Subgroups — D₃×#359513 #72270372

Order 3072.

At least 7136 conjugacy classes of subgroups; only the 2891 normal subgroups are shown.

The subgroup lattice has 846 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72270358	C₂	1	1	yes	maximal, characteristic, complemented
2	D₃×#60064	C₂	1	1	yes	maximal, characteristic, complemented
3	#72270325	C₂	1	2	yes	maximal, complemented
4	#72270321	C₂	1	1	yes	maximal, characteristic, complemented
5	#72270315	C₂	1	1	yes	maximal, characteristic, complemented
6	#72270312	C₂	1	2	yes	maximal, complemented
7	#72270309	C₂	1	4	yes	maximal, complemented
8	#72270300	C₂	1	4	yes	maximal, complemented
9	C₃×#359513	C₂	1	1	yes	maximal, characteristic, complemented
10	D₃×#20584	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂²×D₃×#535	C₂	1	1	yes	maximal, characteristic
12	D₃×#10716	C₂	1	2	yes	maximal, complemented
13	D₃×#10987	C₂	1	4	yes	maximal, complemented
14	D₃×#20598	C₂	1	2	yes	maximal, complemented
15	C₂×D₃×#1910	C₂	1	4	yes	maximal, complemented
16	C₂³×D₃×#41	C₂²	1	1	yes	characteristic
17	C₂⁴×D₃×D₄	C₂²	1	1	yes	characteristic
18	C₂×D₃×#568	C₂²	1	2	yes	complemented
19	C₂²×#5525	C₂²	1	1	yes	characteristic
20	C₂²×#5674	C₄	1	2	yes	complemented
21	C₂²×#5805	C₂²	1	1	yes	characteristic
22	C₂²×#5830	C₂²	1	1	yes	characteristic
23	C₂²×#5715	C₄	1	2	yes	complemented
24	C₂×D₃×#535	C₄	1	2	yes	complemented
25	C₂×D₃×#535	C₄	1	2	yes	complemented
26	C₂×D₃×#535	C₄	1	2	yes	complemented
27	C₂×D₃×#535	C₄	1	2	yes	complemented
28	C₂×D₃×#535	C₂²	1	2	yes	—
29	C₂×D₃×#535	C₂²	1	2	yes	—
30	C₂×D₃×#535	C₂²	1	2	yes	—
31	C₂×D₃×#535	C₂²	1	2	yes	—
32	C₂²×D₃×#127	C₄	1	2	yes	complemented
33	C₂²×D₃×#124	C₄	1	2	yes	complemented
34	C₂²×D₃×#117	C₂²	1	1	yes	characteristic
35	C₂×D₃×#418	C₂²	1	8	yes	complemented
36	C₂×D₃×#410	C₂²	1	2	yes	complemented
37	C₂×D₃×#410	C₂²	1	2	yes	complemented
38	#11658639	C₂²	1	1	yes	characteristic, complemented
39	#11658638	C₂²	1	2	yes	complemented
40	#11658637	C₂²	1	2	yes	complemented
41	#11658636	C₂²	1	2	yes	complemented
42	D₃×#2879	C₂²	1	2	yes	complemented
43	C₂×D₃×#407	C₂²	1	2	yes	—
44	D₃×#2280	C₂²	1	2	yes	—
45	C₂×#71854	C₂²	1	4	yes	complemented
46	C₂×#72025	C₂²	1	4	yes	complemented
47	C₂×#68713	C₂²	1	8	yes	complemented
48	C₂×#70047	C₂²	1	4	yes	complemented
49	C₂×#70330	C₂²	1	8	yes	complemented
50	#10794391	C₂²	1	2	yes	complemented
51	#10794390	C₂²	1	2	yes	complemented
52	#10794389	C₂²	1	2	yes	complemented
53	#10794388	C₂²	1	8	yes	complemented
54	#10794319	C₂²	1	1	yes	characteristic, complemented
55	#10794318	C₂²	1	2	yes	complemented
56	#10794316	C₂²	1	2	yes	complemented
57	#10794316	C₂²	1	2	yes	complemented
58	C₂×D₃×H(3,ℤ/4)	C₂²	1	8	yes	complemented
59	#10701779	C₂²	1	4	yes	complemented
60	#10701778	C₂²	1	4	yes	complemented
61	#10701777	C₂²	1	8	yes	complemented
62	#10701776	C₂²	1	4	yes	complemented
63	#10701775	C₂²	1	8	yes	complemented
64	#10700420	C₂²	1	2	yes	complemented
65	#10700419	C₂²	1	2	yes	complemented
66	#10700418	C₂²	1	2	yes	complemented
67	#10700417	C₂²	1	8	yes	complemented
68	C₂²×C₃×#535	C₂²	1	1	yes	characteristic
69	C₃×#60064	C₂²	1	1	yes	characteristic, complemented
70	C₂×C₃×#1910	C₂²	1	4	yes	complemented
71	C₃×#20598	C₂²	1	2	yes	complemented
72	C₃×#20584	C₂²	1	1	yes	characteristic, complemented
73	C₃×#10987	C₂²	1	4	yes	complemented
74	C₃×#10716	C₂²	1	2	yes	complemented
75	#359513	D₃	1	1	yes	characteristic, direct product factor
76	C₂³×C₃×#41	C₂³	1	1	yes	characteristic
77	C₂⁴×C₃×D₄	C₂³	1	1	yes	characteristic
78	C₂²×D₃×#41	C₂×C₄	1	1	yes	characteristic
79	C₂²×D₃×#41	C₂×C₄	1	1	yes	characteristic
80	C₂²×D₃×#41	C₂×C₄	1	1	yes	characteristic
81	C₂²×D₃×#41	C₂×C₄	1	1	yes	characteristic
82	C₂²×D₃×#41	D₄	1	2	yes	—
83	C₂²×D₃×#41	D₄	1	2	yes	—
84	C₂²×D₃×#41	D₄	1	2	yes	—
85	C₂²×D₃×#41	D₄	1	2	yes	—
86	C₂²×D₃×#41	C₂³	1	1	yes	characteristic
87	C₂²×D₃×#41	C₂³	1	1	yes	characteristic
88	C₂²×D₃×#41	C₂³	1	1	yes	characteristic
89	C₂²×D₃×#41	C₂³	1	1	yes	characteristic
90	C₂³×D₃×Q₈	C₂×C₄	1	1	yes	characteristic
91	C₂³×#239	C₂×C₄	1	1	yes	characteristic
92	C₂³×D₃×D₄	C₂×C₄	1	2	yes	—
93	C₂³×D₃×D₄	C₂×C₄	1	2	yes	—
94	C₂³×D₃×D₄	C₂×C₄	1	2	yes	—
95	C₂³×D₃×D₄	C₂×C₄	1	2	yes	—
96	C₂³×D₃×D₄	C₂×C₄	1	1	yes	characteristic
97	C₂³×D₃×D₄	D₄	1	2	yes	—
98	C₂³×D₃×D₄	C₂³	1	2	yes	—
99	C₂³×D₃×D₄	C₂³	1	2	yes	—
100	C₂³×#237	C₂×C₄	1	1	yes	characteristic
101	C₂³×#237	D₄	1	2	yes	—
102	C₂³×#235	D₄	1	2	yes	—
103	C₂³×#235	C₂³	1	1	yes	characteristic
104	C₂⁴×D₁₂	C₂³	1	1	yes	characteristic
105	C₂⁴×C₄×D₃	D₄	1	2	yes	—
106	C₂⁴×C₄×D₃	C₂³	1	1	yes	characteristic
107	C₂×C₃×#568	C₂³	1	2	yes	complemented
