Subgroups — C₂×#13129406 #16770272

Order 3328.

7258 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13129406	C₂	1	32	yes	maximal, direct product factor
2	C₂×#11719404	C₂	1	2	yes	maximal, complemented
3	C₂×#11719389	C₂	1	2	yes	maximal, complemented
4	C₂×#11719289	C₂	1	2	yes	maximal, complemented
5	C₂×#11719363	C₂	1	4	yes	maximal, complemented
6	C₂×D₄×Dic₂₆	C₂	1	2	yes	maximal, complemented
7	C₂×#11719257	C₂	1	2	yes	maximal, complemented
8	C₂×#11719255	C₂	1	2	yes	maximal, complemented
9	C₂×#11719339	C₂	1	2	yes	maximal, complemented
10	C₂×#11719239	C₂	1	2	yes	maximal, complemented
11	C₂×#11719415	C₂	1	4	yes	maximal, complemented
12	C₂×#11719322	C₂	1	2	yes	maximal, complemented
13	C₂×#11719231	C₂	1	2	yes	maximal, complemented
14	C₂×#11719175	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂²×#88129	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₁₃×#529	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂²×#6127	C₂²	1	2	yes	—
18	C₂³×D₅₂	C₂²	1	1	yes	characteristic
19	C₂³×Dic₂₆	C₂²	1	1	yes	characteristic
20	C₂³×Dic₂₆	C₂²	1	2	yes	complemented
21	C₁₃×#529	C₂²	1	16	yes	complemented
22	C₂×C₁₃×#126	C₂²	1	2	yes	complemented
23	C₂×C₁₃×#125	C₂²	1	1	yes	characteristic, complemented
24	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic, complemented
25	C₂×C₁₃×#123	C₂²	1	2	yes	—
26	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
27	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
28	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
29	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
30	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic, complemented
31	C₂×C₁₃×#117	C₂²	1	2	yes	complemented
32	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
33	C₂×#88200	C₂²	1	4	yes	complemented
34	C₂×#88193	C₂²	1	4	yes	complemented
35	C₂×#88191	C₂²	1	4	yes	—
36	C₂×D₄×Dic₁₃	C₂²	1	4	yes	—
37	C₂×#88184	C₂²	1	2	yes	—
38	C₂²×#6103	C₂²	1	2	yes	—
39	C₂²×#6103	C₂²	1	2	yes	—
40	C₂×#88180	C₂²	1	2	yes	—
41	C₂×#88178	C₂²	1	2	yes	—
42	C₂×#88178	C₂²	1	2	yes	—
43	C₂×#88178	C₂²	1	2	yes	complemented
44	#11719415	C₂²	1	64	yes	complemented
45	#11719404	C₂²	1	32	yes	complemented
46	#11719389	C₂²	1	32	yes	complemented
47	#11719363	C₂²	1	64	yes	complemented
48	#11719339	C₂²	1	32	yes	complemented
49	#11719322	C₂²	1	32	yes	complemented
50	#11719289	C₂²	1	32	yes	complemented
51	#11719257	C₂²	1	32	yes	complemented
52	#11719255	C₂²	1	32	yes	complemented
53	D₄×Dic₂₆	C₂²	1	32	yes	complemented
54	#11719239	C₂²	1	32	yes	complemented
55	#11719231	C₂²	1	32	yes	complemented
56	C₂×#88152	C₂²	1	4	yes	complemented
57	C₂×#88152	C₂²	1	4	yes	complemented
58	C₂×#88152	C₂²	1	4	yes	complemented
59	C₂×#88151	C₂²	1	4	yes	complemented
60	C₂×#88151	C₂²	1	4	yes	complemented
61	C₂×#88150	C₂²	1	4	yes	complemented
62	C₂×#88150	C₂²	1	4	yes	complemented
63	C₂×#88148	C₂²	1	4	yes	—
64	C₂×#88146	C₂²	1	4	yes	complemented
65	C₂×#88142	C₂²	1	4	yes	complemented
66	C₂×#88140	C₂²	1	4	yes	complemented
67	C₂×#88140	C₂²	1	4	yes	complemented
68	C₂×#88139	C₂²	1	4	yes	complemented
69	C₂×#88139	C₂²	1	4	yes	complemented
70	C₂×#88138	C₂²	1	4	yes	—
71	C₂×#88137	C₂²	1	4	yes	complemented
72	C₂×#88135	C₂²	1	4	yes	complemented
73	C₂×C₂²⋊C₄×D₁₃	C₂²	1	4	yes	—
74	C₂×#88132	C₂²	1	4	yes	—
75	C₂×#88132	C₂²	1	4	yes	complemented
76	C₂×#88129	C₂²	1	2	yes	—
77	C₂×#88129	C₂²	1	2	yes	—
78	C₂×#88129	C₂²	1	2	yes	—
79	C₂×#88129	C₂²	1	2	yes	—
80	C₂×#88129	C₂²	1	2	yes	—
81	C₂×#88129	C₂²	1	16	yes	complemented
82	C₂×C₄×D₅₂	C₂²	1	2	yes	—
83	#11719175	C₂²	1	16	yes	complemented
84	C₂×#88124	C₂²	1	2	yes	complemented
85	C₂×#88123	C₂²	1	1	yes	characteristic, complemented
86	C₂×#88123	C₂²	1	2	yes	complemented
87	C₂×#88123	C₂²	1	1	yes	characteristic, complemented
88	C₂×C₄×Dic₂₆	C₂²	1	2	yes	complemented
