Subgroups — C₃×#41426 #10660033

Order 768.

1614 conjugacy classes of subgroups.

The subgroup lattice has 812 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#2835	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#2834	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#2745	C₂	1	2	yes	maximal, complemented
4	C₃×#2744	C₂	1	2	yes	maximal, complemented
5	C₃×#2739	C₂	1	2	yes	maximal, complemented
6	C₃×#2738	C₂	1	2	yes	maximal, complemented
7	C₃×#2652	C₂	1	2	yes	maximal, complemented
8	C₃×#2652	C₂	1	2	yes	maximal, complemented
9	C₃×#2626	C₂	1	1	yes	maximal, characteristic
10	C₃×#2523	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×#2517	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#2505	C₂	1	2	yes	maximal, complemented
13	C₃×#2493	C₂	1	2	yes	maximal, complemented
14	C₃×#2484	C₂	1	2	yes	maximal, complemented
15	C₃×#2483	C₂	1	2	yes	maximal
16	C₃×#2438	C₂	1	2	yes	maximal, complemented
17	C₂×C₃×#397	C₂	1	1	yes	maximal, characteristic
18	C₃×#2342	C₂	1	2	yes	maximal
19	C₃×#2315	C₂	1	1	yes	maximal, characteristic
20	#41426	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
21	C₂×C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
22	C₂×C₃×#117	C₂²	1	2	yes	—
23	C₂²×C₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
24	C₂²×C₃×C₂²⋊C₄	C₂²	1	2	yes	—
25	C₂²×C₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
26	C₂²×C₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
27	C₂²×C₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
28	C₃×#401	C₂²	1	2	yes	complemented
29	C₃×#400	C₂²	1	2	yes	complemented
30	C₃×#400	C₂²	1	2	yes	complemented
31	C₃×#400	C₂²	1	2	yes	complemented
32	C₃×#400	C₂²	1	2	yes	complemented
33	C₃×#400	C₂²	1	2	yes	complemented
34	C₃×#400	C₂²	1	2	yes	complemented
35	C₃×#400	C₂²	1	2	yes	complemented
36	C₃×#400	C₂²	1	2	yes	complemented
37	C₃×#400	C₂²	1	2	yes	complemented
38	C₃×#399	C₂²	1	1	yes	characteristic
39	C₃×#399	C₂²	1	1	yes	characteristic
40	C₃×#398	C₂²	1	2	yes	complemented
41	C₃×#398	C₂²	1	2	yes	complemented
42	C₃×#398	C₂²	1	2	yes	complemented
43	C₃×#398	C₂²	1	2	yes	complemented
44	C₃×#398	C₂²	1	2	yes	complemented
45	C₃×#397	C₂²	1	2	yes	—
46	C₃×#397	C₂²	1	2	yes	—
47	C₃×#397	C₂²	1	1	yes	characteristic
48	C₃×#397	C₂²	1	1	yes	characteristic
49	C₃×#397	C₂²	1	1	yes	characteristic
50	C₃×#397	C₂²	1	1	yes	characteristic
51	C₃×#397	C₂²	1	2	yes	—
52	C₃×#397	C₂²	1	2	yes	—
53	C₃×#397	C₂²	1	2	yes	—
54	C₃×#397	C₂²	1	2	yes	—
55	C₃×#396	C₂²	1	2	yes	—
56	C₃×#396	C₂²	1	2	yes	—
57	C₃×#395	C₂²	1	2	yes	complemented
58	C₃×#393	C₂²	1	1	yes	characteristic
59	C₃×#393	C₂²	1	1	yes	characteristic
60	C₃×#391	C₂²	1	2	yes	complemented
61	C₃×#389	C₂²	1	2	yes	complemented
62	C₃×#389	C₂²	1	2	yes	complemented
63	C₃×#388	C₂²	1	2	yes	—
64	C₃×#388	C₂²	1	2	yes	—
65	C₃×#388	C₂²	1	2	yes	—
66	C₃×#388	C₂²	1	2	yes	—
67	C₃×#387	C₂²	1	2	yes	complemented
68	C₃×#387	C₂²	1	2	yes	complemented
69	C₃×#387	C₂²	1	2	yes	complemented
70	C₃×#387	C₂²	1	2	yes	complemented
71	C₃×#387	C₂²	1	2	yes	complemented
72	C₃×#387	C₂²	1	2	yes	complemented
73	C₃×#387	C₂²	1	2	yes	complemented
74	C₃×#387	C₂²	1	2	yes	complemented
75	C₃×#387	C₂²	1	2	yes	complemented
76	C₃×#387	C₂²	1	2	yes	complemented
