Subgroups — C₁₃×#61631 #15747970

Order 3328.

2222 conjugacy classes of subgroups.

The subgroup lattice has 754 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3538	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3484	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#3310	C₂	1	4	yes	maximal, complemented
4	C₁₃×#3296	C₂	1	4	yes	maximal, complemented
5	D₄×C₁₃×SD₁₆	C₂	1	4	yes	maximal, complemented
6	C₁₃×#3266	C₂	1	4	yes	maximal, complemented
7	C₁₃×#3222	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3200	C₂	1	2	yes	maximal, complemented
9	C₁₃×#3190	C₂	1	2	yes	maximal, complemented
10	C₁₃×#3123	C₂	1	2	yes	maximal, complemented
11	C₁₃×#3009	C₂	1	2	yes	maximal, complemented
12	C₂×C₁₃×#450	C₂	1	2	yes	maximal, complemented
13	C₁₃×#2977	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₁₃×H(5,𝔽₂)	C₂²	1	1	yes	characteristic
15	C₂³×D₄×C₁₃	C₂²	1	1	yes	characteristic
16	C₂×C₁₃×#137	C₂²	1	2	yes	complemented
17	C₂²×C₁₃×SD₁₆	C₂²	1	4	yes	complemented
18	C₂²×C₁₃×SD₁₆	C₂²	1	2	yes	complemented
19	C₁₃×#563	—	2	2	no	—
20	C₁₃×#552	C₂²	1	4	yes	complemented
21	C₁₃×#551	—	2	2	no	—
22	D₄×Q₈×C₁₃	C₂²	1	4	yes	complemented
23	C₁₃×#546	—	2	2	no	—
24	C₁₃×#546	C₂²	1	4	yes	—
25	D₄²×C₁₃	—	2	2	no	—
26	D₄²×C₁₃	C₂²	1	4	yes	—
27	C₁₃×#544	—	2	2	no	—
28	C₁₃×#541	C₂²	1	2	yes	complemented
29	C₁₃×#539	—	2	2	no	—
30	C₁₃×#536	C₂²	1	2	yes	complemented
31	C₁₃×#535	C₂²	1	1	yes	characteristic
32	C₁₃×#535	C₂²	1	1	yes	characteristic
33	C₁₃×#534	—	2	2	no	—
34	C₁₃×#525	C₂²	1	1	yes	characteristic
35	C₁₃×#525	C₂²	1	1	yes	characteristic
36	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
37	C₂×C₁₃×#120	—	2	2	no	—
38	C₁₃×#518	C₂²	1	1	yes	characteristic
39	C₁₃×#497	C₂²	1	2	yes	complemented
40	C₁₃×#492	C₂²	1	2	yes	complemented
41	C₁₃×#490	C₂²	1	2	yes	complemented
42	C₁₃×#488	C₂²	1	2	yes	complemented
43	C₁₃×#485	C₂²	1	4	yes	complemented
44	C₁₃×#483	C₂²	1	2	yes	complemented
45	C₁₃×#482	C₂²	1	4	yes	complemented
46	C₁₃×#480	C₂²	1	2	yes	complemented
47	C₁₃×#478	C₂²	1	4	yes	complemented
48	C₁₃×#468	C₂²	1	4	yes	complemented
49	C₁₃×#467	C₂²	1	4	yes	complemented
50	C₁₃×#465	C₂²	1	4	yes	complemented
51	C₁₃×#465	C₂²	1	4	yes	complemented
52	C₁₃×#464	C₂²	1	4	yes	complemented
53	C₁₃×#461	C₂²	1	4	yes	complemented
54	C₁₃×#460	C₂²	1	4	yes	complemented
55	C₁₃×#452	C₂²	1	4	yes	complemented
56	C₁₃×#452	C₂²	1	4	yes	complemented
57	C₁₃×#451	C₂²	1	2	yes	complemented
58	C₁₃×#450	C₂²	1	4	yes	—
59	C₁₃×#450	C₂²	1	4	yes	complemented
60	C₁₃×#450	C₂²	1	4	yes	complemented
61	C₁₃×#450	C₂²	1	4	yes	complemented
62	C₁₃×#450	C₂²	1	4	yes	complemented
63	C₁₃×#448	C₂²	1	2	yes	complemented
64	C₁₃×#448	C₂²	1	4	yes	complemented
65	C₁₃×#440	C₂²	1	4	yes	complemented
66	C₄×C₁₃×SD₁₆	C₂²	1	4	yes	complemented
67	C₁₃×#435	C₂²	1	4	yes	complemented
68	C₈×D₄×C₁₃	C₂²	1	4	yes	complemented
69	C₁₃×#433	C₂²	1	2	yes	complemented
70	C₁₃×#418	C₂²	1	2	yes	complemented
71	C₁₃×#416	C₂²	1	2	yes	complemented
72	C₂×C₁₃×#102	C₂²	1	4	yes	complemented
73	C₁₃×#408	C₂²	1	2	yes	complemented
74	C₂×C₁₃×C₂²⋊C₈	C₂²	1	2	yes	complemented
75	C₂⁵×C₁₃	—	2	1	no	—
76	C₁₃×H(5,𝔽₂)	—	4	4	no	—
77	C₂×C₁₃×#41	—	2	1	no	—
78	C₂×C₁₃×#41	C₂³	1	2	yes	—
79	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
80	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
81	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
82	C₂²×Q₈×C₁₃	C₂³	1	2	yes	complemented
83	C₂²×D₄×C₁₃	—	2	2	no	—
84	C₂²×D₄×C₁₃	—	2	1	no	—
85	C₂²×D₄×C₁₃	—	2	4	no	—
86	C₂²×D₄×C₁₃	—	2	1	no	—
87	C₂²×D₄×C₁₃	—	2	2	no	—
88	C₂²×D₄×C₁₃	—	4	4	no	—
89	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
90	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
91	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
92	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
