Subgroups — C₁₃×#61332 #15747671

Order 3328.

1862 conjugacy classes of subgroups.

The subgroup lattice has 776 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3506	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3501	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3376	C₂	1	4	yes	maximal, complemented
4	C₁₃×#3373	C₂	1	4	yes	maximal, complemented
5	C₁₃×#3370	C₂	1	4	yes	maximal, complemented
6	C₁₃×#3366	C₂	1	4	yes	maximal, complemented
7	C₁₃×#3136	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3135	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#3084	C₂	1	2	yes	maximal, complemented
10	C₁₃×#3077	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#3041	C₂	1	2	yes	maximal, complemented
12	C₁₃×#3036	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#2961	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#2946	C₂	1	2	yes	maximal, complemented
15	C₂×C₁₃×#442	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	2	yes	—
17	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic
18	C₁₃×#559	C₂²	1	4	yes	complemented
19	C₁₃×#556	C₂²	1	2	yes	complemented
20	C₁₃×#555	—	2	1	no	—
21	C₁₃×#554	—	2	1	no	—
22	C₁₃×#554	—	2	2	no	—
23	C₁₃×#554	C₂²	1	4	yes	complemented
24	C₁₃×#554	C₂²	1	2	yes	complemented
25	C₁₃×#553	—	2	2	no	—
26	C₁₃×#550	C₂²	1	2	yes	complemented
27	D₄×Q₈×C₁₃	—	2	1	no	—
28	D₄×Q₈×C₁₃	C₂²	1	2	yes	complemented
29	C₁₃×#547	—	2	1	no	—
30	C₁₃×#544	C₂²	1	2	yes	—
31	C₁₃×#543	—	2	2	no	—
32	C₁₃×#538	—	2	2	no	—
33	C₁₃×#535	C₂²	1	2	yes	—
34	C₁₃×#533	C₂²	1	1	yes	characteristic
35	C₁₃×#533	C₂²	1	1	yes	characteristic
36	C₁₃×#532	C₂²	1	1	yes	characteristic
37	C₁₃×#525	—	2	2	no	—
38	C₂×C₁₃×C₂²⋊Q₈	—	2	2	no	—
39	C₁₃×#520	C₂²	1	2	yes	—
40	C₁₃×#518	C₂²	1	2	yes	—
41	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
42	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
43	C₁₃×#491	C₂²	1	2	yes	complemented
44	C₁₃×#490	C₂²	1	2	yes	complemented
45	C₁₃×#490	C₂²	1	4	yes	complemented
46	C₁₃×#489	C₂²	1	2	yes	complemented
47	C₁₃×#489	C₂²	1	2	yes	complemented
48	C₁₃×#489	C₂²	1	4	yes	complemented
49	C₁₃×#488	C₂²	1	4	yes	complemented
50	C₁₃×#486	C₂²	1	4	yes	complemented
51	C₁₃×#479	C₂²	1	4	yes	complemented
52	C₁₃×#478	C₂²	1	4	yes	complemented
53	C₁₃×#478	C₂²	1	4	yes	complemented
54	C₁₃×#476	C₂²	1	2	yes	complemented
55	C₁₃×#476	C₂²	1	4	yes	complemented
56	C₁₃×#475	C₂²	1	4	yes	complemented
57	C₁₃×#474	C₂²	1	2	yes	complemented
58	C₁₃×#463	C₂²	1	4	yes	—
59	C₁₃×#463	C₂²	1	4	yes	—
60	C₁₃×#463	C₂²	1	4	yes	complemented
61	C₁₃×#461	C₂²	1	2	yes	complemented
62	C₁₃×#459	C₂²	1	4	yes	—
63	C₁₃×#459	C₂²	1	4	yes	—
64	C₁₃×#459	C₂²	1	2	yes	complemented
65	C₁₃×#446	C₂²	1	4	yes	complemented
66	C₁₃×#446	C₂²	1	4	yes	complemented
67	C₁₃×#442	C₂²	1	4	yes	—
68	C₁₃×#442	C₂²	1	4	yes	—
69	C₁₃×#442	C₂²	1	4	yes	complemented
70	C₁₃×#440	C₂²	1	4	yes	complemented
71	C₄×C₁₃×SD₁₆	C₂²	1	4	yes	complemented
72	C₄×C₁₃×D₈	C₂²	1	4	yes	complemented
73	C₁₃×#428	C₂²	1	2	yes	—
74	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
75	C₁₃×#424	C₂²	1	2	yes	—
76	C₁₃×#423	C₂²	1	1	yes	characteristic
77	C₁₃×#418	C₂²	1	2	yes	—
78	C₁₃×#417	C₂²	1	2	yes	—
79	C₁₃×#416	C₂²	1	2	yes	—
80	C₁₃×#416	C₂²	1	2	yes	—
81	C₂×C₁₃×#102	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	C₂×C₁₃×#41	—	2	2	no	—
86	C₂×C₁₃×#41	C₂³	1	2	yes	—
87	C₂²×Q₈×C₁₃	—	2	2	no	—
88	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
89	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
90	C₂³×C₄×C₁₃	—	2	1	no	—
