Subgroups — D₃×#394022 #72271751

Order 3072.

At least 10414 conjugacy classes of subgroups; only the 1935 normal subgroups are shown.

The subgroup lattice has 793 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72271718	C₂	1	1	yes	maximal, characteristic, complemented
2	#72271710	C₂	1	1	yes	maximal, characteristic, complemented
3	#72271706	C₂	1	1	yes	maximal, characteristic, complemented
4	D₃×#20608	C₂	1	1	yes	maximal, characteristic, complemented
5	#72271680	C₂	1	1	yes	maximal, characteristic, complemented
6	#72271674	C₂	1	2	yes	maximal, complemented
7	#72271671	C₂	1	2	yes	maximal, complemented
8	#72271667	C₂	1	2	yes	maximal, complemented
9	D₃×#11041	C₂	1	2	yes	maximal, complemented
10	#72271650	C₂	1	2	yes	maximal, complemented
11	D₃×#23430	C₂	1	2	yes	maximal, complemented
12	#72271641	C₂	1	1	yes	maximal, characteristic, complemented
13	#72271637	C₂	1	1	yes	maximal, characteristic, complemented
14	#72271632	C₂	1	1	yes	maximal, characteristic, complemented
15	D₃×#10746	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃×#394022	C₂	1	1	yes	maximal, characteristic, complemented
17	D₃×#35527	C₂	1	1	yes	maximal, characteristic, complemented
18	D₃×#11012	C₂	1	2	yes	maximal, complemented
19	C₂×D₃×#3021	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×D₃×#1795	C₂	1	1	yes	maximal, characteristic, complemented
21	C₂×D₃×#2008	C₂	1	2	yes	maximal, complemented
22	C₂×D₃×#3585	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂×D₃×#1910	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×D₃×#585	C₂²	1	1	yes	characteristic
25	C₂²×D₃×H(5,𝔽₂)	C₂²	1	1	yes	characteristic
26	C₂×#87167	C₂²	1	1	yes	characteristic, complemented
27	C₂×#87277	C₂²	1	1	yes	characteristic, complemented
28	C₂×#87298	C₂²	1	1	yes	characteristic, complemented
29	C₂×#87200	C₂²	1	2	yes	complemented
30	C₂×#87192	C₂²	1	2	yes	complemented
31	C₂×D₃×#575	C₂²	1	2	yes	—
32	C₂²×D₃×AGL(1,ℤ/8)	C₂²	1	2	yes	—
33	C₂²×D₃×AGL(1,ℤ/8)	C₂²	1	2	yes	complemented
34	C₂×D₃×#568	C₂²	1	1	yes	characteristic
35	C₂×D₃×#535	C₂²	1	1	yes	characteristic
36	C₂×D₃×#535	C₂²	1	1	yes	characteristic, complemented
37	C₂²×D₃×#127	C₂²	1	1	yes	characteristic, complemented
38	C₂×#78717	C₂²	1	1	yes	characteristic, complemented
39	C₂×#78994	C₂²	1	2	yes	complemented
40	C₂×#84122	C₂²	1	1	yes	characteristic, complemented
41	C₂×#83395	C₂²	1	1	yes	characteristic, complemented
42	C₂×#83957	C₂²	1	2	yes	complemented
43	C₂×D₃×#421	C₂²	1	2	yes	complemented
44	C₂×D₃×#421	C₂²	1	2	yes	complemented
45	C₂×D₃×#418	C₂²	1	2	yes	complemented
46	C₂×D₃×#418	C₂²	1	2	yes	complemented
47	C₂×D₃×#413	C₂²	1	1	yes	characteristic
48	C₂×D₃×#410	C₂²	1	1	yes	characteristic
49	C₂×D₃×#410	C₂²	1	2	yes	complemented
50	#10978444	C₂²	1	1	yes	characteristic, complemented
51	#10978443	C₂²	1	1	yes	characteristic, complemented
52	#10978443	C₂²	1	1	yes	characteristic, complemented
53	#10978442	C₂²	1	1	yes	characteristic, complemented
54	#10978441	C₂²	1	1	yes	characteristic, complemented
55	#10978440	C₂²	1	1	yes	characteristic, complemented
56	#10978440	C₂²	1	1	yes	characteristic, complemented
57	D₃×#2309	C₂²	1	1	yes	characteristic, complemented
58	D₃×#2297	C₂²	1	1	yes	characteristic
59	D₃×#2297	C₂²	1	1	yes	characteristic, complemented
60	D₃×#2297	C₂²	1	2	yes	complemented
61	#10822344	C₂²	1	2	yes	complemented
62	#10822343	C₂²	1	2	yes	complemented
63	#10822343	C₂²	1	2	yes	complemented
64	#10822341	C₂²	1	2	yes	complemented
65	#10822340	C₂²	1	2	yes	complemented
66	#10822339	C₂²	1	2	yes	complemented
67	#10822339	C₂²	1	2	yes	complemented
68	C₂×#69028	C₂²	1	2	yes	complemented
69	C₂×#70331	C₂²	1	2	yes	complemented
70	C₂×#70409	C₂²	1	2	yes	complemented
71	C₂×#71858	C₂²	1	2	yes	complemented
72	C₂×#70050	C₂²	1	2	yes	complemented
73	C₂×#72099	C₂²	1	2	yes	complemented
74	C₂×#72119	C₂²	1	2	yes	complemented
75	C₂×#71854	C₂²	1	1	yes	characteristic, complemented
76	C₂×#72025	C₂²	1	1	yes	characteristic, complemented
77	C₂×#68713	C₂²	1	2	yes	complemented
78	C₂×#70047	C₂²	1	1	yes	characteristic, complemented
79	C₂×#70330	C₂²	1	2	yes	complemented
80	C₂×#70139	C₂²	1	1	yes	characteristic, complemented
81	C₂×#72141	C₂²	1	1	yes	characteristic, complemented
82	C₂×#70414	C₂²	1	2	yes	complemented
83	C₂×#70048	C₂²	1	1	yes	characteristic, complemented
84	C₂×#70327	C₂²	1	2	yes	complemented
85	#10794451	C₂²	1	1	yes	characteristic, complemented
86	#10794450	C₂²	1	2	yes	complemented
87	#10794450	C₂²	1	1	yes	characteristic, complemented
88	#10794449	C₂²	1	1	yes	characteristic, complemented
89	#10794449	C₂²	1	2	yes	complemented
90	C₂×D₃×#344	C₂²	1	2	yes	complemented
91	C₂×D₃×H(3,ℤ/4)	C₂²	1	2	yes	complemented
92	D₃×#1728	C₂²	1	2	yes	complemented
93	#10702102	C₂²	1	2	yes	complemented
