Subgroups — C₃×#37699 #10656306

Order 768.

2476 conjugacy classes of subgroups.

The subgroup lattice has 1142 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#542	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×#532	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#2857	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#2703	C₂	1	2	yes	maximal, complemented
5	C₃×#2691	C₂	1	2	yes	maximal, complemented
6	C₃×#2681	C₂	1	2	yes	maximal, complemented
7	C₃×#2676	C₂	1	2	yes	maximal, complemented
8	C₃×#2640	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×#2620	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#2466	C₂	1	2	yes	maximal, complemented
11	C₃×#2459	C₂	1	2	yes	maximal, complemented
12	C₃×#2450	C₂	1	2	yes	maximal, complemented
13	C₃×#2446	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃×#2445	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃×#2429	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃×#2428	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃×#2425	C₂	1	2	yes	maximal, complemented
18	C₃×#2407	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃×#2407	C₂	1	1	yes	maximal, characteristic, complemented
20	C₃×#2341	C₂	1	1	yes	maximal, characteristic, complemented
21	C₃×#2339	C₂	1	1	yes	maximal, characteristic, complemented
22	C₃×#2326	C₂	1	1	yes	maximal, characteristic, complemented
23	C₃×#2290	C₂	1	1	yes	maximal, characteristic, complemented
24	#37699	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
25	C₂²×C₃×#41	C₂²	1	1	yes	characteristic
26	C₂²×C₃×#41	C₂²	1	1	yes	characteristic
27	C₃×#542	—	2	8	no	—
28	C₃×#532	—	2	8	no	—
29	C₂×C₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
30	C₂×C₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
31	C₂×C₃×#127	C₂²	1	1	yes	characteristic
32	C₂×C₃×#126	C₂²	1	2	yes	—
33	C₂×C₃×#124	C₂²	1	1	yes	characteristic
34	C₂×C₃×#124	C₂²	1	2	yes	—
35	C₂×C₃×#124	C₂²	1	1	yes	characteristic
36	C₂×C₃×#123	C₂²	1	2	yes	—
37	C₂×C₃×#123	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	1	yes	characteristic
41	C₂×C₃×C₂²⋊Q₈	C₂²	1	2	yes	—
42	C₂×C₃×#121	C₂²	1	2	yes	—
43	C₂×C₃×#121	C₂²	1	2	yes	—
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×C₄×Q₈	C₂²	1	1	yes	characteristic
48	C₂×C₃×C₄×Q₈	C₂²	1	1	yes	characteristic
49	C₂×C₃×C₄×D₄	C₂²	1	2	yes	—
50	C₂×C₃×C₄×D₄	C₂²	1	2	yes	—
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×#117	C₂²	1	1	yes	characteristic
55	C₂²×C₃×C₄²	C₂²	1	1	yes	characteristic
56	C₃×#400	C₂²	1	2	yes	—
57	C₃×#398	C₂²	1	2	yes	—
58	C₃×#398	C₂²	1	2	yes	—
59	C₃×#397	C₂²	1	2	yes	—
60	C₃×#397	C₂²	1	2	yes	—
61	C₃×#396	C₂²	1	2	yes	—
62	C₃×#396	C₂²	1	2	yes	—
63	C₃×#396	C₂²	1	2	yes	—
64	C₃×#394	C₂²	1	2	yes	—
65	C₃×#394	C₂²	1	2	yes	—
66	C₃×#394	C₂²	1	2	yes	—
67	C₃×#394	C₂²	1	2	yes	—
68	C₃×#394	C₂²	1	2	yes	—
69	C₃×#394	C₂²	1	2	yes	—
70	C₃×#394	C₂²	1	2	yes	—
71	C₃×#393	C₂²	1	2	yes	—
72	C₃×#393	C₂²	1	2	yes	—
73	C₃×#392	C₂²	1	2	yes	—
74	C₃×#392	C₂²	1	2	yes	—
75	C₃×#392	C₂²	1	2	yes	—
76	C₃×#391	C₂²	1	1	yes	characteristic
77	C₃×#391	C₂²	1	1	yes	characteristic
78	C₃×#391	C₂²	1	1	yes	characteristic
79	C₃×#391	C₂²	1	1	yes	characteristic
80	C₃×#391	C₂²	1	2	yes	—
81	C₃×#390	C₂²	1	1	yes	characteristic
82	C₃×#390	C₂²	1	1	yes	characteristic
83	C₃×#390	C₂²	1	1	yes	characteristic
84	C₃×#390	C₂²	1	1	yes	characteristic
85	C₃×#390	C₂²	1	2	yes	—
86	C₃×#390	C₂²	1	2	yes	—
87	C₃×#389	C₂²	1	2	yes	—
88	C₃×#389	C₂²	1	2	yes	—
89	C₃×#389	C₂²	1	1	yes	characteristic
90	C₃×#389	C₂²	1	1	yes	characteristic
91	C₃×#388	C₂²	1	1	yes	characteristic
92	C₃×#388	C₂²	1	2	yes	—
93	C₃×#388	C₂²	1	2	yes	—
94	C₃×#388	C₂²	1	2	yes	—
95	C₃×#388	C₂²	1	1	yes	characteristic
96	C₃×#387	C₂²	1	2	yes	—
97	C₃×#387	C₂²	1	2	yes	—
98	C₃×#387	C₂²	1	1	yes	characteristic
99	C₃×#387	C₂²	1	1	yes	characteristic
100	C₃×#386	C₂²	1	2	yes	—
101	C₃×#386	C₂²	1	2	yes	—
102	C₃×#386	C₂²	1	1	yes	characteristic
103	C₃×#386	C₂²	1	2	yes	—
104	C₃×#386	C₂²	1	2	yes	—
105	C₃×#386	C₂²	1	2	yes	—
106	C₃×#386	C₂²	1	2	yes	—
107	C₃×#386	C₂²	1	1	yes	characteristic
108	C₃×#385	C₂²	1	2	yes	—
109	C₃×#385	C₂²	1	2	yes	—
110	C₃×#385	C₂²	1	2	yes	—
111	C₃×#385	C₂²	1	2	yes	—
112	C₃×#385	C₂²	1	1	yes	characteristic
113	C₃×#385	C₂²	1	1	yes	characteristic
114	C₃×#384	C₂²	1	1	yes	characteristic
115	C₃×#381	C₂²	1	2	yes	—
116	C₃×#380	C₂²	1	1	yes	characteristic
117	C₃×#380	C₂²	1	1	yes	characteristic
118	C₃×#380	C₂²	1	2	yes	—
119	C₃×#380	C₂²	1	2	yes	—
120	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
121	C₃×C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
