Subgroups — C₂×#13129113 #16770212

Order 3328.

7418 conjugacy classes of subgroups.

The subgroup lattice has 860 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13129113	C₂	1	32	yes	maximal, direct product factor
2	C₂×#11719388	C₂	1	2	yes	maximal, complemented
3	C₂×#11719371	C₂	1	2	yes	maximal, complemented
4	C₂×#11719369	C₂	1	2	yes	maximal, complemented
5	C₂×#11719346	C₂	1	2	yes	maximal, complemented
6	C₂×#11719237	C₂	1	2	yes	maximal, complemented
7	C₂×#11719384	C₂	1	2	yes	maximal, complemented
8	C₂×#11719522	C₂	1	2	yes	maximal, complemented
9	C₂×#11719335	C₂	1	2	yes	maximal, complemented
10	C₂×#11719438	C₂	1	4	yes	maximal, complemented
11	C₂×#11719348	C₂	1	2	yes	maximal, complemented
12	C₂×#11719362	C₂	1	4	yes	maximal, complemented
13	C₂×#11719535	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#11719332	C₂	1	2	yes	maximal, complemented
15	C₂×#11719533	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₁₃×#536	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic
18	C₂³×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
19	C₂²×#6131	C₂²	1	2	yes	—
20	C₂³×D₅₂	C₂²	1	1	yes	characteristic, complemented
21	C₂³×C₄×D₁₃	C₂²	1	1	yes	characteristic, complemented
22	C₁₃×#536	C₂²	1	16	yes	complemented
23	C₂×C₁₃×C₄⋊Q₈	C₂²	1	2	yes	complemented
24	C₂×C₁₃×#124	C₂²	1	2	yes	—
25	C₂×C₁₃×#123	C₂²	1	2	yes	complemented
26	C₂×C₁₃×#123	C₂²	1	2	yes	complemented
27	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
28	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
29	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic, complemented
30	#11719535	C₂²	1	16	yes	complemented
31	#11719533	C₂²	1	16	yes	complemented
32	#11719522	C₂²	1	32	yes	complemented
33	C₂×#88201	C₂²	1	2	yes	complemented
34	C₂×#88201	C₂²	1	2	yes	complemented
35	C₂×#88201	C₂²	1	4	yes	complemented
36	C₂×#88200	C₂²	1	2	yes	complemented
37	C₂×#88200	C₂²	1	4	yes	complemented
38	C₂×#88200	C₂²	1	2	yes	complemented
39	C₂×Q₈×Dic₁₃	C₂²	1	2	yes	complemented
40	C₂×#88194	C₂²	1	2	yes	—
41	C₂×#88192	C₂²	1	2	yes	—
42	C₂×#88191	C₂²	1	1	yes	characteristic
43	C₂×#88191	C₂²	1	2	yes	—
44	C₂×#88191	C₂²	1	1	yes	characteristic, complemented
45	C₂×#88191	C₂²	1	2	yes	complemented
46	C₂×#88189	C₂²	1	1	yes	characteristic
47	C₂×#88189	C₂²	1	1	yes	characteristic, complemented
48	C₂×#88184	C₂²	1	2	yes	—
49	C₂×#88184	C₂²	1	2	yes	complemented
50	C₂×#88184	C₂²	1	4	yes	complemented
51	C₂×C₄×C₂²⋊D₁₃	C₂²	1	2	yes	—
52	C₂×C₄×C₂²⋊D₁₃	C₂²	1	2	yes	complemented
53	C₂×C₄×C₂²⋊D₁₃	C₂²	1	4	yes	complemented
54	C₂×#88180	C₂²	1	1	yes	characteristic, complemented
55	C₂×#88180	C₂²	1	1	yes	characteristic, complemented
56	#11719438	C₂²	1	64	yes	complemented
57	#11719388	C₂²	1	32	yes	complemented
58	#11719384	C₂²	1	32	yes	complemented
59	#11719371	C₂²	1	32	yes	complemented
60	#11719369	C₂²	1	32	yes	complemented
61	#11719362	C₂²	1	64	yes	complemented
62	#11719348	C₂²	1	32	yes	complemented
63	#11719346	C₂²	1	32	yes	complemented
64	#11719335	C₂²	1	32	yes	complemented
65	#11719332	C₂²	1	32	yes	complemented
66	#11719237	C₂²	1	32	yes	complemented
67	C₂×#88152	C₂²	1	4	yes	complemented
68	C₂×#88152	C₂²	1	4	yes	complemented
69	C₂×#88151	C₂²	1	4	yes	complemented
70	C₂×#88149	C₂²	1	4	yes	—
71	C₂×#88149	C₂²	1	2	yes	—
72	C₂×#88148	C₂²	1	4	yes	complemented
73	C₂×#88148	C₂²	1	4	yes	complemented
74	C₂×#88147	C₂²	1	2	yes	complemented
75	C₂×#88147	C₂²	1	4	yes	complemented
76	C₂×#88146	C₂²	1	2	yes	complemented
77	C₂×#88142	C₂²	1	2	yes	complemented
78	C₂×#88141	C₂²	1	4	yes	complemented
79	C₂×#88139	C₂²	1	4	yes	—
80	C₂×#88139	C₂²	1	4	yes	complemented
81	C₂×#88139	C₂²	1	4	yes	complemented
82	C₂×#88138	C₂²	1	4	yes	complemented
83	C₂×#88137	C₂²	1	4	yes	complemented
84	C₂×#88136	C₂²	1	4	yes	—
85	C₂×#88136	C₂²	1	4	yes	complemented
86	C₂×#88135	C₂²	1	4	yes	complemented
87	C₂×C₂²⋊C₄×D₁₃	C₂²	1	4	yes	complemented
