Subgroups — #72255182

Order 1536.

At least 6404 conjugacy classes of subgroups; only the 1081 normal subgroups are shown.

The subgroup lattice has 723 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×D₄×#67	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×#5590	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#73854	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#76755	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#84052	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#82604	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#76753	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×D₃×#392	C₂	1	1	yes	maximal, characteristic, complemented
9	#10746873	C₂	1	1	yes	maximal, characteristic, complemented
10	#10746841	C₂	1	1	yes	maximal, characteristic, complemented
11	#10733591	C₂	1	1	yes	maximal, characteristic, complemented
12	#10733589	C₂	1	1	yes	maximal, characteristic, complemented
13	#10732931	C₂	1	1	yes	maximal, characteristic, complemented
14	#10732921	C₂	1	1	yes	maximal, characteristic, complemented
15	#10732884	C₂	1	1	yes	maximal, characteristic, complemented
16	#10732883	C₂	1	1	yes	maximal, characteristic, complemented
17	#10732878	C₂	1	1	yes	maximal, characteristic, complemented
18	#10732877	C₂	1	1	yes	maximal, characteristic, complemented
19	#10726631	C₂	1	1	yes	maximal, characteristic, complemented
20	#10726629	C₂	1	1	yes	maximal, characteristic, complemented
21	#10726570	C₂	1	1	yes	maximal, characteristic, complemented
22	#10726565	C₂	1	1	yes	maximal, characteristic, complemented
23	#10726564	C₂	1	1	yes	maximal, characteristic, complemented
24	#10726560	C₂	1	1	yes	maximal, characteristic, complemented
25	#10720472	C₂	1	1	yes	maximal, characteristic, complemented
26	#10718640	C₂	1	1	yes	maximal, characteristic, complemented
27	#10718638	C₂	1	1	yes	maximal, characteristic, complemented
28	#10717958	C₂	1	1	yes	maximal, characteristic, complemented
29	#10717955	C₂	1	1	yes	maximal, characteristic, complemented
30	#10717054	C₂	1	1	yes	maximal, characteristic, complemented
31	C₃×#14715	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂⁴×C₃×D₄	C₂²	1	1	yes	characteristic, complemented
33	C₂⁴×#67	C₂²	1	1	yes	characteristic
34	C₂⁴×#67	C₂²	1	1	yes	characteristic, complemented
35	C₂⁴×#67	C₂²	1	1	yes	characteristic, complemented
36	C₂³×D₃×D₄	C₂²	1	1	yes	characteristic, complemented
37	C₂³×D₃×D₄	C₂²	1	1	yes	characteristic, complemented
38	C₂³×D₃×D₄	C₂²	1	1	yes	characteristic, complemented
39	C₂³×D₃×D₄	C₂²	1	1	yes	characteristic, complemented
40	C₂²×C₃×#120	C₂²	1	1	yes	characteristic, complemented
41	C₂²×C₃×#120	C₂²	1	1	yes	characteristic, complemented
42	C₂²×#953	C₂²	1	1	yes	characteristic, complemented
43	C₂²×#953	C₂²	1	1	yes	characteristic, complemented
44	C₂²×#953	C₂²	1	1	yes	characteristic, complemented
45	C₂²×#953	C₂²	1	1	yes	characteristic, complemented
46	C₂²×#938	C₂²	1	1	yes	characteristic
47	C₂²×#937	C₂²	1	1	yes	characteristic
48	C₂²×#937	C₂²	1	1	yes	characteristic
49	C₂²×#937	C₂²	1	1	yes	characteristic, complemented
50	C₂²×#937	C₂²	1	1	yes	characteristic, complemented
51	C₂²×#937	C₂²	1	1	yes	characteristic, complemented
52	C₂²×#937	C₂²	1	1	yes	characteristic, complemented
53	C₂²×#940	C₂²	1	1	yes	characteristic, complemented
54	C₂²×#940	C₂²	1	1	yes	characteristic, complemented
55	C₂²×#939	C₂²	1	1	yes	characteristic, complemented
56	C₂²×#939	C₂²	1	1	yes	characteristic, complemented
57	C₂²×#939	C₂²	1	1	yes	characteristic, complemented
58	C₂²×#939	C₂²	1	1	yes	characteristic, complemented
59	C₂²×D₄×Dic₃	C₂²	1	1	yes	characteristic, complemented
60	C₂²×#930	C₂²	1	1	yes	characteristic, complemented
61	C₂²×C₄×#67	C₂²	1	1	yes	characteristic, complemented
62	C₂²×#884	C₂²	1	1	yes	characteristic
63	C₂²×#884	C₂²	1	1	yes	characteristic, complemented
64	C₂²×#884	C₂²	1	1	yes	characteristic, complemented
65	C₂²×#882	C₂²	1	1	yes	characteristic, complemented
66	C₂²×#882	C₂²	1	1	yes	characteristic, complemented
67	C₂²×#882	C₂²	1	1	yes	characteristic, complemented
68	C₂²×#882	C₂²	1	1	yes	characteristic, complemented
69	C₂²×D₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
70	C₂²×D₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
71	C₂²×D₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
72	C₂²×#67⋊C₄	C₂²	1	1	yes	characteristic, complemented
73	C₂²×#67⋊C₄	C₂²	1	1	yes	characteristic, complemented
74	C₂×C₃×#392	C₂²	1	1	yes	characteristic, complemented
75	C₂×C₃×#392	C₂²	1	1	yes	characteristic, complemented
76	C₂×C₃×#392	C₂²	1	1	yes	characteristic, complemented
77	C₂×C₃×#392	C₂²	1	1	yes	characteristic, complemented
78	C₂×C₃×#386	C₂²	1	1	yes	characteristic, complemented
79	C₂×C₃×#379	C₂²	1	1	yes	characteristic, complemented
80	C₂×C₃×#379	C₂²	1	1	yes	characteristic, complemented
81	C₂×#5247	C₂²	1	1	yes	characteristic, complemented
