Subgroups — C₁₃×#62815 #15749154

Order 3328.

7210 conjugacy classes of subgroups.

The subgroup lattice has 912 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	4	yes	maximal, complemented
2	C₁₃×#3511	C₂	1	4	yes	maximal, complemented
3	C₁₃×#3510	C₂	1	4	yes	maximal, complemented
4	C₁₃×#3509	C₂	1	2	yes	maximal, complemented
5	C₁₃×#3508	C₂	1	2	yes	maximal, complemented
6	C₁₃×#3507	C₂	1	4	yes	maximal, complemented
7	C₁₃×#3506	C₂	1	4	yes	maximal, complemented
8	C₁₃×#3505	C₂	1	8	yes	maximal, complemented
9	C₁₃×#3480	C₂	1	8	yes	maximal, complemented
10	C₁₃×#3475	C₂	1	8	yes	maximal, complemented
11	C₁₃×#3455	C₂	1	4	yes	maximal, complemented
12	C₁₃×#3449	C₂	1	2	yes	maximal, complemented
13	C₁₃×#3444	C₂	1	4	yes	maximal, complemented
14	C₂×C₁₃×#533	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₁₃×#532	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₃×#3428	C₂	1	2	yes	maximal, complemented
17	C₂×C₄×C₁₃×#41	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic
19	C₂²×C₁₃×#41	C₂²	1	2	yes	—
20	C₁₃×#559	C₂²	1	16	yes	complemented
21	C₁₃×#559	C₂²	1	8	yes	complemented
22	C₁₃×#557	C₂²	1	8	yes	complemented
23	C₁₃×#556	C₂²	1	8	yes	complemented
24	C₁₃×#556	C₂²	1	8	yes	complemented
25	C₁₃×#556	C₂²	1	16	yes	complemented
26	C₁₃×#555	C₂²	1	8	yes	complemented
27	C₁₃×#554	C₂²	1	8	yes	complemented
28	C₁₃×#553	C₂²	1	16	yes	complemented
29	C₁₃×#553	C₂²	1	16	yes	complemented
30	C₁₃×#553	C₂²	1	32	yes	complemented
31	C₁₃×#552	C₂²	1	16	yes	complemented
32	C₁₃×#552	C₂²	1	16	yes	complemented
33	C₁₃×#551	C₂²	1	32	yes	complemented
34	C₁₃×#550	C₂²	1	8	yes	complemented
35	C₁₃×#548	C₂²	1	16	yes	complemented
36	C₁₃×#547	C₂²	1	8	yes	complemented
37	C₁₃×#546	C₂²	1	16	yes	complemented
38	C₁₃×#542	C₂²	1	16	yes	complemented
39	C₁₃×#541	C₂²	1	8	yes	complemented
40	C₁₃×#540	C₂²	1	8	yes	complemented
41	C₁₃×#539	C₂²	1	16	yes	complemented
42	C₁₃×#538	C₂²	1	16	yes	complemented
43	C₁₃×#537	C₂²	1	8	yes	complemented
44	C₁₃×#536	C₂²	1	4	yes	—
45	C₁₃×#536	C₂²	1	4	yes	complemented
46	C₁₃×#535	C₂²	1	4	yes	—
47	C₁₃×#535	C₂²	1	4	yes	complemented
48	C₁₃×#534	C₂²	1	8	yes	—
49	C₁₃×#533	C₂²	1	2	yes	complemented
50	C₁₃×#533	C₂²	1	2	yes	complemented
51	C₁₃×#533	C₂²	1	4	yes	complemented
52	C₁₃×#533	C₂²	1	4	yes	complemented
53	C₁₃×#533	C₂²	1	2	yes	complemented
54	C₁₃×#533	C₂²	1	2	yes	complemented
55	C₁₃×#533	C₂²	1	8	yes	complemented
56	C₁₃×#532	C₂²	1	2	yes	—
57	C₁₃×#532	C₂²	1	2	yes	—
58	C₁₃×#532	C₂²	1	4	yes	—
59	C₁₃×#532	C₂²	1	4	yes	complemented
60	C₁₃×#532	C₂²	1	2	yes	complemented
61	C₁₃×#532	C₂²	1	2	yes	complemented
62	C₁₃×#532	C₂²	1	8	yes	complemented
63	C₁₃×#532	C₂²	1	8	yes	complemented
64	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
65	C₂×C₁₃×C₄⋊Q₈	C₂²	1	2	yes	complemented
66	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic, complemented
67	C₁₃×#529	C₂²	1	16	yes	complemented
68	C₁₃×#529	C₂²	1	16	yes	complemented
69	C₁₃×#529	C₂²	1	16	yes	complemented
70	C₁₃×#529	C₂²	1	32	yes	complemented
71	C₂×C₁₃×#125	C₂²	1	2	yes	complemented
72	C₂×C₁₃×#124	C₂²	1	2	yes	complemented
73	C₁₃×#525	C₂²	1	8	yes	—
74	C₁₃×#525	C₂²	1	8	yes	complemented
75	C₁₃×#525	C₂²	1	16	yes	complemented
76	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	4	yes	—
77	C₂×C₁₃×#121	C₂²	1	4	yes	—
78	C₁₃×#520	C₂²	1	8	yes	complemented
79	C₁₃×#520	C₂²	1	8	yes	complemented
80	C₁₃×#519	C₂²	1	4	yes	complemented
81	C₁₃×#518	C₂²	1	8	yes	—
82	C₁₃×#518	C₂²	1	4	yes	complemented
83	C₄×C₁₃×#41	C₂²	1	4	yes	—
84	C₄×C₁₃×#41	C₂²	1	2	yes	—
85	C₄×C₁₃×#41	C₂²	1	2	yes	—
86	C₄×C₁₃×#41	C₂²	1	4	yes	complemented
87	C₄×C₁₃×#41	C₂²	1	2	yes	complemented
88	C₄×C₁₃×#41	C₂²	1	2	yes	complemented
89	C₄×C₁₃×#41	C₂²	1	8	yes	complemented
90	C₄×C₁₃×#41	C₂²	1	8	yes	complemented
91	C₄×C₁₃×#41	C₂²	1	16	yes	complemented
92	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	complemented
93	C₂×C₄×Q₈×C₁₃	C₂²	1	4	yes	complemented
94	C₂×C₄×D₄×C₁₃	C₂²	1	4	yes	—
95	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	complemented
96	C₂×C₄×D₄×C₁₃	C₂²	1	4	yes	complemented
97	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
98	C₂×C₁₃×#117	C₂²	1	2	yes	—
99	C₂×C₁₃×#117	C₂²	1	2	yes	complemented
100	C₂×C₁₃×#117	C₂²	1	8	yes	complemented
101	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
102	C₂²×C₄²×C₁₃	C₂²	1	2	yes	complemented
103	C₂×C₁₃×#41	—	2	8	no	—
104	C₂×C₁₃×#41	—	2	16	no	—
105	C₂×C₁₃×#41	C₂³	1	2	yes	—
106	C₂×C₁₃×#41	C₂³	1	2	yes	—
107	C₂×C₁₃×#41	C₂³	1	4	yes	—
108	C₂×C₁₃×#41	C₂³	1	2	yes	—
109	C₂×C₁₃×#41	C₂³	1	4	yes	—
110	C₂×C₁₃×#41	C₂³	1	2	yes	—
111	C₂×C₁₃×#41	C₂³	1	4	yes	—
112	C₂×C₁₃×#41	C₂³	1	4	yes	—
113	C₂×C₁₃×#41	C₂³	1	16	yes	—
114	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
115	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
116	C₂²×Q₈×C₁₃	C₂³	1	4	yes	—
117	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
118	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
119	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
120	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
121	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
