Subgroups — C₁₃×#61333 #15747672

Order 3328.

1798 conjugacy classes of subgroups.

The subgroup lattice has 752 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3507	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3501	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3376	C₂	1	4	yes	maximal, complemented
4	C₁₃×#3372	C₂	1	4	yes	maximal, complemented
5	C₁₃×#3370	C₂	1	4	yes	maximal, complemented
6	C₁₃×#3367	C₂	1	4	yes	maximal, complemented
7	C₁₃×#3137	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3135	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#3083	C₂	1	2	yes	maximal, complemented
10	C₁₃×#3078	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#3042	C₂	1	2	yes	maximal, complemented
12	C₁₃×#3036	C₂	1	1	yes	maximal, characteristic
13	C₁₃×#2961	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#2946	C₂	1	2	yes	maximal, complemented
15	C₂×C₁₃×#440	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	2	yes	—
17	C₂²×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
18	C₁₃×#559	C₂²	1	2	yes	complemented
19	C₁₃×#557	C₂²	1	2	yes	complemented
20	C₁₃×#556	—	2	1	no	—
21	C₁₃×#556	C₂²	1	4	yes	complemented
22	C₁₃×#554	—	2	1	no	—
23	C₁₃×#554	—	2	1	no	—
24	C₁₃×#554	—	2	2	no	—
25	C₁₃×#554	C₂²	1	4	yes	—
26	C₁₃×#554	C₂²	1	2	yes	—
27	C₁₃×#552	—	2	2	no	—
28	D₄×Q₈×C₁₃	—	2	1	no	—
29	D₄×Q₈×C₁₃	C₂²	1	2	yes	—
30	C₁₃×#544	C₂²	1	2	yes	—
31	C₁₃×#543	—	2	2	no	—
32	C₁₃×#539	—	2	2	no	—
33	C₁₃×#536	C₂²	1	2	yes	—
34	C₁₃×#533	C₂²	1	1	yes	characteristic
35	C₁₃×#533	C₂²	1	1	yes	characteristic
36	C₁₃×#532	C₂²	1	1	yes	characteristic
37	C₁₃×#529	—	2	2	no	—
38	C₂×C₁₃×C₂²⋊Q₈	—	2	2	no	—
39	C₁₃×#520	C₂²	1	2	yes	—
40	C₁₃×#518	C₂²	1	2	yes	—
41	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
42	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
43	C₁₃×#491	C₂²	1	2	yes	complemented
44	C₁₃×#491	C₂²	1	4	yes	complemented
45	C₁₃×#490	C₂²	1	2	yes	complemented
46	C₁₃×#489	C₂²	1	2	yes	complemented
47	C₁₃×#489	C₂²	1	4	yes	complemented
48	C₁₃×#489	C₂²	1	2	yes	complemented
49	C₁₃×#488	C₂²	1	4	yes	complemented
50	C₁₃×#487	C₂²	1	4	yes	complemented
51	C₁₃×#479	C₂²	1	4	yes	complemented
52	C₁₃×#479	C₂²	1	4	yes	complemented
53	C₁₃×#478	C₂²	1	4	yes	complemented
54	C₁₃×#477	C₂²	1	2	yes	complemented
55	C₁₃×#477	C₂²	1	4	yes	complemented
56	C₁₃×#475	C₂²	1	2	yes	complemented
57	C₁₃×#474	C₂²	1	4	yes	complemented
58	C₁₃×#463	C₂²	1	4	yes	—
59	C₁₃×#463	C₂²	1	4	yes	—
60	C₁₃×#463	C₂²	1	4	yes	—
61	C₁₃×#461	C₂²	1	2	yes	—
62	C₁₃×#461	C₂²	1	4	yes	—
63	C₁₃×#461	C₂²	1	4	yes	—
64	C₁₃×#459	C₂²	1	2	yes	—
65	C₁₃×#446	C₂²	1	4	yes	complemented
66	C₁₃×#446	C₂²	1	4	yes	complemented
67	C₁₃×#442	C₂²	1	4	yes	—
68	C₁₃×#440	C₂²	1	4	yes	—
69	C₁₃×#440	C₂²	1	4	yes	—
70	C₁₃×#440	C₂²	1	4	yes	—
71	C₄×C₁₃×SD₁₆	C₂²	1	4	yes	—
72	C₄×C₁₃×D₈	C₂²	1	4	yes	—
73	C₁₃×#428	C₂²	1	2	yes	—
74	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
75	C₁₃×#424	C₂²	1	2	yes	—
76	C₁₃×#423	C₂²	1	1	yes	characteristic
77	C₁₃×#419	C₂²	1	2	yes	—
78	C₁₃×#417	C₂²	1	2	yes	—
79	C₁₃×#416	C₂²	1	2	yes	—
80	C₁₃×#416	C₂²	1	2	yes	—
81	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
82	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
83	C₁₃×#405	C₂²	1	2	yes	—
84	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
85	C₂×C₁₃×#41	C₂³	1	2	yes	—
86	C₂²×Q₈×C₁₃	—	2	2	no	—
87	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
88	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
89	C₂³×C₄×C₁₃	—	2	1	no	—
90	C₁₃×AGL(1,ℤ/8)	—	2	8	no	—