122	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	—
123	C₃×C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
124	C₃×#376	C₂²	1	1	yes	characteristic
125	C₂×C₃×#95	C₂²	1	2	yes	—
126	C₂×#542	C₂×C₃	1	1	yes	characteristic, complemented
127	C₂×#532	C₂×C₃	1	1	yes	characteristic, complemented
128	#2857	C₂×C₃	1	1	yes	characteristic, complemented
129	#2703	C₂×C₃	1	2	yes	complemented
130	#2691	C₂×C₃	1	2	yes	complemented
131	#2681	C₂×C₃	1	2	yes	complemented
132	#2676	C₂×C₃	1	2	yes	complemented
133	#2640	C₂×C₃	1	1	yes	characteristic, complemented
134	#2620	C₂×C₃	1	1	yes	characteristic, complemented
135	#2466	C₂×C₃	1	2	yes	complemented
136	#2459	C₂×C₃	1	2	yes	complemented
137	#2450	C₂×C₃	1	2	yes	complemented
138	#2446	C₂×C₃	1	1	yes	characteristic, complemented
139	#2445	C₂×C₃	1	1	yes	characteristic, complemented
140	#2429	C₂×C₃	1	1	yes	characteristic, complemented
141	#2428	C₂×C₃	1	1	yes	characteristic, complemented
142	#2425	C₂×C₃	1	2	yes	complemented
143	#2407	C₂×C₃	1	1	yes	characteristic, complemented
144	#2407	C₂×C₃	1	1	yes	characteristic, complemented
145	#2341	C₂×C₃	1	1	yes	characteristic, complemented
146	#2339	C₂×C₃	1	1	yes	characteristic, complemented
147	#2326	C₂×C₃	1	1	yes	characteristic, complemented
148	#2290	C₂×C₃	1	1	yes	characteristic, complemented
149	C₂×C₃×#41	—	2	4	no	—
150	C₂×C₃×#41	—	2	4	no	—
151	C₂×C₃×#41	—	2	4	no	—
152	C₂×C₃×#41	—	2	4	no	—
153	C₂×C₃×#41	—	4	2	no	—
154	C₂×C₃×#41	—	4	2	no	—
155	C₂²×C₃×Q₈	C₂³	1	1	yes	characteristic
156	C₂²×C₃×Q₈	C₂³	1	1	yes	characteristic
157	C₂²×C₃×Q₈	C₂³	1	2	yes	—
158	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
159	C₂²×C₃×D₄	C₂³	1	2	yes	—
160	C₂²×C₃×D₄	C₂³	1	2	yes	—
161	C₂²×C₃×D₄	C₂³	1	2	yes	—
162	C₂²×C₃×D₄	C₂³	1	2	yes	—
163	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
164	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
165	C₂²×C₃×D₄	C₂³	1	2	yes	—
166	C₂²×C₃×D₄	C₂³	1	2	yes	—
167	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
168	C₂³×C₃×C₄	C₂³	1	2	yes	—
169	C₂³×C₃×C₄	C₂³	1	2	yes	—
170	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
171	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
172	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
173	C₂³×C₃×C₄	C₂³	1	2	yes	—
174	C₂³×C₃×C₄	C₂³	1	2	yes	—
175	C₃×C₄⋊Q₈	—	2	4	no	—
176	C₃×C₄⋊Q₈	—	2	4	no	—
177	C₃×#127	—	2	4	no	—
178	C₃×#126	—	2	8	no	—
179	C₃×#124	—	2	8	no	—
180	C₃×#124	—	2	4	no	—
181	C₃×#124	D₄	1	8	yes	complemented
182	C₃×#123	—	2	8	no	—
183	C₃×#123	—	4	4	no	—
184	C₃×C₂²⋊Q₈	—	2	4	no	—
185	C₃×C₂²⋊Q₈	—	2	8	no	—
186	C₃×C₂²⋊Q₈	—	4	4	no	—
187	C₃×C₂²⋊Q₈	—	4	2	no	—
188	C₃×#121	—	2	4	no	—
189	C₃×#121	—	2	8	no	—
190	C₃×#121	—	2	8	no	—
191	C₃×#121	—	4	4	no	—
192	C₃×#121	—	4	2	no	—
193	C₃×C₄×Q₈	—	2	4	no	—
194	C₃×C₄×Q₈	—	4	2	no	—
195	C₃×C₄×D₄	—	2	4	no	—
196	C₃×C₄×D₄	—	2	4	no	—
197	C₃×C₄×D₄	—	2	8	no	—
198	C₃×C₄×D₄	—	2	8	no	—
199	C₃×C₄×D₄	—	4	2	no	—
200	C₃×#117	—	2	4	no	—
201	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
202	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
203	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
204	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
205	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
206	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
207	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
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	2	yes	—
213	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
214	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
215	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
216	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
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×C₂²⋊C₄	C₂³	1	1	yes	characteristic
222	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
223	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
224	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
225	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
226	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
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	1	yes	characteristic
234	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
235	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
236	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
237	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
238	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
239	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
240	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
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×C₄²	—	2	4	no	—
