Subgroups — #72248149

Order 1536.

At least 6028 conjugacy classes of subgroups; only the 945 normal subgroups are shown.

The subgroup lattice has 686 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×D₃×#120	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#77689	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#73857	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#73861	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#76895	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#77108	C₂	1	1	yes	maximal, characteristic, complemented
7	#10746889	C₂	1	1	yes	maximal, characteristic, complemented
8	#10746844	C₂	1	1	yes	maximal, characteristic, complemented
9	#10746841	C₂	1	1	yes	maximal, characteristic, complemented
10	#10733191	C₂	1	1	yes	maximal, characteristic, complemented
11	#10733189	C₂	1	1	yes	maximal, characteristic, complemented
12	#10732963	C₂	1	1	yes	maximal, characteristic, complemented
13	#10732962	C₂	1	1	yes	maximal, characteristic, complemented
14	#10732880	C₂	1	1	yes	maximal, characteristic, complemented
15	#10732879	C₂	1	1	yes	maximal, characteristic, complemented
16	#10732873	C₂	1	1	yes	maximal, characteristic, complemented
17	#10732873	C₂	1	1	yes	maximal, characteristic, complemented
18	#10727935	C₂	1	1	yes	maximal, characteristic, complemented
19	#10726771	C₂	1	1	yes	maximal, characteristic, complemented
20	#10726676	C₂	1	1	yes	maximal, characteristic, complemented
21	#10726649	C₂	1	1	yes	maximal, characteristic, complemented
22	#10726589	C₂	1	1	yes	maximal, characteristic, complemented
23	#10726564	C₂	1	1	yes	maximal, characteristic, complemented
24	#10726342	C₂	1	1	yes	maximal, characteristic, complemented
25	#10722473	C₂	1	1	yes	maximal, characteristic, complemented
26	#10722471	C₂	1	1	yes	maximal, characteristic, complemented
27	#10717952	C₂	1	1	yes	maximal, characteristic, complemented
28	#10717952	C₂	1	1	yes	maximal, characteristic, complemented
29	#10717052	C₂	1	1	yes	maximal, characteristic, complemented
30	#10717052	C₂	1	1	yes	maximal, characteristic, complemented
31	C₃×#16255	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂⁶×D₃	C₂²	1	1	yes	characteristic
33	C₂³×D₃×D₄	C₂²	1	1	yes	characteristic
34	C₂³×D₃×D₄	C₂²	1	1	yes	characteristic
35	C₂³×D₃×D₄	C₂²	1	1	yes	characteristic
36	C₂²×C₃×#120	C₂²	1	1	yes	characteristic
37	C₂²×#953	C₂²	1	1	yes	characteristic
38	C₂²×#953	C₂²	1	1	yes	characteristic, complemented
39	C₂²×#937	C₂²	1	1	yes	characteristic
40	C₂²×#937	C₂²	1	1	yes	characteristic
41	C₂²×#937	C₂²	1	1	yes	characteristic
42	C₂²×#895	C₂²	1	1	yes	characteristic, complemented
43	C₂²×#893	C₂²	1	1	yes	characteristic, complemented
44	C₂²×#884	C₂²	1	1	yes	characteristic, complemented
45	C₂²×#884	C₂²	1	1	yes	characteristic, complemented
46	C₂²×#884	C₂²	1	1	yes	characteristic, complemented
47	C₂²×#882	C₂²	1	1	yes	characteristic
48	C₂²×#882	C₂²	1	1	yes	characteristic
49	C₂²×#882	C₂²	1	1	yes	characteristic
50	C₂²×#882	C₂²	1	1	yes	characteristic
51	C₂²×#882	C₂²	1	1	yes	characteristic
52	C₂²×#882	C₂²	1	1	yes	characteristic
53	C₂²×#882	C₂²	1	1	yes	characteristic, complemented
54	C₂²×#882	C₂²	1	1	yes	characteristic, complemented
55	C₂²×#882	C₂²	1	1	yes	characteristic, complemented
56	C₂²×#882	C₂²	1	1	yes	characteristic, complemented
57	C₂²×D₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
58	C₂²×D₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
59	C₂²×D₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
60	C₂²×D₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
61	C₂×C₃×#397	C₂²	1	1	yes	characteristic, complemented
62	C₂×C₃×#394	C₂²	1	1	yes	characteristic, complemented
63	C₂×C₃×#394	C₂²	1	1	yes	characteristic, complemented
64	C₂×C₃×#379	C₂²	1	1	yes	characteristic, complemented
65	C₂×C₃×#379	C₂²	1	1	yes	characteristic, complemented
66	C₂×#5247	C₂²	1	1	yes	characteristic, complemented
67	C₂×#5223	C₂²	1	1	yes	characteristic, complemented
68	C₂×#5223	C₂²	1	1	yes	characteristic, complemented
69	C₂×#5223	C₂²	1	1	yes	characteristic, complemented
70	C₂×#5222	C₂²	1	1	yes	characteristic, complemented
71	C₂×#4993	C₂²	1	1	yes	characteristic, complemented
72	C₂×#4991	C₂²	1	1	yes	characteristic, complemented
73	C₂×#4989	C₂²	1	1	yes	characteristic, complemented
74	C₂×#4959	C₂²	1	1	yes	characteristic, complemented
75	C₂×#4959	C₂²	1	1	yes	characteristic, complemented
76	C₂×#4960	C₂²	1	1	yes	characteristic, complemented
77	C₂×#4960	C₂²	1	1	yes	characteristic, complemented
78	C₂×#4960	C₂²	1	1	yes	characteristic, complemented
79	C₂×#4956	C₂²	1	1	yes	characteristic, complemented
80	C₂×#4956	C₂²	1	1	yes	characteristic, complemented
81	C₂×#4956	C₂²	1	1	yes	characteristic, complemented
82	C₂×#4956	C₂²	1	1	yes	characteristic, complemented
83	C₂×#4956	C₂²	1	1	yes	characteristic, complemented
84	C₂×#4956	C₂²	1	1	yes	characteristic, complemented
85	C₂×#4956	C₂²	1	1	yes	characteristic, complemented
86	C₂×#4955	C₂²	1	1	yes	characteristic
87	C₂×#4955	C₂²	1	1	yes	characteristic
88	C₂×#4955	C₂²	1	1	yes	characteristic
89	C₂×#4955	C₂²	1	1	yes	characteristic
90	C₂×#4955	C₂²	1	1	yes	characteristic
91	C₂×#4955	C₂²	1	1	yes	characteristic
92	C₂×#4955	C₂²	1	1	yes	characteristic
