Subgroups — C₁₃×#61889 #15748228

Order 3328.

1706 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3502	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#556	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#3398	C₂	1	8	yes	maximal, complemented
4	C₁₃×#3369	C₂	1	8	yes	maximal, complemented
5	C₁₃×#3215	C₂	1	4	yes	maximal
6	C₁₃×#3209	C₂	1	2	yes	maximal, complemented
7	C₁₃×#3113	C₂	1	4	yes	maximal, complemented
8	C₁₃×#3101	C₂	1	2	yes	maximal
9	C₁₃×#2983	C₂	1	1	yes	maximal, characteristic, complemented
10	Q₈²×C₁₃	C₂²	1	4	yes	complemented
11	C₁₃×#557	—	2	4	no	—
12	C₁₃×#557	C₂²	1	4	yes	complemented
13	C₁₃×#556	—	2	4	no	—
14	C₁₃×#556	C₂²	1	8	yes	—
15	C₁₃×#544	—	2	1	no	—
16	C₁₃×#544	—	2	2	no	—
17	C₁₃×#533	C₂²	1	2	yes	—
18	C₁₃×#533	C₂²	1	4	yes	—
19	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
20	C₂×C₁₃×#126	—	2	2	no	—
21	C₂×C₁₃×#124	C₂²	1	2	yes	—
22	C₂×C₁₃×C₂²⋊Q₈	—	2	1	no	—
23	C₁₃×#519	—	2	1	no	—
24	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	—
25	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
26	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
27	C₂×C₁₃×#117	—	2	1	no	—
28	C₁₃×#497	C₂²	1	8	yes	—
29	C₁₃×#494	C₂²	1	4	yes	complemented
30	C₁₃×#489	C₂²	1	8	yes	—
31	C₁₃×#487	C₂²	1	4	yes	complemented
32	C₁₃×#483	C₂²	1	4	yes	—
33	C₁₃×#476	C₂²	1	4	yes	—
34	C₁₃×#475	C₂²	1	8	yes	complemented
35	C₁₃×#464	C₂²	1	16	yes	—
36	C₁₃×#462	C₂²	1	8	yes	complemented
37	C₁₃×#462	C₂²	1	8	yes	complemented
38	C₁₃×#461	C₂²	1	4	yes	—
39	C₁₃×#451	C₂²	1	8	yes	—
40	C₁₃×#450	C₂²	1	4	yes	—
41	C₁₃×#446	C₂²	1	8	yes	complemented
42	C₁₃×#441	C₂²	1	16	yes	complemented
43	C₄×C₁₃×SD₁₆	C₂²	1	8	yes	—
44	C₁₃×#432	C₂²	1	4	yes	—
45	C₁₃×#431	C₂²	1	2	yes	—
46	C₂²×Q₈×C₁₃	D₄	1	1	yes	characteristic
47	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
48	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
49	C₂³×C₄×C₁₃	—	2	1	no	—
50	C₂×C₁₃×Q₁₆	C₂³	1	16	yes	—
51	C₂×C₁₃×SD₁₆	C₂³	1	8	yes	—
52	C₁₃×C₄⋊Q₈	—	2	4	no	—
53	C₁₃×C₄⋊Q₈	—	2	8	no	—
54	C₁₃×C₄⋊Q₈	—	2	2	no	—
55	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
56	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
57	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
58	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
59	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
60	C₁₃×#126	—	2	16	no	—
61	C₁₃×#125	—	2	4	no	—
62	C₁₃×#125	—	2	8	no	—
63	C₁₃×#125	—	2	2	no	—
64	C₁₃×#125	—	2	4	no	—
65	C₁₃×#124	—	2	4	no	—
66	C₁₃×#124	C₂³	1	8	yes	—
67	C₁₃×C₂²⋊Q₈	—	2	8	no	—
68	C₁₃×C₂²⋊Q₈	—	2	4	no	—
69	C₁₃×C₂²⋊Q₈	—	2	2	no	—
70	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
