Subgroups — C₃×#36167 #10654774

Order 768.

2028 conjugacy classes of subgroups.

The subgroup lattice has 1040 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#2855	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#2851	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#2848	C₂	1	1	yes	maximal, characteristic
4	C₃×#2577	C₂	1	2	yes	maximal, complemented
5	C₃×#2530	C₂	1	2	yes	maximal, complemented
6	C₃×#2505	C₂	1	2	yes	maximal, complemented
7	C₃×#2503	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#2495	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×#2494	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#2493	C₂	1	2	yes	maximal, complemented
11	C₃×#2493	C₂	1	2	yes	maximal, complemented
12	C₃×#2489	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃×#2483	C₂	1	2	yes	maximal
14	C₃×#2442	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃×#2421	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃×#2360	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃×#2344	C₂	1	1	yes	maximal, characteristic, complemented
18	C₃×#2343	C₂	1	2	yes	maximal, complemented
19	C₃×#2342	C₂	1	2	yes	maximal
20	C₃×C₄×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
21	C₃×#2283	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×C₃×#380	C₂	1	1	yes	maximal, characteristic
23	C₂×C₃×C₄×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic
24	#36167	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
25	C₂⁴×C₃×C₄	C₂²	1	1	yes	characteristic
26	C₂×C₃×#125	C₂²	1	1	yes	characteristic, complemented
27	C₂×C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
28	C₂×C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
29	C₂×C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
30	C₂×C₃×C₄×Q₈	C₂²	1	1	yes	characteristic, complemented
31	C₂×C₃×#117	C₂²	1	2	yes	—
32	C₂²×C₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
33	C₂²×C₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
34	C₂²×C₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
35	C₂²×C₃×C₂²⋊C₄	C₂²	1	2	yes	—
36	C₂²×C₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
37	C₂²×C₃×C₄²	C₂²	1	1	yes	characteristic
38	C₂²×C₃×C₄²	C₂²	1	1	yes	characteristic
39	C₃×#401	C₂²	1	2	yes	complemented
40	C₃×#400	C₂²	1	2	yes	complemented
41	C₃×#400	C₂²	1	2	yes	complemented
42	C₃×#400	C₂²	1	2	yes	complemented
43	C₃×#400	C₂²	1	2	yes	complemented
44	C₃×#400	C₂²	1	2	yes	complemented
45	C₃×#400	C₂²	1	2	yes	complemented
46	C₃×#398	C₂²	1	2	yes	complemented
47	C₃×#397	C₂²	1	2	yes	—
48	C₃×#397	C₂²	1	2	yes	—
49	C₃×#397	C₂²	1	2	yes	—
50	C₃×#397	C₂²	1	2	yes	—
51	C₃×#391	C₂²	1	1	yes	characteristic, complemented
52	C₃×#391	C₂²	1	1	yes	characteristic, complemented
53	C₃×#391	C₂²	1	1	yes	characteristic, complemented
54	C₃×#389	C₂²	1	1	yes	characteristic, complemented
55	C₃×#389	C₂²	1	2	yes	complemented
56	C₃×#389	C₂²	1	1	yes	characteristic, complemented
57	C₃×#389	C₂²	1	1	yes	characteristic, complemented
58	C₃×#389	C₂²	1	1	yes	characteristic, complemented
59	C₃×#389	C₂²	1	1	yes	characteristic, complemented
60	C₃×#388	C₂²	1	2	yes	—
61	C₃×#388	C₂²	1	2	yes	—
62	C₃×#388	C₂²	1	2	yes	—
63	C₃×#388	C₂²	1	2	yes	—
64	C₃×#387	C₂²	1	2	yes	complemented
65	C₃×#387	C₂²	1	2	yes	complemented
66	C₃×#387	C₂²	1	2	yes	complemented
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×#385	C₂²	1	2	yes	—
75	C₃×#385	C₂²	1	2	yes	—
76	C₃×#385	C₂²	1	2	yes	—
77	C₃×#385	C₂²	1	2	yes	—
78	C₃×#385	C₂²	1	2	yes	—
79	C₃×#385	C₂²	1	2	yes	—
80	C₃×#385	C₂²	1	2	yes	—
81	C₃×#385	C₂²	1	2	yes	—
82	C₃×#385	C₂²	1	2	yes	—
83	C₃×#383	C₂²	1	2	yes	complemented
84	C₃×#383	C₂²	1	2	yes	complemented
85	C₃×#382	C₂²	1	1	yes	characteristic, complemented
86	C₃×#382	C₂²	1	2	yes	complemented
87	C₃×#382	C₂²	1	1	yes	characteristic, complemented
88	C₃×#382	C₂²	1	1	yes	characteristic, complemented
89	C₃×#381	C₂²	1	2	yes	—
90	C₃×#381	C₂²	1	2	yes	—
91	C₃×#381	C₂²	1	2	yes	—
92	C₃×#381	C₂²	1	2	yes	—
93	C₃×#381	C₂²	1	2	yes	—
94	C₃×#380	C₂²	1	1	yes	characteristic
95	C₃×#380	C₂²	1	2	yes	—
96	C₃×#380	C₂²	1	1	yes	characteristic
97	C₃×#380	C₂²	1	1	yes	characteristic
98	C₃×#380	C₂²	1	2	yes	—
99	C₃×#380	C₂²	1	1	yes	characteristic
100	C₃×#380	C₂²	1	2	yes	—
101	C₃×#380	C₂²	1	1	yes	characteristic
102	C₃×#380	C₂²	1	1	yes	characteristic
103	C₃×#380	C₂²	1	1	yes	characteristic
104	C₃×#379	C₂²	1	2	yes	—
105	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
106	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
107	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
108	C₃×C₄×C₄⋊C₄	C₂²	1	2	yes	complemented
109	C₃×C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
110	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	—
111	C₃×C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
112	C₃×C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
113	C₃×C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
114	C₃×C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