94	#10702101	C₂²	1	2	yes	complemented
95	#10702101	C₂²	1	2	yes	complemented
96	#10702100	C₂²	1	2	yes	complemented
97	#10702099	C₂²	1	2	yes	complemented
98	#10702098	C₂²	1	2	yes	complemented
99	#10702098	C₂²	1	2	yes	complemented
100	#10701919	C₂²	1	2	yes	complemented
101	#10701918	C₂²	1	2	yes	complemented
102	#10701917	C₂²	1	2	yes	complemented
103	#10701916	C₂²	1	2	yes	complemented
104	#10701915	C₂²	1	2	yes	complemented
105	#10701914	C₂²	1	2	yes	complemented
106	#10701913	C₂²	1	2	yes	complemented
107	#10700537	C₂²	1	1	yes	characteristic, complemented
108	#10700536	C₂²	1	2	yes	complemented
109	#10700535	C₂²	1	1	yes	characteristic, complemented
110	#10700534	C₂²	1	1	yes	characteristic, complemented
111	#10700533	C₂²	1	2	yes	complemented
112	C₂×C₃×#3585	C₂²	1	1	yes	characteristic, complemented
113	C₂×C₃×#3021	C₂²	1	1	yes	characteristic, complemented
114	C₃×#35527	C₂²	1	1	yes	characteristic, complemented
115	C₃×#23430	C₂²	1	2	yes	complemented
116	C₂×C₃×#2008	C₂²	1	2	yes	complemented
117	C₂×C₃×#1910	C₂²	1	1	yes	characteristic, complemented
118	C₂×C₃×#1795	C₂²	1	1	yes	characteristic, complemented
119	C₃×#20608	C₂²	1	1	yes	characteristic, complemented
120	C₃×#11041	C₂²	1	2	yes	complemented
121	C₃×#11012	C₂²	1	2	yes	complemented
122	C₃×#10746	C₂²	1	1	yes	characteristic, complemented
123	#394022	D₃	1	1	yes	characteristic, direct product factor
124	C₂×C₃×#585	C₂³	1	1	yes	characteristic
125	C₂²×C₃×H(5,𝔽₂)	C₂³	1	1	yes	characteristic
126	D₃×#585	D₄	1	8	yes	complemented
127	C₂×#5964	C₂³	1	1	yes	characteristic
128	C₂×#5964	C₂³	1	2	yes	—
129	C₂²×#1009	D₄	1	2	yes	—
130	C₂²×#1009	C₂³	1	1	yes	characteristic
131	C₂²×#1009	C₂³	1	1	yes	characteristic
132	C₂²×D₃×#41	D₄	1	2	yes	—
133	C₂²×D₃×#41	C₂³	1	1	yes	characteristic
134	C₂²×D₃×#41	C₂³	1	2	yes	—
135	C₂²×D₃×#41	C₂³	1	1	yes	characteristic
136	C₂²×#1004	D₄	1	2	yes	—
137	C₂²×#1004	C₂³	1	1	yes	characteristic
138	C₂³×D₃×D₄	D₄	1	2	yes	—
139	C₂³×D₃×D₄	C₂³	1	1	yes	characteristic
140	C₂³×D₃×D₄	C₂³	1	1	yes	characteristic
141	C₂×C₃×#575	C₂³	1	2	yes	—
142	C₂²×C₃×AGL(1,ℤ/8)	C₂³	1	2	yes	—
143	C₂²×C₃×AGL(1,ℤ/8)	C₂³	1	2	yes	complemented
144	C₂×C₃×#568	C₂³	1	1	yes	characteristic
145	C₂×C₃×#535	C₂³	1	1	yes	characteristic
146	C₂×C₃×#535	C₂³	1	1	yes	characteristic, complemented
147	C₂²×C₃×#127	C₂³	1	1	yes	characteristic, complemented
148	C₂×#5830	C₂³	1	1	yes	characteristic
149	C₂×#5830	C₂³	1	1	yes	characteristic, complemented
150	C₂×#5822	C₂³	1	2	yes	—
151	C₂×#5822	C₂³	1	2	yes	—
152	C₂²×#949	C₂³	1	2	yes	—
153	C₂²×#949	C₂³	1	2	yes	complemented
154	C₂×#5819	C₂³	1	1	yes	characteristic
155	C₂×#5805	C₂³	1	1	yes	characteristic
156	C₂×#5805	C₂³	1	1	yes	characteristic, complemented
157	C₂²×#940	C₂³	1	1	yes	characteristic, complemented
158	C₂²×#940	C₂³	1	1	yes	characteristic, complemented
159	C₂²×#932	C₂³	1	2	yes	—
160	C₂²×#932	C₂³	1	2	yes	complemented
161	D₃×#575	D₄	1	16	yes	complemented
162	C₂²×#914	D₄	1	4	yes	complemented
163	C₂²×D₃×SD₁₆	D₄	1	4	yes	complemented
164	C₂²×#911	D₄	1	4	yes	complemented
165	C₂²×D₃×D₈	D₄	1	4	yes	complemented
166	D₃×#568	D₄	1	8	yes	complemented
167	C₂×#5748	C₂³	1	2	yes	—
168	C₂²×#908	C₂³	1	2	yes	—
169	C₂²×#908	C₂³	1	2	yes	complemented
170	C₂×#5745	C₂³	1	2	yes	—
171	C₂²×D₃×M₁₆	C₂³	1	2	yes	—
172	C₂²×D₃×M₁₆	C₂³	1	2	yes	—
173	C₂×#5715	D₄	1	2	yes	—
174	C₂×D₃×#127	D₄	1	2	yes	—
175	C₂×#5674	D₄	1	2	yes	—
176	C₂×D₃×#124	D₄	1	2	yes	—
177	C₂×#5525	C₂³	1	1	yes	characteristic
178	C₂×#5525	C₂³	1	1	yes	characteristic, complemented
179	C₂×D₃×#117	C₂³	1	2	yes	—
180	C₂×D₃×#117	C₂³	1	1	yes	characteristic
181	C₂×D₃×#117	C₂³	1	1	yes	characteristic
182	C₂²×#874	C₂³	1	1	yes	characteristic, complemented
183	C₂²×C₄²×D₃	C₂³	1	1	yes	characteristic
184	C₂×C₃×#421	C₂³	1	2	yes	complemented
185	C₂×C₃×#421	C₂³	1	2	yes	complemented
186	C₂×C₃×#418	C₂³	1	2	yes	complemented
187	C₂×C₃×#418	C₂³	1	2	yes	complemented
188	C₂×C₃×#413	C₂³	1	1	yes	characteristic
189	C₂×C₃×#410	C₂³	1	1	yes	characteristic
190	C₂×C₃×#410	C₂³	1	2	yes	complemented
191	C₃×#2309	C₂³	1	1	yes	characteristic, complemented
192	C₃×#2297	C₂³	1	1	yes	characteristic
193	C₃×#2297	C₂³	1	1	yes	characteristic, complemented
194	C₃×#2297	C₂³	1	2	yes	complemented
195	#84086	C₂³	1	1	yes	characteristic
196	#84086	C₂³	1	1	yes	characteristic, complemented
197	#84086	C₂³	1	2	yes	complemented
198	C₂×#5240	C₂³	1	1	yes	characteristic
199	C₂×#5240	C₂³	1	2	yes	complemented
200	C₂×#5236	C₂³	1	2	yes	complemented
201	C₂×#5236	C₂³	1	2	yes	complemented
202	C₂×#5237	C₂³	1	1	yes	characteristic
203	#84044	C₂³	1	1	yes	characteristic, complemented
204	C₂×#5215	C₂³	1	2	yes	complemented
205	C₂×#5215	C₂³	1	2	yes	complemented
206	C₂×#5139	C₂³	1	2	yes	complemented
207	C₂×#5139	C₂³	1	2	yes	complemented
208	C₂×#5131	C₂³	1	2	yes	complemented
