Subgroups — C₁₃×#60921 #15747260

Order 3328.

1758 conjugacy classes of subgroups.

The subgroup lattice has 514 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3455	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×#541	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3261	C₂	1	4	yes	maximal, complemented
4	C₁₃×#3260	C₂	1	4	yes	maximal, complemented
5	C₁₃×#3258	C₂	1	8	yes	maximal, complemented
6	C₁₃×#3080	C₂	1	2	yes	maximal, complemented
7	C₁₃×#3078	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3056	C₂	1	4	yes	maximal, complemented
9	C₁₃×#3039	C₂	1	2	yes	maximal, complemented
10	C₁₃×#3037	C₂	1	2	yes	maximal, complemented
11	C₁₃×#2905	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₃×#137	C₂²	1	4	yes	—
13	C₂²×C₁₃×M₁₆	C₂²	1	2	yes	—
14	C₁₃×#542	C₂²	1	4	yes	—
15	C₁₃×#541	—	2	4	no	—
16	C₁₃×#541	C₂²	1	4	yes	—
17	C₁₃×#541	C₂²	1	4	yes	—
18	C₁₃×#541	C₂²	1	2	yes	—
19	C₁₃×#540	C₂²	1	2	yes	—
20	C₁₃×#539	—	2	2	no	—
21	C₁₃×#538	—	2	2	no	—
22	C₁₃×#533	C₂²	1	1	yes	characteristic
23	C₁₃×#532	C₂²	1	1	yes	characteristic
24	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
25	C₁₃×#529	—	2	4	no	—
26	C₂×C₁₃×#126	—	2	2	no	—
27	C₂×C₁₃×#125	—	2	2	no	—
28	C₂×C₁₃×#125	C₂²	1	1	yes	characteristic
29	C₁₃×#525	C₂²	1	2	yes	—
30	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
31	C₄×C₁₃×#41	C₂²	1	2	yes	—
32	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	—
33	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
34	C₁₃×#479	C₂²	1	8	yes	complemented
35	C₁₃×#479	C₂²	1	8	yes	complemented
36	C₁₃×#478	C₂²	1	8	yes	complemented
37	C₁₃×#477	C₂²	1	4	yes	complemented
38	C₁₃×#475	C₂²	1	4	yes	complemented
39	C₁₃×#470	C₂²	1	8	yes	—
40	C₁₃×#468	C₂²	1	8	yes	—
41	C₁₃×#467	C₂²	1	8	yes	—
42	C₁₃×#465	C₂²	1	8	yes	—
43	C₁₃×#464	C₂²	1	8	yes	complemented
44	C₁₃×#462	C₂²	1	4	yes	complemented
45	C₁₃×#462	C₂²	1	8	yes	complemented
46	C₁₃×#461	C₂²	1	8	yes	complemented
47	C₁₃×#460	C₂²	1	4	yes	complemented
48	C₁₃×#428	C₂²	1	4	yes	—
49	C₁₃×#424	C₂²	1	4	yes	—
50	C₁₃×#424	C₂²	1	4	yes	—
51	C₁₃×#423	C₂²	1	2	yes	—
52	C₁₃×#423	C₂²	1	2	yes	—
53	C₁₃×#419	C₂²	1	4	yes	—
54	C₁₃×#417	C₂²	1	4	yes	—
55	C₂×C₁₃×#41	C₂³	1	2	yes	—
56	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
57	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
58	C₁₃×#137	—	4	8	no	—
59	C₂×C₁₃×Q₁₆	C₂³	1	8	yes	—
60	C₂×C₁₃×SD₁₆	C₂³	1	8	yes	—
61	C₂×C₁₃×M₁₆	—	4	4	no	—
62	C₂×C₁₃×M₁₆	C₂³	1	4	yes	—
63	C₂×C₁₃×M₁₆	C₂³	1	4	yes	—
64	C₂²×C₈×C₁₃	C₂³	1	4	yes	—
65	C₁₃×C₄⋊Q₈	—	2	2	no	—
66	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
67	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
68	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