91	C₂×C₁₃×SD₁₆	—	2	4	no	—
92	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
93	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
94	C₂×C₁₃×D₈	C₂³	1	4	yes	—
95	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
96	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
97	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
98	C₁₃×C₄⋊Q₈	—	2	2	no	—
99	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
100	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
101	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
102	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
103	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
104	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
105	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
106	C₁₃×#127	C₂³	1	1	yes	characteristic
107	C₁₃×#126	—	2	4	no	—
108	C₁₃×#126	—	2	4	no	—
109	C₁₃×#125	—	2	2	no	—
110	C₁₃×#125	—	2	4	no	—
111	C₁₃×#125	—	2	2	no	—
112	C₁₃×#125	D₄	1	2	yes	—
113	C₁₃×#125	C₂³	1	4	yes	—
114	C₁₃×#125	C₂³	1	2	yes	—
115	C₁₃×#124	—	2	2	no	—
116	C₁₃×#124	C₂³	1	4	yes	—
117	C₁₃×#124	C₂³	1	2	yes	—
118	C₁₃×#123	—	2	4	no	—
119	C₁₃×#123	—	2	4	no	—
120	C₁₃×C₂²⋊Q₈	—	2	2	no	—
121	C₁₃×C₂²⋊Q₈	—	2	4	no	—
122	C₁₃×C₂²⋊Q₈	—	2	4	no	—
123	C₁₃×C₂²⋊Q₈	—	2	1	no	—
124	C₁₃×C₂²⋊Q₈	—	2	1	no	—
125	C₁₃×C₂²⋊Q₈	—	2	2	no	—
126	C₁₃×C₂²⋊Q₈	—	2	4	no	—
127	C₁₃×C₂²⋊Q₈	—	2	2	no	—
128	C₁₃×C₂²⋊Q₈	—	2	2	no	—
129	C₁₃×C₂²⋊Q₈	—	2	4	no	—
130	C₁₃×C₂²⋊Q₈	—	2	4	no	—
131	C₁₃×C₂²⋊Q₈	—	2	4	no	—
132	C₁₃×C₂²⋊Q₈	—	2	4	no	—
133	C₁₃×C₂²⋊Q₈	D₄	1	2	yes	—
134	C₁₃×C₂²⋊Q₈	D₄	1	2	yes	—
135	C₁₃×#121	—	2	1	no	—
136	C₁₃×#121	—	2	1	no	—
137	C₄×Q₈×C₁₃	—	2	2	no	—
138	C₄×Q₈×C₁₃	—	2	1	no	—
139	C₄×Q₈×C₁₃	—	2	1	no	—
140	C₄×Q₈×C₁₃	—	2	1	no	—
141	C₄×Q₈×C₁₃	—	2	1	no	—
142	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
143	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
144	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
145	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
146	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
147	C₄×D₄×C₁₃	—	2	2	no	—
148	C₄×D₄×C₁₃	—	2	2	no	—
149	C₄×D₄×C₁₃	—	2	2	no	—
150	C₄×D₄×C₁₃	—	2	4	no	—
151	C₄×D₄×C₁₃	—	2	1	no	—
152	C₄×D₄×C₁₃	—	2	1	no	—
153	C₄×D₄×C₁₃	—	2	1	no	—
154	C₄×D₄×C₁₃	—	2	1	no	—
155	C₄×D₄×C₁₃	C₂³	1	4	yes	—
156	C₄×D₄×C₁₃	C₂³	1	4	yes	—
157	C₄×D₄×C₁₃	C₂³	1	4	yes	—
158	C₄×D₄×C₁₃	C₂³	1	2	yes	—
159	C₄×D₄×C₁₃	C₂³	1	2	yes	—
160	C₁₃×#117	—	2	2	no	—
161	C₁₃×#117	—	2	4	no	—
162	C₁₃×#117	C₂³	1	2	yes	—
163	C₁₃×#117	C₂³	1	2	yes	—
164	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
165	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
166	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
167	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
168	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
169	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
170	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
171	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
172	C₂×C₄²×C₁₃	—	2	1	no	—
173	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
174	C₁₃×#107	C₂³	1	4	yes	—
175	C₁₃×#107	C₂³	1	4	yes	—
176	C₁₃×#106	C₂³	1	4	yes	—
177	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
178	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
179	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
180	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
181	C₁₃×#103	C₂³	1	4	yes	—
182	C₁₃×#103	C₂³	1	2	yes	—
183	C₁₃×#103	C₂³	1	2	yes	—
184	C₁₃×#103	C₂³	1	2	yes	—