108	C₂×C₃×#535	C₂×C₄	1	2	yes	complemented
109	C₂×C₃×#535	C₂×C₄	1	2	yes	complemented
110	C₂×C₃×#535	C₂³	1	2	yes	—
111	C₂×C₃×#535	C₂³	1	2	yes	—
112	C₂²×C₃×#127	C₂×C₄	1	2	yes	complemented
113	C₂²×C₃×#124	C₂×C₄	1	2	yes	complemented
114	C₂²×C₃×#117	C₂³	1	1	yes	characteristic
115	C₂×#5830	C₂×C₄	1	2	yes	complemented
116	C₂×#5830	C₂×C₄	1	2	yes	complemented
117	C₂×#5830	C₂³	1	2	yes	—
118	C₂×#5830	C₂³	1	2	yes	—
119	C₂×#5819	C₂³	1	2	yes	complemented
120	C₂²×#947	C₂×C₄	1	2	yes	complemented
121	C₂×#5805	C₂×C₄	1	2	yes	complemented
122	C₂×#5805	C₂×C₄	1	2	yes	complemented
123	C₂×#5805	C₂³	1	2	yes	—
124	C₂×#5805	C₂³	1	2	yes	—
125	C₂²×#940	C₂×C₄	1	2	yes	complemented
126	C₂²×#940	C₂×C₄	1	2	yes	complemented
127	C₂²×#936	C₂×C₄	1	2	yes	complemented
128	C₂²×#926	C₂³	1	1	yes	characteristic
129	C₂×#5745	C₂³	1	4	yes	complemented
130	C₂²×D₃×M₁₆	C₂³	1	4	yes	—
131	D₃×#535	D₄	1	32	yes	—
132	C₂×#5715	C₂×C₄	1	4	yes	—
133	C₂×#5715	C₂×C₄	1	4	yes	—
134	C₂×#5715	C₂×C₄	1	4	yes	complemented
135	C₂×#5715	C₂×C₄	1	4	yes	complemented
136	C₂×D₃×#127	C₂×C₄	1	4	yes	—
137	C₂×D₃×#127	C₂×C₄	1	4	yes	—
138	C₂×D₃×#127	C₂×C₄	1	4	yes	complemented
139	C₂×D₃×#127	C₂×C₄	1	4	yes	complemented
140	C₂×#5674	C₂×C₄	1	4	yes	—
141	C₂×#5674	C₂×C₄	1	4	yes	—
142	C₂×#5674	C₂×C₄	1	4	yes	complemented
143	C₂×#5674	C₂×C₄	1	4	yes	complemented
144	C₂×D₃×#124	C₂×C₄	1	4	yes	—
145	C₂×D₃×#124	C₂×C₄	1	4	yes	—
146	C₂×D₃×#124	C₂×C₄	1	4	yes	complemented
147	C₂×D₃×#124	C₂×C₄	1	4	yes	complemented
148	C₂×#5525	C₂×C₄	1	2	yes	complemented
149	C₂×#5525	C₂×C₄	1	2	yes	complemented
150	C₂×#5525	C₂³	1	2	yes	—
151	C₂×#5525	C₂³	1	2	yes	—
152	C₂×D₃×#117	C₂×C₄	1	2	yes	—
153	C₂×D₃×#117	C₂×C₄	1	2	yes	—
154	C₂×D₃×#117	C₂³	1	4	yes	—
155	C₂×D₃×#117	C₂³	1	2	yes	—
156	C₂×D₃×#117	C₂³	1	2	yes	—
157	C₂²×#874	C₂×C₄	1	2	yes	complemented
158	C₂²×#875	C₂×C₄	1	2	yes	complemented
159	C₂²×#872	C₂×C₄	1	2	yes	—
160	C₂²×C₄²×D₃	C₂×C₄	1	2	yes	—
161	C₂×C₃×#418	C₂³	1	8	yes	complemented
162	C₂×C₃×#410	C₂³	1	2	yes	complemented
163	C₂×C₃×#410	C₂³	1	2	yes	complemented
164	C₃×#2879	C₂³	1	2	yes	complemented
165	C₂×C₃×#407	C₂³	1	2	yes	—
166	C₃×#2280	C₂³	1	2	yes	—
167	C₂×#5240	C₂³	1	2	yes	complemented
168	C₂×#5240	C₂³	1	2	yes	complemented
169	#84074	C₂³	1	2	yes	complemented
170	C₂×#5215	C₂³	1	8	yes	complemented
171	#84027	C₂³	1	2	yes	—
172	C₂×#5207	C₂³	1	2	yes	—
173	C₂×#5131	C₂³	1	8	yes	complemented
174	#83762	C₂³	1	4	yes	complemented
175	C₂×#5126	C₂³	1	4	yes	—
176	#82267	C₂³	1	4	yes	—
177	C₂×#5006	C₂³	1	4	yes	complemented
178	C₂×#5006	C₂³	1	4	yes	complemented
179	C₂×#5001	C₂³	1	8	yes	complemented
180	C₂×#4726	D₄	1	8	yes	complemented
181	C₂×D₃×C₂²⋊C₈	D₄	1	8	yes	complemented
182	C₂×C₃×H(3,ℤ/4)	C₂³	1	8	yes	complemented
183	C₂×#4557	C₂³	1	8	yes	complemented
184	C₂×#4531	C₂³	1	8	yes	complemented
185	C₂×#4531	C₂³	1	8	yes	complemented
186	C₂²×#535	C₂×D₃	1	1	yes	characteristic
187	#60064	C₂×D₃	1	1	yes	characteristic, complemented
188	C₂×#1910	C₂×D₃	1	4	yes	complemented
189	#20598	C₂×D₃	1	2	yes	complemented
190	#20584	C₂×D₃	1	1	yes	characteristic, complemented
191	#10987	C₂×D₃	1	4	yes	complemented
192	#10716	C₂×D₃	1	2	yes	complemented
193	C₂⁵×D₃	C₂²⋊C₄	1	2	yes	—
194	C₂⁵×D₃	C₂×D₄	1	1	yes	characteristic
195	C₂²×C₃×#41	C₂²×C₄	1	1	yes	characteristic
196	C₂²×C₃×#41	C₂²×C₄	1	1	yes	characteristic
197	C₂²×C₃×#41	C₂×D₄	1	2	yes	—
198	C₂²×C₃×#41	C₂×D₄	1	2	yes	—
199	C₂²×C₃×#41	C₂⁴	1	1	yes	characteristic
200	C₂²×C₃×#41	C₂⁴	1	1	yes	characteristic
201	C₂³×C₃×Q₈	C₂²×C₄	1	1	yes	characteristic
202	C₂³×C₃×D₄	C₂²×C₄	1	2	yes	—
203	C₂³×C₃×D₄	C₂²×C₄	1	2	yes	—
204	C₂³×C₃×D₄	C₂²×C₄	1	1	yes	characteristic
205	C₂³×C₃×D₄	C₂×D₄	1	2	yes	—
206	C₂³×C₃×D₄	C₂⁴	1	2	yes	—
207	C₂⁴×C₃×C₄	C₂×D₄	1	2	yes	—
208	C₂⁴×C₃×C₄	C₂⁴	1	1	yes	characteristic
209	C₂³×#67	C₂²⋊C₄	1	2	yes	—
210	C₂³×#67	C₂²⋊C₄	1	2	yes	—
211	C₂³×#67	C₂×D₄	1	2	yes	—
212	C₂⁴×Dic₃	C₂²⋊C₄	1	2	yes	—
213	C₂⁴×Dic₃	C₂×D₄	1	1	yes	characteristic
214	C₂×D₃×#41	C₂×D₄	1	16	yes	—
215	C₂²×#239	C₂²⋊C₄	1	2	yes	—
216	C₂²×#239	C₂²⋊C₄	1	2	yes	—
217	C₂²×#239	C₂²×C₄	1	1	yes	characteristic
218	C₂²×#239	C₂²×C₄	1	1	yes	characteristic
219	C₂²×#239	C₂²×C₄	1	1	yes	characteristic
220	C₂²×#239	C₂²×C₄	1	1	yes	characteristic
221	C₂²×D₃×Q₈	C₂²⋊C₄	1	2	yes	—
222	C₂²×D₃×Q₈	C₂²⋊C₄	1	2	yes	—
223	C₂²×D₃×Q₈	C₂²×C₄	1	1	yes	characteristic
224	C₂²×D₃×Q₈	C₂²×C₄	1	1	yes	characteristic
225	C₂²×D₃×Q₈	C₂²×C₄	1	1	yes	characteristic
226	C₂²×D₃×Q₈	C₂²×C₄	1	1	yes	characteristic
227	C₂²×#237	C₂²⋊C₄	1	2	yes	—
228	C₂²×#237	C₂²⋊C₄	1	2	yes	—
229	C₂²×#237	C₂²⋊C₄	1	2	yes	—
230	C₂²×#237	C₂²⋊C₄	1	2	yes	—