115	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	—
116	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	—
117	C₃×C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
118	C₃×C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
119	C₃×C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
120	C₃×#376	C₂²	1	2	yes	complemented
121	C₂×C₃×#95	C₂²	1	1	yes	characteristic
122	C₂×C₃×#95	C₂²	1	2	yes	—
123	C₂×C₃×#95	C₂²	1	1	yes	characteristic
124	#2855	C₂×C₃	1	1	yes	characteristic, complemented
125	#2851	C₂×C₃	1	1	yes	characteristic, complemented
126	#2848	C₂×C₃	1	1	yes	characteristic
127	#2577	C₂×C₃	1	2	yes	complemented
128	#2530	C₂×C₃	1	2	yes	complemented
129	#2505	C₂×C₃	1	2	yes	complemented
130	#2503	C₂×C₃	1	1	yes	characteristic, complemented
131	#2495	C₂×C₃	1	1	yes	characteristic, complemented
132	#2494	C₂×C₃	1	1	yes	characteristic, complemented
133	#2493	C₂×C₃	1	2	yes	complemented
134	#2493	C₂×C₃	1	2	yes	complemented
135	#2489	C₂×C₃	1	1	yes	characteristic, complemented
136	#2483	C₂×C₃	1	2	yes	—
137	#2442	C₂×C₃	1	1	yes	characteristic, complemented
138	#2421	C₂×C₃	1	1	yes	characteristic, complemented
139	#2360	C₂×C₃	1	1	yes	characteristic, complemented
140	#2344	C₂×C₃	1	1	yes	characteristic, complemented
141	#2343	C₂×C₃	1	2	yes	complemented
142	#2342	C₂×C₃	1	2	yes	—
143	C₄×C₂²⋊Q₈	C₂×C₃	1	1	yes	characteristic, complemented
144	#2283	C₂×C₃	1	1	yes	characteristic, complemented
145	C₂×#380	C₂×C₃	1	1	yes	characteristic
146	C₂×C₄×C₂²⋊C₄	C₂×C₃	1	1	yes	characteristic
147	C₂⁵×C₃	C₂³	1	1	yes	characteristic
148	C₂²×C₃×Q₈	C₂³	1	1	yes	characteristic
149	C₂³×C₃×C₄	—	2	4	no	—
150	C₂³×C₃×C₄	—	2	4	no	—
151	C₂³×C₃×C₄	—	4	2	no	—
152	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
153	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
154	C₂³×C₃×C₄	C₂³	1	2	yes	—
155	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
156	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
157	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
158	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
159	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
160	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
161	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
162	C₂³×C₃×C₄	C₂³	1	2	yes	—
163	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
164	C₃×#125	—	4	2	no	—
165	C₃×C₂²⋊Q₈	—	2	4	no	—
166	C₃×C₂²⋊Q₈	—	2	4	no	—
167	C₃×C₂²⋊Q₈	—	4	2	no	—
168	C₃×C₄×Q₈	—	4	2	no	—
169	C₃×#117	—	2	8	no	—
170	C₂×C₃×C₄⋊C₄	—	2	4	no	—
171	C₂×C₃×C₄⋊C₄	—	4	2	no	—
172	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
173	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
174	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
175	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
176	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
177	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
178	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
179	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
180	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
181	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
182	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
183	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
184	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
185	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
186	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
187	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
188	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
189	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
190	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
191	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
192	C₂×C₃×C₂²⋊C₄	—	2	4	no	—
193	C₂×C₃×C₂²⋊C₄	—	2	8	no	—
194	C₂×C₃×C₂²⋊C₄	—	2	4	no	—
195	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
196	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
197	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
198	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
199	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
200	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
201	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
202	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
203	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
204	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
205	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
206	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
207	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
208	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
209	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
210	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
211	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
212	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
213	C₂×C₃×C₄²	—	2	4	no	—
214	C₂×C₃×C₄²	—	4	2	no	—
215	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