93	C₂×#4955	C₂²	1	1	yes	characteristic
94	C₂×#4955	C₂²	1	1	yes	characteristic
95	C₂×#4955	C₂²	1	1	yes	characteristic, complemented
96	C₂×#4955	C₂²	1	1	yes	characteristic, complemented
97	C₂×#4955	C₂²	1	1	yes	characteristic, complemented
98	C₂×#4955	C₂²	1	1	yes	characteristic, complemented
99	C₂×#4955	C₂²	1	1	yes	characteristic, complemented
100	C₂×#4955	C₂²	1	1	yes	characteristic, complemented
101	C₂×#4955	C₂²	1	1	yes	characteristic, complemented
102	C₂×#4955	C₂²	1	1	yes	characteristic, complemented
103	C₂×#4955	C₂²	1	1	yes	characteristic, complemented
104	C₂×#4955	C₂²	1	1	yes	characteristic, complemented
105	C₂×#4955	C₂²	1	1	yes	characteristic, complemented
106	C₂×#4949	C₂²	1	1	yes	characteristic, complemented
107	C₂×#4952	C₂²	1	1	yes	characteristic, complemented
108	C₂×#4952	C₂²	1	1	yes	characteristic, complemented
109	C₂×#4961	C₂²	1	1	yes	characteristic, complemented
110	C₂×#4961	C₂²	1	1	yes	characteristic, complemented
111	C₂×#4961	C₂²	1	1	yes	characteristic, complemented
112	C₂×#4957	C₂²	1	1	yes	characteristic, complemented
113	C₂×#4957	C₂²	1	1	yes	characteristic, complemented
114	C₂×#4675	C₂²	1	1	yes	characteristic, complemented
115	C₂×#4671	C₂²	1	1	yes	characteristic, complemented
116	C₂×#4671	C₂²	1	1	yes	characteristic, complemented
117	C₂×#4665	C₂²	1	1	yes	characteristic, complemented
118	C₂×#4665	C₂²	1	1	yes	characteristic, complemented
119	C₂×#4665	C₂²	1	1	yes	characteristic, complemented
120	C₂×#4665	C₂²	1	1	yes	characteristic, complemented
121	C₂×#4665	C₂²	1	1	yes	characteristic, complemented
122	C₂×#4665	C₂²	1	1	yes	characteristic, complemented
123	C₂×#4665	C₂²	1	1	yes	characteristic, complemented
124	C₂×#4665	C₂²	1	1	yes	characteristic, complemented
125	C₂×#4665	C₂²	1	1	yes	characteristic, complemented
126	C₂×#4668	C₂²	1	1	yes	characteristic, complemented
127	C₂×#4667	C₂²	1	1	yes	characteristic, complemented
128	C₂×#4672	C₂²	1	1	yes	characteristic, complemented
129	C₃×#1440	C₂²	1	1	yes	characteristic, complemented
130	C₃×#1440	C₂²	1	1	yes	characteristic, complemented
131	C₃×#1439	C₂²	1	1	yes	characteristic, complemented
132	C₃×#1439	C₂²	1	1	yes	characteristic, complemented
133	C₃×#1439	C₂²	1	1	yes	characteristic, complemented
134	C₃×#1438	C₂²	1	1	yes	characteristic, complemented
135	C₃×#1438	C₂²	1	1	yes	characteristic, complemented
136	C₃×#1438	C₂²	1	1	yes	characteristic, complemented
137	C₃×#1438	C₂²	1	1	yes	characteristic, complemented
138	#72131	C₂²	1	1	yes	characteristic, complemented
139	#72131	C₂²	1	1	yes	characteristic, complemented
140	#71570	C₂²	1	1	yes	characteristic, complemented
141	#71570	C₂²	1	1	yes	characteristic, complemented
142	#71570	C₂²	1	1	yes	characteristic, complemented
143	#71550	C₂²	1	1	yes	characteristic, complemented
144	#71550	C₂²	1	1	yes	characteristic, complemented
145	#71550	C₂²	1	1	yes	characteristic, complemented
146	#71550	C₂²	1	1	yes	characteristic, complemented
147	#71550	C₂²	1	1	yes	characteristic, complemented
148	#71550	C₂²	1	1	yes	characteristic, complemented
149	#71550	C₂²	1	1	yes	characteristic, complemented
150	#71550	C₂²	1	1	yes	characteristic, complemented
151	#71550	C₂²	1	1	yes	characteristic, complemented
152	#71550	C₂²	1	1	yes	characteristic, complemented
153	#71549	C₂²	1	1	yes	characteristic, complemented
154	#71549	C₂²	1	1	yes	characteristic, complemented
155	#71549	C₂²	1	1	yes	characteristic, complemented
156	#71548	C₂²	1	1	yes	characteristic, complemented
157	#71547	C₂²	1	1	yes	characteristic, complemented
158	#71547	C₂²	1	1	yes	characteristic, complemented
159	#71547	C₂²	1	1	yes	characteristic, complemented
160	#71545	C₂²	1	1	yes	characteristic, complemented
161	#71545	C₂²	1	1	yes	characteristic, complemented
162	#69429	C₂²	1	1	yes	characteristic, complemented
163	#69429	C₂²	1	1	yes	characteristic, complemented
164	#69429	C₂²	1	1	yes	characteristic, complemented
165	#69429	C₂²	1	1	yes	characteristic, complemented
166	#69428	C₂²	1	1	yes	characteristic, complemented
167	#69428	C₂²	1	1	yes	characteristic, complemented
168	#69428	C₂²	1	1	yes	characteristic, complemented
169	#69428	C₂²	1	1	yes	characteristic, complemented
170	#69428	C₂²	1	1	yes	characteristic, complemented
171	#69427	C₂²	1	1	yes	characteristic, complemented
172	#69427	C₂²	1	1	yes	characteristic, complemented
173	#69426	C₂²	1	1	yes	characteristic, complemented
174	#69426	C₂²	1	1	yes	characteristic, complemented
175	#69426	C₂²	1	1	yes	characteristic, complemented
176	#69426	C₂²	1	1	yes	characteristic, complemented
177	#69426	C₂²	1	1	yes	characteristic, complemented
178	#69426	C₂²	1	1	yes	characteristic, complemented
179	(C₂×D₃)⋊#95	C₂²	1	1	yes	characteristic, complemented
180	(C₂×D₃)⋊#95	C₂²	1	1	yes	characteristic, complemented
181	(C₂×D₃)⋊#95	C₂²	1	1	yes	characteristic, complemented
182	(C₂×D₃)⋊#95	C₂²	1	1	yes	characteristic, complemented
183	(C₂×D₃)⋊#95	C₂²	1	1	yes	characteristic, complemented
184	(C₂×D₃)⋊#95	C₂²	1	1	yes	characteristic, complemented
185	#69408	C₂²	1	1	yes	characteristic, complemented
186	#69408	C₂²	1	1	yes	characteristic, complemented
187	#16255	D₃	1	1	yes	characteristic, complemented
188	C₂⁶×C₃	C₂³	1	1	yes	characteristic
189	C₂⁵×D₃	C₂³	1	1	yes	characteristic
190	C₂⁵×D₃	C₂³	1	1	yes	characteristic
