Subgroups — C₂³×#3519 #72289352

Order 1024.

556709 conjugacy classes of subgroups.

The subgroup lattice has 980 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#3519	C₂	1	224	yes	maximal, direct product factor
2	C₂³×#555	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂³×#553	C₂	1	2	yes	maximal, complemented
4	C₂³×#553	C₂	1	2	yes	maximal, complemented
5	C₂³×#554	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂³×#550	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂³×#546	C₂	1	2	yes	maximal, complemented
8	C₂³×#546	C₂	1	4	yes	maximal, complemented
9	C₂³×D₄²	C₂	1	2	yes	maximal, complemented
10	C₂³×D₄²	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂³×#540	C₂	1	2	yes	maximal, complemented
12	C₂³×#538	C₂	1	4	yes	maximal, complemented
13	C₂³×#532	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂³×#529	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂³×#525	C₂	1	2	yes	maximal, complemented
16	C₂⁴×#121	C₂	1	2	yes	maximal, complemented
17	C₂³×#518	C₂	1	2	yes	maximal, complemented
18	C₂⁴×C₄×D₄	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂⁴×#41	C₂²	1	2	yes	complemented
20	C₂⁴×#41	C₂²	1	2	yes	complemented
21	C₂⁵×D₄	C₂²	1	1	yes	characteristic
22	C₂⁵×D₄	C₂²	1	2	yes	—
23	C₂⁵×D₄	C₂²	1	2	yes	complemented
24	C₂⁵×D₄	C₂²	1	4	yes	complemented
25	C₂⁶×C₄	C₂²	1	2	yes	complemented
26	C₂×#3519	C₂²	1	7168	yes	direct product factor
27	C₂²×#555	C₂²	1	112	yes	complemented
28	C₂²×#553	C₂²	1	224	yes	complemented
29	C₂²×#553	C₂²	1	224	yes	complemented
30	C₂²×#554	C₂²	1	112	yes	complemented
31	C₂²×#550	C₂²	1	112	yes	complemented
32	C₂²×#546	C₂²	1	224	yes	complemented
33	C₂²×#546	C₂²	1	448	yes	complemented
34	C₂²×D₄²	C₂²	1	224	yes	complemented
35	C₂²×D₄²	C₂²	1	112	yes	complemented
36	C₂²×#540	C₂²	1	224	yes	complemented
37	C₂²×#538	C₂²	1	448	yes	complemented
38	C₂²×#532	C₂²	1	112	yes	complemented
39	C₂³×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
40	C₂³×#127	C₂²	1	1	yes	characteristic, complemented
41	C₂³×#127	C₂²	1	2	yes	complemented
42	C₂²×#529	C₂²	1	112	yes	complemented
43	C₂³×#126	C₂²	1	2	yes	complemented
44	C₂³×#126	C₂²	1	4	yes	complemented
45	C₂³×#125	C₂²	1	1	yes	characteristic, complemented
46	C₂³×#125	C₂²	1	2	yes	complemented
47	C₂³×#124	C₂²	1	1	yes	characteristic, complemented
48	C₂³×#124	C₂²	1	2	yes	complemented
49	C₂³×#124	C₂²	1	4	yes	complemented
50	C₂²×#525	C₂²	1	224	yes	complemented
51	C₂³×#123	C₂²	1	4	yes	complemented
52	C₂³×#123	C₂²	1	2	yes	complemented
53	C₂³×#123	C₂²	1	4	yes	complemented
54	C₂³×#123	C₂²	1	4	yes	complemented
55	C₂³×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
56	C₂³×C₂²⋊Q₈	C₂²	1	2	yes	complemented
57	C₂³×C₂²⋊Q₈	C₂²	1	4	yes	complemented
58	C₂³×#121	C₂²	1	1	yes	characteristic
59	C₂³×#121	C₂²	1	2	yes	complemented
60	C₂³×#121	C₂²	1	4	yes	complemented
61	C₂³×#121	C₂²	1	4	yes	complemented
62	C₂³×#121	C₂²	1	2	yes	complemented
63	C₂³×#121	C₂²	1	2	yes	complemented
64	C₂³×#121	C₂²	1	2	yes	complemented
65	C₂³×#121	C₂²	1	2	yes	complemented
66	C₂³×#121	C₂²	1	4	yes	complemented
67	C₂³×#121	C₂²	1	4	yes	complemented
68	C₂³×#121	C₂²	1	2	yes	complemented
69	C₂³×#121	C₂²	1	2	yes	complemented
70	C₂³×#121	C₂²	1	4	yes	complemented
71	C₂³×#121	C₂²	1	224	yes	complemented
72	C₂³×#120	C₂²	1	4	yes	complemented
73	C₂³×#120	C₂²	1	4	yes	complemented
74	C₂³×#120	C₂²	1	4	yes	complemented
75	C₂²×#518	C₂²	1	224	yes	complemented
76	C₂³×C₄×Q₈	C₂²	1	1	yes	characteristic, complemented
77	C₂³×C₄×D₄	C₂²	1	1	yes	characteristic
78	C₂³×C₄×D₄	C₂²	1	1	yes	characteristic
79	C₂³×C₄×D₄	C₂²	1	2	yes	—
80	C₂³×C₄×D₄	C₂²	1	2	yes	complemented
81	C₂³×C₄×D₄	C₂²	1	1	yes	characteristic, complemented
82	C₂³×C₄×D₄	C₂²	1	2	yes	complemented
83	C₂³×C₄×D₄	C₂²	1	1	yes	characteristic, complemented
84	C₂³×C₄×D₄	C₂²	1	4	yes	complemented
85	C₂³×C₄×D₄	C₂²	1	2	yes	complemented
86	C₂³×C₄×D₄	C₂²	1	4	yes	complemented
87	C₂³×C₄×D₄	C₂²	1	2	yes	complemented
88	C₂³×C₄×D₄	C₂²	1	4	yes	complemented
89	C₂³×C₄×D₄	C₂²	1	2	yes	complemented
90	C₂³×C₄×D₄	C₂²	1	1	yes	characteristic, complemented
91	C₂³×C₄×D₄	C₂²	1	2	yes	complemented
92	C₂³×C₄×D₄	C₂²	1	112	yes	complemented
93	C₂³×#117	C₂²	1	2	yes	complemented
94	C₂³×#117	C₂²	1	2	yes	complemented
95	C₂³×#117	C₂²	1	2	yes	complemented
96	C₂⁴×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
97	C₂⁴×C₄⋊C₄	C₂²	1	2	yes	complemented
98	C₂⁴×C₂²⋊C₄	C₂²	1	2	yes	complemented
99	C₂⁴×C₂²⋊C₄	C₂²	1	4	yes	complemented
100	C₂⁴×C₂²⋊C₄	C₂²	1	4	yes	complemented
101	C₂⁴×C₄²	C₂²	1	1	yes	characteristic, complemented
102	C₂⁷	C₂³	1	2	yes	—
103	C₂⁷	C₂³	1	4	yes	—
104	C₂³×#41	—	4	32	no	—
105	C₂³×#41	—	4	32	no	—
106	C₂³×#41	C₂³	1	112	yes	complemented
107	C₂³×#41	C₂³	1	112	yes	complemented
108	C₂⁴×Q₈	C₂³	1	1	yes	characteristic
109	C₂⁴×Q₈	C₂³	1	2	yes	—
110	C₂⁴×D₄	—	2	32	no	—
111	C₂⁴×D₄	—	2	64	no	—
112	C₂⁴×D₄	—	4	32	no	—
113	C₂⁴×D₄	—	4	64	no	—
114	C₂⁴×D₄	C₂³	1	2	yes	—
115	C₂⁴×D₄	C₂³	1	4	yes	—
116	C₂⁴×D₄	C₂³	1	1	yes	characteristic
117	C₂⁴×D₄	C₂³	1	2	yes	—
118	C₂⁴×D₄	C₂³	1	56	yes	—