216	C₂×C₃×C₄²	C₂³	1	2	yes	—
217	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
218	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
219	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
220	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
221	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
222	C₂×C₃×C₄²	C₂³	1	2	yes	—
223	C₂×C₃×C₄²	C₂³	1	2	yes	—
224	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
225	C₂×C₃×C₄²	C₂³	1	2	yes	—
226	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
227	C₃×#95	C₂³	1	2	yes	—
228	C₃×#95	C₂³	1	1	yes	characteristic
229	C₃×#95	C₂³	1	1	yes	characteristic
230	C₃×#95	C₂³	1	1	yes	characteristic
231	C₃×#95	C₂³	1	1	yes	characteristic
232	C₃×#95	C₂³	1	1	yes	characteristic
233	C₃×#95	C₂³	1	1	yes	characteristic
234	C₃×#95	C₂³	1	1	yes	characteristic
235	C₃×#95	C₂³	1	1	yes	characteristic
236	C₃×#95	C₂³	1	2	yes	—
237	C₃×#95	C₂³	1	2	yes	—
238	C₃×#95	C₂³	1	2	yes	—
239	C₃×#95	C₂³	1	2	yes	—
240	C₃×#95	C₂³	1	2	yes	—
241	C₃×#95	C₂³	1	2	yes	—
242	C₃×#95	C₂³	1	2	yes	—
243	C₃×#95	C₂³	1	2	yes	—
244	C₃×#95	C₂³	1	2	yes	—
245	C₃×#95	C₂³	1	2	yes	—
246	C₃×#95	C₂³	1	2	yes	—
247	C₃×#95	C₂³	1	2	yes	—
248	C₃×#95	C₂³	1	2	yes	—
249	C₃×#95	C₂³	1	2	yes	—
250	C₃×#95	C₂³	1	2	yes	—
251	C₃×#95	C₂³	1	2	yes	—
252	C₃×#95	C₂³	1	2	yes	—
253	C₃×#95	C₂³	1	2	yes	—
254	C₃×#95	C₂³	1	2	yes	—
255	C₃×#95	C₂³	1	2	yes	—
256	C₃×#95	C₂³	1	2	yes	—
257	C₃×#95	C₂³	1	2	yes	—
258	C₃×#95	C₂³	1	2	yes	—
259	C₃×#95	C₂³	1	2	yes	—
260	C₃×#95	C₂³	1	2	yes	—
261	C₃×#95	C₂³	1	2	yes	—
262	C₂⁴×C₄	C₂²×C₃	1	1	yes	characteristic
263	C₂×#125	C₂²×C₃	1	1	yes	characteristic, complemented
264	C₂×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
265	C₂×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
266	C₂×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
267	C₂×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
268	C₂×#117	C₂²×C₃	1	2	yes	—
269	C₂²×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
270	C₂²×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
271	C₂²×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
272	C₂²×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
273	C₂²×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
274	C₂²×C₄²	C₂²×C₃	1	1	yes	characteristic
275	C₂²×C₄²	C₂²×C₃	1	1	yes	characteristic
276	#401	C₂²×C₃	1	2	yes	complemented
277	#400	C₂²×C₃	1	2	yes	complemented
278	#400	C₂²×C₃	1	2	yes	complemented
279	#400	C₂²×C₃	1	2	yes	complemented
280	#400	C₂²×C₃	1	2	yes	complemented
281	#400	C₂²×C₃	1	2	yes	complemented
282	#400	C₂²×C₃	1	2	yes	complemented
283	#398	C₂²×C₃	1	2	yes	complemented
284	#397	C₂²×C₃	1	2	yes	—
285	#397	C₂²×C₃	1	2	yes	—
286	#397	C₂²×C₃	1	2	yes	—
287	#397	C₂²×C₃	1	2	yes	—
288	#391	C₂²×C₃	1	1	yes	characteristic, complemented
289	#391	C₂²×C₃	1	1	yes	characteristic, complemented
290	#391	C₂²×C₃	1	1	yes	characteristic, complemented
291	#389	C₂²×C₃	1	1	yes	characteristic, complemented
292	#389	C₂²×C₃	1	1	yes	characteristic, complemented
293	#389	C₂²×C₃	1	1	yes	characteristic, complemented
294	#389	C₂²×C₃	1	1	yes	characteristic, complemented
295	#389	C₂²×C₃	1	2	yes	complemented
296	#389	C₂²×C₃	1	1	yes	characteristic, complemented
297	#388	C₂²×C₃	1	2	yes	—
298	#388	C₂²×C₃	1	2	yes	—
299	#388	C₂²×C₃	1	2	yes	—
300	#388	C₂²×C₃	1	2	yes	—
301	#387	C₂²×C₃	1	2	yes	complemented
302	#387	C₂²×C₃	1	2	yes	complemented
303	#387	C₂²×C₃	1	2	yes	complemented
304	#387	C₂²×C₃	1	2	yes	complemented
305	#387	C₂²×C₃	1	2	yes	complemented
306	#387	C₂²×C₃	1	2	yes	complemented
307	#387	C₂²×C₃	1	2	yes	complemented
308	#387	C₂²×C₃	1	2	yes	complemented
309	#387	C₂²×C₃	1	2	yes	complemented
310	#387	C₂²×C₃	1	2	yes	complemented
311	#385	C₂²×C₃	1	2	yes	—
312	#385	C₂²×C₃	1	2	yes	—
313	#385	C₂²×C₃	1	2	yes	—
314	#385	C₂²×C₃	1	2	yes	—
315	#385	C₂²×C₃	1	2	yes	—
316	#385	C₂²×C₃	1	2	yes	—
317	#385	C₂²×C₃	1	2	yes	—
318	#385	C₂²×C₃	1	2	yes	—
319	#385	C₂²×C₃	1	2	yes	—
320	#383	C₂²×C₃	1	2	yes	complemented
321	#383	C₂²×C₃	1	2	yes	complemented
322	#382	C₂²×C₃	1	1	yes	characteristic, complemented
323	#382	C₂²×C₃	1	2	yes	complemented
324	#382	C₂²×C₃	1	1	yes	characteristic, complemented
325	#382	C₂²×C₃	1	1	yes	characteristic, complemented
326	#381	C₂²×C₃	1	2	yes	—
327	#381	C₂²×C₃	1	2	yes	—
328	#381	C₂²×C₃	1	2	yes	—
329	#381	C₂²×C₃	1	2	yes	—
330	#381	C₂²×C₃	1	2	yes	—
331	#380	C₂²×C₃	1	2	yes	—
332	#380	C₂²×C₃	1	1	yes	characteristic
333	#380	C₂²×C₃	1	1	yes	characteristic
334	#380	C₂²×C₃	1	1	yes	characteristic
335	#380	C₂²×C₃	1	1	yes	characteristic
336	#380	C₂²×C₃	1	2	yes	—
337	#380	C₂²×C₃	1	1	yes	characteristic
338	#380	C₂²×C₃	1	1	yes	characteristic
339	#380	C₂²×C₃	1	2	yes	—
340	#380	C₂²×C₃	1	1	yes	characteristic
341	#379	C₂²×C₃	1	2	yes	—
342	C₄×C₄⋊C₄	C₂²×C₃	1	2	yes	complemented
343	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
344	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
345	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
