Subgroups — D₃×#359428 #72271233

Order 3072.

At least 8384 conjugacy classes of subgroups; only the 3263 normal subgroups are shown.

The subgroup lattice has 721 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72271219	C₂	1	4	yes	maximal, complemented
2	#72271214	C₂	1	4	yes	maximal, complemented
3	#72271186	C₂	1	1	yes	maximal, characteristic, complemented
4	#72271165	C₂	1	1	yes	maximal, characteristic, complemented
5	#72271139	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#359428	C₂	1	1	yes	maximal, characteristic, complemented
7	#72271074	C₂	1	2	yes	maximal, complemented
8	#72271046	C₂	1	2	yes	maximal, complemented
9	C₂²×D₃×#379	C₂	1	1	yes	maximal, characteristic, complemented
10	D₃×#10725	C₂	1	2	yes	maximal, complemented
11	D₃×#10965	C₂	1	4	yes	maximal, complemented
12	D₃×#14679	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×D₃×#1781	C₂	1	2	yes	maximal, complemented
14	C₂×D₃×#1898	C₂	1	4	yes	maximal, complemented
15	C₂³×D₃×#120	C₂	1	1	yes	maximal, characteristic
16	C₂⁷×D₃	C₂²	1	1	yes	characteristic
17	C₂⁴×D₃×D₄	C₄	1	2	yes	complemented
18	C₂⁴×D₃×D₄	C₂²	1	1	yes	characteristic
19	C₂³×#882	C₄	1	2	yes	complemented
20	C₂³×#882	C₂²	1	1	yes	characteristic
21	C₂³×#953	C₂²	1	1	yes	characteristic
22	C₂³×#937	C₄	1	2	yes	complemented
23	C₂³×#937	C₂²	1	1	yes	characteristic
24	C₂²×D₃×#120	C₄	1	4	yes	complemented
25	C₂²×D₃×#120	C₄	1	4	yes	complemented
26	C₂²×D₃×#120	C₂²	1	2	yes	—
27	C₂²×D₃×#120	C₂²	1	2	yes	—
28	C₂²×D₃×#120	C₂²	1	2	yes	—
29	C₂²×D₃×#120	C₂²	1	2	yes	—
30	C₂³×D₃×C₂²⋊C₄	C₄	1	2	yes	complemented
31	C₂³×D₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
32	C₂³×D₃×C₂²⋊C₄	C₂²	1	2	yes	complemented
33	C₂²×D₃×#99	C₂²	1	8	yes	complemented
34	C₂²×#5247	C₂²	1	1	yes	characteristic, complemented
35	C₂²×#4955	C₂²	1	2	yes	complemented
36	C₂×D₃×#379	C₂²	1	2	yes	—
37	C₂×D₃×#379	C₂²	1	2	yes	—
38	C₂×D₃×#379	C₂²	1	2	yes	complemented
39	C₂×D₃×#379	C₂²	1	2	yes	complemented
40	C₂×D₃×#379	C₂²	1	2	yes	complemented
41	C₂×D₃×#379	C₂²	1	2	yes	complemented
42	C₂×D₃×#379	C₂²	1	2	yes	complemented
43	C₂×#71670	C₂²	1	4	yes	complemented
44	C₂×#71543	C₂²	1	4	yes	complemented
45	C₂×#68970	C₂²	1	8	yes	complemented
46	C₂×#69496	C₂²	1	4	yes	complemented
47	C₂×#70036	C₂²	1	8	yes	complemented
48	C₂×#72130	C₂²	1	2	yes	complemented
49	C₂×#69498	C₂²	1	2	yes	complemented
50	C₂×#69498	C₂²	1	2	yes	complemented
51	C₂×#70035	C₂²	1	8	yes	complemented
52	C₂×D₃×#342	C₂²	1	8	yes	complemented
53	#10726343	C₂²	1	1	yes	characteristic, complemented
54	#10726342	C₂²	1	2	yes	complemented
55	#10726342	C₂²	1	2	yes	complemented
56	#10726342	C₂²	1	2	yes	complemented
57	#10701679	C₂²	1	4	yes	complemented
58	#10701678	C₂²	1	8	yes	complemented
59	#10701677	C₂²	1	4	yes	complemented
60	#10701677	C₂²	1	4	yes	complemented
61	#10701676	C₂²	1	8	yes	complemented
62	#10700449	C₂²	1	2	yes	complemented
63	#10700448	C₂²	1	2	yes	complemented
64	#10700448	C₂²	1	2	yes	complemented
65	#10700447	C₂²	1	8	yes	complemented
66	C₂³×C₃×#120	C₂²	1	1	yes	characteristic
67	C₂²×C₃×#379	C₂²	1	1	yes	characteristic, complemented
68	C₂×C₃×#1898	C₂²	1	4	yes	complemented
69	C₂×C₃×#1781	C₂²	1	2	yes	complemented
70	C₃×#14679	C₂²	1	1	yes	characteristic, complemented
71	C₃×#10965	C₂²	1	4	yes	complemented
72	C₃×#10725	C₂²	1	2	yes	complemented
73	#359428	D₃	1	1	yes	characteristic, direct product factor
74	C₂⁷×C₃	C₂³	1	1	yes	characteristic
75	C₂⁶×D₃	C₂×C₄	1	2	yes	—
76	C₂⁶×D₃	C₂×C₄	1	2	yes	—
77	C₂⁶×D₃	C₂×C₄	1	2	yes	—
78	C₂⁶×D₃	C₂×C₄	1	2	yes	—
79	C₂⁶×D₃	C₂×C₄	1	1	yes	characteristic, complemented
80	C₂⁶×D₃	D₄	1	2	yes	—
81	C₂⁶×D₃	D₄	1	4	yes	—
82	C₂⁶×D₃	D₄	1	4	yes	—
83	C₂⁶×D₃	D₄	1	2	yes	—
84	C₂⁶×D₃	D₄	1	2	yes	—
85	C₂⁶×D₃	D₄	1	2	yes	—
86	C₂⁶×D₃	C₂³	1	1	yes	characteristic
87	C₂⁶×D₃	C₂³	1	1	yes	characteristic
88	C₂⁶×D₃	C₂³	1	1	yes	characteristic
89	C₂⁶×D₃	C₂³	1	1	yes	characteristic
90	C₂⁶×D₃	C₂³	1	1	yes	characteristic
91	C₂⁶×D₃	C₂³	1	1	yes	characteristic
92	C₂⁴×C₃×D₄	C₂×C₄	1	2	yes	complemented
93	C₂⁴×C₃×D₄	C₂³	1	1	yes	characteristic
94	C₂⁴×#67	C₂×C₄	1	1	yes	characteristic, complemented
95	C₂⁴×#67	C₂×C₄	1	2	yes	complemented
96	C₂⁴×#67	C₂×C₄	1	2	yes	complemented
