Subgroups — C₁₃×#61018 #15747357

Order 3328.

1672 conjugacy classes of subgroups.

The subgroup lattice has 738 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3510	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#3509	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3258	C₂	1	4	yes	maximal, complemented
4	C₁₃×#3240	C₂	1	2	yes	maximal, complemented
5	C₁₃×#3237	C₂	1	2	yes	maximal, complemented
6	C₁₃×#3218	C₂	1	2	yes	maximal, complemented
7	C₁₃×#3215	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3202	C₂	1	2	yes	maximal, complemented
9	C₁₃×#3200	C₂	1	2	yes	maximal
10	C₁₃×#3181	C₂	1	2	yes	maximal, complemented
11	C₁₃×#3172	C₂	1	2	yes	maximal, complemented
12	C₁₃×#3127	C₂	1	2	yes	maximal, complemented
13	C₁₃×#3123	C₂	1	2	yes	maximal, complemented
14	C₁₃×#3121	C₂	1	4	yes	maximal, complemented
15	C₁₃×#2923	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₃×#559	—	2	2	no	—
17	C₁₃×#557	—	2	2	no	—
18	C₁₃×#556	—	2	2	no	—
19	C₁₃×#556	—	2	2	no	—
20	C₁₃×#552	—	2	2	no	—
21	C₁₃×#552	—	2	2	no	—
22	C₁₃×#551	—	2	2	no	—
23	C₁₃×#551	—	2	2	no	—
24	C₁₃×#542	C₂²	1	2	yes	—
25	C₁₃×#542	C₂²	1	2	yes	—
26	C₁₃×#541	C₂²	1	2	yes	—
27	C₁₃×#541	C₂²	1	2	yes	complemented
28	C₁₃×#536	C₂²	1	2	yes	—
29	C₁₃×#536	C₂²	1	1	yes	characteristic
30	C₁₃×#535	C₂²	1	1	yes	characteristic
31	C₁₃×#533	C₂²	1	2	yes	—
32	C₁₃×#533	C₂²	1	1	yes	characteristic
33	C₁₃×#533	C₂²	1	2	yes	complemented
34	C₁₃×#533	C₂²	1	1	yes	characteristic, complemented
35	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
36	C₁₃×#529	C₂²	1	2	yes	—
37	C₁₃×#529	C₂²	1	2	yes	—
38	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic
39	C₁₃×#519	C₂²	1	1	yes	characteristic
40	C₁₃×#519	C₂²	1	2	yes	complemented
41	C₁₃×#518	C₂²	1	1	yes	characteristic
42	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
43	C₁₃×#501	C₂²	1	2	yes	complemented
44	C₁₃×#501	C₂²	1	2	yes	complemented
45	C₁₃×#497	C₂²	1	2	yes	—
46	C₁₃×#497	C₂²	1	2	yes	—
47	C₁₃×#491	C₂²	1	2	yes	complemented
48	C₁₃×#491	C₂²	1	2	yes	complemented
49	C₁₃×#489	C₂²	1	2	yes	—
50	C₁₃×#489	C₂²	1	2	yes	—
51	C₁₃×#485	C₂²	1	4	yes	—
52	C₁₃×#485	C₂²	1	4	yes	—
53	C₁₃×#485	C₂²	1	4	yes	complemented
54	C₁₃×#482	C₂²	1	4	yes	—
55	C₁₃×#479	C₂²	1	4	yes	complemented
56	C₁₃×#478	C₂²	1	4	yes	—
57	C₁₃×#477	C₂²	1	4	yes	complemented
58	C₁₃×#475	C₂²	1	4	yes	complemented
59	C₁₃×#470	C₂²	1	4	yes	complemented
60	C₁₃×#468	C₂²	1	4	yes	—
61	C₁₃×#467	C₂²	1	4	yes	complemented
62	C₁₃×#465	C₂²	1	4	yes	—
63	C₁₃×#464	C₂²	1	4	yes	—
64	C₁₃×#464	C₂²	1	4	yes	—
65	C₁₃×#462	C₂²	1	4	yes	complemented
66	C₁₃×#461	C₂²	1	4	yes	—
67	C₁₃×#451	C₂²	1	4	yes	—
68	C₁₃×#451	C₂²	1	4	yes	complemented
69	C₁₃×#450	C₂²	1	4	yes	—
70	C₁₃×#448	C₂²	1	4	yes	—
71	C₁₃×#441	C₂²	1	4	yes	complemented
72	C₁₃×#440	C₂²	1	4	yes	—
73	C₄×C₁₃×Q₁₆	C₂²	1	4	yes	complemented
74	C₄×C₁₃×SD₁₆	C₂²	1	4	yes	—
75	C₁₃×#433	C₂²	1	2	yes	—
76	C₁₃×#433	C₂²	1	2	yes	complemented
77	C₁₃×#432	C₂²	1	2	yes	—
78	C₁₃×#432	C₂²	1	2	yes	complemented
79	C₁₃×#424	C₂²	1	2	yes	complemented
80	C₁₃×#408	C₂²	1	2	yes	—
81	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic, complemented
82	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic, complemented
83	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
84	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
85	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
86	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
