Subgroups — C₁₃×#62856 #15749195

Order 3328.

7086 conjugacy classes of subgroups.

The subgroup lattice has 784 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3512	C₂	1	8	yes	maximal, complemented
2	C₁₃×#3511	C₂	1	8	yes	maximal, complemented
3	C₁₃×#3505	C₂	1	8	yes	maximal, complemented
4	C₁₃×#3495	C₂	1	8	yes	maximal, complemented
5	C₁₃×#3494	C₂	1	8	yes	maximal, complemented
6	C₁₃×#3493	C₂	1	4	yes	maximal, complemented
7	C₁₃×#3492	C₂	1	4	yes	maximal, complemented
8	C₁₃×#3461	C₂	1	4	yes	maximal, complemented
9	C₁₃×#3460	C₂	1	4	yes	maximal, complemented
10	C₂×C₁₃×#544	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#3449	C₂	1	2	yes	maximal, complemented
12	C₂×C₁₃×#537	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#3428	C₂	1	2	yes	maximal, complemented
14	C₂×C₁₃×#520	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic
16	C₂²×C₁₃×#41	C₂²	1	2	yes	—
17	C₁₃×#556	C₂²	1	16	yes	complemented
18	C₁₃×#555	C₂²	1	16	yes	complemented
19	C₁₃×#554	C₂²	1	16	yes	complemented
20	C₁₃×#553	C₂²	1	16	yes	complemented
21	C₁₃×#553	C₂²	1	16	yes	complemented
22	C₁₃×#553	C₂²	1	32	yes	complemented
23	C₁₃×#553	C₂²	1	16	yes	complemented
24	C₁₃×#552	C₂²	1	16	yes	complemented
25	C₁₃×#552	C₂²	1	16	yes	complemented
26	C₁₃×#552	C₂²	1	16	yes	complemented
27	C₁₃×#551	C₂²	1	32	yes	complemented
28	C₁₃×#548	C₂²	1	16	yes	complemented
29	C₁₃×#547	C₂²	1	16	yes	complemented
30	C₁₃×#546	C₂²	1	16	yes	complemented
31	C₁₃×#544	C₂²	1	4	yes	complemented
32	C₁₃×#544	C₂²	1	4	yes	complemented
33	C₁₃×#544	C₂²	1	8	yes	complemented
34	C₁₃×#542	C₂²	1	16	yes	complemented
35	C₁₃×#542	C₂²	1	16	yes	complemented
36	C₁₃×#541	C₂²	1	16	yes	complemented
37	C₁₃×#540	C₂²	1	16	yes	complemented
38	C₁₃×#539	C₂²	1	16	yes	complemented
39	C₁₃×#538	C₂²	1	16	yes	complemented
40	C₁₃×#537	C₂²	1	4	yes	—
41	C₁₃×#537	C₂²	1	4	yes	—
42	C₁₃×#537	C₂²	1	8	yes	complemented
43	C₁₃×#537	C₂²	1	4	yes	complemented
44	C₁₃×#537	C₂²	1	4	yes	complemented
45	C₁₃×#536	C₂²	1	4	yes	—
46	C₁₃×#536	C₂²	1	4	yes	complemented
47	C₁₃×#535	C₂²	1	4	yes	—
48	C₁₃×#535	C₂²	1	4	yes	complemented
49	C₁₃×#534	C₂²	1	8	yes	—
50	C₁₃×#533	C₂²	1	16	yes	complemented
51	C₁₃×#532	C₂²	1	8	yes	complemented
52	C₁₃×#532	C₂²	1	16	yes	complemented
53	C₂×C₁₃×C₄⋊Q₈	C₂²	1	4	yes	complemented
54	C₁₃×#529	C₂²	1	16	yes	complemented
55	C₁₃×#529	C₂²	1	16	yes	complemented
56	C₁₃×#529	C₂²	1	16	yes	complemented
57	C₂×C₁₃×#125	C₂²	1	4	yes	complemented
58	C₁₃×#525	C₂²	1	8	yes	—
59	C₁₃×#525	C₂²	1	8	yes	complemented
60	C₁₃×#525	C₂²	1	16	yes	complemented
61	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	4	yes	—
62	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	4	yes	complemented
63	C₂×C₁₃×#121	C₂²	1	4	yes	—
64	C₂×C₁₃×#121	C₂²	1	4	yes	complemented
65	C₁₃×#520	C₂²	1	8	yes	—
66	C₁₃×#520	C₂²	1	8	yes	complemented
67	C₁₃×#520	C₂²	1	4	yes	complemented
68	C₁₃×#520	C₂²	1	4	yes	complemented
69	C₁₃×#520	C₂²	1	4	yes	complemented
70	C₁₃×#520	C₂²	1	4	yes	complemented
71	C₁₃×#519	C₂²	1	4	yes	complemented
72	C₁₃×#518	C₂²	1	8	yes	—
73	C₁₃×#518	C₂²	1	4	yes	complemented
74	C₄×C₁₃×#41	C₂²	1	8	yes	complemented
75	C₄×C₁₃×#41	C₂²	1	8	yes	complemented
76	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	complemented
77	C₂×C₄×D₄×C₁₃	C₂²	1	4	yes	—
78	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	complemented
79	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
80	C₂×C₁₃×#117	C₂²	1	2	yes	—
81	C₂×C₁₃×#117	C₂²	1	2	yes	complemented
82	C₂×C₁₃×#117	C₂²	1	8	yes	complemented
83	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
84	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	complemented
85	C₂×C₁₃×#41	—	2	8	no	—
86	C₂×C₁₃×#41	—	2	16	no	—
87	C₂×C₁₃×#41	C₂³	1	4	yes	—
88	C₂×C₁₃×#41	C₂³	1	4	yes	—
89	C₂×C₁₃×#41	C₂³	1	4	yes	—
90	C₂×C₁₃×#41	C₂³	1	4	yes	—
91	C₂×C₁₃×#41	C₂³	1	4	yes	—
92	C₂×C₁₃×#41	C₂³	1	4	yes	—
93	C₂×C₁₃×#41	C₂³	1	16	yes	—
94	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
95	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
96	C₂²×Q₈×C₁₃	C₂³	1	4	yes	—
97	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
98	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
99	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
100	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