250	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
251	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
252	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
253	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
254	C₂×C₃×C₄²	C₂³	1	2	yes	—
255	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
256	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
257	C₂×C₃×C₄²	C₂³	1	2	yes	—
258	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
259	C₃×#95	C₂³	1	1	yes	characteristic
260	C₃×#95	C₂³	1	2	yes	—
261	C₃×#95	C₂³	1	2	yes	—
262	C₃×#95	C₂³	1	2	yes	—
263	C₃×#95	C₂³	1	1	yes	characteristic
264	C₃×#95	C₂³	1	1	yes	characteristic
265	C₃×#95	C₂³	1	1	yes	characteristic
266	C₃×#95	C₂³	1	1	yes	characteristic
267	C₃×#95	C₂³	1	1	yes	characteristic
268	C₃×#95	C₂³	1	2	yes	—
269	C₃×#95	C₂³	1	1	yes	characteristic
270	C₃×#95	C₂³	1	1	yes	characteristic
271	C₃×#95	C₂³	1	1	yes	characteristic
272	C₃×#95	C₂³	1	1	yes	characteristic
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	C₃×#95	C₂³	1	2	yes	—
280	C₃×#95	C₂³	1	2	yes	—
281	C₂²×#41	C₂²×C₃	1	1	yes	characteristic
282	C₂²×#41	C₂²×C₃	1	1	yes	characteristic
283	#542	—	2	8	no	—
284	#532	—	2	8	no	—
285	C₂×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
286	C₂×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
287	C₂×#127	C₂²×C₃	1	1	yes	characteristic
288	C₂×#126	C₂²×C₃	1	2	yes	—
289	C₂×#124	C₂²×C₃	1	1	yes	characteristic
290	C₂×#124	C₂²×C₃	1	2	yes	—
291	C₂×#124	C₂²×C₃	1	1	yes	characteristic
292	C₂×#123	C₂²×C₃	1	2	yes	—
293	C₂×#123	C₂²×C₃	1	2	yes	—
294	C₂×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
295	C₂×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
296	C₂×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
297	C₂×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
298	C₂×#121	C₂²×C₃	1	1	yes	characteristic
299	C₂×#121	C₂²×C₃	1	2	yes	—
300	C₂×#121	C₂²×C₃	1	2	yes	—
301	C₂×#121	C₂²×C₃	1	1	yes	characteristic
302	C₂×#121	C₂²×C₃	1	2	yes	—
303	C₂×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic
304	C₂×C₄×Q₈	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	2	yes	—
308	C₂×C₄×D₄	C₂²×C₃	1	2	yes	—
309	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
310	C₂×#117	C₂²×C₃	1	1	yes	characteristic
311	C₂²×C₄²	C₂²×C₃	1	1	yes	characteristic
312	#400	C₂²×C₃	1	2	yes	—
313	#398	C₂²×C₃	1	2	yes	—
314	#398	C₂²×C₃	1	2	yes	—
315	#397	C₂²×C₃	1	2	yes	—
316	#397	C₂²×C₃	1	2	yes	—
317	#396	C₂²×C₃	1	2	yes	—
318	#396	C₂²×C₃	1	2	yes	—
319	#396	C₂²×C₃	1	2	yes	—
320	#394	C₂²×C₃	1	2	yes	—
321	#394	C₂²×C₃	1	2	yes	—
322	#394	C₂²×C₃	1	2	yes	—
323	#394	C₂²×C₃	1	2	yes	—
324	#394	C₂²×C₃	1	2	yes	—
325	#394	C₂²×C₃	1	2	yes	—
326	#394	C₂²×C₃	1	2	yes	—
327	#393	C₂²×C₃	1	2	yes	—
328	#393	C₂²×C₃	1	2	yes	—
329	#392	C₂²×C₃	1	2	yes	—
330	#392	C₂²×C₃	1	2	yes	—
331	#392	C₂²×C₃	1	2	yes	—
332	#391	C₂²×C₃	1	1	yes	characteristic
333	#391	C₂²×C₃	1	1	yes	characteristic
334	#391	C₂²×C₃	1	1	yes	characteristic
335	#391	C₂²×C₃	1	2	yes	—
336	#391	C₂²×C₃	1	1	yes	characteristic
337	#390	C₂²×C₃	1	1	yes	characteristic
338	#390	C₂²×C₃	1	1	yes	characteristic
339	#390	C₂²×C₃	1	1	yes	characteristic
340	#390	C₂²×C₃	1	2	yes	—
341	#390	C₂²×C₃	1	2	yes	—
342	#390	C₂²×C₃	1	1	yes	characteristic
343	#389	C₂²×C₃	1	2	yes	—
344	#389	C₂²×C₃	1	1	yes	characteristic
345	#389	C₂²×C₃	1	1	yes	characteristic
346	#389	C₂²×C₃	1	2	yes	—
347	#388	C₂²×C₃	1	2	yes	—
348	#388	C₂²×C₃	1	2	yes	—
349	#388	C₂²×C₃	1	1	yes	characteristic
350	#388	C₂²×C₃	1	2	yes	—
351	#388	C₂²×C₃	1	1	yes	characteristic
352	#387	C₂²×C₃	1	2	yes	—
353	#387	C₂²×C₃	1	2	yes	—
354	#387	C₂²×C₃	1	1	yes	characteristic
355	#387	C₂²×C₃	1	1	yes	characteristic
356	#386	C₂²×C₃	1	2	yes	—
357	#386	C₂²×C₃	1	2	yes	—
358	#386	C₂²×C₃	1	2	yes	—
359	#386	C₂²×C₃	1	2	yes	—
360	#386	C₂²×C₃	1	1	yes	characteristic
361	#386	C₂²×C₃	1	2	yes	—
362	#386	C₂²×C₃	1	2	yes	—
363	#386	C₂²×C₃	1	1	yes	characteristic
364	#385	C₂²×C₃	1	2	yes	—
365	#385	C₂²×C₃	1	2	yes	—
366	#385	C₂²×C₃	1	2	yes	—
367	#385	C₂²×C₃	1	2	yes	—
368	#385	C₂²×C₃	1	1	yes	characteristic
369	#385	C₂²×C₃	1	1	yes	characteristic
370	#384	C₂²×C₃	1	1	yes	characteristic
371	#381	C₂²×C₃	1	2	yes	—
372	#380	C₂²×C₃	1	1	yes	characteristic
373	#380	C₂²×C₃	1	1	yes	characteristic
374	#380	C₂²×C₃	1	2	yes	—
375	#380	C₂²×C₃	1	2	yes	—
376	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
377	C₄×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
378	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
379	C₄×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
