Subgroups — C₃×#41412 #10660019

Order 768.

2142 conjugacy classes of subgroups.

The subgroup lattice has 1034 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#554	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×#551	C₂	1	1	yes	maximal, characteristic
3	C₃×#2821	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#2814	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#2721	C₂	1	2	yes	maximal, complemented
6	C₃×#2700	C₂	1	2	yes	maximal, complemented
7	C₃×#2690	C₂	1	2	yes	maximal, complemented
8	C₃×#2680	C₂	1	2	yes	maximal, complemented
9	C₃×#2659	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#2638	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×#2637	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#2623	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃×#2621	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃×#2599	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃×#2561	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃×#2502	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃×#2486	C₂	1	1	yes	maximal, characteristic, complemented
18	C₃×#2438	C₂	1	2	yes	maximal, complemented
19	C₃×#2437	C₂	1	2	yes	maximal, complemented
20	C₃×#2419	C₂	1	2	yes	maximal, complemented
21	C₃×#2418	C₂	1	2	yes	maximal
22	C₂×C₃×#397	C₂	1	1	yes	maximal, characteristic, complemented
23	C₃×#2318	C₂	1	1	yes	maximal, characteristic, complemented
24	#41412	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
25	C₃×#554	—	2	8	no	—
26	C₃×#551	—	2	8	no	—
27	C₂×C₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
28	C₂×C₃×#126	C₂²	1	1	yes	characteristic
29	C₂×C₃×#126	C₂²	1	1	yes	characteristic
30	C₂×C₃×#125	C₂²	1	2	yes	complemented
31	C₂×C₃×#124	C₂²	1	1	yes	characteristic
32	C₂×C₃×#123	C₂²	1	1	yes	characteristic
33	C₂×C₃×#123	C₂²	1	1	yes	characteristic
34	C₂×C₃×#123	C₂²	1	1	yes	characteristic
35	C₂×C₃×#123	C₂²	1	2	yes	—
36	C₂×C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
37	C₂×C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
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×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
42	C₂×C₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
43	C₂×C₃×#120	C₂²	1	1	yes	characteristic
44	C₂×C₃×C₄×Q₈	C₂²	1	1	yes	characteristic, complemented
45	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
46	C₂×C₃×C₄×D₄	C₂²	1	2	yes	—
47	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
48	C₂×C₃×#117	C₂²	1	1	yes	characteristic
49	C₂×C₃×#117	C₂²	1	1	yes	characteristic
50	C₂²×C₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
51	C₂²×C₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
52	C₂²×C₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
53	C₂²×C₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
54	C₂²×C₃×C₂²⋊C₄	C₂²	1	2	yes	—
55	C₃×#400	C₂²	1	2	yes	complemented
56	C₃×#400	C₂²	1	2	yes	complemented
57	C₃×#399	C₂²	1	2	yes	—
58	C₃×#399	C₂²	1	2	yes	—
59	C₃×#398	C₂²	1	1	yes	characteristic, complemented
60	C₃×#398	C₂²	1	2	yes	complemented
61	C₃×#398	C₂²	1	1	yes	characteristic, complemented
62	C₃×#398	C₂²	1	1	yes	characteristic, complemented
63	C₃×#398	C₂²	1	2	yes	complemented
64	C₃×#398	C₂²	1	1	yes	characteristic, complemented
65	C₃×#398	C₂²	1	1	yes	characteristic, complemented
66	C₃×#398	C₂²	1	2	yes	complemented
67	C₃×#398	C₂²	1	1	yes	characteristic, complemented
68	C₃×#398	C₂²	1	2	yes	complemented
69	C₃×#397	C₂²	1	1	yes	characteristic
70	C₃×#397	C₂²	1	2	yes	—
71	C₃×#397	C₂²	1	1	yes	characteristic
72	C₃×#397	C₂²	1	1	yes	characteristic
73	C₃×#397	C₂²	1	1	yes	characteristic
74	C₃×#397	C₂²	1	2	yes	—
75	C₃×#397	C₂²	1	2	yes	—
76	C₃×#397	C₂²	1	1	yes	characteristic
77	C₃×#397	C₂²	1	1	yes	characteristic
78	C₃×#397	C₂²	1	2	yes	complemented
79	C₃×#397	C₂²	1	2	yes	complemented
80	C₃×#396	C₂²	1	2	yes	—
81	C₃×#396	C₂²	1	2	yes	—
82	C₃×#395	C₂²	1	1	yes	characteristic, complemented
83	C₃×#395	C₂²	1	2	yes	complemented
84	C₃×#395	C₂²	1	1	yes	characteristic, complemented
85	C₃×#395	C₂²	1	2	yes	complemented
86	C₃×#394	C₂²	1	2	yes	—
87	C₃×#394	C₂²	1	2	yes	—
88	C₃×#393	C₂²	1	1	yes	characteristic
89	C₃×#393	C₂²	1	1	yes	characteristic
90	C₃×#393	C₂²	1	2	yes	—
91	C₃×#391	C₂²	1	2	yes	complemented
92	C₃×#391	C₂²	1	2	yes	complemented
93	C₃×#389	C₂²	1	2	yes	complemented
94	C₃×#388	C₂²	1	2	yes	—
95	C₃×#388	C₂²	1	2	yes	—
96	C₃×#388	C₂²	1	2	yes	—
97	C₃×#388	C₂²	1	2	yes	—
98	C₃×#388	C₂²	1	2	yes	complemented
99	C₃×#387	C₂²	1	2	yes	complemented
100	C₃×#387	C₂²	1	2	yes	complemented
101	C₃×#387	C₂²	1	2	yes	complemented
102	C₃×#387	C₂²	1	2	yes	complemented
103	C₃×#387	C₂²	1	2	yes	complemented
104	C₃×#386	C₂²	1	2	yes	—
105	C₃×#386	C₂²	1	2	yes	—
106	C₃×#385	C₂²	1	2	yes	—
