Subgroups — C₁₃×#61933 #15748272

Order 3328.

1754 conjugacy classes of subgroups.

The subgroup lattice has 472 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3556	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3508	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#3400	C₂	1	4	yes	maximal, complemented
4	C₁₃×#3392	C₂	1	4	yes	maximal, complemented
5	C₁₃×#3368	C₂	1	4	yes	maximal, complemented
6	C₁₃×#3365	C₂	1	4	yes	maximal, complemented
7	C₁₃×#3222	C₂	1	4	yes	maximal, complemented
8	C₁₃×#3208	C₂	1	2	yes	maximal, complemented
9	C₁₃×#3123	C₂	1	4	yes	maximal, complemented
10	C₁₃×#3107	C₂	1	2	yes	maximal, complemented
11	C₁₃×#2986	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#564	—	2	2	no	—
13	C₁₃×#559	C₂²	1	4	yes	—
14	C₁₃×#557	—	2	2	no	—
15	C₁₃×#557	C₂²	1	4	yes	complemented
16	C₁₃×#557	C₂²	1	4	yes	complemented
17	C₁₃×#550	C₂²	1	4	yes	—
18	C₁₃×#546	—	2	4	no	—
19	C₁₃×#541	—	2	4	no	—
20	C₁₃×#541	C₂²	1	4	yes	—
21	C₁₃×#540	—	2	2	no	—
22	C₁₃×#535	C₂²	1	2	yes	—
23	C₁₃×#533	C₂²	1	2	yes	—
24	C₁₃×#533	C₂²	1	1	yes	characteristic
25	C₁₃×#532	—	2	2	no	—
26	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
27	C₁₃×#518	C₂²	1	2	yes	—
28	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
29	C₁₃×#497	C₂²	1	4	yes	complemented
30	C₁₃×#492	C₂²	1	4	yes	—
31	C₁₃×#492	C₂²	1	4	yes	complemented
32	C₁₃×#490	C₂²	1	4	yes	complemented
33	C₁₃×#488	C₂²	1	4	yes	complemented
34	C₁₃×#486	C₂²	1	4	yes	—
35	C₁₃×#485	C₂²	1	4	yes	—
36	C₁₃×#478	C₂²	1	8	yes	complemented
37	C₁₃×#475	C₂²	1	2	yes	complemented
38	C₁₃×#474	C₂²	1	2	yes	complemented
39	C₁₃×#464	C₂²	1	8	yes	complemented
40	C₁₃×#462	C₂²	1	2	yes	complemented
41	C₁₃×#461	C₂²	1	2	yes	complemented
42	C₁₃×#461	C₂²	1	8	yes	complemented
43	C₁₃×#460	C₂²	1	4	yes	—
44	C₁₃×#460	C₂²	1	4	yes	—
45	C₁₃×#460	C₂²	1	8	yes	complemented
46	C₁₃×#452	C₂²	1	4	yes	—
47	C₁₃×#450	C₂²	1	8	yes	—
48	C₁₃×#446	C₂²	1	4	yes	complemented
49	C₈×Q₈×C₁₃	C₂²	1	4	yes	complemented
50	C₁₃×#440	C₂²	1	8	yes	complemented
51	C₄×C₁₃×Q₁₆	C₂²	1	4	yes	complemented
52	C₄×C₁₃×SD₁₆	C₂²	1	4	yes	complemented
53	C₄×C₁₃×SD₁₆	C₂²	1	8	yes	complemented
54	C₁₃×#433	C₂²	1	4	yes	—
55	C₁₃×#431	C₂²	1	2	yes	—
56	C₂×C₁₃×#41	—	2	4	no	—
57	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
58	C₂²×D₄×C₁₃	—	2	2	no	—
59	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
60	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	—
61	C₂×C₁₃×SD₁₆	C₂³	1	8	yes	—
62	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
