Subgroups — C₁₃×#61017 #15747356

Order 3328.

1792 conjugacy classes of subgroups.

The subgroup lattice has 768 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, complemented
2	C₁₃×#3508	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3257	C₂	1	4	yes	maximal, complemented
4	C₁₃×#3240	C₂	1	2	yes	maximal, complemented
5	C₁₃×#3235	C₂	1	2	yes	maximal, complemented
6	C₁₃×#3217	C₂	1	2	yes	maximal, complemented
7	C₁₃×#3213	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3200	C₂	1	2	yes	maximal, complemented
9	C₁₃×#3199	C₂	1	2	yes	maximal, complemented
10	C₁₃×#3180	C₂	1	2	yes	maximal, complemented
11	C₁₃×#3171	C₂	1	2	yes	maximal, complemented
12	C₁₃×#3126	C₂	1	2	yes	maximal, complemented
13	C₁₃×#3122	C₂	1	2	yes	maximal, complemented
14	C₁₃×#3118	C₂	1	4	yes	maximal, complemented
15	C₁₃×#2923	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₃×#559	—	2	2	no	—
17	C₁₃×#559	—	2	2	no	—
18	C₁₃×#556	—	2	2	no	—
19	C₁₃×#551	—	2	2	no	—
20	C₁₃×#551	—	2	2	no	—
21	C₁₃×#550	—	2	2	no	—
22	C₁₃×#546	—	2	2	no	—
23	C₁₃×#546	—	2	2	no	—
24	C₁₃×#542	C₂²	1	2	yes	—
25	C₁₃×#542	C₂²	1	2	yes	complemented
26	C₁₃×#540	C₂²	1	2	yes	—
27	C₁₃×#540	C₂²	1	2	yes	complemented
28	C₁₃×#536	C₂²	1	1	yes	characteristic
29	C₁₃×#535	C₂²	1	1	yes	characteristic
30	C₁₃×#535	C₂²	1	2	yes	—
31	C₁₃×#533	C₂²	1	1	yes	characteristic, complemented
32	C₁₃×#533	C₂²	1	1	yes	characteristic, complemented
33	C₁₃×#532	C₂²	1	2	yes	—
34	C₁₃×#532	C₂²	1	2	yes	complemented
35	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic, complemented
36	C₁₃×#529	C₂²	1	2	yes	—
37	C₁₃×#529	C₂²	1	2	yes	complemented
38	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic, complemented
39	C₁₃×#519	C₂²	1	1	yes	characteristic, complemented
40	C₁₃×#518	C₂²	1	2	yes	complemented
41	C₁₃×#518	C₂²	1	1	yes	characteristic, complemented
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×#496	C₂²	1	2	yes	—
46	C₁₃×#496	C₂²	1	2	yes	—
47	C₁₃×#490	C₂²	1	2	yes	complemented
48	C₁₃×#490	C₂²	1	2	yes	complemented
49	C₁₃×#489	C₂²	1	2	yes	complemented
50	C₁₃×#489	C₂²	1	2	yes	complemented
51	C₁₃×#485	C₂²	1	4	yes	complemented
52	C₁₃×#482	C₂²	1	4	yes	—
53	C₁₃×#482	C₂²	1	4	yes	complemented
54	C₁₃×#482	C₂²	1	4	yes	complemented
55	C₁₃×#479	C₂²	1	4	yes	complemented
56	C₁₃×#478	C₂²	1	4	yes	complemented
57	C₁₃×#476	C₂²	1	4	yes	complemented
58	C₁₃×#474	C₂²	1	4	yes	complemented
59	C₁₃×#469	C₂²	1	4	yes	complemented
60	C₁₃×#468	C₂²	1	4	yes	complemented
61	C₁₃×#466	C₂²	1	4	yes	complemented
62	C₁₃×#465	C₂²	1	4	yes	complemented
63	C₁₃×#463	C₂²	1	4	yes	complemented
64	C₁₃×#463	C₂²	1	4	yes	complemented
65	C₁₃×#460	C₂²	1	4	yes	complemented
66	C₁₃×#459	C₂²	1	4	yes	—
67	C₁₃×#450	C₂²	1	4	yes	complemented
68	C₁₃×#448	C₂²	1	4	yes	complemented
69	C₁₃×#447	C₂²	1	4	yes	—
70	C₁₃×#447	C₂²	1	4	yes	complemented
71	C₁₃×#442	C₂²	1	4	yes	complemented
72	C₁₃×#440	C₂²	1	4	yes	complemented
73	C₄×C₁₃×SD₁₆	C₂²	1	4	yes	complemented
74	C₄×C₁₃×D₈	C₂²	1	4	yes	complemented
75	C₁₃×#433	C₂²	1	2	yes	complemented
76	C₁₃×#433	C₂²	1	2	yes	complemented
77	C₁₃×#432	C₂²	1	2	yes	complemented
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	—	2	2	no	—
84	C₂×C₁₃×#41	—	2	2	no	—
85	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
86	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
87	C₂²×D₄×C₁₃	—	2	2	no	—
88	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
89	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