97	C₂⁴×#67	C₂³	1	1	yes	characteristic
98	C₂³×D₃×D₄	C₂×C₄	1	4	yes	—
99	C₂³×D₃×D₄	C₂×C₄	1	2	yes	complemented
100	C₂³×D₃×D₄	C₂×C₄	1	4	yes	complemented
101	C₂³×D₃×D₄	C₂×C₄	1	2	yes	complemented
102	C₂³×D₃×D₄	C₂×C₄	1	4	yes	complemented
103	C₂³×D₃×D₄	C₂×C₄	1	4	yes	complemented
104	C₂³×D₃×D₄	C₂³	1	2	yes	—
105	C₂³×D₃×D₄	C₂³	1	2	yes	—
106	C₂⁴×D₁₂	C₂×C₄	1	1	yes	characteristic, complemented
107	C₂⁴×D₁₂	C₂×C₄	1	2	yes	complemented
108	C₂⁴×C₄×D₃	C₂×C₄	1	1	yes	characteristic, complemented
109	C₂⁴×C₄×D₃	C₂×C₄	1	2	yes	complemented
110	C₂²×C₃×#120	C₂×C₄	1	4	yes	complemented
111	C₂²×C₃×#120	C₂³	1	2	yes	—
112	C₂²×C₃×#120	C₂³	1	2	yes	—
113	C₂³×C₃×C₂²⋊C₄	C₂×C₄	1	2	yes	complemented
114	C₂³×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
115	C₂³×C₃×C₂²⋊C₄	C₂³	1	2	yes	complemented
116	C₂²×#953	C₂×C₄	1	4	yes	complemented
117	C₂²×#953	C₂³	1	2	yes	—
118	C₂²×#953	C₂³	1	2	yes	—
119	C₂³×#217	C₂×C₄	1	2	yes	complemented
120	C₂³×#217	C₂³	1	1	yes	characteristic
121	C₂³×#217	C₂³	1	2	yes	complemented
122	C₂²×#937	C₂×C₄	1	4	yes	—
123	C₂²×#937	C₂×C₄	1	4	yes	complemented
124	C₂²×#937	C₂×C₄	1	4	yes	complemented
125	C₂²×#937	C₂×C₄	1	4	yes	complemented
126	C₂²×#937	C₂×C₄	1	4	yes	complemented
127	C₂²×#937	C₂³	1	2	yes	—
128	C₂²×#937	C₂³	1	2	yes	—
129	C₂³×(C₂×D₃)⋊C₄	C₂×C₄	1	2	yes	complemented
130	C₂³×(C₂×D₃)⋊C₄	C₂×C₄	1	2	yes	complemented
131	C₂³×(C₂×D₃)⋊C₄	C₂×C₄	1	2	yes	complemented
132	C₂×D₃×#120	D₄	1	32	yes	—
133	C₂²×#882	C₂×C₄	1	4	yes	—
134	C₂²×#882	C₂×C₄	1	4	yes	complemented
135	C₂²×#882	C₂×C₄	1	4	yes	complemented
136	C₂²×#882	C₂×C₄	1	4	yes	complemented
137	C₂²×#882	C₂×C₄	1	4	yes	complemented
138	C₂²×#882	C₂³	1	2	yes	—
139	C₂²×#882	C₂³	1	2	yes	—
140	C₂²×D₃×C₂²⋊C₄	C₂×C₄	1	4	yes	—
141	C₂²×D₃×C₂²⋊C₄	C₂×C₄	1	2	yes	complemented
142	C₂²×D₃×C₂²⋊C₄	C₂×C₄	1	4	yes	complemented
143	C₂²×D₃×C₂²⋊C₄	C₂×C₄	1	2	yes	complemented
144	C₂²×D₃×C₂²⋊C₄	C₂×C₄	1	4	yes	complemented
145	C₂²×D₃×C₂²⋊C₄	C₂×C₄	1	4	yes	complemented
146	C₂²×D₃×C₂²⋊C₄	C₂³	1	4	yes	—
147	C₂²×D₃×C₂²⋊C₄	C₂³	1	4	yes	—
148	C₂²×D₃×C₂²⋊C₄	C₂³	1	2	yes	—
149	C₂²×D₃×C₂²⋊C₄	C₂³	1	2	yes	—
150	C₂²×D₃×C₂²⋊C₄	C₂³	1	4	yes	complemented
151	C₂²×C₃×#99	C₂³	1	8	yes	complemented
152	C₂×C₃×#379	C₂³	1	2	yes	—
153	C₂×C₃×#379	C₂³	1	2	yes	—
154	C₂×C₃×#379	C₂³	1	2	yes	complemented
155	C₂×C₃×#379	C₂³	1	2	yes	complemented
156	C₂×C₃×#379	C₂³	1	2	yes	complemented
157	C₂×#5247	C₂³	1	2	yes	—
158	C₂×#5247	C₂³	1	2	yes	—
159	C₂×#5247	C₂³	1	2	yes	complemented
160	C₂×#5247	C₂³	1	2	yes	complemented
161	C₂×#5247	C₂³	1	2	yes	complemented
162	C₂²×#834	C₂³	1	8	yes	complemented
163	C₂×#4955	C₂³	1	4	yes	—
164	C₂×#4955	C₂³	1	4	yes	—
165	C₂×#4955	C₂³	1	4	yes	complemented
166	C₂×#4955	C₂³	1	4	yes	complemented
167	C₂×#4955	C₂³	1	4	yes	complemented
168	C₂²×#806	C₂³	1	8	yes	complemented
169	C₂²×#806	C₂³	1	8	yes	complemented
170	D₃×#379	D₄	1	16	yes	complemented
171	C₂×C₃×#342	C₂³	1	8	yes	complemented
172	C₂×#4527	C₂³	1	8	yes	complemented
173	C₂×#4527	C₂³	1	8	yes	complemented
174	C₂×#4526	C₂³	1	8	yes	complemented
175	C₂³×#120	C₂×D₃	1	1	yes	characteristic
176	C₂²×#379	C₂×D₃	1	1	yes	characteristic, complemented
177	C₂×#1898	C₂×D₃	1	4	yes	complemented
178	C₂×#1781	C₂×D₃	1	2	yes	complemented
179	#14679	C₂×D₃	1	1	yes	characteristic, complemented
180	#10965	C₂×D₃	1	4	yes	complemented
181	#10725	C₂×D₃	1	2	yes	complemented
182	C₂⁶×C₃	C₂²×C₄	1	2	yes	—
183	C₂⁶×C₃	C₂²×C₄	1	2	yes	—
184	C₂⁶×C₃	C₂²×C₄	1	1	yes	characteristic, complemented
185	C₂⁶×C₃	C₂×D₄	1	2	yes	—
186	C₂⁶×C₃	C₂×D₄	1	4	yes	—
187	C₂⁶×C₃	C₂×D₄	1	2	yes	—
188	C₂⁶×C₃	C₂⁴	1	1	yes	characteristic
189	C₂⁶×C₃	C₂⁴	1	1	yes	characteristic
190	C₂⁶×C₃	C₂⁴	1	1	yes	characteristic
191	C₂⁵×D₃	C₂²⋊C₄	1	4	yes	—
192	C₂⁵×D₃	C₂²⋊C₄	1	4	yes	—
193	C₂⁵×D₃	C₂²⋊C₄	1	4	yes	—
194	C₂⁵×D₃	C₂²⋊C₄	1	4	yes	—
195	C₂⁵×D₃	C₂²⋊C₄	1	4	yes	—
196	C₂⁵×D₃	C₂²⋊C₄	1	4	yes	—
197	C₂⁵×D₃	C₂²⋊C₄	1	4	yes	—
198	C₂⁵×D₃	C₂²⋊C₄	1	4	yes	—
199	C₂⁵×D₃	C₂²⋊C₄	1	4	yes	—
200	C₂⁵×D₃	C₂²⋊C₄	1	4	yes	—
201	C₂⁵×D₃	C₂²⋊C₄	1	4	yes	—
202	C₂⁵×D₃	C₂²⋊C₄	1	4	yes	—
203	C₂⁵×D₃	C₂²⋊C₄	1	4	yes	—
204	C₂⁵×D₃	C₂²⋊C₄	1	4	yes	—
205	C₂⁵×D₃	C₂²⋊C₄	1	4	yes	—
206	C₂⁵×D₃	C₂²⋊C₄	1	4	yes	—
207	C₂⁵×D₃	C₂²×C₄	1	1	yes	characteristic
208	C₂⁵×D₃	C₂²×C₄	1	2	yes	—
209	C₂⁵×D₃	C₂²×C₄	1	2	yes	—
