Subgroups — C₁₃×#62889 #15749228

Order 3328.

6186 conjugacy classes of subgroups.

The subgroup lattice has 838 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3564	C₂	1	8	yes	maximal, complemented
2	C₁₃×#3563	C₂	1	8	yes	maximal, complemented
3	C₁₃×#3563	C₂	1	8	yes	maximal, complemented
4	C₁₃×#3557	C₂	1	4	yes	maximal, complemented
5	C₁₃×#3556	C₂	1	4	yes	maximal, complemented
6	C₁₃×#3555	C₂	1	8	yes	maximal, complemented
7	C₁₃×#3555	C₂	1	8	yes	maximal, complemented
8	C₁₃×#3509	C₂	1	2	yes	maximal, complemented
9	C₁₃×#3507	C₂	1	2	yes	maximal, complemented
10	C₁₃×#3504	C₂	1	2	yes	maximal, complemented
11	C₁₃×#3502	C₂	1	2	yes	maximal, complemented
12	C₁₃×#3495	C₂	1	4	yes	maximal, complemented
13	C₁₃×#3458	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#3455	C₂	1	1	yes	maximal, characteristic
15	C₂×C₁₃×#541	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₃×#564	C₂²	1	16	yes	complemented
17	C₁₃×#563	C₂²	1	16	yes	—
18	C₁₃×#563	C₂²	1	16	yes	—
19	C₁₃×#563	C₂²	1	16	yes	complemented
20	C₁₃×#559	C₂²	1	4	yes	complemented
21	Q₈²×C₁₃	C₂²	1	4	yes	complemented
22	Q₈²×C₁₃	C₂²	1	4	yes	complemented
23	C₁₃×#557	C₂²	1	4	yes	complemented
24	C₁₃×#557	C₂²	1	16	yes	complemented
25	C₁₃×#557	C₂²	1	8	yes	complemented
26	C₁₃×#557	C₂²	1	8	yes	complemented
27	C₁₃×#557	C₂²	1	8	yes	complemented
28	C₁₃×#557	C₂²	1	4	yes	complemented
29	C₁₃×#557	C₂²	1	8	yes	complemented
30	C₁₃×#557	C₂²	1	4	yes	complemented
31	C₁₃×#556	C₂²	1	16	yes	—
32	C₁₃×#556	C₂²	1	8	yes	—
33	C₁₃×#556	C₂²	1	4	yes	complemented
34	C₁₃×#556	C₂²	1	8	yes	complemented
35	C₁₃×#556	C₂²	1	8	yes	complemented
36	C₁₃×#554	C₂²	1	8	yes	—
37	C₁₃×#554	C₂²	1	16	yes	—
38	C₁₃×#554	C₂²	1	8	yes	complemented
39	C₁₃×#554	C₂²	1	4	yes	complemented
40	C₁₃×#552	C₂²	1	16	yes	—
41	C₁₃×#552	C₂²	1	8	yes	—
42	C₁₃×#552	C₂²	1	8	yes	—
43	C₁₃×#552	C₂²	1	16	yes	—
44	C₁₃×#552	C₂²	1	16	yes	—
45	C₁₃×#552	C₂²	1	8	yes	complemented
46	C₁₃×#552	C₂²	1	16	yes	complemented
47	C₁₃×#551	C₂²	1	16	yes	—
48	C₁₃×#544	C₂²	1	4	yes	—
49	C₁₃×#544	C₂²	1	4	yes	—
50	C₁₃×#544	C₂²	1	4	yes	—
51	C₁₃×#544	C₂²	1	8	yes	—
52	C₁₃×#544	C₂²	1	4	yes	—
53	C₁₃×#544	C₂²	1	16	yes	complemented
54	C₁₃×#544	C₂²	1	8	yes	complemented
55	C₁₃×#543	C₂²	1	4	yes	—
56	C₁₃×#542	C₂²	1	4	yes	—
57	C₁₃×#542	C₂²	1	16	yes	—
58	C₁₃×#542	C₂²	1	8	yes	—
59	C₁₃×#541	C₂²	1	4	yes	—
60	C₁₃×#541	C₂²	1	16	yes	—
61	C₁₃×#541	C₂²	1	8	yes	—
62	C₁₃×#541	C₂²	1	8	yes	—
63	C₁₃×#541	C₂²	1	2	yes	—
64	C₁₃×#541	C₂²	1	4	yes	—
65	C₁₃×#541	C₂²	1	16	yes	—
66	C₁₃×#541	C₂²	1	16	yes	complemented
67	C₁₃×#541	C₂²	1	16	yes	complemented
68	C₁₃×#541	C₂²	1	4	yes	complemented
69	C₁₃×#541	C₂²	1	16	yes	complemented
70	C₁₃×#541	C₂²	1	4	yes	complemented
71	C₁₃×#540	C₂²	1	2	yes	—
72	C₁₃×#539	C₂²	1	16	yes	—
73	C₁₃×#539	C₂²	1	4	yes	—
74	C₁₃×#539	C₂²	1	8	yes	—
75	C₁₃×#538	C₂²	1	4	yes	—
76	C₁₃×#536	C₂²	1	4	yes	—
77	C₁₃×#533	C₂²	1	4	yes	—
78	C₁₃×#533	C₂²	1	8	yes	—
79	C₁₃×#533	C₂²	1	4	yes	—
80	C₁₃×#533	C₂²	1	8	yes	—
81	C₁₃×#533	C₂²	1	1	yes	characteristic
82	C₁₃×#533	C₂²	1	2	yes	—
83	C₁₃×#533	C₂²	1	2	yes	—
84	C₁₃×#533	C₂²	1	4	yes	complemented
85	C₁₃×#533	C₂²	1	8	yes	complemented
86	C₁₃×#532	C₂²	1	1	yes	characteristic
87	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
88	C₁₃×#529	C₂²	1	8	yes	—
89	C₁₃×#529	C₂²	1	8	yes	—
90	C₁₃×#529	C₂²	1	8	yes	—
91	C₂×C₁₃×#126	C₂²	1	4	yes	—
92	C₂×C₁₃×#125	C₂²	1	4	yes	—
93	C₂×C₁₃×#125	C₂²	1	1	yes	characteristic
94	C₂×C₁₃×#125	C₂²	1	4	yes	complemented
95	C₁₃×#525	C₂²	1	2	yes	—
96	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
97	C₁₃×#520	C₂²	1	4	yes	—
98	C₁₃×#519	C₂²	1	4	yes	—
99	C₄×C₁₃×#41	C₂²	1	2	yes	—
100	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	—
101	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
102	C₂×C₁₃×#117	C₂²	1	2	yes	—
103	C₂×C₁₃×#41	C₂³	1	2	yes	—
104	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
105	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
106	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
107	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
108	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
109	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
110	C₁₃×C₄⋊Q₈	C₂³	1	8	yes	—
111	C₁₃×C₄⋊Q₈	C₂³	1	8	yes	—
112	C₁₃×C₄⋊Q₈	C₂³	1	8	yes	—
