Subgroups — C₂×#13129210 #16770558

Order 3328.

8046 conjugacy classes of subgroups.

The subgroup lattice has 964 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13129210	C₂	1	32	yes	maximal, direct product factor
2	C₂×#11719371	C₂	1	4	yes	maximal, complemented
3	C₂×#11719289	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#11719400	C₂	1	2	yes	maximal, complemented
5	C₂×#11719282	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#11719258	C₂	1	2	yes	maximal, complemented
7	C₂×#11719256	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#11719255	C₂	1	2	yes	maximal, complemented
9	C₂×#11719381	C₂	1	2	yes	maximal, complemented
10	C₂×D₄×D₅₂	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×#11719239	C₂	1	2	yes	maximal, complemented
12	C₂×#11719409	C₂	1	4	yes	maximal, complemented
13	C₂×#11719334	C₂	1	2	yes	maximal, complemented
14	C₂×#11719230	C₂	1	2	yes	maximal, complemented
15	C₂×#11719312	C₂	1	2	yes	maximal, complemented
16	C₂×#11719182	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×#11719182	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₁₃×#529	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂²×#6131	C₂²	1	2	yes	complemented
20	C₂²×D₄×D₁₃	C₂²	1	2	yes	—
21	C₂²×#6127	C₂²	1	2	yes	complemented
22	C₂²×#6127	C₂²	1	2	yes	complemented
23	C₂²×#6127	C₂²	1	2	yes	complemented
24	C₂³×D₅₂	C₂²	1	2	yes	—
25	C₁₃×#529	C₂²	1	16	yes	complemented
26	C₂×C₁₃×#126	C₂²	1	2	yes	complemented
27	C₂×C₁₃×#125	C₂²	1	1	yes	characteristic, complemented
28	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic
29	C₂×C₁₃×#123	C₂²	1	2	yes	complemented
30	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
31	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
32	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
33	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
34	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	complemented
35	C₂×C₁₃×#117	C₂²	1	2	yes	complemented
36	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic, complemented
37	C₂×#88200	C₂²	1	2	yes	complemented
38	C₂×#88194	C₂²	1	4	yes	complemented
39	C₂×#88192	C₂²	1	2	yes	—
40	C₂×#88191	C₂²	1	4	yes	complemented
41	C₂×#88184	C₂²	1	2	yes	—
42	C₂×#88184	C₂²	1	1	yes	characteristic
43	C₂×#88184	C₂²	1	1	yes	characteristic, complemented
44	C₂×#88184	C₂²	1	2	yes	complemented
45	C₂×#88184	C₂²	1	2	yes	complemented
46	C₂×#88184	C₂²	1	2	yes	complemented
47	C₂×#88178	C₂²	1	2	yes	complemented
48	#11719409	C₂²	1	64	yes	complemented
49	#11719400	C₂²	1	32	yes	complemented
50	#11719381	C₂²	1	32	yes	complemented
51	#11719371	C₂²	1	64	yes	complemented
52	#11719334	C₂²	1	32	yes	complemented
53	#11719312	C₂²	1	32	yes	complemented
54	#11719289	C₂²	1	16	yes	complemented
55	#11719282	C₂²	1	16	yes	complemented
56	#11719258	C₂²	1	32	yes	complemented
57	#11719256	C₂²	1	16	yes	complemented
58	#11719255	C₂²	1	32	yes	complemented
59	D₄×D₅₂	C₂²	1	16	yes	complemented
60	#11719239	C₂²	1	32	yes	complemented
61	#11719230	C₂²	1	32	yes	complemented
62	C₂×#88152	C₂²	1	4	yes	complemented
63	C₂×#88152	C₂²	1	4	yes	complemented
64	C₂×#88150	C₂²	1	4	yes	complemented
65	C₂×#88149	C₂²	1	2	yes	—
66	C₂×#88149	C₂²	1	2	yes	complemented
67	C₂×#88149	C₂²	1	4	yes	complemented
68	C₂×#88149	C₂²	1	4	yes	complemented
69	C₂×#88149	C₂²	1	4	yes	complemented
70	C₂×#88148	C₂²	1	4	yes	complemented
71	C₂×#88147	C₂²	1	4	yes	complemented
72	C₂×#88146	C₂²	1	2	yes	complemented
73	C₂×C₄⋊C₄×D₁₃	C₂²	1	2	yes	complemented
74	C₂×#88139	C₂²	1	4	yes	complemented
75	C₂×#88138	C₂²	1	4	yes	complemented
76	C₂×#88138	C₂²	1	4	yes	complemented
77	C₂×#88138	C₂²	1	4	yes	complemented
78	C₂×#88137	C₂²	1	4	yes	complemented
79	C₂×#88137	C₂²	1	4	yes	complemented
80	C₂×#88136	C₂²	1	4	yes	—
81	C₂×#88136	C₂²	1	4	yes	complemented
82	C₂×#88136	C₂²	1	4	yes	complemented
83	C₂×C₂²⋊C₄×D₁₃	C₂²	1	4	yes	complemented
84	#11719182	C₂²	1	16	yes	complemented
85	#11719182	C₂²	1	16	yes	complemented
86	C₂×#88129	C₂²	1	2	yes	—
87	C₂×#88129	C₂²	1	2	yes	complemented
88	C₂×#88129	C₂²	1	2	yes	complemented
89	C₂×#88128	C₂²	1	1	yes	characteristic
90	C₂×#88128	C₂²	1	1	yes	characteristic
91	C₂×#88128	C₂²	1	2	yes	complemented
92	C₂×C₄×D₅₂	C₂²	1	1	yes	characteristic
93	C₂×C₄×D₅₂	C₂²	1	2	yes	complemented
94	C₂×C₄×D₅₂	C₂²	1	2	yes	complemented
95	C₂×C₄×D₅₂	C₂²	1	2	yes	complemented
96	C₂×C₄×D₅₂	C₂²	1	1	yes	characteristic, complemented
97	C₂×C₄×D₅₂	C₂²	1	2	yes	complemented
98	C₂×#88123	C₂²	1	1	yes	characteristic, complemented
