Subgroups — C₃×#41959 #10660566

Order 768.

2248 conjugacy classes of subgroups.

The subgroup lattice has 1092 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#553	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×#542	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#2821	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#2816	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#2721	C₂	1	2	yes	maximal, complemented
6	C₃×#2714	C₂	1	2	yes	maximal, complemented
7	C₃×#2676	C₂	1	2	yes	maximal, complemented
8	C₃×#2672	C₂	1	2	yes	maximal, complemented
9	C₃×#2662	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#2656	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×#2636	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#2635	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃×#2631	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃×#2604	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃×#2580	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃×#2564	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃×#2542	C₂	1	1	yes	maximal, characteristic, complemented
18	C₃×#2464	C₂	1	2	yes	maximal, complemented
19	C₃×#2463	C₂	1	2	yes	maximal, complemented
20	C₃×#2449	C₂	1	2	yes	maximal, complemented
21	C₃×#2422	C₂	1	2	yes	maximal, complemented
22	C₃×#2397	C₂	1	1	yes	maximal, characteristic, complemented
23	C₃×#2343	C₂	1	1	yes	maximal, characteristic, complemented
24	#41959	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
25	C₃×#553	—	2	8	no	—
26	C₃×#542	—	2	8	no	—
27	C₂×C₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
28	C₂×C₃×#126	C₂²	1	1	yes	characteristic
29	C₂×C₃×#126	C₂²	1	2	yes	—
30	C₂×C₃×#126	C₂²	1	1	yes	characteristic
31	C₂×C₃×#125	C₂²	1	1	yes	characteristic
32	C₂×C₃×#124	C₂²	1	1	yes	characteristic
33	C₂×C₃×#124	C₂²	1	2	yes	—
34	C₂×C₃×#123	C₂²	1	2	yes	—
35	C₂×C₃×#123	C₂²	1	1	yes	characteristic
36	C₂×C₃×#123	C₂²	1	1	yes	characteristic
37	C₂×C₃×C₂²⋊Q₈	C₂²	1	2	yes	—
38	C₂×C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
39	C₂×C₃×C₂²⋊Q₈	C₂²	1	2	yes	—
40	C₂×C₃×C₂²⋊Q₈	C₂²	1	2	yes	—
41	C₂×C₃×#121	C₂²	1	1	yes	characteristic
42	C₂×C₃×#121	C₂²	1	1	yes	characteristic
43	C₂×C₃×#121	C₂²	1	1	yes	characteristic
44	C₂×C₃×#121	C₂²	1	1	yes	characteristic
45	C₂×C₃×#121	C₂²	1	1	yes	characteristic
46	C₂×C₃×#121	C₂²	1	2	yes	—
47	C₂×C₃×#121	C₂²	1	2	yes	—
48	C₂×C₃×C₄×Q₈	C₂²	1	1	yes	characteristic
49	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
50	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
51	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
52	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
53	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
54	C₂×C₃×C₄×D₄	C₂²	1	2	yes	—
55	C₂×C₃×C₄×D₄	C₂²	1	2	yes	—
56	C₂×C₃×#117	C₂²	1	1	yes	characteristic
57	C₂²×C₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
58	C₃×#400	C₂²	1	1	yes	characteristic
59	C₃×#400	C₂²	1	1	yes	characteristic
60	C₃×#399	C₂²	1	1	yes	characteristic
61	C₃×#399	C₂²	1	1	yes	characteristic
62	C₃×#399	C₂²	1	2	yes	—
63	C₃×#399	C₂²	1	1	yes	characteristic
64	C₃×#399	C₂²	1	1	yes	characteristic
65	C₃×#399	C₂²	1	2	yes	—
66	C₃×#399	C₂²	1	1	yes	characteristic
67	C₃×#399	C₂²	1	1	yes	characteristic
68	C₃×#398	C₂²	1	2	yes	—
69	C₃×#398	C₂²	1	2	yes	—
70	C₃×#397	C₂²	1	2	yes	—
71	C₃×#397	C₂²	1	2	yes	—
72	C₃×#396	C₂²	1	2	yes	—
73	C₃×#396	C₂²	1	2	yes	—
74	C₃×#395	C₂²	1	1	yes	characteristic
75	C₃×#395	C₂²	1	2	yes	—
76	C₃×#394	C₂²	1	1	yes	characteristic
77	C₃×#394	C₂²	1	2	yes	—
78	C₃×#394	C₂²	1	2	yes	—
79	C₃×#394	C₂²	1	2	yes	—
80	C₃×#394	C₂²	1	2	yes	—
81	C₃×#394	C₂²	1	2	yes	—
82	C₃×#394	C₂²	1	2	yes	—
83	C₃×#393	C₂²	1	1	yes	characteristic
84	C₃×#393	C₂²	1	1	yes	characteristic
85	C₃×#393	C₂²	1	1	yes	characteristic
86	C₃×#393	C₂²	1	2	yes	—
87	C₃×#392	C₂²	1	1	yes	characteristic
88	C₃×#392	C₂²	1	1	yes	characteristic
89	C₃×#392	C₂²	1	2	yes	—
90	C₃×#392	C₂²	1	2	yes	—
91	C₃×#392	C₂²	1	1	yes	characteristic
92	C₃×#392	C₂²	1	2	yes	—
93	C₃×#392	C₂²	1	2	yes	—
94	C₃×#390	C₂²	1	2	yes	—
95	C₃×#390	C₂²	1	2	yes	—
96	C₃×#390	C₂²	1	2	yes	—
97	C₃×#389	C₂²	1	2	yes	—
98	C₃×#389	C₂²	1	2	yes	—
99	C₃×#388	C₂²	1	2	yes	—
100	C₃×#388	C₂²	1	2	yes	—
101	C₃×#388	C₂²	1	2	yes	—
102	C₃×#388	C₂²	1	2	yes	—
103	C₃×#387	C₂²	1	2	yes	—
104	C₃×#387	C₂²	1	2	yes	—
105	C₃×#387	C₂²	1	2	yes	—
106	C₃×#387	C₂²	1	2	yes	—
107	C₃×#386	C₂²	1	2	yes	—
108	C₃×#386	C₂²	1	2	yes	—
109	C₃×#386	C₂²	1	2	yes	—
110	C₃×#386	C₂²	1	2	yes	—
111	C₃×#386	C₂²	1	2	yes	—
112	C₃×#385	C₂²	1	2	yes	—
113	C₃×#385	C₂²	1	2	yes	—
114	C₃×#385	C₂²	1	2	yes	—
115	C₃×#385	C₂²	1	2	yes	—
116	C₃×#385	C₂²	1	2	yes	—
117	C₃×#384	C₂²	1	2	yes	—
118	C₃×#383	C₂²	1	1	yes	characteristic
119	C₃×#382	C₂²	1	1	yes	characteristic
120	C₃×#381	C₂²	1	1	yes	characteristic
121	C₃×#380	C₂²	1	2	yes	—
122	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
