Subgroups — C₁₃×#61433 #15747772

Order 3328.

1852 conjugacy classes of subgroups.

The subgroup lattice has 734 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3482	C₂	1	2	yes	maximal, complemented
2	C₁₃×#3393	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3383	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#3364	C₂	1	2	yes	maximal, complemented
5	C₁₃×#3336	C₂	1	2	yes	maximal, complemented
6	C₁₃×#3334	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#3300	C₂	1	4	yes	maximal, complemented
8	C₁₃×#3298	C₂	1	2	yes	maximal, complemented
9	D₄×C₁₃×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#3285	C₂	1	2	yes	maximal, complemented
11	C₁₃×#3170	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#3168	C₂	1	2	yes	maximal, complemented
13	C₁₃×#3108	C₂	1	4	yes	maximal, complemented
14	C₁₃×#3107	C₂	1	2	yes	maximal, complemented
15	C₈×C₁₃×#41	C₂	1	1	yes	maximal, characteristic, complemented
16	C₄×C₁₃×#135	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×C₄×C₁₃×Q₁₆	C₂	1	2	yes	maximal, complemented
18	C₂×C₁₃×#135	C₂²	1	1	yes	characteristic
19	C₂²×C₁₃×Q₁₆	C₂²	1	2	yes	—
20	C₁₃×#557	C₂²	1	2	yes	—
21	C₁₃×#556	—	2	2	no	—
22	C₁₃×#556	C₂²	1	2	yes	—
23	C₁₃×#552	—	2	4	no	—
24	C₁₃×#552	C₂²	1	4	yes	—
25	D₄×Q₈×C₁₃	C₂²	1	2	yes	—
26	C₁₃×#548	C₂²	1	4	yes	—
27	C₁₃×#547	—	2	2	no	—
28	C₁₃×#547	C₂²	1	2	yes	—
29	C₁₃×#533	—	2	2	no	—
30	C₁₃×#533	C₂²	1	2	yes	—
31	C₁₃×#529	—	2	4	no	—
32	C₁₃×#529	C₂²	1	4	yes	—
33	C₄×C₁₃×#41	—	2	2	no	—
34	C₄×C₁₃×#41	C₂²	1	2	yes	—
35	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
36	C₂×C₄×Q₈×C₁₃	C₂²	1	4	yes	—
37	C₁₃×#500	C₂²	1	1	yes	characteristic
38	C₁₃×#499	C₂²	1	2	yes	—
39	C₁₃×#495	C₂²	1	2	yes	—
40	C₁₃×#494	C₂²	1	1	yes	characteristic
41	C₁₃×#488	C₂²	1	4	yes	—
42	C₁₃×#487	C₂²	1	2	yes	—
43	C₁₃×#485	C₂²	1	4	yes	—
44	C₁₃×#483	C₂²	1	4	yes	—
45	C₁₃×#480	C₂²	1	4	yes	—
46	C₁₃×#479	C₂²	1	4	yes	—
47	C₁₃×#479	C₂²	1	4	yes	—
48	C₁₃×#475	C₂²	1	2	yes	—
49	C₁₃×#474	C₂²	1	2	yes	—
50	C₁₃×#467	C₂²	1	2	yes	—
51	C₁₃×#467	C₂²	1	2	yes	—
52	C₁₃×#467	C₂²	1	2	yes	—
53	C₁₃×#466	C₂²	1	2	yes	—
54	C₁₃×#465	C₂²	1	4	yes	—
55	C₁₃×#464	C₂²	1	4	yes	—
56	C₁₃×#464	C₂²	1	4	yes	—
57	C₁₃×#462	C₂²	1	2	yes	—
58	C₁₃×#461	C₂²	1	2	yes	—
59	C₁₃×#452	C₂²	1	4	yes	—
60	C₁₃×#451	C₂²	1	4	yes	—
61	C₁₃×#448	C₂²	1	4	yes	—
62	C₈×Q₈×C₁₃	C₂²	1	1	yes	characteristic
63	C₈×Q₈×C₁₃	C₂²	1	1	yes	characteristic
64	C₄×C₁₃×Q₁₆	C₂²	1	2	yes	—
65	C₄×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
66	C₄×C₁₃×Q₁₆	C₂²	1	4	yes	—
67	C₄×C₁₃×Q₁₆	C₂²	1	2	yes	—
68	C₄×C₁₃×Q₁₆	C₂²	1	4	yes	—
69	C₄×C₁₃×Q₁₆	C₂²	1	2	yes	—
70	C₄×C₁₃×Q₁₆	C₂²	1	2	yes	—
71	C₄×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
72	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	—
73	C₄×C₁₃×SD₁₆	C₂²	1	4	yes	—
74	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	—
75	C₄×C₁₃×D₈	C₂²	1	1	yes	characteristic
76	C₄×C₁₃×D₈	C₂²	1	1	yes	characteristic
77	C₈×D₄×C₁₃	C₂²	1	2	yes	—
78	C₈×D₄×C₁₃	C₂²	1	1	yes	characteristic
79	C₈×D₄×C₁₃	C₂²	1	1	yes	characteristic
80	C₈×D₄×C₁₃	C₂²	1	2	yes	—
81	C₁₃×#431	C₂²	1	1	yes	characteristic
82	C₁₃×#431	C₂²	1	2	yes	—
83	C₁₃×#427	C₂²	1	1	yes	characteristic
84	C₂×C₁₃×#107	C₂²	1	2	yes	—
85	C₁₃×#416	C₂²	1	2	yes	—
86	C₂×C₁₃×#103	C₂²	1	4	yes	—
87	C₂×C₄×C₈×C₁₃	C₂²	1	2	yes	—
88	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
89	C₂×C₁₃×#41	—	2	2	no	—
