Subgroups — C₁₃×#60802 #15747141

Order 3328.

2186 conjugacy classes of subgroups.

The subgroup lattice has 574 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3444	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#532	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3216	C₂	1	4	yes	maximal, complemented
4	C₁₃×#3214	C₂	1	4	yes	maximal, complemented
5	C₁₃×#3212	C₂	1	8	yes	maximal, complemented
6	C₁₃×#3153	C₂	1	2	yes	maximal, complemented
7	C₁₃×#3140	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3039	C₂	1	2	yes	maximal, complemented
9	C₁₃×#3038	C₂	1	2	yes	maximal, complemented
10	C₁₃×#3005	C₂	1	4	yes	maximal, complemented
11	C₁₃×#2920	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₁₃×#41	C₂²	1	2	yes	—
13	C₂×C₁₃×#137	C₂²	1	4	yes	—
14	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	4	yes	—
15	C₁₃×#533	C₂²	1	1	yes	characteristic
16	C₁₃×#533	C₂²	1	2	yes	complemented
17	C₁₃×#532	—	2	2	no	—
18	C₁₃×#532	—	2	2	no	—
19	C₁₃×#532	C₂²	1	1	yes	characteristic
20	C₁₃×#532	C₂²	1	4	yes	—
21	C₁₃×#532	C₂²	1	4	yes	—
22	C₁₃×#532	C₂²	1	2	yes	complemented
23	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
24	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
25	C₁₃×#529	—	2	2	no	—
26	C₁₃×#529	—	2	2	no	—
27	C₁₃×#529	C₂²	1	4	yes	complemented
28	C₂×C₁₃×#124	C₂²	1	2	yes	—
29	C₁₃×#525	—	2	2	no	—
30	C₁₃×#525	C₂²	1	2	yes	—
31	C₂×C₁₃×#121	—	2	2	no	—
32	C₄×C₁₃×#41	—	2	2	no	—
33	C₄×C₁₃×#41	C₂²	1	2	yes	—
34	C₂×C₄×D₄×C₁₃	—	2	2	no	—
35	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
36	C₁₃×#497	C₂²	1	4	yes	complemented
37	C₁₃×#496	C₂²	1	4	yes	complemented
38	C₁₃×#495	C₂²	1	8	yes	complemented
39	C₁₃×#489	C₂²	1	8	yes	complemented
40	C₁₃×#488	C₂²	1	8	yes	complemented
41	C₁₃×#462	C₂²	1	8	yes	complemented
42	C₁₃×#461	C₂²	1	8	yes	complemented
43	C₁₃×#460	C₂²	1	8	yes	complemented
44	C₁₃×#459	C₂²	1	8	yes	complemented
45	C₁₃×#452	C₂²	1	16	yes	complemented
46	C₁₃×#449	C₂²	1	16	yes	complemented
47	C₁₃×#432	C₂²	1	4	yes	complemented
48	C₁₃×#431	C₂²	1	4	yes	complemented
49	C₁₃×#423	C₂²	1	2	yes	—
50	C₁₃×#419	C₂²	1	4	yes	—
51	C₁₃×#418	C₂²	1	4	yes	—
52	C₁₃×#407	C₂²	1	2	yes	—
53	C₄×C₁₃×M₁₆	C₂²	1	2	yes	—
54	C₂×C₁₃×#41	—	2	2	no	—
55	C₂×C₁₃×#41	—	2	4	no	—
56	C₂×C₁₃×#41	—	4	8	no	—
57	C₂×C₁₃×#41	C₂³	1	2	yes	—
58	C₂×C₁₃×#41	C₂³	1	8	yes	—
59	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
60	C₂²×D₄×C₁₃	—	2	2	no	—
61	C₂²×D₄×C₁₃	—	2	2	no	—
62	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
63	C₂³×C₄×C₁₃	—	2	2	no	—
64	C₂³×C₄×C₁₃	D₄	1	2	yes	—