209	C₂×#5131	C₂³	1	2	yes	complemented
210	C₂×#5132	C₂³	1	2	yes	—
211	#82269	C₂³	1	1	yes	characteristic, complemented
212	#82269	C₂³	1	1	yes	characteristic, complemented
213	C₂×#5006	C₂³	1	2	yes	—
214	C₂×#5006	C₂³	1	2	yes	complemented
215	C₂×#5006	C₂³	1	2	yes	complemented
216	#82228	C₂³	1	1	yes	characteristic
217	#82228	C₂³	1	1	yes	characteristic, complemented
218	#82228	C₂³	1	2	yes	complemented
219	C₂×#5005	C₂³	1	2	yes	complemented
220	C₂×#5005	C₂³	1	2	yes	complemented
221	C₂×#5001	C₂³	1	2	yes	complemented
222	C₂×#5001	C₂³	1	2	yes	complemented
223	#82070	C₂³	1	1	yes	characteristic
224	#82070	C₂³	1	1	yes	characteristic, complemented
225	#82070	C₂³	1	2	yes	complemented
226	D₃×#413	D₄	1	8	yes	complemented
227	D₃×#386	D₄	1	4	yes	—
228	#74658	D₄	1	4	yes	—
229	C₂×C₃×#344	C₂³	1	2	yes	complemented
230	C₂×C₃×H(3,ℤ/4)	C₂³	1	2	yes	complemented
231	C₃×#1728	C₂³	1	2	yes	complemented
232	C₂×#4559	C₂³	1	2	yes	complemented
233	C₂×#4556	C₂³	1	2	yes	complemented
234	C₂×#4557	C₂³	1	2	yes	complemented
235	#71979	C₂³	1	2	yes	complemented
236	#71979	C₂³	1	2	yes	complemented
237	C₂×#4533	C₂³	1	2	yes	complemented
238	C₂×#4531	C₂³	1	2	yes	complemented
239	C₂×#4531	C₂³	1	2	yes	complemented
240	#71527	C₂³	1	2	yes	complemented
241	C₂×#3585	C₂×D₃	1	1	yes	characteristic, complemented
242	C₂×#3021	C₂×D₃	1	1	yes	characteristic, complemented
243	#35527	C₂×D₃	1	1	yes	characteristic, complemented
244	#23430	C₂×D₃	1	2	yes	complemented
245	C₂×#2008	C₂×D₃	1	2	yes	complemented
246	C₂×#1910	C₂×D₃	1	1	yes	characteristic, complemented
247	C₂×#1795	C₂×D₃	1	1	yes	characteristic, complemented
248	#20608	C₂×D₃	1	1	yes	characteristic, complemented
249	#11041	C₂×D₃	1	2	yes	complemented
250	#11012	C₂×D₃	1	2	yes	complemented
251	#10746	C₂×D₃	1	1	yes	characteristic, complemented
252	C₃×#585	C₂×D₄	1	4	yes	complemented
253	C₂²×C₃×#41	C₂×D₄	1	2	yes	—
254	C₂²×C₃×#41	C₂⁴	1	2	yes	—
255	C₂²×C₃×#41	C₂⁴	1	1	yes	characteristic
256	C₂²×C₃×#41	C₂⁴	1	1	yes	characteristic
257	C₂³×C₃×D₄	C₂×D₄	1	2	yes	—
258	C₂³×C₃×D₄	C₂⁴	1	1	yes	characteristic
259	C₂³×C₃×D₄	C₂⁴	1	1	yes	characteristic
260	#5964	C₂×D₄	1	4	yes	complemented
261	#5964	C₂×D₄	1	8	yes	complemented
262	C₂×D₃×#41	C₂×D₄	1	8	yes	—
263	C₂×D₃×#41	C₂×D₄	1	8	yes	—
264	C₂×D₃×#41	C₂×D₄	1	8	yes	—
265	C₂×D₃×#41	C₂×D₄	1	4	yes	—
266	C₂×D₃×#41	C₂×D₄	1	4	yes	—
267	C₂×D₃×#41	C₂×D₄	1	4	yes	—
268	C₂×D₃×#41	#41	1	4	yes	—
269	C₂²×#239	C₂×D₄	1	1	yes	characteristic
270	C₂²×#239	C₂×D₄	1	2	yes	—
271	C₂²×#239	C₂×D₄	1	2	yes	—
272	C₂²×#239	C₂×D₄	1	1	yes	characteristic
273	C₂²×D₃×Q₈	C₂×D₄	1	1	yes	characteristic
274	C₂²×D₃×Q₈	C₂×D₄	1	2	yes	—
275	C₂²×D₃×Q₈	C₂×D₄	1	1	yes	characteristic
276	C₂²×#237	C₂×D₄	1	2	yes	—
277	C₂²×#237	C₂×D₄	1	1	yes	characteristic
278	C₂²×#237	C₂×D₄	1	2	yes	—
279	C₂²×#237	C₂×D₄	1	2	yes	—
280	C₂²×#237	C₂×D₄	1	1	yes	characteristic
281	C₂²×D₃×D₄	C₂×D₄	1	2	yes	—
282	C₂²×D₃×D₄	C₂×D₄	1	2	yes	—
283	C₂²×D₃×D₄	C₂×D₄	1	2	yes	—
284	C₂²×D₃×D₄	C₂×D₄	1	1	yes	characteristic
285	C₂²×D₃×D₄	C₂×D₄	1	2	yes	—
286	C₂²×D₃×D₄	C₂×D₄	1	2	yes	—
287	C₂²×D₃×D₄	C₂×D₄	1	4	yes	—
288	C₂²×D₃×D₄	C₂×D₄	1	4	yes	—
289	C₂²×D₃×D₄	C₂×D₄	1	2	yes	—
290	C₂²×D₃×D₄	C₂×D₄	1	2	yes	—
291	C₂²×D₃×D₄	C₂×D₄	1	2	yes	—
292	C₂²×D₃×D₄	C₂×D₄	1	1	yes	characteristic
293	C₂²×#235	C₂×D₄	1	2	yes	—
294	C₂²×#235	C₂×D₄	1	2	yes	—
295	C₂²×#235	C₂⁴	1	1	yes	characteristic
296	C₂²×#235	C₂⁴	1	2	yes	—
297	C₂²×#235	C₂⁴	1	1	yes	characteristic
298	C₂³×D₁₂	C₂×D₄	1	2	yes	—
299	C₂³×D₁₂	C₂⁴	1	1	yes	characteristic
300	C₂³×D₁₂	C₂⁴	1	1	yes	characteristic
301	C₂³×C₄×D₃	C₂×D₄	1	2	yes	—
302	C₂³×C₄×D₃	C₂×D₄	1	2	yes	—
303	C₂³×C₄×D₃	C₂⁴	1	1	yes	characteristic
304	C₃×#575	C₂×D₄	1	8	yes	complemented
305	C₂²×C₃×SD₁₆	C₂×D₄	1	4	yes	complemented
306	C₂²×C₃×D₈	C₂×D₄	1	4	yes	complemented
307	C₃×#568	C₂×D₄	1	4	yes	complemented
308	C₂²×C₃×M₁₆	C₂⁴	1	2	yes	—
309	C₂²×C₃×M₁₆	C₂⁴	1	2	yes	—
310	C₂×C₃×#127	C₂×D₄	1	2	yes	—
311	C₂×C₃×#124	C₂×D₄	1	2	yes	—
312	C₂×C₃×#117	C₂⁴	1	2	yes	—
313	C₂×C₃×#117	C₂⁴	1	1	yes	characteristic
314	C₂×C₃×#117	C₂⁴	1	1	yes	characteristic
315	C₂²×C₃×C₄²	C₂⁴	1	1	yes	characteristic
316	#5822	C₂×D₄	1	8	yes	complemented
317	#5822	C₂×D₄	1	8	yes	complemented
318	#5819	C₂×D₄	1	4	yes	complemented
319	C₂×#947	C₂×D₄	1	2	yes	—
320	C₂²×#215	C₂×D₄	1	4	yes	complemented
321	C₂×#940	C₂×D₄	1	2	yes	—
322	C₂×#940	C₂×D₄	1	2	yes	—
323	C₂×#936	C₂×D₄	1	2	yes	—
324	C₂²×#214	C₂×D₄	1	4	yes	complemented
325	C₂²×#213	C₂×D₄	1	4	yes	complemented
326	C₂²×#213	C₂×D₄	1	4	yes	complemented
327	C₂×#926	C₂⁴	1	2	yes	—
328	C₂×#926	C₂⁴	1	1	yes	characteristic
329	C₂×#926	C₂⁴	1	1	yes	characteristic
330	C₂²×C₄×Dic₃	C₂×D₄	1	2	yes	—
331	C₂²×C₄×Dic₃	C₂⁴	1	1	yes	characteristic
332	C₂²×#208	C₂⁴	1	2	yes	—
333	C₂²×#208	C₂⁴	1	2	yes	—
334	#5748	C₂×D₄	1	8	yes	complemented
335	#5745	C₂×D₄	1	8	yes	complemented