101	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
102	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
103	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
104	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
105	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
106	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
107	C₁₃×C₄⋊Q₈	C₂³	1	16	yes	—
108	C₁₃×C₄⋊Q₈	C₂³	1	16	yes	—
109	C₁₃×C₄⋊Q₈	C₂³	1	8	yes	—
110	C₁₃×#127	C₂³	1	8	yes	—
111	C₁₃×#126	C₂³	1	32	yes	—
112	C₁₃×#126	C₂³	1	32	yes	—
113	C₁₃×#126	C₂³	1	32	yes	—
114	C₁₃×#125	C₂³	1	16	yes	—
115	C₁₃×#125	C₂³	1	16	yes	—
116	C₁₃×#125	C₂³	1	16	yes	—
117	C₁₃×#125	C₂³	1	32	yes	—
118	C₁₃×#124	C₂³	1	8	yes	—
119	C₁₃×#124	C₂³	1	8	yes	—
120	C₁₃×#124	C₂³	1	16	yes	—
121	C₁₃×#124	C₂³	1	32	yes	—
122	C₁₃×#123	C₂³	1	16	yes	—
123	C₁₃×#123	C₂³	1	16	yes	—
124	C₁₃×#123	C₂³	1	32	yes	—
125	C₁₃×#123	C₂³	1	32	yes	—
126	C₁₃×#123	C₂³	1	32	yes	—
127	C₁₃×C₂²⋊Q₈	C₂³	1	16	yes	—
128	C₁₃×C₂²⋊Q₈	C₂³	1	16	yes	—
129	C₁₃×C₂²⋊Q₈	C₂³	1	16	yes	—
130	C₁₃×C₂²⋊Q₈	C₂³	1	16	yes	—
131	C₁₃×C₂²⋊Q₈	C₂³	1	8	yes	—
132	C₁₃×C₂²⋊Q₈	C₂³	1	8	yes	—
133	C₁₃×C₂²⋊Q₈	C₂³	1	8	yes	—
134	C₁₃×C₂²⋊Q₈	C₂³	1	8	yes	—
135	C₁₃×C₂²⋊Q₈	C₂³	1	16	yes	—
136	C₁₃×C₂²⋊Q₈	C₂³	1	32	yes	—
137	C₁₃×#121	C₂³	1	16	yes	—
138	C₁₃×#121	C₂³	1	16	yes	—
139	C₁₃×#121	C₂³	1	16	yes	—
140	C₁₃×#121	C₂³	1	16	yes	—
141	C₁₃×#121	C₂³	1	8	yes	—
142	C₁₃×#121	C₂³	1	8	yes	—
143	C₁₃×#121	C₂³	1	8	yes	—
144	C₁₃×#121	C₂³	1	8	yes	—
145	C₁₃×#121	C₂³	1	16	yes	—
146	C₁₃×#121	C₂³	1	16	yes	—
147	C₁₃×#121	C₂³	1	16	yes	—
148	C₁₃×#121	C₂³	1	32	yes	—
149	C₁₃×#120	C₂³	1	16	yes	—
150	C₁₃×#120	C₂³	1	16	yes	—
151	C₄×Q₈×C₁₃	C₂³	1	16	yes	—
152	C₄×Q₈×C₁₃	C₂³	1	8	yes	—
153	C₄×Q₈×C₁₃	C₂³	1	8	yes	—
154	C₄×Q₈×C₁₃	C₂³	1	8	yes	—
155	C₄×Q₈×C₁₃	C₂³	1	8	yes	—
156	C₄×Q₈×C₁₃	C₂³	1	16	yes	—
157	C₄×D₄×C₁₃	C₂³	1	16	yes	—
158	C₄×D₄×C₁₃	C₂³	1	16	yes	—
159	C₄×D₄×C₁₃	C₂³	1	16	yes	—
160	C₄×D₄×C₁₃	C₂³	1	16	yes	—
161	C₄×D₄×C₁₃	C₂³	1	16	yes	—
162	C₄×D₄×C₁₃	C₂³	1	16	yes	—
163	C₄×D₄×C₁₃	C₂³	1	16	yes	—
164	C₄×D₄×C₁₃	C₂³	1	8	yes	—
165	C₄×D₄×C₁₃	C₂³	1	8	yes	—
166	C₄×D₄×C₁₃	C₂³	1	8	yes	—
167	C₄×D₄×C₁₃	C₂³	1	8	yes	—
168	C₄×D₄×C₁₃	C₂³	1	16	yes	—
169	C₄×D₄×C₁₃	C₂³	1	16	yes	—
170	C₄×D₄×C₁₃	C₂³	1	32	yes	—
171	C₄×D₄×C₁₃	C₂³	1	16	yes	—
172	C₁₃×#117	C₂³	1	4	yes	—
173	C₁₃×#117	C₂³	1	4	yes	—
174	C₁₃×#117	C₂³	1	4	yes	—
175	C₁₃×#117	C₂³	1	4	yes	—
176	C₁₃×#117	C₂³	1	4	yes	—
177	C₁₃×#117	C₂³	1	4	yes	—
178	C₁₃×#117	C₂³	1	16	yes	—
179	C₁₃×#117	C₂³	1	16	yes	—
180	C₁₃×#117	C₂³	1	16	yes	—
181	C₁₃×#117	C₂³	1	8	yes	—
182	C₁₃×#117	C₂³	1	8	yes	—
183	C₁₃×#117	C₂³	1	16	yes	—
184	C₁₃×#117	C₂³	1	32	yes	—
185	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
186	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
187	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
188	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
189	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
190	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
191	C₂×C₁₃×C₄⋊C₄	C₂³	1	16	yes	—
192	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
193	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
194	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
195	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
196	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
197	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
198	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
199	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
200	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
201	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
202	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
203	C₂×C₁₃×C₂²⋊C₄	C₂³	1	16	yes	—
204	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
205	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
206	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
207	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
208	C₂×C₄²×C₁₃	C₂³	1	16	yes	—
209	#62856	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
210	C₂⁴×C₁₃	C₂⁴	1	4	yes	—
211	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
212	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
213	C₁₃×#41	—	2	16	no	—
214	C₁₃×#41	—	2	16	no	—
215	C₁₃×#41	—	2	16	no	—