122	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
123	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
124	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
125	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
126	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
127	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
128	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
129	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
130	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
131	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
132	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
133	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
134	C₁₃×C₄⋊Q₈	C₂³	1	8	yes	—
135	C₁₃×#127	C₂³	1	2	yes	—
136	C₁₃×#127	C₂³	1	2	yes	—
137	C₁₃×#127	C₂³	1	4	yes	—
138	C₁₃×#127	C₂³	1	8	yes	—
139	C₁₃×#126	C₂³	1	32	yes	—
140	C₁₃×#126	C₂³	1	32	yes	—
141	C₁₃×#126	C₂³	1	32	yes	—
142	C₁₃×#125	C₂³	1	4	yes	—
143	C₁₃×#125	C₂³	1	4	yes	—
144	C₁₃×#125	C₂³	1	8	yes	—
145	C₁₃×#125	C₂³	1	16	yes	—
146	C₁₃×#125	C₂³	1	32	yes	—
147	C₁₃×#124	C₂³	1	4	yes	—
148	C₁₃×#124	C₂³	1	4	yes	—
149	C₁₃×#124	C₂³	1	8	yes	—
150	C₁₃×#124	C₂³	1	16	yes	—
151	C₁₃×#124	C₂³	1	32	yes	—
152	C₁₃×#124	C₂³	1	8	yes	—
153	C₁₃×#124	C₂³	1	8	yes	—
154	C₁₃×#123	C₂³	1	16	yes	—
155	C₁₃×#123	C₂³	1	16	yes	—
156	C₁₃×#123	C₂³	1	32	yes	—
157	C₁₃×#123	C₂³	1	32	yes	—
158	C₁₃×#123	C₂³	1	32	yes	—
159	C₁₃×C₂²⋊Q₈	C₂³	1	8	yes	—
160	C₁₃×C₂²⋊Q₈	C₂³	1	8	yes	—
161	C₁₃×C₂²⋊Q₈	C₂³	1	8	yes	—
162	C₁₃×C₂²⋊Q₈	C₂³	1	8	yes	—
163	C₁₃×C₂²⋊Q₈	C₂³	1	16	yes	—
164	C₁₃×C₂²⋊Q₈	C₂³	1	16	yes	—
165	C₁₃×C₂²⋊Q₈	C₂³	1	16	yes	—
166	C₁₃×C₂²⋊Q₈	C₂³	1	32	yes	—
167	C₁₃×#121	C₂³	1	8	yes	—
168	C₁₃×#121	C₂³	1	8	yes	—
169	C₁₃×#121	C₂³	1	8	yes	—
170	C₁₃×#121	C₂³	1	8	yes	—
171	C₁₃×#121	C₂³	1	16	yes	—
172	C₁₃×#121	C₂³	1	16	yes	—
173	C₁₃×#121	C₂³	1	16	yes	—
174	C₁₃×#121	C₂³	1	32	yes	—
175	C₁₃×#121	C₂³	1	32	yes	—
176	C₁₃×#120	C₂³	1	16	yes	—
177	C₁₃×#120	C₂³	1	16	yes	—
178	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
179	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
180	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
181	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
182	C₄×Q₈×C₁₃	C₂³	1	8	yes	—
183	C₄×Q₈×C₁₃	C₂³	1	8	yes	—
184	C₄×Q₈×C₁₃	C₂³	1	8	yes	—
185	C₄×Q₈×C₁₃	C₂³	1	8	yes	—
186	C₄×Q₈×C₁₃	C₂³	1	16	yes	—
187	C₄×Q₈×C₁₃	C₂³	1	16	yes	—
188	C₄×Q₈×C₁₃	C₂³	1	16	yes	—
189	C₄×D₄×C₁₃	C₂³	1	8	yes	—
190	C₄×D₄×C₁₃	C₂³	1	8	yes	—
191	C₄×D₄×C₁₃	C₂³	1	8	yes	—
192	C₄×D₄×C₁₃	C₂³	1	8	yes	—
193	C₄×D₄×C₁₃	C₂³	1	4	yes	—
194	C₄×D₄×C₁₃	C₂³	1	4	yes	—
195	C₄×D₄×C₁₃	C₂³	1	4	yes	—
196	C₄×D₄×C₁₃	C₂³	1	4	yes	—
197	C₄×D₄×C₁₃	C₂³	1	8	yes	—
198	C₄×D₄×C₁₃	C₂³	1	8	yes	—
199	C₄×D₄×C₁₃	C₂³	1	8	yes	—
200	C₄×D₄×C₁₃	C₂³	1	8	yes	—
201	C₄×D₄×C₁₃	C₂³	1	32	yes	—
202	C₄×D₄×C₁₃	C₂³	1	32	yes	—
203	C₄×D₄×C₁₃	C₂³	1	16	yes	—
204	C₄×D₄×C₁₃	C₂³	1	16	yes	—
205	C₄×D₄×C₁₃	C₂³	1	32	yes	—
206	C₄×D₄×C₁₃	C₂³	1	32	yes	—
207	C₄×D₄×C₁₃	C₂³	1	16	yes	—
208	C₁₃×#117	C₂³	1	2	yes	—
209	C₁₃×#117	C₂³	1	4	yes	—
210	C₁₃×#117	C₂³	1	2	yes	—
211	C₁₃×#117	C₂³	1	2	yes	—
212	C₁₃×#117	C₂³	1	2	yes	—
213	C₁₃×#117	C₂³	1	4	yes	—
214	C₁₃×#117	C₂³	1	4	yes	—
215	C₁₃×#117	C₂³	1	4	yes	—
216	C₁₃×#117	C₂³	1	8	yes	—
217	C₁₃×#117	C₂³	1	4	yes	—
218	C₁₃×#117	C₂³	1	4	yes	—
219	C₁₃×#117	C₂³	1	16	yes	—
220	C₁₃×#117	C₂³	1	16	yes	—
221	C₁₃×#117	C₂³	1	16	yes	—
222	C₁₃×#117	C₂³	1	16	yes	—
223	C₁₃×#117	C₂³	1	32	yes	—
224	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
225	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
226	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
227	C₂×C₁₃×C₄⋊C₄	C₂³	1	16	yes	—
228	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
229	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
230	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
231	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
232	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
233	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
234	C₂×C₁₃×C₂²⋊C₄	C₂³	1	16	yes	—
235	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
236	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
237	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
238	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
239	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
240	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
241	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
242	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
243	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
244	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
245	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
246	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
247	C₂×C₄²×C₁₃	C₂³	1	8	yes	—
248	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
249	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
250	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
251	C₂×C₄²×C₁₃	C₂³	1	16	yes	—
252	#62815	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
253	C₂⁴×C₁₃	C₂⁴	1	4	yes	—
254	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
