Subgroups — C₂²×#87239 #72270916

Order 1536.

149300 conjugacy classes of subgroups.

The subgroup lattice has 870 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×#1004	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#87239	C₂	1	96	yes	maximal, direct product factor
3	C₂²×#5806	C₂	1	8	yes	maximal, complemented
4	C₂²×D₄×#67	C₂	1	8	yes	maximal, complemented
5	C₂²×#5805	C₂	1	2	yes	maximal, complemented
6	C₂²×#5804	C₂	1	4	yes	maximal, complemented
7	C₂²×#5791	C₂	1	2	yes	maximal, complemented
8	C₂³×#953	C₂	1	4	yes	maximal, complemented
9	C₂²×#5798	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂⁵×C₃×D₄	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂²×#3484	—	3	1	no	maximal, Sylow
12	C₂⁷×C₃	C₂²	1	2	yes	complemented
13	C₂⁴×C₃×D₄	—	2	32	no	—
14	C₂⁴×C₃×D₄	C₂²	1	1	yes	characteristic
15	C₂⁴×C₃×D₄	C₂²	1	8	yes	complemented
16	C₂⁴×C₃×D₄	C₂²	1	2	yes	complemented
17	C₂⁴×C₃×D₄	C₂²	1	1	yes	characteristic, complemented
18	C₂⁴×C₃×D₄	C₂²	1	48	yes	complemented
19	C₂⁵×C₃×C₄	C₂²	1	1	yes	characteristic, complemented
20	C₂⁴×#67	C₂²	1	4	yes	complemented
21	C₂⁴×#67	C₂²	1	8	yes	complemented
22	C₂²×#1004	—	2	32	no	—
23	C₂²×#1004	C₂²	1	48	yes	complemented
24	C₂³×D₃×D₄	C₂²	1	4	yes	complemented
25	C₂³×#237	C₂²	1	4	yes	complemented
26	C₂³×#235	C₂²	1	2	yes	complemented
27	C₂²×#953	C₂²	1	4	yes	complemented
28	C₂²×#953	C₂²	1	16	yes	complemented
29	C₂²×#953	C₂²	1	8	yes	complemented
30	C₂²×#953	C₂²	1	192	yes	complemented
31	C₂³×#217	C₂²	1	4	yes	complemented
32	C₂³×#217	C₂²	1	8	yes	complemented
33	#87239	C₂²	1	1024	yes	direct product factor
34	C₂×D₄×#67	C₂²	1	384	yes	complemented
35	C₂×#5805	C₂²	1	96	yes	complemented
36	C₂×#5804	C₂²	1	192	yes	complemented
37	C₂²×#938	C₂²	1	8	yes	complemented
38	C₂²×#937	C₂²	1	8	yes	complemented
39	C₂×#5806	C₂²	1	384	yes	complemented
40	C₂²×#940	C₂²	1	4	yes	complemented
41	C₂²×#936	C₂²	1	4	yes	complemented
42	C₂²×#935	C₂²	1	8	yes	complemented
43	C₂²×#939	C₂²	1	16	yes	complemented
44	C₂×#5798	C₂²	1	48	yes	complemented
45	C₂²×D₄×Dic₃	C₂²	1	8	yes	complemented
46	C₂×#5791	C₂²	1	96	yes	complemented
47	C₂²×#929	C₂²	1	4	yes	complemented
48	C₂²×#930	C₂²	1	4	yes	complemented
49	C₂²×#924	C₂²	1	4	yes	complemented
50	C₂²×C₄×#67	C₂²	1	8	yes	complemented
51	C₂²×#926	C₂²	1	2	yes	complemented
52	C₂³×H(5,𝔽₂)	—	3	1	no	—
53	C₂⁵×D₄	D₃	1	1	yes	characteristic, complemented
54	C₂×#3484	—	3	96	no	—
55	C₂²×#546	—	3	8	no	—
56	C₂²×D₄²	—	3	8	no	—
57	C₂²×#535	—	3	2	no	—
58	C₂²×#534	—	3	4	no	—
59	C₂²×#525	—	3	2	no	—
60	C₂³×#120	—	3	4	no	—
61	C₂²×#518	—	3	1	no	—
62	C₂⁶×C₃	—	2	32	no	—
63	C₂⁶×C₃	—	4	32	no	—
64	C₂⁶×C₃	C₂³	1	1	yes	characteristic
65	C₂⁶×C₃	C₂³	1	8	yes	—
66	C₂⁶×C₃	C₂³	1	2	yes	—
67	C₂⁶×C₃	C₂³	1	2	yes	—
68	C₂⁶×C₃	C₂³	1	48	yes	complemented
69	C₂⁵×D₃	C₂³	1	4	yes	complemented
70	C₂³×C₃×D₄	—	2	128	no	—
71	C₂³×C₃×D₄	—	2	768	no	—
72	C₂³×C₃×D₄	—	2	16	no	—
73	C₂³×C₃×D₄	—	2	32	no	—
74	C₂³×C₃×D₄	D₄	1	32	yes	complemented
75	C₂³×C₃×D₄	C₂³	1	8	yes	—
76	C₂³×C₃×D₄	C₂³	1	4	yes	—
77	C₂³×C₃×D₄	C₂³	1	4	yes	—
78	C₂³×C₃×D₄	C₂³	1	24	yes	—
79	C₂³×C₃×D₄	C₂³	1	192	yes	complemented
80	C₂³×C₃×D₄	C₂³	1	48	yes	complemented
81	C₂³×C₃×D₄	C₂³	1	24	yes	complemented
82	C₂³×C₃×D₄	C₂³	1	256	yes	complemented
83	C₂⁴×C₃×C₄	—	2	16	no	—
84	C₂⁴×C₃×C₄	C₂³	1	4	yes	—
85	C₂⁴×C₃×C₄	C₂³	1	1	yes	characteristic
86	C₂⁴×C₃×C₄	C₂³	1	1	yes	characteristic
87	C₂⁴×C₃×C₄	C₂³	1	24	yes	complemented
88	C₂³×#67	—	2	64	no	—
89	C₂³×#67	—	4	64	no	—
90	C₂³×#67	C₂³	1	4	yes	—
91	C₂³×#67	C₂³	1	8	yes	—
92	C₂³×#67	C₂³	1	8	yes	complemented
93	C₂³×#67	C₂³	1	16	yes	complemented
94	C₂³×#67	C₂³	1	96	yes	complemented
95	C₂³×#67	C₂³	1	192	yes	complemented
96	C₂⁴×Dic₃	C₂³	1	4	yes	complemented
97	C₂⁴×Dic₃	C₂³	1	8	yes	complemented
98	C₂×#1004	—	2	768	no	—
99	C₂×#1004	C₂³	1	256	yes	complemented
100	C₂²×#237	—	2	64	no	—
101	C₂²×#237	C₂³	1	96	yes	complemented
102	C₂²×D₃×D₄	—	2	64	no	—
103	C₂²×D₃×D₄	C₂³	1	96	yes	complemented
104	C₂²×#235	—	2	32	no	—
105	C₂²×#235	C₂³	1	48	yes	complemented
