Subgroups — C₁₃×#61377 #15747716

Order 3328.

1742 conjugacy classes of subgroups.

The subgroup lattice has 724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3502	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3501	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#3388	C₂	1	4	yes	maximal, complemented
4	C₁₃×#3388	C₂	1	4	yes	maximal, complemented
5	C₁₃×#3386	C₂	1	4	yes	maximal, complemented
6	C₁₃×#3385	C₂	1	4	yes	maximal, complemented
7	C₁₃×#3164	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3162	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#3082	C₂	1	2	yes	maximal, complemented
10	C₁₃×#3081	C₂	1	2	yes	maximal
11	C₁₃×#3078	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#3077	C₂	1	1	yes	maximal, characteristic
13	C₁₃×#2961	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#2949	C₂	1	2	yes	maximal
15	C₂×C₁₃×#440	C₂	1	1	yes	maximal, characteristic
16	C₂²×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
17	Q₈²×C₁₃	—	2	1	no	—
18	Q₈²×C₁₃	C₂²	1	2	yes	complemented
19	C₁₃×#557	—	2	1	no	—
20	C₁₃×#557	—	2	2	no	—
21	C₁₃×#557	C₂²	1	4	yes	complemented
22	C₁₃×#557	C₂²	1	2	yes	complemented
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	D₄×Q₈×C₁₃	—	2	1	no	—
28	D₄×Q₈×C₁₃	C₂²	1	2	yes	—
29	C₁₃×#544	—	2	2	no	—
30	C₁₃×#544	C₂²	1	2	yes	—
31	C₁₃×#544	C₂²	1	2	yes	—
32	C₁₃×#543	—	2	2	no	—
33	C₁₃×#533	—	2	2	no	—
34	C₁₃×#533	C₂²	1	1	yes	characteristic
35	C₁₃×#533	C₂²	1	1	yes	characteristic
36	C₁₃×#533	C₂²	1	1	yes	characteristic
37	C₂×C₁₃×C₂²⋊Q₈	—	2	2	no	—
38	C₁₃×#519	C₂²	1	2	yes	—
39	C₁₃×#518	C₂²	1	2	yes	—
40	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
41	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
42	C₁₃×#501	C₂²	1	2	yes	complemented
43	C₁₃×#501	C₂²	1	4	yes	complemented
44	C₁₃×#501	C₂²	1	2	yes	complemented
45	C₁₃×#501	C₂²	1	4	yes	complemented
46	C₁₃×#501	C₂²	1	2	yes	complemented
47	C₁₃×#501	C₂²	1	2	yes	complemented
48	C₁₃×#500	C₂²	1	4	yes	complemented
49	C₁₃×#499	C₂²	1	4	yes	complemented
50	C₁₃×#479	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	—
54	C₁₃×#478	C₂²	1	4	yes	—
55	C₁₃×#478	C₂²	1	4	yes	—
56	C₁₃×#477	C₂²	1	2	yes	complemented
57	C₁₃×#477	C₂²	1	4	yes	complemented
58	C₁₃×#476	C₂²	1	2	yes	—
59	C₁₃×#476	C₂²	1	4	yes	—
60	C₁₃×#475	C₂²	1	2	yes	complemented
61	C₁₃×#475	C₂²	1	4	yes	complemented
62	C₁₃×#474	C₂²	1	2	yes	—
63	C₁₃×#474	C₂²	1	4	yes	—
64	C₁₃×#446	C₂²	1	4	yes	complemented
65	C₁₃×#446	C₂²	1	4	yes	complemented
66	C₁₃×#440	C₂²	1	4	yes	—
67	C₁₃×#440	C₂²	1	4	yes	—
68	C₁₃×#440	C₂²	1	4	yes	—
69	C₁₃×#440	C₂²	1	4	yes	—
70	C₄×C₁₃×SD₁₆	C₂²	1	4	yes	—
71	C₄×C₁₃×SD₁₆	C₂²	1	4	yes	—
72	C₁₃×#428	C₂²	1	2	yes	—
73	C₁₃×#428	C₂²	1	2	yes	—
74	C₁₃×#427	C₂²	1	2	yes	—
75	C₁₃×#427	C₂²	1	2	yes	—
76	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
77	C₁₃×#424	C₂²	1	2	yes	—
78	C₁₃×#423	C₂²	1	1	yes	characteristic
79	C₁₃×#419	C₂²	1	2	yes	—
80	C₁₃×#418	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	C₂²×Q₈×C₁₃	—	2	2	no	—
86	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
87	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
88	C₂³×C₄×C₁₃	—	2	1	no	—
89	C₂×C₁₃×SD₁₆	Q₈	1	8	yes	complemented
90	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
91	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
92	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