77	C₃×#387	C₂²	1	2	yes	complemented
78	C₃×#385	C₂²	1	2	yes	—
79	C₃×#385	C₂²	1	1	yes	characteristic
80	C₃×#385	C₂²	1	1	yes	characteristic
81	C₃×#385	C₂²	1	2	yes	—
82	C₃×#385	C₂²	1	2	yes	—
83	C₃×#385	C₂²	1	2	yes	—
84	C₃×#385	C₂²	1	2	yes	—
85	C₃×#385	C₂²	1	2	yes	—
86	C₃×#385	C₂²	1	2	yes	—
87	C₃×#385	C₂²	1	2	yes	—
88	C₃×#385	C₂²	1	2	yes	—
89	C₃×#385	C₂²	1	1	yes	characteristic
90	C₃×#385	C₂²	1	1	yes	characteristic
91	C₃×#383	C₂²	1	2	yes	complemented
92	C₃×#382	C₂²	1	2	yes	complemented
93	C₃×#381	C₂²	1	2	yes	—
94	C₃×#381	C₂²	1	2	yes	—
95	C₃×#381	C₂²	1	2	yes	—
96	C₃×#381	C₂²	1	2	yes	—
97	C₃×#381	C₂²	1	2	yes	—
98	C₃×#380	C₂²	1	1	yes	characteristic
99	C₃×#380	C₂²	1	2	yes	—
100	C₃×#380	C₂²	1	2	yes	—
101	C₃×#380	C₂²	1	2	yes	—
102	C₃×#379	C₂²	1	2	yes	—
103	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	—
104	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	—
105	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	—
106	C₂×C₃×#95	C₂²	1	2	yes	—
107	C₂×C₃×#95	C₂²	1	1	yes	characteristic
108	#2835	C₂×C₃	1	1	yes	characteristic, complemented
109	#2834	C₂×C₃	1	1	yes	characteristic, complemented
110	#2745	C₂×C₃	1	2	yes	complemented
111	#2744	C₂×C₃	1	2	yes	complemented
112	#2739	C₂×C₃	1	2	yes	complemented
113	#2738	C₂×C₃	1	2	yes	complemented
114	#2652	C₂×C₃	1	2	yes	complemented
115	#2652	C₂×C₃	1	2	yes	complemented
116	#2626	C₂×C₃	1	1	yes	characteristic
117	#2523	C₂×C₃	1	1	yes	characteristic, complemented
118	#2517	C₂×C₃	1	1	yes	characteristic, complemented
119	#2505	C₂×C₃	1	2	yes	complemented
120	#2493	C₂×C₃	1	2	yes	complemented
121	#2484	C₂×C₃	1	2	yes	complemented
122	#2483	C₂×C₃	1	2	yes	—
123	#2438	C₂×C₃	1	2	yes	complemented
124	C₂×#397	C₂×C₃	1	1	yes	characteristic
125	#2342	C₂×C₃	1	2	yes	—
126	#2315	C₂×C₃	1	1	yes	characteristic
127	C₂⁵×C₃	C₂³	1	1	yes	characteristic
128	C₂²×C₃×Q₈	C₂³	1	1	yes	characteristic
129	C₂³×C₃×C₄	C₂³	1	2	yes	—
130	C₂³×C₃×C₄	C₂³	1	2	yes	—
131	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
132	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
133	C₂³×C₃×C₄	C₂³	1	2	yes	—
134	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
135	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
136	C₃×C₂²⋊Q₈	—	4	2	no	—
137	C₃×#117	—	4	4	no	—
138	C₂×C₃×C₄⋊C₄	—	4	2	no	—
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	2	yes	—
148	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
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	1	yes	characteristic
155	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
156	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
157	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
158	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
159	C₂×C₃×C₂²⋊C₄	—	2	8	no	—
160	C₂×C₃×C₂²⋊C₄	—	2	4	no	—
161	C₂×C₃×C₂²⋊C₄	—	4	2	no	—
162	C₂×C₃×C₂²⋊C₄	—	4	2	no	—
163	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
164	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
165	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
166	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
167	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
168	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
169	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