191	C₂⁵×D₃	C₂³	1	1	yes	characteristic
192	C₂⁵×D₃	C₂³	1	1	yes	characteristic
193	C₂⁵×D₃	C₂³	1	1	yes	characteristic
194	C₂⁵×D₃	C₂³	1	1	yes	characteristic
195	C₂⁵×D₃	C₂³	1	1	yes	characteristic
196	C₂³×C₃×D₄	C₂³	1	1	yes	characteristic
197	C₂³×C₃×D₄	C₂³	1	1	yes	characteristic
198	C₂³×C₃×D₄	C₂³	1	1	yes	characteristic
199	C₂³×#67	C₂³	1	1	yes	characteristic
200	C₂³×#67	C₂³	1	1	yes	characteristic
201	C₂³×#67	C₂³	1	1	yes	characteristic
202	C₂³×#67	C₂³	1	1	yes	characteristic
203	C₂³×#67	C₂³	1	1	yes	characteristic
204	C₂³×#67	C₂³	1	1	yes	characteristic
205	C₂³×#67	C₂³	1	1	yes	characteristic
206	C₂³×#67	C₂³	1	1	yes	characteristic
207	C₂³×#67	C₂³	1	1	yes	characteristic
208	C₂³×#67	C₂³	1	1	yes	characteristic, complemented
209	C₂²×D₃×D₄	D₄	1	8	yes	complemented
210	C₂³×D₁₂	C₂³	1	1	yes	characteristic
211	C₂³×D₁₂	C₂³	1	1	yes	characteristic
212	C₂³×D₁₂	C₂³	1	1	yes	characteristic
213	C₂³×D₁₂	C₂³	1	1	yes	characteristic
214	C₂³×D₁₂	C₂³	1	1	yes	characteristic
215	C₂³×D₁₂	C₂³	1	1	yes	characteristic
216	C₂³×D₁₂	C₂³	1	1	yes	characteristic
217	C₂³×D₁₂	C₂³	1	1	yes	characteristic, complemented
218	C₂³×C₄×D₃	C₂³	1	1	yes	characteristic
219	C₂³×C₄×D₃	C₂³	1	1	yes	characteristic
220	C₂³×C₄×D₃	C₂³	1	1	yes	characteristic
221	C₂³×C₄×D₃	C₂³	1	1	yes	characteristic, complemented
222	C₂³×C₄×D₃	C₂³	1	1	yes	characteristic, complemented
223	C₂³×C₄×D₃	C₂³	1	1	yes	characteristic, complemented
224	C₂²×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic, complemented
225	C₂²×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic, complemented
226	C₂²×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
227	C₂²×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
228	C₂²×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
229	C₂²×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
230	C₂²×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
231	C₂²×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
232	C₂²×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
233	C₂²×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
234	C₂²×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
235	C₂²×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
236	C₂²×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
237	C₂²×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
238	C₂²×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
239	C₂²×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
240	C₂²×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
241	C₂²×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic, complemented
242	C₂²×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic, complemented
243	C₂²×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic, complemented
244	C₂²×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic, complemented
245	C₂×#953	D₄	1	8	yes	complemented
246	C₂²×#217	C₂³	1	1	yes	characteristic
247	C₂²×#217	C₂³	1	1	yes	characteristic
248	C₂²×#217	C₂³	1	1	yes	characteristic
249	C₂²×#217	C₂³	1	1	yes	characteristic
250	C₂²×#217	C₂³	1	1	yes	characteristic
251	C₂²×#217	C₂³	1	1	yes	characteristic
252	C₂²×#217	C₂³	1	1	yes	characteristic
253	C₂²×#217	C₂³	1	1	yes	characteristic
254	C₂²×#217	C₂³	1	1	yes	characteristic
255	C₂²×#217	C₂³	1	1	yes	characteristic
256	C₂²×#217	C₂³	1	1	yes	characteristic
257	C₂²×#217	C₂³	1	1	yes	characteristic
258	C₂²×#217	C₂³	1	1	yes	characteristic, complemented
259	C₂²×#217	C₂³	1	1	yes	characteristic, complemented
260	C₂²×#217	C₂³	1	1	yes	characteristic, complemented
261	C₂²×(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
262	C₂²×(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
263	C₂²×(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
264	C₂²×(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
265	C₂²×(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
266	C₂²×(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
267	C₂²×(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
268	C₂²×(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
269	C₂²×(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
270	C₂²×(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
271	C₂²×(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
272	C₂²×(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
273	C₂²×(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
274	C₂²×(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
275	C₂²×(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
276	C₂²×(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
277	C₂²×(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
278	C₂²×(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
279	C₂²×(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
280	C₂²×(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
281	C₂²×(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
282	C₂²×(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
283	C₂²×(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
284	C₂²×(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
285	C₂²×(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
286	C₂²×(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