93	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
94	C₁₃×C₄⋊Q₈	—	2	2	no	—
95	C₁₃×C₄⋊Q₈	—	2	4	no	—
96	C₁₃×C₄⋊Q₈	—	2	2	no	—
97	C₁₃×C₄⋊Q₈	—	2	4	no	—
98	C₁₃×C₄⋊Q₈	—	2	2	no	—
99	C₁₃×C₄⋊Q₈	—	2	2	no	—
100	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
101	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
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	4	yes	—
106	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
107	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
108	C₁₃×#125	—	2	4	no	—
109	C₁₃×#125	—	2	4	no	—
110	C₁₃×#125	—	2	4	no	—
111	C₁₃×#125	—	2	2	no	—
112	C₁₃×#125	—	2	2	no	—
113	C₁₃×#125	D₄	1	2	yes	—
114	C₁₃×#125	C₂³	1	4	yes	—
115	C₁₃×#125	C₂³	1	2	yes	—
116	C₁₃×#125	C₂³	1	4	yes	—
117	C₁₃×#125	C₂³	1	2	yes	—
118	C₁₃×C₂²⋊Q₈	—	2	2	no	—
119	C₁₃×C₂²⋊Q₈	—	2	4	no	—
120	C₁₃×C₂²⋊Q₈	—	2	1	no	—
121	C₁₃×C₂²⋊Q₈	—	2	1	no	—
122	C₁₃×C₂²⋊Q₈	—	2	1	no	—
123	C₁₃×C₂²⋊Q₈	—	2	1	no	—
124	C₁₃×C₂²⋊Q₈	—	2	2	no	—
125	C₁₃×C₂²⋊Q₈	—	2	4	no	—
126	C₁₃×C₂²⋊Q₈	—	2	4	no	—
127	C₁₃×C₂²⋊Q₈	—	2	4	no	—
128	C₁₃×C₂²⋊Q₈	—	2	4	no	—
129	C₁₃×C₂²⋊Q₈	—	2	4	no	—
130	C₁₃×C₂²⋊Q₈	—	2	4	no	—
131	C₁₃×C₂²⋊Q₈	D₄	1	2	yes	—
132	C₁₃×C₂²⋊Q₈	D₄	1	2	yes	—
133	C₄×Q₈×C₁₃	—	2	2	no	—
134	C₄×Q₈×C₁₃	—	2	2	no	—
135	C₄×Q₈×C₁₃	—	2	2	no	—
136	C₄×Q₈×C₁₃	—	2	4	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	—	2	1	no	—
143	C₄×Q₈×C₁₃	—	2	1	no	—
144	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
145	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
146	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
147	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
148	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
149	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
150	C₄×D₄×C₁₃	—	2	2	no	—
151	C₄×D₄×C₁₃	—	2	2	no	—
152	C₄×D₄×C₁₃	—	2	1	no	—
153	C₄×D₄×C₁₃	—	2	1	no	—
154	C₄×D₄×C₁₃	C₂³	1	4	yes	—
155	C₄×D₄×C₁₃	C₂³	1	4	yes	—
156	C₄×D₄×C₁₃	C₂³	1	2	yes	—
157	C₄×D₄×C₁₃	C₂³	1	2	yes	—
158	C₁₃×#117	—	2	4	no	—
159	C₁₃×#117	C₂³	1	2	yes	—
160	C₁₃×#117	C₂³	1	2	yes	—
161	C₁₃×#117	C₂³	1	2	yes	—
162	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
163	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
164	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
165	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
166	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
167	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
168	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
169	C₂×C₄²×C₁₃	—	2	1	no	—
170	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
171	C₁₃×#107	C₂³	1	4	yes	—
172	C₁₃×#107	C₂³	1	2	yes	—
173	C₁₃×#107	C₂³	1	2	yes	—
174	C₁₃×#107	C₂³	1	2	yes	—
175	C₁₃×#107	C₂³	1	2	yes	—
176	C₁₃×#107	C₂³	1	4	yes	—
177	C₁₃×#107	C₂³	1	4	yes	—
178	C₁₃×#106	C₂³	1	2	yes	—
179	C₁₃×#106	C₂³	1	2	yes	—
180	C₁₃×#106	C₂³	1	2	yes	—
181	C₁₃×#106	C₂³	1	2	yes	—
182	C₁₃×#106	C₂³	1	4	yes	—
183	C₁₃×#106	C₂³	1	4	yes	—
184	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
185	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
186	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
187	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
188	C₁₃×#103	C₂³	1	4	yes	—
189	C₁₃×#103	C₂³	1	4	yes	—
190	C₁₃×#103	C₂³	1	4	yes	—
191	C₁₃×#102	C₂³	1	4	yes	—
192	C₁₃×#102	C₂³	1	4	yes	—
193	C₁₃×#102	C₂³	1	4	yes	—
194	C₁₃×#97	C₂³	1	2	yes	—