216	C₁₃×#41	—	2	16	no	—
217	C₁₃×#41	—	2	16	no	—
218	C₁₃×#41	—	2	16	no	—
219	C₁₃×#41	—	8	16	no	—
220	C₂×Q₈×C₁₃	—	2	8	no	—
221	C₂×Q₈×C₁₃	—	2	4	no	—
222	C₂×Q₈×C₁₃	—	8	4	no	—
223	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
224	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
225	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
226	C₂×Q₈×C₁₃	C₂⁴	1	16	yes	—
227	C₂×D₄×C₁₃	—	2	8	no	—
228	C₂×D₄×C₁₃	—	2	16	no	—
229	C₂×D₄×C₁₃	—	2	8	no	—
230	C₂×D₄×C₁₃	—	2	4	no	—
231	C₂×D₄×C₁₃	—	8	4	no	—
232	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
233	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
234	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
235	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
236	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
237	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
238	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
239	C₂×D₄×C₁₃	C₂⁴	1	16	yes	—
240	C₂×D₄×C₁₃	C₂⁴	1	16	yes	—
241	C₂×D₄×C₁₃	C₂⁴	1	16	yes	—
242	C₂²×C₄×C₁₃	—	2	16	no	—
243	C₂²×C₄×C₁₃	—	2	8	no	—
244	C₂²×C₄×C₁₃	—	8	2	no	—
245	C₂²×C₄×C₁₃	—	8	4	no	—
246	C₂²×C₄×C₁₃	#41	1	8	yes	complemented
247	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
248	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
249	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
250	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
251	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
252	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
253	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
254	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
255	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
256	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
257	C₂²×C₄×C₁₃	C₂⁴	1	16	yes	—
258	C₂²×C₄×C₁₃	C₂⁴	1	16	yes	—
259	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
260	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
261	C₂²×C₄×C₁₃	C₂⁴	1	16	yes	—
262	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
263	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
264	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
265	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
266	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
267	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
268	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
269	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
270	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
271	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
272	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
273	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
274	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
275	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
276	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
277	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
278	C₁₃×C₄⋊C₄	C₂⁴	1	32	yes	—
279	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
280	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
281	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
282	C₁₃×C₂²⋊C₄	C₂⁴	1	4	yes	—
283	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
284	C₁₃×C₂²⋊C₄	C₂⁴	1	4	yes	—
285	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
286	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
287	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
288	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
289	C₁₃×C₂²⋊C₄	C₂⁴	1	32	yes	—
290	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
291	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
292	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
293	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
294	C₄²×C₁₃	C₂⁴	1	8	yes	—
295	C₄²×C₁₃	C₂⁴	1	8	yes	—
296	C₄²×C₁₃	C₂⁴	1	16	yes	—
297	C₄²×C₁₃	C₂⁴	1	16	yes	—
298	C₄²×C₁₃	C₂⁴	1	16	yes	—
299	C₄²×C₁₃	C₂⁴	1	8	yes	—
300	#3512	C₂×C₁₃	1	8	yes	complemented
301	#3511	C₂×C₁₃	1	8	yes	complemented
302	#3505	C₂×C₁₃	1	8	yes	complemented
303	#3495	C₂×C₁₃	1	8	yes	complemented
304	#3494	C₂×C₁₃	1	8	yes	complemented
305	#3493	C₂×C₁₃	1	4	yes	complemented
306	#3492	C₂×C₁₃	1	4	yes	complemented
307	#3461	C₂×C₁₃	1	4	yes	complemented