123	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	—
124	C₃×#376	C₂²	1	1	yes	characteristic
125	C₂×C₃×#95	C₂²	1	1	yes	characteristic
126	C₂×#553	C₂×C₃	1	1	yes	characteristic, complemented
127	C₂×#542	C₂×C₃	1	1	yes	characteristic, complemented
128	#2821	C₂×C₃	1	1	yes	characteristic, complemented
129	#2816	C₂×C₃	1	1	yes	characteristic, complemented
130	#2721	C₂×C₃	1	2	yes	complemented
131	#2714	C₂×C₃	1	2	yes	complemented
132	#2676	C₂×C₃	1	2	yes	complemented
133	#2672	C₂×C₃	1	2	yes	complemented
134	#2662	C₂×C₃	1	1	yes	characteristic, complemented
135	#2656	C₂×C₃	1	1	yes	characteristic, complemented
136	#2636	C₂×C₃	1	1	yes	characteristic, complemented
137	#2635	C₂×C₃	1	1	yes	characteristic, complemented
138	#2631	C₂×C₃	1	1	yes	characteristic, complemented
139	#2604	C₂×C₃	1	1	yes	characteristic, complemented
140	#2580	C₂×C₃	1	1	yes	characteristic, complemented
141	#2564	C₂×C₃	1	1	yes	characteristic, complemented
142	#2542	C₂×C₃	1	1	yes	characteristic, complemented
143	#2464	C₂×C₃	1	2	yes	complemented
144	#2463	C₂×C₃	1	2	yes	complemented
145	#2449	C₂×C₃	1	2	yes	complemented
146	#2422	C₂×C₃	1	2	yes	complemented
147	#2397	C₂×C₃	1	1	yes	characteristic, complemented
148	#2343	C₂×C₃	1	1	yes	characteristic, complemented
149	C₂²×C₃×Q₈	C₂³	1	1	yes	characteristic
150	C₂²×C₃×Q₈	C₂³	1	2	yes	—
151	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
152	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
153	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
154	C₂²×C₃×D₄	C₂³	1	2	yes	—
155	C₂²×C₃×D₄	C₂³	1	2	yes	—
156	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
157	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
158	C₂²×C₃×D₄	C₂³	1	2	yes	—
159	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
160	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
161	C₂²×C₃×D₄	C₂³	1	2	yes	—
162	C₂³×C₃×C₄	C₂³	1	2	yes	—
163	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
164	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
165	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
166	C₂³×C₃×C₄	C₂³	1	2	yes	—
167	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
168	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
169	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
170	C₃×C₄⋊Q₈	—	2	4	no	—
171	C₃×#126	—	2	8	no	—
172	C₃×#126	—	2	4	no	—
173	C₃×#126	—	2	4	no	—
174	C₃×#125	—	2	4	no	—
175	C₃×#124	—	2	8	no	—
176	C₃×#124	—	2	4	no	—
177	C₃×#123	—	2	8	no	—
178	C₃×#123	—	2	4	no	—
179	C₃×#123	—	2	4	no	—
180	C₃×C₂²⋊Q₈	—	2	4	no	—
181	C₃×C₂²⋊Q₈	—	2	8	no	—
182	C₃×C₂²⋊Q₈	—	4	4	no	—
183	C₃×C₂²⋊Q₈	—	4	4	no	—
184	C₃×#121	—	2	4	no	—
185	C₃×#121	—	2	4	no	—
186	C₃×#121	—	2	4	no	—
187	C₃×#121	—	2	4	no	—
188	C₃×#121	—	2	4	no	—
189	C₃×#121	—	4	4	no	—
190	C₃×#121	—	4	4	no	—
191	C₃×C₄×Q₈	—	2	4	no	—
192	C₃×C₄×D₄	—	2	4	no	—
193	C₃×C₄×D₄	—	2	4	no	—
194	C₃×C₄×D₄	—	2	4	no	—
195	C₃×C₄×D₄	—	2	4	no	—
196	C₃×C₄×D₄	—	2	4	no	—
197	C₃×C₄×D₄	—	4	4	no	—
198	C₃×C₄×D₄	—	4	4	no	—
199	C₃×#117	D₄	1	8	yes	complemented
200	C₂×C₃×C₄⋊C₄	—	2	4	no	—
201	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
202	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
203	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
204	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
205	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
206	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
207	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
208	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
209	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
210	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
211	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
212	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
213	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
214	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
215	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
216	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
217	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
218	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
219	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
220	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
221	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
222	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
223	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
224	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
225	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
226	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
227	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
228	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
229	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
230	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
231	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