113	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
114	C₁₃×C₄⋊Q₈	C₂³	1	8	yes	—
115	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
116	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
117	C₁₃×C₄⋊Q₈	C₂³	1	8	yes	—
118	C₁₃×C₄⋊Q₈	C₂³	1	8	yes	—
119	C₁₃×C₄⋊Q₈	C₂³	1	8	yes	—
120	C₁₃×C₄⋊Q₈	C₂³	1	16	yes	—
121	C₁₃×C₄⋊Q₈	C₂³	1	16	yes	—
122	C₁₃×C₄⋊Q₈	C₂³	1	16	yes	—
123	C₁₃×#127	C₂³	1	1	yes	characteristic
124	C₁₃×#126	C₂³	1	16	yes	—
125	C₁₃×#126	C₂³	1	16	yes	—
126	C₁₃×#126	C₂³	1	8	yes	—
127	C₁₃×#126	C₂³	1	8	yes	—
128	C₁₃×#126	C₂³	1	16	yes	—
129	C₁₃×#126	C₂³	1	16	yes	—
130	C₁₃×#126	C₂³	1	16	yes	—
131	C₁₃×#126	C₂³	1	16	yes	—
132	C₁₃×#126	C₂³	1	16	yes	—
133	C₁₃×#126	C₂³	1	16	yes	—
134	C₁₃×#126	C₂³	1	16	yes	—
135	C₁₃×#126	C₂³	1	16	yes	—
136	C₁₃×#125	C₂³	1	4	yes	—
137	C₁₃×#125	C₂³	1	16	yes	—
138	C₁₃×#125	C₂³	1	16	yes	—
139	C₁₃×#125	C₂³	1	4	yes	—
140	C₁₃×#125	C₂³	1	2	yes	—
141	C₁₃×#125	C₂³	1	16	yes	—
142	C₁₃×#125	C₂³	1	8	yes	—
143	C₁₃×#125	C₂³	1	8	yes	—
144	C₁₃×#125	C₂³	1	8	yes	—
145	C₁₃×#125	C₂³	1	8	yes	—
146	C₁₃×#125	C₂³	1	2	yes	—
147	C₁₃×#125	C₂³	1	16	yes	—
148	C₁₃×#125	C₂³	1	2	yes	—
149	C₁₃×#125	C₂³	1	8	yes	—
150	C₁₃×#125	C₂³	1	16	yes	—
151	C₁₃×#125	C₂³	1	4	yes	—
152	C₁₃×#125	C₂³	1	8	yes	—
153	C₁₃×#125	C₂³	1	16	yes	—
154	C₁₃×#125	C₂³	1	16	yes	—
155	C₁₃×#125	C₂³	1	16	yes	—
156	C₁₃×#125	C₂³	1	16	yes	—
157	C₁₃×#125	C₂³	1	16	yes	—
158	C₁₃×#125	C₂³	1	16	yes	—
159	C₁₃×#125	C₂³	1	16	yes	—
160	C₁₃×#125	C₂³	1	16	yes	—
161	C₁₃×#125	C₂³	1	16	yes	—
162	C₁₃×#124	C₂³	1	8	yes	—
163	C₁₃×#124	C₂³	1	8	yes	—
164	C₁₃×#124	C₂³	1	8	yes	—
165	C₁₃×#124	C₂³	1	2	yes	—
166	C₁₃×#124	C₂³	1	16	yes	—
167	C₁₃×#123	C₂³	1	4	yes	—
168	C₁₃×#123	C₂³	1	16	yes	—
169	C₁₃×#123	C₂³	1	8	yes	—
170	C₁₃×#123	C₂³	1	8	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	4	yes	—
178	C₁₃×C₂²⋊Q₈	C₂³	1	8	yes	—
179	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
180	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
181	C₁₃×C₂²⋊Q₈	C₂³	1	8	yes	—
182	C₁₃×C₂²⋊Q₈	C₂³	1	8	yes	—
183	C₁₃×C₂²⋊Q₈	C₂³	1	16	yes	—
184	C₁₃×C₂²⋊Q₈	C₂³	1	8	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	8	yes	—
189	C₁₃×C₂²⋊Q₈	C₂³	1	8	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×C₂²⋊Q₈	C₂³	1	16	yes	—
194	C₁₃×C₂²⋊Q₈	C₂³	1	16	yes	—
195	C₁₃×C₂²⋊Q₈	C₂³	1	16	yes	—
196	C₁₃×#121	C₂³	1	4	yes	—
197	C₁₃×#121	C₂³	1	4	yes	—
198	C₁₃×#121	C₂³	1	8	yes	—
199	C₁₃×#120	C₂³	1	4	yes	—
200	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
201	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
202	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
203	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
204	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
205	C₄×Q₈×C₁₃	C₂³	1	8	yes	—
206	C₄×Q₈×C₁₃	C₂³	1	8	yes	—
207	C₄×Q₈×C₁₃	C₂³	1	8	yes	—
208	C₄×Q₈×C₁₃	C₂³	1	8	yes	—
209	C₄×Q₈×C₁₃	C₂³	1	8	yes	—
210	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
211	C₄×Q₈×C₁₃	C₂³	1	8	yes	—
212	C₄×Q₈×C₁₃	C₂³	1	8	yes	—
213	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
214	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
215	C₄×Q₈×C₁₃	C₂³	1	16	yes	—
216	C₄×Q₈×C₁₃	C₂³	1	8	yes	—
217	C₄×Q₈×C₁₃	C₂³	1	16	yes	—
218	C₄×Q₈×C₁₃	C₂³	1	8	yes	—
219	C₄×Q₈×C₁₃	C₂³	1	16	yes	—
220	C₄×Q₈×C₁₃	C₂³	1	16	yes	—
221	C₄×D₄×C₁₃	C₂³	1	8	yes	—
222	C₄×D₄×C₁₃	C₂³	1	4	yes	—
223	C₄×D₄×C₁₃	C₂³	1	16	yes	—
224	C₄×D₄×C₁₃	C₂³	1	8	yes	—
225	C₄×D₄×C₁₃	C₂³	1	8	yes	—
226	C₄×D₄×C₁₃	C₂³	1	4	yes	—
227	C₄×D₄×C₁₃	C₂³	1	8	yes	—
228	C₄×D₄×C₁₃	C₂³	1	16	yes	—
229	C₁₃×#117	C₂³	1	4	yes	—
230	C₁₃×#117	C₂³	1	4	yes	—
231	C₁₃×#117	C₂³	1	2	yes	—
232	C₁₃×#117	C₂³	1	2	yes	—
233	C₁₃×#117	C₂³	1	4	yes	—
234	C₁₃×#117	C₂³	1	2	yes	—
235	C₁₃×#117	C₂³	1	4	yes	—
236	C₁₃×#117	C₂³	1	2	yes	—
237	C₁₃×#117	C₂³	1	2	yes	—
238	C₁₃×#117	C₂³	1	4	yes	—
239	C₁₃×#117	C₂³	1	16	yes	—
240	C₁₃×#117	C₂³	1	8	yes	—
241	C₁₃×#117	C₂³	1	16	yes	—
242	C₁₃×#117	C₂³	1	16	yes	—
243	C₁₃×#117	C₂³	1	16	yes	—
244	C₁₃×#117	C₂³	1	16	yes	—
245	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
246	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
247	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
248	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
249	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
250	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
