂×C₃×C₄	H(5,𝔽₂)	1	2	yes	—
561	C₂×C₃×C₄	H(5,𝔽₂)	1	2	yes	—
562	C₂×C₃×C₄	2₋¹⁺⁴	1	2	yes	—
563	C₂×C₃×C₄	2₋¹⁺⁴	1	2	yes	—
564	C₂×C₃×C₄	2₋¹⁺⁴	1	2	yes	—
565	C₂⁴	C₂⁴×C₃	1	2	yes	—
566	C₂×Q₈	—	2	2	no	—
567	C₂×Q₈	—	2	2	no	—
568	C₂×Q₈	—	4	1	no	—
569	C₂×Q₈	—	4	1	no	—
570	C₂×Q₈	—	4	1	no	—
571	C₂×Q₈	—	4	1	no	—
572	C₂×Q₈	—	4	1	no	—
573	C₂×Q₈	—	4	1	no	—
574	C₂×Q₈	C₃×#41	1	4	yes	—
575	C₂×D₄	—	2	2	no	—
576	C₂×D₄	—	4	1	no	—
577	C₂×D₄	—	4	1	no	—
578	C₂²×C₄	—	2	4	no	—
579	C₂²×C₄	—	4	2	no	—
580	C₂²×C₄	—	4	2	no	—
581	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
582	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
583	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
584	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
585	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
586	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
587	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
588	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
589	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
590	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
591	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
592	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
593	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
594	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
595	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
596	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
597	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
598	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
599	C₄⋊C₄	—	2	4	no	—
600	C₄⋊C₄	—	2	4	no	—
601	C₄⋊C₄	—	2	4	no	—
602	C₄⋊C₄	—	2	4	no	—
603	C₄⋊C₄	—	2	4	no	—
604	C₄⋊C₄	—	2	4	no	—
605	C₄⋊C₄	—	2	4	no	—
606	C₄⋊C₄	—	2	4	no	—
607	C₄⋊C₄	—	2	4	no	—
608	C₄⋊C₄	—	2	4	no	—
609	C₄⋊C₄	—	2	2	no	—
610	C₄⋊C₄	—	2	2	no	—
611	C₄⋊C₄	—	2	4	no	—
612	C₄⋊C₄	—	4	2	no	—
613	C₄⋊C₄	—	4	2	no	—
614	C₄⋊C₄	—	4	1	no	—
615	C₄⋊C₄	—	4	1	no	—
616	C₄⋊C₄	—	4	2	no	—
617	C₄⋊C₄	—	4	1	no	—
618	C₄⋊C₄	—	4	1	no	—
619	C₄⋊C₄	—	4	2	no	—
620	C₄⋊C₄	—	4	2	no	—
621	C₄⋊C₄	—	4	2	no	—
622	C₄⋊C₄	—	4	2	no	—
623	C₄⋊C₄	—	4	2	no	—
624	C₄⋊C₄	—	4	2	no	—
625	C₄⋊C₄	—	4	2	no	—
626	C₄⋊C₄	—	4	1	no	—
627	C₄⋊C₄	—	4	1	no	—
628	C₄⋊C₄	—	4	2	no	—
629	C₄⋊C₄	—	4	2	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	—	4	2	no	—
637	C₂²⋊C₄	—	4	2	no	—
638	C₂²⋊C₄	—	4	2	no	—
639	C₂²⋊C₄	—	4	2	no	—
640	C₂²⋊C₄	—	4	2	no	—
641	C₂²⋊C₄	—	4	2	no	—
642	C₂²⋊C₄	—	4	2	no	—
643	C₄²	—	2	2	no	—
644	C₄²	—	2	4	no	—
645	C₄²	—	2	2	no	—
646	C₄²	—	2	4	no	—
647	C₄²	—	2	2	no	—
648	C₄²	—	2	2	no	—
649	C₄²	—	2	2	no	—
650	C₄²	—	2	2	no	—
651	C₄²	—	4	2	no	—
652	C₄²	—	4	2	no	—