87	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	—
88	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	—
89	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
90	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
91	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
92	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
93	C₁₃×C₄⋊Q₈	—	2	1	no	—
94	C₁₃×C₄⋊Q₈	—	2	2	no	—
95	C₁₃×C₄⋊Q₈	—	2	2	no	—
96	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
97	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
98	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
99	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
100	C₁₃×#127	—	2	1	no	—
101	C₁₃×#126	—	2	2	no	—
102	C₁₃×#126	—	2	2	no	—
103	C₁₃×#126	—	2	4	no	—
104	C₁₃×#126	—	2	4	no	—
105	C₁₃×#126	—	2	2	no	—
106	C₁₃×#126	—	2	2	no	—
107	C₁₃×#125	—	2	4	no	—
108	C₁₃×#125	—	2	4	no	—
109	C₁₃×#125	—	2	2	no	—
110	C₁₃×#125	—	2	2	no	—
111	C₁₃×#125	C₂³	1	2	yes	—
112	C₁₃×#125	C₂³	1	2	yes	—
113	C₁₃×#124	—	2	1	no	—
114	C₁₃×#124	—	2	2	no	—
115	C₁₃×#124	—	2	1	no	—
116	C₁₃×#124	—	2	2	no	—
117	C₁₃×#124	—	2	2	no	—
118	C₁₃×#124	—	2	2	no	—
119	C₁₃×#124	C₂³	1	2	yes	—
120	C₁₃×#124	C₂³	1	2	yes	—
121	C₁₃×#123	—	2	1	no	—
122	C₁₃×#123	—	2	1	no	—
123	C₁₃×#123	—	2	2	no	—
124	C₁₃×#123	—	2	2	no	—
125	C₁₃×#123	—	2	2	no	—
126	C₁₃×#123	—	2	2	no	—
127	C₁₃×#123	—	2	2	no	—
128	C₁₃×#123	—	2	2	no	—
129	C₁₃×C₂²⋊Q₈	—	2	2	no	—
130	C₁₃×C₂²⋊Q₈	—	2	2	no	—
131	C₁₃×C₂²⋊Q₈	—	2	2	no	—
132	C₁₃×C₂²⋊Q₈	—	2	2	no	—
133	C₁₃×C₂²⋊Q₈	—	2	2	no	—
134	C₁₃×C₂²⋊Q₈	—	2	2	no	—
135	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
136	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
137	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
138	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
139	C₁₃×#121	C₂³	1	2	yes	—
140	C₁₃×#121	C₂³	1	2	yes	—
141	C₁₃×#120	—	2	1	no	—
142	C₁₃×#120	—	2	1	no	—
143	C₄×Q₈×C₁₃	—	2	2	no	—
144	C₄×Q₈×C₁₃	—	2	4	no	—
145	C₄×Q₈×C₁₃	—	2	2	no	—
146	C₄×Q₈×C₁₃	—	2	2	no	—
147	C₄×Q₈×C₁₃	—	2	2	no	—
148	C₄×Q₈×C₁₃	—	2	2	no	—
149	C₄×Q₈×C₁₃	D₄	1	2	yes	—
150	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
151	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
152	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
153	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
154	C₄×D₄×C₁₃	—	2	2	no	—
155	C₄×D₄×C₁₃	—	2	2	no	—
156	C₄×D₄×C₁₃	—	2	2	no	—
157	C₄×D₄×C₁₃	D₄	1	2	yes	—
158	C₄×D₄×C₁₃	D₄	1	2	yes	—
159	C₄×D₄×C₁₃	D₄	1	2	yes	—
160	C₄×D₄×C₁₃	C₂³	1	2	yes	—
161	C₄×D₄×C₁₃	C₂³	1	2	yes	—
162	C₁₃×#117	—	2	2	no	—
163	C₁₃×#117	—	2	2	no	—
164	C₁₃×#117	—	2	2	no	—
165	C₁₃×#117	—	2	4	no	—
166	C₁₃×#117	—	2	2	no	—
167	C₁₃×#117	—	2	2	no	—
168	C₁₃×#117	C₂³	1	2	yes	—
169	C₁₃×#117	C₂³	1	1	yes	characteristic
170	C₁₃×#117	C₂³	1	1	yes	characteristic
171	C₁₃×#117	C₂³	1	1	yes	characteristic
172	C₁₃×#117	C₂³	1	1	yes	characteristic
173	C₁₃×#117	C₂³	1	1	yes	characteristic
174	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
175	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
176	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
177	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
178	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
179	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
180	C₁₃×#107	C₂³	1	4	yes	—
181	C₁₃×#107	C₂³	1	4	yes	—
182	C₁₃×#106	C₂³	1	4	yes	—
183	C₁₃×#106	C₂³	1	4	yes	—