195	C₁₃×#97	C₂³	1	2	yes	—
196	C₁₃×#97	C₂³	1	4	yes	—
197	C₄×C₈×C₁₃	C₂³	1	4	yes	—
198	#61377	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
199	C₂⁴×C₁₃	—	2	1	no	—
200	C₂×Q₈×C₁₃	—	2	1	no	—
201	C₂×Q₈×C₁₃	—	2	1	no	—
202	C₂×Q₈×C₁₃	—	2	1	no	—
203	C₂×Q₈×C₁₃	—	2	1	no	—
204	C₂×Q₈×C₁₃	—	2	1	no	—
205	C₂×Q₈×C₁₃	—	2	4	no	—
206	C₂×Q₈×C₁₃	—	2	4	no	—
207	C₂×Q₈×C₁₃	—	2	2	no	—
208	C₂×Q₈×C₁₃	—	8	4	no	—
209	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
210	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
211	C₂×Q₈×C₁₃	C₂×Q₈	1	4	yes	complemented
212	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
213	C₂×D₄×C₁₃	—	2	1	no	—
214	C₂×D₄×C₁₃	—	2	2	no	—
215	C₂×D₄×C₁₃	C₂×Q₈	1	4	yes	—
216	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
217	C₂²×C₄×C₁₃	—	2	1	no	—
218	C₂²×C₄×C₁₃	—	2	1	no	—
219	C₂²×C₄×C₁₃	—	2	1	no	—
220	C₂²×C₄×C₁₃	—	2	2	no	—
221	C₂²×C₄×C₁₃	—	2	4	no	—
222	C₂²×C₄×C₁₃	—	2	4	no	—
223	C₂²×C₄×C₁₃	—	2	2	no	—
224	C₂²×C₄×C₁₃	—	8	2	no	—
225	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
226	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
227	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
228	C₁₃×SD₁₆	C₂×Q₈	1	16	yes	complemented
229	C₁₃×M₁₆	—	2	4	no	—
230	C₂×C₈×C₁₃	—	2	2	no	—
231	C₂×C₈×C₁₃	C₂×Q₈	1	4	yes	complemented
232	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
233	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
234	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
235	C₁₃×C₄⋊C₄	—	2	2	no	—
236	C₁₃×C₄⋊C₄	—	2	1	no	—
237	C₁₃×C₄⋊C₄	—	2	2	no	—
238	C₁₃×C₄⋊C₄	—	2	2	no	—
239	C₁₃×C₄⋊C₄	—	2	4	no	—
240	C₁₃×C₄⋊C₄	—	2	4	no	—
241	C₁₃×C₄⋊C₄	—	2	4	no	—
242	C₁₃×C₄⋊C₄	—	2	1	no	—
243	C₁₃×C₄⋊C₄	—	2	1	no	—
244	C₁₃×C₄⋊C₄	—	2	4	no	—
245	C₁₃×C₄⋊C₄	—	2	4	no	—
246	C₁₃×C₄⋊C₄	—	2	2	no	—
247	C₁₃×C₄⋊C₄	—	2	1	no	—
248	C₁₃×C₄⋊C₄	—	2	2	no	—
249	C₁₃×C₄⋊C₄	—	2	1	no	—
250	C₁₃×C₄⋊C₄	—	2	1	no	—
251	C₁₃×C₄⋊C₄	—	2	4	no	—
252	C₁₃×C₄⋊C₄	—	2	4	no	—
253	C₁₃×C₄⋊C₄	—	2	2	no	—
254	C₁₃×C₄⋊C₄	—	2	4	no	—
255	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
256	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
257	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
258	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
259	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
260	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
261	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
262	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
263	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
264	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
265	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
266	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
267	C₁₃×C₂²⋊C₄	—	2	2	no	—
268	C₁₃×C₂²⋊C₄	—	2	2	no	—
269	C₁₃×C₂²⋊C₄	—	2	4	no	—
270	C₁₃×C₂²⋊C₄	—	2	4	no	—
271	C₁₃×C₂²⋊C₄	—	2	2	no	—
272	C₁₃×C₂²⋊C₄	—	2	2	no	—
273	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
274	C₄²×C₁₃	—	2	2	no	—
275	C₄²×C₁₃	—	2	2	no	—
276	C₄²×C₁₃	—	2	4	no	—
277	C₄²×C₁₃	—	2	4	no	—
278	C₄²×C₁₃	—	2	2	no	—
279	C₄²×C₁₃	—	2	2	no	—
280	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
281	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
282	C₄²×C₁₃	C₂⁴	1	4	yes	—
283	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
284	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