90	C₂×C₁₃×#41	D₄	1	1	yes	characteristic
91	C₂×C₁₃×#41	C₂³	1	2	yes	—
92	C₂²×Q₈×C₁₃	C₂³	1	4	yes	—
93	C₁₃×#135	—	2	4	no	—
94	C₂×C₁₃×Q₁₆	—	2	8	no	—
95	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	—
96	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
97	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
98	C₂×C₁₃×Q₁₆	C₂³	1	1	yes	characteristic
99	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
100	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
101	C₂×C₁₃×D₈	C₂³	1	1	yes	characteristic
102	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
103	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
104	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
105	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
106	C₁₃×C₄⋊Q₈	—	2	2	no	—
107	C₁₃×C₄⋊Q₈	—	2	2	no	—
108	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
109	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
110	C₁₃×#126	—	2	4	no	—
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	—	2	2	no	—
116	C₁₃×#125	C₂³	1	4	yes	—
117	C₁₃×#124	—	2	4	no	—
118	C₁₃×#124	C₂³	1	4	yes	—
119	C₁₃×#123	—	2	4	no	—
120	C₁₃×#123	—	2	4	no	—
121	C₁₃×#123	—	2	4	no	—
122	C₁₃×C₂²⋊Q₈	—	2	2	no	—
123	C₁₃×C₂²⋊Q₈	—	2	2	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	C₂³	1	4	yes	—
128	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
129	C₁₃×#121	—	2	4	no	—
130	C₁₃×#121	C₂³	1	4	yes	—
131	C₄×Q₈×C₁₃	—	2	2	no	—
132	C₄×Q₈×C₁₃	—	2	4	no	—
133	C₄×Q₈×C₁₃	—	2	4	no	—
134	C₄×Q₈×C₁₃	—	2	2	no	—
135	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
136	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
137	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
138	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
139	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
140	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
141	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
142	C₄×D₄×C₁₃	—	2	2	no	—
143	C₄×D₄×C₁₃	—	2	4	no	—
144	C₄×D₄×C₁₃	—	2	2	no	—
145	C₄×D₄×C₁₃	—	2	2	no	—
146	C₄×D₄×C₁₃	—	2	4	no	—
147	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
148	C₄×D₄×C₁₃	D₄	1	2	yes	—
149	C₄×D₄×C₁₃	C₂³	1	2	yes	—
150	C₄×D₄×C₁₃	C₂³	1	2	yes	—
151	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
152	C₄×D₄×C₁₃	C₂³	1	2	yes	—
153	C₁₃×#117	—	2	2	no	—
154	C₁₃×#117	—	2	2	no	—
155	C₁₃×#117	—	2	4	no	—
156	C₁₃×#117	—	2	2	no	—
157	C₁₃×#117	—	2	4	no	—
158	C₁₃×#117	D₄	1	2	yes	—
159	C₁₃×#117	D₄	1	1	yes	characteristic
160	C₁₃×#117	C₂³	1	2	yes	—
161	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
162	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
163	C₂×C₄²×C₁₃	—	2	4	no	—
164	C₂×C₄²×C₁₃	—	2	2	no	—
165	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
166	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
167	C₁₃×#107	C₂³	1	1	yes	characteristic
168	C₁₃×#107	C₂³	1	2	yes	—
169	C₁₃×#107	C₂³	1	4	yes	—
170	C₁₃×#107	C₂³	1	1	yes	characteristic
171	C₁₃×#107	C₂³	1	2	yes	—
172	C₁₃×#106	C₂³	1	2	yes	—
173	C₁₃×#106	C₂³	1	4	yes	—
174	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
175	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
176	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
177	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
178	C₁₃×#103	C₂³	1	2	yes	—
179	C₁₃×#103	C₂³	1	4	yes	—
180	C₁₃×#103	C₂³	1	4	yes	—
181	C₁₃×#103	C₂³	1	4	yes	—