93	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
94	C₁₃×#137	—	4	4	no	—
95	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	complemented
96	C₂×C₁₃×SD₁₆	—	4	8	no	—
97	C₂×C₁₃×SD₁₆	—	4	4	no	—
98	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
99	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
100	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
101	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
102	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	complemented
103	C₂×C₁₃×M₁₆	C₂³	1	2	yes	complemented
104	C₂²×C₈×C₁₃	C₂³	1	4	yes	—
105	C₂²×C₈×C₁₃	C₂³	1	2	yes	complemented
106	C₁₃×C₄⋊Q₈	—	2	2	no	—
107	C₁₃×C₄⋊Q₈	—	2	4	no	—
108	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	complemented
109	C₁₃×#127	—	2	1	no	—
110	C₁₃×#127	C₂³	1	2	yes	—
111	C₁₃×#126	—	2	4	no	—
112	C₁₃×#126	—	2	4	no	—
113	C₁₃×#125	—	2	4	no	—
114	C₁₃×#125	—	2	4	no	—
115	C₁₃×#125	C₂³	1	2	yes	complemented
116	C₁₃×#124	—	2	1	no	—
117	C₁₃×#124	—	2	2	no	—
118	C₁₃×#124	C₂³	1	2	yes	—
119	C₁₃×#123	—	2	2	no	—
120	C₁₃×#123	—	2	2	no	—
121	C₁₃×#123	—	2	4	no	—
122	C₁₃×#123	—	2	1	no	—
123	C₁₃×#123	—	2	4	no	—
124	C₁₃×#123	D₄	1	2	yes	—
125	C₁₃×C₂²⋊Q₈	—	2	2	no	—
126	C₁₃×C₂²⋊Q₈	—	2	2	no	—
127	C₁₃×C₂²⋊Q₈	—	2	4	no	—
128	C₁₃×C₂²⋊Q₈	—	2	4	no	—
129	C₁₃×C₂²⋊Q₈	D₄	1	2	yes	—
130	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
131	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
132	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
133	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	complemented
134	C₁₃×#121	—	2	4	no	—
135	C₁₃×#121	—	2	2	no	—
136	C₁₃×#121	—	2	4	no	—
137	C₁₃×#121	D₄	1	2	yes	—
138	C₁₃×#121	C₂³	1	2	yes	—
139	C₁₃×#121	C₂³	1	4	yes	—
140	C₁₃×#120	—	2	1	no	—
141	C₁₃×#120	—	2	2	no	—
142	C₁₃×#120	—	2	4	no	—
143	C₁₃×#120	—	2	2	no	—
144	C₁₃×#120	—	2	4	no	—
145	C₁₃×#120	—	2	4	no	—
146	C₁₃×#120	D₄	1	2	yes	—
147	C₄×Q₈×C₁₃	C₂³	1	4	yes	complemented
148	C₄×D₄×C₁₃	—	2	4	no	—
149	C₄×D₄×C₁₃	—	2	2	no	—
150	C₄×D₄×C₁₃	—	2	2	no	—
151	C₄×D₄×C₁₃	C₂³	1	4	yes	—
152	C₄×D₄×C₁₃	C₂³	1	4	yes	—
153	C₁₃×#117	—	2	4	no	—
154	C₁₃×#117	C₂³	1	1	yes	characteristic
155	C₁₃×#117	C₂³	1	1	yes	characteristic
156	C₁₃×#117	C₂³	1	2	yes	complemented
157	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
158	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
159	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
160	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
161	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
162	C₁₃×#107	C₂³	1	4	yes	complemented
163	C₁₃×#106	C₂³	1	4	yes	complemented
164	C₁₃×C₄⋊C₈	C₂³	1	4	yes	complemented
165	C₁₃×#103	C₂³	1	4	yes	complemented
166	C₁₃×#103	C₂³	1	4	yes	complemented
167	C₁₃×#103	C₂³	1	4	yes	complemented
168	C₁₃×#102	C₂³	1	4	yes	—
169	C₁₃×#102	C₂³	1	4	yes	—
170	C₁₃×#102	C₂³	1	4	yes	—
171	C₁₃×#102	C₂³	1	4	yes	—
172	C₁₃×#102	C₂³	1	4	yes	complemented
173	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
174	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
175	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
176	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	complemented
177	C₁₃×#97	C₂³	1	2	yes	complemented
178	C₄×C₈×C₁₃	C₂³	1	2	yes	complemented
179	#61631	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
180	C₂⁴×C₁₃	—	2	1	no	—
181	C₂⁴×C₁₃	—	2	4	no	—
182	C₂⁴×C₁₃	—	2	1	no	—
183	C₂⁴×C₁₃	—	2	2	no	—
184	C₂⁴×C₁₃	—	4	4	no	—
185	C₂⁴×C₁₃	—	8	4	no	—
186	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
187	C₁₃×#41	—	2	4	no	—
188	C₁₃×#41	—	4	2	no	—
189	C₁₃×#41	—	4	2	no	—
190	C₁₃×#41	—	4	2	no	—
191	C₁₃×#41	—	4	4	no	—
192	C₂×Q₈×C₁₃	—	2	2	no	—
193	C₂×Q₈×C₁₃	—	2	2	no	—
194	C₂×Q₈×C₁₃	—	4	4	no	—
195	C₂×Q₈×C₁₃	—	4	2	no	—
196	C₂×Q₈×C₁₃	—	4	2	no	—