380	#376	C₂²×C₃	1	1	yes	characteristic
381	C₂×#95	C₂²×C₃	1	2	yes	—
382	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
383	C₂⁴×C₃	C₂⁴	1	2	yes	—
384	C₂⁴×C₃	C₂⁴	1	2	yes	—
385	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
386	C₃×#41	—	4	16	no	—
387	C₃×#41	—	4	16	no	—
388	C₂×C₃×Q₈	—	2	2	no	—
389	C₂×C₃×Q₈	—	2	4	no	—
390	C₂×C₃×Q₈	—	2	2	no	—
391	C₂×C₃×Q₈	—	2	2	no	—
392	C₂×C₃×Q₈	—	2	2	no	—
393	C₂×C₃×Q₈	—	2	2	no	—
394	C₂×C₃×Q₈	—	4	2	no	—
395	C₂×C₃×Q₈	—	4	2	no	—
396	C₂×C₃×Q₈	C₂×D₄	1	4	yes	—
397	C₂×C₃×D₄	—	2	4	no	—
398	C₂×C₃×D₄	—	2	4	no	—
399	C₂×C₃×D₄	—	2	4	no	—
400	C₂×C₃×D₄	—	2	2	no	—
401	C₂×C₃×D₄	—	2	4	no	—
402	C₂×C₃×D₄	—	2	4	no	—
403	C₂×C₃×D₄	—	2	4	no	—
404	C₂×C₃×D₄	—	2	4	no	—
405	C₂×C₃×D₄	—	2	2	no	—
406	C₂×C₃×D₄	—	2	2	no	—
407	C₂×C₃×D₄	—	2	2	no	—
408	C₂×C₃×D₄	—	2	2	no	—
409	C₂×C₃×D₄	—	2	4	no	—
410	C₂×C₃×D₄	—	2	2	no	—
411	C₂×C₃×D₄	—	2	4	no	—
412	C₂×C₃×D₄	—	4	2	no	—
413	C₂×C₃×D₄	—	4	2	no	—
414	C₂×C₃×D₄	—	4	1	no	—
415	C₂×C₃×D₄	—	4	1	no	—
416	C₂×C₃×D₄	—	4	2	no	—
417	C₂×C₃×D₄	—	4	2	no	—
418	C₂×C₃×D₄	—	4	2	no	—
419	C₂×C₃×D₄	—	4	2	no	—
420	C₂×C₃×D₄	—	4	2	no	—
421	C₂×C₃×D₄	—	4	2	no	—
422	C₂×C₃×D₄	—	4	2	no	—
423	C₂×C₃×D₄	C₂×D₄	1	4	yes	—
424	C₂²×C₃×C₄	—	2	2	no	—
425	C₂²×C₃×C₄	—	2	2	no	—
426	C₂²×C₃×C₄	—	2	4	no	—
427	C₂²×C₃×C₄	—	2	4	no	—
428	C₂²×C₃×C₄	—	2	2	no	—
429	C₂²×C₃×C₄	—	2	2	no	—
430	C₂²×C₃×C₄	—	2	2	no	—
431	C₂²×C₃×C₄	—	2	4	no	—
432	C₂²×C₃×C₄	—	2	2	no	—
433	C₂²×C₃×C₄	—	2	4	no	—
434	C₂²×C₃×C₄	—	2	4	no	—
435	C₂²×C₃×C₄	—	2	2	no	—
436	C₂²×C₃×C₄	—	2	2	no	—
437	C₂²×C₃×C₄	—	2	2	no	—
438	C₂²×C₃×C₄	—	4	1	no	—
439	C₂²×C₃×C₄	—	4	1	no	—
440	C₂²×C₃×C₄	—	4	2	no	—
441	C₂²×C₃×C₄	—	4	2	no	—
442	C₂²×C₃×C₄	—	4	2	no	—
443	C₂²×C₃×C₄	—	4	2	no	—
444	C₂²×C₃×C₄	—	4	2	no	—
445	C₂²×C₃×C₄	—	4	2	no	—
446	C₂²×C₃×C₄	—	4	2	no	—
447	C₂²×C₃×C₄	#41	1	4	yes	—
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	2	yes	—
453	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
454	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
455	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
456	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
457	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
458	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
459	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
460	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
461	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
462	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
463	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
464	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
465	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
466	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
467	C₃×C₄⋊C₄	—	2	2	no	—
468	C₃×C₄⋊C₄	—	2	2	no	—
469	C₃×C₄⋊C₄	—	2	4	no	—
470	C₃×C₄⋊C₄	—	2	4	no	—
471	C₃×C₄⋊C₄	—	2	2	no	—
472	C₃×C₄⋊C₄	—	2	2	no	—
473	C₃×C₄⋊C₄	—	2	4	no	—
474	C₃×C₄⋊C₄	—	2	4	no	—
475	C₃×C₄⋊C₄	—	2	4	no	—
476	C₃×C₄⋊C₄	—	2	2	no	—
477	C₃×C₄⋊C₄	—	2	2	no	—
478	C₃×C₄⋊C₄	—	2	2	no	—
479	C₃×C₄⋊C₄	—	2	4	no	—
480	C₃×C₄⋊C₄	—	2	4	no	—
481	C₃×C₄⋊C₄	—	2	2	no	—
482	C₃×C₄⋊C₄	—	2	2	no	—
483	C₃×C₄⋊C₄	—	4	2	no	—
484	C₃×C₄⋊C₄	—	4	2	no	—
485	C₃×C₄⋊C₄	—	4	2	no	—
486	C₃×C₄⋊C₄	—	4	2	no	—
487	C₃×C₂²⋊C₄	—	2	4	no	—
488	C₃×C₂²⋊C₄	—	2	4	no	—
489	C₃×C₂²⋊C₄	—	2	2	no	—
490	C₃×C₂²⋊C₄	—	2	2	no	—
491	C₃×C₂²⋊C₄	—	2	2	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	—	2	2	no	—
496	C₃×C₂²⋊C₄	—	2	2	no	—
497	C₃×C₂²⋊C₄	—	2	2	no	—
498	C₃×C₂²⋊C₄	—	4	2	no	—
499	C₃×C₂²⋊C₄	—	4	1	no	—
500	C₃×C₂²⋊C₄	—	4	1	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	—	4	2	no	—
508	C₃×C₂²⋊C₄	—	4	2	no	—
509	C₃×C₂²⋊C₄	—	4	2	no	—
510	C₃×C₂²⋊C₄	—	4	2	no	—
511	C₃×C₂²⋊C₄	—	4	2	no	—
512	C₃×C₂²⋊C₄	—	4	2	no	—
513	C₃×C₂²⋊C₄	C₂×D₄	1	8	yes	—
514	C₃×C₂²⋊C₄	C₂×D₄	1	8	yes	—
515	C₃×C₄²	—	2	2	no	—
516	C₃×C₄²	—	2	2	no	—
517	C₃×C₄²	—	2	2	no	—
518	C₃×C₄²	—	2	2	no	—
519	C₃×C₄²	—	2	4	no	—
520	C₃×C₄²	—	2	2	no	—
521	C₃×C₄²	—	2	2	no	—
522	C₃×C₄²	—	4	2	no	—
523	C₃×C₄²	C₂×D₄	1	4	yes	—
524	C₂×#41	—	2	4	no	—
525	C₂×#41	—	2	4	no	—
526	C₂×#41	—	2	4	no	—
527	C₂×#41	—	2	4	no	—
528	C₂×#41	—	4	2	no	—
529	C₂×#41	—	4	2	no	—
530	C₂²×Q₈	C₂³×C₃	1	1	yes	characteristic
531	C₂²×Q₈	C₂³×C₃	1	1	yes	characteristic
532	C₂²×Q₈	C₂³×C₃	1	2	yes	—
533	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
534	C₂²×D₄	C₂³×C₃	1	2	yes	—
535	C₂²×D₄	C₂³×C₃	1	2	yes	—
536	C₂²×D₄	C₂³×C₃	1	2	yes	—
537	C₂²×D₄	C₂³×C₃	1	2	yes	—
538	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
539	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
540	C₂²×D₄	C₂³×C₃	1	2	yes	—
541	C₂²×D₄	C₂³×C₃	1	2	yes	—