106	C₂³×D₁₂	C₂³	1	2	yes	complemented
107	C₂³×C₄×D₃	C₂³	1	4	yes	complemented
108	C₂³×Dic₆	C₂³	1	2	yes	complemented
109	C₂×#953	C₂³	1	96	yes	complemented
110	C₂×#953	C₂³	1	384	yes	complemented
111	C₂×#953	C₂³	1	192	yes	complemented
112	C₂×#953	C₂³	1	1024	yes	complemented
113	C₂²×#217	C₂³	1	4	yes	—
114	C₂²×#217	C₂³	1	8	yes	—
115	C₂²×#217	C₂³	1	96	yes	complemented
116	C₂²×#217	C₂³	1	192	yes	complemented
117	C₂²×#217	C₂³	1	8	yes	complemented
118	C₂²×#217	C₂³	1	16	yes	complemented
119	#5806	C₂³	1	2048	yes	complemented
120	#5805	C₂³	1	512	yes	complemented
121	#5804	C₂³	1	1024	yes	complemented
122	C₂×#940	C₂³	1	96	yes	complemented
123	C₂×#939	C₂³	1	384	yes	complemented
124	D₄×#67	C₂³	1	2048	yes	complemented
125	C₂×#938	C₂³	1	192	yes	complemented
126	C₂×#937	C₂³	1	192	yes	complemented
127	#5798	C₂³	1	256	yes	complemented
128	C₂×#936	C₂³	1	96	yes	complemented
129	C₂×#935	C₂³	1	192	yes	complemented
130	C₂×D₄×Dic₃	C₂³	1	192	yes	complemented
131	#5791	C₂³	1	512	yes	complemented
132	C₂×#930	C₂³	1	96	yes	complemented
133	C₂×#929	C₂³	1	96	yes	complemented
134	C₂×C₄×#67	C₂³	1	192	yes	complemented
135	C₂²×(C₂×D₃)⋊C₄	C₂³	1	8	yes	complemented
136	C₂×#926	C₂³	1	48	yes	complemented
137	C₂²×C₄⋊Dic₃	C₂³	1	4	yes	complemented
138	C₂×#924	C₂³	1	96	yes	complemented
139	C₂²×Dic₃⋊C₄	C₂³	1	8	yes	complemented
140	C₂²×C₄×Dic₃	C₂³	1	4	yes	complemented
141	C₂⁷	C₂×D₃	1	2	yes	complemented
142	C₂²×H(5,𝔽₂)	—	3	48	no	—
143	C₂²×H(5,𝔽₂)	—	6	32	no	—
144	C₂³×#41	—	3	4	no	—
145	C₂³×#41	—	3	2	no	—
146	C₂⁴×D₄	—	2	32	no	—
147	C₂⁴×D₄	—	3	4	no	—
148	C₂⁴×D₄	—	3	8	no	—
149	C₂⁴×D₄	—	3	4	no	—
150	C₂⁴×D₄	C₂×D₃	1	1	yes	characteristic
151	C₂⁴×D₄	C₂×D₃	1	2	yes	complemented
152	C₂⁴×D₄	C₂×D₃	1	1	yes	characteristic, complemented
153	C₂⁴×D₄	C₂×D₃	1	8	yes	complemented
154	C₂⁴×D₄	C₂×D₃	1	48	yes	complemented
155	C₂⁵×C₄	C₂×D₃	1	1	yes	characteristic, complemented
156	#3484	—	3	1024	no	—
157	C₂×#546	—	3	384	no	—
158	C₂×D₄²	—	3	384	no	—
159	C₂×#535	—	3	96	no	—
160	C₂×#534	—	3	192	no	—
161	C₂²×#127	—	3	4	no	—
162	C₂²×#124	—	3	4	no	—
163	C₂×#525	—	3	96	no	—
164	C₂²×#123	—	3	8	no	—
165	C₂²×#123	—	3	4	no	—
166	C₂²×C₂²⋊Q₈	—	3	4	no	—
167	C₂²×#121	—	3	16	no	—
168	C₂²×#121	—	3	8	no	—
169	C₂²×#121	—	3	4	no	—
170	C₂²×#120	—	3	4	no	—
171	C₂²×#120	—	3	8	no	—
172	C₂²×#120	—	3	16	no	—
173	C₂²×#120	—	3	192	no	—
174	C₂²×#120	—	3	8	no	—
175	C₂×#518	—	3	48	no	—
176	C₂²×C₄×D₄	—	3	8	no	—
177	C₂²×C₄×D₄	—	3	8	no	—
178	C₂²×#117	—	3	2	no	—
179	C₂³×C₂²⋊C₄	—	3	4	no	—
180	C₂³×C₂²⋊C₄	—	3	8	no	—
181	C₂⁵×C₃	—	2	8	no	—
182	C₂⁵×C₃	—	2	16	no	—
183	C₂⁵×C₃	—	2	64	no	—
184	C₂⁵×C₃	—	2	16	no	—
185	C₂⁵×C₃	—	2	384	no	—
186	C₂⁵×C₃	—	2	64	no	—
187	C₂⁵×C₃	—	4	16	no	—
188	C₂⁵×C₃	—	4	32	no	—
189	C₂⁵×C₃	—	4	16	no	—
190	C₂⁵×C₃	—	4	384	no	—
191	C₂⁵×C₃	—	4	512	no	—
192	C₂⁵×C₃	C₂×D₄	1	32	yes	complemented
193	C₂⁵×C₃	C₂⁴	1	4	yes	—
194	C₂⁵×C₃	C₂⁴	1	12	yes	—
195	C₂⁵×C₃	C₂⁴	1	96	yes	—
196	C₂⁵×C₃	C₂⁴	1	4	yes	—
197	C₂⁵×C₃	C₂⁴	1	1	yes	characteristic
198	C₂⁵×C₃	C₂⁴	1	2	yes	—
199	C₂⁵×C₃	C₂⁴	1	24	yes	—
200	C₂⁵×C₃	C₂⁴	1	24	yes	—
201	C₂⁵×C₃	C₂⁴	1	128	yes	complemented
202	C₂⁴×D₃	—	2	32	no	—
203	C₂⁴×D₃	—	4	32	no	—
204	C₂⁴×D₃	C₂⁴	1	4	yes	—
205	C₂⁴×D₃	C₂⁴	1	48	yes	complemented
206	C₂²×C₃×D₄	—	2	64	no	—
207	C₂²×C₃×D₄	—	2	384	no	—
208	C₂²×C₃×D₄	—	2	1536	no	—
209	C₂²×C₃×D₄	—	2	2048	no	—
210	C₂²×C₃×D₄	—	2	32	no	—
211	C₂²×C₃×D₄	—	2	192	no	—
212	C₂²×C₃×D₄	C₂×D₄	1	64	yes	complemented
213	C₂²×C₃×D₄	C₂×D₄	1	384	yes	complemented
214	C₂²×C₃×D₄	C₂⁴	1	96	yes	—
215	C₂²×C₃×D₄	C₂⁴	1	48	yes	—
216	C₂²×C₃×D₄	C₂⁴	1	48	yes	—
217	C₂²×C₃×D₄	C₂⁴	1	64	yes	—
218	C₂²×C₃×D₄	C₂⁴	1	512	yes	complemented
219	C₂²×C₃×D₄	C₂⁴	1	128	yes	complemented
220	C₂²×C₃×D₄	C₂⁴	1	64	yes	complemented
221	C₂³×C₃×C₄	—	2	8	no	—
222	C₂³×C₃×C₄	—	2	32	no	—
223	C₂³×C₃×C₄	—	2	192	no	—
224	C₂³×C₃×C₄	C₂×D₄	1	16	yes	complemented
225	C₂³×C₃×C₄	C₂⁴	1	2	yes	—
226	C₂³×C₃×C₄	C₂⁴	1	48	yes	—
227	C₂³×C₃×C₄	C₂⁴	1	12	yes	—
228	C₂³×C₃×C₄	C₂⁴	1	2	yes	—
229	C₂³×C₃×C₄	C₂⁴	1	12	yes	—