69	C₁₃×#127	C₂³	1	1	yes	characteristic
70	C₁₃×#126	—	2	4	no	—
71	C₁₃×#126	—	2	8	no	—
72	C₁₃×#126	—	2	8	no	—
73	C₁₃×#126	—	2	4	no	—
74	C₁₃×#125	—	2	8	no	—
75	C₁₃×#125	—	2	8	no	—
76	C₁₃×#125	—	2	4	no	—
77	C₁₃×#125	—	2	2	no	—
78	C₁₃×#125	C₂³	1	4	yes	—
79	C₁₃×#125	C₂³	1	2	yes	—
80	C₁₃×#124	—	2	4	no	—
81	C₁₃×#124	C₂³	1	2	yes	—
82	C₁₃×#123	—	2	2	no	—
83	C₁₃×#123	—	2	4	no	—
84	C₁₃×#123	—	2	4	no	—
85	C₁₃×C₂²⋊Q₈	—	2	4	no	—
86	C₁₃×C₂²⋊Q₈	—	2	2	no	—
87	C₁₃×C₂²⋊Q₈	—	2	4	no	—
88	C₁₃×C₂²⋊Q₈	C₂³	1	8	yes	—
89	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
90	C₁₃×#121	—	2	2	no	—
91	C₁₃×#121	—	2	4	no	—
92	C₁₃×#121	C₂³	1	4	yes	—
93	C₁₃×#120	—	2	2	no	—
94	C₄×Q₈×C₁₃	—	2	2	no	—
95	C₄×Q₈×C₁₃	—	2	2	no	—
96	C₄×Q₈×C₁₃	—	2	2	no	—
97	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
98	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
99	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
100	C₄×D₄×C₁₃	—	2	4	no	—
101	C₄×D₄×C₁₃	—	2	4	no	—
102	C₄×D₄×C₁₃	—	2	2	no	—
103	C₄×D₄×C₁₃	C₂³	1	4	yes	—
104	C₁₃×#117	—	2	2	no	—
105	C₁₃×#117	D₄	1	4	yes	—
106	C₁₃×#117	C₂³	1	2	yes	—
107	C₁₃×#117	C₂³	1	2	yes	—
108	C₁₃×#117	C₂³	1	2	yes	—
109	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
110	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
111	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
112	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
113	C₂×C₁₃×C₄⋊C₄	D₄	1	2	yes	—
114	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
115	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
116	C₂×C₁₃×C₂²⋊C₄	D₄	1	2	yes	—
117	C₂×C₄²×C₁₃	—	2	2	no	—
118	C₂×C₄²×C₁₃	—	2	2	no	—
119	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
120	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
121	C₁₃×#107	C₂³	1	8	yes	—
122	C₁₃×#106	C₂³	1	8	yes	—
123	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
124	C₁₃×C₄⋊C₈	C₂³	1	8	yes	—
125	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
126	C₁₃×#103	C₂³	1	8	yes	—
127	C₁₃×#103	C₂³	1	8	yes	—
128	C₁₃×#103	C₂³	1	8	yes	—
129	C₁₃×#102	C₂³	1	8	yes	—
130	#60921	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
131	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
132	C₁₃×#41	—	2	4	no	—
133	C₁₃×#41	—	2	4	no	—
134	C₂×Q₈×C₁₃	—	2	2	no	—
135	C₂×Q₈×C₁₃	—	2	2	no	—
136	C₂×Q₈×C₁₃	—	2	4	no	—
137	C₂×Q₈×C₁₃	—	2	4	no	—
138	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
139	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
140	C₂×D₄×C₁₃	—	2	2	no	—
141	C₂×D₄×C₁₃	—	2	4	no	—
142	C₂×D₄×C₁₃	—	2	2	no	—
143	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
144	C₂²×C₄×C₁₃	—	2	2	no	—
145	C₂²×C₄×C₁₃	—	2	2	no	—
146	C₂²×C₄×C₁₃	—	2	2	no	—
147	C₂²×C₄×C₁₃	—	2	2	no	—
148	C₂²×C₄×C₁₃	—	2	2	no	—
