Subgroups — D₃×#393979 #72272270

Order 3072.

At least 9816 conjugacy classes of subgroups; only the 1955 normal subgroups are shown.

The subgroup lattice has 771 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72272265	C₂	1	1	yes	maximal, characteristic, complemented
2	#72272264	C₂	1	1	yes	maximal, characteristic, complemented
3	#72272260	C₂	1	1	yes	maximal, characteristic, complemented
4	#72272259	C₂	1	1	yes	maximal, characteristic, complemented
5	#72272252	C₂	1	1	yes	maximal, characteristic, complemented
6	#72272242	C₂	1	1	yes	maximal, characteristic, complemented
7	#72271961	C₂	1	4	yes	maximal, complemented
8	#72271951	C₂	1	4	yes	maximal, complemented
9	#72271729	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#393979	C₂	1	1	yes	maximal, characteristic, complemented
11	D₃×#10738	C₂	1	1	yes	maximal, characteristic, complemented
12	D₃×#60359	C₂	1	1	yes	maximal, characteristic, complemented
13	D₃×#20605	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂²×D₃×#535	C₂	1	1	yes	maximal, characteristic, complemented
15	D₃×#20983	C₂	1	1	yes	maximal, characteristic, complemented
16	D₃×#11004	C₂	1	4	yes	maximal, complemented
17	D₃×#20598	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×D₃×#2008	C₂	1	4	yes	maximal, complemented
19	C₂×D₃×#3003	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂³×D₃×#41	C₂²	1	1	yes	characteristic
21	C₂⁴×D₃×D₄	C₂²	1	1	yes	characteristic
22	C₂×D₃×#575	C₂²	1	2	yes	complemented
23	C₂²×D₃×AGL(1,ℤ/8)	C₂²	1	2	yes	complemented
24	C₂²×#5525	C₂²	1	1	yes	characteristic, complemented
25	C₂²×#5805	C₂²	1	1	yes	characteristic, complemented
26	C₂²×#5830	C₂²	1	1	yes	characteristic, complemented
27	C₂×D₃×#535	C₂²	1	4	yes	—
28	C₂×D₃×#535	C₂²	1	4	yes	complemented
29	C₂×D₃×#525	C₂²	1	1	yes	characteristic
30	C₂²×D₃×#117	C₂²	1	1	yes	characteristic
31	#11661584	C₂²	1	1	yes	characteristic, complemented
32	#11661583	C₂²	1	2	yes	complemented
33	#11661581	C₂²	1	1	yes	characteristic, complemented
34	#11661579	C₂²	1	1	yes	characteristic, complemented
35	#11661577	C₂²	1	2	yes	complemented
36	C₂×#78637	C₂²	1	1	yes	characteristic, complemented
37	C₂×#78926	C₂²	1	2	yes	complemented
38	C₂×#84038	C₂²	1	1	yes	characteristic, complemented
39	C₂×#82927	C₂²	1	1	yes	characteristic, complemented
40	C₂×#83944	C₂²	1	2	yes	complemented
41	C₂×D₃×#421	C₂²	1	4	yes	complemented
42	D₃×#2896	C₂²	1	2	yes	complemented
43	C₂×D₃×#418	C₂²	1	2	yes	complemented
44	C₂×D₃×#418	C₂²	1	4	yes	complemented
45	C₂×D₃×#410	C₂²	1	2	yes	complemented
46	C₂×D₃×#407	C₂²	1	1	yes	characteristic
47	C₂×D₃×#407	C₂²	1	1	yes	characteristic
48	D₃×#2280	C₂²	1	1	yes	characteristic
49	C₂×#69028	C₂²	1	4	yes	complemented
50	C₂×#70331	C₂²	1	4	yes	complemented
51	C₂×#70409	C₂²	1	4	yes	complemented
52	C₂×#71858	C₂²	1	4	yes	complemented
53	C₂×#70050	C₂²	1	4	yes	complemented
54	C₂×#72099	C₂²	1	4	yes	complemented
55	C₂×#72119	C₂²	1	4	yes	complemented
56	#10796982	C₂²	1	1	yes	characteristic, complemented
57	#10796981	C₂²	1	1	yes	characteristic, complemented
58	#10796980	C₂²	1	2	yes	complemented
59	#10796979	C₂²	1	1	yes	characteristic, complemented
60	#10796977	C₂²	1	2	yes	complemented
61	#10794437	C₂²	1	1	yes	characteristic, complemented
62	#10794436	C₂²	1	1	yes	characteristic, complemented
63	#10794435	C₂²	1	1	yes	characteristic, complemented
64	#10794434	C₂²	1	4	yes	complemented
65	#10794391	C₂²	1	1	yes	characteristic, complemented
66	#10794390	C₂²	1	1	yes	characteristic, complemented
67	#10794389	C₂²	1	1	yes	characteristic, complemented
68	#10794388	C₂²	1	4	yes	complemented
69	C₂×D₃×#344	C₂²	1	4	yes	complemented
70	D₃×#1740	C₂²	1	2	yes	complemented
71	#10701878	C₂²	1	4	yes	complemented
72	#10701877	C₂²	1	4	yes	complemented
73	#10701876	C₂²	1	4	yes	complemented
74	#10701875	C₂²	1	4	yes	complemented
75	#10701874	C₂²	1	4	yes	complemented
76	#10701873	C₂²	1	4	yes	complemented
77	#10701872	C₂²	1	4	yes	complemented
78	#10700498	C₂²	1	1	yes	characteristic, complemented
79	#10700497	C₂²	1	1	yes	characteristic, complemented
80	#10700496	C₂²	1	1	yes	characteristic, complemented
81	#10700495	C₂²	1	4	yes	complemented
82	C₂²×C₃×#535	C₂²	1	1	yes	characteristic, complemented
83	C₃×#60359	C₂²	1	1	yes	characteristic, complemented
84	C₂×C₃×#3003	C₂²	1	1	yes	characteristic, complemented
85	C₂×C₃×#2008	C₂²	1	4	yes	complemented
86	C₃×#20983	C₂²	1	1	yes	characteristic, complemented
87	C₃×#20605	C₂²	1	1	yes	characteristic, complemented
88	C₃×#20598	C₂²	1	1	yes	characteristic, complemented