232	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
233	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
234	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
235	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
236	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
237	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
238	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
239	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
240	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
241	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
242	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
243	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
244	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
245	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
246	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
247	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
248	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
249	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
250	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
251	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
252	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
253	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
254	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
255	C₂×C₃×C₄²	C₂³	1	2	yes	—
256	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
257	C₂×C₃×C₄²	C₂³	1	2	yes	—
258	C₂×C₃×C₄²	C₂³	1	2	yes	—
259	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
260	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
261	C₃×#95	C₂³	1	1	yes	characteristic
262	C₃×#95	C₂³	1	1	yes	characteristic
263	C₃×#95	C₂³	1	2	yes	—
264	C₃×#95	C₂³	1	1	yes	characteristic
265	C₃×#95	C₂³	1	2	yes	—
266	C₃×#95	C₂³	1	2	yes	—
267	C₃×#95	C₂³	1	2	yes	—
268	C₃×#95	C₂³	1	1	yes	characteristic
269	C₃×#95	C₂³	1	2	yes	—
270	C₃×#95	C₂³	1	2	yes	—
271	C₃×#95	C₂³	1	2	yes	—
272	C₃×#95	C₂³	1	2	yes	—
273	C₃×#95	C₂³	1	2	yes	—
274	C₃×#95	C₂³	1	2	yes	—
275	C₃×#95	C₂³	1	2	yes	—
276	C₃×#95	C₂³	1	2	yes	—
277	C₃×#95	C₂³	1	2	yes	—
278	C₃×#95	C₂³	1	2	yes	—
279	#553	—	2	8	no	—
280	#542	—	2	8	no	—
281	C₂×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
282	C₂×#126	C₂²×C₃	1	1	yes	characteristic
283	C₂×#126	C₂²×C₃	1	1	yes	characteristic
284	C₂×#126	C₂²×C₃	1	2	yes	—
285	C₂×#125	C₂²×C₃	1	1	yes	characteristic
286	C₂×#124	C₂²×C₃	1	1	yes	characteristic
287	C₂×#124	C₂²×C₃	1	2	yes	—
288	C₂×#123	C₂²×C₃	1	1	yes	characteristic
289	C₂×#123	C₂²×C₃	1	1	yes	characteristic
290	C₂×#123	C₂²×C₃	1	2	yes	—
291	C₂×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
292	C₂×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
293	C₂×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
294	C₂×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
295	C₂×#121	C₂²×C₃	1	1	yes	characteristic
296	C₂×#121	C₂²×C₃	1	1	yes	characteristic
297	C₂×#121	C₂²×C₃	1	1	yes	characteristic
298	C₂×#121	C₂²×C₃	1	1	yes	characteristic
299	C₂×#121	C₂²×C₃	1	1	yes	characteristic
300	C₂×#121	C₂²×C₃	1	2	yes	—
301	C₂×#121	C₂²×C₃	1	2	yes	—
302	C₂×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic
303	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
304	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
305	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
306	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
307	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
308	C₂×C₄×D₄	C₂²×C₃	1	2	yes	—
309	C₂×C₄×D₄	C₂²×C₃	1	2	yes	—
310	C₂×#117	C₂²×C₃	1	1	yes	characteristic
311	C₂²×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
312	#400	C₂²×C₃	1	1	yes	characteristic
313	#400	C₂²×C₃	1	1	yes	characteristic
314	#399	C₂²×C₃	1	1	yes	characteristic
315	#399	C₂²×C₃	1	1	yes	characteristic
316	#399	C₂²×C₃	1	1	yes	characteristic
317	#399	C₂²×C₃	1	1	yes	characteristic
318	#399	C₂²×C₃	1	1	yes	characteristic
319	#399	C₂²×C₃	1	1	yes	characteristic
320	#399	C₂²×C₃	1	2	yes	—
321	#399	C₂²×C₃	1	2	yes	—
322	#398	C₂²×C₃	1	2	yes	—
323	#398	C₂²×C₃	1	2	yes	—
324	#397	C₂²×C₃	1	2	yes	—
325	#397	C₂²×C₃	1	2	yes	—
326	#396	C₂²×C₃	1	2	yes	—
327	#396	C₂²×C₃	1	2	yes	—
328	#395	C₂²×C₃	1	1	yes	characteristic
329	#395	C₂²×C₃	1	2	yes	—
330	#394	C₂²×C₃	1	2	yes	—
331	#394	C₂²×C₃	1	2	yes	—
332	#394	C₂²×C₃	1	2	yes	—
333	#394	C₂²×C₃	1	1	yes	characteristic
334	#394	C₂²×C₃	1	2	yes	—
335	#394	C₂²×C₃	1	2	yes	—
336	#394	C₂²×C₃	1	2	yes	—
337	#393	C₂²×C₃	1	1	yes	characteristic
338	#393	C₂²×C₃	1	1	yes	characteristic
339	#393	C₂²×C₃	1	1	yes	characteristic
340	#393	C₂²×C₃	1	2	yes	—
341	#392	C₂²×C₃	1	1	yes	characteristic
342	#392	C₂²×C₃	1	1	yes	characteristic
343	#392	C₂²×C₃	1	2	yes	—
344	#392	C₂²×C₃	1	2	yes	—
345	#392	C₂²×C₃	1	1	yes	characteristic
346	#392	C₂²×C₃	1	2	yes	—
347	#392	C₂²×C₃	1	2	yes	—
348	#390	C₂²×C₃	1	2	yes	—
349	#390	C₂²×C₃	1	2	yes	—