65	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
66	C₁₃×#137	—	4	8	no	—
67	C₁₃×AGL(1,ℤ/8)	—	4	8	no	—
68	C₂×C₁₃×Q₁₆	C₂³	1	8	yes	—
69	C₂×C₁₃×SD₁₆	C₂³	1	8	yes	—
70	C₂×C₁₃×SD₁₆	C₂³	1	8	yes	—
71	C₂×C₁₃×D₈	C₂³	1	8	yes	—
72	C₂×C₁₃×M₁₆	C₂³	1	4	yes	—
73	C₁₃×C₄⋊Q₈	—	2	1	no	—
74	C₁₃×C₄⋊Q₈	—	2	1	no	—
75	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
76	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
77	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
78	C₁₃×#127	—	2	1	no	—
79	C₁₃×#127	—	2	1	no	—
80	C₁₃×#127	C₂³	1	4	yes	—
81	C₁₃×#127	C₂³	1	1	yes	characteristic
82	C₁₃×#126	—	2	4	no	—
83	C₁₃×#125	—	2	2	no	—
84	C₁₃×#125	C₂³	1	2	yes	—
85	C₁₃×#124	—	2	4	no	—
86	C₁₃×#124	—	2	2	no	—
87	C₁₃×#124	C₂³	1	4	yes	—
88	C₁₃×#124	C₂³	1	4	yes	—
89	C₁₃×#124	C₂³	1	2	yes	—
90	C₁₃×#123	—	2	4	no	—
91	C₁₃×#123	—	2	2	no	—
92	C₁₃×C₂²⋊Q₈	—	2	2	no	—
93	C₁₃×C₂²⋊Q₈	—	2	2	no	—
94	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
95	C₁₃×#121	—	2	4	no	—
96	C₁₃×#121	—	2	4	no	—
97	C₁₃×#121	—	2	4	no	—
98	C₁₃×#121	—	2	4	no	—
99	C₁₃×#121	—	2	2	no	—
100	C₁₃×#121	—	2	2	no	—
101	C₁₃×#121	C₂³	1	4	yes	—
102	C₁₃×#120	—	2	2	no	—
103	C₄×Q₈×C₁₃	—	2	2	no	—
104	C₄×Q₈×C₁₃	—	2	2	no	—
105	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
106	C₄×D₄×C₁₃	—	2	4	no	—
107	C₄×D₄×C₁₃	—	2	4	no	—
108	C₄×D₄×C₁₃	—	2	4	no	—
109	C₄×D₄×C₁₃	—	2	4	no	—
110	C₄×D₄×C₁₃	—	2	4	no	—
111	C₄×D₄×C₁₃	—	2	4	no	—
112	C₄×D₄×C₁₃	—	2	4	no	—
113	C₄×D₄×C₁₃	—	2	2	no	—
114	C₄×D₄×C₁₃	—	2	2	no	—
115	C₄×D₄×C₁₃	C₂³	1	4	yes	—
116	C₁₃×#117	—	2	2	no	—
117	C₁₃×#117	—	2	4	no	—
118	C₁₃×#117	—	2	2	no	—
119	C₁₃×#117	C₂³	1	2	yes	—
120	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
121	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
122	C₂×C₄²×C₁₃	—	2	2	no	—
123	C₂×C₄²×C₁₃	D₄	1	2	yes	—
124	C₂×C₄²×C₁₃	D₄	1	2	yes	—
125	C₂×C₄²×C₁₃	D₄	1	2	yes	—
126	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
127	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
128	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
129	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
130	C₁₃×C₄⋊C₈	C₂³	1	8	yes	—
131	C₁₃×#103	C₂³	1	16	yes	—
132	C₁₃×#102	C₂³	1	16	yes	—
133	C₁₃×C₂²⋊C₈	C₂³	1	8	yes	—
134	C₁₃×#97	C₂³	1	4	yes	—
135	C₄×C₈×C₁₃	C₂³	1	4	yes	—
136	#60802	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
137	C₂⁴×C₁₃	—	2	2	no	—
138	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
139	C₁₃×#41	—	2	4	no	—
140	C₁₃×#41	—	2	4	no	—
141	C₁₃×#41	—	4	16	no	—
142	C₁₃×#41	—	4	8	no	—
143	C₁₃×#41	—	4	16	no	—
144	C₂×Q₈×C₁₃	—	2	2	no	—
145	C₂×Q₈×C₁₃	—	2	2	no	—
146	C₂×Q₈×C₁₃	—	2	8	no	—