82	C₂×#5223	C₂²	1	1	yes	characteristic
83	C₂×#5223	C₂²	1	1	yes	characteristic, complemented
84	C₂×#5223	C₂²	1	1	yes	characteristic, complemented
85	C₂×#5223	C₂²	1	1	yes	characteristic, complemented
86	C₂×#5223	C₂²	1	1	yes	characteristic, complemented
87	C₂×#5223	C₂²	1	1	yes	characteristic, complemented
88	C₂×#5223	C₂²	1	1	yes	characteristic, complemented
89	C₂×#5223	C₂²	1	1	yes	characteristic, complemented
90	C₂×#5223	C₂²	1	1	yes	characteristic, complemented
91	C₂×#5223	C₂²	1	1	yes	characteristic, complemented
92	C₂×#5223	C₂²	1	1	yes	characteristic, complemented
93	C₂×#5223	C₂²	1	1	yes	characteristic, complemented
94	C₂×#5222	C₂²	1	1	yes	characteristic, complemented
95	C₂×#5220	C₂²	1	1	yes	characteristic, complemented
96	C₂×#5220	C₂²	1	1	yes	characteristic, complemented
97	C₂×#5220	C₂²	1	1	yes	characteristic, complemented
98	C₂×#5213	C₂²	1	1	yes	characteristic, complemented
99	C₂×#5213	C₂²	1	1	yes	characteristic, complemented
100	C₂×#4959	C₂²	1	1	yes	characteristic, complemented
101	C₂×#4959	C₂²	1	1	yes	characteristic, complemented
102	C₂×#4960	C₂²	1	1	yes	characteristic, complemented
103	C₂×#4960	C₂²	1	1	yes	characteristic, complemented
104	C₂×#4960	C₂²	1	1	yes	characteristic, complemented
105	C₂×#4960	C₂²	1	1	yes	characteristic, complemented
106	C₂×#4960	C₂²	1	1	yes	characteristic, complemented
107	C₂×#4960	C₂²	1	1	yes	characteristic, complemented
108	C₂×#4960	C₂²	1	1	yes	characteristic, complemented
109	C₂×#4960	C₂²	1	1	yes	characteristic, complemented
110	C₂×#4960	C₂²	1	1	yes	characteristic, complemented
111	C₂×#4960	C₂²	1	1	yes	characteristic, complemented
112	C₂×#4960	C₂²	1	1	yes	characteristic, complemented
113	C₂×#4960	C₂²	1	1	yes	characteristic, complemented
114	C₂×#4956	C₂²	1	1	yes	characteristic, complemented
115	C₂×#4956	C₂²	1	1	yes	characteristic, complemented
116	C₂×#4956	C₂²	1	1	yes	characteristic, complemented
117	C₂×#4956	C₂²	1	1	yes	characteristic, complemented
118	C₂×#4956	C₂²	1	1	yes	characteristic, complemented
119	C₂×#4956	C₂²	1	1	yes	characteristic, complemented
120	C₂×#4956	C₂²	1	1	yes	characteristic, complemented
121	C₂×#4956	C₂²	1	1	yes	characteristic, complemented
122	C₂×#4955	C₂²	1	1	yes	characteristic, complemented
123	C₂×#4955	C₂²	1	1	yes	characteristic, complemented
124	C₂×#4955	C₂²	1	1	yes	characteristic, complemented
125	C₂×#4955	C₂²	1	1	yes	characteristic, complemented
126	C₂×#4961	C₂²	1	1	yes	characteristic, complemented
127	C₂×#4958	C₂²	1	1	yes	characteristic, complemented
128	C₂×#4958	C₂²	1	1	yes	characteristic, complemented
129	C₂×#4958	C₂²	1	1	yes	characteristic, complemented
130	C₂×#4946	C₂²	1	1	yes	characteristic, complemented
131	C₂×#4671	C₂²	1	1	yes	characteristic, complemented
132	C₂×#4671	C₂²	1	1	yes	characteristic, complemented
133	C₂×#4665	C₂²	1	1	yes	characteristic, complemented
134	C₂×#4665	C₂²	1	1	yes	characteristic, complemented
135	C₂×#4665	C₂²	1	1	yes	characteristic, complemented
136	C₂×#4668	C₂²	1	1	yes	characteristic, complemented
137	C₂×D₃×#95	C₂²	1	1	yes	characteristic, complemented
138	C₃×#1438	C₂²	1	1	yes	characteristic, complemented
139	C₃×#1438	C₂²	1	1	yes	characteristic, complemented
140	C₃×#1438	C₂²	1	1	yes	characteristic, complemented
141	C₃×#1438	C₂²	1	1	yes	characteristic, complemented
142	C₃×C₂²⋊#95	C₂²	1	1	yes	characteristic, complemented
143	#72131	C₂²	1	1	yes	characteristic, complemented
144	#72131	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	#71550	C₂²	1	1	yes	characteristic, complemented
154	#71550	C₂²	1	1	yes	characteristic, complemented
155	#71550	C₂²	1	1	yes	characteristic, complemented
156	#71550	C₂²	1	1	yes	characteristic, complemented
157	#71550	C₂²	1	1	yes	characteristic, complemented
158	#71549	C₂²	1	1	yes	characteristic, complemented
159	#71548	C₂²	1	1	yes	characteristic, complemented
160	#71547	C₂²	1	1	yes	characteristic, complemented
161	#71547	C₂²	1	1	yes	characteristic, complemented
162	#71547	C₂²	1	1	yes	characteristic, complemented
163	#71547	C₂²	1	1	yes	characteristic, complemented
164	#71545	C₂²	1	1	yes	characteristic, complemented
165	#71545	C₂²	1	1	yes	characteristic, complemented
166	#71545	C₂²	1	1	yes	characteristic, complemented
167	#71544	C₂²	1	1	yes	characteristic, complemented
168	#71544	C₂²	1	1	yes	characteristic, complemented
169	#71544	C₂²	1	1	yes	characteristic, complemented
170	#69428	C₂²	1	1	yes	characteristic, complemented
171	#69428	C₂²	1	1	yes	characteristic, complemented
172	#69428	C₂²	1	1	yes	characteristic, complemented
173	#69428	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	(C₂×D₃)⋊#95	C₂²	1	1	yes	characteristic, complemented
178	(C₂×D₃)⋊#95	C₂²	1	1	yes	characteristic, complemented
179	(C₂×D₃)⋊#95	C₂²	1	1	yes	characteristic, complemented
180	#69411	C₂²	1	1	yes	characteristic, complemented