184	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
185	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
186	C₁₃×#103	C₂³	1	4	yes	—
187	C₁₃×#103	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×#103	C₂³	1	4	yes	—
192	C₁₃×#102	C₂³	1	4	yes	—
193	C₁₃×#102	C₂³	1	4	yes	—
194	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
195	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
196	C₁₃×#97	C₂³	1	2	yes	—
197	C₁₃×#97	C₂³	1	2	yes	—
198	C₁₃×#97	C₂³	1	2	yes	—
199	C₄×C₈×C₁₃	C₂³	1	2	yes	—
200	#61018	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
201	C₂⁴×C₁₃	—	2	1	no	—
202	C₁₃×#41	—	4	2	no	—
203	C₂×Q₈×C₁₃	—	2	2	no	—
204	C₂×Q₈×C₁₃	—	2	1	no	—
205	C₂×Q₈×C₁₃	—	2	2	no	—
206	C₂×Q₈×C₁₃	—	2	2	no	—
207	C₂×Q₈×C₁₃	—	4	2	no	—
208	C₂×Q₈×C₁₃	—	4	2	no	—
209	C₂×Q₈×C₁₃	—	4	2	no	—
210	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
211	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
212	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
213	C₂×D₄×C₁₃	—	2	2	no	—
214	C₂×D₄×C₁₃	—	2	2	no	—
215	C₂×D₄×C₁₃	—	2	1	no	—
216	C₂×D₄×C₁₃	—	4	2	no	—
217	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
218	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
219	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
220	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
221	C₂²×C₄×C₁₃	—	2	1	no	—
222	C₂²×C₄×C₁₃	—	2	2	no	—
223	C₂²×C₄×C₁₃	—	2	2	no	—
224	C₂²×C₄×C₁₃	—	2	2	no	—
225	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
226	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
227	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
228	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
229	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
230	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
231	C₁₃×Q₁₆	—	4	4	no	—
232	C₁₃×Q₁₆	—	4	4	no	—
233	C₁₃×SD₁₆	—	4	4	no	—
234	C₁₃×SD₁₆	—	4	4	no	—
235	C₁₃×M₁₆	—	4	2	no	—
236	C₂×C₈×C₁₃	—	4	2	no	—
237	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
238	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
239	C₁₃×C₄⋊C₄	—	2	2	no	—
240	C₁₃×C₄⋊C₄	—	2	2	no	—
241	C₁₃×C₄⋊C₄	—	2	4	no	—
242	C₁₃×C₄⋊C₄	—	2	2	no	—
243	C₁₃×C₄⋊C₄	—	2	2	no	—
244	C₁₃×C₄⋊C₄	—	2	2	no	—
245	C₁₃×C₄⋊C₄	—	2	2	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	2	no	—
250	C₁₃×C₄⋊C₄	—	2	2	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	4	no	—
255	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
256	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
257	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
258	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
259	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
260	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
261	C₁₃×C₂²⋊C₄	—	2	1	no	—
262	C₁₃×C₂²⋊C₄	—	2	1	no	—
263	C₁₃×C₂²⋊C₄	—	2	2	no	—
264	C₁₃×C₂²⋊C₄	—	2	4	no	—
265	C₁₃×C₂²⋊C₄	—	2	4	no	—
266	C₁₃×C₂²⋊C₄	—	2	2	no	—
267	C₁₃×C₂²⋊C₄	—	2	2	no	—
268	C₁₃×C₂²⋊C₄	—	2	2	no	—
269	C₁₃×C₂²⋊C₄	—	2	2	no	—
270	C₁₃×C₂²⋊C₄	—	2	2	no	—
271	C₁₃×C₂²⋊C₄	—	2	2	no	—
272	C₁₃×C₂²⋊C₄	—	2	2	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	C₂×D₄	1	2	yes	—
277	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
278	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
279	C₄²×C₁₃	—	2	2	no	—
280	C₄²×C₁₃	—	2	2	no	—
281	C₄²×C₁₃	—	2	4	no	—
282	C₄²×C₁₃	—	2	4	no	—
283	C₄²×C₁₃	—	2	1	no	—
284	C₄²×C₁₃	—	2	1	no	—
285	C₄²×C₁₃	—	2	2	no	—
