Subgroups — C₁₃×#60827 #15747166

Order 3328.

2154 conjugacy classes of subgroups.

The subgroup lattice has 670 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×#3498	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3224	C₂	1	8	yes	maximal, complemented
4	C₁₃×#3219	C₂	1	4	yes	maximal, complemented
5	C₁₃×#3217	C₂	1	4	yes	maximal, complemented
6	C₁₃×#3153	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₁₃×#496	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#3138	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#3135	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#3043	C₂	1	2	yes	maximal, complemented
11	C₁₃×#3041	C₂	1	2	yes	maximal, complemented
12	C₁₃×#3009	C₂	1	2	yes	maximal, complemented
13	C₁₃×#3008	C₂	1	2	yes	maximal, complemented
14	C₁₃×#2923	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₁₃×H(5,𝔽₂)	C₂²	1	2	yes	—
16	C₂×C₁₃×#137	C₂²	1	2	yes	complemented
17	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	2	yes	complemented
18	C₂²×C₁₃×SD₁₆	C₂²	1	2	yes	complemented
19	C₂²×C₁₃×D₈	C₂²	1	2	yes	complemented
20	C₁₃×#559	—	2	2	no	—
21	C₁₃×#556	—	2	2	no	—
22	C₁₃×#551	—	2	4	no	—
23	C₁₃×#550	—	2	2	no	—
24	D₄²×C₁₃	—	2	2	no	—
25	D₄²×C₁₃	—	2	4	no	—
26	C₁₃×#542	C₂²	1	4	yes	complemented
27	C₁₃×#536	C₂²	1	1	yes	characteristic
28	C₁₃×#535	C₂²	1	2	yes	—
29	C₁₃×#535	C₂²	1	1	yes	characteristic
30	C₁₃×#535	C₂²	1	4	yes	complemented
31	C₁₃×#533	C₂²	1	1	yes	characteristic, complemented
32	C₁₃×#532	C₂²	1	1	yes	characteristic
33	C₁₃×#532	C₂²	1	2	yes	complemented
34	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
35	C₂×C₁₃×#127	C₂²	1	2	yes	complemented
36	C₁₃×#529	C₂²	1	4	yes	complemented
37	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic, complemented
38	C₁₃×#519	C₂²	1	1	yes	characteristic, complemented
39	C₁₃×#518	C₂²	1	1	yes	characteristic, complemented
40	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
41	C₁₃×#497	C₂²	1	2	yes	complemented
42	C₁₃×#496	C₂²	1	4	yes	complemented
43	C₁₃×#496	C₂²	1	4	yes	complemented
44	C₁₃×#496	C₂²	1	2	yes	complemented
45	C₁₃×#495	C₂²	1	4	yes	complemented
46	C₁₃×#491	C₂²	1	2	yes	complemented
47	C₁₃×#490	C₂²	1	2	yes	complemented
48	C₁₃×#490	C₂²	1	4	yes	complemented
49	C₁₃×#489	C₂²	1	4	yes	complemented
50	C₁₃×#486	C₂²	1	4	yes	complemented
51	C₁₃×#464	C₂²	1	8	yes	complemented
52	C₁₃×#463	C₂²	1	8	yes	complemented
53	C₁₃×#460	C₂²	1	8	yes	complemented
54	C₁₃×#459	C₂²	1	8	yes	complemented
55	C₁₃×#452	C₂²	1	8	yes	complemented
56	C₁₃×#450	C₂²	1	8	yes	complemented
57	C₁₃×#449	C₂²	1	8	yes	complemented
58	C₁₃×#447	C₂²	1	8	yes	complemented
59	C₁₃×#433	C₂²	1	4	yes	complemented
60	C₁₃×#432	C₂²	1	4	yes	complemented
61	C₁₃×#424	C₂²	1	2	yes	complemented
62	C₁₃×#418	C₂²	1	2	yes	complemented
63	C₁₃×#418	C₂²	1	2	yes	complemented
64	C₁₃×#416	C₂²	1	2	yes	complemented
65	C₁₃×#416	C₂²	1	2	yes	complemented
66	C₁₃×#408	C₂²	1	2	yes	—
67	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic, complemented
68	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic, complemented
69	C₁₃×H(5,𝔽₂)	—	4	4	no	—
70	C₁₃×H(5,𝔽₂)	—	4	4	no	—
71	C₂×C₁₃×#41	—	2	2	no	—
72	C₂×C₁₃×#41	C₂³	1	2	yes	—
73	C₂×C₁₃×#41	C₂³	1	4	yes	—
74	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
