Subgroups — C₁₃×#62888 #15749227

Order 3328.

6906 conjugacy classes of subgroups.

The subgroup lattice has 904 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3562	C₂	1	8	yes	maximal, complemented
2	C₁₃×#3560	C₂	1	8	yes	maximal, complemented
3	C₁₃×#3559	C₂	1	8	yes	maximal, complemented
4	C₁₃×#3552	C₂	1	8	yes	maximal, complemented
5	C₁₃×#3541	C₂	1	8	yes	maximal, complemented
6	C₁₃×#3539	C₂	1	4	yes	maximal, complemented
7	C₁₃×#3538	C₂	1	4	yes	maximal, complemented
8	C₁₃×#3512	C₂	1	2	yes	maximal, complemented
9	C₁₃×#3507	C₂	1	2	yes	maximal, complemented
10	C₁₃×#3499	C₂	1	2	yes	maximal, complemented
11	C₁₃×#3497	C₂	1	2	yes	maximal, complemented
12	C₁₃×#3489	C₂	1	4	yes	maximal, complemented
13	C₁₃×#3455	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₁₃×#541	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#3449	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₁₃×2₋¹⁺⁴	C₂²	1	4	yes	complemented
17	C₂²×C₁₃×#41	C₂²	1	2	yes	—
18	C₁₃×#563	C₂²	1	16	yes	complemented
19	C₁₃×#563	C₂²	1	16	yes	complemented
20	C₁₃×#562	C₂²	1	16	yes	complemented
21	C₁₃×#560	C₂²	1	16	yes	complemented
22	C₁₃×#559	C₂²	1	4	yes	complemented
23	C₁₃×#557	C₂²	1	4	yes	complemented
24	C₁₃×#556	C₂²	1	4	yes	complemented
25	C₁₃×#556	C₂²	1	8	yes	complemented
26	C₁₃×#554	C₂²	1	4	yes	complemented
27	C₁₃×#554	C₂²	1	16	yes	complemented
28	C₁₃×#553	C₂²	1	8	yes	complemented
29	C₁₃×#553	C₂²	1	16	yes	complemented
30	C₁₃×#553	C₂²	1	16	yes	complemented
31	C₁₃×#553	C₂²	1	16	yes	complemented
32	C₁₃×#552	C₂²	1	8	yes	complemented
33	C₁₃×#552	C₂²	1	8	yes	complemented
34	C₁₃×#551	C₂²	1	16	yes	complemented
35	C₁₃×#550	C₂²	1	4	yes	complemented
36	C₁₃×#550	C₂²	1	4	yes	complemented
37	D₄×Q₈×C₁₃	C₂²	1	4	yes	complemented
38	D₄×Q₈×C₁₃	C₂²	1	8	yes	complemented
39	D₄×Q₈×C₁₃	C₂²	1	8	yes	complemented
40	D₄×Q₈×C₁₃	C₂²	1	4	yes	complemented
41	C₁₃×#548	C₂²	1	8	yes	—
42	C₁₃×#548	C₂²	1	8	yes	complemented
43	C₁₃×#548	C₂²	1	8	yes	complemented
44	C₁₃×#547	C₂²	1	8	yes	—
45	C₁₃×#547	C₂²	1	8	yes	complemented
46	C₁₃×#547	C₂²	1	16	yes	complemented
47	C₁₃×#547	C₂²	1	16	yes	complemented
48	C₁₃×#546	C₂²	1	16	yes	—
49	C₁₃×#546	C₂²	1	8	yes	complemented
50	C₁₃×#544	C₂²	1	16	yes	complemented
51	C₁₃×#542	C₂²	1	4	yes	complemented
52	C₁₃×#542	C₂²	1	16	yes	complemented
53	C₁₃×#541	C₂²	1	2	yes	complemented
54	C₁₃×#541	C₂²	1	4	yes	complemented
55	C₁₃×#541	C₂²	1	4	yes	complemented
56	C₁₃×#541	C₂²	1	4	yes	complemented
57	C₁₃×#541	C₂²	1	8	yes	complemented
58	C₁₃×#540	C₂²	1	2	yes	complemented
59	C₁₃×#540	C₂²	1	16	yes	complemented
60	C₁₃×#540	C₂²	1	4	yes	complemented
61	C₁₃×#539	C₂²	1	16	yes	complemented
62	C₁₃×#539	C₂²	1	16	yes	complemented
63	C₁₃×#539	C₂²	1	16	yes	complemented
64	C₁₃×#539	C₂²	1	4	yes	complemented
65	C₁₃×#539	C₂²	1	8	yes	complemented
66	C₁₃×#538	C₂²	1	4	yes	—
67	C₁₃×#538	C₂²	1	16	yes	complemented
68	C₁₃×#538	C₂²	1	16	yes	complemented
69	C₁₃×#537	C₂²	1	8	yes	—
70	C₁₃×#537	C₂²	1	4	yes	—
71	C₁₃×#537	C₂²	1	8	yes	complemented
72	C₁₃×#537	C₂²	1	4	yes	complemented
73	C₁₃×#536	C₂²	1	8	yes	—
74	C₁₃×#536	C₂²	1	4	yes	—
75	C₁₃×#536	C₂²	1	8	yes	complemented
76	C₁₃×#536	C₂²	1	4	yes	complemented
77	C₁₃×#535	C₂²	1	4	yes	—
78	C₁₃×#534	C₂²	1	4	yes	—
79	C₁₃×#533	C₂²	1	1	yes	characteristic, complemented
80	C₁₃×#532	C₂²	1	2	yes	—
81	C₁₃×#532	C₂²	1	2	yes	—
82	C₁₃×#532	C₂²	1	8	yes	complemented
83	C₁₃×#532	C₂²	1	4	yes	complemented
84	C₁₃×#532	C₂²	1	1	yes	characteristic, complemented
85	C₂×C₁₃×C₄⋊Q₈	C₂²	1	4	yes	complemented
86	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
87	C₁₃×#529	C₂²	1	8	yes	complemented
88	C₁₃×#529	C₂²	1	8	yes	complemented
89	C₁₃×#529	C₂²	1	8	yes	complemented
90	C₂×C₁₃×#126	C₂²	1	4	yes	—
91	C₂×C₁₃×#125	C₂²	1	4	yes	complemented
92	C₂×C₁₃×#125	C₂²	1	1	yes	characteristic, complemented
93	C₁₃×#525	C₂²	1	4	yes	—
94	C₁₃×#525	C₂²	1	4	yes	—
95	C₁₃×#525	C₂²	1	2	yes	—
96	C₁₃×#525	C₂²	1	8	yes	complemented
97	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
98	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	8	yes	complemented
99	C₁₃×#520	C₂²	1	4	yes	complemented
100	C₄×C₁₃×#41	C₂²	1	2	yes	complemented
101	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	complemented
102	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
103	C₁₃×2₋¹⁺⁴	—	4	16	no	—
104	C₂×C₁₃×#41	—	4	8	no	—
105	C₂×C₁₃×#41	C₂³	1	2	yes	—
106	C₂×C₁₃×#41	C₂³	1	4	yes	—
107	C₂×C₁₃×#41	C₂³	1	4	yes	—
108	C₂×C₁₃×#41	C₂³	1	8	yes	—
109	C₂×C₁₃×#41	C₂³	1	8	yes	—
110	C₂×C₁₃×#41	C₂³	1	16	yes	—
111	C₂×C₁₃×#41	C₂³	1	4	yes	—
112	C₂×C₁₃×#41	C₂³	1	4	yes	—
113	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
114	C₂²×Q₈×C₁₃	C₂³	1	8	yes	—
115	C₂²×Q₈×C₁₃	C₂³	1	8	yes	—
116	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
117	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
118	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
119	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