286	C₄²×C₁₃	C₂×D₄	1	2	yes	—
287	C₄²×C₁₃	C₂×D₄	1	2	yes	—
288	C₄²×C₁₃	C₂×D₄	1	2	yes	—
289	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
290	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
291	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
292	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
293	#3510	C₂×C₁₃	1	1	yes	characteristic
294	#3509	C₂×C₁₃	1	1	yes	characteristic, complemented
295	#3258	C₂×C₁₃	1	4	yes	complemented
296	#3240	C₂×C₁₃	1	2	yes	complemented
297	#3237	C₂×C₁₃	1	2	yes	complemented
298	#3218	C₂×C₁₃	1	2	yes	complemented
299	#3215	C₂×C₁₃	1	2	yes	complemented
300	#3202	C₂×C₁₃	1	2	yes	complemented
301	#3200	C₂×C₁₃	1	2	yes	—
302	#3181	C₂×C₁₃	1	2	yes	complemented
303	#3172	C₂×C₁₃	1	2	yes	complemented
304	#3127	C₂×C₁₃	1	2	yes	complemented
305	#3123	C₂×C₁₃	1	2	yes	complemented
306	#3121	C₂×C₁₃	1	4	yes	complemented
307	#2923	C₂×C₁₃	1	1	yes	characteristic, complemented
308	C₂³×C₁₃	—	2	2	no	—
309	C₂³×C₁₃	—	4	2	no	—
310	C₂³×C₁₃	—	8	2	no	—
311	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
312	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
313	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
314	Q₈×C₁₃	—	2	4	no	—
315	Q₈×C₁₃	—	2	4	no	—
316	Q₈×C₁₃	—	2	4	no	—
317	Q₈×C₁₃	—	4	1	no	—
318	Q₈×C₁₃	—	4	4	no	—
319	Q₈×C₁₃	—	4	2	no	—
320	Q₈×C₁₃	—	4	4	no	—
321	Q₈×C₁₃	—	8	2	no	—
322	D₄×C₁₃	—	2	4	no	—
323	D₄×C₁₃	—	4	1	no	—
324	D₄×C₁₃	—	4	1	no	—
325	D₄×C₁₃	—	4	1	no	—
326	D₄×C₁₃	—	4	2	no	—
327	D₄×C₁₃	—	8	2	no	—
328	D₄×C₁₃	—	8	2	no	—
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	4	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	—	4	2	no	—
338	C₂×C₄×C₁₃	—	4	2	no	—
339	C₂×C₄×C₁₃	—	4	2	no	—
340	C₂×C₄×C₁₃	—	4	4	no	—
341	C₂×C₄×C₁₃	—	4	2	no	—
342	C₂×C₄×C₁₃	—	8	2	no	—
343	C₂×C₄×C₁₃	—	8	2	no	—
344	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
345	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
346	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
347	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
348	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
349	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
350	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
351	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
352	C₈×C₁₃	—	2	4	no	—
353	C₈×C₁₃	—	2	4	no	—
354	#559	—	2	2	no	—
355	#557	—	2	2	no	—
356	#556	—	2	2	no	—
357	#556	—	2	2	no	—
358	#552	—	2	2	no	—
359	#552	—	2	2	no	—
360	#551	—	2	2	no	—
361	#551	—	2	2	no	—
362	#542	C₂²×C₁₃	1	2	yes	—
363	#542	C₂²×C₁₃	1	2	yes	—
364	#541	C₂²×C₁₃	1	2	yes	—
365	#541	C₂²×C₁₃	1	2	yes	complemented
366	#536	C₂²×C₁₃	1	2	yes	—
367	#536	C₂²×C₁₃	1	1	yes	characteristic
368	#535	C₂²×C₁₃	1	1	yes	characteristic
369	#533	C₂²×C₁₃	1	2	yes	—
370	#533	C₂²×C₁₃	1	1	yes	characteristic
371	#533	C₂²×C₁₃	1	2	yes	complemented
372	#533	C₂²×C₁₃	1	1	yes	characteristic, complemented
373	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
374	#529	C₂²×C₁₃	1	2	yes	—
375	#529	C₂²×C₁₃	1	2	yes	—
376	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic
377	#519	C₂²×C₁₃	1	1	yes	characteristic
378	#519	C₂²×C₁₃	1	2	yes	complemented
379	#518	C₂²×C₁₃	1	1	yes	characteristic
380	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
381	#501	C₂²×C₁₃	1	2	yes	complemented
382	#501	C₂²×C₁₃	1	2	yes	complemented
383	#497	C₂²×C₁₃	1	2	yes	—
384	#497	C₂²×C₁₃	1	2	yes	—
385	#491	C₂²×C₁₃	1	2	yes	complemented