88	C₂×#88133	C₂²	1	4	yes	complemented
89	C₂×#88129	C₂²	1	4	yes	complemented
90	C₂×#88126	C₂²	1	4	yes	complemented
91	C₂⁴×D₁₃	C₂³	1	2	yes	—
92	C₂⁴×D₁₃	C₂³	1	1	yes	characteristic
93	C₂×C₁₃×#41	—	4	4	no	—
94	C₂×C₁₃×#41	C₂³	1	8	yes	—
95	C₂²×Q₈×C₁₃	—	4	4	no	—
96	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
97	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
98	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
99	C₂²×Q₈×C₁₃	C₂³	1	8	yes	complemented
100	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
101	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
102	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
103	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
104	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
105	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
106	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
107	C₂²×C₂²⋊D₁₃	C₂³	1	4	yes	—
108	C₂²×C₂²⋊D₁₃	C₂³	1	2	yes	—
109	C₂²×C₂²⋊D₁₃	C₂³	1	2	yes	—
110	C₂²×C₂²⋊D₁₃	C₂³	1	4	yes	—
111	C₂³×Dic₁₃	C₂³	1	1	yes	characteristic
112	C₂×#6131	—	4	8	no	—
113	C₂×#6131	C₂³	1	16	yes	—
114	C₂²×D₅₂	—	4	4	no	—
115	C₂²×D₅₂	C₂³	1	2	yes	—
116	C₂²×D₅₂	C₂³	1	4	yes	—
117	C₂²×D₅₂	C₂³	1	4	yes	—
118	C₂²×D₅₂	C₂³	1	2	yes	—
119	C₂²×D₅₂	C₂³	1	8	yes	complemented
120	C₂²×C₄×D₁₃	—	4	4	no	—
121	C₂²×C₄×D₁₃	C₂³	1	2	yes	—
122	C₂²×C₄×D₁₃	C₂³	1	4	yes	—
123	C₂²×C₄×D₁₃	C₂³	1	4	yes	—
124	C₂²×C₄×D₁₃	C₂³	1	2	yes	—
125	C₂²×C₄×D₁₃	C₂³	1	8	yes	complemented
126	C₂²×Dic₂₆	C₂³	1	4	yes	—
127	C₁₃×C₄⋊Q₈	C₂³	1	16	yes	complemented
128	C₁₃×#124	C₂³	1	16	yes	—
129	C₁₃×#123	C₂³	1	16	yes	complemented
130	C₁₃×#123	C₂³	1	16	yes	complemented
131	C₁₃×C₂²⋊Q₈	C₂³	1	16	yes	complemented
132	C₁₃×C₂²⋊Q₈	C₂³	1	16	yes	complemented
133	C₁₃×#117	C₂³	1	8	yes	complemented
134	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
135	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
136	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
137	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
138	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
139	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
140	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
141	C₂×C₂²⋊Dic₁₃	C₂³	1	2	yes	—
142	C₂×C₂²⋊Dic₁₃	C₂³	1	2	yes	—
143	C₂×C₂²⋊Dic₁₃	C₂³	1	1	yes	characteristic
144	C₂×C₂²⋊Dic₁₃	C₂³	1	1	yes	characteristic
145	C₂×C₂²⋊Dic₁₃	C₂³	1	2	yes	—
146	#88201	C₂³	1	16	yes	complemented
147	#88201	C₂³	1	32	yes	complemented
148	#88201	C₂³	1	16	yes	complemented
149	#88200	C₂³	1	16	yes	complemented
150	#88200	C₂³	1	32	yes	complemented
151	#88200	C₂³	1	16	yes	complemented
152	Q₈×Dic₁₃	C₂³	1	16	yes	complemented
153	#88194	C₂³	1	16	yes	—
154	#88192	C₂³	1	16	yes	—
155	#88191	C₂³	1	8	yes	—
156	#88191	C₂³	1	16	yes	—
157	#88191	C₂³	1	8	yes	complemented
158	#88191	C₂³	1	16	yes	complemented
159	#88189	C₂³	1	8	yes	—
160	#88189	C₂³	1	8	yes	complemented
161	#88184	C₂³	1	16	yes	—
162	#88184	C₂³	1	16	yes	complemented
163	#88184	C₂³	1	32	yes	complemented
164	C₄×C₂²⋊D₁₃	C₂³	1	16	yes	—
165	C₄×C₂²⋊D₁₃	C₂³	1	16	yes	complemented
166	C₄×C₂²⋊D₁₃	C₂³	1	32	yes	complemented
167	C₂×#6103	C₂³	1	4	yes	—
168	C₂×#6103	C₂³	1	4	yes	—
169	C₂×#6103	C₂³	1	2	yes	—
170	C₂×#6103	C₂³	1	4	yes	—
171	C₂×#6103	C₂³	1	4	yes	—
172	C₂×#6103	C₂³	1	4	yes	—
173	C₂×#6103	C₂³	1	4	yes	—
174	C₂×#6103	C₂³	1	4	yes	—
175	C₂×#6103	C₂³	1	4	yes	—
176	C₂×#6103	C₂³	1	2	yes	—
177	#88180	C₂³	1	8	yes	complemented
178	#88180	C₂³	1	8	yes	complemented
179	C₂×C₄⋊Dic₁₃	C₂³	1	4	yes	—
180	C₂×C₄⋊Dic₁₃	C₂³	1	2	yes	—
181	C₂×C₄⋊Dic₁₃	C₂³	1	2	yes	—
182	C₂×#6101	C₂³	1	2	yes	—
183	C₂×#6101	C₂³	1	4	yes	—
184	C₂×#6101	C₂³	1	4	yes	—
185	C₂×#6101	C₂³	1	2	yes	—
186	C₂×C₄×Dic₁₃	C₂³	1	4	yes	—
187	C₂×C₄×Dic₁₃	C₂³	1	4	yes	—
188	C₂×C₄×Dic₁₃	C₂³	1	2	yes	—
189	C₂×C₄×Dic₁₃	C₂³	1	2	yes	—
190	#88152	C₂³	1	32	yes	complemented
191	#88152	C₂³	1	32	yes	complemented
192	#88151	C₂³	1	32	yes	complemented