231	C₂²×#237	C₂²⋊C₄	1	2	yes	—
232	C₂²×#237	C₂²⋊C₄	1	2	yes	—
233	C₂²×#237	C₂²×C₄	1	1	yes	characteristic
234	C₂²×#237	C₂²×C₄	1	1	yes	characteristic
235	C₂²×#237	C₂²×C₄	1	1	yes	characteristic
236	C₂²×#237	C₂²×C₄	1	1	yes	characteristic
237	C₂²×#237	C₂×D₄	1	2	yes	—
238	C₂²×#237	C₂×D₄	1	2	yes	—
239	C₂²×#237	C₂×D₄	1	2	yes	—
240	C₂²×#237	C₂×D₄	1	2	yes	—
241	C₂²×D₃×D₄	C₂²⋊C₄	1	2	yes	—
242	C₂²×D₃×D₄	C₂²⋊C₄	1	2	yes	—
243	C₂²×D₃×D₄	C₂²⋊C₄	1	2	yes	—
244	C₂²×D₃×D₄	C₂²⋊C₄	1	2	yes	—
245	C₂²×D₃×D₄	C₂²⋊C₄	1	2	yes	—
246	C₂²×D₃×D₄	C₂²⋊C₄	1	2	yes	—
247	C₂²×D₃×D₄	C₂²×C₄	1	1	yes	characteristic
248	C₂²×D₃×D₄	C₂²×C₄	1	4	yes	—
249	C₂²×D₃×D₄	C₂²×C₄	1	4	yes	—
250	C₂²×D₃×D₄	C₂²×C₄	1	4	yes	—
251	C₂²×D₃×D₄	C₂²×C₄	1	4	yes	—
252	C₂²×D₃×D₄	C₂²×C₄	1	1	yes	characteristic
253	C₂²×D₃×D₄	C₂²×C₄	1	1	yes	characteristic
254	C₂²×D₃×D₄	C₂²×C₄	1	1	yes	characteristic
255	C₂²×D₃×D₄	C₂×D₄	1	2	yes	—
256	C₂²×D₃×D₄	C₂×D₄	1	2	yes	—
257	C₂²×D₃×D₄	C₂×D₄	1	2	yes	—
258	C₂²×D₃×D₄	C₂×D₄	1	2	yes	—
259	C₂²×D₃×D₄	C₂×D₄	1	16	yes	—
260	C₂²×#235	C₂²⋊C₄	1	2	yes	—
261	C₂²×#235	C₂²⋊C₄	1	2	yes	—
262	C₂²×#235	C₂²⋊C₄	1	2	yes	—
263	C₂²×#235	C₂²⋊C₄	1	2	yes	—
264	C₂²×#235	C₂²×C₄	1	1	yes	characteristic
265	C₂²×#235	C₂²×C₄	1	1	yes	characteristic
266	C₂²×#235	C₂×D₄	1	2	yes	—
267	C₂²×#235	C₂×D₄	1	2	yes	—
268	C₂²×#235	C₂×D₄	1	2	yes	—
269	C₂²×#235	C₂×D₄	1	2	yes	—
270	C₂²×#235	C₂×D₄	1	2	yes	—
271	C₂²×#235	C₂×D₄	1	2	yes	—
272	C₂²×#235	C₂⁴	1	1	yes	characteristic
273	C₂²×#235	C₂⁴	1	1	yes	characteristic
274	C₂³×D₁₂	C₂²⋊C₄	1	2	yes	—
275	C₂³×D₁₂	C₂²×C₄	1	2	yes	—
276	C₂³×D₁₂	C₂²×C₄	1	2	yes	—
277	C₂³×D₁₂	C₂²×C₄	1	1	yes	characteristic
278	C₂³×D₁₂	C₂⁴	1	2	yes	—
279	C₂³×C₄×D₃	C₂²⋊C₄	1	2	yes	—
280	C₂³×C₄×D₃	C₂²⋊C₄	1	2	yes	—
281	C₂³×C₄×D₃	C₂²⋊C₄	1	2	yes	—
282	C₂³×C₄×D₃	C₂²⋊C₄	1	2	yes	—
283	C₂³×C₄×D₃	C₂²⋊C₄	1	2	yes	—
284	C₂³×C₄×D₃	C₂²⋊C₄	1	2	yes	—
285	C₂³×C₄×D₃	C₂²×C₄	1	1	yes	characteristic
286	C₂³×C₄×D₃	C₂²×C₄	1	1	yes	characteristic
287	C₂³×C₄×D₃	C₂²×C₄	1	1	yes	characteristic
288	C₂³×C₄×D₃	C₂²×C₄	1	1	yes	characteristic
289	C₂³×C₄×D₃	C₂×D₄	1	2	yes	—
290	C₂³×C₄×D₃	C₂×D₄	1	2	yes	—
291	C₂³×C₄×D₃	C₂×D₄	1	2	yes	—
292	C₂³×C₄×D₃	C₂×D₄	1	2	yes	—
293	C₂³×C₄×D₃	C₂×D₄	1	1	yes	characteristic
294	C₂³×C₄×D₃	C₂×D₄	1	1	yes	characteristic
295	C₂³×C₄×D₃	C₂×D₄	1	2	yes	—
296	C₂³×C₄×D₃	C₂×D₄	1	1	yes	characteristic
297	C₂³×C₄×D₃	C₂×D₄	1	1	yes	characteristic
298	C₂³×C₄×D₃	C₂×D₄	1	1	yes	characteristic
299	C₂³×C₄×D₃	C₂×D₄	1	1	yes	characteristic
300	C₂³×C₄×D₃	C₂×D₄	1	4	yes	—
301	C₂³×C₄×D₃	C₂×D₄	1	4	yes	—
302	C₂³×C₄×D₃	#41	1	4	yes	—
303	C₂³×C₄×D₃	#41	1	4	yes	—
304	C₂³×C₄×D₃	C₂⁴	1	1	yes	characteristic
305	C₂³×C₄×D₃	C₂⁴	1	1	yes	characteristic
306	C₂³×Dic₆	C₂²⋊C₄	1	2	yes	—
307	C₂³×Dic₆	C₂²×C₄	1	1	yes	characteristic
308	C₂²×C₃×M₁₆	C₂⁴	1	4	yes	—
309	C₃×#535	C₂×D₄	1	16	yes	—
310	C₂×C₃×#127	C₂²×C₄	1	4	yes	—
311	C₂×C₃×#127	C₂²×C₄	1	4	yes	—
312	C₂×C₃×#124	C₂²×C₄	1	4	yes	—
313	C₂×C₃×#124	C₂²×C₄	1	4	yes	—
314	C₂×C₃×#117	C₂²×C₄	1	2	yes	—
315	C₂×C₃×#117	C₂⁴	1	4	yes	—
316	C₂×C₃×#117	C₂⁴	1	2	yes	—
317	C₂²×C₃×C₄²	C₂²×C₄	1	2	yes	—
318	#5830	C₂×D₄	1	16	yes	—
319	C₂×#947	C₂²×C₄	1	4	yes	—
320	C₂×#947	C₂²×C₄	1	4	yes	—
321	#5805	C₂×D₄	1	16	yes	—
322	C₂×#940	C₂²×C₄	1	4	yes	—
323	C₂×#940	C₂²×C₄	1	4	yes	—
324	C₂×#940	C₂²×C₄	1	4	yes	—
325	C₂×#940	C₂²×C₄	1	4	yes	—
326	C₂×#936	C₂²×C₄	1	4	yes	—
327	C₂×#936	C₂²×C₄	1	4	yes	—
328	C₂×#926	C₂²×C₄	1	2	yes	—
329	C₂×#926	C₂⁴	1	4	yes	—
330	C₂×#926	C₂⁴	1	2	yes	—
331	C₂²×C₄×Dic₃	C₂²×C₄	1	2	yes	—
332	C₂²×#208	C₂⁴	1	4	yes	—
333	C₂²×ΓL(1,𝔽₂₅)	C₂×D₄	1	8	yes	complemented
334	C₂²×D₃×C₈	C₂×D₄	1	8	yes	complemented
335	#5715	C₂²⋊C₄	1	32	yes	complemented
336	D₃×#127	C₂²⋊C₄	1	32	yes	complemented
337	#5674	C₂²⋊C₄	1	32	yes	complemented
338	D₃×#124	C₂²⋊C₄	1	32	yes	complemented
339	#5525	C₂×D₄	1	16	yes	—
340	D₃×#117	C₂×D₄	1	16	yes	—
341	C₂×#875	C₂²×C₄	1	4	yes	—
342	C₂×#875	C₂²×C₄	1	4	yes	—
343	C₂×#874	C₂²×C₄	1	4	yes	—
344	C₂×#874	C₂²×C₄	1	4	yes	—
345	C₂×#872	C₂²×C₄	1	4	yes	—
346	C₂×#872	C₂²×C₄	1	4	yes	—
347	C₂×C₄²×D₃	C₂²×C₄	1	4	yes	—
348	C₂×C₄²×D₃	C₂²×C₄	1	4	yes	—
349	C₂×C₃×C₂²⋊C₈	C₂×D₄	1	8	yes	complemented
350	C₂×#830	C₂×D₄	1	8	yes	complemented
351	C₂×(C₂×D₃)⋊C₈	C₂×D₄	1	16	yes	complemented
352	C₂³×#41	C₂²×D₃	1	1	yes	characteristic
353	C₂⁴×D₄	C₂²×D₃	1	1	yes	characteristic
354	C₂×#568	C₂²×D₃	1	2	yes	complemented
355	C₂×#535	C₄×D₃	1	2	yes	complemented
356	C₂×#535	C₄×D₃	1	2	yes	complemented
357	C₂×#535	C₂²×D₃	1	2	yes	—
358	C₂×#535	C₂²×D₃	1	2	yes	—
359	C₂²×#127	C₄×D₃	1	2	yes	complemented
360	C₂²×#124	C₄×D₃	1	2	yes	complemented
361	C₂²×#117	C₂²×D₃	1	1	yes	characteristic
362	C₂×#418	C₂²×D₃	1	8	yes	complemented