181	#69409	C₂²	1	1	yes	characteristic, complemented
182	#69408	C₂²	1	1	yes	characteristic, complemented
183	#69408	C₂²	1	1	yes	characteristic, complemented
184	#69408	C₂²	1	1	yes	characteristic, complemented
185	#69407	C₂²	1	1	yes	characteristic, complemented
186	#69406	C₂²	1	1	yes	characteristic, complemented
187	#14715	D₃	1	1	yes	characteristic, complemented
188	C₂⁶×C₃	C₂³	1	1	yes	characteristic
189	C₂⁶×C₃	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	C₂³×C₃×D₄	C₂³	1	1	yes	characteristic
195	C₂³×C₃×D₄	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×C₃×D₄	C₂³	1	1	yes	characteristic
200	C₂³×C₃×D₄	C₂³	1	1	yes	characteristic
201	C₂³×C₃×D₄	C₂³	1	1	yes	characteristic
202	C₂³×C₃×D₄	C₂³	1	1	yes	characteristic
203	C₂⁴×C₃×C₄	C₂³	1	1	yes	characteristic
204	C₂³×#67	D₄	1	8	yes	complemented
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
209	C₂³×#67	C₂³	1	1	yes	characteristic
210	C₂³×#67	C₂³	1	1	yes	characteristic
211	C₂³×#67	C₂³	1	1	yes	characteristic
212	C₂³×#67	C₂³	1	1	yes	characteristic
213	C₂³×#67	C₂³	1	1	yes	characteristic
214	C₂³×#67	C₂³	1	1	yes	characteristic
215	C₂³×#67	C₂³	1	1	yes	characteristic
216	C₂³×#67	C₂³	1	1	yes	characteristic
217	C₂³×#67	C₂³	1	1	yes	characteristic
218	C₂³×#67	C₂³	1	1	yes	characteristic
219	C₂³×#67	C₂³	1	1	yes	characteristic
220	C₂³×#67	C₂³	1	1	yes	characteristic
221	C₂³×#67	C₂³	1	1	yes	characteristic
222	C₂³×#67	C₂³	1	1	yes	characteristic
223	C₂³×#67	C₂³	1	1	yes	characteristic
224	C₂³×#67	C₂³	1	1	yes	characteristic
225	C₂³×#67	C₂³	1	1	yes	characteristic
226	C₂³×#67	C₂³	1	1	yes	characteristic
227	C₂⁴×Dic₃	C₂³	1	1	yes	characteristic
228	C₂⁴×Dic₃	C₂³	1	1	yes	characteristic
229	C₂⁴×Dic₃	C₂³	1	1	yes	characteristic
230	C₂³×D₁₂	C₂³	1	1	yes	characteristic
231	C₂³×D₁₂	C₂³	1	1	yes	characteristic
232	C₂³×D₁₂	C₂³	1	1	yes	characteristic
233	C₂³×D₁₂	C₂³	1	1	yes	characteristic
234	C₂³×D₁₂	C₂³	1	1	yes	characteristic
235	C₂³×D₁₂	C₂³	1	1	yes	characteristic
236	C₂³×C₄×D₃	C₂³	1	1	yes	characteristic
237	C₂³×C₄×D₃	C₂³	1	1	yes	characteristic
238	C₂³×C₄×D₃	C₂³	1	1	yes	characteristic
239	C₂³×C₄×D₃	C₂³	1	1	yes	characteristic
240	C₂³×C₄×D₃	C₂³	1	1	yes	characteristic
241	C₂²×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
242	C₂²×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
243	C₂²×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
244	C₂²×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
245	C₂²×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
246	C₂²×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
247	C₂²×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
248	C₂²×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
249	C₂²×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
250	C₂²×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
251	C₂²×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
252	C₂²×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
253	C₂²×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
254	C₂²×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
255	C₂²×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
256	C₂²×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
257	C₂²×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
258	C₂²×#217	C₂³	1	1	yes	characteristic
259	C₂²×#217	C₂³	1	1	yes	characteristic
260	C₂²×#217	C₂³	1	1	yes	characteristic
261	C₂²×#217	C₂³	1	1	yes	characteristic
262	C₂²×#217	C₂³	1	1	yes	characteristic
263	C₂²×#217	C₂³	1	1	yes	characteristic
264	C₂²×#217	C₂³	1	1	yes	characteristic
265	C₂²×#217	C₂³	1	1	yes	characteristic
266	C₂²×#217	C₂³	1	1	yes	characteristic
267	C₂²×#217	C₂³	1	1	yes	characteristic
268	C₂²×#217	C₂³	1	1	yes	characteristic
269	C₂²×#217	C₂³	1	1	yes	characteristic
270	C₂²×#217	C₂³	1	1	yes	characteristic
271	C₂²×#217	C₂³	1	1	yes	characteristic
272	C₂²×#217	C₂³	1	1	yes	characteristic
273	C₂²×#217	C₂³	1	1	yes	characteristic
274	C₂²×#217	C₂³	1	1	yes	characteristic
275	C₂²×#217	C₂³	1	1	yes	characteristic
276	C₂²×#217	C₂³	1	1	yes	characteristic
277	C₂×#938	D₄	1	8	yes	complemented
278	C₂×#937	D₄	1	8	yes	complemented
279	C₂×#937	D₄	1	8	yes	complemented
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
296	C₂²×(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
297	C₂²×(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
298	C₂²×(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
299	C₂²×(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
300	C₂²×(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
301	C₂²×(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
302	C₂²×(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
303	C₂²×(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
304	C₂²×(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
305	C₂²×(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