308	#3460	C₂×C₁₃	1	4	yes	complemented
309	C₂×#544	C₂×C₁₃	1	1	yes	characteristic, complemented
310	#3449	C₂×C₁₃	1	2	yes	complemented
311	C₂×#537	C₂×C₁₃	1	1	yes	characteristic, complemented
312	#3428	C₂×C₁₃	1	2	yes	complemented
313	C₂×#520	C₂×C₁₃	1	1	yes	characteristic, complemented
314	C₂³×C₁₃	—	2	4	no	—
315	C₂³×C₁₃	—	2	8	no	—
316	C₂³×C₁₃	—	4	1	no	—
317	C₂³×C₁₃	—	4	2	no	—
318	C₂³×C₁₃	—	4	1	no	—
319	C₂³×C₁₃	—	4	2	no	—
320	C₂³×C₁₃	—	4	4	no	—
321	C₂³×C₁₃	—	4	4	no	—
322	C₂³×C₁₃	C₂×#41	1	4	yes	—
323	C₂³×C₁₃	C₂⁵	1	4	yes	—
324	C₂³×C₁₃	C₂⁵	1	8	yes	—
325	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
326	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
327	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
328	Q₈×C₁₃	—	2	8	no	—
329	Q₈×C₁₃	—	2	8	no	—
330	Q₈×C₁₃	—	2	8	no	—
331	Q₈×C₁₃	—	4	16	no	—
332	D₄×C₁₃	—	2	8	no	—
333	D₄×C₁₃	—	2	16	no	—
334	D₄×C₁₃	—	2	8	no	—
335	D₄×C₁₃	—	2	16	no	—
336	D₄×C₁₃	—	2	8	no	—
337	D₄×C₁₃	—	2	8	no	—
338	D₄×C₁₃	—	2	8	no	—
339	D₄×C₁₃	—	4	16	no	—
340	D₄×C₁₃	—	4	16	no	—
341	D₄×C₁₃	—	4	16	no	—
342	C₂×C₄×C₁₃	—	2	8	no	—
343	C₂×C₄×C₁₃	—	2	4	no	—
344	C₂×C₄×C₁₃	—	2	16	no	—
345	C₂×C₄×C₁₃	—	2	16	no	—
346	C₂×C₄×C₁₃	—	2	16	no	—
347	C₂×C₄×C₁₃	—	4	2	no	—
348	C₂×C₄×C₁₃	—	4	4	no	—
349	C₂×C₄×C₁₃	—	4	4	no	—
350	C₂×C₄×C₁₃	—	4	4	no	—
351	C₂×C₄×C₁₃	—	4	16	no	—
352	C₂×C₄×C₁₃	—	4	2	no	—
353	C₂×C₄×C₁₃	—	4	16	no	—
354	C₂×C₄×C₁₃	—	4	4	no	—
355	C₂×C₄×C₁₃	—	4	4	no	—
356	C₂×C₄×C₁₃	—	4	16	no	—
357	C₂×C₄×C₁₃	C₂×#41	1	8	yes	—
358	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
359	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
360	C₂×C₄×C₁₃	C₂×#41	1	8	yes	—
361	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
362	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
363	C₂×C₄×C₁₃	C₂⁵	1	8	yes	—
364	C₂×C₄×C₁₃	C₂⁵	1	8	yes	—
365	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
366	C₂×C₄×C₁₃	C₂⁵	1	8	yes	—
367	C₂×C₄×C₁₃	C₂⁵	1	8	yes	—
368	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
369	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
370	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic
371	C₂²×#41	C₂²×C₁₃	1	2	yes	—
372	#556	C₂²×C₁₃	1	16	yes	complemented
373	#555	C₂²×C₁₃	1	16	yes	complemented
374	#554	C₂²×C₁₃	1	16	yes	complemented
375	#553	C₂²×C₁₃	1	16	yes	complemented
376	#553	C₂²×C₁₃	1	16	yes	complemented
377	#553	C₂²×C₁₃	1	32	yes	complemented
378	#553	C₂²×C₁₃	1	16	yes	complemented
379	#552	C₂²×C₁₃	1	16	yes	complemented
380	#552	C₂²×C₁₃	1	16	yes	complemented
381	#552	C₂²×C₁₃	1	16	yes	complemented
382	#551	C₂²×C₁₃	1	32	yes	complemented
383	#548	C₂²×C₁₃	1	16	yes	complemented
384	#547	C₂²×C₁₃	1	16	yes	complemented
385	#546	C₂²×C₁₃	1	16	yes	complemented
386	#544	C₂²×C₁₃	1	4	yes	complemented
387	#544	C₂²×C₁₃	1	4	yes	complemented
388	#544	C₂²×C₁₃	1	8	yes	complemented
389	#542	C₂²×C₁₃	1	16	yes	complemented
390	#542	C₂²×C₁₃	1	16	yes	complemented
391	#541	C₂²×C₁₃	1	16	yes	complemented
392	#540	C₂²×C₁₃	1	16	yes	complemented
393	#539	C₂²×C₁₃	1	16	yes	complemented
394	#538	C₂²×C₁₃	1	16	yes	complemented
395	#537	C₂²×C₁₃	1	4	yes	—
396	#537	C₂²×C₁₃	1	4	yes	—
397	#537	C₂²×C₁₃	1	8	yes	complemented
398	#537	C₂²×C₁₃	1	4	yes	complemented
399	#537	C₂²×C₁₃	1	4	yes	complemented
400	#536	C₂²×C₁₃	1	4	yes	—
401	#536	C₂²×C₁₃	1	4	yes	complemented
402	#535	C₂²×C₁₃	1	4	yes	—
403	#535	C₂²×C₁₃	1	4	yes	complemented
404	#534	C₂²×C₁₃	1	8	yes	—
405	#533	C₂²×C₁₃	1	16	yes	complemented
406	#532	C₂²×C₁₃	1	8	yes	complemented
407	#532	C₂²×C₁₃	1	16	yes	complemented
408	C₂×C₄⋊Q₈	C₂²×C₁₃	1	4	yes	complemented
409	#529	C₂²×C₁₃	1	16	yes	complemented
410	#529	C₂²×C₁₃	1	16	yes	complemented
411	#529	C₂²×C₁₃	1	16	yes	complemented
412	C₂×#125	C₂²×C₁₃	1	4	yes	complemented
413	#525	C₂²×C₁₃	1	8	yes	—
414	#525	C₂²×C₁₃	1	8	yes	complemented
415	#525	C₂²×C₁₃	1	16	yes	complemented
416	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	4	yes	—
417	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	4	yes	complemented
418	C₂×#121	C₂²×C₁₃	1	4	yes	—
419	C₂×#121	C₂²×C₁₃	1	4	yes	complemented
420	#520	C₂²×C₁₃	1	8	yes	—
421	#520	C₂²×C₁₃	1	8	yes	complemented
422	#520	C₂²×C₁₃	1	4	yes	complemented
423	#520	C₂²×C₁₃	1	4	yes	complemented
424	#520	C₂²×C₁₃	1	4	yes	complemented
425	#520	C₂²×C₁₃	1	4	yes	complemented