170	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
171	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
172	C₂×C₃×C₂²⋊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	1	yes	characteristic
179	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
180	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
181	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
182	C₂×C₃×C₄²	C₂³	1	2	yes	—
183	C₂×C₃×C₄²	C₂³	1	2	yes	—
184	C₂×C₃×C₄²	C₂³	1	2	yes	—
185	C₂×C₃×C₄²	C₂³	1	2	yes	—
186	C₃×#95	C₂³	1	1	yes	characteristic
187	C₃×#95	C₂³	1	2	yes	—
188	C₃×#95	C₂³	1	2	yes	—
189	C₃×#95	C₂³	1	2	yes	—
190	C₃×#95	C₂³	1	2	yes	—
191	C₃×#95	C₂³	1	2	yes	—
192	C₃×#95	C₂³	1	1	yes	characteristic
193	C₃×#95	C₂³	1	2	yes	—
194	C₃×#95	C₂³	1	2	yes	—
195	C₃×#95	C₂³	1	2	yes	—
196	C₃×#95	C₂³	1	2	yes	—
197	C₃×#95	C₂³	1	2	yes	—
198	C₃×#95	C₂³	1	2	yes	—
199	C₃×#95	C₂³	1	2	yes	—
200	C₃×#95	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
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	C₂×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
222	C₂×#117	C₂²×C₃	1	2	yes	—
223	C₂²×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
224	C₂²×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
225	C₂²×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
226	C₂²×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
227	C₂²×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
228	#401	C₂²×C₃	1	2	yes	complemented
229	#400	C₂²×C₃	1	2	yes	complemented
230	#400	C₂²×C₃	1	2	yes	complemented
231	#400	C₂²×C₃	1	2	yes	complemented
232	#400	C₂²×C₃	1	2	yes	complemented
233	#400	C₂²×C₃	1	2	yes	complemented
234	#400	C₂²×C₃	1	2	yes	complemented
235	#400	C₂²×C₃	1	2	yes	complemented
236	#400	C₂²×C₃	1	2	yes	complemented
237	#400	C₂²×C₃	1	2	yes	complemented
238	#399	C₂²×C₃	1	1	yes	characteristic
239	#399	C₂²×C₃	1	1	yes	characteristic
240	#398	C₂²×C₃	1	2	yes	complemented
241	#398	C₂²×C₃	1	2	yes	complemented
242	#398	C₂²×C₃	1	2	yes	complemented
243	#398	C₂²×C₃	1	2	yes	complemented
244	#398	C₂²×C₃	1	2	yes	complemented
245	#397	C₂²×C₃	1	1	yes	characteristic
246	#397	C₂²×C₃	1	2	yes	—
247	#397	C₂²×C₃	1	2	yes	—
248	#397	C₂²×C₃	1	2	yes	—
249	#397	C₂²×C₃	1	2	yes	—
250	#397	C₂²×C₃	1	1	yes	characteristic
251	#397	C₂²×C₃	1	1	yes	characteristic
252	#397	C₂²×C₃	1	1	yes	characteristic
253	#397	C₂²×C₃	1	2	yes	—
254	#397	C₂²×C₃	1	2	yes	—
255	#396	C₂²×C₃	1	2	yes	—
256	#396	C₂²×C₃	1	2	yes	—
257	#395	C₂²×C₃	1	2	yes	complemented
258	#393	C₂²×C₃	1	1	yes	characteristic
259	#393	C₂²×C₃	1	1	yes	characteristic
260	#391	C₂²×C₃	1	2	yes	complemented
261	#389	C₂²×C₃	1	2	yes	complemented
262	#389	C₂²×C₃	1	2	yes	complemented
263	#388	C₂²×C₃	1	2	yes	—
264	#388	C₂²×C₃	1	2	yes	—
265	#388	C₂²×C₃	1	2	yes	—
266	#388	C₂²×C₃	1	2	yes	—
267	#387	C₂²×C₃	1	2	yes	complemented
268	#387	C₂²×C₃	1	2	yes	complemented
269	#387	C₂²×C₃	1	2	yes	complemented
270	#387	C₂²×C₃	1	2	yes	complemented
271	#387	C₂²×C₃	1	2	yes	complemented
272	#387	C₂²×C₃	1	2	yes	complemented
273	#387	C₂²×C₃	1	2	yes	complemented
274	#387	C₂²×C₃	1	2	yes	complemented
275	#387	C₂²×C₃	1	2	yes	complemented
276	#387	C₂²×C₃	1	2	yes	complemented
277	#387	C₂²×C₃	1	2	yes	complemented