193	#88149	C₂³	1	32	yes	—
194	#88149	C₂³	1	16	yes	—
195	#88148	C₂³	1	32	yes	complemented
196	#88148	C₂³	1	32	yes	complemented
197	#88147	C₂³	1	32	yes	complemented
198	#88147	C₂³	1	16	yes	complemented
199	#88146	C₂³	1	16	yes	complemented
200	#88142	C₂³	1	16	yes	complemented
201	#88141	C₂³	1	32	yes	complemented
202	#88139	C₂³	1	32	yes	—
203	#88139	C₂³	1	32	yes	complemented
204	#88139	C₂³	1	32	yes	complemented
205	#88138	C₂³	1	32	yes	complemented
206	#88137	C₂³	1	32	yes	complemented
207	#88136	C₂³	1	32	yes	—
208	#88136	C₂³	1	32	yes	complemented
209	#88135	C₂³	1	32	yes	complemented
210	C₂²⋊C₄×D₁₃	C₂³	1	32	yes	complemented
211	#88133	C₂³	1	32	yes	complemented
212	#88129	C₂³	1	32	yes	complemented
213	#88126	C₂³	1	32	yes	complemented
214	C₂×#3540	—	13	1	no	maximal, Sylow
215	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
216	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
217	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
218	C₂³×D₁₃	—	4	2	no	—
219	C₂³×D₁₃	—	4	4	no	—
220	C₂³×D₁₃	—	4	4	no	—
221	C₂³×D₁₃	—	4	8	no	—
222	C₂³×D₁₃	C₂⁴	1	2	yes	—
223	C₂³×D₁₃	C₂⁴	1	4	yes	—
224	C₂³×D₁₃	C₂⁴	1	8	yes	—
225	C₂³×D₁₃	C₂⁴	1	4	yes	—
226	C₁₃×#41	—	4	16	no	—
227	C₂×Q₈×C₁₃	—	2	8	no	—
228	C₂×Q₈×C₁₃	—	4	4	no	—
229	C₂×Q₈×C₁₃	—	4	2	no	—
230	C₂×Q₈×C₁₃	—	4	16	no	—
231	C₂×Q₈×C₁₃	C₂⁴	1	8	yes	—
232	C₂×Q₈×C₁₃	C₂⁴	1	8	yes	—
233	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
234	C₂×D₄×C₁₃	—	4	2	no	—
235	C₂×D₄×C₁₃	—	4	2	no	—
236	C₂×D₄×C₁₃	—	4	2	no	—
237	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
238	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
239	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
240	C₂²×C₄×C₁₃	—	2	4	no	—
241	C₂²×C₄×C₁₃	—	2	4	no	—
242	C₂²×C₄×C₁₃	—	2	4	no	—
243	C₂²×C₄×C₁₃	—	4	4	no	—
244	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
245	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
246	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
247	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
248	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
249	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
250	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
251	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
252	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
253	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
254	C₂×C₂²⋊D₁₃	—	4	4	no	—
255	C₂×C₂²⋊D₁₃	—	4	8	no	—
256	C₂×C₂²⋊D₁₃	—	4	8	no	—
257	C₂×C₂²⋊D₁₃	—	4	4	no	—
258	C₂×C₂²⋊D₁₃	C₂⁴	1	16	yes	—
259	C₂×C₂²⋊D₁₃	C₂⁴	1	8	yes	—
260	C₂×C₂²⋊D₁₃	C₂⁴	1	8	yes	—
261	C₂×C₂²⋊D₁₃	C₂⁴	1	16	yes	—
262	C₂²×Dic₁₃	—	4	2	no	—
263	C₂²×Dic₁₃	C₂⁴	1	4	yes	—
264	C₂²×Dic₁₃	C₂⁴	1	2	yes	—
265	C₂²×Dic₁₃	C₂⁴	1	2	yes	—
266	C₂²×Dic₁₃	C₂⁴	1	2	yes	—
267	C₂²×Dic₁₃	C₂⁴	1	4	yes	—
268	#6131	—	4	32	no	—
269	C₂×D₅₂	—	2	8	no	—
270	C₂×D₅₂	—	4	16	no	—
271	C₂×D₅₂	—	4	4	no	—
272	C₂×D₅₂	—	4	8	no	—
273	C₂×D₅₂	—	4	8	no	—
274	C₂×D₅₂	C₂⁴	1	8	yes	—
275	C₂×D₅₂	C₂⁴	1	16	yes	—
276	C₂×D₅₂	C₂⁴	1	16	yes	—
277	C₂×D₅₂	C₂⁴	1	8	yes	—
278	C₂×C₄×D₁₃	—	2	8	no	—
279	C₂×C₄×D₁₃	—	4	16	no	—
280	C₂×C₄×D₁₃	—	4	4	no	—
281	C₂×C₄×D₁₃	—	4	8	no	—
282	C₂×C₄×D₁₃	—	4	8	no	—
283	C₂×C₄×D₁₃	C₂⁴	1	8	yes	—
284	C₂×C₄×D₁₃	C₂⁴	1	16	yes	—
285	C₂×C₄×D₁₃	C₂⁴	1	16	yes	—
286	C₂×C₄×D₁₃	C₂⁴	1	8	yes	—
287	C₂×Dic₂₆	—	4	8	no	—
288	C₂×Dic₂₆	C₂⁴	1	16	yes	—
289	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
290	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
291	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
292	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
293	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
294	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
295	C₄²×C₁₃	C₂⁴	1	8	yes	—
296	C₂²⋊Dic₁₃	C₂⁴	1	8	yes	—
297	C₂²⋊Dic₁₃	C₂⁴	1	8	yes	—
298	C₂²⋊Dic₁₃	C₂⁴	1	4	yes	—
299	C₂²⋊Dic₁₃	C₂⁴	1	4	yes	—
300	C₂²⋊Dic₁₃	C₂⁴	1	8	yes	—
301	#6103	C₂⁴	1	16	yes	—
302	#6103	C₂⁴	1	16	yes	—