89	C₃×#11004	C₂²	1	4	yes	complemented
90	C₃×#10738	C₂²	1	1	yes	characteristic, complemented
91	#393979	D₃	1	1	yes	characteristic, direct product factor
92	C₂³×C₃×#41	C₂³	1	1	yes	characteristic
93	C₂⁴×C₃×D₄	C₂³	1	1	yes	characteristic
94	C₂²×D₃×#41	D₄	1	2	yes	—
95	C₂²×D₃×#41	D₄	1	2	yes	—
96	C₂²×D₃×#41	C₂³	1	2	yes	—
97	C₂²×D₃×#41	C₂³	1	2	yes	—
98	C₂²×D₃×#41	C₂³	1	1	yes	characteristic
99	C₂³×D₃×Q₈	D₄	1	1	yes	characteristic
100	C₂³×#239	D₄	1	1	yes	characteristic
101	C₂³×D₃×D₄	D₄	1	2	yes	—
102	C₂³×D₃×D₄	D₄	1	1	yes	characteristic
103	C₂³×D₃×D₄	D₄	1	2	yes	—
104	C₂³×D₃×D₄	D₄	1	2	yes	—
105	C₂³×D₃×D₄	D₄	1	2	yes	—
106	C₂³×D₃×D₄	C₂³	1	2	yes	—
107	C₂³×D₃×D₄	C₂³	1	2	yes	—
108	C₂³×#237	D₄	1	1	yes	characteristic
109	C₂³×#235	C₂³	1	1	yes	characteristic
110	C₂⁴×D₁₂	C₂³	1	1	yes	characteristic
111	C₂⁴×C₄×D₃	C₂³	1	1	yes	characteristic
112	C₂×C₃×#575	C₂³	1	2	yes	complemented
113	C₂²×C₃×AGL(1,ℤ/8)	C₂³	1	2	yes	complemented
114	C₂×C₃×#535	C₂³	1	4	yes	—
115	C₂×C₃×#525	C₂³	1	1	yes	characteristic
116	C₂²×C₃×#117	C₂³	1	1	yes	characteristic
117	C₂×#5830	C₂³	1	4	yes	—
118	C₂×#5828	C₂³	1	1	yes	characteristic
119	C₂×#5822	C₂³	1	2	yes	complemented
120	C₂×#5822	C₂³	1	2	yes	complemented
121	C₂²×#949	C₂³	1	2	yes	complemented
122	C₂×#5805	C₂³	1	4	yes	—
123	C₂²×#932	C₂³	1	2	yes	complemented
124	C₂×#5791	C₂³	1	1	yes	characteristic
125	C₂²×#926	C₂³	1	1	yes	characteristic
126	C₂×#5748	C₂³	1	2	yes	complemented
127	C₂²×#908	C₂³	1	2	yes	complemented
128	C₂²×D₃×M₁₆	C₂³	1	2	yes	—
129	C₂²×D₃×M₁₆	C₂³	1	2	yes	—
130	D₃×#535	D₄	1	32	yes	complemented
131	C₂×D₃×C₂²⋊Q₈	D₄	1	2	yes	complemented
132	C₂×#5627	D₄	1	2	yes	complemented
133	C₂×D₃×#121	D₄	1	2	yes	complemented
134	C₂×#5606	D₄	1	2	yes	complemented
135	C₂×#5525	C₂³	1	4	yes	—
136	C₂×#5524	C₂³	1	1	yes	characteristic
137	C₂×D₃×#117	D₄	1	2	yes	—
138	C₂×D₃×#117	D₄	1	2	yes	—
139	C₂×D₃×#117	C₂³	1	2	yes	—
140	C₂×D₃×#117	C₂³	1	1	yes	characteristic
141	C₂×D₃×#117	C₂³	1	2	yes	—
142	C₂×D₃×#117	C₂³	1	2	yes	—
143	C₂²×D₃×C₂²⋊C₄	D₄	1	2	yes	—
144	C₂²×#877	D₄	1	2	yes	—
145	C₂×C₃×#421	C₂³	1	4	yes	complemented
146	C₃×#2896	C₂³	1	2	yes	complemented
147	C₂×C₃×#418	C₂³	1	2	yes	complemented
148	C₂×C₃×#418	C₂³	1	4	yes	complemented
149	C₂×C₃×#410	C₂³	1	2	yes	complemented
150	C₂×C₃×#407	C₂³	1	1	yes	characteristic
151	C₂×C₃×#407	C₂³	1	1	yes	characteristic
152	C₃×#2280	C₂³	1	1	yes	characteristic
153	C₂×#5240	C₂³	1	2	yes	complemented
154	C₂×#5236	C₂³	1	4	yes	complemented
155	#84072	C₂³	1	2	yes	complemented
156	C₂×#5215	C₂³	1	2	yes	complemented
157	C₂×#5215	C₂³	1	4	yes	complemented
158	#84027	C₂³	1	1	yes	characteristic
159	C₂×#5207	C₂³	1	1	yes	characteristic
160	C₂×#5207	C₂³	1	1	yes	characteristic
161	C₂×#5139	C₂³	1	4	yes	complemented
162	#83768	C₂³	1	2	yes	complemented
163	C₂×#5131	C₂³	1	2	yes	complemented
164	C₂×#5131	C₂³	1	4	yes	complemented
165	C₂×#5126	C₂³	1	2	yes	—
166	C₂×#5126	C₂³	1	2	yes	—
167	#82267	C₂³	1	2	yes	—
168	C₂×#5006	C₂³	1	2	yes	complemented
169	C₂×#5006	C₂³	1	2	yes	complemented
170	C₂×#5005	C₂³	1	4	yes	complemented
171	#82213	C₂³	1	2	yes	complemented
172	C₂×#5001	C₂³	1	2	yes	complemented
173	C₂×#5001	C₂³	1	4	yes	complemented
174	D₃×#407	D₄	1	4	yes	complemented
175	D₃×#407	D₄	1	4	yes	complemented
176	C₂×#4726	D₄	1	4	yes	complemented
177	C₂×D₃×C₂²⋊C₈	D₄	1	4	yes	complemented
178	C₂×C₃×#344	C₂³	1	4	yes	complemented
179	C₃×#1740	C₂³	1	2	yes	complemented
180	C₂×#4559	C₂³	1	4	yes	complemented
181	C₂×#4556	C₂³	1	4	yes	complemented
182	#71593	C₂³	1	2	yes	complemented
183	#71593	C₂³	1	2	yes	complemented
184	#71592	C₂³	1	2	yes	complemented
185	C₂×#4533	C₂³	1	4	yes	complemented
186	C₂²×#535	C₂×D₃	1	1	yes	characteristic, complemented
187	#60359	C₂×D₃	1	1	yes	characteristic, complemented
188	C₂×#3003	C₂×D₃	1	1	yes	characteristic, complemented
189	C₂×#2008	C₂×D₃	1	4	yes	complemented
190	#20983	C₂×D₃	1	1	yes	characteristic, complemented
191	#20605	C₂×D₃	1	1	yes	characteristic, complemented
192	#20598	C₂×D₃	1	1	yes	characteristic, complemented
193	#11004	C₂×D₃	1	4	yes	complemented
194	#10738	C₂×D₃	1	1	yes	characteristic, complemented
195	C₂⁵×D₃	C₂×D₄	1	1	yes	characteristic
196	C₂²×C₃×#41	C₂×D₄	1	2	yes	—
197	C₂²×C₃×#41	C₂⁴	1	2	yes	—
198	C₂²×C₃×#41	C₂⁴	1	1	yes	characteristic
199	C₂³×C₃×Q₈	C₂×D₄	1	1	yes	characteristic
200	C₂³×C₃×D₄	C₂×D₄	1	1	yes	characteristic
201	C₂³×C₃×D₄	C₂×D₄	1	2	yes	—
202	C₂³×C₃×D₄	C₂×D₄	1	2	yes	—
203	C₂³×C₃×D₄	C₂⁴	1	2	yes	—
204	C₂⁴×C₃×C₄	C₂⁴	1	1	yes	characteristic
205	C₂⁴×Dic₃	C₂×D₄	1	1	yes	characteristic