147	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
148	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
149	C₂×D₄×C₁₃	—	2	2	no	—
150	C₂×D₄×C₁₃	—	2	4	no	—
151	C₂×D₄×C₁₃	—	2	8	no	—
152	C₂×D₄×C₁₃	—	2	2	no	—
153	C₂×D₄×C₁₃	—	2	4	no	—
154	C₂×D₄×C₁₃	—	2	4	no	—
155	C₂×D₄×C₁₃	—	2	2	no	—
156	C₂×D₄×C₁₃	—	2	8	no	—
157	C₂×D₄×C₁₃	—	4	8	no	—
158	C₂×D₄×C₁₃	—	4	8	no	—
159	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
160	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
161	C₂²×C₄×C₁₃	—	2	4	no	—
162	C₂²×C₄×C₁₃	—	2	2	no	—
163	C₂²×C₄×C₁₃	—	2	2	no	—
164	C₂²×C₄×C₁₃	—	2	4	no	—
165	C₂²×C₄×C₁₃	—	2	8	no	—
166	C₂²×C₄×C₁₃	—	4	4	no	—
167	C₂²×C₄×C₁₃	—	4	8	no	—
168	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
169	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
170	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
171	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
172	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
173	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
174	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
175	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
176	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
177	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
178	C₁₃×Q₁₆	—	4	8	no	—
179	C₁₃×SD₁₆	—	4	8	no	—
180	C₁₃×SD₁₆	—	4	8	no	—
181	C₁₃×D₈	—	4	8	no	—
182	C₁₃×M₁₆	—	2	8	no	—
183	C₂×C₈×C₁₃	C₂⁴	1	8	yes	—
184	C₁₃×C₄⋊C₄	—	2	4	no	—
185	C₁₃×C₄⋊C₄	—	2	4	no	—
186	C₁₃×C₄⋊C₄	—	2	2	no	—
187	C₁₃×C₄⋊C₄	—	2	2	no	—
188	C₁₃×C₄⋊C₄	—	2	4	no	—
189	C₁₃×C₄⋊C₄	—	2	4	no	—
190	C₁₃×C₄⋊C₄	—	2	4	no	—
191	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
192	C₁₃×C₂²⋊C₄	—	2	4	no	—
193	C₁₃×C₂²⋊C₄	—	2	2	no	—
194	C₁₃×C₂²⋊C₄	—	2	8	no	—
195	C₁₃×C₂²⋊C₄	—	2	8	no	—
196	C₁₃×C₂²⋊C₄	—	2	4	no	—
197	C₁₃×C₂²⋊C₄	—	2	4	no	—
198	C₁₃×C₂²⋊C₄	—	2	4	no	—
199	C₄²×C₁₃	—	2	4	no	—
200	C₄²×C₁₃	—	2	2	no	—
201	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
202	C₄²×C₁₃	C₂×D₄	1	2	yes	—
203	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
204	C₄²×C₁₃	C₂×D₄	1	2	yes	—
205	C₄²×C₁₃	C₂×D₄	1	2	yes	—
206	C₄²×C₁₃	C₂×D₄	1	2	yes	—
207	C₄²×C₁₃	C₂×D₄	1	2	yes	—
208	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
209	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
210	C₄²×C₁₃	C₂⁴	1	2	yes	—
211	#3444	C₂×C₁₃	1	1	yes	characteristic, complemented
212	C₂×#532	C₂×C₁₃	1	1	yes	characteristic, complemented
213	#3216	C₂×C₁₃	1	4	yes	complemented
214	#3214	C₂×C₁₃	1	4	yes	complemented
215	#3212	C₂×C₁₃	1	8	yes	complemented
216	#3153	C₂×C₁₃	1	2	yes	complemented