363	C₂×#410	C₂²×D₃	1	2	yes	complemented
364	C₂×#410	C₂²×D₃	1	2	yes	complemented
365	#2879	C₂²×D₃	1	2	yes	complemented
366	C₂×#407	C₂²×D₃	1	2	yes	—
367	#2280	C₂²×D₃	1	2	yes	—
368	C₂×H(3,ℤ/4)	C₂²×D₃	1	8	yes	complemented
369	C₂⁵×C₃	C₂×C₂²⋊C₄	1	2	yes	—
370	C₂⁵×C₃	C₂²×D₄	1	1	yes	characteristic
371	C₂⁴×D₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
372	C₂⁴×D₃	C₂×C₂²⋊C₄	1	2	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	2	yes	—
376	C₂⁴×D₃	C₂×C₂²⋊C₄	1	2	yes	—
377	C₂⁴×D₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
378	C₂⁴×D₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
379	C₂⁴×D₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
380	C₂⁴×D₃	#121	1	4	yes	—
381	C₂⁴×D₃	#121	1	4	yes	—
382	C₂⁴×D₃	C₂²×D₄	1	1	yes	characteristic
383	C₂⁴×D₃	C₂²×D₄	1	1	yes	characteristic
384	C₂×C₃×#41	C₂²×D₄	1	8	yes	—
385	C₂²×C₃×Q₈	C₂×C₂²⋊C₄	1	2	yes	—
386	C₂²×C₃×Q₈	C₂³×C₄	1	1	yes	characteristic
387	C₂²×C₃×Q₈	C₂³×C₄	1	1	yes	characteristic
388	C₂²×C₃×D₄	C₂×C₂²⋊C₄	1	2	yes	—
389	C₂²×C₃×D₄	C₂×C₂²⋊C₄	1	2	yes	—
390	C₂²×C₃×D₄	C₂×C₂²⋊C₄	1	2	yes	—
391	C₂²×C₃×D₄	C₂³×C₄	1	1	yes	characteristic
392	C₂²×C₃×D₄	C₂³×C₄	1	4	yes	—
393	C₂²×C₃×D₄	C₂³×C₄	1	1	yes	characteristic
394	C₂²×C₃×D₄	C₂²×D₄	1	2	yes	—
395	C₂²×C₃×D₄	C₂²×D₄	1	2	yes	—
396	C₂²×C₃×D₄	C₂²×D₄	1	8	yes	—
397	C₂³×C₃×C₄	C₂×C₂²⋊C₄	1	2	yes	—
398	C₂³×C₃×C₄	C₂×C₂²⋊C₄	1	2	yes	—
399	C₂³×C₃×C₄	C₂×C₂²⋊C₄	1	2	yes	—
400	C₂³×C₃×C₄	C₂³×C₄	1	1	yes	characteristic
401	C₂³×C₃×C₄	C₂³×C₄	1	1	yes	characteristic
402	C₂³×C₃×C₄	C₂²×D₄	1	2	yes	—
403	C₂³×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
404	C₂³×C₃×C₄	C₂²×D₄	1	2	yes	—
405	C₂³×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
406	C₂³×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
407	C₂³×C₃×C₄	C₂²×D₄	1	4	yes	—
408	C₂³×C₃×C₄	C₂×#41	1	4	yes	—
409	C₂³×C₃×C₄	C₂⁵	1	1	yes	characteristic
410	C₂²×#67	C₂×C₂²⋊C₄	1	2	yes	—
411	C₂²×#67	C₂×C₂²⋊C₄	1	2	yes	—
412	C₂²×#67	C₂×C₂²⋊C₄	1	2	yes	—
413	C₂²×#67	C₂×C₂²⋊C₄	1	2	yes	—
414	C₂²×#67	C₂×C₂²⋊C₄	1	2	yes	—
415	C₂²×#67	C₂×C₂²⋊C₄	1	2	yes	—
416	C₂²×#67	C₂×C₂²⋊C₄	1	2	yes	—
417	C₂²×#67	C₂×C₂²⋊C₄	1	2	yes	—
418	C₂²×#67	C₂×C₂²⋊C₄	1	2	yes	—
419	C₂²×#67	C₂×C₂²⋊C₄	1	2	yes	—
420	C₂²×#67	C₂²×D₄	1	2	yes	—
421	C₂²×#67	C₂²×D₄	1	2	yes	—
422	C₂³×Dic₃	C₂×C₂²⋊C₄	1	2	yes	—
423	C₂³×Dic₃	C₂×C₂²⋊C₄	1	2	yes	—
424	C₂³×Dic₃	C₂×C₂²⋊C₄	1	2	yes	—
425	C₂³×Dic₃	C₂×C₂²⋊C₄	1	2	yes	—
426	C₂³×Dic₃	C₂×C₂²⋊C₄	1	2	yes	—
427	C₂³×Dic₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
428	C₂³×Dic₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
429	C₂³×Dic₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
430	C₂³×Dic₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
431	C₂³×Dic₃	#121	1	4	yes	—
432	C₂³×Dic₃	#121	1	4	yes	—
433	C₂³×Dic₃	C₂²×D₄	1	1	yes	characteristic
434	C₂³×Dic₃	C₂²×D₄	1	1	yes	characteristic
435	C₂×#239	C₂×C₂²⋊C₄	1	8	yes	—
436	C₂×D₃×Q₈	C₂×C₂²⋊C₄	1	8	yes	—
437	C₂×#237	C₂×C₂²⋊C₄	1	8	yes	—
438	C₂×#237	#120	1	16	yes	—
439	C₂×D₃×D₄	C₂×C₂²⋊C₄	1	16	yes	—
440	C₂×D₃×D₄	C₂×C₂²⋊C₄	1	16	yes	—
441	C₂×D₃×D₄	C₂×C₂²⋊C₄	1	8	yes	—
442	C₂×D₃×D₄	#120	1	16	yes	—
443	C₂×#235	#120	1	16	yes	—
444	C₂×#235	C₂²×D₄	1	8	yes	—
445	C₂²×D₁₂	C₂×C₂²⋊C₄	1	2	yes	—
446	C₂²×D₁₂	C₂×C₂²⋊C₄	1	2	yes	—
447	C₂²×D₁₂	C₂×C₂²⋊C₄	1	2	yes	—
448	C₂²×D₁₂	C₂×C₂²⋊C₄	1	2	yes	—
449	C₂²×D₁₂	C₂×C₂²⋊C₄	1	2	yes	—
450	C₂²×D₁₂	C₂³×C₄	1	1	yes	characteristic
451	C₂²×D₁₂	C₂³×C₄	1	4	yes	—
452	C₂²×D₁₂	C₂³×C₄	1	1	yes	characteristic
453	C₂²×D₁₂	C₂²×D₄	1	8	yes	—
454	C₂²×C₄×D₃	C₂×C₂²⋊C₄	1	2	yes	—
455	C₂²×C₄×D₃	C₂×C₂²⋊C₄	1	2	yes	—
456	C₂²×C₄×D₃	C₂×C₂²⋊C₄	1	2	yes	—
457	C₂²×C₄×D₃	C₂×C₂²⋊C₄	1	2	yes	—
458	C₂²×C₄×D₃	C₂×C₂²⋊C₄	1	2	yes	—
459	C₂²×C₄×D₃	C₂×C₂²⋊C₄	1	2	yes	—
460	C₂²×C₄×D₃	C₂×C₂²⋊C₄	1	2	yes	—
461	C₂²×C₄×D₃	C₂×C₂²⋊C₄	1	2	yes	—
462	C₂²×C₄×D₃	C₂×C₂²⋊C₄	1	2	yes	—
463	C₂²×C₄×D₃	C₂×C₂²⋊C₄	1	2	yes	—
464	C₂²×C₄×D₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
465	C₂²×C₄×D₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
466	C₂²×C₄×D₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
467	C₂²×C₄×D₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
468	C₂²×C₄×D₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
469	C₂²×C₄×D₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
470	C₂²×C₄×D₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
471	C₂²×C₄×D₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
472	C₂²×C₄×D₃	C₄×D₄	1	4	yes	—
473	C₂²×C₄×D₃	C₄×D₄	1	4	yes	—
474	C₂²×C₄×D₃	C₄×D₄	1	4	yes	—
475	C₂²×C₄×D₃	C₄×D₄	1	4	yes	—
476	C₂²×C₄×D₃	C₄×D₄	1	4	yes	—
477	C₂²×C₄×D₃	C₄×D₄	1	4	yes	—
