Subgroups — C₁₃×#60673 #15747012

Order 3328.

2050 conjugacy classes of subgroups.

The subgroup lattice has 454 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	2	yes	maximal, complemented
2	C₁₃×#3170	C₂	1	2	yes	maximal, complemented
3	C₁₃×#3169	C₂	1	2	yes	maximal, complemented
4	C₁₃×#3168	C₂	1	8	yes	maximal, complemented
5	C₁₃×#3167	C₂	1	4	yes	maximal, complemented
6	C₁₃×#3160	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#3147	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#3131	C₂	1	2	yes	maximal, complemented
9	C₁₃×#3050	C₂	1	4	yes	maximal, complemented
10	C₄×C₁₃×#135	C₂	1	4	yes	maximal, complemented
11	C₂²×C₄×C₈×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₃×#135	C₂²	1	4	yes	—
13	C₂³×C₈×C₁₃	C₂²	1	2	yes	—
14	C₁₃×#533	C₂²	1	4	yes	—
15	C₁₃×#533	C₂²	1	2	yes	—
16	C₁₃×#532	C₂²	1	2	yes	—
17	C₁₃×#532	C₂²	1	4	yes	—
18	C₁₃×#529	—	2	4	no	—
19	C₁₃×#529	—	2	4	no	—
20	C₁₃×#529	C₂²	1	8	yes	—
21	C₁₃×#525	—	2	4	no	—
22	C₁₃×#525	C₂²	1	4	yes	—
23	C₄×C₁₃×#41	—	2	4	no	—
24	C₄×C₁₃×#41	C₂²	1	4	yes	—
25	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
26	C₁₃×#500	C₂²	1	2	yes	complemented
27	C₁₃×#499	C₂²	1	4	yes	complemented
28	C₁₃×#498	C₂²	1	2	yes	complemented
29	C₁₃×#495	C₂²	1	4	yes	complemented
30	C₁₃×#494	C₂²	1	1	yes	characteristic, complemented
31	C₁₃×#493	C₂²	1	1	yes	characteristic, complemented
32	C₁₃×#492	C₂²	1	2	yes	complemented
33	C₁₃×#488	C₂²	1	8	yes	complemented
34	C₁₃×#487	C₂²	1	4	yes	complemented
35	C₁₃×#486	C₂²	1	4	yes	complemented
36	C₁₃×#467	C₂²	1	8	yes	—
37	C₁₃×#466	C₂²	1	8	yes	—
38	C₁₃×#465	C₂²	1	16	yes	—
39	C₄×C₁₃×Q₁₆	C₂²	1	8	yes	complemented
40	C₄×C₁₃×SD₁₆	C₂²	1	16	yes	complemented
41	C₄×C₁₃×D₈	C₂²	1	8	yes	complemented
42	C₁₃×#427	C₂²	1	4	yes	—
43	C₁₃×#416	C₂²	1	8	yes	—
44	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
45	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
46	C₂×C₄×C₈×C₁₃	C₂²	1	2	yes	—
47	C₂×C₄×C₈×C₁₃	C₂²	1	4	yes	—
48	C₂×C₄×C₈×C₁₃	C₂²	1	2	yes	—
49	C₂×C₄×C₈×C₁₃	C₂²	1	2	yes	—
50	C₂×C₁₃×#41	—	2	4	no	—
51	C₂×C₁₃×#41	C₂³	1	4	yes	—
52	C₂³×C₄×C₁₃	D₄	1	2	yes	—
53	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
54	C₁₃×#135	—	2	16	no	—
55	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	—
56	C₂×C₁₃×SD₁₆	C₂³	1	8	yes	—
57	C₂×C₁₃×D₈	C₂³	1	4	yes	—
58	C₂²×C₈×C₁₃	—	2	8	no	—
59	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
60	C₂²×C₈×C₁₃	C₂³	1	4	yes	—
61	C₂²×C₈×C₁₃	C₂³	1	4	yes	—
62	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
63	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
64	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
65	C₁₃×#127	C₂³	1	2	yes	—
66	C₁₃×#126	—	2	8	no	—
67	C₁₃×#125	—	2	4	no	—
68	C₁₃×#125	C₂³	1	4	yes	—
69	C₁₃×#124	—	2	4	no	—
70	C₁₃×#124	C₂³	1	4	yes	—
71	C₁₃×#123	—	2	8	no	—
72	C₁₃×#123	—	2	4	no	—
73	C₁₃×C₂²⋊Q₈	—	2	4	no	—
74	C₁₃×C₂²⋊Q₈	—	2	4	no	—
75	C₁₃×C₂²⋊Q₈	C₂³	1	8	yes	—
76	C₁₃×#121	—	2	4	no	—
77	C₁₃×#121	—	2	4	no	—
78	C₁₃×#121	C₂³	1	8	yes	—