306	C₂²×(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
307	C₂²×(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
308	C₂²×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
309	C₂²×Dic₃⋊C₄	C₂³	1	1	yes	characteristic
310	C₂²×Dic₃⋊C₄	C₂³	1	1	yes	characteristic
311	C₂²×Dic₃⋊C₄	C₂³	1	1	yes	characteristic
312	C₂²×Dic₃⋊C₄	C₂³	1	1	yes	characteristic
313	C₂²×C₄×Dic₃	C₂³	1	1	yes	characteristic
314	C₂²×C₄×Dic₃	C₂³	1	1	yes	characteristic
315	C₂×#884	D₄	1	8	yes	complemented
316	C₂×C₃×#95	C₂³	1	1	yes	characteristic
317	C₂×C₃×#95	C₂³	1	1	yes	characteristic
318	C₂×C₃×#95	C₂³	1	1	yes	characteristic
319	C₂×C₃×#95	C₂³	1	1	yes	characteristic
320	C₂×C₃×#95	C₂³	1	1	yes	characteristic
321	C₂×C₃×#95	C₂³	1	1	yes	characteristic
322	#5223	D₄	1	8	yes	complemented
323	C₂×C₃⋊#95	C₂³	1	1	yes	characteristic
324	C₂×C₃⋊#95	C₂³	1	1	yes	characteristic
325	C₂×C₃⋊#95	C₂³	1	1	yes	characteristic
326	C₂×C₃⋊#95	C₂³	1	1	yes	characteristic
327	C₂×C₃⋊#95	C₂³	1	1	yes	characteristic
328	C₂×C₃⋊#95	C₂³	1	1	yes	characteristic
329	C₂×C₃⋊#95	C₂³	1	1	yes	characteristic
330	C₂×C₃⋊#95	C₂³	1	1	yes	characteristic
331	C₂×C₃⋊#95	C₂³	1	1	yes	characteristic
332	C₂×C₃⋊#95	C₂³	1	1	yes	characteristic
333	C₂×C₃⋊#95	C₂³	1	1	yes	characteristic
334	C₂×C₃⋊#95	C₂³	1	1	yes	characteristic
335	C₂×C₃⋊#95	C₂³	1	1	yes	characteristic
336	C₂×C₃⋊#95	C₂³	1	1	yes	characteristic
337	C₂×C₃⋊#95	C₂³	1	1	yes	characteristic
338	C₂×C₃⋊#95	C₂³	1	1	yes	characteristic
339	C₂×C₃⋊#95	C₂³	1	1	yes	characteristic
340	C₂×C₃⋊#95	C₂³	1	1	yes	characteristic
341	C₂×C₃⋊#95	C₂³	1	1	yes	characteristic
342	C₂×C₃⋊#95	C₂³	1	1	yes	characteristic
343	C₂×C₃⋊#95	C₂³	1	1	yes	characteristic
344	C₂×C₃⋊#95	C₂³	1	1	yes	characteristic
345	C₂×C₃⋊#95	C₂³	1	1	yes	characteristic
346	C₂×C₃⋊#95	C₂³	1	1	yes	characteristic
347	C₂×C₃⋊#95	C₂³	1	1	yes	characteristic
348	C₂×C₃⋊#95	C₂³	1	1	yes	characteristic
349	C₂⁴×D₄	C₂×D₃	1	1	yes	characteristic, complemented
350	C₂²×#120	C₂×D₃	1	1	yes	characteristic, complemented
351	C₂²×#120	C₂×D₃	1	1	yes	characteristic, complemented
352	C₂×#392	C₂×D₃	1	1	yes	characteristic, complemented
353	C₂×#392	C₂×D₃	1	1	yes	characteristic, complemented
354	C₂×#392	C₂×D₃	1	1	yes	characteristic, complemented
355	C₂×#392	C₂×D₃	1	1	yes	characteristic, complemented
356	C₂×#386	C₂×D₃	1	1	yes	characteristic, complemented
357	C₂×#379	C₂×D₃	1	1	yes	characteristic, complemented
358	C₂×#379	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	#1438	C₂×D₃	1	1	yes	characteristic, complemented
363	C₂²⋊#95	C₂×D₃	1	1	yes	characteristic, complemented
364	C₂⁵×C₃	C₂×D₄	1	4	yes	complemented
365	C₂⁵×C₃	C₂⁴	1	1	yes	characteristic
366	C₂⁵×C₃	C₂⁴	1	1	yes	characteristic
367	C₂⁵×C₃	C₂⁴	1	1	yes	characteristic
368	C₂⁵×C₃	C₂⁴	1	1	yes	characteristic
369	C₂⁵×C₃	C₂⁴	1	1	yes	characteristic
370	C₂⁵×C₃	C₂⁴	1	1	yes	characteristic
371	C₂⁴×D₃	C₂×D₄	1	4	yes	—
372	C₂⁴×D₃	C₂×D₄	1	4	yes	complemented
373	C₂⁴×D₃	C₂×D₄	1	4	yes	complemented
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	C₂⁴×D₃	C₂⁴	1	1	yes	characteristic
379	C₂²×C₃×D₄	C₂×D₄	1	4	yes	complemented
380	C₂²×C₃×D₄	C₂×D₄	1	4	yes	complemented
381	C₂²×C₃×D₄	C₂×D₄	1	4	yes	complemented
382	C₂²×C₃×D₄	C₂×D₄	1	4	yes	complemented
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	C₂³×C₃×C₄	C₂⁴	1	1	yes	characteristic
391	C₂³×C₃×C₄	C₂⁴	1	1	yes	characteristic
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	—
397	C₂²×#67	C₂×D₄	1	4	yes	—
398	C₂²×#67	C₂×D₄	1	4	yes	complemented
399	C₂²×#67	C₂×D₄	1	4	yes	complemented
400	C₂²×#67	C₂×D₄	1	4	yes	complemented
401	C₂²×#67	C₂×D₄	1	4	yes	complemented
402	C₂²×#67	C₂×D₄	1	4	yes	complemented
403	C₂²×#67	C₂×D₄	1	4	yes	complemented
404	C₂²×#67	C₂×D₄	1	4	yes	complemented
405	C₂²×#67	C₂×D₄	1	4	yes	complemented
406	C₂³×Dic₃	C₂×D₄	1	4	yes	complemented
407	C₂³×Dic₃	C₂⁴	1	1	yes	characteristic
408	C₂³×Dic₃	C₂⁴	1	1	yes	characteristic
409	C₂³×Dic₃	C₂⁴	1	1	yes	characteristic
410	C₂³×Dic₃	C₂⁴	1	1	yes	characteristic
411	C₂³×Dic₃	C₂⁴	1	1	yes	characteristic
412	C₂³×Dic₃	C₂⁴	1	1	yes	characteristic
413	C₂³×Dic₃	C₂⁴	1	1	yes	characteristic
414	C₂³×Dic₃	C₂⁴	1	1	yes	characteristic
415	C₂³×Dic₃	C₂⁴	1	1	yes	characteristic
416	C₂³×Dic₃	C₂⁴	1	1	yes	characteristic
417	C₂³×Dic₃	C₂⁴	1	1	yes	characteristic
418	C₂²×D₁₂	C₂×D₄	1	4	yes	complemented
419	C₂²×C₄×D₃	C₂×D₄	1	4	yes	complemented
420	C₂²×C₄×D₃	C₂×D₄	1	4	yes	complemented
421	C₂×C₃×C₂²⋊C₄	C₂×D₄	1	4	yes	complemented
422	C₂×#217	C₂×D₄	1	4	yes	complemented
423	C₂×#217	C₂×D₄	1	4	yes	complemented
424	C₂×#217	C₂×D₄	1	4	yes	complemented
425	C₂×#217	C₂×D₄	1	4	yes	complemented
426	C₂×#217	C₂×D₄	1	4	yes	complemented
427	C₂×#217	C₂×D₄	1	4	yes	complemented
428	C₂×(C₂×D₃)⋊C₄	C₂×D₄	1	4	yes	complemented
429	C₂×(C₂×D₃)⋊C₄	C₂×D₄	1	4	yes	complemented
430	C₂×(C₂×D₃)⋊C₄	C₂×D₄	1	4	yes	complemented
431	C₂×(C₂×D₃)⋊C₄	C₂×D₄	1	4	yes	complemented
432	C₂×(C₂×D₃)⋊C₄	C₂×D₄	1	4	yes	complemented