426	#519	C₂²×C₁₃	1	4	yes	complemented
427	#518	C₂²×C₁₃	1	8	yes	—
428	#518	C₂²×C₁₃	1	4	yes	complemented
429	C₄×#41	C₂²×C₁₃	1	8	yes	complemented
430	C₄×#41	C₂²×C₁₃	1	8	yes	complemented
431	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	complemented
432	C₂×C₄×D₄	C₂²×C₁₃	1	4	yes	—
433	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	complemented
434	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
435	C₂×#117	C₂²×C₁₃	1	2	yes	—
436	C₂×#117	C₂²×C₁₃	1	2	yes	complemented
437	C₂×#117	C₂²×C₁₃	1	8	yes	complemented
438	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
439	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	complemented
440	C₂²×C₁₃	—	2	1	no	—
441	C₂²×C₁₃	—	2	1	no	—
442	C₂²×C₁₃	—	2	1	no	—
443	C₂²×C₁₃	—	2	1	no	—
444	C₂²×C₁₃	—	2	1	no	—
445	C₂²×C₁₃	—	2	1	no	—
446	C₂²×C₁₃	—	2	4	no	—
447	C₂²×C₁₃	—	2	8	no	—
448	C₂²×C₁₃	—	2	4	no	—
449	C₂²×C₁₃	—	2	8	no	—
450	C₂²×C₁₃	—	2	8	no	—
451	C₂²×C₁₃	—	2	4	no	—
452	C₂²×C₁₃	—	4	4	no	—
453	C₂²×C₁₃	—	4	8	no	—
454	C₂²×C₁₃	—	8	8	no	—
455	C₂²×C₁₃	C₂²×#41	1	2	yes	—
456	C₂²×C₁₃	C₂²×#41	1	2	yes	—
457	C₂²×C₁₃	C₂²×#41	1	2	yes	—
458	C₂²×C₁₃	C₂⁶	1	1	yes	characteristic
459	C₄×C₁₃	—	2	8	no	—
460	C₄×C₁₃	—	2	4	no	—
461	C₄×C₁₃	—	2	4	no	—
462	C₄×C₁₃	—	2	8	no	—
463	C₄×C₁₃	—	2	8	no	—
464	C₄×C₁₃	—	2	4	no	—
465	C₄×C₁₃	—	2	8	no	—
466	C₄×C₁₃	C₂²×#41	1	4	yes	—
467	C₄×C₁₃	C₂²×#41	1	4	yes	—
468	C₂×#41	—	2	8	no	—
469	C₂×#41	—	2	16	no	—
470	C₂×#41	C₂³×C₁₃	1	4	yes	—
471	C₂×#41	C₂³×C₁₃	1	4	yes	—
472	C₂×#41	C₂³×C₁₃	1	4	yes	—
473	C₂×#41	C₂³×C₁₃	1	4	yes	—
474	C₂×#41	C₂³×C₁₃	1	4	yes	—
475	C₂×#41	C₂³×C₁₃	1	4	yes	—
476	C₂×#41	C₂³×C₁₃	1	16	yes	—
477	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
478	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
479	C₂²×Q₈	C₂³×C₁₃	1	4	yes	—
480	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
481	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
482	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
483	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
484	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
485	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
486	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
487	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
488	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
489	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
490	C₄⋊Q₈	C₂³×C₁₃	1	16	yes	—
491	C₄⋊Q₈	C₂³×C₁₃	1	16	yes	—
492	C₄⋊Q₈	C₂³×C₁₃	1	8	yes	—
493	#127	C₂³×C₁₃	1	8	yes	—
494	#126	C₂³×C₁₃	1	32	yes	—
495	#126	C₂³×C₁₃	1	32	yes	—
496	#126	C₂³×C₁₃	1	32	yes	—
497	#125	C₂³×C₁₃	1	16	yes	—
498	#125	C₂³×C₁₃	1	16	yes	—
499	#125	C₂³×C₁₃	1	16	yes	—
500	#125	C₂³×C₁₃	1	32	yes	—
501	#124	C₂³×C₁₃	1	8	yes	—
502	#124	C₂³×C₁₃	1	8	yes	—
503	#124	C₂³×C₁₃	1	16	yes	—
504	#124	C₂³×C₁₃	1	32	yes	—
505	#123	C₂³×C₁₃	1	16	yes	—
506	#123	C₂³×C₁₃	1	16	yes	—
507	#123	C₂³×C₁₃	1	32	yes	—
508	#123	C₂³×C₁₃	1	32	yes	—
509	#123	C₂³×C₁₃	1	32	yes	—
510	C₂²⋊Q₈	C₂³×C₁₃	1	16	yes	—
511	C₂²⋊Q₈	C₂³×C₁₃	1	16	yes	—
512	C₂²⋊Q₈	C₂³×C₁₃	1	16	yes	—
513	C₂²⋊Q₈	C₂³×C₁₃	1	16	yes	—
514	C₂²⋊Q₈	C₂³×C₁₃	1	8	yes	—
515	C₂²⋊Q₈	C₂³×C₁₃	1	8	yes	—
516	C₂²⋊Q₈	C₂³×C₁₃	1	8	yes	—
517	C₂²⋊Q₈	C₂³×C₁₃	1	8	yes	—
518	C₂²⋊Q₈	C₂³×C₁₃	1	16	yes	—
519	C₂²⋊Q₈	C₂³×C₁₃	1	32	yes	—
520	#121	C₂³×C₁₃	1	16	yes	—
521	#121	C₂³×C₁₃	1	16	yes	—
522	#121	C₂³×C₁₃	1	16	yes	—
523	#121	C₂³×C₁₃	1	16	yes	—
524	#121	C₂³×C₁₃	1	8	yes	—
525	#121	C₂³×C₁₃	1	8	yes	—
526	#121	C₂³×C₁₃	1	8	yes	—
527	#121	C₂³×C₁₃	1	8	yes	—
528	#121	C₂³×C₁₃	1	16	yes	—
529	#121	C₂³×C₁₃	1	16	yes	—
530	#121	C₂³×C₁₃	1	16	yes	—
531	#121	C₂³×C₁₃	1	32	yes	—
532	#120	C₂³×C₁₃	1	16	yes	—
533	#120	C₂³×C₁₃	1	16	yes	—
534	C₄×Q₈	C₂³×C₁₃	1	16	yes	—
535	C₄×Q₈	C₂³×C₁₃	1	8	yes	—
536	C₄×Q₈	C₂³×C₁₃	1	8	yes	—
537	C₄×Q₈	C₂³×C₁₃	1	8	yes	—
538	C₄×Q₈	C₂³×C₁₃	1	8	yes	—
539	C₄×Q₈	C₂³×C₁₃	1	16	yes	—
540	C₄×D₄	C₂³×C₁₃	1	16	yes	—
541	C₄×D₄	C₂³×C₁₃	1	16	yes	—
542	C₄×D₄	C₂³×C₁₃	1	16	yes	—
543	C₄×D₄	C₂³×C₁₃	1	16	yes	—
544	C₄×D₄	C₂³×C₁₃	1	16	yes	—
545	C₄×D₄	C₂³×C₁₃	1	16	yes	—
546	C₄×D₄	C₂³×C₁₃	1	16	yes	—
547	C₄×D₄	C₂³×C₁₃	1	8	yes	—
548	C₄×D₄	C₂³×C₁₃	1	8	yes	—
549	C₄×D₄	C₂³×C₁₃	1	8	yes	—
550	C₄×D₄	C₂³×C₁₃	1	8	yes	—
551	C₄×D₄	C₂³×C₁₃	1	16	yes	—
552	C₄×D₄	C₂³×C₁₃	1	16	yes	—
553	C₄×D₄	C₂³×C₁₃	1	32	yes	—
554	C₄×D₄	C₂³×C₁₃	1	16	yes	—