185	C₁₃×#103	C₂³	1	2	yes	—
186	C₁₃×#103	C₂³	1	4	yes	—
187	C₁₃×#103	C₂³	1	4	yes	—
188	C₁₃×#103	C₂³	1	4	yes	—
189	C₁₃×#102	C₂³	1	4	yes	—
190	C₁₃×#102	C₂³	1	2	yes	—
191	C₁₃×#102	C₂³	1	2	yes	—
192	C₁₃×#102	C₂³	1	2	yes	—
193	C₁₃×#102	C₂³	1	2	yes	—
194	C₁₃×#102	C₂³	1	4	yes	—
195	C₁₃×#97	C₂³	1	2	yes	—
196	C₁₃×#97	C₂³	1	2	yes	—
197	C₁₃×#97	C₂³	1	4	yes	—
198	C₄×C₈×C₁₃	C₂³	1	4	yes	—
199	#61333	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
200	C₂⁴×C₁₃	—	2	1	no	—
201	C₁₃×#41	—	2	4	no	—
202	C₁₃×#41	—	2	4	no	—
203	C₂×Q₈×C₁₃	—	2	1	no	—
204	C₂×Q₈×C₁₃	—	2	1	no	—
205	C₂×Q₈×C₁₃	—	2	1	no	—
206	C₂×Q₈×C₁₃	—	2	4	no	—
207	C₂×Q₈×C₁₃	—	2	2	no	—
208	C₂×Q₈×C₁₃	—	2	2	no	—
209	C₂×Q₈×C₁₃	—	8	4	no	—
210	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
211	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
212	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
213	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
214	C₂×D₄×C₁₃	—	2	2	no	—
215	C₂×D₄×C₁₃	—	2	1	no	—
216	C₂×D₄×C₁₃	—	2	1	no	—
217	C₂×D₄×C₁₃	—	2	1	no	—
218	C₂×D₄×C₁₃	—	2	2	no	—
219	C₂×D₄×C₁₃	#41	1	4	yes	—
220	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
221	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
222	C₂²×C₄×C₁₃	—	2	1	no	—
223	C₂²×C₄×C₁₃	—	2	1	no	—
224	C₂²×C₄×C₁₃	—	2	1	no	—
225	C₂²×C₄×C₁₃	—	2	2	no	—
226	C₂²×C₄×C₁₃	—	2	2	no	—
227	C₂²×C₄×C₁₃	—	2	4	no	—
228	C₂²×C₄×C₁₃	—	2	4	no	—
229	C₂²×C₄×C₁₃	—	2	2	no	—
230	C₂²×C₄×C₁₃	—	2	4	no	—
231	C₂²×C₄×C₁₃	—	8	2	no	—
232	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
233	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
234	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
235	C₁₃×SD₁₆	—	2	8	no	—
236	C₁₃×SD₁₆	—	2	8	no	—
237	C₁₃×D₈	—	2	8	no	—
238	C₁₃×M₁₆	—	2	4	no	—
239	C₂×C₈×C₁₃	—	2	2	no	—
240	C₂×C₈×C₁₃	—	2	2	no	—
241	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
242	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
243	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
244	C₁₃×C₄⋊C₄	—	2	1	no	—
245	C₁₃×C₄⋊C₄	—	2	2	no	—
246	C₁₃×C₄⋊C₄	—	2	1	no	—
247	C₁₃×C₄⋊C₄	—	2	4	no	—
248	C₁₃×C₄⋊C₄	—	2	2	no	—
249	C₁₃×C₄⋊C₄	—	2	2	no	—
250	C₁₃×C₄⋊C₄	—	2	4	no	—
251	C₁₃×C₄⋊C₄	—	2	4	no	—
252	C₁₃×C₄⋊C₄	—	2	4	no	—
253	C₁₃×C₄⋊C₄	—	2	1	no	—
254	C₁₃×C₄⋊C₄	—	2	4	no	—
255	C₁₃×C₄⋊C₄	—	2	1	no	—
256	C₁₃×C₄⋊C₄	—	2	1	no	—
257	C₁₃×C₄⋊C₄	—	2	2	no	—
258	C₁₃×C₄⋊C₄	—	2	1	no	—
259	C₁₃×C₄⋊C₄	—	2	4	no	—
260	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
261	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
262	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
263	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
264	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
265	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
266	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
267	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
268	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
269	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
270	C₁₃×C₂²⋊C₄	—	2	2	no	—
271	C₁₃×C₂²⋊C₄	—	2	4	no	—
272	C₁₃×C₂²⋊C₄	—	2	4	no	—
273	C₁₃×C₂²⋊C₄	—	2	2	no	—
274	C₁₃×C₂²⋊C₄	—	2	2	no	—
275	C₁₃×C₂²⋊C₄	—	2	2	no	—
276	C₁₃×C₂²⋊C₄	—	2	4	no	—
277	C₁₃×C₂²⋊C₄	—	2	4	no	—
278	C₁₃×C₂²⋊C₄	—	2	2	no	—
279	C₁₃×C₂²⋊C₄	—	2	4	no	—
280	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
281	C₄²×C₁₃	—	2	2	no	—
282	C₄²×C₁₃	—	2	2	no	—
283	C₄²×C₁₃	—	2	4	no	—
284	C₄²×C₁₃	—	2	2	no	—
285	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