542	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
543	C₂³×C₄	C₂³×C₃	1	2	yes	—
544	C₂³×C₄	C₂³×C₃	1	2	yes	—
545	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
546	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
547	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
548	C₂³×C₄	C₂³×C₃	1	2	yes	—
549	C₂³×C₄	C₂³×C₃	1	2	yes	—
550	C₄⋊Q₈	—	2	4	no	—
551	C₄⋊Q₈	—	2	4	no	—
552	#127	—	2	4	no	—
553	#126	—	2	8	no	—
554	#124	—	2	8	no	—
555	#124	—	2	4	no	—
556	#124	C₃×D₄	1	8	yes	complemented
557	#123	—	2	8	no	—
558	#123	—	4	4	no	—
559	C₂²⋊Q₈	—	2	4	no	—
560	C₂²⋊Q₈	—	2	8	no	—
561	C₂²⋊Q₈	—	4	4	no	—
562	C₂²⋊Q₈	—	4	2	no	—
563	#121	—	2	4	no	—
564	#121	—	2	8	no	—
565	#121	—	2	8	no	—
566	#121	—	4	4	no	—
567	#121	—	4	2	no	—
568	C₄×Q₈	—	2	4	no	—
569	C₄×Q₈	—	4	2	no	—
570	C₄×D₄	—	2	4	no	—
571	C₄×D₄	—	2	4	no	—
572	C₄×D₄	—	2	8	no	—
573	C₄×D₄	—	2	8	no	—
574	C₄×D₄	—	4	2	no	—
575	#117	—	2	4	no	—
576	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
577	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
578	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
579	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
580	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
581	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
582	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
583	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
584	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
585	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
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	2	yes	—
591	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
592	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
593	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
594	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
595	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
596	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
597	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
598	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
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	1	yes	characteristic
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	1	yes	characteristic
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	1	yes	characteristic
617	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
618	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
619	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
620	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
621	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
622	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
623	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
624	C₂×C₄²	—	2	4	no	—
625	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
626	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
627	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
628	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
629	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
630	C₂×C₄²	C₂³×C₃	1	2	yes	—
631	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
632	C₂×C₄²	C₂³×C₃	1	2	yes	—
633	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
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	1	yes	characteristic
639	#95	C₂³×C₃	1	1	yes	characteristic
640	#95	C₂³×C₃	1	1	yes	characteristic
641	#95	C₂³×C₃	1	1	yes	characteristic
642	#95	C₂³×C₃	1	1	yes	characteristic
643	#95	C₂³×C₃	1	2	yes	—
644	#95	C₂³×C₃	1	1	yes	characteristic
645	#95	C₂³×C₃	1	1	yes	characteristic
646	#95	C₂³×C₃	1	1	yes	characteristic
647	#95	C₂³×C₃	1	1	yes	characteristic
648	#95	C₂³×C₃	1	2	yes	—
649	#95	C₂³×C₃	1	2	yes	—
650	#95	C₂³×C₃	1	2	yes	—
651	#95	C₂³×C₃	1	2	yes	—
652	#95	C₂³×C₃	1	2	yes	—
653	#95	C₂³×C₃	1	2	yes	—
654	#95	C₂³×C₃	1	2	yes	—
655	#95	C₂³×C₃	1	2	yes	—
656	C₂³×C₃	—	2	1	no	—
657	C₂³×C₃	—	2	2	no	—
658	C₂³×C₃	—	2	1	no	—
659	C₂³×C₃	—	2	2	no	—
660	C₂³×C₃	—	2	2	no	—
661	C₂³×C₃	—	2	1	no	—
662	C₂³×C₃	—	2	1	no	—
663	C₂³×C₃	—	2	2	no	—
664	C₂³×C₃	—	2	1	no	—
665	C₂³×C₃	—	2	1	no	—
666	C₂³×C₃	—	2	2	no	—
667	C₂³×C₃	—	2	2	no	—
668	C₂³×C₃	—	2	1	no	—
669	C₂³×C₃	—	2	2	no	—
670	C₂³×C₃	—	2	1	no	—
671	C₂³×C₃	—	2	2	no	—
672	C₂³×C₃	—	2	1	no	—
673	C₂³×C₃	—	2	2	no	—
674	C₂³×C₃	—	2	1	no	—
675	C₂³×C₃	—	2	2	no	—
676	C₂³×C₃	—	2	1	no	—
677	C₂³×C₃	—	2	2	no	—
678	C₂³×C₃	—	2	2	no	—
679	C₂³×C₃	—	2	2	no	—
680	C₂³×C₃	—	2	1	no	—
681	C₂³×C₃	—	2	1	no	—
682	C₂³×C₃	C₂²×D₄	1	4	yes	—
683	C₂³×C₃	C₂×#41	1	2	yes	—
684	C₂³×C₃	C₂⁵	1	1	yes	characteristic
685	C₃×Q₈	—	2	8	no	—
686	C₃×Q₈	—	4	4	no	—