433	C₂×(C₂×D₃)⋊C₄	C₂×D₄	1	4	yes	complemented
434	C₂×C₄⋊Dic₃	C₂×D₄	1	4	yes	complemented
435	C₂×Dic₃⋊C₄	C₂×D₄	1	4	yes	complemented
436	C₃⋊#95	C₂×D₄	1	4	yes	complemented
437	C₂⁶	C₂²×D₃	1	1	yes	characteristic
438	C₂⁶	C₂²×D₃	1	1	yes	characteristic
439	C₂³×D₄	C₂²×D₃	1	1	yes	characteristic
440	C₂³×D₄	C₂²×D₃	1	1	yes	characteristic
441	C₂³×D₄	C₂²×D₃	1	1	yes	characteristic
442	C₂³×D₄	C₂²×D₃	1	1	yes	characteristic
443	C₂³×D₄	C₂²×D₃	1	1	yes	characteristic
444	C₂³×D₄	C₂²×D₃	1	1	yes	characteristic
445	C₂³×D₄	C₂²×D₃	1	1	yes	characteristic
446	C₂³×D₄	C₂²×D₃	1	1	yes	characteristic
447	C₂³×D₄	C₂²×D₃	1	1	yes	characteristic
448	C₂⁴×C₄	C₂²×D₃	1	1	yes	characteristic
449	C₂²×C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
450	C₂²×C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
451	C₂²×C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
452	C₂²×C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
453	C₂²×C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
454	C₂²×C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
455	C₂²×C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
456	C₂²×C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
457	C₂²×C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
458	C₂²×C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
459	C₂²×C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
460	C₂²×C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
461	C₂²×C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
462	C₂²×C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
463	C₂²×C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
464	C₂²×C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
465	C₂²×C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
466	C₂×#95	C₂²×D₃	1	1	yes	characteristic
467	C₂×#95	C₂²×D₃	1	1	yes	characteristic
468	C₂×#95	C₂²×D₃	1	1	yes	characteristic
469	C₂×#95	C₂²×D₃	1	1	yes	characteristic
470	C₂×#95	C₂²×D₃	1	1	yes	characteristic
471	C₂×#95	C₂²×D₃	1	1	yes	characteristic
472	C₂⁴×C₃	C₂²×D₄	1	2	yes	—
473	C₂⁴×C₃	C₂²×D₄	1	2	yes	—
474	C₂⁴×C₃	C₂²×D₄	1	2	yes	—
475	C₂⁴×C₃	C₂²×D₄	1	2	yes	—
476	C₂⁴×C₃	C₂²×D₄	1	2	yes	—
477	C₂⁴×C₃	C₂²×D₄	1	2	yes	—
478	C₂⁴×C₃	C₂²×D₄	1	2	yes	—
479	C₂⁴×C₃	C₂²×D₄	1	2	yes	—
480	C₂⁴×C₃	C₂²×D₄	1	2	yes	—
481	C₂⁴×C₃	C₂²×D₄	1	2	yes	—
482	C₂⁴×C₃	C₂²×D₄	1	2	yes	—
483	C₂⁴×C₃	C₂²×D₄	1	2	yes	—
484	C₂⁴×C₃	H(5,𝔽₂)	1	2	yes	—
485	C₂⁴×C₃	H(5,𝔽₂)	1	2	yes	—
486	C₂⁴×C₃	C₂⁵	1	1	yes	characteristic
487	C₂³×D₃	C₂²×D₄	1	2	yes	—
488	C₂³×D₃	C₂²×D₄	1	2	yes	—
489	C₂³×D₃	C₂²×D₄	1	2	yes	—
490	C₂³×D₃	C₂²×D₄	1	2	yes	—
491	C₂³×D₃	C₂²×D₄	1	2	yes	—
492	C₂³×D₃	C₂²×D₄	1	2	yes	—
493	C₂³×D₃	C₂²×D₄	1	2	yes	—
494	C₂³×D₃	C₂²×D₄	1	2	yes	—
495	C₂³×D₃	C₂²×D₄	1	2	yes	—
496	C₂³×D₃	C₂²×D₄	1	2	yes	—
497	C₂³×D₃	H(5,𝔽₂)	1	2	yes	—
498	C₂³×D₃	H(5,𝔽₂)	1	2	yes	—
499	C₂³×D₃	H(5,𝔽₂)	1	2	yes	—
500	C₂²×C₃×C₄	C₂²×D₄	1	2	yes	—
501	C₂²×C₃×C₄	C₂²×D₄	1	2	yes	—
502	C₂²×C₃×C₄	C₂²×D₄	1	2	yes	—
503	C₂²×C₃×C₄	C₂²×D₄	1	2	yes	—
504	C₂²×C₃×C₄	C₂²×D₄	1	2	yes	—
505	C₂²×C₃×C₄	C₂²×D₄	1	2	yes	—
506	C₂²×C₃×C₄	H(5,𝔽₂)	1	2	yes	—
507	C₂²×C₃×C₄	H(5,𝔽₂)	1	2	yes	—
508	C₂×#67	#120	1	16	yes	complemented
509	C₂×#67	#120	1	16	yes	complemented
510	C₂²×Dic₃	C₂²×D₄	1	2	yes	—
511	C₂²×Dic₃	C₂²×D₄	1	2	yes	—
512	C₂²×Dic₃	C₂²×D₄	1	2	yes	—
513	C₂²×Dic₃	C₂²×D₄	1	2	yes	—
514	C₂²×Dic₃	C₂²×D₄	1	2	yes	—
515	C₂²×Dic₃	C₂²×D₄	1	2	yes	—
516	C₂²×Dic₃	C₂²×D₄	1	2	yes	—
517	C₂²×Dic₃	C₂²×D₄	1	2	yes	—
518	C₂²×Dic₃	C₂²×D₄	1	2	yes	—
519	C₂²×Dic₃	C₂²×D₄	1	2	yes	—
520	C₂²×Dic₃	C₂²×D₄	1	2	yes	—
521	C₂²×Dic₃	C₂²×D₄	1	2	yes	—
522	C₂²×Dic₃	C₂²×D₄	1	2	yes	—
523	C₂²×Dic₃	C₂²×D₄	1	2	yes	—
524	C₂²×Dic₃	H(5,𝔽₂)	1	2	yes	—
525	C₂⁵	D₃×D₄	1	4	yes	complemented
526	C₂⁵	C₂³×D₃	1	1	yes	characteristic
527	C₂⁵	C₂³×D₃	1	1	yes	characteristic
528	C₂⁵	C₂³×D₃	1	1	yes	characteristic
529	C₂⁵	C₂³×D₃	1	1	yes	characteristic
530	C₂⁵	C₂³×D₃	1	1	yes	characteristic
531	C₂⁵	C₂³×D₃	1	1	yes	characteristic
532	C₂²×D₄	D₃×D₄	1	4	yes	complemented
533	C₂²×D₄	D₃×D₄	1	4	yes	complemented
534	C₂²×D₄	D₃×D₄	1	4	yes	complemented
535	C₂²×D₄	D₃×D₄	1	4	yes	complemented
536	C₂³×C₄	C₂³×D₃	1	1	yes	characteristic
537	C₂³×C₄	C₂³×D₃	1	1	yes	characteristic
538	C₂³×C₄	C₂³×D₃	1	1	yes	characteristic
539	C₂³×C₄	C₂³×D₃	1	1	yes	characteristic
540	C₂³×C₄	C₂³×D₃	1	1	yes	characteristic
541	C₂³×C₄	C₂³×D₃	1	1	yes	characteristic
542	C₂³×C₄	C₂³×D₃	1	1	yes	characteristic
543	C₂³×C₄	C₂³×D₃	1	1	yes	characteristic
544	C₂³×C₄	C₂³×D₃	1	1	yes	characteristic
545	C₂×C₂²⋊C₄	D₃×D₄	1	4	yes	complemented
546	C₂³×C₃	C₂×#120	1	4	yes	—
547	C₂³×C₃	C₂×#120	1	4	yes	—
548	C₂³×C₃	D₄²	1	4	yes	—
549	C₂³×C₃	D₄²	1	4	yes	complemented
550	C₂³×C₃	C₂³×D₄	1	1	yes	characteristic
551	C₂³×C₃	C₂³×D₄	1	1	yes	characteristic
552	C₂³×C₃	C₂³×D₄	1	1	yes	characteristic
553	C₂³×C₃	C₂³×D₄	1	1	yes	characteristic
554	C₂³×C₃	C₂³×D₄	1	1	yes	characteristic
555	C₂³×C₃	C₂³×D₄	1	1	yes	characteristic