119	C₂⁴×D₄	C₂³	1	112	yes	—
120	C₂⁴×D₄	C₂³	1	2	yes	—
121	C₂⁴×D₄	C₂³	1	1	yes	characteristic
122	C₂⁴×D₄	C₂³	1	4	yes	—
123	C₂⁴×D₄	C₂³	1	2	yes	—
124	C₂⁴×D₄	C₂³	1	4	yes	—
125	C₂⁴×D₄	C₂³	1	4	yes	—
126	C₂⁴×D₄	C₂³	1	4	yes	—
127	C₂⁴×D₄	C₂³	1	4	yes	—
128	C₂⁴×D₄	C₂³	1	2	yes	—
129	C₂⁴×D₄	C₂³	1	1	yes	characteristic
130	C₂⁴×D₄	C₂³	1	112	yes	complemented
131	C₂⁴×D₄	C₂³	1	224	yes	complemented
132	C₂⁵×C₄	—	4	32	no	—
133	C₂⁵×C₄	C₂³	1	1	yes	characteristic
134	C₂⁵×C₄	C₂³	1	2	yes	—
135	C₂⁵×C₄	C₂³	1	2	yes	—
136	C₂⁵×C₄	C₂³	1	1	yes	characteristic
137	C₂⁵×C₄	C₂³	1	2	yes	—
138	C₂⁵×C₄	C₂³	1	1	yes	characteristic
139	C₂⁵×C₄	C₂³	1	2	yes	—
140	C₂⁵×C₄	C₂³	1	2	yes	—
141	C₂⁵×C₄	C₂³	1	2	yes	—
142	C₂⁵×C₄	C₂³	1	4	yes	—
143	C₂⁵×C₄	C₂³	1	4	yes	—
144	C₂⁵×C₄	C₂³	1	4	yes	—
145	C₂⁵×C₄	C₂³	1	112	yes	complemented
146	#3519	C₂³	1	32768	yes	direct product factor
147	C₂×#555	C₂³	1	1792	yes	complemented
148	C₂×#554	C₂³	1	1792	yes	complemented
149	C₂×#553	C₂³	1	3584	yes	complemented
150	C₂×#553	C₂³	1	3584	yes	complemented
151	C₂×#550	C₂³	1	1792	yes	complemented
152	C₂×#546	C₂³	1	7168	yes	complemented
153	C₂×#546	C₂³	1	3584	yes	complemented
154	C₂×D₄²	C₂³	1	1792	yes	complemented
155	C₂×D₄²	C₂³	1	3584	yes	complemented
156	C₂×#540	C₂³	1	3584	yes	complemented
157	C₂×#538	C₂³	1	7168	yes	complemented
158	C₂×#532	C₂³	1	1792	yes	complemented
159	C₂²×C₄⋊Q₈	C₂³	1	56	yes	complemented
160	C₂²×#127	C₂³	1	56	yes	complemented
161	C₂²×#127	C₂³	1	112	yes	complemented
162	C₂×#529	C₂³	1	1792	yes	complemented
163	C₂²×#126	C₂³	1	112	yes	complemented
164	C₂²×#126	C₂³	1	224	yes	complemented
165	C₂²×#125	C₂³	1	56	yes	complemented
166	C₂²×#125	C₂³	1	112	yes	complemented
167	C₂²×#124	C₂³	1	56	yes	complemented
168	C₂²×#124	C₂³	1	112	yes	complemented
169	C₂²×#124	C₂³	1	224	yes	complemented
170	C₂×#525	C₂³	1	3584	yes	complemented
171	C₂²×#123	C₂³	1	224	yes	complemented
172	C₂²×#123	C₂³	1	112	yes	complemented
173	C₂²×#123	C₂³	1	224	yes	complemented
174	C₂²×#123	C₂³	1	224	yes	complemented
175	C₂²×C₂²⋊Q₈	C₂³	1	56	yes	complemented
176	C₂²×C₂²⋊Q₈	C₂³	1	112	yes	complemented
177	C₂²×C₂²⋊Q₈	C₂³	1	224	yes	complemented
178	C₂²×#121	C₂³	1	56	yes	—
179	C₂²×#121	C₂³	1	112	yes	complemented
180	C₂²×#121	C₂³	1	224	yes	complemented
181	C₂²×#121	C₂³	1	224	yes	complemented
182	C₂²×#121	C₂³	1	112	yes	complemented
183	C₂²×#121	C₂³	1	112	yes	complemented
184	C₂²×#121	C₂³	1	112	yes	complemented
185	C₂²×#121	C₂³	1	112	yes	complemented
186	C₂²×#121	C₂³	1	224	yes	complemented
187	C₂²×#121	C₂³	1	224	yes	complemented
188	C₂²×#121	C₂³	1	112	yes	complemented
189	C₂²×#121	C₂³	1	112	yes	complemented
190	C₂²×#121	C₂³	1	224	yes	complemented
191	C₂²×#121	C₂³	1	3584	yes	complemented
192	C₂²×#120	C₂³	1	224	yes	complemented
193	C₂²×#120	C₂³	1	224	yes	complemented
194	C₂²×#120	C₂³	1	224	yes	complemented
195	C₂×#518	C₂³	1	3584	yes	complemented
196	C₂²×C₄×Q₈	C₂³	1	56	yes	complemented
197	C₂²×C₄×D₄	C₂³	1	56	yes	—
198	C₂²×C₄×D₄	C₂³	1	56	yes	—
199	C₂²×C₄×D₄	C₂³	1	112	yes	—
200	C₂²×C₄×D₄	C₂³	1	112	yes	complemented
201	C₂²×C₄×D₄	C₂³	1	56	yes	complemented
202	C₂²×C₄×D₄	C₂³	1	112	yes	complemented
203	C₂²×C₄×D₄	C₂³	1	56	yes	complemented
204	C₂²×C₄×D₄	C₂³	1	224	yes	complemented
205	C₂²×C₄×D₄	C₂³	1	112	yes	complemented
206	C₂²×C₄×D₄	C₂³	1	224	yes	complemented
207	C₂²×C₄×D₄	C₂³	1	112	yes	complemented
208	C₂²×C₄×D₄	C₂³	1	224	yes	complemented
209	C₂²×C₄×D₄	C₂³	1	112	yes	complemented
210	C₂²×C₄×D₄	C₂³	1	56	yes	complemented
211	C₂²×C₄×D₄	C₂³	1	112	yes	complemented
212	C₂²×C₄×D₄	C₂³	1	1792	yes	complemented
213	C₂²×#117	C₂³	1	112	yes	complemented
214	C₂²×#117	C₂³	1	112	yes	complemented
215	C₂²×#117	C₂³	1	112	yes	complemented
216	C₂³×C₄⋊C₄	C₂³	1	1	yes	characteristic
217	C₂³×C₄⋊C₄	C₂³	1	1	yes	characteristic
218	C₂³×C₄⋊C₄	C₂³	1	2	yes	—
219	C₂³×C₄⋊C₄	C₂³	1	1	yes	characteristic
220	C₂³×C₄⋊C₄	C₂³	1	2	yes	—
221	C₂³×C₄⋊C₄	C₂³	1	4	yes	—
222	C₂³×C₄⋊C₄	C₂³	1	1	yes	characteristic
223	C₂³×C₄⋊C₄	C₂³	1	2	yes	—
224	C₂³×C₄⋊C₄	C₂³	1	2	yes	—
225	C₂³×C₄⋊C₄	C₂³	1	2	yes	—
226	C₂³×C₄⋊C₄	C₂³	1	2	yes	—
227	C₂³×C₄⋊C₄	C₂³	1	4	yes	—
228	C₂³×C₄⋊C₄	C₂³	1	2	yes	—
229	C₂³×C₄⋊C₄	C₂³	1	56	yes	complemented
230	C₂³×C₄⋊C₄	C₂³	1	112	yes	complemented
231	C₂³×C₂²⋊C₄	C₂³	1	2	yes	—
232	C₂³×C₂²⋊C₄	C₂³	1	2	yes	—
233	C₂³×C₂²⋊C₄	C₂³	1	4	yes	—
234	C₂³×C₂²⋊C₄	C₂³	1	2	yes	—
235	C₂³×C₂²⋊C₄	C₂³	1	2	yes	—
236	C₂³×C₂²⋊C₄	C₂³	1	4	yes	—
237	C₂³×C₂²⋊C₄	C₂³	1	4	yes	—
238	C₂³×C₂²⋊C₄	C₂³	1	2	yes	—
239	C₂³×C₂²⋊C₄	C₂³	1	4	yes	—
240	C₂³×C₂²⋊C₄	C₂³	1	2	yes	—
241	C₂³×C₂²⋊C₄	C₂³	1	4	yes	—
242	C₂³×C₂²⋊C₄	C₂³	1	2	yes	—
243	C₂³×C₂²⋊C₄	C₂³	1	2	yes	—
244	C₂³×C₂²⋊C₄	C₂³	1	2	yes	—
245	C₂³×C₂²⋊C₄	C₂³	1	4	yes	—
246	C₂³×C₂²⋊C₄	C₂³	1	4	yes	—
247	C₂³×C₂²⋊C₄	C₂³	1	112	yes	complemented
248	C₂³×C₂²⋊C₄	C₂³	1	224	yes	complemented
249	C₂³×C₂²⋊C₄	C₂³	1	224	yes	complemented
250	C₂³×C₄²	C₂³	1	1	yes	characteristic
251	C₂³×C₄²	C₂³	1	1	yes	characteristic
252	C₂³×C₄²	C₂³	1	1	yes	characteristic
253	C₂³×C₄²	C₂³	1	1	yes	characteristic
254	C₂³×C₄²	C₂³	1	4	yes	—
255	C₂³×C₄²	C₂³	1	2	yes	—