303	#6103	C₂⁴	1	8	yes	—
304	#6103	C₂⁴	1	16	yes	—
305	#6103	C₂⁴	1	16	yes	—
306	#6103	C₂⁴	1	16	yes	—
307	#6103	C₂⁴	1	16	yes	—
308	#6103	C₂⁴	1	16	yes	—
309	#6103	C₂⁴	1	16	yes	—
310	#6103	C₂⁴	1	8	yes	—
311	C₄⋊Dic₁₃	C₂⁴	1	16	yes	—
312	C₄⋊Dic₁₃	C₂⁴	1	8	yes	—
313	C₄⋊Dic₁₃	C₂⁴	1	8	yes	—
314	#6101	C₂⁴	1	8	yes	—
315	#6101	C₂⁴	1	16	yes	—
316	#6101	C₂⁴	1	16	yes	—
317	#6101	C₂⁴	1	8	yes	—
318	C₄×Dic₁₃	C₂⁴	1	16	yes	—
319	C₄×Dic₁₃	C₂⁴	1	16	yes	—
320	C₄×Dic₁₃	C₂⁴	1	8	yes	—
321	C₄×Dic₁₃	C₂⁴	1	8	yes	—
322	#3540	—	13	32	no	—
323	C₂×H(3,𝔽₄)	—	13	2	no	—
324	C₂×#560	—	13	2	no	—
325	C₂×#559	—	13	2	no	—
326	C₂×#556	—	13	2	no	—
327	C₂×#555	—	13	2	no	—
328	C₂×#551	—	13	2	no	—
329	C₂×#548	—	13	2	no	—
330	C₂×#546	—	13	2	no	—
331	C₂×#542	—	13	4	no	—
332	C₂×#542	—	13	2	no	—
333	C₂×#538	—	13	4	no	—
334	C₂×#536	D₁₃	1	1	yes	characteristic, complemented
335	C₂×#535	—	13	1	no	—
336	C₂×#525	—	13	1	no	—
337	C₂×#525	—	13	2	no	—
338	C₂³×C₁₃	—	2	2	no	—
339	C₂³×C₁₃	—	2	2	no	—
340	C₂³×C₁₃	—	2	2	no	—
341	C₂³×C₁₃	—	2	4	no	—
342	C₂³×C₁₃	—	2	4	no	—
343	C₂³×C₁₃	—	2	4	no	—
344	C₂³×C₁₃	C₂⁵	1	2	yes	—
345	C₂³×C₁₃	C₂⁵	1	2	yes	—
346	C₂³×C₁₃	C₂⁵	1	2	yes	—
347	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
348	C₂²×D₁₃	—	2	4	no	—
349	C₂²×D₁₃	—	2	8	no	—
350	C₂²×D₁₃	—	2	8	no	—
351	C₂²×D₁₃	—	2	4	no	—
352	C₂²×D₁₃	—	2	8	no	—
353	C₂²×D₁₃	—	2	4	no	—
354	C₂²×D₁₃	—	4	4	no	—
355	C₂²×D₁₃	—	4	8	no	—
356	C₂²×D₁₃	—	4	8	no	—
357	C₂²×D₁₃	—	4	16	no	—
358	C₂²×D₁₃	—	4	16	no	—
359	C₂²×D₁₃	—	8	16	no	—
360	C₂²×D₁₃	C₂⁵	1	4	yes	—
361	C₂²×D₁₃	C₂⁵	1	8	yes	—
362	Q₈×C₁₃	—	2	16	no	—
363	Q₈×C₁₃	—	4	8	no	—
364	Q₈×C₁₃	—	4	4	no	—
365	D₄×C₁₃	—	4	4	no	—
366	D₄×C₁₃	—	4	4	no	—
367	D₄×C₁₃	—	4	4	no	—
368	C₂×C₄×C₁₃	—	2	2	no	—
369	C₂×C₄×C₁₃	—	2	8	no	—
370	C₂×C₄×C₁₃	—	2	2	no	—
371	C₂×C₄×C₁₃	—	2	2	no	—
372	C₂×C₄×C₁₃	—	2	8	no	—
373	C₂×C₄×C₁₃	—	2	8	no	—
374	C₂×C₄×C₁₃	—	2	8	no	—
375	C₂×C₄×C₁₃	—	2	8	no	—
376	C₂×C₄×C₁₃	—	4	8	no	—
377	C₂×C₄×C₁₃	H(5,𝔽₂)	1	4	yes	—
378	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
379	C₂×C₄×C₁₃	C₂⁵	1	8	yes	—
380	C₂×C₄×C₁₃	C₂⁵	1	8	yes	—
381	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
382	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
383	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
384	C₂²⋊D₁₃	—	4	8	no	—
385	C₂²⋊D₁₃	—	4	16	no	—
386	C₂²⋊D₁₃	—	4	16	no	—
387	C₂²⋊D₁₃	—	4	8	no	—
388	C₂×Dic₁₃	—	2	4	no	—
389	C₂×Dic₁₃	—	2	4	no	—
390	C₂×Dic₁₃	—	2	8	no	—
391	C₂×Dic₁₃	—	2	4	no	—
392	C₂×Dic₁₃	—	4	4	no	—
393	C₂×Dic₁₃	C₂⁵	1	8	yes	—
394	C₂×Dic₁₃	C₂⁵	1	4	yes	—
395	C₂×Dic₁₃	C₂⁵	1	4	yes	—
396	C₂×Dic₁₃	C₂⁵	1	4	yes	—
397	D₅₂	—	2	16	no	—
398	D₅₂	—	4	8	no	—
399	D₅₂	—	4	16	no	—
400	D₅₂	—	4	16	no	—
401	C₄×D₁₃	—	2	16	no	—
402	C₄×D₁₃	—	4	8	no	—
403	C₄×D₁₃	—	4	16	no	—
404	C₄×D₁₃	—	4	16	no	—
405	Dic₂₆	—	4	16	no	—
406	C₂²×#41	—	13	2	no	—
407	C₂²×#41	C₂×D₁₃	1	1	yes	characteristic
408	C₂³×Q₈	C₂×D₁₃	1	1	yes	characteristic, complemented
409	C₂³×D₄	—	13	1	no	—
410	C₂⁴×C₄	—	13	1	no	—
411	H(3,𝔽₄)	—	13	32	no	—
412	#560	—	13	32	no	—
413	#559	—	13	32	no	—
414	#556	—	13	32	no	—
415	#555	—	13	32	no	—
416	#551	—	13	32	no	—
417	#548	—	13	32	no	—
418	#546	—	13	32	no	—
419	#542	—	13	64	no	—
420	#542	—	13	32	no	—
421	#538	—	13	64	no	—
422	#536	C₂×D₁₃	1	16	yes	complemented
423	#535	—	13	16	no	—
424	C₂×C₄⋊Q₈	—	13	2	no	—
425	C₂×C₄⋊Q₈	C₂×D₁₃	1	2	yes	complemented
426	C₂×#127	—	13	2	no	—
427	C₂×#126	—	13	4	no	—
428	C₂×#126	—	13	4	no	—
429	C₂×#126	—	13	4	no	—
430	C₂×#124	—	13	2	no	—
431	C₂×#124	—	13	2	no	—
432	C₂×#124	—	13	4	no	—
433	C₂×#124	—	13	4	no	—
434	C₂×#124	—	13	4	no	—
435	C₂×#124	—	13	4	no	—
436	C₂×#124	—	13	4	no	—
437	C₂×#124	C₂×D₁₃	1	2	yes	—
438	#525	—	13	16	no	—
439	#525	—	13	32	no	—
440	C₂×#123	—	13	1	no	—
441	C₂×#123	—	13	1	no	—
442	C₂×#123	—	13	4	no	—
443	C₂×#123	—	13	4	no	—
444	C₂×#123	—	13	4	no	—
445	C₂×#123	C₂×D₁₃	1	2	yes	complemented
446	C₂×#123	C₂×D₁₃	1	2	yes	complemented