555	#117	C₂³×C₁₃	1	4	yes	—
556	#117	C₂³×C₁₃	1	4	yes	—
557	#117	C₂³×C₁₃	1	4	yes	—
558	#117	C₂³×C₁₃	1	4	yes	—
559	#117	C₂³×C₁₃	1	4	yes	—
560	#117	C₂³×C₁₃	1	4	yes	—
561	#117	C₂³×C₁₃	1	16	yes	—
562	#117	C₂³×C₁₃	1	16	yes	—
563	#117	C₂³×C₁₃	1	16	yes	—
564	#117	C₂³×C₁₃	1	8	yes	—
565	#117	C₂³×C₁₃	1	8	yes	—
566	#117	C₂³×C₁₃	1	16	yes	—
567	#117	C₂³×C₁₃	1	32	yes	—
568	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
569	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
570	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
571	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
572	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
573	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
574	C₂×C₄⋊C₄	C₂³×C₁₃	1	16	yes	—
575	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
576	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
577	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
578	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
579	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
580	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
581	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
582	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
583	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
584	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
585	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
586	C₂×C₂²⋊C₄	C₂³×C₁₃	1	16	yes	—
587	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
588	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
589	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
590	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
591	C₂×C₄²	C₂³×C₁₃	1	16	yes	—
592	C₂×C₁₃	—	2	2	no	—
593	C₂×C₁₃	—	2	2	no	—
594	C₂×C₁₃	—	2	2	no	—
595	C₂×C₁₃	—	4	4	no	—
596	C₂×C₁₃	—	4	8	no	—
597	C₂×C₁₃	C₂³×#41	1	1	yes	characteristic
598	C₂×C₁₃	H(7,𝔽₂)	1	1	yes	characteristic
599	C₂×C₁₃	2₋¹⁺⁶	1	1	yes	characteristic
600	C₂⁴	C₂⁴×C₁₃	1	4	yes	—
601	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
602	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
603	#41	—	2	16	no	—
604	#41	—	2	16	no	—
605	#41	—	2	16	no	—
606	#41	—	2	16	no	—
607	#41	—	2	16	no	—
608	#41	—	2	16	no	—
609	#41	—	8	16	no	—
610	C₂×Q₈	—	2	8	no	—
611	C₂×Q₈	—	2	4	no	—
612	C₂×Q₈	—	8	4	no	—
613	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
614	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
615	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
616	C₂×Q₈	C₂⁴×C₁₃	1	16	yes	—
617	C₂×D₄	—	2	8	no	—
618	C₂×D₄	—	2	16	no	—
619	C₂×D₄	—	2	8	no	—
620	C₂×D₄	—	2	4	no	—
621	C₂×D₄	—	8	4	no	—
622	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
623	C₂×D₄	C₂⁴×C₁₃	1	8	yes	—
624	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
625	C₂×D₄	C₂⁴×C₁₃	1	8	yes	—
626	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
627	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
628	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
629	C₂×D₄	C₂⁴×C₁₃	1	16	yes	—
630	C₂×D₄	C₂⁴×C₁₃	1	16	yes	—
631	C₂×D₄	C₂⁴×C₁₃	1	16	yes	—
632	C₂²×C₄	—	2	16	no	—
633	C₂²×C₄	—	2	8	no	—
634	C₂²×C₄	—	8	2	no	—
635	C₂²×C₄	—	8	4	no	—
636	C₂²×C₄	C₁₃×#41	1	8	yes	complemented
637	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
638	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
639	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
640	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
641	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
642	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
643	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
644	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
645	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
646	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
647	C₂²×C₄	C₂⁴×C₁₃	1	16	yes	—
648	C₂²×C₄	C₂⁴×C₁₃	1	16	yes	—
649	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
650	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
651	C₂²×C₄	C₂⁴×C₁₃	1	16	yes	—
652	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
653	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
654	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
655	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