256	C₂³×C₄²	C₂³	1	56	yes	complemented
257	C₂⁶	—	2	32	no	—
258	C₂⁶	—	2	32	no	—
259	C₂⁶	—	2	64	no	—
260	C₂⁶	—	4	16	no	—
261	C₂⁶	—	4	32	no	—
262	C₂⁶	—	4	32	no	—
263	C₂⁶	C₂⁴	1	2	yes	—
264	C₂⁶	C₂⁴	1	4	yes	—
265	C₂⁶	C₂⁴	1	2	yes	—
266	C₂⁶	C₂⁴	1	56	yes	—
267	C₂⁶	C₂⁴	1	2	yes	—
268	C₂⁶	C₂⁴	1	1	yes	characteristic
269	C₂⁶	C₂⁴	1	112	yes	—
270	C₂²×#41	—	4	896	no	—
271	C₂²×#41	—	4	896	no	—
272	C₂²×#41	C₂⁴	1	896	yes	complemented
273	C₂²×#41	C₂⁴	1	896	yes	complemented
274	C₂³×Q₈	—	2	16	no	—
275	C₂³×Q₈	—	4	16	no	—
276	C₂³×Q₈	C₂⁴	1	28	yes	—
277	C₂³×Q₈	C₂⁴	1	56	yes	—
278	C₂³×D₄	—	2	32	no	—
279	C₂³×D₄	—	2	64	no	—
280	C₂³×D₄	—	2	32	no	—
281	C₂³×D₄	—	2	64	no	—
282	C₂³×D₄	—	2	896	no	—
283	C₂³×D₄	—	2	1792	no	—
284	C₂³×D₄	—	2	16	no	—
285	C₂³×D₄	—	2	32	no	—
286	C₂³×D₄	—	2	16	no	—
287	C₂³×D₄	—	2	32	no	—
288	C₂³×D₄	—	4	896	no	—
289	C₂³×D₄	—	4	32	no	—
290	C₂³×D₄	—	4	32	no	—
291	C₂³×D₄	—	4	32	no	—
292	C₂³×D₄	—	4	16	no	—
293	C₂³×D₄	—	4	32	no	—
294	C₂³×D₄	—	4	1792	no	—
295	C₂³×D₄	#41	1	32	yes	complemented
296	C₂³×D₄	C₂⁴	1	56	yes	—
297	C₂³×D₄	C₂⁴	1	112	yes	—
298	C₂³×D₄	C₂⁴	1	28	yes	—
299	C₂³×D₄	C₂⁴	1	56	yes	—
300	C₂³×D₄	C₂⁴	1	448	yes	—
301	C₂³×D₄	C₂⁴	1	896	yes	—
302	C₂³×D₄	C₂⁴	1	56	yes	—
303	C₂³×D₄	C₂⁴	1	28	yes	—
304	C₂³×D₄	C₂⁴	1	112	yes	—
305	C₂³×D₄	C₂⁴	1	56	yes	—
306	C₂³×D₄	C₂⁴	1	112	yes	—
307	C₂³×D₄	C₂⁴	1	112	yes	—
308	C₂³×D₄	C₂⁴	1	112	yes	—
309	C₂³×D₄	C₂⁴	1	112	yes	—
310	C₂³×D₄	C₂⁴	1	56	yes	—
311	C₂³×D₄	C₂⁴	1	28	yes	—
312	C₂³×D₄	C₂⁴	1	896	yes	complemented
313	C₂³×D₄	C₂⁴	1	1792	yes	complemented
314	C₂⁴×C₄	—	2	16	no	—
315	C₂⁴×C₄	—	2	16	no	—
316	C₂⁴×C₄	—	2	32	no	—
317	C₂⁴×C₄	—	2	16	no	—
318	C₂⁴×C₄	—	2	32	no	—
319	C₂⁴×C₄	—	2	32	no	—
320	C₂⁴×C₄	—	4	896	no	—
321	C₂⁴×C₄	—	4	16	no	—
322	C₂⁴×C₄	—	4	16	no	—
323	C₂⁴×C₄	—	4	16	no	—
324	C₂⁴×C₄	—	4	32	no	—
325	C₂⁴×C₄	—	4	32	no	—
326	C₂⁴×C₄	—	4	32	no	—
327	C₂⁴×C₄	C₂⁴	1	28	yes	—
328	C₂⁴×C₄	C₂⁴	1	56	yes	—
329	C₂⁴×C₄	C₂⁴	1	56	yes	—
330	C₂⁴×C₄	C₂⁴	1	28	yes	—
331	C₂⁴×C₄	C₂⁴	1	56	yes	—
332	C₂⁴×C₄	C₂⁴	1	28	yes	—
333	C₂⁴×C₄	C₂⁴	1	1	yes	characteristic
334	C₂⁴×C₄	C₂⁴	1	2	yes	—
335	C₂⁴×C₄	C₂⁴	1	1	yes	characteristic
336	C₂⁴×C₄	C₂⁴	1	2	yes	—
337	C₂⁴×C₄	C₂⁴	1	2	yes	—
338	C₂⁴×C₄	C₂⁴	1	4	yes	—
339	C₂⁴×C₄	C₂⁴	1	2	yes	—
340	C₂⁴×C₄	C₂⁴	1	1	yes	characteristic
341	C₂⁴×C₄	C₂⁴	1	1	yes	characteristic
342	C₂⁴×C₄	C₂⁴	1	2	yes	—
343	C₂⁴×C₄	C₂⁴	1	56	yes	—
344	C₂⁴×C₄	C₂⁴	1	56	yes	—
345	C₂⁴×C₄	C₂⁴	1	56	yes	—
346	C₂⁴×C₄	C₂⁴	1	112	yes	—
347	C₂⁴×C₄	C₂⁴	1	112	yes	—
348	C₂⁴×C₄	C₂⁴	1	112	yes	—
349	C₂⁴×C₄	C₂⁴	1	1	yes	characteristic
350	C₂⁴×C₄	C₂⁴	1	1	yes	characteristic
351	C₂⁴×C₄	C₂⁴	1	896	yes	complemented
352	#555	C₂⁴	1	4096	yes	complemented
353	#554	C₂⁴	1	4096	yes	complemented
354	#553	C₂⁴	1	8192	yes	complemented
355	#553	C₂⁴	1	8192	yes	complemented
356	#550	C₂⁴	1	4096	yes	complemented
357	#546	C₂⁴	1	16384	yes	complemented
358	#546	C₂⁴	1	8192	yes	complemented
359	D₄²	C₂⁴	1	4096	yes	complemented
360	D₄²	C₂⁴	1	8192	yes	complemented
361	#540	C₂⁴	1	8192	yes	complemented
362	#538	C₂⁴	1	16384	yes	complemented
363	#532	C₂⁴	1	4096	yes	complemented
364	C₂×C₄⋊Q₈	C₂⁴	1	448	yes	complemented
365	C₂×#127	C₂⁴	1	448	yes	complemented
366	C₂×#127	C₂⁴	1	896	yes	complemented
367	#529	C₂⁴	1	4096	yes	complemented
368	C₂×#126	C₂⁴	1	896	yes	complemented
369	C₂×#126	C₂⁴	1	1792	yes	complemented
370	C₂×#125	C₂⁴	1	448	yes	complemented
371	C₂×#125	C₂⁴	1	896	yes	complemented
372	C₂×#124	C₂⁴	1	448	yes	complemented
373	C₂×#124	C₂⁴	1	896	yes	complemented
374	C₂×#124	C₂⁴	1	1792	yes	complemented
375	#525	C₂⁴	1	8192	yes	complemented
376	C₂×#123	C₂⁴	1	1792	yes	complemented
377	C₂×#123	C₂⁴	1	896	yes	complemented
378	C₂×#123	C₂⁴	1	1792	yes	complemented
379	C₂×#123	C₂⁴	1	1792	yes	complemented
380	C₂×C₂²⋊Q₈	C₂⁴	1	448	yes	complemented
381	C₂×C₂²⋊Q₈	C₂⁴	1	896	yes	complemented
382	C₂×C₂²⋊Q₈	C₂⁴	1	1792	yes	complemented
383	C₂×#121	C₂⁴	1	448	yes	—
384	C₂×#121	C₂⁴	1	896	yes	complemented
385	C₂×#121	C₂⁴	1	1792	yes	complemented
386	C₂×#121	C₂⁴	1	1792	yes	complemented
387	C₂×#121	C₂⁴	1	896	yes	complemented
388	C₂×#121	C₂⁴	1	896	yes	complemented
389	C₂×#121	C₂⁴	1	896	yes	complemented
390	C₂×#121	C₂⁴	1	896	yes	complemented
391	C₂×#121	C₂⁴	1	1792	yes	complemented
392	C₂×#121	C₂⁴	1	1792	yes	complemented
393	C₂×#121	C₂⁴	1	896	yes	complemented
394	C₂×#121	C₂⁴	1	896	yes	complemented
395	C₂×#121	C₂⁴	1	1792	yes	complemented
396	C₂×#121	C₂⁴	1	8192	yes	complemented
397	C₂×#120	C₂⁴	1	1792	yes	complemented
398	C₂×#120	C₂⁴	1	1792	yes	complemented
399	C₂×#120	C₂⁴	1	1792	yes	complemented
400	#518	C₂⁴	1	8192	yes	complemented
401	C₂×C₄×Q₈	C₂⁴	1	448	yes	complemented
402	C₂×C₄×D₄	C₂⁴	1	448	yes	—
403	C₂×C₄×D₄	C₂⁴	1	448	yes	—
404	C₂×C₄×D₄	C₂⁴	1	896	yes	—
405	C₂×C₄×D₄	C₂⁴	1	896	yes	complemented
406	C₂×C₄×D₄	C₂⁴	1	448	yes	complemented
407	C₂×C₄×D₄	C₂⁴	1	896	yes	complemented
408	C₂×C₄×D₄	C₂⁴	1	448	yes	complemented
409	C₂×C₄×D₄	C₂⁴	1	1792	yes	complemented
410	C₂×C₄×D₄	C₂⁴	1	896	yes	complemented
411	C₂×C₄×D₄	C₂⁴	1	1792	yes	complemented
412	C₂×C₄×D₄	C₂⁴	1	896	yes	complemented
413	C₂×C₄×D₄	C₂⁴	1	1792	yes	complemented
