Subgroups — C₁₃×#61375 #15747714

Order 3328.

1706 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3504	C₂	1	2	yes	maximal, complemented
2	C₁₃×#3390	C₂	1	4	yes	maximal, complemented
3	C₁₃×#3389	C₂	1	4	yes	maximal, complemented
4	C₁₃×#3381	C₂	1	8	yes	maximal, complemented
5	C₁₃×#3163	C₂	1	2	yes	maximal, complemented
6	C₂×C₁₃×#499	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#3083	C₂	1	4	yes	maximal, complemented
8	C₁₃×#3080	C₂	1	2	yes	maximal, complemented
9	C₁₃×#2960	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#2952	C₂	1	2	yes	maximal
11	C₄×C₁₃×#135	C₂	1	1	yes	maximal, characteristic
12	C₂×C₁₃×#135	C₂²	1	1	yes	characteristic
13	C₁₃×#557	C₂²	1	8	yes	—
14	C₁₃×#554	—	2	8	no	—
15	C₁₃×#554	C₂²	1	8	yes	—
16	C₁₃×#544	—	2	4	no	—
17	C₁₃×#544	C₂²	1	4	yes	—
18	C₁₃×#533	—	2	2	no	—
19	C₁₃×#533	C₂²	1	1	yes	characteristic
20	C₂×C₁₃×#125	—	2	2	no	—
21	C₂×C₁₃×#125	C₂²	1	2	yes	—
22	C₁₃×#520	C₂²	1	4	yes	—
23	C₄×C₁₃×#41	C₂²	1	2	yes	—
24	C₁₃×#501	C₂²	1	8	yes	—
25	C₁₃×#499	C₂²	1	4	yes	—
26	C₁₃×#499	C₂²	1	4	yes	—
27	C₁₃×#499	C₂²	1	4	yes	—
28	C₁₃×#498	C₂²	1	4	yes	—
29	C₁₃×#479	C₂²	1	8	yes	—
30	C₁₃×#479	C₂²	1	8	yes	—
31	C₁₃×#478	C₂²	1	8	yes	—
32	C₁₃×#478	C₂²	1	8	yes	—
33	C₁₃×#477	C₂²	1	8	yes	—
34	C₁₃×#474	C₂²	1	8	yes	—
35	C₁₃×#446	C₂²	1	4	yes	—
36	C₈×Q₈×C₁₃	C₂²	1	4	yes	—
37	C₁₃×#442	C₂²	1	4	yes	—
38	C₁₃×#441	C₂²	1	4	yes	—
39	C₄×C₁₃×Q₁₆	C₂²	1	2	yes	—
40	C₄×C₁₃×SD₁₆	C₂²	1	4	yes	—
41	C₄×C₁₃×SD₁₆	C₂²	1	8	yes	—
42	C₄×C₁₃×D₈	C₂²	1	2	yes	—
43	C₁₃×#428	C₂²	1	4	yes	—
44	C₁₃×#427	C₂²	1	1	yes	characteristic
45	C₂×C₁₃×#107	C₂²	1	2	yes	—
46	C₂×C₁₃×#106	C₂²	1	2	yes	—
47	C₁₃×#424	C₂²	1	2	yes	—
48	C₁₃×#423	C₂²	1	1	yes	characteristic
49	C₁₃×#417	C₂²	1	4	yes	—
50	C₁₃×#416	C₂²	1	2	yes	—
51	C₁₃×#405	C₂²	1	2	yes	—
52	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
53	C₂×C₁₃×#41	C₂³	1	2	yes	—
54	C₁₃×#135	Q₈	1	8	yes	complemented
55	C₂×C₁₃×Q₁₆	C₂³	1	1	yes	characteristic
56	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
57	C₂×C₁₃×D₈	C₂³	1	1	yes	characteristic
58	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
59	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
60	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
61	C₁₃×C₄⋊Q₈	—	2	8	no	—
62	C₁₃×C₄⋊Q₈	—	2	4	no	—
63	C₁₃×C₄⋊Q₈	D₄	1	2	yes	—
64	C₁₃×C₄⋊Q₈	C₂³	1	8	yes	—
65	C₁₃×#125	—	2	4	no	—
66	C₁₃×#125	—	2	8	no	—
67	C₁₃×#125	—	2	8	no	—
68	C₁₃×#125	—	2	2	no	—
69	C₁₃×#125	—	2	2	no	—
70	C₁₃×#125	D₄	1	2	yes	—