90	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
91	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
92	C₂×C₁₃×D₈	C₂³	1	4	yes	—
93	C₂×C₁₃×D₈	C₂³	1	4	yes	—
94	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
95	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
96	C₁₃×C₄⋊Q₈	—	2	1	no	—
97	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
98	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
99	C₁₃×#127	—	2	2	no	—
100	C₁₃×#127	—	2	1	no	—
101	C₁₃×#127	—	2	2	no	—
102	C₁₃×#127	C₂³	1	2	yes	—
103	C₁₃×#127	C₂³	1	2	yes	—
104	C₁₃×#126	—	2	2	no	—
105	C₁₃×#126	—	2	2	no	—
106	C₁₃×#126	—	2	2	no	—
107	C₁₃×#126	—	2	2	no	—
108	C₁₃×#125	C₂³	1	2	yes	—
109	C₁₃×#125	C₂³	1	2	yes	—
110	C₁₃×#124	—	2	1	no	—
111	C₁₃×#124	—	2	2	no	—
112	C₁₃×#124	—	2	1	no	—
113	C₁₃×#124	—	2	2	no	—
114	C₁₃×#124	—	2	2	no	—
115	C₁₃×#124	—	2	2	no	—
116	C₁₃×#124	—	2	2	no	—
117	C₁₃×#124	—	2	2	no	—
118	C₁₃×#124	C₂³	1	2	yes	—
119	C₁₃×#124	C₂³	1	2	yes	—
120	C₁₃×#123	—	2	1	no	—
121	C₁₃×#123	—	2	1	no	—
122	C₁₃×#123	—	2	2	no	—
123	C₁₃×#123	—	2	2	no	—
124	C₁₃×#123	—	2	4	no	—
125	C₁₃×#123	—	2	4	no	—
126	C₁₃×#123	—	2	2	no	—
127	C₁₃×#123	—	2	2	no	—
128	C₁₃×C₂²⋊Q₈	—	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	C₂³	1	2	yes	—
133	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
134	C₁₃×#121	—	2	2	no	—
135	C₁₃×#121	—	2	2	no	—
136	C₁₃×#121	—	2	4	no	—
137	C₁₃×#121	—	2	4	no	—
138	C₁₃×#121	C₂³	1	2	yes	—
139	C₁₃×#121	C₂³	1	4	yes	—
140	C₁₃×#121	C₂³	1	4	yes	—
141	C₁₃×#121	C₂³	1	2	yes	—
142	C₁₃×#120	—	2	2	no	—
143	C₁₃×#120	—	2	2	no	—
144	C₁₃×#120	—	2	1	no	—
145	C₁₃×#120	—	2	1	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	2	yes	—
151	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
152	C₄×D₄×C₁₃	—	2	2	no	—
153	C₄×D₄×C₁₃	—	2	2	no	—
154	C₄×D₄×C₁₃	—	2	4	no	—
155	C₄×D₄×C₁₃	—	2	2	no	—
156	C₄×D₄×C₁₃	—	2	2	no	—
157	C₄×D₄×C₁₃	—	2	2	no	—
158	C₄×D₄×C₁₃	D₄	1	2	yes	—
159	C₄×D₄×C₁₃	D₄	1	2	yes	—
160	C₄×D₄×C₁₃	D₄	1	2	yes	—
161	C₄×D₄×C₁₃	C₂³	1	2	yes	—
162	C₄×D₄×C₁₃	C₂³	1	4	yes	—
163	C₄×D₄×C₁₃	C₂³	1	2	yes	—
164	C₄×D₄×C₁₃	C₂³	1	4	yes	—
165	C₁₃×#117	—	2	2	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×C₂²⋊C₄	—	2	2	no	—
175	C₂×C₁₃×C₂²⋊C₄	—	2	4	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×#102	C₂³	1	4	yes	—
189	C₁₃×#102	C₂³	1	4	yes	—
190	C₁₃×#102	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×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	#61017	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
201	C₂⁴×C₁₃	—	2	1	no	—
202	C₂⁴×C₁₃	—	2	2	no	—
203	C₁₃×#41	—	4	2	no	—
204	C₁₃×#41	—	8	4	no	—
205	C₁₃×#41	—	8	4	no	—
206	C₂×Q₈×C₁₃	—	2	1	no	—
207	C₂×Q₈×C₁₃	—	2	2	no	—
208	C₂×Q₈×C₁₃	—	2	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×D₄×C₁₃	—	2	2	no	—
213	C₂×D₄×C₁₃	—	2	2	no	—
214	C₂×D₄×C₁₃	—	2	4	no	—
215	C₂×D₄×C₁₃	—	2	4	no	—
216	C₂×D₄×C₁₃	—	2	1	no	—
217	C₂×D₄×C₁₃	—	2	2	no	—
218	C₂×D₄×C₁₃	—	2	2	no	—
219	C₂×D₄×C₁₃	—	2	2	no	—
220	C₂×D₄×C₁₃	—	2	4	no	—
221	C₂×D₄×C₁₃	—	4	2	no	—
222	C₂×D₄×C₁₃	—	4	2	no	—
223	C₂×D₄×C₁₃	—	4	2	no	—
224	C₂×D₄×C₁₃	—	8	4	no	—
225	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
226	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
227	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
228	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
229	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
230	C₂²×C₄×C₁₃	—	2	1	no	—
231	C₂²×C₄×C₁₃	—	2	2	no	—
232	C₂²×C₄×C₁₃	—	2	2	no	—