386	#491	C₂²×C₁₃	1	2	yes	complemented
387	#489	C₂²×C₁₃	1	2	yes	—
388	#489	C₂²×C₁₃	1	2	yes	—
389	#485	C₂²×C₁₃	1	4	yes	—
390	#485	C₂²×C₁₃	1	4	yes	—
391	#485	C₂²×C₁₃	1	4	yes	complemented
392	#482	C₂²×C₁₃	1	4	yes	—
393	#479	C₂²×C₁₃	1	4	yes	complemented
394	#478	C₂²×C₁₃	1	4	yes	—
395	#477	C₂²×C₁₃	1	4	yes	complemented
396	#475	C₂²×C₁₃	1	4	yes	complemented
397	#470	C₂²×C₁₃	1	4	yes	complemented
398	#468	C₂²×C₁₃	1	4	yes	—
399	#467	C₂²×C₁₃	1	4	yes	complemented
400	#465	C₂²×C₁₃	1	4	yes	—
401	#464	C₂²×C₁₃	1	4	yes	—
402	#464	C₂²×C₁₃	1	4	yes	—
403	#462	C₂²×C₁₃	1	4	yes	complemented
404	#461	C₂²×C₁₃	1	4	yes	—
405	#451	C₂²×C₁₃	1	4	yes	—
406	#451	C₂²×C₁₃	1	4	yes	complemented
407	#450	C₂²×C₁₃	1	4	yes	—
408	#448	C₂²×C₁₃	1	4	yes	—
409	#441	C₂²×C₁₃	1	4	yes	complemented
410	#440	C₂²×C₁₃	1	4	yes	—
411	C₄×Q₁₆	C₂²×C₁₃	1	4	yes	complemented
412	C₄×SD₁₆	C₂²×C₁₃	1	4	yes	—
413	#433	C₂²×C₁₃	1	2	yes	—
414	#433	C₂²×C₁₃	1	2	yes	complemented
415	#432	C₂²×C₁₃	1	2	yes	—
416	#432	C₂²×C₁₃	1	2	yes	complemented
417	#424	C₂²×C₁₃	1	2	yes	complemented
418	#408	C₂²×C₁₃	1	2	yes	—
419	C₄×M₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
420	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic, complemented
421	C₂²×C₁₃	—	2	2	no	—
422	C₂²×C₁₃	—	2	2	no	—
423	C₂²×C₁₃	—	2	2	no	—
424	C₂²×C₁₃	—	2	1	no	—
425	C₂²×C₁₃	—	2	1	no	—
426	C₂²×C₁₃	—	2	1	no	—
427	C₂²×C₁₃	—	4	2	no	—
428	C₂²×C₁₃	—	4	2	no	—
429	C₂²×C₁₃	—	4	2	no	—
430	C₂²×C₁₃	—	16	2	no	—
431	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
432	C₄×C₁₃	—	2	2	no	—
433	C₄×C₁₃	—	2	2	no	—
434	C₄×C₁₃	—	2	2	no	—
435	C₄×C₁₃	—	2	2	no	—
436	C₄×C₁₃	—	2	1	no	—
437	C₄×C₁₃	—	2	1	no	—
438	C₄×C₁₃	—	2	1	no	—
439	C₄×C₁₃	—	4	2	no	—
440	C₄×C₁₃	—	4	2	no	—
441	C₄×C₁₃	—	4	4	no	—
442	C₄×C₁₃	—	4	2	no	—
443	C₄×C₁₃	—	4	4	no	—
444	C₄×C₁₃	#585	1	2	yes	—
445	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
446	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
447	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
448	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
449	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	—
450	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	—
451	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
452	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
453	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
454	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
455	C₄⋊Q₈	—	2	1	no	—
456	C₄⋊Q₈	—	2	2	no	—
457	C₄⋊Q₈	—	2	2	no	—
458	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
459	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
460	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
461	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
462	#127	—	2	1	no	—
463	#126	—	2	2	no	—
464	#126	—	2	2	no	—
465	#126	—	2	4	no	—
466	#126	—	2	4	no	—
467	#126	—	2	2	no	—
468	#126	—	2	2	no	—
469	#125	—	2	4	no	—
470	#125	—	2	4	no	—
471	#125	—	2	2	no	—
472	#125	—	2	2	no	—
473	#125	C₂³×C₁₃	1	2	yes	—
474	#125	C₂³×C₁₃	1	2	yes	—
475	#124	—	2	1	no	—
476	#124	—	2	2	no	—
477	#124	—	2	1	no	—
478	#124	—	2	2	no	—
479	#124	—	2	2	no	—
480	#124	—	2	2	no	—
481	#124	C₂³×C₁₃	1	2	yes	—
482	#124	C₂³×C₁₃	1	2	yes	—
483	#123	—	2	1	no	—
484	#123	—	2	1	no	—
485	#123	—	2	2	no	—
486	#123	—	2	2	no	—
487	#123	—	2	2	no	—
488	#123	—	2	2	no	—
489	#123	—	2	2	no	—
490	#123	—	2	2	no	—
491	C₂²⋊Q₈	—	2	2	no	—
492	C₂²⋊Q₈	—	2	2	no	—
493	C₂²⋊Q₈	—	2	2	no	—