278	#385	C₂²×C₃	1	1	yes	characteristic
279	#385	C₂²×C₃	1	1	yes	characteristic
280	#385	C₂²×C₃	1	1	yes	characteristic
281	#385	C₂²×C₃	1	1	yes	characteristic
282	#385	C₂²×C₃	1	2	yes	—
283	#385	C₂²×C₃	1	2	yes	—
284	#385	C₂²×C₃	1	2	yes	—
285	#385	C₂²×C₃	1	2	yes	—
286	#385	C₂²×C₃	1	2	yes	—
287	#385	C₂²×C₃	1	2	yes	—
288	#385	C₂²×C₃	1	2	yes	—
289	#385	C₂²×C₃	1	2	yes	—
290	#385	C₂²×C₃	1	2	yes	—
291	#383	C₂²×C₃	1	2	yes	complemented
292	#382	C₂²×C₃	1	2	yes	complemented
293	#381	C₂²×C₃	1	2	yes	—
294	#381	C₂²×C₃	1	2	yes	—
295	#381	C₂²×C₃	1	2	yes	—
296	#381	C₂²×C₃	1	2	yes	—
297	#381	C₂²×C₃	1	2	yes	—
298	#380	C₂²×C₃	1	2	yes	—
299	#380	C₂²×C₃	1	2	yes	—
300	#380	C₂²×C₃	1	2	yes	—
301	#380	C₂²×C₃	1	1	yes	characteristic
302	#379	C₂²×C₃	1	2	yes	—
303	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
304	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
305	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
306	C₂×#95	C₂²×C₃	1	2	yes	—
307	C₂×#95	C₂²×C₃	1	1	yes	characteristic
308	C₂⁴×C₃	—	2	2	no	—
309	C₂⁴×C₃	—	2	2	no	—
310	C₂⁴×C₃	—	4	2	no	—
311	C₂⁴×C₃	—	4	2	no	—
312	C₂⁴×C₃	#41	1	4	yes	—
313	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
314	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
315	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
316	C₂×C₃×Q₈	—	4	1	no	—
317	C₂×C₃×Q₈	—	4	2	no	—
318	C₂²×C₃×C₄	—	2	4	no	—
319	C₂²×C₃×C₄	—	2	2	no	—
320	C₂²×C₃×C₄	—	2	4	no	—
321	C₂²×C₃×C₄	—	2	4	no	—
322	C₂²×C₃×C₄	—	2	4	no	—
323	C₂²×C₃×C₄	—	2	4	no	—
324	C₂²×C₃×C₄	—	2	2	no	—
325	C₂²×C₃×C₄	—	4	2	no	—
326	C₂²×C₃×C₄	—	4	1	no	—
327	C₂²×C₃×C₄	—	4	1	no	—
328	C₂²×C₃×C₄	—	4	2	no	—
329	C₂²×C₃×C₄	—	4	2	no	—
330	C₂²×C₃×C₄	—	4	2	no	—
331	C₂²×C₃×C₄	—	4	2	no	—
332	C₂²×C₃×C₄	—	4	2	no	—
333	C₂²×C₃×C₄	—	4	2	no	—
334	C₂²×C₃×C₄	—	4	2	no	—
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	2	yes	—
339	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
340	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
341	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
342	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
343	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
344	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
345	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
346	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
347	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
348	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
349	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
350	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
351	C₃×C₄⋊C₄	—	4	1	no	—
352	C₃×C₄⋊C₄	—	4	2	no	—
353	C₃×C₄⋊C₄	—	4	1	no	—
354	C₃×C₄⋊C₄	—	4	2	no	—
355	C₃×C₄⋊C₄	—	4	2	no	—
356	C₃×C₄⋊C₄	—	4	2	no	—
357	C₃×C₄⋊C₄	—	4	2	no	—
358	C₃×C₄⋊C₄	—	4	2	no	—
359	C₃×C₄⋊C₄	—	4	2	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	2	no	—
365	C₃×C₄⋊C₄	—	4	2	no	—
366	C₃×C₄⋊C₄	—	4	2	no	—
367	C₃×C₄⋊C₄	—	4	2	no	—
368	C₃×C₄⋊C₄	—	4	2	no	—
369	C₃×C₄⋊C₄	—	4	1	no	—
370	C₃×C₄⋊C₄	—	4	2	no	—
371	C₃×C₂²⋊C₄	—	2	4	no	—
372	C₃×C₂²⋊C₄	—	2	4	no	—
373	C₃×C₂²⋊C₄	—	2	2	no	—
374	C₃×C₂²⋊C₄	—	2	2	no	—
375	C₃×C₂²⋊C₄	—	2	4	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	—	4	2	no	—
382	C₃×C₂²⋊C₄	—	4	1	no	—
383	C₃×C₂²⋊C₄	—	4	1	no	—