255	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
256	C₁₃×#41	—	2	8	no	—
257	C₁₃×#41	—	2	16	no	—
258	C₁₃×#41	—	2	8	no	—
259	C₁₃×#41	—	2	16	no	—
260	C₁₃×#41	—	2	8	no	—
261	C₁₃×#41	—	2	16	no	—
262	C₁₃×#41	—	2	8	no	—
263	C₁₃×#41	—	2	16	no	—
264	C₁₃×#41	—	4	32	no	—
265	C₂×Q₈×C₁₃	—	2	8	no	—
266	C₂×Q₈×C₁₃	—	2	4	no	—
267	C₂×Q₈×C₁₃	—	4	8	no	—
268	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
269	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
270	C₂×Q₈×C₁₃	C₂⁴	1	8	yes	—
271	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
272	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
273	C₂×Q₈×C₁₃	C₂⁴	1	8	yes	—
274	C₂×D₄×C₁₃	—	2	8	no	—
275	C₂×D₄×C₁₃	—	2	16	no	—
276	C₂×D₄×C₁₃	—	2	8	no	—
277	C₂×D₄×C₁₃	—	2	4	no	—
278	C₂×D₄×C₁₃	—	4	8	no	—
279	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
280	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
281	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
282	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
283	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
284	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
285	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
286	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
287	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
288	C₂×D₄×C₁₃	C₂⁴	1	32	yes	—
289	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
290	C₂²×C₄×C₁₃	—	2	16	no	—
291	C₂²×C₄×C₁₃	—	2	8	no	—
292	C₂²×C₄×C₁₃	—	4	4	no	—
293	C₂²×C₄×C₁₃	—	4	8	no	—
294	C₂²×C₄×C₁₃	#41	1	8	yes	complemented
295	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
296	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
297	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
298	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
299	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
300	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
301	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
302	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
303	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
304	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
305	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
306	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
307	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
308	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
309	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
310	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
311	C₂²×C₄×C₁₃	C₂⁴	1	32	yes	—
312	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
313	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
314	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
315	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
316	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
317	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
318	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
319	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
320	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
321	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
322	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
323	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
324	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
325	C₁₃×C₄⋊C₄	C₂⁴	1	32	yes	—
326	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
327	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
328	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
329	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
330	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
331	C₁₃×C₄⋊C₄	C₂⁴	1	32	yes	—
332	C₁₃×C₂²⋊C₄	C₂⁴	1	4	yes	—
333	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
334	C₁₃×C₂²⋊C₄	C₂⁴	1	4	yes	—
335	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
336	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
337	C₁₃×C₂²⋊C₄	C₂⁴	1	32	yes	—
338	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
339	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
340	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
341	C₁₃×C₂²⋊C₄	C₂⁴	1	32	yes	—
342	C₁₃×C₂²⋊C₄	C₂⁴	1	32	yes	—
343	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
344	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
345	C₄²×C₁₃	C₂⁴	1	4	yes	—
346	C₄²×C₁₃	C₂⁴	1	8	yes	—
347	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
348	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
349	C₄²×C₁₃	C₂⁴	1	2	yes	—
350	C₄²×C₁₃	C₂⁴	1	2	yes	—
351	C₄²×C₁₃	C₂⁴	1	8	yes	—
352	C₄²×C₁₃	C₂⁴	1	2	yes	—
353	C₄²×C₁₃	C₂⁴	1	2	yes	—
354	C₄²×C₁₃	C₂⁴	1	32	yes	—
355	C₄²×C₁₃	C₂⁴	1	8	yes	—
356	C₄²×C₁₃	C₂⁴	1	4	yes	—
357	C₄²×C₁₃	C₂⁴	1	2	yes	—
358	C₄²×C₁₃	C₂⁴	1	2	yes	—
359	C₄²×C₁₃	C₂⁴	1	8	yes	—
360	#3512	C₂×C₁₃	1	4	yes	complemented
361	#3511	C₂×C₁₃	1	4	yes	complemented
362	#3510	C₂×C₁₃	1	4	yes	complemented
363	#3509	C₂×C₁₃	1	2	yes	complemented
364	#3508	C₂×C₁₃	1	2	yes	complemented
365	#3507	C₂×C₁₃	1	4	yes	complemented
366	#3506	C₂×C₁₃	1	4	yes	complemented
367	#3505	C₂×C₁₃	1	8	yes	complemented
368	#3480	C₂×C₁₃	1	8	yes	complemented