79	C₁₃×#120	—	2	4	no	—
80	C₄×Q₈×C₁₃	—	2	4	no	—
81	C₄×Q₈×C₁₃	—	2	4	no	—
82	C₄×Q₈×C₁₃	C₂³	1	8	yes	—
83	C₄×D₄×C₁₃	—	2	8	no	—
84	C₄×D₄×C₁₃	—	2	8	no	—
85	C₄×D₄×C₁₃	—	2	8	no	—
86	C₄×D₄×C₁₃	—	2	4	no	—
87	C₄×D₄×C₁₃	—	2	4	no	—
88	C₄×D₄×C₁₃	C₂³	1	8	yes	—
89	C₁₃×#117	—	2	4	no	—
90	C₁₃×#117	—	2	8	no	—
91	C₁₃×#117	—	2	4	no	—
92	C₁₃×#117	C₂³	1	4	yes	—
93	C₂×C₄²×C₁₃	—	2	4	no	—
94	C₂×C₄²×C₁₃	D₄	1	2	yes	—
95	C₂×C₄²×C₁₃	D₄	1	2	yes	—
96	C₂×C₄²×C₁₃	D₄	1	2	yes	—
97	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
98	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
99	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
100	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
101	C₁₃×#107	C₂³	1	8	yes	—
102	C₁₃×#106	C₂³	1	8	yes	—
103	C₁₃×#103	C₂³	1	16	yes	—
104	C₁₃×#102	C₂³	1	16	yes	—
105	C₄×C₈×C₁₃	C₂³	1	4	yes	—
106	C₄×C₈×C₁₃	C₂³	1	4	yes	—
107	C₄×C₈×C₁₃	C₂³	1	2	yes	—
108	C₄×C₈×C₁₃	C₂³	1	2	yes	—
109	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
110	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
111	C₄×C₈×C₁₃	C₂³	1	2	yes	—
112	#60673	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
113	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
114	C₁₃×#41	—	2	16	no	—
115	C₁₃×#41	—	4	16	no	—
116	C₂×Q₈×C₁₃	—	2	4	no	—
117	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
118	C₂×D₄×C₁₃	—	2	4	no	—
119	C₂×D₄×C₁₃	—	2	8	no	—
120	C₂×D₄×C₁₃	—	2	4	no	—
121	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
122	C₂²×C₄×C₁₃	—	2	8	no	—
123	C₂²×C₄×C₁₃	—	2	4	no	—
124	C₂²×C₄×C₁₃	—	2	4	no	—
125	C₂²×C₄×C₁₃	—	2	8	no	—
126	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
127	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
128	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
129	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
130	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
131	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
132	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
133	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
134	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
135	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
136	C₁₃×Q₁₆	—	2	8	no	—
137	C₁₃×SD₁₆	—	2	16	no	—
138	C₁₃×D₈	—	2	8	no	—
139	C₂×C₈×C₁₃	—	2	4	no	—
140	C₂×C₈×C₁₃	—	2	8	no	—
141	C₂×C₈×C₁₃	—	2	8	no	—
142	C₂×C₈×C₁₃	#41	1	8	yes	complemented
143	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
144	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
145	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
146	C₁₃×C₄⋊C₄	—	2	4	no	—
147	C₁₃×C₄⋊C₄	—	2	4	no	—
148	C₁₃×C₄⋊C₄	—	2	8	no	—
149	C₁₃×C₄⋊C₄	—	2	8	no	—
150	C₁₃×C₄⋊C₄	—	2	8	no	—
151	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
152	C₁₃×C₂²⋊C₄	—	2	8	no	—
153	C₁₃×C₂²⋊C₄	—	2	4	no	—
154	C₁₃×C₂²⋊C₄	—	2	8	no	—
155	C₁₃×C₂²⋊C₄	—	2	8	no	—
156	C₁₃×C₂²⋊C₄	—	2	8	no	—
157	C₄²×C₁₃	—	2	8	no	—
158	C₄²×C₁₃	—	2	4	no	—
159	C₄²×C₁₃	C₂×D₄	1	2	yes	—
160	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