182	C₁₃×#103	C₂³	1	2	yes	—
183	C₁₃×#103	C₂³	1	4	yes	—
184	C₁₃×#103	C₂³	1	4	yes	—
185	C₁₃×#102	C₂³	1	2	yes	—
186	C₁₃×#102	C₂³	1	2	yes	—
187	C₁₃×#102	C₂³	1	4	yes	—
188	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
189	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
190	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
191	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
192	C₄×C₈×C₁₃	C₂³	1	2	yes	—
193	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
194	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
195	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
196	C₄×C₈×C₁₃	C₂³	1	2	yes	—
197	C₄×C₈×C₁₃	C₂³	1	2	yes	—
198	#61433	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
199	C₁₃×#41	—	2	4	no	—
200	C₁₃×#41	—	2	4	no	—
201	C₁₃×#41	—	4	2	no	—
202	C₁₃×#41	—	4	8	no	—
203	C₂×Q₈×C₁₃	—	2	4	no	—
204	C₂×Q₈×C₁₃	—	2	2	no	—
205	C₂×Q₈×C₁₃	—	2	8	no	—
206	C₂×Q₈×C₁₃	—	4	4	no	—
207	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
208	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
209	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
210	C₂×D₄×C₁₃	—	2	2	no	—
211	C₂×D₄×C₁₃	—	2	4	no	—
212	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
213	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
214	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
215	C₂²×C₄×C₁₃	—	2	4	no	—
216	C₂²×C₄×C₁₃	—	2	4	no	—
217	C₂²×C₄×C₁₃	—	2	2	no	—
218	C₂²×C₄×C₁₃	—	2	2	no	—
219	C₂²×C₄×C₁₃	—	2	2	no	—
220	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
221	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
222	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
223	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
224	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
225	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
226	C₁₃×Q₁₆	—	2	8	no	—
227	C₁₃×Q₁₆	—	2	4	no	—
228	C₁₃×Q₁₆	—	4	2	no	—
229	C₁₃×Q₁₆	#41	1	4	yes	complemented
230	C₁₃×SD₁₆	—	2	4	no	—
231	C₁₃×SD₁₆	—	4	4	no	—
232	C₁₃×D₈	—	2	2	no	—
233	C₂×C₈×C₁₃	—	2	4	no	—
234	C₂×C₈×C₁₃	—	2	2	no	—
235	C₂×C₈×C₁₃	—	4	2	no	—
236	C₂×C₈×C₁₃	—	4	1	no	—
237	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
238	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
239	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
240	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
241	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
242	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
243	C₁₃×C₄⋊C₄	—	2	2	no	—
244	C₁₃×C₄⋊C₄	—	2	4	no	—
245	C₁₃×C₄⋊C₄	—	2	4	no	—
246	C₁₃×C₄⋊C₄	—	2	4	no	—
247	C₁₃×C₄⋊C₄	—	2	4	no	—
248	C₁₃×C₄⋊C₄	—	2	2	no	—
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	2	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	C₂×D₄	1	1	yes	characteristic
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	1	yes	characteristic
260	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
261	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
262	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
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	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	C₂×D₄	1	2	yes	—
272	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
273	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
274	C₄²×C₁₃	—	2	2	no	—
275	C₄²×C₁₃	—	2	4	no	—
276	C₄²×C₁₃	—	2	2	no	—
277	C₄²×C₁₃	—	2	4	no	—