149	C₂²×C₄×C₁₃	—	2	4	no	—
150	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
151	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
152	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
153	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
154	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
155	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
156	C₁₃×Q₁₆	—	4	8	no	—
157	C₁₃×SD₁₆	—	4	8	no	—
158	C₁₃×M₁₆	—	2	8	no	—
159	C₁₃×M₁₆	—	4	4	no	—
160	C₂×C₈×C₁₃	—	4	4	no	—
161	C₂×C₈×C₁₃	C₂⁴	1	8	yes	—
162	C₁₃×C₄⋊C₄	—	2	4	no	—
163	C₁₃×C₄⋊C₄	—	2	4	no	—
164	C₁₃×C₄⋊C₄	—	2	8	no	—
165	C₁₃×C₄⋊C₄	—	2	8	no	—
166	C₁₃×C₄⋊C₄	—	2	8	no	—
167	C₁₃×C₄⋊C₄	—	2	2	no	—
168	C₁₃×C₄⋊C₄	—	2	4	no	—
169	C₁₃×C₄⋊C₄	—	2	2	no	—
170	C₁₃×C₄⋊C₄	—	2	4	no	—
171	C₁₃×C₄⋊C₄	—	2	4	no	—
172	C₁₃×C₄⋊C₄	—	2	2	no	—
173	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
174	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
175	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
176	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
177	C₁₃×C₂²⋊C₄	—	2	8	no	—
178	C₁₃×C₂²⋊C₄	—	2	2	no	—
179	C₁₃×C₂²⋊C₄	—	2	4	no	—
180	C₁₃×C₂²⋊C₄	—	2	4	no	—
181	C₁₃×C₂²⋊C₄	—	2	4	no	—
182	C₁₃×C₂²⋊C₄	—	2	4	no	—
183	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
184	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
185	C₄²×C₁₃	—	2	2	no	—
186	C₄²×C₁₃	—	2	4	no	—
187	C₄²×C₁₃	—	2	4	no	—
188	C₄²×C₁₃	—	2	4	no	—
189	C₄²×C₁₃	C₂×D₄	1	2	yes	—
190	C₄²×C₁₃	C₂×D₄	1	2	yes	—
191	C₄²×C₁₃	C₂⁴	1	2	yes	—
192	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
193	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
194	#3455	C₂×C₁₃	1	1	yes	characteristic
195	C₂×#541	C₂×C₁₃	1	1	yes	characteristic, complemented
196	#3261	C₂×C₁₃	1	4	yes	complemented
197	#3260	C₂×C₁₃	1	4	yes	complemented
198	#3258	C₂×C₁₃	1	8	yes	complemented
199	#3080	C₂×C₁₃	1	2	yes	complemented
200	#3078	C₂×C₁₃	1	2	yes	complemented
201	#3056	C₂×C₁₃	1	4	yes	complemented
202	#3039	C₂×C₁₃	1	2	yes	complemented
203	#3037	C₂×C₁₃	1	2	yes	complemented
204	#2905	C₂×C₁₃	1	1	yes	characteristic, complemented
205	C₂³×C₁₃	—	2	2	no	—
206	C₂³×C₁₃	—	2	2	no	—
207	C₂³×C₁₃	—	4	2	no	—
208	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
209	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
210	Q₈×C₁₃	—	2	4	no	—
211	Q₈×C₁₃	—	2	2	no	—
212	Q₈×C₁₃	—	2	4	no	—
213	Q₈×C₁₃	—	2	2	no	—
214	Q₈×C₁₃	—	4	4	no	—
215	Q₈×C₁₃	—	8	2	no	—
216	D₄×C₁₃	—	2	2	no	—
217	D₄×C₁₃	—	2	2	no	—
218	D₄×C₁₃	—	4	4	no	—
219	D₄×C₁₃	—	8	2	no	—
220	D₄×C₁₃	—	8	4	no	—
221	C₂×C₄×C₁₃	—	2	2	no	—
222	C₂×C₄×C₁₃	—	2	4	no	—
223	C₂×C₄×C₁₃	—	2	2	no	—
224	C₂×C₄×C₁₃	—	2	2	no	—
225	C₂×C₄×C₁₃	—	2	2	no	—
226	C₂×C₄×C₁₃	—	2	4	no	—