478	C₂²×C₄×D₃	C₄×D₄	1	4	yes	—
479	C₂²×C₄×D₃	C₄×D₄	1	4	yes	—
480	C₂²×C₄×D₃	#120	1	16	yes	—
481	C₂²×C₄×D₃	#120	1	2	yes	—
482	C₂²×C₄×D₃	#120	1	2	yes	—
483	C₂²×C₄×D₃	#120	1	4	yes	—
484	C₂²×C₄×D₃	#120	1	2	yes	—
485	C₂²×C₄×D₃	#120	1	4	yes	—
486	C₂²×C₄×D₃	#120	1	2	yes	—
487	C₂²×C₄×D₃	#121	1	4	yes	—
488	C₂²×C₄×D₃	#121	1	4	yes	—
489	C₂²×C₄×D₃	#121	1	4	yes	—
490	C₂²×C₄×D₃	#121	1	4	yes	—
491	C₂²×C₄×D₃	#123	1	2	yes	—
492	C₂²×C₄×D₃	#123	1	2	yes	—
493	C₂²×C₄×D₃	#123	1	4	yes	—
494	C₂²×C₄×D₃	#123	1	4	yes	—
495	C₂²×C₄×D₃	#123	1	2	yes	—
496	C₂²×C₄×D₃	#123	1	2	yes	—
497	C₂²×C₄×D₃	C₂³×C₄	1	1	yes	characteristic
498	C₂²×C₄×D₃	C₂³×C₄	1	1	yes	characteristic
499	C₂²×C₄×D₃	C₂³×C₄	1	1	yes	characteristic
500	C₂²×C₄×D₃	C₂³×C₄	1	1	yes	characteristic
501	C₂²×C₄×D₃	C₂²×D₄	1	2	yes	—
502	C₂²×C₄×D₃	C₂²×D₄	1	4	yes	—
503	C₂²×C₄×D₃	C₂²×D₄	1	2	yes	—
504	C₂²×C₄×D₃	C₂²×D₄	1	1	yes	characteristic
505	C₂²×C₄×D₃	C₂²×D₄	1	1	yes	characteristic
506	C₂²×C₄×D₃	C₂²×D₄	1	8	yes	—
507	C₂²×C₄×D₃	C₂²×D₄	1	2	yes	—
508	C₂²×C₄×D₃	C₂²×D₄	1	2	yes	—
509	C₂²×C₄×D₃	C₂²×D₄	1	1	yes	characteristic
510	C₂²×C₄×D₃	C₂²×D₄	1	1	yes	characteristic
511	C₂²×C₄×D₃	C₂×#41	1	4	yes	—
512	C₂²×C₄×D₃	C₂×#41	1	2	yes	—
513	C₂²×C₄×D₃	C₂×#41	1	2	yes	—
514	C₂²×C₄×D₃	H(5,𝔽₂)	1	8	yes	—
515	C₂²×Dic₆	C₂×C₂²⋊C₄	1	2	yes	—
516	C₂²×Dic₆	C₂×C₂²⋊C₄	1	2	yes	—
517	C₂²×Dic₆	C₂×C₂²⋊C₄	1	2	yes	—
518	C₂²×Dic₆	C₂×C₂²⋊C₄	1	2	yes	—
519	C₂²×Dic₆	C₂×C₂²⋊C₄	1	2	yes	—
520	C₂²×Dic₆	C₂³×C₄	1	1	yes	characteristic
521	C₂²×Dic₆	C₂³×C₄	1	1	yes	characteristic
522	C₂²×C₃×C₈	C₂²×D₄	1	8	yes	complemented
523	C₃×#127	C₂×C₂²⋊C₄	1	16	yes	complemented
524	C₃×#124	C₂×C₂²⋊C₄	1	16	yes	complemented
525	C₃×#117	C₂²×D₄	1	8	yes	—
526	C₂×C₃×C₄²	C₂³×C₄	1	4	yes	—
527	#947	C₂×C₂²⋊C₄	1	16	yes	complemented
528	#940	C₂×C₂²⋊C₄	1	16	yes	complemented
529	#940	C₂×C₂²⋊C₄	1	16	yes	complemented
530	#936	C₂×C₂²⋊C₄	1	16	yes	complemented
531	#926	C₂²×D₄	1	8	yes	—
532	C₂×C₄×Dic₃	C₂³×C₄	1	4	yes	—
533	C₂²×C₃⋊C₈	C₂²×D₄	1	8	yes	complemented
534	#875	C₂×C₂²⋊C₄	1	16	yes	complemented
535	#874	C₂×C₂²⋊C₄	1	16	yes	complemented
536	#872	C₂×C₂²⋊C₄	1	16	yes	—
537	C₄²×D₃	C₂×C₂²⋊C₄	1	16	yes	—
538	C₂²×#41	C₂×C₄×D₃	1	1	yes	characteristic
539	C₂²×#41	C₂×C₄×D₃	1	1	yes	characteristic
540	C₂²×#41	D₃×D₄	1	2	yes	—
541	C₂²×#41	D₃×D₄	1	2	yes	—
542	C₂²×#41	C₂³×D₃	1	1	yes	characteristic
543	C₂²×#41	C₂³×D₃	1	1	yes	characteristic
544	C₂³×Q₈	C₂×C₄×D₃	1	1	yes	characteristic
545	C₂³×D₄	C₂×C₄×D₃	1	2	yes	—
546	C₂³×D₄	C₂×C₄×D₃	1	2	yes	—
547	C₂³×D₄	C₂×C₄×D₃	1	1	yes	characteristic
548	C₂³×D₄	D₃×D₄	1	2	yes	—
549	C₂³×D₄	C₂³×D₃	1	2	yes	—
550	C₂⁴×C₄	D₃×D₄	1	2	yes	—
551	C₂⁴×C₄	C₂³×D₃	1	1	yes	characteristic
552	C₂²×M₁₆	C₂³×D₃	1	4	yes	—
553	#535	D₃×D₄	1	16	yes	—
554	C₂×#127	C₂×C₄×D₃	1	4	yes	—
555	C₂×#127	C₂×C₄×D₃	1	4	yes	—
556	C₂×#124	C₂×C₄×D₃	1	4	yes	—
557	C₂×#124	C₂×C₄×D₃	1	4	yes	—
558	C₂×#117	C₂×C₄×D₃	1	2	yes	—
559	C₂×#117	C₂³×D₃	1	4	yes	—
560	C₂×#117	C₂³×D₃	1	2	yes	—
561	C₂²×C₄²	C₂×C₄×D₃	1	2	yes	—
562	C₂×C₂²⋊C₈	D₃×D₄	1	8	yes	complemented
563	C₂⁴×C₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
564	C₂⁴×C₃	C₂²×C₂²⋊C₄	1	2	yes	—
565	C₂⁴×C₃	C₂²×C₂²⋊C₄	1	2	yes	—
566	C₂⁴×C₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
567	C₂⁴×C₃	C₂×#121	1	4	yes	—
568	C₂⁴×C₃	C₂³×D₄	1	1	yes	characteristic
569	C₂³×D₃	#379	1	8	yes	—
570	C₂³×D₃	#386	1	2	yes	—
571	C₂³×D₃	#386	1	2	yes	—
572	C₂³×D₃	#386	1	4	yes	—
573	C₂³×D₃	#386	1	4	yes	—
574	C₂³×D₃	#386	1	2	yes	—
575	C₂³×D₃	#386	1	2	yes	—
576	C₂³×D₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
577	C₂³×D₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
578	C₂³×D₃	C₂²×C₂²⋊C₄	1	2	yes	—
579	C₂³×D₃	C₂²×C₂²⋊C₄	1	2	yes	—
580	C₂³×D₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
581	C₂³×D₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
582	C₂³×D₃	C₂×#120	1	4	yes	—
583	C₂³×D₃	C₂×#121	1	4	yes	—
584	C₂³×D₃	C₂×#121	1	2	yes	—
585	C₂³×D₃	C₂×#121	1	2	yes	—
586	C₂³×D₃	#534	1	4	yes	—
587	C₂×C₃×Q₈	C₂²×C₂²⋊C₄	1	4	yes	—
588	C₂×C₃×D₄	C₂²×C₂²⋊C₄	1	8	yes	—
589	C₂×C₃×D₄	C₂²×C₂²⋊C₄	1	4	yes	—
590	C₂×C₃×D₄	C₂×#120	1	8	yes	—
591	C₂²×C₃×C₄	C₂²×C₂²⋊C₄	1	2	yes	—
592	C₂²×C₃×C₄	C₂²×C₂²⋊C₄	1	2	yes	—
593	C₂²×C₃×C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
594	C₂²×C₃×C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
595	C₂²×C₃×C₄	C₂×C₄×D₄	1	4	yes	—
596	C₂²×C₃×C₄	C₂×C₄×D₄	1	4	yes	—
597	C₂²×C₃×C₄	C₂×#120	1	8	yes	—
598	C₂²×C₃×C₄	C₂×#120	1	2	yes	—
599	C₂²×C₃×C₄	C₂×#120	1	2	yes	—
600	C₂²×C₃×C₄	C₂×#121	1	4	yes	—
601	C₂²×C₃×C₄	C₂×#123	1	2	yes	—
602	C₂²×C₃×C₄	C₂×#123	1	2	yes	—
603	C₂²×C₃×C₄	C₂⁴×C₄	1	1	yes	characteristic