217	#3140	C₂×C₁₃	1	2	yes	complemented
218	#3039	C₂×C₁₃	1	2	yes	complemented
219	#3038	C₂×C₁₃	1	2	yes	complemented
220	#3005	C₂×C₁₃	1	4	yes	complemented
221	#2920	C₂×C₁₃	1	1	yes	characteristic, complemented
222	C₂³×C₁₃	—	2	2	no	—
223	C₂³×C₁₃	—	2	2	no	—
224	C₂³×C₁₃	—	2	4	no	—
225	C₂³×C₁₃	—	4	2	no	—
226	C₂³×C₁₃	—	4	8	no	—
227	C₂³×C₁₃	—	4	4	no	—
228	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
229	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
230	Q₈×C₁₃	—	2	2	no	—
231	Q₈×C₁₃	—	2	8	no	—
232	Q₈×C₁₃	—	2	2	no	—
233	Q₈×C₁₃	—	4	4	no	—
234	Q₈×C₁₃	—	4	4	no	—
235	D₄×C₁₃	—	2	2	no	—
236	D₄×C₁₃	—	2	8	no	—
237	D₄×C₁₃	—	2	2	no	—
238	D₄×C₁₃	—	4	8	no	—
239	D₄×C₁₃	—	4	4	no	—
240	D₄×C₁₃	—	4	16	no	—
241	D₄×C₁₃	—	4	8	no	—
242	D₄×C₁₃	—	4	4	no	—
243	D₄×C₁₃	—	4	4	no	—
244	D₄×C₁₃	—	4	8	no	—
245	C₂×C₄×C₁₃	—	2	2	no	—
246	C₂×C₄×C₁₃	—	2	4	no	—
247	C₂×C₄×C₁₃	—	2	4	no	—
248	C₂×C₄×C₁₃	—	2	4	no	—
249	C₂×C₄×C₁₃	—	2	4	no	—
250	C₂×C₄×C₁₃	—	2	4	no	—
251	C₂×C₄×C₁₃	—	2	2	no	—
252	C₂×C₄×C₁₃	—	2	4	no	—
253	C₂×C₄×C₁₃	—	2	4	no	—
254	C₂×C₄×C₁₃	—	4	2	no	—
255	C₂×C₄×C₁₃	—	4	2	no	—
256	C₂×C₄×C₁₃	—	4	2	no	—
257	C₂×C₄×C₁₃	—	4	16	no	—
258	C₂×C₄×C₁₃	—	4	4	no	—
259	C₂×C₄×C₁₃	—	4	4	no	—
260	C₂×C₄×C₁₃	—	4	8	no	—
261	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
262	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
263	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
264	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
265	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
266	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
267	C₂×C₄×C₁₃	H(5,𝔽₂)	1	4	yes	—
268	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
269	C₈×C₁₃	—	2	8	no	—
270	C₂²×#41	C₂²×C₁₃	1	2	yes	—
271	C₂×#137	C₂²×C₁₃	1	4	yes	—
272	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	4	yes	—
273	#533	C₂²×C₁₃	1	1	yes	characteristic
274	#533	C₂²×C₁₃	1	2	yes	complemented
275	#532	—	2	2	no	—
276	#532	—	2	2	no	—
277	#532	C₂²×C₁₃	1	1	yes	characteristic
278	#532	C₂²×C₁₃	1	4	yes	—
279	#532	C₂²×C₁₃	1	4	yes	—
280	#532	C₂²×C₁₃	1	2	yes	complemented
281	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
282	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
283	#529	—	2	2	no	—
284	#529	—	2	2	no	—
285	#529	C₂²×C₁₃	1	4	yes	complemented
286	C₂×#124	C₂²×C₁₃	1	2	yes	—
287	#525	—	2	2	no	—
288	#525	C₂²×C₁₃	1	2	yes	—
289	C₂×#121	—	2	2	no	—
290	C₄×#41	—	2	2	no	—
291	C₄×#41	C₂²×C₁₃	1	2	yes	—
292	C₂×C₄×D₄	—	2	2	no	—
293	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
294	#497	C₂²×C₁₃	1	4	yes	complemented