71	C₄×Q₈×C₁₃	—	2	4	no	—
72	C₄×Q₈×C₁₃	—	2	4	no	—
73	C₄×Q₈×C₁₃	—	2	4	no	—
74	C₄×Q₈×C₁₃	—	2	2	no	—
75	C₄×Q₈×C₁₃	—	2	4	no	—
76	C₄×Q₈×C₁₃	D₄	1	4	yes	—
77	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
78	C₄×Q₈×C₁₃	C₂³	1	8	yes	—
79	C₄×Q₈×C₁₃	C₂³	1	8	yes	—
80	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
81	C₄×D₄×C₁₃	—	2	2	no	—
82	C₄×D₄×C₁₃	C₂³	1	4	yes	—
83	C₁₃×#117	—	2	4	no	—
84	C₁₃×#117	—	2	2	no	—
85	C₁₃×#117	—	2	8	no	—
86	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
87	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
88	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
89	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
90	C₂×C₁₃×C₄⋊C₄	D₄	1	2	yes	—
91	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
92	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
93	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
94	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
95	C₂×C₄²×C₁₃	—	2	2	no	—
96	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
97	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
98	C₁₃×#106	C₂³	1	8	yes	—
99	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
100	C₁₃×C₄⋊C₈	C₂³	1	8	yes	—
101	C₁₃×#103	C₂³	1	8	yes	—
102	C₁₃×#103	C₂³	1	16	yes	—
103	C₁₃×#102	C₂³	1	8	yes	—
104	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
105	C₁₃×#97	C₂³	1	8	yes	—
106	C₄×C₈×C₁₃	C₂³	1	4	yes	—
107	#61889	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
108	C₂⁴×C₁₃	—	2	1	no	—
109	C₂×Q₈×C₁₃	—	2	4	no	—
110	C₂×Q₈×C₁₃	—	2	2	no	—
111	C₂×Q₈×C₁₃	—	2	4	no	—
112	C₂×Q₈×C₁₃	—	2	2	no	—
113	C₂×Q₈×C₁₃	—	4	4	no	—
114	C₂×Q₈×C₁₃	C₂×D₄	1	4	yes	—
115	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
116	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
117	C₂×D₄×C₁₃	—	2	1	no	—
118	C₂×D₄×C₁₃	—	4	2	no	—
119	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
120	C₂²×C₄×C₁₃	—	2	1	no	—
121	C₂²×C₄×C₁₃	—	2	2	no	—
122	C₂²×C₄×C₁₃	—	2	4	no	—
123	C₂²×C₄×C₁₃	—	4	4	no	—
124	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
125	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
126	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
127	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
128	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
129	C₁₃×Q₁₆	—	4	16	no	—
130	C₁₃×SD₁₆	—	4	8	no	—
131	C₂×C₈×C₁₃	C₂⁴	1	8	yes	—
132	C₁₃×C₄⋊C₄	—	2	4	no	—
133	C₁₃×C₄⋊C₄	—	2	8	no	—
134	C₁₃×C₄⋊C₄	—	2	4	no	—
135	C₁₃×C₄⋊C₄	—	2	1	no	—
136	C₁₃×C₄⋊C₄	—	2	4	no	—
137	C₁₃×C₄⋊C₄	—	2	2	no	—
138	C₁₃×C₄⋊C₄	—	2	4	no	—
139	C₁₃×C₄⋊C₄	—	2	2	no	—
140	C₁₃×C₄⋊C₄	—	2	4	no	—