346	C₄×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
347	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
348	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
349	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
350	C₄×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
351	C₄×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
352	C₄×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
353	C₄×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
354	C₄×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
355	C₄×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
356	C₄×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
357	#376	C₂²×C₃	1	2	yes	complemented
358	C₂×#95	C₂²×C₃	1	2	yes	—
359	C₂×#95	C₂²×C₃	1	1	yes	characteristic
360	C₂×#95	C₂²×C₃	1	1	yes	characteristic
361	C₂⁴×C₃	—	2	2	no	—
362	C₂⁴×C₃	—	2	2	no	—
363	C₂⁴×C₃	—	2	2	no	—
364	C₂⁴×C₃	—	2	2	no	—
365	C₂⁴×C₃	—	4	1	no	—
366	C₂⁴×C₃	—	4	1	no	—
367	C₂⁴×C₃	#41	1	4	yes	—
368	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
369	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
370	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
371	C₂×C₃×Q₈	—	2	2	no	—
372	C₂×C₃×Q₈	—	2	2	no	—
373	C₂×C₃×Q₈	—	2	2	no	—
374	C₂²×C₃×C₄	—	2	2	no	—
375	C₂²×C₃×C₄	—	2	2	no	—
376	C₂²×C₃×C₄	—	2	2	no	—
377	C₂²×C₃×C₄	—	2	2	no	—
378	C₂²×C₃×C₄	—	2	2	no	—
379	C₂²×C₃×C₄	—	2	2	no	—
380	C₂²×C₃×C₄	—	2	2	no	—
381	C₂²×C₃×C₄	—	2	4	no	—
382	C₂²×C₃×C₄	—	2	2	no	—
383	C₂²×C₃×C₄	—	2	4	no	—
384	C₂²×C₃×C₄	—	2	4	no	—
385	C₂²×C₃×C₄	—	2	2	no	—
386	C₂²×C₃×C₄	—	2	2	no	—
387	C₂²×C₃×C₄	—	2	2	no	—
388	C₂²×C₃×C₄	—	2	2	no	—
389	C₂²×C₃×C₄	—	2	4	no	—
390	C₂²×C₃×C₄	—	2	2	no	—
391	C₂²×C₃×C₄	—	2	2	no	—
392	C₂²×C₃×C₄	—	2	2	no	—
393	C₂²×C₃×C₄	—	2	2	no	—
394	C₂²×C₃×C₄	—	2	2	no	—
395	C₂²×C₃×C₄	—	2	2	no	—
396	C₂²×C₃×C₄	—	2	2	no	—
397	C₂²×C₃×C₄	—	2	2	no	—
398	C₂²×C₃×C₄	—	2	2	no	—
399	C₂²×C₃×C₄	—	4	1	no	—
400	C₂²×C₃×C₄	—	4	1	no	—
401	C₂²×C₃×C₄	—	4	1	no	—
402	C₂²×C₃×C₄	—	4	1	no	—
403	C₂²×C₃×C₄	—	4	1	no	—
404	C₂²×C₃×C₄	—	4	1	no	—
405	C₂²×C₃×C₄	—	4	1	no	—
406	C₂²×C₃×C₄	—	4	16	no	—
407	C₂²×C₃×C₄	—	4	2	no	—
408	C₂²×C₃×C₄	—	4	2	no	—
409	C₂²×C₃×C₄	#41	1	4	yes	—
410	C₂²×C₃×C₄	#41	1	4	yes	—
411	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
412	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
413	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
414	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
415	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
416	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
417	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
418	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
419	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
420	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
421	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
422	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
423	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
424	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
425	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
426	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
427	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
428	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
429	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
430	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
431	C₃×C₄⋊C₄	—	2	4	no	—
432	C₃×C₄⋊C₄	—	2	2	no	—
433	C₃×C₄⋊C₄	—	2	2	no	—
434	C₃×C₄⋊C₄	—	2	4	no	—
435	C₃×C₄⋊C₄	—	2	4	no	—
436	C₃×C₄⋊C₄	—	2	2	no	—
437	C₃×C₄⋊C₄	—	2	2	no	—
438	C₃×C₄⋊C₄	—	2	4	no	—
439	C₃×C₄⋊C₄	—	2	4	no	—
440	C₃×C₄⋊C₄	—	2	2	no	—
441	C₃×C₄⋊C₄	—	2	2	no	—
442	C₃×C₄⋊C₄	—	2	2	no	—
443	C₃×C₄⋊C₄	—	4	2	no	—
444	C₃×C₄⋊C₄	—	4	2	no	—
445	C₃×C₄⋊C₄	—	4	2	no	—
446	C₃×C₄⋊C₄	—	4	2	no	—
447	C₃×C₄⋊C₄	—	4	2	no	—
448	C₃×C₄⋊C₄	—	4	2	no	—
449	C₃×C₄⋊C₄	—	4	2	no	—
450	C₃×C₄⋊C₄	—	4	2	no	—
451	C₃×C₂²⋊C₄	—	2	2	no	—
452	C₃×C₂²⋊C₄	—	2	2	no	—
453	C₃×C₂²⋊C₄	—	2	4	no	—
454	C₃×C₂²⋊C₄	—	2	4	no	—
455	C₃×C₂²⋊C₄	—	2	2	no	—
456	C₃×C₂²⋊C₄	—	2	2	no	—
457	C₃×C₂²⋊C₄	—	2	2	no	—
458	C₃×C₂²⋊C₄	—	2	4	no	—
459	C₃×C₂²⋊C₄	—	2	4	no	—
460	C₃×C₂²⋊C₄	—	2	4	no	—
461	C₃×C₂²⋊C₄	—	2	4	no	—
462	C₃×C₂²⋊C₄	—	2	4	no	—
463	C₃×C₂²⋊C₄	—	2	4	no	—
464	C₃×C₂²⋊C₄	—	2	2	no	—
465	C₃×C₂²⋊C₄	—	2	2	no	—
466	C₃×C₂²⋊C₄	—	4	2	no	—
467	C₃×C₂²⋊C₄	—	4	2	no	—
468	C₃×C₂²⋊C₄	#41	1	4	yes	—
469	C₃×C₄²	—	2	2	no	—
470	C₃×C₄²	—	2	2	no	—
471	C₃×C₄²	—	2	2	no	—
472	C₃×C₄²	—	2	2	no	—
473	C₃×C₄²	—	2	4	no	—
474	C₃×C₄²	—	2	4	no	—
475	C₃×C₄²	—	2	2	no	—
476	C₃×C₄²	—	2	2	no	—
477	C₃×C₄²	—	4	1	no	—
478	C₃×C₄²	—	4	1	no	—
479	C₃×C₄²	—	4	2	no	—
480	C₃×C₄²	—	4	2	no	—
481	C₂⁵	C₂³×C₃	1	1	yes	characteristic
482	C₂²×Q₈	C₂³×C₃	1	1	yes	characteristic
483	C₂³×C₄	—	2	4	no	—
484	C₂³×C₄	—	2	4	no	—
485	C₂³×C₄	—	4	2	no	—
486	C₂³×C₄	C₂³×C₃	1	2	yes	—
487	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
488	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
489	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