206	C₂×D₃×#41	C₂×D₄	1	16	yes	—
207	C₂²×#239	C₂×D₄	1	2	yes	—
208	C₂²×#239	C₂×D₄	1	2	yes	—
209	C₂²×#239	C₂×D₄	1	1	yes	characteristic, complemented
210	C₂²×D₃×Q₈	C₂×D₄	1	2	yes	—
211	C₂²×D₃×Q₈	C₂×D₄	1	2	yes	—
212	C₂²×D₃×Q₈	C₂×D₄	1	1	yes	characteristic, complemented
213	C₂²×#237	C₂×D₄	1	2	yes	—
214	C₂²×#237	C₂×D₄	1	2	yes	—
215	C₂²×#237	C₂×D₄	1	1	yes	characteristic, complemented
216	C₂²×D₃×D₄	C₂×D₄	1	16	yes	—
217	C₂²×D₃×D₄	C₂×D₄	1	4	yes	—
218	C₂²×D₃×D₄	C₂×D₄	1	4	yes	—
219	C₂²×D₃×D₄	C₂×D₄	1	2	yes	—
220	C₂²×D₃×D₄	C₂×D₄	1	4	yes	—
221	C₂²×D₃×D₄	C₂×D₄	1	4	yes	—
222	C₂²×D₃×D₄	C₂×D₄	1	2	yes	—
223	C₂²×D₃×D₄	C₂×D₄	1	1	yes	characteristic, complemented
224	C₂²×#235	C₂×D₄	1	2	yes	—
225	C₂²×#235	C₂⁴	1	2	yes	—
226	C₂²×#235	C₂⁴	1	1	yes	characteristic
227	C₂³×D₁₂	C₂×D₄	1	2	yes	—
228	C₂³×D₁₂	C₂×D₄	1	2	yes	—
229	C₂³×D₁₂	C₂×D₄	1	1	yes	characteristic
230	C₂³×D₁₂	C₂⁴	1	2	yes	—
231	C₂³×C₄×D₃	C₂×D₄	1	2	yes	—
232	C₂³×C₄×D₃	C₂×D₄	1	2	yes	—
233	C₂³×C₄×D₃	C₂×D₄	1	1	yes	characteristic
234	C₂³×C₄×D₃	C₂×D₄	1	1	yes	characteristic
235	C₂³×C₄×D₃	C₂×D₄	1	1	yes	characteristic
236	C₂³×C₄×D₃	C₂×D₄	1	1	yes	characteristic
237	C₂³×C₄×D₃	C₂×D₄	1	1	yes	characteristic
238	C₂³×C₄×D₃	C₂×D₄	1	1	yes	characteristic
239	C₂³×C₄×D₃	C₂×D₄	1	1	yes	characteristic
240	C₂³×C₄×D₃	C₂×D₄	1	1	yes	characteristic
241	C₂³×C₄×D₃	C₂×D₄	1	1	yes	characteristic
242	C₂³×C₄×D₃	C₂×D₄	1	1	yes	characteristic
243	C₂³×C₄×D₃	C₂×D₄	1	2	yes	—
244	C₂³×C₄×D₃	C₂×D₄	1	2	yes	—
245	C₂³×C₄×D₃	C₂×D₄	1	2	yes	—
246	C₂³×C₄×D₃	C₂×D₄	1	2	yes	—
247	C₂³×C₄×D₃	#41	1	2	yes	—
248	C₂³×C₄×D₃	#41	1	2	yes	—
249	C₂³×C₄×D₃	C₂⁴	1	1	yes	characteristic
250	C₂³×C₄×D₃	C₂⁴	1	1	yes	characteristic
251	C₂³×Dic₆	C₂×D₄	1	1	yes	characteristic
252	C₂²×C₃×M₁₆	C₂⁴	1	2	yes	—
253	C₂²×C₃×M₁₆	C₂⁴	1	2	yes	—
254	C₃×#535	C₂×D₄	1	16	yes	complemented
255	C₂×C₃×C₂²⋊Q₈	C₂×D₄	1	2	yes	complemented
256	C₂×C₃×#121	C₂×D₄	1	2	yes	complemented
257	C₂×C₃×#117	C₂×D₄	1	2	yes	—
258	C₂×C₃×#117	C₂⁴	1	2	yes	—
259	C₂×C₃×#117	C₂⁴	1	1	yes	characteristic
260	C₂×C₃×#117	C₂⁴	1	2	yes	—
261	C₂²×C₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
262	C₂²×#217	C₂×D₄	1	2	yes	—
263	#5830	C₂×D₄	1	16	yes	complemented
264	C₂×#946	C₂×D₄	1	2	yes	complemented
265	#5805	C₂×D₄	1	16	yes	complemented
266	C₂×#938	C₂×D₄	1	2	yes	complemented
267	C₂×#930	C₂×D₄	1	2	yes	complemented
268	C₂×#926	C₂×D₄	1	2	yes	—
269	C₂×#926	C₂⁴	1	2	yes	—
270	C₂×#926	C₂⁴	1	2	yes	—
271	C₂×#926	C₂⁴	1	1	yes	characteristic
272	C₂×#924	C₂×D₄	1	2	yes	complemented
273	C₂²×#208	C₂⁴	1	2	yes	—
274	C₂²×#208	C₂⁴	1	2	yes	—
275	C₂×D₃×M₁₆	C₂×D₄	1	4	yes	complemented
276	C₂×D₃×M₁₆	C₂×D₄	1	4	yes	complemented
277	C₂²×ΓL(1,𝔽₂₅)	C₂×D₄	1	4	yes	complemented
278	C₂²×D₃×C₈	C₂×D₄	1	4	yes	complemented
279	#5525	C₂×D₄	1	16	yes	complemented
280	D₃×#117	C₂×D₄	1	16	yes	—
281	C₂×#897	C₂×D₄	1	2	yes	complemented
282	C₂×#895	C₂×D₄	1	2	yes	complemented
283	C₂×#892	C₂×D₄	1	2	yes	complemented
284	C₂×D₃×C₄⋊C₄	C₂×D₄	1	2	yes	complemented
285	C₂×D₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
286	C₂×D₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
287	C₂×#877	C₂×D₄	1	4	yes	—
288	C₂×#877	C₂×D₄	1	4	yes	—
289	C₃×#407	C₂×D₄	1	4	yes	complemented
290	C₂×C₃×C₂²⋊C₈	C₂×D₄	1	4	yes	complemented
291	#5207	C₂×D₄	1	4	yes	complemented
292	C₂×#830	C₂×D₄	1	4	yes	complemented
293	#5126	C₂×D₄	1	8	yes	complemented
294	C₂×(C₂×D₃)⋊C₈	C₂×D₄	1	8	yes	complemented
295	C₂³×#41	C₂²×D₃	1	1	yes	characteristic
296	C₂⁴×D₄	C₂²×D₃	1	1	yes	characteristic
297	C₂×#575	C₂²×D₃	1	2	yes	complemented
298	C₂²×AGL(1,ℤ/8)	C₂²×D₃	1	2	yes	complemented
299	C₂×#535	C₂²×D₃	1	4	yes	—
300	C₂×#525	C₂²×D₃	1	1	yes	characteristic
301	C₂²×#117	C₂²×D₃	1	1	yes	characteristic
302	C₂×#421	C₂²×D₃	1	4	yes	complemented
303	#2896	C₂²×D₃	1	2	yes	complemented
304	C₂×#418	C₂²×D₃	1	2	yes	complemented
305	C₂×#418	C₂²×D₃	1	4	yes	complemented
306	C₂×#410	C₂²×D₃	1	2	yes	complemented
307	C₂×#407	C₂²×D₃	1	1	yes	characteristic
308	C₂×#407	C₂²×D₃	1	1	yes	characteristic
309	#2280	C₂²×D₃	1	1	yes	characteristic
310	C₂×#344	C₂²×D₃	1	4	yes	complemented
311	#1740	C₂²×D₃	1	2	yes	complemented
312	C₂⁵×C₃	C₂²×D₄	1	1	yes	characteristic
313	C₂⁴×D₃	#120	1	1	yes	characteristic
314	C₂⁴×D₃	#120	1	1	yes	characteristic
315	C₂⁴×D₃	#120	1	1	yes	characteristic
316	C₂⁴×D₃	#120	1	1	yes	characteristic
317	C₂⁴×D₃	#121	1	2	yes	—
318	C₂⁴×D₃	#121	1	2	yes	—
319	C₂⁴×D₃	#127	1	2	yes	—
320	C₂⁴×D₃	#127	1	2	yes	—
321	C₂⁴×D₃	C₂²×D₄	1	1	yes	characteristic
322	C₂⁴×D₃	C₂²×D₄	1	1	yes	characteristic
323	C₂×C₃×#41	C₂²×D₄	1	8	yes	—