141	C₁₃×C₄⋊C₄	—	2	4	no	—
142	C₁₃×C₄⋊C₄	—	2	2	no	—
143	C₁₃×C₄⋊C₄	—	2	8	no	—
144	C₁₃×C₄⋊C₄	—	2	4	no	—
145	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
146	C₁₃×C₄⋊C₄	C₂×D₄	1	8	yes	—
147	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
148	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
149	C₁₃×C₂²⋊C₄	—	2	4	no	—
150	C₁₃×C₂²⋊C₄	—	2	8	no	—
151	C₁₃×C₂²⋊C₄	—	2	4	no	—
152	C₁₃×C₂²⋊C₄	—	2	8	no	—
153	C₄²×C₁₃	—	2	8	no	—
154	C₄²×C₁₃	—	2	8	no	—
155	C₄²×C₁₃	—	2	4	no	—
156	C₄²×C₁₃	C₂×D₄	1	2	yes	—
157	C₄²×C₁₃	C₂×D₄	1	4	yes	—
158	C₄²×C₁₃	C₂⁴	1	2	yes	—
159	C₄²×C₁₃	C₂⁴	1	4	yes	—
160	#3502	C₂×C₁₃	1	1	yes	characteristic, complemented
161	C₂×#556	C₂×C₁₃	1	1	yes	characteristic
162	#3398	C₂×C₁₃	1	8	yes	complemented
163	#3369	C₂×C₁₃	1	8	yes	complemented
164	#3215	C₂×C₁₃	1	4	yes	—
165	#3209	C₂×C₁₃	1	2	yes	complemented
166	#3113	C₂×C₁₃	1	4	yes	complemented
167	#3101	C₂×C₁₃	1	2	yes	—
168	#2983	C₂×C₁₃	1	1	yes	characteristic, complemented
169	C₂³×C₁₃	—	2	2	no	—
170	C₂³×C₁₃	—	4	2	no	—
171	C₂³×C₁₃	—	4	2	no	—
172	C₂³×C₁₃	—	4	2	no	—
173	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
174	Q₈×C₁₃	—	2	8	no	—
175	Q₈×C₁₃	—	2	8	no	—
176	Q₈×C₁₃	—	2	8	no	—
177	Q₈×C₁₃	—	4	4	no	—
178	Q₈×C₁₃	—	8	4	no	—
179	Q₈×C₁₃	—	8	2	no	—
180	D₄×C₁₃	—	2	4	no	—
181	D₄×C₁₃	—	4	2	no	—
182	C₂×C₄×C₁₃	—	2	4	no	—
183	C₂×C₄×C₁₃	—	2	2	no	—
184	C₂×C₄×C₁₃	—	2	2	no	—
185	C₂×C₄×C₁₃	—	2	4	no	—
186	C₂×C₄×C₁₃	—	2	4	no	—
187	C₂×C₄×C₁₃	—	2	4	no	—
188	C₂×C₄×C₁₃	—	4	2	no	—
189	C₂×C₄×C₁₃	—	4	1	no	—
190	C₂×C₄×C₁₃	—	4	4	no	—
191	C₂×C₄×C₁₃	—	4	2	no	—
192	C₂×C₄×C₁₃	—	4	8	no	—
193	C₂×C₄×C₁₃	#137	1	4	yes	—
194	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
195	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
196	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
197	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
198	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
199	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
200	C₈×C₁₃	—	2	8	no	—
201	Q₈²	C₂²×C₁₃	1	4	yes	complemented
202	#557	—	2	4	no	—
203	#557	C₂²×C₁₃	1	4	yes	complemented
204	#556	—	2	4	no	—
205	#556	C₂²×C₁₃	1	8	yes	—
206	#544	—	2	1	no	—
207	#544	—	2	2	no	—
208	#533	C₂²×C₁₃	1	2	yes	—
209	#533	C₂²×C₁₃	1	4	yes	—
210	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
211	C₂×#126	—	2	2	no	—
212	C₂×#124	C₂²×C₁₃	1	2	yes	—
213	C₂×C₂²⋊Q₈	—	2	1	no	—
214	#519	—	2	1	no	—
215	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	—
216	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
217	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
218	C₂×#117	—	2	1	no	—