350	#390	C₂²×C₃	1	2	yes	—
351	#389	C₂²×C₃	1	2	yes	—
352	#389	C₂²×C₃	1	2	yes	—
353	#388	C₂²×C₃	1	2	yes	—
354	#388	C₂²×C₃	1	2	yes	—
355	#388	C₂²×C₃	1	2	yes	—
356	#388	C₂²×C₃	1	2	yes	—
357	#387	C₂²×C₃	1	2	yes	—
358	#387	C₂²×C₃	1	2	yes	—
359	#387	C₂²×C₃	1	2	yes	—
360	#387	C₂²×C₃	1	2	yes	—
361	#386	C₂²×C₃	1	2	yes	—
362	#386	C₂²×C₃	1	2	yes	—
363	#386	C₂²×C₃	1	2	yes	—
364	#386	C₂²×C₃	1	2	yes	—
365	#386	C₂²×C₃	1	2	yes	—
366	#385	C₂²×C₃	1	2	yes	—
367	#385	C₂²×C₃	1	2	yes	—
368	#385	C₂²×C₃	1	2	yes	—
369	#385	C₂²×C₃	1	2	yes	—
370	#385	C₂²×C₃	1	2	yes	—
371	#384	C₂²×C₃	1	2	yes	—
372	#383	C₂²×C₃	1	1	yes	characteristic
373	#382	C₂²×C₃	1	1	yes	characteristic
374	#381	C₂²×C₃	1	1	yes	characteristic
375	#380	C₂²×C₃	1	2	yes	—
376	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
377	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
378	#376	C₂²×C₃	1	1	yes	characteristic
379	C₂×#95	C₂²×C₃	1	1	yes	characteristic
380	C₂⁴×C₃	C₂⁴	1	2	yes	—
381	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
382	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
383	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
384	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
385	C₂×C₃×Q₈	—	2	2	no	—
386	C₂×C₃×Q₈	—	2	4	no	—
387	C₂×C₃×Q₈	—	4	2	no	—
388	C₂×C₃×Q₈	—	4	2	no	—
389	C₂×C₃×Q₈	—	4	2	no	—
390	C₂×C₃×D₄	—	2	2	no	—
391	C₂×C₃×D₄	—	2	2	no	—
392	C₂×C₃×D₄	—	2	2	no	—
393	C₂×C₃×D₄	—	2	2	no	—
394	C₂×C₃×D₄	—	2	4	no	—
395	C₂×C₃×D₄	—	2	2	no	—
396	C₂×C₃×D₄	—	2	2	no	—
397	C₂×C₃×D₄	—	2	4	no	—
398	C₂×C₃×D₄	—	2	2	no	—
399	C₂×C₃×D₄	—	2	2	no	—
400	C₂×C₃×D₄	—	2	2	no	—
401	C₂×C₃×D₄	—	2	2	no	—
402	C₂×C₃×D₄	—	2	4	no	—
403	C₂×C₃×D₄	—	4	2	no	—
404	C₂×C₃×D₄	—	4	1	no	—
405	C₂×C₃×D₄	—	4	2	no	—
406	C₂×C₃×D₄	—	4	1	no	—
407	C₂×C₃×D₄	—	4	2	no	—
408	C₂×C₃×D₄	—	4	2	no	—
409	C₂×C₃×D₄	—	4	2	no	—
410	C₂×C₃×D₄	—	4	1	no	—
411	C₂×C₃×D₄	—	4	2	no	—
412	C₂×C₃×D₄	—	4	2	no	—
413	C₂×C₃×D₄	—	4	2	no	—
414	C₂×C₃×D₄	—	4	2	no	—
415	C₂×C₃×D₄	—	4	2	no	—
416	C₂×C₃×D₄	—	4	2	no	—
417	C₂×C₃×D₄	—	4	2	no	—
418	C₂×C₃×D₄	—	4	2	no	—
419	C₂²×C₃×C₄	—	2	2	no	—
420	C₂²×C₃×C₄	—	2	2	no	—
421	C₂²×C₃×C₄	—	2	2	no	—
422	C₂²×C₃×C₄	—	2	2	no	—
423	C₂²×C₃×C₄	—	2	2	no	—
424	C₂²×C₃×C₄	—	2	4	no	—
425	C₂²×C₃×C₄	—	2	4	no	—
426	C₂²×C₃×C₄	—	4	2	no	—
427	C₂²×C₃×C₄	—	4	2	no	—
428	C₂²×C₃×C₄	—	4	2	no	—
429	C₂²×C₃×C₄	—	4	2	no	—
430	C₂²×C₃×C₄	—	4	2	no	—
431	C₂²×C₃×C₄	—	4	2	no	—
432	C₂²×C₃×C₄	—	4	2	no	—
433	C₂²×C₃×C₄	—	4	2	no	—
434	C₂²×C₃×C₄	—	4	2	no	—
435	C₂²×C₃×C₄	—	4	2	no	—
436	C₂²×C₃×C₄	C₂×D₄	1	4	yes	—
437	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
438	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
439	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
440	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
441	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
442	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
443	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
444	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
445	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
446	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
447	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
448	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
449	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
450	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
451	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
452	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
453	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
454	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
455	C₃×C₄⋊C₄	—	2	2	no	—
456	C₃×C₄⋊C₄	—	2	2	no	—
457	C₃×C₄⋊C₄	—	2	2	no	—
458	C₃×C₄⋊C₄	—	2	2	no	—
459	C₃×C₄⋊C₄	—	2	2	no	—
460	C₃×C₄⋊C₄	—	2	2	no	—
461	C₃×C₄⋊C₄	—	2	2	no	—
462	C₃×C₄⋊C₄	—	2	2	no	—
463	C₃×C₄⋊C₄	—	2	4	no	—
464	C₃×C₄⋊C₄	—	2	2	no	—
465	C₃×C₄⋊C₄	—	2	2	no	—
466	C₃×C₄⋊C₄	—	2	4	no	—
467	C₃×C₄⋊C₄	—	2	4	no	—
468	C₃×C₄⋊C₄	—	2	4	no	—
469	C₃×C₄⋊C₄	—	2	4	no	—
470	C₃×C₄⋊C₄	—	2	4	no	—
471	C₃×C₄⋊C₄	—	4	2	no	—
472	C₃×C₄⋊C₄	—	4	2	no	—
473	C₃×C₄⋊C₄	—	4	2	no	—
474	C₃×C₄⋊C₄	—	4	2	no	—
475	C₃×C₄⋊C₄	—	4	2	no	—
476	C₃×C₄⋊C₄	—	4	2	no	—
477	C₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
478	C₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
479	C₃×C₂²⋊C₄	—	2	2	no	—
480	C₃×C₂²⋊C₄	—	2	4	no	—
481	C₃×C₂²⋊C₄	—	2	2	no	—
482	C₃×C₂²⋊C₄	—	2	2	no	—
483	C₃×C₂²⋊C₄	—	2	2	no	—
484	C₃×C₂²⋊C₄	—	2	2	no	—
485	C₃×C₂²⋊C₄	—	2	2	no	—
486	C₃×C₂²⋊C₄	—	2	4	no	—
487	C₃×C₂²⋊C₄	—	2	4	no	—
488	C₃×C₂²⋊C₄	—	2	2	no	—
489	C₃×C₂²⋊C₄	—	2	2	no	—
490	C₃×C₂²⋊C₄	—	2	4	no	—
491	C₃×C₂²⋊C₄	—	2	4	no	—
492	C₃×C₂²⋊C₄	—	2	4	no	—
493	C₃×C₂²⋊C₄	—	2	4	no	—
494	C₃×C₂²⋊C₄	—	2	4	no	—
495	C₃×C₂²⋊C₄	—	4	2	no	—
496	C₃×C₂²⋊C₄	—	4	2	no	—
497	C₃×C₂²⋊C₄	—	4	2	no	—
498	C₃×C₂²⋊C₄	—	4	2	no	—
499	C₃×C₂²⋊C₄	—	4	2	no	—
500	C₃×C₂²⋊C₄	—	4	2	no	—
501	C₃×C₂²⋊C₄	—	4	2	no	—
502	C₃×C₂²⋊C₄	—	4	2	no	—
503	C₃×C₂²⋊C₄	—	4	2	no	—