653	C₄²	—	4	2	no	—
654	C₄²	—	4	1	no	—
655	C₂²×C₃	—	4	2	no	—
656	C₂²×C₃	—	4	2	no	—
657	C₂²×C₃	—	4	2	no	—
658	C₂²×C₃	—	4	2	no	—
659	C₂²×C₃	—	4	2	no	—
660	C₂²×C₃	—	4	2	no	—
661	C₂²×C₃	—	4	2	no	—
662	C₂²×C₃	C₂²×#41	1	1	yes	characteristic
663	C₂²×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
664	C₂²×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
665	C₂²×C₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
666	C₂²×C₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
667	C₂²×C₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
668	C₂²×C₃	#585	1	1	yes	characteristic
669	C₃×C₄	—	2	4	no	—
670	C₃×C₄	—	2	2	no	—
671	C₃×C₄	—	2	2	no	—
672	C₃×C₄	—	2	2	no	—
673	C₃×C₄	—	2	2	no	—
674	C₃×C₄	—	2	2	no	—
675	C₃×C₄	—	2	2	no	—
676	C₃×C₄	—	4	2	no	—
677	C₃×C₄	—	4	2	no	—
678	C₃×C₄	—	4	2	no	—
679	C₃×C₄	—	4	2	no	—
680	C₃×C₄	—	4	2	no	—
681	C₃×C₄	—	4	1	no	—
682	C₃×C₄	—	4	2	no	—
683	C₃×C₄	—	4	2	no	—
684	C₃×C₄	—	4	2	no	—
685	C₃×C₄	—	4	2	no	—
686	C₃×C₄	—	4	2	no	—
687	C₂³	—	2	2	no	—
688	C₂³	—	2	2	no	—
689	C₂³	—	2	2	no	—
690	C₂³	—	2	2	no	—
691	C₂³	—	2	2	no	—
692	C₂³	—	2	2	no	—
693	C₂³	—	2	2	no	—
694	C₂³	C₂⁵×C₃	1	1	yes	characteristic
695	Q₈	—	4	4	no	—
696	Q₈	—	4	4	no	—
697	Q₈	—	8	2	no	—
698	D₄	—	8	2	no	—
699	C₂×C₄	—	2	1	no	—
700	C₂×C₄	—	2	1	no	—
701	C₂×C₄	—	2	2	no	—
702	C₂×C₄	—	2	1	no	—
703	C₂×C₄	—	2	1	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	1	no	—
709	C₂×C₄	—	2	1	no	—
710	C₂×C₄	—	2	1	no	—
711	C₂×C₄	—	2	1	no	—
712	C₂×C₄	—	2	2	no	—
713	C₂×C₄	—	2	2	no	—
714	C₂×C₄	—	2	2	no	—
715	C₂×C₄	—	2	2	no	—
716	C₂×C₄	—	2	2	no	—
717	C₂×C₄	—	2	1	no	—
718	C₂×C₄	—	2	2	no	—
719	C₂×C₄	—	2	2	no	—
720	C₂×C₄	—	2	2	no	—
721	C₂×C₄	—	2	1	no	—
722	C₂×C₄	—	2	2	no	—
723	C₂×C₄	—	2	2	no	—
724	C₂×C₄	—	2	2	no	—
725	C₂×C₄	—	2	2	no	—
726	C₂×C₄	—	2	2	no	—
727	C₂×C₄	—	2	2	no	—
728	C₂×C₄	—	2	2	no	—
729	C₂×C₄	—	2	2	no	—
730	C₂×C₄	—	2	2	no	—
731	C₂×C₄	—	2	2	no	—
732	C₂×C₄	—	2	1	no	—
733	C₂×C₄	—	2	2	no	—
734	C₂×C₄	—	2	2	no	—
735	C₂×C₄	—	2	2	no	—
736	C₂×C₄	—	2	2	no	—
737	C₂×C₄	—	2	2	no	—
738	C₂×C₄	—	2	2	no	—
739	C₂×C₄	—	2	2	no	—
740	C₂×C₄	—	2	2	no	—
741	C₂×C₄	—	2	2	no	—
742	C₂×C₄	—	2	2	no	—
743	C₂×C₄	—	2	2	no	—
744	C₂×C₄	—	2	2	no	—
745	C₂×C₄	—	2	2	no	—
746	C₂×C₄	—	4	8	no	—
747	C₂×C₄	C₂×C₃×#41	1	2	yes	—
748	C₂×C₄	C₂×C₃×#41	1	4	yes	—
749	C₂×C₄	C₃×H(5,𝔽₂)	1	2	yes	—
750	C₂×C₄	C₃×H(5,𝔽₂)	1	2	yes	—
751	C₂×C₄	C₃×2₋¹⁺⁴	1	2	yes	—
752	C₂×C₄	C₃×2₋¹⁺⁴	1	2	yes	—
753	C₂×C₄	C₃×2₋¹⁺⁴	1	2	yes	—
754	C₂×C₃	—	8	2	no	—
755	C₂×C₃	#3459	1	1	yes	characteristic
756	C₂×C₃	#3522	1	1	yes	characteristic
757	C₂×C₃	#3523	1	1	yes	characteristic
758	C₂×C₃	#3544	1	1	yes	characteristic
759	C₂×C₃	#3548	1	1	yes	characteristic