556	C₂³×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
557	C₂³×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
558	C₂³×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
559	C₂³×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
560	C₂³×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
561	C₂³×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
562	C₂³×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
563	C₂³×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
564	C₂³×C₃	#585	1	1	yes	characteristic
565	C₂²×D₃	C₂×#120	1	4	yes	—
566	C₂²×D₃	C₂×#120	1	4	yes	—
567	C₂²×D₃	#534	1	4	yes	—
568	C₂²×D₃	D₄²	1	4	yes	—
569	C₂²×D₃	D₄²	1	4	yes	—
570	C₂²×D₃	D₄²	1	4	yes	—
571	C₂²×D₃	D₄²	1	4	yes	—
572	C₂²×D₃	D₄²	1	4	yes	complemented
573	C₂×C₃×C₄	D₄²	1	4	yes	complemented
574	C₂×Dic₃	C₂×#120	1	4	yes	—
575	C₂×Dic₃	C₂×#120	1	4	yes	—
576	C₂×Dic₃	D₄²	1	4	yes	complemented
577	C₂⁴	C₂×D₃×D₄	1	2	yes	—
578	C₂⁴	C₂×D₃×D₄	1	2	yes	—
579	C₂⁴	C₂×D₃×D₄	1	2	yes	—
580	C₂⁴	C₂×D₃×D₄	1	2	yes	—
581	C₂⁴	C₂×D₃×D₄	1	2	yes	—
582	C₂⁴	C₂×D₃×D₄	1	2	yes	—
583	C₂⁴	C₂×D₃×D₄	1	2	yes	—
584	C₂⁴	C₂×D₃×D₄	1	2	yes	—
585	C₂⁴	C₂×D₃×D₄	1	2	yes	—
586	C₂⁴	C₂×D₃×D₄	1	2	yes	—
587	C₂⁴	C₂×D₃×D₄	1	2	yes	—
588	C₂⁴	C₂×D₃×D₄	1	2	yes	—
589	C₂⁴	#1004	1	2	yes	—
590	C₂⁴	#1004	1	2	yes	—
591	C₂⁴	C₂⁴×D₃	1	1	yes	characteristic
592	C₂²×C₄	C₂×D₃×D₄	1	2	yes	—
593	C₂²×C₄	C₂×D₃×D₄	1	2	yes	—
594	C₂²×C₄	C₂×D₃×D₄	1	2	yes	—
595	C₂²×C₄	C₂×D₃×D₄	1	2	yes	—
596	C₂²×C₄	C₂×D₃×D₄	1	2	yes	—
597	C₂²×C₄	C₂×D₃×D₄	1	2	yes	—
598	C₂²×C₄	#1004	1	2	yes	—
599	C₂²×C₄	#1004	1	2	yes	—
600	C₂²×C₃	C₂²×#120	1	1	yes	characteristic
601	C₂²×C₃	C₂²×#120	1	1	yes	characteristic
602	C₂²×C₃	C₂×#534	1	1	yes	characteristic
603	C₂²×C₃	C₂×D₄²	1	1	yes	characteristic
604	C₂²×C₃	C₂×D₄²	1	1	yes	characteristic
605	C₂²×C₃	C₂×D₄²	1	1	yes	characteristic
606	C₂²×C₃	C₂×D₄²	1	1	yes	characteristic
607	C₂²×C₃	C₂×D₄²	1	1	yes	characteristic
608	C₂²×C₃	C₂×D₄²	1	1	yes	characteristic
609	C₂²×C₃	C₂×D₄²	1	1	yes	characteristic
610	C₂²×C₃	C₂×D₄²	1	1	yes	characteristic
611	C₂²×C₃	C₂×D₄²	1	1	yes	characteristic
612	C₂²×C₃	#3484	1	1	yes	characteristic
613	C₂²×C₃	#3484	1	1	yes	characteristic
614	C₂²×C₃	#3484	1	1	yes	characteristic
615	C₂²×C₃	#3484	1	1	yes	characteristic
616	C₂²×C₃	#3484	1	1	yes	characteristic
617	C₂²×C₃	#3484	1	1	yes	characteristic
618	C₂²×C₃	#3484	1	1	yes	characteristic
619	C₂²×C₃	#3484	1	1	yes	characteristic
620	C₂²×C₃	#3484	1	1	yes	characteristic
621	C₂²×C₃	#3488	1	1	yes	characteristic
622	C₂²×C₃	#3488	1	1	yes	characteristic
623	C₂²×C₃	#3488	1	1	yes	characteristic
624	C₂²×C₃	#3496	1	1	yes	characteristic
625	C₂²×C₃	#3496	1	1	yes	characteristic
626	C₂²×C₃	#3496	1	1	yes	characteristic
627	C₂²×C₃	#3498	1	1	yes	characteristic
628	C₂²×C₃	#3498	1	1	yes	characteristic
629	C₂²×C₃	#3532	1	1	yes	characteristic
630	C₂²×C₃	#3534	1	1	yes	characteristic
631	C₂²×C₃	#3537	1	1	yes	characteristic
632	C₂²×C₃	#3537	1	1	yes	characteristic
633	C₂²×C₃	#3537	1	1	yes	characteristic
634	C₂²×C₃	#3543	1	1	yes	characteristic
635	C₂×D₃	#2403	1	8	yes	complemented
636	C₂³	D₃×#120	1	4	yes	—
637	C₂³	D₃×#120	1	4	yes	—
638	C₂³	#5590	1	4	yes	—
639	C₂³	#5590	1	4	yes	complemented
640	C₂³	C₂²×D₃×D₄	1	1	yes	characteristic
641	C₂³	C₂²×D₃×D₄	1	1	yes	characteristic
642	C₂³	C₂²×D₃×D₄	1	1	yes	characteristic
643	C₂³	C₂²×D₃×D₄	1	1	yes	characteristic
644	C₂³	C₂²×D₃×D₄	1	1	yes	characteristic
645	C₂³	C₂²×D₃×D₄	1	1	yes	characteristic
646	C₂³	C₂×#1004	1	1	yes	characteristic
647	C₂³	C₂×#1004	1	1	yes	characteristic
648	C₂³	C₂×#1004	1	1	yes	characteristic
649	C₂³	C₂×#1004	1	1	yes	characteristic
650	C₂³	#5964	1	1	yes	characteristic
651	C₂³	D₃×H(5,𝔽₂)	1	1	yes	characteristic
652	C₂³	D₃×H(5,𝔽₂)	1	1	yes	characteristic
653	C₂³	D₃×H(5,𝔽₂)	1	1	yes	characteristic
654	C₂³	D₃×H(5,𝔽₂)	1	1	yes	characteristic
655	C₂×C₄	#5590	1	4	yes	complemented
656	C₂×C₃	C₂×#2403	1	1	yes	characteristic
657	C₂×C₃	#35680	1	1	yes	characteristic
658	C₂×C₃	#35680	1	1	yes	characteristic
659	C₂×C₃	D₄×#120	1	1	yes	characteristic
660	C₂×C₃	D₄×#120	1	1	yes	characteristic
661	C₂×C₃	#37672	1	1	yes	characteristic
662	C₂×C₃	#40584	1	1	yes	characteristic
663	C₂×C₃	#42996	1	1	yes	characteristic
664	C₂×C₃	#43001	1	1	yes	characteristic
665	C₂×C₃	#43001	1	1	yes	characteristic
666	C₂×C₃	#43098	1	1	yes	characteristic
667	C₂×C₃	#58990	1	1	yes	characteristic
668	C₂×C₃	#58997	1	1	yes	characteristic
669	C₂×C₃	#58997	1	1	yes	characteristic
670	C₂×C₃	#59126	1	1	yes	characteristic
671	C₂²	C₂×D₃×#120	1	1	yes	characteristic
672	C₂²	C₂×D₃×#120	1	1	yes	characteristic
673	C₂²	C₂×#5590	1	1	yes	characteristic
674	C₂²	C₂×#5590	1	1	yes	characteristic
675	C₂²	C₂×#5590	1	1	yes	characteristic
676	C₂²	#85919	1	1	yes	characteristic
677	C₂²	#85919	1	1	yes	characteristic
678	C₂²	#85919	1	1	yes	characteristic
679	C₂²	#85919	1	1	yes	characteristic
680	C₂²	#85949	1	1	yes	characteristic