197	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
198	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
199	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
200	C₂×D₄×C₁₃	—	2	4	no	—
201	C₂×D₄×C₁₃	—	2	8	no	—
202	C₂×D₄×C₁₃	—	2	4	no	—
203	C₂×D₄×C₁₃	—	2	2	no	—
204	C₂×D₄×C₁₃	—	2	1	no	—
205	C₂×D₄×C₁₃	—	2	2	no	—
206	C₂×D₄×C₁₃	—	2	4	no	—
207	C₂×D₄×C₁₃	—	2	1	no	—
208	C₂×D₄×C₁₃	—	2	2	no	—
209	C₂×D₄×C₁₃	—	2	4	no	—
210	C₂×D₄×C₁₃	—	2	1	no	—
211	C₂×D₄×C₁₃	—	2	4	no	—
212	C₂×D₄×C₁₃	—	4	4	no	—
213	C₂×D₄×C₁₃	—	4	2	no	—
214	C₂×D₄×C₁₃	—	4	2	no	—
215	C₂×D₄×C₁₃	—	4	8	no	—
216	C₂×D₄×C₁₃	—	4	4	no	—
217	C₂×D₄×C₁₃	—	4	4	no	—
218	C₂×D₄×C₁₃	—	4	8	no	—
219	C₂×D₄×C₁₃	—	8	8	no	—
220	C₂×D₄×C₁₃	C₂×D₄	1	4	yes	—
221	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
222	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
223	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
224	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
225	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
226	C₂²×C₄×C₁₃	—	2	2	no	—
227	C₂²×C₄×C₁₃	—	2	2	no	—
228	C₂²×C₄×C₁₃	—	2	2	no	—
229	C₂²×C₄×C₁₃	—	2	2	no	—
230	C₂²×C₄×C₁₃	—	2	1	no	—
231	C₂²×C₄×C₁₃	—	2	4	no	—
232	C₂²×C₄×C₁₃	—	4	2	no	—
233	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
234	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
235	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
236	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
237	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
238	C₁₃×Q₁₆	—	4	4	no	—
239	C₁₃×SD₁₆	—	2	8	no	—
240	C₁₃×SD₁₆	—	2	8	no	—
241	C₁₃×SD₁₆	—	4	4	no	—
242	C₁₃×SD₁₆	—	4	4	no	—
243	C₁₃×SD₁₆	—	4	4	no	—
244	C₁₃×M₁₆	—	4	2	no	—
245	C₂×C₈×C₁₃	—	4	4	no	—
246	C₂×C₈×C₁₃	—	4	2	no	—
247	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
248	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
249	C₁₃×C₄⋊C₄	—	2	4	no	—
250	C₁₃×C₄⋊C₄	—	2	4	no	—
251	C₁₃×C₄⋊C₄	—	2	2	no	—
252	C₁₃×C₄⋊C₄	—	2	4	no	—
253	C₁₃×C₄⋊C₄	—	2	4	no	—
254	C₁₃×C₄⋊C₄	—	2	2	no	—
255	C₁₃×C₄⋊C₄	—	2	4	no	—
256	C₁₃×C₄⋊C₄	—	2	4	no	—
257	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
258	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
259	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
260	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
261	C₁₃×C₂²⋊C₄	—	2	1	no	—
262	C₁₃×C₂²⋊C₄	—	2	2	no	—
263	C₁₃×C₂²⋊C₄	—	2	4	no	—
264	C₁₃×C₂²⋊C₄	—	2	4	no	—
265	C₁₃×C₂²⋊C₄	—	2	2	no	—
266	C₁₃×C₂²⋊C₄	—	2	4	no	—
267	C₁₃×C₂²⋊C₄	—	2	4	no	—
268	C₁₃×C₂²⋊C₄	—	2	4	no	—
269	C₁₃×C₂²⋊C₄	—	2	4	no	—
270	C₁₃×C₂²⋊C₄	—	2	2	no	—
271	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
272	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
273	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
274	C₄²×C₁₃	—	2	2	no	—
275	C₄²×C₁₃	—	2	4	no	—
276	C₄²×C₁₃	—	2	1	no	—
277	C₄²×C₁₃	C₂⁴	1	2	yes	—
278	#3538	C₂×C₁₃	1	1	yes	characteristic, complemented
279	#3484	C₂×C₁₃	1	1	yes	characteristic
280	#3310	C₂×C₁₃	1	4	yes	complemented
281	#3296	C₂×C₁₃	1	4	yes	complemented
282	D₄×SD₁₆	C₂×C₁₃	1	4	yes	complemented
283	#3266	C₂×C₁₃	1	4	yes	complemented
284	#3222	C₂×C₁₃	1	2	yes	complemented
285	#3200	C₂×C₁₃	1	2	yes	complemented
286	#3190	C₂×C₁₃	1	2	yes	complemented
287	#3123	C₂×C₁₃	1	2	yes	complemented
288	#3009	C₂×C₁₃	1	2	yes	complemented
289	C₂×#450	C₂×C₁₃	1	2	yes	complemented
290	#2977	C₂×C₁₃	1	1	yes	characteristic, complemented
291	C₂³×C₁₃	—	2	4	no	—
292	C₂³×C₁₃	—	2	4	no	—
293	C₂³×C₁₃	—	2	2	no	—
294	C₂³×C₁₃	—	2	2	no	—
295	C₂³×C₁₃	—	2	1	no	—
296	C₂³×C₁₃	—	4	1	no	—
297	C₂³×C₁₃	—	4	8	no	—
298	C₂³×C₁₃	—	4	4	no	—
299	C₂³×C₁₃	—	4	2	no	—
300	C₂³×C₁₃	—	4	8	no	—
301	C₂³×C₁₃	—	8	4	no	—
302	C₂³×C₁₃	—	8	2	no	—
303	C₂³×C₁₃	—	8	2	no	—
304	C₂³×C₁₃	—	8	4	no	—
305	C₂³×C₁₃	—	8	16	no	—