63	C₂×C₁₃×SD₁₆	C₂³	1	8	yes	—
64	C₁₃×C₄⋊Q₈	—	2	4	no	—
65	C₁₃×C₄⋊Q₈	D₄	1	2	yes	—
66	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
67	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
68	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
69	C₁₃×#127	—	2	1	no	—
70	C₁₃×#127	—	2	1	no	—
71	C₁₃×#127	C₂³	1	4	yes	—
72	C₁₃×#127	C₂³	1	4	yes	—
73	C₁₃×#126	—	2	8	no	—
74	C₁₃×#125	—	2	4	no	—
75	C₁₃×#125	—	2	8	no	—
76	C₁₃×#125	—	2	8	no	—
77	C₁₃×#125	—	2	8	no	—
78	C₁₃×#125	—	2	2	no	—
79	C₁₃×#125	D₄	1	2	yes	—
80	C₁₃×#125	C₂³	1	4	yes	—
81	C₁₃×#124	—	2	4	no	—
82	C₁₃×#124	C₂³	1	4	yes	—
83	C₁₃×#123	—	2	8	no	—
84	C₁₃×C₂²⋊Q₈	—	2	2	no	—
85	C₁₃×C₂²⋊Q₈	D₄	1	4	yes	—
86	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
87	C₁₃×#121	—	2	4	no	—
88	C₁₃×#121	—	2	4	no	—
89	C₁₃×#121	—	2	8	no	—
90	C₁₃×#120	—	2	4	no	—
91	C₄×Q₈×C₁₃	—	2	4	no	—
92	C₄×Q₈×C₁₃	—	2	4	no	—
93	C₄×Q₈×C₁₃	—	2	2	no	—
94	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
95	C₄×Q₈×C₁₃	C₂³	1	8	yes	—
96	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
97	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
98	C₄×D₄×C₁₃	—	2	2	no	—
99	C₄×D₄×C₁₃	—	2	4	no	—
100	C₄×D₄×C₁₃	—	2	4	no	—
101	C₄×D₄×C₁₃	C₂³	1	2	yes	—
102	C₄×D₄×C₁₃	C₂³	1	8	yes	—
103	C₁₃×#117	—	2	2	no	—
104	C₁₃×#117	—	2	1	no	—
105	C₁₃×#117	C₂³	1	1	yes	characteristic
106	C₁₃×#117	C₂³	1	2	yes	—
107	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
108	C₂×C₄²×C₁₃	—	2	1	no	—
109	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
110	C₁₃×#107	C₂³	1	4	yes	—
111	C₁₃×#106	C₂³	1	4	yes	—
112	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
113	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
114	C₁₃×C₄⋊C₈	C₂³	1	8	yes	—
115	C₁₃×#103	C₂³	1	4	yes	—
116	C₁₃×#103	C₂³	1	4	yes	—
117	C₁₃×#103	C₂³	1	4	yes	—
118	C₁₃×#102	C₂³	1	8	yes	—
119	C₁₃×#102	C₂³	1	4	yes	—
120	C₁₃×#102	C₂³	1	8	yes	—
121	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
122	C₁₃×#97	C₂³	1	4	yes	—
123	C₄×C₈×C₁₃	C₂³	1	4	yes	—
124	C₄×C₈×C₁₃	C₂³	1	4	yes	—
125	#61933	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
126	C₂⁴×C₁₃	—	2	2	no	—
127	C₁₃×#41	—	4	2	no	—
128	C₁₃×#41	—	8	8	no	—
129	C₂×Q₈×C₁₃	—	2	2	no	—
130	C₂×Q₈×C₁₃	C₂×D₄	1	4	yes	—
131	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
132	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
133	C₂×D₄×C₁₃	—	2	1	no	—
134	C₂×D₄×C₁₃	—	2	2	no	—
135	C₂×D₄×C₁₃	—	2	4	no	—
136	C₂×D₄×C₁₃	—	2	8	no	—
137	C₂×D₄×C₁₃	—	2	4	no	—
138	C₂×D₄×C₁₃	—	4	4	no	—
139	C₂×D₄×C₁₃	—	8	4	no	—