227	C₂×C₄×C₁₃	—	2	4	no	—
228	C₂×C₄×C₁₃	—	2	4	no	—
229	C₂×C₄×C₁₃	—	4	2	no	—
230	C₂×C₄×C₁₃	—	4	2	no	—
231	C₂×C₄×C₁₃	—	4	4	no	—
232	C₂×C₄×C₁₃	—	4	4	no	—
233	C₂×C₄×C₁₃	—	4	4	no	—
234	C₂×C₄×C₁₃	—	8	4	no	—
235	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
236	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
237	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
238	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
239	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
240	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
241	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
242	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
243	C₈×C₁₃	—	2	8	no	—
244	C₂×#137	C₂²×C₁₃	1	4	yes	—
245	C₂²×M₁₆	C₂²×C₁₃	1	2	yes	—
246	#542	C₂²×C₁₃	1	4	yes	—
247	#541	—	2	4	no	—
248	#541	C₂²×C₁₃	1	4	yes	—
249	#541	C₂²×C₁₃	1	4	yes	—
250	#541	C₂²×C₁₃	1	2	yes	—
251	#540	C₂²×C₁₃	1	2	yes	—
252	#539	—	2	2	no	—
253	#538	—	2	2	no	—
254	#533	C₂²×C₁₃	1	1	yes	characteristic
255	#532	C₂²×C₁₃	1	1	yes	characteristic
256	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
257	#529	—	2	4	no	—
258	C₂×#126	—	2	2	no	—
259	C₂×#125	—	2	2	no	—
260	C₂×#125	C₂²×C₁₃	1	1	yes	characteristic
261	#525	C₂²×C₁₃	1	2	yes	—
262	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
263	C₄×#41	C₂²×C₁₃	1	2	yes	—
264	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	—
265	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
266	#479	C₂²×C₁₃	1	8	yes	complemented
267	#479	C₂²×C₁₃	1	8	yes	complemented
268	#478	C₂²×C₁₃	1	8	yes	complemented
269	#477	C₂²×C₁₃	1	4	yes	complemented
270	#475	C₂²×C₁₃	1	4	yes	complemented
271	#470	C₂²×C₁₃	1	8	yes	—
272	#468	C₂²×C₁₃	1	8	yes	—
273	#467	C₂²×C₁₃	1	8	yes	—
274	#465	C₂²×C₁₃	1	8	yes	—
275	#464	C₂²×C₁₃	1	8	yes	complemented
276	#462	C₂²×C₁₃	1	8	yes	complemented
277	#462	C₂²×C₁₃	1	4	yes	complemented
278	#461	C₂²×C₁₃	1	8	yes	complemented
279	#460	C₂²×C₁₃	1	4	yes	complemented
280	#428	C₂²×C₁₃	1	4	yes	—
281	#424	C₂²×C₁₃	1	4	yes	—
282	#424	C₂²×C₁₃	1	4	yes	—
283	#423	C₂²×C₁₃	1	2	yes	—
284	#423	C₂²×C₁₃	1	2	yes	—
285	#419	C₂²×C₁₃	1	4	yes	—
286	#417	C₂²×C₁₃	1	4	yes	—
287	C₂²×C₁₃	—	2	2	no	—
288	C₂²×C₁₃	—	2	4	no	—
289	C₂²×C₁₃	—	2	2	no	—
290	C₂²×C₁₃	—	4	4	no	—
291	C₂²×C₁₃	—	4	2	no	—
292	C₂²×C₁₃	—	8	2	no	—
293	C₂²×C₁₃	#537	1	2	yes	—
294	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
295	C₄×C₁₃	—	2	4	no	—
296	C₄×C₁₃	—	2	2	no	—
297	C₄×C₁₃	—	2	2	no	—
298	C₄×C₁₃	—	2	2	no	—
299	C₄×C₁₃	—	4	4	no	—
300	C₄×C₁₃	—	4	4	no	—
301	C₄×C₁₃	—	4	2	no	—
302	C₄×C₁₃	—	4	4	no	—
303	C₄×C₁₃	#537	1	2	yes	—
304	C₄×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
305	C₄×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