71	C₁₃×#125	C₂³	1	8	yes	—
72	C₁₃×#125	C₂³	1	8	yes	—
73	C₁₃×C₂²⋊Q₈	—	2	8	no	—
74	C₁₃×C₂²⋊Q₈	—	2	8	no	—
75	C₁₃×C₂²⋊Q₈	—	2	8	no	—
76	C₁₃×C₂²⋊Q₈	—	2	8	no	—
77	C₁₃×C₂²⋊Q₈	D₄	1	4	yes	—
78	C₄×Q₈×C₁₃	—	2	8	no	—
79	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
80	C₄×Q₈×C₁₃	C₂³	1	8	yes	—
81	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
82	C₄×D₄×C₁₃	—	2	4	no	—
83	C₄×D₄×C₁₃	—	2	8	no	—
84	C₄×D₄×C₁₃	C₂³	1	4	yes	—
85	C₄×D₄×C₁₃	C₂³	1	8	yes	—
86	C₁₃×#117	—	2	4	no	—
87	C₁₃×#117	—	2	2	no	—
88	C₁₃×#117	C₂³	1	2	yes	—
89	C₁₃×#117	C₂³	1	2	yes	—
90	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
91	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
92	C₂×C₁₃×C₄⋊C₄	—	2	8	no	—
93	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
94	C₂×C₄²×C₁₃	—	2	2	no	—
95	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
96	C₁₃×#107	C₂³	1	4	yes	—
97	C₁₃×#107	C₂³	1	4	yes	—
98	C₁₃×#107	C₂³	1	2	yes	—
99	C₁₃×#107	C₂³	1	8	yes	—
100	C₁₃×#106	C₂³	1	4	yes	—
101	C₁₃×#106	C₂³	1	4	yes	—
102	C₁₃×#106	C₂³	1	2	yes	—
103	C₁₃×#106	C₂³	1	8	yes	—
104	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
105	C₁₃×C₄⋊C₈	C₂³	1	8	yes	—
106	C₁₃×#103	C₂³	1	4	yes	—
107	C₁₃×#103	C₂³	1	8	yes	—
108	C₁₃×#102	C₂³	1	4	yes	—
109	C₁₃×#102	C₂³	1	8	yes	—
110	C₁₃×#97	C₂³	1	4	yes	—
111	C₄×C₈×C₁₃	C₂³	1	2	yes	—
112	C₄×C₈×C₁₃	C₂³	1	2	yes	—
113	C₄×C₈×C₁₃	C₂³	1	4	yes	—
114	#61375	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
115	C₁₃×#41	—	2	4	no	—
116	C₁₃×#41	C₂×Q₈	1	8	yes	—
117	C₂×Q₈×C₁₃	—	2	8	no	—
118	C₂×Q₈×C₁₃	C₂×D₄	1	4	yes	—
119	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
120	C₂×D₄×C₁₃	—	2	2	no	—
121	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
122	C₂²×C₄×C₁₃	—	2	2	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	C₂⁴	1	1	yes	characteristic
128	C₁₃×Q₁₆	C₂×Q₈	1	4	yes	—
129	C₁₃×SD₁₆	C₂×Q₈	1	8	yes	—
130	C₁₃×D₈	C₂×Q₈	1	4	yes	—
131	C₁₃×M₁₆	—	2	4	no	—
132	C₂×C₈×C₁₃	—	2	2	no	—
133	C₂×C₈×C₁₃	C₂×Q₈	1	4	yes	—
134	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
135	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
136	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
137	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
138	C₁₃×C₄⋊C₄	—	2	8	no	—
139	C₁₃×C₄⋊C₄	—	2	4	no	—
140	C₁₃×C₄⋊C₄	—	2	8	no	—
141	C₁₃×C₄⋊C₄	—	2	8	no	—
142	C₁₃×C₄⋊C₄	—	2	8	no	—
143	C₁₃×C₄⋊C₄	—	2	8	no	—
144	C₁₃×C₄⋊C₄	—	2	4	no	—
145	C₁₃×C₄⋊C₄	—	2	8	no	—
146	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