336	C₂×D₃×M₁₆	C₂×D₄	1	8	yes	—
337	C₂×D₃×M₁₆	C₂×D₄	1	8	yes	—
338	C₂×D₃×M₁₆	C₂×D₄	1	8	yes	—
339	C₂²×D₂₄	C₂×D₄	1	4	yes	complemented
340	C₂²×#204	C₂×D₄	1	4	yes	complemented
341	C₂²×ΓL(1,𝔽₂₅)	C₂×D₄	1	4	yes	—
342	C₂²×D₃×C₈	C₂×D₄	1	4	yes	—
343	C₂×D₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
344	C₂×#877	C₂×D₄	1	2	yes	—
345	C₂×#875	C₂×D₄	1	2	yes	—
346	C₂×#874	C₂×D₄	1	2	yes	—
347	C₂×#872	C₂×D₄	1	2	yes	—
348	C₂×C₄²×D₃	C₂×D₄	1	2	yes	—
349	C₃×#413	C₂×D₄	1	4	yes	complemented
350	C₃×#386	C₂×D₄	1	4	yes	—
351	#5237	C₂×D₄	1	4	yes	complemented
352	#5220	C₂×D₄	1	4	yes	—
353	#5213	C₂×D₄	1	4	yes	—
354	#5132	C₂×D₄	1	8	yes	complemented
355	#4958	C₂×D₄	1	4	yes	—
356	C₂×#585	C₂²×D₃	1	1	yes	characteristic
357	C₂²×H(5,𝔽₂)	C₂²×D₃	1	1	yes	characteristic
358	C₂×#575	C₂²×D₃	1	2	yes	—
359	C₂²×AGL(1,ℤ/8)	C₂²×D₃	1	2	yes	—
360	C₂²×AGL(1,ℤ/8)	C₂²×D₃	1	2	yes	complemented
361	C₂×#568	C₂²×D₃	1	1	yes	characteristic
362	C₂×#535	C₂²×D₃	1	1	yes	characteristic
363	C₂×#535	C₂²×D₃	1	1	yes	characteristic, complemented
364	C₂²×#127	C₂²×D₃	1	1	yes	characteristic, complemented
365	C₂×#421	C₂²×D₃	1	2	yes	complemented
366	C₂×#421	C₂²×D₃	1	2	yes	complemented
367	C₂×#418	C₂²×D₃	1	2	yes	complemented
368	C₂×#418	C₂²×D₃	1	2	yes	complemented
369	C₂×#413	C₂²×D₃	1	1	yes	characteristic
370	C₂×#410	C₂²×D₃	1	1	yes	characteristic
371	C₂×#410	C₂²×D₃	1	2	yes	complemented
372	#2309	C₂²×D₃	1	1	yes	characteristic, complemented
373	#2297	C₂²×D₃	1	1	yes	characteristic
374	#2297	C₂²×D₃	1	1	yes	characteristic, complemented
375	#2297	C₂²×D₃	1	2	yes	complemented
376	C₂×#344	C₂²×D₃	1	2	yes	complemented
377	C₂×H(3,ℤ/4)	C₂²×D₃	1	2	yes	complemented
378	#1728	C₂²×D₃	1	2	yes	complemented
379	C₂⁴×D₃	#120	1	2	yes	—
380	C₂⁴×D₃	C₂²×D₄	1	1	yes	characteristic
381	C₂×C₃×#41	C₂²×D₄	1	4	yes	—
382	C₂×C₃×#41	C₂²×D₄	1	4	yes	—
383	C₂×C₃×#41	C₂²×D₄	1	4	yes	—
384	C₂×C₃×#41	C₂²×D₄	1	2	yes	—
385	C₂×C₃×#41	C₂²×D₄	1	2	yes	—
386	C₂×C₃×#41	C₂²×D₄	1	2	yes	—
387	C₂×C₃×#41	C₂×#41	1	2	yes	—
388	C₂²×C₃×Q₈	C₂²×D₄	1	1	yes	characteristic
389	C₂²×C₃×Q₈	C₂²×D₄	1	2	yes	—
390	C₂²×C₃×Q₈	C₂²×D₄	1	1	yes	characteristic
391	C₂²×C₃×D₄	C₂²×D₄	1	2	yes	—
392	C₂²×C₃×D₄	C₂²×D₄	1	2	yes	—
393	C₂²×C₃×D₄	C₂²×D₄	1	4	yes	—
394	C₂²×C₃×D₄	C₂²×D₄	1	1	yes	characteristic
395	C₂²×C₃×D₄	C₂²×D₄	1	2	yes	—
396	C₂²×C₃×D₄	C₂²×D₄	1	2	yes	—
397	C₂²×C₃×D₄	C₂²×D₄	1	1	yes	characteristic
398	C₂³×C₃×C₄	C₂²×D₄	1	2	yes	—
399	C₂³×C₃×C₄	C₂²×D₄	1	2	yes	—
400	C₂³×C₃×C₄	C₂⁵	1	1	yes	characteristic
401	C₂²×#67	#120	1	2	yes	—
402	C₂²×#67	#120	1	2	yes	—
403	C₂²×#67	C₂²×D₄	1	2	yes	—
404	C₂³×Dic₃	#120	1	2	yes	—
405	C₂³×Dic₃	C₂²×D₄	1	2	yes	—
406	C₂³×Dic₃	C₂²×D₄	1	1	yes	characteristic
407	C₂×#239	#120	1	4	yes	—
408	C₂×#239	#120	1	4	yes	—
409	C₂×#239	#120	1	8	yes	complemented
410	C₂×#239	#121	1	4	yes	—
411	C₂×D₃×Q₈	#120	1	4	yes	—
412	C₂×D₃×Q₈	#120	1	4	yes	—
413	C₂×D₃×Q₈	#120	1	8	yes	complemented
414	C₂×D₃×Q₈	#121	1	4	yes	—
415	C₂×#237	#120	1	4	yes	—
416	C₂×#237	#120	1	4	yes	—
417	C₂×#237	#120	1	8	yes	complemented
418	C₂×#237	#121	1	4	yes	—
419	C₂×#237	#121	1	8	yes	—
420	C₂×#237	#127	1	8	yes	—
421	C₂×D₃×D₄	#120	1	4	yes	—
422	C₂×D₃×D₄	#120	1	4	yes	—
423	C₂×D₃×D₄	#120	1	4	yes	—
424	C₂×D₃×D₄	#120	1	8	yes	—
425	C₂×D₃×D₄	#120	1	4	yes	—
426	C₂×D₃×D₄	#120	1	8	yes	complemented
427	C₂×D₃×D₄	#121	1	4	yes	—
428	C₂×D₃×D₄	#121	1	8	yes	—
429	C₂×D₃×D₄	#127	1	8	yes	—
430	C₂×#235	#120	1	8	yes	—
431	C₂×#235	#121	1	8	yes	—
432	C₂×#235	C₂²×D₄	1	4	yes	—
433	C₂×#235	C₂²×D₄	1	2	yes	—
434	C₂×#235	C₂²×D₄	1	2	yes	—
435	C₂×#235	C₂²×D₄	1	4	yes	—
436	C₂×#235	C₂²×D₄	1	4	yes	—
437	C₂×#235	C₂²×D₄	1	2	yes	—
438	C₂×#235	C₂×#41	1	2	yes	—
439	C₂²×D₁₂	#120	1	2	yes	—
440	C₂²×D₁₂	C₂²×D₄	1	2	yes	—
441	C₂²×D₁₂	C₂²×D₄	1	1	yes	characteristic
442	C₂²×D₁₂	C₂²×D₄	1	2	yes	—
443	C₂²×D₁₂	C₂²×D₄	1	4	yes	—
444	C₂²×D₁₂	C₂²×D₄	1	2	yes	—
445	C₂²×D₁₂	C₂²×D₄	1	1	yes	characteristic
446	C₂²×C₄×D₃	#120	1	8	yes	—
447	C₂²×C₄×D₃	#120	1	2	yes	—
448	C₂²×C₄×D₃	#120	1	2	yes	—
449	C₂²×C₄×D₃	#121	1	8	yes	—
450	C₂²×C₄×D₃	C₂²×D₄	1	2	yes	—
451	C₂²×C₄×D₃	C₂²×D₄	1	2	yes	—
452	C₂²×C₄×D₃	C₂²×D₄	1	1	yes	characteristic
453	C₂²×C₄×D₃	C₂²×D₄	1	1	yes	characteristic
454	C₂²×C₄×D₃	C₂²×D₄	1	2	yes	—
455	C₂²×C₄×D₃	C₂²×D₄	1	4	yes	—
456	C₂²×C₄×D₃	C₂²×D₄	1	2	yes	—
457	C₂²×C₄×D₃	C₂²×D₄	1	2	yes	—
458	C₂²×C₄×D₃	C₂²×D₄	1	1	yes	characteristic
459	C₂²×C₄×D₃	C₂²×D₄	1	1	yes	characteristic
460	C₂²×C₄×D₃	C₂²×D₄	1	2	yes	—
461	C₂²×C₄×D₃	C₂×#41	1	2	yes	—
462	C₂²×C₄×D₃	H(5,𝔽₂)	1	2	yes	—
463	C₂²×C₄×D₃	H(5,𝔽₂)	1	2	yes	—
464	C₂²×C₄×D₃	H(5,𝔽₂)	1	4	yes	—
465	C₂²×Dic₆	#120	1	2	yes	—
466	C₂²×Dic₆	C₂²×D₄	1	1	yes	characteristic
467	C₂²×Dic₆	C₂²×D₄	1	2	yes	—
468	C₂²×Dic₆	C₂²×D₄	1	1	yes	characteristic
469	C₂×C₃×M₁₆	C₂²×D₄	1	4	yes	—
470	C₂×C₃×M₁₆	C₂²×D₄	1	4	yes	—
471	C₂×C₃×M₁₆	C₂²×D₄	1	4	yes	—