161	C₄²×C₁₃	C₂×D₄	1	2	yes	—
162	C₄²×C₁₃	C₂×D₄	1	2	yes	—
163	C₄²×C₁₃	C₂×D₄	1	2	yes	—
164	C₄²×C₁₃	C₂×D₄	1	2	yes	—
165	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
166	C₄²×C₁₃	C₂⁴	1	2	yes	—
167	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
168	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
169	#3444	C₂×C₁₃	1	2	yes	complemented
170	#3170	C₂×C₁₃	1	2	yes	complemented
171	#3169	C₂×C₁₃	1	2	yes	complemented
172	#3168	C₂×C₁₃	1	8	yes	complemented
173	#3167	C₂×C₁₃	1	4	yes	complemented
174	#3160	C₂×C₁₃	1	1	yes	characteristic, complemented
175	#3147	C₂×C₁₃	1	1	yes	characteristic, complemented
176	#3131	C₂×C₁₃	1	2	yes	complemented
177	#3050	C₂×C₁₃	1	4	yes	complemented
178	C₄×#135	C₂×C₁₃	1	4	yes	complemented
179	C₂²×C₄×C₈	C₂×C₁₃	1	1	yes	characteristic, complemented
180	C₂³×C₁₃	—	2	2	no	—
181	C₂³×C₁₃	—	2	4	no	—
182	C₂³×C₁₃	—	2	4	no	—
183	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
184	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
185	Q₈×C₁₃	—	2	8	no	—
186	Q₈×C₁₃	—	4	8	no	—
187	D₄×C₁₃	—	2	8	no	—
188	D₄×C₁₃	—	4	8	no	—
189	D₄×C₁₃	—	4	16	no	—
190	D₄×C₁₃	—	4	8	no	—
191	C₂×C₄×C₁₃	—	2	2	no	—
192	C₂×C₄×C₁₃	—	2	4	no	—
193	C₂×C₄×C₁₃	—	2	4	no	—
194	C₂×C₄×C₁₃	—	2	4	no	—
195	C₂×C₄×C₁₃	—	2	4	no	—
196	C₂×C₄×C₁₃	—	2	4	no	—
197	C₂×C₄×C₁₃	—	2	4	no	—
198	C₂×C₄×C₁₃	—	2	4	no	—
199	C₂×C₄×C₁₃	—	2	4	no	—
200	C₂×C₄×C₁₃	—	2	8	no	—
201	C₂×C₄×C₁₃	—	4	8	no	—
202	C₂×C₄×C₁₃	—	4	16	no	—
203	C₂×C₄×C₁₃	#135	1	8	yes	complemented
204	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
205	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
206	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
207	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
208	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
209	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
210	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
211	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
212	C₈×C₁₃	—	2	4	no	—
213	C₈×C₁₃	C₂×#41	1	4	yes	—
214	C₈×C₁₃	C₂×#41	1	4	yes	—
215	C₂×#135	C₂²×C₁₃	1	4	yes	—
216	C₂³×C₈	C₂²×C₁₃	1	2	yes	—
217	#533	C₂²×C₁₃	1	4	yes	—
218	#533	C₂²×C₁₃	1	2	yes	—
219	#532	C₂²×C₁₃	1	2	yes	—
220	#532	C₂²×C₁₃	1	4	yes	—
221	#529	—	2	4	no	—
222	#529	—	2	4	no	—
223	#529	C₂²×C₁₃	1	8	yes	—
224	#525	—	2	4	no	—
225	#525	C₂²×C₁₃	1	4	yes	—
226	C₄×#41	—	2	4	no	—
227	C₄×#41	C₂²×C₁₃	1	4	yes	—
228	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
229	#500	C₂²×C₁₃	1	2	yes	complemented
230	#499	C₂²×C₁₃	1	4	yes	complemented
231	#498	C₂²×C₁₃	1	2	yes	complemented
232	#495	C₂²×C₁₃	1	4	yes	complemented
233	#494	C₂²×C₁₃	1	1	yes	characteristic, complemented
234	#493	C₂²×C₁₃	1	1	yes	characteristic, complemented
235	#492	C₂²×C₁₃	1	2	yes	complemented
236	#488	C₂²×C₁₃	1	8	yes	complemented
237	#487	C₂²×C₁₃	1	4	yes	complemented
238	#486	C₂²×C₁₃	1	4	yes	complemented
239	#467	C₂²×C₁₃	1	8	yes	—
240	#466	C₂²×C₁₃	1	8	yes	—
241	#465	C₂²×C₁₃	1	16	yes	—
242	C₄×Q₁₆	C₂²×C₁₃	1	8	yes	complemented