504	C₃×C₂²⋊C₄	—	4	2	no	—
505	C₃×C₂²⋊C₄	—	4	2	no	—
506	C₃×C₂²⋊C₄	—	4	2	no	—
507	C₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
508	C₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
509	C₃×C₄²	—	2	2	no	—
510	C₃×C₄²	—	2	4	no	—
511	C₃×C₄²	—	2	4	no	—
512	C₃×C₄²	—	4	2	no	—
513	C₃×C₄²	C₂×D₄	1	4	yes	—
514	C₃×C₄²	C₂×D₄	1	4	yes	—
515	C₂²×Q₈	C₂³×C₃	1	1	yes	characteristic
516	C₂²×Q₈	C₂³×C₃	1	2	yes	—
517	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
518	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
519	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
520	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
521	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
522	C₂²×D₄	C₂³×C₃	1	2	yes	—
523	C₂²×D₄	C₂³×C₃	1	2	yes	—
524	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
525	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
526	C₂²×D₄	C₂³×C₃	1	2	yes	—
527	C₂²×D₄	C₂³×C₃	1	2	yes	—
528	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
529	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
530	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
531	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
532	C₂³×C₄	C₂³×C₃	1	2	yes	—
533	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
534	C₂³×C₄	C₂³×C₃	1	2	yes	—
535	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
536	C₄⋊Q₈	—	2	4	no	—
537	#126	—	2	8	no	—
538	#126	—	2	4	no	—
539	#126	—	2	4	no	—
540	#125	—	2	4	no	—
541	#124	—	2	8	no	—
542	#124	—	2	4	no	—
543	#123	—	2	8	no	—
544	#123	—	2	4	no	—
545	#123	—	2	4	no	—
546	C₂²⋊Q₈	—	2	4	no	—
547	C₂²⋊Q₈	—	2	8	no	—
548	C₂²⋊Q₈	—	4	4	no	—
549	C₂²⋊Q₈	—	4	4	no	—
550	#121	—	2	4	no	—
551	#121	—	2	4	no	—
552	#121	—	2	4	no	—
553	#121	—	2	4	no	—
554	#121	—	2	4	no	—
555	#121	—	4	4	no	—
556	#121	—	4	4	no	—
557	C₄×Q₈	—	2	4	no	—
558	C₄×D₄	—	2	4	no	—
559	C₄×D₄	—	2	4	no	—
560	C₄×D₄	—	2	4	no	—
561	C₄×D₄	—	2	4	no	—
562	C₄×D₄	—	2	4	no	—
563	C₄×D₄	—	4	4	no	—
564	C₄×D₄	—	4	4	no	—
565	#117	C₃×D₄	1	8	yes	complemented
566	C₂×C₄⋊C₄	—	2	4	no	—
567	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
568	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
569	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
570	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
571	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
572	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
573	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
574	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
575	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
576	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
577	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
578	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
579	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
580	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
581	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
582	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
583	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
584	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
585	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
586	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
587	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
588	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
589	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
590	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
591	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
592	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
593	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
594	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
595	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
596	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
597	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
598	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
599	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
600	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
601	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
602	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
603	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
604	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
605	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
606	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
607	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
608	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
609	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
610	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
611	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
612	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
613	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
614	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