75	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
76	C₂²×D₄×C₁₃	—	2	4	no	—
77	C₂²×D₄×C₁₃	—	2	2	no	—
78	C₂²×D₄×C₁₃	—	2	2	no	—
79	C₂²×D₄×C₁₃	—	2	4	no	—
80	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
81	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
82	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
83	C₁₃×#137	—	4	4	no	—
84	C₁₃×AGL(1,ℤ/8)	—	4	4	no	—
85	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	—
86	C₂×C₁₃×SD₁₆	—	4	4	no	—
87	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
88	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
89	C₂×C₁₃×SD₁₆	C₂³	1	8	yes	—
90	C₂×C₁₃×D₈	—	4	4	no	—
91	C₂×C₁₃×D₈	C₂³	1	4	yes	—
92	C₂×C₁₃×D₈	C₂³	1	8	yes	—
93	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
94	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
95	C₁₃×C₄⋊Q₈	—	2	1	no	—
96	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
97	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
98	C₁₃×#127	—	2	1	no	—
99	C₁₃×#127	—	2	2	no	—
100	C₁₃×#127	—	2	4	no	—
101	C₁₃×#127	C₂³	1	4	yes	—
102	C₁₃×#127	C₂³	1	2	yes	—
103	C₁₃×#127	C₂³	1	2	yes	—
104	C₁₃×#127	C₂³	1	1	yes	characteristic
105	C₁₃×#126	—	2	4	no	—
106	C₁₃×#126	—	2	4	no	—
107	C₁₃×#125	C₂³	1	2	yes	—
108	C₁₃×#124	—	2	1	no	—
109	C₁₃×#124	—	2	1	no	—
110	C₁₃×#124	—	2	4	no	—
111	C₁₃×#124	—	2	2	no	—
112	C₁₃×#124	C₂³	1	4	yes	—
113	C₁₃×#124	C₂³	1	2	yes	—
114	C₁₃×#124	C₂³	1	2	yes	—
115	C₁₃×#124	C₂³	1	2	yes	—
116	C₁₃×#123	—	2	2	no	—
117	C₁₃×#123	—	2	4	no	—
118	C₁₃×#123	—	2	4	no	—
119	C₁₃×C₂²⋊Q₈	—	2	2	no	—
120	C₁₃×C₂²⋊Q₈	—	2	4	no	—
121	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
122	C₁₃×#121	—	2	2	no	—
123	C₁₃×#121	—	2	4	no	—
124	C₁₃×#121	—	2	4	no	—
125	C₁₃×#121	—	2	8	no	—
126	C₁₃×#121	C₂³	1	4	yes	—
127	C₁₃×#120	—	2	2	no	—
128	C₁₃×#120	—	2	4	no	—
129	C₁₃×#120	—	2	8	no	—
130	C₄×Q₈×C₁₃	—	2	2	no	—
131	C₄×Q₈×C₁₃	—	2	2	no	—
132	C₄×Q₈×C₁₃	D₄	1	2	yes	—
133	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
134	C₄×D₄×C₁₃	—	2	4	no	—
135	C₄×D₄×C₁₃	—	2	2	no	—
136	C₄×D₄×C₁₃	—	2	2	no	—
137	C₄×D₄×C₁₃	—	2	4	no	—
138	C₄×D₄×C₁₃	D₄	1	4	yes	—
139	C₄×D₄×C₁₃	D₄	1	2	yes	—
140	C₄×D₄×C₁₃	C₂³	1	4	yes	—
141	C₁₃×#117	—	2	2	no	—
142	C₁₃×#117	—	2	4	no	—
143	C₁₃×#117	C₂³	1	1	yes	characteristic
144	C₁₃×#117	C₂³	1	1	yes	characteristic
145	C₁₃×#117	C₂³	1	1	yes	characteristic
146	C₁₃×#117	C₂³	1	2	yes	—
147	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
148	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
149	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
150	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
151	C₁₃×C₄⋊C₈	C₂³	1	8	yes	—
152	C₁₃×#103	C₂³	1	4	yes	—
153	C₁₃×#103	C₂³	1	4	yes	—
154	C₁₃×#102	C₂³	1	4	yes	—
155	C₁₃×#102	C₂³	1	4	yes	—
156	C₁₃×#102	C₂³	1	8	yes	—
157	C₁₃×#102	C₂³	1	8	yes	—
158	C₁₃×C₂²⋊C₈	C₂³	1	8	yes	—
159	C₁₃×#97	C₂³	1	2	yes	—
160	C₁₃×#97	C₂³	1	2	yes	—
161	C₁₃×#97	C₂³	1	2	yes	—
162	C₄×C₈×C₁₃	C₂³	1	2	yes	—
163	#60827	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
164	C₂⁴×C₁₃	—	2	1	no	—
165	C₂⁴×C₁₃	—	2	4	no	—
166	C₂⁴×C₁₃	—	2	2	no	—
167	C₁₃×#41	—	2	4	no	—
168	C₁₃×#41	—	2	4	no	—
169	C₁₃×#41	—	2	4	no	—
170	C₁₃×#41	—	4	4	no	—
171	C₁₃×#41	—	4	4	no	—
172	C₁₃×#41	—	4	8	no	—