219	#497	C₂²×C₁₃	1	8	yes	—
220	#494	C₂²×C₁₃	1	4	yes	complemented
221	#489	C₂²×C₁₃	1	8	yes	—
222	#487	C₂²×C₁₃	1	4	yes	complemented
223	#483	C₂²×C₁₃	1	4	yes	—
224	#476	C₂²×C₁₃	1	4	yes	—
225	#475	C₂²×C₁₃	1	8	yes	complemented
226	#464	C₂²×C₁₃	1	16	yes	—
227	#462	C₂²×C₁₃	1	8	yes	complemented
228	#462	C₂²×C₁₃	1	8	yes	complemented
229	#461	C₂²×C₁₃	1	4	yes	—
230	#451	C₂²×C₁₃	1	8	yes	—
231	#450	C₂²×C₁₃	1	4	yes	—
232	#446	C₂²×C₁₃	1	8	yes	complemented
233	#441	C₂²×C₁₃	1	16	yes	complemented
234	C₄×SD₁₆	C₂²×C₁₃	1	8	yes	—
235	#432	C₂²×C₁₃	1	4	yes	—
236	#431	C₂²×C₁₃	1	2	yes	—
237	C₂²×C₁₃	—	2	1	no	—
238	C₂²×C₁₃	—	2	1	no	—
239	C₂²×C₁₃	—	4	2	no	—
240	C₂²×C₁₃	—	4	2	no	—
241	C₂²×C₁₃	—	4	2	no	—
242	C₂²×C₁₃	—	8	4	no	—
243	C₂²×C₁₃	C₂×#137	1	2	yes	—
244	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
245	C₄×C₁₃	—	2	4	no	—
246	C₄×C₁₃	—	2	2	no	—
247	C₄×C₁₃	—	2	1	no	—
248	C₄×C₁₃	—	2	4	no	—
249	C₄×C₁₃	—	4	4	no	—
250	C₄×C₁₃	—	4	4	no	—
251	C₄×C₁₃	—	4	4	no	—
252	C₄×C₁₃	—	4	2	no	—
253	C₄×C₁₃	C₂×#137	1	4	yes	—
254	C₄×C₁₃	#585	1	2	yes	—
255	C₂²×Q₈	D₄×C₁₃	1	1	yes	characteristic
256	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
257	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
258	C₂³×C₄	—	2	1	no	—
259	C₂×Q₁₆	C₂³×C₁₃	1	16	yes	—
260	C₂×SD₁₆	C₂³×C₁₃	1	8	yes	—
261	C₄⋊Q₈	—	2	4	no	—
262	C₄⋊Q₈	—	2	8	no	—
263	C₄⋊Q₈	—	2	2	no	—
264	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
265	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
266	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
267	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
268	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
269	#126	—	2	16	no	—
270	#125	—	2	4	no	—
271	#125	—	2	8	no	—
272	#125	—	2	2	no	—
273	#125	—	2	4	no	—
274	#124	—	2	4	no	—
275	#124	C₂³×C₁₃	1	8	yes	—
276	C₂²⋊Q₈	—	2	8	no	—
277	C₂²⋊Q₈	—	2	4	no	—
278	C₂²⋊Q₈	—	2	2	no	—
279	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
280	C₄×Q₈	—	2	4	no	—
281	C₄×Q₈	—	2	4	no	—
282	C₄×Q₈	—	2	4	no	—
283	C₄×Q₈	—	2	2	no	—
284	C₄×Q₈	—	2	4	no	—
285	C₄×Q₈	D₄×C₁₃	1	4	yes	—
286	C₄×Q₈	C₂³×C₁₃	1	8	yes	—
287	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
288	C₄×Q₈	C₂³×C₁₃	1	8	yes	—
289	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
290	C₄×D₄	—	2	2	no	—
291	C₄×D₄	C₂³×C₁₃	1	4	yes	—
292	#117	—	2	4	no	—
293	#117	—	2	2	no	—
294	#117	—	2	8	no	—
295	C₂×C₄⋊C₄	—	2	1	no	—
296	C₂×C₄⋊C₄	—	2	2	no	—
297	C₂×C₄⋊C₄	—	2	1	no	—
298	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
299	C₂×C₄⋊C₄	D₄×C₁₃	1	2	yes	—
300	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
301	C₂×C₂²⋊C₄	—	2	2	no	—