251	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
252	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
253	C₂×C₁₃×C₄⋊C₄	C₂³	1	16	yes	—
254	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
255	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
256	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
257	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
258	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
259	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
260	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
261	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
262	#62889	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
263	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
264	C₁₃×#41	—	2	8	no	—
265	C₂×Q₈×C₁₃	—	2	8	no	—
266	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
267	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
268	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
269	C₂×Q₈×C₁₃	C₂⁴	1	8	yes	—
270	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
271	C₂×Q₈×C₁₃	C₂⁴	1	16	yes	—
272	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
273	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
274	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
275	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
276	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
277	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
278	C₂²×C₄×C₁₃	—	2	4	no	—
279	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
280	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
281	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
282	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
283	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
284	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
285	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
286	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
287	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
288	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
289	C₂²×C₄×C₁₃	C₂⁴	1	16	yes	—
290	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
291	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
292	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
293	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
294	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
295	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
296	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
297	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
298	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
299	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
300	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
301	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
302	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
303	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
304	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
305	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
306	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
307	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
308	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
309	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
310	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
311	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
312	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
313	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
314	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
315	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
316	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
317	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
318	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
319	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
320	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
321	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
322	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
323	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
324	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
325	C₁₃×C₂²⋊C₄	C₂⁴	1	4	yes	—
326	C₁₃×C₂²⋊C₄	C₂⁴	1	4	yes	—