306	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
307	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
308	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
309	Q₈×C₁₃	—	2	4	no	—
310	Q₈×C₁₃	—	2	4	no	—
311	Q₈×C₁₃	—	2	2	no	—
312	Q₈×C₁₃	—	4	1	no	—
313	Q₈×C₁₃	—	8	2	no	—
314	Q₈×C₁₃	—	8	2	no	—
315	D₄×C₁₃	—	2	4	no	—
316	D₄×C₁₃	—	2	8	no	—
317	D₄×C₁₃	—	2	2	no	—
318	D₄×C₁₃	—	2	4	no	—
319	D₄×C₁₃	—	2	2	no	—
320	D₄×C₁₃	—	4	1	no	—
321	D₄×C₁₃	—	4	2	no	—
322	D₄×C₁₃	—	4	8	no	—
323	D₄×C₁₃	—	4	4	no	—
324	D₄×C₁₃	—	4	2	no	—
325	D₄×C₁₃	—	4	4	no	—
326	D₄×C₁₃	—	4	2	no	—
327	D₄×C₁₃	—	4	4	no	—
328	D₄×C₁₃	—	8	4	no	—
329	D₄×C₁₃	—	8	4	no	—
330	D₄×C₁₃	H(5,𝔽₂)	1	4	yes	—
331	C₂×C₄×C₁₃	—	2	4	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	—	2	4	no	—
336	C₂×C₄×C₁₃	—	2	2	no	—
337	C₂×C₄×C₁₃	—	2	4	no	—
338	C₂×C₄×C₁₃	—	2	1	no	—
339	C₂×C₄×C₁₃	—	4	2	no	—
340	C₂×C₄×C₁₃	—	4	1	no	—
341	C₂×C₄×C₁₃	—	4	4	no	—
342	C₂×C₄×C₁₃	—	4	2	no	—
343	C₂×C₄×C₁₃	—	4	4	no	—
344	C₂×C₄×C₁₃	—	8	4	no	—
345	C₂×C₄×C₁₃	—	8	2	no	—
346	C₂×C₄×C₁₃	—	8	2	no	—
347	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
348	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
349	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
350	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
351	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
352	C₈×C₁₃	—	2	4	no	—
353	C₈×C₁₃	—	2	4	no	—
354	C₂×H(5,𝔽₂)	C₂²×C₁₃	1	1	yes	characteristic
355	C₂³×D₄	C₂²×C₁₃	1	1	yes	characteristic
356	C₂×#137	C₂²×C₁₃	1	2	yes	complemented
357	C₂²×SD₁₆	C₂²×C₁₃	1	4	yes	complemented
358	C₂²×SD₁₆	C₂²×C₁₃	1	2	yes	complemented
359	#563	—	2	2	no	—
360	#552	C₂²×C₁₃	1	4	yes	complemented
361	#551	—	2	2	no	—
362	D₄×Q₈	C₂²×C₁₃	1	4	yes	complemented
363	#546	—	2	2	no	—
364	#546	C₂²×C₁₃	1	4	yes	—
365	D₄²	—	2	2	no	—
366	D₄²	C₂²×C₁₃	1	4	yes	—
367	#544	—	2	2	no	—
368	#541	C₂²×C₁₃	1	2	yes	complemented
369	#539	—	2	2	no	—
370	#536	C₂²×C₁₃	1	2	yes	complemented
371	#535	C₂²×C₁₃	1	1	yes	characteristic
372	#535	C₂²×C₁₃	1	1	yes	characteristic
373	#534	—	2	2	no	—
374	#525	C₂²×C₁₃	1	1	yes	characteristic
375	#525	C₂²×C₁₃	1	1	yes	characteristic
376	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	complemented
377	C₂×#120	—	2	2	no	—
378	#518	C₂²×C₁₃	1	1	yes	characteristic
379	#497	C₂²×C₁₃	1	2	yes	complemented
380	#492	C₂²×C₁₃	1	2	yes	complemented
381	#490	C₂²×C₁₃	1	2	yes	complemented
382	#488	C₂²×C₁₃	1	2	yes	complemented
383	#485	C₂²×C₁₃	1	4	yes	complemented
384	#483	C₂²×C₁₃	1	2	yes	complemented
385	#482	C₂²×C₁₃	1	4	yes	complemented
386	#480	C₂²×C₁₃	1	2	yes	complemented
387	#478	C₂²×C₁₃	1	4	yes	complemented
388	#468	C₂²×C₁₃	1	4	yes	complemented
389	#467	C₂²×C₁₃	1	4	yes	complemented
390	#465	C₂²×C₁₃	1	4	yes	complemented
391	#465	C₂²×C₁₃	1	4	yes	complemented
392	#464	C₂²×C₁₃	1	4	yes	complemented
393	#461	C₂²×C₁₃	1	4	yes	complemented
394	#460	C₂²×C₁₃	1	4	yes	complemented
395	#452	C₂²×C₁₃	1	4	yes	complemented
396	#452	C₂²×C₁₃	1	4	yes	complemented
397	#451	C₂²×C₁₃	1	2	yes	complemented
398	#450	C₂²×C₁₃	1	4	yes	—
399	#450	C₂²×C₁₃	1	4	yes	complemented
400	#450	C₂²×C₁₃	1	4	yes	complemented
401	#450	C₂²×C₁₃	1	4	yes	complemented
402	#450	C₂²×C₁₃	1	4	yes	complemented
403	#448	C₂²×C₁₃	1	2	yes	complemented
404	#448	C₂²×C₁₃	1	4	yes	complemented
405	#440	C₂²×C₁₃	1	4	yes	complemented
406	C₄×SD₁₆	C₂²×C₁₃	1	4	yes	complemented
407	#435	C₂²×C₁₃	1	4	yes	complemented
408	C₈×D₄	C₂²×C₁₃	1	4	yes	complemented
409	#433	C₂²×C₁₃	1	2	yes	complemented
410	#418	C₂²×C₁₃	1	2	yes	complemented
411	#416	C₂²×C₁₃	1	2	yes	complemented
412	C₂×#102	C₂²×C₁₃	1	4	yes	complemented
413	#408	C₂²×C₁₃	1	2	yes	complemented
414	C₂×C₂²⋊C₈	C₂²×C₁₃	1	2	yes	complemented
415	C₂²×C₁₃	—	2	2	no	—
416	C₂²×C₁₃	—	2	2	no	—
417	C₂²×C₁₃	—	2	1	no	—