173	C₂×Q₈×C₁₃	—	2	1	no	—
174	C₂×Q₈×C₁₃	—	2	2	no	—
175	C₂×Q₈×C₁₃	—	2	4	no	—
176	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
177	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
178	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
179	C₂×D₄×C₁₃	—	2	4	no	—
180	C₂×D₄×C₁₃	—	2	2	no	—
181	C₂×D₄×C₁₃	—	2	4	no	—
182	C₂×D₄×C₁₃	—	2	1	no	—
183	C₂×D₄×C₁₃	—	2	2	no	—
184	C₂×D₄×C₁₃	—	2	4	no	—
185	C₂×D₄×C₁₃	—	2	4	no	—
186	C₂×D₄×C₁₃	—	2	2	no	—
187	C₂×D₄×C₁₃	—	2	8	no	—
188	C₂×D₄×C₁₃	—	2	4	no	—
189	C₂×D₄×C₁₃	—	2	4	no	—
190	C₂×D₄×C₁₃	—	2	4	no	—
191	C₂×D₄×C₁₃	—	2	4	no	—
192	C₂×D₄×C₁₃	—	4	4	no	—
193	C₂×D₄×C₁₃	—	4	4	no	—
194	C₂×D₄×C₁₃	—	4	16	no	—
195	C₂×D₄×C₁₃	—	4	8	no	—
196	C₂×D₄×C₁₃	—	8	4	no	—
197	C₂×D₄×C₁₃	—	8	8	no	—
198	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
199	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
200	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
201	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
202	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
203	C₂²×C₄×C₁₃	—	2	1	no	—
204	C₂²×C₄×C₁₃	—	2	4	no	—
205	C₂²×C₄×C₁₃	—	2	2	no	—
206	C₂²×C₄×C₁₃	—	2	4	no	—
207	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
208	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
209	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
210	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
211	C₁₃×Q₁₆	—	4	4	no	—
212	C₁₃×SD₁₆	—	4	8	no	—
213	C₁₃×SD₁₆	—	4	4	no	—
214	C₁₃×SD₁₆	—	4	4	no	—
215	C₁₃×D₈	—	4	8	no	—
216	C₁₃×D₈	—	4	4	no	—
217	C₁₃×M₁₆	—	2	4	no	—
218	C₂×C₈×C₁₃	—	2	4	no	—
219	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
220	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
221	C₁₃×C₄⋊C₄	—	2	2	no	—
222	C₁₃×C₄⋊C₄	—	2	4	no	—
223	C₁₃×C₄⋊C₄	—	2	4	no	—
224	C₁₃×C₄⋊C₄	—	2	2	no	—
225	C₁₃×C₄⋊C₄	—	2	2	no	—
226	C₁₃×C₄⋊C₄	—	2	2	no	—
227	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
228	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
229	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
230	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
231	C₁₃×C₂²⋊C₄	—	2	1	no	—
232	C₁₃×C₂²⋊C₄	—	2	1	no	—
233	C₁₃×C₂²⋊C₄	—	2	4	no	—
234	C₁₃×C₂²⋊C₄	—	2	4	no	—
235	C₁₃×C₂²⋊C₄	—	2	4	no	—
236	C₁₃×C₂²⋊C₄	—	2	4	no	—
237	C₁₃×C₂²⋊C₄	—	2	4	no	—
238	C₁₃×C₂²⋊C₄	—	2	8	no	—
239	C₁₃×C₂²⋊C₄	—	2	4	no	—
240	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
241	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
242	C₄²×C₁₃	—	2	4	no	—
243	C₄²×C₁₃	—	2	1	no	—
244	C₄²×C₁₃	—	2	1	no	—
245	C₄²×C₁₃	C₂×D₄	1	4	yes	—
246	C₄²×C₁₃	C₂×D₄	1	2	yes	—
247	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
248	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
249	C₄²×C₁₃	C₂⁴	1	2	yes	—
250	#3510	C₂×C₁₃	1	1	yes	characteristic, complemented
251	#3498	C₂×C₁₃	1	1	yes	characteristic, complemented
252	#3224	C₂×C₁₃	1	8	yes	complemented
253	#3219	C₂×C₁₃	1	4	yes	complemented
254	#3217	C₂×C₁₃	1	4	yes	complemented
255	#3153	C₂×C₁₃	1	1	yes	characteristic, complemented
256	C₂×#496	C₂×C₁₃	1	1	yes	characteristic, complemented
257	#3138	C₂×C₁₃	1	1	yes	characteristic, complemented
258	#3135	C₂×C₁₃	1	1	yes	characteristic, complemented
259	#3043	C₂×C₁₃	1	2	yes	complemented