120	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
121	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
122	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
123	C₁₃×C₄⋊Q₈	C₂³	1	8	yes	—
124	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
125	C₁₃×C₄⋊Q₈	C₂³	1	16	yes	—
126	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
127	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
128	C₁₃×C₄⋊Q₈	C₂³	1	8	yes	—
129	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
130	C₁₃×C₄⋊Q₈	C₂³	1	16	yes	—
131	C₁₃×#127	C₂³	1	2	yes	—
132	C₁₃×#127	C₂³	1	2	yes	—
133	C₁₃×#127	C₂³	1	1	yes	characteristic
134	C₁₃×#127	C₂³	1	8	yes	—
135	C₁₃×#126	C₂³	1	16	yes	—
136	C₁₃×#126	C₂³	1	16	yes	—
137	C₁₃×#126	C₂³	1	8	yes	—
138	C₁₃×#126	C₂³	1	16	yes	—
139	C₁₃×#126	C₂³	1	16	yes	—
140	C₁₃×#126	C₂³	1	8	yes	—
141	C₁₃×#126	C₂³	1	16	yes	—
142	C₁₃×#126	C₂³	1	16	yes	—
143	C₁₃×#125	C₂³	1	4	yes	—
144	C₁₃×#125	C₂³	1	16	yes	—
145	C₁₃×#125	C₂³	1	4	yes	—
146	C₁₃×#125	C₂³	1	16	yes	—
147	C₁₃×#125	C₂³	1	8	yes	—
148	C₁₃×#125	C₂³	1	8	yes	—
149	C₁₃×#125	C₂³	1	2	yes	—
150	C₁₃×#125	C₂³	1	16	yes	—
151	C₁₃×#125	C₂³	1	16	yes	—
152	C₁₃×#124	C₂³	1	4	yes	—
153	C₁₃×#124	C₂³	1	8	yes	—
154	C₁₃×#124	C₂³	1	8	yes	—
155	C₁₃×#124	C₂³	1	4	yes	—
156	C₁₃×#124	C₂³	1	8	yes	—
157	C₁₃×#124	C₂³	1	16	yes	—
158	C₁₃×#124	C₂³	1	2	yes	—
159	C₁₃×#124	C₂³	1	16	yes	—
160	C₁₃×#123	C₂³	1	8	yes	—
161	C₁₃×#123	C₂³	1	8	yes	—
162	C₁₃×#123	C₂³	1	4	yes	—
163	C₁₃×#123	C₂³	1	16	yes	—
164	C₁₃×#123	C₂³	1	16	yes	—
165	C₁₃×#123	C₂³	1	8	yes	—
166	C₁₃×#123	C₂³	1	8	yes	—
167	C₁₃×#123	C₂³	1	16	yes	—
168	C₁₃×#123	C₂³	1	16	yes	—
169	C₁₃×#123	C₂³	1	16	yes	—
170	C₁₃×#123	C₂³	1	16	yes	—
171	C₁₃×#123	C₂³	1	16	yes	—
172	C₁₃×#123	C₂³	1	16	yes	—
173	C₁₃×#123	C₂³	1	16	yes	—
174	C₁₃×C₂²⋊Q₈	C₂³	1	8	yes	—
175	C₁₃×C₂²⋊Q₈	C₂³	1	8	yes	—
176	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
177	C₁₃×C₂²⋊Q₈	C₂³	1	8	yes	—
178	C₁₃×C₂²⋊Q₈	C₂³	1	8	yes	—
179	C₁₃×C₂²⋊Q₈	C₂³	1	16	yes	—
180	C₁₃×C₂²⋊Q₈	C₂³	1	16	yes	—
181	C₁₃×C₂²⋊Q₈	C₂³	1	8	yes	—
182	C₁₃×C₂²⋊Q₈	C₂³	1	8	yes	—
183	C₁₃×C₂²⋊Q₈	C₂³	1	8	yes	—
184	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
185	C₁₃×C₂²⋊Q₈	C₂³	1	8	yes	—
186	C₁₃×C₂²⋊Q₈	C₂³	1	8	yes	—
187	C₁₃×C₂²⋊Q₈	C₂³	1	16	yes	—
188	C₁₃×C₂²⋊Q₈	C₂³	1	16	yes	—
189	C₁₃×C₂²⋊Q₈	C₂³	1	16	yes	—
190	C₁₃×C₂²⋊Q₈	C₂³	1	16	yes	—
191	C₁₃×C₂²⋊Q₈	C₂³	1	16	yes	—
192	C₁₃×C₂²⋊Q₈	C₂³	1	16	yes	—
193	C₁₃×#121	C₂³	1	4	yes	—
194	C₁₃×#121	C₂³	1	8	yes	—
195	C₁₃×#121	C₂³	1	8	yes	—
196	C₁₃×#121	C₂³	1	8	yes	—
197	C₁₃×#121	C₂³	1	4	yes	—
198	C₁₃×#121	C₂³	1	8	yes	—
199	C₁₃×#121	C₂³	1	8	yes	—
200	C₁₃×#121	C₂³	1	4	yes	—
201	C₁₃×#121	C₂³	1	8	yes	—
202	C₁₃×#121	C₂³	1	4	yes	—
203	C₁₃×#121	C₂³	1	16	yes	—
204	C₁₃×#121	C₂³	1	16	yes	—
205	C₁₃×#121	C₂³	1	16	yes	—
206	C₁₃×#121	C₂³	1	16	yes	—
207	C₁₃×#121	C₂³	1	16	yes	—
208	C₁₃×#121	C₂³	1	16	yes	—
209	C₁₃×#121	C₂³	1	16	yes	—
210	C₁₃×#121	C₂³	1	16	yes	—
211	C₁₃×#120	C₂³	1	8	yes	—
212	C₁₃×#120	C₂³	1	8	yes	—
213	C₁₃×#120	C₂³	1	4	yes	—
214	C₁₃×#120	C₂³	1	16	yes	—
215	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
216	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
217	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
218	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
219	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
220	C₄×Q₈×C₁₃	C₂³	1	8	yes	—
221	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
222	C₄×Q₈×C₁₃	C₂³	1	8	yes	—
223	C₄×D₄×C₁₃	C₂³	1	8	yes	—
224	C₄×D₄×C₁₃	C₂³	1	4	yes	—
225	C₄×D₄×C₁₃	C₂³	1	16	yes	—
226	C₄×D₄×C₁₃	C₂³	1	8	yes	—
227	C₄×D₄×C₁₃	C₂³	1	8	yes	—
228	C₄×D₄×C₁₃	C₂³	1	4	yes	—
229	C₄×D₄×C₁₃	C₂³	1	4	yes	—
230	C₄×D₄×C₁₃	C₂³	1	8	yes	—
231	C₄×D₄×C₁₃	C₂³	1	16	yes	—
232	C₄×D₄×C₁₃	C₂³	1	16	yes	—
233	C₄×D₄×C₁₃	C₂³	1	4	yes	—
234	C₄×D₄×C₁₃	C₂³	1	8	yes	—
235	C₄×D₄×C₁₃	C₂³	1	16	yes	—
236	C₄×D₄×C₁₃	C₂³	1	16	yes	—
237	C₄×D₄×C₁₃	C₂³	1	16	yes	—
238	C₄×D₄×C₁₃	C₂³	1	8	yes	—
239	C₄×D₄×C₁₃	C₂³	1	8	yes	—
240	C₁₃×#117	C₂³	1	2	yes	—
241	C₁₃×#117	C₂³	1	2	yes	—
242	C₁₃×#117	C₂³	1	4	yes	—
243	C₁₃×#117	C₂³	1	2	yes	—
244	C₁₃×#117	C₂³	1	4	yes	—
245	C₁₃×#117	C₂³	1	8	yes	—
246	C₁₃×#117	C₂³	1	16	yes	—
247	C₁₃×#117	C₂³	1	16	yes	—
248	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
249	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
250	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
251	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
252	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
253	C₂×C₁₃×C₄⋊C₄	C₂³	1	16	yes	—
254	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
255	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
256	C₂×C₁₃×C₄⋊C₄	C₂³	1	16	yes	—
257	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
258	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
259	C₂×C₁₃×C₂²⋊C₄	C₂³	1	16	yes	—
260	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
261	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