324	C₂²×C₃×Q₈	C₂²×D₄	1	2	yes	—
325	C₂²×C₃×Q₈	C₂²×D₄	1	1	yes	characteristic, complemented
326	C₂²×C₃×D₄	C₂²×D₄	1	8	yes	—
327	C₂²×C₃×D₄	C₂²×D₄	1	4	yes	—
328	C₂²×C₃×D₄	C₂²×D₄	1	2	yes	—
329	C₂²×C₃×D₄	C₂²×D₄	1	1	yes	characteristic, complemented
330	C₂³×C₃×C₄	C₂²×D₄	1	2	yes	—
331	C₂³×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
332	C₂³×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
333	C₂³×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
334	C₂³×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
335	C₂³×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
336	C₂³×C₃×C₄	C₂²×D₄	1	2	yes	—
337	C₂³×C₃×C₄	C₂²×D₄	1	2	yes	—
338	C₂³×C₃×C₄	C₂×#41	1	2	yes	—
339	C₂³×C₃×C₄	C₂⁵	1	1	yes	characteristic
340	C₂³×Dic₃	#120	1	1	yes	characteristic
341	C₂³×Dic₃	#120	1	1	yes	characteristic
342	C₂³×Dic₃	#120	1	1	yes	characteristic
343	C₂³×Dic₃	#120	1	1	yes	characteristic
344	C₂³×Dic₃	#121	1	2	yes	—
345	C₂³×Dic₃	#121	1	2	yes	—
346	C₂³×Dic₃	#127	1	2	yes	—
347	C₂³×Dic₃	#127	1	2	yes	—
348	C₂³×Dic₃	C₂²×D₄	1	1	yes	characteristic
349	C₂³×Dic₃	C₂²×D₄	1	1	yes	characteristic
350	C₂×#239	#120	1	8	yes	—
351	C₂×D₃×Q₈	#120	1	8	yes	—
352	C₂×#237	#120	1	8	yes	—
353	C₂×D₃×D₄	#120	1	16	yes	—
354	C₂×D₃×D₄	#120	1	16	yes	—
355	C₂×D₃×D₄	#120	1	8	yes	—
356	C₂×#235	C₂²×D₄	1	8	yes	—
357	C₂²×D₁₂	C₂²×D₄	1	8	yes	—
358	C₂²×D₁₂	C₂²×D₄	1	4	yes	—
359	C₂²×D₁₂	C₂²×D₄	1	2	yes	—
360	C₂²×D₁₂	C₂²×D₄	1	1	yes	characteristic, complemented
361	C₂²×C₄×D₃	#120	1	2	yes	—
362	C₂²×C₄×D₃	#120	1	2	yes	—
363	C₂²×C₄×D₃	#120	1	2	yes	—
364	C₂²×C₄×D₃	#120	1	2	yes	—
365	C₂²×C₄×D₃	#120	1	2	yes	—
366	C₂²×C₄×D₃	#120	1	2	yes	—
367	C₂²×C₄×D₃	#120	1	2	yes	—
368	C₂²×C₄×D₃	#120	1	2	yes	—
369	C₂²×C₄×D₃	#120	1	2	yes	—
370	C₂²×C₄×D₃	#120	1	2	yes	—
371	C₂²×C₄×D₃	#120	1	2	yes	—
372	C₂²×C₄×D₃	#120	1	2	yes	—
373	C₂²×C₄×D₃	#120	1	2	yes	—
374	C₂²×C₄×D₃	#120	1	2	yes	—
375	C₂²×C₄×D₃	#120	1	2	yes	—
376	C₂²×C₄×D₃	#120	1	2	yes	—
377	C₂²×C₄×D₃	#120	1	1	yes	characteristic
378	C₂²×C₄×D₃	#120	1	1	yes	characteristic
379	C₂²×C₄×D₃	#120	1	1	yes	characteristic
380	C₂²×C₄×D₃	#120	1	1	yes	characteristic
381	C₂²×C₄×D₃	#120	1	1	yes	characteristic
382	C₂²×C₄×D₃	#120	1	1	yes	characteristic
383	C₂²×C₄×D₃	#120	1	1	yes	characteristic
384	C₂²×C₄×D₃	#120	1	1	yes	characteristic
385	C₂²×C₄×D₃	#121	1	2	yes	—
386	C₂²×C₄×D₃	#121	1	2	yes	—
387	C₂²×C₄×D₃	#121	1	2	yes	—
388	C₂²×C₄×D₃	#121	1	2	yes	—
389	C₂²×C₄×D₃	#121	1	2	yes	—
390	C₂²×C₄×D₃	#121	1	2	yes	—
391	C₂²×C₄×D₃	#121	1	2	yes	—
392	C₂²×C₄×D₃	#121	1	2	yes	—
393	C₂²×C₄×D₃	#121	1	2	yes	—
394	C₂²×C₄×D₃	#121	1	2	yes	—
395	C₂²×C₄×D₃	#121	1	2	yes	—
396	C₂²×C₄×D₃	#121	1	2	yes	—
397	C₂²×C₄×D₃	#121	1	2	yes	—
398	C₂²×C₄×D₃	#121	1	2	yes	—
399	C₂²×C₄×D₃	#121	1	2	yes	—
400	C₂²×C₄×D₃	#121	1	2	yes	—
401	C₂²×C₄×D₃	#121	1	2	yes	—
402	C₂²×C₄×D₃	#121	1	2	yes	—
403	C₂²×C₄×D₃	#121	1	2	yes	—
404	C₂²×C₄×D₃	#121	1	2	yes	—
405	C₂²×C₄×D₃	#127	1	2	yes	—
406	C₂²×C₄×D₃	#127	1	2	yes	—
407	C₂²×C₄×D₃	#127	1	2	yes	—
408	C₂²×C₄×D₃	#127	1	2	yes	—
409	C₂²×C₄×D₃	C₂²×D₄	1	2	yes	—
410	C₂²×C₄×D₃	C₂²×D₄	1	1	yes	characteristic
411	C₂²×C₄×D₃	C₂²×D₄	1	1	yes	characteristic
412	C₂²×C₄×D₃	C₂²×D₄	1	1	yes	characteristic
413	C₂²×C₄×D₃	C₂²×D₄	1	1	yes	characteristic
414	C₂²×C₄×D₃	C₂²×D₄	1	2	yes	—
415	C₂²×C₄×D₃	C₂²×D₄	1	2	yes	—
416	C₂²×C₄×D₃	C₂²×D₄	1	1	yes	characteristic
417	C₂²×C₄×D₃	C₂²×D₄	1	1	yes	characteristic
418	C₂²×C₄×D₃	C₂²×D₄	1	1	yes	characteristic
419	C₂²×C₄×D₃	C₂²×D₄	1	1	yes	characteristic
420	C₂²×C₄×D₃	C₂²×D₄	1	1	yes	characteristic
421	C₂²×C₄×D₃	C₂²×D₄	1	1	yes	characteristic
422	C₂²×C₄×D₃	C₂²×D₄	1	8	yes	—
423	C₂²×C₄×D₃	C₂²×D₄	1	1	yes	characteristic
424	C₂²×C₄×D₃	C₂²×D₄	1	1	yes	characteristic
425	C₂²×C₄×D₃	C₂²×D₄	1	1	yes	characteristic
426	C₂²×C₄×D₃	C₂²×D₄	1	1	yes	characteristic
427	C₂²×C₄×D₃	C₂×#41	1	2	yes	—
428	C₂²×C₄×D₃	C₂×#41	1	1	yes	characteristic
429	C₂²×C₄×D₃	C₂×#41	1	1	yes	characteristic
430	C₂²×C₄×D₃	H(5,𝔽₂)	1	8	yes	—
431	C₂²×Dic₆	C₂²×D₄	1	2	yes	—
432	C₂²×Dic₆	C₂²×D₄	1	1	yes	characteristic, complemented
433	C₂×C₃×M₁₆	C₂²×D₄	1	4	yes	complemented
434	C₂²×C₃×C₈	C₂²×D₄	1	4	yes	complemented
435	C₃×#117	C₂²×D₄	1	8	yes	—
436	C₂×C₃×C₄⋊C₄	C₂²×D₄	1	2	yes	complemented
437	C₂×C₃×C₂²⋊C₄	C₂²×D₄	1	4	yes	—
438	C₂×#217	C₂²×D₄	1	4	yes	—
439	#926	C₂²×D₄	1	8	yes	—
440	C₂×C₄⋊Dic₃	C₂²×D₄	1	2	yes	complemented
441	C₂×#208	C₂²×D₄	1	4	yes	complemented
442	C₂²×C₃⋊C₈	C₂²×D₄	1	4	yes	complemented
443	D₃×C₂²⋊C₄	#120	1	16	yes	—
444	#877	#120	1	16	yes	—
445	C₂²×#41	D₃×D₄	1	2	yes	—
446	C₂²×#41	C₂³×D₃	1	2	yes	—
447	C₂²×#41	C₂³×D₃	1	1	yes	characteristic