414	C₂×C₄×D₄	C₂⁴	1	896	yes	complemented
415	C₂×C₄×D₄	C₂⁴	1	448	yes	complemented
416	C₂×C₄×D₄	C₂⁴	1	896	yes	complemented
417	C₂×C₄×D₄	C₂⁴	1	4096	yes	complemented
418	C₂×#117	C₂⁴	1	896	yes	complemented
419	C₂×#117	C₂⁴	1	896	yes	complemented
420	C₂×#117	C₂⁴	1	896	yes	complemented
421	C₂²×C₄⋊C₄	C₂⁴	1	28	yes	—
422	C₂²×C₄⋊C₄	C₂⁴	1	28	yes	—
423	C₂²×C₄⋊C₄	C₂⁴	1	56	yes	—
424	C₂²×C₄⋊C₄	C₂⁴	1	28	yes	—
425	C₂²×C₄⋊C₄	C₂⁴	1	56	yes	—
426	C₂²×C₄⋊C₄	C₂⁴	1	112	yes	—
427	C₂²×C₄⋊C₄	C₂⁴	1	28	yes	—
428	C₂²×C₄⋊C₄	C₂⁴	1	56	yes	—
429	C₂²×C₄⋊C₄	C₂⁴	1	56	yes	—
430	C₂²×C₄⋊C₄	C₂⁴	1	56	yes	—
431	C₂²×C₄⋊C₄	C₂⁴	1	56	yes	—
432	C₂²×C₄⋊C₄	C₂⁴	1	112	yes	—
433	C₂²×C₄⋊C₄	C₂⁴	1	56	yes	—
434	C₂²×C₄⋊C₄	C₂⁴	1	448	yes	complemented
435	C₂²×C₄⋊C₄	C₂⁴	1	896	yes	complemented
436	C₂²×C₂²⋊C₄	C₂⁴	1	56	yes	—
437	C₂²×C₂²⋊C₄	C₂⁴	1	56	yes	—
438	C₂²×C₂²⋊C₄	C₂⁴	1	112	yes	—
439	C₂²×C₂²⋊C₄	C₂⁴	1	56	yes	—
440	C₂²×C₂²⋊C₄	C₂⁴	1	56	yes	—
441	C₂²×C₂²⋊C₄	C₂⁴	1	112	yes	—
442	C₂²×C₂²⋊C₄	C₂⁴	1	112	yes	—
443	C₂²×C₂²⋊C₄	C₂⁴	1	56	yes	—
444	C₂²×C₂²⋊C₄	C₂⁴	1	112	yes	—
445	C₂²×C₂²⋊C₄	C₂⁴	1	56	yes	—
446	C₂²×C₂²⋊C₄	C₂⁴	1	112	yes	—
447	C₂²×C₂²⋊C₄	C₂⁴	1	56	yes	—
448	C₂²×C₂²⋊C₄	C₂⁴	1	56	yes	—
449	C₂²×C₂²⋊C₄	C₂⁴	1	56	yes	—
450	C₂²×C₂²⋊C₄	C₂⁴	1	112	yes	—
451	C₂²×C₂²⋊C₄	C₂⁴	1	112	yes	—
452	C₂²×C₂²⋊C₄	C₂⁴	1	896	yes	complemented
453	C₂²×C₂²⋊C₄	C₂⁴	1	1792	yes	complemented
454	C₂²×C₂²⋊C₄	C₂⁴	1	1792	yes	complemented
455	C₂²×C₄²	C₂⁴	1	28	yes	—
456	C₂²×C₄²	C₂⁴	1	28	yes	—
457	C₂²×C₄²	C₂⁴	1	28	yes	—
458	C₂²×C₄²	C₂⁴	1	28	yes	—
459	C₂²×C₄²	C₂⁴	1	112	yes	—
460	C₂²×C₄²	C₂⁴	1	56	yes	—
461	C₂²×C₄²	C₂⁴	1	448	yes	complemented
462	C₂⁵	—	2	8	no	—
463	C₂⁵	—	2	8	no	—
464	C₂⁵	—	2	16	no	—
465	C₂⁵	—	2	16	no	—
466	C₂⁵	—	2	16	no	—
467	C₂⁵	—	2	448	no	—
468	C₂⁵	—	2	16	no	—
469	C₂⁵	—	2	32	no	—
470	C₂⁵	—	2	16	no	—
471	C₂⁵	—	2	32	no	—
472	C₂⁵	—	2	32	no	—
473	C₂⁵	—	2	16	no	—
474	C₂⁵	—	2	16	no	—
475	C₂⁵	—	2	448	no	—
476	C₂⁵	—	2	16	no	—
477	C₂⁵	—	2	896	no	—
478	C₂⁵	—	4	224	no	—
479	C₂⁵	—	4	448	no	—
480	C₂⁵	—	4	448	no	—
481	C₂⁵	—	4	512	no	—
482	C₂⁵	—	8	512	no	—
483	C₂⁵	C₂×#41	1	32	yes	—
484	C₂⁵	H(5,𝔽₂)	1	16	yes	—
485	C₂⁵	C₂⁵	1	28	yes	—
486	C₂⁵	C₂⁵	1	28	yes	—
487	C₂⁵	C₂⁵	1	56	yes	—
488	C₂⁵	C₂⁵	1	224	yes	—
489	C₂⁵	C₂⁵	1	28	yes	—
490	C₂⁵	C₂⁵	1	14	yes	—
491	C₂⁵	C₂⁵	1	448	yes	—
492	C₂⁵	C₂⁵	1	1	yes	characteristic
493	C₂×#41	—	4	3584	no	—
494	C₂×#41	—	4	3584	no	—
495	C₂×#41	C₂⁵	1	1024	yes	complemented
496	C₂×#41	C₂⁵	1	1024	yes	complemented
497	C₂²×Q₈	—	2	224	no	—
498	C₂²×Q₈	—	4	224	no	—
499	C₂²×Q₈	C₂⁵	1	112	yes	—
500	C₂²×Q₈	C₂⁵	1	224	yes	—
501	C₂²×D₄	—	2	448	no	—
502	C₂²×D₄	—	2	896	no	—
503	C₂²×D₄	—	2	448	no	—
504	C₂²×D₄	—	2	896	no	—
505	C₂²×D₄	—	2	3584	no	—
506	C₂²×D₄	—	2	7168	no	—
507	C₂²×D₄	—	2	224	no	—
508	C₂²×D₄	—	2	448	no	—
509	C₂²×D₄	—	2	224	no	—
510	C₂²×D₄	—	2	448	no	—
511	C₂²×D₄	—	4	3584	no	—
512	C₂²×D₄	—	4	448	no	—
513	C₂²×D₄	—	4	448	no	—
514	C₂²×D₄	—	4	448	no	—
515	C₂²×D₄	—	4	224	no	—
516	C₂²×D₄	—	4	448	no	—
517	C₂²×D₄	—	4	7168	no	—
518	C₂²×D₄	C₂×#41	1	448	yes	complemented
519	C₂²×D₄	C₂⁵	1	224	yes	—
520	C₂²×D₄	C₂⁵	1	448	yes	—
521	C₂²×D₄	C₂⁵	1	112	yes	—
522	C₂²×D₄	C₂⁵	1	224	yes	—
523	C₂²×D₄	C₂⁵	1	512	yes	—
524	C₂²×D₄	C₂⁵	1	448	yes	—
525	C₂²×D₄	C₂⁵	1	224	yes	—
526	C₂²×D₄	C₂⁵	1	112	yes	—
527	C₂²×D₄	C₂⁵	1	224	yes	—
528	C₂²×D₄	C₂⁵	1	1024	yes	—
529	C₂²×D₄	C₂⁵	1	448	yes	—
530	C₂²×D₄	C₂⁵	1	224	yes	—
531	C₂²×D₄	C₂⁵	1	448	yes	—
532	C₂²×D₄	C₂⁵	1	448	yes	—
533	C₂²×D₄	C₂⁵	1	448	yes	—
534	C₂²×D₄	C₂⁵	1	112	yes	—
535	C₂²×D₄	C₂⁵	1	1024	yes	complemented
536	C₂²×D₄	C₂⁵	1	2048	yes	complemented
537	C₂³×C₄	—	2	8	no	—
538	C₂³×C₄	—	2	16	no	—
539	C₂³×C₄	—	2	8	no	—
540	C₂³×C₄	—	2	8	no	—
541	C₂³×C₄	—	2	16	no	—
542	C₂³×C₄	—	2	16	no	—
543	C₂³×C₄	—	2	8	no	—
544	C₂³×C₄	—	2	224	no	—
545	C₂³×C₄	—	2	16	no	—
546	C₂³×C₄	—	2	32	no	—
547	C₂³×C₄	—	2	16	no	—
548	C₂³×C₄	—	2	224	no	—
549	C₂³×C₄	—	2	448	no	—
550	C₂³×C₄	—	2	224	no	—
551	C₂³×C₄	—	2	448	no	—
552	C₂³×C₄	—	2	448	no	—
553	C₂³×C₄	—	4	3584	no	—
554	C₂³×C₄	—	4	224	no	—
555	C₂³×C₄	—	4	224	no	—
556	C₂³×C₄	—	4	224	no	—
557	C₂³×C₄	—	4	448	no	—
558	C₂³×C₄	—	4	448	no	—
559	C₂³×C₄	—	4	448	no	—
560	C₂³×C₄	C₂×#41	1	16	yes	—
561	C₂³×C₄	H(5,𝔽₂)	1	16	yes	—
562	C₂³×C₄	C₂⁵	1	28	yes	—
563	C₂³×C₄	C₂⁵	1	14	yes	—
564	C₂³×C₄	C₂⁵	1	14	yes	—
565	C₂³×C₄	C₂⁵	1	28	yes	—
566	C₂³×C₄	C₂⁵	1	14	yes	—
567	C₂³×C₄	C₂⁵	1	14	yes	—
568	C₂³×C₄	C₂⁵	1	56	yes	—
569	C₂³×C₄	C₂⁵	1	28	yes	—
570	C₂³×C₄	C₂⁵	1	28	yes	—
571	C₂³×C₄	C₂⁵	1	28	yes	—
572	C₂³×C₄	C₂⁵	1	112	yes	—
573	C₂³×C₄	C₂⁵	1	224	yes	—
574	C₂³×C₄	C₂⁵	1	112	yes	—
575	C₂³×C₄	C₂⁵	1	224	yes	—
576	C₂³×C₄	C₂⁵	1	224	yes	—
577	C₂³×C₄	C₂⁵	1	112	yes	—
578	C₂³×C₄	C₂⁵	1	224	yes	—
579	C₂³×C₄	C₂⁵	1	448	yes	—
580	C₂³×C₄	C₂⁵	1	224	yes	—
581	C₂³×C₄	C₂⁵	1	448	yes	—
582	C₂³×C₄	C₂⁵	1	448	yes	—
583	C₂³×C₄	C₂⁵	1	224	yes	—
584	C₂³×C₄	C₂⁵	1	14	yes	—
585	C₂³×C₄	C₂⁵	1	14	yes	—
586	C₂³×C₄	C₂⁵	1	1024	yes	complemented
587	C₄⋊Q₈	C₂⁵	1	512	yes	complemented
588	#127	C₂⁵	1	512	yes	complemented
589	#127	C₂⁵	1	1024	yes	complemented
590	#126	C₂⁵	1	1024	yes	complemented