230	C₂³×C₃×C₄	C₂⁴	1	64	yes	complemented
231	C₂²×#67	—	2	32	no	—
232	C₂²×#67	—	2	64	no	—
233	C₂²×#67	—	2	768	no	—
234	C₂²×#67	—	2	64	no	—
235	C₂²×#67	—	4	64	no	—
236	C₂²×#67	—	4	768	no	—
237	C₂²×#67	C₂⁴	1	48	yes	—
238	C₂²×#67	C₂⁴	1	96	yes	—
239	C₂²×#67	C₂⁴	1	96	yes	complemented
240	C₂²×#67	C₂⁴	1	192	yes	complemented
241	C₂²×#67	C₂⁴	1	256	yes	complemented
242	C₂²×#67	C₂⁴	1	512	yes	complemented
243	C₂³×Dic₃	—	2	32	no	—
244	C₂³×Dic₃	—	4	32	no	—
245	C₂³×Dic₃	C₂⁴	1	4	yes	—
246	C₂³×Dic₃	C₂⁴	1	8	yes	—
247	C₂³×Dic₃	C₂⁴	1	48	yes	complemented
248	C₂³×Dic₃	C₂⁴	1	96	yes	complemented
249	#1004	—	2	2048	no	—
250	C₂×#237	—	2	768	no	—
251	C₂×#237	C₂⁴	1	256	yes	complemented
252	C₂×D₃×D₄	—	2	768	no	—
253	C₂×D₃×D₄	C₂⁴	1	256	yes	complemented
254	C₂×#235	—	2	384	no	—
255	C₂×#235	C₂⁴	1	128	yes	complemented
256	C₂²×D₁₂	—	2	16	no	—
257	C₂²×D₁₂	C₂⁴	1	24	yes	complemented
258	C₂²×C₄×D₃	—	2	32	no	—
259	C₂²×C₄×D₃	C₂⁴	1	48	yes	complemented
260	C₂²×Dic₆	—	2	16	no	—
261	C₂²×Dic₆	C₂⁴	1	24	yes	complemented
262	#953	C₂⁴	1	256	yes	complemented
263	#953	C₂⁴	1	1024	yes	complemented
264	#953	C₂⁴	1	512	yes	complemented
265	C₂×#217	C₂⁴	1	96	yes	—
266	C₂×#217	C₂⁴	1	48	yes	—
267	C₂×#217	C₂⁴	1	256	yes	complemented
268	C₂×#217	C₂⁴	1	512	yes	complemented
269	C₂×#217	C₂⁴	1	96	yes	complemented
270	C₂×#217	C₂⁴	1	192	yes	complemented
271	#940	C₂⁴	1	256	yes	complemented
272	#939	C₂⁴	1	1024	yes	complemented
273	#938	C₂⁴	1	512	yes	complemented
274	#937	C₂⁴	1	512	yes	complemented
275	#936	C₂⁴	1	256	yes	complemented
276	#935	C₂⁴	1	512	yes	complemented
277	D₄×Dic₃	C₂⁴	1	512	yes	complemented
278	#930	C₂⁴	1	256	yes	complemented
279	#929	C₂⁴	1	256	yes	complemented
280	C₄×#67	C₂⁴	1	512	yes	complemented
281	C₂×(C₂×D₃)⋊C₄	C₂⁴	1	96	yes	complemented
282	#926	C₂⁴	1	128	yes	complemented
283	C₂×C₄⋊Dic₃	C₂⁴	1	48	yes	complemented
284	#924	C₂⁴	1	256	yes	complemented
285	C₂×Dic₃⋊C₄	C₂⁴	1	96	yes	complemented
286	C₂×C₄×Dic₃	C₂⁴	1	48	yes	complemented
287	C₂⁶	—	2	32	no	—
288	C₂⁶	—	3	4	no	—
289	C₂⁶	—	4	32	no	—
290	C₂⁶	C₂²×D₃	1	1	yes	characteristic
291	C₂⁶	C₂²×D₃	1	8	yes	—
292	C₂⁶	C₂²×D₃	1	2	yes	—
293	C₂⁶	C₂²×D₃	1	2	yes	—
294	C₂⁶	C₂²×D₃	1	48	yes	complemented
295	C₂×H(5,𝔽₂)	—	3	256	no	—
296	C₂×H(5,𝔽₂)	—	6	768	no	—
297	C₂²×#41	—	3	96	no	—
298	C₂²×#41	—	3	48	no	—
299	C₂²×#41	—	6	64	no	—
300	C₂²×#41	—	6	32	no	—
301	C₂³×Q₈	—	3	2	no	—
302	C₂³×D₄	—	2	32	no	—
303	C₂³×D₄	—	2	128	no	—
304	C₂³×D₄	—	2	768	no	—
305	C₂³×D₄	—	2	16	no	—
306	C₂³×D₄	—	3	4	no	—
307	C₂³×D₄	—	3	8	no	—
308	C₂³×D₄	—	3	8	no	—
309	C₂³×D₄	—	3	96	no	—
310	C₂³×D₄	—	3	16	no	—
311	C₂³×D₄	—	3	192	no	—
312	C₂³×D₄	—	3	96	no	—
313	C₂³×D₄	—	3	2	no	—
314	C₂³×D₄	—	6	64	no	—
315	C₂³×D₄	—	6	64	no	—
316	C₂³×D₄	—	12	64	no	—
317	C₂³×D₄	#67	1	32	yes	complemented
318	C₂³×D₄	C₂²×D₃	1	8	yes	—
319	C₂³×D₄	C₂²×D₃	1	4	yes	—
320	C₂³×D₄	C₂²×D₃	1	4	yes	—
321	C₂³×D₄	C₂²×D₃	1	24	yes	—
322	C₂³×D₄	C₂²×D₃	1	48	yes	complemented
323	C₂³×D₄	C₂²×D₃	1	24	yes	complemented
324	C₂³×D₄	C₂²×D₃	1	192	yes	complemented
325	C₂³×D₄	C₂²×D₃	1	256	yes	complemented
326	C₂⁴×C₄	—	2	16	no	—
327	C₂⁴×C₄	—	3	4	no	—
328	C₂⁴×C₄	—	3	8	no	—
329	C₂⁴×C₄	—	3	4	no	—
330	C₂⁴×C₄	C₂²×D₃	1	4	yes	—
331	C₂⁴×C₄	C₂²×D₃	1	1	yes	characteristic
332	C₂⁴×C₄	C₂²×D₃	1	1	yes	characteristic
333	C₂⁴×C₄	C₂²×D₃	1	24	yes	complemented
334	#546	—	3	2048	no	—
335	D₄²	—	3	2048	no	—
336	#535	—	3	512	no	—
337	#534	—	3	1024	no	—
338	C₂×#127	—	3	96	no	—
339	C₂×#124	—	3	96	no	—
340	#525	—	3	512	no	—
341	C₂×#123	—	3	192	no	—
342	C₂×#123	—	3	96	no	—
343	C₂×C₂²⋊Q₈	—	3	96	no	—
344	C₂×#121	—	3	384	no	—
345	C₂×#121	—	3	192	no	—
346	C₂×#121	—	3	96	no	—
347	C₂×#120	—	3	96	no	—
348	C₂×#120	—	3	192	no	—
349	C₂×#120	—	3	384	no	—
350	C₂×#120	—	3	1024	no	—
351	C₂×#120	—	3	192	no	—
352	#518	—	3	256	no	—
353	C₂×C₄×D₄	—	3	192	no	—
354	C₂×C₄×D₄	—	3	192	no	—
355	C₂×#117	—	3	48	no	—
356	C₂²×C₄⋊C₄	—	3	4	no	—
357	C₂²×C₄⋊C₄	—	3	8	no	—
358	C₂²×C₂²⋊C₄	—	3	4	no	—
359	C₂²×C₂²⋊C₄	—	3	8	no	—
360	C₂²×C₂²⋊C₄	—	3	8	no	—
361	C₂²×C₂²⋊C₄	—	3	96	no	—