448	C₂³×Q₈	D₃×D₄	1	1	yes	characteristic
449	C₂³×D₄	D₃×D₄	1	2	yes	—
450	C₂³×D₄	D₃×D₄	1	2	yes	—
451	C₂³×D₄	D₃×D₄	1	1	yes	characteristic
452	C₂³×D₄	C₂³×D₃	1	2	yes	—
453	C₂⁴×C₄	C₂³×D₃	1	1	yes	characteristic
454	C₂²×M₁₆	C₂³×D₃	1	2	yes	—
455	C₂²×M₁₆	C₂³×D₃	1	2	yes	—
456	#535	D₃×D₄	1	16	yes	complemented
457	C₂×C₂²⋊Q₈	D₃×D₄	1	2	yes	complemented
458	C₂×#121	D₃×D₄	1	2	yes	complemented
459	C₂×#117	D₃×D₄	1	2	yes	—
460	C₂×#117	C₂³×D₃	1	2	yes	—
461	C₂×#117	C₂³×D₃	1	1	yes	characteristic
462	C₂×#117	C₂³×D₃	1	2	yes	—
463	C₂²×C₂²⋊C₄	D₃×D₄	1	2	yes	—
464	#407	D₃×D₄	1	4	yes	complemented
465	C₂×C₂²⋊C₈	D₃×D₄	1	4	yes	complemented
466	C₂⁴×C₃	C₂×#120	1	1	yes	characteristic
467	C₂⁴×C₃	C₂×#120	1	1	yes	characteristic
468	C₂⁴×C₃	C₂×#121	1	2	yes	—
469	C₂⁴×C₃	C₂×#127	1	2	yes	—
470	C₂⁴×C₃	C₂³×D₄	1	1	yes	characteristic
471	C₂³×D₃	#392	1	2	yes	—
472	C₂³×D₃	#392	1	2	yes	—
473	C₂³×D₃	#392	1	2	yes	—
474	C₂³×D₃	#392	1	2	yes	—
475	C₂³×D₃	#392	1	2	yes	—
476	C₂³×D₃	#392	1	2	yes	—
477	C₂³×D₃	#392	1	2	yes	—
478	C₂³×D₃	#392	1	2	yes	—
479	C₂³×D₃	C₂×#120	1	1	yes	characteristic
480	C₂³×D₃	C₂×#120	1	1	yes	characteristic
481	C₂³×D₃	C₂×#120	1	1	yes	characteristic
482	C₂³×D₃	C₂×#120	1	1	yes	characteristic
483	C₂³×D₃	C₂×#120	1	4	yes	—
484	C₂³×D₃	C₂×#121	1	2	yes	—
485	C₂³×D₃	C₂×#121	1	1	yes	characteristic
486	C₂³×D₃	C₂×#121	1	1	yes	characteristic
487	C₂³×D₃	C₂×#127	1	2	yes	—
488	C₂³×D₃	C₂×#127	1	1	yes	characteristic
489	C₂³×D₃	C₂×#127	1	1	yes	characteristic
490	C₂³×D₃	#535	1	4	yes	—
491	C₂×C₃×Q₈	C₂×#120	1	4	yes	—
492	C₂×C₃×D₄	C₂×#120	1	8	yes	—
493	C₂×C₃×D₄	C₂×#120	1	4	yes	—
494	C₂²×C₃×C₄	C₂×#120	1	1	yes	characteristic
495	C₂²×C₃×C₄	C₂×#120	1	1	yes	characteristic
496	C₂²×C₃×C₄	C₂×#120	1	2	yes	—
497	C₂²×C₃×C₄	C₂×#120	1	2	yes	—
498	C₂²×C₃×C₄	C₂×#120	1	2	yes	—
499	C₂²×C₃×C₄	C₂×#120	1	2	yes	—
500	C₂²×C₃×C₄	C₂×#121	1	2	yes	—
501	C₂²×C₃×C₄	C₂×#121	1	2	yes	—
502	C₂²×C₃×C₄	C₂×#121	1	2	yes	—
503	C₂²×C₃×C₄	C₂×#121	1	2	yes	—
504	C₂²×C₃×C₄	C₂×#121	1	2	yes	—
505	C₂²×C₃×C₄	C₂×#127	1	2	yes	—
506	C₂²×C₃×C₄	C₂³×D₄	1	1	yes	characteristic
507	C₂²×C₃×C₄	C₂³×D₄	1	1	yes	characteristic
508	C₂²×C₃×C₄	C₂³×D₄	1	1	yes	characteristic
509	C₂²×C₃×C₄	C₂³×D₄	1	4	yes	—
510	C₂²×C₃×C₄	C₂³×D₄	1	1	yes	characteristic
511	C₂²×C₃×C₄	C₂³×D₄	1	1	yes	characteristic
512	C₂²×C₃×C₄	C₂²×#41	1	1	yes	characteristic
513	C₂²×C₃×C₄	C₂×H(5,𝔽₂)	1	4	yes	—
514	C₂²×Dic₃	#392	1	2	yes	—
515	C₂²×Dic₃	#392	1	2	yes	—
516	C₂²×Dic₃	#392	1	2	yes	—
517	C₂²×Dic₃	#392	1	2	yes	—
518	C₂²×Dic₃	#392	1	2	yes	—
519	C₂²×Dic₃	#392	1	2	yes	—
520	C₂²×Dic₃	#392	1	2	yes	—
521	C₂²×Dic₃	#392	1	2	yes	—
522	C₂²×Dic₃	C₂×#120	1	1	yes	characteristic
523	C₂²×Dic₃	C₂×#120	1	1	yes	characteristic
524	C₂²×Dic₃	C₂×#120	1	1	yes	characteristic
525	C₂²×Dic₃	C₂×#120	1	1	yes	characteristic
526	C₂²×Dic₃	C₂×#120	1	4	yes	—
527	C₂²×Dic₃	C₂×#121	1	2	yes	—
528	C₂²×Dic₃	C₂×#121	1	1	yes	characteristic
529	C₂²×Dic₃	C₂×#121	1	1	yes	characteristic
530	C₂²×Dic₃	C₂×#127	1	2	yes	—
531	C₂²×Dic₃	C₂×#127	1	1	yes	characteristic
532	C₂²×Dic₃	C₂×#127	1	1	yes	characteristic
533	C₂²×Dic₃	#535	1	4	yes	—
534	C₂×D₁₂	C₂×#120	1	4	yes	—
535	C₂×D₁₂	C₂×#120	1	8	yes	—
536	C₂×C₄×D₃	#392	1	2	yes	—
537	C₂×C₄×D₃	#392	1	2	yes	—
538	C₂×C₄×D₃	#392	1	2	yes	—
539	C₂×C₄×D₃	#392	1	2	yes	—
540	C₂×C₄×D₃	#392	1	2	yes	—
541	C₂×C₄×D₃	#392	1	2	yes	—
542	C₂×C₄×D₃	#392	1	2	yes	—
543	C₂×C₄×D₃	#392	1	2	yes	—
544	C₂×C₄×D₃	#392	1	2	yes	—
545	C₂×C₄×D₃	#392	1	2	yes	—
546	C₂×C₄×D₃	#392	1	2	yes	—
547	C₂×C₄×D₃	#392	1	2	yes	—
548	C₂×C₄×D₃	#392	1	2	yes	—
549	C₂×C₄×D₃	#392	1	2	yes	—
550	C₂×C₄×D₃	#392	1	2	yes	—
551	C₂×C₄×D₃	#392	1	2	yes	—
552	C₂×C₄×D₃	C₂×#120	1	2	yes	—
553	C₂×C₄×D₃	C₂×#120	1	2	yes	—
554	C₂×C₄×D₃	C₂×#120	1	2	yes	—
555	C₂×C₄×D₃	C₂×#120	1	2	yes	—
556	C₂×C₄×D₃	C₂×#120	1	1	yes	characteristic
557	C₂×C₄×D₃	C₂×#120	1	1	yes	characteristic
558	C₂×C₄×D₃	C₂×#120	1	1	yes	characteristic
559	C₂×C₄×D₃	C₂×#120	1	1	yes	characteristic
560	C₂×C₄×D₃	C₂×#120	1	1	yes	characteristic
561	C₂×C₄×D₃	C₂×#120	1	1	yes	characteristic
562	C₂×C₄×D₃	C₂×#120	1	1	yes	characteristic
563	C₂×C₄×D₃	C₂×#120	1	1	yes	characteristic
564	C₂×C₄×D₃	C₂×#120	1	4	yes	—
565	C₂×C₄×D₃	C₂×#120	1	4	yes	—
566	C₂×C₄×D₃	C₂×#120	1	4	yes	—
567	C₂×C₄×D₃	C₂×#120	1	4	yes	—
568	C₂×C₄×D₃	C₂×#121	1	2	yes	—
569	C₂×C₄×D₃	C₂×#121	1	2	yes	—
570	C₂×C₄×D₃	C₂×#121	1	2	yes	—
571	C₂×C₄×D₃	C₂×#121	1	2	yes	—
572	C₂×C₄×D₃	C₂×#121	1	1	yes	characteristic
573	C₂×C₄×D₃	C₂×#121	1	1	yes	characteristic
574	C₂×C₄×D₃	C₂×#121	1	1	yes	characteristic
575	C₂×C₄×D₃	C₂×#121	1	1	yes	characteristic