447	C₂×C₂²⋊Q₈	—	13	2	no	—
448	C₂×C₂²⋊Q₈	—	13	2	no	—
449	C₂×C₂²⋊Q₈	—	13	4	no	—
450	C₂×C₂²⋊Q₈	—	13	4	no	—
451	C₂×C₂²⋊Q₈	C₂×D₁₃	1	2	yes	complemented
452	C₂×C₂²⋊Q₈	C₂×D₁₃	1	2	yes	complemented
453	C₂×#121	—	13	2	no	—
454	C₂×#121	—	13	2	no	—
455	C₂×#121	—	13	2	no	—
456	C₂×#121	—	13	4	no	—
457	C₂×#121	—	13	2	no	—
458	C₂×#121	—	13	4	no	—
459	C₂×#121	—	13	4	no	—
460	C₂×#120	—	13	1	no	—
461	C₂×#120	—	13	2	no	—
462	C₂×#120	—	13	1	no	—
463	C₂×#120	—	13	2	no	—
464	C₂×#120	—	13	4	no	—
465	C₂×#120	—	13	4	no	—
466	C₂×C₄×Q₈	—	13	2	no	—
467	C₂×C₄×Q₈	—	13	4	no	—
468	C₂×C₄×D₄	—	13	2	no	—
469	C₂×C₄×D₄	—	13	2	no	—
470	C₂×C₄×D₄	—	13	4	no	—
471	C₂×C₄×D₄	—	13	4	no	—
472	C₂×C₄×D₄	—	13	2	no	—
473	C₂×C₄×D₄	—	13	4	no	—
474	C₂×#117	—	13	1	no	—
475	C₂×#117	—	13	1	no	—
476	C₂×#117	—	13	2	no	—
477	C₂×#117	—	13	4	no	—
478	C₂×#117	C₂×D₁₃	1	1	yes	characteristic, complemented
479	C₂²×C₂²⋊C₄	—	13	4	no	—
480	C₂²×C₁₃	—	2	2	no	—
481	C₂²×C₁₃	—	2	2	no	—
482	C₂²×C₁₃	—	2	2	no	—
483	C₂²×C₁₃	—	2	4	no	—
484	C₂²×C₁₃	—	2	4	no	—
485	C₂²×C₁₃	—	2	4	no	—
486	C₂²×C₁₃	—	4	4	no	—
487	C₂²×C₁₃	—	4	4	no	—
488	C₂²×C₁₃	—	4	4	no	—
489	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
490	C₂²×C₁₃	#585	1	4	yes	—
491	C₂²×C₁₃	C₂⁶	1	1	yes	characteristic
492	C₂×D₁₃	—	2	4	no	—
493	C₂×D₁₃	—	2	8	no	—
494	C₂×D₁₃	—	2	8	no	—
495	C₂×D₁₃	—	2	4	no	—
496	C₂×D₁₃	—	2	8	no	—
497	C₂×D₁₃	—	2	4	no	—
498	C₂×D₁₃	—	4	16	no	—
499	C₂×D₁₃	—	4	8	no	—
500	C₂×D₁₃	—	4	16	no	—
501	C₂×D₁₃	—	8	16	no	—
502	C₄×C₁₃	—	2	2	no	—
503	C₄×C₁₃	—	2	8	no	—
504	C₄×C₁₃	—	2	2	no	—
505	C₄×C₁₃	—	2	2	no	—
506	C₄×C₁₃	—	2	8	no	—
507	C₄×C₁₃	C₂×H(5,𝔽₂)	1	4	yes	—
508	Dic₁₃	—	2	4	no	—
509	Dic₁₃	—	2	4	no	—
510	Dic₁₃	—	2	8	no	—
511	Dic₁₃	—	2	4	no	—
512	C₂⁵	—	13	2	no	—
513	C₂⁵	—	13	1	no	—
514	C₂×#41	—	4	4	no	—
515	C₂×#41	—	13	16	no	—
516	C₂×#41	—	52	8	no	—
517	C₂×#41	C₂²×D₁₃	1	8	yes	—
518	C₂²×Q₈	—	4	4	no	—
519	C₂²×Q₈	—	13	4	no	—
520	C₂²×Q₈	C₂²×D₁₃	1	2	yes	—
521	C₂²×Q₈	C₂²×D₁₃	1	2	yes	—
522	C₂²×Q₈	C₂²×D₁₃	1	1	yes	characteristic
523	C₂²×Q₈	C₂²×D₁₃	1	8	yes	complemented
524	C₂²×D₄	—	13	2	no	—
525	C₂²×D₄	—	13	4	no	—
526	C₂²×D₄	—	13	2	no	—
527	C₂²×D₄	—	13	4	no	—
528	C₂²×D₄	—	13	2	no	—
529	C₂²×D₄	—	13	4	no	—
530	C₂²×D₄	—	13	4	no	—
531	C₂²×D₄	—	13	2	no	—
532	C₂²×D₄	—	13	8	no	—
533	C₂²×D₄	—	52	4	no	—
534	C₂²×D₄	C₂²×D₁₃	1	1	yes	characteristic
535	C₂²×D₄	C₂²×D₁₃	1	1	yes	characteristic
536	C₂²×D₄	C₂²×D₁₃	1	1	yes	characteristic
537	C₂³×C₄	—	13	1	no	—
538	C₂³×C₄	—	13	2	no	—
539	C₂³×C₄	—	13	4	no	—
540	C₂³×C₄	—	13	4	no	—
541	C₂³×C₄	—	13	2	no	—
542	C₂³×C₄	—	13	8	no	—
543	C₂³×C₄	—	52	4	no	—
544	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
545	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
546	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
547	C₂³×C₄	C₂²×D₁₃	1	2	yes	—
548	C₄⋊Q₈	—	13	16	no	—
549	C₄⋊Q₈	C₂²×D₁₃	1	16	yes	complemented
550	#127	—	13	16	no	—
551	#126	—	13	32	no	—
552	#126	—	13	32	no	—
553	#126	—	13	32	no	—
554	#124	—	13	16	no	—
555	#124	—	13	16	no	—
556	#124	—	13	32	no	—
557	#124	—	13	32	no	—
558	#124	—	13	32	no	—
559	#124	—	13	32	no	—
560	#124	—	13	32	no	—
561	#124	C₂²×D₁₃	1	16	yes	—
562	#123	—	13	8	no	—
563	#123	—	13	8	no	—
564	#123	—	13	32	no	—
565	#123	—	13	32	no	—
566	#123	—	13	32	no	—
567	#123	C₂²×D₁₃	1	16	yes	complemented
568	#123	C₂²×D₁₃	1	16	yes	complemented
569	C₂²⋊Q₈	—	13	16	no	—
570	C₂²⋊Q₈	—	13	16	no	—
571	C₂²⋊Q₈	—	13	32	no	—
572	C₂²⋊Q₈	—	13	32	no	—
573	C₂²⋊Q₈	C₂²×D₁₃	1	16	yes	complemented
574	C₂²⋊Q₈	C₂²×D₁₃	1	16	yes	complemented
575	#121	—	13	16	no	—
576	#121	—	13	16	no	—
577	#121	—	13	16	no	—
578	#121	—	13	32	no	—
579	#121	—	13	16	no	—
580	#121	—	13	32	no	—
581	#121	—	13	32	no	—
582	#120	—	13	8	no	—
583	#120	—	13	8	no	—
584	#120	—	13	16	no	—
585	#120	—	13	16	no	—
586	#120	—	13	32	no	—
587	#120	—	13	32	no	—
588	C₄×Q₈	—	13	16	no	—
589	C₄×Q₈	—	13	32	no	—
590	C₄×D₄	—	13	16	no	—
591	C₄×D₄	—	13	16	no	—
592	C₄×D₄	—	13	32	no	—