490	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
491	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
492	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
493	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
494	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
495	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
496	C₂³×C₄	C₂³×C₃	1	2	yes	—
497	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
498	#125	—	4	2	no	—
499	C₂²⋊Q₈	—	2	4	no	—
500	C₂²⋊Q₈	—	2	4	no	—
501	C₂²⋊Q₈	—	4	2	no	—
502	C₄×Q₈	—	4	2	no	—
503	#117	—	2	8	no	—
504	C₂×C₄⋊C₄	—	2	4	no	—
505	C₂×C₄⋊C₄	—	4	2	no	—
506	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
507	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
508	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
509	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
510	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
511	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
512	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
513	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
514	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
515	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
516	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
517	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
518	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
519	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
520	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
521	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
522	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
523	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
524	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
525	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
526	C₂×C₂²⋊C₄	—	2	4	no	—
527	C₂×C₂²⋊C₄	—	2	8	no	—
528	C₂×C₂²⋊C₄	—	2	4	no	—
529	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
530	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
531	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
532	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
533	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
534	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
535	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
536	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
537	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
538	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
539	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
540	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
541	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
542	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
543	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
544	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
545	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
546	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
547	C₂×C₄²	—	2	4	no	—
548	C₂×C₄²	—	4	2	no	—
549	C₂×C₄²	C₂³×C₃	1	2	yes	—
550	C₂×C₄²	C₂³×C₃	1	2	yes	—
551	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
552	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
553	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
554	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
555	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
556	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
557	C₂×C₄²	C₂³×C₃	1	2	yes	—
558	C₂×C₄²	C₂³×C₃	1	2	yes	—
559	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
560	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
561	#95	C₂³×C₃	1	2	yes	—
562	#95	C₂³×C₃	1	1	yes	characteristic
563	#95	C₂³×C₃	1	1	yes	characteristic
564	#95	C₂³×C₃	1	1	yes	characteristic
565	#95	C₂³×C₃	1	1	yes	characteristic
566	#95	C₂³×C₃	1	1	yes	characteristic
567	#95	C₂³×C₃	1	1	yes	characteristic
568	#95	C₂³×C₃	1	1	yes	characteristic
569	#95	C₂³×C₃	1	1	yes	characteristic
570	#95	C₂³×C₃	1	2	yes	—
571	#95	C₂³×C₃	1	2	yes	—
572	#95	C₂³×C₃	1	2	yes	—
573	#95	C₂³×C₃	1	2	yes	—
574	#95	C₂³×C₃	1	2	yes	—
575	#95	C₂³×C₃	1	2	yes	—
576	#95	C₂³×C₃	1	2	yes	—
577	#95	C₂³×C₃	1	2	yes	—
578	#95	C₂³×C₃	1	2	yes	—
579	#95	C₂³×C₃	1	2	yes	—
580	#95	C₂³×C₃	1	2	yes	—
581	#95	C₂³×C₃	1	2	yes	—
582	#95	C₂³×C₃	1	2	yes	—
583	#95	C₂³×C₃	1	2	yes	—
584	#95	C₂³×C₃	1	2	yes	—
585	#95	C₂³×C₃	1	2	yes	—
586	#95	C₂³×C₃	1	2	yes	—
587	#95	C₂³×C₃	1	2	yes	—
588	#95	C₂³×C₃	1	2	yes	—
589	#95	C₂³×C₃	1	2	yes	—
590	#95	C₂³×C₃	1	2	yes	—
591	#95	C₂³×C₃	1	2	yes	—
592	#95	C₂³×C₃	1	2	yes	—
593	#95	C₂³×C₃	1	2	yes	—
594	#95	C₂³×C₃	1	2	yes	—
595	#95	C₂³×C₃	1	2	yes	—
596	C₂³×C₃	—	2	1	no	—
597	C₂³×C₃	—	2	1	no	—
598	C₂³×C₃	—	2	1	no	—
599	C₂³×C₃	—	2	1	no	—
600	C₂³×C₃	—	2	1	no	—
601	C₂³×C₃	—	2	1	no	—
602	C₂³×C₃	—	2	1	no	—
603	C₂³×C₃	—	2	1	no	—
604	C₂³×C₃	—	2	8	no	—
605	C₂³×C₃	—	2	8	no	—
606	C₂³×C₃	—	2	1	no	—
607	C₂³×C₃	—	2	1	no	—
608	C₂³×C₃	—	2	1	no	—
609	C₂³×C₃	—	2	1	no	—
610	C₂³×C₃	—	2	1	no	—
611	C₂³×C₃	—	2	1	no	—