472	C₂²×C₃×C₈	C₂²×D₄	1	4	yes	—
473	C₂×C₃×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
474	C₂×C₃×C₄²	C₂²×D₄	1	2	yes	—
475	C₂×#217	C₂²×D₄	1	2	yes	—
476	C₂×C₄×Dic₃	C₂²×D₄	1	2	yes	—
477	C₂×#208	C₂²×D₄	1	4	yes	—
478	C₂×#208	C₂²×D₄	1	4	yes	—
479	C₂×#208	C₂²×D₄	1	4	yes	—
480	C₂²×C₃⋊C₈	C₂²×D₄	1	4	yes	—
481	C₂×ΓL(1,𝔽₂₅)	#120	1	16	yes	complemented
482	C₂×D₃×C₈	#120	1	16	yes	complemented
483	#585	D₃×D₄	1	4	yes	complemented
484	C₂²×#41	D₃×D₄	1	2	yes	—
485	C₂²×#41	C₂³×D₃	1	1	yes	characteristic
486	C₂²×#41	C₂³×D₃	1	2	yes	—
487	C₂²×#41	C₂³×D₃	1	1	yes	characteristic
488	C₂³×D₄	D₃×D₄	1	2	yes	—
489	C₂³×D₄	C₂³×D₃	1	1	yes	characteristic
490	C₂³×D₄	C₂³×D₃	1	1	yes	characteristic
491	#575	D₃×D₄	1	8	yes	complemented
492	C₂²×SD₁₆	D₃×D₄	1	4	yes	complemented
493	C₂²×D₈	D₃×D₄	1	4	yes	complemented
494	#568	D₃×D₄	1	4	yes	complemented
495	C₂²×M₁₆	C₂³×D₃	1	2	yes	—
496	C₂²×M₁₆	C₂³×D₃	1	2	yes	—
497	C₂×#127	D₃×D₄	1	2	yes	—
498	C₂×#124	D₃×D₄	1	2	yes	—
499	C₂×#117	C₂³×D₃	1	2	yes	—
500	C₂×#117	C₂³×D₃	1	1	yes	characteristic
501	C₂×#117	C₂³×D₃	1	1	yes	characteristic
502	C₂²×C₄²	C₂³×D₃	1	1	yes	characteristic
503	#413	D₃×D₄	1	4	yes	complemented
504	#386	D₃×D₄	1	4	yes	—
505	C₂⁴×C₃	C₂×#120	1	2	yes	—
506	C₂⁴×C₃	C₂³×D₄	1	1	yes	characteristic
507	C₂³×D₃	#392	1	8	yes	—
508	C₂³×D₃	C₂×#120	1	1	yes	characteristic
509	C₂³×D₃	C₂×#120	1	2	yes	—
510	C₂³×D₃	C₂×#120	1	1	yes	characteristic
511	C₂³×D₃	C₂×#121	1	2	yes	—
512	C₂³×D₃	C₂×#127	1	2	yes	—
513	C₂³×D₃	D₄²	1	2	yes	—
514	C₂³×D₃	D₄²	1	4	yes	—
515	C₂³×D₃	D₄²	1	2	yes	—
516	C₂×C₃×Q₈	C₂×#120	1	2	yes	—
517	C₂×C₃×Q₈	C₂×#120	1	2	yes	—
518	C₂×C₃×Q₈	C₂×#120	1	4	yes	complemented
519	C₂×C₃×Q₈	C₂×#121	1	2	yes	—
520	C₂×C₃×D₄	C₂×#120	1	4	yes	—
521	C₂×C₃×D₄	C₂×#120	1	2	yes	—
522	C₂×C₃×D₄	C₂×#120	1	2	yes	—
523	C₂×C₃×D₄	C₂×#120	1	4	yes	complemented
524	C₂×C₃×D₄	C₂×#121	1	4	yes	—
525	C₂×C₃×D₄	C₂×#121	1	2	yes	—
526	C₂×C₃×D₄	C₂×#127	1	4	yes	—
527	C₂²×C₃×C₄	C₂×#120	1	2	yes	—
528	C₂²×C₃×C₄	C₂×#120	1	4	yes	—
529	C₂²×C₃×C₄	C₂×#121	1	4	yes	—
530	C₂²×C₃×C₄	C₂³×D₄	1	1	yes	characteristic
531	C₂²×C₃×C₄	C₂³×D₄	1	1	yes	characteristic
532	C₂²×C₃×C₄	C₂³×D₄	1	1	yes	characteristic
533	C₂²×C₃×C₄	C₂³×D₄	1	2	yes	—
534	C₂²×C₃×C₄	C₂³×D₄	1	2	yes	—
535	C₂²×C₃×C₄	C₂³×D₄	1	1	yes	characteristic
536	C₂²×C₃×C₄	C₂³×D₄	1	1	yes	characteristic
537	C₂²×C₃×C₄	C₂²×#41	1	1	yes	characteristic
538	C₂²×C₃×C₄	C₂×H(5,𝔽₂)	1	2	yes	—
539	C₂²×C₃×C₄	C₂×H(5,𝔽₂)	1	2	yes	—
540	C₂×#67	#392	1	8	yes	—
541	C₂×#67	#392	1	8	yes	—
542	C₂×#67	C₂×#121	1	4	yes	—
543	C₂×#67	C₂×#127	1	4	yes	—
544	C₂²×Dic₃	#392	1	8	yes	—
545	C₂²×Dic₃	C₂×#120	1	2	yes	—
546	C₂²×Dic₃	C₂×#120	1	1	yes	characteristic
547	C₂²×Dic₃	C₂×#120	1	1	yes	characteristic
548	C₂²×Dic₃	C₂×#121	1	2	yes	—
549	C₂²×Dic₃	C₂×#127	1	2	yes	—
550	C₂²×Dic₃	D₄²	1	4	yes	—
551	C₂²×Dic₃	D₄²	1	2	yes	—
552	C₂²×Dic₃	D₄²	1	2	yes	—
553	C₂×D₁₂	#392	1	8	yes	—
554	C₂×D₁₂	C₂×#120	1	4	yes	—
555	C₂×D₁₂	C₂×#120	1	2	yes	—
556	C₂×D₁₂	C₂×#120	1	2	yes	—
557	C₂×D₁₂	C₂×#120	1	4	yes	complemented
558	C₂×D₁₂	C₂×#121	1	2	yes	—
559	C₂×C₄×D₃	#392	1	8	yes	—
560	C₂×C₄×D₃	#392	1	8	yes	—
561	C₂×C₄×D₃	C₂×#120	1	4	yes	—
562	C₂×C₄×D₃	C₂×#120	1	2	yes	—
563	C₂×C₄×D₃	C₂×#120	1	2	yes	—
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×#120	1	1	yes	characteristic
569	C₂×C₄×D₃	C₂×#120	1	2	yes	—
570	C₂×C₄×D₃	C₂×#120	1	1	yes	characteristic
571	C₂×C₄×D₃	C₂×#120	1	2	yes	—
572	C₂×C₄×D₃	C₂×#120	1	2	yes	—
573	C₂×C₄×D₃	C₂×#120	1	2	yes	—
574	C₂×C₄×D₃	C₂×#120	1	2	yes	—
575	C₂×C₄×D₃	C₂×#121	1	4	yes	—
576	C₂×C₄×D₃	C₂×#121	1	2	yes	—
577	C₂×C₄×D₃	C₂×#121	1	2	yes	—
578	C₂×C₄×D₃	C₂×#121	1	2	yes	—
579	C₂×C₄×D₃	C₂×#121	1	2	yes	—
580	C₂×C₄×D₃	#534	1	4	yes	—
581	C₂×C₄×D₃	#534	1	4	yes	—
582	C₂×C₄×D₃	#534	1	1	yes	characteristic
583	C₂×C₄×D₃	#534	1	1	yes	characteristic
584	C₂×C₄×D₃	#534	1	2	yes	—
585	C₂×C₄×D₃	#534	1	2	yes	—
586	C₂×C₄×D₃	#534	1	2	yes	—
587	C₂×C₄×D₃	#535	1	4	yes	—
588	C₂×C₄×D₃	#535	1	4	yes	—
589	C₂×C₄×D₃	D₄²	1	2	yes	—
590	C₂×C₄×D₃	D₄²	1	2	yes	—
591	C₂×C₄×D₃	D₄²	1	2	yes	—
592	C₂×C₄×D₃	D₄²	1	2	yes	—
593	C₂×C₄×D₃	D₄²	1	4	yes	—
594	C₂×C₄×D₃	D₄²	1	4	yes	—
595	C₂×C₄×D₃	D₄²	1	4	yes	—
596	C₂×C₄×D₃	D₄²	1	4	yes	—
597	C₂×C₄×D₃	D₄²	1	4	yes	—
598	C₂×C₄×D₃	D₄²	1	4	yes	—
599	C₂×C₄×D₃	#546	1	4	yes	—
600	C₂×C₄×D₃	#546	1	4	yes	—
601	C₂×C₄×D₃	#546	1	4	yes	—
602	C₂×C₄×D₃	#546	1	4	yes	—
603	C₂×Dic₆	#392	1	8	yes	—
604	C₂×Dic₆	C₂×#120	1	2	yes	—
605	C₂×Dic₆	C₂×#120	1	2	yes	—
606	C₂×Dic₆	C₂×#120	1	4	yes	complemented
607	C₂×Dic₆	C₂×#121	1	2	yes	—
608	C₂×C₃×C₈	C₂×#120	1	8	yes	complemented
609	C₂×C₃⋊C₈	C₂×#120	1	8	yes	complemented
610	C₂×#41	C₂×D₃×D₄	1	4	yes	—
611	C₂×#41	C₂×D₃×D₄	1	4	yes	—
612	C₂×#41	C₂×D₃×D₄	1	4	yes	—
613	C₂×#41	C₂×D₃×D₄	1	2	yes	—
614	C₂×#41	C₂×D₃×D₄	1	2	yes	—
615	C₂×#41	C₂×D₃×D₄	1	2	yes	—
616	C₂×#41	D₃×#41	1	2	yes	—