287	C₂²×(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
288	C₂²×(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
289	C₂²×(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
290	C₂²×(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
291	C₂²×(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
292	C₂²×(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
293	C₂²×(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
294	C₂²×(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
295	C₂²×(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic, complemented
296	C₂²×(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic, complemented
297	C₂²×(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic, complemented
298	C₂²×(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic, complemented
299	C₂²×(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic, complemented
300	C₂²×(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic, complemented
301	C₂²×(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic, complemented
302	C₂²×(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic, complemented
303	C₂²×(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic, complemented
304	C₂²×(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic, complemented
305	C₂²×C₄⋊Dic₃	C₂³	1	1	yes	characteristic, complemented
306	C₂²×Dic₃⋊C₄	C₂³	1	1	yes	characteristic, complemented
307	C₂²×Dic₃⋊C₄	C₂³	1	1	yes	characteristic, complemented
308	C₂²×Dic₃⋊C₄	C₂³	1	1	yes	characteristic, complemented
309	C₂²×Dic₃⋊C₄	C₂³	1	1	yes	characteristic, complemented
310	C₂²×C₄×Dic₃	C₂³	1	1	yes	characteristic, complemented
311	C₂×#882	D₄	1	8	yes	complemented
312	C₂×#882	D₄	1	8	yes	complemented
313	C₂×C₃×#95	C₂³	1	1	yes	characteristic, complemented
314	C₂×C₃×#95	C₂³	1	1	yes	characteristic, complemented
315	C₂×C₃×#95	C₂³	1	1	yes	characteristic, complemented
316	C₂×C₃×#95	C₂³	1	1	yes	characteristic, complemented
317	C₂×C₃×#95	C₂³	1	1	yes	characteristic, complemented
318	C₂×C₃×#95	C₂³	1	1	yes	characteristic, complemented
319	C₂×C₃×#95	C₂³	1	1	yes	characteristic, complemented
320	C₂×C₃×#95	C₂³	1	1	yes	characteristic, complemented
321	C₂×C₃×#95	C₂³	1	1	yes	characteristic, complemented
322	C₂×C₃×#95	C₂³	1	1	yes	characteristic, complemented
323	C₂×C₃⋊#95	C₂³	1	1	yes	characteristic, complemented
324	C₂×C₃⋊#95	C₂³	1	1	yes	characteristic, complemented
325	C₂×C₃⋊#95	C₂³	1	1	yes	characteristic, complemented
326	C₂×C₃⋊#95	C₂³	1	1	yes	characteristic, complemented
327	C₂×C₃⋊#95	C₂³	1	1	yes	characteristic, complemented
328	C₂×C₃⋊#95	C₂³	1	1	yes	characteristic, complemented
329	C₂×C₃⋊#95	C₂³	1	1	yes	characteristic, complemented
330	C₂×C₃⋊#95	C₂³	1	1	yes	characteristic, complemented
331	C₂×C₃⋊#95	C₂³	1	1	yes	characteristic, complemented
332	C₂×C₃⋊#95	C₂³	1	1	yes	characteristic, complemented
333	C₂×C₃⋊#95	C₂³	1	1	yes	characteristic, complemented
334	C₂×C₃⋊#95	C₂³	1	1	yes	characteristic, complemented
335	C₂×C₃⋊#95	C₂³	1	1	yes	characteristic, complemented
336	C₂×C₃⋊#95	C₂³	1	1	yes	characteristic, complemented
337	C₂×C₃⋊#95	C₂³	1	1	yes	characteristic, complemented
338	C₂×C₃⋊#95	C₂³	1	1	yes	characteristic, complemented
339	C₂×C₃⋊#95	C₂³	1	1	yes	characteristic, complemented
340	C₂×C₃⋊#95	C₂³	1	1	yes	characteristic, complemented
341	C₂×C₃⋊#95	C₂³	1	1	yes	characteristic, complemented
342	C₂×C₃⋊#95	C₂³	1	1	yes	characteristic, complemented
343	C₂×C₃⋊#95	C₂³	1	1	yes	characteristic, complemented
344	C₂×C₃⋊#95	C₂³	1	1	yes	characteristic, complemented
345	C₂×C₃⋊#95	C₂³	1	1	yes	characteristic, complemented
346	C₂×C₃⋊#95	C₂³	1	1	yes	characteristic, complemented
347	C₂²×#120	C₂×D₃	1	1	yes	characteristic
348	C₂×#397	C₂×D₃	1	1	yes	characteristic, complemented
349	C₂×#394	C₂×D₃	1	1	yes	characteristic, complemented
350	C₂×#394	C₂×D₃	1	1	yes	characteristic, complemented
351	C₂×#379	C₂×D₃	1	1	yes	characteristic, complemented
352	C₂×#379	C₂×D₃	1	1	yes	characteristic, complemented
353	#1440	C₂×D₃	1	1	yes	characteristic, complemented
354	#1440	C₂×D₃	1	1	yes	characteristic, complemented
355	#1439	C₂×D₃	1	1	yes	characteristic, complemented
356	#1439	C₂×D₃	1	1	yes	characteristic, complemented
357	#1439	C₂×D₃	1	1	yes	characteristic, complemented
358	#1438	C₂×D₃	1	1	yes	characteristic, complemented
359	#1438	C₂×D₃	1	1	yes	characteristic, complemented
360	#1438	C₂×D₃	1	1	yes	characteristic, complemented
361	#1438	C₂×D₃	1	1	yes	characteristic, complemented
362	C₂⁵×C₃	C₂×D₄	1	4	yes	—
363	C₂⁵×C₃	C₂⁴	1	1	yes	characteristic
364	C₂⁵×C₃	C₂⁴	1	1	yes	characteristic
365	C₂⁵×C₃	C₂⁴	1	1	yes	characteristic
366	C₂⁵×C₃	C₂⁴	1	1	yes	characteristic
367	C₂⁴×D₃	C₂×D₄	1	4	yes	—
368	C₂⁴×D₃	C₂×D₄	1	4	yes	—
369	C₂⁴×D₃	C₂×D₄	1	4	yes	—
370	C₂⁴×D₃	C₂×D₄	1	4	yes	—
371	C₂⁴×D₃	#41	1	4	yes	—
372	C₂⁴×D₃	C₂⁴	1	1	yes	characteristic
373	C₂⁴×D₃	C₂⁴	1	1	yes	characteristic
374	C₂⁴×D₃	C₂⁴	1	1	yes	characteristic
375	C₂⁴×D₃	C₂⁴	1	1	yes	characteristic
376	C₂⁴×D₃	C₂⁴	1	1	yes	characteristic
377	C₂⁴×D₃	C₂⁴	1	1	yes	characteristic
378	C₂²×C₃×D₄	C₂×D₄	1	4	yes	—
379	C₂³×C₃×C₄	C₂⁴	1	1	yes	characteristic
380	C₂³×C₃×C₄	C₂⁴	1	1	yes	characteristic
381	C₂³×C₃×C₄	C₂⁴	1	1	yes	characteristic
382	C₂³×C₃×C₄	C₂⁴	1	1	yes	characteristic