384	C₃×C₂²⋊C₄	—	4	1	no	—
385	C₃×C₂²⋊C₄	—	4	1	no	—
386	C₃×C₂²⋊C₄	—	4	2	no	—
387	C₃×C₂²⋊C₄	—	4	2	no	—
388	C₃×C₂²⋊C₄	—	4	2	no	—
389	C₃×C₂²⋊C₄	—	4	2	no	—
390	C₃×C₄²	—	4	2	no	—
391	C₃×C₄²	—	4	2	no	—
392	C₃×C₄²	—	4	2	no	—
393	C₃×C₄²	—	4	2	no	—
394	C₂⁵	C₂³×C₃	1	1	yes	characteristic
395	C₂²×Q₈	C₂³×C₃	1	1	yes	characteristic
396	C₂³×C₄	C₂³×C₃	1	2	yes	—
397	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
398	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
399	C₂³×C₄	C₂³×C₃	1	2	yes	—
400	C₂³×C₄	C₂³×C₃	1	2	yes	—
401	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
402	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
403	C₂²⋊Q₈	—	4	2	no	—
404	#117	—	4	4	no	—
405	C₂×C₄⋊C₄	—	4	2	no	—
406	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
407	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
408	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
409	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
410	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
411	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
412	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
413	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
414	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
415	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
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×C₂²⋊C₄	—	2	8	no	—
427	C₂×C₂²⋊C₄	—	2	4	no	—
428	C₂×C₂²⋊C₄	—	4	2	no	—
429	C₂×C₂²⋊C₄	—	4	2	no	—
430	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
431	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
432	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
433	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
434	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
435	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
436	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
437	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
438	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
439	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
440	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
441	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
442	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
443	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
444	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
445	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
446	C₂×C₂²⋊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×C₄²	C₂³×C₃	1	2	yes	—
450	C₂×C₄²	C₂³×C₃	1	2	yes	—
451	C₂×C₄²	C₂³×C₃	1	2	yes	—
452	C₂×C₄²	C₂³×C₃	1	2	yes	—
453	#95	C₂³×C₃	1	1	yes	characteristic
454	#95	C₂³×C₃	1	2	yes	—
455	#95	C₂³×C₃	1	2	yes	—
456	#95	C₂³×C₃	1	2	yes	—
457	#95	C₂³×C₃	1	2	yes	—
458	#95	C₂³×C₃	1	2	yes	—
459	#95	C₂³×C₃	1	1	yes	characteristic
460	#95	C₂³×C₃	1	2	yes	—
461	#95	C₂³×C₃	1	2	yes	—
462	#95	C₂³×C₃	1	2	yes	—
463	#95	C₂³×C₃	1	2	yes	—
464	#95	C₂³×C₃	1	2	yes	—
465	#95	C₂³×C₃	1	2	yes	—
466	#95	C₂³×C₃	1	2	yes	—
467	#95	C₂³×C₃	1	1	yes	characteristic
468	#95	C₂³×C₃	1	2	yes	—
469	#95	C₂³×C₃	1	2	yes	—
470	#95	C₂³×C₃	1	2	yes	—
471	#95	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	C₂³×C₃	—	2	2	no	—
489	C₂³×C₃	—	2	2	no	—
490	C₂³×C₃	—	2	1	no	—