327	C₁₃×C₂²⋊C₄	C₂⁴	1	4	yes	—
328	C₁₃×C₂²⋊C₄	C₂⁴	1	4	yes	—
329	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
330	C₁₃×C₂²⋊C₄	C₂⁴	1	4	yes	—
331	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
332	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
333	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
334	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
335	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
336	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
337	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
338	C₄²×C₁₃	C₂⁴	1	2	yes	—
339	C₄²×C₁₃	C₂⁴	1	4	yes	—
340	C₄²×C₁₃	C₂⁴	1	2	yes	—
341	C₄²×C₁₃	C₂⁴	1	4	yes	—
342	C₄²×C₁₃	C₂⁴	1	2	yes	—
343	C₄²×C₁₃	C₂⁴	1	8	yes	—
344	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
345	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
346	C₄²×C₁₃	C₂⁴	1	8	yes	—
347	C₄²×C₁₃	C₂⁴	1	4	yes	—
348	C₄²×C₁₃	C₂⁴	1	8	yes	—
349	C₄²×C₁₃	C₂⁴	1	8	yes	—
350	C₄²×C₁₃	C₂⁴	1	16	yes	—
351	C₄²×C₁₃	C₂⁴	1	16	yes	—
352	C₄²×C₁₃	C₂⁴	1	16	yes	—
353	#3564	C₂×C₁₃	1	8	yes	complemented
354	#3563	C₂×C₁₃	1	8	yes	complemented
355	#3563	C₂×C₁₃	1	8	yes	complemented
356	#3557	C₂×C₁₃	1	4	yes	complemented
357	#3556	C₂×C₁₃	1	4	yes	complemented
358	#3555	C₂×C₁₃	1	8	yes	complemented
359	#3555	C₂×C₁₃	1	8	yes	complemented
360	#3509	C₂×C₁₃	1	2	yes	complemented
361	#3507	C₂×C₁₃	1	2	yes	complemented
362	#3504	C₂×C₁₃	1	2	yes	complemented
363	#3502	C₂×C₁₃	1	2	yes	complemented
364	#3495	C₂×C₁₃	1	4	yes	complemented
365	#3458	C₂×C₁₃	1	1	yes	characteristic, complemented
366	#3455	C₂×C₁₃	1	1	yes	characteristic
367	C₂×#541	C₂×C₁₃	1	1	yes	characteristic, complemented
368	C₂³×C₁₃	—	2	2	no	—
369	C₂³×C₁₃	—	4	2	no	—
370	C₂³×C₁₃	C₂⁵	1	2	yes	—
371	C₂³×C₁₃	C₂⁵	1	4	yes	—
372	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
373	Q₈×C₁₃	—	2	8	no	—
374	Q₈×C₁₃	—	2	8	no	—
375	Q₈×C₁₃	—	2	4	no	—
376	Q₈×C₁₃	—	4	8	no	—
377	Q₈×C₁₃	—	4	4	no	—
378	Q₈×C₁₃	—	4	16	no	—
379	Q₈×C₁₃	—	4	4	no	—
380	Q₈×C₁₃	—	4	4	no	—
381	D₄×C₁₃	—	2	8	no	—
382	D₄×C₁₃	—	2	4	no	—
383	D₄×C₁₃	—	4	4	no	—
384	D₄×C₁₃	—	4	8	no	—
385	C₂×C₄×C₁₃	—	2	2	no	—
386	C₂×C₄×C₁₃	—	2	8	no	—
387	C₂×C₄×C₁₃	—	2	4	no	—
388	C₂×C₄×C₁₃	—	2	4	no	—
389	C₂×C₄×C₁₃	—	2	8	no	—
390	C₂×C₄×C₁₃	—	4	2	no	—
391	C₂×C₄×C₁₃	—	4	4	no	—
392	C₂×C₄×C₁₃	—	4	16	no	—
393	C₂×C₄×C₁₃	—	4	8	no	—
394	C₂×C₄×C₁₃	—	4	8	no	—
395	C₂×C₄×C₁₃	—	4	2	no	—
396	C₂×C₄×C₁₃	2₋¹⁺⁴	1	4	yes	—
397	C₂×C₄×C₁₃	C₂⁵	1	8	yes	—
398	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
399	C₂×C₄×C₁₃	C₂⁵	1	8	yes	—
400	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
401	C₂×C₄×C₁₃	C₂⁵	1	8	yes	—
402	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
403	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
404	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
405	C₂×C₄×C₁₃	C₂⁵	1	8	yes	—
406	C₂×C₄×C₁₃	C₂⁵	1	8	yes	—
407	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
408	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
409	#564	C₂²×C₁₃	1	16	yes	complemented
410	#563	C₂²×C₁₃	1	16	yes	—
411	#563	C₂²×C₁₃	1	16	yes	—
412	#563	C₂²×C₁₃	1	16	yes	complemented
413	#559	C₂²×C₁₃	1	4	yes	complemented
414	Q₈²	C₂²×C₁₃	1	4	yes	complemented
415	Q₈²	C₂²×C₁₃	1	4	yes	complemented
416	#557	C₂²×C₁₃	1	4	yes	complemented
417	#557	C₂²×C₁₃	1	8	yes	complemented
418	#557	C₂²×C₁₃	1	8	yes	complemented
419	#557	C₂²×C₁₃	1	4	yes	complemented
420	#557	C₂²×C₁₃	1	8	yes	complemented
421	#557	C₂²×C₁₃	1	4	yes	complemented
422	#557	C₂²×C₁₃	1	8	yes	complemented
423	#557	C₂²×C₁₃	1	16	yes	complemented
424	#556	C₂²×C₁₃	1	8	yes	—
425	#556	C₂²×C₁₃	1	16	yes	—
426	#556	C₂²×C₁₃	1	4	yes	complemented
427	#556	C₂²×C₁₃	1	8	yes	complemented
428	#556	C₂²×C₁₃	1	8	yes	complemented
429	#554	C₂²×C₁₃	1	8	yes	—
430	#554	C₂²×C₁₃	1	16	yes	—
431	#554	C₂²×C₁₃	1	8	yes	complemented
432	#554	C₂²×C₁₃	1	4	yes	complemented
433	#552	C₂²×C₁₃	1	8	yes	—
434	#552	C₂²×C₁₃	1	8	yes	—
435	#552	C₂²×C₁₃	1	16	yes	—
436	#552	C₂²×C₁₃	1	16	yes	—
437	#552	C₂²×C₁₃	1	16	yes	—
438	#552	C₂²×C₁₃	1	8	yes	complemented
439	#552	C₂²×C₁₃	1	16	yes	complemented
440	#551	C₂²×C₁₃	1	16	yes	—
441	#544	C₂²×C₁₃	1	4	yes	—
442	#544	C₂²×C₁₃	1	4	yes	—
443	#544	C₂²×C₁₃	1	4	yes	—
444	#544	C₂²×C₁₃	1	4	yes	—
445	#544	C₂²×C₁₃	1	8	yes	—
446	#544	C₂²×C₁₃	1	8	yes	complemented