306	C₂×#41	C₂³×C₁₃	1	2	yes	—
307	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
308	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
309	#137	—	4	8	no	—
310	C₂×Q₁₆	C₂³×C₁₃	1	8	yes	—
311	C₂×SD₁₆	C₂³×C₁₃	1	8	yes	—
312	C₂×M₁₆	—	4	4	no	—
313	C₂×M₁₆	C₂³×C₁₃	1	4	yes	—
314	C₂×M₁₆	C₂³×C₁₃	1	4	yes	—
315	C₂²×C₈	C₂³×C₁₃	1	4	yes	—
316	C₄⋊Q₈	—	2	2	no	—
317	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
318	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
319	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
320	#127	C₂³×C₁₃	1	1	yes	characteristic
321	#126	—	2	4	no	—
322	#126	—	2	8	no	—
323	#126	—	2	8	no	—
324	#126	—	2	4	no	—
325	#125	—	2	8	no	—
326	#125	—	2	8	no	—
327	#125	—	2	4	no	—
328	#125	—	2	2	no	—
329	#125	C₂³×C₁₃	1	4	yes	—
330	#125	C₂³×C₁₃	1	2	yes	—
331	#124	—	2	4	no	—
332	#124	C₂³×C₁₃	1	2	yes	—
333	#123	—	2	2	no	—
334	#123	—	2	4	no	—
335	#123	—	2	4	no	—
336	C₂²⋊Q₈	—	2	4	no	—
337	C₂²⋊Q₈	—	2	2	no	—
338	C₂²⋊Q₈	—	2	4	no	—
339	C₂²⋊Q₈	C₂³×C₁₃	1	8	yes	—
340	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
341	#121	—	2	2	no	—
342	#121	—	2	4	no	—
343	#121	C₂³×C₁₃	1	4	yes	—
344	#120	—	2	2	no	—
345	C₄×Q₈	—	2	2	no	—
346	C₄×Q₈	—	2	2	no	—
347	C₄×Q₈	—	2	2	no	—
348	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
349	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
350	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
351	C₄×D₄	—	2	4	no	—
352	C₄×D₄	—	2	4	no	—
353	C₄×D₄	—	2	2	no	—
354	C₄×D₄	C₂³×C₁₃	1	4	yes	—
355	#117	—	2	2	no	—
356	#117	D₄×C₁₃	1	4	yes	—
357	#117	C₂³×C₁₃	1	2	yes	—
358	#117	C₂³×C₁₃	1	2	yes	—
359	#117	C₂³×C₁₃	1	2	yes	—
360	C₂×C₄⋊C₄	—	2	2	no	—
361	C₂×C₄⋊C₄	—	2	2	no	—
362	C₂×C₄⋊C₄	—	2	2	no	—
363	C₂×C₄⋊C₄	—	2	2	no	—
364	C₂×C₄⋊C₄	D₄×C₁₃	1	2	yes	—
365	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
366	C₂×C₂²⋊C₄	—	2	2	no	—
367	C₂×C₂²⋊C₄	D₄×C₁₃	1	2	yes	—
368	C₂×C₄²	—	2	2	no	—
369	C₂×C₄²	—	2	2	no	—
370	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
371	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
372	#107	C₂³×C₁₃	1	8	yes	—
373	#106	C₂³×C₁₃	1	8	yes	—
374	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
375	C₄⋊C₈	C₂³×C₁₃	1	8	yes	—
376	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
377	#103	C₂³×C₁₃	1	8	yes	—
378	#103	C₂³×C₁₃	1	8	yes	—
379	#103	C₂³×C₁₃	1	8	yes	—
380	#102	C₂³×C₁₃	1	8	yes	—
381	C₂×C₁₃	—	2	2	no	—
382	C₂×C₁₃	—	4	2	no	—
383	C₂×C₁₃	—	8	2	no	—
384	C₂×C₁₃	C₂×#537	1	1	yes	characteristic
385	C₂×C₁₃	#3586	1	2	yes	—
386	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
387	#41	—	2	4	no	—
388	#41	—	2	4	no	—
389	C₂×Q₈	—	2	2	no	—
390	C₂×Q₈	—	2	2	no	—
391	C₂×Q₈	—	2	4	no	—
392	C₂×Q₈	—	2	4	no	—
393	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