210	C₂⁵×D₃	C₂²×C₄	1	2	yes	—
211	C₂⁵×D₃	C₂²×C₄	1	2	yes	—
212	C₂⁵×D₃	C₂²×C₄	1	2	yes	—
213	C₂⁵×D₃	C₂²×C₄	1	2	yes	—
214	C₂⁵×D₃	C₂²×C₄	1	2	yes	—
215	C₂⁵×D₃	C₂²×C₄	1	2	yes	—
216	C₂⁵×D₃	C₂²×C₄	1	2	yes	—
217	C₂⁵×D₃	C₂²×C₄	1	2	yes	—
218	C₂⁵×D₃	C₂²×C₄	1	2	yes	—
219	C₂⁵×D₃	C₂²×C₄	1	1	yes	characteristic
220	C₂⁵×D₃	C₂²×C₄	1	1	yes	characteristic
221	C₂⁵×D₃	C₂²×C₄	1	1	yes	characteristic
222	C₂⁵×D₃	C₂²×C₄	1	1	yes	characteristic, complemented
223	C₂⁵×D₃	C₂²×C₄	1	2	yes	complemented
224	C₂⁵×D₃	C₂×D₄	1	1	yes	characteristic
225	C₂⁵×D₃	C₂×D₄	1	2	yes	—
226	C₂⁵×D₃	C₂×D₄	1	2	yes	—
227	C₂⁵×D₃	C₂×D₄	1	2	yes	—
228	C₂⁵×D₃	C₂×D₄	1	2	yes	—
229	C₂⁵×D₃	C₂×D₄	1	2	yes	—
230	C₂⁵×D₃	C₂×D₄	1	2	yes	—
231	C₂⁵×D₃	C₂×D₄	1	2	yes	—
232	C₂⁵×D₃	C₂×D₄	1	2	yes	—
233	C₂⁵×D₃	C₂×D₄	1	2	yes	—
234	C₂⁵×D₃	C₂×D₄	1	2	yes	—
235	C₂⁵×D₃	C₂×D₄	1	4	yes	—
236	C₂⁵×D₃	C₂×D₄	1	4	yes	—
237	C₂⁵×D₃	C₂×D₄	1	4	yes	—
238	C₂⁵×D₃	C₂×D₄	1	2	yes	—
239	C₂⁵×D₃	C₂×D₄	1	2	yes	—
240	C₂⁵×D₃	C₂×D₄	1	2	yes	—
241	C₂⁵×D₃	C₂×D₄	1	16	yes	—
242	C₂⁵×D₃	C₂×D₄	1	1	yes	characteristic
243	C₂⁵×D₃	C₂×D₄	1	1	yes	characteristic
244	C₂⁵×D₃	C₂×D₄	1	1	yes	characteristic
245	C₂⁵×D₃	C₂×D₄	1	2	yes	—
246	C₂⁵×D₃	C₂×D₄	1	2	yes	—
247	C₂⁵×D₃	C₂×D₄	1	2	yes	—
248	C₂⁵×D₃	C₂×D₄	1	8	yes	—
249	C₂⁵×D₃	#41	1	8	yes	—
250	C₂⁵×D₃	C₂⁴	1	1	yes	characteristic
251	C₂⁵×D₃	C₂⁴	1	1	yes	characteristic
252	C₂⁵×D₃	C₂⁴	1	1	yes	characteristic
253	C₂⁵×D₃	C₂⁴	1	1	yes	characteristic
254	C₂³×C₃×D₄	C₂²×C₄	1	4	yes	—
255	C₂³×C₃×D₄	C₂²×C₄	1	2	yes	complemented
256	C₂³×C₃×D₄	C₂²×C₄	1	4	yes	complemented
257	C₂³×C₃×D₄	C₂⁴	1	2	yes	—
258	C₂⁴×C₃×C₄	C₂²×C₄	1	1	yes	characteristic, complemented
259	C₂⁴×C₃×C₄	C₂²×C₄	1	2	yes	complemented
260	C₂³×#67	C₂²×C₄	1	2	yes	—
261	C₂³×#67	C₂²×C₄	1	4	yes	—
262	C₂³×#67	C₂²×C₄	1	4	yes	—
263	C₂³×#67	C₂²×C₄	1	2	yes	complemented
264	C₂³×#67	C₂²×C₄	1	2	yes	complemented
265	C₂³×#67	C₂²×C₄	1	4	yes	complemented
266	C₂³×#67	C₂²×C₄	1	4	yes	complemented
267	C₂³×#67	C₂⁴	1	2	yes	—
268	C₂⁴×Dic₃	C₂²×C₄	1	1	yes	characteristic, complemented
269	C₂⁴×Dic₃	C₂²×C₄	1	2	yes	complemented
270	C₂²×D₃×D₄	C₂²⋊C₄	1	32	yes	complemented
271	C₂²×D₃×D₄	C₂×D₄	1	16	yes	—
272	C₂³×D₁₂	C₂²×C₄	1	2	yes	—
273	C₂³×D₁₂	C₂²×C₄	1	4	yes	—
274	C₂³×D₁₂	C₂²×C₄	1	2	yes	complemented
275	C₂³×D₁₂	C₂²×C₄	1	4	yes	complemented
276	C₂³×C₄×D₃	C₂²×C₄	1	2	yes	—
277	C₂³×C₄×D₃	C₂²×C₄	1	4	yes	—
278	C₂³×C₄×D₃	C₂²×C₄	1	2	yes	complemented
279	C₂³×C₄×D₃	C₂²×C₄	1	4	yes	complemented
280	C₂×C₃×#120	C₂×D₄	1	16	yes	—
281	C₂²×C₃×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
282	C₂²×C₃×C₂²⋊C₄	C₂²×C₄	1	4	yes	complemented
283	C₂²×C₃×C₂²⋊C₄	C₂²×C₄	1	2	yes	complemented
284	C₂²×C₃×C₂²⋊C₄	C₂⁴	1	4	yes	—
285	C₂²×C₃×C₂²⋊C₄	C₂⁴	1	4	yes	—
286	C₂²×C₃×C₂²⋊C₄	C₂⁴	1	2	yes	—
287	C₂×#953	C₂×D₄	1	16	yes	—
288	C₂²×#217	C₂²×C₄	1	4	yes	—
289	C₂²×#217	C₂²×C₄	1	4	yes	complemented
290	C₂²×#217	C₂²×C₄	1	2	yes	complemented
291	C₂²×#217	C₂⁴	1	4	yes	—
292	C₂²×#217	C₂⁴	1	4	yes	—
293	C₂²×#217	C₂⁴	1	2	yes	—
294	C₂×#937	C₂²⋊C₄	1	32	yes	complemented
295	C₂×#937	C₂×D₄	1	16	yes	—
296	C₂²×(C₂×D₃)⋊C₄	C₂²×C₄	1	4	yes	—
297	C₂²×(C₂×D₃)⋊C₄	C₂²×C₄	1	4	yes	—
298	C₂²×(C₂×D₃)⋊C₄	C₂²×C₄	1	4	yes	—
299	C₂²×(C₂×D₃)⋊C₄	C₂²×C₄	1	4	yes	complemented
300	C₂²×(C₂×D₃)⋊C₄	C₂²×C₄	1	4	yes	complemented
301	C₂²×(C₂×D₃)⋊C₄	C₂²×C₄	1	4	yes	complemented
302	C₂×#882	C₂²⋊C₄	1	32	yes	complemented
303	C₂×#882	C₂×D₄	1	16	yes	—
304	C₂×D₃×C₂²⋊C₄	C₂²⋊C₄	1	32	yes	complemented
305	C₂×D₃×C₂²⋊C₄	C₂×D₄	1	16	yes	—
306	C₂×D₃×C₂²⋊C₄	C₂×D₄	1	16	yes	complemented
307	C₃×#379	C₂×D₄	1	8	yes	complemented
308	#5247	C₂×D₄	1	8	yes	complemented
309	#4955	C₂×D₄	1	16	yes	complemented
310	C₂⁷	C₂²×D₃	1	1	yes	characteristic
311	C₂⁴×D₄	C₄×D₃	1	2	yes	complemented
312	C₂⁴×D₄	C₂²×D₃	1	1	yes	characteristic
313	C₂²×#120	C₄×D₃	1	4	yes	complemented
314	C₂²×#120	C₂²×D₃	1	2	yes	—
315	C₂²×#120	C₂²×D₃	1	2	yes	—
316	C₂³×C₂²⋊C₄	C₄×D₃	1	2	yes	complemented
317	C₂³×C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
318	C₂³×C₂²⋊C₄	C₂²×D₃	1	2	yes	complemented
319	C₂²×#99	C₂²×D₃	1	8	yes	complemented
320	C₂×#379	C₂²×D₃	1	2	yes	—
321	C₂×#379	C₂²×D₃	1	2	yes	—
322	C₂×#379	C₂²×D₃	1	2	yes	complemented
323	C₂×#379	C₂²×D₃	1	2	yes	complemented
324	C₂×#379	C₂²×D₃	1	2	yes	complemented