418	C₂²×C₁₃	—	2	2	no	—
419	C₂²×C₁₃	—	2	4	no	—
420	C₂²×C₁₃	—	2	4	no	—
421	C₂²×C₁₃	—	2	2	no	—
422	C₂²×C₁₃	—	4	4	no	—
423	C₂²×C₁₃	—	4	4	no	—
424	C₂²×C₁₃	—	4	1	no	—
425	C₂²×C₁₃	—	4	2	no	—
426	C₂²×C₁₃	—	4	2	no	—
427	C₂²×C₁₃	—	4	4	no	—
428	C₂²×C₁₃	—	8	16	no	—
429	C₂²×C₁₃	—	8	4	no	—
430	C₂²×C₁₃	—	8	4	no	—
431	C₂²×C₁₃	—	16	4	no	—
432	C₂²×C₁₃	#577	1	4	yes	—
433	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
434	C₄×C₁₃	—	2	1	no	—
435	C₄×C₁₃	—	2	2	no	—
436	C₄×C₁₃	—	2	2	no	—
437	C₄×C₁₃	—	2	4	no	—
438	C₄×C₁₃	—	4	1	no	—
439	C₄×C₁₃	—	4	4	no	—
440	C₄×C₁₃	—	4	4	no	—
441	C₄×C₁₃	—	4	2	no	—
442	C₄×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
443	C₂⁵	—	2	1	no	—
444	H(5,𝔽₂)	—	4	4	no	—
445	C₂×#41	—	2	1	no	—
446	C₂×#41	C₂³×C₁₃	1	2	yes	—
447	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
448	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
449	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
450	C₂²×Q₈	C₂³×C₁₃	1	2	yes	complemented
451	C₂²×D₄	—	2	2	no	—
452	C₂²×D₄	—	2	1	no	—
453	C₂²×D₄	—	2	4	no	—
454	C₂²×D₄	—	2	1	no	—
455	C₂²×D₄	—	2	2	no	—
456	C₂²×D₄	—	4	4	no	—
457	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
458	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
459	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
460	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
461	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
462	#137	—	4	4	no	—
463	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	complemented
464	C₂×SD₁₆	—	4	8	no	—
465	C₂×SD₁₆	—	4	4	no	—
466	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
467	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
468	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
469	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
470	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	complemented
471	C₂×M₁₆	C₂³×C₁₃	1	2	yes	complemented
472	C₂²×C₈	C₂³×C₁₃	1	4	yes	—
473	C₂²×C₈	C₂³×C₁₃	1	2	yes	complemented
474	C₄⋊Q₈	—	2	2	no	—
475	C₄⋊Q₈	—	2	4	no	—
476	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	complemented
477	#127	—	2	1	no	—
478	#127	C₂³×C₁₃	1	2	yes	—
479	#126	—	2	4	no	—
480	#126	—	2	4	no	—
481	#125	—	2	4	no	—
482	#125	—	2	4	no	—
483	#125	C₂³×C₁₃	1	2	yes	complemented
484	#124	—	2	1	no	—
485	#124	—	2	2	no	—
486	#124	C₂³×C₁₃	1	2	yes	—
487	#123	—	2	2	no	—
488	#123	—	2	2	no	—
489	#123	—	2	4	no	—
490	#123	—	2	1	no	—
491	#123	—	2	4	no	—
492	#123	D₄×C₁₃	1	2	yes	—
493	C₂²⋊Q₈	—	2	2	no	—
494	C₂²⋊Q₈	—	2	2	no	—
495	C₂²⋊Q₈	—	2	4	no	—
496	C₂²⋊Q₈	—	2	4	no	—
497	C₂²⋊Q₈	D₄×C₁₃	1	2	yes	—
498	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
499	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
500	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
501	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	complemented
502	#121	—	2	4	no	—
503	#121	—	2	2	no	—
504	#121	—	2	4	no	—
505	#121	D₄×C₁₃	1	2	yes	—
506	#121	C₂³×C₁₃	1	2	yes	—
507	#121	C₂³×C₁₃	1	4	yes	—
508	#120	—	2	1	no	—
509	#120	—	2	2	no	—
510	#120	—	2	4	no	—
511	#120	—	2	2	no	—
512	#120	—	2	4	no	—
513	#120	—	2	4	no	—
514	#120	D₄×C₁₃	1	2	yes	—
515	C₄×Q₈	C₂³×C₁₃	1	4	yes	complemented
516	C₄×D₄	—	2	4	no	—
517	C₄×D₄	—	2	2	no	—
518	C₄×D₄	—	2	2	no	—
519	C₄×D₄	C₂³×C₁₃	1	4	yes	—
520	C₄×D₄	C₂³×C₁₃	1	4	yes	—
521	#117	—	2	4	no	—
522	#117	C₂³×C₁₃	1	1	yes	characteristic
523	#117	C₂³×C₁₃	1	1	yes	characteristic
524	#117	C₂³×C₁₃	1	2	yes	complemented
525	C₂×C₄⋊C₄	—	2	2	no	—
526	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
527	C₂×C₂²⋊C₄	—	2	2	no	—
528	C₂×C₂²⋊C₄	—	2	2	no	—
529	C₂×C₂²⋊C₄	—	2	4	no	—
530	#107	C₂³×C₁₃	1	4	yes	complemented
531	#106	C₂³×C₁₃	1	4	yes	complemented
532	C₄⋊C₈	C₂³×C₁₃	1	4	yes	complemented
533	#103	C₂³×C₁₃	1	4	yes	complemented