147	C₁₃×C₄⋊C₄	C₂×D₄	1	8	yes	—
148	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
149	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
150	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
151	C₁₃×C₂²⋊C₄	—	2	2	no	—
152	C₁₃×C₂²⋊C₄	—	2	4	no	—
153	C₁₃×C₂²⋊C₄	—	2	8	no	—
154	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
155	C₄²×C₁₃	—	2	2	no	—
156	C₄²×C₁₃	—	2	4	no	—
157	C₄²×C₁₃	—	2	8	no	—
158	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
159	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
160	C₄²×C₁₃	C₂⁴	1	2	yes	—
161	C₄²×C₁₃	C₂⁴	1	4	yes	—
162	#3504	C₂×C₁₃	1	2	yes	complemented
163	#3390	C₂×C₁₃	1	4	yes	complemented
164	#3389	C₂×C₁₃	1	4	yes	complemented
165	#3381	C₂×C₁₃	1	8	yes	complemented
166	#3163	C₂×C₁₃	1	2	yes	complemented
167	C₂×#499	C₂×C₁₃	1	1	yes	characteristic, complemented
168	#3083	C₂×C₁₃	1	4	yes	complemented
169	#3080	C₂×C₁₃	1	2	yes	complemented
170	#2960	C₂×C₁₃	1	1	yes	characteristic, complemented
171	#2952	C₂×C₁₃	1	2	yes	—
172	C₄×#135	C₂×C₁₃	1	1	yes	characteristic
173	C₂³×C₁₃	—	2	2	no	—
174	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
175	Q₈×C₁₃	—	2	2	no	—
176	Q₈×C₁₃	—	4	4	no	—
177	Q₈×C₁₃	—	8	8	no	—
178	Q₈×C₁₃	C₂²×Q₈	1	4	yes	—
179	D₄×C₁₃	—	2	8	no	—
180	D₄×C₁₃	—	2	2	no	—
181	D₄×C₁₃	C₂²×Q₈	1	4	yes	—
182	C₂×C₄×C₁₃	—	2	2	no	—
183	C₂×C₄×C₁₃	—	2	8	no	—
184	C₂×C₄×C₁₃	—	2	4	no	—
185	C₂×C₄×C₁₃	—	2	8	no	—
186	C₂×C₄×C₁₃	—	4	2	no	—
187	C₂×C₄×C₁₃	—	8	4	no	—
188	C₂×C₄×C₁₃	—	8	8	no	—
189	C₂×C₄×C₁₃	—	8	4	no	—
190	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
191	C₂×C₄×C₁₃	C₂²×D₄	1	8	yes	—
192	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
193	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
194	C₂×C₄×C₁₃	C₂²×Q₈	1	2	yes	—
195	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
196	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
197	C₈×C₁₃	—	2	2	no	—
198	C₈×C₁₃	—	2	4	no	—
199	C₈×C₁₃	C₂²×Q₈	1	2	yes	—
200	C₈×C₁₃	C₂²×Q₈	1	2	yes	—
201	C₂×#135	C₂²×C₁₃	1	1	yes	characteristic
202	#557	C₂²×C₁₃	1	8	yes	—
203	#554	—	2	8	no	—
204	#554	C₂²×C₁₃	1	8	yes	—
205	#544	—	2	4	no	—
206	#544	C₂²×C₁₃	1	4	yes	—
207	#533	—	2	2	no	—
208	#533	C₂²×C₁₃	1	1	yes	characteristic
209	C₂×#125	—	2	2	no	—
210	C₂×#125	C₂²×C₁₃	1	2	yes	—
211	#520	C₂²×C₁₃	1	4	yes	—
212	C₄×#41	C₂²×C₁₃	1	2	yes	—
213	#501	C₂²×C₁₃	1	8	yes	—
214	#499	C₂²×C₁₃	1	4	yes	—
215	#499	C₂²×C₁₃	1	4	yes	—
216	#499	C₂²×C₁₃	1	4	yes	—