325	C₂×#342	C₂²×D₃	1	8	yes	complemented
326	C₂⁵×C₃	C₂×C₂²⋊C₄	1	4	yes	—
327	C₂⁵×C₃	C₂×C₂²⋊C₄	1	4	yes	—
328	C₂⁵×C₃	C₂×C₂²⋊C₄	1	4	yes	—
329	C₂⁵×C₃	C₂×C₂²⋊C₄	1	4	yes	—
330	C₂⁵×C₃	C₂³×C₄	1	1	yes	characteristic
331	C₂⁵×C₃	C₂³×C₄	1	2	yes	—
332	C₂⁵×C₃	C₂³×C₄	1	2	yes	—
333	C₂⁵×C₃	C₂³×C₄	1	2	yes	—
334	C₂⁵×C₃	C₂³×C₄	1	1	yes	characteristic
335	C₂⁵×C₃	C₂²×D₄	1	1	yes	characteristic
336	C₂⁵×C₃	C₂²×D₄	1	2	yes	—
337	C₂⁵×C₃	C₂²×D₄	1	2	yes	—
338	C₂⁵×C₃	C₂²×D₄	1	2	yes	—
339	C₂⁵×C₃	C₂²×D₄	1	2	yes	—
340	C₂⁵×C₃	C₂²×D₄	1	2	yes	—
341	C₂⁵×C₃	C₂²×D₄	1	8	yes	—
342	C₂⁵×C₃	C₂²×D₄	1	1	yes	characteristic
343	C₂⁵×C₃	C₂²×D₄	1	4	yes	—
344	C₂⁵×C₃	C₂×#41	1	4	yes	—
345	C₂⁵×C₃	C₂⁵	1	1	yes	characteristic
346	C₂⁴×D₃	#99	1	32	yes	complemented
347	C₂⁴×D₃	C₂×C₂²⋊C₄	1	2	yes	—
348	C₂⁴×D₃	C₂×C₂²⋊C₄	1	2	yes	—
349	C₂⁴×D₃	C₂×C₂²⋊C₄	1	2	yes	—
350	C₂⁴×D₃	C₂×C₂²⋊C₄	1	2	yes	—
351	C₂⁴×D₃	C₂×C₂²⋊C₄	1	4	yes	—
352	C₂⁴×D₃	C₂×C₂²⋊C₄	1	4	yes	—
353	C₂⁴×D₃	C₂×C₂²⋊C₄	1	4	yes	—
354	C₂⁴×D₃	C₂×C₂²⋊C₄	1	4	yes	—
355	C₂⁴×D₃	C₂×C₂²⋊C₄	1	4	yes	—
356	C₂⁴×D₃	C₂×C₂²⋊C₄	1	4	yes	—
357	C₂⁴×D₃	C₂×C₂²⋊C₄	1	4	yes	—
358	C₂⁴×D₃	C₂×C₂²⋊C₄	1	4	yes	—
359	C₂⁴×D₃	C₂×C₂²⋊C₄	1	4	yes	—
360	C₂⁴×D₃	C₂×C₂²⋊C₄	1	4	yes	—
361	C₂⁴×D₃	C₂×C₂²⋊C₄	1	2	yes	—
362	C₂⁴×D₃	C₂×C₂²⋊C₄	1	2	yes	—
363	C₂⁴×D₃	C₂×C₂²⋊C₄	1	16	yes	—
364	C₂⁴×D₃	C₂×C₂²⋊C₄	1	2	yes	—
365	C₂⁴×D₃	C₂×C₂²⋊C₄	1	2	yes	—
366	C₂⁴×D₃	C₂×C₂²⋊C₄	1	2	yes	—
367	C₂⁴×D₃	C₂×C₂²⋊C₄	1	2	yes	—
368	C₂⁴×D₃	C₂×C₂²⋊C₄	1	2	yes	—
369	C₂⁴×D₃	C₂×C₂²⋊C₄	1	2	yes	—
370	C₂⁴×D₃	C₂×C₂²⋊C₄	1	4	yes	—
371	C₂⁴×D₃	C₂×C₂²⋊C₄	1	4	yes	—
372	C₂⁴×D₃	C₂×C₂²⋊C₄	1	4	yes	—
373	C₂⁴×D₃	C₂×C₂²⋊C₄	1	2	yes	—
374	C₂⁴×D₃	C₂×C₂²⋊C₄	1	2	yes	—
375	C₂⁴×D₃	C₂×C₂²⋊C₄	1	4	yes	—
376	C₂⁴×D₃	C₂×C₂²⋊C₄	1	4	yes	—
377	C₂⁴×D₃	C₂×C₂²⋊C₄	1	4	yes	—
378	C₂⁴×D₃	C₂×C₂²⋊C₄	1	16	yes	—
379	C₂⁴×D₃	C₂×C₂²⋊C₄	1	2	yes	—
380	C₂⁴×D₃	C₂×C₂²⋊C₄	1	2	yes	—
381	C₂⁴×D₃	C₂×C₂²⋊C₄	1	8	yes	complemented
382	C₂⁴×D₃	C₄×D₄	1	8	yes	—
383	C₂⁴×D₃	C₄×D₄	1	8	yes	—
384	C₂⁴×D₃	C₄×D₄	1	8	yes	—
385	C₂⁴×D₃	C₄×D₄	1	8	yes	—
386	C₂⁴×D₃	#120	1	8	yes	—
387	C₂⁴×D₃	#120	1	16	yes	—
388	C₂⁴×D₃	#120	1	8	yes	—
389	C₂⁴×D₃	#120	1	16	yes	—
390	C₂⁴×D₃	#120	1	8	yes	—
391	C₂⁴×D₃	#120	1	8	yes	—
392	C₂⁴×D₃	#120	1	8	yes	—
393	C₂⁴×D₃	#120	1	8	yes	—
394	C₂⁴×D₃	#121	1	16	yes	—
395	C₂⁴×D₃	#121	1	16	yes	—
396	C₂⁴×D₃	#123	1	8	yes	—
397	C₂⁴×D₃	#123	1	8	yes	—
398	C₂⁴×D₃	C₂³×C₄	1	1	yes	characteristic
399	C₂⁴×D₃	C₂³×C₄	1	2	yes	—
400	C₂⁴×D₃	C₂³×C₄	1	2	yes	—
401	C₂⁴×D₃	C₂³×C₄	1	1	yes	characteristic
402	C₂⁴×D₃	C₂³×C₄	1	2	yes	—
403	C₂⁴×D₃	C₂³×C₄	1	1	yes	characteristic
404	C₂⁴×D₃	C₂³×C₄	1	1	yes	characteristic
405	C₂⁴×D₃	C₂²×D₄	1	1	yes	characteristic
406	C₂⁴×D₃	C₂²×D₄	1	2	yes	—
407	C₂⁴×D₃	C₂²×D₄	1	2	yes	—
408	C₂⁴×D₃	C₂²×D₄	1	2	yes	—
409	C₂⁴×D₃	C₂²×D₄	1	2	yes	—
410	C₂⁴×D₃	C₂²×D₄	1	2	yes	—
411	C₂⁴×D₃	C₂²×D₄	1	1	yes	characteristic
412	C₂⁴×D₃	C₂²×D₄	1	1	yes	characteristic
413	C₂⁴×D₃	C₂²×D₄	1	8	yes	—
414	C₂⁴×D₃	C₂²×D₄	1	1	yes	characteristic
415	C₂⁴×D₃	C₂²×D₄	1	4	yes	—
416	C₂⁴×D₃	C₂²×D₄	1	1	yes	characteristic
417	C₂⁴×D₃	C₂²×D₄	1	1	yes	characteristic
418	C₂⁴×D₃	C₂²×D₄	1	8	yes	—
419	C₂⁴×D₃	C₂²×D₄	1	4	yes	—
420	C₂⁴×D₃	C₂×#41	1	4	yes	—
421	C₂⁴×D₃	C₂×#41	1	4	yes	—
422	C₂⁴×D₃	H(5,𝔽₂)	1	8	yes	—
423	C₂²×C₃×D₄	C₂×C₂²⋊C₄	1	16	yes	complemented
424	C₂²×C₃×D₄	C₂²×D₄	1	8	yes	—
425	C₂³×C₃×C₄	C₂³×C₄	1	2	yes	—
426	C₂³×C₃×C₄	C₂³×C₄	1	4	yes	—
427	C₂²×#67	C₂×C₂²⋊C₄	1	8	yes	complemented
428	C₂²×#67	C₂×C₂²⋊C₄	1	16	yes	complemented
429	C₂²×#67	C₂×C₂²⋊C₄	1	16	yes	complemented
430	C₂²×#67	C₂²×D₄	1	8	yes	—
431	C₂³×Dic₃	C₂³×C₄	1	2	yes	—
432	C₂³×Dic₃	C₂³×C₄	1	4	yes	—
433	C₂²×D₁₂	C₂×C₂²⋊C₄	1	8	yes	complemented
434	C₂²×D₁₂	C₂×C₂²⋊C₄	1	16	yes	complemented
435	C₂²×C₄×D₃	C₂×C₂²⋊C₄	1	8	yes	complemented
436	C₂²×C₄×D₃	C₂×C₂²⋊C₄	1	16	yes	complemented
437	C₂×C₃×C₂²⋊C₄	C₂×C₂²⋊C₄	1	16	yes	complemented
438	C₂×C₃×C₂²⋊C₄	C₂²×D₄	1	8	yes	—
439	C₂×C₃×C₂²⋊C₄	C₂²×D₄	1	8	yes	complemented
440	C₂×#217	C₂×C₂²⋊C₄	1	16	yes	complemented
441	C₂×#217	C₂²×D₄	1	8	yes	—
442	C₂×#217	C₂²×D₄	1	8	yes	complemented
443	C₂×(C₂×D₃)⋊C₄	C₂×C₂²⋊C₄	1	16	yes	complemented
444	C₂×(C₂×D₃)⋊C₄	C₂×C₂²⋊C₄	1	16	yes	complemented
445	C₂×(C₂×D₃)⋊C₄	C₂×C₂²⋊C₄	1	16	yes	complemented
446	C₂⁶	C₂×C₄×D₃	1	2	yes	—
447	C₂⁶	C₂×C₄×D₃	1	2	yes	—