285	#3502	C₂×C₁₃	1	1	yes	characteristic, complemented
286	#3501	C₂×C₁₃	1	1	yes	characteristic
287	#3388	C₂×C₁₃	1	4	yes	complemented
288	#3388	C₂×C₁₃	1	4	yes	complemented
289	#3386	C₂×C₁₃	1	4	yes	complemented
290	#3385	C₂×C₁₃	1	4	yes	complemented
291	#3164	C₂×C₁₃	1	2	yes	complemented
292	#3162	C₂×C₁₃	1	1	yes	characteristic, complemented
293	#3082	C₂×C₁₃	1	2	yes	complemented
294	#3081	C₂×C₁₃	1	2	yes	—
295	#3078	C₂×C₁₃	1	1	yes	characteristic, complemented
296	#3077	C₂×C₁₃	1	1	yes	characteristic
297	#2961	C₂×C₁₃	1	1	yes	characteristic, complemented
298	#2949	C₂×C₁₃	1	2	yes	—
299	C₂×#440	C₂×C₁₃	1	1	yes	characteristic
300	C₂³×C₁₃	—	2	2	no	—
301	C₂³×C₁₃	—	2	4	no	—
302	C₂³×C₁₃	—	8	1	no	—
303	C₂³×C₁₃	—	8	1	no	—
304	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
305	Q₈×C₁₃	—	2	4	no	—
306	Q₈×C₁₃	—	2	2	no	—
307	Q₈×C₁₃	—	4	2	no	—
308	Q₈×C₁₃	—	4	2	no	—
309	Q₈×C₁₃	—	4	2	no	—
310	Q₈×C₁₃	—	4	2	no	—
311	Q₈×C₁₃	—	8	1	no	—
312	Q₈×C₁₃	—	8	4	no	—
313	Q₈×C₁₃	—	8	1	no	—
314	Q₈×C₁₃	—	8	4	no	—
315	Q₈×C₁₃	C₂²×Q₈	1	4	yes	—
316	D₄×C₁₃	—	2	4	no	—
317	D₄×C₁₃	—	2	2	no	—
318	D₄×C₁₃	C₂²×Q₈	1	4	yes	—
319	C₂×C₄×C₁₃	—	2	4	no	—
320	C₂×C₄×C₁₃	—	2	2	no	—
321	C₂×C₄×C₁₃	—	2	2	no	—
322	C₂×C₄×C₁₃	—	2	2	no	—
323	C₂×C₄×C₁₃	—	2	2	no	—
324	C₂×C₄×C₁₃	—	2	2	no	—
325	C₂×C₄×C₁₃	—	2	2	no	—
326	C₂×C₄×C₁₃	—	2	2	no	—
327	C₂×C₄×C₁₃	—	4	1	no	—
328	C₂×C₄×C₁₃	—	4	1	no	—
329	C₂×C₄×C₁₃	—	4	4	no	—
330	C₂×C₄×C₁₃	—	8	4	no	—
331	C₂×C₄×C₁₃	—	8	2	no	—
332	C₂×C₄×C₁₃	—	8	4	no	—
333	C₂×C₄×C₁₃	—	8	1	no	—
334	C₂×C₄×C₁₃	—	8	1	no	—
335	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
336	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
337	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
338	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
339	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
340	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
341	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
342	C₂×C₄×C₁₃	C₂²×Q₈	1	2	yes	—
343	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
344	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
345	C₈×C₁₃	—	2	2	no	—
346	C₈×C₁₃	—	2	4	no	—
347	C₈×C₁₃	C₂²×Q₈	1	4	yes	—
348	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
349	Q₈²	—	2	1	no	—
350	Q₈²	C₂²×C₁₃	1	2	yes	complemented
351	#557	—	2	1	no	—
352	#557	—	2	2	no	—
353	#557	C₂²×C₁₃	1	4	yes	complemented
354	#557	C₂²×C₁₃	1	2	yes	complemented
355	#554	—	2	1	no	—
356	#554	—	2	2	no	—
357	#554	C₂²×C₁₃	1	4	yes	—
358	#554	C₂²×C₁₃	1	2	yes	—
359	D₄×Q₈	—	2	1	no	—
360	D₄×Q₈	C₂²×C₁₃	1	2	yes	—
361	#544	—	2	2	no	—
362	#544	C₂²×C₁₃	1	2	yes	—
363	#544	C₂²×C₁₃	1	2	yes	—
364	#543	—	2	2	no	—
365	#533	—	2	2	no	—
366	#533	C₂²×C₁₃	1	1	yes	characteristic
367	#533	C₂²×C₁₃	1	1	yes	characteristic
368	#533	C₂²×C₁₃	1	1	yes	characteristic
369	C₂×C₂²⋊Q₈	—	2	2	no	—
370	#519	C₂²×C₁₃	1	2	yes	—
371	#518	C₂²×C₁₃	1	2	yes	—
372	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
373	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
374	#501	C₂²×C₁₃	1	2	yes	complemented
375	#501	C₂²×C₁₃	1	4	yes	complemented
376	#501	C₂²×C₁₃	1	2	yes	complemented
377	#501	C₂²×C₁₃	1	4	yes	complemented
378	#501	C₂²×C₁₃	1	2	yes	complemented
379	#501	C₂²×C₁₃	1	2	yes	complemented
380	#500	C₂²×C₁₃	1	4	yes	complemented
381	#499	C₂²×C₁₃	1	4	yes	complemented
382	#479	C₂²×C₁₃	1	4	yes	complemented