593	C₄×D₄	—	13	32	no	—
594	C₄×D₄	—	13	16	no	—
595	C₄×D₄	—	13	32	no	—
596	#117	—	13	8	no	—
597	#117	—	13	8	no	—
598	#117	—	13	16	no	—
599	#117	—	13	32	no	—
600	#117	C₂²×D₁₃	1	8	yes	complemented
601	C₂×C₄⋊C₄	—	13	2	no	—
602	C₂×C₄⋊C₄	—	13	2	no	—
603	C₂×C₄⋊C₄	—	13	2	no	—
604	C₂×C₄⋊C₄	—	13	4	no	—
605	C₂×C₄⋊C₄	—	13	4	no	—
606	C₂×C₄⋊C₄	—	13	2	no	—
607	C₂×C₄⋊C₄	—	13	4	no	—
608	C₂×C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
609	C₂×C₄⋊C₄	C₂²×D₁₃	1	4	yes	—
610	C₂×C₄⋊C₄	C₂²×D₁₃	1	4	yes	—
611	C₂×C₂²⋊C₄	—	13	2	no	—
612	C₂×C₂²⋊C₄	—	13	2	no	—
613	C₂×C₂²⋊C₄	—	13	1	no	—
614	C₂×C₂²⋊C₄	—	13	1	no	—
615	C₂×C₂²⋊C₄	—	13	2	no	—
616	C₂×C₂²⋊C₄	—	13	4	no	—
617	C₂×C₂²⋊C₄	—	13	4	no	—
618	C₂×C₂²⋊C₄	—	13	4	no	—
619	C₂×C₂²⋊C₄	—	13	4	no	—
620	C₂×C₂²⋊C₄	—	13	2	no	—
621	C₂×C₂²⋊C₄	—	13	4	no	—
622	C₂×C₂²⋊C₄	—	13	4	no	—
623	C₂×C₂²⋊C₄	—	13	4	no	—
624	C₂×C₂²⋊C₄	—	13	2	no	—
625	C₂×C₂²⋊C₄	—	13	4	no	—
626	C₂×C₂²⋊C₄	—	13	32	no	—
627	C₂×C₂²⋊C₄	C₂²×D₁₃	1	4	yes	—
628	C₂×C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
629	C₂×C₂²⋊C₄	C₂²×D₁₃	1	4	yes	—
630	C₂×C₄²	—	13	4	no	—
631	C₂×C₄²	—	13	2	no	—
632	C₂×C₄²	—	13	2	no	—
633	C₂×C₄²	—	13	4	no	—
634	C₂×C₄²	C₂²×D₁₃	1	2	yes	—
635	C₂×C₁₃	—	4	2	no	—
636	C₂×C₁₃	—	4	2	no	—
637	C₂×C₁₃	—	4	2	no	—
638	C₂×C₁₃	#3540	1	4	yes	complemented
639	C₂×C₁₃	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
640	C₂×C₁₃	C₂×#585	1	2	yes	—
641	D₁₃	—	4	4	no	—
642	D₁₃	—	4	8	no	—
643	C₂⁴	—	13	2	no	—
644	C₂⁴	—	13	4	no	—
645	C₂⁴	—	13	8	no	—
646	C₂⁴	—	13	4	no	—
647	C₂⁴	—	52	2	no	—
648	C₂⁴	—	52	4	no	—
649	C₂⁴	—	52	4	no	—
650	C₂⁴	—	52	8	no	—
651	C₂⁴	C₂³×D₁₃	1	1	yes	characteristic
652	C₂⁴	C₂³×D₁₃	1	1	yes	characteristic
653	C₂⁴	C₂³×D₁₃	1	1	yes	characteristic
654	#41	—	4	16	no	—
655	#41	—	52	32	no	—
656	C₂×Q₈	—	2	8	no	—
657	C₂×Q₈	—	4	4	no	—
658	C₂×Q₈	—	4	2	no	—
659	C₂×Q₈	—	4	16	no	—
660	C₂×Q₈	—	13	16	no	—
661	C₂×Q₈	—	52	8	no	—
662	C₂×Q₈	C₂³×D₁₃	1	8	yes	—
663	C₂×Q₈	C₂³×D₁₃	1	8	yes	—
664	C₂×Q₈	C₂³×D₁₃	1	4	yes	—
665	C₂×D₄	—	4	2	no	—
666	C₂×D₄	—	4	2	no	—
667	C₂×D₄	—	4	2	no	—
668	C₂×D₄	—	13	8	no	—
669	C₂×D₄	—	13	16	no	—
670	C₂×D₄	—	13	8	no	—
671	C₂×D₄	—	13	16	no	—
672	C₂×D₄	—	13	8	no	—
673	C₂×D₄	—	13	16	no	—
674	C₂×D₄	—	13	16	no	—
675	C₂×D₄	—	13	8	no	—
676	C₂×D₄	—	26	8	no	—
677	C₂×D₄	—	52	16	no	—
678	C₂×D₄	—	52	4	no	—
679	C₂×D₄	—	52	8	no	—
680	C₂×D₄	—	52	8	no	—
681	C₂×D₄	—	52	4	no	—
682	C₂×D₄	—	52	8	no	—
683	C₂×D₄	—	52	8	no	—
684	C₂×D₄	—	52	4	no	—
685	C₂×D₄	C₂³×D₁₃	1	4	yes	—
686	C₂×D₄	C₂³×D₁₃	1	4	yes	—
687	C₂×D₄	C₂³×D₁₃	1	4	yes	—
688	C₂²×C₄	—	2	4	no	—
689	C₂²×C₄	—	2	4	no	—
690	C₂²×C₄	—	2	4	no	—
691	C₂²×C₄	—	4	4	no	—
692	C₂²×C₄	—	13	2	no	—
693	C₂²×C₄	—	13	4	no	—
694	C₂²×C₄	—	13	2	no	—
695	C₂²×C₄	—	13	2	no	—
696	C₂²×C₄	—	13	4	no	—
697	C₂²×C₄	—	13	8	no	—
698	C₂²×C₄	—	13	16	no	—
699	C₂²×C₄	—	13	16	no	—
700	C₂²×C₄	—	13	8	no	—
701	C₂²×C₄	—	26	8	no	—
702	C₂²×C₄	—	52	16	no	—
703	C₂²×C₄	—	52	4	no	—
704	C₂²×C₄	—	52	8	no	—
705	C₂²×C₄	—	52	8	no	—
706	C₂²×C₄	—	52	2	no	—
707	C₂²×C₄	C₂³×D₁₃	1	4	yes	—
708	C₂²×C₄	C₂³×D₁₃	1	4	yes	—
709	C₂²×C₄	C₂³×D₁₃	1	4	yes	—
710	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
711	C₂²×C₄	C₂³×D₁₃	1	4	yes	—
712	C₂²×C₄	C₂³×D₁₃	1	4	yes	—
713	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
714	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
715	C₂²×C₄	C₂³×D₁₃	1	8	yes	—
716	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
717	C₄⋊C₄	—	13	8	no	—
718	C₄⋊C₄	—	13	8	no	—
719	C₄⋊C₄	—	13	8	no	—
720	C₄⋊C₄	—	13	16	no	—
721	C₄⋊C₄	—	13	16	no	—
722	C₄⋊C₄	—	13	8	no	—
723	C₄⋊C₄	—	13	16	no	—
724	C₄⋊C₄	C₂³×D₁₃	1	8	yes	—
725	C₄⋊C₄	C₂³×D₁₃	1	16	yes	—
726	C₄⋊C₄	C₂³×D₁₃	1	16	yes	—
727	C₂²⋊C₄	—	13	8	no	—
728	C₂²⋊C₄	—	13	8	no	—
729	C₂²⋊C₄	—	13	4	no	—
730	C₂²⋊C₄	—	13	4	no	—
731	C₂²⋊C₄	—	13	8	no	—
732	C₂²⋊C₄	—	13	16	no	—
733	C₂²⋊C₄	—	13	16	no	—
734	C₂²⋊C₄	—	13	16	no	—
735	C₂²⋊C₄	—	13	16	no	—
736	C₂²⋊C₄	—	13	8	no	—
737	C₂²⋊C₄	—	13	16	no	—