99	C₂×#88123	C₂²	1	1	yes	characteristic, complemented
100	C₂×C₄×Dic₂₆	C₂²	1	2	yes	complemented
101	C₂⁴×D₁₃	C₂³	1	4	yes	—
102	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
103	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
104	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
105	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
106	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
107	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
108	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
109	C₂²×C₂²⋊D₁₃	C₂³	1	4	yes	—
110	C₂²×C₂²⋊D₁₃	C₂³	1	4	yes	—
111	C₂²×C₂²⋊D₁₃	C₂³	1	2	yes	—
112	C₂²×C₂²⋊D₁₃	C₂³	1	4	yes	—
113	C₂²×C₂²⋊D₁₃	C₂³	1	2	yes	—
114	C₂×#6131	—	4	8	no	—
115	C₂×#6131	C₂³	1	16	yes	complemented
116	C₂×D₄×D₁₃	—	4	8	no	—
117	C₂×D₄×D₁₃	C₂³	1	16	yes	—
118	C₂×#6127	—	4	8	no	—
119	C₂×#6127	—	4	8	no	—
120	C₂×#6127	—	4	8	no	—
121	C₂×#6127	C₂³	1	16	yes	complemented
122	C₂×#6127	C₂³	1	16	yes	complemented
123	C₂×#6127	C₂³	1	16	yes	complemented
124	C₂²×D₅₂	—	4	8	no	—
125	C₂²×D₅₂	C₂³	1	1	yes	characteristic
126	C₂²×D₅₂	C₂³	1	1	yes	characteristic
127	C₂²×D₅₂	C₂³	1	2	yes	—
128	C₂²×D₅₂	C₂³	1	2	yes	—
129	C₂²×D₅₂	C₂³	1	2	yes	—
130	C₂²×D₅₂	C₂³	1	2	yes	—
131	C₂²×D₅₂	C₂³	1	2	yes	—
132	C₂²×D₅₂	C₂³	1	4	yes	—
133	C₂²×D₅₂	C₂³	1	4	yes	—
134	C₂²×D₅₂	C₂³	1	4	yes	—
135	C₂²×D₅₂	C₂³	1	16	yes	—
136	C₂²×C₄×D₁₃	C₂³	1	2	yes	—
137	C₂²×C₄×D₁₃	C₂³	1	2	yes	—
138	C₂²×C₄×D₁₃	C₂³	1	4	yes	—
139	C₂²×C₄×D₁₃	C₂³	1	4	yes	—
140	C₂²×C₄×D₁₃	C₂³	1	4	yes	—
141	C₂²×Dic₂₆	C₂³	1	2	yes	—
142	C₂²×Dic₂₆	C₂³	1	2	yes	—
143	C₁₃×#126	C₂³	1	16	yes	complemented
144	C₁₃×#125	C₂³	1	8	yes	complemented
145	C₁₃×#124	C₂³	1	8	yes	—
146	C₁₃×#123	C₂³	1	16	yes	complemented
147	C₁₃×C₂²⋊Q₈	C₂³	1	8	yes	complemented
148	C₁₃×#121	C₂³	1	8	yes	—
149	C₄×Q₈×C₁₃	C₂³	1	8	yes	complemented
150	C₄×D₄×C₁₃	C₂³	1	8	yes	—
151	C₄×D₄×C₁₃	C₂³	1	16	yes	complemented
152	C₁₃×#117	C₂³	1	16	yes	complemented
153	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
154	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
155	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
156	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
157	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
158	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
159	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
160	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
161	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
162	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
163	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
164	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
165	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
166	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
167	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
168	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
169	C₂×C₄²×C₁₃	C₂³	1	8	yes	complemented
170	C₂×C₂²⋊Dic₁₃	C₂³	1	4	yes	—
171	#88200	C₂³	1	16	yes	complemented
172	#88194	C₂³	1	32	yes	complemented
173	#88192	C₂³	1	16	yes	—
174	#88191	C₂³	1	32	yes	complemented
175	#88184	C₂³	1	8	yes	—
176	#88184	C₂³	1	16	yes	—
177	#88184	C₂³	1	8	yes	complemented
178	#88184	C₂³	1	16	yes	complemented
179	#88184	C₂³	1	16	yes	complemented
180	#88184	C₂³	1	16	yes	complemented
181	C₂×#6103	C₂³	1	2	yes	—
182	C₂×#6103	C₂³	1	2	yes	—
183	C₂×#6103	C₂³	1	4	yes	—
184	C₂×#6103	C₂³	1	4	yes	—
185	C₂×#6103	C₂³	1	2	yes	—
186	C₂×#6103	C₂³	1	2	yes	—
187	C₂×#6103	C₂³	1	4	yes	—
188	C₂×#6103	C₂³	1	4	yes	—
189	C₂×#6103	C₂³	1	4	yes	—
190	C₂×#6103	C₂³	1	4	yes	—
191	C₂×C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
192	C₂×C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
193	C₂×C₄⋊Dic₁₃	C₂³	1	2	yes	—
194	C₂×C₄⋊Dic₁₃	C₂³	1	2	yes	—
195	C₂×C₄⋊Dic₁₃	C₂³	1	2	yes	—
196	#88178	C₂³	1	16	yes	complemented
197	C₂×#6101	C₂³	1	4	yes	—
198	C₂×#6101	C₂³	1	4	yes	—
199	C₂×C₄×Dic₁₃	C₂³	1	4	yes	—
200	#88152	C₂³	1	32	yes	complemented
201	#88152	C₂³	1	32	yes	complemented
202	#88150	C₂³	1	32	yes	complemented
203	#88149	C₂³	1	16	yes	—
204	#88149	C₂³	1	32	yes	complemented
205	#88149	C₂³	1	32	yes	complemented
206	#88149	C₂³	1	16	yes	complemented
207	#88149	C₂³	1	32	yes	complemented
208	#88148	C₂³	1	32	yes	complemented
209	#88147	C₂³	1	32	yes	complemented
210	#88146	C₂³	1	16	yes	complemented
211	C₄⋊C₄×D₁₃	C₂³	1	16	yes	complemented
212	#88139	C₂³	1	32	yes	complemented
213	#88138	C₂³	1	32	yes	complemented
214	#88138	C₂³	1	32	yes	complemented