383	C₂³×C₃×C₄	C₂⁴	1	1	yes	characteristic
384	C₂³×C₃×C₄	C₂⁴	1	1	yes	characteristic
385	C₂³×C₃×C₄	C₂⁴	1	1	yes	characteristic
386	C₂³×C₃×C₄	C₂⁴	1	1	yes	characteristic
387	C₂³×C₃×C₄	C₂⁴	1	1	yes	characteristic
388	C₂³×C₃×C₄	C₂⁴	1	1	yes	characteristic
389	C₂³×C₃×C₄	C₂⁴	1	1	yes	characteristic
390	C₂²×#67	C₂×D₄	1	4	yes	—
391	C₂²×#67	C₂×D₄	1	4	yes	—
392	C₂²×#67	C₂×D₄	1	4	yes	—
393	C₂²×#67	C₂×D₄	1	4	yes	—
394	C₂²×#67	C₂×D₄	1	4	yes	—
395	C₂²×#67	C₂×D₄	1	4	yes	—
396	C₂²×#67	C₂×D₄	1	4	yes	complemented
397	C₂³×Dic₃	C₂⁴	1	1	yes	characteristic
398	C₂³×Dic₃	C₂⁴	1	1	yes	characteristic
399	C₂³×Dic₃	C₂⁴	1	1	yes	characteristic
400	C₂³×Dic₃	C₂⁴	1	1	yes	characteristic
401	C₂³×Dic₃	C₂⁴	1	1	yes	characteristic
402	C₂³×Dic₃	C₂⁴	1	1	yes	characteristic
403	C₂³×Dic₃	C₂⁴	1	1	yes	characteristic
404	C₂³×Dic₃	C₂⁴	1	1	yes	characteristic
405	C₂³×Dic₃	C₂⁴	1	1	yes	characteristic
406	C₂³×Dic₃	C₂⁴	1	1	yes	characteristic
407	C₂²×D₁₂	C₂×D₄	1	4	yes	—
408	C₂²×D₁₂	C₂×D₄	1	4	yes	—
409	C₂²×D₁₂	C₂×D₄	1	4	yes	—
410	C₂²×D₁₂	C₂×D₄	1	4	yes	—
411	C₂²×D₁₂	C₂×D₄	1	4	yes	complemented
412	C₂²×C₄×D₃	C₂×D₄	1	4	yes	—
413	C₂×C₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
414	C₂×C₃×C₂²⋊C₄	C₂×D₄	1	4	yes	complemented
415	C₂×#217	C₂×D₄	1	4	yes	—
416	C₂×#217	C₂×D₄	1	4	yes	—
417	C₂×#217	C₂×D₄	1	4	yes	—
418	C₂×(C₂×D₃)⋊C₄	C₂×D₄	1	4	yes	—
419	C₂×(C₂×D₃)⋊C₄	C₂×D₄	1	4	yes	—
420	C₂×(C₂×D₃)⋊C₄	C₂×D₄	1	4	yes	—
421	C₂×(C₂×D₃)⋊C₄	C₂×D₄	1	4	yes	complemented
422	C₂⁶	C₂²×D₃	1	1	yes	characteristic
423	C₂³×D₄	C₂²×D₃	1	1	yes	characteristic
424	C₂³×D₄	C₂²×D₃	1	1	yes	characteristic
425	C₂³×D₄	C₂²×D₃	1	1	yes	characteristic
426	C₂²×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic, complemented
427	C₂²×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic, complemented
428	C₂²×C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
429	C₂²×C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
430	C₂²×C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
431	C₂²×C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
432	C₂²×C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
433	C₂²×C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
434	C₂²×C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
435	C₂²×C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
436	C₂²×C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
437	C₂²×C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
438	C₂²×C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
439	C₂²×C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
440	C₂²×C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
441	C₂²×C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
442	C₂²×C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
443	C₂²×C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic, complemented
444	C₂²×C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic, complemented
445	C₂²×C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic, complemented
446	C₂²×C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic, complemented
447	C₂×#95	C₂²×D₃	1	1	yes	characteristic, complemented
448	C₂×#95	C₂²×D₃	1	1	yes	characteristic, complemented
449	C₂×#95	C₂²×D₃	1	1	yes	characteristic, complemented
450	C₂×#95	C₂²×D₃	1	1	yes	characteristic, complemented
451	C₂×#95	C₂²×D₃	1	1	yes	characteristic, complemented
452	C₂×#95	C₂²×D₃	1	1	yes	characteristic, complemented
453	C₂×#95	C₂²×D₃	1	1	yes	characteristic, complemented
454	C₂×#95	C₂²×D₃	1	1	yes	characteristic, complemented
455	C₂×#95	C₂²×D₃	1	1	yes	characteristic, complemented
456	C₂×#95	C₂²×D₃	1	1	yes	characteristic, complemented
457	C₂⁴×C₃	C₂²×D₄	1	2	yes	—
458	C₂⁴×C₃	C₂²×D₄	1	2	yes	—
459	C₂⁴×C₃	C₂²×D₄	1	2	yes	—
460	C₂⁴×C₃	C₂²×D₄	1	2	yes	—
461	C₂⁴×C₃	C₂²×D₄	1	2	yes	—
462	C₂⁴×C₃	C₂²×D₄	1	2	yes	—
463	C₂⁴×C₃	C₂²×D₄	1	2	yes	—
464	C₂⁴×C₃	C₂×#41	1	2	yes	—
465	C₂⁴×C₃	H(5,𝔽₂)	1	2	yes	—
466	C₂⁴×C₃	H(5,𝔽₂)	1	2	yes	—
467	C₂⁴×C₃	C₂⁵	1	1	yes	characteristic
468	C₂³×D₃	C₂²×D₄	1	2	yes	—
469	C₂³×D₃	C₂²×D₄	1	2	yes	—
470	C₂³×D₃	C₂²×D₄	1	2	yes	—
471	C₂³×D₃	C₂²×D₄	1	2	yes	—
472	C₂³×D₃	C₂²×D₄	1	2	yes	—
473	C₂³×D₃	C₂²×D₄	1	2	yes	—
474	C₂³×D₃	C₂²×D₄	1	2	yes	—
475	C₂³×D₃	C₂²×D₄	1	2	yes	—
476	C₂³×D₃	C₂²×D₄	1	2	yes	—
477	C₂³×D₃	C₂²×D₄	1	2	yes	—
478	C₂³×D₃	C₂×#41	1	2	yes	—
479	C₂³×D₃	C₂×#41	1	2	yes	—
480	C₂³×D₃	H(5,𝔽₂)	1	2	yes	—
481	C₂³×D₃	H(5,𝔽₂)	1	2	yes	—
482	C₂³×D₃	H(5,𝔽₂)	1	2	yes	—
483	C₂³×D₃	H(5,𝔽₂)	1	2	yes	—
484	C₂³×D₃	H(5,𝔽₂)	1	2	yes	—
485	C₂³×D₃	H(5,𝔽₂)	1	2	yes	—
486	C₂³×D₃	H(5,𝔽₂)	1	2	yes	—
487	C₂³×D₃	H(5,𝔽₂)	1	2	yes	—
488	C₂²×C₃×C₄	C₂²×D₄	1	2	yes	—
489	C₂²×C₃×C₄	C₂²×D₄	1	2	yes	—
490	C₂²×C₃×C₄	C₂²×D₄	1	2	yes	—
491	C₂²×C₃×C₄	C₂²×D₄	1	2	yes	—
492	C₂²×C₃×C₄	C₂²×D₄	1	2	yes	—
493	C₂×#67	#120	1	16	yes	complemented
494	C₂²×Dic₃	C₂²×D₄	1	2	yes	—
495	C₂²×Dic₃	C₂²×D₄	1	2	yes	—
496	C₂²×Dic₃	C₂²×D₄	1	2	yes	—
497	C₂²×Dic₃	C₂²×D₄	1	2	yes	—
498	C₂²×Dic₃	C₂²×D₄	1	2	yes	—
499	C₂²×Dic₃	C₂²×D₄	1	2	yes	—
500	C₂⁵	D₃×D₄	1	4	yes	—
501	C₂⁵	C₂³×D₃	1	1	yes	characteristic
502	C₂⁵	C₂³×D₃	1	1	yes	characteristic
503	C₂⁵	C₂³×D₃	1	1	yes	characteristic
504	C₂⁵	C₂³×D₃	1	1	yes	characteristic
505	C₂²×D₄	D₃×D₄	1	4	yes	—
506	C₂³×C₄	C₂³×D₃	1	1	yes	characteristic
507	C₂³×C₄	C₂³×D₃	1	1	yes	characteristic
508	C₂³×C₄	C₂³×D₃	1	1	yes	characteristic