233	C₂²×C₄×C₁₃	—	2	4	no	—
234	C₂²×C₄×C₁₃	—	2	4	no	—
235	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
236	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
237	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
238	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
239	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
240	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
241	C₁₃×SD₁₆	—	4	4	no	—
242	C₁₃×SD₁₆	—	4	4	no	—
243	C₁₃×D₈	—	4	4	no	—
244	C₁₃×D₈	—	4	4	no	—
245	C₁₃×M₁₆	—	4	2	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	2	no	—
250	C₁₃×C₄⋊C₄	—	2	2	no	—
251	C₁₃×C₄⋊C₄	—	2	2	no	—
252	C₁₃×C₄⋊C₄	—	2	2	no	—
253	C₁₃×C₄⋊C₄	—	2	2	no	—
254	C₁₃×C₄⋊C₄	—	2	2	no	—
255	C₁₃×C₄⋊C₄	—	2	2	no	—
256	C₁₃×C₄⋊C₄	—	2	4	no	—
257	C₁₃×C₄⋊C₄	—	2	2	no	—
258	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
259	C₁₃×C₄⋊C₄	C₂×D₄	1	2	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	4	yes	—
264	C₁₃×C₂²⋊C₄	—	2	2	no	—
265	C₁₃×C₂²⋊C₄	—	2	1	no	—
266	C₁₃×C₂²⋊C₄	—	2	1	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	4	no	—
272	C₁₃×C₂²⋊C₄	—	2	4	no	—
273	C₁₃×C₂²⋊C₄	—	2	2	no	—
274	C₁₃×C₂²⋊C₄	—	2	2	no	—
275	C₁₃×C₂²⋊C₄	—	2	2	no	—
276	C₁₃×C₂²⋊C₄	—	2	2	no	—
277	C₁₃×C₂²⋊C₄	—	2	2	no	—
278	C₁₃×C₂²⋊C₄	—	2	2	no	—
279	C₁₃×C₂²⋊C₄	—	2	4	no	—
280	C₁₃×C₂²⋊C₄	—	2	4	no	—
281	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
282	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
283	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
284	C₄²×C₁₃	—	2	2	no	—
285	C₄²×C₁₃	—	2	2	no	—
286	C₄²×C₁₃	—	2	2	no	—
287	C₄²×C₁₃	—	2	1	no	—
288	C₄²×C₁₃	—	2	1	no	—
289	C₄²×C₁₃	C₂×D₄	1	2	yes	—
290	C₄²×C₁₃	C₂×D₄	1	2	yes	—
291	C₄²×C₁₃	C₂×D₄	1	2	yes	—
292	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
293	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
294	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
295	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
296	#3510	C₂×C₁₃	1	1	yes	characteristic, complemented
297	#3508	C₂×C₁₃	1	1	yes	characteristic, complemented
298	#3257	C₂×C₁₃	1	4	yes	complemented
299	#3240	C₂×C₁₃	1	2	yes	complemented
300	#3235	C₂×C₁₃	1	2	yes	complemented
301	#3217	C₂×C₁₃	1	2	yes	complemented
302	#3213	C₂×C₁₃	1	2	yes	complemented
303	#3200	C₂×C₁₃	1	2	yes	complemented
304	#3199	C₂×C₁₃	1	2	yes	complemented
305	#3180	C₂×C₁₃	1	2	yes	complemented
306	#3171	C₂×C₁₃	1	2	yes	complemented
307	#3126	C₂×C₁₃	1	2	yes	complemented
308	#3122	C₂×C₁₃	1	2	yes	complemented
309	#3118	C₂×C₁₃	1	4	yes	complemented
310	#2923	C₂×C₁₃	1	1	yes	characteristic, complemented
311	C₂³×C₁₃	—	2	2	no	—
312	C₂³×C₁₃	—	2	4	no	—
313	C₂³×C₁₃	—	4	2	no	—
314	C₂³×C₁₃	—	4	4	no	—
315	C₂³×C₁₃	—	8	4	no	—
316	C₂³×C₁₃	—	8	2	no	—
317	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
318	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
319	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
320	Q₈×C₁₃	—	2	4	no	—
321	Q₈×C₁₃	—	4	1	no	—
322	Q₈×C₁₃	—	4	2	no	—
323	Q₈×C₁₃	—	4	4	no	—
324	Q₈×C₁₃	—	8	2	no	—
325	D₄×C₁₃	—	2	4	no	—
326	D₄×C₁₃	—	2	4	no	—
327	D₄×C₁₃	—	2	4	no	—
328	D₄×C₁₃	—	4	1	no	—
329	D₄×C₁₃	—	4	1	no	—
330	D₄×C₁₃	—	4	1	no	—
331	D₄×C₁₃	—	4	4	no	—
332	D₄×C₁₃	—	4	2	no	—
333	D₄×C₁₃	—	4	4	no	—
334	D₄×C₁₃	—	4	4	no	—
335	D₄×C₁₃	—	8	4	no	—
336	D₄×C₁₃	—	8	2	no	—
337	D₄×C₁₃	—	8	2	no	—
338	D₄×C₁₃	—	8	4	no	—
339	D₄×C₁₃	—	8	4	no	—
340	C₂×C₄×C₁₃	—	2	2	no	—
341	C₂×C₄×C₁₃	—	2	2	no	—
342	C₂×C₄×C₁₃	—	2	2	no	—
343	C₂×C₄×C₁₃	—	2	2	no	—