687	C₃×Q₈	—	8	4	no	—
688	C₃×D₄	—	2	8	no	—
689	C₃×D₄	—	4	8	no	—
690	C₃×D₄	—	4	8	no	—
691	C₃×D₄	—	4	8	no	—
692	C₃×D₄	—	4	8	no	—
693	C₃×D₄	—	4	4	no	—
694	C₃×D₄	—	4	4	no	—
695	C₃×D₄	—	8	4	no	—
696	C₃×D₄	—	8	4	no	—
697	C₂×C₃×C₄	—	2	1	no	—
698	C₂×C₃×C₄	—	2	1	no	—
699	C₂×C₃×C₄	—	2	1	no	—
700	C₂×C₃×C₄	—	2	2	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	1	no	—
705	C₂×C₃×C₄	—	2	1	no	—
706	C₂×C₃×C₄	—	2	1	no	—
707	C₂×C₃×C₄	—	2	1	no	—
708	C₂×C₃×C₄	—	2	1	no	—
709	C₂×C₃×C₄	—	2	8	no	—
710	C₂×C₃×C₄	—	2	1	no	—
711	C₂×C₃×C₄	—	2	1	no	—
712	C₂×C₃×C₄	—	2	2	no	—
713	C₂×C₃×C₄	—	2	1	no	—
714	C₂×C₃×C₄	—	2	2	no	—
715	C₂×C₃×C₄	—	2	2	no	—
716	C₂×C₃×C₄	—	2	1	no	—
717	C₂×C₃×C₄	—	2	1	no	—
718	C₂×C₃×C₄	—	2	1	no	—
719	C₂×C₃×C₄	—	2	2	no	—
720	C₂×C₃×C₄	—	2	1	no	—
721	C₂×C₃×C₄	—	2	1	no	—
722	C₂×C₃×C₄	—	2	2	no	—
723	C₂×C₃×C₄	—	2	1	no	—
724	C₂×C₃×C₄	—	2	1	no	—
725	C₂×C₃×C₄	—	2	2	no	—
726	C₂×C₃×C₄	—	2	1	no	—
727	C₂×C₃×C₄	—	2	2	no	—
728	C₂×C₃×C₄	—	2	2	no	—
729	C₂×C₃×C₄	—	2	2	no	—
730	C₂×C₃×C₄	—	2	1	no	—
731	C₂×C₃×C₄	—	2	2	no	—
732	C₂×C₃×C₄	—	2	2	no	—
733	C₂×C₃×C₄	—	2	1	no	—
734	C₂×C₃×C₄	—	2	1	no	—
735	C₂×C₃×C₄	—	2	1	no	—
736	C₂×C₃×C₄	—	2	1	no	—
737	C₂×C₃×C₄	—	2	1	no	—
738	C₂×C₃×C₄	—	2	2	no	—
739	C₂×C₃×C₄	—	2	1	no	—
740	C₂×C₃×C₄	—	2	1	no	—
741	C₂×C₃×C₄	—	2	1	no	—
742	C₂×C₃×C₄	—	2	1	no	—
743	C₂×C₃×C₄	—	2	2	no	—
744	C₂×C₃×C₄	—	2	2	no	—
745	C₂×C₃×C₄	—	2	2	no	—
746	C₂×C₃×C₄	—	4	4	no	—
747	C₂×C₃×C₄	—	4	4	no	—
748	C₂×C₃×C₄	—	4	8	no	—
749	C₂×C₃×C₄	—	4	8	no	—
750	C₂×C₃×C₄	—	4	4	no	—
751	C₂×C₃×C₄	—	8	4	no	—
752	C₂×C₃×C₄	—	8	4	no	—
753	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
754	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
755	C₂×C₃×C₄	C₂²×D₄	1	4	yes	—
756	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
757	C₂×C₃×C₄	C₂×#41	1	2	yes	—
758	C₂×C₃×C₄	C₂×#41	1	2	yes	—
759	C₂×C₃×C₄	H(5,𝔽₂)	1	2	yes	—
760	C₂×C₃×C₄	H(5,𝔽₂)	1	2	yes	—
761	C₂×C₃×C₄	2₋¹⁺⁴	1	2	yes	—
762	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
763	C₂⁴	C₂⁴×C₃	1	2	yes	—
764	C₂⁴	C₂⁴×C₃	1	2	yes	—
765	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
766	#41	—	4	16	no	—
767	#41	—	4	16	no	—
768	C₂×Q₈	—	2	2	no	—
769	C₂×Q₈	—	2	4	no	—
770	C₂×Q₈	—	2	2	no	—
771	C₂×Q₈	—	2	2	no	—
772	C₂×Q₈	—	2	2	no	—
773	C₂×Q₈	—	2	2	no	—
774	C₂×Q₈	—	4	2	no	—
775	C₂×Q₈	—	4	2	no	—
776	C₂×Q₈	C₂×C₃×D₄	1	4	yes	—
777	C₂×D₄	—	2	4	no	—
778	C₂×D₄	—	2	4	no	—
779	C₂×D₄	—	2	4	no	—
780	C₂×D₄	—	2	2	no	—
781	C₂×D₄	—	2	4	no	—
782	C₂×D₄	—	2	4	no	—
783	C₂×D₄	—	2	4	no	—
784	C₂×D₄	—	2	4	no	—
785	C₂×D₄	—	2	2	no	—
786	C₂×D₄	—	2	2	no	—
787	C₂×D₄	—	2	2	no	—
788	C₂×D₄	—	2	2	no	—
789	C₂×D₄	—	2	4	no	—
790	C₂×D₄	—	2	2	no	—
791	C₂×D₄	—	2	4	no	—
792	C₂×D₄	—	4	2	no	—
793	C₂×D₄	—	4	2	no	—
794	C₂×D₄	—	4	2	no	—
795	C₂×D₄	—	4	2	no	—
796	C₂×D₄	—	4	1	no	—
797	C₂×D₄	—	4	1	no	—
798	C₂×D₄	—	4	2	no	—
799	C₂×D₄	—	4	2	no	—
800	C₂×D₄	—	4	2	no	—
801	C₂×D₄	—	4	2	no	—
802	C₂×D₄	—	4	2	no	—
803	C₂×D₄	C₂×C₃×D₄	1	4	yes	—
804	C₂²×C₄	—	2	2	no	—
805	C₂²×C₄	—	2	2	no	—
806	C₂²×C₄	—	2	4	no	—
807	C₂²×C₄	—	2	4	no	—
808	C₂²×C₄	—	2	2	no	—
809	C₂²×C₄	—	2	2	no	—
810	C₂²×C₄	—	2	2	no	—
811	C₂²×C₄	—	2	4	no	—
812	C₂²×C₄	—	2	2	no	—
813	C₂²×C₄	—	2	4	no	—
814	C₂²×C₄	—	2	4	no	—
815	C₂²×C₄	—	2	2	no	—
816	C₂²×C₄	—	2	2	no	—
817	C₂²×C₄	—	2	2	no	—
818	C₂²×C₄	—	4	2	no	—
819	C₂²×C₄	—	4	2	no	—
820	C₂²×C₄	—	4	1	no	—
821	C₂²×C₄	—	4	1	no	—
822	C₂²×C₄	—	4	2	no	—
823	C₂²×C₄	—	4	2	no	—
824	C₂²×C₄	—	4	2	no	—
825	C₂²×C₄	—	4	2	no	—
826	C₂²×C₄	—	4	2	no	—
827	C₂²×C₄	C₃×#41	1	4	yes	—
828	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
829	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
830	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
831	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
832	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
833	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
834	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
835	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
836	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
837	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
838	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
839	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
840	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
841	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
842	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
843	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
844	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
845	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
846	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