617	C₂²×Q₈	C₂×D₃×D₄	1	1	yes	characteristic
618	C₂²×Q₈	C₂×D₃×D₄	1	2	yes	—
619	C₂²×Q₈	C₂×D₃×D₄	1	1	yes	characteristic
620	C₂²×D₄	C₂×D₃×D₄	1	2	yes	—
621	C₂²×D₄	C₂×D₃×D₄	1	4	yes	—
622	C₂²×D₄	C₂×D₃×D₄	1	1	yes	characteristic
623	C₂²×D₄	C₂×D₃×D₄	1	2	yes	—
624	C₂²×D₄	C₂×D₃×D₄	1	2	yes	—
625	C₂²×D₄	C₂×D₃×D₄	1	1	yes	characteristic
626	C₂²×D₄	C₂×D₃×D₄	1	2	yes	—
627	C₂³×C₄	C₂×D₃×D₄	1	2	yes	—
628	C₂³×C₄	C₂×D₃×D₄	1	2	yes	—
629	C₂³×C₄	C₂⁴×D₃	1	1	yes	characteristic
630	C₂×M₁₆	C₂×D₃×D₄	1	4	yes	—
631	C₂×M₁₆	C₂×D₃×D₄	1	4	yes	—
632	C₂×M₁₆	C₂×D₃×D₄	1	4	yes	—
633	C₂²×C₈	C₂×D₃×D₄	1	4	yes	—
634	C₂×C₂²⋊C₄	C₂×D₃×D₄	1	2	yes	—
635	C₂×C₄²	C₂×D₃×D₄	1	2	yes	—
636	C₂³×C₃	C₂×#392	1	4	yes	—
637	C₂³×C₃	C₂²×#120	1	1	yes	characteristic
638	C₂³×C₃	C₂²×#121	1	1	yes	characteristic
639	C₂³×C₃	C₂²×#127	1	1	yes	characteristic
640	C₂³×C₃	C₂×D₄²	1	2	yes	—
641	C₂³×C₃	C₂×D₄²	1	2	yes	—
642	C₂²×D₃	C₂×#392	1	2	yes	—
643	C₂²×D₃	C₂×#392	1	4	yes	—
644	C₂²×D₃	C₂×#392	1	2	yes	—
645	C₂²×D₃	#2403	1	2	yes	—
646	C₂²×D₃	#2403	1	1	yes	characteristic
647	C₂²×D₃	#2403	1	2	yes	—
648	C₂²×D₃	#2403	1	2	yes	—
649	C₂²×D₃	#2403	1	1	yes	characteristic
650	C₂²×D₃	#2410	1	4	yes	—
651	C₂²×D₃	#2410	1	4	yes	—
652	C₂²×D₃	#2433	1	4	yes	—
653	C₂²×D₃	#2433	1	4	yes	—
654	C₂×C₃×C₄	C₂×#392	1	4	yes	—
655	C₂×C₃×C₄	C₂²×#120	1	2	yes	—
656	C₂×C₃×C₄	C₂²×#120	1	1	yes	characteristic
657	C₂×C₃×C₄	C₂²×#120	1	1	yes	characteristic
658	C₂×C₃×C₄	C₂²×#120	1	2	yes	—
659	C₂×C₃×C₄	C₂²×#120	1	1	yes	characteristic
660	C₂×C₃×C₄	C₂²×#120	1	1	yes	characteristic
661	C₂×C₃×C₄	C₂²×#121	1	1	yes	characteristic
662	C₂×C₃×C₄	C₂²×#121	1	1	yes	characteristic
663	C₂×C₃×C₄	C₂×#534	1	2	yes	—
664	C₂×C₃×C₄	C₂×#534	1	1	yes	characteristic
665	C₂×C₃×C₄	C₂×#534	1	1	yes	characteristic
666	C₂×C₃×C₄	C₂×#535	1	2	yes	—
667	C₂×C₃×C₄	C₂×D₄²	1	2	yes	—
668	C₂×C₃×C₄	C₂×D₄²	1	2	yes	—
669	C₂×C₃×C₄	C₂×D₄²	1	2	yes	—
670	C₂×C₃×C₄	C₂×D₄²	1	2	yes	—
671	C₂×C₃×C₄	C₂×#546	1	2	yes	—
672	C₂×C₃×C₄	C₂×#546	1	2	yes	—
673	C₂×Dic₃	C₂×#392	1	4	yes	—
674	C₂×Dic₃	C₂×#392	1	2	yes	—
675	C₂×Dic₃	C₂×#392	1	2	yes	—
676	C₂×Dic₃	#2403	1	2	yes	—
677	C₂×Dic₃	#2403	1	2	yes	—
678	C₂×Dic₃	#2403	1	1	yes	characteristic
679	C₂×Dic₃	#2403	1	1	yes	characteristic
680	C₂×Dic₃	#2403	1	2	yes	—
681	C₂×Dic₃	#2410	1	4	yes	—
682	C₂×Dic₃	#2410	1	4	yes	—
683	C₂×Dic₃	#2433	1	4	yes	—
684	C₂×Dic₃	#2433	1	4	yes	—
685	C₄×D₃	#2403	1	4	yes	—
686	C₄×D₃	#2403	1	4	yes	—
687	C₄×D₃	#2403	1	4	yes	—
688	C₄×D₃	#2403	1	4	yes	—
689	C₄×D₃	#2408	1	4	yes	—
690	C₄×D₃	#2408	1	4	yes	—
691	C₄×D₃	#2408	1	4	yes	—
692	C₄×D₃	#2408	1	4	yes	—
693	C₄×D₃	#2410	1	2	yes	—
694	C₄×D₃	#2410	1	2	yes	—
695	C₄×D₃	#2410	1	2	yes	—
696	C₄×D₃	#2410	1	2	yes	—
697	C₄×D₃	#2410	1	4	yes	—
698	C₄×D₃	#2410	1	4	yes	—
699	C₄×D₃	#2613	1	2	yes	—
700	C₄×D₃	#2613	1	2	yes	—
701	C₄×D₃	#2613	1	4	yes	—
702	C₄×D₃	#2846	1	2	yes	—
703	C₄×D₃	#2846	1	4	yes	—
704	C₄×D₃	#2846	1	2	yes	—
705	C₂⁴	D₃×#120	1	2	yes	—
706	C₂⁴	C₂²×D₃×D₄	1	1	yes	characteristic
707	C₂×Q₈	D₃×#120	1	2	yes	—
708	C₂×Q₈	D₃×#120	1	2	yes	—
709	C₂×Q₈	D₃×#120	1	4	yes	complemented
710	C₂×Q₈	D₃×#121	1	2	yes	—
711	C₂×D₄	D₃×#120	1	4	yes	—
712	C₂×D₄	D₃×#120	1	2	yes	—
713	C₂×D₄	D₃×#120	1	2	yes	—
714	C₂×D₄	D₃×#120	1	4	yes	complemented
715	C₂×D₄	D₃×#121	1	2	yes	—
716	C₂×D₄	D₃×#121	1	4	yes	—
717	C₂×D₄	D₃×#127	1	4	yes	—
718	C₂²×C₄	D₃×#120	1	4	yes	—
719	C₂²×C₄	D₃×#120	1	2	yes	—
720	C₂²×C₄	D₃×#121	1	4	yes	—
721	C₂²×C₄	C₂²×D₃×D₄	1	1	yes	characteristic
722	C₂²×C₄	C₂²×D₃×D₄	1	1	yes	characteristic
723	C₂²×C₄	C₂²×D₃×D₄	1	1	yes	characteristic
724	C₂²×C₄	C₂²×D₃×D₄	1	1	yes	characteristic
725	C₂²×C₄	C₂²×D₃×D₄	1	1	yes	characteristic
726	C₂²×C₄	C₂²×D₃×D₄	1	2	yes	—
727	C₂²×C₄	C₂²×D₃×D₄	1	2	yes	—
728	C₂²×C₄	C₂×D₃×#41	1	1	yes	characteristic
729	C₂²×C₄	D₃×H(5,𝔽₂)	1	2	yes	—
730	C₂²×C₄	D₃×H(5,𝔽₂)	1	2	yes	—
731	C₂×C₈	D₃×#120	1	8	yes	complemented
732	C₂²×C₃	C₂²×#392	1	1	yes	characteristic
733	C₂²×C₃	C₂×#2403	1	1	yes	characteristic
734	C₂²×C₃	C₂×#2403	1	1	yes	characteristic
735	C₂²×C₃	C₂×#2410	1	2	yes	—
736	C₂²×C₃	C₂×#2433	1	2	yes	—
737	C₂×D₃	#14715	1	2	yes	—
738	C₂×D₃	#14715	1	4	yes	—
739	C₂×D₃	#14715	1	2	yes	—
740	C₂×D₃	#23882	1	4	yes	—
741	C₃×C₄	C₂×#2613	1	1	yes	characteristic
742	C₃×C₄	C₂×#2403	1	2	yes	—
743	C₃×C₄	C₂×#2410	1	1	yes	characteristic
744	C₃×C₄	C₂×#2410	1	1	yes	characteristic
745	C₃×C₄	C₂×#2408	1	2	yes	—
746	C₃×C₄	C₂×#2846	1	1	yes	characteristic
747	Dic₃	#14715	1	4	yes	—
748	Dic₃	#14715	1	2	yes	—
749	Dic₃	#14715	1	2	yes	—
750	C₂³	D₃×#392	1	4	yes	—
751	C₂³	C₂×D₃×#120	1	1	yes	characteristic
752	C₂³	C₂×D₃×#121	1	1	yes	characteristic
753	C₂³	C₂×D₃×#127	1	1	yes	characteristic
754	C₂³	D₃×D₄²	1	2	yes	—
755	C₂³	D₃×D₄²	1	2	yes	—
756	C₂×C₄	D₃×#392	1	4	yes	—
757	C₂×C₄	C₂×D₃×#120	1	2	yes	—
758	C₂×C₄	C₂×D₃×#120	1	1	yes	characteristic
759	C₂×C₄	C₂×D₃×#120	1	1	yes	characteristic