217	#498	C₂²×C₁₃	1	4	yes	—
218	#479	C₂²×C₁₃	1	8	yes	—
219	#479	C₂²×C₁₃	1	8	yes	—
220	#478	C₂²×C₁₃	1	8	yes	—
221	#478	C₂²×C₁₃	1	8	yes	—
222	#477	C₂²×C₁₃	1	8	yes	—
223	#474	C₂²×C₁₃	1	8	yes	—
224	#446	C₂²×C₁₃	1	4	yes	—
225	C₈×Q₈	C₂²×C₁₃	1	4	yes	—
226	#442	C₂²×C₁₃	1	4	yes	—
227	#441	C₂²×C₁₃	1	4	yes	—
228	C₄×Q₁₆	C₂²×C₁₃	1	2	yes	—
229	C₄×SD₁₆	C₂²×C₁₃	1	4	yes	—
230	C₄×SD₁₆	C₂²×C₁₃	1	8	yes	—
231	C₄×D₈	C₂²×C₁₃	1	2	yes	—
232	#428	C₂²×C₁₃	1	4	yes	—
233	#427	C₂²×C₁₃	1	1	yes	characteristic
234	C₂×#107	C₂²×C₁₃	1	2	yes	—
235	C₂×#106	C₂²×C₁₃	1	2	yes	—
236	#424	C₂²×C₁₃	1	2	yes	—
237	#423	C₂²×C₁₃	1	1	yes	characteristic
238	#417	C₂²×C₁₃	1	4	yes	—
239	#416	C₂²×C₁₃	1	2	yes	—
240	#405	C₂²×C₁₃	1	2	yes	—
241	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
242	C₂²×C₁₃	—	2	2	no	—
243	C₂²×C₁₃	—	2	4	no	—
244	C₂²×C₁₃	—	4	4	no	—
245	C₂²×C₁₃	D₄×Q₈	1	2	yes	—
246	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
247	C₄×C₁₃	—	2	2	no	—
248	C₄×C₁₃	—	2	2	no	—
249	C₄×C₁₃	—	2	8	no	—
250	C₄×C₁₃	—	2	4	no	—
251	C₄×C₁₃	—	4	8	no	—
252	C₄×C₁₃	—	4	4	no	—
253	C₄×C₁₃	D₄×Q₈	1	2	yes	—
254	C₄×C₁₃	C₂³×Q₈	1	1	yes	characteristic
255	C₄×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
256	C₂×#41	C₂³×C₁₃	1	2	yes	—
257	#135	Q₈×C₁₃	1	8	yes	complemented
258	C₂×Q₁₆	C₂³×C₁₃	1	1	yes	characteristic
259	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
260	C₂×D₈	C₂³×C₁₃	1	1	yes	characteristic
261	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
262	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
263	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
264	C₄⋊Q₈	—	2	8	no	—
265	C₄⋊Q₈	—	2	4	no	—
266	C₄⋊Q₈	D₄×C₁₃	1	2	yes	—
267	C₄⋊Q₈	C₂³×C₁₃	1	8	yes	—
268	#125	—	2	4	no	—
269	#125	—	2	8	no	—
270	#125	—	2	8	no	—
271	#125	—	2	2	no	—
272	#125	—	2	2	no	—
273	#125	D₄×C₁₃	1	2	yes	—
274	#125	C₂³×C₁₃	1	8	yes	—
275	#125	C₂³×C₁₃	1	8	yes	—
276	C₂²⋊Q₈	—	2	8	no	—
277	C₂²⋊Q₈	—	2	8	no	—
278	C₂²⋊Q₈	—	2	8	no	—
279	C₂²⋊Q₈	—	2	8	no	—
280	C₂²⋊Q₈	D₄×C₁₃	1	4	yes	—
281	C₄×Q₈	—	2	8	no	—
282	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
283	C₄×Q₈	C₂³×C₁₃	1	8	yes	—
284	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
285	C₄×D₄	—	2	4	no	—
286	C₄×D₄	—	2	8	no	—
287	C₄×D₄	C₂³×C₁₃	1	4	yes	—
288	C₄×D₄	C₂³×C₁₃	1	8	yes	—
289	#117	—	2	4	no	—
290	#117	—	2	2	no	—
291	#117	C₂³×C₁₃	1	2	yes	—
292	#117	C₂³×C₁₃	1	2	yes	—
293	C₂×C₄⋊C₄	—	2	4	no	—
294	C₂×C₄⋊C₄	—	2	4	no	—
295	C₂×C₄⋊C₄	—	2	8	no	—