91	C₂³×C₄×C₁₃	—	2	1	no	—
92	C₁₃×AGL(1,ℤ/8)	—	2	8	no	—
93	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
94	C₂×C₁₃×D₈	—	2	4	no	—
95	C₂×C₁₃×D₈	C₂³	1	4	yes	—
96	C₂×C₁₃×D₈	C₂³	1	4	yes	—
97	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
98	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
99	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
100	C₁₃×C₄⋊Q₈	—	2	2	no	—
101	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
102	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
103	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
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×#127	C₂³	1	4	yes	—
108	C₁₃×#127	C₂³	1	1	yes	characteristic
109	C₁₃×#126	—	2	4	no	—
110	C₁₃×#125	—	2	2	no	—
111	C₁₃×#125	D₄	1	2	yes	—
112	C₁₃×#125	C₂³	1	2	yes	—
113	C₁₃×#125	C₂³	1	4	yes	—
114	C₁₃×#124	—	2	4	no	—
115	C₁₃×#124	C₂³	1	4	yes	—
116	C₁₃×#124	C₂³	1	2	yes	—
117	C₁₃×#123	—	2	4	no	—
118	C₁₃×#123	—	2	4	no	—
119	C₁₃×C₂²⋊Q₈	—	2	2	no	—
120	C₁₃×C₂²⋊Q₈	—	2	2	no	—
121	C₁₃×C₂²⋊Q₈	—	2	4	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	D₄	1	2	yes	—
131	C₁₃×C₂²⋊Q₈	D₄	1	2	yes	—
132	C₁₃×#121	—	2	1	no	—
133	C₁₃×#121	—	2	1	no	—
134	C₁₃×#121	—	2	2	no	—
135	C₁₃×#121	—	2	2	no	—
136	C₁₃×#121	—	2	2	no	—
137	C₁₃×#121	—	2	4	no	—
138	C₁₃×#120	—	2	4	no	—
139	C₄×Q₈×C₁₃	—	2	1	no	—
140	C₄×Q₈×C₁₃	—	2	1	no	—
141	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
142	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
143	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
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	—	2	4	no	—
148	C₄×D₄×C₁₃	—	2	1	no	—
149	C₄×D₄×C₁₃	—	2	1	no	—
150	C₄×D₄×C₁₃	—	2	1	no	—
151	C₄×D₄×C₁₃	—	2	1	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	4	yes	—
157	C₄×D₄×C₁₃	C₂³	1	2	yes	—
158	C₄×D₄×C₁₃	C₂³	1	2	yes	—
159	C₄×D₄×C₁₃	C₂³	1	2	yes	—
160	C₄×D₄×C₁₃	C₂³	1	2	yes	—
161	C₁₃×#117	—	2	2	no	—
162	C₁₃×#117	—	2	2	no	—
163	C₁₃×#117	C₂³	1	2	yes	—
164	C₁₃×#117	C₂³	1	2	yes	—
165	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
166	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
167	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
168	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
169	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
170	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
171	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
172	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
173	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
174	C₁₃×#107	C₂³	1	4	yes	—
175	C₁₃×#106	C₂³	1	4	yes	—
176	C₁₃×#106	C₂³	1	4	yes	—
177	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
178	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
179	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
180	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
181	C₁₃×#103	C₂³	1	2	yes	—
182	C₁₃×#103	C₂³	1	2	yes	—
183	C₁₃×#103	C₂³	1	2	yes	—
184	C₁₃×#103	C₂³	1	2	yes	—
185	C₁₃×#103	C₂³	1	4	yes	—
186	C₁₃×#102	C₂³	1	4	yes	—
187	C₁₃×#102	C₂³	1	4	yes	—
188	C₁₃×#102	C₂³	1	2	yes	—
189	C₁₃×#102	C₂³	1	2	yes	—
190	C₁₃×#102	C₂³	1	2	yes	—
191	C₁₃×#102	C₂³	1	2	yes	—
192	C₁₃×#102	C₂³	1	4	yes	—
193	C₁₃×#102	C₂³	1	4	yes	—
194	C₁₃×#102	C₂³	1	4	yes	—
195	C₁₃×#97	C₂³	1	2	yes	—
196	C₁₃×#97	C₂³	1	2	yes	—
197	C₁₃×#97	C₂³	1	4	yes	—
198	C₄×C₈×C₁₃	C₂³	1	4	yes	—
199	#61332	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
200	C₂⁴×C₁₃	—	2	1	no	—
201	C₂⁴×C₁₃	—	2	1	no	—
202	C₁₃×#41	—	2	4	no	—
203	C₁₃×#41	—	2	4	no	—