760	C₂×C₄	C₂×D₃×#120	1	2	yes	—
761	C₂×C₄	C₂×D₃×#120	1	1	yes	characteristic
762	C₂×C₄	C₂×D₃×#120	1	1	yes	characteristic
763	C₂×C₄	C₂×D₃×#121	1	1	yes	characteristic
764	C₂×C₄	C₂×D₃×#121	1	1	yes	characteristic
765	C₂×C₄	D₃×#534	1	2	yes	—
766	C₂×C₄	D₃×#534	1	1	yes	characteristic
767	C₂×C₄	D₃×#534	1	1	yes	characteristic
768	C₂×C₄	D₃×#535	1	2	yes	—
769	C₂×C₄	D₃×D₄²	1	2	yes	—
770	C₂×C₄	D₃×D₄²	1	2	yes	—
771	C₂×C₄	D₃×D₄²	1	2	yes	—
772	C₂×C₄	D₃×D₄²	1	2	yes	—
773	C₂×C₄	D₃×#546	1	2	yes	—
774	C₂×C₄	D₃×#546	1	2	yes	—
775	C₂×C₃	C₂×#14715	1	1	yes	characteristic
776	C₂×C₃	C₂×#23882	1	2	yes	—
777	D₃	#394022	1	4	yes	direct product factor
778	C₂²	C₂×D₃×#392	1	1	yes	characteristic
779	C₂²	D₃×#2403	1	1	yes	characteristic
780	C₂²	D₃×#2403	1	1	yes	characteristic
781	C₂²	D₃×#2410	1	2	yes	—
782	C₂²	D₃×#2433	1	2	yes	—
783	C₄	D₃×#2613	1	1	yes	characteristic
784	C₄	D₃×#2403	1	2	yes	—
785	C₄	D₃×#2410	1	1	yes	characteristic
786	C₄	D₃×#2410	1	1	yes	characteristic
787	C₄	D₃×#2408	1	2	yes	—
788	C₄	D₃×#2846	1	1	yes	characteristic
789	C₃	C₂×#394022	1	1	yes	characteristic, complemented, Sylow
790	C₂	D₃×#23882	1	2	yes	—
791	C₂	D₃×#14715	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₃×#2403
commutator, cosocle	C₂³×C₃×C₄	C₂⁵
Frattini	C₂³×C₄	C₂⁴×D₃
Fitting	C₃×#394022	C₂
socle	C₂²×C₃	C₂×#2403
hypercenter	#394022	D₃
hypocenter	C₃	C₂×#394022
LCS	G ▷ C₂³×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂² ◁ C₂³×C₄ ◁ #394022

Complements

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

N	H ≅ G/N	type
1. #72271718	C₂	semidirect
2. #72271710	C₂	semidirect
3. #72271706	C₂	semidirect
4. D₃×#20608	C₂	semidirect
5. #72271680	C₂	semidirect
6. #72271674	C₂	semidirect
7. #72271671	C₂	semidirect
8. #72271667	C₂	semidirect
9. D₃×#11041	C₂	semidirect
10. #72271650	C₂	semidirect
11. D₃×#23430	C₂	semidirect
12. #72271641	C₂	semidirect
13. #72271637	C₂	semidirect
14. #72271632	C₂	semidirect
15. D₃×#10746	C₂	semidirect
16. C₃×#394022	C₂	semidirect
17. D₃×#35527	C₂	semidirect
18. D₃×#11012	C₂	semidirect
19. C₂×D₃×#3021	C₂	semidirect
20. C₂×D₃×#1795	C₂	semidirect
21. C₂×D₃×#2008	C₂	semidirect
22. C₂×D₃×#3585	C₂	semidirect
23. C₂×D₃×#1910	C₂	semidirect
26. C₂×#87167	C₂²	semidirect
27. C₂×#87277	C₂²	semidirect
28. C₂×#87298	C₂²	semidirect
29. C₂×#87200	C₂²	semidirect
30. C₂×#87192	C₂²	semidirect
33. C₂²×D₃×AGL(1,ℤ/8)	C₂²	semidirect
36. C₂×D₃×#535	C₂²	semidirect
37. C₂²×D₃×#127	C₂²	semidirect
38. C₂×#78717	C₂²	semidirect
39. C₂×#78994	C₂²	semidirect
40. C₂×#84122	C₂²	semidirect
41. C₂×#83395	C₂²	semidirect
42. C₂×#83957	C₂²	semidirect
43. C₂×D₃×#421	C₂²	semidirect
44. C₂×D₃×#421	C₂²	semidirect
45. C₂×D₃×#418	C₂²	semidirect
46. C₂×D₃×#418	C₂²	semidirect
49. C₂×D₃×#410	C₂²	semidirect
50. #10978444	C₂²	semidirect
51. #10978443	C₂²	semidirect
52. #10978443	C₂²	semidirect
53. #10978442	C₂²	semidirect
54. #10978441	C₂²	semidirect
55. #10978440	C₂²	semidirect
56. #10978440	C₂²	semidirect
57. D₃×#2309	C₂²	semidirect
59. D₃×#2297	C₂²	semidirect
60. D₃×#2297	C₂²	semidirect
61. #10822344	C₂²	semidirect
62. #10822343	C₂²	semidirect
63. #10822343	C₂²	semidirect
64. #10822341	C₂²	semidirect
65. #10822340	C₂²	semidirect
66. #10822339	C₂²	semidirect
67. #10822339	C₂²	semidirect
68. C₂×#69028	C₂²	semidirect
69. C₂×#70331	C₂²	semidirect
70. C₂×#70409	C₂²	semidirect
71. C₂×#71858	C₂²	semidirect
72. C₂×#70050	C₂²	semidirect
73. C₂×#72099	C₂²	semidirect
74. C₂×#72119	C₂²	semidirect
75. C₂×#71854	C₂²	semidirect
76. C₂×#72025	C₂²	semidirect
77. C₂×#68713	C₂²	semidirect
78. C₂×#70047	C₂²	semidirect
79. C₂×#70330	C₂²	semidirect
80. C₂×#70139	C₂²	semidirect
81. C₂×#72141	C₂²	semidirect
82. C₂×#70414	C₂²	semidirect
83. C₂×#70048	C₂²	semidirect
84. C₂×#70327	C₂²	semidirect
85. #10794451	C₂²	semidirect
86. #10794450	C₂²	semidirect
87. #10794450	C₂²	semidirect
88. #10794449	C₂²	semidirect
89. #10794449	C₂²	semidirect
90. C₂×D₃×#344	C₂²	semidirect
91. C₂×D₃×H(3,ℤ/4)	C₂²	semidirect
92. D₃×#1728	C₂²	semidirect
93. #10702102	C₂²	semidirect
94. #10702101	C₂²	semidirect
95. #10702101	C₂²	semidirect
96. #10702100	C₂²	semidirect
97. #10702099	C₂²	semidirect
98. #10702098	C₂²	semidirect
99. #10702098	C₂²	semidirect
100. #10701919	C₂²	semidirect
101. #10701918	C₂²	semidirect
102. #10701917	C₂²	semidirect
103. #10701916	C₂²	semidirect
104. #10701915	C₂²	semidirect
105. #10701914	C₂²	semidirect
106. #10701913	C₂²	semidirect
107. #10700537	C₂²	semidirect
108. #10700536	C₂²	semidirect
109. #10700535	C₂²	semidirect
110. #10700534	C₂²	semidirect
111. #10700533	C₂²	semidirect
112. C₂×C₃×#3585	C₂²	semidirect
113. C₂×C₃×#3021	C₂²	semidirect
114. C₃×#35527	C₂²	semidirect
115. C₃×#23430	C₂²	semidirect
116. C₂×C₃×#2008	C₂²	semidirect
117. C₂×C₃×#1910	C₂²	semidirect