295	#496	C₂²×C₁₃	1	4	yes	complemented
296	#495	C₂²×C₁₃	1	8	yes	complemented
297	#489	C₂²×C₁₃	1	8	yes	complemented
298	#488	C₂²×C₁₃	1	8	yes	complemented
299	#462	C₂²×C₁₃	1	8	yes	complemented
300	#461	C₂²×C₁₃	1	8	yes	complemented
301	#460	C₂²×C₁₃	1	8	yes	complemented
302	#459	C₂²×C₁₃	1	8	yes	complemented
303	#452	C₂²×C₁₃	1	16	yes	complemented
304	#449	C₂²×C₁₃	1	16	yes	complemented
305	#432	C₂²×C₁₃	1	4	yes	complemented
306	#431	C₂²×C₁₃	1	4	yes	complemented
307	#423	C₂²×C₁₃	1	2	yes	—
308	#419	C₂²×C₁₃	1	4	yes	—
309	#418	C₂²×C₁₃	1	4	yes	—
310	#407	C₂²×C₁₃	1	2	yes	—
311	C₄×M₁₆	C₂²×C₁₃	1	2	yes	—
312	C₂²×C₁₃	—	2	2	no	—
313	C₂²×C₁₃	—	2	2	no	—
314	C₂²×C₁₃	—	2	2	no	—
315	C₂²×C₁₃	—	2	2	no	—
316	C₂²×C₁₃	—	4	4	no	—
317	C₂²×C₁₃	—	4	4	no	—
318	C₂²×C₁₃	—	4	2	no	—
319	C₂²×C₁₃	—	4	4	no	—
320	C₂²×C₁₃	—	4	8	no	—
321	C₂²×C₁₃	—	8	8	no	—
322	C₂²×C₁₃	#535	1	2	yes	—
323	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
324	C₄×C₁₃	—	2	2	no	—
325	C₄×C₁₃	—	2	2	no	—
326	C₄×C₁₃	—	2	2	no	—
327	C₄×C₁₃	—	2	2	no	—
328	C₄×C₁₃	—	4	4	no	—
329	C₄×C₁₃	—	4	2	no	—
330	C₄×C₁₃	—	4	4	no	—
331	C₄×C₁₃	#535	1	2	yes	—
332	C₄×C₁₃	#575	1	4	yes	—
333	C₄×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
334	C₂×#41	—	2	2	no	—
335	C₂×#41	—	2	4	no	—
336	C₂×#41	—	4	8	no	—
337	C₂×#41	C₂³×C₁₃	1	2	yes	—
338	C₂×#41	C₂³×C₁₃	1	8	yes	—
339	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
340	C₂²×D₄	—	2	2	no	—
341	C₂²×D₄	—	2	2	no	—
342	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
343	C₂³×C₄	—	2	2	no	—
344	C₂³×C₄	D₄×C₁₃	1	2	yes	—
345	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
346	#137	—	4	8	no	—
347	AGL(1,ℤ/8)	—	4	8	no	—
348	C₂×Q₁₆	C₂³×C₁₃	1	8	yes	—
349	C₂×SD₁₆	C₂³×C₁₃	1	8	yes	—
350	C₂×SD₁₆	C₂³×C₁₃	1	8	yes	—
351	C₂×D₈	C₂³×C₁₃	1	8	yes	—
352	C₂×M₁₆	C₂³×C₁₃	1	4	yes	—
353	C₄⋊Q₈	—	2	1	no	—
354	C₄⋊Q₈	—	2	1	no	—
355	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
356	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
357	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
358	#127	—	2	1	no	—
359	#127	—	2	1	no	—
360	#127	C₂³×C₁₃	1	4	yes	—
361	#127	C₂³×C₁₃	1	1	yes	characteristic
362	#126	—	2	4	no	—
363	#125	—	2	2	no	—
364	#125	C₂³×C₁₃	1	2	yes	—
365	#124	—	2	4	no	—
366	#124	—	2	2	no	—
367	#124	C₂³×C₁₃	1	4	yes	—
368	#124	C₂³×C₁₃	1	4	yes	—
369	#124	C₂³×C₁₃	1	2	yes	—
370	#123	—	2	4	no	—
371	#123	—	2	2	no	—
372	C₂²⋊Q₈	—	2	2	no	—
373	C₂²⋊Q₈	—	2	2	no	—
374	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
375	#121	—	2	4	no	—
376	#121	—	2	4	no	—
377	#121	—	2	4	no	—
378	#121	—	2	4	no	—
379	#121	—	2	2	no	—