612	C₂³×C₃	—	4	4	no	—
613	C₂³×C₃	—	4	4	no	—
614	C₂³×C₃	—	4	4	no	—
615	C₂³×C₃	—	4	4	no	—
616	C₂³×C₃	—	4	4	no	—
617	C₂³×C₃	C₂×#41	1	2	yes	—
618	C₂³×C₃	C₂×#41	1	2	yes	—
619	C₂³×C₃	C₂×#41	1	2	yes	—
620	C₂³×C₃	C₂×#41	1	2	yes	—
621	C₂³×C₃	C₂×#41	1	2	yes	—
622	C₂³×C₃	C₂×#41	1	2	yes	—
623	C₂³×C₃	2₋¹⁺⁴	1	2	yes	—
624	C₂³×C₃	C₂⁵	1	1	yes	characteristic
625	C₃×Q₈	—	4	4	no	—
626	C₂×C₃×C₄	—	2	1	no	—
627	C₂×C₃×C₄	—	2	1	no	—
628	C₂×C₃×C₄	—	2	1	no	—
629	C₂×C₃×C₄	—	2	1	no	—
630	C₂×C₃×C₄	—	2	1	no	—
631	C₂×C₃×C₄	—	2	1	no	—
632	C₂×C₃×C₄	—	2	1	no	—
633	C₂×C₃×C₄	—	2	1	no	—
634	C₂×C₃×C₄	—	2	8	no	—
635	C₂×C₃×C₄	—	2	8	no	—
636	C₂×C₃×C₄	—	2	2	no	—
637	C₂×C₃×C₄	—	2	1	no	—
638	C₂×C₃×C₄	—	2	1	no	—
639	C₂×C₃×C₄	—	2	1	no	—
640	C₂×C₃×C₄	—	2	2	no	—
641	C₂×C₃×C₄	—	2	2	no	—
642	C₂×C₃×C₄	—	2	2	no	—
643	C₂×C₃×C₄	—	2	2	no	—
644	C₂×C₃×C₄	—	2	1	no	—
645	C₂×C₃×C₄	—	2	1	no	—
646	C₂×C₃×C₄	—	2	1	no	—
647	C₂×C₃×C₄	—	2	1	no	—
648	C₂×C₃×C₄	—	2	1	no	—
649	C₂×C₃×C₄	—	2	2	no	—
650	C₂×C₃×C₄	—	2	2	no	—
651	C₂×C₃×C₄	—	2	1	no	—
652	C₂×C₃×C₄	—	2	2	no	—
653	C₂×C₃×C₄	—	2	2	no	—
654	C₂×C₃×C₄	—	2	2	no	—
655	C₂×C₃×C₄	—	2	2	no	—
656	C₂×C₃×C₄	—	2	2	no	—
657	C₂×C₃×C₄	—	2	2	no	—
658	C₂×C₃×C₄	—	2	2	no	—
659	C₂×C₃×C₄	—	2	1	no	—
660	C₂×C₃×C₄	—	2	1	no	—
661	C₂×C₃×C₄	—	2	1	no	—
662	C₂×C₃×C₄	—	2	1	no	—
663	C₂×C₃×C₄	—	2	1	no	—
664	C₂×C₃×C₄	—	2	2	no	—
665	C₂×C₃×C₄	—	2	2	no	—
666	C₂×C₃×C₄	—	2	2	no	—
667	C₂×C₃×C₄	—	2	2	no	—
668	C₂×C₃×C₄	—	2	1	no	—
669	C₂×C₃×C₄	—	2	2	no	—
670	C₂×C₃×C₄	—	2	2	no	—
671	C₂×C₃×C₄	—	2	1	no	—
672	C₂×C₃×C₄	—	2	1	no	—
673	C₂×C₃×C₄	—	2	1	no	—
674	C₂×C₃×C₄	—	2	2	no	—
675	C₂×C₃×C₄	—	2	2	no	—
676	C₂×C₃×C₄	—	2	2	no	—
677	C₂×C₃×C₄	—	2	1	no	—
678	C₂×C₃×C₄	—	2	1	no	—
679	C₂×C₃×C₄	—	2	1	no	—
680	C₂×C₃×C₄	—	2	2	no	—
681	C₂×C₃×C₄	—	4	4	no	—
682	C₂×C₃×C₄	—	4	4	no	—
683	C₂×C₃×C₄	—	4	4	no	—
684	C₂×C₃×C₄	—	4	4	no	—
685	C₂×C₃×C₄	—	4	4	no	—
686	C₂×C₃×C₄	—	4	4	no	—
687	C₂×C₃×C₄	—	4	8	no	—
688	C₂×C₃×C₄	—	4	4	no	—
689	C₂×C₃×C₄	—	4	4	no	—
690	C₂×C₃×C₄	—	8	4	no	—
691	C₂×C₃×C₄	C₂×#41	1	2	yes	—
692	C₂×C₃×C₄	C₂×#41	1	2	yes	—
693	C₂×C₃×C₄	C₂×#41	1	2	yes	—
694	C₂×C₃×C₄	C₂×#41	1	2	yes	—
695	C₂×C₃×C₄	C₂×#41	1	2	yes	—
696	C₂×C₃×C₄	C₂×#41	1	2	yes	—
697	C₂×C₃×C₄	H(5,𝔽₂)	1	2	yes	—
698	C₂⁴	—	2	2	no	—
699	C₂⁴	—	2	2	no	—
700	C₂⁴	—	2	2	no	—
701	C₂⁴	—	2	2	no	—
702	C₂⁴	—	4	1	no	—
703	C₂⁴	—	4	1	no	—
704	C₂⁴	C₃×#41	1	4	yes	—
705	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
706	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
707	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
708	C₂×Q₈	—	2	2	no	—
709	C₂×Q₈	—	2	2	no	—
710	C₂×Q₈	—	2	2	no	—
711	C₂²×C₄	—	2	2	no	—
712	C₂²×C₄	—	2	2	no	—
713	C₂²×C₄	—	2	2	no	—
714	C₂²×C₄	—	2	2	no	—
715	C₂²×C₄	—	2	2	no	—
716	C₂²×C₄	—	2	2	no	—
717	C₂²×C₄	—	2	2	no	—
718	C₂²×C₄	—	2	4	no	—
719	C₂²×C₄	—	2	2	no	—
720	C₂²×C₄	—	2	4	no	—
721	C₂²×C₄	—	2	4	no	—
722	C₂²×C₄	—	2	2	no	—
723	C₂²×C₄	—	2	2	no	—
724	C₂²×C₄	—	2	2	no	—
725	C₂²×C₄	—	2	2	no	—
726	C₂²×C₄	—	2	4	no	—
727	C₂²×C₄	—	2	2	no	—
728	C₂²×C₄	—	2	2	no	—
729	C₂²×C₄	—	2	2	no	—
730	C₂²×C₄	—	2	2	no	—
731	C₂²×C₄	—	2	2	no	—
732	C₂²×C₄	—	2	2	no	—
733	C₂²×C₄	—	2	2	no	—
734	C₂²×C₄	—	2	2	no	—
735	C₂²×C₄	—	2	2	no	—
736	C₂²×C₄	—	4	1	no	—
737	C₂²×C₄	—	4	1	no	—
738	C₂²×C₄	—	4	1	no	—
739	C₂²×C₄	—	4	1	no	—
740	C₂²×C₄	—	4	1	no	—
741	C₂²×C₄	—	4	1	no	—
742	C₂²×C₄	—	4	1	no	—
743	C₂²×C₄	—	4	16	no	—
744	C₂²×C₄	—	4	2	no	—
745	C₂²×C₄	—	4	2	no	—
746	C₂²×C₄	C₃×#41	1	4	yes	—
747	C₂²×C₄	C₃×#41	1	4	yes	—
748	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
749	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
750	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
751	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
752	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
753	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
754	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
755	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
756	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
757	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
758	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
759	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
760	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
761	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
762	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
763	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
764	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
765	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
766	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
767	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
768	C₄⋊C₄	—	2	4	no	—
769	C₄⋊C₄	—	2	2	no	—
770	C₄⋊C₄	—	2	2	no	—
771	C₄⋊C₄	—	2	4	no	—
772	C₄⋊C₄	—	2	4	no	—
773	C₄⋊C₄	—	2	2	no	—
774	C₄⋊C₄	—	2	2	no	—
775	C₄⋊C₄	—	2	4	no	—
776	C₄⋊C₄	—	2	4	no	—
777	C₄⋊C₄	—	2	2	no	—
778	C₄⋊C₄	—	2	2	no	—
779	C₄⋊C₄	—	2	2	no	—
780	C₄⋊C₄	—	4	2	no	—
781	C₄⋊C₄	—	4	2	no	—
782	C₄⋊C₄	—	4	2	no	—
783	C₄⋊C₄	—	4	2	no	—