89	C₂×C₄×Dic₂₆	C₂²	1	2	yes	complemented
90	C₂×C₄×Dic₂₆	C₂²	1	2	yes	complemented
91	C₂⁴×D₁₃	C₂³	1	2	yes	—
92	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
93	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
94	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
95	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
96	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
97	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
98	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
99	C₂²×C₂²⋊D₁₃	C₂³	1	4	yes	—
100	C₂²×C₂²⋊D₁₃	C₂³	1	4	yes	—
101	C₂³×Dic₁₃	C₂³	1	2	yes	—
102	C₂³×Dic₁₃	C₂³	1	4	yes	—
103	C₂×#6127	—	4	8	no	—
104	C₂×#6127	C₂³	1	16	yes	—
105	C₂²×D₅₂	—	4	4	no	—
106	C₂²×D₅₂	C₂³	1	2	yes	—
107	C₂²×D₅₂	C₂³	1	2	yes	—
108	C₂²×D₅₂	C₂³	1	8	yes	—
109	C₂²×C₄×D₁₃	C₂³	1	4	yes	—
110	C₂²×C₄×D₁₃	C₂³	1	4	yes	—
111	C₂²×Dic₂₆	—	4	4	no	—
112	C₂²×Dic₂₆	—	4	8	no	—
113	C₂²×Dic₂₆	C₂³	1	2	yes	—
114	C₂²×Dic₂₆	C₂³	1	2	yes	—
115	C₂²×Dic₂₆	C₂³	1	2	yes	—
116	C₂²×Dic₂₆	C₂³	1	2	yes	—
117	C₂²×Dic₂₆	C₂³	1	8	yes	—
118	C₂²×Dic₂₆	C₂³	1	4	yes	—
119	C₂²×Dic₂₆	C₂³	1	16	yes	complemented
120	C₁₃×#126	C₂³	1	16	yes	complemented
121	C₁₃×#125	C₂³	1	8	yes	complemented
122	C₁₃×#124	C₂³	1	8	yes	complemented
123	C₁₃×#123	C₂³	1	16	yes	—
124	C₁₃×C₂²⋊Q₈	C₂³	1	8	yes	—
125	C₁₃×#121	C₂³	1	8	yes	—
126	C₄×Q₈×C₁₃	C₂³	1	8	yes	complemented
127	C₄×D₄×C₁₃	C₂³	1	16	yes	—
128	C₄×D₄×C₁₃	C₂³	1	8	yes	complemented
129	C₁₃×#117	C₂³	1	16	yes	complemented
130	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
131	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
132	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
133	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
134	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
135	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
136	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
137	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
138	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
139	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
140	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
141	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
142	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
143	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
144	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
145	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
146	C₂×C₄²×C₁₃	C₂³	1	8	yes	—
147	C₂×C₂²⋊Dic₁₃	C₂³	1	4	yes	—
148	C₂×C₂²⋊Dic₁₃	C₂³	1	4	yes	—
149	#88200	C₂³	1	32	yes	complemented
150	#88193	C₂³	1	32	yes	complemented
151	#88191	C₂³	1	32	yes	—
152	D₄×Dic₁₃	C₂³	1	32	yes	—
153	#88184	C₂³	1	16	yes	—
154	C₂×#6103	C₂³	1	4	yes	—
155	C₂×#6103	C₂³	1	4	yes	—
156	C₂×#6103	C₂³	1	4	yes	—
157	C₂×#6103	C₂³	1	4	yes	—
158	C₂×#6103	C₂³	1	4	yes	—
159	C₂×#6103	C₂³	1	4	yes	—
160	C₂×#6103	C₂³	1	4	yes	—
161	C₂×#6103	C₂³	1	16	yes	—
162	C₂×#6103	C₂³	1	16	yes	—
163	C₂×#6103	C₂³	1	4	yes	—
164	#88180	C₂³	1	16	yes	—
165	C₂×C₄⋊Dic₁₃	C₂³	1	2	yes	—
166	C₂×C₄⋊Dic₁₃	C₂³	1	2	yes	—
167	C₂×C₄⋊Dic₁₃	C₂³	1	2	yes	—
168	C₂×C₄⋊Dic₁₃	C₂³	1	2	yes	—
169	C₂×C₄⋊Dic₁₃	C₂³	1	4	yes	—
170	C₂×C₄⋊Dic₁₃	C₂³	1	4	yes	—
171	#88178	C₂³	1	16	yes	—
172	#88178	C₂³	1	16	yes	—
173	#88178	C₂³	1	16	yes	complemented
174	C₂×#6101	C₂³	1	4	yes	—
175	C₂×#6101	C₂³	1	4	yes	—
176	C₂×#6101	C₂³	1	4	yes	—
177	C₂×#6101	C₂³	1	4	yes	—
178	C₂×C₄×Dic₁₃	C₂³	1	4	yes	—
179	C₂×C₄×Dic₁₃	C₂³	1	4	yes	—
180	#88152	C₂³	1	32	yes	complemented
181	#88152	C₂³	1	32	yes	complemented
182	#88152	C₂³	1	32	yes	complemented
183	#88151	C₂³	1	32	yes	complemented
184	#88151	C₂³	1	32	yes	complemented
185	#88150	C₂³	1	32	yes	complemented
186	#88150	C₂³	1	32	yes	complemented
187	#88148	C₂³	1	32	yes	—
188	#88146	C₂³	1	32	yes	complemented