576	C₂×C₄×D₃	C₂×#121	1	1	yes	characteristic
577	C₂×C₄×D₃	C₂×#121	1	1	yes	characteristic
578	C₂×C₄×D₃	C₂×#121	1	1	yes	characteristic
579	C₂×C₄×D₃	C₂×#121	1	1	yes	characteristic
580	C₂×C₄×D₃	#534	1	4	yes	—
581	C₂×C₄×D₃	#534	1	4	yes	—
582	C₂×C₄×D₃	#534	1	4	yes	—
583	C₂×C₄×D₃	#534	1	4	yes	—
584	C₂×C₄×D₃	D₄²	1	8	yes	—
585	C₂×C₄×D₃	D₄²	1	8	yes	—
586	C₂×C₄×D₃	D₄²	1	8	yes	—
587	C₂×C₄×D₃	D₄²	1	8	yes	—
588	C₂×C₄×D₃	D₄²	1	8	yes	—
589	C₂×C₄×D₃	D₄²	1	8	yes	—
590	C₂×C₄×D₃	#546	1	8	yes	—
591	C₂×C₄×D₃	#546	1	8	yes	—
592	C₂×Dic₆	C₂×#120	1	4	yes	—
593	C₃×C₂²⋊C₄	C₂×#120	1	8	yes	—
594	#217	C₂×#120	1	8	yes	—
595	C₂⁵	C₂×D₃×D₄	1	1	yes	characteristic
596	C₂×#41	C₂×D₃×D₄	1	8	yes	—
597	C₂²×Q₈	C₂×D₃×D₄	1	2	yes	—
598	C₂²×Q₈	C₂×D₃×D₄	1	1	yes	characteristic, complemented
599	C₂²×D₄	C₂×D₃×D₄	1	4	yes	—
600	C₂²×D₄	C₂×D₃×D₄	1	2	yes	—
601	C₂²×D₄	C₂×D₃×D₄	1	8	yes	—
602	C₂²×D₄	C₂×D₃×D₄	1	1	yes	characteristic, complemented
603	C₂³×C₄	C₂×D₃×D₄	1	2	yes	—
604	C₂³×C₄	C₂×D₃×D₄	1	2	yes	—
605	C₂³×C₄	C₂×D₃×D₄	1	2	yes	—
606	C₂³×C₄	C₂×D₃×D₄	1	1	yes	characteristic
607	C₂³×C₄	C₂×D₃×D₄	1	1	yes	characteristic
608	C₂³×C₄	C₂×D₃×D₄	1	1	yes	characteristic
609	C₂³×C₄	C₂×D₃×D₄	1	1	yes	characteristic
610	C₂³×C₄	C₂×D₃×D₄	1	1	yes	characteristic
611	C₂³×C₄	D₃×#41	1	2	yes	—
612	C₂³×C₄	C₂⁴×D₃	1	1	yes	characteristic
613	C₂×M₁₆	C₂×D₃×D₄	1	4	yes	complemented
614	C₂²×C₈	C₂×D₃×D₄	1	4	yes	complemented
615	#117	C₂×D₃×D₄	1	8	yes	—
616	C₂×C₄⋊C₄	C₂×D₃×D₄	1	2	yes	complemented
617	C₂×C₂²⋊C₄	C₂×D₃×D₄	1	4	yes	—
618	C₂³×C₃	C₂×#392	1	2	yes	—
619	C₂³×C₃	C₂×#392	1	2	yes	—
620	C₂³×C₃	C₂²×#120	1	1	yes	characteristic
621	C₂³×C₃	C₂²×#120	1	2	yes	—
622	C₂³×C₃	C₂²×#121	1	1	yes	characteristic
623	C₂³×C₃	C₂²×#127	1	1	yes	characteristic
624	C₂³×C₃	C₂×#535	1	2	yes	—
625	C₂²×D₃	#2008	1	8	yes	complemented
626	C₂²×D₃	C₂×#392	1	2	yes	—
627	C₂²×D₃	C₂×#392	1	2	yes	—
628	C₂²×D₃	C₂×#392	1	1	yes	characteristic
629	C₂²×D₃	C₂×#392	1	1	yes	characteristic
630	C₂²×D₃	C₂×#392	1	1	yes	characteristic
631	C₂²×D₃	C₂×#392	1	1	yes	characteristic
632	C₂²×D₃	#2408	1	4	yes	—
633	C₂²×D₃	#2408	1	4	yes	—
634	C₂²×D₃	#2433	1	4	yes	—
635	C₂²×D₃	#2433	1	4	yes	—
636	C₂²×D₃	#2613	1	2	yes	—
637	C₂²×D₃	#2613	1	2	yes	—
638	C₂²×D₃	#2846	1	2	yes	—
639	C₂²×D₃	#2846	1	2	yes	—
640	C₂×C₃×C₄	C₂×#392	1	2	yes	—
641	C₂×C₃×C₄	C₂×#392	1	2	yes	—
642	C₂×C₃×C₄	C₂²×#120	1	1	yes	characteristic
643	C₂×C₃×C₄	C₂²×#120	1	1	yes	characteristic
644	C₂×C₃×C₄	C₂²×#120	1	2	yes	—
645	C₂×C₃×C₄	C₂²×#120	1	2	yes	—
646	C₂×C₃×C₄	C₂²×#121	1	1	yes	characteristic
647	C₂×C₃×C₄	C₂²×#121	1	1	yes	characteristic
648	C₂×C₃×C₄	C₂×#534	1	2	yes	—
649	C₂×C₃×C₄	C₂×#534	1	2	yes	—
650	C₂×C₃×C₄	C₂×D₄²	1	4	yes	—
651	C₂×C₃×C₄	C₂×D₄²	1	4	yes	—
652	C₂×C₃×C₄	C₂×D₄²	1	4	yes	—
653	C₂×C₃×C₄	C₂×#546	1	4	yes	—
654	C₂×Dic₃	C₂×#392	1	2	yes	—
655	C₂×Dic₃	C₂×#392	1	2	yes	—
656	C₂×Dic₃	C₂×#392	1	1	yes	characteristic
657	C₂×Dic₃	C₂×#392	1	1	yes	characteristic
658	C₂×Dic₃	C₂×#392	1	1	yes	characteristic
659	C₂×Dic₃	C₂×#392	1	1	yes	characteristic
660	C₂×Dic₃	#2408	1	4	yes	—
661	C₂×Dic₃	#2408	1	4	yes	—
662	C₂×Dic₃	#2433	1	4	yes	—
663	C₂×Dic₃	#2433	1	4	yes	—
664	C₂×Dic₃	#2613	1	2	yes	—
665	C₂×Dic₃	#2613	1	2	yes	—
666	C₂×Dic₃	#2846	1	2	yes	—
667	C₂×Dic₃	#2846	1	2	yes	—
668	C₄×D₃	#2403	1	4	yes	—
669	C₄×D₃	#2403	1	4	yes	—
670	C₄×D₃	#2403	1	4	yes	—
671	C₄×D₃	#2403	1	4	yes	—
672	C₄×D₃	#2403	1	4	yes	—
673	C₄×D₃	#2403	1	4	yes	—
674	C₄×D₃	#2403	1	4	yes	—
675	C₄×D₃	#2403	1	4	yes	—
676	C₄×D₃	#2410	1	4	yes	—
677	C₄×D₃	#2410	1	4	yes	—
678	C₄×D₃	#2410	1	4	yes	—
679	C₄×D₃	#2410	1	4	yes	—
680	C₄×D₃	#2410	1	4	yes	—
681	C₄×D₃	#2410	1	4	yes	—
682	C₄×D₃	#2410	1	4	yes	—
683	C₄×D₃	#2410	1	4	yes	—
684	C₂⁴	D₃×#120	1	1	yes	characteristic
685	C₂⁴	D₃×#120	1	1	yes	characteristic
686	C₂⁴	D₃×#121	1	2	yes	—
687	C₂⁴	D₃×#127	1	2	yes	—
688	C₂⁴	C₂²×D₃×D₄	1	1	yes	characteristic
689	C₂×Q₈	D₃×#120	1	4	yes	—
690	C₂×D₄	D₃×#120	1	8	yes	—
691	C₂×D₄	D₃×#120	1	4	yes	—
692	C₂²×C₄	D₃×#120	1	2	yes	—
693	C₂²×C₄	D₃×#120	1	2	yes	—
694	C₂²×C₄	D₃×#120	1	2	yes	—
695	C₂²×C₄	D₃×#120	1	2	yes	—
696	C₂²×C₄	D₃×#120	1	1	yes	characteristic
697	C₂²×C₄	D₃×#120	1	1	yes	characteristic
698	C₂²×C₄	D₃×#121	1	2	yes	—
699	C₂²×C₄	D₃×#121	1	2	yes	—
700	C₂²×C₄	D₃×#121	1	2	yes	—
701	C₂²×C₄	D₃×#121	1	2	yes	—
702	C₂²×C₄	D₃×#121	1	2	yes	—
703	C₂²×C₄	D₃×#127	1	2	yes	—
704	C₂²×C₄	C₂²×D₃×D₄	1	1	yes	characteristic
705	C₂²×C₄	C₂²×D₃×D₄	1	1	yes	characteristic
706	C₂²×C₄	C₂²×D₃×D₄	1	1	yes	characteristic
707	C₂²×C₄	C₂²×D₃×D₄	1	1	yes	characteristic
708	C₂²×C₄	C₂²×D₃×D₄	1	1	yes	characteristic