262	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
263	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
264	#62888	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
265	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
266	C₂⁴×C₁₃	C₂⁴	1	4	yes	—
267	C₁₃×#41	—	2	16	no	—
268	C₁₃×#41	—	2	8	no	—
269	C₁₃×#41	—	4	8	no	—
270	C₁₃×#41	—	4	8	no	—
271	C₁₃×#41	—	4	32	no	—
272	C₁₃×#41	—	4	8	no	—
273	C₁₃×#41	—	4	16	no	—
274	C₁₃×#41	—	4	16	no	—
275	C₂×Q₈×C₁₃	—	2	8	no	—
276	C₂×Q₈×C₁₃	—	4	4	no	—
277	C₂×Q₈×C₁₃	—	4	16	no	—
278	C₂×Q₈×C₁₃	—	4	16	no	—
279	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
280	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
281	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
282	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
283	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
284	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
285	C₂×Q₈×C₁₃	C₂⁴	1	16	yes	—
286	C₂×D₄×C₁₃	—	4	4	no	—
287	C₂×D₄×C₁₃	—	4	8	no	—
288	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
289	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
290	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
291	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
292	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
293	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
294	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
295	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
296	C₂×D₄×C₁₃	C₂⁴	1	16	yes	—
297	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
298	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
299	C₂×D₄×C₁₃	C₂⁴	1	16	yes	—
300	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
301	C₂²×C₄×C₁₃	—	2	4	no	—
302	C₂²×C₄×C₁₃	—	4	8	no	—
303	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
304	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
305	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
306	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
307	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
308	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
309	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
310	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
311	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
312	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
313	C₂²×C₄×C₁₃	C₂⁴	1	16	yes	—
314	C₂²×C₄×C₁₃	C₂⁴	1	16	yes	—
315	C₂²×C₄×C₁₃	C₂⁴	1	16	yes	—
316	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
317	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
318	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
319	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
320	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
321	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
322	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
323	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
324	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
325	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
326	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
327	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
328	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
329	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
330	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
331	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
332	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
333	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
334	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
335	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
336	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
337	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
338	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
339	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
340	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
341	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
342	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
343	C₁₃×C₂²⋊C₄	C₂⁴	1	4	yes	—
344	C₁₃×C₂²⋊C₄	C₂⁴	1	4	yes	—
345	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
346	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
347	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
348	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
349	C₁₃×C₂²⋊C₄	C₂⁴	1	4	yes	—
350	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
351	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
352	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
353	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
354	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
355	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
356	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
357	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
358	C₄²×C₁₃	C₂⁴	1	2	yes	—