380	#121	—	2	2	no	—
381	#121	C₂³×C₁₃	1	4	yes	—
382	#120	—	2	2	no	—
383	C₄×Q₈	—	2	2	no	—
384	C₄×Q₈	—	2	2	no	—
385	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
386	C₄×D₄	—	2	4	no	—
387	C₄×D₄	—	2	4	no	—
388	C₄×D₄	—	2	4	no	—
389	C₄×D₄	—	2	4	no	—
390	C₄×D₄	—	2	4	no	—
391	C₄×D₄	—	2	4	no	—
392	C₄×D₄	—	2	4	no	—
393	C₄×D₄	—	2	2	no	—
394	C₄×D₄	—	2	2	no	—
395	C₄×D₄	C₂³×C₁₃	1	4	yes	—
396	#117	—	2	2	no	—
397	#117	—	2	4	no	—
398	#117	—	2	2	no	—
399	#117	C₂³×C₁₃	1	2	yes	—
400	C₂×C₄⋊C₄	—	2	2	no	—
401	C₂×C₂²⋊C₄	—	2	4	no	—
402	C₂×C₄²	—	2	2	no	—
403	C₂×C₄²	D₄×C₁₃	1	2	yes	—
404	C₂×C₄²	D₄×C₁₃	1	2	yes	—
405	C₂×C₄²	D₄×C₁₃	1	2	yes	—
406	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
407	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
408	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
409	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
410	C₄⋊C₈	C₂³×C₁₃	1	8	yes	—
411	#103	C₂³×C₁₃	1	16	yes	—
412	#102	C₂³×C₁₃	1	16	yes	—
413	C₂²⋊C₈	C₂³×C₁₃	1	8	yes	—
414	#97	C₂³×C₁₃	1	4	yes	—
415	C₄×C₈	C₂³×C₁₃	1	4	yes	—
416	C₂×C₁₃	—	2	2	no	—
417	C₂×C₁₃	—	4	2	no	—
418	C₂×C₁₃	—	8	2	no	—
419	C₂×C₁₃	—	8	4	no	—
420	C₂×C₁₃	C₂×#535	1	1	yes	characteristic
421	C₂×C₁₃	C₂×#575	1	2	yes	—
422	C₂⁴	—	2	2	no	—
423	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
424	#41	—	2	4	no	—
425	#41	—	2	4	no	—
426	#41	—	4	16	no	—
427	#41	—	4	16	no	—
428	#41	—	4	8	no	—
429	C₂×Q₈	—	2	2	no	—
430	C₂×Q₈	—	2	2	no	—
431	C₂×Q₈	—	2	8	no	—
432	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
433	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
434	C₂×D₄	—	2	2	no	—
435	C₂×D₄	—	2	4	no	—
436	C₂×D₄	—	2	8	no	—
437	C₂×D₄	—	2	2	no	—
438	C₂×D₄	—	2	4	no	—
439	C₂×D₄	—	2	4	no	—
440	C₂×D₄	—	2	2	no	—
441	C₂×D₄	—	2	8	no	—
442	C₂×D₄	—	4	8	no	—
443	C₂×D₄	—	4	8	no	—
444	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
445	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
446	C₂²×C₄	—	2	4	no	—
447	C₂²×C₄	—	2	2	no	—
448	C₂²×C₄	—	2	2	no	—
449	C₂²×C₄	—	2	4	no	—
450	C₂²×C₄	—	2	8	no	—
451	C₂²×C₄	—	4	4	no	—
452	C₂²×C₄	—	4	8	no	—
453	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
454	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
455	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
456	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
457	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
458	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
459	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
460	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