243	C₄×SD₁₆	C₂²×C₁₃	1	16	yes	complemented
244	C₄×D₈	C₂²×C₁₃	1	8	yes	complemented
245	#427	C₂²×C₁₃	1	4	yes	—
246	#416	C₂²×C₁₃	1	8	yes	—
247	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
248	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
249	C₂×C₄×C₈	C₂²×C₁₃	1	2	yes	—
250	C₂×C₄×C₈	C₂²×C₁₃	1	4	yes	—
251	C₂×C₄×C₈	C₂²×C₁₃	1	2	yes	—
252	C₂×C₄×C₈	C₂²×C₁₃	1	2	yes	—
253	C₂²×C₁₃	—	2	8	no	—
254	C₂²×C₁₃	—	2	2	no	—
255	C₂²×C₁₃	—	2	2	no	—
256	C₂²×C₁₃	—	2	2	no	—
257	C₂²×C₁₃	—	4	4	no	—
258	C₂²×C₁₃	—	4	8	no	—
259	C₂²×C₁₃	#532	1	2	yes	—
260	C₂²×C₁₃	C₂×#135	1	4	yes	—
261	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
262	C₄×C₁₃	—	2	2	no	—
263	C₄×C₁₃	—	2	2	no	—
264	C₄×C₁₃	—	2	2	no	—
265	C₄×C₁₃	—	4	4	no	—
266	C₄×C₁₃	—	4	8	no	—
267	C₄×C₁₃	#532	1	2	yes	—
268	C₄×C₁₃	C₂×#135	1	4	yes	—
269	C₄×C₁₃	C₂×#135	1	4	yes	—
270	C₄×C₁₃	C₂²×#41	1	2	yes	—
271	C₂×#41	—	2	4	no	—
272	C₂×#41	C₂³×C₁₃	1	4	yes	—
273	C₂³×C₄	D₄×C₁₃	1	2	yes	—
274	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
275	#135	—	2	16	no	—
276	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	—
277	C₂×SD₁₆	C₂³×C₁₃	1	8	yes	—
278	C₂×D₈	C₂³×C₁₃	1	4	yes	—
279	C₂²×C₈	—	2	8	no	—
280	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
281	C₂²×C₈	C₂³×C₁₃	1	4	yes	—
282	C₂²×C₈	C₂³×C₁₃	1	4	yes	—
283	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
284	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
285	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
286	#127	C₂³×C₁₃	1	2	yes	—
287	#126	—	2	8	no	—
288	#125	—	2	4	no	—
289	#125	C₂³×C₁₃	1	4	yes	—
290	#124	—	2	4	no	—
291	#124	C₂³×C₁₃	1	4	yes	—
292	#123	—	2	8	no	—
293	#123	—	2	4	no	—
294	C₂²⋊Q₈	—	2	4	no	—
295	C₂²⋊Q₈	—	2	4	no	—
296	C₂²⋊Q₈	C₂³×C₁₃	1	8	yes	—
297	#121	—	2	4	no	—
298	#121	—	2	4	no	—
299	#121	C₂³×C₁₃	1	8	yes	—
300	#120	—	2	4	no	—
301	C₄×Q₈	—	2	4	no	—
302	C₄×Q₈	—	2	4	no	—
303	C₄×Q₈	C₂³×C₁₃	1	8	yes	—
304	C₄×D₄	—	2	8	no	—
305	C₄×D₄	—	2	8	no	—
306	C₄×D₄	—	2	8	no	—
307	C₄×D₄	—	2	4	no	—
308	C₄×D₄	—	2	4	no	—
309	C₄×D₄	C₂³×C₁₃	1	8	yes	—
310	#117	—	2	4	no	—
311	#117	—	2	8	no	—
312	#117	—	2	4	no	—
313	#117	C₂³×C₁₃	1	4	yes	—
314	C₂×C₄²	—	2	4	no	—
315	C₂×C₄²	D₄×C₁₃	1	2	yes	—
316	C₂×C₄²	D₄×C₁₃	1	2	yes	—
317	C₂×C₄²	D₄×C₁₃	1	2	yes	—
318	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
319	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
320	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
321	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
322	#107	C₂³×C₁₃	1	8	yes	—
323	#106	C₂³×C₁₃	1	8	yes	—
324	#103	C₂³×C₁₃	1	16	yes	—
325	#102	C₂³×C₁₃	1	16	yes	—
326	C₄×C₈	C₂³×C₁₃	1	4	yes	—
327	C₄×C₈	C₂³×C₁₃	1	4	yes	—
328	C₄×C₈	C₂³×C₁₃	1	2	yes	—
329	C₄×C₈	C₂³×C₁₃	1	2	yes	—
330	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
331	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
332	C₄×C₈	C₂³×C₁₃	1	2	yes	—
333	C₂×C₁₃	—	2	2	no	—
334	C₂×C₁₃	—	2	4	no	—
335	C₂×C₁₃	—	8	4	no	—
336	C₂×C₁₃	C₂×#532	1	1	yes	characteristic
337	C₂×C₁₃	C₂²×#135	1	2	yes	—