278	C₄²×C₁₃	—	2	2	no	—
279	C₄²×C₁₃	—	2	4	no	—
280	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
281	C₄²×C₁₃	C₂×D₄	1	2	yes	—
282	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
283	C₄²×C₁₃	C₂×D₄	1	2	yes	—
284	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
285	C₄²×C₁₃	C₂⁴	1	2	yes	—
286	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
287	#3482	C₂×C₁₃	1	2	yes	complemented
288	#3393	C₂×C₁₃	1	1	yes	characteristic, complemented
289	#3383	C₂×C₁₃	1	1	yes	characteristic, complemented
290	#3364	C₂×C₁₃	1	2	yes	complemented
291	#3336	C₂×C₁₃	1	2	yes	complemented
292	#3334	C₂×C₁₃	1	1	yes	characteristic, complemented
293	#3300	C₂×C₁₃	1	4	yes	complemented
294	#3298	C₂×C₁₃	1	2	yes	complemented
295	D₄×Q₁₆	C₂×C₁₃	1	1	yes	characteristic, complemented
296	#3285	C₂×C₁₃	1	2	yes	complemented
297	#3170	C₂×C₁₃	1	1	yes	characteristic, complemented
298	#3168	C₂×C₁₃	1	2	yes	complemented
299	#3108	C₂×C₁₃	1	4	yes	complemented
300	#3107	C₂×C₁₃	1	2	yes	complemented
301	C₈×#41	C₂×C₁₃	1	1	yes	characteristic, complemented
302	C₄×#135	C₂×C₁₃	1	1	yes	characteristic, complemented
303	C₂×C₄×Q₁₆	C₂×C₁₃	1	2	yes	complemented
304	C₂³×C₁₃	—	2	2	no	—
305	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
306	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
307	Q₈×C₁₃	—	2	2	no	—
308	Q₈×C₁₃	—	2	2	no	—
309	Q₈×C₁₃	—	2	4	no	—
310	Q₈×C₁₃	—	2	4	no	—
311	Q₈×C₁₃	—	4	8	no	—
312	Q₈×C₁₃	—	4	4	no	—
313	Q₈×C₁₃	C₂×#41	1	4	yes	—
314	D₄×C₁₃	—	2	4	no	—
315	D₄×C₁₃	—	2	2	no	—
316	D₄×C₁₃	—	2	2	no	—
317	D₄×C₁₃	—	4	4	no	—
318	D₄×C₁₃	—	4	8	no	—
319	D₄×C₁₃	#135	1	4	yes	complemented
320	C₂×C₄×C₁₃	—	2	4	no	—
321	C₂×C₄×C₁₃	—	2	2	no	—
322	C₂×C₄×C₁₃	—	2	2	no	—
323	C₂×C₄×C₁₃	—	2	4	no	—
324	C₂×C₄×C₁₃	—	2	2	no	—
325	C₂×C₄×C₁₃	—	2	2	no	—
326	C₂×C₄×C₁₃	—	2	1	no	—
327	C₂×C₄×C₁₃	—	2	2	no	—
328	C₂×C₄×C₁₃	—	2	1	no	—
329	C₂×C₄×C₁₃	—	2	2	no	—
330	C₂×C₄×C₁₃	—	2	2	no	—
331	C₂×C₄×C₁₃	—	2	4	no	—
332	C₂×C₄×C₁₃	—	2	4	no	—
333	C₂×C₄×C₁₃	—	4	4	no	—
334	C₂×C₄×C₁₃	—	4	8	no	—
335	C₂×C₄×C₁₃	—	4	8	no	—
336	C₂×C₄×C₁₃	—	4	4	no	—
337	C₂×C₄×C₁₃	—	4	4	no	—
338	C₂×C₄×C₁₃	C₂²×D₄	1	2	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	2	yes	—
342	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
343	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
344	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
345	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
346	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
347	C₈×C₁₃	—	2	1	no	—
348	C₈×C₁₃	—	2	2	no	—
349	C₈×C₁₃	—	2	1	no	—
350	C₈×C₁₃	—	2	2	no	—
351	C₈×C₁₃	—	2	1	no	—
352	C₈×C₁₃	C₂×#41	1	2	yes	—
353	C₂×#135	C₂²×C₁₃	1	1	yes	characteristic
354	C₂²×Q₁₆	C₂²×C₁₃	1	2	yes	—
355	#557	C₂²×C₁₃	1	2	yes	—
356	#556	—	2	2	no	—
357	#556	C₂²×C₁₃	1	2	yes	—
358	#552	—	2	4	no	—
359	#552	C₂²×C₁₃	1	4	yes	—
360	D₄×Q₈	C₂²×C₁₃	1	2	yes	—
361	#548	C₂²×C₁₃	1	4	yes	—
362	#547	—	2	2	no	—
363	#547	C₂²×C₁₃	1	2	yes	—
364	#533	—	2	2	no	—
365	#533	C₂²×C₁₃	1	2	yes	—
366	#529	—	2	4	no	—
367	#529	C₂²×C₁₃	1	4	yes	—
368	C₄×#41	—	2	2	no	—
369	C₄×#41	C₂²×C₁₃	1	2	yes	—
370	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
371	C₂×C₄×Q₈	C₂²×C₁₃	1	4	yes	—
372	#500	C₂²×C₁₃	1	1	yes	characteristic
373	#499	C₂²×C₁₃	1	2	yes	—
374	#495	C₂²×C₁₃	1	2	yes	—
375	#494	C₂²×C₁₃	1	1	yes	characteristic
376	#488	C₂²×C₁₃	1	4	yes	—
377	#487	C₂²×C₁₃	1	2	yes	—
378	#485	C₂²×C₁₃	1	4	yes	—