534	#103	C₂³×C₁₃	1	4	yes	complemented
535	#103	C₂³×C₁₃	1	4	yes	complemented
536	#102	C₂³×C₁₃	1	4	yes	—
537	#102	C₂³×C₁₃	1	4	yes	—
538	#102	C₂³×C₁₃	1	4	yes	—
539	#102	C₂³×C₁₃	1	4	yes	—
540	#102	C₂³×C₁₃	1	4	yes	complemented
541	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
542	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
543	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
544	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	complemented
545	#97	C₂³×C₁₃	1	2	yes	complemented
546	C₄×C₈	C₂³×C₁₃	1	2	yes	complemented
547	C₂×C₁₃	—	2	4	no	—
548	C₂×C₁₃	—	4	1	no	—
549	C₂×C₁₃	—	4	2	no	—
550	C₂×C₁₃	—	4	4	no	—
551	C₂×C₁₃	—	8	2	no	—
552	C₂×C₁₃	—	8	1	no	—
553	C₂×C₁₃	#3484	1	1	yes	characteristic
554	C₂×C₁₃	C₂×#577	1	2	yes	—
555	C₂⁴	—	2	1	no	—
556	C₂⁴	—	2	4	no	—
557	C₂⁴	—	2	1	no	—
558	C₂⁴	—	2	2	no	—
559	C₂⁴	—	4	4	no	—
560	C₂⁴	—	8	4	no	—
561	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
562	#41	—	2	4	no	—
563	#41	—	4	2	no	—
564	#41	—	4	2	no	—
565	#41	—	4	2	no	—
566	#41	—	4	4	no	—
567	C₂×Q₈	—	2	2	no	—
568	C₂×Q₈	—	2	2	no	—
569	C₂×Q₈	—	4	4	no	—
570	C₂×Q₈	—	4	2	no	—
571	C₂×Q₈	—	4	2	no	—
572	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
573	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
574	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
575	C₂×D₄	—	2	4	no	—
576	C₂×D₄	—	2	8	no	—
577	C₂×D₄	—	2	4	no	—
578	C₂×D₄	—	2	2	no	—
579	C₂×D₄	—	2	1	no	—
580	C₂×D₄	—	2	2	no	—
581	C₂×D₄	—	2	4	no	—
582	C₂×D₄	—	2	1	no	—
583	C₂×D₄	—	2	2	no	—
584	C₂×D₄	—	2	4	no	—
585	C₂×D₄	—	2	1	no	—
586	C₂×D₄	—	2	4	no	—
587	C₂×D₄	—	4	4	no	—
588	C₂×D₄	—	4	2	no	—
589	C₂×D₄	—	4	2	no	—
590	C₂×D₄	—	4	8	no	—
591	C₂×D₄	—	4	4	no	—
592	C₂×D₄	—	4	4	no	—
593	C₂×D₄	—	4	8	no	—
594	C₂×D₄	—	8	8	no	—
595	C₂×D₄	C₂×D₄×C₁₃	1	4	yes	—
596	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
597	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
598	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
599	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
600	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
601	C₂²×C₄	—	2	2	no	—
602	C₂²×C₄	—	2	2	no	—
603	C₂²×C₄	—	2	2	no	—
604	C₂²×C₄	—	2	2	no	—
605	C₂²×C₄	—	2	1	no	—
606	C₂²×C₄	—	2	4	no	—
607	C₂²×C₄	—	4	2	no	—
608	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
609	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
610	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
611	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
612	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
613	Q₁₆	—	4	4	no	—
614	SD₁₆	—	2	8	no	—
615	SD₁₆	—	2	8	no	—
616	SD₁₆	—	4	4	no	—
617	SD₁₆	—	4	4	no	—
618	SD₁₆	—	4	4	no	—
619	M₁₆	—	4	2	no	—
620	C₂×C₈	—	4	4	no	—
621	C₂×C₈	—	4	2	no	—
622	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
623	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
624	C₄⋊C₄	—	2	4	no	—
625	C₄⋊C₄	—	2	4	no	—
626	C₄⋊C₄	—	2	2	no	—
627	C₄⋊C₄	—	2	4	no	—
628	C₄⋊C₄	—	2	4	no	—
629	C₄⋊C₄	—	2	2	no	—
630	C₄⋊C₄	—	2	4	no	—
631	C₄⋊C₄	—	2	4	no	—
632	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
633	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
634	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
635	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
636	C₂²⋊C₄	—	2	1	no	—
637	C₂²⋊C₄	—	2	2	no	—
638	C₂²⋊C₄	—	2	4	no	—
639	C₂²⋊C₄	—	2	4	no	—
640	C₂²⋊C₄	—	2	2	no	—
641	C₂²⋊C₄	—	2	4	no	—
642	C₂²⋊C₄	—	2	4	no	—
643	C₂²⋊C₄	—	2	4	no	—
644	C₂²⋊C₄	—	2	4	no	—
645	C₂²⋊C₄	—	2	2	no	—
646	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
647	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
648	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
649	C₄²	—	2	2	no	—
650	C₄²	—	2	4	no	—
651	C₄²	—	2	1	no	—
652	C₄²	C₂⁴×C₁₃	1	2	yes	—