215	#88138	C₂³	1	32	yes	complemented
216	#88137	C₂³	1	32	yes	complemented
217	#88137	C₂³	1	32	yes	complemented
218	#88136	C₂³	1	32	yes	—
219	#88136	C₂³	1	32	yes	complemented
220	#88136	C₂³	1	32	yes	complemented
221	C₂²⋊C₄×D₁₃	C₂³	1	32	yes	complemented
222	#88129	C₂³	1	16	yes	—
223	#88129	C₂³	1	16	yes	complemented
224	#88129	C₂³	1	16	yes	complemented
225	#88128	C₂³	1	8	yes	—
226	#88128	C₂³	1	8	yes	—
227	#88128	C₂³	1	16	yes	complemented
228	C₄×D₅₂	C₂³	1	8	yes	—
229	C₄×D₅₂	C₂³	1	8	yes	complemented
230	C₄×D₅₂	C₂³	1	16	yes	complemented
231	C₄×D₅₂	C₂³	1	16	yes	complemented
232	C₄×D₅₂	C₂³	1	16	yes	complemented
233	C₄×D₅₂	C₂³	1	16	yes	complemented
234	#88123	C₂³	1	8	yes	complemented
235	#88123	C₂³	1	8	yes	complemented
236	C₄×Dic₂₆	C₂³	1	16	yes	complemented
237	C₂×#3546	—	13	1	no	maximal, Sylow
238	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
239	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
240	C₂³×D₁₃	—	4	8	no	—
241	C₂³×D₁₃	—	4	8	no	—
242	C₂³×D₁₃	—	4	8	no	—
243	C₂³×D₁₃	C₂⁴	1	2	yes	—
244	C₂³×D₁₃	C₂⁴	1	4	yes	—
245	C₂³×D₁₃	C₂⁴	1	2	yes	—
246	C₂³×D₁₃	C₂⁴	1	16	yes	—
247	C₂×Q₈×C₁₃	—	2	4	no	—
248	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
249	C₂×D₄×C₁₃	—	2	4	no	—
250	C₂×D₄×C₁₃	—	4	4	no	—
251	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
252	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
253	C₂²×C₄×C₁₃	—	2	8	no	—
254	C₂²×C₄×C₁₃	—	2	4	no	—
255	C₂²×C₄×C₁₃	—	2	4	no	—
256	C₂²×C₄×C₁₃	—	4	2	no	—
257	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
258	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
259	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
260	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
261	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
262	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
263	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
264	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
265	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
266	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
267	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
268	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
269	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
270	C₂×C₂²⋊D₁₃	—	4	8	no	—
271	C₂×C₂²⋊D₁₃	—	4	8	no	—
272	C₂×C₂²⋊D₁₃	—	4	4	no	—
273	C₂×C₂²⋊D₁₃	—	4	4	no	—
274	C₂×C₂²⋊D₁₃	—	4	8	no	—
275	C₂×C₂²⋊D₁₃	C₂⁴	1	16	yes	—
276	C₂×C₂²⋊D₁₃	C₂⁴	1	16	yes	—
277	C₂×C₂²⋊D₁₃	C₂⁴	1	8	yes	—
278	C₂×C₂²⋊D₁₃	C₂⁴	1	16	yes	—
279	C₂×C₂²⋊D₁₃	C₂⁴	1	8	yes	—
280	C₂²×Dic₁₃	C₂⁴	1	2	yes	—
281	C₂²×Dic₁₃	C₂⁴	1	4	yes	—
282	C₂²×Dic₁₃	C₂⁴	1	2	yes	—
283	#6131	—	4	32	no	—
284	D₄×D₁₃	—	4	32	no	—
285	#6127	—	4	32	no	—
286	#6127	—	4	32	no	—
287	#6127	—	4	32	no	—
288	C₂×D₅₂	—	2	4	no	—
289	C₂×D₅₂	—	2	8	no	—
290	C₂×D₅₂	—	2	4	no	—
291	C₂×D₅₂	—	2	8	no	—
292	C₂×D₅₂	—	4	32	no	—
293	C₂×D₅₂	—	4	8	no	—
294	C₂×D₅₂	—	4	4	no	—
295	C₂×D₅₂	—	4	4	no	—
296	C₂×D₅₂	—	4	8	no	—
297	C₂×D₅₂	—	4	4	no	—
298	C₂×D₅₂	—	4	8	no	—
299	C₂×D₅₂	C₂⁴	1	4	yes	—
300	C₂×D₅₂	C₂⁴	1	4	yes	—
301	C₂×D₅₂	C₂⁴	1	8	yes	—
302	C₂×D₅₂	C₂⁴	1	8	yes	—
303	C₂×D₅₂	C₂⁴	1	8	yes	—
304	C₂×D₅₂	C₂⁴	1	8	yes	—
305	C₂×D₅₂	C₂⁴	1	8	yes	—
306	C₂×D₅₂	C₂⁴	1	16	yes	—
307	C₂×D₅₂	C₂⁴	1	16	yes	—
308	C₂×D₅₂	C₂⁴	1	16	yes	—
309	C₂×C₄×D₁₃	—	2	8	no	—
310	C₂×C₄×D₁₃	—	2	8	no	—
311	C₂×C₄×D₁₃	—	4	8	no	—
312	C₂×C₄×D₁₃	—	4	8	no	—
313	C₂×C₄×D₁₃	—	4	8	no	—
314	C₂×C₄×D₁₃	C₂⁴	1	8	yes	—
315	C₂×C₄×D₁₃	C₂⁴	1	8	yes	—
316	C₂×C₄×D₁₃	C₂⁴	1	16	yes	—
317	C₂×C₄×D₁₃	C₂⁴	1	16	yes	—
318	C₂×C₄×D₁₃	C₂⁴	1	16	yes	—
319	C₂×Dic₂₆	—	2	8	no	—
320	C₂×Dic₂₆	—	4	4	no	—
321	C₂×Dic₂₆	C₂⁴	1	8	yes	—
322	C₂×Dic₂₆	C₂⁴	1	8	yes	—
323	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
324	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
325	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
326	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
327	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
328	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
329	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
330	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
331	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
332	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
333	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
334	C₄²×C₁₃	C₂⁴	1	8	yes	—
335	C₄²×C₁₃	C₂⁴	1	4	yes	—
336	C₄²×C₁₃	C₂⁴	1	4	yes	—
337	C₄²×C₁₃	C₂⁴	1	4	yes	—
338	C₄²×C₁₃	C₂⁴	1	4	yes	—
339	C₂²⋊Dic₁₃	C₂⁴	1	16	yes	—
340	#6103	C₂⁴	1	8	yes	—