509	C₂³×C₄	C₂³×D₃	1	1	yes	characteristic
510	C₂³×C₄	C₂³×D₃	1	1	yes	characteristic
511	C₂³×C₄	C₂³×D₃	1	1	yes	characteristic
512	C₂³×C₄	C₂³×D₃	1	1	yes	characteristic
513	C₂³×C₄	C₂³×D₃	1	1	yes	characteristic
514	C₂³×C₄	C₂³×D₃	1	1	yes	characteristic
515	C₂³×C₄	C₂³×D₃	1	1	yes	characteristic
516	C₂³×C₄	C₂³×D₃	1	1	yes	characteristic
517	C₂×C₂²⋊C₄	D₃×D₄	1	4	yes	—
518	C₂×C₂²⋊C₄	D₃×D₄	1	4	yes	complemented
519	C₂³×C₃	C₂×#120	1	4	yes	—
520	C₂³×C₃	D₄²	1	4	yes	—
521	C₂³×C₃	#546	1	4	yes	—
522	C₂³×C₃	C₂³×D₄	1	1	yes	characteristic
523	C₂³×C₃	C₂³×D₄	1	1	yes	characteristic
524	C₂³×C₃	C₂³×D₄	1	1	yes	characteristic
525	C₂³×C₃	C₂³×D₄	1	1	yes	characteristic
526	C₂³×C₃	C₂²×#41	1	1	yes	characteristic
527	C₂³×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
528	C₂³×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
529	C₂³×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
530	C₂³×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
531	C₂³×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
532	C₂³×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
533	C₂³×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
534	C₂³×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
535	C₂³×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
536	C₂³×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
537	C₂²×D₃	C₂×#120	1	4	yes	—
538	C₂²×D₃	#534	1	4	yes	—
539	C₂²×D₃	#534	1	4	yes	—
540	C₂²×D₃	#534	1	4	yes	—
541	C₂²×D₃	#538	1	4	yes	—
542	C₂²×D₃	D₄²	1	4	yes	—
543	C₂²×D₃	D₄²	1	4	yes	—
544	C₂²×D₃	#546	1	4	yes	—
545	C₂²×D₃	#546	1	4	yes	—
546	C₂²×D₃	#546	1	4	yes	—
547	C₂²×D₃	#560	1	4	yes	—
548	C₂×Dic₃	C₂×#120	1	4	yes	—
549	C₂⁴	C₂×D₃×D₄	1	2	yes	—
550	C₂⁴	C₂×D₃×D₄	1	2	yes	—
551	C₂⁴	C₂×D₃×D₄	1	2	yes	—
552	C₂⁴	C₂×D₃×D₄	1	2	yes	—
553	C₂⁴	C₂×D₃×D₄	1	2	yes	—
554	C₂⁴	C₂×D₃×D₄	1	2	yes	—
555	C₂⁴	C₂×D₃×D₄	1	2	yes	—
556	C₂⁴	D₃×#41	1	2	yes	—
557	C₂⁴	#1009	1	2	yes	—
558	C₂⁴	#1009	1	2	yes	—
559	C₂⁴	C₂⁴×D₃	1	1	yes	characteristic
560	C₂²×C₄	C₂×D₃×D₄	1	2	yes	—
561	C₂²×C₄	C₂×D₃×D₄	1	2	yes	—
562	C₂²×C₄	C₂×D₃×D₄	1	2	yes	—
563	C₂²×C₄	C₂×D₃×D₄	1	2	yes	—
564	C₂²×C₄	C₂×D₃×D₄	1	2	yes	—
565	C₂²×C₃	C₂²×#120	1	1	yes	characteristic
566	C₂²×C₃	C₂×#534	1	1	yes	characteristic
567	C₂²×C₃	C₂×#534	1	1	yes	characteristic
568	C₂²×C₃	C₂×#534	1	1	yes	characteristic
569	C₂²×C₃	C₂×#538	1	1	yes	characteristic
570	C₂²×C₃	C₂×D₄²	1	1	yes	characteristic
571	C₂²×C₃	C₂×D₄²	1	1	yes	characteristic
572	C₂²×C₃	C₂×D₄²	1	1	yes	characteristic
573	C₂²×C₃	C₂×#546	1	1	yes	characteristic
574	C₂²×C₃	C₂×#546	1	1	yes	characteristic
575	C₂²×C₃	C₂×#546	1	1	yes	characteristic
576	C₂²×C₃	C₂×#546	1	1	yes	characteristic
577	C₂²×C₃	#3484	1	1	yes	characteristic
578	C₂²×C₃	#3484	1	1	yes	characteristic
579	C₂²×C₃	#3484	1	1	yes	characteristic
580	C₂²×C₃	#3484	1	1	yes	characteristic
581	C₂²×C₃	#3484	1	1	yes	characteristic
582	C₂²×C₃	#3484	1	1	yes	characteristic
583	C₂²×C₃	#3484	1	1	yes	characteristic
584	C₂²×C₃	#3484	1	1	yes	characteristic
585	C₂²×C₃	#3484	1	1	yes	characteristic
586	C₂²×C₃	#3484	1	1	yes	characteristic
587	C₂²×C₃	#3484	1	1	yes	characteristic
588	C₂²×C₃	#3484	1	1	yes	characteristic
589	C₂²×C₃	#3490	1	1	yes	characteristic
590	C₂²×C₃	#3490	1	1	yes	characteristic
591	C₂²×C₃	C₂×#560	1	1	yes	characteristic
592	C₂²×C₃	#3532	1	1	yes	characteristic
593	C₂²×C₃	#3532	1	1	yes	characteristic
594	C₂²×C₃	#3532	1	1	yes	characteristic
595	C₂²×C₃	#3532	1	1	yes	characteristic
596	C₂²×C₃	#3532	1	1	yes	characteristic
597	C₂²×C₃	#3532	1	1	yes	characteristic
598	C₂²×C₃	#3532	1	1	yes	characteristic
599	C₂²×C₃	#3532	1	1	yes	characteristic
600	C₂×D₃	#2668	1	8	yes	complemented
601	C₂³	D₃×#120	1	4	yes	—
602	C₂³	#5609	1	4	yes	—
603	C₂³	#5654	1	4	yes	—
604	C₂³	C₂²×D₃×D₄	1	1	yes	characteristic
605	C₂³	C₂²×D₃×D₄	1	1	yes	characteristic
606	C₂³	C₂²×D₃×D₄	1	1	yes	characteristic
607	C₂³	C₂²×D₃×D₄	1	1	yes	characteristic
608	C₂³	C₂×D₃×#41	1	1	yes	characteristic
609	C₂³	C₂×#1009	1	1	yes	characteristic
610	C₂³	C₂×#1009	1	1	yes	characteristic
611	C₂³	D₃×H(5,𝔽₂)	1	1	yes	characteristic
612	C₂³	D₃×H(5,𝔽₂)	1	1	yes	characteristic
613	C₂³	D₃×H(5,𝔽₂)	1	1	yes	characteristic
614	C₂³	D₃×H(5,𝔽₂)	1	1	yes	characteristic
615	C₂³	D₃×H(5,𝔽₂)	1	1	yes	characteristic
616	C₂³	D₃×H(5,𝔽₂)	1	1	yes	characteristic
617	C₂³	D₃×H(5,𝔽₂)	1	1	yes	characteristic
618	C₂³	D₃×H(5,𝔽₂)	1	1	yes	characteristic
619	C₂×C₃	#34980	1	1	yes	characteristic
620	C₂×C₃	D₄×#120	1	1	yes	characteristic
621	C₂×C₃	#36152	1	1	yes	characteristic
622	C₂×C₃	#36702	1	1	yes	characteristic
623	C₂×C₃	#37644	1	1	yes	characteristic
624	C₂×C₃	#37644	1	1	yes	characteristic
625	C₂×C₃	#37644	1	1	yes	characteristic
626	C₂×C₃	#37660	1	1	yes	characteristic
627	C₂×C₃	#37660	1	1	yes	characteristic
628	C₂×C₃	#37832	1	1	yes	characteristic
629	C₂×C₃	#45438	1	1	yes	characteristic
630	C₂×C₃	#45438	1	1	yes	characteristic
631	C₂×C₃	C₂×#2668	1	1	yes	characteristic
632	C₂×C₃	#58991	1	1	yes	characteristic
633	C₂×C₃	#58991	1	1	yes	characteristic
634	C₂²	C₂×D₃×#120	1	1	yes	characteristic
635	C₂²	C₂×#5609	1	1	yes	characteristic
636	C₂²	C₂×#5654	1	1	yes	characteristic
637	C₂²	D₃×#534	1	1	yes	characteristic
638	C₂²	D₃×#534	1	1	yes	characteristic
639	C₂²	D₃×#534	1	1	yes	characteristic
640	C₂²	#86308	1	1	yes	characteristic