359	C₄²×C₁₃	C₂⁴	1	2	yes	—
360	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
361	C₄²×C₁₃	C₂⁴	1	4	yes	—
362	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
363	C₄²×C₁₃	C₂⁴	1	8	yes	—
364	C₄²×C₁₃	C₂⁴	1	2	yes	—
365	C₄²×C₁₃	C₂⁴	1	8	yes	—
366	C₄²×C₁₃	C₂⁴	1	8	yes	—
367	C₄²×C₁₃	C₂⁴	1	16	yes	—
368	#3562	C₂×C₁₃	1	8	yes	complemented
369	#3560	C₂×C₁₃	1	8	yes	complemented
370	#3559	C₂×C₁₃	1	8	yes	complemented
371	#3552	C₂×C₁₃	1	8	yes	complemented
372	#3541	C₂×C₁₃	1	8	yes	complemented
373	#3539	C₂×C₁₃	1	4	yes	complemented
374	#3538	C₂×C₁₃	1	4	yes	complemented
375	#3512	C₂×C₁₃	1	2	yes	complemented
376	#3507	C₂×C₁₃	1	2	yes	complemented
377	#3499	C₂×C₁₃	1	2	yes	complemented
378	#3497	C₂×C₁₃	1	2	yes	complemented
379	#3489	C₂×C₁₃	1	4	yes	complemented
380	#3455	C₂×C₁₃	1	1	yes	characteristic, complemented
381	C₂×#541	C₂×C₁₃	1	1	yes	characteristic, complemented
382	#3449	C₂×C₁₃	1	1	yes	characteristic, complemented
383	C₂³×C₁₃	—	2	2	no	—
384	C₂³×C₁₃	—	4	4	no	—
385	C₂³×C₁₃	—	4	2	no	—
386	C₂³×C₁₃	—	4	8	no	—
387	C₂³×C₁₃	C₂⁵	1	2	yes	—
388	C₂³×C₁₃	C₂⁵	1	8	yes	—
389	C₂³×C₁₃	C₂⁵	1	4	yes	—
390	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
391	Q₈×C₁₃	—	2	8	no	—
392	Q₈×C₁₃	—	2	8	no	—
393	Q₈×C₁₃	—	2	4	no	—
394	Q₈×C₁₃	—	2	8	no	—
395	Q₈×C₁₃	—	4	16	no	—
396	Q₈×C₁₃	—	4	4	no	—
397	Q₈×C₁₃	—	4	4	no	—
398	D₄×C₁₃	—	2	16	no	—
399	D₄×C₁₃	—	2	8	no	—
400	D₄×C₁₃	—	2	8	no	—
401	D₄×C₁₃	—	2	4	no	—
402	D₄×C₁₃	—	4	4	no	—
403	D₄×C₁₃	—	4	8	no	—
404	D₄×C₁₃	—	4	8	no	—
405	D₄×C₁₃	—	4	16	no	—
406	D₄×C₁₃	—	4	8	no	—
407	D₄×C₁₃	—	4	4	no	—
408	D₄×C₁₃	—	4	4	no	—
409	D₄×C₁₃	—	4	4	no	—
410	D₄×C₁₃	—	4	16	no	—
411	C₂×C₄×C₁₃	—	2	2	no	—
412	C₂×C₄×C₁₃	—	2	8	no	—
413	C₂×C₄×C₁₃	—	2	4	no	—
414	C₂×C₄×C₁₃	—	2	4	no	—
415	C₂×C₄×C₁₃	—	2	16	no	—
416	C₂×C₄×C₁₃	—	2	8	no	—
417	C₂×C₄×C₁₃	—	4	4	no	—
418	C₂×C₄×C₁₃	—	4	8	no	—
419	C₂×C₄×C₁₃	—	4	2	no	—
420	C₂×C₄×C₁₃	—	4	4	no	—
421	C₂×C₄×C₁₃	—	4	16	no	—
422	C₂×C₄×C₁₃	—	4	8	no	—
423	C₂×C₄×C₁₃	—	4	2	no	—
424	C₂×C₄×C₁₃	—	4	16	no	—
425	C₂×C₄×C₁₃	—	4	16	no	—
426	C₂×C₄×C₁₃	H(5,𝔽₂)	1	4	yes	—
427	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
428	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
429	C₂×C₄×C₁₃	C₂⁵	1	8	yes	—
430	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
431	C₂×C₄×C₁₃	C₂⁵	1	8	yes	—
432	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
433	C₂×C₄×C₁₃	C₂⁵	1	8	yes	—
434	C₂×C₄×C₁₃	C₂⁵	1	8	yes	—
435	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
436	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
437	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
438	C₂×2₋¹⁺⁴	C₂²×C₁₃	1	4	yes	complemented
439	C₂²×#41	C₂²×C₁₃	1	2	yes	—
440	#563	C₂²×C₁₃	1	16	yes	complemented
441	#563	C₂²×C₁₃	1	16	yes	complemented
442	#562	C₂²×C₁₃	1	16	yes	complemented
443	#560	C₂²×C₁₃	1	16	yes	complemented
444	#559	C₂²×C₁₃	1	4	yes	complemented
445	#557	C₂²×C₁₃	1	4	yes	complemented
446	#556	C₂²×C₁₃	1	4	yes	complemented
447	#556	C₂²×C₁₃	1	8	yes	complemented
448	#554	C₂²×C₁₃	1	4	yes	complemented
449	#554	C₂²×C₁₃	1	16	yes	complemented
450	#553	C₂²×C₁₃	1	8	yes	complemented
451	#553	C₂²×C₁₃	1	16	yes	complemented
452	#553	C₂²×C₁₃	1	16	yes	complemented
453	#553	C₂²×C₁₃	1	16	yes	complemented
454	#552	C₂²×C₁₃	1	8	yes	complemented
455	#552	C₂²×C₁₃	1	8	yes	complemented
456	#551	C₂²×C₁₃	1	16	yes	complemented
457	#550	C₂²×C₁₃	1	4	yes	complemented
458	#550	C₂²×C₁₃	1	4	yes	complemented
459	D₄×Q₈	C₂²×C₁₃	1	8	yes	complemented
460	D₄×Q₈	C₂²×C₁₃	1	4	yes	complemented
461	D₄×Q₈	C₂²×C₁₃	1	4	yes	complemented
462	D₄×Q₈	C₂²×C₁₃	1	8	yes	complemented
463	#548	C₂²×C₁₃	1	8	yes	—
464	#548	C₂²×C₁₃	1	8	yes	complemented
465	#548	C₂²×C₁₃	1	8	yes	complemented
466	#547	C₂²×C₁₃	1	8	yes	—
467	#547	C₂²×C₁₃	1	16	yes	complemented
468	#547	C₂²×C₁₃	1	8	yes	complemented
469	#547	C₂²×C₁₃	1	16	yes	complemented
470	#546	C₂²×C₁₃	1	16	yes	—
471	#546	C₂²×C₁₃	1	8	yes	complemented
472	#544	C₂²×C₁₃	1	16	yes	complemented
473	#542	C₂²×C₁₃	1	4	yes	complemented
474	#542	C₂²×C₁₃	1	16	yes	complemented
475	#541	C₂²×C₁₃	1	4	yes	complemented
476	#541	C₂²×C₁₃	1	4	yes	complemented
477	#541	C₂²×C₁₃	1	8	yes	complemented
478	#541	C₂²×C₁₃	1	2	yes	complemented
479	#541	C₂²×C₁₃	1	4	yes	complemented
480	#540	C₂²×C₁₃	1	2	yes	complemented
481	#540	C₂²×C₁₃	1	4	yes	complemented
482	#540	C₂²×C₁₃	1	16	yes	complemented
483	#539	C₂²×C₁₃	1	4	yes	complemented
484	#539	C₂²×C₁₃	1	8	yes	complemented
485	#539	C₂²×C₁₃	1	16	yes	complemented
486	#539	C₂²×C₁₃	1	16	yes	complemented
487	#539	C₂²×C₁₃	1	16	yes	complemented
488	#538	C₂²×C₁₃	1	4	yes	—
489	#538	C₂²×C₁₃	1	16	yes	complemented
490	#538	C₂²×C₁₃	1	16	yes	complemented
491	#537	C₂²×C₁₃	1	4	yes	—
492	#537	C₂²×C₁₃	1	8	yes	—
493	#537	C₂²×C₁₃	1	4	yes	complemented
494	#537	C₂²×C₁₃	1	8	yes	complemented
495	#536	C₂²×C₁₃	1	4	yes	—
496	#536	C₂²×C₁₃	1	8	yes	—
497	#536	C₂²×C₁₃	1	4	yes	complemented
498	#536	C₂²×C₁₃	1	8	yes	complemented