369	#3475	C₂×C₁₃	1	8	yes	complemented
370	#3455	C₂×C₁₃	1	4	yes	complemented
371	#3449	C₂×C₁₃	1	2	yes	complemented
372	#3444	C₂×C₁₃	1	4	yes	complemented
373	C₂×#533	C₂×C₁₃	1	1	yes	characteristic, complemented
374	C₂×#532	C₂×C₁₃	1	1	yes	characteristic, complemented
375	#3428	C₂×C₁₃	1	2	yes	complemented
376	C₂×C₄×#41	C₂×C₁₃	1	1	yes	characteristic, complemented
377	C₂³×C₁₃	—	2	4	no	—
378	C₂³×C₁₃	—	2	8	no	—
379	C₂³×C₁₃	—	4	2	no	—
380	C₂³×C₁₃	—	4	4	no	—
381	C₂³×C₁₃	—	4	8	no	—
382	C₂³×C₁₃	C₂×#41	1	4	yes	—
383	C₂³×C₁₃	C₂⁵	1	4	yes	—
384	C₂³×C₁₃	C₂⁵	1	8	yes	—
385	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
386	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
387	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
388	Q₈×C₁₃	—	2	4	no	—
389	Q₈×C₁₃	—	2	8	no	—
390	Q₈×C₁₃	—	2	8	no	—
391	Q₈×C₁₃	—	2	4	no	—
392	Q₈×C₁₃	—	2	16	no	—
393	Q₈×C₁₃	—	4	8	no	—
394	D₄×C₁₃	—	2	8	no	—
395	D₄×C₁₃	—	2	16	no	—
396	D₄×C₁₃	—	2	8	no	—
397	D₄×C₁₃	—	2	16	no	—
398	D₄×C₁₃	—	2	4	no	—
399	D₄×C₁₃	—	2	8	no	—
400	D₄×C₁₃	—	2	4	no	—
401	D₄×C₁₃	—	2	8	no	—
402	D₄×C₁₃	—	2	16	no	—
403	D₄×C₁₃	—	4	8	no	—
404	D₄×C₁₃	—	4	32	no	—
405	C₂×C₄×C₁₃	—	2	8	no	—
406	C₂×C₄×C₁₃	—	2	4	no	—
407	C₂×C₄×C₁₃	—	2	8	no	—
408	C₂×C₄×C₁₃	—	2	16	no	—
409	C₂×C₄×C₁₃	—	2	16	no	—
410	C₂×C₄×C₁₃	—	2	8	no	—
411	C₂×C₄×C₁₃	—	2	4	no	—
412	C₂×C₄×C₁₃	—	2	4	no	—
413	C₂×C₄×C₁₃	—	2	4	no	—
414	C₂×C₄×C₁₃	—	2	16	no	—
415	C₂×C₄×C₁₃	—	4	4	no	—
416	C₂×C₄×C₁₃	—	4	8	no	—
417	C₂×C₄×C₁₃	—	4	2	no	—
418	C₂×C₄×C₁₃	—	4	2	no	—
419	C₂×C₄×C₁₃	—	4	2	no	—
420	C₂×C₄×C₁₃	—	4	8	no	—
421	C₂×C₄×C₁₃	—	4	32	no	—
422	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
423	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
424	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
425	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
426	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
427	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
428	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
429	C₂×C₄×C₁₃	C₂⁵	1	8	yes	—
430	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
431	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
432	C₂×C₄×C₁₃	C₂⁵	1	8	yes	—
433	C₂×C₄×C₁₃	C₂⁵	1	16	yes	—
434	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
435	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
436	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
437	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
438	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
439	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
440	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic
441	C₂²×#41	C₂²×C₁₃	1	2	yes	—
442	#559	C₂²×C₁₃	1	16	yes	complemented
443	#559	C₂²×C₁₃	1	8	yes	complemented
444	#557	C₂²×C₁₃	1	8	yes	complemented
445	#556	C₂²×C₁₃	1	8	yes	complemented
446	#556	C₂²×C₁₃	1	8	yes	complemented
447	#556	C₂²×C₁₃	1	16	yes	complemented
448	#555	C₂²×C₁₃	1	8	yes	complemented
449	#554	C₂²×C₁₃	1	8	yes	complemented
450	#553	C₂²×C₁₃	1	16	yes	complemented
451	#553	C₂²×C₁₃	1	16	yes	complemented
452	#553	C₂²×C₁₃	1	32	yes	complemented
453	#552	C₂²×C₁₃	1	16	yes	complemented
454	#552	C₂²×C₁₃	1	16	yes	complemented
455	#551	C₂²×C₁₃	1	32	yes	complemented
456	#550	C₂²×C₁₃	1	8	yes	complemented
457	#548	C₂²×C₁₃	1	16	yes	complemented
458	#547	C₂²×C₁₃	1	8	yes	complemented
459	#546	C₂²×C₁₃	1	16	yes	complemented
460	#542	C₂²×C₁₃	1	16	yes	complemented
461	#541	C₂²×C₁₃	1	8	yes	complemented
462	#540	C₂²×C₁₃	1	8	yes	complemented
463	#539	C₂²×C₁₃	1	16	yes	complemented
464	#538	C₂²×C₁₃	1	16	yes	complemented
465	#537	C₂²×C₁₃	1	8	yes	complemented
466	#536	C₂²×C₁₃	1	4	yes	—
467	#536	C₂²×C₁₃	1	4	yes	complemented
468	#535	C₂²×C₁₃	1	4	yes	—
469	#535	C₂²×C₁₃	1	4	yes	complemented
470	#534	C₂²×C₁₃	1	8	yes	—
471	#533	C₂²×C₁₃	1	2	yes	complemented
472	#533	C₂²×C₁₃	1	2	yes	complemented
473	#533	C₂²×C₁₃	1	4	yes	complemented
474	#533	C₂²×C₁₃	1	4	yes	complemented
475	#533	C₂²×C₁₃	1	2	yes	complemented
476	#533	C₂²×C₁₃	1	2	yes	complemented
477	#533	C₂²×C₁₃	1	8	yes	complemented
478	#532	C₂²×C₁₃	1	2	yes	—
479	#532	C₂²×C₁₃	1	2	yes	—
480	#532	C₂²×C₁₃	1	4	yes	—
481	#532	C₂²×C₁₃	1	4	yes	complemented
482	#532	C₂²×C₁₃	1	2	yes	complemented
483	#532	C₂²×C₁₃	1	2	yes	complemented
484	#532	C₂²×C₁₃	1	8	yes	complemented
485	#532	C₂²×C₁₃	1	8	yes	complemented
486	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
487	C₂×C₄⋊Q₈	C₂²×C₁₃	1	2	yes	complemented
488	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic, complemented
489	#529	C₂²×C₁₃	1	16	yes	complemented
490	#529	C₂²×C₁₃	1	16	yes	complemented
491	#529	C₂²×C₁₃	1	16	yes	complemented
492	#529	C₂²×C₁₃	1	32	yes	complemented
493	C₂×#125	C₂²×C₁₃	1	2	yes	complemented
494	C₂×#124	C₂²×C₁₃	1	2	yes	complemented
495	#525	C₂²×C₁₃	1	8	yes	—
496	#525	C₂²×C₁₃	1	8	yes	complemented
497	#525	C₂²×C₁₃	1	16	yes	complemented
498	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	4	yes	—
499	C₂×#121	C₂²×C₁₃	1	4	yes	—
500	#520	C₂²×C₁₃	1	8	yes	complemented
501	#520	C₂²×C₁₃	1	8	yes	complemented
502	#519	C₂²×C₁₃	1	4	yes	complemented
503	#518	C₂²×C₁₃	1	8	yes	—