338	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
339	#41	—	2	16	no	—
340	#41	—	4	16	no	—
341	C₂×Q₈	—	2	4	no	—
342	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
343	C₂×D₄	—	2	4	no	—
344	C₂×D₄	—	2	8	no	—
345	C₂×D₄	—	2	4	no	—
346	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
347	C₂²×C₄	—	2	8	no	—
348	C₂²×C₄	—	2	4	no	—
349	C₂²×C₄	—	2	4	no	—
350	C₂²×C₄	—	2	8	no	—
351	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
352	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
353	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
354	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
355	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
356	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
357	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
358	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
359	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
360	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
361	Q₁₆	—	2	8	no	—
362	SD₁₆	—	2	16	no	—
363	D₈	—	2	8	no	—
364	C₂×C₈	—	2	4	no	—
365	C₂×C₈	—	2	8	no	—
366	C₂×C₈	—	2	8	no	—
367	C₂×C₈	C₁₃×#41	1	8	yes	complemented
368	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
369	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
370	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
371	C₄⋊C₄	—	2	4	no	—
372	C₄⋊C₄	—	2	4	no	—
373	C₄⋊C₄	—	2	8	no	—
374	C₄⋊C₄	—	2	8	no	—
375	C₄⋊C₄	—	2	8	no	—
376	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
377	C₂²⋊C₄	—	2	8	no	—
378	C₂²⋊C₄	—	2	4	no	—
379	C₂²⋊C₄	—	2	8	no	—
380	C₂²⋊C₄	—	2	8	no	—
381	C₂²⋊C₄	—	2	8	no	—
382	C₄²	—	2	8	no	—
383	C₄²	—	2	4	no	—
384	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
385	C₄²	C₂×D₄×C₁₃	1	2	yes	—
386	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
387	C₄²	C₂×D₄×C₁₃	1	2	yes	—
388	C₄²	C₂×D₄×C₁₃	1	2	yes	—
389	C₄²	C₂×D₄×C₁₃	1	2	yes	—
390	C₄²	C₂×D₄×C₁₃	1	2	yes	—
391	C₄²	C₂⁴×C₁₃	1	2	yes	—
392	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
393	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
394	C₁₃	#60673	1	1	yes	characteristic, direct product factor, Sylow
395	C₂³	—	2	2	no	—
396	C₂³	—	2	4	no	—
397	C₂³	—	2	4	no	—
398	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
399	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
400	Q₈	—	2	8	no	—
401	Q₈	—	4	8	no	—
402	D₄	—	2	8	no	—
403	D₄	—	4	8	no	—
404	D₄	—	4	16	no	—
405	D₄	—	4	8	no	—
406	C₂×C₄	—	2	2	no	—
407	C₂×C₄	—	2	4	no	—
408	C₂×C₄	—	2	4	no	—
409	C₂×C₄	—	2	4	no	—
410	C₂×C₄	—	2	4	no	—
411	C₂×C₄	—	2	4	no	—
412	C₂×C₄	—	2	4	no	—
413	C₂×C₄	—	2	4	no	—
414	C₂×C₄	—	2	4	no	—
415	C₂×C₄	—	2	8	no	—
416	C₂×C₄	—	4	8	no	—
417	C₂×C₄	—	4	16	no	—
418	C₂×C₄	C₁₃×#135	1	8	yes	complemented
419	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
420	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
421	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
422	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