189	#88142	C₂³	1	32	yes	complemented
190	#88140	C₂³	1	32	yes	complemented
191	#88140	C₂³	1	32	yes	complemented
192	#88139	C₂³	1	32	yes	complemented
193	#88139	C₂³	1	32	yes	complemented
194	#88138	C₂³	1	32	yes	—
195	#88137	C₂³	1	32	yes	complemented
196	#88135	C₂³	1	32	yes	complemented
197	C₂²⋊C₄×D₁₃	C₂³	1	32	yes	—
198	#88132	C₂³	1	32	yes	—
199	#88132	C₂³	1	32	yes	complemented
200	#88129	C₂³	1	16	yes	—
201	#88129	C₂³	1	16	yes	—
202	#88129	C₂³	1	16	yes	—
203	#88129	C₂³	1	16	yes	—
204	#88129	C₂³	1	16	yes	—
205	C₄×D₅₂	C₂³	1	16	yes	—
206	#88124	C₂³	1	16	yes	complemented
207	#88123	C₂³	1	8	yes	complemented
208	#88123	C₂³	1	8	yes	complemented
209	#88123	C₂³	1	16	yes	complemented
210	C₄×Dic₂₆	C₂³	1	16	yes	complemented
211	C₄×Dic₂₆	C₂³	1	16	yes	complemented
212	C₄×Dic₂₆	C₂³	1	16	yes	complemented
213	C₂×#3561	—	13	1	no	maximal, Sylow
214	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
215	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
216	C₂³×D₁₃	—	2	8	no	—
217	C₂³×D₁₃	—	4	4	no	—
218	C₂³×D₁₃	—	4	4	no	—
219	C₂³×D₁₃	C₂⁴	1	4	yes	—
220	C₂³×D₁₃	C₂⁴	1	8	yes	—
221	C₂×Q₈×C₁₃	—	4	2	no	—
222	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
223	C₂×D₄×C₁₃	—	2	8	no	—
224	C₂×D₄×C₁₃	—	4	2	no	—
225	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
226	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
227	C₂²×C₄×C₁₃	—	2	4	no	—
228	C₂²×C₄×C₁₃	—	2	4	no	—
229	C₂²×C₄×C₁₃	—	2	8	no	—
230	C₂²×C₄×C₁₃	—	4	2	no	—
231	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
232	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
233	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
234	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
235	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
236	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
237	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
238	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
239	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
240	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
241	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
242	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
243	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
244	C₂×C₂²⋊D₁₃	—	4	8	no	—
245	C₂×C₂²⋊D₁₃	—	4	8	no	—
246	C₂×C₂²⋊D₁₃	C₂⁴	1	16	yes	—
247	C₂×C₂²⋊D₁₃	C₂⁴	1	16	yes	—
248	C₂²×Dic₁₃	—	4	4	no	—
249	C₂²×Dic₁₃	—	4	8	no	—
250	C₂²×Dic₁₃	C₂⁴	1	4	yes	—
251	C₂²×Dic₁₃	C₂⁴	1	4	yes	—
252	C₂²×Dic₁₃	C₂⁴	1	4	yes	—
253	C₂²×Dic₁₃	C₂⁴	1	8	yes	—
254	C₂²×Dic₁₃	C₂⁴	1	16	yes	—
255	#6127	—	4	32	no	—
256	C₂×D₅₂	—	2	8	no	—
257	C₂×D₅₂	—	4	16	no	—
258	C₂×D₅₂	—	4	4	no	—
259	C₂×D₅₂	C₂⁴	1	8	yes	—
260	C₂×D₅₂	C₂⁴	1	8	yes	—
261	C₂×C₄×D₁₃	—	4	8	no	—
262	C₂×C₄×D₁₃	—	4	8	no	—
263	C₂×C₄×D₁₃	C₂⁴	1	16	yes	—
264	C₂×C₄×D₁₃	C₂⁴	1	16	yes	—
265	C₂×Dic₂₆	—	2	8	no	—
266	C₂×Dic₂₆	—	2	8	no	—
267	C₂×Dic₂₆	—	4	16	no	—
268	C₂×Dic₂₆	—	4	32	no	—
269	C₂×Dic₂₆	—	4	4	no	—
270	C₂×Dic₂₆	—	4	8	no	—
271	C₂×Dic₂₆	—	4	4	no	—
272	C₂×Dic₂₆	C₂⁴	1	8	yes	—
273	C₂×Dic₂₆	C₂⁴	1	8	yes	—
274	C₂×Dic₂₆	C₂⁴	1	8	yes	—
275	C₂×Dic₂₆	C₂⁴	1	8	yes	—
276	C₂×Dic₂₆	C₂⁴	1	16	yes	—
277	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
278	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
279	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
280	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
281	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
282	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
283	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
284	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
285	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
286	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
287	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