760	C₂×C₃	#3561	1	1	yes	characteristic
761	C₂×C₃	#3563	1	1	yes	characteristic
762	C₂²	—	4	2	no	—
763	C₂²	—	4	2	no	—
764	C₂²	—	4	2	no	—
765	C₂²	—	4	2	no	—
766	C₂²	—	4	2	no	—
767	C₂²	—	4	2	no	—
768	C₂²	—	4	2	no	—
769	C₂²	C₂²×C₃×#41	1	1	yes	characteristic
770	C₂²	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
771	C₂²	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
772	C₂²	C₂×C₃×2₋¹⁺⁴	1	1	yes	characteristic
773	C₂²	C₂×C₃×2₋¹⁺⁴	1	1	yes	characteristic
774	C₂²	C₂×C₃×2₋¹⁺⁴	1	1	yes	characteristic
775	C₂²	C₃×#585	1	1	yes	characteristic
776	C₄	—	2	4	no	—
777	C₄	—	2	2	no	—
778	C₄	—	2	2	no	—
779	C₄	—	2	2	no	—
780	C₄	—	2	2	no	—
781	C₄	—	2	2	no	—
782	C₄	—	2	2	no	—
783	C₄	—	4	2	no	—
784	C₄	—	4	2	no	—
785	C₄	—	4	2	no	—
786	C₄	—	4	2	no	—
787	C₄	—	4	2	no	—
788	C₄	—	4	1	no	—
789	C₄	—	4	2	no	—
790	C₄	—	4	2	no	—
791	C₄	—	4	2	no	—
792	C₄	—	4	2	no	—
793	C₄	—	4	2	no	—
794	C₃	#37265	1	1	yes	characteristic, direct product factor, Sylow
795	C₂	—	8	2	no	—
796	C₂	C₃×#3459	1	1	yes	characteristic
797	C₂	C₃×#3522	1	1	yes	characteristic
798	C₂	C₃×#3523	1	1	yes	characteristic
799	C₂	C₃×#3544	1	1	yes	characteristic
800	C₂	C₃×#3548	1	1	yes	characteristic
801	C₂	C₃×#3561	1	1	yes	characteristic
802	C₂	C₃×#3563	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₃	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₃
prime radical	C₂²×C₃×D₄	C₂³
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×#2864	C₂	semidirect
4. C₃×#2806	C₂	semidirect
5. C₃×#2806	C₂	semidirect
6. C₃×#2773	C₂	semidirect
7. C₃×#2768	C₂	semidirect
9. C₃×#2729	C₂	semidirect
10. C₃×#2726	C₂	semidirect
11. C₃×#2721	C₂	semidirect
13. C₃×#2637	C₂	semidirect
14. C₃×#2520	C₂	semidirect
15. C₃×#2519	C₂	semidirect
17. C₃×#2478	C₂	semidirect
18. C₃×#2323	C₂	semidirect
19. C₃×C₄×C₄⋊Q₈	C₂	semidirect
20. #37265	C₃	direct (N × H)
108. #2864	C₂×C₃	semidirect
111. #2806	C₂×C₃	semidirect
112. #2806	C₂×C₃	semidirect
113. #2773	C₂×C₃	semidirect
114. #2768	C₂×C₃	semidirect
116. #2729	C₂×C₃	semidirect
117. #2726	C₂×C₃	semidirect
118. #2721	C₂×C₃	semidirect
120. #2637	C₂×C₃	semidirect
121. #2520	C₂×C₃	semidirect
122. #2519	C₂×C₃	semidirect
124. #2478	C₂×C₃	semidirect
125. #2323	C₂×C₃	semidirect
126. C₄×C₄⋊Q₈	C₂×C₃	semidirect
794. C₃	#37265	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×#2864	2
C₃×#2861	2
C₃×#2808	2
C₃×#2806	2
C₃×#2773	2
C₃×#2768	2
C₃×#2732	2
C₃×#2729	2
C₃×#2726	2
C₃×#2721	2
C₃×#2715	2
C₃×#2637	2
C₃×#2520	2
C₃×#2519	2
C₃×#2479	2
C₃×#2478	2
C₃×#2323	2
C₃×C₄×C₄⋊Q₈	2
#37265	3

Subgroups — C3×#37265 #10655872

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#37265 #10655872