344	C₂×C₄×C₁₃	—	2	2	no	—
345	C₂×C₄×C₁₃	—	2	2	no	—
346	C₂×C₄×C₁₃	—	2	4	no	—
347	C₂×C₄×C₁₃	—	4	2	no	—
348	C₂×C₄×C₁₃	—	4	2	no	—
349	C₂×C₄×C₁₃	—	4	2	no	—
350	C₂×C₄×C₁₃	—	4	2	no	—
351	C₂×C₄×C₁₃	—	8	2	no	—
352	C₂×C₄×C₁₃	—	8	2	no	—
353	C₂×C₄×C₁₃	—	8	4	no	—
354	C₂×C₄×C₁₃	—	8	4	no	—
355	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
356	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
357	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
358	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
359	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
360	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
361	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
362	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
363	C₈×C₁₃	—	2	4	no	—
364	C₈×C₁₃	—	2	4	no	—
365	#559	—	2	2	no	—
366	#559	—	2	2	no	—
367	#556	—	2	2	no	—
368	#551	—	2	2	no	—
369	#551	—	2	2	no	—
370	#550	—	2	2	no	—
371	#546	—	2	2	no	—
372	#546	—	2	2	no	—
373	#542	C₂²×C₁₃	1	2	yes	—
374	#542	C₂²×C₁₃	1	2	yes	complemented
375	#540	C₂²×C₁₃	1	2	yes	—
376	#540	C₂²×C₁₃	1	2	yes	complemented
377	#536	C₂²×C₁₃	1	1	yes	characteristic
378	#535	C₂²×C₁₃	1	1	yes	characteristic
379	#535	C₂²×C₁₃	1	2	yes	—
380	#533	C₂²×C₁₃	1	1	yes	characteristic, complemented
381	#533	C₂²×C₁₃	1	1	yes	characteristic, complemented
382	#532	C₂²×C₁₃	1	2	yes	—
383	#532	C₂²×C₁₃	1	2	yes	complemented
384	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic, complemented
385	#529	C₂²×C₁₃	1	2	yes	—
386	#529	C₂²×C₁₃	1	2	yes	complemented
387	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic, complemented
388	#519	C₂²×C₁₃	1	1	yes	characteristic, complemented
389	#518	C₂²×C₁₃	1	2	yes	complemented
390	#518	C₂²×C₁₃	1	1	yes	characteristic, complemented
391	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
392	#501	C₂²×C₁₃	1	2	yes	complemented
393	#501	C₂²×C₁₃	1	2	yes	complemented
394	#496	C₂²×C₁₃	1	2	yes	—
395	#496	C₂²×C₁₃	1	2	yes	—
396	#490	C₂²×C₁₃	1	2	yes	complemented
397	#490	C₂²×C₁₃	1	2	yes	complemented
398	#489	C₂²×C₁₃	1	2	yes	complemented
399	#489	C₂²×C₁₃	1	2	yes	complemented
400	#485	C₂²×C₁₃	1	4	yes	complemented
401	#482	C₂²×C₁₃	1	4	yes	—
402	#482	C₂²×C₁₃	1	4	yes	complemented
403	#482	C₂²×C₁₃	1	4	yes	complemented
404	#479	C₂²×C₁₃	1	4	yes	complemented
405	#478	C₂²×C₁₃	1	4	yes	complemented
406	#476	C₂²×C₁₃	1	4	yes	complemented
407	#474	C₂²×C₁₃	1	4	yes	complemented
408	#469	C₂²×C₁₃	1	4	yes	complemented
409	#468	C₂²×C₁₃	1	4	yes	complemented
410	#466	C₂²×C₁₃	1	4	yes	complemented
411	#465	C₂²×C₁₃	1	4	yes	complemented
412	#463	C₂²×C₁₃	1	4	yes	complemented
413	#463	C₂²×C₁₃	1	4	yes	complemented
414	#460	C₂²×C₁₃	1	4	yes	complemented
415	#459	C₂²×C₁₃	1	4	yes	—
416	#450	C₂²×C₁₃	1	4	yes	complemented
417	#448	C₂²×C₁₃	1	4	yes	complemented
418	#447	C₂²×C₁₃	1	4	yes	—
419	#447	C₂²×C₁₃	1	4	yes	complemented
420	#442	C₂²×C₁₃	1	4	yes	complemented
421	#440	C₂²×C₁₃	1	4	yes	complemented
422	C₄×SD₁₆	C₂²×C₁₃	1	4	yes	complemented
423	C₄×D₈	C₂²×C₁₃	1	4	yes	complemented
424	#433	C₂²×C₁₃	1	2	yes	complemented
425	#433	C₂²×C₁₃	1	2	yes	complemented
426	#432	C₂²×C₁₃	1	2	yes	complemented
427	#432	C₂²×C₁₃	1	2	yes	complemented
428	#424	C₂²×C₁₃	1	2	yes	complemented
429	#408	C₂²×C₁₃	1	2	yes	—
430	C₄×M₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
431	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic, complemented
432	C₂²×C₁₃	—	2	2	no	—
433	C₂²×C₁₃	—	2	2	no	—
434	C₂²×C₁₃	—	2	2	no	—