341	#6103	C₂⁴	1	8	yes	—
342	#6103	C₂⁴	1	16	yes	—
343	#6103	C₂⁴	1	16	yes	—
344	#6103	C₂⁴	1	8	yes	—
345	#6103	C₂⁴	1	8	yes	—
346	#6103	C₂⁴	1	16	yes	—
347	#6103	C₂⁴	1	16	yes	—
348	#6103	C₂⁴	1	16	yes	—
349	#6103	C₂⁴	1	16	yes	—
350	C₄⋊Dic₁₃	C₂⁴	1	4	yes	—
351	C₄⋊Dic₁₃	C₂⁴	1	4	yes	—
352	C₄⋊Dic₁₃	C₂⁴	1	8	yes	—
353	C₄⋊Dic₁₃	C₂⁴	1	8	yes	—
354	C₄⋊Dic₁₃	C₂⁴	1	8	yes	—
355	#6101	C₂⁴	1	16	yes	—
356	#6101	C₂⁴	1	16	yes	—
357	C₄×Dic₁₃	C₂⁴	1	16	yes	—
358	#3546	—	13	32	no	—
359	C₂×#560	—	13	4	no	—
360	C₂×#556	—	13	1	no	—
361	C₂×#553	—	13	2	no	—
362	C₂×#550	—	13	1	no	—
363	C₂×#550	—	13	2	no	—
364	C₂×#547	—	13	1	no	—
365	C₂×#546	—	13	2	no	—
366	C₂×#546	—	13	2	no	—
367	C₂×D₄²	—	13	1	no	—
368	C₂×#542	—	13	2	no	—
369	C₂×#538	—	13	4	no	—
370	C₂×#537	—	13	2	no	—
371	C₂×#535	—	13	2	no	—
372	C₂×#535	—	13	2	no	—
373	C₂×#532	—	13	1	no	—
374	C₂×#532	—	13	1	no	—
375	C₂×#529	D₁₃	1	1	yes	characteristic, complemented
376	C₂³×C₁₃	—	2	2	no	—
377	C₂³×C₁₃	—	2	2	no	—
378	C₂³×C₁₃	—	2	4	no	—
379	C₂³×C₁₃	—	2	4	no	—
380	C₂³×C₁₃	—	2	2	no	—
381	C₂³×C₁₃	—	2	4	no	—
382	C₂³×C₁₃	C₂⁵	1	4	yes	—
383	C₂³×C₁₃	C₂⁵	1	2	yes	—
384	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
385	C₂²×D₁₃	—	2	4	no	—
386	C₂²×D₁₃	—	2	4	no	—
387	C₂²×D₁₃	—	2	4	no	—
388	C₂²×D₁₃	—	2	8	no	—
389	C₂²×D₁₃	—	2	8	no	—
390	C₂²×D₁₃	—	2	4	no	—
391	C₂²×D₁₃	—	2	4	no	—
392	C₂²×D₁₃	—	2	8	no	—
393	C₂²×D₁₃	—	2	4	no	—
394	C₂²×D₁₃	—	4	16	no	—
395	C₂²×D₁₃	—	4	16	no	—
396	C₂²×D₁₃	—	4	16	no	—
397	C₂²×D₁₃	—	8	32	no	—
398	C₂²×D₁₃	C₂⁵	1	4	yes	—
399	C₂²×D₁₃	C₂⁵	1	8	yes	—
400	C₂²×D₁₃	C₂⁵	1	4	yes	—
401	Q₈×C₁₃	—	2	8	no	—
402	D₄×C₁₃	—	2	8	no	—
403	D₄×C₁₃	—	4	8	no	—
404	C₂×C₄×C₁₃	—	2	2	no	—
405	C₂×C₄×C₁₃	—	2	2	no	—
406	C₂×C₄×C₁₃	—	2	4	no	—
407	C₂×C₄×C₁₃	—	2	4	no	—
408	C₂×C₄×C₁₃	—	2	2	no	—
409	C₂×C₄×C₁₃	—	2	2	no	—
410	C₂×C₄×C₁₃	—	2	4	no	—
411	C₂×C₄×C₁₃	—	2	16	no	—
412	C₂×C₄×C₁₃	—	2	8	no	—
413	C₂×C₄×C₁₃	—	2	8	no	—
414	C₂×C₄×C₁₃	—	4	4	no	—
415	C₂×C₄×C₁₃	H(5,𝔽₂)	1	4	yes	—
416	C₂×C₄×C₁₃	H(5,𝔽₂)	1	4	yes	—
417	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
418	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
419	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
420	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
421	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
422	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
423	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
424	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
425	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
426	C₂²⋊D₁₃	—	4	16	no	—
427	C₂²⋊D₁₃	—	4	16	no	—
428	C₂²⋊D₁₃	—	4	8	no	—
429	C₂²⋊D₁₃	—	4	8	no	—
430	C₂²⋊D₁₃	—	4	16	no	—
431	C₂×Dic₁₃	—	2	8	no	—
432	C₂×Dic₁₃	—	2	4	no	—
433	C₂×Dic₁₃	—	2	4	no	—
434	C₂×Dic₁₃	C₂⁵	1	4	yes	—
435	C₂×Dic₁₃	C₂⁵	1	8	yes	—
436	C₂×Dic₁₃	C₂⁵	1	4	yes	—
437	D₅₂	—	2	8	no	—
438	D₅₂	—	2	16	no	—
439	D₅₂	—	2	8	no	—
440	D₅₂	—	2	16	no	—
441	D₅₂	—	4	16	no	—
442	D₅₂	—	4	8	no	—
443	D₅₂	—	4	8	no	—
444	D₅₂	—	4	16	no	—
445	D₅₂	—	4	8	no	—
446	D₅₂	—	4	16	no	—
447	C₄×D₁₃	—	2	16	no	—
448	C₄×D₁₃	—	2	16	no	—
449	C₄×D₁₃	—	4	16	no	—
450	C₄×D₁₃	—	4	16	no	—
451	C₄×D₁₃	—	4	16	no	—
452	Dic₂₆	—	2	16	no	—
453	Dic₂₆	—	4	8	no	—
454	C₂²×#41	—	13	2	no	—
455	C₂²×#41	—	13	2	no	—
456	C₂²×#41	—	13	2	no	—
457	C₂²×#41	—	13	2	no	—
458	C₂³×D₄	—	13	2	no	—
459	C₂³×D₄	—	13	2	no	—
460	#560	—	13	64	no	—
461	#556	—	13	16	no	—
462	#553	—	13	32	no	—
463	#550	—	13	16	no	—
464	#550	—	13	32	no	—
465	#547	—	13	16	no	—
466	#546	—	13	32	no	—
467	#546	—	13	32	no	—
468	D₄²	—	13	16	no	—
469	#542	—	13	32	no	—
470	#538	—	13	64	no	—
471	#537	—	13	32	no	—
472	#535	—	13	32	no	—
473	#535	—	13	32	no	—
474	#532	—	13	16	no	—
475	#532	—	13	16	no	—
476	C₂×C₄⋊Q₈	—	13	1	no	—
477	C₂×C₄⋊Q₈	—	13	1	no	—
478	C₂×#127	—	13	4	no	—
479	C₂×#127	—	13	1	no	—
480	C₂×#127	—	13	1	no	—
481	C₂×#127	—	13	2	no	—
482	#529	C₂×D₁₃	1	16	yes	complemented
483	C₂×#126	—	13	4	no	—
484	C₂×#126	—	13	4	no	—
485	C₂×#126	C₂×D₁₃	1	2	yes	complemented
486	C₂×#125	C₂×D₁₃	1	1	yes	characteristic, complemented
487	C₂×#124	—	13	4	no	—
488	C₂×#124	—	13	2	no	—
489	C₂×#124	—	13	2	no	—
490	C₂×#124	—	13	2	no	—
491	C₂×#124	C₂×D₁₃	1	1	yes	characteristic
492	C₂×#123	—	13	4	no	—
493	C₂×#123	—	13	4	no	—
494	C₂×#123	—	13	4	no	—
495	C₂×#123	C₂×D₁₃	1	2	yes	complemented
496	C₂×C₂²⋊Q₈	—	13	2	no	—
497	C₂×C₂²⋊Q₈	—	13	2	no	—
498	C₂×C₂²⋊Q₈	—	13	4	no	—
499	C₂×C₂²⋊Q₈	C₂×D₁₃	1	1	yes	characteristic, complemented
500	C₂×#121	—	13	2	no	—
501	C₂×#121	—	13	1	no	—
502	C₂×#121	—	13	2	no	—