604	C₂²×C₃×C₄	C₂³×D₄	1	4	yes	—
605	C₂²×C₃×C₄	C₂³×D₄	1	2	yes	—
606	C₂²×C₃×C₄	C₂³×D₄	1	1	yes	characteristic
607	C₂²×C₃×C₄	C₂²×#41	1	2	yes	—
608	C₂²×C₃×C₄	C₂×H(5,𝔽₂)	1	4	yes	—
609	C₂×#67	#379	1	8	yes	—
610	C₂×#67	#379	1	8	yes	—
611	C₂×#67	C₂×#120	1	8	yes	—
612	C₂²×Dic₃	#379	1	8	yes	—
613	C₂²×Dic₃	#386	1	4	yes	—
614	C₂²×Dic₃	#386	1	2	yes	—
615	C₂²×Dic₃	#386	1	2	yes	—
616	C₂²×Dic₃	#386	1	2	yes	—
617	C₂²×Dic₃	#386	1	2	yes	—
618	C₂²×Dic₃	#386	1	4	yes	—
619	C₂²×Dic₃	C₂²×C₂²⋊C₄	1	2	yes	—
620	C₂²×Dic₃	C₂²×C₂²⋊C₄	1	2	yes	—
621	C₂²×Dic₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
622	C₂²×Dic₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
623	C₂²×Dic₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
624	C₂²×Dic₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
625	C₂²×Dic₃	C₂×#120	1	4	yes	—
626	C₂²×Dic₃	C₂×#121	1	4	yes	—
627	C₂²×Dic₃	C₂×#121	1	2	yes	—
628	C₂²×Dic₃	C₂×#121	1	2	yes	—
629	C₂²×Dic₃	#534	1	4	yes	—
630	C₂×D₁₂	#379	1	8	yes	—
631	C₂×D₁₂	C₂²×C₂²⋊C₄	1	8	yes	—
632	C₂×D₁₂	C₂²×C₂²⋊C₄	1	4	yes	—
633	C₂×C₄×D₃	#379	1	8	yes	—
634	C₂×C₄×D₃	#379	1	8	yes	—
635	C₂×C₄×D₃	#386	1	2	yes	—
636	C₂×C₄×D₃	#386	1	2	yes	—
637	C₂×C₄×D₃	#386	1	2	yes	—
638	C₂×C₄×D₃	#386	1	2	yes	—
639	C₂×C₄×D₃	#386	1	4	yes	—
640	C₂×C₄×D₃	#386	1	4	yes	—
641	C₂×C₄×D₃	#386	1	2	yes	—
642	C₂×C₄×D₃	#386	1	2	yes	—
643	C₂×C₄×D₃	#386	1	4	yes	—
644	C₂×C₄×D₃	#386	1	4	yes	—
645	C₂×C₄×D₃	#386	1	2	yes	—
646	C₂×C₄×D₃	#386	1	2	yes	—
647	C₂×C₄×D₃	C₂²×C₂²⋊C₄	1	4	yes	—
648	C₂×C₄×D₃	C₂²×C₂²⋊C₄	1	4	yes	—
649	C₂×C₄×D₃	C₂×C₄×D₄	1	4	yes	—
650	C₂×C₄×D₃	C₂×C₄×D₄	1	4	yes	—
651	C₂×C₄×D₃	C₂×C₄×D₄	1	2	yes	—
652	C₂×C₄×D₃	C₂×C₄×D₄	1	2	yes	—
653	C₂×C₄×D₃	C₂×C₄×D₄	1	2	yes	—
654	C₂×C₄×D₃	C₂×C₄×D₄	1	2	yes	—
655	C₂×C₄×D₃	#518	1	4	yes	—
656	C₂×C₄×D₃	#518	1	4	yes	—
657	C₂×C₄×D₃	C₂×#120	1	8	yes	—
658	C₂×C₄×D₃	C₂×#120	1	2	yes	—
659	C₂×C₄×D₃	C₂×#120	1	2	yes	—
660	C₂×C₄×D₃	C₂×#120	1	1	yes	characteristic
661	C₂×C₄×D₃	C₂×#120	1	2	yes	—
662	C₂×C₄×D₃	C₂×#120	1	1	yes	characteristic
663	C₂×C₄×D₃	C₂×#120	1	4	yes	—
664	C₂×C₄×D₃	C₂×#120	1	4	yes	—
665	C₂×C₄×D₃	C₂×#123	1	2	yes	—
666	C₂×C₄×D₃	C₂×#123	1	2	yes	—
667	C₂×C₄×D₃	C₂×#123	1	1	yes	characteristic
668	C₂×C₄×D₃	C₂×#123	1	1	yes	characteristic
669	C₂×C₄×D₃	C₂×#123	1	2	yes	—
670	C₂×C₄×D₃	#534	1	4	yes	—
671	C₂×C₄×D₃	#534	1	4	yes	—
672	C₂×C₄×D₃	D₄²	1	16	yes	—
673	C₂×C₄×D₃	D₄²	1	16	yes	—
674	C₂×C₄×D₃	#546	1	16	yes	—
675	C₂×C₄×D₃	#546	1	16	yes	—
676	C₂×Dic₆	#379	1	8	yes	—
677	C₂×Dic₆	C₂²×C₂²⋊C₄	1	4	yes	—
678	C₃×C₄²	C₂²×C₂²⋊C₄	1	8	yes	—
679	C₄×Dic₃	C₂²×C₂²⋊C₄	1	8	yes	—
680	C₂⁵	D₃×C₂²⋊C₄	1	2	yes	—
681	C₂⁵	C₂×D₃×D₄	1	1	yes	characteristic
682	C₂×#41	C₂×D₃×D₄	1	8	yes	—
683	C₂²×Q₈	D₃×C₂²⋊C₄	1	2	yes	—
684	C₂²×Q₈	C₂²×C₄×D₃	1	1	yes	characteristic
685	C₂²×Q₈	C₂²×C₄×D₃	1	1	yes	characteristic
686	C₂²×D₄	D₃×C₂²⋊C₄	1	2	yes	—
687	C₂²×D₄	D₃×C₂²⋊C₄	1	2	yes	—
688	C₂²×D₄	D₃×C₂²⋊C₄	1	2	yes	—
689	C₂²×D₄	C₂²×C₄×D₃	1	1	yes	characteristic
690	C₂²×D₄	C₂²×C₄×D₃	1	4	yes	—
691	C₂²×D₄	C₂²×C₄×D₃	1	1	yes	characteristic
692	C₂²×D₄	C₂×D₃×D₄	1	8	yes	—
693	C₂²×D₄	C₂×D₃×D₄	1	2	yes	—
694	C₂²×D₄	C₂×D₃×D₄	1	2	yes	—
695	C₂³×C₄	D₃×C₂²⋊C₄	1	2	yes	—
696	C₂³×C₄	D₃×C₂²⋊C₄	1	2	yes	—
697	C₂³×C₄	D₃×C₂²⋊C₄	1	2	yes	—
698	C₂³×C₄	C₂²×C₄×D₃	1	1	yes	characteristic
699	C₂³×C₄	C₂²×C₄×D₃	1	1	yes	characteristic
700	C₂³×C₄	C₂×D₃×D₄	1	2	yes	—
701	C₂³×C₄	C₂×D₃×D₄	1	1	yes	characteristic
702	C₂³×C₄	C₂×D₃×D₄	1	1	yes	characteristic
703	C₂³×C₄	C₂×D₃×D₄	1	2	yes	—
704	C₂³×C₄	C₂×D₃×D₄	1	4	yes	—
705	C₂³×C₄	C₂×D₃×D₄	1	1	yes	characteristic
706	C₂³×C₄	D₃×#41	1	4	yes	—
707	C₂³×C₄	C₂⁴×D₃	1	1	yes	characteristic
708	C₂²×C₈	C₂×D₃×D₄	1	8	yes	complemented
709	#127	D₃×C₂²⋊C₄	1	16	yes	complemented
710	#124	D₃×C₂²⋊C₄	1	16	yes	complemented
711	#117	C₂×D₃×D₄	1	8	yes	—
712	C₂×C₄²	C₂²×C₄×D₃	1	4	yes	—
713	C₂³×C₃	C₂×#379	1	4	yes	—
714	C₂³×C₃	C₂×#386	1	2	yes	—
715	C₂³×C₃	C₂×#386	1	2	yes	—
716	C₂³×C₃	C₂³×C₂²⋊C₄	1	1	yes	characteristic
717	C₂³×C₃	C₂²×#120	1	2	yes	—
718	C₂³×C₃	C₂²×#121	1	2	yes	—
719	C₂³×C₃	C₂×#534	1	2	yes	—
720	C₂²×D₃	#1910	1	8	yes	complemented
721	C₂²×D₃	C₂×#379	1	2	yes	—
722	C₂²×D₃	C₂×#379	1	4	yes	—
723	C₂²×D₃	C₂×#379	1	2	yes	—
724	C₂²×D₃	C₂×#386	1	2	yes	—
725	C₂²×D₃	C₂×#386	1	2	yes	—
726	C₂²×D₃	C₂×#386	1	1	yes	characteristic
727	C₂²×D₃	C₂×#386	1	2	yes	—
728	C₂²×D₃	C₂×#386	1	1	yes	characteristic
729	C₂²×D₃	#2308	1	2	yes	—
730	C₂²×D₃	#2308	1	2	yes	—
731	C₂²×D₃	#2410	1	8	yes	—
732	C₂²×D₃	#2410	1	8	yes	—
733	C₂×C₃×C₄	C₂×#379	1	4	yes	—
734	C₂×C₃×C₄	C₂×#386	1	2	yes	—
735	C₂×C₃×C₄	C₂×#386	1	2	yes	—
736	C₂×C₃×C₄	C₂³×C₂²⋊C₄	1	2	yes	—
737	C₂×C₃×C₄	C₂²×C₄×D₄	1	2	yes	—