288	C₄²×C₁₃	C₂⁴	1	4	yes	—
289	C₄²×C₁₃	C₂⁴	1	4	yes	—
290	C₄²×C₁₃	C₂⁴	1	8	yes	—
291	C₄²×C₁₃	C₂⁴	1	4	yes	—
292	C₄²×C₁₃	C₂⁴	1	4	yes	—
293	C₂²⋊Dic₁₃	C₂⁴	1	16	yes	—
294	C₂²⋊Dic₁₃	C₂⁴	1	16	yes	—
295	#6103	C₂⁴	1	16	yes	—
296	#6103	C₂⁴	1	16	yes	—
297	#6103	C₂⁴	1	16	yes	—
298	#6103	C₂⁴	1	16	yes	—
299	#6103	C₂⁴	1	16	yes	—
300	#6103	C₂⁴	1	16	yes	—
301	#6103	C₂⁴	1	16	yes	—
302	#6103	C₂⁴	1	16	yes	—
303	C₄⋊Dic₁₃	C₂⁴	1	8	yes	—
304	C₄⋊Dic₁₃	C₂⁴	1	8	yes	—
305	C₄⋊Dic₁₃	C₂⁴	1	8	yes	—
306	C₄⋊Dic₁₃	C₂⁴	1	8	yes	—
307	C₄⋊Dic₁₃	C₂⁴	1	16	yes	—
308	C₄⋊Dic₁₃	C₂⁴	1	16	yes	—
309	#6101	C₂⁴	1	16	yes	—
310	#6101	C₂⁴	1	16	yes	—
311	#6101	C₂⁴	1	16	yes	—
312	#6101	C₂⁴	1	16	yes	—
313	C₄×Dic₁₃	C₂⁴	1	16	yes	—
314	C₄×Dic₁₃	C₂⁴	1	16	yes	—
315	#3561	—	13	32	no	—
316	C₂×#563	—	13	2	no	—
317	C₂×#562	—	13	2	no	—
318	C₂×#556	—	13	2	no	—
319	C₂×#551	—	13	4	no	—
320	C₂×D₄×Q₈	—	13	2	no	—
321	C₂×#548	—	13	2	no	—
322	C₂×#546	—	13	2	no	—
323	C₂×#543	—	13	2	no	—
324	C₂×#542	—	13	4	no	—
325	C₂×#542	—	13	2	no	—
326	C₂×#538	—	13	2	no	—
327	C₂×#536	—	13	2	no	—
328	C₂×#533	—	13	1	no	—
329	C₂×#529	D₁₃	1	1	yes	characteristic, complemented
330	C₂²×#124	—	13	1	no	—
331	C₂³×C₁₃	—	2	2	no	—
332	C₂³×C₁₃	—	2	2	no	—
333	C₂³×C₁₃	—	2	4	no	—
334	C₂³×C₁₃	—	2	4	no	—
335	C₂³×C₁₃	—	2	4	no	—
336	C₂³×C₁₃	2₋¹⁺⁴	1	4	yes	—
337	C₂³×C₁₃	C₂⁵	1	4	yes	—
338	C₂³×C₁₃	C₂⁵	1	2	yes	—
339	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
340	C₂²×D₁₃	—	2	8	no	—
341	C₂²×D₁₃	—	2	8	no	—
342	C₂²×D₁₃	—	2	8	no	—
343	C₂²×D₁₃	—	2	16	no	—
344	C₂²×D₁₃	—	4	8	no	—
345	C₂²×D₁₃	—	4	8	no	—
346	C₂²×D₁₃	—	8	16	no	—
347	C₂²×D₁₃	C₂⁵	1	8	yes	—
348	Q₈×C₁₃	—	4	4	no	—
349	D₄×C₁₃	—	2	16	no	—
350	D₄×C₁₃	—	4	4	no	—
351	C₂×C₄×C₁₃	—	2	4	no	—
352	C₂×C₄×C₁₃	—	2	2	no	—
353	C₂×C₄×C₁₃	—	2	8	no	—
354	C₂×C₄×C₁₃	—	2	2	no	—
355	C₂×C₄×C₁₃	—	2	2	no	—
356	C₂×C₄×C₁₃	—	2	4	no	—
357	C₂×C₄×C₁₃	—	2	2	no	—
358	C₂×C₄×C₁₃	—	2	4	no	—
359	C₂×C₄×C₁₃	—	2	2	no	—
360	C₂×C₄×C₁₃	—	2	8	no	—
361	C₂×C₄×C₁₃	—	2	16	no	—
362	C₂×C₄×C₁₃	—	4	4	no	—
363	C₂×C₄×C₁₃	H(5,𝔽₂)	1	4	yes	—
364	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
365	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
366	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
367	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
368	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
369	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
370	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
371	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
372	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
373	C₂²⋊D₁₃	—	4	16	no	—
374	C₂²⋊D₁₃	—	4	16	no	—
375	C₂×Dic₁₃	—	2	8	no	—
376	C₂×Dic₁₃	—	2	8	no	—
377	C₂×Dic₁₃	—	2	8	no	—
378	C₂×Dic₁₃	—	4	8	no	—
379	C₂×Dic₁₃	—	4	16	no	—
380	C₂×Dic₁₃	C₂⁵	1	8	yes	—
381	C₂×Dic₁₃	C₂⁵	1	8	yes	—
382	C₂×Dic₁₃	C₂⁵	1	8	yes	—
383	D₅₂	—	2	16	no	—
384	D₅₂	—	4	8	no	—
385	C₄×D₁₃	—	4	16	no	—
386	C₄×D₁₃	—	4	16	no	—
387	Dic₂₆	—	2	16	no	—
388	Dic₂₆	—	2	16	no	—
389	Dic₂₆	—	4	8	no	—
390	Dic₂₆	—	4	16	no	—
391	Dic₂₆	—	4	8	no	—
392	C₂²×#41	—	13	2	no	—
393	C₂³×Q₈	—	13	1	no	—
394	C₂³×Q₈	—	13	2	no	—
395	C₂³×D₄	—	13	1	no	—
396	#563	—	13	32	no	—
397	#562	—	13	32	no	—
398	#556	—	13	32	no	—
399	#551	—	13	64	no	—
400	D₄×Q₈	—	13	32	no	—
401	#548	—	13	32	no	—
402	#546	—	13	32	no	—
403	#543	—	13	32	no	—
404	#542	—	13	64	no	—
405	#542	—	13	32	no	—
406	#538	—	13	32	no	—
407	#536	—	13	32	no	—
408	#533	—	13	16	no	—
409	C₂×C₄⋊Q₈	—	13	4	no	—
410	C₂×C₄⋊Q₈	—	13	1	no	—
411	C₂×C₄⋊Q₈	—	13	1	no	—
412	C₂×C₄⋊Q₈	—	13	2	no	—
413	#529	C₂×D₁₃	1	16	yes	complemented
414	C₂×#126	—	13	4	no	—
415	C₂×#126	—	13	4	no	—
416	C₂×#126	—	13	4	no	—
417	C₂×#126	C₂×D₁₃	1	2	yes	complemented
418	C₂×#125	—	13	2	no	—
419	C₂×#125	C₂×D₁₃	1	1	yes	characteristic, complemented
420	C₂×#124	—	13	4	no	—
421	C₂×#124	—	13	4	no	—