503	C₂×#121	—	13	2	no	—
504	C₂×#121	—	13	1	no	—
505	C₂×#121	—	13	2	no	—
506	C₂×#121	—	13	2	no	—
507	C₂×#121	—	13	2	no	—
508	C₂×#121	—	13	4	no	—
509	C₂×#121	—	13	2	no	—
510	C₂×#121	—	13	4	no	—
511	C₂×#121	—	13	4	no	—
512	C₂×#121	—	13	4	no	—
513	C₂×#121	—	13	4	no	—
514	C₂×#121	—	13	4	no	—
515	C₂×#121	C₂×D₁₃	1	1	yes	characteristic
516	C₂×#120	—	13	4	no	—
517	C₂×#120	—	13	4	no	—
518	C₂×#120	—	13	4	no	—
519	C₂×#120	—	13	4	no	—
520	C₂×C₄×Q₈	—	13	2	no	—
521	C₂×C₄×Q₈	C₂×D₁₃	1	1	yes	characteristic, complemented
522	C₂×C₄×D₄	—	13	4	no	—
523	C₂×C₄×D₄	—	13	1	no	—
524	C₂×C₄×D₄	—	13	2	no	—
525	C₂×C₄×D₄	—	13	2	no	—
526	C₂×C₄×D₄	—	13	2	no	—
527	C₂×C₄×D₄	—	13	1	no	—
528	C₂×C₄×D₄	—	13	2	no	—
529	C₂×C₄×D₄	C₂×D₁₃	1	1	yes	characteristic
530	C₂×C₄×D₄	C₂×D₁₃	1	2	yes	complemented
531	C₂×#117	—	13	2	no	—
532	C₂×#117	C₂×D₁₃	1	2	yes	complemented
533	C₂²×C₄⋊C₄	—	13	2	no	—
534	C₂²×C₂²⋊C₄	—	13	4	no	—
535	C₂²×C₄²	C₂×D₁₃	1	1	yes	characteristic, complemented
536	C₂²×C₁₃	—	2	2	no	—
537	C₂²×C₁₃	—	2	2	no	—
538	C₂²×C₁₃	—	2	4	no	—
539	C₂²×C₁₃	—	2	4	no	—
540	C₂²×C₁₃	—	2	2	no	—
541	C₂²×C₁₃	—	2	4	no	—
542	C₂²×C₁₃	—	4	8	no	—
543	C₂²×C₁₃	—	4	4	no	—
544	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
545	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
546	C₂²×C₁₃	#585	1	2	yes	—
547	C₂²×C₁₃	C₂⁶	1	1	yes	characteristic
548	C₂×D₁₃	—	2	4	no	—
549	C₂×D₁₃	—	2	4	no	—
550	C₂×D₁₃	—	2	4	no	—
551	C₂×D₁₃	—	2	8	no	—
552	C₂×D₁₃	—	2	8	no	—
553	C₂×D₁₃	—	2	4	no	—
554	C₂×D₁₃	—	2	4	no	—
555	C₂×D₁₃	—	2	8	no	—
556	C₂×D₁₃	—	2	4	no	—
557	C₂×D₁₃	—	4	8	no	—
558	C₂×D₁₃	—	4	16	no	—
559	C₂×D₁₃	—	4	8	no	—
560	C₂×D₁₃	—	8	32	no	—
561	C₄×C₁₃	—	2	2	no	—
562	C₄×C₁₃	—	2	2	no	—
563	C₄×C₁₃	—	2	4	no	—
564	C₄×C₁₃	—	2	4	no	—
565	C₄×C₁₃	—	2	2	no	—
566	C₄×C₁₃	—	2	2	no	—
567	C₄×C₁₃	—	2	4	no	—
568	C₄×C₁₃	C₂×H(5,𝔽₂)	1	4	yes	—
569	C₄×C₁₃	C₂×H(5,𝔽₂)	1	4	yes	—
570	Dic₁₃	—	2	8	no	—
571	Dic₁₃	—	2	4	no	—
572	Dic₁₃	—	2	4	no	—
573	C₂⁵	—	13	4	no	—
574	C₂×#41	—	13	16	no	—
575	C₂×#41	—	13	16	no	—
576	C₂×#41	—	13	16	no	—
577	C₂×#41	—	13	16	no	—
578	C₂×#41	—	52	8	no	—
579	C₂×#41	—	52	8	no	—
580	C₂×#41	—	52	8	no	—
581	C₂×#41	—	52	8	no	—
582	C₂²×Q₈	—	13	2	no	—
583	C₂²×Q₈	—	13	2	no	—
584	C₂²×Q₈	C₂²×D₁₃	1	1	yes	characteristic
585	C₂²×D₄	—	13	2	no	—
586	C₂²×D₄	—	13	4	no	—
587	C₂²×D₄	—	13	4	no	—
588	C₂²×D₄	—	13	4	no	—
589	C₂²×D₄	—	13	2	no	—
590	C₂²×D₄	—	13	16	no	—
591	C₂²×D₄	—	13	2	no	—
592	C₂²×D₄	—	13	1	no	—
593	C₂²×D₄	—	13	2	no	—
594	C₂²×D₄	—	13	1	no	—
595	C₂²×D₄	—	13	2	no	—
596	C₂²×D₄	—	13	2	no	—
597	C₂²×D₄	—	13	4	no	—
598	C₂²×D₄	—	13	2	no	—
599	C₂²×D₄	—	13	4	no	—
600	C₂²×D₄	—	13	4	no	—
601	C₂²×D₄	—	13	16	no	—
602	C₂²×D₄	—	52	8	no	—
603	C₂²×D₄	—	52	8	no	—
604	C₂²×D₄	C₂²×D₁₃	1	1	yes	characteristic
605	C₂²×D₄	C₂²×D₁₃	1	2	yes	—
606	C₂³×C₄	—	13	2	no	—
607	C₂³×C₄	—	13	2	no	—
608	C₂³×C₄	—	13	4	no	—
609	C₂³×C₄	—	13	4	no	—
610	C₂³×C₄	—	13	4	no	—
611	C₂³×C₄	C₂²×D₁₃	1	2	yes	—
612	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
613	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
614	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
615	C₄⋊Q₈	—	13	8	no	—
616	C₄⋊Q₈	—	13	8	no	—
617	#127	—	13	32	no	—
618	#127	—	13	8	no	—
619	#127	—	13	8	no	—
620	#127	—	13	16	no	—
621	#126	—	13	32	no	—
622	#126	—	13	32	no	—
623	#126	C₂²×D₁₃	1	16	yes	complemented
624	#125	C₂²×D₁₃	1	8	yes	complemented
625	#124	—	13	32	no	—
626	#124	—	13	16	no	—
627	#124	—	13	16	no	—
628	#124	—	13	16	no	—
629	#124	C₂²×D₁₃	1	8	yes	—
630	#123	—	13	32	no	—
631	#123	—	13	32	no	—
632	#123	—	13	32	no	—
633	#123	C₂²×D₁₃	1	16	yes	complemented
634	C₂²⋊Q₈	—	13	16	no	—
635	C₂²⋊Q₈	—	13	16	no	—
636	C₂²⋊Q₈	—	13	32	no	—
637	C₂²⋊Q₈	C₂²×D₁₃	1	8	yes	complemented
638	#121	—	13	16	no	—
639	#121	—	13	16	no	—
640	#121	—	13	8	no	—
641	#121	—	13	8	no	—
642	#121	—	13	16	no	—
643	#121	—	13	16	no	—
644	#121	—	13	16	no	—
645	#121	—	13	32	no	—
646	#121	—	13	16	no	—
647	#121	—	13	32	no	—
648	#121	—	13	16	no	—
649	#121	—	13	32	no	—
650	#121	—	13	32	no	—
651	#121	—	13	32	no	—
652	#121	—	13	32	no	—
653	#121	C₂²×D₁₃	1	8	yes	—
654	#120	—	13	32	no	—
655	#120	—	13	32	no	—
656	#120	—	13	32	no	—
657	#120	—	13	32	no	—
658	C₄×Q₈	—	13	16	no	—
659	C₄×Q₈	C₂²×D₁₃	1	8	yes	complemented
660	C₄×D₄	—	13	32	no	—
661	C₄×D₄	—	13	16	no	—
662	C₄×D₄	—	13	8	no	—
663	C₄×D₄	—	13	16	no	—
664	C₄×D₄	—	13	16	no	—
665	C₄×D₄	—	13	8	no	—
666	C₄×D₄	—	13	16	no	—
667	C₄×D₄	C₂²×D₁₃	1	8	yes	—
668	C₄×D₄	C₂²×D₁₃	1	16	yes	complemented
669	#117	—	13	16	no	—
670	#117	C₂²×D₁₃	1	16	yes	complemented