107	C₃×#385	C₂²	1	2	yes	—
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	complemented
112	C₃×#384	C₂²	1	2	yes	complemented
113	C₃×#383	C₂²	1	1	yes	characteristic, complemented
114	C₃×#382	C₂²	1	1	yes	characteristic, complemented
115	C₃×#381	C₂²	1	2	yes	—
116	C₃×#381	C₂²	1	1	yes	characteristic, complemented
117	C₃×#381	C₂²	1	2	yes	complemented
118	C₃×#380	C₂²	1	2	yes	—
119	C₃×#380	C₂²	1	2	yes	—
120	C₃×#380	C₂²	1	2	yes	—
121	C₃×#380	C₂²	1	1	yes	characteristic, complemented
122	C₃×#379	C₂²	1	2	yes	—
123	C₃×C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
124	C₂×C₃×#95	C₂²	1	1	yes	characteristic
125	C₂×C₃×#95	C₂²	1	2	yes	—
126	C₂×#554	C₂×C₃	1	1	yes	characteristic, complemented
127	C₂×#551	C₂×C₃	1	1	yes	characteristic
128	#2821	C₂×C₃	1	1	yes	characteristic, complemented
129	#2814	C₂×C₃	1	1	yes	characteristic, complemented
130	#2721	C₂×C₃	1	2	yes	complemented
131	#2700	C₂×C₃	1	2	yes	complemented
132	#2690	C₂×C₃	1	2	yes	complemented
133	#2680	C₂×C₃	1	2	yes	complemented
134	#2659	C₂×C₃	1	1	yes	characteristic, complemented
135	#2638	C₂×C₃	1	1	yes	characteristic, complemented
136	#2637	C₂×C₃	1	1	yes	characteristic, complemented
137	#2623	C₂×C₃	1	1	yes	characteristic, complemented
138	#2621	C₂×C₃	1	1	yes	characteristic, complemented
139	#2599	C₂×C₃	1	1	yes	characteristic, complemented
140	#2561	C₂×C₃	1	1	yes	characteristic, complemented
141	#2502	C₂×C₃	1	1	yes	characteristic, complemented
142	#2486	C₂×C₃	1	1	yes	characteristic, complemented
143	#2438	C₂×C₃	1	2	yes	complemented
144	#2437	C₂×C₃	1	2	yes	complemented
145	#2419	C₂×C₃	1	2	yes	complemented
146	#2418	C₂×C₃	1	2	yes	—
147	C₂×#397	C₂×C₃	1	1	yes	characteristic, complemented
148	#2318	C₂×C₃	1	1	yes	characteristic, complemented
149	C₂⁵×C₃	C₂³	1	1	yes	characteristic
150	C₂²×C₃×Q₈	C₂³	1	1	yes	characteristic
151	C₂²×C₃×Q₈	C₂³	1	2	yes	—
152	C₂²×C₃×Q₈	C₂³	1	1	yes	characteristic
153	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
154	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
155	C₂²×C₃×D₄	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	2	yes	—
159	C₂³×C₃×C₄	C₂³	1	2	yes	—
160	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
161	C₂³×C₃×C₄	C₂³	1	2	yes	—
162	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
163	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
164	C₃×C₄⋊Q₈	—	2	4	no	—
165	C₃×#126	—	2	4	no	—
166	C₃×#126	—	2	4	no	—
167	C₃×#125	—	2	8	no	—
168	C₃×#124	—	2	4	no	—
169	C₃×#123	—	2	4	no	—
170	C₃×#123	—	2	4	no	—
171	C₃×#123	—	2	4	no	—
172	C₃×#123	—	4	4	no	—
173	C₃×C₂²⋊Q₈	—	2	4	no	—
174	C₃×C₂²⋊Q₈	—	2	4	no	—
175	C₃×C₂²⋊Q₈	—	2	4	no	—
176	C₃×C₂²⋊Q₈	—	2	4	no	—
177	C₃×C₂²⋊Q₈	—	2	8	no	—
178	C₃×C₂²⋊Q₈	—	2	8	no	—
179	C₃×C₂²⋊Q₈	—	4	4	no	—
180	C₃×#120	—	2	4	no	—
181	C₃×C₄×Q₈	—	2	4	no	—
182	C₃×C₄×D₄	—	2	8	no	—
183	C₃×C₄×D₄	—	2	4	no	—
184	C₃×C₄×D₄	D₄	1	8	yes	—
185	C₃×#117	—	2	4	no	—
186	C₃×#117	—	2	4	no	—
187	C₂×C₃×C₄⋊C₄	—	2	4	no	—
188	C₂×C₃×C₄⋊C₄	—	2	4	no	—
189	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
190	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
191	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
192	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
193	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
194	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
195	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
196	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
197	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
198	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
199	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
200	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
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	2	yes	—
204	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
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	2	yes	—
208	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
209	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
210	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
211	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
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	1	yes	characteristic
216	C₂×C₃×C₂²⋊C₄	—	2	4	no	—
217	C₂×C₃×C₂²⋊C₄	—	2	4	no	—
218	C₂×C₃×C₂²⋊C₄	—	4	4	no	—
219	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
220	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
221	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
222	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
223	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
224	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
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	1	yes	characteristic