656	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
657	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
658	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
659	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
660	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
661	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
662	C₄⋊C₄	C₂⁴×C₁₃	1	16	yes	—
663	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
664	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
665	C₄⋊C₄	C₂⁴×C₁₃	1	16	yes	—
666	C₄⋊C₄	C₂⁴×C₁₃	1	16	yes	—
667	C₄⋊C₄	C₂⁴×C₁₃	1	16	yes	—
668	C₄⋊C₄	C₂⁴×C₁₃	1	32	yes	—
669	C₄⋊C₄	C₂⁴×C₁₃	1	16	yes	—
670	C₄⋊C₄	C₂⁴×C₁₃	1	16	yes	—
671	C₄⋊C₄	C₂⁴×C₁₃	1	16	yes	—
672	C₂²⋊C₄	C₂⁴×C₁₃	1	4	yes	—
673	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
674	C₂²⋊C₄	C₂⁴×C₁₃	1	4	yes	—
675	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
676	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
677	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
678	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
679	C₂²⋊C₄	C₂⁴×C₁₃	1	32	yes	—
680	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
681	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
682	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
683	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
684	C₄²	C₂⁴×C₁₃	1	8	yes	—
685	C₄²	C₂⁴×C₁₃	1	8	yes	—
686	C₄²	C₂⁴×C₁₃	1	16	yes	—
687	C₄²	C₂⁴×C₁₃	1	16	yes	—
688	C₄²	C₂⁴×C₁₃	1	16	yes	—
689	C₄²	C₂⁴×C₁₃	1	8	yes	—
690	C₁₃	#62856	1	1	yes	characteristic, direct product factor, Sylow
691	C₂³	—	2	4	no	—
692	C₂³	—	2	8	no	—
693	C₂³	—	4	1	no	—
694	C₂³	—	4	2	no	—
695	C₂³	—	4	1	no	—
696	C₂³	—	4	2	no	—
697	C₂³	—	4	4	no	—
698	C₂³	—	4	4	no	—
699	C₂³	C₂×C₁₃×#41	1	4	yes	—
700	C₂³	C₂⁵×C₁₃	1	4	yes	—
701	C₂³	C₂⁵×C₁₃	1	8	yes	—
702	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
703	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
704	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
705	Q₈	—	2	8	no	—
706	Q₈	—	2	8	no	—
707	Q₈	—	2	8	no	—
708	Q₈	—	4	16	no	—
709	D₄	—	2	8	no	—
710	D₄	—	2	16	no	—
711	D₄	—	2	8	no	—
712	D₄	—	2	16	no	—
713	D₄	—	2	8	no	—
714	D₄	—	2	8	no	—
715	D₄	—	2	8	no	—
716	D₄	—	4	16	no	—
717	D₄	—	4	16	no	—
718	D₄	—	4	16	no	—
719	C₂×C₄	—	2	8	no	—
720	C₂×C₄	—	2	4	no	—
721	C₂×C₄	—	2	16	no	—
722	C₂×C₄	—	2	16	no	—
723	C₂×C₄	—	2	16	no	—
724	C₂×C₄	—	4	2	no	—
725	C₂×C₄	—	4	4	no	—
726	C₂×C₄	—	4	4	no	—
727	C₂×C₄	—	4	4	no	—
728	C₂×C₄	—	4	16	no	—
729	C₂×C₄	—	4	2	no	—
730	C₂×C₄	—	4	16	no	—
731	C₂×C₄	—	4	4	no	—
732	C₂×C₄	—	4	4	no	—
733	C₂×C₄	—	4	16	no	—
734	C₂×C₄	C₂×C₁₃×#41	1	8	yes	—
735	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
736	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
737	C₂×C₄	C₂×C₁₃×#41	1	8	yes	—
738	C₂×C₄	C₂⁵×C₁₃	1	4	yes	—
739	C₂×C₄	C₂⁵×C₁₃	1	4	yes	—
740	C₂×C₄	C₂⁵×C₁₃	1	8	yes	—
741	C₂×C₄	C₂⁵×C₁₃	1	8	yes	—
742	C₂×C₄	C₂⁵×C₁₃	1	4	yes	—
743	C₂×C₄	C₂⁵×C₁₃	1	8	yes	—
744	C₂×C₄	C₂⁵×C₁₃	1	8	yes	—
745	C₂×C₄	C₂⁵×C₁₃	1	2	yes	—
746	C₂×C₄	C₂⁵×C₁₃	1	2	yes	—
747	C₂²	—	2	1	no	—
748	C₂²	—	2	1	no	—
749	C₂²	—	2	1	no	—
750	C₂²	—	2	1	no	—
751	C₂²	—	2	1	no	—
752	C₂²	—	2	1	no	—
753	C₂²	—	2	4	no	—
754	C₂²	—	2	8	no	—
755	C₂²	—	2	4	no	—
756	C₂²	—	2	8	no	—
757	C₂²	—	2	8	no	—
758	C₂²	—	2	4	no	—
759	C₂²	—	4	4	no	—
760	C₂²	—	4	8	no	—
761	C₂²	—	8	8	no	—
762	C₂²	C₂²×C₁₃×#41	1	2	yes	—
763	C₂²	C₂²×C₁₃×#41	1	2	yes	—
764	C₂²	C₂²×C₁₃×#41	1	2	yes	—
765	C₂²	C₂⁶×C₁₃	1	1	yes	characteristic
766	C₄	—	2	8	no	—
767	C₄	—	2	4	no	—
768	C₄	—	2	4	no	—
769	C₄	—	2	8	no	—
770	C₄	—	2	8	no	—
771	C₄	—	2	4	no	—
772	C₄	—	2	8	no	—
773	C₄	C₂²×C₁₃×#41	1	4	yes	—
774	C₄	C₂²×C₁₃×#41	1	4	yes	—
775	C₂	—	2	2	no	—
776	C₂	—	2	2	no	—
777	C₂	—	2	2	no	—
778	C₂	—	4	4	no	—
779	C₂	—	4	8	no	—
780	C₂	C₂³×C₁₃×#41	1	1	yes	characteristic
781	C₂	C₁₃×H(7,𝔽₂)	1	1	yes	characteristic
782	C₂	C₁₃×2₋¹⁺⁶	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂⁶
commutator, Frattini, cosocle	C₂²	C₂⁶×C₁₃
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3512	C₂	semidirect
2. C₁₃×#3511	C₂	semidirect
3. C₁₃×#3505	C₂	semidirect
4. C₁₃×#3495	C₂	semidirect
5. C₁₃×#3494	C₂	semidirect
6. C₁₃×#3493	C₂	semidirect
7. C₁₃×#3492	C₂	semidirect
8. C₁₃×#3461	C₂	semidirect
9. C₁₃×#3460	C₂	semidirect
10. C₂×C₁₃×#544	C₂	semidirect