591	#126	C₂⁵	1	2048	yes	complemented
592	#125	C₂⁵	1	512	yes	complemented
593	#125	C₂⁵	1	1024	yes	complemented
594	#124	C₂⁵	1	512	yes	complemented
595	#124	C₂⁵	1	1024	yes	complemented
596	#124	C₂⁵	1	2048	yes	complemented
597	#123	C₂⁵	1	2048	yes	complemented
598	#123	C₂⁵	1	1024	yes	complemented
599	#123	C₂⁵	1	2048	yes	complemented
600	#123	C₂⁵	1	2048	yes	complemented
601	C₂²⋊Q₈	C₂⁵	1	512	yes	complemented
602	C₂²⋊Q₈	C₂⁵	1	1024	yes	complemented
603	C₂²⋊Q₈	C₂⁵	1	2048	yes	complemented
604	#121	C₂⁵	1	512	yes	—
605	#121	C₂⁵	1	1024	yes	complemented
606	#121	C₂⁵	1	2048	yes	complemented
607	#121	C₂⁵	1	2048	yes	complemented
608	#121	C₂⁵	1	1024	yes	complemented
609	#121	C₂⁵	1	1024	yes	complemented
610	#121	C₂⁵	1	1024	yes	complemented
611	#121	C₂⁵	1	1024	yes	complemented
612	#121	C₂⁵	1	2048	yes	complemented
613	#121	C₂⁵	1	2048	yes	complemented
614	#121	C₂⁵	1	1024	yes	complemented
615	#121	C₂⁵	1	1024	yes	complemented
616	#121	C₂⁵	1	2048	yes	complemented
617	#120	C₂⁵	1	2048	yes	complemented
618	#120	C₂⁵	1	2048	yes	complemented
619	#120	C₂⁵	1	2048	yes	complemented
620	C₄×Q₈	C₂⁵	1	512	yes	complemented
621	C₄×D₄	C₂⁵	1	512	yes	—
622	C₄×D₄	C₂⁵	1	512	yes	—
623	C₄×D₄	C₂⁵	1	1024	yes	—
624	C₄×D₄	C₂⁵	1	1024	yes	complemented
625	C₄×D₄	C₂⁵	1	512	yes	complemented
626	C₄×D₄	C₂⁵	1	1024	yes	complemented
627	C₄×D₄	C₂⁵	1	512	yes	complemented
628	C₄×D₄	C₂⁵	1	2048	yes	complemented
629	C₄×D₄	C₂⁵	1	1024	yes	complemented
630	C₄×D₄	C₂⁵	1	2048	yes	complemented
631	C₄×D₄	C₂⁵	1	1024	yes	complemented
632	C₄×D₄	C₂⁵	1	2048	yes	complemented
633	C₄×D₄	C₂⁵	1	1024	yes	complemented
634	C₄×D₄	C₂⁵	1	512	yes	complemented
635	C₄×D₄	C₂⁵	1	1024	yes	complemented
636	#117	C₂⁵	1	1024	yes	complemented
637	#117	C₂⁵	1	1024	yes	complemented
638	#117	C₂⁵	1	1024	yes	complemented
639	C₂×C₄⋊C₄	C₂⁵	1	112	yes	—
640	C₂×C₄⋊C₄	C₂⁵	1	112	yes	—
641	C₂×C₄⋊C₄	C₂⁵	1	224	yes	—
642	C₂×C₄⋊C₄	C₂⁵	1	112	yes	—
643	C₂×C₄⋊C₄	C₂⁵	1	224	yes	—
644	C₂×C₄⋊C₄	C₂⁵	1	448	yes	—
645	C₂×C₄⋊C₄	C₂⁵	1	112	yes	—
646	C₂×C₄⋊C₄	C₂⁵	1	224	yes	—
647	C₂×C₄⋊C₄	C₂⁵	1	224	yes	—
648	C₂×C₄⋊C₄	C₂⁵	1	224	yes	—
649	C₂×C₄⋊C₄	C₂⁵	1	224	yes	—
650	C₂×C₄⋊C₄	C₂⁵	1	448	yes	—
651	C₂×C₄⋊C₄	C₂⁵	1	224	yes	—
652	C₂×C₄⋊C₄	C₂⁵	1	512	yes	complemented
653	C₂×C₄⋊C₄	C₂⁵	1	1024	yes	complemented
654	C₂×C₂²⋊C₄	C₂⁵	1	224	yes	—
655	C₂×C₂²⋊C₄	C₂⁵	1	224	yes	—
656	C₂×C₂²⋊C₄	C₂⁵	1	448	yes	—
657	C₂×C₂²⋊C₄	C₂⁵	1	224	yes	—
658	C₂×C₂²⋊C₄	C₂⁵	1	224	yes	—
659	C₂×C₂²⋊C₄	C₂⁵	1	448	yes	—
660	C₂×C₂²⋊C₄	C₂⁵	1	448	yes	—
661	C₂×C₂²⋊C₄	C₂⁵	1	224	yes	—
662	C₂×C₂²⋊C₄	C₂⁵	1	448	yes	—
663	C₂×C₂²⋊C₄	C₂⁵	1	224	yes	—
664	C₂×C₂²⋊C₄	C₂⁵	1	448	yes	—
665	C₂×C₂²⋊C₄	C₂⁵	1	224	yes	—
666	C₂×C₂²⋊C₄	C₂⁵	1	224	yes	—
667	C₂×C₂²⋊C₄	C₂⁵	1	224	yes	—
668	C₂×C₂²⋊C₄	C₂⁵	1	448	yes	—
669	C₂×C₂²⋊C₄	C₂⁵	1	448	yes	—
670	C₂×C₂²⋊C₄	C₂⁵	1	1024	yes	complemented
671	C₂×C₂²⋊C₄	C₂⁵	1	2048	yes	complemented
672	C₂×C₂²⋊C₄	C₂⁵	1	2048	yes	complemented
673	C₂×C₄²	C₂⁵	1	112	yes	—
674	C₂×C₄²	C₂⁵	1	448	yes	—
675	C₂×C₄²	C₂⁵	1	224	yes	—
676	C₂×C₄²	C₂⁵	1	112	yes	—
677	C₂×C₄²	C₂⁵	1	112	yes	—
678	C₂×C₄²	C₂⁵	1	112	yes	—
679	C₂×C₄²	C₂⁵	1	512	yes	complemented
680	C₂⁴	—	2	56	no	—
681	C₂⁴	—	2	56	no	—
682	C₂⁴	—	2	112	no	—
683	C₂⁴	—	2	112	no	—
684	C₂⁴	—	2	128	no	—
685	C₂⁴	—	2	256	no	—
686	C₂⁴	—	2	112	no	—
687	C₂⁴	—	2	896	no	—
688	C₂⁴	—	2	112	no	—
689	C₂⁴	—	2	224	no	—
690	C₂⁴	—	2	112	no	—
691	C₂⁴	—	2	224	no	—
692	C₂⁴	—	2	224	no	—
693	C₂⁴	—	2	112	no	—
694	C₂⁴	—	2	112	no	—
695	C₂⁴	—	2	896	no	—
696	C₂⁴	—	2	112	no	—
697	C₂⁴	—	2	1792	no	—
698	C₂⁴	—	4	448	no	—
699	C₂⁴	—	4	896	no	—
700	C₂⁴	—	4	896	no	—
701	C₂⁴	—	4	3584	no	—
702	C₂⁴	—	4	128	no	—
703	C₂⁴	—	4	256	no	—
704	C₂⁴	—	4	128	no	—
705	C₂⁴	—	8	3584	no	—
706	C₂⁴	C₂²×#41	1	224	yes	—
707	C₂⁴	C₂²×#41	1	8	yes	—
708	C₂⁴	C₂×H(5,𝔽₂)	1	112	yes	—
709	C₂⁴	C₂×H(5,𝔽₂)	1	8	yes	—
710	C₂⁴	C₂×H(5,𝔽₂)	1	8	yes	—
711	C₂⁴	C₂⁶	1	56	yes	—
712	C₂⁴	C₂⁶	1	56	yes	—
713	C₂⁴	C₂⁶	1	112	yes	—
714	C₂⁴	C₂⁶	1	128	yes	—
715	C₂⁴	C₂⁶	1	56	yes	—
716	C₂⁴	C₂⁶	1	28	yes	—
717	C₂⁴	C₂⁶	1	256	yes	—
718	C₂⁴	C₂⁶	1	7	yes	—
719	#41	—	4	2048	no	—
720	#41	—	4	2048	no	—
721	C₂×Q₈	—	2	448	no	—
722	C₂×Q₈	—	4	448	no	—
723	C₂×Q₈	C₂⁶	1	64	yes	—
724	C₂×Q₈	C₂⁶	1	128	yes	—
725	C₂×D₄	—	2	896	no	—
726	C₂×D₄	—	2	1792	no	—
727	C₂×D₄	—	2	896	no	—
728	C₂×D₄	—	2	1792	no	—
729	C₂×D₄	—	2	2048	no	—
730	C₂×D₄	—	2	4096	no	—
731	C₂×D₄	—	2	448	no	—
732	C₂×D₄	—	2	896	no	—
733	C₂×D₄	—	2	448	no	—
734	C₂×D₄	—	2	896	no	—
735	C₂×D₄	—	4	2048	no	—
736	C₂×D₄	—	4	896	no	—
737	C₂×D₄	—	4	896	no	—
738	C₂×D₄	—	4	896	no	—
739	C₂×D₄	—	4	448	no	—
740	C₂×D₄	—	4	896	no	—
741	C₂×D₄	—	4	4096	no	—
742	C₂×D₄	C₂²×#41	1	896	yes	complemented
743	C₂×D₄	C₂⁶	1	128	yes	—
744	C₂×D₄	C₂⁶	1	256	yes	—
745	C₂×D₄	C₂⁶	1	64	yes	—
746	C₂×D₄	C₂⁶	1	128	yes	—
747	C₂×D₄	C₂⁶	1	256	yes	—
748	C₂×D₄	C₂⁶	1	128	yes	—
749	C₂×D₄	C₂⁶	1	64	yes	—
750	C₂×D₄	C₂⁶	1	128	yes	—
751	C₂×D₄	C₂⁶	1	256	yes	—
752	C₂×D₄	C₂⁶	1	128	yes	—
753	C₂×D₄	C₂⁶	1	256	yes	—
754	C₂×D₄	C₂⁶	1	256	yes	—
755	C₂×D₄	C₂⁶	1	256	yes	—
756	C₂×D₄	C₂⁶	1	64	yes	—
757	C₂²×C₄	—	2	56	no	—
758	C₂²×C₄	—	2	112	no	—