296	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
297	C₂×C₄²	—	2	2	no	—
298	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
299	#107	C₂³×C₁₃	1	4	yes	—
300	#107	C₂³×C₁₃	1	4	yes	—
301	#107	C₂³×C₁₃	1	2	yes	—
302	#107	C₂³×C₁₃	1	8	yes	—
303	#106	C₂³×C₁₃	1	4	yes	—
304	#106	C₂³×C₁₃	1	4	yes	—
305	#106	C₂³×C₁₃	1	2	yes	—
306	#106	C₂³×C₁₃	1	8	yes	—
307	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
308	C₄⋊C₈	C₂³×C₁₃	1	8	yes	—
309	#103	C₂³×C₁₃	1	4	yes	—
310	#103	C₂³×C₁₃	1	8	yes	—
311	#102	C₂³×C₁₃	1	4	yes	—
312	#102	C₂³×C₁₃	1	8	yes	—
313	#97	C₂³×C₁₃	1	4	yes	—
314	C₄×C₈	C₂³×C₁₃	1	2	yes	—
315	C₄×C₈	C₂³×C₁₃	1	2	yes	—
316	C₄×C₈	C₂³×C₁₃	1	4	yes	—
317	C₂×C₁₃	—	2	2	no	—
318	C₂×C₁₃	—	4	4	no	—
319	C₂×C₁₃	C₂×D₄×Q₈	1	1	yes	characteristic
320	C₂×C₁₃	#3584	1	2	yes	—
321	#41	—	2	4	no	—
322	#41	C₂×Q₈×C₁₃	1	8	yes	—
323	C₂×Q₈	—	2	8	no	—
324	C₂×Q₈	C₂×D₄×C₁₃	1	4	yes	—
325	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
326	C₂×D₄	—	2	2	no	—
327	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
328	C₂²×C₄	—	2	2	no	—
329	C₂²×C₄	—	2	4	no	—
330	C₂²×C₄	—	2	4	no	—
331	C₂²×C₄	—	2	8	no	—
332	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
333	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
334	Q₁₆	C₂×Q₈×C₁₃	1	4	yes	—
335	SD₁₆	C₂×Q₈×C₁₃	1	8	yes	—
336	D₈	C₂×Q₈×C₁₃	1	4	yes	—
337	M₁₆	—	2	4	no	—
338	C₂×C₈	—	2	2	no	—
339	C₂×C₈	C₂×Q₈×C₁₃	1	4	yes	—
340	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
341	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
342	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
343	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
344	C₄⋊C₄	—	2	8	no	—
345	C₄⋊C₄	—	2	4	no	—
346	C₄⋊C₄	—	2	8	no	—
347	C₄⋊C₄	—	2	8	no	—
348	C₄⋊C₄	—	2	8	no	—
349	C₄⋊C₄	—	2	8	no	—
350	C₄⋊C₄	—	2	4	no	—
351	C₄⋊C₄	—	2	8	no	—
352	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
353	C₄⋊C₄	C₂×D₄×C₁₃	1	8	yes	—
354	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
355	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
356	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
357	C₂²⋊C₄	—	2	2	no	—
358	C₂²⋊C₄	—	2	4	no	—
359	C₂²⋊C₄	—	2	8	no	—
360	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
361	C₄²	—	2	2	no	—
362	C₄²	—	2	4	no	—
363	C₄²	—	2	8	no	—
364	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
365	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
366	C₄²	C₂⁴×C₁₃	1	2	yes	—
367	C₄²	C₂⁴×C₁₃	1	4	yes	—