423	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
424	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
425	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
426	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
427	C₈	—	2	4	no	—
428	C₈	C₂×C₁₃×#41	1	4	yes	—
429	C₈	C₂×C₁₃×#41	1	4	yes	—
430	C₂²	—	2	8	no	—
431	C₂²	—	2	2	no	—
432	C₂²	—	2	2	no	—
433	C₂²	—	2	2	no	—
434	C₂²	—	4	8	no	—
435	C₂²	—	4	4	no	—
436	C₂²	C₁₃×#532	1	2	yes	—
437	C₂²	C₂×C₁₃×#135	1	4	yes	—
438	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
439	C₄	—	2	2	no	—
440	C₄	—	2	2	no	—
441	C₄	—	2	2	no	—
442	C₄	—	4	8	no	—
443	C₄	—	4	4	no	—
444	C₄	C₁₃×#532	1	2	yes	—
445	C₄	C₂×C₁₃×#135	1	4	yes	—
446	C₄	C₂×C₁₃×#135	1	4	yes	—
447	C₄	C₂²×C₁₃×#41	1	2	yes	—
448	C₂	—	2	2	no	—
449	C₂	—	2	4	no	—
450	C₂	—	8	4	no	—
451	C₂	C₂×C₁₃×#532	1	1	yes	characteristic
452	C₂	C₂²×C₁₃×#135	1	2	yes	—

	subgroup	G/H
center	C₄²×C₁₃	C₂×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
socle	C₂²×C₁₃	C₂³×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄²×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. C₁₃×#3170	C₂	semidirect
3. C₁₃×#3169	C₂	semidirect
4. C₁₃×#3168	C₂	semidirect
5. C₁₃×#3167	C₂	semidirect
6. C₁₃×#3160	C₂	semidirect
7. C₁₃×#3147	C₂	semidirect
8. C₁₃×#3131	C₂	semidirect
9. C₁₃×#3050	C₂	semidirect
10. C₄×C₁₃×#135	C₂	semidirect
11. C₂²×C₄×C₈×C₁₃	C₂	semidirect
26. C₁₃×#500	C₂²	semidirect
27. C₁₃×#499	C₂²	semidirect
28. C₁₃×#498	C₂²	semidirect
29. C₁₃×#495	C₂²	semidirect
30. C₁₃×#494	C₂²	semidirect
31. C₁₃×#493	C₂²	semidirect
32. C₁₃×#492	C₂²	semidirect
33. C₁₃×#488	C₂²	semidirect
34. C₁₃×#487	C₂²	semidirect
35. C₁₃×#486	C₂²	semidirect
39. C₄×C₁₃×Q₁₆	C₂²	semidirect
40. C₄×C₁₃×SD₁₆	C₂²	semidirect
41. C₄×C₁₃×D₈	C₂²	semidirect
112. #60673	C₁₃	direct (N × H)
142. C₂×C₈×C₁₃	#41	semidirect
169. #3444	C₂×C₁₃	semidirect
170. #3170	C₂×C₁₃	semidirect
171. #3169	C₂×C₁₃	semidirect
172. #3168	C₂×C₁₃	semidirect
173. #3167	C₂×C₁₃	semidirect
174. #3160	C₂×C₁₃	semidirect
175. #3147	C₂×C₁₃	semidirect
176. #3131	C₂×C₁₃	semidirect
177. #3050	C₂×C₁₃	semidirect
178. C₄×#135	C₂×C₁₃	semidirect
179. C₂²×C₄×C₈	C₂×C₁₃	semidirect
203. C₂×C₄×C₁₃	#135	semidirect
229. #500	C₂²×C₁₃	semidirect
230. #499	C₂²×C₁₃	semidirect
231. #498	C₂²×C₁₃	semidirect
232. #495	C₂²×C₁₃	semidirect
233. #494	C₂²×C₁₃	semidirect
234. #493	C₂²×C₁₃	semidirect
235. #492	C₂²×C₁₃	semidirect
236. #488	C₂²×C₁₃	semidirect
237. #487	C₂²×C₁₃	semidirect
238. #486	C₂²×C₁₃	semidirect
242. C₄×Q₁₆	C₂²×C₁₃	semidirect
243. C₄×SD₁₆	C₂²×C₁₃	semidirect
244. C₄×D₈	C₂²×C₁₃	semidirect
367. C₂×C₈	C₁₃×#41	semidirect
394. C₁₃	#60673	direct (N × H)
418. C₂×C₄	C₁₃×#135	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₁₃×#3444	2
C₁₃×#3170	2
C₁₃×#3169	2
C₁₃×#3168	2
C₁₃×#3167	2
C₁₃×#3160	2
C₁₃×#3147	2
C₁₃×#3131	2
C₁₃×#3050	2
C₄×C₁₃×#135	2
C₂²×C₄×C₈×C₁₃	2
#60673	13

Subgroups — C13×#60673 #15747012

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#60673 #15747012