260	#3041	C₂×C₁₃	1	2	yes	complemented
261	#3009	C₂×C₁₃	1	2	yes	complemented
262	#3008	C₂×C₁₃	1	2	yes	complemented
263	#2923	C₂×C₁₃	1	1	yes	characteristic, complemented
264	C₂³×C₁₃	—	2	2	no	—
265	C₂³×C₁₃	—	2	4	no	—
266	C₂³×C₁₃	—	2	2	no	—
267	C₂³×C₁₃	—	4	8	no	—
268	C₂³×C₁₃	—	4	4	no	—
269	C₂³×C₁₃	—	4	2	no	—
270	C₂³×C₁₃	—	8	4	no	—
271	C₂³×C₁₃	—	8	8	no	—
272	C₂³×C₁₃	—	8	2	no	—
273	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
274	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
275	Q₈×C₁₃	—	2	2	no	—
276	Q₈×C₁₃	—	2	4	no	—
277	Q₈×C₁₃	—	2	2	no	—
278	Q₈×C₁₃	—	2	2	no	—
279	Q₈×C₁₃	—	4	2	no	—
280	Q₈×C₁₃	—	8	2	no	—
281	D₄×C₁₃	—	2	4	no	—
282	D₄×C₁₃	—	2	2	no	—
283	D₄×C₁₃	—	2	4	no	—
284	D₄×C₁₃	—	2	4	no	—
285	D₄×C₁₃	—	2	2	no	—
286	D₄×C₁₃	—	2	4	no	—
287	D₄×C₁₃	—	2	2	no	—
288	D₄×C₁₃	—	4	8	no	—
289	D₄×C₁₃	—	4	4	no	—
290	D₄×C₁₃	—	4	8	no	—
291	D₄×C₁₃	—	4	8	no	—
292	D₄×C₁₃	—	4	4	no	—
293	D₄×C₁₃	—	4	2	no	—
294	D₄×C₁₃	—	4	4	no	—
295	D₄×C₁₃	—	8	8	no	—
296	D₄×C₁₃	—	8	4	no	—
297	D₄×C₁₃	—	8	4	no	—
298	C₂×C₄×C₁₃	—	2	4	no	—
299	C₂×C₄×C₁₃	—	2	2	no	—
300	C₂×C₄×C₁₃	—	2	2	no	—
301	C₂×C₄×C₁₃	—	2	2	no	—
302	C₂×C₄×C₁₃	—	2	2	no	—
303	C₂×C₄×C₁₃	—	4	4	no	—
304	C₂×C₄×C₁₃	—	4	2	no	—
305	C₂×C₄×C₁₃	—	4	8	no	—
306	C₂×C₄×C₁₃	—	4	2	no	—
307	C₂×C₄×C₁₃	—	4	4	no	—
308	C₂×C₄×C₁₃	—	8	4	no	—
309	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
310	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
311	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
312	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
313	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
314	C₂×C₄×C₁₃	H(5,𝔽₂)	1	4	yes	—
315	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
316	C₈×C₁₃	—	2	4	no	—
317	C₈×C₁₃	—	2	4	no	—
318	C₂×H(5,𝔽₂)	C₂²×C₁₃	1	2	yes	—
319	C₂×#137	C₂²×C₁₃	1	2	yes	complemented
320	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	2	yes	complemented
321	C₂²×SD₁₆	C₂²×C₁₃	1	2	yes	complemented
322	C₂²×D₈	C₂²×C₁₃	1	2	yes	complemented
323	#559	—	2	2	no	—
324	#556	—	2	2	no	—
325	#551	—	2	4	no	—
326	#550	—	2	2	no	—
327	D₄²	—	2	2	no	—
328	D₄²	—	2	4	no	—
329	#542	C₂²×C₁₃	1	4	yes	complemented
330	#536	C₂²×C₁₃	1	1	yes	characteristic
331	#535	C₂²×C₁₃	1	2	yes	—
332	#535	C₂²×C₁₃	1	1	yes	characteristic
333	#535	C₂²×C₁₃	1	4	yes	complemented
334	#533	C₂²×C₁₃	1	1	yes	characteristic, complemented
335	#532	C₂²×C₁₃	1	1	yes	characteristic
336	#532	C₂²×C₁₃	1	2	yes	complemented
337	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
338	C₂×#127	C₂²×C₁₃	1	2	yes	complemented
339	#529	C₂²×C₁₃	1	4	yes	complemented
340	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic, complemented
341	#519	C₂²×C₁₃	1	1	yes	characteristic, complemented
342	#518	C₂²×C₁₃	1	1	yes	characteristic, complemented
343	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
344	#497	C₂²×C₁₃	1	2	yes	complemented
345	#496	C₂²×C₁₃	1	4	yes	complemented
346	#496	C₂²×C₁₃	1	4	yes	complemented
347	#496	C₂²×C₁₃	1	2	yes	complemented
348	#495	C₂²×C₁₃	1	4	yes	complemented
349	#491	C₂²×C₁₃	1	2	yes	complemented
350	#490	C₂²×C₁₃	1	2	yes	complemented
351	#490	C₂²×C₁₃	1	4	yes	complemented
352	#489	C₂²×C₁₃	1	4	yes	complemented
353	#486	C₂²×C₁₃	1	4	yes	complemented
354	#464	C₂²×C₁₃	1	8	yes	complemented