671	C₂×C₄⋊C₄	—	13	2	no	—
672	C₂×C₄⋊C₄	—	13	4	no	—
673	C₂×C₄⋊C₄	—	13	1	no	—
674	C₂×C₄⋊C₄	—	13	1	no	—
675	C₂×C₄⋊C₄	—	13	2	no	—
676	C₂×C₄⋊C₄	—	13	2	no	—
677	C₂×C₄⋊C₄	—	13	4	no	—
678	C₂×C₄⋊C₄	—	13	16	no	—
679	C₂×C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
680	C₂×C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
681	C₂×C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
682	C₂×C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
683	C₂×C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
684	C₂×C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
685	C₂×C₂²⋊C₄	—	13	4	no	—
686	C₂×C₂²⋊C₄	—	13	2	no	—
687	C₂×C₂²⋊C₄	—	13	4	no	—
688	C₂×C₂²⋊C₄	—	13	4	no	—
689	C₂×C₂²⋊C₄	—	13	2	no	—
690	C₂×C₂²⋊C₄	—	13	2	no	—
691	C₂×C₂²⋊C₄	—	13	4	no	—
692	C₂×C₂²⋊C₄	—	13	4	no	—
693	C₂×C₂²⋊C₄	—	13	4	no	—
694	C₂×C₂²⋊C₄	—	13	4	no	—
695	C₂×C₂²⋊C₄	—	13	2	no	—
696	C₂×C₂²⋊C₄	—	13	32	no	—
697	C₂×C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
698	C₂×C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
699	C₂×C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
700	C₂×C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
701	C₂×C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
702	C₂×C₄²	—	13	4	no	—
703	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
704	C₂×C₄²	C₂²×D₁₃	1	2	yes	—
705	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
706	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
707	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
708	C₂×C₄²	C₂²×D₁₃	1	8	yes	complemented
709	C₂×C₁₃	—	4	4	no	—
710	C₂×C₁₃	—	4	2	no	—
711	C₂×C₁₃	#3546	1	4	yes	complemented
712	C₂×C₁₃	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
713	C₂×C₁₃	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
714	C₂×C₁₃	C₂×#585	1	1	yes	characteristic
715	D₁₃	—	4	4	no	—
716	D₁₃	—	4	8	no	—
717	D₁₃	—	4	4	no	—
718	C₂⁴	—	13	2	no	—
719	C₂⁴	—	13	4	no	—
720	C₂⁴	—	13	2	no	—
721	C₂⁴	—	13	16	no	—
722	C₂⁴	—	52	8	no	—
723	C₂⁴	—	52	8	no	—
724	C₂⁴	—	52	8	no	—
725	C₂⁴	C₂³×D₁₃	1	2	yes	—
726	C₂⁴	C₂³×D₁₃	1	1	yes	characteristic
727	#41	—	52	32	no	—
728	#41	—	52	32	no	—
729	#41	—	52	32	no	—
730	#41	—	52	32	no	—
731	C₂×Q₈	—	2	4	no	—
732	C₂×Q₈	—	13	8	no	—
733	C₂×Q₈	—	13	8	no	—
734	C₂×Q₈	—	26	8	no	—
735	C₂×Q₈	—	52	4	no	—
736	C₂×Q₈	C₂³×D₁₃	1	4	yes	—
737	C₂×D₄	—	2	4	no	—
738	C₂×D₄	—	4	4	no	—
739	C₂×D₄	—	13	8	no	—
740	C₂×D₄	—	13	16	no	—
741	C₂×D₄	—	13	16	no	—
742	C₂×D₄	—	13	16	no	—
743	C₂×D₄	—	13	8	no	—
744	C₂×D₄	—	13	8	no	—
745	C₂×D₄	—	13	4	no	—
746	C₂×D₄	—	13	8	no	—
747	C₂×D₄	—	13	4	no	—
748	C₂×D₄	—	13	8	no	—
749	C₂×D₄	—	13	8	no	—
750	C₂×D₄	—	13	16	no	—
751	C₂×D₄	—	13	8	no	—
752	C₂×D₄	—	13	16	no	—
753	C₂×D₄	—	13	16	no	—
754	C₂×D₄	—	26	4	no	—
755	C₂×D₄	—	26	8	no	—
756	C₂×D₄	—	26	8	no	—
757	C₂×D₄	—	26	4	no	—
758	C₂×D₄	—	52	32	no	—
759	C₂×D₄	—	52	8	no	—
760	C₂×D₄	—	52	4	no	—
761	C₂×D₄	—	52	8	no	—
762	C₂×D₄	—	52	4	no	—
763	C₂×D₄	—	52	4	no	—
764	C₂×D₄	—	52	8	no	—
765	C₂×D₄	—	52	32	no	—
766	C₂×D₄	—	52	8	no	—
767	C₂×D₄	—	52	4	no	—
768	C₂×D₄	—	52	4	no	—
769	C₂×D₄	—	52	8	no	—
770	C₂×D₄	—	52	8	no	—
771	C₂×D₄	C₂³×D₁₃	1	4	yes	—
772	C₂×D₄	C₂³×D₁₃	1	8	yes	—
773	C₂²×C₄	—	2	8	no	—
774	C₂²×C₄	—	2	4	no	—
775	C₂²×C₄	—	2	4	no	—
776	C₂²×C₄	—	4	2	no	—
777	C₂²×C₄	—	13	2	no	—
778	C₂²×C₄	—	13	4	no	—
779	C₂²×C₄	—	13	2	no	—
780	C₂²×C₄	—	13	8	no	—
781	C₂²×C₄	—	13	8	no	—
782	C₂²×C₄	—	13	16	no	—
783	C₂²×C₄	—	13	16	no	—
784	C₂²×C₄	—	13	16	no	—
785	C₂²×C₄	—	26	8	no	—
786	C₂²×C₄	—	26	8	no	—
787	C₂²×C₄	—	52	8	no	—
788	C₂²×C₄	—	52	8	no	—
789	C₂²×C₄	—	52	8	no	—
790	C₂²×C₄	C₂³×D₁₃	1	4	yes	—
791	C₂²×C₄	C₂³×D₁₃	1	4	yes	—
792	C₂²×C₄	C₂³×D₁₃	1	8	yes	—
793	C₂²×C₄	C₂³×D₁₃	1	2	yes	—
794	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
795	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
796	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
797	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
798	C₂²×C₄	C₂³×D₁₃	1	2	yes	—
799	C₂²×C₄	C₂³×D₁₃	1	2	yes	—
800	C₂²×C₄	C₂³×D₁₃	1	4	yes	—
801	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
802	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
803	C₄⋊C₄	—	13	8	no	—
804	C₄⋊C₄	—	13	16	no	—
805	C₄⋊C₄	—	13	4	no	—
806	C₄⋊C₄	—	13	4	no	—
807	C₄⋊C₄	—	13	8	no	—
808	C₄⋊C₄	—	13	8	no	—
809	C₄⋊C₄	—	13	16	no	—
810	C₄⋊C₄	C₂³×D₁₃	1	4	yes	—
811	C₄⋊C₄	C₂³×D₁₃	1	4	yes	—
812	C₄⋊C₄	C₂³×D₁₃	1	8	yes	—
813	C₄⋊C₄	C₂³×D₁₃	1	8	yes	—
814	C₄⋊C₄	C₂³×D₁₃	1	8	yes	—
815	C₄⋊C₄	C₂³×D₁₃	1	8	yes	—
816	C₂²⋊C₄	—	13	16	no	—