383	#479	C₂²×C₁₃	1	4	yes	complemented
384	#479	C₂²×C₁₃	1	4	yes	complemented
385	#478	C₂²×C₁₃	1	4	yes	—
386	#478	C₂²×C₁₃	1	4	yes	—
387	#478	C₂²×C₁₃	1	4	yes	—
388	#477	C₂²×C₁₃	1	2	yes	complemented
389	#477	C₂²×C₁₃	1	4	yes	complemented
390	#476	C₂²×C₁₃	1	2	yes	—
391	#476	C₂²×C₁₃	1	4	yes	—
392	#475	C₂²×C₁₃	1	2	yes	complemented
393	#475	C₂²×C₁₃	1	4	yes	complemented
394	#474	C₂²×C₁₃	1	2	yes	—
395	#474	C₂²×C₁₃	1	4	yes	—
396	#446	C₂²×C₁₃	1	4	yes	complemented
397	#446	C₂²×C₁₃	1	4	yes	complemented
398	#440	C₂²×C₁₃	1	4	yes	—
399	#440	C₂²×C₁₃	1	4	yes	—
400	#440	C₂²×C₁₃	1	4	yes	—
401	#440	C₂²×C₁₃	1	4	yes	—
402	C₄×SD₁₆	C₂²×C₁₃	1	4	yes	—
403	C₄×SD₁₆	C₂²×C₁₃	1	4	yes	—
404	#428	C₂²×C₁₃	1	2	yes	—
405	#428	C₂²×C₁₃	1	2	yes	—
406	#427	C₂²×C₁₃	1	2	yes	—
407	#427	C₂²×C₁₃	1	2	yes	—
408	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
409	#424	C₂²×C₁₃	1	2	yes	—
410	#423	C₂²×C₁₃	1	1	yes	characteristic
411	#419	C₂²×C₁₃	1	2	yes	—
412	#418	C₂²×C₁₃	1	2	yes	—
413	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
414	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
415	#405	C₂²×C₁₃	1	2	yes	—
416	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
417	C₂²×C₁₃	—	2	1	no	—
418	C₂²×C₁₃	—	2	1	no	—
419	C₂²×C₁₃	—	2	4	no	—
420	C₂²×C₁₃	—	4	2	no	—
421	C₂²×C₁₃	—	4	2	no	—
422	C₂²×C₁₃	—	8	4	no	—
423	C₂²×C₁₃	D₄×Q₈	1	2	yes	—
424	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
425	C₄×C₁₃	—	2	1	no	—
426	C₄×C₁₃	—	2	1	no	—
427	C₄×C₁₃	—	2	4	no	—
428	C₄×C₁₃	—	2	1	no	—
429	C₄×C₁₃	—	2	1	no	—
430	C₄×C₁₃	—	2	4	no	—
431	C₄×C₁₃	—	2	4	no	—
432	C₄×C₁₃	—	4	2	no	—
433	C₄×C₁₃	—	4	2	no	—
434	C₄×C₁₃	—	4	2	no	—
435	C₄×C₁₃	—	4	2	no	—
436	C₄×C₁₃	—	4	2	no	—
437	C₄×C₁₃	—	4	2	no	—
438	C₄×C₁₃	D₄×Q₈	1	2	yes	—
439	C₄×C₁₃	C₂³×Q₈	1	1	yes	characteristic
440	C₄×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
441	C₂²×Q₈	—	2	2	no	—
442	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
443	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
444	C₂³×C₄	—	2	1	no	—
445	C₂×SD₁₆	Q₈×C₁₃	1	8	yes	complemented
446	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
447	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
448	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
449	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
450	C₄⋊Q₈	—	2	2	no	—
451	C₄⋊Q₈	—	2	4	no	—
452	C₄⋊Q₈	—	2	2	no	—
453	C₄⋊Q₈	—	2	4	no	—
454	C₄⋊Q₈	—	2	2	no	—
455	C₄⋊Q₈	—	2	2	no	—
456	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
457	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
458	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
459	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
460	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
461	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
462	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
463	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
464	#125	—	2	4	no	—
465	#125	—	2	4	no	—
466	#125	—	2	4	no	—
467	#125	—	2	2	no	—
468	#125	—	2	2	no	—
469	#125	D₄×C₁₃	1	2	yes	—
470	#125	C₂³×C₁₃	1	2	yes	—
471	#125	C₂³×C₁₃	1	2	yes	—
472	#125	C₂³×C₁₃	1	4	yes	—
473	#125	C₂³×C₁₃	1	4	yes	—
474	C₂²⋊Q₈	—	2	2	no	—
475	C₂²⋊Q₈	—	2	4	no	—
476	C₂²⋊Q₈	—	2	1	no	—
477	C₂²⋊Q₈	—	2	1	no	—
478	C₂²⋊Q₈	—	2	1	no	—
479	C₂²⋊Q₈	—	2	1	no	—
480	C₂²⋊Q₈	—	2	2	no	—
481	C₂²⋊Q₈	—	2	4	no	—
482	C₂²⋊Q₈	—	2	4	no	—
483	C₂²⋊Q₈	—	2	4	no	—