709	C₂²×C₄	C₂²×D₃×D₄	1	4	yes	—
710	C₂²×C₄	C₂×D₃×#41	1	1	yes	characteristic
711	C₂²×C₄	D₃×H(5,𝔽₂)	1	4	yes	—
712	C₂²⋊C₄	D₃×#120	1	8	yes	—
713	C₂²×C₃	C₂×#2008	1	4	yes	complemented
714	C₂²×C₃	C₂²×#392	1	1	yes	characteristic
715	C₂²×C₃	C₂×#2613	1	1	yes	characteristic
716	C₂²×C₃	C₂×#2408	1	2	yes	—
717	C₂²×C₃	C₂×#2433	1	2	yes	—
718	C₂²×C₃	C₂×#2846	1	1	yes	characteristic
719	C₂×D₃	#14715	1	2	yes	—
720	C₂×D₃	#14715	1	2	yes	—
721	C₂×D₃	#14715	1	2	yes	—
722	C₂×D₃	#14715	1	2	yes	—
723	C₂×D₃	C₂×#2008	1	4	yes	—
724	C₂×D₃	C₂×#2008	1	4	yes	complemented
725	C₃×C₄	C₂×#2403	1	2	yes	—
726	C₃×C₄	C₂×#2403	1	2	yes	—
727	C₃×C₄	C₂×#2410	1	2	yes	—
728	C₃×C₄	C₂×#2410	1	2	yes	—
729	Dic₃	#14715	1	2	yes	—
730	Dic₃	#14715	1	2	yes	—
731	Dic₃	#14715	1	2	yes	—
732	Dic₃	#14715	1	2	yes	—
733	C₂³	D₃×#392	1	2	yes	—
734	C₂³	D₃×#392	1	2	yes	—
735	C₂³	C₂×D₃×#120	1	1	yes	characteristic
736	C₂³	C₂×D₃×#120	1	2	yes	—
737	C₂³	C₂×D₃×#121	1	1	yes	characteristic
738	C₂³	C₂×D₃×#127	1	1	yes	characteristic
739	C₂³	D₃×#535	1	2	yes	—
740	C₂×C₄	D₃×#392	1	2	yes	—
741	C₂×C₄	D₃×#392	1	2	yes	—
742	C₂×C₄	C₂×D₃×#120	1	1	yes	characteristic
743	C₂×C₄	C₂×D₃×#120	1	1	yes	characteristic
744	C₂×C₄	C₂×D₃×#120	1	2	yes	—
745	C₂×C₄	C₂×D₃×#120	1	2	yes	—
746	C₂×C₄	C₂×D₃×#121	1	1	yes	characteristic
747	C₂×C₄	C₂×D₃×#121	1	1	yes	characteristic
748	C₂×C₄	D₃×#534	1	2	yes	—
749	C₂×C₄	D₃×#534	1	2	yes	—
750	C₂×C₄	D₃×D₄²	1	4	yes	—
751	C₂×C₄	D₃×D₄²	1	4	yes	—
752	C₂×C₄	D₃×D₄²	1	4	yes	—
753	C₂×C₄	D₃×#546	1	4	yes	—
754	C₂×C₃	C₂×#14715	1	1	yes	characteristic
755	C₂×C₃	C₂²×#2008	1	2	yes	—
756	D₃	#393979	1	4	yes	direct product factor
757	C₂²	D₃×#2008	1	4	yes	complemented
758	C₂²	C₂×D₃×#392	1	1	yes	characteristic
759	C₂²	D₃×#2613	1	1	yes	characteristic
760	C₂²	D₃×#2408	1	2	yes	—
761	C₂²	D₃×#2433	1	2	yes	—
762	C₂²	D₃×#2846	1	1	yes	characteristic
763	C₄	D₃×#2403	1	2	yes	—
764	C₄	D₃×#2403	1	2	yes	—
765	C₄	D₃×#2410	1	2	yes	—
766	C₄	D₃×#2410	1	2	yes	—
767	C₃	C₂×#393979	1	1	yes	characteristic, complemented, Sylow
768	C₂	D₃×#14715	1	1	yes	characteristic
769	C₂	C₂×D₃×#2008	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂×D₃×#392
commutator, cosocle	C₂³×C₃×C₄	C₂⁵
Frattini	C₂³×C₄	C₂⁴×D₃
Fitting	C₃×#393979	C₂
socle	C₂²×C₃	C₂²×#392
hypercenter	#393979	D₃
hypocenter	C₃	C₂×#393979
LCS	G ▷ C₂³×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂² ◁ C₂⁴×C₄ ◁ #393979

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. #72272265	C₂	semidirect
2. #72272264	C₂	semidirect
3. #72272260	C₂	semidirect
4. #72272259	C₂	semidirect
5. #72272252	C₂	semidirect
6. #72272242	C₂	semidirect
7. #72271961	C₂	semidirect
8. #72271951	C₂	semidirect
9. #72271729	C₂	semidirect
10. C₃×#393979	C₂	semidirect
11. D₃×#10738	C₂	semidirect
12. D₃×#60359	C₂	semidirect
13. D₃×#20605	C₂	semidirect
14. C₂²×D₃×#535	C₂	semidirect
15. D₃×#20983	C₂	semidirect
16. D₃×#11004	C₂	semidirect
17. D₃×#20598	C₂	semidirect
18. C₂×D₃×#2008	C₂	semidirect
19. C₂×D₃×#3003	C₂	semidirect
22. C₂×D₃×#575	C₂²	semidirect
23. C₂²×D₃×AGL(1,ℤ/8)	C₂²	semidirect
24. C₂²×#5525	C₂²	semidirect
25. C₂²×#5805	C₂²	semidirect
26. C₂²×#5830	C₂²	semidirect
28. C₂×D₃×#535	C₂²	semidirect
31. #11661584	C₂²	semidirect
32. #11661583	C₂²	semidirect
33. #11661581	C₂²	semidirect
34. #11661579	C₂²	semidirect
35. #11661577	C₂²	semidirect
36. C₂×#78637	C₂²	semidirect
37. C₂×#78926	C₂²	semidirect
38. C₂×#84038	C₂²	semidirect
39. C₂×#82927	C₂²	semidirect
40. C₂×#83944	C₂²	semidirect
41. C₂×D₃×#421	C₂²	semidirect
42. D₃×#2896	C₂²	semidirect
43. C₂×D₃×#418	C₂²	semidirect
44. C₂×D₃×#418	C₂²	semidirect
45. C₂×D₃×#410	C₂²	semidirect
49. C₂×#69028	C₂²	semidirect
50. C₂×#70331	C₂²	semidirect
51. C₂×#70409	C₂²	semidirect
52. C₂×#71858	C₂²	semidirect
53. C₂×#70050	C₂²	semidirect
54. C₂×#72099	C₂²	semidirect
55. C₂×#72119	C₂²	semidirect
56. #10796982	C₂²	semidirect
57. #10796981	C₂²	semidirect
58. #10796980	C₂²	semidirect
59. #10796979	C₂²	semidirect
60. #10796977	C₂²	semidirect
61. #10794437	C₂²	semidirect
62. #10794436	C₂²	semidirect
63. #10794435	C₂²	semidirect
64. #10794434	C₂²	semidirect
65. #10794391	C₂²	semidirect
66. #10794390	C₂²	semidirect
67. #10794389	C₂²	semidirect
68. #10794388	C₂²	semidirect
69. C₂×D₃×#344	C₂²	semidirect
70. D₃×#1740	C₂²	semidirect
71. #10701878	C₂²	semidirect
72. #10701877	C₂²	semidirect
73. #10701876	C₂²	semidirect
74. #10701875	C₂²	semidirect
75. #10701874	C₂²	semidirect
76. #10701873	C₂²	semidirect
77. #10701872	C₂²	semidirect
78. #10700498	C₂²	semidirect