447	#544	C₂²×C₁₃	1	16	yes	complemented
448	#543	C₂²×C₁₃	1	4	yes	—
449	#542	C₂²×C₁₃	1	4	yes	—
450	#542	C₂²×C₁₃	1	8	yes	—
451	#542	C₂²×C₁₃	1	16	yes	—
452	#541	C₂²×C₁₃	1	4	yes	—
453	#541	C₂²×C₁₃	1	8	yes	—
454	#541	C₂²×C₁₃	1	4	yes	—
455	#541	C₂²×C₁₃	1	2	yes	—
456	#541	C₂²×C₁₃	1	8	yes	—
457	#541	C₂²×C₁₃	1	16	yes	—
458	#541	C₂²×C₁₃	1	16	yes	—
459	#541	C₂²×C₁₃	1	4	yes	complemented
460	#541	C₂²×C₁₃	1	4	yes	complemented
461	#541	C₂²×C₁₃	1	16	yes	complemented
462	#541	C₂²×C₁₃	1	16	yes	complemented
463	#541	C₂²×C₁₃	1	16	yes	complemented
464	#540	C₂²×C₁₃	1	2	yes	—
465	#539	C₂²×C₁₃	1	4	yes	—
466	#539	C₂²×C₁₃	1	8	yes	—
467	#539	C₂²×C₁₃	1	16	yes	—
468	#538	C₂²×C₁₃	1	4	yes	—
469	#536	C₂²×C₁₃	1	4	yes	—
470	#533	C₂²×C₁₃	1	1	yes	characteristic
471	#533	C₂²×C₁₃	1	2	yes	—
472	#533	C₂²×C₁₃	1	2	yes	—
473	#533	C₂²×C₁₃	1	4	yes	—
474	#533	C₂²×C₁₃	1	4	yes	—
475	#533	C₂²×C₁₃	1	8	yes	—
476	#533	C₂²×C₁₃	1	8	yes	—
477	#533	C₂²×C₁₃	1	4	yes	complemented
478	#533	C₂²×C₁₃	1	8	yes	complemented
479	#532	C₂²×C₁₃	1	1	yes	characteristic
480	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
481	#529	C₂²×C₁₃	1	8	yes	—
482	#529	C₂²×C₁₃	1	8	yes	—
483	#529	C₂²×C₁₃	1	8	yes	—
484	C₂×#126	C₂²×C₁₃	1	4	yes	—
485	C₂×#125	C₂²×C₁₃	1	1	yes	characteristic
486	C₂×#125	C₂²×C₁₃	1	4	yes	—
487	C₂×#125	C₂²×C₁₃	1	4	yes	complemented
488	#525	C₂²×C₁₃	1	2	yes	—
489	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
490	#520	C₂²×C₁₃	1	4	yes	—
491	#519	C₂²×C₁₃	1	4	yes	—
492	C₄×#41	C₂²×C₁₃	1	2	yes	—
493	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	—
494	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
495	C₂×#117	C₂²×C₁₃	1	2	yes	—
496	C₂²×C₁₃	—	2	2	no	—
497	C₂²×C₁₃	—	2	2	no	—
498	C₂²×C₁₃	—	2	4	no	—
499	C₂²×C₁₃	—	2	8	no	—
500	C₂²×C₁₃	—	2	4	no	—
501	C₂²×C₁₃	—	8	2	no	—
502	C₂²×C₁₃	C₂×2₋¹⁺⁴	1	2	yes	—
503	C₂²×C₁₃	C₂⁶	1	1	yes	characteristic
504	C₄×C₁₃	—	2	2	no	—
505	C₄×C₁₃	—	2	4	no	—
506	C₄×C₁₃	—	2	8	no	—
507	C₄×C₁₃	—	2	8	no	—
508	C₄×C₁₃	—	2	4	no	—
509	C₄×C₁₃	—	2	8	no	—
510	C₄×C₁₃	—	2	2	no	—
511	C₄×C₁₃	—	2	8	no	—
512	C₄×C₁₃	—	2	8	no	—
513	C₄×C₁₃	—	2	2	no	—
514	C₄×C₁₃	C₂×2₋¹⁺⁴	1	2	yes	—
515	C₄×C₁₃	C₂×2₋¹⁺⁴	1	2	yes	—
516	C₂×#41	C₂³×C₁₃	1	2	yes	—
517	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
518	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
519	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
520	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
521	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
522	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
523	C₄⋊Q₈	C₂³×C₁₃	1	8	yes	—
524	C₄⋊Q₈	C₂³×C₁₃	1	8	yes	—
525	C₄⋊Q₈	C₂³×C₁₃	1	8	yes	—
526	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
527	C₄⋊Q₈	C₂³×C₁₃	1	8	yes	—
528	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
529	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
530	C₄⋊Q₈	C₂³×C₁₃	1	8	yes	—
531	C₄⋊Q₈	C₂³×C₁₃	1	8	yes	—
532	C₄⋊Q₈	C₂³×C₁₃	1	8	yes	—
533	C₄⋊Q₈	C₂³×C₁₃	1	16	yes	—
534	C₄⋊Q₈	C₂³×C₁₃	1	16	yes	—
535	C₄⋊Q₈	C₂³×C₁₃	1	16	yes	—
536	#127	C₂³×C₁₃	1	1	yes	characteristic
537	#126	C₂³×C₁₃	1	16	yes	—
538	#126	C₂³×C₁₃	1	16	yes	—
539	#126	C₂³×C₁₃	1	8	yes	—
540	#126	C₂³×C₁₃	1	8	yes	—
541	#126	C₂³×C₁₃	1	16	yes	—
542	#126	C₂³×C₁₃	1	16	yes	—
543	#126	C₂³×C₁₃	1	16	yes	—
544	#126	C₂³×C₁₃	1	16	yes	—
545	#126	C₂³×C₁₃	1	16	yes	—
546	#126	C₂³×C₁₃	1	16	yes	—
547	#126	C₂³×C₁₃	1	16	yes	—
548	#126	C₂³×C₁₃	1	16	yes	—
549	#125	C₂³×C₁₃	1	4	yes	—
550	#125	C₂³×C₁₃	1	16	yes	—
551	#125	C₂³×C₁₃	1	16	yes	—
552	#125	C₂³×C₁₃	1	4	yes	—
553	#125	C₂³×C₁₃	1	2	yes	—
554	#125	C₂³×C₁₃	1	16	yes	—
555	#125	C₂³×C₁₃	1	8	yes	—
556	#125	C₂³×C₁₃	1	8	yes	—
557	#125	C₂³×C₁₃	1	8	yes	—
558	#125	C₂³×C₁₃	1	8	yes	—
559	#125	C₂³×C₁₃	1	2	yes	—
560	#125	C₂³×C₁₃	1	16	yes	—
561	#125	C₂³×C₁₃	1	2	yes	—
562	#125	C₂³×C₁₃	1	8	yes	—
563	#125	C₂³×C₁₃	1	16	yes	—
564	#125	C₂³×C₁₃	1	4	yes	—
565	#125	C₂³×C₁₃	1	8	yes	—
566	#125	C₂³×C₁₃	1	16	yes	—
567	#125	C₂³×C₁₃	1	16	yes	—
568	#125	C₂³×C₁₃	1	16	yes	—
569	#125	C₂³×C₁₃	1	16	yes	—
570	#125	C₂³×C₁₃	1	16	yes	—
571	#125	C₂³×C₁₃	1	16	yes	—
572	#125	C₂³×C₁₃	1	16	yes	—
573	#125	C₂³×C₁₃	1	16	yes	—
574	#125	C₂³×C₁₃	1	16	yes	—
575	#124	C₂³×C₁₃	1	8	yes	—
576	#124	C₂³×C₁₃	1	8	yes	—
577	#124	C₂³×C₁₃	1	8	yes	—
578	#124	C₂³×C₁₃	1	2	yes	—