641	C₂²	#86308	1	1	yes	characteristic
642	C₂²	#86308	1	1	yes	characteristic
643	C₂²	#86308	1	1	yes	characteristic
644	C₂²	#86330	1	1	yes	characteristic
645	C₂²	#86330	1	1	yes	characteristic
646	C₂²	#86330	1	1	yes	characteristic
647	C₂²	D₃×#538	1	1	yes	characteristic
648	C₂²	#86414	1	1	yes	characteristic
649	C₂²	#86418	1	1	yes	characteristic
650	C₂²	#86418	1	1	yes	characteristic
651	C₂²	#86418	1	1	yes	characteristic
652	C₂²	#86418	1	1	yes	characteristic
653	C₂²	D₃×D₄²	1	1	yes	characteristic
654	C₂²	D₃×D₄²	1	1	yes	characteristic
655	C₂²	D₃×#546	1	1	yes	characteristic
656	C₂²	D₃×#546	1	1	yes	characteristic
657	C₂²	D₃×#546	1	1	yes	characteristic
658	C₂²	#86662	1	1	yes	characteristic
659	C₂²	#86662	1	1	yes	characteristic
660	C₂²	#86662	1	1	yes	characteristic
661	C₂²	#86662	1	1	yes	characteristic
662	C₂²	#86662	1	1	yes	characteristic
663	C₂²	#86815	1	1	yes	characteristic
664	C₂²	#86818	1	1	yes	characteristic
665	C₂²	D₃×#560	1	1	yes	characteristic
666	C₂²	#87080	1	1	yes	characteristic
667	C₂²	#87080	1	1	yes	characteristic
668	C₂²	#87090	1	1	yes	characteristic
669	C₃	#846041	1	1	yes	characteristic, complemented, Sylow
670	C₂	#10967717	1	1	yes	characteristic
671	C₂	#10990482	1	1	yes	characteristic
672	C₂	#10991600	1	1	yes	characteristic
673	C₂	#11001921	1	1	yes	characteristic
674	C₂	#11023811	1	1	yes	characteristic
675	C₂	#11023811	1	1	yes	characteristic
676	C₂	#11023813	1	1	yes	characteristic
677	C₂	#11024179	1	1	yes	characteristic
678	C₂	#11024181	1	1	yes	characteristic
679	C₂	#11028519	1	1	yes	characteristic
680	C₂	#11235212	1	1	yes	characteristic
681	C₂	#11235219	1	1	yes	characteristic
682	C₂	D₃×#2668	1	1	yes	characteristic
683	C₂	#11632809	1	1	yes	characteristic
684	C₂	#11632812	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂⁴	C₂⁴×D₃
commutator, socle, cosocle	C₂⁴×C₃	C₂⁵
Fitting	C₃×#16255	C₂
hypercenter	#16255	D₃
hypocenter	C₃	#846041
LCS	G ▷ C₂⁴×C₃ ▷ C₃
UCS	C₁ ◁ C₂⁴ ◁ #16255

Complements

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

N	H ≅ G/N	type
1. C₂²×D₃×#120	C₂	semidirect
2. C₂×#77689	C₂	semidirect
3. C₂×#73857	C₂	semidirect
4. C₂×#73861	C₂	semidirect
5. C₂×#76895	C₂	semidirect
6. C₂×#77108	C₂	semidirect
7. #10746889	C₂	semidirect
8. #10746844	C₂	semidirect
9. #10746841	C₂	semidirect
10. #10733191	C₂	semidirect
11. #10733189	C₂	semidirect
12. #10732963	C₂	semidirect
13. #10732962	C₂	semidirect
14. #10732880	C₂	semidirect
15. #10732879	C₂	semidirect
16. #10732873	C₂	semidirect
17. #10732873	C₂	semidirect
18. #10727935	C₂	semidirect
19. #10726771	C₂	semidirect
20. #10726676	C₂	semidirect
21. #10726649	C₂	semidirect
22. #10726589	C₂	semidirect
23. #10726564	C₂	semidirect
24. #10726342	C₂	semidirect
25. #10722473	C₂	semidirect
26. #10722471	C₂	semidirect
27. #10717952	C₂	semidirect
28. #10717952	C₂	semidirect
29. #10717052	C₂	semidirect
30. #10717052	C₂	semidirect
31. C₃×#16255	C₂	semidirect
38. C₂²×#953	C₂²	semidirect
42. C₂²×#895	C₂²	semidirect
43. C₂²×#893	C₂²	semidirect
44. C₂²×#884	C₂²	semidirect
45. C₂²×#884	C₂²	semidirect
46. C₂²×#884	C₂²	semidirect
53. C₂²×#882	C₂²	semidirect
54. C₂²×#882	C₂²	semidirect
55. C₂²×#882	C₂²	semidirect
56. C₂²×#882	C₂²	semidirect
60. C₂²×D₃×C₂²⋊C₄	C₂²	semidirect
61. C₂×C₃×#397	C₂²	semidirect
62. C₂×C₃×#394	C₂²	semidirect
63. C₂×C₃×#394	C₂²	semidirect
64. C₂×C₃×#379	C₂²	semidirect
65. C₂×C₃×#379	C₂²	semidirect
66. C₂×#5247	C₂²	semidirect
67. C₂×#5223	C₂²	semidirect
68. C₂×#5223	C₂²	semidirect
69. C₂×#5223	C₂²	semidirect
70. C₂×#5222	C₂²	semidirect
71. C₂×#4993	C₂²	semidirect
72. C₂×#4991	C₂²	semidirect
73. C₂×#4989	C₂²	semidirect
74. C₂×#4959	C₂²	semidirect
75. C₂×#4959	C₂²	semidirect
76. C₂×#4960	C₂²	semidirect
77. C₂×#4960	C₂²	semidirect
78. C₂×#4960	C₂²	semidirect
79. C₂×#4956	C₂²	semidirect
80. C₂×#4956	C₂²	semidirect
81. C₂×#4956	C₂²	semidirect
82. C₂×#4956	C₂²	semidirect
83. C₂×#4956	C₂²	semidirect
84. C₂×#4956	C₂²	semidirect
85. C₂×#4956	C₂²	semidirect
95. C₂×#4955	C₂²	semidirect
96. C₂×#4955	C₂²	semidirect
97. C₂×#4955	C₂²	semidirect
98. C₂×#4955	C₂²	semidirect
99. C₂×#4955	C₂²	semidirect
100. C₂×#4955	C₂²	semidirect
101. C₂×#4955	C₂²	semidirect
102. C₂×#4955	C₂²	semidirect
103. C₂×#4955	C₂²	semidirect
104. C₂×#4955	C₂²	semidirect
105. C₂×#4955	C₂²	semidirect
106. C₂×#4949	C₂²	semidirect
107. C₂×#4952	C₂²	semidirect
108. C₂×#4952	C₂²	semidirect
109. C₂×#4961	C₂²	semidirect
110. C₂×#4961	C₂²	semidirect
111. C₂×#4961	C₂²	semidirect
112. C₂×#4957	C₂²	semidirect
113. C₂×#4957	C₂²	semidirect
114. C₂×#4675	C₂²	semidirect
115. C₂×#4671	C₂²	semidirect
116. C₂×#4671	C₂²	semidirect
117. C₂×#4665	C₂²	semidirect
118. C₂×#4665	C₂²	semidirect
119. C₂×#4665	C₂²	semidirect
120. C₂×#4665	C₂²	semidirect
121. C₂×#4665	C₂²	semidirect
122. C₂×#4665	C₂²	semidirect
123. C₂×#4665	C₂²	semidirect
124. C₂×#4665	C₂²	semidirect
125. C₂×#4665	C₂²	semidirect
126. C₂×#4668	C₂²	semidirect
127. C₂×#4667	C₂²	semidirect
128. C₂×#4672	C₂²	semidirect
129. C₃×#1440	C₂²	semidirect
130. C₃×#1440	C₂²	semidirect
131. C₃×#1439	C₂²	semidirect
132. C₃×#1439	C₂²	semidirect
133. C₃×#1439	C₂²	semidirect
134. C₃×#1438	C₂²	semidirect
135. C₃×#1438	C₂²	semidirect
136. C₃×#1438	C₂²	semidirect