494	C₂²⋊Q₈	—	2	2	no	—
495	C₂²⋊Q₈	—	2	2	no	—
496	C₂²⋊Q₈	—	2	2	no	—
497	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
498	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
499	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
500	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
501	#121	C₂³×C₁₃	1	2	yes	—
502	#121	C₂³×C₁₃	1	2	yes	—
503	#120	—	2	1	no	—
504	#120	—	2	1	no	—
505	C₄×Q₈	—	2	2	no	—
506	C₄×Q₈	—	2	4	no	—
507	C₄×Q₈	—	2	2	no	—
508	C₄×Q₈	—	2	2	no	—
509	C₄×Q₈	—	2	2	no	—
510	C₄×Q₈	—	2	2	no	—
511	C₄×Q₈	D₄×C₁₃	1	2	yes	—
512	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
513	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
514	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
515	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
516	C₄×D₄	—	2	2	no	—
517	C₄×D₄	—	2	2	no	—
518	C₄×D₄	—	2	2	no	—
519	C₄×D₄	D₄×C₁₃	1	2	yes	—
520	C₄×D₄	D₄×C₁₃	1	2	yes	—
521	C₄×D₄	D₄×C₁₃	1	2	yes	—
522	C₄×D₄	C₂³×C₁₃	1	2	yes	—
523	C₄×D₄	C₂³×C₁₃	1	2	yes	—
524	#117	—	2	2	no	—
525	#117	—	2	2	no	—
526	#117	—	2	2	no	—
527	#117	—	2	4	no	—
528	#117	—	2	2	no	—
529	#117	—	2	2	no	—
530	#117	C₂³×C₁₃	1	1	yes	characteristic
531	#117	C₂³×C₁₃	1	1	yes	characteristic
532	#117	C₂³×C₁₃	1	2	yes	—
533	#117	C₂³×C₁₃	1	1	yes	characteristic
534	#117	C₂³×C₁₃	1	1	yes	characteristic
535	#117	C₂³×C₁₃	1	1	yes	characteristic
536	C₂×C₄⋊C₄	—	2	2	no	—
537	C₂×C₂²⋊C₄	—	2	2	no	—
538	C₂×C₂²⋊C₄	—	2	2	no	—
539	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
540	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
541	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
542	#107	C₂³×C₁₃	1	4	yes	—
543	#107	C₂³×C₁₃	1	4	yes	—
544	#106	C₂³×C₁₃	1	4	yes	—
545	#106	C₂³×C₁₃	1	4	yes	—
546	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
547	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
548	#103	C₂³×C₁₃	1	4	yes	—
549	#103	C₂³×C₁₃	1	4	yes	—
550	#103	C₂³×C₁₃	1	4	yes	—
551	#103	C₂³×C₁₃	1	4	yes	—
552	#103	C₂³×C₁₃	1	4	yes	—
553	#103	C₂³×C₁₃	1	4	yes	—
554	#102	C₂³×C₁₃	1	4	yes	—
555	#102	C₂³×C₁₃	1	4	yes	—
556	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
557	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
558	#97	C₂³×C₁₃	1	2	yes	—
559	#97	C₂³×C₁₃	1	2	yes	—
560	#97	C₂³×C₁₃	1	2	yes	—
561	C₄×C₈	C₂³×C₁₃	1	2	yes	—
562	C₂×C₁₃	—	4	1	no	—
563	C₂×C₁₃	—	4	1	no	—
564	C₂×C₁₃	—	4	1	no	—
565	C₂×C₁₃	—	8	2	no	—
566	C₂×C₁₃	#3449	1	1	yes	characteristic
567	C₂×C₁₃	#3586	1	2	yes	—
568	C₂⁴	—	2	1	no	—
569	#41	—	4	2	no	—
570	C₂×Q₈	—	2	2	no	—
571	C₂×Q₈	—	2	1	no	—
572	C₂×Q₈	—	2	2	no	—
573	C₂×Q₈	—	2	2	no	—
574	C₂×Q₈	—	4	2	no	—
575	C₂×Q₈	—	4	2	no	—
576	C₂×Q₈	—	4	2	no	—
577	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
578	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
579	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
580	C₂×D₄	—	2	2	no	—
581	C₂×D₄	—	2	2	no	—
582	C₂×D₄	—	2	1	no	—
583	C₂×D₄	—	4	2	no	—
584	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
585	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
586	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
587	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
588	C₂²×C₄	—	2	1	no	—
589	C₂²×C₄	—	2	2	no	—
590	C₂²×C₄	—	2	2	no	—
591	C₂²×C₄	—	2	2	no	—
592	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
593	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
594	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