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	1	yes	characteristic
231	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
235	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
236	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
245	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
246	C₂×C₃×C₄²	C₂³	1	2	yes	—
247	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
248	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
249	C₂×C₃×C₄²	C₂³	1	2	yes	—
250	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
251	C₃×#95	C₂³	1	1	yes	characteristic
252	C₃×#95	C₂³	1	1	yes	characteristic
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	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	2	yes	—
264	C₃×#95	C₂³	1	2	yes	—
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	2	yes	—
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	#554	—	2	8	no	—
277	#551	—	2	8	no	—
278	C₂×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
279	C₂×#126	C₂²×C₃	1	1	yes	characteristic
280	C₂×#126	C₂²×C₃	1	1	yes	characteristic
281	C₂×#125	C₂²×C₃	1	2	yes	complemented
282	C₂×#124	C₂²×C₃	1	1	yes	characteristic
283	C₂×#123	C₂²×C₃	1	1	yes	characteristic
284	C₂×#123	C₂²×C₃	1	1	yes	characteristic
285	C₂×#123	C₂²×C₃	1	1	yes	characteristic
286	C₂×#123	C₂²×C₃	1	2	yes	—
287	C₂×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
288	C₂×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
289	C₂×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
290	C₂×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
291	C₂×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
292	C₂×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
293	C₂×C₂²⋊Q₈	C₂²×C₃	1	2	yes	complemented
294	C₂×#120	C₂²×C₃	1	1	yes	characteristic
295	C₂×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
296	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
297	C₂×C₄×D₄	C₂²×C₃	1	2	yes	—
298	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
299	C₂×#117	C₂²×C₃	1	1	yes	characteristic
300	C₂×#117	C₂²×C₃	1	1	yes	characteristic
301	C₂²×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
302	C₂²×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
303	C₂²×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
304	C₂²×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
305	C₂²×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
306	#400	C₂²×C₃	1	2	yes	complemented
307	#400	C₂²×C₃	1	2	yes	complemented
308	#399	C₂²×C₃	1	2	yes	—
309	#399	C₂²×C₃	1	2	yes	—
310	#398	C₂²×C₃	1	1	yes	characteristic, complemented
311	#398	C₂²×C₃	1	1	yes	characteristic, complemented
312	#398	C₂²×C₃	1	1	yes	characteristic, complemented
313	#398	C₂²×C₃	1	1	yes	characteristic, complemented
314	#398	C₂²×C₃	1	2	yes	complemented
315	#398	C₂²×C₃	1	1	yes	characteristic, complemented
316	#398	C₂²×C₃	1	2	yes	complemented
317	#398	C₂²×C₃	1	1	yes	characteristic, complemented
318	#398	C₂²×C₃	1	2	yes	complemented
319	#398	C₂²×C₃	1	2	yes	complemented
320	#397	C₂²×C₃	1	1	yes	characteristic
321	#397	C₂²×C₃	1	1	yes	characteristic
322	#397	C₂²×C₃	1	1	yes	characteristic
323	#397	C₂²×C₃	1	1	yes	characteristic
324	#397	C₂²×C₃	1	1	yes	characteristic
325	#397	C₂²×C₃	1	2	yes	—
326	#397	C₂²×C₃	1	1	yes	characteristic
327	#397	C₂²×C₃	1	2	yes	—
328	#397	C₂²×C₃	1	2	yes	—
329	#397	C₂²×C₃	1	2	yes	complemented
330	#397	C₂²×C₃	1	2	yes	complemented
331	#396	C₂²×C₃	1	2	yes	—
332	#396	C₂²×C₃	1	2	yes	—
333	#395	C₂²×C₃	1	2	yes	complemented
334	#395	C₂²×C₃	1	1	yes	characteristic, complemented
335	#395	C₂²×C₃	1	1	yes	characteristic, complemented
336	#395	C₂²×C₃	1	2	yes	complemented
337	#394	C₂²×C₃	1	2	yes	—
338	#394	C₂²×C₃	1	2	yes	—
339	#393	C₂²×C₃	1	1	yes	characteristic
340	#393	C₂²×C₃	1	1	yes	characteristic
341	#393	C₂²×C₃	1	2	yes	—
342	#391	C₂²×C₃	1	2	yes	complemented
343	#391	C₂²×C₃	1	2	yes	complemented
344	#389	C₂²×C₃	1	2	yes	complemented
345	#388	C₂²×C₃	1	2	yes	—
346	#388	C₂²×C₃	1	2	yes	—
347	#388	C₂²×C₃	1	2	yes	—
348	#388	C₂²×C₃	1	2	yes	—
349	#388	C₂²×C₃	1	2	yes	complemented
350	#387	C₂²×C₃	1	2	yes	complemented
351	#387	C₂²×C₃	1	2	yes	complemented
352	#387	C₂²×C₃	1	2	yes	complemented
353	#387	C₂²×C₃	1	2	yes	complemented
354	#387	C₂²×C₃	1	2	yes	complemented
355	#386	C₂²×C₃	1	2	yes	—
356	#386	C₂²×C₃	1	2	yes	—
357	#385	C₂²×C₃	1	2	yes	—
358	#385	C₂²×C₃	1	2	yes	—
359	#385	C₂²×C₃	1	2	yes	—
360	#385	C₂²×C₃	1	2	yes	—
361	#385	C₂²×C₃	1	2	yes	—
362	#385	C₂²×C₃	1	2	yes	complemented
363	#384	C₂²×C₃	1	2	yes	complemented
364	#383	C₂²×C₃	1	1	yes	characteristic, complemented
365	#382	C₂²×C₃	1	1	yes	characteristic, complemented
366	#381	C₂²×C₃	1	2	yes	—
367	#381	C₂²×C₃	1	1	yes	characteristic, complemented
368	#381	C₂²×C₃	1	2	yes	complemented