461	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
462	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
463	Q₁₆	—	4	8	no	—
464	SD₁₆	—	4	8	no	—
465	SD₁₆	—	4	8	no	—
466	D₈	—	4	8	no	—
467	M₁₆	—	2	8	no	—
468	C₂×C₈	C₂⁴×C₁₃	1	8	yes	—
469	C₄⋊C₄	—	2	4	no	—
470	C₄⋊C₄	—	2	4	no	—
471	C₄⋊C₄	—	2	2	no	—
472	C₄⋊C₄	—	2	2	no	—
473	C₄⋊C₄	—	2	4	no	—
474	C₄⋊C₄	—	2	4	no	—
475	C₄⋊C₄	—	2	4	no	—
476	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
477	C₂²⋊C₄	—	2	4	no	—
478	C₂²⋊C₄	—	2	2	no	—
479	C₂²⋊C₄	—	2	8	no	—
480	C₂²⋊C₄	—	2	8	no	—
481	C₂²⋊C₄	—	2	4	no	—
482	C₂²⋊C₄	—	2	4	no	—
483	C₂²⋊C₄	—	2	4	no	—
484	C₄²	—	2	4	no	—
485	C₄²	—	2	2	no	—
486	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
487	C₄²	C₂×D₄×C₁₃	1	2	yes	—
488	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
489	C₄²	C₂×D₄×C₁₃	1	2	yes	—
490	C₄²	C₂×D₄×C₁₃	1	2	yes	—
491	C₄²	C₂×D₄×C₁₃	1	2	yes	—
492	C₄²	C₂×D₄×C₁₃	1	2	yes	—
493	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
494	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
495	C₄²	C₂⁴×C₁₃	1	2	yes	—
496	C₁₃	#60802	1	1	yes	characteristic, direct product factor, Sylow
497	C₂³	—	2	2	no	—
498	C₂³	—	2	2	no	—
499	C₂³	—	2	4	no	—
500	C₂³	—	4	2	no	—
501	C₂³	—	4	8	no	—
502	C₂³	—	4	4	no	—
503	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
504	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
505	Q₈	—	2	2	no	—
506	Q₈	—	2	8	no	—
507	Q₈	—	2	2	no	—
508	Q₈	—	4	4	no	—
509	Q₈	—	4	4	no	—
510	D₄	—	2	2	no	—
511	D₄	—	2	8	no	—
512	D₄	—	2	2	no	—
513	D₄	—	4	8	no	—
514	D₄	—	4	4	no	—
515	D₄	—	4	16	no	—
516	D₄	—	4	8	no	—
517	D₄	—	4	4	no	—
518	D₄	—	4	4	no	—
519	D₄	—	4	8	no	—
520	C₂×C₄	—	2	2	no	—
521	C₂×C₄	—	2	4	no	—
522	C₂×C₄	—	2	4	no	—
523	C₂×C₄	—	2	4	no	—
524	C₂×C₄	—	2	4	no	—
525	C₂×C₄	—	2	4	no	—
526	C₂×C₄	—	2	2	no	—
527	C₂×C₄	—	2	4	no	—
528	C₂×C₄	—	2	4	no	—
529	C₂×C₄	—	4	2	no	—
530	C₂×C₄	—	4	2	no	—
531	C₂×C₄	—	4	2	no	—
532	C₂×C₄	—	4	16	no	—
533	C₂×C₄	—	4	4	no	—
534	C₂×C₄	—	4	4	no	—
535	C₂×C₄	—	4	8	no	—
536	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
537	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
538	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
539	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
540	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
541	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
542	C₂×C₄	C₁₃×H(5,𝔽₂)	1	4	yes	—
543	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
544	C₈	—	2	8	no	—
545	C₂²	—	2	2	no	—
546	C₂²	—	2	2	no	—
547	C₂²	—	2	2	no	—
548	C₂²	—	2	2	no	—
549	C₂²	—	4	4	no	—
550	C₂²	—	4	4	no	—
551	C₂²	—	4	8	no	—