362	C₂²×C₂²⋊C₄	—	3	16	no	—
363	C₂²×C₂²⋊C₄	—	3	192	no	—
364	C₂²×C₂²⋊C₄	—	3	8	no	—
365	C₂²×C₄²	—	3	4	no	—
366	C₂⁴×C₃	—	2	128	no	—
367	C₂⁴×C₃	—	2	48	no	—
368	C₂⁴×C₃	—	2	8	no	—
369	C₂⁴×C₃	—	2	8	no	—
370	C₂⁴×C₃	—	2	8	no	—
371	C₂⁴×C₃	—	2	32	no	—
372	C₂⁴×C₃	—	2	96	no	—
373	C₂⁴×C₃	—	2	384	no	—
374	C₂⁴×C₃	—	2	96	no	—
375	C₂⁴×C₃	—	2	16	no	—
376	C₂⁴×C₃	—	2	512	no	—
377	C₂⁴×C₃	—	2	32	no	—
378	C₂⁴×C₃	—	2	384	no	—
379	C₂⁴×C₃	—	4	128	no	—
380	C₂⁴×C₃	—	4	96	no	—
381	C₂⁴×C₃	—	4	192	no	—
382	C₂⁴×C₃	—	4	96	no	—
383	C₂⁴×C₃	—	4	512	no	—
384	C₂⁴×C₃	—	4	512	no	—
385	C₂⁴×C₃	—	4	3072	no	—
386	C₂⁴×C₃	—	4	128	no	—
387	C₂⁴×C₃	C₂²×D₄	1	8	yes	—
388	C₂⁴×C₃	C₂²×D₄	1	32	yes	—
389	C₂⁴×C₃	C₂²×D₄	1	192	yes	complemented
390	C₂⁴×C₃	H(5,𝔽₂)	1	16	yes	complemented
391	C₂⁴×C₃	C₂⁵	1	24	yes	—
392	C₂⁴×C₃	C₂⁵	1	16	yes	—
393	C₂⁴×C₃	C₂⁵	1	128	yes	—
394	C₂⁴×C₃	C₂⁵	1	6	yes	—
395	C₂⁴×C₃	C₂⁵	1	24	yes	—
396	C₂⁴×C₃	C₂⁵	1	12	yes	—
397	C₂⁴×C₃	C₂⁵	1	32	yes	—
398	C₂⁴×C₃	C₂⁵	1	32	yes	—
399	C₂⁴×C₃	C₂⁵	1	1	yes	characteristic
400	C₂³×D₃	—	2	16	no	—
401	C₂³×D₃	—	2	32	no	—
402	C₂³×D₃	—	2	192	no	—
403	C₂³×D₃	—	4	192	no	—
404	C₂³×D₃	—	8	128	no	—
405	C₂³×D₃	C₂⁵	1	24	yes	—
406	C₂³×D₃	C₂⁵	1	64	yes	complemented
407	C₂×C₃×D₄	—	2	384	no	—
408	C₂×C₃×D₄	—	2	512	no	—
409	C₂×C₃×D₄	—	2	2048	no	—
410	C₂×C₃×D₄	—	2	192	no	—
411	C₂×C₃×D₄	—	2	256	no	—
412	C₂×C₃×D₄	C₂²×D₄	1	384	yes	complemented
413	C₂×C₃×D₄	C₂²×D₄	1	512	yes	complemented
414	C₂×C₃×D₄	C₂⁵	1	128	yes	—
415	C₂×C₃×D₄	C₂⁵	1	64	yes	—
416	C₂×C₃×D₄	C₂⁵	1	64	yes	—
417	C₂²×C₃×C₄	—	2	48	no	—
418	C₂²×C₃×C₄	—	2	8	no	—
419	C₂²×C₃×C₄	—	2	192	no	—
420	C₂²×C₃×C₄	—	2	256	no	—
421	C₂²×C₃×C₄	C₂²×D₄	1	16	yes	—
422	C₂²×C₃×C₄	C₂²×D₄	1	96	yes	complemented
423	C₂²×C₃×C₄	C₂⁵	1	12	yes	—
424	C₂²×C₃×C₄	C₂⁵	1	64	yes	—
425	C₂²×C₃×C₄	C₂⁵	1	16	yes	—
426	C₂²×C₃×C₄	C₂⁵	1	12	yes	—
427	C₂²×C₃×C₄	C₂⁵	1	16	yes	—
428	C₂×#67	—	2	192	no	—
429	C₂×#67	—	2	384	no	—
430	C₂×#67	—	2	1024	no	—
431	C₂×#67	—	2	384	no	—
432	C₂×#67	—	4	384	no	—
433	C₂×#67	—	4	1024	no	—
434	C₂×#67	C₂⁵	1	128	yes	—
435	C₂×#67	C₂⁵	1	64	yes	—
436	C₂×#67	C₂⁵	1	128	yes	complemented
437	C₂×#67	C₂⁵	1	256	yes	complemented
438	C₂²×Dic₃	—	2	16	no	—
439	C₂²×Dic₃	—	2	192	no	—
440	C₂²×Dic₃	—	2	32	no	—
441	C₂²×Dic₃	—	4	192	no	—
442	C₂²×Dic₃	C₂⁵	1	48	yes	—
443	C₂²×Dic₃	C₂⁵	1	24	yes	—
444	C₂²×Dic₃	C₂⁵	1	64	yes	complemented
445	C₂²×Dic₃	C₂⁵	1	128	yes	complemented
446	#237	—	2	1024	no	—
447	D₃×D₄	—	2	1024	no	—
448	#235	—	2	512	no	—
449	C₂×D₁₂	—	2	96	no	—
450	C₂×D₁₂	C₂⁵	1	32	yes	complemented
451	C₂×C₄×D₃	—	2	192	no	—
452	C₂×C₄×D₃	C₂⁵	1	64	yes	complemented
453	C₂×Dic₆	—	2	96	no	—
454	C₂×Dic₆	C₂⁵	1	32	yes	complemented
455	#217	C₂⁵	1	128	yes	—
456	#217	C₂⁵	1	64	yes	—
457	#217	C₂⁵	1	128	yes	complemented
458	#217	C₂⁵	1	256	yes	complemented
459	(C₂×D₃)⋊C₄	C₂⁵	1	128	yes	complemented
460	C₄⋊Dic₃	C₂⁵	1	64	yes	complemented
461	Dic₃⋊C₄	C₂⁵	1	128	yes	complemented
462	C₄×Dic₃	C₂⁵	1	64	yes	complemented
463	C₂⁵	—	2	16	no	—
464	C₂⁵	—	2	8	no	—
465	C₂⁵	—	2	64	no	—
466	C₂⁵	—	2	64	no	—
467	C₂⁵	—	2	16	no	—
468	C₂⁵	—	2	384	no	—
469	C₂⁵	—	3	4	no	—
470	C₂⁵	—	3	48	no	—
471	C₂⁵	—	4	16	no	—
472	C₂⁵	—	4	32	no	—
473	C₂⁵	—	4	16	no	—
474	C₂⁵	—	4	384	no	—
475	C₂⁵	—	4	512	no	—
476	C₂⁵	—	6	32	no	—
477	C₂⁵	—	12	32	no	—
478	C₂⁵	C₂×#67	1	32	yes	complemented
479	C₂⁵	C₂³×D₃	1	12	yes	—
480	C₂⁵	C₂³×D₃	1	4	yes	—
481	C₂⁵	C₂³×D₃	1	96	yes	—
482	C₂⁵	C₂³×D₃	1	2	yes	—
483	C₂⁵	C₂³×D₃	1	1	yes	characteristic
484	C₂⁵	C₂³×D₃	1	4	yes	—
485	C₂⁵	C₂³×D₃	1	24	yes	—
486	C₂⁵	C₂³×D₃	1	24	yes	—
487	C₂⁵	C₂³×D₃	1	128	yes	complemented
488	H(5,𝔽₂)	—	6	2048	no	—
489	C₂×#41	—	3	256	no	—
490	C₂×#41	—	3	128	no	—
491	C₂×#41	—	6	768	no	—
492	C₂×#41	—	6	384	no	—
493	C₂²×Q₈	—	3	24	no	—
494	C₂²×Q₈	—	6	16	no	—
495	C₂²×D₄	—	2	64	no	—
496	C₂²×D₄	—	2	384	no	—
497	C₂²×D₄	—	2	1536	no	—
498	C₂²×D₄	—	2	2048	no	—
499	C₂²×D₄	—	2	32	no	—
500	C₂²×D₄	—	2	192	no	—
501	C₂²×D₄	—	3	96	no	—
502	C₂²×D₄	—	3	48	no	—
503	C₂²×D₄	—	3	96	no	—
504	C₂²×D₄	—	3	256	no	—
505	C₂²×D₄	—	3	192	no	—