369	#380	C₂²×C₃	1	2	yes	—
370	#380	C₂²×C₃	1	2	yes	—
371	#380	C₂²×C₃	1	2	yes	—
372	#380	C₂²×C₃	1	1	yes	characteristic, complemented
373	#379	C₂²×C₃	1	2	yes	—
374	C₄×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
375	C₂×#95	C₂²×C₃	1	1	yes	characteristic
376	C₂×#95	C₂²×C₃	1	2	yes	—
377	C₂⁴×C₃	—	2	2	no	—
378	C₂⁴×C₃	—	2	2	no	—
379	C₂⁴×C₃	—	2	4	no	—
380	C₂⁴×C₃	—	4	2	no	—
381	C₂⁴×C₃	—	4	1	no	—
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	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
386	C₂×C₃×Q₈	—	2	2	no	—
387	C₂×C₃×Q₈	—	2	2	no	—
388	C₂×C₃×Q₈	—	2	4	no	—
389	C₂×C₃×Q₈	—	4	2	no	—
390	C₂×C₃×Q₈	—	4	2	no	—
391	C₂×C₃×Q₈	—	4	2	no	—
392	C₂×C₃×Q₈	—	4	2	no	—
393	C₂×C₃×D₄	—	2	4	no	—
394	C₂×C₃×D₄	—	2	2	no	—
395	C₂×C₃×D₄	—	2	2	no	—
396	C₂×C₃×D₄	—	2	2	no	—
397	C₂×C₃×D₄	—	4	1	no	—
398	C₂×C₃×D₄	—	4	2	no	—
399	C₂×C₃×D₄	C₂×D₄	1	4	yes	—
400	C₂²×C₃×C₄	—	2	2	no	—
401	C₂²×C₃×C₄	—	2	2	no	—
402	C₂²×C₃×C₄	—	2	4	no	—
403	C₂²×C₃×C₄	—	2	4	no	—
404	C₂²×C₃×C₄	—	2	4	no	—
405	C₂²×C₃×C₄	—	2	4	no	—
406	C₂²×C₃×C₄	—	2	2	no	—
407	C₂²×C₃×C₄	—	2	2	no	—
408	C₂²×C₃×C₄	—	4	2	no	—
409	C₂²×C₃×C₄	—	4	2	no	—
410	C₂²×C₃×C₄	—	4	1	no	—
411	C₂²×C₃×C₄	—	4	2	no	—
412	C₂²×C₃×C₄	—	4	2	no	—
413	C₂²×C₃×C₄	—	4	2	no	—
414	C₂²×C₃×C₄	—	4	2	no	—
415	C₂²×C₃×C₄	—	4	2	no	—
416	C₂²×C₃×C₄	—	4	2	no	—
417	C₂²×C₃×C₄	—	4	2	no	—
418	C₂²×C₃×C₄	C₂×D₄	1	4	yes	—
419	C₂²×C₃×C₄	C₂×D₄	1	4	yes	—
420	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
421	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
422	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
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	2	yes	—
429	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
430	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
431	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
432	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
433	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
434	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
435	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
436	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
437	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
438	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
439	C₃×C₄⋊C₄	—	2	2	no	—
440	C₃×C₄⋊C₄	—	2	4	no	—
441	C₃×C₄⋊C₄	—	2	4	no	—
442	C₃×C₄⋊C₄	—	2	2	no	—
443	C₃×C₄⋊C₄	—	2	2	no	—
444	C₃×C₄⋊C₄	—	2	2	no	—
445	C₃×C₄⋊C₄	—	2	2	no	—
446	C₃×C₄⋊C₄	—	2	2	no	—
447	C₃×C₄⋊C₄	—	2	2	no	—
448	C₃×C₄⋊C₄	—	2	2	no	—
449	C₃×C₄⋊C₄	—	2	4	no	—
450	C₃×C₄⋊C₄	—	2	4	no	—
451	C₃×C₄⋊C₄	—	2	4	no	—
452	C₃×C₄⋊C₄	—	2	4	no	—
453	C₃×C₄⋊C₄	—	2	2	no	—
454	C₃×C₄⋊C₄	—	2	2	no	—
455	C₃×C₄⋊C₄	—	4	2	no	—
456	C₃×C₄⋊C₄	—	4	2	no	—
457	C₃×C₄⋊C₄	—	4	2	no	—
458	C₃×C₄⋊C₄	—	4	2	no	—
459	C₃×C₄⋊C₄	—	4	2	no	—
460	C₃×C₄⋊C₄	—	4	2	no	—
461	C₃×C₄⋊C₄	—	4	2	no	—
462	C₃×C₄⋊C₄	—	4	2	no	—
463	C₃×C₄⋊C₄	—	4	2	no	—
464	C₃×C₄⋊C₄	—	4	2	no	—
465	C₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
466	C₃×C₂²⋊C₄	—	2	2	no	—
467	C₃×C₂²⋊C₄	—	2	2	no	—
468	C₃×C₂²⋊C₄	—	2	4	no	—
469	C₃×C₂²⋊C₄	—	2	4	no	—
470	C₃×C₂²⋊C₄	—	2	2	no	—
471	C₃×C₂²⋊C₄	—	2	2	no	—
472	C₃×C₂²⋊C₄	—	2	4	no	—
473	C₃×C₂²⋊C₄	—	2	4	no	—
474	C₃×C₂²⋊C₄	—	2	4	no	—
475	C₃×C₂²⋊C₄	—	2	4	no	—
476	C₃×C₂²⋊C₄	—	2	2	no	—
477	C₃×C₂²⋊C₄	—	2	2	no	—
478	C₃×C₂²⋊C₄	—	2	2	no	—
479	C₃×C₂²⋊C₄	—	2	2	no	—
480	C₃×C₂²⋊C₄	—	2	2	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	—	4	2	no	—
485	C₃×C₂²⋊C₄	—	4	2	no	—
486	C₃×C₂²⋊C₄	—	4	2	no	—
487	C₃×C₂²⋊C₄	—	4	2	no	—
488	C₃×C₂²⋊C₄	—	4	2	no	—
489	C₃×C₂²⋊C₄	—	4	2	no	—
490	C₃×C₂²⋊C₄	—	4	2	no	—
491	C₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
492	C₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
493	C₃×C₄²	—	2	2	no	—
494	C₃×C₄²	—	2	2	no	—
495	C₃×C₄²	—	2	4	no	—
496	C₃×C₄²	—	4	2	no	—
497	C₃×C₄²	C₂×D₄	1	4	yes	—
498	C₂⁵	C₂³×C₃	1	1	yes	characteristic
499	C₂²×Q₈	C₂³×C₃	1	1	yes	characteristic
500	C₂²×Q₈	C₂³×C₃	1	2	yes	—
501	C₂²×Q₈	C₂³×C₃	1	1	yes	characteristic
502	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
503	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
504	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
505	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
506	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
507	C₂³×C₄	C₂³×C₃	1	2	yes	—
508	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
509	C₂³×C₄	C₂³×C₃	1	2	yes	—
510	C₂³×C₄	C₂³×C₃	1	2	yes	—
511	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
512	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
513	C₄⋊Q₈	—	2	4	no	—
514	#126	—	2	4	no	—
515	#126	—	2	4	no	—
516	#125	—	2	8	no	—
517	#124	—	2	4	no	—
518	#123	—	2	4	no	—
519	#123	—	2	4	no	—
520	#123	—	2	4	no	—
521	#123	—	4	4	no	—
522	C₂²⋊Q₈	—	2	4	no	—