448	C₂⁶	C₂×C₄×D₃	1	1	yes	characteristic, complemented
449	C₂⁶	D₃×D₄	1	2	yes	—
450	C₂⁶	D₃×D₄	1	4	yes	—
451	C₂⁶	D₃×D₄	1	2	yes	—
452	C₂⁶	C₂³×D₃	1	1	yes	characteristic
453	C₂⁶	C₂³×D₃	1	1	yes	characteristic
454	C₂⁶	C₂³×D₃	1	1	yes	characteristic
455	C₂³×D₄	C₂×C₄×D₃	1	4	yes	—
456	C₂³×D₄	C₂×C₄×D₃	1	2	yes	complemented
457	C₂³×D₄	C₂×C₄×D₃	1	4	yes	complemented
458	C₂³×D₄	C₂³×D₃	1	2	yes	—
459	C₂⁴×C₄	C₂×C₄×D₃	1	1	yes	characteristic, complemented
460	C₂⁴×C₄	C₂×C₄×D₃	1	2	yes	complemented
461	C₂×#120	D₃×D₄	1	16	yes	—
462	C₂²×C₂²⋊C₄	C₂×C₄×D₃	1	4	yes	—
463	C₂²×C₂²⋊C₄	C₂×C₄×D₃	1	4	yes	complemented
464	C₂²×C₂²⋊C₄	C₂×C₄×D₃	1	2	yes	complemented
465	C₂²×C₂²⋊C₄	C₂³×D₃	1	4	yes	—
466	C₂²×C₂²⋊C₄	C₂³×D₃	1	4	yes	—
467	C₂²×C₂²⋊C₄	C₂³×D₃	1	2	yes	—
468	#379	D₃×D₄	1	8	yes	complemented
469	C₂⁴×C₃	C₂×#99	1	16	yes	complemented
470	C₂⁴×C₃	C₂²×C₂²⋊C₄	1	4	yes	—
471	C₂⁴×C₃	C₂²×C₂²⋊C₄	1	2	yes	—
472	C₂⁴×C₃	C₂²×C₂²⋊C₄	1	2	yes	—
473	C₂⁴×C₃	C₂²×C₂²⋊C₄	1	8	yes	—
474	C₂⁴×C₃	C₂²×C₂²⋊C₄	1	2	yes	—
475	C₂⁴×C₃	C₂²×C₂²⋊C₄	1	2	yes	—
476	C₂⁴×C₃	C₂²×C₂²⋊C₄	1	4	yes	complemented
477	C₂⁴×C₃	C₂×C₄×D₄	1	4	yes	—
478	C₂⁴×C₃	C₂×C₄×D₄	1	4	yes	—
479	C₂⁴×C₃	C₂×#120	1	4	yes	—
480	C₂⁴×C₃	C₂×#120	1	8	yes	—
481	C₂⁴×C₃	C₂×#120	1	4	yes	—
482	C₂⁴×C₃	C₂×#120	1	4	yes	—
483	C₂⁴×C₃	C₂×#121	1	8	yes	—
484	C₂⁴×C₃	C₂×#123	1	4	yes	—
485	C₂⁴×C₃	C₂⁴×C₄	1	1	yes	characteristic
486	C₂⁴×C₃	C₂³×D₄	1	1	yes	characteristic
487	C₂⁴×C₃	C₂³×D₄	1	1	yes	characteristic
488	C₂⁴×C₃	C₂³×D₄	1	4	yes	—
489	C₂⁴×C₃	C₂³×D₄	1	2	yes	—
490	C₂⁴×C₃	C₂²×#41	1	2	yes	—
491	C₂⁴×C₃	C₂×H(5,𝔽₂)	1	4	yes	—
492	C₂³×D₃	#379	1	8	yes	—
493	C₂³×D₃	#379	1	8	yes	—
494	C₂³×D₃	#379	1	8	yes	—
495	C₂³×D₃	#379	1	8	yes	—
496	C₂³×D₃	#379	1	8	yes	—
497	C₂³×D₃	#379	1	8	yes	—
498	C₂³×D₃	#379	1	8	yes	—
499	C₂³×D₃	#379	1	8	yes	—
500	C₂³×D₃	#386	1	8	yes	—
501	C₂³×D₃	#386	1	8	yes	—
502	C₂³×D₃	#386	1	8	yes	—
503	C₂³×D₃	#386	1	8	yes	—
504	C₂³×D₃	#386	1	8	yes	—
505	C₂³×D₃	#386	1	8	yes	—
506	C₂³×D₃	#386	1	8	yes	—
507	C₂³×D₃	#386	1	8	yes	—
508	C₂³×D₃	C₂×#99	1	16	yes	—
509	C₂³×D₃	C₂×#99	1	16	yes	—
510	C₂³×D₃	C₂×#99	1	16	yes	—
511	C₂³×D₃	C₂×#99	1	16	yes	complemented
512	C₂³×D₃	C₂×#99	1	16	yes	complemented
513	C₂³×D₃	C₂×#99	1	16	yes	complemented
514	C₂³×D₃	C₂²×C₂²⋊C₄	1	4	yes	—
515	C₂³×D₃	C₂²×C₂²⋊C₄	1	2	yes	—
516	C₂³×D₃	C₂²×C₂²⋊C₄	1	2	yes	—
517	C₂³×D₃	C₂²×C₂²⋊C₄	1	8	yes	—
518	C₂³×D₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
519	C₂³×D₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
520	C₂³×D₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
521	C₂³×D₃	C₂²×C₂²⋊C₄	1	4	yes	—
522	C₂³×D₃	C₂²×C₂²⋊C₄	1	2	yes	—
523	C₂³×D₃	C₂²×C₂²⋊C₄	1	2	yes	—
524	C₂³×D₃	C₂²×C₂²⋊C₄	1	4	yes	—
525	C₂³×D₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
526	C₂³×D₃	C₂²×C₂²⋊C₄	1	4	yes	complemented
527	C₂³×D₃	C₂×C₄×D₄	1	4	yes	—
528	C₂³×D₃	C₂×C₄×D₄	1	4	yes	—
529	C₂³×D₃	C₂×C₄×D₄	1	4	yes	—
530	C₂³×D₃	C₂×C₄×D₄	1	4	yes	—
531	C₂³×D₃	#518	1	4	yes	—
532	C₂³×D₃	#518	1	4	yes	—
533	C₂³×D₃	C₂×#120	1	4	yes	—
534	C₂³×D₃	C₂×#120	1	8	yes	—
535	C₂³×D₃	C₂×#120	1	4	yes	—
536	C₂³×D₃	C₂×#120	1	2	yes	—
537	C₂³×D₃	C₂×#120	1	4	yes	—
538	C₂³×D₃	C₂×#120	1	4	yes	—
539	C₂³×D₃	C₂×#120	1	4	yes	—
540	C₂³×D₃	C₂×#120	1	2	yes	—
541	C₂³×D₃	C₂×#120	1	4	yes	—
542	C₂³×D₃	C₂×#120	1	4	yes	—
543	C₂³×D₃	C₂×#121	1	8	yes	—
544	C₂³×D₃	C₂×#121	1	4	yes	—
545	C₂³×D₃	C₂×#121	1	4	yes	—
546	C₂³×D₃	C₂×#123	1	4	yes	—
547	C₂³×D₃	C₂×#123	1	2	yes	—
548	C₂³×D₃	C₂×#123	1	2	yes	—
549	C₂³×D₃	#534	1	4	yes	—
550	C₂³×D₃	#534	1	4	yes	—
551	C₂³×D₃	#534	1	4	yes	—
552	C₂³×D₃	#534	1	4	yes	—
553	C₂³×D₃	D₄²	1	32	yes	—
554	C₂³×D₃	#546	1	32	yes	—
555	C₂²×C₃×C₄	C₂²×C₂²⋊C₄	1	4	yes	complemented
556	C₂²×C₃×C₄	C₂²×C₂²⋊C₄	1	8	yes	complemented
557	C₂²×Dic₃	C₂²×C₂²⋊C₄	1	4	yes	complemented
558	C₂²×Dic₃	C₂²×C₂²⋊C₄	1	8	yes	complemented
559	C₂⁵	D₃×C₂²⋊C₄	1	4	yes	—
560	C₂⁵	D₃×C₂²⋊C₄	1	4	yes	—
561	C₂⁵	D₃×C₂²⋊C₄	1	4	yes	—
562	C₂⁵	D₃×C₂²⋊C₄	1	4	yes	—
563	C₂⁵	C₂²×C₄×D₃	1	1	yes	characteristic
564	C₂⁵	C₂²×C₄×D₃	1	2	yes	—
565	C₂⁵	C₂²×C₄×D₃	1	2	yes	—
566	C₂⁵	C₂²×C₄×D₃	1	2	yes	—
567	C₂⁵	C₂²×C₄×D₃	1	1	yes	characteristic
568	C₂⁵	C₂×D₃×D₄	1	1	yes	characteristic
569	C₂⁵	C₂×D₃×D₄	1	2	yes	—
570	C₂⁵	C₂×D₃×D₄	1	2	yes	—
571	C₂⁵	C₂×D₃×D₄	1	2	yes	—