302	C₂×C₂²⋊C₄	—	2	1	no	—
303	C₂×C₂²⋊C₄	—	2	2	no	—
304	C₂×C₄²	—	2	2	no	—
305	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
306	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
307	#106	C₂³×C₁₃	1	8	yes	—
308	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
309	C₄⋊C₈	C₂³×C₁₃	1	8	yes	—
310	#103	C₂³×C₁₃	1	8	yes	—
311	#103	C₂³×C₁₃	1	16	yes	—
312	#102	C₂³×C₁₃	1	8	yes	—
313	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
314	#97	C₂³×C₁₃	1	8	yes	—
315	C₄×C₈	C₂³×C₁₃	1	4	yes	—
316	C₂×C₁₃	—	2	2	no	—
317	C₂×C₁₃	—	8	2	no	—
318	C₂×C₁₃	#3487	1	1	yes	characteristic
319	C₂×C₁₃	C₂²×#137	1	1	yes	characteristic
320	C₂×C₁₃	#3586	1	1	yes	characteristic
321	C₂⁴	—	2	1	no	—
322	C₂×Q₈	—	2	4	no	—
323	C₂×Q₈	—	2	2	no	—
324	C₂×Q₈	—	2	4	no	—
325	C₂×Q₈	—	2	2	no	—
326	C₂×Q₈	—	4	4	no	—
327	C₂×Q₈	C₂×D₄×C₁₃	1	4	yes	—
328	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
329	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
330	C₂×D₄	—	2	1	no	—
331	C₂×D₄	—	4	2	no	—
332	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
333	C₂²×C₄	—	2	1	no	—
334	C₂²×C₄	—	2	2	no	—
335	C₂²×C₄	—	2	4	no	—
336	C₂²×C₄	—	4	4	no	—
337	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
338	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
339	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
340	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
341	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
342	Q₁₆	—	4	16	no	—
343	SD₁₆	—	4	8	no	—
344	C₂×C₈	C₂⁴×C₁₃	1	8	yes	—
345	C₄⋊C₄	—	2	4	no	—
346	C₄⋊C₄	—	2	8	no	—
347	C₄⋊C₄	—	2	4	no	—
348	C₄⋊C₄	—	2	1	no	—
349	C₄⋊C₄	—	2	4	no	—
350	C₄⋊C₄	—	2	2	no	—
351	C₄⋊C₄	—	2	4	no	—
352	C₄⋊C₄	—	2	2	no	—
353	C₄⋊C₄	—	2	4	no	—
354	C₄⋊C₄	—	2	4	no	—
355	C₄⋊C₄	—	2	2	no	—
356	C₄⋊C₄	—	2	8	no	—
357	C₄⋊C₄	—	2	4	no	—
358	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
359	C₄⋊C₄	C₂×D₄×C₁₃	1	8	yes	—
360	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
361	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
362	C₂²⋊C₄	—	2	4	no	—
363	C₂²⋊C₄	—	2	8	no	—
364	C₂²⋊C₄	—	2	4	no	—
365	C₂²⋊C₄	—	2	8	no	—
366	C₄²	—	2	8	no	—
367	C₄²	—	2	8	no	—
368	C₄²	—	2	4	no	—
369	C₄²	C₂×D₄×C₁₃	1	2	yes	—
370	C₄²	C₂×D₄×C₁₃	1	4	yes	—
371	C₄²	C₂⁴×C₁₃	1	2	yes	—
372	C₄²	C₂⁴×C₁₃	1	4	yes	—
373	C₁₃	#61889	1	1	yes	characteristic, direct product factor, Sylow
374	C₂³	—	2	2	no	—
375	C₂³	—	4	2	no	—
376	C₂³	—	4	2	no	—
377	C₂³	—	4	2	no	—
378	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
379	Q₈	—	2	8	no	—
380	Q₈	—	2	8	no	—
381	Q₈	—	2	8	no	—
382	Q₈	—	4	4	no	—
383	Q₈	—	8	4	no	—
384	Q₈	—	8	2	no	—
385	D₄	—	2	4	no	—