615	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
616	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
617	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
618	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
619	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
620	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
621	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
622	C₂×C₄²	C₂³×C₃	1	2	yes	—
623	C₂×C₄²	C₂³×C₃	1	2	yes	—
624	C₂×C₄²	C₂³×C₃	1	2	yes	—
625	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
626	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
627	#95	C₂³×C₃	1	1	yes	characteristic
628	#95	C₂³×C₃	1	1	yes	characteristic
629	#95	C₂³×C₃	1	2	yes	—
630	#95	C₂³×C₃	1	1	yes	characteristic
631	#95	C₂³×C₃	1	2	yes	—
632	#95	C₂³×C₃	1	2	yes	—
633	#95	C₂³×C₃	1	2	yes	—
634	#95	C₂³×C₃	1	1	yes	characteristic
635	#95	C₂³×C₃	1	2	yes	—
636	#95	C₂³×C₃	1	2	yes	—
637	#95	C₂³×C₃	1	2	yes	—
638	#95	C₂³×C₃	1	2	yes	—
639	#95	C₂³×C₃	1	2	yes	—
640	#95	C₂³×C₃	1	2	yes	—
641	#95	C₂³×C₃	1	2	yes	—
642	#95	C₂³×C₃	1	2	yes	—
643	#95	C₂³×C₃	1	2	yes	—
644	#95	C₂³×C₃	1	2	yes	—
645	C₂³×C₃	—	2	1	no	—
646	C₂³×C₃	—	2	2	no	—
647	C₂³×C₃	—	2	2	no	—
648	C₂³×C₃	—	2	1	no	—
649	C₂³×C₃	—	2	2	no	—
650	C₂³×C₃	—	2	2	no	—
651	C₂³×C₃	—	2	1	no	—
652	C₂³×C₃	—	2	1	no	—
653	C₂³×C₃	—	2	2	no	—
654	C₂³×C₃	—	2	1	no	—
655	C₂³×C₃	—	2	1	no	—
656	C₂³×C₃	—	2	2	no	—
657	C₂³×C₃	—	2	2	no	—
658	C₂³×C₃	—	2	2	no	—
659	C₂³×C₃	—	2	2	no	—
660	C₂³×C₃	—	2	1	no	—
661	C₂³×C₃	—	2	1	no	—
662	C₂³×C₃	—	2	2	no	—
663	C₂³×C₃	—	2	2	no	—
664	C₂³×C₃	—	2	2	no	—
665	C₂³×C₃	—	2	2	no	—
666	C₂³×C₃	—	2	2	no	—
667	C₂³×C₃	—	2	2	no	—
668	C₂³×C₃	—	2	1	no	—
669	C₂³×C₃	—	2	1	no	—
670	C₂³×C₃	C₂²×D₄	1	2	yes	—
671	C₂³×C₃	2₋¹⁺⁴	1	2	yes	—
672	C₂³×C₃	C₂⁵	1	1	yes	characteristic
673	C₃×Q₈	—	4	4	no	—
674	C₃×Q₈	—	8	4	no	—
675	C₃×D₄	—	4	4	no	—
676	C₃×D₄	—	4	4	no	—
677	C₃×D₄	—	4	4	no	—
678	C₃×D₄	—	4	4	no	—
679	C₃×D₄	—	4	8	no	—
680	C₃×D₄	—	4	4	no	—
681	C₃×D₄	—	4	8	no	—
682	C₃×D₄	—	8	2	no	—
683	C₃×D₄	—	8	2	no	—
684	C₃×D₄	—	8	4	no	—
685	C₃×D₄	—	8	4	no	—
686	C₂×C₃×C₄	—	2	2	no	—
687	C₂×C₃×C₄	—	2	2	no	—
688	C₂×C₃×C₄	—	2	1	no	—
689	C₂×C₃×C₄	—	2	1	no	—
690	C₂×C₃×C₄	—	2	1	no	—
691	C₂×C₃×C₄	—	2	2	no	—
692	C₂×C₃×C₄	—	2	1	no	—
693	C₂×C₃×C₄	—	2	2	no	—
694	C₂×C₃×C₄	—	2	2	no	—
695	C₂×C₃×C₄	—	2	2	no	—
696	C₂×C₃×C₄	—	2	2	no	—
697	C₂×C₃×C₄	—	2	1	no	—
698	C₂×C₃×C₄	—	2	1	no	—
699	C₂×C₃×C₄	—	2	2	no	—
700	C₂×C₃×C₄	—	2	1	no	—
701	C₂×C₃×C₄	—	2	2	no	—
702	C₂×C₃×C₄	—	2	1	no	—
703	C₂×C₃×C₄	—	2	1	no	—
704	C₂×C₃×C₄	—	2	2	no	—
705	C₂×C₃×C₄	—	2	2	no	—
706	C₂×C₃×C₄	—	2	2	no	—
707	C₂×C₃×C₄	—	2	2	no	—
708	C₂×C₃×C₄	—	2	2	no	—
709	C₂×C₃×C₄	—	2	2	no	—
710	C₂×C₃×C₄	—	2	2	no	—
711	C₂×C₃×C₄	—	2	2	no	—
712	C₂×C₃×C₄	—	2	2	no	—
713	C₂×C₃×C₄	—	2	2	no	—
714	C₂×C₃×C₄	—	2	1	no	—
715	C₂×C₃×C₄	—	2	2	no	—
716	C₂×C₃×C₄	—	2	2	no	—
717	C₂×C₃×C₄	—	2	2	no	—
718	C₂×C₃×C₄	—	2	1	no	—
719	C₂×C₃×C₄	—	2	2	no	—
720	C₂×C₃×C₄	—	2	2	no	—
721	C₂×C₃×C₄	—	2	2	no	—
722	C₂×C₃×C₄	—	2	2	no	—
723	C₂×C₃×C₄	—	2	2	no	—
724	C₂×C₃×C₄	—	2	2	no	—
725	C₂×C₃×C₄	—	4	4	no	—
726	C₂×C₃×C₄	—	4	4	no	—
727	C₂×C₃×C₄	—	8	2	no	—
728	C₂×C₃×C₄	—	8	2	no	—
729	C₂×C₃×C₄	—	8	4	no	—
730	C₂×C₃×C₄	—	8	2	no	—
731	C₂×C₃×C₄	—	8	2	no	—
732	C₂×C₃×C₄	—	8	4	no	—
733	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
734	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
735	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
736	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
737	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
738	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
739	C₂×C₃×C₄	H(5,𝔽₂)	1	4	yes	—
740	C₂⁴	C₂⁴×C₃	1	2	yes	—
741	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
742	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
743	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
744	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
745	C₂×Q₈	—	2	2	no	—
746	C₂×Q₈	—	2	4	no	—
747	C₂×Q₈	—	4	2	no	—
748	C₂×Q₈	—	4	2	no	—
749	C₂×Q₈	—	4	2	no	—
750	C₂×D₄	—	2	2	no	—
751	C₂×D₄	—	2	2	no	—
752	C₂×D₄	—	2	2	no	—
753	C₂×D₄	—	2	2	no	—
754	C₂×D₄	—	2	4	no	—
755	C₂×D₄	—	2	2	no	—
756	C₂×D₄	—	2	2	no	—
757	C₂×D₄	—	2	4	no	—
758	C₂×D₄	—	2	2	no	—
759	C₂×D₄	—	2	2	no	—
760	C₂×D₄	—	2	2	no	—
761	C₂×D₄	—	2	2	no	—
762	C₂×D₄	—	2	4	no	—
763	C₂×D₄	—	4	2	no	—
764	C₂×D₄	—	4	1	no	—
765	C₂×D₄	—	4	2	no	—
766	C₂×D₄	—	4	1	no	—
767	C₂×D₄	—	4	2	no	—
768	C₂×D₄	—	4	2	no	—
769	C₂×D₄	—	4	2	no	—
770	C₂×D₄	—	4	1	no	—
771	C₂×D₄	—	4	2	no	—
772	C₂×D₄	—	4	2	no	—
773	C₂×D₄	—	4	2	no	—
774	C₂×D₄	—	4	2	no	—
775	C₂×D₄	—	4	2	no	—
776	C₂×D₄	—	4	2	no	—
777	C₂×D₄	—	4	2	no	—
778	C₂×D₄	—	4	2	no	—
779	C₂²×C₄	—	2	2	no	—
780	C₂²×C₄	—	2	2	no	—
781	C₂²×C₄	—	2	2	no	—
782	C₂²×C₄	—	2	2	no	—
783	C₂²×C₄	—	2	2	no	—
784	C₂²×C₄	—	2	4	no	—
785	C₂²×C₄	—	2	4	no	—
786	C₂²×C₄	—	4	2	no	—
787	C₂²×C₄	—	4	2	no	—
788	C₂²×C₄	—	4	2	no	—
789	C₂²×C₄	—	4	2	no	—