11. C₁₃×#3449	C₂	semidirect
12. C₂×C₁₃×#537	C₂	semidirect
13. C₁₃×#3428	C₂	semidirect
14. C₂×C₁₃×#520	C₂	semidirect
17. C₁₃×#556	C₂²	semidirect
18. C₁₃×#555	C₂²	semidirect
19. C₁₃×#554	C₂²	semidirect
20. C₁₃×#553	C₂²	semidirect
21. C₁₃×#553	C₂²	semidirect
22. C₁₃×#553	C₂²	semidirect
23. C₁₃×#553	C₂²	semidirect
24. C₁₃×#552	C₂²	semidirect
25. C₁₃×#552	C₂²	semidirect
26. C₁₃×#552	C₂²	semidirect
27. C₁₃×#551	C₂²	semidirect
28. C₁₃×#548	C₂²	semidirect
29. C₁₃×#547	C₂²	semidirect
30. C₁₃×#546	C₂²	semidirect
31. C₁₃×#544	C₂²	semidirect
32. C₁₃×#544	C₂²	semidirect
33. C₁₃×#544	C₂²	semidirect
34. C₁₃×#542	C₂²	semidirect
35. C₁₃×#542	C₂²	semidirect
36. C₁₃×#541	C₂²	semidirect
37. C₁₃×#540	C₂²	semidirect
38. C₁₃×#539	C₂²	semidirect
39. C₁₃×#538	C₂²	semidirect
42. C₁₃×#537	C₂²	semidirect
43. C₁₃×#537	C₂²	semidirect
44. C₁₃×#537	C₂²	semidirect
46. C₁₃×#536	C₂²	semidirect
48. C₁₃×#535	C₂²	semidirect
50. C₁₃×#533	C₂²	semidirect
51. C₁₃×#532	C₂²	semidirect
52. C₁₃×#532	C₂²	semidirect
53. C₂×C₁₃×C₄⋊Q₈	C₂²	semidirect
54. C₁₃×#529	C₂²	semidirect
55. C₁₃×#529	C₂²	semidirect
56. C₁₃×#529	C₂²	semidirect
57. C₂×C₁₃×#125	C₂²	semidirect
59. C₁₃×#525	C₂²	semidirect
60. C₁₃×#525	C₂²	semidirect
62. C₂×C₁₃×C₂²⋊Q₈	C₂²	semidirect
64. C₂×C₁₃×#121	C₂²	semidirect
66. C₁₃×#520	C₂²	semidirect
67. C₁₃×#520	C₂²	semidirect
68. C₁₃×#520	C₂²	semidirect
69. C₁₃×#520	C₂²	semidirect
70. C₁₃×#520	C₂²	semidirect
71. C₁₃×#519	C₂²	semidirect
73. C₁₃×#518	C₂²	semidirect
74. C₄×C₁₃×#41	C₂²	semidirect
75. C₄×C₁₃×#41	C₂²	semidirect
76. C₂×C₄×Q₈×C₁₃	C₂²	semidirect
78. C₂×C₄×D₄×C₁₃	C₂²	semidirect
81. C₂×C₁₃×#117	C₂²	semidirect
82. C₂×C₁₃×#117	C₂²	semidirect
84. C₂²×C₁₃×C₄⋊C₄	C₂²	semidirect
209. #62856	C₁₃	direct (N × H)
246. C₂²×C₄×C₁₃	#41	semidirect
300. #3512	C₂×C₁₃	semidirect
301. #3511	C₂×C₁₃	semidirect
302. #3505	C₂×C₁₃	semidirect
303. #3495	C₂×C₁₃	semidirect
304. #3494	C₂×C₁₃	semidirect
305. #3493	C₂×C₁₃	semidirect
306. #3492	C₂×C₁₃	semidirect
307. #3461	C₂×C₁₃	semidirect
308. #3460	C₂×C₁₃	semidirect
309. C₂×#544	C₂×C₁₃	semidirect
310. #3449	C₂×C₁₃	semidirect
311. C₂×#537	C₂×C₁₃	semidirect
312. #3428	C₂×C₁₃	semidirect
313. C₂×#520	C₂×C₁₃	semidirect
372. #556	C₂²×C₁₃	semidirect
373. #555	C₂²×C₁₃	semidirect
374. #554	C₂²×C₁₃	semidirect
375. #553	C₂²×C₁₃	semidirect
376. #553	C₂²×C₁₃	semidirect
377. #553	C₂²×C₁₃	semidirect
378. #553	C₂²×C₁₃	semidirect
379. #552	C₂²×C₁₃	semidirect
380. #552	C₂²×C₁₃	semidirect
381. #552	C₂²×C₁₃	semidirect
382. #551	C₂²×C₁₃	semidirect
383. #548	C₂²×C₁₃	semidirect
384. #547	C₂²×C₁₃	semidirect
385. #546	C₂²×C₁₃	semidirect
386. #544	C₂²×C₁₃	semidirect
387. #544	C₂²×C₁₃	semidirect
388. #544	C₂²×C₁₃	semidirect
389. #542	C₂²×C₁₃	semidirect
390. #542	C₂²×C₁₃	semidirect
391. #541	C₂²×C₁₃	semidirect
392. #540	C₂²×C₁₃	semidirect
393. #539	C₂²×C₁₃	semidirect
394. #538	C₂²×C₁₃	semidirect
397. #537	C₂²×C₁₃	semidirect
398. #537	C₂²×C₁₃	semidirect
399. #537	C₂²×C₁₃	semidirect
401. #536	C₂²×C₁₃	semidirect
403. #535	C₂²×C₁₃	semidirect
405. #533	C₂²×C₁₃	semidirect
406. #532	C₂²×C₁₃	semidirect
407. #532	C₂²×C₁₃	semidirect
408. C₂×C₄⋊Q₈	C₂²×C₁₃	semidirect
409. #529	C₂²×C₁₃	semidirect
410. #529	C₂²×C₁₃	semidirect
411. #529	C₂²×C₁₃	semidirect
412. C₂×#125	C₂²×C₁₃	semidirect
414. #525	C₂²×C₁₃	semidirect
415. #525	C₂²×C₁₃	semidirect
417. C₂×C₂²⋊Q₈	C₂²×C₁₃	semidirect
419. C₂×#121	C₂²×C₁₃	semidirect
421. #520	C₂²×C₁₃	semidirect
422. #520	C₂²×C₁₃	semidirect
423. #520	C₂²×C₁₃	semidirect
424. #520	C₂²×C₁₃	semidirect
425. #520	C₂²×C₁₃	semidirect
426. #519	C₂²×C₁₃	semidirect
428. #518	C₂²×C₁₃	semidirect
429. C₄×#41	C₂²×C₁₃	semidirect
430. C₄×#41	C₂²×C₁₃	semidirect
431. C₂×C₄×Q₈	C₂²×C₁₃	semidirect
433. C₂×C₄×D₄	C₂²×C₁₃	semidirect
436. C₂×#117	C₂²×C₁₃	semidirect
437. C₂×#117	C₂²×C₁₃	semidirect
439. C₂²×C₄⋊C₄	C₂²×C₁₃	semidirect
636. C₂²×C₄	C₁₃×#41	semidirect
690. C₁₃	#62856	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₃×#3512	2
C₁₃×#3511	2
C₁₃×#3505	2
C₁₃×#3495	2
C₁₃×#3494	2
C₁₃×#3493	2
C₁₃×#3492	2
C₁₃×#3461	2
C₁₃×#3460	2
C₂×C₁₃×#544	2
C₁₃×#3449	2
C₂×C₁₃×#537	2
C₁₃×#3428	2
C₂×C₁₃×#520	2
#62856	13

Subgroups — C13×#62856 #15749195

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#62856 #15749195