435	C₂²×C₁₃	—	2	1	no	—
436	C₂²×C₁₃	—	2	1	no	—
437	C₂²×C₁₃	—	2	1	no	—
438	C₂²×C₁₃	—	4	4	no	—
439	C₂²×C₁₃	—	4	4	no	—
440	C₂²×C₁₃	—	4	2	no	—
441	C₂²×C₁₃	—	4	2	no	—
442	C₂²×C₁₃	—	4	2	no	—
443	C₂²×C₁₃	—	4	4	no	—
444	C₂²×C₁₃	—	16	2	no	—
445	C₂²×C₁₃	—	16	4	no	—
446	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
447	C₄×C₁₃	—	2	2	no	—
448	C₄×C₁₃	—	2	2	no	—
449	C₄×C₁₃	—	2	2	no	—
450	C₄×C₁₃	—	2	2	no	—
451	C₄×C₁₃	—	2	1	no	—
452	C₄×C₁₃	—	2	1	no	—
453	C₄×C₁₃	—	2	1	no	—
454	C₄×C₁₃	—	4	4	no	—
455	C₄×C₁₃	—	4	2	no	—
456	C₄×C₁₃	—	4	2	no	—
457	C₄×C₁₃	—	4	2	no	—
458	C₄×C₁₃	#585	1	2	yes	—
459	C₂×#41	—	2	2	no	—
460	C₂×#41	—	2	2	no	—
461	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
462	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
463	C₂²×D₄	—	2	2	no	—
464	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
465	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
466	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
467	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
468	C₂×D₈	C₂³×C₁₃	1	4	yes	—
469	C₂×D₈	C₂³×C₁₃	1	4	yes	—
470	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
471	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
472	C₄⋊Q₈	—	2	1	no	—
473	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
474	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
475	#127	—	2	2	no	—
476	#127	—	2	1	no	—
477	#127	—	2	2	no	—
478	#127	C₂³×C₁₃	1	2	yes	—
479	#127	C₂³×C₁₃	1	2	yes	—
480	#126	—	2	2	no	—
481	#126	—	2	2	no	—
482	#126	—	2	2	no	—
483	#126	—	2	2	no	—
484	#125	C₂³×C₁₃	1	2	yes	—
485	#125	C₂³×C₁₃	1	2	yes	—
486	#124	—	2	1	no	—
487	#124	—	2	2	no	—
488	#124	—	2	1	no	—
489	#124	—	2	2	no	—
490	#124	—	2	2	no	—
491	#124	—	2	2	no	—
492	#124	—	2	2	no	—
493	#124	—	2	2	no	—
494	#124	C₂³×C₁₃	1	2	yes	—
495	#124	C₂³×C₁₃	1	2	yes	—
496	#123	—	2	1	no	—
497	#123	—	2	1	no	—
498	#123	—	2	2	no	—
499	#123	—	2	2	no	—
500	#123	—	2	4	no	—
501	#123	—	2	4	no	—
502	#123	—	2	2	no	—
503	#123	—	2	2	no	—
504	C₂²⋊Q₈	—	2	2	no	—
505	C₂²⋊Q₈	—	2	2	no	—
506	C₂²⋊Q₈	—	2	2	no	—
507	C₂²⋊Q₈	—	2	2	no	—
508	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
509	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
510	#121	—	2	2	no	—
511	#121	—	2	2	no	—
512	#121	—	2	4	no	—
513	#121	—	2	4	no	—
514	#121	C₂³×C₁₃	1	2	yes	—
515	#121	C₂³×C₁₃	1	2	yes	—
516	#121	C₂³×C₁₃	1	4	yes	—
517	#121	C₂³×C₁₃	1	4	yes	—
518	#120	—	2	2	no	—
519	#120	—	2	2	no	—
520	#120	—	2	1	no	—
521	#120	—	2	1	no	—
522	C₄×Q₈	—	2	2	no	—
523	C₄×Q₈	—	2	2	no	—
524	C₄×Q₈	—	2	2	no	—
525	C₄×Q₈	D₄×C₁₃	1	2	yes	—
526	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
527	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
528	C₄×D₄	—	2	2	no	—
529	C₄×D₄	—	2	2	no	—
530	C₄×D₄	—	2	4	no	—
531	C₄×D₄	—	2	2	no	—
532	C₄×D₄	—	2	2	no	—
533	C₄×D₄	—	2	2	no	—
534	C₄×D₄	D₄×C₁₃	1	2	yes	—
535	C₄×D₄	D₄×C₁₃	1	2	yes	—
536	C₄×D₄	D₄×C₁₃	1	2	yes	—
537	C₄×D₄	C₂³×C₁₃	1	2	yes	—
538	C₄×D₄	C₂³×C₁₃	1	2	yes	—
539	C₄×D₄	C₂³×C₁₃	1	4	yes	—
540	C₄×D₄	C₂³×C₁₃	1	4	yes	—
541	#117	—	2	2	no	—
542	#117	—	2	2	no	—
543	#117	—	2	2	no	—
544	#117	C₂³×C₁₃	1	2	yes	—
545	#117	C₂³×C₁₃	1	1	yes	characteristic
546	#117	C₂³×C₁₃	1	1	yes	characteristic
547	#117	C₂³×C₁₃	1	1	yes	characteristic
548	#117	C₂³×C₁₃	1	1	yes	characteristic
549	#117	C₂³×C₁₃	1	1	yes	characteristic
550	C₂×C₂²⋊C₄	—	2	2	no	—
551	C₂×C₂²⋊C₄	—	2	4	no	—
552	C₂×C₂²⋊C₄	—	2	2	no	—
553	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