759	C₂²×C₄	—	2	56	no	—
760	C₂²×C₄	—	2	56	no	—
761	C₂²×C₄	—	2	112	no	—
762	C₂²×C₄	—	2	112	no	—
763	C₂²×C₄	—	2	56	no	—
764	C₂²×C₄	—	2	448	no	—
765	C₂²×C₄	—	2	112	no	—
766	C₂²×C₄	—	2	224	no	—
767	C₂²×C₄	—	2	112	no	—
768	C₂²×C₄	—	2	448	no	—
769	C₂²×C₄	—	2	896	no	—
770	C₂²×C₄	—	2	448	no	—
771	C₂²×C₄	—	2	896	no	—
772	C₂²×C₄	—	2	896	no	—
773	C₂²×C₄	—	4	2048	no	—
774	C₂²×C₄	—	4	448	no	—
775	C₂²×C₄	—	4	448	no	—
776	C₂²×C₄	—	4	448	no	—
777	C₂²×C₄	—	4	896	no	—
778	C₂²×C₄	—	4	896	no	—
779	C₂²×C₄	—	4	896	no	—
780	C₂²×C₄	C₂²×#41	1	112	yes	—
781	C₂²×C₄	C₂×H(5,𝔽₂)	1	112	yes	—
782	C₂²×C₄	C₂⁶	1	56	yes	—
783	C₂²×C₄	C₂⁶	1	28	yes	—
784	C₂²×C₄	C₂⁶	1	28	yes	—
785	C₂²×C₄	C₂⁶	1	28	yes	—
786	C₂²×C₄	C₂⁶	1	56	yes	—
787	C₂²×C₄	C₂⁶	1	28	yes	—
788	C₂²×C₄	C₂⁶	1	112	yes	—
789	C₂²×C₄	C₂⁶	1	56	yes	—
790	C₂²×C₄	C₂⁶	1	56	yes	—
791	C₂²×C₄	C₂⁶	1	64	yes	—
792	C₂²×C₄	C₂⁶	1	64	yes	—
793	C₂²×C₄	C₂⁶	1	64	yes	—
794	C₂²×C₄	C₂⁶	1	56	yes	—
795	C₂²×C₄	C₂⁶	1	128	yes	—
796	C₂²×C₄	C₂⁶	1	128	yes	—
797	C₂²×C₄	C₂⁶	1	128	yes	—
798	C₂²×C₄	C₂⁶	1	128	yes	—
799	C₂²×C₄	C₂⁶	1	256	yes	—
800	C₂²×C₄	C₂⁶	1	128	yes	—
801	C₂²×C₄	C₂⁶	1	256	yes	—
802	C₂²×C₄	C₂⁶	1	256	yes	—
803	C₂²×C₄	C₂⁶	1	128	yes	—
804	C₂²×C₄	C₂⁶	1	28	yes	—
805	C₂²×C₄	C₂⁶	1	28	yes	—
806	C₄⋊C₄	C₂⁶	1	64	yes	—
807	C₄⋊C₄	C₂⁶	1	64	yes	—
808	C₄⋊C₄	C₂⁶	1	128	yes	—
809	C₄⋊C₄	C₂⁶	1	64	yes	—
810	C₄⋊C₄	C₂⁶	1	128	yes	—
811	C₄⋊C₄	C₂⁶	1	256	yes	—
812	C₄⋊C₄	C₂⁶	1	64	yes	—
813	C₄⋊C₄	C₂⁶	1	128	yes	—
814	C₄⋊C₄	C₂⁶	1	128	yes	—
815	C₄⋊C₄	C₂⁶	1	128	yes	—
816	C₄⋊C₄	C₂⁶	1	128	yes	—
817	C₄⋊C₄	C₂⁶	1	256	yes	—
818	C₄⋊C₄	C₂⁶	1	128	yes	—
819	C₂²⋊C₄	C₂⁶	1	128	yes	—
820	C₂²⋊C₄	C₂⁶	1	128	yes	—
821	C₂²⋊C₄	C₂⁶	1	256	yes	—
822	C₂²⋊C₄	C₂⁶	1	128	yes	—
823	C₂²⋊C₄	C₂⁶	1	128	yes	—
824	C₂²⋊C₄	C₂⁶	1	256	yes	—
825	C₂²⋊C₄	C₂⁶	1	256	yes	—
826	C₂²⋊C₄	C₂⁶	1	128	yes	—
827	C₂²⋊C₄	C₂⁶	1	256	yes	—
828	C₂²⋊C₄	C₂⁶	1	128	yes	—
829	C₂²⋊C₄	C₂⁶	1	256	yes	—
830	C₂²⋊C₄	C₂⁶	1	128	yes	—
831	C₂²⋊C₄	C₂⁶	1	128	yes	—
832	C₂²⋊C₄	C₂⁶	1	128	yes	—
833	C₂²⋊C₄	C₂⁶	1	256	yes	—
834	C₂²⋊C₄	C₂⁶	1	256	yes	—
835	C₄²	C₂⁶	1	64	yes	—
836	C₄²	C₂⁶	1	64	yes	—
837	C₄²	C₂⁶	1	64	yes	—
838	C₄²	C₂⁶	1	64	yes	—
839	C₄²	C₂⁶	1	256	yes	—
840	C₄²	C₂⁶	1	128	yes	—
841	C₂³	—	2	448	no	—
842	C₂³	—	2	896	no	—
843	C₂³	—	2	56	no	—
844	C₂³	—	2	56	no	—
845	C₂³	—	2	112	no	—
846	C₂³	—	2	112	no	—
847	C₂³	—	2	112	no	—
848	C₂³	—	2	256	no	—
849	C₂³	—	2	112	no	—
850	C₂³	—	2	224	no	—
851	C₂³	—	2	112	no	—
852	C₂³	—	2	224	no	—
853	C₂³	—	2	224	no	—
854	C₂³	—	2	112	no	—
855	C₂³	—	2	112	no	—
856	C₂³	—	2	256	no	—
857	C₂³	—	2	112	no	—
858	C₂³	—	2	512	no	—
859	C₂³	—	4	128	no	—
860	C₂³	—	4	256	no	—
861	C₂³	—	4	256	no	—
862	C₂³	—	4	3584	no	—
863	C₂³	—	4	448	no	—
864	C₂³	—	4	896	no	—
865	C₂³	—	4	448	no	—
866	C₂³	—	8	3584	no	—
867	C₂³	#3519	1	64	yes	direct product factor
868	C₂³	C₂³×#41	1	224	yes	—
869	C₂³	C₂³×#41	1	28	yes	—
870	C₂³	C₂²×H(5,𝔽₂)	1	112	yes	—
871	C₂³	C₂²×H(5,𝔽₂)	1	28	yes	—
872	C₂³	C₂²×H(5,𝔽₂)	1	28	yes	—
873	C₂³	C₂⁷	1	16	yes	—
874	C₂³	C₂⁷	1	16	yes	—
875	C₂³	C₂⁷	1	32	yes	—
876	C₂³	C₂⁷	1	16	yes	—
877	C₂³	C₂⁷	1	8	yes	—
878	C₂³	C₂⁷	1	7	yes	—
879	Q₈	—	2	128	no	—
880	Q₈	—	4	128	no	—
881	D₄	—	2	256	no	—
882	D₄	—	2	512	no	—
883	D₄	—	2	256	no	—
884	D₄	—	2	512	no	—
885	D₄	—	2	128	no	—
886	D₄	—	2	256	no	—
887	D₄	—	2	128	no	—
888	D₄	—	2	256	no	—
889	D₄	—	4	256	no	—
890	D₄	—	4	256	no	—
891	D₄	—	4	256	no	—
892	D₄	—	4	128	no	—
893	D₄	—	4	256	no	—
894	D₄	C₂³×#41	1	256	yes	complemented
895	C₂×C₄	—	2	56	no	—
896	C₂×C₄	—	2	112	no	—
897	C₂×C₄	—	2	56	no	—
898	C₂×C₄	—	2	56	no	—
899	C₂×C₄	—	2	112	no	—
900	C₂×C₄	—	2	112	no	—
901	C₂×C₄	—	2	56	no	—
902	C₂×C₄	—	2	128	no	—
903	C₂×C₄	—	2	112	no	—
904	C₂×C₄	—	2	224	no	—
905	C₂×C₄	—	2	112	no	—
906	C₂×C₄	—	2	128	no	—
907	C₂×C₄	—	2	256	no	—
908	C₂×C₄	—	2	128	no	—
909	C₂×C₄	—	2	256	no	—
910	C₂×C₄	—	2	256	no	—
911	C₂×C₄	—	4	128	no	—
912	C₂×C₄	—	4	128	no	—
913	C₂×C₄	—	4	128	no	—
914	C₂×C₄	—	4	256	no	—
915	C₂×C₄	—	4	256	no	—
916	C₂×C₄	—	4	256	no	—
917	C₂×C₄	C₂³×#41	1	112	yes	—
918	C₂×C₄	C₂²×H(5,𝔽₂)	1	112	yes	—
919	C₂×C₄	C₂⁷	1	8	yes	—
920	C₂×C₄	C₂⁷	1	16	yes	—
921	C₂×C₄	C₂⁷	1	8	yes	—
922	C₂×C₄	C₂⁷	1	8	yes	—
923	C₂×C₄	C₂⁷	1	16	yes	—
924	C₂×C₄	C₂⁷	1	8	yes	—
925	C₂×C₄	C₂⁷	1	32	yes	—
926	C₂×C₄	C₂⁷	1	16	yes	—
927	C₂×C₄	C₂⁷	1	16	yes	—
928	C₂×C₄	C₂⁷	1	16	yes	—
929	C₂×C₄	C₂⁷	1	8	yes	—
930	C₂×C₄	C₂⁷	1	8	yes	—
931	C₂²	—	2	224	no	—
932	C₂²	—	2	448	no	—
933	C₂²	—	2	8	no	—
934	C₂²	—	2	8	no	—
935	C₂²	—	2	16	no	—
936	C₂²	—	2	16	no	—
937	C₂²	—	2	16	no	—
938	C₂²	—	2	16	no	—
939	C₂²	—	2	32	no	—
940	C₂²	—	2	16	no	—
941	C₂²	—	2	32	no	—
942	C₂²	—	2	32	no	—
943	C₂²	—	2	16	no	—
944	C₂²	—	2	16	no	—
945	C₂²	—	2	16	no	—
946	C₂²	—	4	512	no	—
947	C₂²	—	4	224	no	—
948	C₂²	—	4	448	no	—
949	C₂²	—	4	224	no	—
950	C₂²	—	8	512	no	—
951	C₂²	C₂×#3519	1	112	yes	direct product factor
952	C₂²	C₂⁴×#41	1	32	yes	—
953	C₂²	C₂⁴×#41	1	14	yes	—
954	C₂²	C₂³×H(5,𝔽₂)	1	16	yes	—
955	C₂²	C₂³×H(5,𝔽₂)	1	14	yes	—
956	C₂²	C₂³×H(5,𝔽₂)	1	14	yes	—
957	C₂²	C₂⁸	1	1	yes	characteristic
958	C₄	—	2	8	no	—
959	C₄	—	2	16	no	—
960	C₄	—	2	8	no	—