484	C₂²⋊Q₈	—	2	4	no	—
485	C₂²⋊Q₈	—	2	4	no	—
486	C₂²⋊Q₈	—	2	4	no	—
487	C₂²⋊Q₈	D₄×C₁₃	1	2	yes	—
488	C₂²⋊Q₈	D₄×C₁₃	1	2	yes	—
489	C₄×Q₈	—	2	2	no	—
490	C₄×Q₈	—	2	2	no	—
491	C₄×Q₈	—	2	2	no	—
492	C₄×Q₈	—	2	4	no	—
493	C₄×Q₈	—	2	2	no	—
494	C₄×Q₈	—	2	1	no	—
495	C₄×Q₈	—	2	1	no	—
496	C₄×Q₈	—	2	1	no	—
497	C₄×Q₈	—	2	1	no	—
498	C₄×Q₈	—	2	1	no	—
499	C₄×Q₈	—	2	1	no	—
500	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
501	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
502	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
503	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
504	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
505	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
506	C₄×D₄	—	2	2	no	—
507	C₄×D₄	—	2	2	no	—
508	C₄×D₄	—	2	1	no	—
509	C₄×D₄	—	2	1	no	—
510	C₄×D₄	C₂³×C₁₃	1	2	yes	—
511	C₄×D₄	C₂³×C₁₃	1	2	yes	—
512	C₄×D₄	C₂³×C₁₃	1	4	yes	—
513	C₄×D₄	C₂³×C₁₃	1	4	yes	—
514	#117	—	2	4	no	—
515	#117	C₂³×C₁₃	1	2	yes	—
516	#117	C₂³×C₁₃	1	2	yes	—
517	#117	C₂³×C₁₃	1	2	yes	—
518	C₂×C₄⋊C₄	—	2	1	no	—
519	C₂×C₄⋊C₄	—	2	4	no	—
520	C₂×C₄⋊C₄	—	2	2	no	—
521	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
522	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
523	C₂×C₂²⋊C₄	—	2	1	no	—
524	C₂×C₂²⋊C₄	—	2	4	no	—
525	C₂×C₄²	—	2	1	no	—
526	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
527	#107	C₂³×C₁₃	1	4	yes	—
528	#107	C₂³×C₁₃	1	2	yes	—
529	#107	C₂³×C₁₃	1	2	yes	—
530	#107	C₂³×C₁₃	1	2	yes	—
531	#107	C₂³×C₁₃	1	2	yes	—
532	#107	C₂³×C₁₃	1	4	yes	—
533	#107	C₂³×C₁₃	1	4	yes	—
534	#106	C₂³×C₁₃	1	2	yes	—
535	#106	C₂³×C₁₃	1	2	yes	—
536	#106	C₂³×C₁₃	1	2	yes	—
537	#106	C₂³×C₁₃	1	2	yes	—
538	#106	C₂³×C₁₃	1	4	yes	—
539	#106	C₂³×C₁₃	1	4	yes	—
540	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
541	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
542	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
543	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
544	#103	C₂³×C₁₃	1	4	yes	—
545	#103	C₂³×C₁₃	1	4	yes	—
546	#103	C₂³×C₁₃	1	4	yes	—
547	#102	C₂³×C₁₃	1	4	yes	—
548	#102	C₂³×C₁₃	1	4	yes	—
549	#102	C₂³×C₁₃	1	4	yes	—
550	#97	C₂³×C₁₃	1	2	yes	—
551	#97	C₂³×C₁₃	1	2	yes	—
552	#97	C₂³×C₁₃	1	4	yes	—
553	C₄×C₈	C₂³×C₁₃	1	4	yes	—
554	C₂×C₁₃	—	2	2	no	—
555	C₂×C₁₃	—	4	4	no	—
556	C₂×C₁₃	C₂×D₄×Q₈	1	1	yes	characteristic
557	C₂×C₁₃	#3585	1	1	yes	characteristic
558	C₂×C₁₃	#3586	1	1	yes	characteristic
559	C₂⁴	—	2	1	no	—
560	C₂×Q₈	—	2	1	no	—
561	C₂×Q₈	—	2	1	no	—
562	C₂×Q₈	—	2	1	no	—
563	C₂×Q₈	—	2	1	no	—
564	C₂×Q₈	—	2	1	no	—
565	C₂×Q₈	—	2	4	no	—
566	C₂×Q₈	—	2	4	no	—
567	C₂×Q₈	—	2	2	no	—
568	C₂×Q₈	—	8	4	no	—
569	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
570	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
571	C₂×Q₈	C₂×Q₈×C₁₃	1	4	yes	complemented
572	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
573	C₂×D₄	—	2	1	no	—
574	C₂×D₄	—	2	2	no	—
575	C₂×D₄	C₂×Q₈×C₁₃	1	4	yes	—
576	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
577	C₂²×C₄	—	2	1	no	—
578	C₂²×C₄	—	2	1	no	—
579	C₂²×C₄	—	2	1	no	—
580	C₂²×C₄	—	2	2	no	—
581	C₂²×C₄	—	2	4	no	—
582	C₂²×C₄	—	2	4	no	—
583	C₂²×C₄	—	2	2	no	—
584	C₂²×C₄	—	8	2	no	—
585	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
586	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
587	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
588	SD₁₆	C₂×Q₈×C₁₃	1	16	yes	complemented