355	#463	C₂²×C₁₃	1	8	yes	complemented
356	#460	C₂²×C₁₃	1	8	yes	complemented
357	#459	C₂²×C₁₃	1	8	yes	complemented
358	#452	C₂²×C₁₃	1	8	yes	complemented
359	#450	C₂²×C₁₃	1	8	yes	complemented
360	#449	C₂²×C₁₃	1	8	yes	complemented
361	#447	C₂²×C₁₃	1	8	yes	complemented
362	#433	C₂²×C₁₃	1	4	yes	complemented
363	#432	C₂²×C₁₃	1	4	yes	complemented
364	#424	C₂²×C₁₃	1	2	yes	complemented
365	#418	C₂²×C₁₃	1	2	yes	complemented
366	#418	C₂²×C₁₃	1	2	yes	complemented
367	#416	C₂²×C₁₃	1	2	yes	complemented
368	#416	C₂²×C₁₃	1	2	yes	complemented
369	#408	C₂²×C₁₃	1	2	yes	—
370	C₄×M₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
371	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic, complemented
372	C₂²×C₁₃	—	2	2	no	—
373	C₂²×C₁₃	—	2	4	no	—
374	C₂²×C₁₃	—	2	2	no	—
375	C₂²×C₁₃	—	4	4	no	—
376	C₂²×C₁₃	—	4	8	no	—
377	C₂²×C₁₃	—	4	4	no	—
378	C₂²×C₁₃	—	4	4	no	—
379	C₂²×C₁₃	—	4	2	no	—
380	C₂²×C₁₃	—	4	2	no	—
381	C₂²×C₁₃	—	16	2	no	—
382	C₂²×C₁₃	—	16	4	no	—
383	C₂²×C₁₃	—	16	8	no	—
384	C₂²×C₁₃	#535	1	2	yes	—
385	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
386	C₄×C₁₃	—	2	2	no	—
387	C₄×C₁₃	—	2	4	no	—
388	C₄×C₁₃	—	2	2	no	—
389	C₄×C₁₃	—	2	2	no	—
390	C₄×C₁₃	—	4	2	no	—
391	C₄×C₁₃	—	4	2	no	—
392	C₄×C₁₃	—	4	2	no	—
393	C₄×C₁₃	—	4	2	no	—
394	C₄×C₁₃	#535	1	2	yes	—
395	C₄×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
396	H(5,𝔽₂)	—	4	4	no	—
397	H(5,𝔽₂)	—	4	4	no	—
398	C₂×#41	—	2	2	no	—
399	C₂×#41	C₂³×C₁₃	1	2	yes	—
400	C₂×#41	C₂³×C₁₃	1	4	yes	—
401	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
402	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
403	C₂²×D₄	—	2	4	no	—
404	C₂²×D₄	—	2	2	no	—
405	C₂²×D₄	—	2	2	no	—
406	C₂²×D₄	—	2	4	no	—
407	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
408	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
409	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
410	#137	—	4	4	no	—
411	AGL(1,ℤ/8)	—	4	4	no	—
412	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	—
413	C₂×SD₁₆	—	4	4	no	—
414	C₂×SD₁₆	C₂³×C₁₃	1	8	yes	—
415	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
416	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
417	C₂×D₈	—	4	4	no	—
418	C₂×D₈	C₂³×C₁₃	1	8	yes	—
419	C₂×D₈	C₂³×C₁₃	1	4	yes	—
420	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
421	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
422	C₄⋊Q₈	—	2	1	no	—
423	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
424	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
425	#127	—	2	1	no	—
426	#127	—	2	2	no	—
427	#127	—	2	4	no	—
428	#127	C₂³×C₁₃	1	2	yes	—
429	#127	C₂³×C₁₃	1	2	yes	—
430	#127	C₂³×C₁₃	1	1	yes	characteristic
431	#127	C₂³×C₁₃	1	4	yes	—
432	#126	—	2	4	no	—
433	#126	—	2	4	no	—
434	#125	C₂³×C₁₃	1	2	yes	—
435	#124	—	2	1	no	—
436	#124	—	2	1	no	—
437	#124	—	2	4	no	—
438	#124	—	2	2	no	—
439	#124	C₂³×C₁₃	1	2	yes	—
440	#124	C₂³×C₁₃	1	2	yes	—
441	#124	C₂³×C₁₃	1	2	yes	—
442	#124	C₂³×C₁₃	1	4	yes	—
443	#123	—	2	2	no	—
444	#123	—	2	4	no	—
445	#123	—	2	4	no	—
446	C₂²⋊Q₈	—	2	2	no	—
447	C₂²⋊Q₈	—	2	4	no	—
448	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
449	#121	—	2	2	no	—
450	#121	—	2	4	no	—
451	#121	—	2	4	no	—
452	#121	—	2	8	no	—
453	#121	C₂³×C₁₃	1	4	yes	—