653	C₁₃	#61631	1	1	yes	characteristic, direct product factor, Sylow
654	C₂³	—	2	4	no	—
655	C₂³	—	2	4	no	—
656	C₂³	—	2	2	no	—
657	C₂³	—	2	2	no	—
658	C₂³	—	2	1	no	—
659	C₂³	—	4	1	no	—
660	C₂³	—	4	8	no	—
661	C₂³	—	4	4	no	—
662	C₂³	—	4	2	no	—
663	C₂³	—	4	8	no	—
664	C₂³	—	8	4	no	—
665	C₂³	—	8	2	no	—
666	C₂³	—	8	2	no	—
667	C₂³	—	8	4	no	—
668	C₂³	—	8	16	no	—
669	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
670	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
671	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
672	Q₈	—	2	4	no	—
673	Q₈	—	2	4	no	—
674	Q₈	—	2	2	no	—
675	Q₈	—	4	1	no	—
676	Q₈	—	8	2	no	—
677	Q₈	—	8	2	no	—
678	D₄	—	2	4	no	—
679	D₄	—	2	8	no	—
680	D₄	—	2	2	no	—
681	D₄	—	2	4	no	—
682	D₄	—	2	2	no	—
683	D₄	—	4	1	no	—
684	D₄	—	4	2	no	—
685	D₄	—	4	8	no	—
686	D₄	—	4	4	no	—
687	D₄	—	4	2	no	—
688	D₄	—	4	4	no	—
689	D₄	—	4	2	no	—
690	D₄	—	4	4	no	—
691	D₄	—	8	4	no	—
692	D₄	—	8	4	no	—
693	D₄	C₁₃×H(5,𝔽₂)	1	4	yes	—
694	C₂×C₄	—	2	4	no	—
695	C₂×C₄	—	2	2	no	—
696	C₂×C₄	—	2	2	no	—
697	C₂×C₄	—	2	2	no	—
698	C₂×C₄	—	2	4	no	—
699	C₂×C₄	—	2	2	no	—
700	C₂×C₄	—	2	4	no	—
701	C₂×C₄	—	2	1	no	—
702	C₂×C₄	—	4	2	no	—
703	C₂×C₄	—	4	1	no	—
704	C₂×C₄	—	4	4	no	—
705	C₂×C₄	—	4	2	no	—
706	C₂×C₄	—	4	4	no	—
707	C₂×C₄	—	8	4	no	—
708	C₂×C₄	—	8	2	no	—
709	C₂×C₄	—	8	2	no	—
710	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
711	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
712	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
713	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
714	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
715	C₈	—	2	4	no	—
716	C₈	—	2	4	no	—
717	C₂²	—	2	2	no	—
718	C₂²	—	2	2	no	—
719	C₂²	—	2	4	no	—
720	C₂²	—	2	2	no	—
721	C₂²	—	2	1	no	—
722	C₂²	—	2	2	no	—
723	C₂²	—	2	4	no	—
724	C₂²	—	4	4	no	—
725	C₂²	—	4	4	no	—
726	C₂²	—	4	2	no	—
727	C₂²	—	4	4	no	—
728	C₂²	—	4	1	no	—
729	C₂²	—	4	2	no	—
730	C₂²	—	8	16	no	—
731	C₂²	—	8	4	no	—
732	C₂²	—	8	4	no	—
733	C₂²	—	16	4	no	—
734	C₂²	C₁₃×#577	1	4	yes	—
735	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
736	C₄	—	2	4	no	—
737	C₄	—	2	1	no	—
738	C₄	—	2	2	no	—
739	C₄	—	2	2	no	—
740	C₄	—	4	4	no	—
741	C₄	—	4	2	no	—
742	C₄	—	4	1	no	—
743	C₄	—	4	4	no	—
744	C₄	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
745	C₂	—	2	4	no	—
746	C₂	—	4	1	no	—
747	C₂	—	4	2	no	—
748	C₂	—	4	4	no	—
749	C₂	—	8	2	no	—
750	C₂	—	8	1	no	—
751	C₂	C₁₃×#3484	1	1	yes	characteristic
752	C₂	C₂×C₁₃×#577	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
prime radical	C₁₃×#3484	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₁₃×#525 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3538	C₂	semidirect
3. C₁₃×#3310	C₂	semidirect
4. C₁₃×#3296	C₂	semidirect
5. D₄×C₁₃×SD₁₆	C₂	semidirect
6. C₁₃×#3266	C₂	semidirect
7. C₁₃×#3222	C₂	semidirect
8. C₁₃×#3200	C₂	semidirect
9. C₁₃×#3190	C₂	semidirect
10. C₁₃×#3123	C₂	semidirect
11. C₁₃×#3009	C₂	semidirect
12. C₂×C₁₃×#450	C₂	semidirect
13. C₁₃×#2977	C₂	semidirect
16. C₂×C₁₃×#137	C₂²	semidirect
17. C₂²×C₁₃×SD₁₆	C₂²	semidirect
18. C₂²×C₁₃×SD₁₆	C₂²	semidirect
20. C₁₃×#552	C₂²	semidirect
22. D₄×Q₈×C₁₃	C₂²	semidirect
28. C₁₃×#541	C₂²	semidirect
30. C₁₃×#536	C₂²	semidirect
36. C₂×C₁₃×C₂²⋊Q₈	C₂²	semidirect
39. C₁₃×#497	C₂²	semidirect
40. C₁₃×#492	C₂²	semidirect
41. C₁₃×#490	C₂²	semidirect
42. C₁₃×#488	C₂²	semidirect
43. C₁₃×#485	C₂²	semidirect
44. C₁₃×#483	C₂²	semidirect
45. C₁₃×#482	C₂²	semidirect
46. C₁₃×#480	C₂²	semidirect
47. C₁₃×#478	C₂²	semidirect
48. C₁₃×#468	C₂²	semidirect
49. C₁₃×#467	C₂²	semidirect
50. C₁₃×#465	C₂²	semidirect
51. C₁₃×#465	C₂²	semidirect
52. C₁₃×#464	C₂²	semidirect
53. C₁₃×#461	C₂²	semidirect
54. C₁₃×#460	C₂²	semidirect
55. C₁₃×#452	C₂²	semidirect
56. C₁₃×#452	C₂²	semidirect
57. C₁₃×#451	C₂²	semidirect