394	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
395	C₂×D₄	—	2	2	no	—
396	C₂×D₄	—	2	4	no	—
397	C₂×D₄	—	2	2	no	—
398	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
399	C₂²×C₄	—	2	2	no	—
400	C₂²×C₄	—	2	2	no	—
401	C₂²×C₄	—	2	2	no	—
402	C₂²×C₄	—	2	2	no	—
403	C₂²×C₄	—	2	2	no	—
404	C₂²×C₄	—	2	4	no	—
405	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
406	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
407	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
408	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
409	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
410	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
411	Q₁₆	—	4	8	no	—
412	SD₁₆	—	4	8	no	—
413	M₁₆	—	2	8	no	—
414	M₁₆	—	4	4	no	—
415	C₂×C₈	—	4	4	no	—
416	C₂×C₈	C₂⁴×C₁₃	1	8	yes	—
417	C₄⋊C₄	—	2	4	no	—
418	C₄⋊C₄	—	2	4	no	—
419	C₄⋊C₄	—	2	8	no	—
420	C₄⋊C₄	—	2	8	no	—
421	C₄⋊C₄	—	2	8	no	—
422	C₄⋊C₄	—	2	2	no	—
423	C₄⋊C₄	—	2	4	no	—
424	C₄⋊C₄	—	2	2	no	—
425	C₄⋊C₄	—	2	4	no	—
426	C₄⋊C₄	—	2	4	no	—
427	C₄⋊C₄	—	2	2	no	—
428	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
429	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
430	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
431	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
432	C₂²⋊C₄	—	2	8	no	—
433	C₂²⋊C₄	—	2	2	no	—
434	C₂²⋊C₄	—	2	4	no	—
435	C₂²⋊C₄	—	2	4	no	—
436	C₂²⋊C₄	—	2	4	no	—
437	C₂²⋊C₄	—	2	4	no	—
438	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
439	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
440	C₄²	—	2	2	no	—
441	C₄²	—	2	4	no	—
442	C₄²	—	2	4	no	—
443	C₄²	—	2	4	no	—
444	C₄²	C₂×D₄×C₁₃	1	2	yes	—
445	C₄²	C₂×D₄×C₁₃	1	2	yes	—
446	C₄²	C₂⁴×C₁₃	1	2	yes	—
447	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
448	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
449	C₁₃	#60921	1	1	yes	characteristic, direct product factor, Sylow
450	C₂³	—	2	2	no	—
451	C₂³	—	2	2	no	—
452	C₂³	—	4	2	no	—
453	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
454	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
455	Q₈	—	2	4	no	—
456	Q₈	—	2	2	no	—
457	Q₈	—	2	4	no	—
458	Q₈	—	2	2	no	—
459	Q₈	—	4	4	no	—
460	Q₈	—	8	2	no	—
461	D₄	—	2	2	no	—
462	D₄	—	2	2	no	—
463	D₄	—	4	4	no	—
464	D₄	—	8	2	no	—
465	D₄	—	8	4	no	—
466	C₂×C₄	—	2	2	no	—
467	C₂×C₄	—	2	4	no	—
468	C₂×C₄	—	2	2	no	—
469	C₂×C₄	—	2	2	no	—
470	C₂×C₄	—	2	2	no	—
471	C₂×C₄	—	2	4	no	—
472	C₂×C₄	—	2	4	no	—
473	C₂×C₄	—	2	4	no	—
474	C₂×C₄	—	4	2	no	—
475	C₂×C₄	—	4	2	no	—
476	C₂×C₄	—	4	4	no	—
477	C₂×C₄	—	4	4	no	—
478	C₂×C₄	—	4	4	no	—
479	C₂×C₄	—	8	4	no	—
480	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
481	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