504	#518	C₂²×C₁₃	1	4	yes	complemented
505	C₄×#41	C₂²×C₁₃	1	4	yes	—
506	C₄×#41	C₂²×C₁₃	1	2	yes	—
507	C₄×#41	C₂²×C₁₃	1	2	yes	—
508	C₄×#41	C₂²×C₁₃	1	4	yes	complemented
509	C₄×#41	C₂²×C₁₃	1	2	yes	complemented
510	C₄×#41	C₂²×C₁₃	1	2	yes	complemented
511	C₄×#41	C₂²×C₁₃	1	8	yes	complemented
512	C₄×#41	C₂²×C₁₃	1	8	yes	complemented
513	C₄×#41	C₂²×C₁₃	1	16	yes	complemented
514	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	complemented
515	C₂×C₄×Q₈	C₂²×C₁₃	1	4	yes	complemented
516	C₂×C₄×D₄	C₂²×C₁₃	1	4	yes	—
517	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	complemented
518	C₂×C₄×D₄	C₂²×C₁₃	1	4	yes	complemented
519	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
520	C₂×#117	C₂²×C₁₃	1	2	yes	—
521	C₂×#117	C₂²×C₁₃	1	2	yes	complemented
522	C₂×#117	C₂²×C₁₃	1	8	yes	complemented
523	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
524	C₂²×C₄²	C₂²×C₁₃	1	2	yes	complemented
525	C₂²×C₁₃	—	2	2	no	—
526	C₂²×C₁₃	—	2	2	no	—
527	C₂²×C₁₃	—	2	2	no	—
528	C₂²×C₁₃	—	2	4	no	—
529	C₂²×C₁₃	—	2	8	no	—
530	C₂²×C₁₃	—	2	8	no	—
531	C₂²×C₁₃	—	2	16	no	—
532	C₂²×C₁₃	—	4	4	no	—
533	C₂²×C₁₃	—	4	8	no	—
534	C₂²×C₁₃	—	8	8	no	—
535	C₂²×C₁₃	C₂²×#41	1	2	yes	—
536	C₂²×C₁₃	C₂²×#41	1	2	yes	—
537	C₂²×C₁₃	C₂²×#41	1	2	yes	—
538	C₂²×C₁₃	C₂⁶	1	1	yes	characteristic
539	C₄×C₁₃	—	2	8	no	—
540	C₄×C₁₃	—	2	4	no	—
541	C₄×C₁₃	—	2	2	no	—
542	C₄×C₁₃	—	2	8	no	—
543	C₄×C₁₃	—	2	2	no	—
544	C₄×C₁₃	—	2	2	no	—
545	C₄×C₁₃	—	2	16	no	—
546	C₄×C₁₃	C₂²×#41	1	2	yes	—
547	C₄×C₁₃	C₂²×#41	1	2	yes	—
548	C₄×C₁₃	C₂²×#41	1	2	yes	—
549	C₄×C₁₃	C₂²×#41	1	2	yes	—
550	C₄×C₁₃	#585	1	4	yes	—
551	C₂×#41	—	2	8	no	—
552	C₂×#41	—	2	16	no	—
553	C₂×#41	C₂³×C₁₃	1	2	yes	—
554	C₂×#41	C₂³×C₁₃	1	2	yes	—
555	C₂×#41	C₂³×C₁₃	1	4	yes	—
556	C₂×#41	C₂³×C₁₃	1	2	yes	—
557	C₂×#41	C₂³×C₁₃	1	4	yes	—
558	C₂×#41	C₂³×C₁₃	1	2	yes	—
559	C₂×#41	C₂³×C₁₃	1	4	yes	—
560	C₂×#41	C₂³×C₁₃	1	4	yes	—
561	C₂×#41	C₂³×C₁₃	1	16	yes	—
562	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
563	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
564	C₂²×Q₈	C₂³×C₁₃	1	4	yes	—
565	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
566	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
567	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
568	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
569	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
570	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
571	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
572	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
573	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
574	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
575	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
576	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
577	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
578	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
579	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
580	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
581	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
582	C₄⋊Q₈	C₂³×C₁₃	1	8	yes	—
583	#127	C₂³×C₁₃	1	2	yes	—
584	#127	C₂³×C₁₃	1	2	yes	—
585	#127	C₂³×C₁₃	1	4	yes	—
586	#127	C₂³×C₁₃	1	8	yes	—
587	#126	C₂³×C₁₃	1	32	yes	—
588	#126	C₂³×C₁₃	1	32	yes	—
589	#126	C₂³×C₁₃	1	32	yes	—
590	#125	C₂³×C₁₃	1	4	yes	—
591	#125	C₂³×C₁₃	1	4	yes	—
592	#125	C₂³×C₁₃	1	8	yes	—
593	#125	C₂³×C₁₃	1	16	yes	—
594	#125	C₂³×C₁₃	1	32	yes	—
595	#124	C₂³×C₁₃	1	4	yes	—
596	#124	C₂³×C₁₃	1	4	yes	—
597	#124	C₂³×C₁₃	1	8	yes	—
598	#124	C₂³×C₁₃	1	16	yes	—
599	#124	C₂³×C₁₃	1	32	yes	—
600	#124	C₂³×C₁₃	1	8	yes	—
601	#124	C₂³×C₁₃	1	8	yes	—
602	#123	C₂³×C₁₃	1	16	yes	—
603	#123	C₂³×C₁₃	1	16	yes	—
604	#123	C₂³×C₁₃	1	32	yes	—
605	#123	C₂³×C₁₃	1	32	yes	—
606	#123	C₂³×C₁₃	1	32	yes	—
607	C₂²⋊Q₈	C₂³×C₁₃	1	8	yes	—
608	C₂²⋊Q₈	C₂³×C₁₃	1	8	yes	—
609	C₂²⋊Q₈	C₂³×C₁₃	1	8	yes	—
610	C₂²⋊Q₈	C₂³×C₁₃	1	8	yes	—
611	C₂²⋊Q₈	C₂³×C₁₃	1	16	yes	—
612	C₂²⋊Q₈	C₂³×C₁₃	1	16	yes	—
613	C₂²⋊Q₈	C₂³×C₁₃	1	16	yes	—
614	C₂²⋊Q₈	C₂³×C₁₃	1	32	yes	—
615	#121	C₂³×C₁₃	1	8	yes	—
616	#121	C₂³×C₁₃	1	8	yes	—
617	#121	C₂³×C₁₃	1	8	yes	—
618	#121	C₂³×C₁₃	1	8	yes	—
619	#121	C₂³×C₁₃	1	16	yes	—
620	#121	C₂³×C₁₃	1	16	yes	—
621	#121	C₂³×C₁₃	1	16	yes	—
622	#121	C₂³×C₁₃	1	32	yes	—
623	#121	C₂³×C₁₃	1	32	yes	—
624	#120	C₂³×C₁₃	1	16	yes	—
625	#120	C₂³×C₁₃	1	16	yes	—
626	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
627	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
628	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
629	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
630	C₄×Q₈	C₂³×C₁₃	1	8	yes	—
631	C₄×Q₈	C₂³×C₁₃	1	8	yes	—
632	C₄×Q₈	C₂³×C₁₃	1	8	yes	—
633	C₄×Q₈	C₂³×C₁₃	1	8	yes	—
634	C₄×Q₈	C₂³×C₁₃	1	16	yes	—
635	C₄×Q₈	C₂³×C₁₃	1	16	yes	—
636	C₄×Q₈	C₂³×C₁₃	1	16	yes	—
637	C₄×D₄	C₂³×C₁₃	1	8	yes	—
638	C₄×D₄	C₂³×C₁₃	1	8	yes	—
639	C₄×D₄	C₂³×C₁₃	1	8	yes	—
640	C₄×D₄	C₂³×C₁₃	1	8	yes	—
641	C₄×D₄	C₂³×C₁₃	1	4	yes	—
642	C₄×D₄	C₂³×C₁₃	1	4	yes	—
643	C₄×D₄	C₂³×C₁₃	1	4	yes	—
644	C₄×D₄	C₂³×C₁₃	1	4	yes	—
645	C₄×D₄	C₂³×C₁₃	1	8	yes	—
646	C₄×D₄	C₂³×C₁₃	1	8	yes	—
647	C₄×D₄	C₂³×C₁₃	1	8	yes	—
648	C₄×D₄	C₂³×C₁₃	1	8	yes	—