379	#483	C₂²×C₁₃	1	4	yes	—
380	#480	C₂²×C₁₃	1	4	yes	—
381	#479	C₂²×C₁₃	1	4	yes	—
382	#479	C₂²×C₁₃	1	4	yes	—
383	#475	C₂²×C₁₃	1	2	yes	—
384	#474	C₂²×C₁₃	1	2	yes	—
385	#467	C₂²×C₁₃	1	2	yes	—
386	#467	C₂²×C₁₃	1	2	yes	—
387	#467	C₂²×C₁₃	1	2	yes	—
388	#466	C₂²×C₁₃	1	2	yes	—
389	#465	C₂²×C₁₃	1	4	yes	—
390	#464	C₂²×C₁₃	1	4	yes	—
391	#464	C₂²×C₁₃	1	4	yes	—
392	#462	C₂²×C₁₃	1	2	yes	—
393	#461	C₂²×C₁₃	1	2	yes	—
394	#452	C₂²×C₁₃	1	4	yes	—
395	#451	C₂²×C₁₃	1	4	yes	—
396	#448	C₂²×C₁₃	1	4	yes	—
397	C₈×Q₈	C₂²×C₁₃	1	1	yes	characteristic
398	C₈×Q₈	C₂²×C₁₃	1	1	yes	characteristic
399	C₄×Q₁₆	C₂²×C₁₃	1	2	yes	—
400	C₄×Q₁₆	C₂²×C₁₃	1	4	yes	—
401	C₄×Q₁₆	C₂²×C₁₃	1	2	yes	—
402	C₄×Q₁₆	C₂²×C₁₃	1	4	yes	—
403	C₄×Q₁₆	C₂²×C₁₃	1	2	yes	—
404	C₄×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
405	C₄×Q₁₆	C₂²×C₁₃	1	2	yes	—
406	C₄×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
407	C₄×SD₁₆	C₂²×C₁₃	1	4	yes	—
408	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	—
409	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	—
410	C₄×D₈	C₂²×C₁₃	1	1	yes	characteristic
411	C₄×D₈	C₂²×C₁₃	1	1	yes	characteristic
412	C₈×D₄	C₂²×C₁₃	1	1	yes	characteristic
413	C₈×D₄	C₂²×C₁₃	1	2	yes	—
414	C₈×D₄	C₂²×C₁₃	1	1	yes	characteristic
415	C₈×D₄	C₂²×C₁₃	1	2	yes	—
416	#431	C₂²×C₁₃	1	1	yes	characteristic
417	#431	C₂²×C₁₃	1	2	yes	—
418	#427	C₂²×C₁₃	1	1	yes	characteristic
419	C₂×#107	C₂²×C₁₃	1	2	yes	—
420	#416	C₂²×C₁₃	1	2	yes	—
421	C₂×#103	C₂²×C₁₃	1	4	yes	—
422	C₂×C₄×C₈	C₂²×C₁₃	1	2	yes	—
423	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
424	C₂²×C₁₃	—	2	2	no	—
425	C₂²×C₁₃	—	2	2	no	—
426	C₂²×C₁₃	—	2	1	no	—
427	C₂²×C₁₃	—	2	1	no	—
428	C₂²×C₁₃	—	2	1	no	—
429	C₂²×C₁₃	—	4	2	no	—
430	C₂²×C₁₃	—	4	2	no	—
431	C₂²×C₁₃	—	4	2	no	—
432	C₂²×C₁₃	C₂×#135	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	4	no	—
437	C₄×C₁₃	—	2	1	no	—
438	C₄×C₁₃	—	2	2	no	—
439	C₄×C₁₃	—	2	2	no	—
440	C₄×C₁₃	—	2	1	no	—
441	C₄×C₁₃	—	4	4	no	—
442	C₄×C₁₃	—	4	2	no	—
443	C₄×C₁₃	—	4	4	no	—
444	C₄×C₁₃	—	4	2	no	—
445	C₄×C₁₃	C₂×#135	1	2	yes	—
446	C₄×C₁₃	#578	1	2	yes	—
447	C₄×C₁₃	C₂²×#41	1	1	yes	characteristic
448	C₄×C₁₃	#585	1	1	yes	characteristic
449	C₂×#41	—	2	2	no	—
450	C₂×#41	D₄×C₁₃	1	1	yes	characteristic
451	C₂×#41	C₂³×C₁₃	1	2	yes	—
452	C₂²×Q₈	C₂³×C₁₃	1	4	yes	—
453	#135	—	2	4	no	—
454	C₂×Q₁₆	—	2	8	no	—
455	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	—
456	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
457	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
458	C₂×Q₁₆	C₂³×C₁₃	1	1	yes	characteristic
459	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
460	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
461	C₂×D₈	C₂³×C₁₃	1	1	yes	characteristic
462	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
463	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
464	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
465	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
466	C₄⋊Q₈	—	2	2	no	—
467	C₄⋊Q₈	—	2	2	no	—
468	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
469	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
470	#126	—	2	4	no	—
471	#126	—	2	4	no	—
472	#126	—	2	4	no	—
473	#125	—	2	4	no	—
474	#125	—	2	4	no	—
475	#125	—	2	2	no	—
476	#125	C₂³×C₁₃	1	4	yes	—
477	#124	—	2	4	no	—
478	#124	C₂³×C₁₃	1	4	yes	—
479	#123	—	2	4	no	—
480	#123	—	2	4	no	—
481	#123	—	2	4	no	—