506	C₂²×D₄	—	3	512	no	—
507	C₂²×D₄	—	3	256	no	—
508	C₂²×D₄	—	3	24	no	—
509	C₂²×D₄	—	6	64	no	—
510	C₂²×D₄	—	6	32	no	—
511	C₂²×D₄	—	6	64	no	—
512	C₂²×D₄	—	6	768	no	—
513	C₂²×D₄	—	6	768	no	—
514	C₂²×D₄	—	6	16	no	—
515	C₂²×D₄	—	12	64	no	—
516	C₂²×D₄	—	12	768	no	—
517	C₂²×D₄	C₂×#67	1	64	yes	complemented
518	C₂²×D₄	C₂×#67	1	384	yes	complemented
519	C₂²×D₄	C₂³×D₃	1	96	yes	—
520	C₂²×D₄	C₂³×D₃	1	48	yes	—
521	C₂²×D₄	C₂³×D₃	1	48	yes	—
522	C₂²×D₄	C₂³×D₃	1	64	yes	—
523	C₂²×D₄	C₂³×D₃	1	128	yes	complemented
524	C₂²×D₄	C₂³×D₃	1	64	yes	complemented
525	C₂²×D₄	C₂³×D₃	1	512	yes	complemented
526	C₂³×C₄	—	2	8	no	—
527	C₂³×C₄	—	2	32	no	—
528	C₂³×C₄	—	2	192	no	—
529	C₂³×C₄	—	3	48	no	—
530	C₂³×C₄	—	3	8	no	—
531	C₂³×C₄	—	3	4	no	—
532	C₂³×C₄	—	3	96	no	—
533	C₂³×C₄	—	3	48	no	—
534	C₂³×C₄	—	6	32	no	—
535	C₂³×C₄	—	6	32	no	—
536	C₂³×C₄	—	12	32	no	—
537	C₂³×C₄	C₂×#67	1	16	yes	complemented
538	C₂³×C₄	C₂³×D₃	1	48	yes	—
539	C₂³×C₄	C₂³×D₃	1	12	yes	—
540	C₂³×C₄	C₂³×D₃	1	2	yes	—
541	C₂³×C₄	C₂³×D₃	1	2	yes	—
542	C₂³×C₄	C₂³×D₃	1	12	yes	—
543	C₂³×C₄	C₂³×D₃	1	64	yes	complemented
544	#127	—	3	256	no	—
545	#124	—	3	256	no	—
546	#123	—	3	512	no	—
547	#123	—	3	256	no	—
548	C₂²⋊Q₈	—	3	256	no	—
549	#121	—	3	1024	no	—
550	#121	—	3	512	no	—
551	#121	—	3	256	no	—
552	#120	—	3	256	no	—
553	#120	—	3	512	no	—
554	#120	—	3	1024	no	—
555	#120	—	3	512	no	—
556	C₄×D₄	—	3	512	no	—
557	C₄×D₄	—	3	512	no	—
558	#117	—	3	128	no	—
559	C₂×C₄⋊C₄	—	3	48	no	—
560	C₂×C₄⋊C₄	—	3	96	no	—
561	C₂×C₂²⋊C₄	—	3	48	no	—
562	C₂×C₂²⋊C₄	—	3	96	no	—
563	C₂×C₂²⋊C₄	—	3	96	no	—
564	C₂×C₂²⋊C₄	—	3	256	no	—
565	C₂×C₂²⋊C₄	—	3	192	no	—
566	C₂×C₂²⋊C₄	—	3	512	no	—
567	C₂×C₂²⋊C₄	—	3	96	no	—
568	C₂×C₄²	—	3	48	no	—
569	C₂³×C₃	—	2	384	no	—
570	C₂³×C₃	—	2	32	no	—
571	C₂³×C₃	—	2	24	no	—
572	C₂³×C₃	—	2	96	no	—
573	C₂³×C₃	—	2	24	no	—
574	C₂³×C₃	—	2	24	no	—
575	C₂³×C₃	—	2	64	no	—
576	C₂³×C₃	—	2	128	no	—
577	C₂³×C₃	—	2	32	no	—
578	C₂³×C₃	—	2	64	no	—
579	C₂³×C₃	—	2	256	no	—
580	C₂³×C₃	—	2	64	no	—
581	C₂³×C₃	—	2	48	no	—
582	C₂³×C₃	—	2	96	no	—
583	C₂³×C₃	—	2	256	no	—
584	C₂³×C₃	—	4	384	no	—
585	C₂³×C₃	—	4	64	no	—
586	C₂³×C₃	—	4	128	no	—
587	C₂³×C₃	—	4	64	no	—
588	C₂³×C₃	—	4	1536	no	—
589	C₂³×C₃	—	4	2048	no	—
590	C₂³×C₃	—	4	384	no	—
591	C₂³×C₃	—	4	64	no	—
592	C₂³×C₃	C₂³×D₄	1	96	yes	—
593	C₂³×C₃	C₂³×D₄	1	24	yes	—
594	C₂³×C₃	C₂³×D₄	1	4	yes	—
595	C₂³×C₃	C₂³×D₄	1	128	yes	complemented
596	C₂³×C₃	C₂×H(5,𝔽₂)	1	8	yes	—
597	C₂³×C₃	C₂×H(5,𝔽₂)	1	48	yes	complemented
598	C₂³×C₃	C₂⁶	1	16	yes	—
599	C₂³×C₃	C₂⁶	1	4	yes	—
600	C₂³×C₃	C₂⁶	1	16	yes	—
601	C₂³×C₃	C₂⁶	1	8	yes	—
602	C₂³×C₃	C₂⁶	1	3	yes	—
603	C₂²×D₃	—	2	48	no	—
604	C₂²×D₃	—	2	96	no	—
605	C₂²×D₃	—	2	128	no	—
606	C₂²×D₃	—	4	128	no	—
607	C₂²×D₃	—	4	64	no	—
608	C₂²×D₃	—	8	384	no	—
609	C₂²×D₃	C₂⁶	1	16	yes	—
610	C₃×D₄	—	2	256	no	—
611	C₃×D₄	—	2	128	no	—
612	C₃×D₄	C₂³×D₄	1	256	yes	complemented
613	C₂×C₃×C₄	—	2	32	no	—
614	C₂×C₃×C₄	—	2	24	no	—
615	C₂×C₃×C₄	—	2	128	no	—
616	C₂×C₃×C₄	C₂³×D₄	1	48	yes	—
617	C₂×C₃×C₄	C₂³×D₄	1	64	yes	complemented
618	C₂×C₃×C₄	C₂⁶	1	8	yes	—
619	C₂×C₃×C₄	C₂⁶	1	8	yes	—
620	#67	—	2	128	no	—
621	#67	—	2	256	no	—
622	#67	—	2	256	no	—
623	#67	—	4	256	no	—
624	C₂×Dic₃	—	2	48	no	—
625	C₂×Dic₃	—	2	128	no	—
626	C₂×Dic₃	—	2	96	no	—
627	C₂×Dic₃	—	4	128	no	—
628	C₂×Dic₃	C₂⁶	1	32	yes	—
629	C₂×Dic₃	C₂⁶	1	16	yes	—
630	D₁₂	—	2	64	no	—
631	C₄×D₃	—	2	128	no	—
632	Dic₆	—	2	64	no	—
633	C₂⁴	—	2	128	no	—
634	C₂⁴	—	2	32	no	—
635	C₂⁴	—	2	8	no	—
636	C₂⁴	—	2	8	no	—
637	C₂⁴	—	2	96	no	—
638	C₂⁴	—	2	48	no	—
639	C₂⁴	—	2	8	no	—
640	C₂⁴	—	2	32	no	—
641	C₂⁴	—	2	384	no	—
642	C₂⁴	—	2	384	no	—
643	C₂⁴	—	2	96	no	—
644	C₂⁴	—	2	16	no	—
645	C₂⁴	—	2	512	no	—
646	C₂⁴	—	3	24	no	—
647	C₂⁴	—	3	64	no	—
648	C₂⁴	—	4	128	no	—
649	C₂⁴	—	4	96	no	—
650	C₂⁴	—	4	192	no	—
651	C₂⁴	—	4	96	no	—
652	C₂⁴	—	4	512	no	—
653	C₂⁴	—	4	512	no	—
654	C₂⁴	—	4	3072	no	—
655	C₂⁴	—	4	128	no	—
656	C₂⁴	—	6	32	no	—
657	C₂⁴	—	6	16	no	—
658	C₂⁴	—	6	192	no	—
659	C₂⁴	—	12	192	no	—
660	C₂⁴	—	24	128	no	—