649	C₄×D₄	C₂³×C₁₃	1	32	yes	—
650	C₄×D₄	C₂³×C₁₃	1	32	yes	—
651	C₄×D₄	C₂³×C₁₃	1	16	yes	—
652	C₄×D₄	C₂³×C₁₃	1	16	yes	—
653	C₄×D₄	C₂³×C₁₃	1	32	yes	—
654	C₄×D₄	C₂³×C₁₃	1	32	yes	—
655	C₄×D₄	C₂³×C₁₃	1	16	yes	—
656	#117	C₂³×C₁₃	1	2	yes	—
657	#117	C₂³×C₁₃	1	4	yes	—
658	#117	C₂³×C₁₃	1	2	yes	—
659	#117	C₂³×C₁₃	1	2	yes	—
660	#117	C₂³×C₁₃	1	2	yes	—
661	#117	C₂³×C₁₃	1	4	yes	—
662	#117	C₂³×C₁₃	1	4	yes	—
663	#117	C₂³×C₁₃	1	4	yes	—
664	#117	C₂³×C₁₃	1	8	yes	—
665	#117	C₂³×C₁₃	1	4	yes	—
666	#117	C₂³×C₁₃	1	4	yes	—
667	#117	C₂³×C₁₃	1	16	yes	—
668	#117	C₂³×C₁₃	1	16	yes	—
669	#117	C₂³×C₁₃	1	16	yes	—
670	#117	C₂³×C₁₃	1	16	yes	—
671	#117	C₂³×C₁₃	1	32	yes	—
672	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
673	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
674	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
675	C₂×C₄⋊C₄	C₂³×C₁₃	1	16	yes	—
676	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
677	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
678	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
679	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
680	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
681	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
682	C₂×C₂²⋊C₄	C₂³×C₁₃	1	16	yes	—
683	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
684	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
685	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
686	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
687	C₂×C₄²	C₂³×C₁₃	1	16	yes	—
688	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
689	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
690	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
691	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
692	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
693	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
694	C₂×C₄²	C₂³×C₁₃	1	8	yes	—
695	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
696	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
697	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
698	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
699	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
700	C₂×C₁₃	—	2	2	no	—
701	C₂×C₁₃	—	2	2	no	—
702	C₂×C₁₃	—	2	2	no	—
703	C₂×C₁₃	—	4	4	no	—
704	C₂×C₁₃	—	4	8	no	—
705	C₂×C₁₃	C₂³×#41	1	1	yes	characteristic
706	C₂×C₁₃	C₂×#585	1	2	yes	—
707	C₂⁴	C₂⁴×C₁₃	1	4	yes	—
708	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
709	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
710	#41	—	2	8	no	—
711	#41	—	2	16	no	—
712	#41	—	2	8	no	—
713	#41	—	2	16	no	—
714	#41	—	2	8	no	—
715	#41	—	2	16	no	—
716	#41	—	2	8	no	—
717	#41	—	2	16	no	—
718	#41	—	4	32	no	—
719	C₂×Q₈	—	2	8	no	—
720	C₂×Q₈	—	2	4	no	—
721	C₂×Q₈	—	4	8	no	—
722	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
723	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
724	C₂×Q₈	C₂⁴×C₁₃	1	8	yes	—
725	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
726	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
727	C₂×Q₈	C₂⁴×C₁₃	1	8	yes	—
728	C₂×D₄	—	2	8	no	—
729	C₂×D₄	—	2	16	no	—
730	C₂×D₄	—	2	8	no	—
731	C₂×D₄	—	2	4	no	—
732	C₂×D₄	—	4	8	no	—
733	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
734	C₂×D₄	C₂⁴×C₁₃	1	8	yes	—
735	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
736	C₂×D₄	C₂⁴×C₁₃	1	8	yes	—
737	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
738	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
739	C₂×D₄	C₂⁴×C₁₃	1	8	yes	—
740	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
741	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
742	C₂×D₄	C₂⁴×C₁₃	1	32	yes	—
743	C₂×D₄	C₂⁴×C₁₃	1	8	yes	—
744	C₂²×C₄	—	2	16	no	—
745	C₂²×C₄	—	2	8	no	—
746	C₂²×C₄	—	4	4	no	—
747	C₂²×C₄	—	4	8	no	—
748	C₂²×C₄	C₁₃×#41	1	8	yes	complemented
749	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
750	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
751	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
752	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
753	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
754	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
755	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
756	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
757	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
758	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
759	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
760	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
761	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
762	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
763	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
764	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
765	C₂²×C₄	C₂⁴×C₁₃	1	32	yes	—
766	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
767	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
768	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
769	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
770	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