204	C₁₃×#41	—	8	4	no	—
205	C₂×Q₈×C₁₃	—	2	1	no	—
206	C₂×Q₈×C₁₃	—	2	1	no	—
207	C₂×Q₈×C₁₃	—	2	4	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	C₂⁴	1	2	yes	—
212	C₂×D₄×C₁₃	—	2	2	no	—
213	C₂×D₄×C₁₃	—	2	1	no	—
214	C₂×D₄×C₁₃	—	2	1	no	—
215	C₂×D₄×C₁₃	—	2	1	no	—
216	C₂×D₄×C₁₃	—	2	4	no	—
217	C₂×D₄×C₁₃	—	2	1	no	—
218	C₂×D₄×C₁₃	—	2	4	no	—
219	C₂×D₄×C₁₃	—	2	2	no	—
220	C₂×D₄×C₁₃	—	2	2	no	—
221	C₂×D₄×C₁₃	—	2	2	no	—
222	C₂×D₄×C₁₃	#41	1	4	yes	complemented
223	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
224	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
225	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
226	C₂²×C₄×C₁₃	—	2	1	no	—
227	C₂²×C₄×C₁₃	—	2	1	no	—
228	C₂²×C₄×C₁₃	—	2	2	no	—
229	C₂²×C₄×C₁₃	—	2	2	no	—
230	C₂²×C₄×C₁₃	—	2	2	no	—
231	C₂²×C₄×C₁₃	—	2	4	no	—
232	C₂²×C₄×C₁₃	—	2	4	no	—
233	C₂²×C₄×C₁₃	—	2	2	no	—
234	C₂²×C₄×C₁₃	—	2	4	no	—
235	C₂²×C₄×C₁₃	—	2	2	no	—
236	C₂²×C₄×C₁₃	—	8	2	no	—
237	C₂²×C₄×C₁₃	—	8	2	no	—
238	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
239	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
240	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
241	C₁₃×SD₁₆	—	2	8	no	—
242	C₁₃×D₈	—	2	8	no	—
243	C₁₃×D₈	—	2	8	no	—
244	C₁₃×M₁₆	—	2	4	no	—
245	C₂×C₈×C₁₃	—	2	2	no	—
246	C₂×C₈×C₁₃	—	2	2	no	—
247	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
248	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
249	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
250	C₁₃×C₄⋊C₄	—	2	1	no	—
251	C₁₃×C₄⋊C₄	—	2	2	no	—
252	C₁₃×C₄⋊C₄	—	2	1	no	—
253	C₁₃×C₄⋊C₄	—	2	4	no	—
254	C₁₃×C₄⋊C₄	—	2	4	no	—
255	C₁₃×C₄⋊C₄	—	2	4	no	—
256	C₁₃×C₄⋊C₄	—	2	4	no	—
257	C₁₃×C₄⋊C₄	—	2	1	no	—
258	C₁₃×C₄⋊C₄	—	2	1	no	—
259	C₁₃×C₄⋊C₄	—	2	1	no	—
260	C₁₃×C₄⋊C₄	—	2	2	no	—
261	C₁₃×C₄⋊C₄	—	2	1	no	—
262	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
263	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
264	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
265	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
266	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
267	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
268	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
269	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
270	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
271	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
272	C₁₃×C₂²⋊C₄	—	2	2	no	—
273	C₁₃×C₂²⋊C₄	—	2	2	no	—
274	C₁₃×C₂²⋊C₄	—	2	4	no	—
275	C₁₃×C₂²⋊C₄	—	2	4	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	—	2	2	no	—
282	C₁₃×C₂²⋊C₄	—	2	4	no	—
283	C₁₃×C₂²⋊C₄	—	2	2	no	—
284	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
285	C₄²×C₁₃	—	2	4	no	—
286	C₄²×C₁₃	—	2	2	no	—
287	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
288	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
289	C₄²×C₁₃	C₂⁴	1	4	yes	—
290	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
291	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
292	#3506	C₂×C₁₃	1	1	yes	characteristic, complemented
293	#3501	C₂×C₁₃	1	1	yes	characteristic, complemented
294	#3376	C₂×C₁₃	1	4	yes	complemented
295	#3373	C₂×C₁₃	1	4	yes	complemented
296	#3370	C₂×C₁₃	1	4	yes	complemented
297	#3366	C₂×C₁₃	1	4	yes	complemented
298	#3136	C₂×C₁₃	1	2	yes	complemented
299	#3135	C₂×C₁₃	1	1	yes	characteristic, complemented
300	#3084	C₂×C₁₃	1	2	yes	complemented
301	#3077	C₂×C₁₃	1	1	yes	characteristic, complemented
302	#3041	C₂×C₁₃	1	2	yes	complemented
303	#3036	C₂×C₁₃	1	1	yes	characteristic, complemented