784	C₄⋊C₄	—	4	2	no	—
785	C₄⋊C₄	—	4	2	no	—
786	C₄⋊C₄	—	4	2	no	—
787	C₄⋊C₄	—	4	2	no	—
788	C₂²⋊C₄	—	2	2	no	—
789	C₂²⋊C₄	—	2	2	no	—
790	C₂²⋊C₄	—	2	4	no	—
791	C₂²⋊C₄	—	2	4	no	—
792	C₂²⋊C₄	—	2	2	no	—
793	C₂²⋊C₄	—	2	2	no	—
794	C₂²⋊C₄	—	2	2	no	—
795	C₂²⋊C₄	—	2	4	no	—
796	C₂²⋊C₄	—	2	4	no	—
797	C₂²⋊C₄	—	2	4	no	—
798	C₂²⋊C₄	—	2	4	no	—
799	C₂²⋊C₄	—	2	4	no	—
800	C₂²⋊C₄	—	2	4	no	—
801	C₂²⋊C₄	—	2	2	no	—
802	C₂²⋊C₄	—	2	2	no	—
803	C₂²⋊C₄	—	4	2	no	—
804	C₂²⋊C₄	—	4	2	no	—
805	C₂²⋊C₄	C₃×#41	1	4	yes	—
806	C₄²	—	2	2	no	—
807	C₄²	—	2	2	no	—
808	C₄²	—	2	2	no	—
809	C₄²	—	2	2	no	—
810	C₄²	—	2	4	no	—
811	C₄²	—	2	4	no	—
812	C₄²	—	2	2	no	—
813	C₄²	—	2	2	no	—
814	C₄²	—	4	1	no	—
815	C₄²	—	4	1	no	—
816	C₄²	—	4	2	no	—
817	C₄²	—	4	2	no	—
818	C₂²×C₃	—	2	2	no	—
819	C₂²×C₃	—	2	2	no	—
820	C₂²×C₃	—	2	2	no	—
821	C₂²×C₃	—	2	2	no	—
822	C₂²×C₃	—	2	2	no	—
823	C₂²×C₃	—	2	2	no	—
824	C₂²×C₃	—	2	2	no	—
825	C₂²×C₃	—	2	2	no	—
826	C₂²×C₃	—	2	2	no	—
827	C₂²×C₃	—	2	2	no	—
828	C₂²×C₃	—	2	2	no	—
829	C₂²×C₃	—	2	2	no	—
830	C₂²×C₃	—	2	2	no	—
831	C₂²×C₃	—	2	2	no	—
832	C₂²×C₃	—	2	2	no	—
833	C₂²×C₃	—	4	16	no	—
834	C₂²×C₃	—	4	1	no	—
835	C₂²×C₃	—	4	1	no	—
836	C₂²×C₃	—	4	1	no	—
837	C₂²×C₃	—	4	1	no	—
838	C₂²×C₃	#529	1	4	yes	—
839	C₂²×C₃	#552	1	4	yes	—
840	C₂²×C₃	C₂²×#41	1	1	yes	characteristic
841	C₂²×C₃	C₂²×#41	1	1	yes	characteristic
842	C₂²×C₃	C₂²×#41	1	1	yes	characteristic
843	C₂²×C₃	C₂²×#41	1	1	yes	characteristic
844	C₂²×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
845	C₂²×C₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
846	C₂²×C₃	#585	1	1	yes	characteristic
847	C₃×C₄	—	2	2	no	—
848	C₃×C₄	—	2	2	no	—
849	C₃×C₄	—	2	2	no	—
850	C₃×C₄	—	2	2	no	—
851	C₃×C₄	—	4	2	no	—
852	C₃×C₄	—	4	2	no	—
853	C₃×C₄	—	4	1	no	—
854	C₃×C₄	—	4	2	no	—
855	C₃×C₄	—	4	1	no	—
856	C₃×C₄	—	4	1	no	—
857	C₃×C₄	—	4	2	no	—
858	C₃×C₄	—	4	1	no	—
859	C₃×C₄	—	4	2	no	—
860	C₃×C₄	—	4	1	no	—
861	C₃×C₄	—	4	1	no	—
862	C₃×C₄	—	4	2	no	—
863	C₃×C₄	—	4	2	no	—
864	C₃×C₄	—	4	2	no	—
865	C₃×C₄	—	4	1	no	—
866	C₃×C₄	#551	1	4	yes	—
867	C₂³	—	2	1	no	—
868	C₂³	—	2	1	no	—
869	C₂³	—	2	1	no	—
870	C₂³	—	2	1	no	—
871	C₂³	—	2	1	no	—
872	C₂³	—	2	1	no	—
873	C₂³	—	2	1	no	—
874	C₂³	—	2	1	no	—
875	C₂³	—	2	1	no	—
876	C₂³	—	2	1	no	—
877	C₂³	—	2	1	no	—
878	C₂³	—	2	1	no	—
879	C₂³	—	2	1	no	—
880	C₂³	—	2	1	no	—
881	C₂³	—	2	8	no	—
882	C₂³	—	2	8	no	—
883	C₂³	—	4	4	no	—
884	C₂³	—	4	4	no	—
885	C₂³	—	4	4	no	—
886	C₂³	—	4	4	no	—
887	C₂³	—	4	4	no	—
888	C₂³	C₂×C₃×#41	1	2	yes	—
889	C₂³	C₂×C₃×#41	1	2	yes	—
890	C₂³	C₂×C₃×#41	1	2	yes	—
891	C₂³	C₂×C₃×#41	1	2	yes	—
892	C₂³	C₂×C₃×#41	1	2	yes	—
893	C₂³	C₂×C₃×#41	1	2	yes	—
894	C₂³	C₃×2₋¹⁺⁴	1	2	yes	—
895	C₂³	C₂⁵×C₃	1	1	yes	characteristic
896	Q₈	—	4	4	no	—
897	C₂×C₄	—	2	1	no	—
898	C₂×C₄	—	2	1	no	—
899	C₂×C₄	—	2	1	no	—
900	C₂×C₄	—	2	1	no	—
901	C₂×C₄	—	2	1	no	—
902	C₂×C₄	—	2	1	no	—
903	C₂×C₄	—	2	1	no	—
904	C₂×C₄	—	2	1	no	—
905	C₂×C₄	—	2	8	no	—
906	C₂×C₄	—	2	8	no	—
907	C₂×C₄	—	2	2	no	—
908	C₂×C₄	—	2	1	no	—
909	C₂×C₄	—	2	1	no	—
910	C₂×C₄	—	2	1	no	—
911	C₂×C₄	—	2	2	no	—
912	C₂×C₄	—	2	2	no	—
913	C₂×C₄	—	2	2	no	—
914	C₂×C₄	—	2	2	no	—
915	C₂×C₄	—	2	1	no	—
916	C₂×C₄	—	2	1	no	—
917	C₂×C₄	—	2	1	no	—
918	C₂×C₄	—	2	1	no	—
919	C₂×C₄	—	2	1	no	—
920	C₂×C₄	—	2	2	no	—
921	C₂×C₄	—	2	2	no	—
922	C₂×C₄	—	2	1	no	—
923	C₂×C₄	—	2	2	no	—
924	C₂×C₄	—	2	2	no	—
925	C₂×C₄	—	2	2	no	—
926	C₂×C₄	—	2	2	no	—
927	C₂×C₄	—	2	2	no	—
928	C₂×C₄	—	2	2	no	—
929	C₂×C₄	—	2	2	no	—
930	C₂×C₄	—	2	1	no	—
931	C₂×C₄	—	2	1	no	—
932	C₂×C₄	—	2	1	no	—
933	C₂×C₄	—	2	1	no	—
934	C₂×C₄	—	2	1	no	—
935	C₂×C₄	—	2	2	no	—
936	C₂×C₄	—	2	2	no	—
937	C₂×C₄	—	2	2	no	—
938	C₂×C₄	—	2	2	no	—
939	C₂×C₄	—	2	1	no	—
940	C₂×C₄	—	2	2	no	—
941	C₂×C₄	—	2	2	no	—
942	C₂×C₄	—	2	1	no	—
943	C₂×C₄	—	2	1	no	—
944	C₂×C₄	—	2	1	no	—
945	C₂×C₄	—	2	2	no	—
946	C₂×C₄	—	2	2	no	—
947	C₂×C₄	—	2	2	no	—
948	C₂×C₄	—	2	1	no	—
949	C₂×C₄	—	2	1	no	—
950	C₂×C₄	—	2	1	no	—
951	C₂×C₄	—	2	2	no	—
952	C₂×C₄	—	4	4	no	—
953	C₂×C₄	—	4	4	no	—
954	C₂×C₄	—	4	4	no	—
955	C₂×C₄	—	4	4	no	—
956	C₂×C₄	—	4	4	no	—
957	C₂×C₄	—	4	4	no	—
958	C₂×C₄	—	4	8	no	—
959	C₂×C₄	—	4	4	no	—
960	C₂×C₄	—	4	4	no	—
961	C₂×C₄	—	8	4	no	—
962	C₂×C₄	C₂×C₃×#41	1	2	yes	—
963	C₂×C₄	C₂×C₃×#41	1	2	yes	—
964	C₂×C₄	C₂×C₃×#41	1	2	yes	—
965	C₂×C₄	C₂×C₃×#41	1	2	yes	—
966	C₂×C₄	C₂×C₃×#41	1	2	yes	—
967	C₂×C₄	C₂×C₃×#41	1	2	yes	—
968	C₂×C₄	C₃×H(5,𝔽₂)	1	2	yes	—
969	C₂×C₃	—	2	4	no	—
970	C₂×C₃	—	2	4	no	—
971	C₂×C₃	—	4	2	no	—
972	C₂×C₃	C₂×#529	1	1	yes	characteristic
973	C₂×C₃	C₂×#551	1	1	yes	characteristic
974	C₂×C₃	C₂×#552	1	1	yes	characteristic
975	C₂×C₃	#3475	1	1	yes	characteristic
976	C₂×C₃	#3495	1	1	yes	characteristic
977	C₂×C₃	#3505	1	1	yes	characteristic
978	C₂×C₃	#3520	1	1	yes	characteristic
979	C₂²	—	2	2	no	—
980	C₂²	—	2	2	no	—
981	C₂²	—	2	2	no	—
982	C₂²	—	2	2	no	—
983	C₂²	—	2	2	no	—
984	C₂²	—	2	2	no	—
985	C₂²	—	2	2	no	—
986	C₂²	—	2	2	no	—
987	C₂²	—	2	2	no	—
988	C₂²	—	2	2	no	—
989	C₂²	—	2	2	no	—
990	C₂²	—	2	2	no	—
991	C₂²	—	2	2	no	—
992	C₂²	—	2	2	no	—
993	C₂²	—	2	2	no	—
994	C₂²	—	4	16	no	—