552	C₂²	—	4	4	no	—
553	C₂²	—	4	2	no	—
554	C₂²	—	8	8	no	—
555	C₂²	C₁₃×#535	1	2	yes	—
556	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
557	C₄	—	2	2	no	—
558	C₄	—	2	2	no	—
559	C₄	—	2	2	no	—
560	C₄	—	2	2	no	—
561	C₄	—	4	4	no	—
562	C₄	—	4	4	no	—
563	C₄	—	4	2	no	—
564	C₄	C₁₃×#535	1	2	yes	—
565	C₄	C₁₃×#575	1	4	yes	—
566	C₄	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
567	C₂	—	2	2	no	—
568	C₂	—	4	2	no	—
569	C₂	—	8	4	no	—
570	C₂	—	8	2	no	—
571	C₂	C₂×C₁₃×#535	1	1	yes	characteristic
572	C₂	C₂×C₁₃×#575	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 ◁ C₂²×C₄²×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3444	C₂	semidirect
2. C₂×C₁₃×#532	C₂	semidirect
3. C₁₃×#3216	C₂	semidirect
4. C₁₃×#3214	C₂	semidirect
5. C₁₃×#3212	C₂	semidirect
6. C₁₃×#3153	C₂	semidirect
7. C₁₃×#3140	C₂	semidirect
8. C₁₃×#3039	C₂	semidirect
9. C₁₃×#3038	C₂	semidirect
10. C₁₃×#3005	C₂	semidirect
11. C₁₃×#2920	C₂	semidirect
16. C₁₃×#533	C₂²	semidirect
22. C₁₃×#532	C₂²	semidirect
27. C₁₃×#529	C₂²	semidirect
36. C₁₃×#497	C₂²	semidirect
37. C₁₃×#496	C₂²	semidirect
38. C₁₃×#495	C₂²	semidirect
39. C₁₃×#489	C₂²	semidirect
40. C₁₃×#488	C₂²	semidirect
41. C₁₃×#462	C₂²	semidirect
42. C₁₃×#461	C₂²	semidirect
43. C₁₃×#460	C₂²	semidirect
44. C₁₃×#459	C₂²	semidirect
45. C₁₃×#452	C₂²	semidirect
46. C₁₃×#449	C₂²	semidirect
47. C₁₃×#432	C₂²	semidirect
48. C₁₃×#431	C₂²	semidirect
136. #60802	C₁₃	direct (N × H)
211. #3444	C₂×C₁₃	semidirect
212. C₂×#532	C₂×C₁₃	semidirect
213. #3216	C₂×C₁₃	semidirect
214. #3214	C₂×C₁₃	semidirect
215. #3212	C₂×C₁₃	semidirect
216. #3153	C₂×C₁₃	semidirect
217. #3140	C₂×C₁₃	semidirect
218. #3039	C₂×C₁₃	semidirect
219. #3038	C₂×C₁₃	semidirect
220. #3005	C₂×C₁₃	semidirect
221. #2920	C₂×C₁₃	semidirect
274. #533	C₂²×C₁₃	semidirect
280. #532	C₂²×C₁₃	semidirect
285. #529	C₂²×C₁₃	semidirect
294. #497	C₂²×C₁₃	semidirect
295. #496	C₂²×C₁₃	semidirect
296. #495	C₂²×C₁₃	semidirect
297. #489	C₂²×C₁₃	semidirect
298. #488	C₂²×C₁₃	semidirect
299. #462	C₂²×C₁₃	semidirect
300. #461	C₂²×C₁₃	semidirect
301. #460	C₂²×C₁₃	semidirect
302. #459	C₂²×C₁₃	semidirect
303. #452	C₂²×C₁₃	semidirect
304. #449	C₂²×C₁₃	semidirect
305. #432	C₂²×C₁₃	semidirect
306. #431	C₂²×C₁₃	semidirect
496. C₁₃	#60802	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×#3444	2
C₂×C₁₃×#532	2
C₁₃×#3216	2
C₁₃×#3214	2
C₁₃×#3212	2
C₁₃×#3153	2
C₁₃×#3140	2
C₁₃×#3039	2
C₁₃×#3038	2
C₁₃×#3005	2
C₁₃×#2920	2
#60802	13

Subgroups — C13×#60802 #15747141

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#60802 #15747141