961	C₄	—	2	8	no	—
962	C₄	—	2	16	no	—
963	C₄	—	2	16	no	—
964	C₄	—	2	8	no	—
965	C₄	—	2	16	no	—
966	C₄	—	2	32	no	—
967	C₄	—	2	16	no	—
968	C₄	C₂⁴×#41	1	16	yes	—
969	C₄	C₂³×H(5,𝔽₂)	1	16	yes	—
970	C₂	—	2	16	no	—
971	C₂	—	2	32	no	—
972	C₂	—	4	16	no	—
973	C₂	—	4	32	no	—
974	C₂	—	4	16	no	—
975	C₂	C₂²×#3519	1	28	yes	direct product factor
976	C₂	C₂⁵×#41	1	1	yes	characteristic
977	C₂	C₂⁴×H(5,𝔽₂)	1	1	yes	characteristic
978	C₂	C₂⁴×H(5,𝔽₂)	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂⁵	C₂⁵
commutator, Frattini, cosocle	C₂²	C₂⁸
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂⁵ ◁ G
LECS	G ▷ C₂² ▷ C₁

Complements

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

N	H ≅ G/N	type
1. C₂²×#3519	C₂	direct (N × H)
2. C₂³×#555	C₂	semidirect
3. C₂³×#553	C₂	semidirect
4. C₂³×#553	C₂	semidirect
5. C₂³×#554	C₂	semidirect
6. C₂³×#550	C₂	semidirect
7. C₂³×#546	C₂	semidirect
8. C₂³×#546	C₂	semidirect
9. C₂³×D₄²	C₂	semidirect
10. C₂³×D₄²	C₂	semidirect
11. C₂³×#540	C₂	semidirect
12. C₂³×#538	C₂	semidirect
13. C₂³×#532	C₂	semidirect
14. C₂³×#529	C₂	semidirect
15. C₂³×#525	C₂	semidirect
16. C₂⁴×#121	C₂	semidirect
17. C₂³×#518	C₂	semidirect
18. C₂⁴×C₄×D₄	C₂	semidirect
19. C₂⁴×#41	C₂²	semidirect
20. C₂⁴×#41	C₂²	semidirect
23. C₂⁵×D₄	C₂²	semidirect
24. C₂⁵×D₄	C₂²	semidirect
25. C₂⁶×C₄	C₂²	semidirect
26. C₂×#3519	C₂²	direct (N × H)
27. C₂²×#555	C₂²	semidirect
28. C₂²×#553	C₂²	semidirect
29. C₂²×#553	C₂²	semidirect
30. C₂²×#554	C₂²	semidirect
31. C₂²×#550	C₂²	semidirect
32. C₂²×#546	C₂²	semidirect
33. C₂²×#546	C₂²	semidirect
34. C₂²×D₄²	C₂²	semidirect
35. C₂²×D₄²	C₂²	semidirect
36. C₂²×#540	C₂²	semidirect
37. C₂²×#538	C₂²	semidirect
38. C₂²×#532	C₂²	semidirect
39. C₂³×C₄⋊Q₈	C₂²	semidirect
40. C₂³×#127	C₂²	semidirect
41. C₂³×#127	C₂²	semidirect
42. C₂²×#529	C₂²	semidirect
43. C₂³×#126	C₂²	semidirect
44. C₂³×#126	C₂²	semidirect
45. C₂³×#125	C₂²	semidirect
46. C₂³×#125	C₂²	semidirect
47. C₂³×#124	C₂²	semidirect
48. C₂³×#124	C₂²	semidirect
49. C₂³×#124	C₂²	semidirect
50. C₂²×#525	C₂²	semidirect
51. C₂³×#123	C₂²	semidirect
52. C₂³×#123	C₂²	semidirect
53. C₂³×#123	C₂²	semidirect
54. C₂³×#123	C₂²	semidirect
55. C₂³×C₂²⋊Q₈	C₂²	semidirect
56. C₂³×C₂²⋊Q₈	C₂²	semidirect
57. C₂³×C₂²⋊Q₈	C₂²	semidirect
59. C₂³×#121	C₂²	semidirect
60. C₂³×#121	C₂²	semidirect
61. C₂³×#121	C₂²	semidirect
62. C₂³×#121	C₂²	semidirect
63. C₂³×#121	C₂²	semidirect
64. C₂³×#121	C₂²	semidirect
65. C₂³×#121	C₂²	semidirect
66. C₂³×#121	C₂²	semidirect
67. C₂³×#121	C₂²	semidirect
68. C₂³×#121	C₂²	semidirect
69. C₂³×#121	C₂²	semidirect
70. C₂³×#121	C₂²	semidirect
71. C₂³×#121	C₂²	semidirect
72. C₂³×#120	C₂²	semidirect
73. C₂³×#120	C₂²	semidirect
74. C₂³×#120	C₂²	semidirect
75. C₂²×#518	C₂²	semidirect
76. C₂³×C₄×Q₈	C₂²	semidirect
80. C₂³×C₄×D₄	C₂²	semidirect
81. C₂³×C₄×D₄	C₂²	semidirect
82. C₂³×C₄×D₄	C₂²	semidirect
83. C₂³×C₄×D₄	C₂²	semidirect
84. C₂³×C₄×D₄	C₂²	semidirect
85. C₂³×C₄×D₄	C₂²	semidirect
86. C₂³×C₄×D₄	C₂²	semidirect
87. C₂³×C₄×D₄	C₂²	semidirect
88. C₂³×C₄×D₄	C₂²	semidirect
89. C₂³×C₄×D₄	C₂²	semidirect
90. C₂³×C₄×D₄	C₂²	semidirect
91. C₂³×C₄×D₄	C₂²	semidirect
92. C₂³×C₄×D₄	C₂²	semidirect
93. C₂³×#117	C₂²	semidirect
94. C₂³×#117	C₂²	semidirect
95. C₂³×#117	C₂²	semidirect
96. C₂⁴×C₄⋊C₄	C₂²	semidirect
97. C₂⁴×C₄⋊C₄	C₂²	semidirect
98. C₂⁴×C₂²⋊C₄	C₂²	semidirect
99. C₂⁴×C₂²⋊C₄	C₂²	semidirect
100. C₂⁴×C₂²⋊C₄	C₂²	semidirect
101. C₂⁴×C₄²	C₂²	semidirect
106. C₂³×#41	C₂³	semidirect
107. C₂³×#41	C₂³	semidirect
130. C₂⁴×D₄	C₂³	semidirect
131. C₂⁴×D₄	C₂³	semidirect
145. C₂⁵×C₄	C₂³	semidirect
146. #3519	C₂³	direct (N × H)
147. C₂×#555	C₂³	semidirect
148. C₂×#554	C₂³	semidirect
149. C₂×#553	C₂³	semidirect
150. C₂×#553	C₂³	semidirect
151. C₂×#550	C₂³	semidirect
152. C₂×#546	C₂³	semidirect
153. C₂×#546	C₂³	semidirect
154. C₂×D₄²	C₂³	semidirect
155. C₂×D₄²	C₂³	semidirect
156. C₂×#540	C₂³	semidirect
157. C₂×#538	C₂³	semidirect
158. C₂×#532	C₂³	semidirect
159. C₂²×C₄⋊Q₈	C₂³	semidirect
160. C₂²×#127	C₂³	semidirect
161. C₂²×#127	C₂³	semidirect
162. C₂×#529	C₂³	semidirect
163. C₂²×#126	C₂³	semidirect
164. C₂²×#126	C₂³	semidirect
165. C₂²×#125	C₂³	semidirect
166. C₂²×#125	C₂³	semidirect
167. C₂²×#124	C₂³	semidirect
168. C₂²×#124	C₂³	semidirect
169. C₂²×#124	C₂³	semidirect
170. C₂×#525	C₂³	semidirect
171. C₂²×#123	C₂³	semidirect
172. C₂²×#123	C₂³	semidirect
173. C₂²×#123	C₂³	semidirect
174. C₂²×#123	C₂³	semidirect
175. C₂²×C₂²⋊Q₈	C₂³	semidirect
176. C₂²×C₂²⋊Q₈	C₂³	semidirect
177. C₂²×C₂²⋊Q₈	C₂³	semidirect
179. C₂²×#121	C₂³	semidirect
180. C₂²×#121	C₂³	semidirect
181. C₂²×#121	C₂³	semidirect
182. C₂²×#121	C₂³	semidirect
183. C₂²×#121	C₂³	semidirect
184. C₂²×#121	C₂³	semidirect
185. C₂²×#121	C₂³	semidirect
186. C₂²×#121	C₂³	semidirect
187. C₂²×#121	C₂³	semidirect
188. C₂²×#121	C₂³	semidirect
189. C₂²×#121	C₂³	semidirect
190. C₂²×#121	C₂³	semidirect
191. C₂²×#121	C₂³	semidirect
192. C₂²×#120	C₂³	semidirect
193. C₂²×#120	C₂³	semidirect
194. C₂²×#120	C₂³	semidirect