499	#535	C₂²×C₁₃	1	4	yes	—
500	#534	C₂²×C₁₃	1	4	yes	—
501	#533	C₂²×C₁₃	1	1	yes	characteristic, complemented
502	#532	C₂²×C₁₃	1	2	yes	—
503	#532	C₂²×C₁₃	1	2	yes	—
504	#532	C₂²×C₁₃	1	1	yes	characteristic, complemented
505	#532	C₂²×C₁₃	1	8	yes	complemented
506	#532	C₂²×C₁₃	1	4	yes	complemented
507	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
508	C₂×C₄⋊Q₈	C₂²×C₁₃	1	4	yes	complemented
509	#529	C₂²×C₁₃	1	8	yes	complemented
510	#529	C₂²×C₁₃	1	8	yes	complemented
511	#529	C₂²×C₁₃	1	8	yes	complemented
512	C₂×#126	C₂²×C₁₃	1	4	yes	—
513	C₂×#125	C₂²×C₁₃	1	1	yes	characteristic, complemented
514	C₂×#125	C₂²×C₁₃	1	4	yes	complemented
515	#525	C₂²×C₁₃	1	4	yes	—
516	#525	C₂²×C₁₃	1	4	yes	—
517	#525	C₂²×C₁₃	1	2	yes	—
518	#525	C₂²×C₁₃	1	8	yes	complemented
519	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
520	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	8	yes	complemented
521	#520	C₂²×C₁₃	1	4	yes	complemented
522	C₄×#41	C₂²×C₁₃	1	2	yes	complemented
523	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	complemented
524	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
525	C₂²×C₁₃	—	2	2	no	—
526	C₂²×C₁₃	—	2	2	no	—
527	C₂²×C₁₃	—	2	4	no	—
528	C₂²×C₁₃	—	2	8	no	—
529	C₂²×C₁₃	—	2	8	no	—
530	C₂²×C₁₃	—	2	8	no	—
531	C₂²×C₁₃	—	2	8	no	—
532	C₂²×C₁₃	—	2	4	no	—
533	C₂²×C₁₃	—	8	2	no	—
534	C₂²×C₁₃	—	8	8	no	—
535	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
536	C₂²×C₁₃	C₂⁶	1	1	yes	characteristic
537	C₄×C₁₃	—	2	2	no	—
538	C₄×C₁₃	—	2	8	no	—
539	C₄×C₁₃	—	2	4	no	—
540	C₄×C₁₃	—	2	8	no	—
541	C₄×C₁₃	—	2	8	no	—
542	C₄×C₁₃	—	2	4	no	—
543	C₄×C₁₃	—	2	8	no	—
544	C₄×C₁₃	—	2	2	no	—
545	C₄×C₁₃	—	2	2	no	—
546	C₄×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
547	C₄×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
548	2₋¹⁺⁴	—	4	16	no	—
549	C₂×#41	—	4	8	no	—
550	C₂×#41	C₂³×C₁₃	1	2	yes	—
551	C₂×#41	C₂³×C₁₃	1	4	yes	—
552	C₂×#41	C₂³×C₁₃	1	4	yes	—
553	C₂×#41	C₂³×C₁₃	1	8	yes	—
554	C₂×#41	C₂³×C₁₃	1	8	yes	—
555	C₂×#41	C₂³×C₁₃	1	16	yes	—
556	C₂×#41	C₂³×C₁₃	1	4	yes	—
557	C₂×#41	C₂³×C₁₃	1	4	yes	—
558	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
559	C₂²×Q₈	C₂³×C₁₃	1	8	yes	—
560	C₂²×Q₈	C₂³×C₁₃	1	8	yes	—
561	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
562	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
563	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
564	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
565	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
566	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
567	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
568	C₄⋊Q₈	C₂³×C₁₃	1	8	yes	—
569	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
570	C₄⋊Q₈	C₂³×C₁₃	1	16	yes	—
571	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
572	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
573	C₄⋊Q₈	C₂³×C₁₃	1	8	yes	—
574	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
575	C₄⋊Q₈	C₂³×C₁₃	1	16	yes	—
576	#127	C₂³×C₁₃	1	2	yes	—
577	#127	C₂³×C₁₃	1	2	yes	—
578	#127	C₂³×C₁₃	1	1	yes	characteristic
579	#127	C₂³×C₁₃	1	8	yes	—
580	#126	C₂³×C₁₃	1	16	yes	—
581	#126	C₂³×C₁₃	1	16	yes	—
582	#126	C₂³×C₁₃	1	8	yes	—
583	#126	C₂³×C₁₃	1	16	yes	—
584	#126	C₂³×C₁₃	1	16	yes	—
585	#126	C₂³×C₁₃	1	8	yes	—
586	#126	C₂³×C₁₃	1	16	yes	—
587	#126	C₂³×C₁₃	1	16	yes	—
588	#125	C₂³×C₁₃	1	4	yes	—
589	#125	C₂³×C₁₃	1	16	yes	—
590	#125	C₂³×C₁₃	1	4	yes	—
591	#125	C₂³×C₁₃	1	16	yes	—
592	#125	C₂³×C₁₃	1	8	yes	—
593	#125	C₂³×C₁₃	1	8	yes	—
594	#125	C₂³×C₁₃	1	2	yes	—
595	#125	C₂³×C₁₃	1	16	yes	—
596	#125	C₂³×C₁₃	1	16	yes	—
597	#124	C₂³×C₁₃	1	4	yes	—
598	#124	C₂³×C₁₃	1	8	yes	—
599	#124	C₂³×C₁₃	1	8	yes	—
600	#124	C₂³×C₁₃	1	4	yes	—
601	#124	C₂³×C₁₃	1	8	yes	—
602	#124	C₂³×C₁₃	1	16	yes	—
603	#124	C₂³×C₁₃	1	2	yes	—
604	#124	C₂³×C₁₃	1	16	yes	—
605	#123	C₂³×C₁₃	1	8	yes	—
606	#123	C₂³×C₁₃	1	8	yes	—
607	#123	C₂³×C₁₃	1	4	yes	—
608	#123	C₂³×C₁₃	1	16	yes	—
609	#123	C₂³×C₁₃	1	16	yes	—
610	#123	C₂³×C₁₃	1	8	yes	—
611	#123	C₂³×C₁₃	1	8	yes	—
612	#123	C₂³×C₁₃	1	16	yes	—
613	#123	C₂³×C₁₃	1	16	yes	—
614	#123	C₂³×C₁₃	1	16	yes	—
615	#123	C₂³×C₁₃	1	16	yes	—
616	#123	C₂³×C₁₃	1	16	yes	—
617	#123	C₂³×C₁₃	1	16	yes	—
618	#123	C₂³×C₁₃	1	16	yes	—
619	C₂²⋊Q₈	C₂³×C₁₃	1	8	yes	—
620	C₂²⋊Q₈	C₂³×C₁₃	1	8	yes	—
621	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
622	C₂²⋊Q₈	C₂³×C₁₃	1	8	yes	—
623	C₂²⋊Q₈	C₂³×C₁₃	1	8	yes	—
624	C₂²⋊Q₈	C₂³×C₁₃	1	16	yes	—
625	C₂²⋊Q₈	C₂³×C₁₃	1	16	yes	—
626	C₂²⋊Q₈	C₂³×C₁₃	1	8	yes	—
627	C₂²⋊Q₈	C₂³×C₁₃	1	8	yes	—
628	C₂²⋊Q₈	C₂³×C₁₃	1	8	yes	—
629	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
630	C₂²⋊Q₈	C₂³×C₁₃	1	8	yes	—
631	C₂²⋊Q₈	C₂³×C₁₃	1	8	yes	—
632	C₂²⋊Q₈	C₂³×C₁₃	1	16	yes	—
633	C₂²⋊Q₈	C₂³×C₁₃	1	16	yes	—
634	C₂²⋊Q₈	C₂³×C₁₃	1	16	yes	—
635	C₂²⋊Q₈	C₂³×C₁₃	1	16	yes	—
636	C₂²⋊Q₈	C₂³×C₁₃	1	16	yes	—
637	C₂²⋊Q₈	C₂³×C₁₃	1	16	yes	—
638	#121	C₂³×C₁₃	1	4	yes	—
639	#121	C₂³×C₁₃	1	8	yes	—
640	#121	C₂³×C₁₃	1	8	yes	—