738	C₂×C₃×C₄	C₂×#518	1	2	yes	—
739	C₂×C₃×C₄	C₂²×#120	1	1	yes	characteristic
740	C₂×C₃×C₄	C₂²×#120	1	2	yes	—
741	C₂×C₃×C₄	C₂²×#123	1	1	yes	characteristic
742	C₂×C₃×C₄	C₂×#534	1	2	yes	—
743	C₂×C₃×C₄	C₂×D₄²	1	8	yes	—
744	C₂×C₃×C₄	C₂×#546	1	8	yes	—
745	C₂×Dic₃	C₂×#379	1	4	yes	—
746	C₂×Dic₃	C₂×#379	1	2	yes	—
747	C₂×Dic₃	C₂×#379	1	2	yes	—
748	C₂×Dic₃	C₂×#386	1	2	yes	—
749	C₂×Dic₃	C₂×#386	1	2	yes	—
750	C₂×Dic₃	C₂×#386	1	2	yes	—
751	C₂×Dic₃	C₂×#386	1	1	yes	characteristic
752	C₂×Dic₃	C₂×#386	1	1	yes	characteristic
753	C₂×Dic₃	#2308	1	2	yes	—
754	C₂×Dic₃	#2308	1	2	yes	—
755	C₂×Dic₃	#2410	1	8	yes	—
756	C₂×Dic₃	#2410	1	8	yes	—
757	C₄×D₃	D₄×C₂²⋊C₄	1	8	yes	—
758	C₄×D₃	D₄×C₂²⋊C₄	1	8	yes	—
759	C₄×D₃	D₄×C₂²⋊C₄	1	8	yes	—
760	C₄×D₃	D₄×C₂²⋊C₄	1	8	yes	—
761	C₄×D₃	#2403	1	4	yes	—
762	C₄×D₃	#2403	1	8	yes	—
763	C₄×D₃	#2403	1	4	yes	—
764	C₄×D₃	#2405	1	4	yes	—
765	C₄×D₃	#2405	1	4	yes	—
766	C₄×D₃	#2405	1	8	yes	—
767	C₂⁴	C₂×D₃×C₂²⋊C₄	1	1	yes	characteristic
768	C₂⁴	C₂×D₃×C₂²⋊C₄	1	2	yes	—
769	C₂⁴	C₂×D₃×C₂²⋊C₄	1	2	yes	—
770	C₂⁴	C₂×D₃×C₂²⋊C₄	1	1	yes	characteristic
771	C₂⁴	D₃×#121	1	4	yes	—
772	C₂⁴	C₂²×D₃×D₄	1	1	yes	characteristic
773	C₂×Q₈	C₂×D₃×C₂²⋊C₄	1	4	yes	—
774	C₂×D₄	C₂×D₃×C₂²⋊C₄	1	8	yes	—
775	C₂×D₄	C₂×D₃×C₂²⋊C₄	1	4	yes	—
776	C₂×D₄	D₃×#120	1	8	yes	—
777	C₂²×C₄	C₂×D₃×C₂²⋊C₄	1	2	yes	—
778	C₂²×C₄	C₂×D₃×C₂²⋊C₄	1	2	yes	—
779	C₂²×C₄	C₂×D₃×C₂²⋊C₄	1	1	yes	characteristic
780	C₂²×C₄	C₂×D₃×C₂²⋊C₄	1	1	yes	characteristic
781	C₂²×C₄	C₄×D₃×D₄	1	4	yes	—
782	C₂²×C₄	C₄×D₃×D₄	1	4	yes	—
783	C₂²×C₄	D₃×#120	1	8	yes	—
784	C₂²×C₄	D₃×#120	1	2	yes	—
785	C₂²×C₄	D₃×#120	1	2	yes	—
786	C₂²×C₄	D₃×#121	1	4	yes	—
787	C₂²×C₄	D₃×#123	1	2	yes	—
788	C₂²×C₄	D₃×#123	1	2	yes	—
789	C₂²×C₄	C₂³×C₄×D₃	1	1	yes	characteristic
790	C₂²×C₄	C₂²×D₃×D₄	1	2	yes	—
791	C₂²×C₄	C₂²×D₃×D₄	1	1	yes	characteristic
792	C₂²×C₄	C₂²×D₃×D₄	1	4	yes	—
793	C₂²×C₄	C₂×D₃×#41	1	2	yes	—
794	C₂²×C₄	D₃×H(5,𝔽₂)	1	4	yes	—
795	C₄²	C₂×D₃×C₂²⋊C₄	1	8	yes	—
796	C₂²×C₃	C₂×#1910	1	4	yes	complemented
797	C₂²×C₃	C₂²×#379	1	1	yes	characteristic
798	C₂²×C₃	C₂²×#386	1	1	yes	characteristic
799	C₂²×C₃	C₂×#2308	1	1	yes	characteristic
800	C₂²×C₃	C₂×#2410	1	4	yes	—
801	C₂×D₃	#13867	1	2	yes	—
802	C₂×D₃	#13867	1	4	yes	—
803	C₂×D₃	#13867	1	2	yes	—
804	C₂×D₃	C₂×#1910	1	4	yes	—
805	C₂×D₃	C₂×#1910	1	4	yes	complemented
806	C₃×C₄	C₂×D₄×C₂²⋊C₄	1	4	yes	—
807	C₃×C₄	C₂×#2403	1	2	yes	—
808	C₃×C₄	C₂×#2405	1	2	yes	—
809	Dic₃	#13867	1	4	yes	—
810	Dic₃	#13867	1	2	yes	—
811	Dic₃	#13867	1	2	yes	—
812	C₂³	D₃×#379	1	4	yes	—
813	C₂³	D₃×#386	1	2	yes	—
814	C₂³	D₃×#386	1	2	yes	—
815	C₂³	C₂²×D₃×C₂²⋊C₄	1	1	yes	characteristic
816	C₂³	C₂×D₃×#120	1	2	yes	—
817	C₂³	C₂×D₃×#121	1	2	yes	—
818	C₂³	D₃×#534	1	2	yes	—
819	C₂×C₄	D₃×#379	1	4	yes	—
820	C₂×C₄	D₃×#386	1	2	yes	—
821	C₂×C₄	D₃×#386	1	2	yes	—
822	C₂×C₄	C₂²×D₃×C₂²⋊C₄	1	2	yes	—
823	C₂×C₄	C₂×C₄×D₃×D₄	1	2	yes	—
824	C₂×C₄	D₃×#518	1	2	yes	—
825	C₂×C₄	C₂×D₃×#120	1	2	yes	—
826	C₂×C₄	C₂×D₃×#120	1	1	yes	characteristic
827	C₂×C₄	C₂×D₃×#123	1	1	yes	characteristic
828	C₂×C₄	D₃×#534	1	2	yes	—
829	C₂×C₄	D₃×D₄²	1	8	yes	—
830	C₂×C₄	D₃×#546	1	8	yes	—
831	C₂×C₃	C₂×#13867	1	1	yes	characteristic
832	C₂×C₃	C₂²×#1910	1	2	yes	—
833	D₃	#359513	1	4	yes	direct product factor
834	C₂²	D₃×#1910	1	4	yes	complemented
835	C₂²	C₂×D₃×#379	1	1	yes	characteristic
836	C₂²	C₂×D₃×#386	1	1	yes	characteristic
837	C₂²	D₃×#2308	1	1	yes	characteristic
838	C₂²	D₃×#2410	1	4	yes	—
839	C₄	D₃×D₄×C₂²⋊C₄	1	4	yes	—
840	C₄	D₃×#2403	1	2	yes	—
841	C₄	D₃×#2405	1	2	yes	—
842	C₃	C₂×#359513	1	1	yes	characteristic, complemented, Sylow
843	C₂	C₂×D₃×#1910	1	2	yes	—
844	C₂	D₃×#13867	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₃×#386
commutator	C₂²×C₃×C₄	C₂⁴×C₄
Frattini	C₂³×C₄	C₂⁴×D₃
Fitting	C₃×#359513	C₂
socle	C₂²×C₃	C₂²×#386
prime radical	C₂²×D₃×#535	C₂
cosocle	C₂³×C₃×C₄	C₂⁵
hypercenter	#359513	D₃
hypocenter	C₃	C₂×#359513
LCS	G ▷ C₂²×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂² ◁ C₂⁴×C₄ ◁ #359513

Complements

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

N	H ≅ G/N	type
1. #72270358	C₂	semidirect
2. D₃×#60064	C₂	semidirect
3. #72270325	C₂	semidirect
4. #72270321	C₂	semidirect
5. #72270315	C₂	semidirect
6. #72270312	C₂	semidirect
7. #72270309	C₂	semidirect
8. #72270300	C₂	semidirect
9. C₃×#359513	C₂	semidirect
10. D₃×#20584	C₂	semidirect
12. D₃×#10716	C₂	semidirect
13. D₃×#10987	C₂	semidirect
14. D₃×#20598	C₂	semidirect
15. C₂×D₃×#1910	C₂	semidirect
18. C₂×D₃×#568	C₂²	semidirect
20. C₂²×#5674	C₄	semidirect
23. C₂²×#5715	C₄	semidirect
24. C₂×D₃×#535	C₄	semidirect
25. C₂×D₃×#535	C₄	semidirect