661	C₂⁴	#1004	1	16	yes	complemented
662	C₂⁴	C₂²×#67	1	8	yes	—
663	C₂⁴	C₂²×#67	1	32	yes	—
664	C₂⁴	C₂²×#67	1	192	yes	complemented
665	C₂⁴	C₂⁴×D₃	1	24	yes	—
666	C₂⁴	C₂⁴×D₃	1	16	yes	—
667	C₂⁴	C₂⁴×D₃	1	128	yes	—
668	C₂⁴	C₂⁴×D₃	1	12	yes	—
669	C₂⁴	C₂⁴×D₃	1	6	yes	—
670	C₂⁴	C₂⁴×D₃	1	24	yes	—
671	C₂⁴	C₂⁴×D₃	1	32	yes	—
672	C₂⁴	C₂⁴×D₃	1	32	yes	—
673	C₂⁴	C₂⁴×D₃	1	1	yes	characteristic
674	#41	—	6	1024	no	—
675	#41	—	6	512	no	—
676	C₂×Q₈	—	3	32	no	—
677	C₂×Q₈	—	6	96	no	—
678	C₂×D₄	—	2	384	no	—
679	C₂×D₄	—	2	512	no	—
680	C₂×D₄	—	2	2048	no	—
681	C₂×D₄	—	2	192	no	—
682	C₂×D₄	—	2	256	no	—
683	C₂×D₄	—	3	128	no	—
684	C₂×D₄	—	3	64	no	—
685	C₂×D₄	—	3	128	no	—
686	C₂×D₄	—	3	256	no	—
687	C₂×D₄	—	3	32	no	—
688	C₂×D₄	—	6	384	no	—
689	C₂×D₄	—	6	192	no	—
690	C₂×D₄	—	6	384	no	—
691	C₂×D₄	—	6	1024	no	—
692	C₂×D₄	—	6	1024	no	—
693	C₂×D₄	—	6	96	no	—
694	C₂×D₄	—	12	384	no	—
695	C₂×D₄	—	12	1024	no	—
696	C₂×D₄	C₂²×#67	1	384	yes	complemented
697	C₂×D₄	C₂²×#67	1	512	yes	complemented
698	C₂×D₄	C₂⁴×D₃	1	128	yes	—
699	C₂×D₄	C₂⁴×D₃	1	64	yes	—
700	C₂×D₄	C₂⁴×D₃	1	64	yes	—
701	C₂²×C₄	—	2	48	no	—
702	C₂²×C₄	—	2	8	no	—
703	C₂²×C₄	—	2	192	no	—
704	C₂²×C₄	—	2	256	no	—
705	C₂²×C₄	—	3	48	no	—
706	C₂²×C₄	—	3	24	no	—
707	C₂²×C₄	—	3	64	no	—
708	C₂²×C₄	—	3	128	no	—
709	C₂²×C₄	—	3	64	no	—
710	C₂²×C₄	—	6	32	no	—
711	C₂²×C₄	—	6	16	no	—
712	C₂²×C₄	—	6	192	no	—
713	C₂²×C₄	—	6	192	no	—
714	C₂²×C₄	—	12	192	no	—
715	C₂²×C₄	C₂²×#67	1	16	yes	—
716	C₂²×C₄	C₂²×#67	1	96	yes	complemented
717	C₂²×C₄	C₂⁴×D₃	1	12	yes	—
718	C₂²×C₄	C₂⁴×D₃	1	64	yes	—
719	C₂²×C₄	C₂⁴×D₃	1	16	yes	—
720	C₂²×C₄	C₂⁴×D₃	1	12	yes	—
721	C₂²×C₄	C₂⁴×D₃	1	16	yes	—
722	C₄⋊C₄	—	3	64	no	—
723	C₄⋊C₄	—	3	128	no	—
724	C₂²⋊C₄	—	3	64	no	—
725	C₂²⋊C₄	—	3	128	no	—
726	C₂²⋊C₄	—	3	128	no	—
727	C₂²⋊C₄	—	3	256	no	—
728	C₂²⋊C₄	—	3	128	no	—
729	C₄²	—	3	64	no	—
730	C₂²×C₃	—	2	128	no	—
731	C₂²×C₃	—	2	192	no	—
732	C₂²×C₃	—	2	48	no	—
733	C₂²×C₃	—	2	96	no	—
734	C₂²×C₃	—	2	8	no	—
735	C₂²×C₃	—	2	32	no	—
736	C₂²×C₃	—	2	8	no	—
737	C₂²×C₃	—	2	8	no	—
738	C₂²×C₃	—	2	16	no	—
739	C₂²×C₃	—	2	32	no	—
740	C₂²×C₃	—	4	128	no	—
741	C₂²×C₃	—	4	512	no	—
742	C₂²×C₃	—	4	128	no	—
743	C₂²×C₃	—	4	96	no	—
744	C₂²×C₃	#3484	1	16	yes	complemented
745	C₂²×C₃	C₂⁴×D₄	1	32	yes	—
746	C₂²×C₃	C₂⁴×D₄	1	8	yes	—
747	C₂²×C₃	C₂⁴×D₄	1	6	yes	—
748	C₂²×C₃	C₂²×H(5,𝔽₂)	1	12	yes	—
749	C₂²×C₃	C₂²×H(5,𝔽₂)	1	16	yes	complemented
750	C₂²×C₃	C₂⁷	1	1	yes	characteristic
751	C₂×D₃	—	2	16	no	—
752	C₂×D₃	—	2	32	no	—
753	C₂×D₃	—	4	96	no	—
754	C₂×D₃	—	8	128	no	—
755	C₃×C₄	—	2	8	no	—
756	C₃×C₄	C₂⁴×D₄	1	16	yes	—
757	Dic₃	—	2	16	no	—
758	Dic₃	—	2	32	no	—
759	C₂³	—	2	384	no	—
760	C₂³	—	2	96	no	—
761	C₂³	—	2	24	no	—
762	C₂³	—	2	24	no	—
763	C₂³	—	2	64	no	—
764	C₂³	—	2	32	no	—
765	C₂³	—	2	24	no	—
766	C₂³	—	2	64	no	—
767	C₂³	—	2	32	no	—
768	C₂³	—	2	128	no	—
769	C₂³	—	2	96	no	—
770	C₂³	—	2	256	no	—
771	C₂³	—	2	256	no	—
772	C₂³	—	2	64	no	—
773	C₂³	—	2	48	no	—
774	C₂³	—	3	16	no	—
775	C₂³	—	4	384	no	—
776	C₂³	—	4	64	no	—
777	C₂³	—	4	128	no	—
778	C₂³	—	4	64	no	—
779	C₂³	—	4	1536	no	—
780	C₂³	—	4	2048	no	—
781	C₂³	—	4	384	no	—
782	C₂³	—	4	64	no	—
783	C₂³	—	6	96	no	—
784	C₂³	—	6	48	no	—
785	C₂³	—	6	128	no	—
786	C₂³	—	12	128	no	—
787	C₂³	—	12	64	no	—
788	C₂³	—	24	384	no	—
789	C₂³	C₂×#1004	1	8	yes	—
790	C₂³	C₂×#1004	1	48	yes	complemented
791	C₂³	C₂³×#67	1	24	yes	—
792	C₂³	C₂³×#67	1	96	yes	—
793	C₂³	C₂³×#67	1	4	yes	—
794	C₂³	C₂³×#67	1	128	yes	complemented
795	C₂³	C₂⁵×D₃	1	16	yes	—
796	C₂³	C₂⁵×D₃	1	8	yes	—
797	C₂³	C₂⁵×D₃	1	4	yes	—
798	C₂³	C₂⁵×D₃	1	16	yes	—
799	C₂³	C₂⁵×D₃	1	3	yes	—
800	Q₈	—	6	64	no	—
801	D₄	—	2	256	no	—
802	D₄	—	2	128	no	—
803	D₄	—	6	256	no	—
804	D₄	—	6	128	no	—
805	D₄	—	6	256	no	—
806	D₄	—	6	64	no	—
807	D₄	—	12	256	no	—
808	D₄	C₂³×#67	1	256	yes	complemented
809	C₂×C₄	—	2	32	no	—
810	C₂×C₄	—	2	24	no	—
811	C₂×C₄	—	2	128	no	—
812	C₂×C₄	—	3	32	no	—
813	C₂×C₄	—	3	16	no	—
814	C₂×C₄	—	6	96	no	—
815	C₂×C₄	—	6	48	no	—
816	C₂×C₄	—	6	128	no	—
817	C₂×C₄	—	6	128	no	—
818	C₂×C₄	—	12	128	no	—