523	C₂²⋊Q₈	—	2	4	no	—
524	C₂²⋊Q₈	—	2	4	no	—
525	C₂²⋊Q₈	—	2	4	no	—
526	C₂²⋊Q₈	—	2	8	no	—
527	C₂²⋊Q₈	—	2	8	no	—
528	C₂²⋊Q₈	—	4	4	no	—
529	#120	—	2	4	no	—
530	C₄×Q₈	—	2	4	no	—
531	C₄×D₄	—	2	8	no	—
532	C₄×D₄	—	2	4	no	—
533	C₄×D₄	C₃×D₄	1	8	yes	—
534	#117	—	2	4	no	—
535	#117	—	2	4	no	—
536	C₂×C₄⋊C₄	—	2	4	no	—
537	C₂×C₄⋊C₄	—	2	4	no	—
538	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
539	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
540	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
541	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
542	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
543	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
544	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
545	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
546	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
547	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
548	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
549	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
550	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
551	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
552	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
553	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
554	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
555	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
556	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
557	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
558	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
559	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
560	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
561	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
562	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
563	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
564	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
565	C₂×C₂²⋊C₄	—	2	4	no	—
566	C₂×C₂²⋊C₄	—	2	4	no	—
567	C₂×C₂²⋊C₄	—	4	4	no	—
568	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
569	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
570	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
571	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
572	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
573	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
574	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
575	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
576	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
577	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
578	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
579	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
580	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
581	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
582	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
583	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
584	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
585	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
586	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
587	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
588	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
589	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
590	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
591	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
592	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
593	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
594	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
595	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
596	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
597	C₂×C₄²	C₂³×C₃	1	2	yes	—
598	C₂×C₄²	C₂³×C₃	1	2	yes	—
599	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
600	#95	C₂³×C₃	1	1	yes	characteristic
601	#95	C₂³×C₃	1	1	yes	characteristic
602	#95	C₂³×C₃	1	2	yes	—
603	#95	C₂³×C₃	1	2	yes	—
604	#95	C₂³×C₃	1	2	yes	—
605	#95	C₂³×C₃	1	2	yes	—
606	#95	C₂³×C₃	1	2	yes	—
607	#95	C₂³×C₃	1	1	yes	characteristic
608	#95	C₂³×C₃	1	1	yes	characteristic
609	#95	C₂³×C₃	1	2	yes	—
610	#95	C₂³×C₃	1	2	yes	—
611	#95	C₂³×C₃	1	2	yes	—
612	#95	C₂³×C₃	1	2	yes	—
613	#95	C₂³×C₃	1	2	yes	—
614	#95	C₂³×C₃	1	2	yes	—
615	#95	C₂³×C₃	1	2	yes	—
616	#95	C₂³×C₃	1	2	yes	—
617	#95	C₂³×C₃	1	2	yes	—
618	#95	C₂³×C₃	1	2	yes	—
619	#95	C₂³×C₃	1	2	yes	—
620	#95	C₂³×C₃	1	2	yes	—
621	#95	C₂³×C₃	1	2	yes	—
622	#95	C₂³×C₃	1	2	yes	—
623	#95	C₂³×C₃	1	2	yes	—
624	#95	C₂³×C₃	1	2	yes	—
625	C₂³×C₃	—	2	1	no	—
626	C₂³×C₃	—	2	2	no	—
627	C₂³×C₃	—	2	1	no	—
628	C₂³×C₃	—	2	1	no	—
629	C₂³×C₃	—	2	1	no	—
630	C₂³×C₃	—	2	2	no	—
631	C₂³×C₃	—	2	2	no	—