681	C₂²	#85950	1	1	yes	characteristic
682	C₂²	#85950	1	1	yes	characteristic
683	C₂²	#86195	1	1	yes	characteristic
684	C₂²	#86301	1	1	yes	characteristic
685	C₂²	D₃×#534	1	1	yes	characteristic
686	C₂²	#86308	1	1	yes	characteristic
687	C₂²	#86310	1	1	yes	characteristic
688	C₂²	#86334	1	1	yes	characteristic
689	C₂²	#86336	1	1	yes	characteristic
690	C₂²	#86608	1	1	yes	characteristic
691	C₂²	D₃×D₄²	1	1	yes	characteristic
692	C₂²	D₃×D₄²	1	1	yes	characteristic
693	C₂²	D₃×D₄²	1	1	yes	characteristic
694	C₂²	D₃×D₄²	1	1	yes	characteristic
695	C₂²	D₃×D₄²	1	1	yes	characteristic
696	C₂²	D₃×D₄²	1	1	yes	characteristic
697	C₂²	#86620	1	1	yes	characteristic
698	C₂²	#86620	1	1	yes	characteristic
699	C₂²	#86620	1	1	yes	characteristic
700	C₂²	#86620	1	1	yes	characteristic
701	C₂²	#86623	1	1	yes	characteristic
702	C₂²	#86629	1	1	yes	characteristic
703	C₂²	#86629	1	1	yes	characteristic
704	C₂²	#86665	1	1	yes	characteristic
705	C₂²	#86669	1	1	yes	characteristic
706	C₃	#772778	1	1	yes	characteristic, complemented, Sylow
707	C₂	D₃×#2403	1	1	yes	characteristic
708	C₂	#10981240	1	1	yes	characteristic
709	C₂	#10981252	1	1	yes	characteristic
710	C₂	#10990476	1	1	yes	characteristic
711	C₂	#10990485	1	1	yes	characteristic
712	C₂	#11024467	1	1	yes	characteristic
713	C₂	#11100275	1	1	yes	characteristic
714	C₂	#11166951	1	1	yes	characteristic
715	C₂	#11167082	1	1	yes	characteristic
716	C₂	#11167097	1	1	yes	characteristic
717	C₂	#11169873	1	1	yes	characteristic
718	C₂	#11632788	1	1	yes	characteristic
719	C₂	#11632939	1	1	yes	characteristic
720	C₂	#11632944	1	1	yes	characteristic
721	C₂	#11635870	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂⁴	C₂⁴×D₃
commutator, socle, cosocle	C₂⁴×C₃	C₂⁵
Fitting	C₃×#14715	C₂
hypercenter	#14715	D₃
hypocenter	C₃	#772778
LCS	G ▷ C₂⁴×C₃ ▷ C₃
UCS	C₁ ◁ C₂⁴ ◁ #14715

Complements

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

N	H ≅ G/N	type
1. C₂²×D₄×#67	C₂	semidirect
2. C₂²×#5590	C₂	semidirect
3. C₂×#73854	C₂	semidirect
4. C₂×#76755	C₂	semidirect
5. C₂×#84052	C₂	semidirect
6. C₂×#82604	C₂	semidirect
7. C₂×#76753	C₂	semidirect
8. C₂×D₃×#392	C₂	semidirect
9. #10746873	C₂	semidirect
10. #10746841	C₂	semidirect
11. #10733591	C₂	semidirect
12. #10733589	C₂	semidirect
13. #10732931	C₂	semidirect
14. #10732921	C₂	semidirect
15. #10732884	C₂	semidirect
16. #10732883	C₂	semidirect
17. #10732878	C₂	semidirect
18. #10732877	C₂	semidirect
19. #10726631	C₂	semidirect
20. #10726629	C₂	semidirect
21. #10726570	C₂	semidirect
22. #10726565	C₂	semidirect
23. #10726564	C₂	semidirect
24. #10726560	C₂	semidirect
25. #10720472	C₂	semidirect
26. #10718640	C₂	semidirect
27. #10718638	C₂	semidirect
28. #10717958	C₂	semidirect
29. #10717955	C₂	semidirect
30. #10717054	C₂	semidirect
31. C₃×#14715	C₂	semidirect
32. C₂⁴×C₃×D₄	C₂²	semidirect
34. C₂⁴×#67	C₂²	semidirect
35. C₂⁴×#67	C₂²	semidirect
36. C₂³×D₃×D₄	C₂²	semidirect
37. C₂³×D₃×D₄	C₂²	semidirect
38. C₂³×D₃×D₄	C₂²	semidirect
39. C₂³×D₃×D₄	C₂²	semidirect
40. C₂²×C₃×#120	C₂²	semidirect
41. C₂²×C₃×#120	C₂²	semidirect
42. C₂²×#953	C₂²	semidirect
43. C₂²×#953	C₂²	semidirect
44. C₂²×#953	C₂²	semidirect
45. C₂²×#953	C₂²	semidirect
49. C₂²×#937	C₂²	semidirect
50. C₂²×#937	C₂²	semidirect
51. C₂²×#937	C₂²	semidirect
52. C₂²×#937	C₂²	semidirect
53. C₂²×#940	C₂²	semidirect
54. C₂²×#940	C₂²	semidirect
55. C₂²×#939	C₂²	semidirect
56. C₂²×#939	C₂²	semidirect
57. C₂²×#939	C₂²	semidirect
58. C₂²×#939	C₂²	semidirect
59. C₂²×D₄×Dic₃	C₂²	semidirect
60. C₂²×#930	C₂²	semidirect
61. C₂²×C₄×#67	C₂²	semidirect
63. C₂²×#884	C₂²	semidirect
64. C₂²×#884	C₂²	semidirect
65. C₂²×#882	C₂²	semidirect
66. C₂²×#882	C₂²	semidirect
67. C₂²×#882	C₂²	semidirect
68. C₂²×#882	C₂²	semidirect
69. C₂²×D₃×C₂²⋊C₄	C₂²	semidirect
70. C₂²×D₃×C₂²⋊C₄	C₂²	semidirect
71. C₂²×D₃×C₂²⋊C₄	C₂²	semidirect
72. C₂²×#67⋊C₄	C₂²	semidirect
73. C₂²×#67⋊C₄	C₂²	semidirect
74. C₂×C₃×#392	C₂²	semidirect
75. C₂×C₃×#392	C₂²	semidirect
76. C₂×C₃×#392	C₂²	semidirect
77. C₂×C₃×#392	C₂²	semidirect
78. C₂×C₃×#386	C₂²	semidirect
79. C₂×C₃×#379	C₂²	semidirect
80. C₂×C₃×#379	C₂²	semidirect
81. C₂×#5247	C₂²	semidirect
83. C₂×#5223	C₂²	semidirect
84. C₂×#5223	C₂²	semidirect
85. C₂×#5223	C₂²	semidirect
86. C₂×#5223	C₂²	semidirect
87. C₂×#5223	C₂²	semidirect
88. C₂×#5223	C₂²	semidirect
89. C₂×#5223	C₂²	semidirect
90. C₂×#5223	C₂²	semidirect
91. C₂×#5223	C₂²	semidirect
92. C₂×#5223	C₂²	semidirect
93. C₂×#5223	C₂²	semidirect
94. C₂×#5222	C₂²	semidirect
95. C₂×#5220	C₂²	semidirect
96. C₂×#5220	C₂²	semidirect
97. C₂×#5220	C₂²	semidirect
98. C₂×#5213	C₂²	semidirect
99. C₂×#5213	C₂²	semidirect
100. C₂×#4959	C₂²	semidirect
101. C₂×#4959	C₂²	semidirect
102. C₂×#4960	C₂²	semidirect
103. C₂×#4960	C₂²	semidirect
104. C₂×#4960	C₂²	semidirect
105. C₂×#4960	C₂²	semidirect
106. C₂×#4960	C₂²	semidirect