819	C₂×C₄	C₂³×#67	1	48	yes	—
820	C₂×C₄	C₂³×#67	1	64	yes	complemented
821	C₂×C₄	C₂⁵×D₃	1	8	yes	—
822	C₂×C₄	C₂⁵×D₃	1	8	yes	—
823	C₂×C₃	—	2	32	no	—
824	C₂×C₃	—	2	8	no	—
825	C₂×C₃	—	2	16	no	—
826	C₂×C₃	—	4	16	no	—
827	C₂×C₃	C₂×#3484	1	12	yes	complemented
828	C₂×C₃	C₂⁵×D₄	1	1	yes	characteristic
829	C₂×C₃	C₂³×H(5,𝔽₂)	1	2	yes	—
830	D₃	—	4	16	no	—
831	C₂²	—	2	128	no	—
832	C₂²	—	2	96	no	—
833	C₂²	—	2	48	no	—
834	C₂²	—	2	192	no	—
835	C₂²	—	2	8	no	—
836	C₂²	—	2	32	no	—
837	C₂²	—	2	8	no	—
838	C₂²	—	2	8	no	—
839	C₂²	—	2	16	no	—
840	C₂²	—	2	32	no	—
841	C₂²	—	4	128	no	—
842	C₂²	—	4	512	no	—
843	C₂²	—	4	128	no	—
844	C₂²	—	4	96	no	—
845	C₂²	—	6	16	no	—
846	C₂²	—	6	32	no	—
847	C₂²	—	12	96	no	—
848	C₂²	—	24	128	no	—
849	C₂²	#87239	1	16	yes	direct product factor
850	C₂²	C₂²×#1004	1	12	yes	—
851	C₂²	C₂²×#1004	1	16	yes	complemented
852	C₂²	C₂⁴×#67	1	8	yes	—
853	C₂²	C₂⁴×#67	1	32	yes	—
854	C₂²	C₂⁴×#67	1	6	yes	—
855	C₂²	C₂⁶×D₃	1	1	yes	characteristic
856	C₄	—	2	8	no	—
857	C₄	—	6	16	no	—
858	C₄	—	6	32	no	—
859	C₄	C₂⁴×#67	1	16	yes	—
860	C₃	C₂²×#3484	1	1	yes	characteristic, complemented, Sylow
861	C₂	—	2	16	no	—
862	C₂	—	2	8	no	—
863	C₂	—	2	32	no	—
864	C₂	—	4	16	no	—
865	C₂	—	12	16	no	—
866	C₂	C₂×#87239	1	12	yes	direct product factor
867	C₂	C₂⁵×#67	1	1	yes	characteristic
868	C₂	C₂³×#1004	1	2	yes	—

	subgroup	G/H
center	C₂⁴	C₂⁴×D₃
commutator, cosocle	C₂²×C₃	C₂⁷
Frattini	C₂²	C₂⁶×D₃
Fitting	C₂⁵×C₃×D₄	C₂
socle	C₂⁴×C₃	C₂⁵
hypercenter	C₂⁵×D₄	D₃
hypocenter	C₃	C₂²×#3484
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂⁴ ◁ C₂⁵×D₄

Complements

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

N	H ≅ G/N	type
1. C₂³×#1004	C₂	semidirect
2. C₂×#87239	C₂	direct (N × H)
3. C₂²×#5806	C₂	semidirect
4. C₂²×D₄×#67	C₂	semidirect
5. C₂²×#5805	C₂	semidirect
6. C₂²×#5804	C₂	semidirect
7. C₂²×#5791	C₂	semidirect
8. C₂³×#953	C₂	semidirect
9. C₂²×#5798	C₂	semidirect
10. C₂⁵×C₃×D₄	C₂	semidirect
12. C₂⁷×C₃	C₂²	semidirect
15. C₂⁴×C₃×D₄	C₂²	semidirect
16. C₂⁴×C₃×D₄	C₂²	semidirect
17. C₂⁴×C₃×D₄	C₂²	semidirect
18. C₂⁴×C₃×D₄	C₂²	semidirect
19. C₂⁵×C₃×C₄	C₂²	semidirect
20. C₂⁴×#67	C₂²	semidirect
21. C₂⁴×#67	C₂²	semidirect
23. C₂²×#1004	C₂²	semidirect
24. C₂³×D₃×D₄	C₂²	semidirect
25. C₂³×#237	C₂²	semidirect
26. C₂³×#235	C₂²	semidirect
27. C₂²×#953	C₂²	semidirect
28. C₂²×#953	C₂²	semidirect
29. C₂²×#953	C₂²	semidirect
30. C₂²×#953	C₂²	semidirect
31. C₂³×#217	C₂²	semidirect
32. C₂³×#217	C₂²	semidirect
33. #87239	C₂²	direct (N × H)
34. C₂×D₄×#67	C₂²	semidirect
35. C₂×#5805	C₂²	semidirect
36. C₂×#5804	C₂²	semidirect
37. C₂²×#938	C₂²	semidirect
38. C₂²×#937	C₂²	semidirect
39. C₂×#5806	C₂²	semidirect
40. C₂²×#940	C₂²	semidirect
41. C₂²×#936	C₂²	semidirect
42. C₂²×#935	C₂²	semidirect
43. C₂²×#939	C₂²	semidirect
44. C₂×#5798	C₂²	semidirect
45. C₂²×D₄×Dic₃	C₂²	semidirect
46. C₂×#5791	C₂²	semidirect
47. C₂²×#929	C₂²	semidirect
48. C₂²×#930	C₂²	semidirect
49. C₂²×#924	C₂²	semidirect
50. C₂²×C₄×#67	C₂²	semidirect
51. C₂²×#926	C₂²	semidirect
53. C₂⁵×D₄	D₃	semidirect
68. C₂⁶×C₃	C₂³	semidirect
69. C₂⁵×D₃	C₂³	semidirect
74. C₂³×C₃×D₄	D₄	semidirect
79. C₂³×C₃×D₄	C₂³	semidirect
80. C₂³×C₃×D₄	C₂³	semidirect
81. C₂³×C₃×D₄	C₂³	semidirect
82. C₂³×C₃×D₄	C₂³	semidirect
87. C₂⁴×C₃×C₄	C₂³	semidirect
92. C₂³×#67	C₂³	semidirect
93. C₂³×#67	C₂³	semidirect
94. C₂³×#67	C₂³	semidirect
95. C₂³×#67	C₂³	semidirect
96. C₂⁴×Dic₃	C₂³	semidirect
97. C₂⁴×Dic₃	C₂³	semidirect
99. C₂×#1004	C₂³	semidirect
101. C₂²×#237	C₂³	semidirect
103. C₂²×D₃×D₄	C₂³	semidirect
105. C₂²×#235	C₂³	semidirect
106. C₂³×D₁₂	C₂³	semidirect
107. C₂³×C₄×D₃	C₂³	semidirect
108. C₂³×Dic₆	C₂³	semidirect
109. C₂×#953	C₂³	semidirect
110. C₂×#953	C₂³	semidirect
111. C₂×#953	C₂³	semidirect
112. C₂×#953	C₂³	semidirect
115. C₂²×#217	C₂³	semidirect
116. C₂²×#217	C₂³	semidirect
117. C₂²×#217	C₂³	semidirect
118. C₂²×#217	C₂³	semidirect
119. #5806	C₂³	semidirect
120. #5805	C₂³	semidirect
121. #5804	C₂³	semidirect