482	C₂²⋊Q₈	—	2	2	no	—
483	C₂²⋊Q₈	—	2	2	no	—
484	C₂²⋊Q₈	—	2	2	no	—
485	C₂²⋊Q₈	—	2	4	no	—
486	C₂²⋊Q₈	—	2	4	no	—
487	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
488	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
489	#121	—	2	4	no	—
490	#121	C₂³×C₁₃	1	4	yes	—
491	C₄×Q₈	—	2	2	no	—
492	C₄×Q₈	—	2	4	no	—
493	C₄×Q₈	—	2	4	no	—
494	C₄×Q₈	—	2	2	no	—
495	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
496	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
497	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
498	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
499	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
500	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
501	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
502	C₄×D₄	—	2	2	no	—
503	C₄×D₄	—	2	4	no	—
504	C₄×D₄	—	2	2	no	—
505	C₄×D₄	—	2	2	no	—
506	C₄×D₄	—	2	4	no	—
507	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
508	C₄×D₄	D₄×C₁₃	1	2	yes	—
509	C₄×D₄	C₂³×C₁₃	1	2	yes	—
510	C₄×D₄	C₂³×C₁₃	1	2	yes	—
511	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
512	C₄×D₄	C₂³×C₁₃	1	2	yes	—
513	#117	—	2	2	no	—
514	#117	—	2	2	no	—
515	#117	—	2	4	no	—
516	#117	—	2	2	no	—
517	#117	—	2	4	no	—
518	#117	D₄×C₁₃	1	2	yes	—
519	#117	D₄×C₁₃	1	1	yes	characteristic
520	#117	C₂³×C₁₃	1	2	yes	—
521	C₂×C₄⋊C₄	—	2	4	no	—
522	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
523	C₂×C₄²	—	2	4	no	—
524	C₂×C₄²	—	2	2	no	—
525	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
526	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
527	#107	C₂³×C₁₃	1	1	yes	characteristic
528	#107	C₂³×C₁₃	1	2	yes	—
529	#107	C₂³×C₁₃	1	4	yes	—
530	#107	C₂³×C₁₃	1	1	yes	characteristic
531	#107	C₂³×C₁₃	1	2	yes	—
532	#106	C₂³×C₁₃	1	2	yes	—
533	#106	C₂³×C₁₃	1	4	yes	—
534	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
535	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
536	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
537	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
538	#103	C₂³×C₁₃	1	2	yes	—
539	#103	C₂³×C₁₃	1	4	yes	—
540	#103	C₂³×C₁₃	1	4	yes	—
541	#103	C₂³×C₁₃	1	4	yes	—
542	#103	C₂³×C₁₃	1	2	yes	—
543	#103	C₂³×C₁₃	1	4	yes	—
544	#103	C₂³×C₁₃	1	4	yes	—
545	#102	C₂³×C₁₃	1	2	yes	—
546	#102	C₂³×C₁₃	1	2	yes	—
547	#102	C₂³×C₁₃	1	4	yes	—
548	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
549	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
550	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
551	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
552	C₄×C₈	C₂³×C₁₃	1	2	yes	—
553	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
554	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
555	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
556	C₄×C₈	C₂³×C₁₃	1	2	yes	—
557	C₄×C₈	C₂³×C₁₃	1	2	yes	—
558	C₂×C₁₃	—	2	4	no	—
559	C₂×C₁₃	—	4	1	no	—
560	C₂×C₁₃	—	8	2	no	—
561	C₂×C₁₃	D₄×#41	1	1	yes	characteristic
562	C₂×C₁₃	C₂²×#135	1	1	yes	characteristic
563	C₂×C₁₃	C₂×#578	1	1	yes	characteristic
564	#41	—	2	4	no	—
565	#41	—	2	4	no	—
566	#41	—	4	2	no	—
567	#41	—	4	8	no	—
568	C₂×Q₈	—	2	4	no	—
569	C₂×Q₈	—	2	2	no	—
570	C₂×Q₈	—	2	8	no	—
571	C₂×Q₈	—	4	4	no	—
572	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
573	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
574	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
575	C₂×D₄	—	2	2	no	—