641	#121	C₂³×C₁₃	1	8	yes	—
642	#121	C₂³×C₁₃	1	4	yes	—
643	#121	C₂³×C₁₃	1	8	yes	—
644	#121	C₂³×C₁₃	1	8	yes	—
645	#121	C₂³×C₁₃	1	4	yes	—
646	#121	C₂³×C₁₃	1	8	yes	—
647	#121	C₂³×C₁₃	1	4	yes	—
648	#121	C₂³×C₁₃	1	16	yes	—
649	#121	C₂³×C₁₃	1	16	yes	—
650	#121	C₂³×C₁₃	1	16	yes	—
651	#121	C₂³×C₁₃	1	16	yes	—
652	#121	C₂³×C₁₃	1	16	yes	—
653	#121	C₂³×C₁₃	1	16	yes	—
654	#121	C₂³×C₁₃	1	16	yes	—
655	#121	C₂³×C₁₃	1	16	yes	—
656	#120	C₂³×C₁₃	1	8	yes	—
657	#120	C₂³×C₁₃	1	8	yes	—
658	#120	C₂³×C₁₃	1	4	yes	—
659	#120	C₂³×C₁₃	1	16	yes	—
660	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
661	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
662	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
663	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
664	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
665	C₄×Q₈	C₂³×C₁₃	1	8	yes	—
666	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
667	C₄×Q₈	C₂³×C₁₃	1	8	yes	—
668	C₄×D₄	C₂³×C₁₃	1	8	yes	—
669	C₄×D₄	C₂³×C₁₃	1	4	yes	—
670	C₄×D₄	C₂³×C₁₃	1	16	yes	—
671	C₄×D₄	C₂³×C₁₃	1	8	yes	—
672	C₄×D₄	C₂³×C₁₃	1	8	yes	—
673	C₄×D₄	C₂³×C₁₃	1	4	yes	—
674	C₄×D₄	C₂³×C₁₃	1	4	yes	—
675	C₄×D₄	C₂³×C₁₃	1	8	yes	—
676	C₄×D₄	C₂³×C₁₃	1	16	yes	—
677	C₄×D₄	C₂³×C₁₃	1	16	yes	—
678	C₄×D₄	C₂³×C₁₃	1	4	yes	—
679	C₄×D₄	C₂³×C₁₃	1	8	yes	—
680	C₄×D₄	C₂³×C₁₃	1	16	yes	—
681	C₄×D₄	C₂³×C₁₃	1	16	yes	—
682	C₄×D₄	C₂³×C₁₃	1	16	yes	—
683	C₄×D₄	C₂³×C₁₃	1	8	yes	—
684	C₄×D₄	C₂³×C₁₃	1	8	yes	—
685	#117	C₂³×C₁₃	1	2	yes	—
686	#117	C₂³×C₁₃	1	2	yes	—
687	#117	C₂³×C₁₃	1	4	yes	—
688	#117	C₂³×C₁₃	1	2	yes	—
689	#117	C₂³×C₁₃	1	4	yes	—
690	#117	C₂³×C₁₃	1	8	yes	—
691	#117	C₂³×C₁₃	1	16	yes	—
692	#117	C₂³×C₁₃	1	16	yes	—
693	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
694	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
695	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
696	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
697	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
698	C₂×C₄⋊C₄	C₂³×C₁₃	1	16	yes	—
699	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
700	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
701	C₂×C₄⋊C₄	C₂³×C₁₃	1	16	yes	—
702	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
703	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
704	C₂×C₂²⋊C₄	C₂³×C₁₃	1	16	yes	—
705	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
706	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
707	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
708	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
709	C₂×C₁₃	—	2	2	no	—
710	C₂×C₁₃	—	4	4	no	—
711	C₂×C₁₃	—	4	8	no	—
712	C₂×C₁₃	—	4	2	no	—
713	C₂×C₁₃	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
714	C₂×C₁₃	2₋¹⁺⁶	1	2	yes	—
715	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
716	C₂⁴	C₂⁴×C₁₃	1	4	yes	—
717	#41	—	2	16	no	—
718	#41	—	2	8	no	—
719	#41	—	4	8	no	—
720	#41	—	4	8	no	—
721	#41	—	4	32	no	—
722	#41	—	4	8	no	—
723	#41	—	4	16	no	—
724	#41	—	4	16	no	—
725	C₂×Q₈	—	2	8	no	—
726	C₂×Q₈	—	4	4	no	—
727	C₂×Q₈	—	4	16	no	—
728	C₂×Q₈	—	4	16	no	—
729	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
730	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
731	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
732	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
733	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
734	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
735	C₂×Q₈	C₂⁴×C₁₃	1	16	yes	—
736	C₂×D₄	—	4	4	no	—
737	C₂×D₄	—	4	8	no	—
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	8	yes	—
743	C₂×D₄	C₂⁴×C₁₃	1	8	yes	—
744	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
745	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
746	C₂×D₄	C₂⁴×C₁₃	1	16	yes	—
747	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
748	C₂×D₄	C₂⁴×C₁₃	1	8	yes	—
749	C₂×D₄	C₂⁴×C₁₃	1	16	yes	—
750	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
751	C₂²×C₄	—	2	4	no	—
752	C₂²×C₄	—	4	8	no	—
753	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
754	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
755	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
756	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
757	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
758	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
759	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
760	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
761	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
762	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
763	C₂²×C₄	C₂⁴×C₁₃	1	16	yes	—
764	C₂²×C₄	C₂⁴×C₁₃	1	16	yes	—
765	C₂²×C₄	C₂⁴×C₁₃	1	16	yes	—
766	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
767	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
768	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
769	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