491	C₂³×C₃	—	2	1	no	—
492	C₂³×C₃	—	2	1	no	—
493	C₂³×C₃	—	2	1	no	—
494	C₂³×C₃	—	2	2	no	—
495	C₂³×C₃	—	2	2	no	—
496	C₂³×C₃	—	2	2	no	—
497	C₂³×C₃	—	2	2	no	—
498	C₂³×C₃	—	2	8	no	—
499	C₂³×C₃	—	4	8	no	—
500	C₂³×C₃	—	8	2	no	—
501	C₂³×C₃	—	8	2	no	—
502	C₂³×C₃	—	8	4	no	—
503	C₂³×C₃	C₂×#41	1	2	yes	—
504	C₂³×C₃	C₂×#41	1	2	yes	—
505	C₂³×C₃	C₂×#41	1	2	yes	—
506	C₂³×C₃	H(5,𝔽₂)	1	2	yes	—
507	C₂³×C₃	2₋¹⁺⁴	1	2	yes	—
508	C₂³×C₃	C₂⁵	1	1	yes	characteristic
509	C₃×Q₈	—	8	2	no	—
510	C₂×C₃×C₄	—	2	2	no	—
511	C₂×C₃×C₄	—	2	2	no	—
512	C₂×C₃×C₄	—	2	2	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	2	no	—
518	C₂×C₃×C₄	—	2	2	no	—
519	C₂×C₃×C₄	—	2	2	no	—
520	C₂×C₃×C₄	—	2	2	no	—
521	C₂×C₃×C₄	—	2	1	no	—
522	C₂×C₃×C₄	—	2	1	no	—
523	C₂×C₃×C₄	—	2	1	no	—
524	C₂×C₃×C₄	—	2	1	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	2	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	2	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	2	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	—	4	4	no	—
555	C₂×C₃×C₄	—	4	8	no	—
556	C₂×C₃×C₄	—	8	4	no	—
557	C₂×C₃×C₄	—	8	4	no	—
558	C₂×C₃×C₄	—	8	2	no	—
559	C₂×C₃×C₄	—	8	2	no	—
560	C₂×C₃×C₄	—	8	2	no	—
561	C₂⁴	—	2	2	no	—
562	C₂⁴	—	2	2	no	—
563	C₂⁴	—	4	2	no	—
564	C₂⁴	—	4	2	no	—
565	C₂⁴	C₃×#41	1	4	yes	—
566	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
567	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
568	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
569	C₂×Q₈	—	4	1	no	—
570	C₂×Q₈	—	4	2	no	—
571	C₂²×C₄	—	2	4	no	—
572	C₂²×C₄	—	2	2	no	—
573	C₂²×C₄	—	2	4	no	—
574	C₂²×C₄	—	2	4	no	—
575	C₂²×C₄	—	2	4	no	—
576	C₂²×C₄	—	2	4	no	—
577	C₂²×C₄	—	2	2	no	—
578	C₂²×C₄	—	4	2	no	—
579	C₂²×C₄	—	4	1	no	—
580	C₂²×C₄	—	4	1	no	—
581	C₂²×C₄	—	4	2	no	—
582	C₂²×C₄	—	4	2	no	—
583	C₂²×C₄	—	4	2	no	—
584	C₂²×C₄	—	4	2	no	—
585	C₂²×C₄	—	4	2	no	—
586	C₂²×C₄	—	4	2	no	—
587	C₂²×C₄	—	4	2	no	—
588	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
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	2	yes	—
593	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
594	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
595	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
596	C₂²×C₄	C₂⁴×C₃	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	2	yes	—
600	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
601	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
602	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
603	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
604	C₄⋊C₄	—	4	1	no	—
605	C₄⋊C₄	—	4	2	no	—
606	C₄⋊C₄	—	4	1	no	—
607	C₄⋊C₄	—	4	2	no	—
608	C₄⋊C₄	—	4	2	no	—
609	C₄⋊C₄	—	4	1	no	—
610	C₄⋊C₄	—	4	2	no	—
611	C₄⋊C₄	—	4	2	no	—
612	C₄⋊C₄	—	4	2	no	—
613	C₄⋊C₄	—	4	2	no	—
614	C₄⋊C₄	—	4	2	no	—
615	C₄⋊C₄	—	4	2	no	—
616	C₄⋊C₄	—	4	2	no	—
617	C₄⋊C₄	—	4	2	no	—
618	C₄⋊C₄	—	4	2	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	C₂²⋊C₄	—	2	4	no	—
625	C₂²⋊C₄	—	2	4	no	—
626	C₂²⋊C₄	—	2	2	no	—
627	C₂²⋊C₄	—	2	2	no	—
628	C₂²⋊C₄	—	2	4	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	—	4	2	no	—
635	C₂²⋊C₄	—	4	1	no	—
636	C₂²⋊C₄	—	4	1	no	—
637	C₂²⋊C₄	—	4	1	no	—
638	C₂²⋊C₄	—	4	1	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	—	4	2	no	—
644	C₄²	—	4	2	no	—
645	C₄²	—	4	2	no	—