771	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
772	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
773	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
774	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
775	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
776	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
777	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
778	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
779	C₄⋊C₄	C₂⁴×C₁₃	1	32	yes	—
780	C₄⋊C₄	C₂⁴×C₁₃	1	16	yes	—
781	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
782	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
783	C₄⋊C₄	C₂⁴×C₁₃	1	16	yes	—
784	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
785	C₄⋊C₄	C₂⁴×C₁₃	1	32	yes	—
786	C₂²⋊C₄	C₂⁴×C₁₃	1	4	yes	—
787	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
788	C₂²⋊C₄	C₂⁴×C₁₃	1	4	yes	—
789	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
790	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
791	C₂²⋊C₄	C₂⁴×C₁₃	1	32	yes	—
792	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
793	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
794	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
795	C₂²⋊C₄	C₂⁴×C₁₃	1	32	yes	—
796	C₂²⋊C₄	C₂⁴×C₁₃	1	32	yes	—
797	C₄²	C₂⁴×C₁₃	1	4	yes	—
798	C₄²	C₂⁴×C₁₃	1	2	yes	—
799	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
800	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
801	C₄²	C₂⁴×C₁₃	1	4	yes	—
802	C₄²	C₂⁴×C₁₃	1	2	yes	—
803	C₄²	C₂⁴×C₁₃	1	8	yes	—
804	C₄²	C₂⁴×C₁₃	1	8	yes	—
805	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
806	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
807	C₄²	C₂⁴×C₁₃	1	2	yes	—
808	C₄²	C₂⁴×C₁₃	1	2	yes	—
809	C₄²	C₂⁴×C₁₃	1	8	yes	—
810	C₄²	C₂⁴×C₁₃	1	2	yes	—
811	C₄²	C₂⁴×C₁₃	1	2	yes	—
812	C₄²	C₂⁴×C₁₃	1	32	yes	—
813	C₄²	C₂⁴×C₁₃	1	8	yes	—
814	C₁₃	#62815	1	1	yes	characteristic, direct product factor, Sylow
815	C₂³	—	2	4	no	—
816	C₂³	—	2	8	no	—
817	C₂³	—	4	2	no	—
818	C₂³	—	4	4	no	—
819	C₂³	—	4	8	no	—
820	C₂³	C₂×C₁₃×#41	1	4	yes	—
821	C₂³	C₂⁵×C₁₃	1	4	yes	—
822	C₂³	C₂⁵×C₁₃	1	8	yes	—
823	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
824	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
825	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
826	Q₈	—	2	4	no	—
827	Q₈	—	2	8	no	—
828	Q₈	—	2	8	no	—
829	Q₈	—	2	4	no	—
830	Q₈	—	2	16	no	—
831	Q₈	—	4	8	no	—
832	D₄	—	2	8	no	—
833	D₄	—	2	16	no	—
834	D₄	—	2	8	no	—
835	D₄	—	2	16	no	—
836	D₄	—	2	4	no	—
837	D₄	—	2	8	no	—
838	D₄	—	2	4	no	—
839	D₄	—	2	8	no	—
840	D₄	—	2	16	no	—
841	D₄	—	4	8	no	—
842	D₄	—	4	32	no	—
843	C₂×C₄	—	2	8	no	—
844	C₂×C₄	—	2	4	no	—
845	C₂×C₄	—	2	8	no	—
846	C₂×C₄	—	2	16	no	—
847	C₂×C₄	—	2	16	no	—
848	C₂×C₄	—	2	8	no	—
849	C₂×C₄	—	2	4	no	—
850	C₂×C₄	—	2	4	no	—
851	C₂×C₄	—	2	4	no	—
852	C₂×C₄	—	2	16	no	—
853	C₂×C₄	—	4	4	no	—
854	C₂×C₄	—	4	8	no	—
855	C₂×C₄	—	4	2	no	—
856	C₂×C₄	—	4	2	no	—
857	C₂×C₄	—	4	2	no	—
858	C₂×C₄	—	4	8	no	—
859	C₂×C₄	—	4	32	no	—
860	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
861	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
862	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
863	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
864	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
865	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
866	C₂×C₄	C₂⁵×C₁₃	1	8	yes	—
867	C₂×C₄	C₂⁵×C₁₃	1	2	yes	—
868	C₂×C₄	C₂⁵×C₁₃	1	2	yes	—
869	C₂×C₄	C₂⁵×C₁₃	1	4	yes	—
870	C₂×C₄	C₂⁵×C₁₃	1	8	yes	—
871	C₂×C₄	C₂⁵×C₁₃	1	16	yes	—
872	C₂×C₄	C₂⁵×C₁₃	1	2	yes	—
873	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
874	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
875	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
876	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
877	C₂×C₄	C₂⁵×C₁₃	1	2	yes	—
878	C₂²	—	2	2	no	—
879	C₂²	—	2	2	no	—
880	C₂²	—	2	2	no	—
881	C₂²	—	2	4	no	—
882	C₂²	—	2	8	no	—
883	C₂²	—	2	8	no	—
884	C₂²	—	2	16	no	—
885	C₂²	—	4	4	no	—
886	C₂²	—	4	8	no	—
887	C₂²	—	8	8	no	—
888	C₂²	C₂²×C₁₃×#41	1	2	yes	—
889	C₂²	C₂²×C₁₃×#41	1	2	yes	—
890	C₂²	C₂²×C₁₃×#41	1	2	yes	—
891	C₂²	C₂⁶×C₁₃	1	1	yes	characteristic
892	C₄	—	2	8	no	—
893	C₄	—	2	4	no	—
894	C₄	—	2	2	no	—
895	C₄	—	2	8	no	—
896	C₄	—	2	2	no	—
897	C₄	—	2	2	no	—
898	C₄	—	2	16	no	—
899	C₄	C₂²×C₁₃×#41	1	2	yes	—
900	C₄	C₂²×C₁₃×#41	1	2	yes	—
901	C₄	C₂²×C₁₃×#41	1	2	yes	—
902	C₄	C₂²×C₁₃×#41	1	2	yes	—
903	C₄	C₁₃×#585	1	4	yes	—
904	C₂	—	2	2	no	—
905	C₂	—	2	2	no	—
906	C₂	—	2	2	no	—
907	C₂	—	4	4	no	—
908	C₂	—	4	8	no	—
909	C₂	C₂³×C₁₃×#41	1	1	yes	characteristic
910	C₂	C₂×C₁₃×#585	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₁₃	C₂⁵
commutator, Frattini, cosocle	C₂²	C₂⁶×C₁₃
socle	C₂²×C₁₃	C₂⁶
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×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×#3510	C₂	semidirect
4. C₁₃×#3509	C₂	semidirect
5. C₁₃×#3508	C₂	semidirect
6. C₁₃×#3507	C₂	semidirect
7. C₁₃×#3506	C₂	semidirect
8. C₁₃×#3505	C₂	semidirect
9. C₁₃×#3480	C₂	semidirect
10. C₁₃×#3475	C₂	semidirect
11. C₁₃×#3455	C₂	semidirect
12. C₁₃×#3449	C₂	semidirect