995	C₂²	—	4	1	no	—
996	C₂²	—	4	1	no	—
997	C₂²	—	4	1	no	—
998	C₂²	—	4	1	no	—
999	C₂²	C₃×#529	1	4	yes	—
1000	C₂²	C₃×#552	1	4	yes	—
1001	C₂²	C₂²×C₃×#41	1	1	yes	characteristic
1002	C₂²	C₂²×C₃×#41	1	1	yes	characteristic
1003	C₂²	C₂²×C₃×#41	1	1	yes	characteristic
1004	C₂²	C₂²×C₃×#41	1	1	yes	characteristic
1005	C₂²	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
1006	C₂²	C₂×C₃×2₋¹⁺⁴	1	1	yes	characteristic
1007	C₂²	C₃×#585	1	1	yes	characteristic
1008	C₄	—	2	2	no	—
1009	C₄	—	2	2	no	—
1010	C₄	—	2	2	no	—
1011	C₄	—	2	2	no	—
1012	C₄	—	4	2	no	—
1013	C₄	—	4	2	no	—
1014	C₄	—	4	1	no	—
1015	C₄	—	4	2	no	—
1016	C₄	—	4	1	no	—
1017	C₄	—	4	1	no	—
1018	C₄	—	4	1	no	—
1019	C₄	—	4	2	no	—
1020	C₄	—	4	2	no	—
1021	C₄	—	4	1	no	—
1022	C₄	—	4	1	no	—
1023	C₄	—	4	2	no	—
1024	C₄	—	4	2	no	—
1025	C₄	—	4	1	no	—
1026	C₄	—	4	2	no	—
1027	C₄	C₃×#551	1	4	yes	—
1028	C₃	#36167	1	1	yes	characteristic, direct product factor, Sylow
1029	C₂	—	2	4	no	—
1030	C₂	—	2	4	no	—
1031	C₂	—	4	2	no	—
1032	C₂	C₂×C₃×#529	1	1	yes	characteristic
1033	C₂	C₂×C₃×#551	1	1	yes	characteristic
1034	C₂	C₂×C₃×#552	1	1	yes	characteristic
1035	C₂	C₃×#3475	1	1	yes	characteristic
1036	C₂	C₃×#3495	1	1	yes	characteristic
1037	C₂	C₃×#3505	1	1	yes	characteristic
1038	C₂	C₃×#3520	1	1	yes	characteristic

	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×#2855	C₂	semidirect
2. C₃×#2851	C₂	semidirect
4. C₃×#2577	C₂	semidirect
5. C₃×#2530	C₂	semidirect
6. C₃×#2505	C₂	semidirect
7. C₃×#2503	C₂	semidirect
8. C₃×#2495	C₂	semidirect
9. C₃×#2494	C₂	semidirect
10. C₃×#2493	C₂	semidirect
11. C₃×#2493	C₂	semidirect
12. C₃×#2489	C₂	semidirect
14. C₃×#2442	C₂	semidirect
15. C₃×#2421	C₂	semidirect
16. C₃×#2360	C₂	semidirect
17. C₃×#2344	C₂	semidirect
18. C₃×#2343	C₂	semidirect
20. C₃×C₄×C₂²⋊Q₈	C₂	semidirect
21. C₃×#2283	C₂	semidirect
24. #36167	C₃	direct (N × H)
26. C₂×C₃×#125	C₂²	semidirect
30. C₂×C₃×C₄×Q₈	C₂²	semidirect
39. C₃×#401	C₂²	semidirect
40. C₃×#400	C₂²	semidirect
41. C₃×#400	C₂²	semidirect
42. C₃×#400	C₂²	semidirect
43. C₃×#400	C₂²	semidirect
44. C₃×#400	C₂²	semidirect
45. C₃×#400	C₂²	semidirect
46. C₃×#398	C₂²	semidirect
51. C₃×#391	C₂²	semidirect
52. C₃×#391	C₂²	semidirect
53. C₃×#391	C₂²	semidirect
54. C₃×#389	C₂²	semidirect
55. C₃×#389	C₂²	semidirect
56. C₃×#389	C₂²	semidirect
57. C₃×#389	C₂²	semidirect
58. C₃×#389	C₂²	semidirect
59. C₃×#389	C₂²	semidirect
64. C₃×#387	C₂²	semidirect
65. C₃×#387	C₂²	semidirect
66. C₃×#387	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
83. C₃×#383	C₂²	semidirect
84. C₃×#383	C₂²	semidirect
85. C₃×#382	C₂²	semidirect
86. C₃×#382	C₂²	semidirect
87. C₃×#382	C₂²	semidirect
88. C₃×#382	C₂²	semidirect
105. C₃×C₄×C₄⋊C₄	C₂²	semidirect
106. C₃×C₄×C₄⋊C₄	C₂²	semidirect
107. C₃×C₄×C₄⋊C₄	C₂²	semidirect
108. C₃×C₄×C₄⋊C₄	C₂²	semidirect
120. C₃×#376	C₂²	semidirect
124. #2855	C₂×C₃	semidirect
125. #2851	C₂×C₃	semidirect
127. #2577	C₂×C₃	semidirect
128. #2530	C₂×C₃	semidirect
129. #2505	C₂×C₃	semidirect
130. #2503	C₂×C₃	semidirect
131. #2495	C₂×C₃	semidirect
132. #2494	C₂×C₃	semidirect
133. #2493	C₂×C₃	semidirect
134. #2493	C₂×C₃	semidirect
135. #2489	C₂×C₃	semidirect
137. #2442	C₂×C₃	semidirect
138. #2421	C₂×C₃	semidirect
139. #2360	C₂×C₃	semidirect
140. #2344	C₂×C₃	semidirect
141. #2343	C₂×C₃	semidirect
143. C₄×C₂²⋊Q₈	C₂×C₃	semidirect
144. #2283	C₂×C₃	semidirect
263. C₂×#125	C₂²×C₃	semidirect
267. C₂×C₄×Q₈	C₂²×C₃	semidirect
276. #401	C₂²×C₃	semidirect
277. #400	C₂²×C₃	semidirect
278. #400	C₂²×C₃	semidirect
279. #400	C₂²×C₃	semidirect
280. #400	C₂²×C₃	semidirect
281. #400	C₂²×C₃	semidirect
282. #400	C₂²×C₃	semidirect
283. #398	C₂²×C₃	semidirect
288. #391	C₂²×C₃	semidirect
289. #391	C₂²×C₃	semidirect
290. #391	C₂²×C₃	semidirect
291. #389	C₂²×C₃	semidirect
292. #389	C₂²×C₃	semidirect
293. #389	C₂²×C₃	semidirect
294. #389	C₂²×C₃	semidirect
295. #389	C₂²×C₃	semidirect
296. #389	C₂²×C₃	semidirect
301. #387	C₂²×C₃	semidirect
302. #387	C₂²×C₃	semidirect
303. #387	C₂²×C₃	semidirect
304. #387	C₂²×C₃	semidirect
305. #387	C₂²×C₃	semidirect
306. #387	C₂²×C₃	semidirect
307. #387	C₂²×C₃	semidirect
308. #387	C₂²×C₃	semidirect
309. #387	C₂²×C₃	semidirect
310. #387	C₂²×C₃	semidirect
320. #383	C₂²×C₃	semidirect
321. #383	C₂²×C₃	semidirect
322. #382	C₂²×C₃	semidirect
323. #382	C₂²×C₃	semidirect
324. #382	C₂²×C₃	semidirect
325. #382	C₂²×C₃	semidirect
342. C₄×C₄⋊C₄	C₂²×C₃	semidirect
343. C₄×C₄⋊C₄	C₂²×C₃	semidirect
344. C₄×C₄⋊C₄	C₂²×C₃	semidirect
345. C₄×C₄⋊C₄	C₂²×C₃	semidirect
357. #376	C₂²×C₃	semidirect
1028. C₃	#36167	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×#2855	2
C₃×#2851	2
C₃×#2848	2
C₃×#2577	2
C₃×#2530	2
C₃×#2505	2
C₃×#2503	2
C₃×#2495	2
C₃×#2494	2
C₃×#2493	2
C₃×#2489	2
C₃×#2483	2
C₃×#2442	2
C₃×#2421	2
C₃×#2360	2
C₃×#2344	2
C₃×#2343	2
C₃×#2342	2
C₃×C₄×C₂²⋊Q₈	2
C₃×#2283	2
C₂×C₃×#380	2
C₂×C₃×C₄×C₂²⋊C₄	2
#36167	3

Subgroups — C3×#36167 #10654774

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#36167 #10654774