286	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
287	C₄²×C₁₃	C₂⁴	1	4	yes	—
288	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
289	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
290	#3507	C₂×C₁₃	1	1	yes	characteristic, complemented
291	#3501	C₂×C₁₃	1	1	yes	characteristic, complemented
292	#3376	C₂×C₁₃	1	4	yes	complemented
293	#3372	C₂×C₁₃	1	4	yes	complemented
294	#3370	C₂×C₁₃	1	4	yes	complemented
295	#3367	C₂×C₁₃	1	4	yes	complemented
296	#3137	C₂×C₁₃	1	2	yes	complemented
297	#3135	C₂×C₁₃	1	1	yes	characteristic, complemented
298	#3083	C₂×C₁₃	1	2	yes	complemented
299	#3078	C₂×C₁₃	1	1	yes	characteristic, complemented
300	#3042	C₂×C₁₃	1	2	yes	complemented
301	#3036	C₂×C₁₃	1	1	yes	characteristic
302	#2961	C₂×C₁₃	1	1	yes	characteristic, complemented
303	#2946	C₂×C₁₃	1	2	yes	complemented
304	C₂×#440	C₂×C₁₃	1	1	yes	characteristic, complemented
305	C₂³×C₁₃	—	2	2	no	—
306	C₂³×C₁₃	—	2	4	no	—
307	C₂³×C₁₃	—	2	2	no	—
308	C₂³×C₁₃	—	8	1	no	—
309	C₂³×C₁₃	—	8	1	no	—
310	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
311	Q₈×C₁₃	—	2	2	no	—
312	Q₈×C₁₃	—	2	2	no	—
313	Q₈×C₁₃	—	2	2	no	—
314	Q₈×C₁₃	—	2	2	no	—
315	Q₈×C₁₃	—	4	2	no	—
316	Q₈×C₁₃	—	4	2	no	—
317	Q₈×C₁₃	—	4	2	no	—
318	Q₈×C₁₃	—	4	2	no	—
319	Q₈×C₁₃	—	8	1	no	—
320	Q₈×C₁₃	—	8	4	no	—
321	D₄×C₁₃	—	2	4	no	—
322	D₄×C₁₃	—	2	2	no	—
323	D₄×C₁₃	—	2	2	no	—
324	D₄×C₁₃	—	2	2	no	—
325	D₄×C₁₃	—	4	2	no	—
326	D₄×C₁₃	—	4	4	no	—
327	D₄×C₁₃	—	8	1	no	—
328	D₄×C₁₃	C₂×#41	1	4	yes	—
329	C₂×C₄×C₁₃	—	2	2	no	—
330	C₂×C₄×C₁₃	—	2	2	no	—
331	C₂×C₄×C₁₃	—	2	2	no	—
332	C₂×C₄×C₁₃	—	2	2	no	—
333	C₂×C₄×C₁₃	—	2	2	no	—
334	C₂×C₄×C₁₃	—	2	2	no	—
335	C₂×C₄×C₁₃	—	4	1	no	—
336	C₂×C₄×C₁₃	—	4	1	no	—
337	C₂×C₄×C₁₃	—	4	4	no	—
338	C₂×C₄×C₁₃	—	4	2	no	—
339	C₂×C₄×C₁₃	—	4	4	no	—
340	C₂×C₄×C₁₃	—	8	4	no	—
341	C₂×C₄×C₁₃	—	8	4	no	—
342	C₂×C₄×C₁₃	—	8	2	no	—
343	C₂×C₄×C₁₃	—	8	4	no	—
344	C₂×C₄×C₁₃	—	8	1	no	—
345	C₂×C₄×C₁₃	—	8	1	no	—
346	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
347	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
348	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
349	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
350	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
351	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
352	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
353	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
354	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
355	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
356	C₈×C₁₃	—	2	2	no	—
357	C₈×C₁₃	—	2	4	no	—
358	C₈×C₁₃	—	2	2	no	—
359	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	2	yes	—
360	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
361	#559	C₂²×C₁₃	1	2	yes	complemented
362	#557	C₂²×C₁₃	1	2	yes	complemented
363	#556	—	2	1	no	—
364	#556	C₂²×C₁₃	1	4	yes	complemented
365	#554	—	2	1	no	—
366	#554	—	2	1	no	—
367	#554	—	2	2	no	—
368	#554	C₂²×C₁₃	1	4	yes	—
369	#554	C₂²×C₁₃	1	2	yes	—
370	#552	—	2	2	no	—
371	D₄×Q₈	—	2	1	no	—
372	D₄×Q₈	C₂²×C₁₃	1	2	yes	—
373	#544	C₂²×C₁₃	1	2	yes	—
374	#543	—	2	2	no	—
375	#539	—	2	2	no	—
376	#536	C₂²×C₁₃	1	2	yes	—
377	#533	C₂²×C₁₃	1	1	yes	characteristic
378	#533	C₂²×C₁₃	1	1	yes	characteristic
379	#532	C₂²×C₁₃	1	1	yes	characteristic
380	#529	—	2	2	no	—
381	C₂×C₂²⋊Q₈	—	2	2	no	—
382	#520	C₂²×C₁₃	1	2	yes	—
383	#518	C₂²×C₁₃	1	2	yes	—
384	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
385	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
386	#491	C₂²×C₁₃	1	2	yes	complemented