738	C₂²⋊C₄	—	13	16	no	—
739	C₂²⋊C₄	—	13	16	no	—
740	C₂²⋊C₄	—	13	8	no	—
741	C₂²⋊C₄	—	13	16	no	—
742	C₂²⋊C₄	C₂³×D₁₃	1	16	yes	—
743	C₂²⋊C₄	C₂³×D₁₃	1	8	yes	—
744	C₂²⋊C₄	C₂³×D₁₃	1	16	yes	—
745	C₄²	—	13	16	no	—
746	C₄²	—	13	8	no	—
747	C₄²	—	13	8	no	—
748	C₄²	—	13	16	no	—
749	C₄²	C₂³×D₁₃	1	8	yes	—
750	C₁₃	C₂×#3540	1	1	yes	characteristic, complemented, Sylow
751	C₂³	—	2	2	no	—
752	C₂³	—	2	2	no	—
753	C₂³	—	2	2	no	—
754	C₂³	—	2	4	no	—
755	C₂³	—	2	4	no	—
756	C₂³	—	2	4	no	—
757	C₂³	—	13	4	no	—
758	C₂³	—	13	8	no	—
759	C₂³	—	26	4	no	—
760	C₂³	—	26	8	no	—
761	C₂³	—	26	8	no	—
762	C₂³	—	26	4	no	—
763	C₂³	—	26	4	no	—
764	C₂³	—	26	8	no	—
765	C₂³	—	52	4	no	—
766	C₂³	—	52	8	no	—
767	C₂³	—	52	8	no	—
768	C₂³	—	52	16	no	—
769	C₂³	—	52	16	no	—
770	C₂³	—	104	16	no	—
771	C₂³	C₂⁴×D₁₃	1	2	yes	—
772	C₂³	C₂⁴×D₁₃	1	2	yes	—
773	C₂³	C₂⁴×D₁₃	1	2	yes	—
774	C₂³	C₂⁴×D₁₃	1	1	yes	characteristic
775	Q₈	—	2	16	no	—
776	Q₈	—	4	8	no	—
777	Q₈	—	4	4	no	—
778	Q₈	—	52	16	no	—
779	D₄	—	4	4	no	—
780	D₄	—	4	4	no	—
781	D₄	—	4	4	no	—
782	D₄	—	26	16	no	—
783	D₄	—	52	16	no	—
784	D₄	—	52	8	no	—
785	D₄	—	52	16	no	—
786	D₄	—	52	8	no	—
787	D₄	—	52	16	no	—
788	D₄	—	52	16	no	—
789	D₄	—	52	8	no	—
790	C₂×C₄	—	2	2	no	—
791	C₂×C₄	—	2	2	no	—
792	C₂×C₄	—	2	2	no	—
793	C₂×C₄	—	2	8	no	—
794	C₂×C₄	—	2	8	no	—
795	C₂×C₄	—	2	8	no	—
796	C₂×C₄	—	2	8	no	—
797	C₂×C₄	—	2	8	no	—
798	C₂×C₄	—	4	8	no	—
799	C₂×C₄	—	13	4	no	—
800	C₂×C₄	—	13	8	no	—
801	C₂×C₄	—	13	4	no	—
802	C₂×C₄	—	13	4	no	—
803	C₂×C₄	—	26	4	no	—
804	C₂×C₄	—	26	4	no	—
805	C₂×C₄	—	26	8	no	—
806	C₂×C₄	—	26	4	no	—
807	C₂×C₄	—	26	16	no	—
808	C₂×C₄	—	52	16	no	—
809	C₂×C₄	—	52	8	no	—
810	C₂×C₄	—	52	16	no	—
811	C₂×C₄	—	52	4	no	—
812	C₂×C₄	#88251	1	4	yes	—
813	C₂×C₄	C₂⁴×D₁₃	1	2	yes	—
814	C₂×C₄	C₂⁴×D₁₃	1	8	yes	—
815	C₂×C₄	C₂⁴×D₁₃	1	8	yes	—
816	C₂×C₄	C₂⁴×D₁₃	1	2	yes	—
817	C₂×C₄	C₂⁴×D₁₃	1	2	yes	—
818	C₂×C₄	C₂⁴×D₁₃	1	2	yes	—
819	C₂²	—	2	2	no	—
820	C₂²	—	2	2	no	—
821	C₂²	—	2	2	no	—
822	C₂²	—	2	4	no	—
823	C₂²	—	2	4	no	—
824	C₂²	—	2	4	no	—
825	C₂²	—	4	4	no	—
826	C₂²	—	4	4	no	—
827	C₂²	—	4	4	no	—
828	C₂²	—	26	4	no	—
829	C₂²	—	26	8	no	—
830	C₂²	—	26	8	no	—
831	C₂²	—	26	4	no	—
832	C₂²	—	26	4	no	—
833	C₂²	—	26	8	no	—
834	C₂²	—	52	16	no	—
835	C₂²	—	52	8	no	—
836	C₂²	—	52	16	no	—
837	C₂²	—	104	16	no	—
838	C₂²	C₂×#88251	1	2	yes	—
839	C₂²	#11719652	1	4	yes	—
840	C₂²	C₂⁵×D₁₃	1	1	yes	characteristic
841	C₄	—	2	2	no	—
842	C₄	—	2	2	no	—
843	C₄	—	2	2	no	—
844	C₄	—	2	8	no	—
845	C₄	—	2	8	no	—
846	C₄	—	26	4	no	—
847	C₄	—	26	4	no	—
848	C₄	—	26	8	no	—
849	C₄	—	26	4	no	—
850	C₄	C₂×#88251	1	4	yes	—
851	C₂	—	4	2	no	—
852	C₂	—	4	2	no	—
853	C₂	—	4	2	no	—
854	C₂	—	52	4	no	—
855	C₂	—	52	8	no	—
856	C₂	#13129113	1	4	yes	direct product factor
857	C₂	C₂²×#88251	1	1	yes	characteristic
858	C₂	C₂×#11719652	1	2	yes	—

	subgroup	G/H
center	C₂³	C₂⁴×D₁₃
commutator, cosocle	C₂²×C₁₃	C₂⁶
Frattini	C₂²	C₂⁵×D₁₃
Fitting	C₂×C₁₃×#536	C₂
socle	C₂³×C₁₃	C₂⁵
hypercenter	C₂×#536	D₁₃
hypocenter	C₁₃	C₂×#3540
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂³ ◁ C₂×#536

Complements

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

N	H ≅ G/N	type
1. #13129113	C₂	direct (N × H)
2. C₂×#11719388	C₂	semidirect
3. C₂×#11719371	C₂	semidirect
4. C₂×#11719369	C₂	semidirect
5. C₂×#11719346	C₂	semidirect
6. C₂×#11719237	C₂	semidirect
7. C₂×#11719384	C₂	semidirect
8. C₂×#11719522	C₂	semidirect
9. C₂×#11719335	C₂	semidirect
10. C₂×#11719438	C₂	semidirect
11. C₂×#11719348	C₂	semidirect
12. C₂×#11719362	C₂	semidirect
13. C₂×#11719535	C₂	semidirect
14. C₂×#11719332	C₂	semidirect
15. C₂×#11719533	C₂	semidirect
16. C₂×C₁₃×#536	C₂	semidirect
18. C₂³×Q₈×C₁₃	C₂²	semidirect
20. C₂³×D₅₂	C₂²	semidirect
21. C₂³×C₄×D₁₃	C₂²	semidirect
22. C₁₃×#536	C₂²	semidirect
23. C₂×C₁₃×C₄⋊Q₈	C₂²	semidirect
25. C₂×C₁₃×#123	C₂²	semidirect
26. C₂×C₁₃×#123	C₂²	semidirect
27. C₂×C₁₃×C₂²⋊Q₈	C₂²	semidirect
28. C₂×C₁₃×C₂²⋊Q₈	C₂²	semidirect