646	C₄²	—	4	2	no	—
647	C₂²×C₃	—	2	4	no	—
648	C₂²×C₃	—	2	2	no	—
649	C₂²×C₃	—	2	2	no	—
650	C₂²×C₃	—	2	4	no	—
651	C₂²×C₃	—	2	2	no	—
652	C₂²×C₃	—	2	2	no	—
653	C₂²×C₃	—	2	4	no	—
654	C₂²×C₃	—	2	4	no	—
655	C₂²×C₃	—	4	1	no	—
656	C₂²×C₃	—	4	1	no	—
657	C₂²×C₃	—	4	1	no	—
658	C₂²×C₃	—	4	1	no	—
659	C₂²×C₃	—	4	2	no	—
660	C₂²×C₃	—	4	2	no	—
661	C₂²×C₃	—	8	8	no	—
662	C₂²×C₃	#539	1	4	yes	—
663	C₂²×C₃	C₂²×#41	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	#585	1	2	yes	—
667	C₂²×C₃	#585	1	2	yes	—
668	C₃×C₄	—	4	2	no	—
669	C₃×C₄	—	4	2	no	—
670	C₃×C₄	—	4	2	no	—
671	C₃×C₄	—	4	2	no	—
672	C₃×C₄	—	4	2	no	—
673	C₃×C₄	—	4	2	no	—
674	C₃×C₄	—	4	2	no	—
675	C₃×C₄	—	4	1	no	—
676	C₃×C₄	—	4	1	no	—
677	C₃×C₄	—	4	2	no	—
678	C₃×C₄	—	4	2	no	—
679	C₃×C₄	—	4	1	no	—
680	C₃×C₄	—	4	1	no	—
681	C₃×C₄	—	4	2	no	—
682	C₃×C₄	—	4	2	no	—
683	C₃×C₄	—	4	2	no	—
684	C₂³	—	2	2	no	—
685	C₂³	—	2	2	no	—
686	C₂³	—	2	1	no	—
687	C₂³	—	2	1	no	—
688	C₂³	—	2	1	no	—
689	C₂³	—	2	1	no	—
690	C₂³	—	2	2	no	—
691	C₂³	—	2	2	no	—
692	C₂³	—	2	2	no	—
693	C₂³	—	2	2	no	—
694	C₂³	—	2	8	no	—
695	C₂³	—	4	8	no	—
696	C₂³	—	8	2	no	—
697	C₂³	—	8	2	no	—
698	C₂³	—	8	4	no	—
699	C₂³	C₂×C₃×#41	1	2	yes	—
700	C₂³	C₂×C₃×#41	1	2	yes	—
701	C₂³	C₂×C₃×#41	1	2	yes	—
702	C₂³	C₃×H(5,𝔽₂)	1	2	yes	—
703	C₂³	C₃×2₋¹⁺⁴	1	2	yes	—
704	C₂³	C₂⁵×C₃	1	1	yes	characteristic
705	Q₈	—	8	2	no	—
706	C₂×C₄	—	2	2	no	—
707	C₂×C₄	—	2	2	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	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	1	no	—
719	C₂×C₄	—	2	1	no	—
720	C₂×C₄	—	2	1	no	—
721	C₂×C₄	—	2	2	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	2	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	—	2	2	no	—
747	C₂×C₄	—	2	2	no	—
748	C₂×C₄	—	2	2	no	—
749	C₂×C₄	—	2	2	no	—
750	C₂×C₄	—	4	4	no	—
751	C₂×C₄	—	4	8	no	—
752	C₂×C₄	—	8	4	no	—
753	C₂×C₄	—	8	4	no	—
754	C₂×C₄	—	8	2	no	—
755	C₂×C₄	—	8	2	no	—
756	C₂×C₄	—	8	2	no	—
757	C₂×C₃	—	2	4	no	—
758	C₂×C₃	—	4	2	no	—
759	C₂×C₃	—	4	2	no	—
760	C₂×C₃	C₂×#539	1	1	yes	characteristic
761	C₂×C₃	#3491	1	2	yes	—
762	C₂×C₃	#3533	1	1	yes	characteristic
763	C₂×C₃	#3545	1	1	yes	characteristic
764	C₂×C₃	#3564	1	2	yes	—
765	C₂²	—	2	4	no	—
766	C₂²	—	2	2	no	—
767	C₂²	—	2	2	no	—
768	C₂²	—	2	4	no	—
769	C₂²	—	2	2	no	—
770	C₂²	—	2	2	no	—
771	C₂²	—	2	4	no	—
772	C₂²	—	2	4	no	—
773	C₂²	—	4	1	no	—
774	C₂²	—	4	1	no	—
775	C₂²	—	4	1	no	—
776	C₂²	—	4	1	no	—
777	C₂²	—	4	2	no	—
778	C₂²	—	4	2	no	—
779	C₂²	—	8	8	no	—
780	C₂²	C₃×#539	1	4	yes	—
781	C₂²	C₂²×C₃×#41	1	1	yes	characteristic
782	C₂²	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
783	C₂²	C₂×C₃×2₋¹⁺⁴	1	1	yes	characteristic
784	C₂²	C₃×#585	1	2	yes	—
785	C₂²	C₃×#585	1	2	yes	—
786	C₄	—	4	2	no	—
787	C₄	—	4	2	no	—
788	C₄	—	4	2	no	—
789	C₄	—	4	2	no	—
790	C₄	—	4	2	no	—
791	C₄	—	4	2	no	—
792	C₄	—	4	1	no	—
793	C₄	—	4	1	no	—
794	C₄	—	4	2	no	—
795	C₄	—	4	2	no	—
796	C₄	—	4	1	no	—
797	C₄	—	4	2	no	—
798	C₄	—	4	1	no	—
799	C₄	—	4	2	no	—
800	C₄	—	4	2	no	—
801	C₄	—	4	2	no	—
802	C₃	#41426	1	1	yes	characteristic, direct product factor, Sylow
803	C₂	—	2	4	no	—
804	C₂	—	4	2	no	—
805	C₂	—	4	2	no	—
806	C₂	C₂×C₃×#539	1	1	yes	characteristic
807	C₂	C₃×#3491	1	2	yes	—
808	C₂	C₃×#3533	1	1	yes	characteristic
809	C₂	C₃×#3545	1	1	yes	characteristic