387	#491	C₂²×C₁₃	1	4	yes	complemented
388	#490	C₂²×C₁₃	1	2	yes	complemented
389	#489	C₂²×C₁₃	1	2	yes	complemented
390	#489	C₂²×C₁₃	1	4	yes	complemented
391	#489	C₂²×C₁₃	1	2	yes	complemented
392	#488	C₂²×C₁₃	1	4	yes	complemented
393	#487	C₂²×C₁₃	1	4	yes	complemented
394	#479	C₂²×C₁₃	1	4	yes	complemented
395	#479	C₂²×C₁₃	1	4	yes	complemented
396	#478	C₂²×C₁₃	1	4	yes	complemented
397	#477	C₂²×C₁₃	1	2	yes	complemented
398	#477	C₂²×C₁₃	1	4	yes	complemented
399	#475	C₂²×C₁₃	1	2	yes	complemented
400	#474	C₂²×C₁₃	1	4	yes	complemented
401	#463	C₂²×C₁₃	1	4	yes	—
402	#463	C₂²×C₁₃	1	4	yes	—
403	#463	C₂²×C₁₃	1	4	yes	—
404	#461	C₂²×C₁₃	1	4	yes	—
405	#461	C₂²×C₁₃	1	2	yes	—
406	#461	C₂²×C₁₃	1	4	yes	—
407	#459	C₂²×C₁₃	1	2	yes	—
408	#446	C₂²×C₁₃	1	4	yes	complemented
409	#446	C₂²×C₁₃	1	4	yes	complemented
410	#442	C₂²×C₁₃	1	4	yes	—
411	#440	C₂²×C₁₃	1	4	yes	—
412	#440	C₂²×C₁₃	1	4	yes	—
413	#440	C₂²×C₁₃	1	4	yes	—
414	C₄×SD₁₆	C₂²×C₁₃	1	4	yes	—
415	C₄×D₈	C₂²×C₁₃	1	4	yes	—
416	#428	C₂²×C₁₃	1	2	yes	—
417	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
418	#424	C₂²×C₁₃	1	2	yes	—
419	#423	C₂²×C₁₃	1	1	yes	characteristic
420	#419	C₂²×C₁₃	1	2	yes	—
421	#417	C₂²×C₁₃	1	2	yes	—
422	#416	C₂²×C₁₃	1	2	yes	—
423	#416	C₂²×C₁₃	1	2	yes	—
424	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
425	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
426	#405	C₂²×C₁₃	1	2	yes	—
427	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
428	C₂²×C₁₃	—	2	1	no	—
429	C₂²×C₁₃	—	2	1	no	—
430	C₂²×C₁₃	—	2	4	no	—
431	C₂²×C₁₃	—	4	2	no	—
432	C₂²×C₁₃	—	4	2	no	—
433	C₂²×C₁₃	—	4	2	no	—
434	C₂²×C₁₃	—	4	2	no	—
435	C₂²×C₁₃	—	4	2	no	—
436	C₂²×C₁₃	—	8	4	no	—
437	C₂²×C₁₃	#548	1	2	yes	—
438	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
439	C₄×C₁₃	—	2	1	no	—
440	C₄×C₁₃	—	2	1	no	—
441	C₄×C₁₃	—	2	4	no	—
442	C₄×C₁₃	—	2	1	no	—
443	C₄×C₁₃	—	2	1	no	—
444	C₄×C₁₃	—	2	4	no	—
445	C₄×C₁₃	—	4	2	no	—
446	C₄×C₁₃	—	4	2	no	—
447	C₄×C₁₃	—	4	2	no	—
448	C₄×C₁₃	—	4	2	no	—
449	C₄×C₁₃	—	4	2	no	—
450	C₄×C₁₃	—	4	2	no	—
451	C₄×C₁₃	#548	1	2	yes	—
452	C₄×C₁₃	C₂²×#41	1	1	yes	characteristic
453	C₄×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
454	C₂×#41	C₂³×C₁₃	1	2	yes	—
455	C₂²×Q₈	—	2	2	no	—
456	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
457	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
458	C₂³×C₄	—	2	1	no	—
459	AGL(1,ℤ/8)	—	2	8	no	—
460	C₂×SD₁₆	—	2	4	no	—
461	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
462	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
463	C₂×D₈	C₂³×C₁₃	1	4	yes	—
464	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
465	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
466	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
467	C₄⋊Q₈	—	2	2	no	—
468	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
469	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
470	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
471	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
472	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
473	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
474	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
475	#127	C₂³×C₁₃	1	1	yes	characteristic
476	#126	—	2	4	no	—
477	#126	—	2	4	no	—
478	#125	—	2	2	no	—
479	#125	—	2	4	no	—
480	#125	—	2	2	no	—
481	#125	D₄×C₁₃	1	2	yes	—
482	#125	C₂³×C₁₃	1	2	yes	—
483	#125	C₂³×C₁₃	1	4	yes	—
484	#124	—	2	2	no	—
485	#124	C₂³×C₁₃	1	2	yes	—
486	#124	C₂³×C₁₃	1	4	yes	—
487	#123	—	2	4	no	—