304	#2961	C₂×C₁₃	1	1	yes	characteristic, complemented
305	#2946	C₂×C₁₃	1	2	yes	complemented
306	C₂×#442	C₂×C₁₃	1	1	yes	characteristic, complemented
307	C₂³×C₁₃	—	2	2	no	—
308	C₂³×C₁₃	—	2	4	no	—
309	C₂³×C₁₃	—	2	2	no	—
310	C₂³×C₁₃	—	2	2	no	—
311	C₂³×C₁₃	—	4	2	no	—
312	C₂³×C₁₃	—	8	1	no	—
313	C₂³×C₁₃	—	8	1	no	—
314	C₂³×C₁₃	—	8	1	no	—
315	C₂³×C₁₃	—	8	1	no	—
316	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
317	Q₈×C₁₃	—	2	2	no	—
318	Q₈×C₁₃	—	2	2	no	—
319	Q₈×C₁₃	—	4	2	no	—
320	Q₈×C₁₃	—	4	2	no	—
321	Q₈×C₁₃	—	4	2	no	—
322	Q₈×C₁₃	—	8	1	no	—
323	Q₈×C₁₃	—	8	4	no	—
324	D₄×C₁₃	—	2	4	no	—
325	D₄×C₁₃	—	2	2	no	—
326	D₄×C₁₃	—	2	2	no	—
327	D₄×C₁₃	—	2	2	no	—
328	D₄×C₁₃	—	2	2	no	—
329	D₄×C₁₃	—	2	2	no	—
330	D₄×C₁₃	—	4	2	no	—
331	D₄×C₁₃	—	4	4	no	—
332	D₄×C₁₃	—	4	2	no	—
333	D₄×C₁₃	—	8	1	no	—
334	D₄×C₁₃	—	8	4	no	—
335	D₄×C₁₃	—	8	4	no	—
336	D₄×C₁₃	C₂×#41	1	4	yes	—
337	C₂×C₄×C₁₃	—	2	2	no	—
338	C₂×C₄×C₁₃	—	2	2	no	—
339	C₂×C₄×C₁₃	—	2	2	no	—
340	C₂×C₄×C₁₃	—	2	2	no	—
341	C₂×C₄×C₁₃	—	2	2	no	—
342	C₂×C₄×C₁₃	—	4	1	no	—
343	C₂×C₄×C₁₃	—	4	1	no	—
344	C₂×C₄×C₁₃	—	4	4	no	—
345	C₂×C₄×C₁₃	—	4	4	no	—
346	C₂×C₄×C₁₃	—	4	4	no	—
347	C₂×C₄×C₁₃	—	8	4	no	—
348	C₂×C₄×C₁₃	—	8	2	no	—
349	C₂×C₄×C₁₃	—	8	2	no	—
350	C₂×C₄×C₁₃	—	8	4	no	—
351	C₂×C₄×C₁₃	—	8	4	no	—
352	C₂×C₄×C₁₃	—	8	1	no	—
353	C₂×C₄×C₁₃	—	8	1	no	—
354	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
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	1	yes	characteristic
358	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
359	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
360	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
361	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
362	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
363	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
364	C₈×C₁₃	—	2	2	no	—
365	C₈×C₁₃	—	2	4	no	—
366	C₈×C₁₃	—	2	2	no	—
367	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	2	yes	—
368	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic
369	#559	C₂²×C₁₃	1	4	yes	complemented
370	#556	C₂²×C₁₃	1	2	yes	complemented
371	#555	—	2	1	no	—
372	#554	—	2	1	no	—
373	#554	—	2	2	no	—
374	#554	C₂²×C₁₃	1	4	yes	complemented
375	#554	C₂²×C₁₃	1	2	yes	complemented
376	#553	—	2	2	no	—
377	#550	C₂²×C₁₃	1	2	yes	complemented
378	D₄×Q₈	—	2	1	no	—
379	D₄×Q₈	C₂²×C₁₃	1	2	yes	complemented
380	#547	—	2	1	no	—
381	#544	C₂²×C₁₃	1	2	yes	—
382	#543	—	2	2	no	—
383	#538	—	2	2	no	—
384	#535	C₂²×C₁₃	1	2	yes	—
385	#533	C₂²×C₁₃	1	1	yes	characteristic
386	#533	C₂²×C₁₃	1	1	yes	characteristic
387	#532	C₂²×C₁₃	1	1	yes	characteristic
388	#525	—	2	2	no	—
389	C₂×C₂²⋊Q₈	—	2	2	no	—
390	#520	C₂²×C₁₃	1	2	yes	—
391	#518	C₂²×C₁₃	1	2	yes	—
392	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
393	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
394	#491	C₂²×C₁₃	1	2	yes	complemented
395	#490	C₂²×C₁₃	1	2	yes	complemented
396	#490	C₂²×C₁₃	1	4	yes	complemented
397	#489	C₂²×C₁₃	1	2	yes	complemented
398	#489	C₂²×C₁₃	1	2	yes	complemented
399	#489	C₂²×C₁₃	1	4	yes	complemented
400	#488	C₂²×C₁₃	1	4	yes	complemented
401	#486	C₂²×C₁₃	1	4	yes	complemented
402	#479	C₂²×C₁₃	1	4	yes	complemented
403	#478	C₂²×C₁₃	1	4	yes	complemented
404	#478	C₂²×C₁₃	1	4	yes	complemented
405	#476	C₂²×C₁₃	1	2	yes	complemented
406	#476	C₂²×C₁₃	1	4	yes	complemented
407	#475	C₂²×C₁₃	1	4	yes	complemented
408	#474	C₂²×C₁₃	1	2	yes	complemented
409	#463	C₂²×C₁₃	1	4	yes	—
410	#463	C₂²×C₁₃	1	4	yes	—
411	#463	C₂²×C₁₃	1	4	yes	complemented