422	C₂×#124	—	13	2	no	—
423	C₂×#124	—	13	2	no	—
424	C₂×#124	—	13	2	no	—
425	C₂×#124	—	13	2	no	—
426	C₂×#124	—	13	2	no	—
427	C₂×#124	—	13	16	no	—
428	C₂×#124	C₂×D₁₃	1	1	yes	characteristic, complemented
429	C₂×#123	—	13	4	no	—
430	C₂×#123	—	13	4	no	—
431	C₂×#123	—	13	4	no	—
432	C₂×#123	—	13	4	no	—
433	C₂×#123	C₂×D₁₃	1	2	yes	—
434	C₂×C₂²⋊Q₈	—	13	4	no	—
435	C₂×C₂²⋊Q₈	—	13	2	no	—
436	C₂×C₂²⋊Q₈	—	13	2	no	—
437	C₂×C₂²⋊Q₈	—	13	2	no	—
438	C₂×C₂²⋊Q₈	—	13	4	no	—
439	C₂×C₂²⋊Q₈	—	13	4	no	—
440	C₂×C₂²⋊Q₈	—	13	4	no	—
441	C₂×C₂²⋊Q₈	—	13	4	no	—
442	C₂×C₂²⋊Q₈	—	13	4	no	—
443	C₂×C₂²⋊Q₈	—	13	4	no	—
444	C₂×C₂²⋊Q₈	C₂×D₁₃	1	1	yes	characteristic
445	C₂×#121	—	13	4	no	—
446	C₂×#121	—	13	2	no	—
447	C₂×#121	—	13	4	no	—
448	C₂×#121	C₂×D₁₃	1	1	yes	characteristic
449	C₂×#120	—	13	4	no	—
450	C₂×C₄×Q₈	—	13	2	no	—
451	C₂×C₄×Q₈	—	13	2	no	—
452	C₂×C₄×Q₈	—	13	2	no	—
453	C₂×C₄×Q₈	C₂×D₁₃	1	1	yes	characteristic, complemented
454	C₂×C₄×D₄	—	13	4	no	—
455	C₂×C₄×D₄	—	13	4	no	—
456	C₂×C₄×D₄	—	13	2	no	—
457	C₂×C₄×D₄	C₂×D₁₃	1	2	yes	—
458	C₂×C₄×D₄	C₂×D₁₃	1	1	yes	characteristic, complemented
459	C₂×#117	—	13	2	no	—
460	C₂×#117	—	13	4	no	—
461	C₂×#117	C₂×D₁₃	1	2	yes	complemented
462	C₂²×C₂²⋊C₄	—	13	2	no	—
463	C₂²×C₂²⋊C₄	—	13	2	no	—
464	C₂²×C₂²⋊C₄	—	13	4	no	—
465	C₂²×C₄²	C₂×D₁₃	1	1	yes	characteristic
466	C₂²×C₁₃	—	2	2	no	—
467	C₂²×C₁₃	—	2	2	no	—
468	C₂²×C₁₃	—	2	8	no	—
469	C₂²×C₁₃	—	2	4	no	—
470	C₂²×C₁₃	—	2	4	no	—
471	C₂²×C₁₃	—	2	4	no	—
472	C₂²×C₁₃	—	4	8	no	—
473	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
474	C₂²×C₁₃	C₂×2₋¹⁺⁴	1	4	yes	—
475	C₂²×C₁₃	C₂×2₋¹⁺⁴	1	2	yes	—
476	C₂²×C₁₃	#585	1	2	yes	—
477	C₂²×C₁₃	C₂⁶	1	1	yes	characteristic
478	C₂×D₁₃	—	2	8	no	—
479	C₂×D₁₃	—	2	8	no	—
480	C₂×D₁₃	—	2	8	no	—
481	C₂×D₁₃	—	4	16	no	—
482	C₂×D₁₃	—	8	16	no	—
483	C₄×C₁₃	—	2	4	no	—
484	C₄×C₁₃	—	2	2	no	—
485	C₄×C₁₃	—	2	2	no	—
486	C₄×C₁₃	—	2	2	no	—
487	C₄×C₁₃	—	2	4	no	—
488	C₄×C₁₃	—	2	2	no	—
489	C₄×C₁₃	—	2	4	no	—
490	C₄×C₁₃	—	2	2	no	—
491	C₄×C₁₃	C₂×H(5,𝔽₂)	1	4	yes	—
492	Dic₁₃	—	2	8	no	—
493	Dic₁₃	—	2	8	no	—
494	Dic₁₃	—	2	8	no	—
495	C₂⁵	—	13	2	no	—
496	C₂×#41	—	13	16	no	—
497	C₂×#41	—	52	8	no	—
498	C₂²×Q₈	—	13	2	no	—
499	C₂²×Q₈	—	13	2	no	—
500	C₂²×Q₈	—	13	2	no	—
501	C₂²×Q₈	—	13	4	no	—
502	C₂²×Q₈	—	13	2	no	—
503	C₂²×Q₈	—	13	8	no	—
504	C₂²×Q₈	—	13	16	no	—
505	C₂²×Q₈	—	52	4	no	—
506	C₂²×Q₈	—	52	8	no	—
507	C₂²×Q₈	C₂²×D₁₃	1	1	yes	characteristic
508	C₂²×D₄	—	13	4	no	—
509	C₂²×D₄	—	13	4	no	—
510	C₂²×D₄	—	13	2	no	—
511	C₂²×D₄	—	13	2	no	—
512	C₂²×D₄	—	13	8	no	—
513	C₂²×D₄	—	52	4	no	—
514	C₂²×D₄	C₂²×D₁₃	1	2	yes	—
515	C₂²×D₄	C₂²×D₁₃	1	1	yes	characteristic
516	C₂³×C₄	—	13	2	no	—
517	C₂³×C₄	—	13	4	no	—
518	C₂³×C₄	—	13	4	no	—
519	C₂³×C₄	—	13	4	no	—
520	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
521	C₂³×C₄	C₂²×D₁₃	1	2	yes	—
522	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
523	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
524	C₄⋊Q₈	—	13	32	no	—
525	C₄⋊Q₈	—	13	8	no	—
526	C₄⋊Q₈	—	13	8	no	—
527	C₄⋊Q₈	—	13	16	no	—
528	#126	—	13	32	no	—
529	#126	—	13	32	no	—
530	#126	—	13	32	no	—
531	#126	C₂²×D₁₃	1	16	yes	complemented
532	#125	—	13	16	no	—
533	#125	C₂²×D₁₃	1	8	yes	complemented
534	#124	—	13	32	no	—
535	#124	—	13	32	no	—
536	#124	—	13	16	no	—
537	#124	—	13	16	no	—
538	#124	—	13	16	no	—
539	#124	—	13	16	no	—
540	#124	—	13	16	no	—
541	#124	C₂²×D₁₃	1	8	yes	complemented
542	#123	—	13	32	no	—
543	#123	—	13	32	no	—
544	#123	—	13	32	no	—
545	#123	—	13	32	no	—
546	#123	C₂²×D₁₃	1	16	yes	—
547	C₂²⋊Q₈	—	13	32	no	—
548	C₂²⋊Q₈	—	13	16	no	—
549	C₂²⋊Q₈	—	13	16	no	—
550	C₂²⋊Q₈	—	13	16	no	—
551	C₂²⋊Q₈	—	13	32	no	—
552	C₂²⋊Q₈	—	13	32	no	—
553	C₂²⋊Q₈	—	13	32	no	—
554	C₂²⋊Q₈	—	13	32	no	—
555	C₂²⋊Q₈	—	13	32	no	—
556	C₂²⋊Q₈	—	13	32	no	—
557	C₂²⋊Q₈	C₂²×D₁₃	1	8	yes	—
558	#121	—	13	32	no	—