579	#124	C₂³×C₁₃	1	16	yes	—
580	#123	C₂³×C₁₃	1	4	yes	—
581	#123	C₂³×C₁₃	1	16	yes	—
582	#123	C₂³×C₁₃	1	8	yes	—
583	#123	C₂³×C₁₃	1	8	yes	—
584	#123	C₂³×C₁₃	1	16	yes	—
585	#123	C₂³×C₁₃	1	16	yes	—
586	#123	C₂³×C₁₃	1	16	yes	—
587	C₂²⋊Q₈	C₂³×C₁₃	1	8	yes	—
588	C₂²⋊Q₈	C₂³×C₁₃	1	8	yes	—
589	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
590	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
591	C₂²⋊Q₈	C₂³×C₁₃	1	8	yes	—
592	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
593	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
594	C₂²⋊Q₈	C₂³×C₁₃	1	8	yes	—
595	C₂²⋊Q₈	C₂³×C₁₃	1	8	yes	—
596	C₂²⋊Q₈	C₂³×C₁₃	1	16	yes	—
597	C₂²⋊Q₈	C₂³×C₁₃	1	8	yes	—
598	C₂²⋊Q₈	C₂³×C₁₃	1	8	yes	—
599	C₂²⋊Q₈	C₂³×C₁₃	1	8	yes	—
600	C₂²⋊Q₈	C₂³×C₁₃	1	16	yes	—
601	C₂²⋊Q₈	C₂³×C₁₃	1	8	yes	—
602	C₂²⋊Q₈	C₂³×C₁₃	1	8	yes	—
603	C₂²⋊Q₈	C₂³×C₁₃	1	16	yes	—
604	C₂²⋊Q₈	C₂³×C₁₃	1	16	yes	—
605	C₂²⋊Q₈	C₂³×C₁₃	1	16	yes	—
606	C₂²⋊Q₈	C₂³×C₁₃	1	16	yes	—
607	C₂²⋊Q₈	C₂³×C₁₃	1	16	yes	—
608	C₂²⋊Q₈	C₂³×C₁₃	1	16	yes	—
609	#121	C₂³×C₁₃	1	4	yes	—
610	#121	C₂³×C₁₃	1	4	yes	—
611	#121	C₂³×C₁₃	1	8	yes	—
612	#120	C₂³×C₁₃	1	4	yes	—
613	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
614	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
615	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
616	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
617	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
618	C₄×Q₈	C₂³×C₁₃	1	8	yes	—
619	C₄×Q₈	C₂³×C₁₃	1	8	yes	—
620	C₄×Q₈	C₂³×C₁₃	1	8	yes	—
621	C₄×Q₈	C₂³×C₁₃	1	8	yes	—
622	C₄×Q₈	C₂³×C₁₃	1	8	yes	—
623	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
624	C₄×Q₈	C₂³×C₁₃	1	8	yes	—
625	C₄×Q₈	C₂³×C₁₃	1	8	yes	—
626	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
627	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
628	C₄×Q₈	C₂³×C₁₃	1	16	yes	—
629	C₄×Q₈	C₂³×C₁₃	1	8	yes	—
630	C₄×Q₈	C₂³×C₁₃	1	16	yes	—
631	C₄×Q₈	C₂³×C₁₃	1	8	yes	—
632	C₄×Q₈	C₂³×C₁₃	1	16	yes	—
633	C₄×Q₈	C₂³×C₁₃	1	16	yes	—
634	C₄×D₄	C₂³×C₁₃	1	8	yes	—
635	C₄×D₄	C₂³×C₁₃	1	4	yes	—
636	C₄×D₄	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	4	yes	—
640	C₄×D₄	C₂³×C₁₃	1	8	yes	—
641	C₄×D₄	C₂³×C₁₃	1	16	yes	—
642	#117	C₂³×C₁₃	1	4	yes	—
643	#117	C₂³×C₁₃	1	4	yes	—
644	#117	C₂³×C₁₃	1	2	yes	—
645	#117	C₂³×C₁₃	1	2	yes	—
646	#117	C₂³×C₁₃	1	4	yes	—
647	#117	C₂³×C₁₃	1	2	yes	—
648	#117	C₂³×C₁₃	1	4	yes	—
649	#117	C₂³×C₁₃	1	2	yes	—
650	#117	C₂³×C₁₃	1	2	yes	—
651	#117	C₂³×C₁₃	1	4	yes	—
652	#117	C₂³×C₁₃	1	16	yes	—
653	#117	C₂³×C₁₃	1	8	yes	—
654	#117	C₂³×C₁₃	1	16	yes	—
655	#117	C₂³×C₁₃	1	16	yes	—
656	#117	C₂³×C₁₃	1	16	yes	—
657	#117	C₂³×C₁₃	1	16	yes	—
658	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
659	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
660	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
661	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
662	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
663	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
664	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
665	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
666	C₂×C₄⋊C₄	C₂³×C₁₃	1	16	yes	—
667	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
668	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
669	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
670	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
671	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
672	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
673	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
674	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
675	C₂×C₁₃	—	2	2	no	—
676	C₂×C₁₃	—	4	4	no	—
677	C₂×C₁₃	—	4	2	no	—
678	C₂×C₁₃	C₂²×2₋¹⁺⁴	1	1	yes	characteristic
679	C₂×C₁₃	2₋¹⁺⁶	1	2	yes	—
680	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
681	#41	—	2	8	no	—
682	C₂×Q₈	—	2	8	no	—
683	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
684	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
685	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
686	C₂×Q₈	C₂⁴×C₁₃	1	8	yes	—
687	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
688	C₂×Q₈	C₂⁴×C₁₃	1	16	yes	—
689	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
690	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