59. C₁₃×#450	C₂²	semidirect
60. C₁₃×#450	C₂²	semidirect
61. C₁₃×#450	C₂²	semidirect
62. C₁₃×#450	C₂²	semidirect
63. C₁₃×#448	C₂²	semidirect
64. C₁₃×#448	C₂²	semidirect
65. C₁₃×#440	C₂²	semidirect
66. C₄×C₁₃×SD₁₆	C₂²	semidirect
67. C₁₃×#435	C₂²	semidirect
68. C₈×D₄×C₁₃	C₂²	semidirect
69. C₁₃×#433	C₂²	semidirect
70. C₁₃×#418	C₂²	semidirect
71. C₁₃×#416	C₂²	semidirect
72. C₂×C₁₃×#102	C₂²	semidirect
73. C₁₃×#408	C₂²	semidirect
74. C₂×C₁₃×C₂²⋊C₈	C₂²	semidirect
82. C₂²×Q₈×C₁₃	C₂³	semidirect
95. C₂×C₁₃×Q₁₆	C₂³	semidirect
102. C₂×C₁₃×SD₁₆	C₂³	semidirect
103. C₂×C₁₃×M₁₆	C₂³	semidirect
105. C₂²×C₈×C₁₃	C₂³	semidirect
108. C₁₃×C₄⋊Q₈	C₂³	semidirect
115. C₁₃×#125	C₂³	semidirect
133. C₁₃×C₂²⋊Q₈	C₂³	semidirect
147. C₄×Q₈×C₁₃	C₂³	semidirect
156. C₁₃×#117	C₂³	semidirect
162. C₁₃×#107	C₂³	semidirect
163. C₁₃×#106	C₂³	semidirect
164. C₁₃×C₄⋊C₈	C₂³	semidirect
165. C₁₃×#103	C₂³	semidirect
166. C₁₃×#103	C₂³	semidirect
167. C₁₃×#103	C₂³	semidirect
172. C₁₃×#102	C₂³	semidirect
176. C₁₃×C₂²⋊C₈	C₂³	semidirect
177. C₁₃×#97	C₂³	semidirect
178. C₄×C₈×C₁₃	C₂³	semidirect
179. #61631	C₁₃	direct (N × H)
278. #3538	C₂×C₁₃	semidirect
280. #3310	C₂×C₁₃	semidirect
281. #3296	C₂×C₁₃	semidirect
282. D₄×SD₁₆	C₂×C₁₃	semidirect
283. #3266	C₂×C₁₃	semidirect
284. #3222	C₂×C₁₃	semidirect
285. #3200	C₂×C₁₃	semidirect
286. #3190	C₂×C₁₃	semidirect
287. #3123	C₂×C₁₃	semidirect
288. #3009	C₂×C₁₃	semidirect
289. C₂×#450	C₂×C₁₃	semidirect
290. #2977	C₂×C₁₃	semidirect
356. C₂×#137	C₂²×C₁₃	semidirect
357. C₂²×SD₁₆	C₂²×C₁₃	semidirect
358. C₂²×SD₁₆	C₂²×C₁₃	semidirect
360. #552	C₂²×C₁₃	semidirect
362. D₄×Q₈	C₂²×C₁₃	semidirect
368. #541	C₂²×C₁₃	semidirect
370. #536	C₂²×C₁₃	semidirect
376. C₂×C₂²⋊Q₈	C₂²×C₁₃	semidirect
379. #497	C₂²×C₁₃	semidirect
380. #492	C₂²×C₁₃	semidirect
381. #490	C₂²×C₁₃	semidirect
382. #488	C₂²×C₁₃	semidirect
383. #485	C₂²×C₁₃	semidirect
384. #483	C₂²×C₁₃	semidirect
385. #482	C₂²×C₁₃	semidirect
386. #480	C₂²×C₁₃	semidirect
387. #478	C₂²×C₁₃	semidirect
388. #468	C₂²×C₁₃	semidirect
389. #467	C₂²×C₁₃	semidirect
390. #465	C₂²×C₁₃	semidirect
391. #465	C₂²×C₁₃	semidirect
392. #464	C₂²×C₁₃	semidirect
393. #461	C₂²×C₁₃	semidirect
394. #460	C₂²×C₁₃	semidirect
395. #452	C₂²×C₁₃	semidirect
396. #452	C₂²×C₁₃	semidirect
397. #451	C₂²×C₁₃	semidirect
399. #450	C₂²×C₁₃	semidirect
400. #450	C₂²×C₁₃	semidirect
401. #450	C₂²×C₁₃	semidirect
402. #450	C₂²×C₁₃	semidirect
403. #448	C₂²×C₁₃	semidirect
404. #448	C₂²×C₁₃	semidirect
405. #440	C₂²×C₁₃	semidirect
406. C₄×SD₁₆	C₂²×C₁₃	semidirect
407. #435	C₂²×C₁₃	semidirect
408. C₈×D₄	C₂²×C₁₃	semidirect
409. #433	C₂²×C₁₃	semidirect
410. #418	C₂²×C₁₃	semidirect
411. #416	C₂²×C₁₃	semidirect
412. C₂×#102	C₂²×C₁₃	semidirect
413. #408	C₂²×C₁₃	semidirect
414. C₂×C₂²⋊C₈	C₂²×C₁₃	semidirect
450. C₂²×Q₈	C₂³×C₁₃	semidirect
463. C₂×Q₁₆	C₂³×C₁₃	semidirect
470. C₂×SD₁₆	C₂³×C₁₃	semidirect
471. C₂×M₁₆	C₂³×C₁₃	semidirect
473. C₂²×C₈	C₂³×C₁₃	semidirect
476. C₄⋊Q₈	C₂³×C₁₃	semidirect
483. #125	C₂³×C₁₃	semidirect
501. C₂²⋊Q₈	C₂³×C₁₃	semidirect
515. C₄×Q₈	C₂³×C₁₃	semidirect
524. #117	C₂³×C₁₃	semidirect
530. #107	C₂³×C₁₃	semidirect
531. #106	C₂³×C₁₃	semidirect
532. C₄⋊C₈	C₂³×C₁₃	semidirect
533. #103	C₂³×C₁₃	semidirect
534. #103	C₂³×C₁₃	semidirect
535. #103	C₂³×C₁₃	semidirect
540. #102	C₂³×C₁₃	semidirect
544. C₂²⋊C₈	C₂³×C₁₃	semidirect
545. #97	C₂³×C₁₃	semidirect
546. C₄×C₈	C₂³×C₁₃	semidirect
653. C₁₃	#61631	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×#3538	2
C₁₃×#3484	2
C₁₃×#3310	2
C₁₃×#3296	2
D₄×C₁₃×SD₁₆	2
C₁₃×#3266	2
C₁₃×#3222	2
C₁₃×#3200	2
C₁₃×#3190	2
C₁₃×#3123	2
C₁₃×#3009	2
C₂×C₁₃×#450	2
C₁₃×#2977	2
#61631	13

Subgroups — C13×#61631 #15747970

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61631 #15747970