572	C₂⁵	C₂×D₃×D₄	1	2	yes	—
573	C₂⁵	C₂×D₃×D₄	1	2	yes	—
574	C₂⁵	C₂×D₃×D₄	1	1	yes	characteristic
575	C₂⁵	C₂×D₃×D₄	1	8	yes	—
576	C₂⁵	C₂×D₃×D₄	1	4	yes	—
577	C₂⁵	D₃×#41	1	4	yes	—
578	C₂⁵	C₂⁴×D₃	1	1	yes	characteristic
579	C₂²×D₄	D₃×C₂²⋊C₄	1	16	yes	complemented
580	C₂²×D₄	C₂×D₃×D₄	1	8	yes	—
581	C₂³×C₄	C₂²×C₄×D₃	1	2	yes	—
582	C₂³×C₄	C₂²×C₄×D₃	1	4	yes	—
583	C₂×C₂²⋊C₄	D₃×C₂²⋊C₄	1	16	yes	complemented
584	C₂×C₂²⋊C₄	C₂×D₃×D₄	1	8	yes	—
585	C₂×C₂²⋊C₄	C₂×D₃×D₄	1	8	yes	complemented
586	C₂³×C₃	C₂×#379	1	4	yes	—
587	C₂³×C₃	C₂×#379	1	4	yes	—
588	C₂³×C₃	C₂×#386	1	4	yes	—
589	C₂³×C₃	C₂×#386	1	4	yes	—
590	C₂³×C₃	C₂²×#99	1	8	yes	—
591	C₂³×C₃	C₂²×#99	1	8	yes	—
592	C₂³×C₃	C₂²×#99	1	8	yes	—
593	C₂³×C₃	C₂³×C₂²⋊C₄	1	2	yes	—
594	C₂³×C₃	C₂³×C₂²⋊C₄	1	1	yes	characteristic
595	C₂³×C₃	C₂²×C₄×D₄	1	2	yes	—
596	C₂³×C₃	C₂×#518	1	2	yes	—
597	C₂³×C₃	C₂²×#120	1	1	yes	characteristic
598	C₂³×C₃	C₂²×#120	1	2	yes	—
599	C₂³×C₃	C₂²×#120	1	2	yes	—
600	C₂³×C₃	C₂²×#121	1	2	yes	—
601	C₂³×C₃	C₂²×#123	1	1	yes	characteristic
602	C₂³×C₃	C₂×#534	1	2	yes	—
603	C₂³×C₃	C₂×#534	1	2	yes	—
604	C₂³×C₃	C₂×D₄²	1	8	yes	—
605	C₂³×C₃	C₂×#546	1	8	yes	—
606	C₂²×D₃	#1781	1	32	yes	complemented
607	C₂²×D₃	#1898	1	32	yes	complemented
608	C₂²×D₃	C₂×#379	1	4	yes	—
609	C₂²×D₃	C₂×#379	1	2	yes	—
610	C₂²×D₃	C₂×#379	1	2	yes	—
611	C₂²×D₃	C₂×#379	1	2	yes	—
612	C₂²×D₃	C₂×#379	1	4	yes	—
613	C₂²×D₃	C₂×#379	1	2	yes	—
614	C₂²×D₃	C₂×#386	1	4	yes	—
615	C₂²×D₃	C₂×#386	1	2	yes	—
616	C₂²×D₃	C₂×#386	1	2	yes	—
617	C₂²×D₃	C₂×#386	1	2	yes	—
618	C₂²×D₃	C₂×#386	1	4	yes	—
619	C₂²×D₃	C₂×#386	1	2	yes	—
620	C₂²×D₃	#2308	1	2	yes	—
621	C₂²×D₃	#2308	1	2	yes	—
622	C₂²×D₃	#2308	1	2	yes	—
623	C₂²×D₃	#2308	1	2	yes	—
624	C₂²×D₃	D₄×C₂²⋊C₄	1	16	yes	—
625	C₂²×D₃	D₄×C₂²⋊C₄	1	16	yes	—
626	C₂²×D₃	#2403	1	8	yes	—
627	C₂²×D₃	#2403	1	8	yes	—
628	C₂²×D₃	#2405	1	8	yes	—
629	C₂²×D₃	#2405	1	8	yes	—
630	C₂²×D₃	#2410	1	16	yes	—
631	C₂²×D₃	#2410	1	16	yes	—
632	C₂²×D₃	C₂²×#99	1	8	yes	—
633	C₂²×D₃	C₂²×#99	1	8	yes	—
634	C₂²×D₃	C₂²×#99	1	8	yes	—
635	C₂²×D₃	C₂²×#99	1	8	yes	—
636	C₂⁴	D₃×#99	1	16	yes	complemented
637	C₂⁴	C₂×D₃×C₂²⋊C₄	1	4	yes	—
638	C₂⁴	C₂×D₃×C₂²⋊C₄	1	2	yes	—
639	C₂⁴	C₂×D₃×C₂²⋊C₄	1	2	yes	—
640	C₂⁴	C₂×D₃×C₂²⋊C₄	1	8	yes	—
641	C₂⁴	C₂×D₃×C₂²⋊C₄	1	2	yes	—
642	C₂⁴	C₂×D₃×C₂²⋊C₄	1	2	yes	—
643	C₂⁴	C₂×D₃×C₂²⋊C₄	1	4	yes	complemented
644	C₂⁴	C₄×D₃×D₄	1	4	yes	—
645	C₂⁴	C₄×D₃×D₄	1	4	yes	—
646	C₂⁴	D₃×#120	1	4	yes	—
647	C₂⁴	D₃×#120	1	8	yes	—
648	C₂⁴	D₃×#120	1	4	yes	—
649	C₂⁴	D₃×#120	1	4	yes	—
650	C₂⁴	D₃×#121	1	8	yes	—
651	C₂⁴	D₃×#123	1	4	yes	—
652	C₂⁴	C₂³×C₄×D₃	1	1	yes	characteristic
653	C₂⁴	C₂²×D₃×D₄	1	1	yes	characteristic
654	C₂⁴	C₂²×D₃×D₄	1	1	yes	characteristic
655	C₂⁴	C₂²×D₃×D₄	1	2	yes	—
656	C₂⁴	C₂²×D₃×D₄	1	4	yes	—
657	C₂⁴	C₂×D₃×#41	1	2	yes	—
658	C₂⁴	D₃×H(5,𝔽₂)	1	4	yes	—
659	C₂²×C₄	C₂×D₃×C₂²⋊C₄	1	4	yes	complemented
660	C₂²×C₄	C₂×D₃×C₂²⋊C₄	1	8	yes	complemented
661	C₂²×C₃	C₂×#1781	1	8	yes	complemented
662	C₂²×C₃	C₂×#1898	1	8	yes	complemented
663	C₂²×C₃	C₂²×#379	1	1	yes	characteristic
664	C₂²×C₃	C₂²×#386	1	1	yes	characteristic
665	C₂²×C₃	C₂×#2308	1	1	yes	characteristic
666	C₂²×C₃	C₂×D₄×C₂²⋊C₄	1	4	yes	—
667	C₂²×C₃	C₂×#2403	1	2	yes	—
668	C₂²×C₃	C₂×#2410	1	4	yes	—
669	C₂²×C₃	C₂×#2405	1	2	yes	—
670	C₂²×C₃	C₂³×#99	1	4	yes	—
671	C₂×D₃	#13867	1	4	yes	—
672	C₂×D₃	#13867	1	4	yes	—
673	C₂×D₃	#13867	1	4	yes	—
674	C₂×D₃	#13867	1	4	yes	—
675	C₂×D₃	C₂×#1781	1	8	yes	—
676	C₂×D₃	C₂×#1781	1	8	yes	complemented
677	C₂×D₃	C₂×#1898	1	8	yes	—
678	C₂×D₃	C₂×#1898	1	8	yes	complemented
679	C₂×D₃	#21746	1	8	yes	—
680	C₂³	D₃×#379	1	4	yes	—
681	C₂³	D₃×#379	1	4	yes	—
682	C₂³	D₃×#386	1	4	yes	—
683	C₂³	D₃×#386	1	4	yes	—
684	C₂³	C₂×D₃×#99	1	8	yes	—
685	C₂³	C₂×D₃×#99	1	8	yes	—
686	C₂³	C₂×D₃×#99	1	8	yes	—
687	C₂³	C₂²×D₃×C₂²⋊C₄	1	2	yes	—
688	C₂³	C₂²×D₃×C₂²⋊C₄	1	1	yes	characteristic
689	C₂³	C₂×C₄×D₃×D₄	1	2	yes	—
690	C₂³	D₃×#518	1	2	yes	—
691	C₂³	C₂×D₃×#120	1	1	yes	characteristic
692	C₂³	C₂×D₃×#120	1	2	yes	—
693	C₂³	C₂×D₃×#120	1	2	yes	—
694	C₂³	C₂×D₃×#121	1	2	yes	—
695	C₂³	C₂×D₃×#123	1	1	yes	characteristic
696	C₂³	D₃×#534	1	2	yes	—
697	C₂³	D₃×#534	1	2	yes	—
698	C₂³	D₃×D₄²	1	8	yes	—
699	C₂³	D₃×#546	1	8	yes	—
700	C₂×C₃	C₂×#13867	1	1	yes	characteristic