554	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
555	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
556	#107	C₂³×C₁₃	1	4	yes	—
557	#107	C₂³×C₁₃	1	4	yes	—
558	#106	C₂³×C₁₃	1	4	yes	—
559	#106	C₂³×C₁₃	1	4	yes	—
560	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
561	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
562	#103	C₂³×C₁₃	1	4	yes	—
563	#103	C₂³×C₁₃	1	4	yes	—
564	#102	C₂³×C₁₃	1	4	yes	—
565	#102	C₂³×C₁₃	1	4	yes	—
566	#102	C₂³×C₁₃	1	4	yes	—
567	#102	C₂³×C₁₃	1	4	yes	—
568	#102	C₂³×C₁₃	1	4	yes	—
569	#102	C₂³×C₁₃	1	4	yes	—
570	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
571	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
572	#97	C₂³×C₁₃	1	2	yes	—
573	#97	C₂³×C₁₃	1	2	yes	—
574	#97	C₂³×C₁₃	1	2	yes	—
575	C₄×C₈	C₂³×C₁₃	1	2	yes	—
576	C₂×C₁₃	—	4	1	no	—
577	C₂×C₁₃	—	4	1	no	—
578	C₂×C₁₃	—	4	1	no	—
579	C₂×C₁₃	—	8	4	no	—
580	C₂×C₁₃	—	8	2	no	—
581	C₂×C₁₃	#3449	1	1	yes	characteristic
582	C₂×C₁₃	#3585	1	2	yes	—
583	C₂⁴	—	2	1	no	—
584	C₂⁴	—	2	2	no	—
585	#41	—	4	2	no	—
586	#41	—	8	4	no	—
587	#41	—	8	4	no	—
588	C₂×Q₈	—	2	1	no	—
589	C₂×Q₈	—	2	2	no	—
590	C₂×Q₈	—	2	2	no	—
591	C₂×Q₈	—	4	2	no	—
592	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
593	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
594	C₂×D₄	—	2	2	no	—
595	C₂×D₄	—	2	2	no	—
596	C₂×D₄	—	2	4	no	—
597	C₂×D₄	—	2	4	no	—
598	C₂×D₄	—	2	1	no	—
599	C₂×D₄	—	2	2	no	—
600	C₂×D₄	—	2	2	no	—
601	C₂×D₄	—	2	2	no	—
602	C₂×D₄	—	2	4	no	—
603	C₂×D₄	—	4	2	no	—
604	C₂×D₄	—	4	2	no	—
605	C₂×D₄	—	4	2	no	—
606	C₂×D₄	—	8	4	no	—
607	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
608	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
609	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
610	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
611	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
612	C₂²×C₄	—	2	1	no	—
613	C₂²×C₄	—	2	2	no	—
614	C₂²×C₄	—	2	2	no	—
615	C₂²×C₄	—	2	4	no	—
616	C₂²×C₄	—	2	4	no	—
617	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
618	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
619	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
620	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
621	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
622	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
623	SD₁₆	—	4	4	no	—
624	SD₁₆	—	4	4	no	—
625	D₈	—	4	4	no	—
626	D₈	—	4	4	no	—
627	M₁₆	—	4	2	no	—
628	C₂×C₈	—	4	2	no	—
629	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
630	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
631	C₄⋊C₄	—	2	2	no	—
632	C₄⋊C₄	—	2	2	no	—
633	C₄⋊C₄	—	2	2	no	—
634	C₄⋊C₄	—	2	2	no	—
635	C₄⋊C₄	—	2	2	no	—
636	C₄⋊C₄	—	2	2	no	—
637	C₄⋊C₄	—	2	2	no	—
638	C₄⋊C₄	—	2	4	no	—
639	C₄⋊C₄	—	2	2	no	—
640	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
641	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
642	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
643	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
644	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
645	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
646	C₂²⋊C₄	—	2	2	no	—
647	C₂²⋊C₄	—	2	1	no	—
648	C₂²⋊C₄	—	2	1	no	—
649	C₂²⋊C₄	—	2	2	no	—
650	C₂²⋊C₄	—	2	2	no	—
651	C₂²⋊C₄	—	2	2	no	—
652	C₂²⋊C₄	—	2	2	no	—
653	C₂²⋊C₄	—	2	4	no	—
654	C₂²⋊C₄	—	2	4	no	—
655	C₂²⋊C₄	—	2	2	no	—
656	C₂²⋊C₄	—	2	2	no	—
657	C₂²⋊C₄	—	2	2	no	—
658	C₂²⋊C₄	—	2	2	no	—
659	C₂²⋊C₄	—	2	2	no	—
660	C₂²⋊C₄	—	2	2	no	—