118. C₂×C₃×#1795	C₂²	semidirect
119. C₃×#20608	C₂²	semidirect
120. C₃×#11041	C₂²	semidirect
121. C₃×#11012	C₂²	semidirect
122. C₃×#10746	C₂²	semidirect
123. #394022	D₃	direct (N × H)
126. D₃×#585	D₄	semidirect
143. C₂²×C₃×AGL(1,ℤ/8)	C₂³	semidirect
146. C₂×C₃×#535	C₂³	semidirect
147. C₂²×C₃×#127	C₂³	semidirect
149. C₂×#5830	C₂³	semidirect
153. C₂²×#949	C₂³	semidirect
156. C₂×#5805	C₂³	semidirect
157. C₂²×#940	C₂³	semidirect
158. C₂²×#940	C₂³	semidirect
160. C₂²×#932	C₂³	semidirect
161. D₃×#575	D₄	semidirect
162. C₂²×#914	D₄	semidirect
163. C₂²×D₃×SD₁₆	D₄	semidirect
164. C₂²×#911	D₄	semidirect
165. C₂²×D₃×D₈	D₄	semidirect
166. D₃×#568	D₄	semidirect
169. C₂²×#908	C₂³	semidirect
178. C₂×#5525	C₂³	semidirect
182. C₂²×#874	C₂³	semidirect
184. C₂×C₃×#421	C₂³	semidirect
185. C₂×C₃×#421	C₂³	semidirect
186. C₂×C₃×#418	C₂³	semidirect
187. C₂×C₃×#418	C₂³	semidirect
190. C₂×C₃×#410	C₂³	semidirect
191. C₃×#2309	C₂³	semidirect
193. C₃×#2297	C₂³	semidirect
194. C₃×#2297	C₂³	semidirect
196. #84086	C₂³	semidirect
197. #84086	C₂³	semidirect
199. C₂×#5240	C₂³	semidirect
200. C₂×#5236	C₂³	semidirect
201. C₂×#5236	C₂³	semidirect
203. #84044	C₂³	semidirect
204. C₂×#5215	C₂³	semidirect
205. C₂×#5215	C₂³	semidirect
206. C₂×#5139	C₂³	semidirect
207. C₂×#5139	C₂³	semidirect
208. C₂×#5131	C₂³	semidirect
209. C₂×#5131	C₂³	semidirect
211. #82269	C₂³	semidirect
212. #82269	C₂³	semidirect
214. C₂×#5006	C₂³	semidirect
215. C₂×#5006	C₂³	semidirect
217. #82228	C₂³	semidirect
218. #82228	C₂³	semidirect
219. C₂×#5005	C₂³	semidirect
220. C₂×#5005	C₂³	semidirect
221. C₂×#5001	C₂³	semidirect
222. C₂×#5001	C₂³	semidirect
224. #82070	C₂³	semidirect
225. #82070	C₂³	semidirect
226. D₃×#413	D₄	semidirect
229. C₂×C₃×#344	C₂³	semidirect
230. C₂×C₃×H(3,ℤ/4)	C₂³	semidirect
231. C₃×#1728	C₂³	semidirect
232. C₂×#4559	C₂³	semidirect
233. C₂×#4556	C₂³	semidirect
234. C₂×#4557	C₂³	semidirect
235. #71979	C₂³	semidirect
236. #71979	C₂³	semidirect
237. C₂×#4533	C₂³	semidirect
238. C₂×#4531	C₂³	semidirect
239. C₂×#4531	C₂³	semidirect
240. #71527	C₂³	semidirect
241. C₂×#3585	C₂×D₃	semidirect
242. C₂×#3021	C₂×D₃	semidirect
243. #35527	C₂×D₃	semidirect
244. #23430	C₂×D₃	semidirect
245. C₂×#2008	C₂×D₃	semidirect
246. C₂×#1910	C₂×D₃	semidirect
247. C₂×#1795	C₂×D₃	semidirect
248. #20608	C₂×D₃	semidirect
249. #11041	C₂×D₃	semidirect
250. #11012	C₂×D₃	semidirect
251. #10746	C₂×D₃	semidirect
252. C₃×#585	C₂×D₄	semidirect
260. #5964	C₂×D₄	semidirect
261. #5964	C₂×D₄	semidirect
304. C₃×#575	C₂×D₄	semidirect
305. C₂²×C₃×SD₁₆	C₂×D₄	semidirect
306. C₂²×C₃×D₈	C₂×D₄	semidirect
307. C₃×#568	C₂×D₄	semidirect
316. #5822	C₂×D₄	semidirect
317. #5822	C₂×D₄	semidirect
318. #5819	C₂×D₄	semidirect
320. C₂²×#215	C₂×D₄	semidirect
324. C₂²×#214	C₂×D₄	semidirect
325. C₂²×#213	C₂×D₄	semidirect
326. C₂²×#213	C₂×D₄	semidirect
334. #5748	C₂×D₄	semidirect
335. #5745	C₂×D₄	semidirect
339. C₂²×D₂₄	C₂×D₄	semidirect
340. C₂²×#204	C₂×D₄	semidirect
349. C₃×#413	C₂×D₄	semidirect
351. #5237	C₂×D₄	semidirect
354. #5132	C₂×D₄	semidirect
360. C₂²×AGL(1,ℤ/8)	C₂²×D₃	semidirect
363. C₂×#535	C₂²×D₃	semidirect
364. C₂²×#127	C₂²×D₃	semidirect
365. C₂×#421	C₂²×D₃	semidirect
366. C₂×#421	C₂²×D₃	semidirect
367. C₂×#418	C₂²×D₃	semidirect
368. C₂×#418	C₂²×D₃	semidirect
371. C₂×#410	C₂²×D₃	semidirect
372. #2309	C₂²×D₃	semidirect
374. #2297	C₂²×D₃	semidirect
375. #2297	C₂²×D₃	semidirect
376. C₂×#344	C₂²×D₃	semidirect
377. C₂×H(3,ℤ/4)	C₂²×D₃	semidirect
378. #1728	C₂²×D₃	semidirect
409. C₂×#239	#120	semidirect
413. C₂×D₃×Q₈	#120	semidirect
417. C₂×#237	#120	semidirect
426. C₂×D₃×D₄	#120	semidirect
481. C₂×ΓL(1,𝔽₂₅)	#120	semidirect
482. C₂×D₃×C₈	#120	semidirect
483. #585	D₃×D₄	semidirect
491. #575	D₃×D₄	semidirect
492. C₂²×SD₁₆	D₃×D₄	semidirect
493. C₂²×D₈	D₃×D₄	semidirect
494. #568	D₃×D₄	semidirect
503. #413	D₃×D₄	semidirect
518. C₂×C₃×Q₈	C₂×#120	semidirect
523. C₂×C₃×D₄	C₂×#120	semidirect
557. C₂×D₁₂	C₂×#120	semidirect
606. C₂×Dic₆	C₂×#120	semidirect
608. C₂×C₃×C₈	C₂×#120	semidirect
609. C₂×C₃⋊C₈	C₂×#120	semidirect
709. C₂×Q₈	D₃×#120	semidirect
714. C₂×D₄	D₃×#120	semidirect
731. C₂×C₈	D₃×#120	semidirect
777. D₃	#394022	direct (N × H)
789. C₃	C₂×#394022	semidirect

Maximal subgroups

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

subgroup	index
#72271718	2
#72271710	2
#72271706	2
D₃×#20608	2
#72271680	2
#72271674	2
#72271671	2
#72271667	2
D₃×#11041	2
#72271650	2
D₃×#23430	2
#72271641	2
#72271637	2
#72271632	2
D₃×#10746	2
C₃×#394022	2
D₃×#35527	2
D₃×#11012	2
C₂×D₃×#3021	2
C₂×D₃×#1795	2
C₂×D₃×#2008	2
C₂×D₃×#3585	2
C₂×D₃×#1910	2
C₂×#394022	3

Subgroups — D3×#394022 #72271751

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃×#394022 #72271751