632	C₂³×C₃	—	2	2	no	—
633	C₂³×C₃	—	2	2	no	—
634	C₂³×C₃	—	2	1	no	—
635	C₂³×C₃	—	2	1	no	—
636	C₂³×C₃	—	2	1	no	—
637	C₂³×C₃	—	2	1	no	—
638	C₂³×C₃	—	2	2	no	—
639	C₂³×C₃	—	2	1	no	—
640	C₂³×C₃	—	2	2	no	—
641	C₂³×C₃	—	4	4	no	—
642	C₂³×C₃	—	4	8	no	—
643	C₂³×C₃	—	4	4	no	—
644	C₂³×C₃	—	8	2	no	—
645	C₂³×C₃	—	8	4	no	—
646	C₂³×C₃	C₂²×D₄	1	2	yes	—
647	C₂³×C₃	C₂²×D₄	1	2	yes	—
648	C₂³×C₃	H(5,𝔽₂)	1	2	yes	—
649	C₂³×C₃	2₋¹⁺⁴	1	4	yes	—
650	C₂³×C₃	C₂⁵	1	1	yes	characteristic
651	C₃×Q₈	—	4	4	no	—
652	C₃×Q₈	—	8	2	no	—
653	C₃×Q₈	—	8	4	no	—
654	C₃×D₄	—	2	8	no	—
655	C₃×D₄	—	4	4	no	—
656	C₃×D₄	—	8	2	no	—
657	C₂×C₃×C₄	—	2	1	no	—
658	C₂×C₃×C₄	—	2	2	no	—
659	C₂×C₃×C₄	—	2	2	no	—
660	C₂×C₃×C₄	—	2	2	no	—
661	C₂×C₃×C₄	—	2	2	no	—
662	C₂×C₃×C₄	—	2	1	no	—
663	C₂×C₃×C₄	—	2	1	no	—
664	C₂×C₃×C₄	—	2	1	no	—
665	C₂×C₃×C₄	—	2	2	no	—
666	C₂×C₃×C₄	—	2	1	no	—
667	C₂×C₃×C₄	—	2	2	no	—
668	C₂×C₃×C₄	—	2	1	no	—
669	C₂×C₃×C₄	—	2	1	no	—
670	C₂×C₃×C₄	—	2	1	no	—
671	C₂×C₃×C₄	—	2	2	no	—
672	C₂×C₃×C₄	—	2	2	no	—
673	C₂×C₃×C₄	—	2	2	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	2	no	—
678	C₂×C₃×C₄	—	2	2	no	—
679	C₂×C₃×C₄	—	2	1	no	—
680	C₂×C₃×C₄	—	2	1	no	—
681	C₂×C₃×C₄	—	2	2	no	—
682	C₂×C₃×C₄	—	2	2	no	—
683	C₂×C₃×C₄	—	2	2	no	—
684	C₂×C₃×C₄	—	2	2	no	—
685	C₂×C₃×C₄	—	2	2	no	—
686	C₂×C₃×C₄	—	2	2	no	—
687	C₂×C₃×C₄	—	2	2	no	—
688	C₂×C₃×C₄	—	2	2	no	—
689	C₂×C₃×C₄	—	2	2	no	—
690	C₂×C₃×C₄	—	2	2	no	—
691	C₂×C₃×C₄	—	2	2	no	—
692	C₂×C₃×C₄	—	2	2	no	—
693	C₂×C₃×C₄	—	2	2	no	—
694	C₂×C₃×C₄	—	2	1	no	—
695	C₂×C₃×C₄	—	2	2	no	—
696	C₂×C₃×C₄	—	2	1	no	—
697	C₂×C₃×C₄	—	2	2	no	—
698	C₂×C₃×C₄	—	2	2	no	—
699	C₂×C₃×C₄	—	2	2	no	—
700	C₂×C₃×C₄	—	2	2	no	—
701	C₂×C₃×C₄	—	4	4	no	—
702	C₂×C₃×C₄	—	4	4	no	—
703	C₂×C₃×C₄	—	4	4	no	—
704	C₂×C₃×C₄	—	4	4	no	—
705	C₂×C₃×C₄	—	8	2	no	—
706	C₂×C₃×C₄	—	8	4	no	—
707	C₂×C₃×C₄	—	8	4	no	—
708	C₂×C₃×C₄	—	8	4	no	—
709	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
710	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
711	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
712	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
713	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
714	C₂⁴	—	2	2	no	—
715	C₂⁴	—	2	2	no	—
716	C₂⁴	—	2	4	no	—
717	C₂⁴	—	4	2	no	—
718	C₂⁴	—	4	1	no	—
719	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
720	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
721	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
722	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
723	C₂×Q₈	—	2	2	no	—
724	C₂×Q₈	—	2	2	no	—
725	C₂×Q₈	—	2	4	no	—
726	C₂×Q₈	—	4	2	no	—
727	C₂×Q₈	—	4	2	no	—
728	C₂×Q₈	—	4	2	no	—
729	C₂×Q₈	—	4	2	no	—
730	C₂×D₄	—	2	4	no	—
731	C₂×D₄	—	2	2	no	—
732	C₂×D₄	—	2	2	no	—
733	C₂×D₄	—	2	2	no	—
734	C₂×D₄	—	4	1	no	—
735	C₂×D₄	—	4	2	no	—
736	C₂×D₄	C₂×C₃×D₄	1	4	yes	—
737	C₂²×C₄	—	2	2	no	—
738	C₂²×C₄	—	2	2	no	—
739	C₂²×C₄	—	2	4	no	—
740	C₂²×C₄	—	2	4	no	—
741	C₂²×C₄	—	2	4	no	—
742	C₂²×C₄	—	2	4	no	—
743	C₂²×C₄	—	2	2	no	—
744	C₂²×C₄	—	2	2	no	—
745	C₂²×C₄	—	4	2	no	—
746	C₂²×C₄	—	4	2	no	—
747	C₂²×C₄	—	4	1	no	—
748	C₂²×C₄	—	4	2	no	—
749	C₂²×C₄	—	4	2	no	—
750	C₂²×C₄	—	4	2	no	—
751	C₂²×C₄	—	4	2	no	—
752	C₂²×C₄	—	4	2	no	—
753	C₂²×C₄	—	4	2	no	—
754	C₂²×C₄	—	4	2	no	—
755	C₂²×C₄	C₂×C₃×D₄	1	4	yes	—
756	C₂²×C₄	C₂×C₃×D₄	1	4	yes	—
757	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
758	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
759	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
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	2	yes	—
766	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
767	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
768	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
769	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
770	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
771	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
772	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
773	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
774	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
775	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
776	C₄⋊C₄	—	2	2	no	—
777	C₄⋊C₄	—	2	4	no	—
778	C₄⋊C₄	—	2	4	no	—
779	C₄⋊C₄	—	2	2	no	—
780	C₄⋊C₄	—	2	2	no	—
781	C₄⋊C₄	—	2	2	no	—
782	C₄⋊C₄	—	2	2	no	—
783	C₄⋊C₄	—	2	2	no	—
784	C₄⋊C₄	—	2	2	no	—
785	C₄⋊C₄	—	2	2	no	—
786	C₄⋊C₄	—	2	4	no	—
787	C₄⋊C₄	—	2	4	no	—
788	C₄⋊C₄	—	2	4	no	—
789	C₄⋊C₄	—	2	4	no	—
790	C₄⋊C₄	—	2	2	no	—
791	C₄⋊C₄	—	2	2	no	—
792	C₄⋊C₄	—	4	2	no	—
793	C₄⋊C₄	—	4	2	no	—
794	C₄⋊C₄	—	4	2	no	—
795	C₄⋊C₄	—	4	2	no	—
796	C₄⋊C₄	—	4	2	no	—
797	C₄⋊C₄	—	4	2	no	—
798	C₄⋊C₄	—	4	2	no	—
799	C₄⋊C₄	—	4	2	no	—
800	C₄⋊C₄	—	4	2	no	—
801	C₄⋊C₄	—	4	2	no	—
802	C₄⋊C₄	C₂×C₃×D₄	1	4	yes	—
803	C₂²⋊C₄	—	2	2	no	—
804	C₂²⋊C₄	—	2	2	no	—