790	C₂²×C₄	—	4	2	no	—
791	C₂²×C₄	—	4	2	no	—
792	C₂²×C₄	—	4	2	no	—
793	C₂²×C₄	—	4	2	no	—
794	C₂²×C₄	—	4	2	no	—
795	C₂²×C₄	—	4	2	no	—
796	C₂²×C₄	C₂×C₃×D₄	1	4	yes	—
797	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
798	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
799	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
800	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
801	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
802	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
803	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
804	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
805	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
806	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
807	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
808	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
809	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
810	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
811	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
812	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
813	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
814	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
815	C₄⋊C₄	—	2	2	no	—
816	C₄⋊C₄	—	2	2	no	—
817	C₄⋊C₄	—	2	2	no	—
818	C₄⋊C₄	—	2	2	no	—
819	C₄⋊C₄	—	2	2	no	—
820	C₄⋊C₄	—	2	2	no	—
821	C₄⋊C₄	—	2	2	no	—
822	C₄⋊C₄	—	2	2	no	—
823	C₄⋊C₄	—	2	4	no	—
824	C₄⋊C₄	—	2	2	no	—
825	C₄⋊C₄	—	2	2	no	—
826	C₄⋊C₄	—	2	4	no	—
827	C₄⋊C₄	—	2	4	no	—
828	C₄⋊C₄	—	2	4	no	—
829	C₄⋊C₄	—	2	4	no	—
830	C₄⋊C₄	—	2	4	no	—
831	C₄⋊C₄	—	4	2	no	—
832	C₄⋊C₄	—	4	2	no	—
833	C₄⋊C₄	—	4	2	no	—
834	C₄⋊C₄	—	4	2	no	—
835	C₄⋊C₄	—	4	2	no	—
836	C₄⋊C₄	—	4	2	no	—
837	C₄⋊C₄	C₂×C₃×D₄	1	4	yes	—
838	C₄⋊C₄	C₂×C₃×D₄	1	4	yes	—
839	C₂²⋊C₄	—	2	2	no	—
840	C₂²⋊C₄	—	2	4	no	—
841	C₂²⋊C₄	—	2	2	no	—
842	C₂²⋊C₄	—	2	2	no	—
843	C₂²⋊C₄	—	2	2	no	—
844	C₂²⋊C₄	—	2	2	no	—
845	C₂²⋊C₄	—	2	2	no	—
846	C₂²⋊C₄	—	2	4	no	—
847	C₂²⋊C₄	—	2	4	no	—
848	C₂²⋊C₄	—	2	2	no	—
849	C₂²⋊C₄	—	2	2	no	—
850	C₂²⋊C₄	—	2	4	no	—
851	C₂²⋊C₄	—	2	4	no	—
852	C₂²⋊C₄	—	2	4	no	—
853	C₂²⋊C₄	—	2	4	no	—
854	C₂²⋊C₄	—	2	4	no	—
855	C₂²⋊C₄	—	4	2	no	—
856	C₂²⋊C₄	—	4	2	no	—
857	C₂²⋊C₄	—	4	2	no	—
858	C₂²⋊C₄	—	4	2	no	—
859	C₂²⋊C₄	—	4	2	no	—
860	C₂²⋊C₄	—	4	2	no	—
861	C₂²⋊C₄	—	4	2	no	—
862	C₂²⋊C₄	—	4	2	no	—
863	C₂²⋊C₄	—	4	2	no	—
864	C₂²⋊C₄	—	4	2	no	—
865	C₂²⋊C₄	—	4	2	no	—
866	C₂²⋊C₄	—	4	2	no	—
867	C₂²⋊C₄	C₂×C₃×D₄	1	4	yes	—
868	C₂²⋊C₄	C₂×C₃×D₄	1	4	yes	—
869	C₄²	—	2	2	no	—
870	C₄²	—	2	4	no	—
871	C₄²	—	2	4	no	—
872	C₄²	—	4	2	no	—
873	C₄²	C₂×C₃×D₄	1	4	yes	—
874	C₄²	C₂×C₃×D₄	1	4	yes	—
875	C₂²×C₃	—	2	2	no	—
876	C₂²×C₃	—	2	2	no	—
877	C₂²×C₃	—	2	2	no	—
878	C₂²×C₃	—	2	2	no	—
879	C₂²×C₃	—	2	4	no	—
880	C₂²×C₃	—	4	1	no	—
881	C₂²×C₃	—	4	1	no	—
882	C₂²×C₃	—	4	2	no	—
883	C₂²×C₃	—	4	2	no	—
884	C₂²×C₃	—	4	2	no	—
885	C₂²×C₃	—	4	2	no	—
886	C₂²×C₃	—	4	1	no	—
887	C₂²×C₃	—	4	1	no	—
888	C₂²×C₃	—	4	1	no	—
889	C₂²×C₃	—	4	1	no	—
890	C₂²×C₃	—	4	2	no	—
891	C₂²×C₃	—	4	2	no	—
892	C₂²×C₃	—	4	1	no	—
893	C₂²×C₃	—	4	1	no	—
894	C₂²×C₃	—	4	2	no	—
895	C₂²×C₃	—	4	2	no	—
896	C₂²×C₃	—	4	2	no	—
897	C₂²×C₃	—	4	2	no	—
898	C₂²×C₃	—	4	2	no	—
899	C₂²×C₃	—	4	2	no	—
900	C₂²×C₃	—	4	2	no	—
901	C₂²×C₃	—	4	2	no	—
902	C₂²×C₃	C₂³×D₄	1	1	yes	characteristic
903	C₂²×C₃	C₂×H(5,𝔽₂)	1	2	yes	—
904	C₂²×C₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
905	C₂²×C₃	#585	1	2	yes	—
906	C₂²×C₃	#585	1	1	yes	characteristic
907	C₃×C₄	—	2	2	no	—
908	C₃×C₄	—	2	2	no	—
909	C₃×C₄	—	2	2	no	—
910	C₃×C₄	—	2	2	no	—
911	C₃×C₄	—	2	2	no	—
912	C₃×C₄	—	2	2	no	—
913	C₃×C₄	—	2	4	no	—
914	C₃×C₄	—	4	1	no	—
915	C₃×C₄	—	4	2	no	—
916	C₃×C₄	—	4	1	no	—
917	C₃×C₄	—	4	1	no	—
918	C₃×C₄	—	4	1	no	—
919	C₃×C₄	—	4	1	no	—
920	C₃×C₄	—	4	2	no	—
921	C₃×C₄	—	4	2	no	—
922	C₃×C₄	—	4	2	no	—
923	C₃×C₄	—	4	2	no	—
924	C₃×C₄	—	4	2	no	—
925	C₂³	—	2	1	no	—
926	C₂³	—	2	2	no	—
927	C₂³	—	2	2	no	—
928	C₂³	—	2	1	no	—
929	C₂³	—	2	2	no	—
930	C₂³	—	2	2	no	—
931	C₂³	—	2	1	no	—
932	C₂³	—	2	1	no	—
933	C₂³	—	2	2	no	—
934	C₂³	—	2	1	no	—
935	C₂³	—	2	1	no	—
936	C₂³	—	2	2	no	—
937	C₂³	—	2	2	no	—
938	C₂³	—	2	2	no	—
939	C₂³	—	2	2	no	—
940	C₂³	—	2	1	no	—
941	C₂³	—	2	1	no	—
942	C₂³	—	2	2	no	—
943	C₂³	—	2	2	no	—
944	C₂³	—	2	2	no	—
945	C₂³	—	2	2	no	—
946	C₂³	—	2	2	no	—
947	C₂³	—	2	2	no	—
948	C₂³	—	2	1	no	—
949	C₂³	—	2	1	no	—
950	C₂³	C₂²×C₃×D₄	1	2	yes	—
951	C₂³	C₃×2₋¹⁺⁴	1	2	yes	—
952	C₂³	C₂⁵×C₃	1	1	yes	characteristic
953	Q₈	—	4	4	no	—
954	Q₈	—	8	4	no	—
955	D₄	—	4	4	no	—
956	D₄	—	4	4	no	—
957	D₄	—	4	4	no	—
958	D₄	—	4	4	no	—
959	D₄	—	4	8	no	—
960	D₄	—	4	4	no	—
961	D₄	—	4	8	no	—
962	D₄	—	8	2	no	—
963	D₄	—	8	2	no	—
964	D₄	—	8	4	no	—
965	D₄	—	8	4	no	—
966	C₂×C₄	—	2	2	no	—
967	C₂×C₄	—	2	2	no	—
968	C₂×C₄	—	2	1	no	—
969	C₂×C₄	—	2	1	no	—
970	C₂×C₄	—	2	1	no	—
971	C₂×C₄	—	2	2	no	—
972	C₂×C₄	—	2	1	no	—
973	C₂×C₄	—	2	2	no	—
974	C₂×C₄	—	2	2	no	—
975	C₂×C₄	—	2	2	no	—
976	C₂×C₄	—	2	2	no	—
977	C₂×C₄	—	2	1	no	—