122. C₂×#940	C₂³	semidirect
123. C₂×#939	C₂³	semidirect
124. D₄×#67	C₂³	semidirect
125. C₂×#938	C₂³	semidirect
126. C₂×#937	C₂³	semidirect
127. #5798	C₂³	semidirect
128. C₂×#936	C₂³	semidirect
129. C₂×#935	C₂³	semidirect
130. C₂×D₄×Dic₃	C₂³	semidirect
131. #5791	C₂³	semidirect
132. C₂×#930	C₂³	semidirect
133. C₂×#929	C₂³	semidirect
134. C₂×C₄×#67	C₂³	semidirect
135. C₂²×(C₂×D₃)⋊C₄	C₂³	semidirect
136. C₂×#926	C₂³	semidirect
137. C₂²×C₄⋊Dic₃	C₂³	semidirect
138. C₂×#924	C₂³	semidirect
139. C₂²×Dic₃⋊C₄	C₂³	semidirect
140. C₂²×C₄×Dic₃	C₂³	semidirect
141. C₂⁷	C₂×D₃	semidirect
151. C₂⁴×D₄	C₂×D₃	semidirect
152. C₂⁴×D₄	C₂×D₃	semidirect
153. C₂⁴×D₄	C₂×D₃	semidirect
154. C₂⁴×D₄	C₂×D₃	semidirect
155. C₂⁵×C₄	C₂×D₃	semidirect
192. C₂⁵×C₃	C₂×D₄	semidirect
201. C₂⁵×C₃	C₂⁴	semidirect
205. C₂⁴×D₃	C₂⁴	semidirect
212. C₂²×C₃×D₄	C₂×D₄	semidirect
213. C₂²×C₃×D₄	C₂×D₄	semidirect
218. C₂²×C₃×D₄	C₂⁴	semidirect
219. C₂²×C₃×D₄	C₂⁴	semidirect
220. C₂²×C₃×D₄	C₂⁴	semidirect
224. C₂³×C₃×C₄	C₂×D₄	semidirect
230. C₂³×C₃×C₄	C₂⁴	semidirect
239. C₂²×#67	C₂⁴	semidirect
240. C₂²×#67	C₂⁴	semidirect
241. C₂²×#67	C₂⁴	semidirect
242. C₂²×#67	C₂⁴	semidirect
247. C₂³×Dic₃	C₂⁴	semidirect
248. C₂³×Dic₃	C₂⁴	semidirect
251. C₂×#237	C₂⁴	semidirect
253. C₂×D₃×D₄	C₂⁴	semidirect
255. C₂×#235	C₂⁴	semidirect
257. C₂²×D₁₂	C₂⁴	semidirect
259. C₂²×C₄×D₃	C₂⁴	semidirect
261. C₂²×Dic₆	C₂⁴	semidirect
262. #953	C₂⁴	semidirect
263. #953	C₂⁴	semidirect
264. #953	C₂⁴	semidirect
267. C₂×#217	C₂⁴	semidirect
268. C₂×#217	C₂⁴	semidirect
269. C₂×#217	C₂⁴	semidirect
270. C₂×#217	C₂⁴	semidirect
271. #940	C₂⁴	semidirect
272. #939	C₂⁴	semidirect
273. #938	C₂⁴	semidirect
274. #937	C₂⁴	semidirect
275. #936	C₂⁴	semidirect
276. #935	C₂⁴	semidirect
277. D₄×Dic₃	C₂⁴	semidirect
278. #930	C₂⁴	semidirect
279. #929	C₂⁴	semidirect
280. C₄×#67	C₂⁴	semidirect
281. C₂×(C₂×D₃)⋊C₄	C₂⁴	semidirect
282. #926	C₂⁴	semidirect
283. C₂×C₄⋊Dic₃	C₂⁴	semidirect
284. #924	C₂⁴	semidirect
285. C₂×Dic₃⋊C₄	C₂⁴	semidirect
286. C₂×C₄×Dic₃	C₂⁴	semidirect
294. C₂⁶	C₂²×D₃	semidirect
317. C₂³×D₄	#67	semidirect
322. C₂³×D₄	C₂²×D₃	semidirect
323. C₂³×D₄	C₂²×D₃	semidirect
324. C₂³×D₄	C₂²×D₃	semidirect
325. C₂³×D₄	C₂²×D₃	semidirect
333. C₂⁴×C₄	C₂²×D₃	semidirect
389. C₂⁴×C₃	C₂²×D₄	semidirect
390. C₂⁴×C₃	H(5,𝔽₂)	semidirect
406. C₂³×D₃	C₂⁵	semidirect
412. C₂×C₃×D₄	C₂²×D₄	semidirect
413. C₂×C₃×D₄	C₂²×D₄	semidirect
422. C₂²×C₃×C₄	C₂²×D₄	semidirect
436. C₂×#67	C₂⁵	semidirect
437. C₂×#67	C₂⁵	semidirect
444. C₂²×Dic₃	C₂⁵	semidirect
445. C₂²×Dic₃	C₂⁵	semidirect
450. C₂×D₁₂	C₂⁵	semidirect
452. C₂×C₄×D₃	C₂⁵	semidirect
454. C₂×Dic₆	C₂⁵	semidirect
457. #217	C₂⁵	semidirect
458. #217	C₂⁵	semidirect
459. (C₂×D₃)⋊C₄	C₂⁵	semidirect
460. C₄⋊Dic₃	C₂⁵	semidirect
461. Dic₃⋊C₄	C₂⁵	semidirect
462. C₄×Dic₃	C₂⁵	semidirect
478. C₂⁵	C₂×#67	semidirect
487. C₂⁵	C₂³×D₃	semidirect
517. C₂²×D₄	C₂×#67	semidirect
518. C₂²×D₄	C₂×#67	semidirect
523. C₂²×D₄	C₂³×D₃	semidirect
524. C₂²×D₄	C₂³×D₃	semidirect
525. C₂²×D₄	C₂³×D₃	semidirect
537. C₂³×C₄	C₂×#67	semidirect
543. C₂³×C₄	C₂³×D₃	semidirect
595. C₂³×C₃	C₂³×D₄	semidirect
597. C₂³×C₃	C₂×H(5,𝔽₂)	semidirect
612. C₃×D₄	C₂³×D₄	semidirect
617. C₂×C₃×C₄	C₂³×D₄	semidirect
661. C₂⁴	#1004	semidirect
664. C₂⁴	C₂²×#67	semidirect
696. C₂×D₄	C₂²×#67	semidirect
697. C₂×D₄	C₂²×#67	semidirect
716. C₂²×C₄	C₂²×#67	semidirect
744. C₂²×C₃	#3484	semidirect
749. C₂²×C₃	C₂²×H(5,𝔽₂)	semidirect
790. C₂³	C₂×#1004	semidirect
794. C₂³	C₂³×#67	semidirect
808. D₄	C₂³×#67	semidirect
820. C₂×C₄	C₂³×#67	semidirect
827. C₂×C₃	C₂×#3484	semidirect
849. C₂²	#87239	direct (N × H)
851. C₂²	C₂²×#1004	semidirect
860. C₃	C₂²×#3484	semidirect
866. C₂	C₂×#87239	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×#1004	2
C₂×#87239	2
C₂²×#5806	2
C₂²×D₄×#67	2
C₂²×#5805	2
C₂²×#5804	2
C₂²×#5791	2
C₂³×#953	2
C₂²×#5798	2
C₂⁵×C₃×D₄	2
C₂²×#3484	3

Subgroups — C22×#87239 #72270916

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×#87239 #72270916