412	#461	C₂²×C₁₃	1	2	yes	complemented
413	#459	C₂²×C₁₃	1	4	yes	—
414	#459	C₂²×C₁₃	1	4	yes	—
415	#459	C₂²×C₁₃	1	2	yes	complemented
416	#446	C₂²×C₁₃	1	4	yes	complemented
417	#446	C₂²×C₁₃	1	4	yes	complemented
418	#442	C₂²×C₁₃	1	4	yes	—
419	#442	C₂²×C₁₃	1	4	yes	—
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	#428	C₂²×C₁₃	1	2	yes	—
425	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
426	#424	C₂²×C₁₃	1	2	yes	—
427	#423	C₂²×C₁₃	1	1	yes	characteristic
428	#418	C₂²×C₁₃	1	2	yes	—
429	#417	C₂²×C₁₃	1	2	yes	—
430	#416	C₂²×C₁₃	1	2	yes	—
431	#416	C₂²×C₁₃	1	2	yes	—
432	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
433	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
434	#405	C₂²×C₁₃	1	2	yes	—
435	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
436	C₂²×C₁₃	—	2	1	no	—
437	C₂²×C₁₃	—	2	1	no	—
438	C₂²×C₁₃	—	2	4	no	—
439	C₂²×C₁₃	—	4	2	no	—
440	C₂²×C₁₃	—	4	2	no	—
441	C₂²×C₁₃	—	4	2	no	—
442	C₂²×C₁₃	—	4	2	no	—
443	C₂²×C₁₃	—	4	2	no	—
444	C₂²×C₁₃	—	4	2	no	—
445	C₂²×C₁₃	—	4	2	no	—
446	C₂²×C₁₃	—	4	2	no	—
447	C₂²×C₁₃	—	8	4	no	—
448	C₂²×C₁₃	—	8	4	no	—
449	C₂²×C₁₃	#548	1	2	yes	—
450	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
451	C₄×C₁₃	—	2	1	no	—
452	C₄×C₁₃	—	2	1	no	—
453	C₄×C₁₃	—	2	1	no	—
454	C₄×C₁₃	—	2	1	no	—
455	C₄×C₁₃	—	2	4	no	—
456	C₄×C₁₃	—	2	4	no	—
457	C₄×C₁₃	—	4	2	no	—
458	C₄×C₁₃	—	4	2	no	—
459	C₄×C₁₃	—	4	2	no	—
460	C₄×C₁₃	—	4	2	no	—
461	C₄×C₁₃	—	4	2	no	—
462	C₄×C₁₃	#548	1	2	yes	—
463	C₄×C₁₃	C₂²×#41	1	1	yes	characteristic
464	C₄×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
465	C₂×#41	—	2	2	no	—
466	C₂×#41	C₂³×C₁₃	1	2	yes	—
467	C₂²×Q₈	—	2	2	no	—
468	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
469	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
470	C₂³×C₄	—	2	1	no	—
471	C₂³×C₄	—	2	1	no	—
472	AGL(1,ℤ/8)	—	2	8	no	—
473	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
474	C₂×D₈	—	2	4	no	—
475	C₂×D₈	C₂³×C₁₃	1	4	yes	—
476	C₂×D₈	C₂³×C₁₃	1	4	yes	—
477	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
478	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
479	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
480	C₄⋊Q₈	—	2	2	no	—
481	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
482	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
483	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
484	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
485	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
486	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
487	#127	C₂³×C₁₃	1	1	yes	characteristic
488	#127	C₂³×C₁₃	1	4	yes	—
489	#126	—	2	4	no	—
490	#125	—	2	2	no	—
491	#125	D₄×C₁₃	1	2	yes	—
492	#125	C₂³×C₁₃	1	2	yes	—
493	#125	C₂³×C₁₃	1	4	yes	—
494	#124	—	2	4	no	—
495	#124	C₂³×C₁₃	1	2	yes	—
496	#124	C₂³×C₁₃	1	4	yes	—
497	#123	—	2	4	no	—
498	#123	—	2	4	no	—
499	C₂²⋊Q₈	—	2	2	no	—
500	C₂²⋊Q₈	—	2	2	no	—
501	C₂²⋊Q₈	—	2	4	no	—
502	C₂²⋊Q₈	—	2	1	no	—
503	C₂²⋊Q₈	—	2	1	no	—
504	C₂²⋊Q₈	—	2	2	no	—
505	C₂²⋊Q₈	—	2	4	no	—
506	C₂²⋊Q₈	—	2	4	no	—
507	C₂²⋊Q₈	—	2	4	no	—
508	C₂²⋊Q₈	—	2	4	no	—
509	C₂²⋊Q₈	—	2	4	no	—
510	C₂²⋊Q₈	D₄×C₁₃	1	2	yes	—
511	C₂²⋊Q₈	D₄×C₁₃	1	2	yes	—
512	#121	—	2	1	no	—
513	#121	—	2	1	no	—
514	#121	—	2	2	no	—
515	#121	—	2	2	no	—
516	#121	—	2	2	no	—
517	#121	—	2	4	no	—
518	#120	—	2	4	no	—
519	C₄×Q₈	—	2	1	no	—
520	C₄×Q₈	—	2	1	no	—
521	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
522	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
523	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