817	C₂²⋊C₄	—	13	8	no	—
818	C₂²⋊C₄	—	13	16	no	—
819	C₂²⋊C₄	—	13	16	no	—
820	C₂²⋊C₄	—	13	8	no	—
821	C₂²⋊C₄	—	13	8	no	—
822	C₂²⋊C₄	—	13	16	no	—
823	C₂²⋊C₄	—	13	16	no	—
824	C₂²⋊C₄	—	13	16	no	—
825	C₂²⋊C₄	—	13	16	no	—
826	C₂²⋊C₄	—	13	8	no	—
827	C₂²⋊C₄	C₂³×D₁₃	1	8	yes	—
828	C₂²⋊C₄	C₂³×D₁₃	1	8	yes	—
829	C₂²⋊C₄	C₂³×D₁₃	1	8	yes	—
830	C₂²⋊C₄	C₂³×D₁₃	1	8	yes	—
831	C₂²⋊C₄	C₂³×D₁₃	1	8	yes	—
832	C₄²	—	13	16	no	—
833	C₄²	C₂³×D₁₃	1	4	yes	—
834	C₄²	C₂³×D₁₃	1	4	yes	—
835	C₄²	C₂³×D₁₃	1	4	yes	—
836	C₄²	C₂³×D₁₃	1	4	yes	—
837	C₄²	C₂³×D₁₃	1	8	yes	—
838	C₁₃	C₂×#3546	1	1	yes	characteristic, complemented, Sylow
839	C₂³	—	2	2	no	—
840	C₂³	—	2	2	no	—
841	C₂³	—	2	4	no	—
842	C₂³	—	2	4	no	—
843	C₂³	—	2	2	no	—
844	C₂³	—	2	4	no	—
845	C₂³	—	13	4	no	—
846	C₂³	—	13	8	no	—
847	C₂³	—	13	4	no	—
848	C₂³	—	26	4	no	—
849	C₂³	—	26	4	no	—
850	C₂³	—	26	4	no	—
851	C₂³	—	26	8	no	—
852	C₂³	—	26	8	no	—
853	C₂³	—	26	4	no	—
854	C₂³	—	26	4	no	—
855	C₂³	—	26	8	no	—
856	C₂³	—	26	4	no	—
857	C₂³	—	52	16	no	—
858	C₂³	—	52	16	no	—
859	C₂³	—	52	16	no	—
860	C₂³	—	104	32	no	—
861	C₂³	C₂⁴×D₁₃	1	4	yes	—
862	C₂³	C₂⁴×D₁₃	1	2	yes	—
863	C₂³	C₂⁴×D₁₃	1	1	yes	characteristic
864	Q₈	—	2	8	no	—
865	Q₈	—	26	16	no	—
866	Q₈	—	52	8	no	—
867	D₄	—	2	8	no	—
868	D₄	—	4	8	no	—
869	D₄	—	26	8	no	—
870	D₄	—	26	16	no	—
871	D₄	—	26	16	no	—
872	D₄	—	26	8	no	—
873	D₄	—	52	8	no	—
874	D₄	—	52	8	no	—
875	D₄	—	52	16	no	—
876	D₄	—	52	16	no	—
877	D₄	—	52	8	no	—
878	D₄	—	52	16	no	—
879	D₄	—	52	16	no	—
880	D₄	—	52	8	no	—
881	D₄	—	52	8	no	—
882	D₄	—	52	16	no	—
883	D₄	—	52	16	no	—
884	C₂×C₄	—	2	2	no	—
885	C₂×C₄	—	2	4	no	—
886	C₂×C₄	—	2	2	no	—
887	C₂×C₄	—	2	4	no	—
888	C₂×C₄	—	2	2	no	—
889	C₂×C₄	—	2	2	no	—
890	C₂×C₄	—	2	4	no	—
891	C₂×C₄	—	2	16	no	—
892	C₂×C₄	—	2	8	no	—
893	C₂×C₄	—	2	8	no	—
894	C₂×C₄	—	4	4	no	—
895	C₂×C₄	—	13	4	no	—
896	C₂×C₄	—	13	8	no	—
897	C₂×C₄	—	13	4	no	—
898	C₂×C₄	—	26	4	no	—
899	C₂×C₄	—	26	4	no	—
900	C₂×C₄	—	26	8	no	—
901	C₂×C₄	—	26	16	no	—
902	C₂×C₄	—	26	16	no	—
903	C₂×C₄	—	52	16	no	—
904	C₂×C₄	—	52	16	no	—
905	C₂×C₄	—	52	16	no	—
906	C₂×C₄	#88256	1	4	yes	—
907	C₂×C₄	#88256	1	4	yes	—
908	C₂×C₄	C₂⁴×D₁₃	1	4	yes	—
909	C₂×C₄	C₂⁴×D₁₃	1	2	yes	—
910	C₂×C₄	C₂⁴×D₁₃	1	2	yes	—
911	C₂×C₄	C₂⁴×D₁₃	1	2	yes	—
912	C₂×C₄	C₂⁴×D₁₃	1	2	yes	—
913	C₂×C₄	C₂⁴×D₁₃	1	4	yes	—
914	C₂×C₄	C₂⁴×D₁₃	1	4	yes	—
915	C₂×C₄	C₂⁴×D₁₃	1	2	yes	—
916	C₂×C₄	C₂⁴×D₁₃	1	2	yes	—
917	C₂²	—	2	2	no	—
918	C₂²	—	2	2	no	—
919	C₂²	—	2	4	no	—
920	C₂²	—	2	4	no	—
921	C₂²	—	2	2	no	—
922	C₂²	—	2	4	no	—
923	C₂²	—	4	4	no	—
924	C₂²	—	4	8	no	—
925	C₂²	—	26	4	no	—
926	C₂²	—	26	4	no	—
927	C₂²	—	26	4	no	—
928	C₂²	—	26	8	no	—
929	C₂²	—	26	8	no	—
930	C₂²	—	26	4	no	—
931	C₂²	—	26	4	no	—
932	C₂²	—	26	8	no	—
933	C₂²	—	26	4	no	—
934	C₂²	—	52	8	no	—
935	C₂²	—	52	16	no	—
936	C₂²	—	52	8	no	—
937	C₂²	—	104	32	no	—
938	C₂²	C₂×#88256	1	2	yes	—
939	C₂²	C₂×#88256	1	2	yes	—
940	C₂²	#11719648	1	2	yes	—
941	C₂²	C₂⁵×D₁₃	1	1	yes	characteristic
942	C₄	—	2	2	no	—
943	C₄	—	2	4	no	—
944	C₄	—	2	2	no	—
945	C₄	—	2	4	no	—
946	C₄	—	2	2	no	—
947	C₄	—	2	2	no	—
948	C₄	—	2	4	no	—
949	C₄	—	26	4	no	—
950	C₄	—	26	4	no	—
951	C₄	—	26	8	no	—
952	C₄	C₂×#88256	1	4	yes	—
953	C₄	C₂×#88256	1	4	yes	—
954	C₂	—	4	4	no	—
955	C₂	—	4	2	no	—
956	C₂	—	52	4	no	—
957	C₂	—	52	8	no	—
958	C₂	—	52	4	no	—
959	C₂	#13129210	1	4	yes	direct product factor
960	C₂	C₂²×#88256	1	1	yes	characteristic
961	C₂	C₂²×#88256	1	1	yes	characteristic
962	C₂	C₂×#11719648	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂⁴×D₁₃
commutator, cosocle	C₂²×C₁₃	C₂⁶
Frattini	C₂²	C₂⁵×D₁₃
Fitting	C₂×C₁₃×#529	C₂
socle	C₂³×C₁₃	C₂⁵
hypercenter	C₂×#529	D₁₃
hypocenter	C₁₃	C₂×#3546
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂³ ◁ C₂×#529

Complements

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

N	H ≅ G/N	type
1. #13129210	C₂	direct (N × H)
2. C₂×#11719371	C₂	semidirect
3. C₂×#11719289	C₂	semidirect
4. C₂×#11719400	C₂	semidirect
5. C₂×#11719282	C₂	semidirect
6. C₂×#11719258	C₂	semidirect
7. C₂×#11719256	C₂	semidirect
8. C₂×#11719255	C₂	semidirect
9. C₂×#11719381	C₂	semidirect
10. C₂×D₄×D₅₂	C₂	semidirect
11. C₂×#11719239	C₂	semidirect
12. C₂×#11719409	C₂	semidirect
13. C₂×#11719334	C₂	semidirect
14. C₂×#11719230	C₂	semidirect
15. C₂×#11719312	C₂	semidirect
16. C₂×#11719182	C₂	semidirect
17. C₂×#11719182	C₂	semidirect
18. C₂×C₁₃×#529	C₂	semidirect
19. C₂²×#6131	C₂²	semidirect
21. C₂²×#6127	C₂²	semidirect
22. C₂²×#6127	C₂²	semidirect
23. C₂²×#6127	C₂²	semidirect
25. C₁₃×#529	C₂²	semidirect