978	C₂×C₄	—	2	1	no	—
979	C₂×C₄	—	2	2	no	—
980	C₂×C₄	—	2	1	no	—
981	C₂×C₄	—	2	2	no	—
982	C₂×C₄	—	2	1	no	—
983	C₂×C₄	—	2	1	no	—
984	C₂×C₄	—	2	2	no	—
985	C₂×C₄	—	2	2	no	—
986	C₂×C₄	—	2	2	no	—
987	C₂×C₄	—	2	2	no	—
988	C₂×C₄	—	2	2	no	—
989	C₂×C₄	—	2	2	no	—
990	C₂×C₄	—	2	2	no	—
991	C₂×C₄	—	2	2	no	—
992	C₂×C₄	—	2	2	no	—
993	C₂×C₄	—	2	2	no	—
994	C₂×C₄	—	2	1	no	—
995	C₂×C₄	—	2	2	no	—
996	C₂×C₄	—	2	2	no	—
997	C₂×C₄	—	2	2	no	—
998	C₂×C₄	—	2	1	no	—
999	C₂×C₄	—	2	2	no	—
1000	C₂×C₄	—	2	2	no	—
1001	C₂×C₄	—	2	2	no	—
1002	C₂×C₄	—	2	2	no	—
1003	C₂×C₄	—	2	2	no	—
1004	C₂×C₄	—	2	2	no	—
1005	C₂×C₄	—	4	4	no	—
1006	C₂×C₄	—	4	4	no	—
1007	C₂×C₄	—	8	2	no	—
1008	C₂×C₄	—	8	2	no	—
1009	C₂×C₄	—	8	4	no	—
1010	C₂×C₄	—	8	2	no	—
1011	C₂×C₄	—	8	2	no	—
1012	C₂×C₄	—	8	4	no	—
1013	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
1014	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
1015	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
1016	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
1017	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
1018	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
1019	C₂×C₄	C₃×H(5,𝔽₂)	1	4	yes	—
1020	C₂×C₃	—	4	2	no	—
1021	C₂×C₃	—	4	2	no	—
1022	C₂×C₃	—	8	1	no	—
1023	C₂×C₃	—	8	1	no	—
1024	C₂×C₃	—	8	2	no	—
1025	C₂×C₃	#3449	1	1	yes	characteristic
1026	C₂×C₃	#3489	1	1	yes	characteristic
1027	C₂×C₃	#3498	1	1	yes	characteristic
1028	C₂×C₃	#3533	1	2	yes	—
1029	C₂×C₃	#3541	1	2	yes	—
1030	C₂²	—	2	2	no	—
1031	C₂²	—	2	2	no	—
1032	C₂²	—	2	2	no	—
1033	C₂²	—	2	2	no	—
1034	C₂²	—	2	4	no	—
1035	C₂²	—	4	1	no	—
1036	C₂²	—	4	1	no	—
1037	C₂²	—	4	2	no	—
1038	C₂²	—	4	2	no	—
1039	C₂²	—	4	2	no	—
1040	C₂²	—	4	2	no	—
1041	C₂²	—	4	1	no	—
1042	C₂²	—	4	1	no	—
1043	C₂²	—	4	1	no	—
1044	C₂²	—	4	1	no	—
1045	C₂²	—	4	2	no	—
1046	C₂²	—	4	2	no	—
1047	C₂²	—	4	1	no	—
1048	C₂²	—	4	1	no	—
1049	C₂²	—	4	2	no	—
1050	C₂²	—	4	2	no	—
1051	C₂²	—	4	2	no	—
1052	C₂²	—	4	2	no	—
1053	C₂²	—	4	2	no	—
1054	C₂²	—	4	2	no	—
1055	C₂²	—	4	2	no	—
1056	C₂²	—	4	2	no	—
1057	C₂²	C₂³×C₃×D₄	1	1	yes	characteristic
1058	C₂²	C₂×C₃×H(5,𝔽₂)	1	2	yes	—
1059	C₂²	C₂×C₃×2₋¹⁺⁴	1	1	yes	characteristic
1060	C₂²	C₃×#585	1	2	yes	—
1061	C₂²	C₃×#585	1	1	yes	characteristic
1062	C₄	—	2	2	no	—
1063	C₄	—	2	2	no	—
1064	C₄	—	2	2	no	—
1065	C₄	—	2	2	no	—
1066	C₄	—	2	2	no	—
1067	C₄	—	2	2	no	—
1068	C₄	—	2	4	no	—
1069	C₄	—	4	1	no	—
1070	C₄	—	4	2	no	—
1071	C₄	—	4	1	no	—
1072	C₄	—	4	1	no	—
1073	C₄	—	4	1	no	—
1074	C₄	—	4	1	no	—
1075	C₄	—	4	2	no	—
1076	C₄	—	4	2	no	—
1077	C₄	—	4	2	no	—
1078	C₄	—	4	2	no	—
1079	C₄	—	4	2	no	—
1080	C₃	#41959	1	1	yes	characteristic, direct product factor, Sylow
1081	C₂	—	4	2	no	—
1082	C₂	—	4	2	no	—
1083	C₂	—	8	1	no	—
1084	C₂	—	8	1	no	—
1085	C₂	—	8	2	no	—
1086	C₂	C₃×#3449	1	1	yes	characteristic
1087	C₂	C₃×#3489	1	1	yes	characteristic
1088	C₂	C₃×#3498	1	1	yes	characteristic
1089	C₂	C₃×#3533	1	2	yes	—
1090	C₂	C₃×#3541	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₃	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₃
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. C₂×C₃×#553	C₂	semidirect
2. C₂×C₃×#542	C₂	semidirect
3. C₃×#2821	C₂	semidirect
4. C₃×#2816	C₂	semidirect
5. C₃×#2721	C₂	semidirect
6. C₃×#2714	C₂	semidirect
7. C₃×#2676	C₂	semidirect
8. C₃×#2672	C₂	semidirect
9. C₃×#2662	C₂	semidirect
10. C₃×#2656	C₂	semidirect
11. C₃×#2636	C₂	semidirect
12. C₃×#2635	C₂	semidirect
13. C₃×#2631	C₂	semidirect
14. C₃×#2604	C₂	semidirect
15. C₃×#2580	C₂	semidirect
16. C₃×#2564	C₂	semidirect
17. C₃×#2542	C₂	semidirect
18. C₃×#2464	C₂	semidirect
19. C₃×#2463	C₂	semidirect
20. C₃×#2449	C₂	semidirect
21. C₃×#2422	C₂	semidirect
22. C₃×#2397	C₂	semidirect
23. C₃×#2343	C₂	semidirect
24. #41959	C₃	direct (N × H)
126. C₂×#553	C₂×C₃	semidirect
127. C₂×#542	C₂×C₃	semidirect
128. #2821	C₂×C₃	semidirect
129. #2816	C₂×C₃	semidirect
130. #2721	C₂×C₃	semidirect
131. #2714	C₂×C₃	semidirect
132. #2676	C₂×C₃	semidirect
133. #2672	C₂×C₃	semidirect
134. #2662	C₂×C₃	semidirect
135. #2656	C₂×C₃	semidirect
136. #2636	C₂×C₃	semidirect
137. #2635	C₂×C₃	semidirect
138. #2631	C₂×C₃	semidirect
139. #2604	C₂×C₃	semidirect
140. #2580	C₂×C₃	semidirect
141. #2564	C₂×C₃	semidirect
142. #2542	C₂×C₃	semidirect
143. #2464	C₂×C₃	semidirect
144. #2463	C₂×C₃	semidirect
145. #2449	C₂×C₃	semidirect
146. #2422	C₂×C₃	semidirect
147. #2397	C₂×C₃	semidirect
148. #2343	C₂×C₃	semidirect
199. C₃×#117	D₄	semidirect
565. #117	C₃×D₄	semidirect
1080. C₃	#41959	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₃×#553	2
C₂×C₃×#542	2
C₃×#2821	2
C₃×#2816	2
C₃×#2721	2
C₃×#2714	2
C₃×#2676	2
C₃×#2672	2
C₃×#2662	2
C₃×#2656	2
C₃×#2636	2
C₃×#2635	2
C₃×#2631	2
C₃×#2604	2
C₃×#2580	2
C₃×#2564	2
C₃×#2542	2
C₃×#2464	2
C₃×#2463	2
C₃×#2449	2
C₃×#2422	2
C₃×#2397	2
C₃×#2343	2
#41959	3

Subgroups — C3×#41959 #10660566

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#41959 #10660566