770	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
771	C₄⋊C₄	C₂⁴×C₁₃	1	16	yes	—
772	C₄⋊C₄	C₂⁴×C₁₃	1	16	yes	—
773	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
774	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
775	C₄⋊C₄	C₂⁴×C₁₃	1	16	yes	—
776	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
777	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
778	C₄⋊C₄	C₂⁴×C₁₃	1	16	yes	—
779	C₄⋊C₄	C₂⁴×C₁₃	1	16	yes	—
780	C₄⋊C₄	C₂⁴×C₁₃	1	16	yes	—
781	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
782	C₄⋊C₄	C₂⁴×C₁₃	1	16	yes	—
783	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
784	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
785	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
786	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
787	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
788	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
789	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
790	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
791	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
792	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
793	C₂²⋊C₄	C₂⁴×C₁₃	1	4	yes	—
794	C₂²⋊C₄	C₂⁴×C₁₃	1	4	yes	—
795	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
796	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
797	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
798	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
799	C₂²⋊C₄	C₂⁴×C₁₃	1	4	yes	—
800	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
801	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
802	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
803	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
804	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
805	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
806	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
807	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
808	C₄²	C₂⁴×C₁₃	1	2	yes	—
809	C₄²	C₂⁴×C₁₃	1	2	yes	—
810	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
811	C₄²	C₂⁴×C₁₃	1	4	yes	—
812	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
813	C₄²	C₂⁴×C₁₃	1	8	yes	—
814	C₄²	C₂⁴×C₁₃	1	2	yes	—
815	C₄²	C₂⁴×C₁₃	1	8	yes	—
816	C₄²	C₂⁴×C₁₃	1	8	yes	—
817	C₄²	C₂⁴×C₁₃	1	16	yes	—
818	C₁₃	#62888	1	1	yes	characteristic, direct product factor, Sylow
819	C₂³	—	2	2	no	—
820	C₂³	—	4	4	no	—
821	C₂³	—	4	2	no	—
822	C₂³	—	4	8	no	—
823	C₂³	C₂⁵×C₁₃	1	2	yes	—
824	C₂³	C₂⁵×C₁₃	1	8	yes	—
825	C₂³	C₂⁵×C₁₃	1	4	yes	—
826	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
827	Q₈	—	2	8	no	—
828	Q₈	—	2	8	no	—
829	Q₈	—	2	4	no	—
830	Q₈	—	2	8	no	—
831	Q₈	—	4	16	no	—
832	Q₈	—	4	4	no	—
833	Q₈	—	4	4	no	—
834	D₄	—	2	16	no	—
835	D₄	—	2	8	no	—
836	D₄	—	2	8	no	—
837	D₄	—	2	4	no	—
838	D₄	—	4	4	no	—
839	D₄	—	4	8	no	—
840	D₄	—	4	8	no	—
841	D₄	—	4	16	no	—
842	D₄	—	4	8	no	—
843	D₄	—	4	4	no	—
844	D₄	—	4	4	no	—
845	D₄	—	4	4	no	—
846	D₄	—	4	16	no	—
847	C₂×C₄	—	2	2	no	—
848	C₂×C₄	—	2	8	no	—
849	C₂×C₄	—	2	4	no	—
850	C₂×C₄	—	2	4	no	—
851	C₂×C₄	—	2	16	no	—
852	C₂×C₄	—	2	8	no	—
853	C₂×C₄	—	4	4	no	—
854	C₂×C₄	—	4	8	no	—
855	C₂×C₄	—	4	2	no	—
856	C₂×C₄	—	4	4	no	—
857	C₂×C₄	—	4	16	no	—
858	C₂×C₄	—	4	8	no	—
859	C₂×C₄	—	4	2	no	—
860	C₂×C₄	—	4	16	no	—
861	C₂×C₄	—	4	16	no	—
862	C₂×C₄	C₁₃×H(5,𝔽₂)	1	4	yes	—
863	C₂×C₄	C₂⁵×C₁₃	1	2	yes	—
864	C₂×C₄	C₂⁵×C₁₃	1	2	yes	—
865	C₂×C₄	C₂⁵×C₁₃	1	8	yes	—
866	C₂×C₄	C₂⁵×C₁₃	1	4	yes	—
867	C₂×C₄	C₂⁵×C₁₃	1	8	yes	—
868	C₂×C₄	C₂⁵×C₁₃	1	4	yes	—
869	C₂×C₄	C₂⁵×C₁₃	1	8	yes	—
870	C₂×C₄	C₂⁵×C₁₃	1	8	yes	—
871	C₂×C₄	C₂⁵×C₁₃	1	2	yes	—
872	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
873	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
874	C₂²	—	2	2	no	—
875	C₂²	—	2	2	no	—
876	C₂²	—	2	4	no	—
877	C₂²	—	2	8	no	—
878	C₂²	—	2	8	no	—
879	C₂²	—	2	8	no	—
880	C₂²	—	2	8	no	—
881	C₂²	—	2	4	no	—
882	C₂²	—	8	2	no	—
883	C₂²	—	8	8	no	—
884	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
885	C₂²	C₂⁶×C₁₃	1	1	yes	characteristic
886	C₄	—	2	2	no	—
887	C₄	—	2	8	no	—
888	C₄	—	2	4	no	—
889	C₄	—	2	8	no	—
890	C₄	—	2	8	no	—
891	C₄	—	2	4	no	—
892	C₄	—	2	8	no	—
893	C₄	—	2	2	no	—
894	C₄	—	2	2	no	—
895	C₄	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
896	C₄	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
897	C₂	—	2	2	no	—
898	C₂	—	4	2	no	—
899	C₂	—	4	8	no	—
900	C₂	—	4	4	no	—
901	C₂	C₂²×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
902	C₂	C₁₃×2₋¹⁺⁶	1	2	yes	—

	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×#3562	C₂	semidirect
2. C₁₃×#3560	C₂	semidirect
3. C₁₃×#3559	C₂	semidirect
4. C₁₃×#3552	C₂	semidirect
5. C₁₃×#3541	C₂	semidirect
6. C₁₃×#3539	C₂	semidirect
7. C₁₃×#3538	C₂	semidirect
8. C₁₃×#3512	C₂	semidirect
9. C₁₃×#3507	C₂	semidirect
10. C₁₃×#3499	C₂	semidirect
11. C₁₃×#3497	C₂	semidirect
12. C₁₃×#3489	C₂	semidirect
13. C₁₃×#3455	C₂	semidirect
14. C₂×C₁₃×#541	C₂	semidirect
15. C₁₃×#3449	C₂	semidirect