482	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
483	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
484	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
485	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
486	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
487	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
488	C₈	—	2	8	no	—
489	C₂²	—	2	2	no	—
490	C₂²	—	2	4	no	—
491	C₂²	—	2	2	no	—
492	C₂²	—	4	4	no	—
493	C₂²	—	4	2	no	—
494	C₂²	—	8	2	no	—
495	C₂²	C₁₃×#537	1	2	yes	—
496	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
497	C₄	—	2	4	no	—
498	C₄	—	2	2	no	—
499	C₄	—	2	2	no	—
500	C₄	—	2	2	no	—
501	C₄	—	4	4	no	—
502	C₄	—	4	4	no	—
503	C₄	—	4	2	no	—
504	C₄	—	4	4	no	—
505	C₄	C₁₃×#537	1	2	yes	—
506	C₄	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
507	C₄	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
508	C₂	—	2	2	no	—
509	C₂	—	4	2	no	—
510	C₂	—	8	2	no	—
511	C₂	C₂×C₁₃×#537	1	1	yes	characteristic
512	C₂	C₁₃×#3586	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
prime radical	C₁₃×#3455	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂×C₁₃×#117 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₃×#541	C₂	semidirect
3. C₁₃×#3261	C₂	semidirect
4. C₁₃×#3260	C₂	semidirect
5. C₁₃×#3258	C₂	semidirect
6. C₁₃×#3080	C₂	semidirect
7. C₁₃×#3078	C₂	semidirect
8. C₁₃×#3056	C₂	semidirect
9. C₁₃×#3039	C₂	semidirect
10. C₁₃×#3037	C₂	semidirect
11. C₁₃×#2905	C₂	semidirect
34. C₁₃×#479	C₂²	semidirect
35. C₁₃×#479	C₂²	semidirect
36. C₁₃×#478	C₂²	semidirect
37. C₁₃×#477	C₂²	semidirect
38. C₁₃×#475	C₂²	semidirect
43. C₁₃×#464	C₂²	semidirect
44. C₁₃×#462	C₂²	semidirect
45. C₁₃×#462	C₂²	semidirect
46. C₁₃×#461	C₂²	semidirect
47. C₁₃×#460	C₂²	semidirect
130. #60921	C₁₃	direct (N × H)
195. C₂×#541	C₂×C₁₃	semidirect
196. #3261	C₂×C₁₃	semidirect
197. #3260	C₂×C₁₃	semidirect
198. #3258	C₂×C₁₃	semidirect
199. #3080	C₂×C₁₃	semidirect
200. #3078	C₂×C₁₃	semidirect
201. #3056	C₂×C₁₃	semidirect
202. #3039	C₂×C₁₃	semidirect
203. #3037	C₂×C₁₃	semidirect
204. #2905	C₂×C₁₃	semidirect
266. #479	C₂²×C₁₃	semidirect
267. #479	C₂²×C₁₃	semidirect
268. #478	C₂²×C₁₃	semidirect
269. #477	C₂²×C₁₃	semidirect
270. #475	C₂²×C₁₃	semidirect
275. #464	C₂²×C₁₃	semidirect
276. #462	C₂²×C₁₃	semidirect
277. #462	C₂²×C₁₃	semidirect
278. #461	C₂²×C₁₃	semidirect
279. #460	C₂²×C₁₃	semidirect
449. C₁₃	#60921	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×#3455	2
C₂×C₁₃×#541	2
C₁₃×#3261	2
C₁₃×#3260	2
C₁₃×#3258	2
C₁₃×#3080	2
C₁₃×#3078	2
C₁₃×#3056	2
C₁₃×#3039	2
C₁₃×#3037	2
C₁₃×#2905	2
#60921	13

Subgroups — C13×#60921 #15747260

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#60921 #15747260