29. C₂×C₁₃×#117	C₂²	semidirect
30. #11719535	C₂²	semidirect
31. #11719533	C₂²	semidirect
32. #11719522	C₂²	semidirect
33. C₂×#88201	C₂²	semidirect
34. C₂×#88201	C₂²	semidirect
35. C₂×#88201	C₂²	semidirect
36. C₂×#88200	C₂²	semidirect
37. C₂×#88200	C₂²	semidirect
38. C₂×#88200	C₂²	semidirect
39. C₂×Q₈×Dic₁₃	C₂²	semidirect
44. C₂×#88191	C₂²	semidirect
45. C₂×#88191	C₂²	semidirect
47. C₂×#88189	C₂²	semidirect
49. C₂×#88184	C₂²	semidirect
50. C₂×#88184	C₂²	semidirect
52. C₂×C₄×C₂²⋊D₁₃	C₂²	semidirect
53. C₂×C₄×C₂²⋊D₁₃	C₂²	semidirect
54. C₂×#88180	C₂²	semidirect
55. C₂×#88180	C₂²	semidirect
56. #11719438	C₂²	semidirect
57. #11719388	C₂²	semidirect
58. #11719384	C₂²	semidirect
59. #11719371	C₂²	semidirect
60. #11719369	C₂²	semidirect
61. #11719362	C₂²	semidirect
62. #11719348	C₂²	semidirect
63. #11719346	C₂²	semidirect
64. #11719335	C₂²	semidirect
65. #11719332	C₂²	semidirect
66. #11719237	C₂²	semidirect
67. C₂×#88152	C₂²	semidirect
68. C₂×#88152	C₂²	semidirect
69. C₂×#88151	C₂²	semidirect
72. C₂×#88148	C₂²	semidirect
73. C₂×#88148	C₂²	semidirect
74. C₂×#88147	C₂²	semidirect
75. C₂×#88147	C₂²	semidirect
76. C₂×#88146	C₂²	semidirect
77. C₂×#88142	C₂²	semidirect
78. C₂×#88141	C₂²	semidirect
80. C₂×#88139	C₂²	semidirect
81. C₂×#88139	C₂²	semidirect
82. C₂×#88138	C₂²	semidirect
83. C₂×#88137	C₂²	semidirect
85. C₂×#88136	C₂²	semidirect
86. C₂×#88135	C₂²	semidirect
87. C₂×C₂²⋊C₄×D₁₃	C₂²	semidirect
88. C₂×#88133	C₂²	semidirect
89. C₂×#88129	C₂²	semidirect
90. C₂×#88126	C₂²	semidirect
99. C₂²×Q₈×C₁₃	C₂³	semidirect
119. C₂²×D₅₂	C₂³	semidirect
125. C₂²×C₄×D₁₃	C₂³	semidirect
127. C₁₃×C₄⋊Q₈	C₂³	semidirect
129. C₁₃×#123	C₂³	semidirect
130. C₁₃×#123	C₂³	semidirect
131. C₁₃×C₂²⋊Q₈	C₂³	semidirect
132. C₁₃×C₂²⋊Q₈	C₂³	semidirect
133. C₁₃×#117	C₂³	semidirect
146. #88201	C₂³	semidirect
147. #88201	C₂³	semidirect
148. #88201	C₂³	semidirect
149. #88200	C₂³	semidirect
150. #88200	C₂³	semidirect
151. #88200	C₂³	semidirect
152. Q₈×Dic₁₃	C₂³	semidirect
157. #88191	C₂³	semidirect
158. #88191	C₂³	semidirect
160. #88189	C₂³	semidirect
162. #88184	C₂³	semidirect
163. #88184	C₂³	semidirect
165. C₄×C₂²⋊D₁₃	C₂³	semidirect
166. C₄×C₂²⋊D₁₃	C₂³	semidirect
177. #88180	C₂³	semidirect
178. #88180	C₂³	semidirect
190. #88152	C₂³	semidirect
191. #88152	C₂³	semidirect
192. #88151	C₂³	semidirect
195. #88148	C₂³	semidirect
196. #88148	C₂³	semidirect
197. #88147	C₂³	semidirect
198. #88147	C₂³	semidirect
199. #88146	C₂³	semidirect
200. #88142	C₂³	semidirect
201. #88141	C₂³	semidirect
203. #88139	C₂³	semidirect
204. #88139	C₂³	semidirect
205. #88138	C₂³	semidirect
206. #88137	C₂³	semidirect
208. #88136	C₂³	semidirect
209. #88135	C₂³	semidirect
210. C₂²⋊C₄×D₁₃	C₂³	semidirect
211. #88133	C₂³	semidirect
212. #88129	C₂³	semidirect
213. #88126	C₂³	semidirect
334. C₂×#536	D₁₃	semidirect
408. C₂³×Q₈	C₂×D₁₃	semidirect
422. #536	C₂×D₁₃	semidirect
425. C₂×C₄⋊Q₈	C₂×D₁₃	semidirect
445. C₂×#123	C₂×D₁₃	semidirect
446. C₂×#123	C₂×D₁₃	semidirect
451. C₂×C₂²⋊Q₈	C₂×D₁₃	semidirect
452. C₂×C₂²⋊Q₈	C₂×D₁₃	semidirect
478. C₂×#117	C₂×D₁₃	semidirect
523. C₂²×Q₈	C₂²×D₁₃	semidirect
549. C₄⋊Q₈	C₂²×D₁₃	semidirect
567. #123	C₂²×D₁₃	semidirect
568. #123	C₂²×D₁₃	semidirect
573. C₂²⋊Q₈	C₂²×D₁₃	semidirect
574. C₂²⋊Q₈	C₂²×D₁₃	semidirect
600. #117	C₂²×D₁₃	semidirect
638. C₂×C₁₃	#3540	semidirect
750. C₁₃	C₂×#3540	semidirect
856. C₂	#13129113	direct (N × H)

Maximal subgroups

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

subgroup	index
#13129113	2
C₂×#11719388	2
C₂×#11719371	2
C₂×#11719369	2
C₂×#11719346	2
C₂×#11719237	2
C₂×#11719384	2
C₂×#11719522	2
C₂×#11719335	2
C₂×#11719438	2
C₂×#11719348	2
C₂×#11719362	2
C₂×#11719535	2
C₂×#11719332	2
C₂×#11719533	2
C₂×C₁₃×#536	2
C₂×#3540	13

Subgroups — C2×#13129113 #16770212

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13129113 #16770212