79. #10700497	C₂²	semidirect
80. #10700496	C₂²	semidirect
81. #10700495	C₂²	semidirect
82. C₂²×C₃×#535	C₂²	semidirect
83. C₃×#60359	C₂²	semidirect
84. C₂×C₃×#3003	C₂²	semidirect
85. C₂×C₃×#2008	C₂²	semidirect
86. C₃×#20983	C₂²	semidirect
87. C₃×#20605	C₂²	semidirect
88. C₃×#20598	C₂²	semidirect
89. C₃×#11004	C₂²	semidirect
90. C₃×#10738	C₂²	semidirect
91. #393979	D₃	direct (N × H)
112. C₂×C₃×#575	C₂³	semidirect
113. C₂²×C₃×AGL(1,ℤ/8)	C₂³	semidirect
119. C₂×#5822	C₂³	semidirect
120. C₂×#5822	C₂³	semidirect
121. C₂²×#949	C₂³	semidirect
123. C₂²×#932	C₂³	semidirect
126. C₂×#5748	C₂³	semidirect
127. C₂²×#908	C₂³	semidirect
130. D₃×#535	D₄	semidirect
131. C₂×D₃×C₂²⋊Q₈	D₄	semidirect
132. C₂×#5627	D₄	semidirect
133. C₂×D₃×#121	D₄	semidirect
134. C₂×#5606	D₄	semidirect
145. C₂×C₃×#421	C₂³	semidirect
146. C₃×#2896	C₂³	semidirect
147. C₂×C₃×#418	C₂³	semidirect
148. C₂×C₃×#418	C₂³	semidirect
149. C₂×C₃×#410	C₂³	semidirect
153. C₂×#5240	C₂³	semidirect
154. C₂×#5236	C₂³	semidirect
155. #84072	C₂³	semidirect
156. C₂×#5215	C₂³	semidirect
157. C₂×#5215	C₂³	semidirect
161. C₂×#5139	C₂³	semidirect
162. #83768	C₂³	semidirect
163. C₂×#5131	C₂³	semidirect
164. C₂×#5131	C₂³	semidirect
168. C₂×#5006	C₂³	semidirect
169. C₂×#5006	C₂³	semidirect
170. C₂×#5005	C₂³	semidirect
171. #82213	C₂³	semidirect
172. C₂×#5001	C₂³	semidirect
173. C₂×#5001	C₂³	semidirect
174. D₃×#407	D₄	semidirect
175. D₃×#407	D₄	semidirect
176. C₂×#4726	D₄	semidirect
177. C₂×D₃×C₂²⋊C₈	D₄	semidirect
178. C₂×C₃×#344	C₂³	semidirect
179. C₃×#1740	C₂³	semidirect
180. C₂×#4559	C₂³	semidirect
181. C₂×#4556	C₂³	semidirect
182. #71593	C₂³	semidirect
183. #71593	C₂³	semidirect
184. #71592	C₂³	semidirect
185. C₂×#4533	C₂³	semidirect
186. C₂²×#535	C₂×D₃	semidirect
187. #60359	C₂×D₃	semidirect
188. C₂×#3003	C₂×D₃	semidirect
189. C₂×#2008	C₂×D₃	semidirect
190. #20983	C₂×D₃	semidirect
191. #20605	C₂×D₃	semidirect
192. #20598	C₂×D₃	semidirect
193. #11004	C₂×D₃	semidirect
194. #10738	C₂×D₃	semidirect
209. C₂²×#239	C₂×D₄	semidirect
212. C₂²×D₃×Q₈	C₂×D₄	semidirect
215. C₂²×#237	C₂×D₄	semidirect
223. C₂²×D₃×D₄	C₂×D₄	semidirect
254. C₃×#535	C₂×D₄	semidirect
255. C₂×C₃×C₂²⋊Q₈	C₂×D₄	semidirect
256. C₂×C₃×#121	C₂×D₄	semidirect
263. #5830	C₂×D₄	semidirect
264. C₂×#946	C₂×D₄	semidirect
265. #5805	C₂×D₄	semidirect
266. C₂×#938	C₂×D₄	semidirect
267. C₂×#930	C₂×D₄	semidirect
272. C₂×#924	C₂×D₄	semidirect
275. C₂×D₃×M₁₆	C₂×D₄	semidirect
276. C₂×D₃×M₁₆	C₂×D₄	semidirect
277. C₂²×ΓL(1,𝔽₂₅)	C₂×D₄	semidirect
278. C₂²×D₃×C₈	C₂×D₄	semidirect
279. #5525	C₂×D₄	semidirect
281. C₂×#897	C₂×D₄	semidirect
282. C₂×#895	C₂×D₄	semidirect
283. C₂×#892	C₂×D₄	semidirect
284. C₂×D₃×C₄⋊C₄	C₂×D₄	semidirect
289. C₃×#407	C₂×D₄	semidirect
290. C₂×C₃×C₂²⋊C₈	C₂×D₄	semidirect
291. #5207	C₂×D₄	semidirect
292. C₂×#830	C₂×D₄	semidirect
293. #5126	C₂×D₄	semidirect
294. C₂×(C₂×D₃)⋊C₈	C₂×D₄	semidirect
297. C₂×#575	C₂²×D₃	semidirect
298. C₂²×AGL(1,ℤ/8)	C₂²×D₃	semidirect
302. C₂×#421	C₂²×D₃	semidirect
303. #2896	C₂²×D₃	semidirect
304. C₂×#418	C₂²×D₃	semidirect
305. C₂×#418	C₂²×D₃	semidirect
306. C₂×#410	C₂²×D₃	semidirect
310. C₂×#344	C₂²×D₃	semidirect
311. #1740	C₂²×D₃	semidirect
325. C₂²×C₃×Q₈	C₂²×D₄	semidirect
329. C₂²×C₃×D₄	C₂²×D₄	semidirect
360. C₂²×D₁₂	C₂²×D₄	semidirect
432. C₂²×Dic₆	C₂²×D₄	semidirect
433. C₂×C₃×M₁₆	C₂²×D₄	semidirect
434. C₂²×C₃×C₈	C₂²×D₄	semidirect
436. C₂×C₃×C₄⋊C₄	C₂²×D₄	semidirect
440. C₂×C₄⋊Dic₃	C₂²×D₄	semidirect
441. C₂×#208	C₂²×D₄	semidirect
442. C₂²×C₃⋊C₈	C₂²×D₄	semidirect
456. #535	D₃×D₄	semidirect
457. C₂×C₂²⋊Q₈	D₃×D₄	semidirect
458. C₂×#121	D₃×D₄	semidirect
464. #407	D₃×D₄	semidirect
465. C₂×C₂²⋊C₈	D₃×D₄	semidirect
598. C₂²×Q₈	C₂×D₃×D₄	semidirect
602. C₂²×D₄	C₂×D₃×D₄	semidirect
613. C₂×M₁₆	C₂×D₃×D₄	semidirect
614. C₂²×C₈	C₂×D₃×D₄	semidirect
616. C₂×C₄⋊C₄	C₂×D₃×D₄	semidirect
625. C₂²×D₃	#2008	semidirect
713. C₂²×C₃	C₂×#2008	semidirect
724. C₂×D₃	C₂×#2008	semidirect
756. D₃	#393979	direct (N × H)
757. C₂²	D₃×#2008	semidirect
767. C₃	C₂×#393979	semidirect

Maximal subgroups

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

subgroup	index
#72272265	2
#72272264	2
#72272260	2
#72272259	2
#72272252	2
#72272242	2
#72271961	2
#72271951	2
#72271729	2
C₃×#393979	2
D₃×#10738	2
D₃×#60359	2
D₃×#20605	2
C₂²×D₃×#535	2
D₃×#20983	2
D₃×#11004	2
D₃×#20598	2
C₂×D₃×#2008	2
C₂×D₃×#3003	2
C₂×#393979	3

Subgroups — D3×#393979 #72272270

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃×#393979 #72272270