691	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
692	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
693	C₂×D₄	C₂⁴×C₁₃	1	8	yes	—
694	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
695	C₂²×C₄	—	2	4	no	—
696	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
697	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
698	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
699	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
700	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
701	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
702	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
703	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
704	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
705	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
706	C₂²×C₄	C₂⁴×C₁₃	1	16	yes	—
707	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
708	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
709	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
710	C₄⋊C₄	C₂⁴×C₁₃	1	16	yes	—
711	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
712	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
713	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
714	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
715	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
716	C₄⋊C₄	C₂⁴×C₁₃	1	16	yes	—
717	C₄⋊C₄	C₂⁴×C₁₃	1	16	yes	—
718	C₄⋊C₄	C₂⁴×C₁₃	1	16	yes	—
719	C₄⋊C₄	C₂⁴×C₁₃	1	16	yes	—
720	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
721	C₄⋊C₄	C₂⁴×C₁₃	1	16	yes	—
722	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
723	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
724	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
725	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
726	C₄⋊C₄	C₂⁴×C₁₃	1	16	yes	—
727	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
728	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
729	C₄⋊C₄	C₂⁴×C₁₃	1	16	yes	—
730	C₄⋊C₄	C₂⁴×C₁₃	1	16	yes	—
731	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
732	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
733	C₄⋊C₄	C₂⁴×C₁₃	1	16	yes	—
734	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
735	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
736	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
737	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
738	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
739	C₄⋊C₄	C₂⁴×C₁₃	1	16	yes	—
740	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
741	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
742	C₂²⋊C₄	C₂⁴×C₁₃	1	4	yes	—
743	C₂²⋊C₄	C₂⁴×C₁₃	1	4	yes	—
744	C₂²⋊C₄	C₂⁴×C₁₃	1	4	yes	—
745	C₂²⋊C₄	C₂⁴×C₁₃	1	4	yes	—
746	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
747	C₂²⋊C₄	C₂⁴×C₁₃	1	4	yes	—
748	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
749	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
750	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
751	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
752	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
753	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
754	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
755	C₄²	C₂⁴×C₁₃	1	2	yes	—
756	C₄²	C₂⁴×C₁₃	1	4	yes	—
757	C₄²	C₂⁴×C₁₃	1	2	yes	—
758	C₄²	C₂⁴×C₁₃	1	4	yes	—
759	C₄²	C₂⁴×C₁₃	1	2	yes	—
760	C₄²	C₂⁴×C₁₃	1	8	yes	—
761	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
762	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
763	C₄²	C₂⁴×C₁₃	1	8	yes	—
764	C₄²	C₂⁴×C₁₃	1	4	yes	—
765	C₄²	C₂⁴×C₁₃	1	8	yes	—
766	C₄²	C₂⁴×C₁₃	1	8	yes	—
767	C₄²	C₂⁴×C₁₃	1	16	yes	—
768	C₄²	C₂⁴×C₁₃	1	16	yes	—
769	C₄²	C₂⁴×C₁₃	1	16	yes	—
770	C₁₃	#62889	1	1	yes	characteristic, direct product factor, Sylow
771	C₂³	—	2	2	no	—
772	C₂³	—	4	2	no	—
773	C₂³	C₂⁵×C₁₃	1	2	yes	—
774	C₂³	C₂⁵×C₁₃	1	4	yes	—
775	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
776	Q₈	—	2	8	no	—
777	Q₈	—	2	8	no	—
778	Q₈	—	2	4	no	—
779	Q₈	—	4	8	no	—
780	Q₈	—	4	4	no	—
781	Q₈	—	4	16	no	—
782	Q₈	—	4	4	no	—
783	Q₈	—	4	4	no	—
784	D₄	—	2	8	no	—
785	D₄	—	2	4	no	—
786	D₄	—	4	4	no	—
787	D₄	—	4	8	no	—
788	C₂×C₄	—	2	2	no	—
789	C₂×C₄	—	2	8	no	—
790	C₂×C₄	—	2	4	no	—
791	C₂×C₄	—	2	4	no	—
792	C₂×C₄	—	2	8	no	—