661	C₂²⋊C₄	—	2	4	no	—
662	C₂²⋊C₄	—	2	4	no	—
663	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
664	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
665	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
666	C₄²	—	2	2	no	—
667	C₄²	—	2	2	no	—
668	C₄²	—	2	2	no	—
669	C₄²	—	2	1	no	—
670	C₄²	—	2	1	no	—
671	C₄²	C₂×D₄×C₁₃	1	2	yes	—
672	C₄²	C₂×D₄×C₁₃	1	2	yes	—
673	C₄²	C₂×D₄×C₁₃	1	2	yes	—
674	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
675	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
676	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
677	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
678	C₁₃	#61017	1	1	yes	characteristic, direct product factor, Sylow
679	C₂³	—	2	2	no	—
680	C₂³	—	2	4	no	—
681	C₂³	—	4	2	no	—
682	C₂³	—	4	4	no	—
683	C₂³	—	8	4	no	—
684	C₂³	—	8	2	no	—
685	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
686	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
687	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
688	Q₈	—	2	4	no	—
689	Q₈	—	4	1	no	—
690	Q₈	—	4	2	no	—
691	Q₈	—	4	4	no	—
692	Q₈	—	8	2	no	—
693	D₄	—	2	4	no	—
694	D₄	—	2	4	no	—
695	D₄	—	2	4	no	—
696	D₄	—	4	1	no	—
697	D₄	—	4	1	no	—
698	D₄	—	4	1	no	—
699	D₄	—	4	4	no	—
700	D₄	—	4	2	no	—
701	D₄	—	4	4	no	—
702	D₄	—	4	4	no	—
703	D₄	—	8	4	no	—
704	D₄	—	8	2	no	—
705	D₄	—	8	2	no	—
706	D₄	—	8	4	no	—
707	D₄	—	8	4	no	—
708	C₂×C₄	—	2	2	no	—
709	C₂×C₄	—	2	2	no	—
710	C₂×C₄	—	2	2	no	—
711	C₂×C₄	—	2	2	no	—
712	C₂×C₄	—	2	2	no	—
713	C₂×C₄	—	2	2	no	—
714	C₂×C₄	—	2	4	no	—
715	C₂×C₄	—	4	2	no	—
716	C₂×C₄	—	4	2	no	—
717	C₂×C₄	—	4	2	no	—
718	C₂×C₄	—	4	2	no	—
719	C₂×C₄	—	8	2	no	—
720	C₂×C₄	—	8	2	no	—
721	C₂×C₄	—	8	4	no	—
722	C₂×C₄	—	8	4	no	—
723	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
724	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
725	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
726	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
727	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
728	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
729	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
730	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
731	C₈	—	2	4	no	—
732	C₈	—	2	4	no	—
733	C₂²	—	2	2	no	—
734	C₂²	—	2	2	no	—
735	C₂²	—	2	2	no	—
736	C₂²	—	2	1	no	—
737	C₂²	—	2	1	no	—
738	C₂²	—	2	1	no	—
739	C₂²	—	4	4	no	—
740	C₂²	—	4	4	no	—
741	C₂²	—	4	2	no	—
742	C₂²	—	4	2	no	—
743	C₂²	—	4	2	no	—
744	C₂²	—	4	4	no	—
745	C₂²	—	16	4	no	—
746	C₂²	—	16	2	no	—
747	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
748	C₄	—	2	2	no	—
749	C₄	—	2	2	no	—
750	C₄	—	2	2	no	—
751	C₄	—	2	2	no	—
752	C₄	—	2	1	no	—
753	C₄	—	2	1	no	—
754	C₄	—	2	1	no	—
755	C₄	—	4	4	no	—
756	C₄	—	4	2	no	—
757	C₄	—	4	2	no	—
758	C₄	—	4	2	no	—
759	C₄	C₁₃×#585	1	2	yes	—
760	C₂	—	4	1	no	—
761	C₂	—	4	1	no	—
762	C₂	—	4	1	no	—
763	C₂	—	8	4	no	—
764	C₂	—	8	2	no	—
765	C₂	C₁₃×#3449	1	1	yes	characteristic
766	C₂	C₁₃×#3585	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
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
1. C₁₃×#3510	C₂	semidirect
2. C₁₃×#3508	C₂	semidirect
3. C₁₃×#3257	C₂	semidirect
4. C₁₃×#3240	C₂	semidirect
5. C₁₃×#3235	C₂	semidirect
6. C₁₃×#3217	C₂	semidirect
7. C₁₃×#3213	C₂	semidirect
8. C₁₃×#3200	C₂	semidirect
9. C₁₃×#3199	C₂	semidirect
10. C₁₃×#3180	C₂	semidirect
11. C₁₃×#3171	C₂	semidirect
12. C₁₃×#3126	C₂	semidirect
13. C₁₃×#3122	C₂	semidirect
14. C₁₃×#3118	C₂	semidirect