701	C₂×C₃	C₂²×#1781	1	2	yes	—
702	C₂×C₃	C₂²×#1898	1	2	yes	—
703	C₂×C₃	C₂×#21746	1	2	yes	—
704	D₃	#359428	1	8	yes	direct product factor
705	C₂²	D₃×#1781	1	8	yes	complemented
706	C₂²	D₃×#1898	1	8	yes	complemented
707	C₂²	C₂×D₃×#379	1	1	yes	characteristic
708	C₂²	C₂×D₃×#386	1	1	yes	characteristic
709	C₂²	D₃×#2308	1	1	yes	characteristic
710	C₂²	D₃×D₄×C₂²⋊C₄	1	4	yes	—
711	C₂²	D₃×#2403	1	2	yes	—
712	C₂²	D₃×#2410	1	4	yes	—
713	C₂²	D₃×#2405	1	2	yes	—
714	C₂²	C₂²×D₃×#99	1	4	yes	—
715	C₃	C₂×#359428	1	1	yes	characteristic, complemented, Sylow
716	C₂	C₂×D₃×#1898	1	2	yes	—
717	C₂	C₂×D₃×#1781	1	2	yes	—
718	C₂	D₃×#21746	1	2	yes	—
719	C₂	D₃×#13867	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂²×D₃×C₂²⋊C₄
commutator	C₂⁴×C₃	C₂⁴×C₄
Frattini	C₂⁵	C₂⁴×D₃
Fitting	C₃×#359428	C₂
socle	C₂³×C₃	C₂³×C₂²⋊C₄
prime radical	C₂³×D₃×#120	C₂
cosocle	C₂⁵×C₃	C₂⁵
hypercenter	#359428	D₃
hypocenter	C₃	C₂×#359428
LCS	G ▷ C₂⁴×C₃ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂³ ◁ C₂⁷ ◁ #359428

Complements

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

N	H ≅ G/N	type
1. #72271219	C₂	semidirect
2. #72271214	C₂	semidirect
3. #72271186	C₂	semidirect
4. #72271165	C₂	semidirect
5. #72271139	C₂	semidirect
6. C₃×#359428	C₂	semidirect
7. #72271074	C₂	semidirect
8. #72271046	C₂	semidirect
9. C₂²×D₃×#379	C₂	semidirect
10. D₃×#10725	C₂	semidirect
11. D₃×#10965	C₂	semidirect
12. D₃×#14679	C₂	semidirect
13. C₂×D₃×#1781	C₂	semidirect
14. C₂×D₃×#1898	C₂	semidirect
17. C₂⁴×D₃×D₄	C₄	semidirect
19. C₂³×#882	C₄	semidirect
22. C₂³×#937	C₄	semidirect
24. C₂²×D₃×#120	C₄	semidirect
25. C₂²×D₃×#120	C₄	semidirect
30. C₂³×D₃×C₂²⋊C₄	C₄	semidirect
32. C₂³×D₃×C₂²⋊C₄	C₂²	semidirect
33. C₂²×D₃×#99	C₂²	semidirect
34. C₂²×#5247	C₂²	semidirect
35. C₂²×#4955	C₂²	semidirect
38. C₂×D₃×#379	C₂²	semidirect
39. C₂×D₃×#379	C₂²	semidirect
40. C₂×D₃×#379	C₂²	semidirect
41. C₂×D₃×#379	C₂²	semidirect
42. C₂×D₃×#379	C₂²	semidirect
43. C₂×#71670	C₂²	semidirect
44. C₂×#71543	C₂²	semidirect
45. C₂×#68970	C₂²	semidirect
46. C₂×#69496	C₂²	semidirect
47. C₂×#70036	C₂²	semidirect
48. C₂×#72130	C₂²	semidirect
49. C₂×#69498	C₂²	semidirect
50. C₂×#69498	C₂²	semidirect
51. C₂×#70035	C₂²	semidirect
52. C₂×D₃×#342	C₂²	semidirect
53. #10726343	C₂²	semidirect
54. #10726342	C₂²	semidirect
55. #10726342	C₂²	semidirect
56. #10726342	C₂²	semidirect
57. #10701679	C₂²	semidirect
58. #10701678	C₂²	semidirect
59. #10701677	C₂²	semidirect
60. #10701677	C₂²	semidirect
61. #10701676	C₂²	semidirect
62. #10700449	C₂²	semidirect
63. #10700448	C₂²	semidirect
64. #10700448	C₂²	semidirect
65. #10700447	C₂²	semidirect
67. C₂²×C₃×#379	C₂²	semidirect
68. C₂×C₃×#1898	C₂²	semidirect
69. C₂×C₃×#1781	C₂²	semidirect
70. C₃×#14679	C₂²	semidirect
71. C₃×#10965	C₂²	semidirect
72. C₃×#10725	C₂²	semidirect
73. #359428	D₃	direct (N × H)
79. C₂⁶×D₃	C₂×C₄	semidirect
92. C₂⁴×C₃×D₄	C₂×C₄	semidirect
94. C₂⁴×#67	C₂×C₄	semidirect
95. C₂⁴×#67	C₂×C₄	semidirect
96. C₂⁴×#67	C₂×C₄	semidirect
99. C₂³×D₃×D₄	C₂×C₄	semidirect
100. C₂³×D₃×D₄	C₂×C₄	semidirect
101. C₂³×D₃×D₄	C₂×C₄	semidirect
102. C₂³×D₃×D₄	C₂×C₄	semidirect
103. C₂³×D₃×D₄	C₂×C₄	semidirect
106. C₂⁴×D₁₂	C₂×C₄	semidirect
107. C₂⁴×D₁₂	C₂×C₄	semidirect
108. C₂⁴×C₄×D₃	C₂×C₄	semidirect
109. C₂⁴×C₄×D₃	C₂×C₄	semidirect
110. C₂²×C₃×#120	C₂×C₄	semidirect
113. C₂³×C₃×C₂²⋊C₄	C₂×C₄	semidirect
115. C₂³×C₃×C₂²⋊C₄	C₂³	semidirect
116. C₂²×#953	C₂×C₄	semidirect
119. C₂³×#217	C₂×C₄	semidirect
121. C₂³×#217	C₂³	semidirect
123. C₂²×#937	C₂×C₄	semidirect
124. C₂²×#937	C₂×C₄	semidirect
125. C₂²×#937	C₂×C₄	semidirect
126. C₂²×#937	C₂×C₄	semidirect
129. C₂³×(C₂×D₃)⋊C₄	C₂×C₄	semidirect
130. C₂³×(C₂×D₃)⋊C₄	C₂×C₄	semidirect
131. C₂³×(C₂×D₃)⋊C₄	C₂×C₄	semidirect
134. C₂²×#882	C₂×C₄	semidirect
135. C₂²×#882	C₂×C₄	semidirect
136. C₂²×#882	C₂×C₄	semidirect
137. C₂²×#882	C₂×C₄	semidirect
141. C₂²×D₃×C₂²⋊C₄	C₂×C₄	semidirect
142. C₂²×D₃×C₂²⋊C₄	C₂×C₄	semidirect
143. C₂²×D₃×C₂²⋊C₄	C₂×C₄	semidirect
144. C₂²×D₃×C₂²⋊C₄	C₂×C₄	semidirect
145. C₂²×D₃×C₂²⋊C₄	C₂×C₄	semidirect
150. C₂²×D₃×C₂²⋊C₄	C₂³	semidirect
151. C₂²×C₃×#99	C₂³	semidirect
154. C₂×C₃×#379	C₂³	semidirect
155. C₂×C₃×#379	C₂³	semidirect