454	#120	—	2	2	no	—
455	#120	—	2	4	no	—
456	#120	—	2	8	no	—
457	C₄×Q₈	—	2	2	no	—
458	C₄×Q₈	—	2	2	no	—
459	C₄×Q₈	D₄×C₁₃	1	2	yes	—
460	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
461	C₄×D₄	—	2	4	no	—
462	C₄×D₄	—	2	2	no	—
463	C₄×D₄	—	2	2	no	—
464	C₄×D₄	—	2	4	no	—
465	C₄×D₄	D₄×C₁₃	1	4	yes	—
466	C₄×D₄	D₄×C₁₃	1	2	yes	—
467	C₄×D₄	C₂³×C₁₃	1	4	yes	—
468	#117	—	2	2	no	—
469	#117	—	2	4	no	—
470	#117	C₂³×C₁₃	1	1	yes	characteristic
471	#117	C₂³×C₁₃	1	1	yes	characteristic
472	#117	C₂³×C₁₃	1	1	yes	characteristic
473	#117	C₂³×C₁₃	1	2	yes	—
474	C₂×C₂²⋊C₄	—	2	2	no	—
475	C₂×C₂²⋊C₄	—	2	2	no	—
476	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
477	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
478	C₄⋊C₈	C₂³×C₁₃	1	8	yes	—
479	#103	C₂³×C₁₃	1	4	yes	—
480	#103	C₂³×C₁₃	1	4	yes	—
481	#102	C₂³×C₁₃	1	4	yes	—
482	#102	C₂³×C₁₃	1	4	yes	—
483	#102	C₂³×C₁₃	1	8	yes	—
484	#102	C₂³×C₁₃	1	8	yes	—
485	C₂²⋊C₈	C₂³×C₁₃	1	8	yes	—
486	#97	C₂³×C₁₃	1	2	yes	—
487	#97	C₂³×C₁₃	1	2	yes	—
488	#97	C₂³×C₁₃	1	2	yes	—
489	C₄×C₈	C₂³×C₁₃	1	2	yes	—
490	C₂×C₁₃	—	2	2	no	—
491	C₂×C₁₃	—	4	2	no	—
492	C₂×C₁₃	—	8	2	no	—
493	C₂×C₁₃	—	8	4	no	—
494	C₂×C₁₃	—	8	2	no	—
495	C₂×C₁₃	C₂×#535	1	1	yes	characteristic
496	C₂×C₁₃	#3585	1	2	yes	—
497	C₂⁴	—	2	1	no	—
498	C₂⁴	—	2	4	no	—
499	C₂⁴	—	2	2	no	—
500	#41	—	2	4	no	—
501	#41	—	2	4	no	—
502	#41	—	2	4	no	—
503	#41	—	4	4	no	—
504	#41	—	4	4	no	—
505	#41	—	4	8	no	—
506	C₂×Q₈	—	2	1	no	—
507	C₂×Q₈	—	2	2	no	—
508	C₂×Q₈	—	2	4	no	—
509	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
510	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
511	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
512	C₂×D₄	—	2	4	no	—
513	C₂×D₄	—	2	2	no	—
514	C₂×D₄	—	2	4	no	—
515	C₂×D₄	—	2	1	no	—
516	C₂×D₄	—	2	2	no	—
517	C₂×D₄	—	2	4	no	—
518	C₂×D₄	—	2	4	no	—
519	C₂×D₄	—	2	2	no	—
520	C₂×D₄	—	2	8	no	—
521	C₂×D₄	—	2	4	no	—
522	C₂×D₄	—	2	4	no	—
523	C₂×D₄	—	2	4	no	—
524	C₂×D₄	—	2	4	no	—
525	C₂×D₄	—	4	4	no	—
526	C₂×D₄	—	4	4	no	—
527	C₂×D₄	—	4	16	no	—
528	C₂×D₄	—	4	8	no	—
529	C₂×D₄	—	8	4	no	—
530	C₂×D₄	—	8	8	no	—
531	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
532	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
533	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
534	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
535	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
536	C₂²×C₄	—	2	1	no	—
537	C₂²×C₄	—	2	4	no	—
538	C₂²×C₄	—	2	2	no	—
539	C₂²×C₄	—	2	4	no	—
540	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
541	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
542	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
543	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
544	Q₁₆	—	4	4	no	—
545	SD₁₆	—	4	8	no	—
546	SD₁₆	—	4	4	no	—
547	SD₁₆	—	4	4	no	—
548	D₈	—	4	8	no	—
549	D₈	—	4	4	no	—
550	M₁₆	—	2	4	no	—
551	C₂×C₈	—	2	4	no	—
552	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
553	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
554	C₄⋊C₄	—	2	2	no	—
555	C₄⋊C₄	—	2	4	no	—
556	C₄⋊C₄	—	2	4	no	—
557	C₄⋊C₄	—	2	2	no	—
558	C₄⋊C₄	—	2	2	no	—
559	C₄⋊C₄	—	2	2	no	—
560	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
561	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