524	C₄×D₄	—	2	2	no	—
525	C₄×D₄	—	2	2	no	—
526	C₄×D₄	—	2	4	no	—
527	C₄×D₄	—	2	4	no	—
528	C₄×D₄	—	2	1	no	—
529	C₄×D₄	—	2	1	no	—
530	C₄×D₄	—	2	1	no	—
531	C₄×D₄	—	2	1	no	—
532	C₄×D₄	—	2	1	no	—
533	C₄×D₄	—	2	1	no	—
534	C₄×D₄	C₂³×C₁₃	1	2	yes	—
535	C₄×D₄	C₂³×C₁₃	1	2	yes	—
536	C₄×D₄	C₂³×C₁₃	1	2	yes	—
537	C₄×D₄	C₂³×C₁₃	1	2	yes	—
538	C₄×D₄	C₂³×C₁₃	1	4	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	C₂³×C₁₃	1	2	yes	—
544	#117	C₂³×C₁₃	1	2	yes	—
545	C₂×C₄⋊C₄	—	2	2	no	—
546	C₂×C₄⋊C₄	—	2	4	no	—
547	C₂×C₄⋊C₄	—	2	2	no	—
548	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
549	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
550	C₂×C₂²⋊C₄	—	2	1	no	—
551	C₂×C₂²⋊C₄	—	2	1	no	—
552	C₂×C₂²⋊C₄	—	2	4	no	—
553	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
554	#107	C₂³×C₁₃	1	4	yes	—
555	#106	C₂³×C₁₃	1	4	yes	—
556	#106	C₂³×C₁₃	1	4	yes	—
557	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
558	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
559	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
560	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
561	#103	C₂³×C₁₃	1	2	yes	—
562	#103	C₂³×C₁₃	1	2	yes	—
563	#103	C₂³×C₁₃	1	2	yes	—
564	#103	C₂³×C₁₃	1	2	yes	—
565	#103	C₂³×C₁₃	1	4	yes	—
566	#102	C₂³×C₁₃	1	4	yes	—
567	#102	C₂³×C₁₃	1	4	yes	—
568	#102	C₂³×C₁₃	1	2	yes	—
569	#102	C₂³×C₁₃	1	2	yes	—
570	#102	C₂³×C₁₃	1	2	yes	—
571	#102	C₂³×C₁₃	1	2	yes	—
572	#102	C₂³×C₁₃	1	4	yes	—
573	#102	C₂³×C₁₃	1	4	yes	—
574	#102	C₂³×C₁₃	1	4	yes	—
575	#97	C₂³×C₁₃	1	2	yes	—
576	#97	C₂³×C₁₃	1	2	yes	—
577	#97	C₂³×C₁₃	1	4	yes	—
578	C₄×C₈	C₂³×C₁₃	1	4	yes	—
579	C₂×C₁₃	—	2	2	no	—
580	C₂×C₁₃	—	4	4	no	—
581	C₂×C₁₃	—	8	2	no	—
582	C₂×C₁₃	—	8	2	no	—
583	C₂×C₁₃	C₂×#548	1	1	yes	characteristic
584	C₂×C₁₃	#3585	1	1	yes	characteristic
585	C₂×C₁₃	#3585	1	1	yes	characteristic
586	C₂⁴	—	2	1	no	—
587	C₂⁴	—	2	1	no	—
588	#41	—	2	4	no	—
589	#41	—	2	4	no	—
590	#41	—	8	4	no	—
591	C₂×Q₈	—	2	1	no	—
592	C₂×Q₈	—	2	1	no	—
593	C₂×Q₈	—	2	4	no	—
594	C₂×Q₈	—	8	4	no	—
595	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
596	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
597	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
598	C₂×D₄	—	2	2	no	—
599	C₂×D₄	—	2	1	no	—
600	C₂×D₄	—	2	1	no	—
601	C₂×D₄	—	2	1	no	—
602	C₂×D₄	—	2	4	no	—
603	C₂×D₄	—	2	1	no	—
604	C₂×D₄	—	2	4	no	—
605	C₂×D₄	—	2	2	no	—
606	C₂×D₄	—	2	2	no	—
607	C₂×D₄	—	2	2	no	—
608	C₂×D₄	C₁₃×#41	1	4	yes	complemented
609	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
610	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
611	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
612	C₂²×C₄	—	2	1	no	—
613	C₂²×C₄	—	2	1	no	—
614	C₂²×C₄	—	2	2	no	—
615	C₂²×C₄	—	2	2	no	—
616	C₂²×C₄	—	2	2	no	—
617	C₂²×C₄	—	2	4	no	—
618	C₂²×C₄	—	2	4	no	—
619	C₂²×C₄	—	2	2	no	—
620	C₂²×C₄	—	2	4	no	—
621	C₂²×C₄	—	2	2	no	—
622	C₂²×C₄	—	8	2	no	—
623	C₂²×C₄	—	8	2	no	—
624	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
625	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
626	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
627	SD₁₆	—	2	8	no	—
628	D₈	—	2	8	no	—
629	D₈	—	2	8	no	—
630	M₁₆	—	2	4	no	—
631	C₂×C₈	—	2	2	no	—
632	C₂×C₈	—	2	2	no	—
633	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
634	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
635	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
636	C₄⋊C₄	—	2	1	no	—
637	C₄⋊C₄	—	2	2	no	—
638	C₄⋊C₄	—	2	1	no	—
639	C₄⋊C₄	—	2	4	no	—
640	C₄⋊C₄	—	2	4	no	—