810	C₂	C₃×#3564	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₃	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₃
prime radical	C₂⁵×C₃	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×#2835	C₂	semidirect
2. C₃×#2834	C₂	semidirect
3. C₃×#2745	C₂	semidirect
4. C₃×#2744	C₂	semidirect
5. C₃×#2739	C₂	semidirect
6. C₃×#2738	C₂	semidirect
7. C₃×#2652	C₂	semidirect
8. C₃×#2652	C₂	semidirect
10. C₃×#2523	C₂	semidirect
11. C₃×#2517	C₂	semidirect
12. C₃×#2505	C₂	semidirect
13. C₃×#2493	C₂	semidirect
14. C₃×#2484	C₂	semidirect
16. C₃×#2438	C₂	semidirect
20. #41426	C₃	direct (N × H)
28. C₃×#401	C₂²	semidirect
29. C₃×#400	C₂²	semidirect
30. C₃×#400	C₂²	semidirect
31. C₃×#400	C₂²	semidirect
32. C₃×#400	C₂²	semidirect
33. C₃×#400	C₂²	semidirect
34. C₃×#400	C₂²	semidirect
35. C₃×#400	C₂²	semidirect
36. C₃×#400	C₂²	semidirect
37. C₃×#400	C₂²	semidirect
40. C₃×#398	C₂²	semidirect
41. C₃×#398	C₂²	semidirect
42. C₃×#398	C₂²	semidirect
43. C₃×#398	C₂²	semidirect
44. C₃×#398	C₂²	semidirect
57. C₃×#395	C₂²	semidirect
60. C₃×#391	C₂²	semidirect
61. C₃×#389	C₂²	semidirect
62. C₃×#389	C₂²	semidirect
67. C₃×#387	C₂²	semidirect
68. C₃×#387	C₂²	semidirect
69. C₃×#387	C₂²	semidirect
70. C₃×#387	C₂²	semidirect
71. C₃×#387	C₂²	semidirect
72. C₃×#387	C₂²	semidirect
73. C₃×#387	C₂²	semidirect
74. C₃×#387	C₂²	semidirect
75. C₃×#387	C₂²	semidirect
76. C₃×#387	C₂²	semidirect
77. C₃×#387	C₂²	semidirect
91. C₃×#383	C₂²	semidirect
92. C₃×#382	C₂²	semidirect
108. #2835	C₂×C₃	semidirect
109. #2834	C₂×C₃	semidirect
110. #2745	C₂×C₃	semidirect
111. #2744	C₂×C₃	semidirect
112. #2739	C₂×C₃	semidirect
113. #2738	C₂×C₃	semidirect
114. #2652	C₂×C₃	semidirect
115. #2652	C₂×C₃	semidirect
117. #2523	C₂×C₃	semidirect
118. #2517	C₂×C₃	semidirect
119. #2505	C₂×C₃	semidirect
120. #2493	C₂×C₃	semidirect
121. #2484	C₂×C₃	semidirect
123. #2438	C₂×C₃	semidirect
228. #401	C₂²×C₃	semidirect
229. #400	C₂²×C₃	semidirect
230. #400	C₂²×C₃	semidirect
231. #400	C₂²×C₃	semidirect
232. #400	C₂²×C₃	semidirect
233. #400	C₂²×C₃	semidirect
234. #400	C₂²×C₃	semidirect
235. #400	C₂²×C₃	semidirect
236. #400	C₂²×C₃	semidirect
237. #400	C₂²×C₃	semidirect
240. #398	C₂²×C₃	semidirect
241. #398	C₂²×C₃	semidirect
242. #398	C₂²×C₃	semidirect
243. #398	C₂²×C₃	semidirect
244. #398	C₂²×C₃	semidirect
257. #395	C₂²×C₃	semidirect
260. #391	C₂²×C₃	semidirect
261. #389	C₂²×C₃	semidirect
262. #389	C₂²×C₃	semidirect
267. #387	C₂²×C₃	semidirect
268. #387	C₂²×C₃	semidirect
269. #387	C₂²×C₃	semidirect
270. #387	C₂²×C₃	semidirect
271. #387	C₂²×C₃	semidirect
272. #387	C₂²×C₃	semidirect
273. #387	C₂²×C₃	semidirect
274. #387	C₂²×C₃	semidirect
275. #387	C₂²×C₃	semidirect
276. #387	C₂²×C₃	semidirect
277. #387	C₂²×C₃	semidirect
291. #383	C₂²×C₃	semidirect
292. #382	C₂²×C₃	semidirect
802. C₃	#41426	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×#2835	2
C₃×#2834	2
C₃×#2745	2
C₃×#2744	2
C₃×#2739	2
C₃×#2738	2
C₃×#2652	2
C₃×#2626	2
C₃×#2523	2
C₃×#2517	2
C₃×#2505	2
C₃×#2493	2
C₃×#2484	2
C₃×#2483	2
C₃×#2438	2
C₂×C₃×#397	2
C₃×#2342	2
C₃×#2315	2
#41426	3

Subgroups — C3×#41426 #10660033

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#41426 #10660033