16. C₂×C₁₃×2₋¹⁺⁴	C₂²	semidirect
18. C₁₃×#563	C₂²	semidirect
19. C₁₃×#563	C₂²	semidirect
20. C₁₃×#562	C₂²	semidirect
21. C₁₃×#560	C₂²	semidirect
22. C₁₃×#559	C₂²	semidirect
23. C₁₃×#557	C₂²	semidirect
24. C₁₃×#556	C₂²	semidirect
25. C₁₃×#556	C₂²	semidirect
26. C₁₃×#554	C₂²	semidirect
27. C₁₃×#554	C₂²	semidirect
28. C₁₃×#553	C₂²	semidirect
29. C₁₃×#553	C₂²	semidirect
30. C₁₃×#553	C₂²	semidirect
31. C₁₃×#553	C₂²	semidirect
32. C₁₃×#552	C₂²	semidirect
33. C₁₃×#552	C₂²	semidirect
34. C₁₃×#551	C₂²	semidirect
35. C₁₃×#550	C₂²	semidirect
36. C₁₃×#550	C₂²	semidirect
37. D₄×Q₈×C₁₃	C₂²	semidirect
38. D₄×Q₈×C₁₃	C₂²	semidirect
39. D₄×Q₈×C₁₃	C₂²	semidirect
40. D₄×Q₈×C₁₃	C₂²	semidirect
42. C₁₃×#548	C₂²	semidirect
43. C₁₃×#548	C₂²	semidirect
45. C₁₃×#547	C₂²	semidirect
46. C₁₃×#547	C₂²	semidirect
47. C₁₃×#547	C₂²	semidirect
49. C₁₃×#546	C₂²	semidirect
50. C₁₃×#544	C₂²	semidirect
51. C₁₃×#542	C₂²	semidirect
52. C₁₃×#542	C₂²	semidirect
53. C₁₃×#541	C₂²	semidirect
54. C₁₃×#541	C₂²	semidirect
55. C₁₃×#541	C₂²	semidirect
56. C₁₃×#541	C₂²	semidirect
57. C₁₃×#541	C₂²	semidirect
58. C₁₃×#540	C₂²	semidirect
59. C₁₃×#540	C₂²	semidirect
60. C₁₃×#540	C₂²	semidirect
61. C₁₃×#539	C₂²	semidirect
62. C₁₃×#539	C₂²	semidirect
63. C₁₃×#539	C₂²	semidirect
64. C₁₃×#539	C₂²	semidirect
65. C₁₃×#539	C₂²	semidirect
67. C₁₃×#538	C₂²	semidirect
68. C₁₃×#538	C₂²	semidirect
71. C₁₃×#537	C₂²	semidirect
72. C₁₃×#537	C₂²	semidirect
75. C₁₃×#536	C₂²	semidirect
76. C₁₃×#536	C₂²	semidirect
79. C₁₃×#533	C₂²	semidirect
82. C₁₃×#532	C₂²	semidirect
83. C₁₃×#532	C₂²	semidirect
84. C₁₃×#532	C₂²	semidirect
85. C₂×C₁₃×C₄⋊Q₈	C₂²	semidirect
86. C₂×C₁₃×C₄⋊Q₈	C₂²	semidirect
87. C₁₃×#529	C₂²	semidirect
88. C₁₃×#529	C₂²	semidirect
89. C₁₃×#529	C₂²	semidirect
91. C₂×C₁₃×#125	C₂²	semidirect
92. C₂×C₁₃×#125	C₂²	semidirect
96. C₁₃×#525	C₂²	semidirect
98. C₂×C₁₃×C₂²⋊Q₈	C₂²	semidirect
99. C₁₃×#520	C₂²	semidirect
100. C₄×C₁₃×#41	C₂²	semidirect
101. C₂×C₄×Q₈×C₁₃	C₂²	semidirect
264. #62888	C₁₃	direct (N × H)
368. #3562	C₂×C₁₃	semidirect
369. #3560	C₂×C₁₃	semidirect
370. #3559	C₂×C₁₃	semidirect
371. #3552	C₂×C₁₃	semidirect
372. #3541	C₂×C₁₃	semidirect
373. #3539	C₂×C₁₃	semidirect
374. #3538	C₂×C₁₃	semidirect
375. #3512	C₂×C₁₃	semidirect
376. #3507	C₂×C₁₃	semidirect
377. #3499	C₂×C₁₃	semidirect
378. #3497	C₂×C₁₃	semidirect
379. #3489	C₂×C₁₃	semidirect
380. #3455	C₂×C₁₃	semidirect
381. C₂×#541	C₂×C₁₃	semidirect
382. #3449	C₂×C₁₃	semidirect
438. C₂×2₋¹⁺⁴	C₂²×C₁₃	semidirect
440. #563	C₂²×C₁₃	semidirect
441. #563	C₂²×C₁₃	semidirect
442. #562	C₂²×C₁₃	semidirect
443. #560	C₂²×C₁₃	semidirect
444. #559	C₂²×C₁₃	semidirect
445. #557	C₂²×C₁₃	semidirect
446. #556	C₂²×C₁₃	semidirect
447. #556	C₂²×C₁₃	semidirect
448. #554	C₂²×C₁₃	semidirect
449. #554	C₂²×C₁₃	semidirect
450. #553	C₂²×C₁₃	semidirect
451. #553	C₂²×C₁₃	semidirect
452. #553	C₂²×C₁₃	semidirect
453. #553	C₂²×C₁₃	semidirect
454. #552	C₂²×C₁₃	semidirect
455. #552	C₂²×C₁₃	semidirect
456. #551	C₂²×C₁₃	semidirect
457. #550	C₂²×C₁₃	semidirect
458. #550	C₂²×C₁₃	semidirect
459. D₄×Q₈	C₂²×C₁₃	semidirect
460. D₄×Q₈	C₂²×C₁₃	semidirect
461. D₄×Q₈	C₂²×C₁₃	semidirect
462. D₄×Q₈	C₂²×C₁₃	semidirect
464. #548	C₂²×C₁₃	semidirect
465. #548	C₂²×C₁₃	semidirect
467. #547	C₂²×C₁₃	semidirect
468. #547	C₂²×C₁₃	semidirect
469. #547	C₂²×C₁₃	semidirect
471. #546	C₂²×C₁₃	semidirect
472. #544	C₂²×C₁₃	semidirect
473. #542	C₂²×C₁₃	semidirect
474. #542	C₂²×C₁₃	semidirect
475. #541	C₂²×C₁₃	semidirect
476. #541	C₂²×C₁₃	semidirect
477. #541	C₂²×C₁₃	semidirect
478. #541	C₂²×C₁₃	semidirect
479. #541	C₂²×C₁₃	semidirect
480. #540	C₂²×C₁₃	semidirect
481. #540	C₂²×C₁₃	semidirect
482. #540	C₂²×C₁₃	semidirect
483. #539	C₂²×C₁₃	semidirect
484. #539	C₂²×C₁₃	semidirect
485. #539	C₂²×C₁₃	semidirect
486. #539	C₂²×C₁₃	semidirect
487. #539	C₂²×C₁₃	semidirect
489. #538	C₂²×C₁₃	semidirect
490. #538	C₂²×C₁₃	semidirect
493. #537	C₂²×C₁₃	semidirect
494. #537	C₂²×C₁₃	semidirect
497. #536	C₂²×C₁₃	semidirect
498. #536	C₂²×C₁₃	semidirect
501. #533	C₂²×C₁₃	semidirect
504. #532	C₂²×C₁₃	semidirect
505. #532	C₂²×C₁₃	semidirect
506. #532	C₂²×C₁₃	semidirect
507. C₂×C₄⋊Q₈	C₂²×C₁₃	semidirect
508. C₂×C₄⋊Q₈	C₂²×C₁₃	semidirect
509. #529	C₂²×C₁₃	semidirect
510. #529	C₂²×C₁₃	semidirect
511. #529	C₂²×C₁₃	semidirect
513. C₂×#125	C₂²×C₁₃	semidirect
514. C₂×#125	C₂²×C₁₃	semidirect
518. #525	C₂²×C₁₃	semidirect
520. C₂×C₂²⋊Q₈	C₂²×C₁₃	semidirect
521. #520	C₂²×C₁₃	semidirect
522. C₄×#41	C₂²×C₁₃	semidirect
523. C₂×C₄×Q₈	C₂²×C₁₃	semidirect
818. C₁₃	#62888	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×#3562	2
C₁₃×#3560	2
C₁₃×#3559	2
C₁₃×#3552	2
C₁₃×#3541	2
C₁₃×#3539	2
C₁₃×#3538	2
C₁₃×#3512	2
C₁₃×#3507	2
C₁₃×#3499	2
C₁₃×#3497	2
C₁₃×#3489	2
C₁₃×#3455	2
C₂×C₁₃×#541	2
C₁₃×#3449	2
#62888	13

Subgroups — C13×#62888 #15749227

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#62888 #15749227