805	C₂²⋊C₄	—	2	4	no	—
806	C₂²⋊C₄	—	2	4	no	—
807	C₂²⋊C₄	—	2	2	no	—
808	C₂²⋊C₄	—	2	2	no	—
809	C₂²⋊C₄	—	2	4	no	—
810	C₂²⋊C₄	—	2	4	no	—
811	C₂²⋊C₄	—	2	4	no	—
812	C₂²⋊C₄	—	2	4	no	—
813	C₂²⋊C₄	—	2	2	no	—
814	C₂²⋊C₄	—	2	2	no	—
815	C₂²⋊C₄	—	2	2	no	—
816	C₂²⋊C₄	—	2	2	no	—
817	C₂²⋊C₄	—	2	2	no	—
818	C₂²⋊C₄	—	2	2	no	—
819	C₂²⋊C₄	—	2	2	no	—
820	C₂²⋊C₄	—	2	2	no	—
821	C₂²⋊C₄	—	4	2	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	—	4	2	no	—
828	C₂²⋊C₄	C₂×C₃×D₄	1	4	yes	—
829	C₂²⋊C₄	C₂×C₃×D₄	1	4	yes	—
830	C₄²	—	2	2	no	—
831	C₄²	—	2	2	no	—
832	C₄²	—	2	4	no	—
833	C₄²	—	4	2	no	—
834	C₄²	C₂×C₃×D₄	1	4	yes	—
835	C₂²×C₃	—	2	2	no	—
836	C₂²×C₃	—	2	2	no	—
837	C₂²×C₃	—	2	4	no	—
838	C₂²×C₃	—	2	4	no	—
839	C₂²×C₃	—	2	2	no	—
840	C₂²×C₃	—	2	2	no	—
841	C₂²×C₃	—	2	2	no	—
842	C₂²×C₃	—	2	2	no	—
843	C₂²×C₃	—	2	4	no	—
844	C₂²×C₃	—	4	1	no	—
845	C₂²×C₃	—	4	1	no	—
846	C₂²×C₃	—	4	2	no	—
847	C₂²×C₃	—	4	2	no	—
848	C₂²×C₃	—	4	2	no	—
849	C₂²×C₃	—	4	1	no	—
850	C₂²×C₃	—	4	1	no	—
851	C₂²×C₃	—	4	1	no	—
852	C₂²×C₃	—	4	2	no	—
853	C₂²×C₃	—	4	2	no	—
854	C₂²×C₃	—	8	8	no	—
855	C₂²×C₃	#536	1	4	yes	—
856	C₂²×C₃	C₂³×D₄	1	1	yes	characteristic
857	C₂²×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
858	C₂²×C₃	C₂×2₋¹⁺⁴	1	2	yes	—
859	C₂²×C₃	#585	1	2	yes	—
860	C₂²×C₃	#585	1	1	yes	characteristic
861	C₃×C₄	—	2	2	no	—
862	C₃×C₄	—	2	2	no	—
863	C₃×C₄	—	2	2	no	—
864	C₃×C₄	—	2	2	no	—
865	C₃×C₄	—	2	2	no	—
866	C₃×C₄	—	4	1	no	—
867	C₃×C₄	—	4	1	no	—
868	C₃×C₄	—	4	1	no	—
869	C₃×C₄	—	4	1	no	—
870	C₃×C₄	—	4	2	no	—
871	C₃×C₄	—	4	1	no	—
872	C₃×C₄	—	4	2	no	—
873	C₃×C₄	—	4	2	no	—
874	C₃×C₄	—	4	2	no	—
875	C₃×C₄	—	4	1	no	—
876	C₃×C₄	—	4	2	no	—
877	C₃×C₄	—	4	2	no	—
878	C₃×C₄	—	4	2	no	—
879	C₃×C₄	—	4	2	no	—
880	C₂³	—	2	1	no	—
881	C₂³	—	2	2	no	—
882	C₂³	—	2	1	no	—
883	C₂³	—	2	1	no	—
884	C₂³	—	2	1	no	—
885	C₂³	—	2	2	no	—
886	C₂³	—	2	2	no	—
887	C₂³	—	2	2	no	—
888	C₂³	—	2	2	no	—
889	C₂³	—	2	1	no	—
890	C₂³	—	2	1	no	—
891	C₂³	—	2	1	no	—
892	C₂³	—	2	1	no	—
893	C₂³	—	2	2	no	—
894	C₂³	—	2	1	no	—
895	C₂³	—	2	2	no	—
896	C₂³	—	4	4	no	—
897	C₂³	—	4	8	no	—
898	C₂³	—	4	4	no	—
899	C₂³	—	8	2	no	—
900	C₂³	—	8	4	no	—
901	C₂³	C₂²×C₃×D₄	1	2	yes	—
902	C₂³	C₂²×C₃×D₄	1	2	yes	—
903	C₂³	C₃×H(5,𝔽₂)	1	2	yes	—
904	C₂³	C₃×2₋¹⁺⁴	1	4	yes	—
905	C₂³	C₂⁵×C₃	1	1	yes	characteristic
906	Q₈	—	4	4	no	—
907	Q₈	—	8	2	no	—
908	Q₈	—	8	4	no	—
909	D₄	—	2	8	no	—
910	D₄	—	4	4	no	—
911	D₄	—	8	2	no	—
912	C₂×C₄	—	2	1	no	—
913	C₂×C₄	—	2	2	no	—
914	C₂×C₄	—	2	2	no	—
915	C₂×C₄	—	2	2	no	—
916	C₂×C₄	—	2	2	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	1	no	—
922	C₂×C₄	—	2	2	no	—
923	C₂×C₄	—	2	1	no	—
924	C₂×C₄	—	2	1	no	—
925	C₂×C₄	—	2	1	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	2	no	—
931	C₂×C₄	—	2	2	no	—
932	C₂×C₄	—	2	2	no	—
933	C₂×C₄	—	2	2	no	—
934	C₂×C₄	—	2	1	no	—
935	C₂×C₄	—	2	1	no	—
936	C₂×C₄	—	2	2	no	—
937	C₂×C₄	—	2	2	no	—
938	C₂×C₄	—	2	2	no	—
939	C₂×C₄	—	2	2	no	—
940	C₂×C₄	—	2	2	no	—
941	C₂×C₄	—	2	2	no	—
942	C₂×C₄	—	2	2	no	—
943	C₂×C₄	—	2	2	no	—
944	C₂×C₄	—	2	2	no	—
945	C₂×C₄	—	2	2	no	—
946	C₂×C₄	—	2	2	no	—
947	C₂×C₄	—	2	2	no	—
948	C₂×C₄	—	2	2	no	—
949	C₂×C₄	—	2	1	no	—
950	C₂×C₄	—	2	2	no	—
951	C₂×C₄	—	2	1	no	—
952	C₂×C₄	—	2	2	no	—
953	C₂×C₄	—	2	2	no	—
954	C₂×C₄	—	2	2	no	—
955	C₂×C₄	—	2	2	no	—
956	C₂×C₄	—	4	4	no	—
957	C₂×C₄	—	4	4	no	—
958	C₂×C₄	—	4	4	no	—
959	C₂×C₄	—	4	4	no	—
960	C₂×C₄	—	8	2	no	—
961	C₂×C₄	—	8	4	no	—
962	C₂×C₄	—	8	4	no	—
963	C₂×C₄	—	8	4	no	—
964	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
965	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
966	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
967	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
968	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
969	C₂×C₃	—	2	4	no	—
970	C₂×C₃	—	4	2	no	—
971	C₂×C₃	—	4	2	no	—
972	C₂×C₃	—	8	1	no	—
973	C₂×C₃	C₂×#536	1	1	yes	characteristic
974	C₂×C₃	#3485	1	1	yes	characteristic
975	C₂×C₃	#3488	1	1	yes	characteristic
976	C₂×C₃	#3535	1	2	yes	—
977	C₂×C₃	#3564	1	2	yes	—
978	C₂²	—	2	2	no	—
979	C₂²	—	2	2	no	—
980	C₂²	—	2	4	no	—
981	C₂²	—	2	4	no	—
982	C₂²	—	2	2	no	—
983	C₂²	—	2	2	no	—
984	C₂²	—	2	2	no	—
985	C₂²	—	2	2	no	—
986	C₂²	—	2	4	no	—
987	C₂²	—	4	1	no	—
988	C₂²	—	4	1	no	—
989	C₂²	—	4	2	no	—
990	C₂²	—	4	2	no	—
991	C₂²	—	4	2	no	—
992	C₂²	—	4	1	no	—
993	C₂²	—	4	1	no	—
994	C₂²	—	4	1	no	—
995	C₂²	—	4	2	no	—
996	C₂²	—	4	2	no	—
997	C₂²	—	8	8	no	—
998	C₂²	C₃×#536	1	4	yes	—
999	C₂²	C₂³×C₃×D₄	1	1	yes	characteristic
1000	C₂²	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
1001	C₂²	C₂×C₃×2₋¹⁺⁴	1	2	yes	—
1002	C₂²	C₃×#585	1	2	yes	—
1003	C₂²	C₃×#585	1	1	yes	characteristic
1004	C₄	—	2	2	no	—
1005	C₄	—	2	2	no	—
1006	C₄	—	2	2	no	—
1007	C₄	—	2	2	no	—
1008	C₄	—	2	2	no	—
1009	C₄	—	4	1	no	—
1010	C₄	—	4	1	no	—