137. C₃×#1438	C₂²	semidirect
138. #72131	C₂²	semidirect
139. #72131	C₂²	semidirect
140. #71570	C₂²	semidirect
141. #71570	C₂²	semidirect
142. #71570	C₂²	semidirect
143. #71550	C₂²	semidirect
144. #71550	C₂²	semidirect
145. #71550	C₂²	semidirect
146. #71550	C₂²	semidirect
147. #71550	C₂²	semidirect
148. #71550	C₂²	semidirect
149. #71550	C₂²	semidirect
150. #71550	C₂²	semidirect
151. #71550	C₂²	semidirect
152. #71550	C₂²	semidirect
153. #71549	C₂²	semidirect
154. #71549	C₂²	semidirect
155. #71549	C₂²	semidirect
156. #71548	C₂²	semidirect
157. #71547	C₂²	semidirect
158. #71547	C₂²	semidirect
159. #71547	C₂²	semidirect
160. #71545	C₂²	semidirect
161. #71545	C₂²	semidirect
162. #69429	C₂²	semidirect
163. #69429	C₂²	semidirect
164. #69429	C₂²	semidirect
165. #69429	C₂²	semidirect
166. #69428	C₂²	semidirect
167. #69428	C₂²	semidirect
168. #69428	C₂²	semidirect
169. #69428	C₂²	semidirect
170. #69428	C₂²	semidirect
171. #69427	C₂²	semidirect
172. #69427	C₂²	semidirect
173. #69426	C₂²	semidirect
174. #69426	C₂²	semidirect
175. #69426	C₂²	semidirect
176. #69426	C₂²	semidirect
177. #69426	C₂²	semidirect
178. #69426	C₂²	semidirect
179. (C₂×D₃)⋊#95	C₂²	semidirect
180. (C₂×D₃)⋊#95	C₂²	semidirect
181. (C₂×D₃)⋊#95	C₂²	semidirect
182. (C₂×D₃)⋊#95	C₂²	semidirect
183. (C₂×D₃)⋊#95	C₂²	semidirect
184. (C₂×D₃)⋊#95	C₂²	semidirect
185. #69408	C₂²	semidirect
186. #69408	C₂²	semidirect
187. #16255	D₃	semidirect
208. C₂³×#67	C₂³	semidirect
209. C₂²×D₃×D₄	D₄	semidirect
217. C₂³×D₁₂	C₂³	semidirect
221. C₂³×C₄×D₃	C₂³	semidirect
222. C₂³×C₄×D₃	C₂³	semidirect
223. C₂³×C₄×D₃	C₂³	semidirect
224. C₂²×C₃×C₄⋊C₄	C₂³	semidirect
225. C₂²×C₃×C₄⋊C₄	C₂³	semidirect
241. C₂²×C₃×C₂²⋊C₄	C₂³	semidirect
242. C₂²×C₃×C₂²⋊C₄	C₂³	semidirect
243. C₂²×C₃×C₂²⋊C₄	C₂³	semidirect
244. C₂²×C₃×C₂²⋊C₄	C₂³	semidirect
245. C₂×#953	D₄	semidirect
258. C₂²×#217	C₂³	semidirect
259. C₂²×#217	C₂³	semidirect
260. C₂²×#217	C₂³	semidirect
295. C₂²×(C₂×D₃)⋊C₄	C₂³	semidirect
296. C₂²×(C₂×D₃)⋊C₄	C₂³	semidirect
297. C₂²×(C₂×D₃)⋊C₄	C₂³	semidirect
298. C₂²×(C₂×D₃)⋊C₄	C₂³	semidirect
299. C₂²×(C₂×D₃)⋊C₄	C₂³	semidirect
300. C₂²×(C₂×D₃)⋊C₄	C₂³	semidirect
301. C₂²×(C₂×D₃)⋊C₄	C₂³	semidirect
302. C₂²×(C₂×D₃)⋊C₄	C₂³	semidirect
303. C₂²×(C₂×D₃)⋊C₄	C₂³	semidirect
304. C₂²×(C₂×D₃)⋊C₄	C₂³	semidirect
305. C₂²×C₄⋊Dic₃	C₂³	semidirect
306. C₂²×Dic₃⋊C₄	C₂³	semidirect
307. C₂²×Dic₃⋊C₄	C₂³	semidirect
308. C₂²×Dic₃⋊C₄	C₂³	semidirect
309. C₂²×Dic₃⋊C₄	C₂³	semidirect
310. C₂²×C₄×Dic₃	C₂³	semidirect
311. C₂×#882	D₄	semidirect
312. C₂×#882	D₄	semidirect
313. C₂×C₃×#95	C₂³	semidirect
314. C₂×C₃×#95	C₂³	semidirect
315. C₂×C₃×#95	C₂³	semidirect
316. C₂×C₃×#95	C₂³	semidirect
317. C₂×C₃×#95	C₂³	semidirect
318. C₂×C₃×#95	C₂³	semidirect
319. C₂×C₃×#95	C₂³	semidirect
320. C₂×C₃×#95	C₂³	semidirect
321. C₂×C₃×#95	C₂³	semidirect
322. C₂×C₃×#95	C₂³	semidirect
323. C₂×C₃⋊#95	C₂³	semidirect
324. C₂×C₃⋊#95	C₂³	semidirect
325. C₂×C₃⋊#95	C₂³	semidirect
326. C₂×C₃⋊#95	C₂³	semidirect
327. C₂×C₃⋊#95	C₂³	semidirect
328. C₂×C₃⋊#95	C₂³	semidirect
329. C₂×C₃⋊#95	C₂³	semidirect
330. C₂×C₃⋊#95	C₂³	semidirect
331. C₂×C₃⋊#95	C₂³	semidirect
332. C₂×C₃⋊#95	C₂³	semidirect
333. C₂×C₃⋊#95	C₂³	semidirect
334. C₂×C₃⋊#95	C₂³	semidirect
335. C₂×C₃⋊#95	C₂³	semidirect
336. C₂×C₃⋊#95	C₂³	semidirect
337. C₂×C₃⋊#95	C₂³	semidirect
338. C₂×C₃⋊#95	C₂³	semidirect
339. C₂×C₃⋊#95	C₂³	semidirect
340. C₂×C₃⋊#95	C₂³	semidirect
341. C₂×C₃⋊#95	C₂³	semidirect
342. C₂×C₃⋊#95	C₂³	semidirect
343. C₂×C₃⋊#95	C₂³	semidirect
344. C₂×C₃⋊#95	C₂³	semidirect
345. C₂×C₃⋊#95	C₂³	semidirect
346. C₂×C₃⋊#95	C₂³	semidirect
348. C₂×#397	C₂×D₃	semidirect
349. C₂×#394	C₂×D₃	semidirect
350. C₂×#394	C₂×D₃	semidirect
351. C₂×#379	C₂×D₃	semidirect
352. C₂×#379	C₂×D₃	semidirect
353. #1440	C₂×D₃	semidirect
354. #1440	C₂×D₃	semidirect
355. #1439	C₂×D₃	semidirect
356. #1439	C₂×D₃	semidirect
357. #1439	C₂×D₃	semidirect
358. #1438	C₂×D₃	semidirect
359. #1438	C₂×D₃	semidirect
360. #1438	C₂×D₃	semidirect
361. #1438	C₂×D₃	semidirect
396. C₂²×#67	C₂×D₄	semidirect
411. C₂²×D₁₂	C₂×D₄	semidirect
414. C₂×C₃×C₂²⋊C₄	C₂×D₄	semidirect
421. C₂×(C₂×D₃)⋊C₄	C₂×D₄	semidirect
426. C₂²×C₄⋊C₄	C₂²×D₃	semidirect
427. C₂²×C₄⋊C₄	C₂²×D₃	semidirect
443. C₂²×C₂²⋊C₄	C₂²×D₃	semidirect
444. C₂²×C₂²⋊C₄	C₂²×D₃	semidirect
445. C₂²×C₂²⋊C₄	C₂²×D₃	semidirect
446. C₂²×C₂²⋊C₄	C₂²×D₃	semidirect
447. C₂×#95	C₂²×D₃	semidirect
448. C₂×#95	C₂²×D₃	semidirect
449. C₂×#95	C₂²×D₃	semidirect
450. C₂×#95	C₂²×D₃	semidirect
451. C₂×#95	C₂²×D₃	semidirect
452. C₂×#95	C₂²×D₃	semidirect
453. C₂×#95	C₂²×D₃	semidirect
454. C₂×#95	C₂²×D₃	semidirect
455. C₂×#95	C₂²×D₃	semidirect
456. C₂×#95	C₂²×D₃	semidirect
493. C₂×#67	#120	semidirect
518. C₂×C₂²⋊C₄	D₃×D₄	semidirect
600. C₂×D₃	#2668	semidirect
669. C₃	#846041	semidirect

Maximal subgroups

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

subgroup	index
C₂²×D₃×#120	2
C₂×#77689	2
C₂×#73857	2
C₂×#73861	2
C₂×#76895	2
C₂×#77108	2
#10746889	2
#10746844	2
#10746841	2
#10733191	2
#10733189	2
#10732963	2
#10732962	2
#10732880	2
#10732879	2
#10732873	2
#10727935	2
#10726771	2
#10726676	2
#10726649	2
#10726589	2
#10726564	2
#10726342	2
#10722473	2
#10722471	2
#10717952	2
#10717052	2
C₃×#16255	2
#846041	3