847	C₄⋊C₄	—	2	2	no	—
848	C₄⋊C₄	—	2	2	no	—
849	C₄⋊C₄	—	2	4	no	—
850	C₄⋊C₄	—	2	4	no	—
851	C₄⋊C₄	—	2	2	no	—
852	C₄⋊C₄	—	2	2	no	—
853	C₄⋊C₄	—	2	4	no	—
854	C₄⋊C₄	—	2	4	no	—
855	C₄⋊C₄	—	2	4	no	—
856	C₄⋊C₄	—	2	2	no	—
857	C₄⋊C₄	—	2	2	no	—
858	C₄⋊C₄	—	2	2	no	—
859	C₄⋊C₄	—	2	4	no	—
860	C₄⋊C₄	—	2	4	no	—
861	C₄⋊C₄	—	2	2	no	—
862	C₄⋊C₄	—	2	2	no	—
863	C₄⋊C₄	—	4	2	no	—
864	C₄⋊C₄	—	4	2	no	—
865	C₄⋊C₄	—	4	2	no	—
866	C₄⋊C₄	—	4	2	no	—
867	C₂²⋊C₄	—	2	4	no	—
868	C₂²⋊C₄	—	2	4	no	—
869	C₂²⋊C₄	—	2	2	no	—
870	C₂²⋊C₄	—	2	2	no	—
871	C₂²⋊C₄	—	2	2	no	—
872	C₂²⋊C₄	—	2	4	no	—
873	C₂²⋊C₄	—	2	4	no	—
874	C₂²⋊C₄	—	2	4	no	—
875	C₂²⋊C₄	—	2	2	no	—
876	C₂²⋊C₄	—	2	2	no	—
877	C₂²⋊C₄	—	2	2	no	—
878	C₂²⋊C₄	—	4	2	no	—
879	C₂²⋊C₄	—	4	2	no	—
880	C₂²⋊C₄	—	4	2	no	—
881	C₂²⋊C₄	—	4	2	no	—
882	C₂²⋊C₄	—	4	2	no	—
883	C₂²⋊C₄	—	4	2	no	—
884	C₂²⋊C₄	—	4	2	no	—
885	C₂²⋊C₄	—	4	2	no	—
886	C₂²⋊C₄	—	4	2	no	—
887	C₂²⋊C₄	—	4	2	no	—
888	C₂²⋊C₄	—	4	1	no	—
889	C₂²⋊C₄	—	4	1	no	—
890	C₂²⋊C₄	—	4	2	no	—
891	C₂²⋊C₄	—	4	2	no	—
892	C₂²⋊C₄	—	4	2	no	—
893	C₂²⋊C₄	C₂×C₃×D₄	1	8	yes	—
894	C₂²⋊C₄	C₂×C₃×D₄	1	8	yes	—
895	C₄²	—	2	2	no	—
896	C₄²	—	2	2	no	—
897	C₄²	—	2	2	no	—
898	C₄²	—	2	2	no	—
899	C₄²	—	2	4	no	—
900	C₄²	—	2	2	no	—
901	C₄²	—	2	2	no	—
902	C₄²	—	4	2	no	—
903	C₄²	C₂×C₃×D₄	1	4	yes	—
904	C₂²×C₃	—	2	2	no	—
905	C₂²×C₃	—	2	2	no	—
906	C₂²×C₃	—	2	4	no	—
907	C₂²×C₃	—	2	4	no	—
908	C₂²×C₃	—	2	4	no	—
909	C₂²×C₃	—	2	2	no	—
910	C₂²×C₃	—	4	2	no	—
911	C₂²×C₃	—	4	1	no	—
912	C₂²×C₃	—	4	1	no	—
913	C₂²×C₃	—	4	2	no	—
914	C₂²×C₃	—	4	2	no	—
915	C₂²×C₃	—	4	1	no	—
916	C₂²×C₃	—	4	2	no	—
917	C₂²×C₃	—	4	1	no	—
918	C₂²×C₃	—	4	1	no	—
919	C₂²×C₃	—	4	2	no	—
920	C₂²×C₃	—	4	2	no	—
921	C₂²×C₃	—	4	1	no	—
922	C₂²×C₃	—	4	2	no	—
923	C₂²×C₃	—	4	1	no	—
924	C₂²×C₃	—	4	2	no	—
925	C₂²×C₃	—	4	1	no	—
926	C₂²×C₃	—	4	1	no	—
927	C₂²×C₃	—	4	2	no	—
928	C₂²×C₃	—	4	1	no	—
929	C₂²×C₃	—	4	2	no	—
930	C₂²×C₃	—	4	1	no	—
931	C₂²×C₃	—	4	2	no	—
932	C₂²×C₃	C₂³×D₄	1	1	yes	characteristic
933	C₂²×C₃	C₂²×#41	1	1	yes	characteristic
934	C₂²×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
935	C₂²×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
936	C₂²×C₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
937	C₂²×C₃	#585	1	1	yes	characteristic
938	C₂²×C₃	#585	1	1	yes	characteristic
939	C₃×C₄	—	2	2	no	—
940	C₃×C₄	—	2	4	no	—
941	C₃×C₄	—	2	2	no	—
942	C₃×C₄	—	2	2	no	—
943	C₃×C₄	—	2	2	no	—
944	C₃×C₄	—	2	2	no	—
945	C₃×C₄	—	4	1	no	—
946	C₃×C₄	—	4	1	no	—
947	C₃×C₄	—	4	2	no	—
948	C₃×C₄	—	4	1	no	—
949	C₃×C₄	—	4	2	no	—
950	C₃×C₄	—	4	2	no	—
951	C₃×C₄	—	4	1	no	—
952	C₃×C₄	—	4	1	no	—
953	C₃×C₄	—	4	2	no	—
954	C₃×C₄	—	4	1	no	—
955	C₃×C₄	—	4	2	no	—
956	C₃×C₄	—	4	1	no	—
957	C₃×C₄	#546	1	4	yes	—
958	C₂³	—	2	1	no	—
959	C₂³	—	2	2	no	—
960	C₂³	—	2	1	no	—
961	C₂³	—	2	2	no	—
962	C₂³	—	2	2	no	—
963	C₂³	—	2	1	no	—
964	C₂³	—	2	1	no	—
965	C₂³	—	2	2	no	—
966	C₂³	—	2	1	no	—
967	C₂³	—	2	1	no	—
968	C₂³	—	2	2	no	—
969	C₂³	—	2	2	no	—
970	C₂³	—	2	1	no	—
971	C₂³	—	2	2	no	—
972	C₂³	—	2	1	no	—
973	C₂³	—	2	2	no	—
974	C₂³	—	2	1	no	—
975	C₂³	—	2	2	no	—
976	C₂³	—	2	1	no	—
977	C₂³	—	2	2	no	—
978	C₂³	—	2	1	no	—
979	C₂³	—	2	2	no	—
980	C₂³	—	2	2	no	—
981	C₂³	—	2	2	no	—
982	C₂³	—	2	1	no	—
983	C₂³	—	2	1	no	—
984	C₂³	C₂²×C₃×D₄	1	4	yes	—
985	C₂³	C₂×C₃×#41	1	2	yes	—
986	C₂³	C₂⁵×C₃	1	1	yes	characteristic
987	Q₈	—	2	8	no	—
988	Q₈	—	4	4	no	—
989	Q₈	—	8	4	no	—
990	D₄	—	2	8	no	—
991	D₄	—	4	8	no	—
992	D₄	—	4	8	no	—
993	D₄	—	4	8	no	—
994	D₄	—	4	8	no	—
995	D₄	—	4	4	no	—
996	D₄	—	4	4	no	—
997	D₄	—	8	4	no	—
998	D₄	—	8	4	no	—
999	C₂×C₄	—	2	1	no	—
1000	C₂×C₄	—	2	1	no	—
1001	C₂×C₄	—	2	1	no	—
1002	C₂×C₄	—	2	2	no	—
1003	C₂×C₄	—	2	2	no	—
1004	C₂×C₄	—	2	1	no	—
1005	C₂×C₄	—	2	1	no	—
1006	C₂×C₄	—	2	1	no	—
1007	C₂×C₄	—	2	1	no	—
1008	C₂×C₄	—	2	1	no	—
1009	C₂×C₄	—	2	1	no	—
1010	C₂×C₄	—	2	1	no	—
1011	C₂×C₄	—	2	8	no	—
1012	C₂×C₄	—	2	1	no	—
1013	C₂×C₄	—	2	1	no	—
1014	C₂×C₄	—	2	2	no	—
1015	C₂×C₄	—	2	1	no	—
1016	C₂×C₄	—	2	2	no	—
1017	C₂×C₄	—	2	2	no	—
1018	C₂×C₄	—	2	1	no	—
1019	C₂×C₄	—	2	1	no	—
1020	C₂×C₄	—	2	1	no	—
1021	C₂×C₄	—	2	2	no	—
1022	C₂×C₄	—	2	1	no	—
1023	C₂×C₄	—	2	1	no	—
1024	C₂×C₄	—	2	2	no	—
1025	C₂×C₄	—	2	1	no	—
1026	C₂×C₄	—	2	1	no	—
1027	C₂×C₄	—	2	2	no	—
1028	C₂×C₄	—	2	1	no	—
1029	C₂×C₄	—	2	2	no	—
1030	C₂×C₄	—	2	2	no	—
1031	C₂×C₄	—	2	2	no	—
1032	C₂×C₄	—	2	1	no	—
1033	C₂×C₄	—	2	2	no	—
1034	C₂×C₄	—	2	2	no	—
1035	C₂×C₄	—	2	1	no	—
1036	C₂×C₄	—	2	1	no	—
1037	C₂×C₄	—	2	1	no	—
1038	C₂×C₄	—	2	1	no	—
1039	C₂×C₄	—	2	1	no	—
1040	C₂×C₄	—	2	2	no	—
1041	C₂×C₄	—	2	1	no	—
1042	C₂×C₄	—	2	1	no	—
1043	C₂×C₄	—	2	1	no	—
1044	C₂×C₄	—	2	1	no	—