1011	C₄	—	4	1	no	—
1012	C₄	—	4	1	no	—
1013	C₄	—	4	2	no	—
1014	C₄	—	4	1	no	—
1015	C₄	—	4	2	no	—
1016	C₄	—	4	2	no	—
1017	C₄	—	4	2	no	—
1018	C₄	—	4	1	no	—
1019	C₄	—	4	2	no	—
1020	C₄	—	4	2	no	—
1021	C₄	—	4	2	no	—
1022	C₄	—	4	2	no	—
1023	C₃	#41412	1	1	yes	characteristic, direct product factor, Sylow
1024	C₂	—	2	4	no	—
1025	C₂	—	4	2	no	—
1026	C₂	—	4	2	no	—
1027	C₂	—	8	1	no	—
1028	C₂	C₂×C₃×#536	1	1	yes	characteristic
1029	C₂	C₃×#3485	1	1	yes	characteristic
1030	C₂	C₃×#3488	1	1	yes	characteristic
1031	C₂	C₃×#3535	1	2	yes	—
1032	C₂	C₃×#3564	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₃	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₃
prime radical	C₂×C₃×#120	C₂²
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×#554	C₂	semidirect
3. C₃×#2821	C₂	semidirect
4. C₃×#2814	C₂	semidirect
5. C₃×#2721	C₂	semidirect
6. C₃×#2700	C₂	semidirect
7. C₃×#2690	C₂	semidirect
8. C₃×#2680	C₂	semidirect
9. C₃×#2659	C₂	semidirect
10. C₃×#2638	C₂	semidirect
11. C₃×#2637	C₂	semidirect
12. C₃×#2623	C₂	semidirect
13. C₃×#2621	C₂	semidirect
14. C₃×#2599	C₂	semidirect
15. C₃×#2561	C₂	semidirect
16. C₃×#2502	C₂	semidirect
17. C₃×#2486	C₂	semidirect
18. C₃×#2438	C₂	semidirect
19. C₃×#2437	C₂	semidirect
20. C₃×#2419	C₂	semidirect
22. C₂×C₃×#397	C₂	semidirect
23. C₃×#2318	C₂	semidirect
24. #41412	C₃	direct (N × H)
27. C₂×C₃×C₄⋊Q₈	C₂²	semidirect
30. C₂×C₃×#125	C₂²	semidirect
41. C₂×C₃×C₂²⋊Q₈	C₂²	semidirect
42. C₂×C₃×C₂²⋊Q₈	C₂²	semidirect
44. C₂×C₃×C₄×Q₈	C₂²	semidirect
51. C₂²×C₃×C₄⋊C₄	C₂²	semidirect
55. C₃×#400	C₂²	semidirect
56. C₃×#400	C₂²	semidirect
59. C₃×#398	C₂²	semidirect
60. C₃×#398	C₂²	semidirect
61. C₃×#398	C₂²	semidirect
62. C₃×#398	C₂²	semidirect
63. C₃×#398	C₂²	semidirect
64. C₃×#398	C₂²	semidirect
65. C₃×#398	C₂²	semidirect
66. C₃×#398	C₂²	semidirect
67. C₃×#398	C₂²	semidirect
68. C₃×#398	C₂²	semidirect
78. C₃×#397	C₂²	semidirect
79. C₃×#397	C₂²	semidirect
82. C₃×#395	C₂²	semidirect
83. C₃×#395	C₂²	semidirect
84. C₃×#395	C₂²	semidirect
85. C₃×#395	C₂²	semidirect
91. C₃×#391	C₂²	semidirect
92. C₃×#391	C₂²	semidirect
93. C₃×#389	C₂²	semidirect
98. C₃×#388	C₂²	semidirect
99. C₃×#387	C₂²	semidirect
100. C₃×#387	C₂²	semidirect
101. C₃×#387	C₂²	semidirect
102. C₃×#387	C₂²	semidirect
103. C₃×#387	C₂²	semidirect
111. C₃×#385	C₂²	semidirect
112. C₃×#384	C₂²	semidirect
113. C₃×#383	C₂²	semidirect
114. C₃×#382	C₂²	semidirect
116. C₃×#381	C₂²	semidirect
117. C₃×#381	C₂²	semidirect
121. C₃×#380	C₂²	semidirect
126. C₂×#554	C₂×C₃	semidirect
128. #2821	C₂×C₃	semidirect
129. #2814	C₂×C₃	semidirect
130. #2721	C₂×C₃	semidirect
131. #2700	C₂×C₃	semidirect
132. #2690	C₂×C₃	semidirect
133. #2680	C₂×C₃	semidirect
134. #2659	C₂×C₃	semidirect
135. #2638	C₂×C₃	semidirect
136. #2637	C₂×C₃	semidirect
137. #2623	C₂×C₃	semidirect
138. #2621	C₂×C₃	semidirect
139. #2599	C₂×C₃	semidirect
140. #2561	C₂×C₃	semidirect
141. #2502	C₂×C₃	semidirect
142. #2486	C₂×C₃	semidirect
143. #2438	C₂×C₃	semidirect
144. #2437	C₂×C₃	semidirect
145. #2419	C₂×C₃	semidirect
147. C₂×#397	C₂×C₃	semidirect
148. #2318	C₂×C₃	semidirect
278. C₂×C₄⋊Q₈	C₂²×C₃	semidirect
281. C₂×#125	C₂²×C₃	semidirect
292. C₂×C₂²⋊Q₈	C₂²×C₃	semidirect
293. C₂×C₂²⋊Q₈	C₂²×C₃	semidirect
295. C₂×C₄×Q₈	C₂²×C₃	semidirect
302. C₂²×C₄⋊C₄	C₂²×C₃	semidirect
306. #400	C₂²×C₃	semidirect
307. #400	C₂²×C₃	semidirect
310. #398	C₂²×C₃	semidirect
311. #398	C₂²×C₃	semidirect
312. #398	C₂²×C₃	semidirect
313. #398	C₂²×C₃	semidirect
314. #398	C₂²×C₃	semidirect
315. #398	C₂²×C₃	semidirect
316. #398	C₂²×C₃	semidirect
317. #398	C₂²×C₃	semidirect
318. #398	C₂²×C₃	semidirect
319. #398	C₂²×C₃	semidirect
329. #397	C₂²×C₃	semidirect
330. #397	C₂²×C₃	semidirect
333. #395	C₂²×C₃	semidirect
334. #395	C₂²×C₃	semidirect
335. #395	C₂²×C₃	semidirect
336. #395	C₂²×C₃	semidirect
342. #391	C₂²×C₃	semidirect
343. #391	C₂²×C₃	semidirect
344. #389	C₂²×C₃	semidirect
349. #388	C₂²×C₃	semidirect
350. #387	C₂²×C₃	semidirect
351. #387	C₂²×C₃	semidirect
352. #387	C₂²×C₃	semidirect
353. #387	C₂²×C₃	semidirect
354. #387	C₂²×C₃	semidirect
362. #385	C₂²×C₃	semidirect
363. #384	C₂²×C₃	semidirect
364. #383	C₂²×C₃	semidirect
365. #382	C₂²×C₃	semidirect
367. #381	C₂²×C₃	semidirect
368. #381	C₂²×C₃	semidirect
372. #380	C₂²×C₃	semidirect
1023. C₃	#41412	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×#554	2
C₂×C₃×#551	2
C₃×#2821	2
C₃×#2814	2
C₃×#2721	2
C₃×#2700	2
C₃×#2690	2
C₃×#2680	2
C₃×#2659	2
C₃×#2638	2
C₃×#2637	2
C₃×#2623	2
C₃×#2621	2
C₃×#2599	2
C₃×#2561	2
C₃×#2502	2
C₃×#2486	2
C₃×#2438	2
C₃×#2437	2
C₃×#2419	2
C₃×#2418	2
C₂×C₃×#397	2
C₃×#2318	2
#41412	3

Subgroups — C3×#41412 #10660019

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#41412 #10660019