562	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
563	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
564	C₂²⋊C₄	—	2	1	no	—
565	C₂²⋊C₄	—	2	1	no	—
566	C₂²⋊C₄	—	2	4	no	—
567	C₂²⋊C₄	—	2	4	no	—
568	C₂²⋊C₄	—	2	4	no	—
569	C₂²⋊C₄	—	2	4	no	—
570	C₂²⋊C₄	—	2	4	no	—
571	C₂²⋊C₄	—	2	8	no	—
572	C₂²⋊C₄	—	2	4	no	—
573	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
574	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
575	C₄²	—	2	4	no	—
576	C₄²	—	2	1	no	—
577	C₄²	—	2	1	no	—
578	C₄²	C₂×D₄×C₁₃	1	4	yes	—
579	C₄²	C₂×D₄×C₁₃	1	2	yes	—
580	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
581	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
582	C₄²	C₂⁴×C₁₃	1	2	yes	—
583	C₁₃	#60827	1	1	yes	characteristic, direct product factor, Sylow
584	C₂³	—	2	2	no	—
585	C₂³	—	2	4	no	—
586	C₂³	—	2	2	no	—
587	C₂³	—	4	8	no	—
588	C₂³	—	4	4	no	—
589	C₂³	—	4	2	no	—
590	C₂³	—	8	4	no	—
591	C₂³	—	8	8	no	—
592	C₂³	—	8	2	no	—
593	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
594	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
595	Q₈	—	2	2	no	—
596	Q₈	—	2	4	no	—
597	Q₈	—	2	2	no	—
598	Q₈	—	2	2	no	—
599	Q₈	—	4	2	no	—
600	Q₈	—	8	2	no	—
601	D₄	—	2	4	no	—
602	D₄	—	2	2	no	—
603	D₄	—	2	4	no	—
604	D₄	—	2	4	no	—
605	D₄	—	2	2	no	—
606	D₄	—	2	4	no	—
607	D₄	—	2	2	no	—
608	D₄	—	4	8	no	—
609	D₄	—	4	4	no	—
610	D₄	—	4	8	no	—
611	D₄	—	4	8	no	—
612	D₄	—	4	4	no	—
613	D₄	—	4	4	no	—
614	D₄	—	4	2	no	—
615	D₄	—	8	8	no	—
616	D₄	—	8	4	no	—
617	D₄	—	8	4	no	—
618	C₂×C₄	—	2	4	no	—
619	C₂×C₄	—	2	2	no	—
620	C₂×C₄	—	2	2	no	—
621	C₂×C₄	—	2	2	no	—
622	C₂×C₄	—	2	2	no	—
623	C₂×C₄	—	4	4	no	—
624	C₂×C₄	—	4	2	no	—
625	C₂×C₄	—	4	8	no	—
626	C₂×C₄	—	4	2	no	—
627	C₂×C₄	—	4	4	no	—
628	C₂×C₄	—	8	4	no	—
629	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
630	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
631	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
632	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
633	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
634	C₂×C₄	C₁₃×H(5,𝔽₂)	1	4	yes	—
635	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
636	C₈	—	2	4	no	—
637	C₈	—	2	4	no	—
638	C₂²	—	2	2	no	—
639	C₂²	—	2	4	no	—
640	C₂²	—	2	2	no	—
641	C₂²	—	4	4	no	—
642	C₂²	—	4	8	no	—
643	C₂²	—	4	4	no	—
644	C₂²	—	4	4	no	—
645	C₂²	—	4	2	no	—
646	C₂²	—	4	2	no	—
647	C₂²	—	16	4	no	—
648	C₂²	—	16	2	no	—
649	C₂²	—	16	8	no	—
650	C₂²	C₁₃×#535	1	2	yes	—
651	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
652	C₄	—	2	2	no	—
653	C₄	—	2	4	no	—
654	C₄	—	2	2	no	—
655	C₄	—	2	2	no	—
656	C₄	—	4	2	no	—
657	C₄	—	4	2	no	—
658	C₄	—	4	2	no	—
659	C₄	—	4	2	no	—
660	C₄	C₁₃×#535	1	2	yes	—
661	C₄	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
662	C₂	—	2	2	no	—
663	C₂	—	4	2	no	—
664	C₂	—	8	4	no	—
665	C₂	—	8	2	no	—
666	C₂	—	8	2	no	—
667	C₂	C₂×C₁₃×#535	1	1	yes	characteristic
668	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×#3498	C₂	semidirect
3. C₁₃×#3224	C₂	semidirect
4. C₁₃×#3219	C₂	semidirect
5. C₁₃×#3217	C₂	semidirect
6. C₁₃×#3153	C₂	semidirect
7. C₂×C₁₃×#496	C₂	semidirect
8. C₁₃×#3138	C₂	semidirect
9. C₁₃×#3135	C₂	semidirect
10. C₁₃×#3043	C₂	semidirect
11. C₁₃×#3041	C₂	semidirect
12. C₁₃×#3009	C₂	semidirect
13. C₁₃×#3008	C₂	semidirect