589	M₁₆	—	2	4	no	—
590	C₂×C₈	—	2	2	no	—
591	C₂×C₈	C₂×Q₈×C₁₃	1	4	yes	complemented
592	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
593	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
594	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
595	C₄⋊C₄	—	2	2	no	—
596	C₄⋊C₄	—	2	1	no	—
597	C₄⋊C₄	—	2	2	no	—
598	C₄⋊C₄	—	2	2	no	—
599	C₄⋊C₄	—	2	4	no	—
600	C₄⋊C₄	—	2	4	no	—
601	C₄⋊C₄	—	2	4	no	—
602	C₄⋊C₄	—	2	1	no	—
603	C₄⋊C₄	—	2	1	no	—
604	C₄⋊C₄	—	2	4	no	—
605	C₄⋊C₄	—	2	4	no	—
606	C₄⋊C₄	—	2	2	no	—
607	C₄⋊C₄	—	2	1	no	—
608	C₄⋊C₄	—	2	2	no	—
609	C₄⋊C₄	—	2	1	no	—
610	C₄⋊C₄	—	2	1	no	—
611	C₄⋊C₄	—	2	4	no	—
612	C₄⋊C₄	—	2	4	no	—
613	C₄⋊C₄	—	2	2	no	—
614	C₄⋊C₄	—	2	4	no	—
615	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
616	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
617	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
618	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
619	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
620	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
621	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
622	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
623	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
624	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
625	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
626	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
627	C₂²⋊C₄	—	2	2	no	—
628	C₂²⋊C₄	—	2	2	no	—
629	C₂²⋊C₄	—	2	4	no	—
630	C₂²⋊C₄	—	2	4	no	—
631	C₂²⋊C₄	—	2	2	no	—
632	C₂²⋊C₄	—	2	2	no	—
633	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
634	C₄²	—	2	2	no	—
635	C₄²	—	2	2	no	—
636	C₄²	—	2	4	no	—
637	C₄²	—	2	4	no	—
638	C₄²	—	2	2	no	—
639	C₄²	—	2	2	no	—
640	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
641	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
642	C₄²	C₂⁴×C₁₃	1	4	yes	—
643	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
644	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
645	C₁₃	#61377	1	1	yes	characteristic, direct product factor, Sylow
646	C₂³	—	2	2	no	—
647	C₂³	—	2	4	no	—
648	C₂³	—	8	1	no	—
649	C₂³	—	8	1	no	—
650	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
651	Q₈	—	2	4	no	—
652	Q₈	—	2	2	no	—
653	Q₈	—	4	2	no	—
654	Q₈	—	4	2	no	—
655	Q₈	—	4	2	no	—
656	Q₈	—	4	2	no	—
657	Q₈	—	8	4	no	—
658	Q₈	—	8	1	no	—
659	Q₈	—	8	4	no	—
660	Q₈	—	8	1	no	—
661	Q₈	C₂²×Q₈×C₁₃	1	4	yes	—
662	D₄	—	2	4	no	—
663	D₄	—	2	2	no	—
664	D₄	C₂²×Q₈×C₁₃	1	4	yes	—
665	C₂×C₄	—	2	4	no	—
666	C₂×C₄	—	2	2	no	—
667	C₂×C₄	—	2	2	no	—
668	C₂×C₄	—	2	2	no	—
669	C₂×C₄	—	2	2	no	—
670	C₂×C₄	—	2	2	no	—
671	C₂×C₄	—	2	2	no	—
672	C₂×C₄	—	2	2	no	—
673	C₂×C₄	—	4	1	no	—
674	C₂×C₄	—	4	1	no	—
675	C₂×C₄	—	4	4	no	—
676	C₂×C₄	—	8	2	no	—
677	C₂×C₄	—	8	4	no	—
678	C₂×C₄	—	8	4	no	—
679	C₂×C₄	—	8	1	no	—
680	C₂×C₄	—	8	1	no	—
681	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
682	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
683	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
684	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
685	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
686	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
687	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
688	C₂×C₄	C₂²×Q₈×C₁₃	1	2	yes	—
689	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