13. C₁₃×#3444	C₂	semidirect
14. C₂×C₁₃×#533	C₂	semidirect
15. C₂×C₁₃×#532	C₂	semidirect
16. C₁₃×#3428	C₂	semidirect
17. C₂×C₄×C₁₃×#41	C₂	semidirect
20. C₁₃×#559	C₂²	semidirect
21. C₁₃×#559	C₂²	semidirect
22. C₁₃×#557	C₂²	semidirect
23. C₁₃×#556	C₂²	semidirect
24. C₁₃×#556	C₂²	semidirect
25. C₁₃×#556	C₂²	semidirect
26. C₁₃×#555	C₂²	semidirect
27. C₁₃×#554	C₂²	semidirect
28. C₁₃×#553	C₂²	semidirect
29. C₁₃×#553	C₂²	semidirect
30. C₁₃×#553	C₂²	semidirect
31. C₁₃×#552	C₂²	semidirect
32. C₁₃×#552	C₂²	semidirect
33. C₁₃×#551	C₂²	semidirect
34. C₁₃×#550	C₂²	semidirect
35. C₁₃×#548	C₂²	semidirect
36. C₁₃×#547	C₂²	semidirect
37. C₁₃×#546	C₂²	semidirect
38. C₁₃×#542	C₂²	semidirect
39. C₁₃×#541	C₂²	semidirect
40. C₁₃×#540	C₂²	semidirect
41. C₁₃×#539	C₂²	semidirect
42. C₁₃×#538	C₂²	semidirect
43. C₁₃×#537	C₂²	semidirect
45. C₁₃×#536	C₂²	semidirect
47. C₁₃×#535	C₂²	semidirect
49. C₁₃×#533	C₂²	semidirect
50. C₁₃×#533	C₂²	semidirect
51. C₁₃×#533	C₂²	semidirect
52. C₁₃×#533	C₂²	semidirect
53. C₁₃×#533	C₂²	semidirect
54. C₁₃×#533	C₂²	semidirect
55. C₁₃×#533	C₂²	semidirect
59. C₁₃×#532	C₂²	semidirect
60. C₁₃×#532	C₂²	semidirect
61. C₁₃×#532	C₂²	semidirect
62. C₁₃×#532	C₂²	semidirect
63. C₁₃×#532	C₂²	semidirect
64. C₂×C₁₃×C₄⋊Q₈	C₂²	semidirect
65. C₂×C₁₃×C₄⋊Q₈	C₂²	semidirect
66. C₂×C₁₃×#127	C₂²	semidirect
67. C₁₃×#529	C₂²	semidirect
68. C₁₃×#529	C₂²	semidirect
69. C₁₃×#529	C₂²	semidirect
70. C₁₃×#529	C₂²	semidirect
71. C₂×C₁₃×#125	C₂²	semidirect
72. C₂×C₁₃×#124	C₂²	semidirect
74. C₁₃×#525	C₂²	semidirect
75. C₁₃×#525	C₂²	semidirect
78. C₁₃×#520	C₂²	semidirect
79. C₁₃×#520	C₂²	semidirect
80. C₁₃×#519	C₂²	semidirect
82. C₁₃×#518	C₂²	semidirect
86. C₄×C₁₃×#41	C₂²	semidirect
87. C₄×C₁₃×#41	C₂²	semidirect
88. C₄×C₁₃×#41	C₂²	semidirect
89. C₄×C₁₃×#41	C₂²	semidirect
90. C₄×C₁₃×#41	C₂²	semidirect
91. C₄×C₁₃×#41	C₂²	semidirect
92. C₂×C₄×Q₈×C₁₃	C₂²	semidirect
93. C₂×C₄×Q₈×C₁₃	C₂²	semidirect
95. C₂×C₄×D₄×C₁₃	C₂²	semidirect
96. C₂×C₄×D₄×C₁₃	C₂²	semidirect
99. C₂×C₁₃×#117	C₂²	semidirect
100. C₂×C₁₃×#117	C₂²	semidirect
102. C₂²×C₄²×C₁₃	C₂²	semidirect
252. #62815	C₁₃	direct (N × H)
294. C₂²×C₄×C₁₃	#41	semidirect
360. #3512	C₂×C₁₃	semidirect
361. #3511	C₂×C₁₃	semidirect
362. #3510	C₂×C₁₃	semidirect
363. #3509	C₂×C₁₃	semidirect
364. #3508	C₂×C₁₃	semidirect
365. #3507	C₂×C₁₃	semidirect
366. #3506	C₂×C₁₃	semidirect
367. #3505	C₂×C₁₃	semidirect
368. #3480	C₂×C₁₃	semidirect
369. #3475	C₂×C₁₃	semidirect
370. #3455	C₂×C₁₃	semidirect
371. #3449	C₂×C₁₃	semidirect
372. #3444	C₂×C₁₃	semidirect
373. C₂×#533	C₂×C₁₃	semidirect
374. C₂×#532	C₂×C₁₃	semidirect
375. #3428	C₂×C₁₃	semidirect
376. C₂×C₄×#41	C₂×C₁₃	semidirect
442. #559	C₂²×C₁₃	semidirect
443. #559	C₂²×C₁₃	semidirect
444. #557	C₂²×C₁₃	semidirect
445. #556	C₂²×C₁₃	semidirect
446. #556	C₂²×C₁₃	semidirect
447. #556	C₂²×C₁₃	semidirect
448. #555	C₂²×C₁₃	semidirect
449. #554	C₂²×C₁₃	semidirect
450. #553	C₂²×C₁₃	semidirect
451. #553	C₂²×C₁₃	semidirect
452. #553	C₂²×C₁₃	semidirect
453. #552	C₂²×C₁₃	semidirect
454. #552	C₂²×C₁₃	semidirect
455. #551	C₂²×C₁₃	semidirect
456. #550	C₂²×C₁₃	semidirect
457. #548	C₂²×C₁₃	semidirect
458. #547	C₂²×C₁₃	semidirect
459. #546	C₂²×C₁₃	semidirect
460. #542	C₂²×C₁₃	semidirect
461. #541	C₂²×C₁₃	semidirect
462. #540	C₂²×C₁₃	semidirect
463. #539	C₂²×C₁₃	semidirect
464. #538	C₂²×C₁₃	semidirect
465. #537	C₂²×C₁₃	semidirect
467. #536	C₂²×C₁₃	semidirect
469. #535	C₂²×C₁₃	semidirect
471. #533	C₂²×C₁₃	semidirect
472. #533	C₂²×C₁₃	semidirect
473. #533	C₂²×C₁₃	semidirect
474. #533	C₂²×C₁₃	semidirect
475. #533	C₂²×C₁₃	semidirect
476. #533	C₂²×C₁₃	semidirect
477. #533	C₂²×C₁₃	semidirect
481. #532	C₂²×C₁₃	semidirect
482. #532	C₂²×C₁₃	semidirect
483. #532	C₂²×C₁₃	semidirect
484. #532	C₂²×C₁₃	semidirect
485. #532	C₂²×C₁₃	semidirect
486. C₂×C₄⋊Q₈	C₂²×C₁₃	semidirect
487. C₂×C₄⋊Q₈	C₂²×C₁₃	semidirect
488. C₂×#127	C₂²×C₁₃	semidirect
489. #529	C₂²×C₁₃	semidirect
490. #529	C₂²×C₁₃	semidirect
491. #529	C₂²×C₁₃	semidirect
492. #529	C₂²×C₁₃	semidirect
493. C₂×#125	C₂²×C₁₃	semidirect
494. C₂×#124	C₂²×C₁₃	semidirect
496. #525	C₂²×C₁₃	semidirect
497. #525	C₂²×C₁₃	semidirect
500. #520	C₂²×C₁₃	semidirect
501. #520	C₂²×C₁₃	semidirect
502. #519	C₂²×C₁₃	semidirect
504. #518	C₂²×C₁₃	semidirect
508. C₄×#41	C₂²×C₁₃	semidirect
509. C₄×#41	C₂²×C₁₃	semidirect
510. C₄×#41	C₂²×C₁₃	semidirect
511. C₄×#41	C₂²×C₁₃	semidirect
512. C₄×#41	C₂²×C₁₃	semidirect
513. C₄×#41	C₂²×C₁₃	semidirect
514. C₂×C₄×Q₈	C₂²×C₁₃	semidirect
515. C₂×C₄×Q₈	C₂²×C₁₃	semidirect
517. C₂×C₄×D₄	C₂²×C₁₃	semidirect
518. C₂×C₄×D₄	C₂²×C₁₃	semidirect
521. C₂×#117	C₂²×C₁₃	semidirect
522. C₂×#117	C₂²×C₁₃	semidirect
524. C₂²×C₄²	C₂²×C₁₃	semidirect
748. C₂²×C₄	C₁₃×#41	semidirect
814. C₁₃	#62815	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×#3510	2
C₁₃×#3509	2
C₁₃×#3508	2
C₁₃×#3507	2
C₁₃×#3506	2
C₁₃×#3505	2
C₁₃×#3480	2
C₁₃×#3475	2
C₁₃×#3455	2
C₁₃×#3449	2
C₁₃×#3444	2
C₂×C₁₃×#533	2
C₂×C₁₃×#532	2
C₁₃×#3428	2
C₂×C₄×C₁₃×#41	2
#62815	13

Subgroups — C13×#62815 #15749154

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#62815 #15749154