156. C₂×C₃×#379	C₂³	semidirect
159. C₂×#5247	C₂³	semidirect
160. C₂×#5247	C₂³	semidirect
161. C₂×#5247	C₂³	semidirect
162. C₂²×#834	C₂³	semidirect
165. C₂×#4955	C₂³	semidirect
166. C₂×#4955	C₂³	semidirect
167. C₂×#4955	C₂³	semidirect
168. C₂²×#806	C₂³	semidirect
169. C₂²×#806	C₂³	semidirect
170. D₃×#379	D₄	semidirect
171. C₂×C₃×#342	C₂³	semidirect
172. C₂×#4527	C₂³	semidirect
173. C₂×#4527	C₂³	semidirect
174. C₂×#4526	C₂³	semidirect
176. C₂²×#379	C₂×D₃	semidirect
177. C₂×#1898	C₂×D₃	semidirect
178. C₂×#1781	C₂×D₃	semidirect
179. #14679	C₂×D₃	semidirect
180. #10965	C₂×D₃	semidirect
181. #10725	C₂×D₃	semidirect
184. C₂⁶×C₃	C₂²×C₄	semidirect
222. C₂⁵×D₃	C₂²×C₄	semidirect
223. C₂⁵×D₃	C₂²×C₄	semidirect
255. C₂³×C₃×D₄	C₂²×C₄	semidirect
256. C₂³×C₃×D₄	C₂²×C₄	semidirect
258. C₂⁴×C₃×C₄	C₂²×C₄	semidirect
259. C₂⁴×C₃×C₄	C₂²×C₄	semidirect
263. C₂³×#67	C₂²×C₄	semidirect
264. C₂³×#67	C₂²×C₄	semidirect
265. C₂³×#67	C₂²×C₄	semidirect
266. C₂³×#67	C₂²×C₄	semidirect
268. C₂⁴×Dic₃	C₂²×C₄	semidirect
269. C₂⁴×Dic₃	C₂²×C₄	semidirect
270. C₂²×D₃×D₄	C₂²⋊C₄	semidirect
274. C₂³×D₁₂	C₂²×C₄	semidirect
275. C₂³×D₁₂	C₂²×C₄	semidirect
278. C₂³×C₄×D₃	C₂²×C₄	semidirect
279. C₂³×C₄×D₃	C₂²×C₄	semidirect
282. C₂²×C₃×C₂²⋊C₄	C₂²×C₄	semidirect
283. C₂²×C₃×C₂²⋊C₄	C₂²×C₄	semidirect
289. C₂²×#217	C₂²×C₄	semidirect
290. C₂²×#217	C₂²×C₄	semidirect
294. C₂×#937	C₂²⋊C₄	semidirect
299. C₂²×(C₂×D₃)⋊C₄	C₂²×C₄	semidirect
300. C₂²×(C₂×D₃)⋊C₄	C₂²×C₄	semidirect
301. C₂²×(C₂×D₃)⋊C₄	C₂²×C₄	semidirect
302. C₂×#882	C₂²⋊C₄	semidirect
304. C₂×D₃×C₂²⋊C₄	C₂²⋊C₄	semidirect
306. C₂×D₃×C₂²⋊C₄	C₂×D₄	semidirect
307. C₃×#379	C₂×D₄	semidirect
308. #5247	C₂×D₄	semidirect
309. #4955	C₂×D₄	semidirect
311. C₂⁴×D₄	C₄×D₃	semidirect
313. C₂²×#120	C₄×D₃	semidirect
316. C₂³×C₂²⋊C₄	C₄×D₃	semidirect
318. C₂³×C₂²⋊C₄	C₂²×D₃	semidirect
319. C₂²×#99	C₂²×D₃	semidirect
322. C₂×#379	C₂²×D₃	semidirect
323. C₂×#379	C₂²×D₃	semidirect
324. C₂×#379	C₂²×D₃	semidirect
325. C₂×#342	C₂²×D₃	semidirect
346. C₂⁴×D₃	#99	semidirect
381. C₂⁴×D₃	C₂×C₂²⋊C₄	semidirect
423. C₂²×C₃×D₄	C₂×C₂²⋊C₄	semidirect
427. C₂²×#67	C₂×C₂²⋊C₄	semidirect
428. C₂²×#67	C₂×C₂²⋊C₄	semidirect
429. C₂²×#67	C₂×C₂²⋊C₄	semidirect
433. C₂²×D₁₂	C₂×C₂²⋊C₄	semidirect
434. C₂²×D₁₂	C₂×C₂²⋊C₄	semidirect
435. C₂²×C₄×D₃	C₂×C₂²⋊C₄	semidirect
436. C₂²×C₄×D₃	C₂×C₂²⋊C₄	semidirect
437. C₂×C₃×C₂²⋊C₄	C₂×C₂²⋊C₄	semidirect
439. C₂×C₃×C₂²⋊C₄	C₂²×D₄	semidirect
440. C₂×#217	C₂×C₂²⋊C₄	semidirect
442. C₂×#217	C₂²×D₄	semidirect
443. C₂×(C₂×D₃)⋊C₄	C₂×C₂²⋊C₄	semidirect
444. C₂×(C₂×D₃)⋊C₄	C₂×C₂²⋊C₄	semidirect
445. C₂×(C₂×D₃)⋊C₄	C₂×C₂²⋊C₄	semidirect
448. C₂⁶	C₂×C₄×D₃	semidirect
456. C₂³×D₄	C₂×C₄×D₃	semidirect
457. C₂³×D₄	C₂×C₄×D₃	semidirect
459. C₂⁴×C₄	C₂×C₄×D₃	semidirect
460. C₂⁴×C₄	C₂×C₄×D₃	semidirect
463. C₂²×C₂²⋊C₄	C₂×C₄×D₃	semidirect
464. C₂²×C₂²⋊C₄	C₂×C₄×D₃	semidirect
468. #379	D₃×D₄	semidirect
469. C₂⁴×C₃	C₂×#99	semidirect
476. C₂⁴×C₃	C₂²×C₂²⋊C₄	semidirect
511. C₂³×D₃	C₂×#99	semidirect
512. C₂³×D₃	C₂×#99	semidirect
513. C₂³×D₃	C₂×#99	semidirect
526. C₂³×D₃	C₂²×C₂²⋊C₄	semidirect
555. C₂²×C₃×C₄	C₂²×C₂²⋊C₄	semidirect
556. C₂²×C₃×C₄	C₂²×C₂²⋊C₄	semidirect
557. C₂²×Dic₃	C₂²×C₂²⋊C₄	semidirect
558. C₂²×Dic₃	C₂²×C₂²⋊C₄	semidirect
579. C₂²×D₄	D₃×C₂²⋊C₄	semidirect
583. C₂×C₂²⋊C₄	D₃×C₂²⋊C₄	semidirect
585. C₂×C₂²⋊C₄	C₂×D₃×D₄	semidirect
606. C₂²×D₃	#1781	semidirect
607. C₂²×D₃	#1898	semidirect
636. C₂⁴	D₃×#99	semidirect
643. C₂⁴	C₂×D₃×C₂²⋊C₄	semidirect
659. C₂²×C₄	C₂×D₃×C₂²⋊C₄	semidirect
660. C₂²×C₄	C₂×D₃×C₂²⋊C₄	semidirect
661. C₂²×C₃	C₂×#1781	semidirect
662. C₂²×C₃	C₂×#1898	semidirect
676. C₂×D₃	C₂×#1781	semidirect
678. C₂×D₃	C₂×#1898	semidirect
704. D₃	#359428	direct (N × H)
705. C₂²	D₃×#1781	semidirect
706. C₂²	D₃×#1898	semidirect
715. C₃	C₂×#359428	semidirect

Maximal subgroups

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

subgroup	index
#72271219	2
#72271214	2
#72271186	2
#72271165	2
#72271139	2
C₃×#359428	2
#72271074	2
#72271046	2
C₂²×D₃×#379	2
D₃×#10725	2
D₃×#10965	2
D₃×#14679	2
C₂×D₃×#1781	2
C₂×D₃×#1898	2
C₂³×D₃×#120	2
C₂×#359428	3

Subgroups — D3×#359428 #72271233

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃×#359428 #72271233