26. C₂×C₁₃×#126	C₂²	semidirect
27. C₂×C₁₃×#125	C₂²	semidirect
29. C₂×C₁₃×#123	C₂²	semidirect
30. C₂×C₁₃×C₂²⋊Q₈	C₂²	semidirect
32. C₂×C₄×Q₈×C₁₃	C₂²	semidirect
34. C₂×C₄×D₄×C₁₃	C₂²	semidirect
35. C₂×C₁₃×#117	C₂²	semidirect
36. C₂²×C₄²×C₁₃	C₂²	semidirect
37. C₂×#88200	C₂²	semidirect
38. C₂×#88194	C₂²	semidirect
40. C₂×#88191	C₂²	semidirect
43. C₂×#88184	C₂²	semidirect
44. C₂×#88184	C₂²	semidirect
45. C₂×#88184	C₂²	semidirect
46. C₂×#88184	C₂²	semidirect
47. C₂×#88178	C₂²	semidirect
48. #11719409	C₂²	semidirect
49. #11719400	C₂²	semidirect
50. #11719381	C₂²	semidirect
51. #11719371	C₂²	semidirect
52. #11719334	C₂²	semidirect
53. #11719312	C₂²	semidirect
54. #11719289	C₂²	semidirect
55. #11719282	C₂²	semidirect
56. #11719258	C₂²	semidirect
57. #11719256	C₂²	semidirect
58. #11719255	C₂²	semidirect
59. D₄×D₅₂	C₂²	semidirect
60. #11719239	C₂²	semidirect
61. #11719230	C₂²	semidirect
62. C₂×#88152	C₂²	semidirect
63. C₂×#88152	C₂²	semidirect
64. C₂×#88150	C₂²	semidirect
66. C₂×#88149	C₂²	semidirect
67. C₂×#88149	C₂²	semidirect
68. C₂×#88149	C₂²	semidirect
69. C₂×#88149	C₂²	semidirect
70. C₂×#88148	C₂²	semidirect
71. C₂×#88147	C₂²	semidirect
72. C₂×#88146	C₂²	semidirect
73. C₂×C₄⋊C₄×D₁₃	C₂²	semidirect
74. C₂×#88139	C₂²	semidirect
75. C₂×#88138	C₂²	semidirect
76. C₂×#88138	C₂²	semidirect
77. C₂×#88138	C₂²	semidirect
78. C₂×#88137	C₂²	semidirect
79. C₂×#88137	C₂²	semidirect
81. C₂×#88136	C₂²	semidirect
82. C₂×#88136	C₂²	semidirect
83. C₂×C₂²⋊C₄×D₁₃	C₂²	semidirect
84. #11719182	C₂²	semidirect
85. #11719182	C₂²	semidirect
87. C₂×#88129	C₂²	semidirect
88. C₂×#88129	C₂²	semidirect
91. C₂×#88128	C₂²	semidirect
93. C₂×C₄×D₅₂	C₂²	semidirect
94. C₂×C₄×D₅₂	C₂²	semidirect
95. C₂×C₄×D₅₂	C₂²	semidirect
96. C₂×C₄×D₅₂	C₂²	semidirect
97. C₂×C₄×D₅₂	C₂²	semidirect
98. C₂×#88123	C₂²	semidirect
99. C₂×#88123	C₂²	semidirect
100. C₂×C₄×Dic₂₆	C₂²	semidirect
115. C₂×#6131	C₂³	semidirect
121. C₂×#6127	C₂³	semidirect
122. C₂×#6127	C₂³	semidirect
123. C₂×#6127	C₂³	semidirect
143. C₁₃×#126	C₂³	semidirect
144. C₁₃×#125	C₂³	semidirect
146. C₁₃×#123	C₂³	semidirect
147. C₁₃×C₂²⋊Q₈	C₂³	semidirect
149. C₄×Q₈×C₁₃	C₂³	semidirect
151. C₄×D₄×C₁₃	C₂³	semidirect
152. C₁₃×#117	C₂³	semidirect
169. C₂×C₄²×C₁₃	C₂³	semidirect
171. #88200	C₂³	semidirect
172. #88194	C₂³	semidirect
174. #88191	C₂³	semidirect
177. #88184	C₂³	semidirect
178. #88184	C₂³	semidirect
179. #88184	C₂³	semidirect
180. #88184	C₂³	semidirect
196. #88178	C₂³	semidirect
200. #88152	C₂³	semidirect
201. #88152	C₂³	semidirect
202. #88150	C₂³	semidirect
204. #88149	C₂³	semidirect
205. #88149	C₂³	semidirect
206. #88149	C₂³	semidirect
207. #88149	C₂³	semidirect
208. #88148	C₂³	semidirect
209. #88147	C₂³	semidirect
210. #88146	C₂³	semidirect
211. C₄⋊C₄×D₁₃	C₂³	semidirect
212. #88139	C₂³	semidirect
213. #88138	C₂³	semidirect
214. #88138	C₂³	semidirect
215. #88138	C₂³	semidirect
216. #88137	C₂³	semidirect
217. #88137	C₂³	semidirect
219. #88136	C₂³	semidirect
220. #88136	C₂³	semidirect
221. C₂²⋊C₄×D₁₃	C₂³	semidirect
223. #88129	C₂³	semidirect
224. #88129	C₂³	semidirect
227. #88128	C₂³	semidirect
229. C₄×D₅₂	C₂³	semidirect
230. C₄×D₅₂	C₂³	semidirect
231. C₄×D₅₂	C₂³	semidirect
232. C₄×D₅₂	C₂³	semidirect
233. C₄×D₅₂	C₂³	semidirect
234. #88123	C₂³	semidirect
235. #88123	C₂³	semidirect
236. C₄×Dic₂₆	C₂³	semidirect
375. C₂×#529	D₁₃	semidirect
482. #529	C₂×D₁₃	semidirect
485. C₂×#126	C₂×D₁₃	semidirect
486. C₂×#125	C₂×D₁₃	semidirect
495. C₂×#123	C₂×D₁₃	semidirect
499. C₂×C₂²⋊Q₈	C₂×D₁₃	semidirect
521. C₂×C₄×Q₈	C₂×D₁₃	semidirect
530. C₂×C₄×D₄	C₂×D₁₃	semidirect
532. C₂×#117	C₂×D₁₃	semidirect
535. C₂²×C₄²	C₂×D₁₃	semidirect
623. #126	C₂²×D₁₃	semidirect
624. #125	C₂²×D₁₃	semidirect
633. #123	C₂²×D₁₃	semidirect
637. C₂²⋊Q₈	C₂²×D₁₃	semidirect
659. C₄×Q₈	C₂²×D₁₃	semidirect
668. C₄×D₄	C₂²×D₁₃	semidirect
670. #117	C₂²×D₁₃	semidirect
708. C₂×C₄²	C₂²×D₁₃	semidirect
711. C₂×C₁₃	#3546	semidirect
838. C₁₃	C₂×#3546	semidirect
959. C₂	#13129210	direct (N × H)

Maximal subgroups

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

subgroup	index
#13129210	2
C₂×#11719371	2
C₂×#11719289	2
C₂×#11719400	2
C₂×#11719282	2
C₂×#11719258	2
C₂×#11719256	2
C₂×#11719255	2
C₂×#11719381	2
C₂×D₄×D₅₂	2
C₂×#11719239	2
C₂×#11719409	2
C₂×#11719334	2
C₂×#11719230	2
C₂×#11719312	2
C₂×#11719182	2
C₂×C₁₃×#529	2
C₂×#3546	13

Subgroups — C2×#13129210 #16770558

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13129210 #16770558