15. C₁₃×#2923	C₂	semidirect
25. C₁₃×#542	C₂²	semidirect
27. C₁₃×#540	C₂²	semidirect
31. C₁₃×#533	C₂²	semidirect
32. C₁₃×#533	C₂²	semidirect
34. C₁₃×#532	C₂²	semidirect
35. C₂×C₁₃×#127	C₂²	semidirect
37. C₁₃×#529	C₂²	semidirect
38. C₂×C₁₃×#124	C₂²	semidirect
39. C₁₃×#519	C₂²	semidirect
40. C₁₃×#518	C₂²	semidirect
41. C₁₃×#518	C₂²	semidirect
43. C₁₃×#501	C₂²	semidirect
44. C₁₃×#501	C₂²	semidirect
47. C₁₃×#490	C₂²	semidirect
48. C₁₃×#490	C₂²	semidirect
49. C₁₃×#489	C₂²	semidirect
50. C₁₃×#489	C₂²	semidirect
51. C₁₃×#485	C₂²	semidirect
53. C₁₃×#482	C₂²	semidirect
54. C₁₃×#482	C₂²	semidirect
55. C₁₃×#479	C₂²	semidirect
56. C₁₃×#478	C₂²	semidirect
57. C₁₃×#476	C₂²	semidirect
58. C₁₃×#474	C₂²	semidirect
59. C₁₃×#469	C₂²	semidirect
60. C₁₃×#468	C₂²	semidirect
61. C₁₃×#466	C₂²	semidirect
62. C₁₃×#465	C₂²	semidirect
63. C₁₃×#463	C₂²	semidirect
64. C₁₃×#463	C₂²	semidirect
65. C₁₃×#460	C₂²	semidirect
67. C₁₃×#450	C₂²	semidirect
68. C₁₃×#448	C₂²	semidirect
70. C₁₃×#447	C₂²	semidirect
71. C₁₃×#442	C₂²	semidirect
72. C₁₃×#440	C₂²	semidirect
73. C₄×C₁₃×SD₁₆	C₂²	semidirect
74. C₄×C₁₃×D₈	C₂²	semidirect
75. C₁₃×#433	C₂²	semidirect
76. C₁₃×#433	C₂²	semidirect
77. C₁₃×#432	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. #61017	C₁₃	direct (N × H)
296. #3510	C₂×C₁₃	semidirect
297. #3508	C₂×C₁₃	semidirect
298. #3257	C₂×C₁₃	semidirect
299. #3240	C₂×C₁₃	semidirect
300. #3235	C₂×C₁₃	semidirect
301. #3217	C₂×C₁₃	semidirect
302. #3213	C₂×C₁₃	semidirect
303. #3200	C₂×C₁₃	semidirect
304. #3199	C₂×C₁₃	semidirect
305. #3180	C₂×C₁₃	semidirect
306. #3171	C₂×C₁₃	semidirect
307. #3126	C₂×C₁₃	semidirect
308. #3122	C₂×C₁₃	semidirect
309. #3118	C₂×C₁₃	semidirect
310. #2923	C₂×C₁₃	semidirect
374. #542	C₂²×C₁₃	semidirect
376. #540	C₂²×C₁₃	semidirect
380. #533	C₂²×C₁₃	semidirect
381. #533	C₂²×C₁₃	semidirect
383. #532	C₂²×C₁₃	semidirect
384. C₂×#127	C₂²×C₁₃	semidirect
386. #529	C₂²×C₁₃	semidirect
387. C₂×#124	C₂²×C₁₃	semidirect
388. #519	C₂²×C₁₃	semidirect
389. #518	C₂²×C₁₃	semidirect
390. #518	C₂²×C₁₃	semidirect
392. #501	C₂²×C₁₃	semidirect
393. #501	C₂²×C₁₃	semidirect
396. #490	C₂²×C₁₃	semidirect
397. #490	C₂²×C₁₃	semidirect
398. #489	C₂²×C₁₃	semidirect
399. #489	C₂²×C₁₃	semidirect
400. #485	C₂²×C₁₃	semidirect
402. #482	C₂²×C₁₃	semidirect
403. #482	C₂²×C₁₃	semidirect
404. #479	C₂²×C₁₃	semidirect
405. #478	C₂²×C₁₃	semidirect
406. #476	C₂²×C₁₃	semidirect
407. #474	C₂²×C₁₃	semidirect
408. #469	C₂²×C₁₃	semidirect
409. #468	C₂²×C₁₃	semidirect
410. #466	C₂²×C₁₃	semidirect
411. #465	C₂²×C₁₃	semidirect
412. #463	C₂²×C₁₃	semidirect
413. #463	C₂²×C₁₃	semidirect
414. #460	C₂²×C₁₃	semidirect
416. #450	C₂²×C₁₃	semidirect
417. #448	C₂²×C₁₃	semidirect
419. #447	C₂²×C₁₃	semidirect
420. #442	C₂²×C₁₃	semidirect
421. #440	C₂²×C₁₃	semidirect
422. C₄×SD₁₆	C₂²×C₁₃	semidirect
423. C₄×D₈	C₂²×C₁₃	semidirect
424. #433	C₂²×C₁₃	semidirect
425. #433	C₂²×C₁₃	semidirect
426. #432	C₂²×C₁₃	semidirect
427. #432	C₂²×C₁₃	semidirect
428. #424	C₂²×C₁₃	semidirect
430. C₄×M₁₆	C₂²×C₁₃	semidirect
431. C₂×#97	C₂²×C₁₃	semidirect
678. C₁₃	#61017	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×#3508	2
C₁₃×#3257	2
C₁₃×#3240	2
C₁₃×#3235	2
C₁₃×#3217	2
C₁₃×#3213	2
C₁₃×#3200	2
C₁₃×#3199	2
C₁₃×#3180	2
C₁₃×#3171	2
C₁₃×#3126	2
C₁₃×#3122	2
C₁₃×#3118	2
C₁₃×#2923	2
#61017	13

Subgroups — C13×#61017 #15747356

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61017 #15747356