26. C₂×D₃×#535	C₄	semidirect
27. C₂×D₃×#535	C₄	semidirect
32. C₂²×D₃×#127	C₄	semidirect
33. C₂²×D₃×#124	C₄	semidirect
35. C₂×D₃×#418	C₂²	semidirect
36. C₂×D₃×#410	C₂²	semidirect
37. C₂×D₃×#410	C₂²	semidirect
38. #11658639	C₂²	semidirect
39. #11658638	C₂²	semidirect
40. #11658637	C₂²	semidirect
41. #11658636	C₂²	semidirect
42. D₃×#2879	C₂²	semidirect
45. C₂×#71854	C₂²	semidirect
46. C₂×#72025	C₂²	semidirect
47. C₂×#68713	C₂²	semidirect
48. C₂×#70047	C₂²	semidirect
49. C₂×#70330	C₂²	semidirect
50. #10794391	C₂²	semidirect
51. #10794390	C₂²	semidirect
52. #10794389	C₂²	semidirect
53. #10794388	C₂²	semidirect
54. #10794319	C₂²	semidirect
55. #10794318	C₂²	semidirect
56. #10794316	C₂²	semidirect
57. #10794316	C₂²	semidirect
58. C₂×D₃×H(3,ℤ/4)	C₂²	semidirect
59. #10701779	C₂²	semidirect
60. #10701778	C₂²	semidirect
61. #10701777	C₂²	semidirect
62. #10701776	C₂²	semidirect
63. #10701775	C₂²	semidirect
64. #10700420	C₂²	semidirect
65. #10700419	C₂²	semidirect
66. #10700418	C₂²	semidirect
67. #10700417	C₂²	semidirect
69. C₃×#60064	C₂²	semidirect
70. C₂×C₃×#1910	C₂²	semidirect
71. C₃×#20598	C₂²	semidirect
72. C₃×#20584	C₂²	semidirect
73. C₃×#10987	C₂²	semidirect
74. C₃×#10716	C₂²	semidirect
75. #359513	D₃	direct (N × H)
107. C₂×C₃×#568	C₂³	semidirect
108. C₂×C₃×#535	C₂×C₄	semidirect
109. C₂×C₃×#535	C₂×C₄	semidirect
112. C₂²×C₃×#127	C₂×C₄	semidirect
113. C₂²×C₃×#124	C₂×C₄	semidirect
115. C₂×#5830	C₂×C₄	semidirect
116. C₂×#5830	C₂×C₄	semidirect
119. C₂×#5819	C₂³	semidirect
120. C₂²×#947	C₂×C₄	semidirect
121. C₂×#5805	C₂×C₄	semidirect
122. C₂×#5805	C₂×C₄	semidirect
125. C₂²×#940	C₂×C₄	semidirect
126. C₂²×#940	C₂×C₄	semidirect
127. C₂²×#936	C₂×C₄	semidirect
129. C₂×#5745	C₂³	semidirect
134. C₂×#5715	C₂×C₄	semidirect
135. C₂×#5715	C₂×C₄	semidirect
138. C₂×D₃×#127	C₂×C₄	semidirect
139. C₂×D₃×#127	C₂×C₄	semidirect
142. C₂×#5674	C₂×C₄	semidirect
143. C₂×#5674	C₂×C₄	semidirect
146. C₂×D₃×#124	C₂×C₄	semidirect
147. C₂×D₃×#124	C₂×C₄	semidirect
148. C₂×#5525	C₂×C₄	semidirect
149. C₂×#5525	C₂×C₄	semidirect
157. C₂²×#874	C₂×C₄	semidirect
158. C₂²×#875	C₂×C₄	semidirect
161. C₂×C₃×#418	C₂³	semidirect
162. C₂×C₃×#410	C₂³	semidirect
163. C₂×C₃×#410	C₂³	semidirect
164. C₃×#2879	C₂³	semidirect
167. C₂×#5240	C₂³	semidirect
168. C₂×#5240	C₂³	semidirect
169. #84074	C₂³	semidirect
170. C₂×#5215	C₂³	semidirect
173. C₂×#5131	C₂³	semidirect
174. #83762	C₂³	semidirect
177. C₂×#5006	C₂³	semidirect
178. C₂×#5006	C₂³	semidirect
179. C₂×#5001	C₂³	semidirect
180. C₂×#4726	D₄	semidirect
181. C₂×D₃×C₂²⋊C₈	D₄	semidirect
182. C₂×C₃×H(3,ℤ/4)	C₂³	semidirect
183. C₂×#4557	C₂³	semidirect
184. C₂×#4531	C₂³	semidirect
185. C₂×#4531	C₂³	semidirect
187. #60064	C₂×D₃	semidirect
188. C₂×#1910	C₂×D₃	semidirect
189. #20598	C₂×D₃	semidirect
190. #20584	C₂×D₃	semidirect
191. #10987	C₂×D₃	semidirect
192. #10716	C₂×D₃	semidirect
333. C₂²×ΓL(1,𝔽₂₅)	C₂×D₄	semidirect
334. C₂²×D₃×C₈	C₂×D₄	semidirect
335. #5715	C₂²⋊C₄	semidirect
336. D₃×#127	C₂²⋊C₄	semidirect
337. #5674	C₂²⋊C₄	semidirect
338. D₃×#124	C₂²⋊C₄	semidirect
349. C₂×C₃×C₂²⋊C₈	C₂×D₄	semidirect
350. C₂×#830	C₂×D₄	semidirect
351. C₂×(C₂×D₃)⋊C₈	C₂×D₄	semidirect
354. C₂×#568	C₂²×D₃	semidirect
355. C₂×#535	C₄×D₃	semidirect
356. C₂×#535	C₄×D₃	semidirect
359. C₂²×#127	C₄×D₃	semidirect
360. C₂²×#124	C₄×D₃	semidirect
362. C₂×#418	C₂²×D₃	semidirect
363. C₂×#410	C₂²×D₃	semidirect
364. C₂×#410	C₂²×D₃	semidirect
365. #2879	C₂²×D₃	semidirect
368. C₂×H(3,ℤ/4)	C₂²×D₃	semidirect
522. C₂²×C₃×C₈	C₂²×D₄	semidirect
523. C₃×#127	C₂×C₂²⋊C₄	semidirect
524. C₃×#124	C₂×C₂²⋊C₄	semidirect
527. #947	C₂×C₂²⋊C₄	semidirect
528. #940	C₂×C₂²⋊C₄	semidirect
529. #940	C₂×C₂²⋊C₄	semidirect
530. #936	C₂×C₂²⋊C₄	semidirect
533. C₂²×C₃⋊C₈	C₂²×D₄	semidirect
534. #875	C₂×C₂²⋊C₄	semidirect
535. #874	C₂×C₂²⋊C₄	semidirect
562. C₂×C₂²⋊C₈	D₃×D₄	semidirect
708. C₂²×C₈	C₂×D₃×D₄	semidirect
709. #127	D₃×C₂²⋊C₄	semidirect
710. #124	D₃×C₂²⋊C₄	semidirect
720. C₂²×D₃	#1910	semidirect
796. C₂²×C₃	C₂×#1910	semidirect
805. C₂×D₃	C₂×#1910	semidirect
833. D₃	#359513	direct (N × H)
834. C₂²	D₃×#1910	semidirect
842. C₃	C₂×#359513	semidirect

Maximal subgroups

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

subgroup	index
#72270358	2
D₃×#60064	2
#72270325	2
#72270321	2
#72270315	2
#72270312	2
#72270309	2
#72270300	2
C₃×#359513	2
D₃×#20584	2
C₂²×D₃×#535	2
D₃×#10716	2
D₃×#10987	2
D₃×#20598	2
C₂×D₃×#1910	2
C₂×#359513	3

Subgroups — D3×#359513 #72270372

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃×#359513 #72270372