690	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
691	C₈	—	2	2	no	—
692	C₈	—	2	4	no	—
693	C₈	C₂²×Q₈×C₁₃	1	4	yes	—
694	C₂²	—	2	1	no	—
695	C₂²	—	2	1	no	—
696	C₂²	—	2	4	no	—
697	C₂²	—	4	2	no	—
698	C₂²	—	4	2	no	—
699	C₂²	—	8	4	no	—
700	C₂²	D₄×Q₈×C₁₃	1	2	yes	—
701	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
702	C₄	—	2	1	no	—
703	C₄	—	2	1	no	—
704	C₄	—	2	4	no	—
705	C₄	—	2	1	no	—
706	C₄	—	2	1	no	—
707	C₄	—	2	4	no	—
708	C₄	—	2	4	no	—
709	C₄	—	4	2	no	—
710	C₄	—	4	2	no	—
711	C₄	—	4	2	no	—
712	C₄	—	4	2	no	—
713	C₄	—	4	2	no	—
714	C₄	—	4	2	no	—
715	C₄	D₄×Q₈×C₁₃	1	2	yes	—
716	C₄	C₂³×Q₈×C₁₃	1	1	yes	characteristic
717	C₄	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
718	C₂	—	2	2	no	—
719	C₂	—	4	4	no	—
720	C₂	C₂×D₄×Q₈×C₁₃	1	1	yes	characteristic
721	C₂	C₁₃×#3585	1	1	yes	characteristic
722	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	C₂²×D₄×C₁₃	C₂³
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×#3502	C₂	semidirect
3. C₁₃×#3388	C₂	semidirect
4. C₁₃×#3388	C₂	semidirect
5. C₁₃×#3386	C₂	semidirect
6. C₁₃×#3385	C₂	semidirect
7. C₁₃×#3164	C₂	semidirect
8. C₁₃×#3162	C₂	semidirect
9. C₁₃×#3082	C₂	semidirect
11. C₁₃×#3078	C₂	semidirect
13. C₁₃×#2961	C₂	semidirect
18. Q₈²×C₁₃	C₂²	semidirect
21. C₁₃×#557	C₂²	semidirect
22. C₁₃×#557	C₂²	semidirect
42. C₁₃×#501	C₂²	semidirect
43. C₁₃×#501	C₂²	semidirect
44. C₁₃×#501	C₂²	semidirect
45. C₁₃×#501	C₂²	semidirect
46. C₁₃×#501	C₂²	semidirect
47. C₁₃×#501	C₂²	semidirect
48. C₁₃×#500	C₂²	semidirect
49. C₁₃×#499	C₂²	semidirect
50. C₁₃×#479	C₂²	semidirect
51. C₁₃×#479	C₂²	semidirect
52. C₁₃×#479	C₂²	semidirect
56. C₁₃×#477	C₂²	semidirect
57. C₁₃×#477	C₂²	semidirect
60. C₁₃×#475	C₂²	semidirect
61. C₁₃×#475	C₂²	semidirect
64. C₁₃×#446	C₂²	semidirect
65. C₁₃×#446	C₂²	semidirect
89. C₂×C₁₃×SD₁₆	Q₈	semidirect
198. #61377	C₁₃	direct (N × H)
211. C₂×Q₈×C₁₃	C₂×Q₈	semidirect
228. C₁₃×SD₁₆	C₂×Q₈	semidirect
231. C₂×C₈×C₁₃	C₂×Q₈	semidirect
285. #3502	C₂×C₁₃	semidirect
287. #3388	C₂×C₁₃	semidirect
288. #3388	C₂×C₁₃	semidirect
289. #3386	C₂×C₁₃	semidirect
290. #3385	C₂×C₁₃	semidirect
291. #3164	C₂×C₁₃	semidirect
292. #3162	C₂×C₁₃	semidirect
293. #3082	C₂×C₁₃	semidirect
295. #3078	C₂×C₁₃	semidirect
297. #2961	C₂×C₁₃	semidirect
350. Q₈²	C₂²×C₁₃	semidirect
353. #557	C₂²×C₁₃	semidirect
354. #557	C₂²×C₁₃	semidirect
374. #501	C₂²×C₁₃	semidirect
375. #501	C₂²×C₁₃	semidirect
376. #501	C₂²×C₁₃	semidirect
377. #501	C₂²×C₁₃	semidirect
378. #501	C₂²×C₁₃	semidirect
379. #501	C₂²×C₁₃	semidirect
380. #500	C₂²×C₁₃	semidirect
381. #499	C₂²×C₁₃	semidirect
382. #479	C₂²×C₁₃	semidirect
383. #479	C₂²×C₁₃	semidirect
384. #479	C₂²×C₁₃	semidirect
388. #477	C₂²×C₁₃	semidirect
389. #477	C₂²×C₁₃	semidirect
392. #475	C₂²×C₁₃	semidirect
393. #475	C₂²×C₁₃	semidirect
396. #446	C₂²×C₁₃	semidirect
397. #446	C₂²×C₁₃	semidirect
445. C₂×SD₁₆	Q₈×C₁₃	semidirect
571. C₂×Q₈	C₂×Q₈×C₁₃	semidirect
588. SD₁₆	C₂×Q₈×C₁₃	semidirect
591. C₂×C₈	C₂×Q₈×C₁₃	semidirect
645. C₁₃	#61377	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×#3502	2
C₁₃×#3501	2
C₁₃×#3388	2
C₁₃×#3386	2
C₁₃×#3385	2
C₁₃×#3164	2
C₁₃×#3162	2
C₁₃×#3082	2
C₁₃×#3081	2
C₁₃×#3078	2
C₁₃×#3077	2
C₁₃×#2961	2
C₁₃×#2949	2
C₂×C₁₃×#440	2
#61377	13

Subgroups — C13×#61377 #15747716

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61377 #15747716