595	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
596	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
597	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
598	Q₁₆	—	4	4	no	—
599	Q₁₆	—	4	4	no	—
600	SD₁₆	—	4	4	no	—
601	SD₁₆	—	4	4	no	—
602	M₁₆	—	4	2	no	—
603	C₂×C₈	—	4	2	no	—
604	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
605	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
606	C₄⋊C₄	—	2	2	no	—
607	C₄⋊C₄	—	2	2	no	—
608	C₄⋊C₄	—	2	4	no	—
609	C₄⋊C₄	—	2	2	no	—
610	C₄⋊C₄	—	2	2	no	—
611	C₄⋊C₄	—	2	2	no	—
612	C₄⋊C₄	—	2	2	no	—
613	C₄⋊C₄	—	2	4	no	—
614	C₄⋊C₄	—	2	4	no	—
615	C₄⋊C₄	—	2	2	no	—
616	C₄⋊C₄	—	2	2	no	—
617	C₄⋊C₄	—	2	2	no	—
618	C₄⋊C₄	—	2	2	no	—
619	C₄⋊C₄	—	2	4	no	—
620	C₄⋊C₄	—	2	4	no	—
621	C₄⋊C₄	—	2	4	no	—
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	2	yes	—
625	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
626	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
627	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
628	C₂²⋊C₄	—	2	1	no	—
629	C₂²⋊C₄	—	2	1	no	—
630	C₂²⋊C₄	—	2	2	no	—
631	C₂²⋊C₄	—	2	4	no	—
632	C₂²⋊C₄	—	2	4	no	—
633	C₂²⋊C₄	—	2	2	no	—
634	C₂²⋊C₄	—	2	2	no	—
635	C₂²⋊C₄	—	2	2	no	—
636	C₂²⋊C₄	—	2	2	no	—
637	C₂²⋊C₄	—	2	2	no	—
638	C₂²⋊C₄	—	2	2	no	—
639	C₂²⋊C₄	—	2	2	no	—
640	C₂²⋊C₄	—	2	2	no	—
641	C₂²⋊C₄	—	2	2	no	—
642	C₂²⋊C₄	—	2	2	no	—
643	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
644	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
645	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
646	C₄²	—	2	2	no	—
647	C₄²	—	2	2	no	—
648	C₄²	—	2	4	no	—
649	C₄²	—	2	4	no	—
650	C₄²	—	2	1	no	—
651	C₄²	—	2	1	no	—
652	C₄²	—	2	2	no	—
653	C₄²	C₂×D₄×C₁₃	1	2	yes	—
654	C₄²	C₂×D₄×C₁₃	1	2	yes	—
655	C₄²	C₂×D₄×C₁₃	1	2	yes	—
656	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
657	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
658	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
659	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
660	C₁₃	#61018	1	1	yes	characteristic, direct product factor, Sylow
661	C₂³	—	2	2	no	—
662	C₂³	—	4	2	no	—
663	C₂³	—	8	2	no	—
664	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
665	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
666	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
667	Q₈	—	2	4	no	—
668	Q₈	—	2	4	no	—
669	Q₈	—	2	4	no	—
670	Q₈	—	4	1	no	—
671	Q₈	—	4	2	no	—
672	Q₈	—	4	4	no	—
673	Q₈	—	4	4	no	—
674	Q₈	—	8	2	no	—
675	D₄	—	2	4	no	—
676	D₄	—	4	1	no	—
677	D₄	—	4	1	no	—
678	D₄	—	4	1	no	—
679	D₄	—	4	2	no	—
680	D₄	—	8	2	no	—
681	D₄	—	8	2	no	—
682	C₂×C₄	—	2	2	no	—
683	C₂×C₄	—	2	2	no	—
684	C₂×C₄	—	2	2	no	—
685	C₂×C₄	—	2	4	no	—
686	C₂×C₄	—	2	2	no	—
687	C₂×C₄	—	2	2	no	—
688	C₂×C₄	—	2	4	no	—
689	C₂×C₄	—	2	2	no	—
690	C₂×C₄	—	4	2	no	—
691	C₂×C₄	—	4	2	no	—
692	C₂×C₄	—	4	2	no	—
693	C₂×C₄	—	4	4	no	—
694	C₂×C₄	—	4	2	no	—
695	C₂×C₄	—	8	2	no	—
696	C₂×C₄	—	8	2	no	—
697	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
698	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
699	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
700	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
701	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
702	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
703	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
704	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
705	C₈	—	2	4	no	—
706	C₈	—	2	4	no	—