559	#121	—	13	16	no	—
560	#121	—	13	32	no	—
561	#121	C₂²×D₁₃	1	8	yes	—
562	#120	—	13	32	no	—
563	C₄×Q₈	—	13	16	no	—
564	C₄×Q₈	—	13	16	no	—
565	C₄×Q₈	—	13	16	no	—
566	C₄×Q₈	C₂²×D₁₃	1	8	yes	complemented
567	C₄×D₄	—	13	32	no	—
568	C₄×D₄	—	13	32	no	—
569	C₄×D₄	—	13	16	no	—
570	C₄×D₄	C₂²×D₁₃	1	16	yes	—
571	C₄×D₄	C₂²×D₁₃	1	8	yes	complemented
572	#117	—	13	16	no	—
573	#117	—	13	32	no	—
574	#117	C₂²×D₁₃	1	16	yes	complemented
575	C₂×C₄⋊C₄	—	13	4	no	—
576	C₂×C₄⋊C₄	—	13	2	no	—
577	C₂×C₄⋊C₄	—	13	2	no	—
578	C₂×C₄⋊C₄	—	13	2	no	—
579	C₂×C₄⋊C₄	—	13	4	no	—
580	C₂×C₄⋊C₄	—	13	4	no	—
581	C₂×C₄⋊C₄	—	13	4	no	—
582	C₂×C₄⋊C₄	—	13	4	no	—
583	C₂×C₄⋊C₄	—	13	4	no	—
584	C₂×C₄⋊C₄	—	13	2	no	—
585	C₂×C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
586	C₂×C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
587	C₂×C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
588	C₂×C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
589	C₂×C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
590	C₂×C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
591	C₂×C₂²⋊C₄	—	13	4	no	—
592	C₂×C₂²⋊C₄	—	13	4	no	—
593	C₂×C₂²⋊C₄	—	13	4	no	—
594	C₂×C₂²⋊C₄	—	13	4	no	—
595	C₂×C₂²⋊C₄	—	13	4	no	—
596	C₂×C₂²⋊C₄	—	13	4	no	—
597	C₂×C₂²⋊C₄	—	13	4	no	—
598	C₂×C₂²⋊C₄	—	13	4	no	—
599	C₂×C₂²⋊C₄	—	13	16	no	—
600	C₂×C₂²⋊C₄	—	13	16	no	—
601	C₂×C₂²⋊C₄	—	13	4	no	—
602	C₂×C₂²⋊C₄	—	13	4	no	—
603	C₂×C₂²⋊C₄	—	13	32	no	—
604	C₂×C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
605	C₂×C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
606	C₂×C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
607	C₂×C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
608	C₂×C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
609	C₂×C₄²	—	13	4	no	—
610	C₂×C₄²	—	13	4	no	—
611	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
612	C₂×C₄²	C₂²×D₁₃	1	2	yes	—
613	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
614	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
615	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
616	C₂×C₄²	C₂²×D₁₃	1	8	yes	—
617	C₂×C₁₃	—	2	4	no	—
618	C₂×C₁₃	—	4	4	no	—
619	C₂×C₁₃	#3561	1	4	yes	complemented
620	C₂×C₁₃	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
621	C₂×C₁₃	C₂²×2₋¹⁺⁴	1	1	yes	characteristic
622	C₂×C₁₃	C₂×#585	1	1	yes	characteristic
623	D₁₃	—	4	8	no	—
624	C₂⁴	—	13	4	no	—
625	C₂⁴	—	13	8	no	—
626	C₂⁴	—	26	8	no	—
627	C₂⁴	—	52	4	no	—
628	C₂⁴	—	52	4	no	—
629	C₂⁴	C₂³×D₁₃	1	2	yes	—
630	C₂⁴	C₂³×D₁₃	1	1	yes	characteristic
631	#41	—	52	32	no	—
632	C₂×Q₈	—	4	2	no	—
633	C₂×Q₈	—	13	8	no	—
634	C₂×Q₈	—	13	8	no	—
635	C₂×Q₈	—	13	8	no	—
636	C₂×Q₈	—	13	16	no	—
637	C₂×Q₈	—	13	8	no	—
638	C₂×Q₈	—	26	8	no	—
639	C₂×Q₈	—	26	8	no	—
640	C₂×Q₈	—	52	8	no	—
641	C₂×Q₈	—	52	4	no	—
642	C₂×Q₈	—	52	4	no	—
643	C₂×Q₈	—	52	16	no	—
644	C₂×Q₈	—	52	32	no	—
645	C₂×Q₈	C₂³×D₁₃	1	4	yes	—
646	C₂×D₄	—	2	8	no	—
647	C₂×D₄	—	4	2	no	—
648	C₂×D₄	—	13	16	no	—
649	C₂×D₄	—	13	16	no	—
650	C₂×D₄	—	13	8	no	—
651	C₂×D₄	—	13	8	no	—
652	C₂×D₄	—	26	8	no	—
653	C₂×D₄	—	52	16	no	—
654	C₂×D₄	—	52	4	no	—
655	C₂×D₄	—	52	8	no	—
656	C₂×D₄	—	52	8	no	—
657	C₂×D₄	C₂³×D₁₃	1	8	yes	—
658	C₂×D₄	C₂³×D₁₃	1	4	yes	—
659	C₂²×C₄	—	2	4	no	—
660	C₂²×C₄	—	2	4	no	—
661	C₂²×C₄	—	2	8	no	—
662	C₂²×C₄	—	4	2	no	—
663	C₂²×C₄	—	13	4	no	—
664	C₂²×C₄	—	13	4	no	—
665	C₂²×C₄	—	13	4	no	—
666	C₂²×C₄	—	13	8	no	—
667	C₂²×C₄	—	13	16	no	—
668	C₂²×C₄	—	13	16	no	—
669	C₂²×C₄	—	13	16	no	—
670	C₂²×C₄	—	52	8	no	—
671	C₂²×C₄	—	52	8	no	—
672	C₂²×C₄	—	52	8	no	—
673	C₂²×C₄	—	52	4	no	—
674	C₂²×C₄	C₂³×D₁₃	1	4	yes	—
675	C₂²×C₄	C₂³×D₁₃	1	4	yes	—
676	C₂²×C₄	C₂³×D₁₃	1	8	yes	—
677	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
678	C₂²×C₄	C₂³×D₁₃	1	2	yes	—
679	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