488	#123	—	2	4	no	—
489	C₂²⋊Q₈	—	2	2	no	—
490	C₂²⋊Q₈	—	2	4	no	—
491	C₂²⋊Q₈	—	2	4	no	—
492	C₂²⋊Q₈	—	2	1	no	—
493	C₂²⋊Q₈	—	2	1	no	—
494	C₂²⋊Q₈	—	2	2	no	—
495	C₂²⋊Q₈	—	2	4	no	—
496	C₂²⋊Q₈	—	2	2	no	—
497	C₂²⋊Q₈	—	2	2	no	—
498	C₂²⋊Q₈	—	2	4	no	—
499	C₂²⋊Q₈	—	2	4	no	—
500	C₂²⋊Q₈	—	2	4	no	—
501	C₂²⋊Q₈	—	2	4	no	—
502	C₂²⋊Q₈	D₄×C₁₃	1	2	yes	—
503	C₂²⋊Q₈	D₄×C₁₃	1	2	yes	—
504	#121	—	2	1	no	—
505	#121	—	2	1	no	—
506	C₄×Q₈	—	2	2	no	—
507	C₄×Q₈	—	2	1	no	—
508	C₄×Q₈	—	2	1	no	—
509	C₄×Q₈	—	2	1	no	—
510	C₄×Q₈	—	2	1	no	—
511	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
512	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
513	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
514	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
515	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
516	C₄×D₄	—	2	2	no	—
517	C₄×D₄	—	2	2	no	—
518	C₄×D₄	—	2	2	no	—
519	C₄×D₄	—	2	4	no	—
520	C₄×D₄	—	2	1	no	—
521	C₄×D₄	—	2	1	no	—
522	C₄×D₄	—	2	1	no	—
523	C₄×D₄	—	2	1	no	—
524	C₄×D₄	C₂³×C₁₃	1	2	yes	—
525	C₄×D₄	C₂³×C₁₃	1	2	yes	—
526	C₄×D₄	C₂³×C₁₃	1	4	yes	—
527	C₄×D₄	C₂³×C₁₃	1	4	yes	—
528	C₄×D₄	C₂³×C₁₃	1	4	yes	—
529	#117	—	2	2	no	—
530	#117	—	2	4	no	—
531	#117	C₂³×C₁₃	1	2	yes	—
532	#117	C₂³×C₁₃	1	2	yes	—
533	C₂×C₄⋊C₄	—	2	1	no	—
534	C₂×C₄⋊C₄	—	2	2	no	—
535	C₂×C₄⋊C₄	—	2	4	no	—
536	C₂×C₄⋊C₄	—	2	2	no	—
537	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
538	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
539	C₂×C₂²⋊C₄	—	2	1	no	—
540	C₂×C₂²⋊C₄	—	2	4	no	—
541	C₂×C₄²	—	2	1	no	—
542	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
543	#107	C₂³×C₁₃	1	4	yes	—
544	#107	C₂³×C₁₃	1	4	yes	—
545	#106	C₂³×C₁₃	1	4	yes	—
546	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
547	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
548	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
549	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
550	#103	C₂³×C₁₃	1	4	yes	—
551	#103	C₂³×C₁₃	1	2	yes	—
552	#103	C₂³×C₁₃	1	2	yes	—
553	#103	C₂³×C₁₃	1	2	yes	—
554	#103	C₂³×C₁₃	1	2	yes	—
555	#103	C₂³×C₁₃	1	4	yes	—
556	#103	C₂³×C₁₃	1	4	yes	—
557	#103	C₂³×C₁₃	1	4	yes	—
558	#102	C₂³×C₁₃	1	4	yes	—
559	#102	C₂³×C₁₃	1	2	yes	—
560	#102	C₂³×C₁₃	1	2	yes	—
561	#102	C₂³×C₁₃	1	2	yes	—
562	#102	C₂³×C₁₃	1	2	yes	—
563	#102	C₂³×C₁₃	1	4	yes	—
564	#97	C₂³×C₁₃	1	2	yes	—
565	#97	C₂³×C₁₃	1	2	yes	—
566	#97	C₂³×C₁₃	1	4	yes	—
567	C₄×C₈	C₂³×C₁₃	1	4	yes	—
568	C₂×C₁₃	—	2	2	no	—
569	C₂×C₁₃	—	4	4	no	—
570	C₂×C₁₃	—	8	2	no	—
571	C₂×C₁₃	C₂×#548	1	1	yes	characteristic
572	C₂×C₁₃	#3585	1	1	yes	characteristic
573	C₂×C₁₃	#3586	1	1	yes	characteristic
574	C₂⁴	—	2	1	no	—
575	#41	—	2	4	no	—
576	#41	—	2	4	no	—
577	C₂×Q₈	—	2	1	no	—
578	C₂×Q₈	—	2	1	no	—
579	C₂×Q₈	—	2	1	no	—
580	C₂×Q₈	—	2	4	no	—
581	C₂×Q₈	—	2	2	no	—
582	C₂×Q₈	—	2	2	no	—
583	C₂×Q₈	—	8	4	no	—
584	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
585	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
586	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
587	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
588	C₂×D₄	—	2	2	no	—
589	C₂×D₄	—	2	1	no	—
590	C₂×D₄	—	2	1	no	—
591	C₂×D₄	—	2	1	no	—
592	C₂×D₄	—	2	2	no	—
593	C₂×D₄	C₁₃×#41	1	4	yes	—
594	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
595	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
596	C₂²×C₄	—	2	1	no	—
597	C₂²×C₄	—	2	1	no	—
598	C₂²×C₄	—	2	1	no	—
599	C₂²×C₄	—	2	2	no	—
600	C₂²×C₄	—	2	2	no	—
601	C₂²×C₄	—	2	4	no	—
602	C₂²×C₄	—	2	4	no	—
603	C₂²×C₄	—	2	2	no	—
604	C₂²×C₄	—	2	4	no	—