368	C₁₃	#61375	1	1	yes	characteristic, direct product factor, Sylow
369	C₂³	—	2	2	no	—
370	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
371	Q₈	—	2	2	no	—
372	Q₈	—	4	4	no	—
373	Q₈	—	8	8	no	—
374	Q₈	C₂²×Q₈×C₁₃	1	4	yes	—
375	D₄	—	2	8	no	—
376	D₄	—	2	2	no	—
377	D₄	C₂²×Q₈×C₁₃	1	4	yes	—
378	C₂×C₄	—	2	2	no	—
379	C₂×C₄	—	2	8	no	—
380	C₂×C₄	—	2	4	no	—
381	C₂×C₄	—	2	8	no	—
382	C₂×C₄	—	4	2	no	—
383	C₂×C₄	—	8	4	no	—
384	C₂×C₄	—	8	8	no	—
385	C₂×C₄	—	8	4	no	—
386	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
387	C₂×C₄	C₂²×D₄×C₁₃	1	8	yes	—
388	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
389	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
390	C₂×C₄	C₂²×Q₈×C₁₃	1	2	yes	—
391	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
392	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
393	C₈	—	2	2	no	—
394	C₈	—	2	4	no	—
395	C₈	C₂²×Q₈×C₁₃	1	2	yes	—
396	C₈	C₂²×Q₈×C₁₃	1	2	yes	—
397	C₂²	—	2	2	no	—
398	C₂²	—	2	4	no	—
399	C₂²	—	4	4	no	—
400	C₂²	D₄×Q₈×C₁₃	1	2	yes	—
401	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
402	C₄	—	2	2	no	—
403	C₄	—	2	2	no	—
404	C₄	—	2	8	no	—
405	C₄	—	2	4	no	—
406	C₄	—	4	8	no	—
407	C₄	—	4	4	no	—
408	C₄	D₄×Q₈×C₁₃	1	2	yes	—
409	C₄	C₂³×Q₈×C₁₃	1	1	yes	characteristic
410	C₄	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
411	C₂	—	2	2	no	—
412	C₂	—	4	4	no	—
413	C₂	C₂×D₄×Q₈×C₁₃	1	1	yes	characteristic
414	C₂	C₁₃×#3584	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
prime radical	C₂×C₁₃×#135	C₂²
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×#3504	C₂	semidirect
2. C₁₃×#3390	C₂	semidirect
3. C₁₃×#3389	C₂	semidirect
4. C₁₃×#3381	C₂	semidirect
5. C₁₃×#3163	C₂	semidirect
6. C₂×C₁₃×#499	C₂	semidirect
7. C₁₃×#3083	C₂	semidirect
8. C₁₃×#3080	C₂	semidirect
9. C₁₃×#2960	C₂	semidirect
54. C₁₃×#135	Q₈	semidirect
114. #61375	C₁₃	direct (N × H)
162. #3504	C₂×C₁₃	semidirect
163. #3390	C₂×C₁₃	semidirect
164. #3389	C₂×C₁₃	semidirect
165. #3381	C₂×C₁₃	semidirect
166. #3163	C₂×C₁₃	semidirect
167. C₂×#499	C₂×C₁₃	semidirect
168. #3083	C₂×C₁₃	semidirect
169. #3080	C₂×C₁₃	semidirect
170. #2960	C₂×C₁₃	semidirect
257. #135	Q₈×C₁₃	semidirect
368. C₁₃	#61375	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×#3504	2
C₁₃×#3390	2
C₁₃×#3389	2
C₁₃×#3381	2
C₁₃×#3163	2
C₂×C₁₃×#499	2
C₁₃×#3083	2
C₁₃×#3080	2
C₁₃×#2960	2
C₁₃×#2952	2
C₄×C₁₃×#135	2
#61375	13

Subgroups — C13×#61375 #15747714

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61375 #15747714