386	D₄	—	4	2	no	—
387	C₂×C₄	—	2	4	no	—
388	C₂×C₄	—	2	2	no	—
389	C₂×C₄	—	2	2	no	—
390	C₂×C₄	—	2	4	no	—
391	C₂×C₄	—	2	4	no	—
392	C₂×C₄	—	2	4	no	—
393	C₂×C₄	—	4	2	no	—
394	C₂×C₄	—	4	1	no	—
395	C₂×C₄	—	4	4	no	—
396	C₂×C₄	—	4	2	no	—
397	C₂×C₄	—	4	8	no	—
398	C₂×C₄	C₁₃×#137	1	4	yes	—
399	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
400	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
401	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
402	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
403	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
404	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
405	C₈	—	2	8	no	—
406	C₂²	—	2	1	no	—
407	C₂²	—	2	1	no	—
408	C₂²	—	4	2	no	—
409	C₂²	—	4	2	no	—
410	C₂²	—	4	2	no	—
411	C₂²	—	8	4	no	—
412	C₂²	C₂×C₁₃×#137	1	2	yes	—
413	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
414	C₄	—	2	4	no	—
415	C₄	—	2	4	no	—
416	C₄	—	2	2	no	—
417	C₄	—	2	1	no	—
418	C₄	—	4	2	no	—
419	C₄	—	4	4	no	—
420	C₄	—	4	4	no	—
421	C₄	—	4	4	no	—
422	C₄	C₂×C₁₃×#137	1	4	yes	—
423	C₄	C₁₃×#585	1	2	yes	—
424	C₂	—	2	2	no	—
425	C₂	—	8	2	no	—
426	C₂	C₁₃×#3487	1	1	yes	characteristic
427	C₂	C₂²×C₁₃×#137	1	1	yes	characteristic
428	C₂	C₁₃×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
prime radical	C₂²×D₄×C₁₃	C₂³
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂×C₄×Q₈×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3502	C₂	semidirect
3. C₁₃×#3398	C₂	semidirect
4. C₁₃×#3369	C₂	semidirect
6. C₁₃×#3209	C₂	semidirect
7. C₁₃×#3113	C₂	semidirect
9. C₁₃×#2983	C₂	semidirect
10. Q₈²×C₁₃	C₂²	semidirect
12. C₁₃×#557	C₂²	semidirect
29. C₁₃×#494	C₂²	semidirect
31. C₁₃×#487	C₂²	semidirect
34. C₁₃×#475	C₂²	semidirect
36. C₁₃×#462	C₂²	semidirect
37. C₁₃×#462	C₂²	semidirect
41. C₁₃×#446	C₂²	semidirect
42. C₁₃×#441	C₂²	semidirect
107. #61889	C₁₃	direct (N × H)
160. #3502	C₂×C₁₃	semidirect
162. #3398	C₂×C₁₃	semidirect
163. #3369	C₂×C₁₃	semidirect
165. #3209	C₂×C₁₃	semidirect
166. #3113	C₂×C₁₃	semidirect
168. #2983	C₂×C₁₃	semidirect
201. Q₈²	C₂²×C₁₃	semidirect
203. #557	C₂²×C₁₃	semidirect
220. #494	C₂²×C₁₃	semidirect
222. #487	C₂²×C₁₃	semidirect
225. #475	C₂²×C₁₃	semidirect
227. #462	C₂²×C₁₃	semidirect
228. #462	C₂²×C₁₃	semidirect
232. #446	C₂²×C₁₃	semidirect
233. #441	C₂²×C₁₃	semidirect
373. C₁₃	#61889	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×#3502	2
C₂×C₁₃×#556	2
C₁₃×#3398	2
C₁₃×#3369	2
C₁₃×#3215	2
C₁₃×#3209	2
C₁₃×#3113	2
C₁₃×#3101	2
C₁₃×#2983	2
#61889	13

Subgroups — C13×#61889 #15748228

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61889 #15748228