576	C₂×D₄	—	2	4	no	—
577	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
578	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
579	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
580	C₂²×C₄	—	2	4	no	—
581	C₂²×C₄	—	2	4	no	—
582	C₂²×C₄	—	2	2	no	—
583	C₂²×C₄	—	2	2	no	—
584	C₂²×C₄	—	2	2	no	—
585	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
586	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
587	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
588	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
589	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
590	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
591	Q₁₆	—	2	8	no	—
592	Q₁₆	—	2	4	no	—
593	Q₁₆	—	4	2	no	—
594	Q₁₆	C₁₃×#41	1	4	yes	complemented
595	SD₁₆	—	2	4	no	—
596	SD₁₆	—	4	4	no	—
597	D₈	—	2	2	no	—
598	C₂×C₈	—	2	4	no	—
599	C₂×C₈	—	2	2	no	—
600	C₂×C₈	—	4	2	no	—
601	C₂×C₈	—	4	1	no	—
602	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
603	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
604	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
605	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
606	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
607	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
608	C₄⋊C₄	—	2	2	no	—
609	C₄⋊C₄	—	2	4	no	—
610	C₄⋊C₄	—	2	4	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	—	2	4	no	—
616	C₄⋊C₄	—	2	2	no	—
617	C₄⋊C₄	—	2	2	no	—
618	C₄⋊C₄	—	2	4	no	—
619	C₄⋊C₄	—	2	2	no	—
620	C₄⋊C₄	—	2	4	no	—
621	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
622	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
623	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
624	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
625	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
626	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
627	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
628	C₂²⋊C₄	—	2	4	no	—
629	C₂²⋊C₄	—	2	4	no	—
630	C₂²⋊C₄	—	2	2	no	—
631	C₂²⋊C₄	—	2	4	no	—
632	C₂²⋊C₄	—	2	2	no	—
633	C₂²⋊C₄	—	2	2	no	—
634	C₂²⋊C₄	—	2	4	no	—
635	C₂²⋊C₄	—	2	4	no	—
636	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
637	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
638	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
639	C₄²	—	2	2	no	—
640	C₄²	—	2	2	no	—
641	C₄²	—	2	4	no	—
642	C₄²	—	2	4	no	—
643	C₄²	—	2	2	no	—
644	C₄²	—	2	4	no	—
645	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
646	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
647	C₄²	C₂×D₄×C₁₃	1	2	yes	—
648	C₄²	C₂×D₄×C₁₃	1	2	yes	—
649	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
650	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
651	C₄²	C₂⁴×C₁₃	1	2	yes	—
652	C₁₃	#61433	1	1	yes	characteristic, direct product factor, Sylow
653	C₂³	—	2	2	no	—
654	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
655	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
656	Q₈	—	2	2	no	—
657	Q₈	—	2	2	no	—
658	Q₈	—	2	4	no	—
659	Q₈	—	2	4	no	—
660	Q₈	—	4	8	no	—
661	Q₈	—	4	4	no	—
662	Q₈	C₂×C₁₃×#41	1	4	yes	—
663	D₄	—	2	4	no	—
664	D₄	—	2	2	no	—
665	D₄	—	2	2	no	—
666	D₄	—	4	4	no	—
667	D₄	—	4	8	no	—
668	D₄	C₁₃×#135	1	4	yes	complemented
669	C₂×C₄	—	2	4	no	—
670	C₂×C₄	—	2	2	no	—
671	C₂×C₄	—	2	2	no	—
672	C₂×C₄	—	2	4	no	—
673	C₂×C₄	—	2	2	no	—
674	C₂×C₄	—	2	2	no	—
675	C₂×C₄	—	2	1	no	—
676	C₂×C₄	—	2	2	no	—