1045	C₂×C₄	—	2	2	no	—
1046	C₂×C₄	—	2	2	no	—
1047	C₂×C₄	—	2	2	no	—
1048	C₂×C₄	—	4	8	no	—
1049	C₂×C₄	—	4	4	no	—
1050	C₂×C₄	—	4	4	no	—
1051	C₂×C₄	—	4	8	no	—
1052	C₂×C₄	—	4	4	no	—
1053	C₂×C₄	—	8	4	no	—
1054	C₂×C₄	—	8	4	no	—
1055	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
1056	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
1057	C₂×C₄	C₂²×C₃×D₄	1	4	yes	—
1058	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
1059	C₂×C₄	C₂×C₃×#41	1	2	yes	—
1060	C₂×C₄	C₂×C₃×#41	1	2	yes	—
1061	C₂×C₄	C₃×H(5,𝔽₂)	1	2	yes	—
1062	C₂×C₄	C₃×H(5,𝔽₂)	1	2	yes	—
1063	C₂×C₄	C₃×2₋¹⁺⁴	1	2	yes	—
1064	C₂×C₃	—	4	2	no	—
1065	C₂×C₃	—	4	4	no	—
1066	C₂×C₃	—	8	1	no	—
1067	C₂×C₃	—	8	2	no	—
1068	C₂×C₃	#3455	1	1	yes	characteristic
1069	C₂×C₃	C₂×#546	1	1	yes	characteristic
1070	C₂×C₃	#3488	1	1	yes	characteristic
1071	C₂×C₃	#3489	1	1	yes	characteristic
1072	C₂×C₃	#3511	1	1	yes	characteristic
1073	C₂×C₃	#3546	1	1	yes	characteristic
1074	C₂×C₃	#3554	1	1	yes	characteristic
1075	C₂²	—	2	2	no	—
1076	C₂²	—	2	2	no	—
1077	C₂²	—	2	4	no	—
1078	C₂²	—	2	4	no	—
1079	C₂²	—	2	4	no	—
1080	C₂²	—	2	2	no	—
1081	C₂²	—	4	2	no	—
1082	C₂²	—	4	1	no	—
1083	C₂²	—	4	1	no	—
1084	C₂²	—	4	2	no	—
1085	C₂²	—	4	2	no	—
1086	C₂²	—	4	1	no	—
1087	C₂²	—	4	2	no	—
1088	C₂²	—	4	1	no	—
1089	C₂²	—	4	1	no	—
1090	C₂²	—	4	2	no	—
1091	C₂²	—	4	2	no	—
1092	C₂²	—	4	1	no	—
1093	C₂²	—	4	2	no	—
1094	C₂²	—	4	1	no	—
1095	C₂²	—	4	2	no	—
1096	C₂²	—	4	1	no	—
1097	C₂²	—	4	1	no	—
1098	C₂²	—	4	2	no	—
1099	C₂²	—	4	1	no	—
1100	C₂²	—	4	2	no	—
1101	C₂²	—	4	1	no	—
1102	C₂²	—	4	2	no	—
1103	C₂²	C₂³×C₃×D₄	1	1	yes	characteristic
1104	C₂²	C₂²×C₃×#41	1	1	yes	characteristic
1105	C₂²	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
1106	C₂²	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
1107	C₂²	C₂×C₃×2₋¹⁺⁴	1	1	yes	characteristic
1108	C₂²	C₃×#585	1	1	yes	characteristic
1109	C₂²	C₃×#585	1	1	yes	characteristic
1110	C₄	—	2	2	no	—
1111	C₄	—	2	4	no	—
1112	C₄	—	2	2	no	—
1113	C₄	—	2	2	no	—
1114	C₄	—	2	2	no	—
1115	C₄	—	2	2	no	—
1116	C₄	—	4	1	no	—
1117	C₄	—	4	2	no	—
1118	C₄	—	4	1	no	—
1119	C₄	—	4	1	no	—
1120	C₄	—	4	2	no	—
1121	C₄	—	4	2	no	—
1122	C₄	—	4	1	no	—
1123	C₄	—	4	1	no	—
1124	C₄	—	4	1	no	—
1125	C₄	—	4	2	no	—
1126	C₄	—	4	2	no	—
1127	C₄	—	4	1	no	—
1128	C₄	C₃×#546	1	4	yes	—
1129	C₃	#37699	1	1	yes	characteristic, direct product factor, Sylow
1130	C₂	—	4	2	no	—
1131	C₂	—	4	4	no	—
1132	C₂	—	8	1	no	—
1133	C₂	—	8	2	no	—
1134	C₂	C₃×#3455	1	1	yes	characteristic
1135	C₂	C₂×C₃×#546	1	1	yes	characteristic
1136	C₂	C₃×#3488	1	1	yes	characteristic
1137	C₂	C₃×#3489	1	1	yes	characteristic
1138	C₂	C₃×#3511	1	1	yes	characteristic
1139	C₂	C₃×#3546	1	1	yes	characteristic
1140	C₂	C₃×#3554	1	1	yes	characteristic

	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×#542	C₂	semidirect
2. C₂×C₃×#532	C₂	semidirect
3. C₃×#2857	C₂	semidirect
4. C₃×#2703	C₂	semidirect
5. C₃×#2691	C₂	semidirect
6. C₃×#2681	C₂	semidirect
7. C₃×#2676	C₂	semidirect
8. C₃×#2640	C₂	semidirect
9. C₃×#2620	C₂	semidirect
10. C₃×#2466	C₂	semidirect
11. C₃×#2459	C₂	semidirect
12. C₃×#2450	C₂	semidirect
13. C₃×#2446	C₂	semidirect
14. C₃×#2445	C₂	semidirect
15. C₃×#2429	C₂	semidirect
16. C₃×#2428	C₂	semidirect
17. C₃×#2425	C₂	semidirect
18. C₃×#2407	C₂	semidirect
19. C₃×#2407	C₂	semidirect
20. C₃×#2341	C₂	semidirect
21. C₃×#2339	C₂	semidirect
22. C₃×#2326	C₂	semidirect
23. C₃×#2290	C₂	semidirect
24. #37699	C₃	direct (N × H)
126. C₂×#542	C₂×C₃	semidirect
127. C₂×#532	C₂×C₃	semidirect
128. #2857	C₂×C₃	semidirect
129. #2703	C₂×C₃	semidirect
130. #2691	C₂×C₃	semidirect
131. #2681	C₂×C₃	semidirect
132. #2676	C₂×C₃	semidirect
133. #2640	C₂×C₃	semidirect
134. #2620	C₂×C₃	semidirect
135. #2466	C₂×C₃	semidirect
136. #2459	C₂×C₃	semidirect
137. #2450	C₂×C₃	semidirect
138. #2446	C₂×C₃	semidirect
139. #2445	C₂×C₃	semidirect
140. #2429	C₂×C₃	semidirect
141. #2428	C₂×C₃	semidirect
142. #2425	C₂×C₃	semidirect
143. #2407	C₂×C₃	semidirect
144. #2407	C₂×C₃	semidirect
145. #2341	C₂×C₃	semidirect
146. #2339	C₂×C₃	semidirect
147. #2326	C₂×C₃	semidirect
148. #2290	C₂×C₃	semidirect
181. C₃×#124	D₄	semidirect
556. #124	C₃×D₄	semidirect
1129. C₃	#37699	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×#542	2
C₂×C₃×#532	2
C₃×#2857	2
C₃×#2703	2
C₃×#2691	2
C₃×#2681	2
C₃×#2676	2
C₃×#2640	2
C₃×#2620	2
C₃×#2466	2
C₃×#2459	2
C₃×#2450	2
C₃×#2446	2
C₃×#2445	2
C₃×#2429	2
C₃×#2428	2
C₃×#2425	2
C₃×#2407	2
C₃×#2341	2
C₃×#2339	2
C₃×#2326	2
C₃×#2290	2
#37699	3

Subgroups — C3×#37699 #10656306

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#37699 #10656306