793	C₂×C₄	—	4	2	no	—
794	C₂×C₄	—	4	4	no	—
795	C₂×C₄	—	4	16	no	—
796	C₂×C₄	—	4	8	no	—
797	C₂×C₄	—	4	8	no	—
798	C₂×C₄	—	4	2	no	—
799	C₂×C₄	C₁₃×2₋¹⁺⁴	1	4	yes	—
800	C₂×C₄	C₂⁵×C₁₃	1	8	yes	—
801	C₂×C₄	C₂⁵×C₁₃	1	2	yes	—
802	C₂×C₄	C₂⁵×C₁₃	1	8	yes	—
803	C₂×C₄	C₂⁵×C₁₃	1	4	yes	—
804	C₂×C₄	C₂⁵×C₁₃	1	8	yes	—
805	C₂×C₄	C₂⁵×C₁₃	1	2	yes	—
806	C₂×C₄	C₂⁵×C₁₃	1	2	yes	—
807	C₂×C₄	C₂⁵×C₁₃	1	4	yes	—
808	C₂×C₄	C₂⁵×C₁₃	1	8	yes	—
809	C₂×C₄	C₂⁵×C₁₃	1	8	yes	—
810	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
811	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
812	C₂²	—	2	2	no	—
813	C₂²	—	2	2	no	—
814	C₂²	—	2	4	no	—
815	C₂²	—	2	8	no	—
816	C₂²	—	2	4	no	—
817	C₂²	—	8	2	no	—
818	C₂²	C₂×C₁₃×2₋¹⁺⁴	1	2	yes	—
819	C₂²	C₂⁶×C₁₃	1	1	yes	characteristic
820	C₄	—	2	2	no	—
821	C₄	—	2	4	no	—
822	C₄	—	2	8	no	—
823	C₄	—	2	8	no	—
824	C₄	—	2	4	no	—
825	C₄	—	2	8	no	—
826	C₄	—	2	2	no	—
827	C₄	—	2	8	no	—
828	C₄	—	2	8	no	—
829	C₄	—	2	2	no	—
830	C₄	C₂×C₁₃×2₋¹⁺⁴	1	2	yes	—
831	C₄	C₂×C₁₃×2₋¹⁺⁴	1	2	yes	—
832	C₂	—	2	2	no	—
833	C₂	—	4	2	no	—
834	C₂	—	4	4	no	—
835	C₂	C₂²×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
836	C₂	C₁₃×2₋¹⁺⁶	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂⁶
commutator, Frattini, cosocle	C₂²	C₂⁶×C₁₃
prime radical	C₁₃×#3455	C₂
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×#3564	C₂	semidirect
2. C₁₃×#3563	C₂	semidirect
3. C₁₃×#3563	C₂	semidirect
4. C₁₃×#3557	C₂	semidirect
5. C₁₃×#3556	C₂	semidirect
6. C₁₃×#3555	C₂	semidirect
7. C₁₃×#3555	C₂	semidirect
8. C₁₃×#3509	C₂	semidirect
9. C₁₃×#3507	C₂	semidirect
10. C₁₃×#3504	C₂	semidirect
11. C₁₃×#3502	C₂	semidirect
12. C₁₃×#3495	C₂	semidirect
13. C₁₃×#3458	C₂	semidirect
15. C₂×C₁₃×#541	C₂	semidirect
16. C₁₃×#564	C₂²	semidirect
19. C₁₃×#563	C₂²	semidirect
20. C₁₃×#559	C₂²	semidirect
21. Q₈²×C₁₃	C₂²	semidirect
22. Q₈²×C₁₃	C₂²	semidirect
23. C₁₃×#557	C₂²	semidirect
24. C₁₃×#557	C₂²	semidirect
25. C₁₃×#557	C₂²	semidirect
26. C₁₃×#557	C₂²	semidirect
27. C₁₃×#557	C₂²	semidirect
28. C₁₃×#557	C₂²	semidirect
29. C₁₃×#557	C₂²	semidirect
30. C₁₃×#557	C₂²	semidirect
33. C₁₃×#556	C₂²	semidirect
34. C₁₃×#556	C₂²	semidirect
35. C₁₃×#556	C₂²	semidirect
38. C₁₃×#554	C₂²	semidirect
39. C₁₃×#554	C₂²	semidirect
45. C₁₃×#552	C₂²	semidirect
46. C₁₃×#552	C₂²	semidirect
53. C₁₃×#544	C₂²	semidirect
54. C₁₃×#544	C₂²	semidirect
66. C₁₃×#541	C₂²	semidirect
67. C₁₃×#541	C₂²	semidirect
68. C₁₃×#541	C₂²	semidirect
69. C₁₃×#541	C₂²	semidirect
70. C₁₃×#541	C₂²	semidirect
84. C₁₃×#533	C₂²	semidirect
85. C₁₃×#533	C₂²	semidirect
94. C₂×C₁₃×#125	C₂²	semidirect
262. #62889	C₁₃	direct (N × H)
353. #3564	C₂×C₁₃	semidirect
354. #3563	C₂×C₁₃	semidirect
355. #3563	C₂×C₁₃	semidirect
356. #3557	C₂×C₁₃	semidirect
357. #3556	C₂×C₁₃	semidirect
358. #3555	C₂×C₁₃	semidirect
359. #3555	C₂×C₁₃	semidirect
360. #3509	C₂×C₁₃	semidirect
361. #3507	C₂×C₁₃	semidirect
362. #3504	C₂×C₁₃	semidirect
363. #3502	C₂×C₁₃	semidirect
364. #3495	C₂×C₁₃	semidirect
365. #3458	C₂×C₁₃	semidirect
367. C₂×#541	C₂×C₁₃	semidirect
409. #564	C₂²×C₁₃	semidirect
412. #563	C₂²×C₁₃	semidirect
413. #559	C₂²×C₁₃	semidirect
414. Q₈²	C₂²×C₁₃	semidirect
415. Q₈²	C₂²×C₁₃	semidirect
416. #557	C₂²×C₁₃	semidirect
417. #557	C₂²×C₁₃	semidirect
418. #557	C₂²×C₁₃	semidirect
419. #557	C₂²×C₁₃	semidirect
420. #557	C₂²×C₁₃	semidirect
421. #557	C₂²×C₁₃	semidirect
422. #557	C₂²×C₁₃	semidirect
423. #557	C₂²×C₁₃	semidirect
426. #556	C₂²×C₁₃	semidirect
427. #556	C₂²×C₁₃	semidirect
428. #556	C₂²×C₁₃	semidirect
431. #554	C₂²×C₁₃	semidirect
432. #554	C₂²×C₁₃	semidirect
438. #552	C₂²×C₁₃	semidirect
439. #552	C₂²×C₁₃	semidirect
446. #544	C₂²×C₁₃	semidirect
447. #544	C₂²×C₁₃	semidirect
459. #541	C₂²×C₁₃	semidirect
460. #541	C₂²×C₁₃	semidirect
461. #541	C₂²×C₁₃	semidirect
462. #541	C₂²×C₁₃	semidirect
463. #541	C₂²×C₁₃	semidirect
477. #533	C₂²×C₁₃	semidirect
478. #533	C₂²×C₁₃	semidirect
487. C₂×#125	C₂²×C₁₃	semidirect
770. C₁₃	#62889	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×#3564	2
C₁₃×#3563	2
C₁₃×#3557	2
C₁₃×#3556	2
C₁₃×#3555	2
C₁₃×#3509	2
C₁₃×#3507	2
C₁₃×#3504	2
C₁₃×#3502	2
C₁₃×#3495	2
C₁₃×#3458	2
C₁₃×#3455	2
C₂×C₁₃×#541	2
#62889	13

Subgroups — C13×#62889 #15749228

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#62889 #15749228