677	C₂×C₄	—	2	1	no	—
678	C₂×C₄	—	2	2	no	—
679	C₂×C₄	—	2	2	no	—
680	C₂×C₄	—	2	4	no	—
681	C₂×C₄	—	2	4	no	—
682	C₂×C₄	—	4	4	no	—
683	C₂×C₄	—	4	8	no	—
684	C₂×C₄	—	4	8	no	—
685	C₂×C₄	—	4	4	no	—
686	C₂×C₄	—	4	4	no	—
687	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
688	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
689	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
690	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
691	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
692	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
693	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
694	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
695	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
696	C₈	—	2	1	no	—
697	C₈	—	2	2	no	—
698	C₈	—	2	1	no	—
699	C₈	—	2	2	no	—
700	C₈	—	2	1	no	—
701	C₈	C₂×C₁₃×#41	1	2	yes	—
702	C₂²	—	2	2	no	—
703	C₂²	—	2	2	no	—
704	C₂²	—	2	1	no	—
705	C₂²	—	2	1	no	—
706	C₂²	—	2	1	no	—
707	C₂²	—	4	2	no	—
708	C₂²	—	4	2	no	—
709	C₂²	—	4	2	no	—
710	C₂²	C₂×C₁₃×#135	1	4	yes	—
711	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
712	C₄	—	2	1	no	—
713	C₄	—	2	2	no	—
714	C₄	—	2	2	no	—
715	C₄	—	2	1	no	—
716	C₄	—	2	1	no	—
717	C₄	—	2	2	no	—
718	C₄	—	2	4	no	—
719	C₄	—	4	2	no	—
720	C₄	—	4	4	no	—
721	C₄	—	4	2	no	—
722	C₄	—	4	4	no	—
723	C₄	C₂×C₁₃×#135	1	2	yes	—
724	C₄	C₁₃×#578	1	2	yes	—
725	C₄	C₂²×C₁₃×#41	1	1	yes	characteristic
726	C₄	C₁₃×#585	1	1	yes	characteristic
727	C₂	—	2	4	no	—
728	C₂	—	4	1	no	—
729	C₂	—	8	2	no	—
730	C₂	D₄×C₁₃×#41	1	1	yes	characteristic
731	C₂	C₂²×C₁₃×#135	1	1	yes	characteristic
732	C₂	C₂×C₁₃×#578	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
socle	C₂²×C₁₃	C₂³×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₃ ◁ C₄×C₁₃×#41 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3482	C₂	semidirect
2. C₁₃×#3393	C₂	semidirect
3. C₁₃×#3383	C₂	semidirect
4. C₁₃×#3364	C₂	semidirect
5. C₁₃×#3336	C₂	semidirect
6. C₁₃×#3334	C₂	semidirect
7. C₁₃×#3300	C₂	semidirect
8. C₁₃×#3298	C₂	semidirect
9. D₄×C₁₃×Q₁₆	C₂	semidirect
10. C₁₃×#3285	C₂	semidirect
11. C₁₃×#3170	C₂	semidirect
12. C₁₃×#3168	C₂	semidirect
13. C₁₃×#3108	C₂	semidirect
14. C₁₃×#3107	C₂	semidirect
15. C₈×C₁₃×#41	C₂	semidirect
16. C₄×C₁₃×#135	C₂	semidirect
17. C₂×C₄×C₁₃×Q₁₆	C₂	semidirect
198. #61433	C₁₃	direct (N × H)
229. C₁₃×Q₁₆	#41	semidirect
287. #3482	C₂×C₁₃	semidirect
288. #3393	C₂×C₁₃	semidirect
289. #3383	C₂×C₁₃	semidirect
290. #3364	C₂×C₁₃	semidirect
291. #3336	C₂×C₁₃	semidirect
292. #3334	C₂×C₁₃	semidirect
293. #3300	C₂×C₁₃	semidirect
294. #3298	C₂×C₁₃	semidirect
295. D₄×Q₁₆	C₂×C₁₃	semidirect
296. #3285	C₂×C₁₃	semidirect
297. #3170	C₂×C₁₃	semidirect
298. #3168	C₂×C₁₃	semidirect
299. #3108	C₂×C₁₃	semidirect
300. #3107	C₂×C₁₃	semidirect
301. C₈×#41	C₂×C₁₃	semidirect
302. C₄×#135	C₂×C₁₃	semidirect
303. C₂×C₄×Q₁₆	C₂×C₁₃	semidirect
319. D₄×C₁₃	#135	semidirect
594. Q₁₆	C₁₃×#41	semidirect
652. C₁₃	#61433	direct (N × H)
668. D₄	C₁₃×#135	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₁₃×#3482	2
C₁₃×#3393	2
C₁₃×#3383	2
C₁₃×#3364	2
C₁₃×#3336	2
C₁₃×#3334	2
C₁₃×#3300	2
C₁₃×#3298	2
D₄×C₁₃×Q₁₆	2
C₁₃×#3285	2
C₁₃×#3170	2
C₁₃×#3168	2
C₁₃×#3108	2
C₁₃×#3107	2
C₈×C₁₃×#41	2
C₄×C₁₃×#135	2
C₂×C₄×C₁₃×Q₁₆	2
#61433	13

Subgroups — C13×#61433 #15747772

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61433 #15747772