605	C₂²×C₄	—	8	2	no	—
606	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
607	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
608	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
609	SD₁₆	—	2	8	no	—
610	SD₁₆	—	2	8	no	—
611	D₈	—	2	8	no	—
612	M₁₆	—	2	4	no	—
613	C₂×C₈	—	2	2	no	—
614	C₂×C₈	—	2	2	no	—
615	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
616	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
617	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
618	C₄⋊C₄	—	2	1	no	—
619	C₄⋊C₄	—	2	2	no	—
620	C₄⋊C₄	—	2	1	no	—
621	C₄⋊C₄	—	2	4	no	—
622	C₄⋊C₄	—	2	2	no	—
623	C₄⋊C₄	—	2	2	no	—
624	C₄⋊C₄	—	2	4	no	—
625	C₄⋊C₄	—	2	4	no	—
626	C₄⋊C₄	—	2	4	no	—
627	C₄⋊C₄	—	2	1	no	—
628	C₄⋊C₄	—	2	4	no	—
629	C₄⋊C₄	—	2	1	no	—
630	C₄⋊C₄	—	2	1	no	—
631	C₄⋊C₄	—	2	2	no	—
632	C₄⋊C₄	—	2	1	no	—
633	C₄⋊C₄	—	2	4	no	—
634	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
635	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
636	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
637	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
638	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
639	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
640	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
641	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
642	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
643	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
644	C₂²⋊C₄	—	2	2	no	—
645	C₂²⋊C₄	—	2	4	no	—
646	C₂²⋊C₄	—	2	4	no	—
647	C₂²⋊C₄	—	2	2	no	—
648	C₂²⋊C₄	—	2	2	no	—
649	C₂²⋊C₄	—	2	2	no	—
650	C₂²⋊C₄	—	2	4	no	—
651	C₂²⋊C₄	—	2	4	no	—
652	C₂²⋊C₄	—	2	2	no	—
653	C₂²⋊C₄	—	2	4	no	—
654	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
655	C₄²	—	2	2	no	—
656	C₄²	—	2	2	no	—
657	C₄²	—	2	4	no	—
658	C₄²	—	2	2	no	—
659	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
660	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
661	C₄²	C₂⁴×C₁₃	1	4	yes	—
662	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
663	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
664	C₁₃	#61333	1	1	yes	characteristic, direct product factor, Sylow
665	C₂³	—	2	2	no	—
666	C₂³	—	2	4	no	—
667	C₂³	—	2	2	no	—
668	C₂³	—	8	1	no	—
669	C₂³	—	8	1	no	—
670	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
671	Q₈	—	2	2	no	—
672	Q₈	—	2	2	no	—
673	Q₈	—	2	2	no	—
674	Q₈	—	2	2	no	—
675	Q₈	—	4	2	no	—
676	Q₈	—	4	2	no	—
677	Q₈	—	4	2	no	—
678	Q₈	—	4	2	no	—
679	Q₈	—	8	4	no	—
680	Q₈	—	8	1	no	—
681	D₄	—	2	4	no	—
682	D₄	—	2	2	no	—
683	D₄	—	2	2	no	—
684	D₄	—	2	2	no	—
685	D₄	—	4	2	no	—
686	D₄	—	4	4	no	—
687	D₄	—	8	1	no	—
688	D₄	C₂×C₁₃×#41	1	4	yes	—
689	C₂×C₄	—	2	2	no	—
690	C₂×C₄	—	2	2	no	—
691	C₂×C₄	—	2	2	no	—
692	C₂×C₄	—	2	2	no	—
693	C₂×C₄	—	2	2	no	—
694	C₂×C₄	—	2	2	no	—
695	C₂×C₄	—	4	1	no	—
696	C₂×C₄	—	4	1	no	—
697	C₂×C₄	—	4	4	no	—
698	C₂×C₄	—	4	2	no	—
699	C₂×C₄	—	4	4	no	—
700	C₂×C₄	—	8	2	no	—
701	C₂×C₄	—	8	4	no	—
702	C₂×C₄	—	8	4	no	—
703	C₂×C₄	—	8	4	no	—
704	C₂×C₄	—	8	1	no	—
705	C₂×C₄	—	8	1	no	—
706	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
707	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
708	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
709	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
710	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
711	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
712	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
713	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