195. C₂×#518	C₂³	semidirect
196. C₂²×C₄×Q₈	C₂³	semidirect
200. C₂²×C₄×D₄	C₂³	semidirect
201. C₂²×C₄×D₄	C₂³	semidirect
202. C₂²×C₄×D₄	C₂³	semidirect
203. C₂²×C₄×D₄	C₂³	semidirect
204. C₂²×C₄×D₄	C₂³	semidirect
205. C₂²×C₄×D₄	C₂³	semidirect
206. C₂²×C₄×D₄	C₂³	semidirect
207. C₂²×C₄×D₄	C₂³	semidirect
208. C₂²×C₄×D₄	C₂³	semidirect
209. C₂²×C₄×D₄	C₂³	semidirect
210. C₂²×C₄×D₄	C₂³	semidirect
211. C₂²×C₄×D₄	C₂³	semidirect
212. C₂²×C₄×D₄	C₂³	semidirect
213. C₂²×#117	C₂³	semidirect
214. C₂²×#117	C₂³	semidirect
215. C₂²×#117	C₂³	semidirect
229. C₂³×C₄⋊C₄	C₂³	semidirect
230. C₂³×C₄⋊C₄	C₂³	semidirect
247. C₂³×C₂²⋊C₄	C₂³	semidirect
248. C₂³×C₂²⋊C₄	C₂³	semidirect
249. C₂³×C₂²⋊C₄	C₂³	semidirect
256. C₂³×C₄²	C₂³	semidirect
272. C₂²×#41	C₂⁴	semidirect
273. C₂²×#41	C₂⁴	semidirect
295. C₂³×D₄	#41	semidirect
312. C₂³×D₄	C₂⁴	semidirect
313. C₂³×D₄	C₂⁴	semidirect
351. C₂⁴×C₄	C₂⁴	semidirect
352. #555	C₂⁴	semidirect
353. #554	C₂⁴	semidirect
354. #553	C₂⁴	semidirect
355. #553	C₂⁴	semidirect
356. #550	C₂⁴	semidirect
357. #546	C₂⁴	semidirect
358. #546	C₂⁴	semidirect
359. D₄²	C₂⁴	semidirect
360. D₄²	C₂⁴	semidirect
361. #540	C₂⁴	semidirect
362. #538	C₂⁴	semidirect
363. #532	C₂⁴	semidirect
364. C₂×C₄⋊Q₈	C₂⁴	semidirect
365. C₂×#127	C₂⁴	semidirect
366. C₂×#127	C₂⁴	semidirect
367. #529	C₂⁴	semidirect
368. C₂×#126	C₂⁴	semidirect
369. C₂×#126	C₂⁴	semidirect
370. C₂×#125	C₂⁴	semidirect
371. C₂×#125	C₂⁴	semidirect
372. C₂×#124	C₂⁴	semidirect
373. C₂×#124	C₂⁴	semidirect
374. C₂×#124	C₂⁴	semidirect
375. #525	C₂⁴	semidirect
376. C₂×#123	C₂⁴	semidirect
377. C₂×#123	C₂⁴	semidirect
378. C₂×#123	C₂⁴	semidirect
379. C₂×#123	C₂⁴	semidirect
380. C₂×C₂²⋊Q₈	C₂⁴	semidirect
381. C₂×C₂²⋊Q₈	C₂⁴	semidirect
382. C₂×C₂²⋊Q₈	C₂⁴	semidirect
384. C₂×#121	C₂⁴	semidirect
385. C₂×#121	C₂⁴	semidirect
386. C₂×#121	C₂⁴	semidirect
387. C₂×#121	C₂⁴	semidirect
388. C₂×#121	C₂⁴	semidirect
389. C₂×#121	C₂⁴	semidirect
390. C₂×#121	C₂⁴	semidirect
391. C₂×#121	C₂⁴	semidirect
392. C₂×#121	C₂⁴	semidirect
393. C₂×#121	C₂⁴	semidirect
394. C₂×#121	C₂⁴	semidirect
395. C₂×#121	C₂⁴	semidirect
396. C₂×#121	C₂⁴	semidirect
397. C₂×#120	C₂⁴	semidirect
398. C₂×#120	C₂⁴	semidirect
399. C₂×#120	C₂⁴	semidirect
400. #518	C₂⁴	semidirect
401. C₂×C₄×Q₈	C₂⁴	semidirect
405. C₂×C₄×D₄	C₂⁴	semidirect
406. C₂×C₄×D₄	C₂⁴	semidirect
407. C₂×C₄×D₄	C₂⁴	semidirect
408. C₂×C₄×D₄	C₂⁴	semidirect
409. C₂×C₄×D₄	C₂⁴	semidirect
410. C₂×C₄×D₄	C₂⁴	semidirect
411. C₂×C₄×D₄	C₂⁴	semidirect
412. C₂×C₄×D₄	C₂⁴	semidirect
413. C₂×C₄×D₄	C₂⁴	semidirect
414. C₂×C₄×D₄	C₂⁴	semidirect
415. C₂×C₄×D₄	C₂⁴	semidirect
416. C₂×C₄×D₄	C₂⁴	semidirect
417. C₂×C₄×D₄	C₂⁴	semidirect
418. C₂×#117	C₂⁴	semidirect
419. C₂×#117	C₂⁴	semidirect
420. C₂×#117	C₂⁴	semidirect
434. C₂²×C₄⋊C₄	C₂⁴	semidirect
435. C₂²×C₄⋊C₄	C₂⁴	semidirect
452. C₂²×C₂²⋊C₄	C₂⁴	semidirect
453. C₂²×C₂²⋊C₄	C₂⁴	semidirect
454. C₂²×C₂²⋊C₄	C₂⁴	semidirect
461. C₂²×C₄²	C₂⁴	semidirect
495. C₂×#41	C₂⁵	semidirect
496. C₂×#41	C₂⁵	semidirect
518. C₂²×D₄	C₂×#41	semidirect
535. C₂²×D₄	C₂⁵	semidirect
536. C₂²×D₄	C₂⁵	semidirect
586. C₂³×C₄	C₂⁵	semidirect
587. C₄⋊Q₈	C₂⁵	semidirect
588. #127	C₂⁵	semidirect
589. #127	C₂⁵	semidirect
590. #126	C₂⁵	semidirect
591. #126	C₂⁵	semidirect
592. #125	C₂⁵	semidirect
593. #125	C₂⁵	semidirect
594. #124	C₂⁵	semidirect
595. #124	C₂⁵	semidirect
596. #124	C₂⁵	semidirect
597. #123	C₂⁵	semidirect
598. #123	C₂⁵	semidirect
599. #123	C₂⁵	semidirect
600. #123	C₂⁵	semidirect
601. C₂²⋊Q₈	C₂⁵	semidirect
602. C₂²⋊Q₈	C₂⁵	semidirect
603. C₂²⋊Q₈	C₂⁵	semidirect
605. #121	C₂⁵	semidirect
606. #121	C₂⁵	semidirect
607. #121	C₂⁵	semidirect
608. #121	C₂⁵	semidirect
609. #121	C₂⁵	semidirect
610. #121	C₂⁵	semidirect
611. #121	C₂⁵	semidirect
612. #121	C₂⁵	semidirect
613. #121	C₂⁵	semidirect
614. #121	C₂⁵	semidirect
615. #121	C₂⁵	semidirect
616. #121	C₂⁵	semidirect
617. #120	C₂⁵	semidirect
618. #120	C₂⁵	semidirect
619. #120	C₂⁵	semidirect
620. C₄×Q₈	C₂⁵	semidirect
624. C₄×D₄	C₂⁵	semidirect
625. C₄×D₄	C₂⁵	semidirect
626. C₄×D₄	C₂⁵	semidirect
627. C₄×D₄	C₂⁵	semidirect
628. C₄×D₄	C₂⁵	semidirect
629. C₄×D₄	C₂⁵	semidirect
630. C₄×D₄	C₂⁵	semidirect
631. C₄×D₄	C₂⁵	semidirect
632. C₄×D₄	C₂⁵	semidirect
633. C₄×D₄	C₂⁵	semidirect
634. C₄×D₄	C₂⁵	semidirect
635. C₄×D₄	C₂⁵	semidirect
636. #117	C₂⁵	semidirect
637. #117	C₂⁵	semidirect
638. #117	C₂⁵	semidirect
652. C₂×C₄⋊C₄	C₂⁵	semidirect
653. C₂×C₄⋊C₄	C₂⁵	semidirect
670. C₂×C₂²⋊C₄	C₂⁵	semidirect
671. C₂×C₂²⋊C₄	C₂⁵	semidirect
672. C₂×C₂²⋊C₄	C₂⁵	semidirect
679. C₂×C₄²	C₂⁵	semidirect
742. C₂×D₄	C₂²×#41	semidirect
867. C₂³	#3519	direct (N × H)
894. D₄	C₂³×#41	semidirect
951. C₂²	C₂×#3519	direct (N × H)
975. C₂	C₂²×#3519	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×#3519	2
C₂³×#555	2
C₂³×#553	2
C₂³×#554	2
C₂³×#550	2
C₂³×#546	2
C₂³×D₄²	2
C₂³×#540	2
C₂³×#538	2
C₂³×#532	2
C₂³×#529	2
C₂³×#525	2
C₂⁴×#121	2
C₂³×#518	2
C₂⁴×C₄×D₄	2

Subgroups — C23×#3519 #72289352

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂³×#3519 #72289352