707	C₂²	—	2	2	no	—
708	C₂²	—	2	2	no	—
709	C₂²	—	2	2	no	—
710	C₂²	—	2	1	no	—
711	C₂²	—	2	1	no	—
712	C₂²	—	2	1	no	—
713	C₂²	—	4	2	no	—
714	C₂²	—	4	2	no	—
715	C₂²	—	4	2	no	—
716	C₂²	—	16	2	no	—
717	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
718	C₄	—	2	2	no	—
719	C₄	—	2	2	no	—
720	C₄	—	2	2	no	—
721	C₄	—	2	2	no	—
722	C₄	—	2	1	no	—
723	C₄	—	2	1	no	—
724	C₄	—	2	1	no	—
725	C₄	—	4	2	no	—
726	C₄	—	4	2	no	—
727	C₄	—	4	4	no	—
728	C₄	—	4	2	no	—
729	C₄	—	4	4	no	—
730	C₄	C₁₃×#585	1	2	yes	—
731	C₂	—	4	1	no	—
732	C₂	—	4	1	no	—
733	C₂	—	4	1	no	—
734	C₂	—	8	2	no	—
735	C₂	C₁₃×#3449	1	1	yes	characteristic
736	C₂	C₁₃×#3586	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
prime radical	C₁₃×#535	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₄×C₁₃×#41 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₃×#3509	C₂	semidirect
3. C₁₃×#3258	C₂	semidirect
4. C₁₃×#3240	C₂	semidirect
5. C₁₃×#3237	C₂	semidirect
6. C₁₃×#3218	C₂	semidirect
7. C₁₃×#3215	C₂	semidirect
8. C₁₃×#3202	C₂	semidirect
10. C₁₃×#3181	C₂	semidirect
11. C₁₃×#3172	C₂	semidirect
12. C₁₃×#3127	C₂	semidirect
13. C₁₃×#3123	C₂	semidirect
14. C₁₃×#3121	C₂	semidirect
15. C₁₃×#2923	C₂	semidirect
27. C₁₃×#541	C₂²	semidirect
33. C₁₃×#533	C₂²	semidirect
34. C₁₃×#533	C₂²	semidirect
35. C₂×C₁₃×C₄⋊Q₈	C₂²	semidirect
40. C₁₃×#519	C₂²	semidirect
43. C₁₃×#501	C₂²	semidirect
44. C₁₃×#501	C₂²	semidirect
47. C₁₃×#491	C₂²	semidirect
48. C₁₃×#491	C₂²	semidirect
53. C₁₃×#485	C₂²	semidirect
55. C₁₃×#479	C₂²	semidirect
57. C₁₃×#477	C₂²	semidirect
58. C₁₃×#475	C₂²	semidirect
59. C₁₃×#470	C₂²	semidirect
61. C₁₃×#467	C₂²	semidirect
65. C₁₃×#462	C₂²	semidirect
68. C₁₃×#451	C₂²	semidirect
71. C₁₃×#441	C₂²	semidirect
73. C₄×C₁₃×Q₁₆	C₂²	semidirect
76. C₁₃×#433	C₂²	semidirect
78. C₁₃×#432	C₂²	semidirect
79. C₁₃×#424	C₂²	semidirect
81. C₄×C₁₃×M₁₆	C₂²	semidirect
82. C₂×C₁₃×#97	C₂²	semidirect
200. #61018	C₁₃	direct (N × H)
294. #3509	C₂×C₁₃	semidirect
295. #3258	C₂×C₁₃	semidirect
296. #3240	C₂×C₁₃	semidirect
297. #3237	C₂×C₁₃	semidirect
298. #3218	C₂×C₁₃	semidirect
299. #3215	C₂×C₁₃	semidirect
300. #3202	C₂×C₁₃	semidirect
302. #3181	C₂×C₁₃	semidirect
303. #3172	C₂×C₁₃	semidirect
304. #3127	C₂×C₁₃	semidirect
305. #3123	C₂×C₁₃	semidirect
306. #3121	C₂×C₁₃	semidirect
307. #2923	C₂×C₁₃	semidirect
365. #541	C₂²×C₁₃	semidirect
371. #533	C₂²×C₁₃	semidirect
372. #533	C₂²×C₁₃	semidirect
373. C₂×C₄⋊Q₈	C₂²×C₁₃	semidirect
378. #519	C₂²×C₁₃	semidirect
381. #501	C₂²×C₁₃	semidirect
382. #501	C₂²×C₁₃	semidirect
385. #491	C₂²×C₁₃	semidirect
386. #491	C₂²×C₁₃	semidirect
391. #485	C₂²×C₁₃	semidirect
393. #479	C₂²×C₁₃	semidirect
395. #477	C₂²×C₁₃	semidirect
396. #475	C₂²×C₁₃	semidirect
397. #470	C₂²×C₁₃	semidirect
399. #467	C₂²×C₁₃	semidirect
403. #462	C₂²×C₁₃	semidirect
406. #451	C₂²×C₁₃	semidirect
409. #441	C₂²×C₁₃	semidirect
411. C₄×Q₁₆	C₂²×C₁₃	semidirect
414. #433	C₂²×C₁₃	semidirect
416. #432	C₂²×C₁₃	semidirect
417. #424	C₂²×C₁₃	semidirect
419. C₄×M₁₆	C₂²×C₁₃	semidirect
420. C₂×#97	C₂²×C₁₃	semidirect
660. C₁₃	#61018	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×#3510	2
C₁₃×#3509	2
C₁₃×#3258	2
C₁₃×#3240	2
C₁₃×#3237	2
C₁₃×#3218	2
C₁₃×#3215	2
C₁₃×#3202	2
C₁₃×#3200	2
C₁₃×#3181	2
C₁₃×#3172	2
C₁₃×#3127	2
C₁₃×#3123	2
C₁₃×#3121	2
C₁₃×#2923	2
#61018	13

Subgroups — C13×#61018 #15747357

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61018 #15747357