641	C₄⋊C₄	—	2	4	no	—
642	C₄⋊C₄	—	2	4	no	—
643	C₄⋊C₄	—	2	1	no	—
644	C₄⋊C₄	—	2	1	no	—
645	C₄⋊C₄	—	2	1	no	—
646	C₄⋊C₄	—	2	2	no	—
647	C₄⋊C₄	—	2	1	no	—
648	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
649	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
650	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
651	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
652	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
653	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
654	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
655	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
656	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
657	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
658	C₂²⋊C₄	—	2	2	no	—
659	C₂²⋊C₄	—	2	2	no	—
660	C₂²⋊C₄	—	2	4	no	—
661	C₂²⋊C₄	—	2	4	no	—
662	C₂²⋊C₄	—	2	2	no	—
663	C₂²⋊C₄	—	2	2	no	—
664	C₂²⋊C₄	—	2	2	no	—
665	C₂²⋊C₄	—	2	4	no	—
666	C₂²⋊C₄	—	2	4	no	—
667	C₂²⋊C₄	—	2	2	no	—
668	C₂²⋊C₄	—	2	4	no	—
669	C₂²⋊C₄	—	2	2	no	—
670	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
671	C₄²	—	2	4	no	—
672	C₄²	—	2	2	no	—
673	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
674	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
675	C₄²	C₂⁴×C₁₃	1	4	yes	—
676	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
677	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
678	C₁₃	#61332	1	1	yes	characteristic, direct product factor, Sylow
679	C₂³	—	2	2	no	—
680	C₂³	—	2	4	no	—
681	C₂³	—	2	2	no	—
682	C₂³	—	2	2	no	—
683	C₂³	—	4	2	no	—
684	C₂³	—	8	1	no	—
685	C₂³	—	8	1	no	—
686	C₂³	—	8	1	no	—
687	C₂³	—	8	1	no	—
688	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
689	Q₈	—	2	2	no	—
690	Q₈	—	2	2	no	—
691	Q₈	—	4	2	no	—
692	Q₈	—	4	2	no	—
693	Q₈	—	4	2	no	—
694	Q₈	—	8	4	no	—
695	Q₈	—	8	1	no	—
696	D₄	—	2	4	no	—
697	D₄	—	2	2	no	—
698	D₄	—	2	2	no	—
699	D₄	—	2	2	no	—
700	D₄	—	2	2	no	—
701	D₄	—	2	2	no	—
702	D₄	—	4	2	no	—
703	D₄	—	4	4	no	—
704	D₄	—	4	2	no	—
705	D₄	—	8	1	no	—
706	D₄	—	8	4	no	—
707	D₄	—	8	4	no	—
708	D₄	C₂×C₁₃×#41	1	4	yes	—
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	—	4	1	no	—
715	C₂×C₄	—	4	1	no	—
716	C₂×C₄	—	4	4	no	—
717	C₂×C₄	—	4	4	no	—
718	C₂×C₄	—	4	4	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	—	8	4	no	—
724	C₂×C₄	—	8	1	no	—
725	C₂×C₄	—	8	1	no	—
726	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
727	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
728	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
729	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
730	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
731	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
732	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
733	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
734	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
735	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
736	C₈	—	2	2	no	—
737	C₈	—	2	4	no	—
738	C₈	—	2	2	no	—
739	C₂²	—	2	1	no	—
740	C₂²	—	2	1	no	—
741	C₂²	—	2	4	no	—
742	C₂²	—	4	2	no	—
743	C₂²	—	4	2	no	—
744	C₂²	—	4	2	no	—
745	C₂²	—	4	2	no	—
746	C₂²	—	4	2	no	—
747	C₂²	—	4	2	no	—
748	C₂²	—	4	2	no	—
749	C₂²	—	4	2	no	—
750	C₂²	—	8	4	no	—
751	C₂²	—	8	4	no	—
752	C₂²	C₁₃×#548	1	2	yes	—
753	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
754	C₄	—	2	1	no	—
755	C₄	—	2	1	no	—
756	C₄	—	2	1	no	—
757	C₄	—	2	1	no	—
758	C₄	—	2	4	no	—
759	C₄	—	2	4	no	—
760	C₄	—	4	2	no	—
761	C₄	—	4	2	no	—
762	C₄	—	4	2	no	—