680	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
681	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
682	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
683	C₂²×C₄	C₂³×D₁₃	1	2	yes	—
684	C₂²×C₄	C₂³×D₁₃	1	2	yes	—
685	C₂²×C₄	C₂³×D₁₃	1	4	yes	—
686	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
687	C₄⋊C₄	—	13	16	no	—
688	C₄⋊C₄	—	13	8	no	—
689	C₄⋊C₄	—	13	8	no	—
690	C₄⋊C₄	—	13	8	no	—
691	C₄⋊C₄	—	13	16	no	—
692	C₄⋊C₄	—	13	16	no	—
693	C₄⋊C₄	—	13	16	no	—
694	C₄⋊C₄	—	13	16	no	—
695	C₄⋊C₄	—	13	16	no	—
696	C₄⋊C₄	—	13	8	no	—
697	C₄⋊C₄	C₂³×D₁₃	1	8	yes	—
698	C₄⋊C₄	C₂³×D₁₃	1	8	yes	—
699	C₄⋊C₄	C₂³×D₁₃	1	8	yes	—
700	C₄⋊C₄	C₂³×D₁₃	1	8	yes	—
701	C₄⋊C₄	C₂³×D₁₃	1	4	yes	—
702	C₄⋊C₄	C₂³×D₁₃	1	4	yes	—
703	C₂²⋊C₄	—	13	16	no	—
704	C₂²⋊C₄	—	13	16	no	—
705	C₂²⋊C₄	—	13	16	no	—
706	C₂²⋊C₄	—	13	16	no	—
707	C₂²⋊C₄	—	13	16	no	—
708	C₂²⋊C₄	—	13	16	no	—
709	C₂²⋊C₄	—	13	16	no	—
710	C₂²⋊C₄	—	13	16	no	—
711	C₂²⋊C₄	—	13	16	no	—
712	C₂²⋊C₄	—	13	16	no	—
713	C₂²⋊C₄	C₂³×D₁₃	1	8	yes	—
714	C₂²⋊C₄	C₂³×D₁₃	1	8	yes	—
715	C₂²⋊C₄	C₂³×D₁₃	1	8	yes	—
716	C₂²⋊C₄	C₂³×D₁₃	1	8	yes	—
717	C₂²⋊C₄	C₂³×D₁₃	1	8	yes	—
718	C₄²	—	13	16	no	—
719	C₄²	—	13	16	no	—
720	C₄²	C₂³×D₁₃	1	4	yes	—
721	C₄²	C₂³×D₁₃	1	4	yes	—
722	C₄²	C₂³×D₁₃	1	4	yes	—
723	C₄²	C₂³×D₁₃	1	4	yes	—
724	C₄²	C₂³×D₁₃	1	8	yes	—
725	C₁₃	C₂×#3561	1	1	yes	characteristic, complemented, Sylow
726	C₂³	—	2	2	no	—
727	C₂³	—	2	2	no	—
728	C₂³	—	2	4	no	—
729	C₂³	—	2	4	no	—
730	C₂³	—	2	4	no	—
731	C₂³	—	13	8	no	—
732	C₂³	—	26	8	no	—
733	C₂³	—	26	8	no	—
734	C₂³	—	26	8	no	—
735	C₂³	—	26	16	no	—
736	C₂³	—	52	8	no	—
737	C₂³	—	52	8	no	—
738	C₂³	—	104	16	no	—
739	C₂³	#88257	1	4	yes	—
740	C₂³	C₂⁴×D₁₃	1	4	yes	—
741	C₂³	C₂⁴×D₁₃	1	2	yes	—
742	C₂³	C₂⁴×D₁₃	1	1	yes	characteristic
743	Q₈	—	4	4	no	—
744	Q₈	—	26	16	no	—
745	Q₈	—	26	16	no	—
746	Q₈	—	52	8	no	—
747	Q₈	—	52	16	no	—
748	Q₈	—	52	8	no	—
749	D₄	—	2	16	no	—
750	D₄	—	4	4	no	—
751	D₄	—	26	16	no	—
752	D₄	—	52	8	no	—
753	D₄	—	52	16	no	—
754	D₄	—	52	16	no	—
755	C₂×C₄	—	2	4	no	—
756	C₂×C₄	—	2	2	no	—
757	C₂×C₄	—	2	8	no	—
758	C₂×C₄	—	2	2	no	—
759	C₂×C₄	—	2	2	no	—
760	C₂×C₄	—	2	4	no	—
761	C₂×C₄	—	2	2	no	—
762	C₂×C₄	—	2	2	no	—
763	C₂×C₄	—	2	4	no	—
764	C₂×C₄	—	2	8	no	—
765	C₂×C₄	—	2	16	no	—
766	C₂×C₄	—	4	4	no	—
767	C₂×C₄	—	13	8	no	—
768	C₂×C₄	—	13	8	no	—
769	C₂×C₄	—	13	8	no	—
770	C₂×C₄	—	26	8	no	—
771	C₂×C₄	—	26	8	no	—
772	C₂×C₄	—	26	8	no	—
773	C₂×C₄	—	52	16	no	—
774	C₂×C₄	—	52	16	no	—
775	C₂×C₄	—	52	16	no	—
776	C₂×C₄	—	52	8	no	—
777	C₂×C₄	#88256	1	4	yes	—
778	C₂×C₄	C₂⁴×D₁₃	1	2	yes	—
779	C₂×C₄	C₂⁴×D₁₃	1	4	yes	—
780	C₂×C₄	C₂⁴×D₁₃	1	2	yes	—
781	C₂×C₄	C₂⁴×D₁₃	1	2	yes	—
782	C₂×C₄	C₂⁴×D₁₃	1	2	yes	—
783	C₂×C₄	C₂⁴×D₁₃	1	2	yes	—
784	C₂×C₄	C₂⁴×D₁₃	1	4	yes	—
785	C₂×C₄	C₂⁴×D₁₃	1	4	yes	—
786	C₂×C₄	C₂⁴×D₁₃	1	2	yes	—
787	C₂²	—	2	2	no	—
788	C₂²	—	2	2	no	—
789	C₂²	—	2	8	no	—
790	C₂²	—	2	4	no	—
791	C₂²	—	2	4	no	—
792	C₂²	—	2	4	no	—
793	C₂²	—	4	8	no	—
794	C₂²	—	26	8	no	—
795	C₂²	—	26	8	no	—
796	C₂²	—	26	8	no	—
797	C₂²	—	52	16	no	—
798	C₂²	—	104	16	no	—
799	C₂²	C₂×#88256	1	2	yes	—
800	C₂²	C₂×#88257	1	4	yes	—
801	C₂²	C₂×#88257	1	2	yes	—
802	C₂²	#11719648	1	2	yes	—
803	C₂²	C₂⁵×D₁₃	1	1	yes	characteristic
804	C₄	—	2	4	no	—
805	C₄	—	2	2	no	—
806	C₄	—	2	2	no	—
807	C₄	—	2	2	no	—
808	C₄	—	2	4	no	—
809	C₄	—	2	2	no	—
810	C₄	—	2	2	no	—
811	C₄	—	2	4	no	—
812	C₄	—	26	8	no	—
813	C₄	—	26	8	no	—
814	C₄	—	26	8	no	—
815	C₄	C₂×#88256	1	4	yes	—
816	C₂	—	2	4	no	—
817	C₂	—	4	4	no	—
818	C₂	—	52	8	no	—
819	C₂	#13129406	1	4	yes	direct product factor
820	C₂	C₂²×#88256	1	1	yes	characteristic
821	C₂	C₂²×#88257	1	1	yes	characteristic
822	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×#3561
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. #13129406	C₂	direct (N × H)
2. C₂×#11719404	C₂	semidirect
3. C₂×#11719389	C₂	semidirect