107. C₂×#4960	C₂²	semidirect
108. C₂×#4960	C₂²	semidirect
109. C₂×#4960	C₂²	semidirect
110. C₂×#4960	C₂²	semidirect
111. C₂×#4960	C₂²	semidirect
112. C₂×#4960	C₂²	semidirect
113. C₂×#4960	C₂²	semidirect
114. C₂×#4956	C₂²	semidirect
115. C₂×#4956	C₂²	semidirect
116. C₂×#4956	C₂²	semidirect
117. C₂×#4956	C₂²	semidirect
118. C₂×#4956	C₂²	semidirect
119. C₂×#4956	C₂²	semidirect
120. C₂×#4956	C₂²	semidirect
121. C₂×#4956	C₂²	semidirect
122. C₂×#4955	C₂²	semidirect
123. C₂×#4955	C₂²	semidirect
124. C₂×#4955	C₂²	semidirect
125. C₂×#4955	C₂²	semidirect
126. C₂×#4961	C₂²	semidirect
127. C₂×#4958	C₂²	semidirect
128. C₂×#4958	C₂²	semidirect
129. C₂×#4958	C₂²	semidirect
130. C₂×#4946	C₂²	semidirect
131. C₂×#4671	C₂²	semidirect
132. C₂×#4671	C₂²	semidirect
133. C₂×#4665	C₂²	semidirect
134. C₂×#4665	C₂²	semidirect
135. C₂×#4665	C₂²	semidirect
136. C₂×#4668	C₂²	semidirect
137. C₂×D₃×#95	C₂²	semidirect
138. C₃×#1438	C₂²	semidirect
139. C₃×#1438	C₂²	semidirect
140. C₃×#1438	C₂²	semidirect
141. C₃×#1438	C₂²	semidirect
142. C₃×C₂²⋊#95	C₂²	semidirect
143. #72131	C₂²	semidirect
144. #72131	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. #71550	C₂²	semidirect
154. #71550	C₂²	semidirect
155. #71550	C₂²	semidirect
156. #71550	C₂²	semidirect
157. #71550	C₂²	semidirect
158. #71549	C₂²	semidirect
159. #71548	C₂²	semidirect
160. #71547	C₂²	semidirect
161. #71547	C₂²	semidirect
162. #71547	C₂²	semidirect
163. #71547	C₂²	semidirect
164. #71545	C₂²	semidirect
165. #71545	C₂²	semidirect
166. #71545	C₂²	semidirect
167. #71544	C₂²	semidirect
168. #71544	C₂²	semidirect
169. #71544	C₂²	semidirect
170. #69428	C₂²	semidirect
171. #69428	C₂²	semidirect
172. #69428	C₂²	semidirect
173. #69428	C₂²	semidirect
174. #69426	C₂²	semidirect
175. #69426	C₂²	semidirect
176. #69426	C₂²	semidirect
177. (C₂×D₃)⋊#95	C₂²	semidirect
178. (C₂×D₃)⋊#95	C₂²	semidirect
179. (C₂×D₃)⋊#95	C₂²	semidirect
180. #69411	C₂²	semidirect
181. #69409	C₂²	semidirect
182. #69408	C₂²	semidirect
183. #69408	C₂²	semidirect
184. #69408	C₂²	semidirect
185. #69407	C₂²	semidirect
186. #69406	C₂²	semidirect
187. #14715	D₃	semidirect
204. C₂³×#67	D₄	semidirect
277. C₂×#938	D₄	semidirect
278. C₂×#937	D₄	semidirect
279. C₂×#937	D₄	semidirect
315. C₂×#884	D₄	semidirect
322. #5223	D₄	semidirect
349. C₂⁴×D₄	C₂×D₃	semidirect
350. C₂²×#120	C₂×D₃	semidirect
351. C₂²×#120	C₂×D₃	semidirect
352. C₂×#392	C₂×D₃	semidirect
353. C₂×#392	C₂×D₃	semidirect
354. C₂×#392	C₂×D₃	semidirect
355. C₂×#392	C₂×D₃	semidirect
356. C₂×#386	C₂×D₃	semidirect
357. C₂×#379	C₂×D₃	semidirect
358. C₂×#379	C₂×D₃	semidirect
359. #1438	C₂×D₃	semidirect
360. #1438	C₂×D₃	semidirect
361. #1438	C₂×D₃	semidirect
362. #1438	C₂×D₃	semidirect
363. C₂²⋊#95	C₂×D₃	semidirect
364. C₂⁵×C₃	C₂×D₄	semidirect
372. C₂⁴×D₃	C₂×D₄	semidirect
373. C₂⁴×D₃	C₂×D₄	semidirect
379. C₂²×C₃×D₄	C₂×D₄	semidirect
380. C₂²×C₃×D₄	C₂×D₄	semidirect
381. C₂²×C₃×D₄	C₂×D₄	semidirect
382. C₂²×C₃×D₄	C₂×D₄	semidirect
398. C₂²×#67	C₂×D₄	semidirect
399. C₂²×#67	C₂×D₄	semidirect
400. C₂²×#67	C₂×D₄	semidirect
401. C₂²×#67	C₂×D₄	semidirect
402. C₂²×#67	C₂×D₄	semidirect
403. C₂²×#67	C₂×D₄	semidirect
404. C₂²×#67	C₂×D₄	semidirect
405. C₂²×#67	C₂×D₄	semidirect
406. C₂³×Dic₃	C₂×D₄	semidirect
418. C₂²×D₁₂	C₂×D₄	semidirect
419. C₂²×C₄×D₃	C₂×D₄	semidirect
420. C₂²×C₄×D₃	C₂×D₄	semidirect
421. C₂×C₃×C₂²⋊C₄	C₂×D₄	semidirect
422. C₂×#217	C₂×D₄	semidirect
423. C₂×#217	C₂×D₄	semidirect
424. C₂×#217	C₂×D₄	semidirect
425. C₂×#217	C₂×D₄	semidirect
426. C₂×#217	C₂×D₄	semidirect
427. C₂×#217	C₂×D₄	semidirect
428. C₂×(C₂×D₃)⋊C₄	C₂×D₄	semidirect
429. C₂×(C₂×D₃)⋊C₄	C₂×D₄	semidirect
430. C₂×(C₂×D₃)⋊C₄	C₂×D₄	semidirect
431. C₂×(C₂×D₃)⋊C₄	C₂×D₄	semidirect
432. C₂×(C₂×D₃)⋊C₄	C₂×D₄	semidirect
433. C₂×(C₂×D₃)⋊C₄	C₂×D₄	semidirect
434. C₂×C₄⋊Dic₃	C₂×D₄	semidirect
435. C₂×Dic₃⋊C₄	C₂×D₄	semidirect
436. C₃⋊#95	C₂×D₄	semidirect
508. C₂×#67	#120	semidirect
509. C₂×#67	#120	semidirect
525. C₂⁵	D₃×D₄	semidirect
532. C₂²×D₄	D₃×D₄	semidirect
533. C₂²×D₄	D₃×D₄	semidirect
534. C₂²×D₄	D₃×D₄	semidirect
535. C₂²×D₄	D₃×D₄	semidirect
545. C₂×C₂²⋊C₄	D₃×D₄	semidirect
549. C₂³×C₃	D₄²	semidirect
572. C₂²×D₃	D₄²	semidirect
573. C₂×C₃×C₄	D₄²	semidirect
576. C₂×Dic₃	D₄²	semidirect
635. C₂×D₃	#2403	semidirect
639. C₂³	#5590	semidirect
655. C₂×C₄	#5590	semidirect
706. C₃	#772778	semidirect

Maximal subgroups

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

subgroup	index
C₂²×D₄×#67	2
C₂²×#5590	2
C₂×#73854	2
C₂×#76755	2
C₂×#84052	2
C₂×#82604	2
C₂×#76753	2
C₂×D₃×#392	2
#10746873	2
#10746841	2
#10733591	2
#10733589	2
#10732931	2
#10732921	2
#10732884	2
#10732883	2
#10732878	2
#10732877	2
#10726631	2
#10726629	2
#10726570	2
#10726565	2
#10726564	2
#10726560	2
#10720472	2
#10718640	2
#10718638	2
#10717958	2
#10717955	2
#10717054	2
C₃×#14715	2
#772778	3