714	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
715	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
716	C₈	—	2	2	no	—
717	C₈	—	2	4	no	—
718	C₈	—	2	2	no	—
719	C₂²	—	2	1	no	—
720	C₂²	—	2	1	no	—
721	C₂²	—	2	4	no	—
722	C₂²	—	4	2	no	—
723	C₂²	—	4	2	no	—
724	C₂²	—	4	2	no	—
725	C₂²	—	4	2	no	—
726	C₂²	—	4	2	no	—
727	C₂²	—	8	4	no	—
728	C₂²	C₁₃×#548	1	2	yes	—
729	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
730	C₄	—	2	1	no	—
731	C₄	—	2	1	no	—
732	C₄	—	2	4	no	—
733	C₄	—	2	1	no	—
734	C₄	—	2	1	no	—
735	C₄	—	2	4	no	—
736	C₄	—	4	2	no	—
737	C₄	—	4	2	no	—
738	C₄	—	4	2	no	—
739	C₄	—	4	2	no	—
740	C₄	—	4	2	no	—
741	C₄	—	4	2	no	—
742	C₄	C₁₃×#548	1	2	yes	—
743	C₄	C₂²×C₁₃×#41	1	1	yes	characteristic
744	C₄	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
745	C₂	—	2	2	no	—
746	C₂	—	4	4	no	—
747	C₂	—	8	2	no	—
748	C₂	C₂×C₁₃×#548	1	1	yes	characteristic
749	C₂	C₁₃×#3585	1	1	yes	characteristic
750	C₂	C₁₃×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
prime radical	C₁₃×#3036	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₁₃×#533 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3507	C₂	semidirect
2. C₁₃×#3501	C₂	semidirect
3. C₁₃×#3376	C₂	semidirect
4. C₁₃×#3372	C₂	semidirect
5. C₁₃×#3370	C₂	semidirect
6. C₁₃×#3367	C₂	semidirect
7. C₁₃×#3137	C₂	semidirect
8. C₁₃×#3135	C₂	semidirect
9. C₁₃×#3083	C₂	semidirect
10. C₁₃×#3078	C₂	semidirect
11. C₁₃×#3042	C₂	semidirect
13. C₁₃×#2961	C₂	semidirect
14. C₁₃×#2946	C₂	semidirect
15. C₂×C₁₃×#440	C₂	semidirect
18. C₁₃×#559	C₂²	semidirect
19. C₁₃×#557	C₂²	semidirect
21. C₁₃×#556	C₂²	semidirect
43. C₁₃×#491	C₂²	semidirect
44. C₁₃×#491	C₂²	semidirect
45. C₁₃×#490	C₂²	semidirect
46. C₁₃×#489	C₂²	semidirect
47. C₁₃×#489	C₂²	semidirect
48. C₁₃×#489	C₂²	semidirect
49. C₁₃×#488	C₂²	semidirect
50. C₁₃×#487	C₂²	semidirect
51. C₁₃×#479	C₂²	semidirect
52. C₁₃×#479	C₂²	semidirect
53. C₁₃×#478	C₂²	semidirect
54. C₁₃×#477	C₂²	semidirect
55. C₁₃×#477	C₂²	semidirect
56. C₁₃×#475	C₂²	semidirect
57. C₁₃×#474	C₂²	semidirect
65. C₁₃×#446	C₂²	semidirect
66. C₁₃×#446	C₂²	semidirect
199. #61333	C₁₃	direct (N × H)
290. #3507	C₂×C₁₃	semidirect
291. #3501	C₂×C₁₃	semidirect
292. #3376	C₂×C₁₃	semidirect
293. #3372	C₂×C₁₃	semidirect
294. #3370	C₂×C₁₃	semidirect
295. #3367	C₂×C₁₃	semidirect
296. #3137	C₂×C₁₃	semidirect
297. #3135	C₂×C₁₃	semidirect
298. #3083	C₂×C₁₃	semidirect
299. #3078	C₂×C₁₃	semidirect
300. #3042	C₂×C₁₃	semidirect
302. #2961	C₂×C₁₃	semidirect
303. #2946	C₂×C₁₃	semidirect
304. C₂×#440	C₂×C₁₃	semidirect
361. #559	C₂²×C₁₃	semidirect
362. #557	C₂²×C₁₃	semidirect
364. #556	C₂²×C₁₃	semidirect
386. #491	C₂²×C₁₃	semidirect
387. #491	C₂²×C₁₃	semidirect
388. #490	C₂²×C₁₃	semidirect
389. #489	C₂²×C₁₃	semidirect
390. #489	C₂²×C₁₃	semidirect
391. #489	C₂²×C₁₃	semidirect
392. #488	C₂²×C₁₃	semidirect
393. #487	C₂²×C₁₃	semidirect
394. #479	C₂²×C₁₃	semidirect
395. #479	C₂²×C₁₃	semidirect
396. #478	C₂²×C₁₃	semidirect
397. #477	C₂²×C₁₃	semidirect
398. #477	C₂²×C₁₃	semidirect
399. #475	C₂²×C₁₃	semidirect
400. #474	C₂²×C₁₃	semidirect
408. #446	C₂²×C₁₃	semidirect
409. #446	C₂²×C₁₃	semidirect
664. C₁₃	#61333	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×#3507	2
C₁₃×#3501	2
C₁₃×#3376	2
C₁₃×#3372	2
C₁₃×#3370	2
C₁₃×#3367	2
C₁₃×#3137	2
C₁₃×#3135	2
C₁₃×#3083	2
C₁₃×#3078	2
C₁₃×#3042	2
C₁₃×#3036	2
C₁₃×#2961	2
C₁₃×#2946	2
C₂×C₁₃×#440	2
#61333	13

Subgroups — C13×#61333 #15747672

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61333 #15747672