4. C₂×#11719289	C₂	semidirect
5. C₂×#11719363	C₂	semidirect
6. C₂×D₄×Dic₂₆	C₂	semidirect
7. C₂×#11719257	C₂	semidirect
8. C₂×#11719255	C₂	semidirect
9. C₂×#11719339	C₂	semidirect
10. C₂×#11719239	C₂	semidirect
11. C₂×#11719415	C₂	semidirect
12. C₂×#11719322	C₂	semidirect
13. C₂×#11719231	C₂	semidirect
14. C₂×#11719175	C₂	semidirect
15. C₂²×#88129	C₂	semidirect
16. C₂×C₁₃×#529	C₂	semidirect
20. C₂³×Dic₂₆	C₂²	semidirect
21. C₁₃×#529	C₂²	semidirect
22. C₂×C₁₃×#126	C₂²	semidirect
23. C₂×C₁₃×#125	C₂²	semidirect
24. C₂×C₁₃×#124	C₂²	semidirect
28. C₂×C₄×Q₈×C₁₃	C₂²	semidirect
30. C₂×C₄×D₄×C₁₃	C₂²	semidirect
31. C₂×C₁₃×#117	C₂²	semidirect
33. C₂×#88200	C₂²	semidirect
34. C₂×#88193	C₂²	semidirect
43. C₂×#88178	C₂²	semidirect
44. #11719415	C₂²	semidirect
45. #11719404	C₂²	semidirect
46. #11719389	C₂²	semidirect
47. #11719363	C₂²	semidirect
48. #11719339	C₂²	semidirect
49. #11719322	C₂²	semidirect
50. #11719289	C₂²	semidirect
51. #11719257	C₂²	semidirect
52. #11719255	C₂²	semidirect
53. D₄×Dic₂₆	C₂²	semidirect
54. #11719239	C₂²	semidirect
55. #11719231	C₂²	semidirect
56. C₂×#88152	C₂²	semidirect
57. C₂×#88152	C₂²	semidirect
58. C₂×#88152	C₂²	semidirect
59. C₂×#88151	C₂²	semidirect
60. C₂×#88151	C₂²	semidirect
61. C₂×#88150	C₂²	semidirect
62. C₂×#88150	C₂²	semidirect
64. C₂×#88146	C₂²	semidirect
65. C₂×#88142	C₂²	semidirect
66. C₂×#88140	C₂²	semidirect
67. C₂×#88140	C₂²	semidirect
68. C₂×#88139	C₂²	semidirect
69. C₂×#88139	C₂²	semidirect
71. C₂×#88137	C₂²	semidirect
72. C₂×#88135	C₂²	semidirect
75. C₂×#88132	C₂²	semidirect
81. C₂×#88129	C₂²	semidirect
83. #11719175	C₂²	semidirect
84. C₂×#88124	C₂²	semidirect
85. C₂×#88123	C₂²	semidirect
86. C₂×#88123	C₂²	semidirect
87. C₂×#88123	C₂²	semidirect
88. C₂×C₄×Dic₂₆	C₂²	semidirect
89. C₂×C₄×Dic₂₆	C₂²	semidirect
90. C₂×C₄×Dic₂₆	C₂²	semidirect
119. C₂²×Dic₂₆	C₂³	semidirect
120. C₁₃×#126	C₂³	semidirect
121. C₁₃×#125	C₂³	semidirect
122. C₁₃×#124	C₂³	semidirect
126. C₄×Q₈×C₁₃	C₂³	semidirect
128. C₄×D₄×C₁₃	C₂³	semidirect
129. C₁₃×#117	C₂³	semidirect
149. #88200	C₂³	semidirect
150. #88193	C₂³	semidirect
173. #88178	C₂³	semidirect
180. #88152	C₂³	semidirect
181. #88152	C₂³	semidirect
182. #88152	C₂³	semidirect
183. #88151	C₂³	semidirect
184. #88151	C₂³	semidirect
185. #88150	C₂³	semidirect
186. #88150	C₂³	semidirect
188. #88146	C₂³	semidirect
189. #88142	C₂³	semidirect
190. #88140	C₂³	semidirect
191. #88140	C₂³	semidirect
192. #88139	C₂³	semidirect
193. #88139	C₂³	semidirect
195. #88137	C₂³	semidirect
196. #88135	C₂³	semidirect
199. #88132	C₂³	semidirect
206. #88124	C₂³	semidirect
207. #88123	C₂³	semidirect
208. #88123	C₂³	semidirect
209. #88123	C₂³	semidirect
210. C₄×Dic₂₆	C₂³	semidirect
211. C₄×Dic₂₆	C₂³	semidirect
212. C₄×Dic₂₆	C₂³	semidirect
329. C₂×#529	D₁₃	semidirect
413. #529	C₂×D₁₃	semidirect
417. C₂×#126	C₂×D₁₃	semidirect
419. C₂×#125	C₂×D₁₃	semidirect
428. C₂×#124	C₂×D₁₃	semidirect
453. C₂×C₄×Q₈	C₂×D₁₃	semidirect
458. C₂×C₄×D₄	C₂×D₁₃	semidirect
461. C₂×#117	C₂×D₁₃	semidirect
531. #126	C₂²×D₁₃	semidirect
533. #125	C₂²×D₁₃	semidirect
541. #124	C₂²×D₁₃	semidirect
566. C₄×Q₈	C₂²×D₁₃	semidirect
571. C₄×D₄	C₂²×D₁₃	semidirect
574. #117	C₂²×D₁₃	semidirect
619. C₂×C₁₃	#3561	semidirect
725. C₁₃	C₂×#3561	semidirect
819. C₂	#13129406	direct (N × H)

Maximal subgroups

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

subgroup	index
#13129406	2
C₂×#11719404	2
C₂×#11719389	2
C₂×#11719289	2
C₂×#11719363	2
C₂×D₄×Dic₂₆	2
C₂×#11719257	2
C₂×#11719255	2
C₂×#11719339	2
C₂×#11719239	2
C₂×#11719415	2
C₂×#11719322	2
C₂×#11719231	2
C₂×#11719175	2
C₂²×#88129	2
C₂×C₁₃×#529	2
C₂×#3561	13

Subgroups — C2×#13129406 #16770272

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13129406 #16770272