763	C₄	—	4	2	no	—
764	C₄	—	4	2	no	—
765	C₄	C₁₃×#548	1	2	yes	—
766	C₄	C₂²×C₁₃×#41	1	1	yes	characteristic
767	C₄	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
768	C₂	—	2	2	no	—
769	C₂	—	4	4	no	—
770	C₂	—	8	2	no	—
771	C₂	—	8	2	no	—
772	C₂	C₂×C₁₃×#548	1	1	yes	characteristic
773	C₂	C₁₃×#3585	1	1	yes	characteristic
774	C₂	C₁₃×#3585	1	1	yes	characteristic

	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 ◁ C₁₃×#533 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3506	C₂	semidirect
2. C₁₃×#3501	C₂	semidirect
3. C₁₃×#3376	C₂	semidirect
4. C₁₃×#3373	C₂	semidirect
5. C₁₃×#3370	C₂	semidirect
6. C₁₃×#3366	C₂	semidirect
7. C₁₃×#3136	C₂	semidirect
8. C₁₃×#3135	C₂	semidirect
9. C₁₃×#3084	C₂	semidirect
10. C₁₃×#3077	C₂	semidirect
11. C₁₃×#3041	C₂	semidirect
12. C₁₃×#3036	C₂	semidirect
13. C₁₃×#2961	C₂	semidirect
14. C₁₃×#2946	C₂	semidirect
15. C₂×C₁₃×#442	C₂	semidirect
18. C₁₃×#559	C₂²	semidirect
19. C₁₃×#556	C₂²	semidirect
23. C₁₃×#554	C₂²	semidirect
24. C₁₃×#554	C₂²	semidirect
26. C₁₃×#550	C₂²	semidirect
28. D₄×Q₈×C₁₃	C₂²	semidirect
43. C₁₃×#491	C₂²	semidirect
44. C₁₃×#490	C₂²	semidirect
45. C₁₃×#490	C₂²	semidirect
46. C₁₃×#489	C₂²	semidirect
47. C₁₃×#489	C₂²	semidirect
48. C₁₃×#489	C₂²	semidirect
49. C₁₃×#488	C₂²	semidirect
50. C₁₃×#486	C₂²	semidirect
51. C₁₃×#479	C₂²	semidirect
52. C₁₃×#478	C₂²	semidirect
53. C₁₃×#478	C₂²	semidirect
54. C₁₃×#476	C₂²	semidirect
55. C₁₃×#476	C₂²	semidirect
56. C₁₃×#475	C₂²	semidirect
57. C₁₃×#474	C₂²	semidirect
60. C₁₃×#463	C₂²	semidirect
61. C₁₃×#461	C₂²	semidirect
64. C₁₃×#459	C₂²	semidirect
65. C₁₃×#446	C₂²	semidirect
66. C₁₃×#446	C₂²	semidirect
69. C₁₃×#442	C₂²	semidirect
70. C₁₃×#440	C₂²	semidirect
71. C₄×C₁₃×SD₁₆	C₂²	semidirect
72. C₄×C₁₃×D₈	C₂²	semidirect
199. #61332	C₁₃	direct (N × H)
222. C₂×D₄×C₁₃	#41	semidirect
292. #3506	C₂×C₁₃	semidirect
293. #3501	C₂×C₁₃	semidirect
294. #3376	C₂×C₁₃	semidirect
295. #3373	C₂×C₁₃	semidirect
296. #3370	C₂×C₁₃	semidirect
297. #3366	C₂×C₁₃	semidirect
298. #3136	C₂×C₁₃	semidirect
299. #3135	C₂×C₁₃	semidirect
300. #3084	C₂×C₁₃	semidirect
301. #3077	C₂×C₁₃	semidirect
302. #3041	C₂×C₁₃	semidirect
303. #3036	C₂×C₁₃	semidirect
304. #2961	C₂×C₁₃	semidirect
305. #2946	C₂×C₁₃	semidirect
306. C₂×#442	C₂×C₁₃	semidirect
369. #559	C₂²×C₁₃	semidirect
370. #556	C₂²×C₁₃	semidirect
374. #554	C₂²×C₁₃	semidirect
375. #554	C₂²×C₁₃	semidirect
377. #550	C₂²×C₁₃	semidirect
379. D₄×Q₈	C₂²×C₁₃	semidirect
394. #491	C₂²×C₁₃	semidirect
395. #490	C₂²×C₁₃	semidirect
396. #490	C₂²×C₁₃	semidirect
397. #489	C₂²×C₁₃	semidirect
398. #489	C₂²×C₁₃	semidirect
399. #489	C₂²×C₁₃	semidirect
400. #488	C₂²×C₁₃	semidirect
401. #486	C₂²×C₁₃	semidirect
402. #479	C₂²×C₁₃	semidirect
403. #478	C₂²×C₁₃	semidirect
404. #478	C₂²×C₁₃	semidirect
405. #476	C₂²×C₁₃	semidirect
406. #476	C₂²×C₁₃	semidirect
407. #475	C₂²×C₁₃	semidirect
408. #474	C₂²×C₁₃	semidirect
411. #463	C₂²×C₁₃	semidirect
412. #461	C₂²×C₁₃	semidirect
415. #459	C₂²×C₁₃	semidirect
416. #446	C₂²×C₁₃	semidirect
417. #446	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
608. C₂×D₄	C₁₃×#41	semidirect
678. C₁₃	#61332	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×#3506	2
C₁₃×#3501	2
C₁₃×#3376	2
C₁₃×#3373	2
C₁₃×#3370	2
C₁₃×#3366	2
C₁₃×#3136	2
C₁₃×#3135	2
C₁₃×#3084	2
C₁₃×#3077	2
C₁₃×#3041	2
C₁₃×#3036	2
C₁₃×#2961	2
C₁₃×#2946	2
C₂×C₁₃×#442	2
#61332	13

Subgroups — C13×#61332 #15747671

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61332 #15747671