14. C₁₃×#2923	C₂	semidirect
16. C₂×C₁₃×#137	C₂²	semidirect
17. C₂×C₁₃×AGL(1,ℤ/8)	C₂²	semidirect
18. C₂²×C₁₃×SD₁₆	C₂²	semidirect
19. C₂²×C₁₃×D₈	C₂²	semidirect
26. C₁₃×#542	C₂²	semidirect
30. C₁₃×#535	C₂²	semidirect
31. C₁₃×#533	C₂²	semidirect
33. C₁₃×#532	C₂²	semidirect
35. C₂×C₁₃×#127	C₂²	semidirect
36. C₁₃×#529	C₂²	semidirect
37. C₂×C₁₃×#124	C₂²	semidirect
38. C₁₃×#519	C₂²	semidirect
39. C₁₃×#518	C₂²	semidirect
41. C₁₃×#497	C₂²	semidirect
42. C₁₃×#496	C₂²	semidirect
43. C₁₃×#496	C₂²	semidirect
44. C₁₃×#496	C₂²	semidirect
45. C₁₃×#495	C₂²	semidirect
46. C₁₃×#491	C₂²	semidirect
47. C₁₃×#490	C₂²	semidirect
48. C₁₃×#490	C₂²	semidirect
49. C₁₃×#489	C₂²	semidirect
50. C₁₃×#486	C₂²	semidirect
51. C₁₃×#464	C₂²	semidirect
52. C₁₃×#463	C₂²	semidirect
53. C₁₃×#460	C₂²	semidirect
54. C₁₃×#459	C₂²	semidirect
55. C₁₃×#452	C₂²	semidirect
56. C₁₃×#450	C₂²	semidirect
57. C₁₃×#449	C₂²	semidirect
58. C₁₃×#447	C₂²	semidirect
59. C₁₃×#433	C₂²	semidirect
60. C₁₃×#432	C₂²	semidirect
61. C₁₃×#424	C₂²	semidirect
62. C₁₃×#418	C₂²	semidirect
63. C₁₃×#418	C₂²	semidirect
64. C₁₃×#416	C₂²	semidirect
65. C₁₃×#416	C₂²	semidirect
67. C₄×C₁₃×M₁₆	C₂²	semidirect
68. C₂×C₁₃×#97	C₂²	semidirect
163. #60827	C₁₃	direct (N × H)
250. #3510	C₂×C₁₃	semidirect
251. #3498	C₂×C₁₃	semidirect
252. #3224	C₂×C₁₃	semidirect
253. #3219	C₂×C₁₃	semidirect
254. #3217	C₂×C₁₃	semidirect
255. #3153	C₂×C₁₃	semidirect
256. C₂×#496	C₂×C₁₃	semidirect
257. #3138	C₂×C₁₃	semidirect
258. #3135	C₂×C₁₃	semidirect
259. #3043	C₂×C₁₃	semidirect
260. #3041	C₂×C₁₃	semidirect
261. #3009	C₂×C₁₃	semidirect
262. #3008	C₂×C₁₃	semidirect
263. #2923	C₂×C₁₃	semidirect
319. C₂×#137	C₂²×C₁₃	semidirect
320. C₂×AGL(1,ℤ/8)	C₂²×C₁₃	semidirect
321. C₂²×SD₁₆	C₂²×C₁₃	semidirect
322. C₂²×D₈	C₂²×C₁₃	semidirect
329. #542	C₂²×C₁₃	semidirect
333. #535	C₂²×C₁₃	semidirect
334. #533	C₂²×C₁₃	semidirect
336. #532	C₂²×C₁₃	semidirect
338. C₂×#127	C₂²×C₁₃	semidirect
339. #529	C₂²×C₁₃	semidirect
340. C₂×#124	C₂²×C₁₃	semidirect
341. #519	C₂²×C₁₃	semidirect
342. #518	C₂²×C₁₃	semidirect
344. #497	C₂²×C₁₃	semidirect
345. #496	C₂²×C₁₃	semidirect
346. #496	C₂²×C₁₃	semidirect
347. #496	C₂²×C₁₃	semidirect
348. #495	C₂²×C₁₃	semidirect
349. #491	C₂²×C₁₃	semidirect
350. #490	C₂²×C₁₃	semidirect
351. #490	C₂²×C₁₃	semidirect
352. #489	C₂²×C₁₃	semidirect
353. #486	C₂²×C₁₃	semidirect
354. #464	C₂²×C₁₃	semidirect
355. #463	C₂²×C₁₃	semidirect
356. #460	C₂²×C₁₃	semidirect
357. #459	C₂²×C₁₃	semidirect
358. #452	C₂²×C₁₃	semidirect
359. #450	C₂²×C₁₃	semidirect
360. #449	C₂²×C₁₃	semidirect
361. #447	C₂²×C₁₃	semidirect
362. #433	C₂²×C₁₃	semidirect
363. #432	C₂²×C₁₃	semidirect
364. #424	C₂²×C₁₃	semidirect
365. #418	C₂²×C₁₃	semidirect
366. #418	C₂²×C₁₃	semidirect
367. #416	C₂²×C₁₃	semidirect
368. #416	C₂²×C₁₃	semidirect
370. C₄×M₁₆	C₂²×C₁₃	semidirect
371. C₂×#97	C₂²×C₁₃	semidirect
583. C₁₃	#60827	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×#3498	2
C₁₃×#3224	2
C₁₃×#3219	2
C₁₃×#3217	2
C₁₃×#3153	2
C₂×C₁₃×#496	2
C₁₃×#3138	2
C₁₃×#3135	2
C₁₃×#3043	2
C₁₃×#3041	2
C₁₃×#3009	2
C₁₃×#3008	2
C₁₃×#2923	2
#60827	13

Subgroups — C13×#60827 #15747166

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#60827 #15747166