140	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
141	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
142	C₂²×C₄×C₁₃	—	2	1	no	—
143	C₂²×C₄×C₁₃	—	2	2	no	—
144	C₂²×C₄×C₁₃	—	2	8	no	—
145	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
146	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
147	C₁₃×Q₁₆	—	4	4	no	—
148	C₁₃×SD₁₆	—	4	8	no	—
149	C₁₃×SD₁₆	—	4	4	no	—
150	C₁₃×SD₁₆	—	4	8	no	—
151	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
152	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
153	C₁₃×C₄⋊C₄	—	2	2	no	—
154	C₁₃×C₄⋊C₄	—	2	2	no	—
155	C₁₃×C₄⋊C₄	—	2	2	no	—
156	C₁₃×C₄⋊C₄	—	2	2	no	—
157	C₁₃×C₄⋊C₄	—	2	4	no	—
158	C₁₃×C₄⋊C₄	—	2	8	no	—
159	C₁₃×C₄⋊C₄	—	2	8	no	—
160	C₁₃×C₄⋊C₄	—	2	4	no	—
161	C₁₃×C₄⋊C₄	—	2	8	no	—
162	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
163	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
164	C₁₃×C₄⋊C₄	C₂×D₄	1	8	yes	—
165	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
166	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
167	C₁₃×C₂²⋊C₄	—	2	1	no	—
168	C₁₃×C₂²⋊C₄	—	2	4	no	—
169	C₁₃×C₂²⋊C₄	—	2	8	no	—
170	C₁₃×C₂²⋊C₄	—	2	2	no	—
171	C₁₃×C₂²⋊C₄	—	2	8	no	—
172	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
173	C₄²×C₁₃	—	2	1	no	—
174	C₄²×C₁₃	—	2	2	no	—
175	C₄²×C₁₃	—	2	4	no	—
176	C₄²×C₁₃	—	2	8	no	—
177	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
178	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
179	C₄²×C₁₃	C₂⁴	1	2	yes	—
180	C₄²×C₁₃	C₂⁴	1	4	yes	—
181	#3556	C₂×C₁₃	1	1	yes	characteristic, complemented
182	#3508	C₂×C₁₃	1	1	yes	characteristic
183	#3400	C₂×C₁₃	1	4	yes	complemented
184	#3392	C₂×C₁₃	1	4	yes	complemented
185	#3368	C₂×C₁₃	1	4	yes	complemented
186	#3365	C₂×C₁₃	1	4	yes	complemented
187	#3222	C₂×C₁₃	1	4	yes	complemented
188	#3208	C₂×C₁₃	1	2	yes	complemented
189	#3123	C₂×C₁₃	1	4	yes	complemented
190	#3107	C₂×C₁₃	1	2	yes	complemented
191	#2986	C₂×C₁₃	1	1	yes	characteristic, complemented
192	C₂³×C₁₃	—	2	4	no	—
193	C₂³×C₁₃	—	2	1	no	—
194	C₂³×C₁₃	—	4	4	no	—
195	C₂³×C₁₃	—	8	4	no	—
196	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
197	Q₈×C₁₃	—	2	8	no	—
198	Q₈×C₁₃	—	2	4	no	—
199	Q₈×C₁₃	—	2	4	no	—
200	Q₈×C₁₃	—	2	2	no	—
201	Q₈×C₁₃	—	4	4	no	—
202	D₄×C₁₃	—	2	8	no	—
203	D₄×C₁₃	—	2	2	no	—
204	D₄×C₁₃	—	4	4	no	—
205	D₄×C₁₃	—	4	2	no	—
206	D₄×C₁₃	—	4	8	no	—
207	D₄×C₁₃	—	8	4	no	—
208	D₄×C₁₃	—	8	8	no	—
209	C₂×C₄×C₁₃	—	2	4	no	—
210	C₂×C₄×C₁₃	—	2	2	no	—
211	C₂×C₄×C₁₃	—	2	4	no	—
212	C₂×C₄×C₁₃	—	2	4	no	—
213	C₂×C₄×C₁₃	—	2	1	no	—
214	C₂×C₄×C₁₃	—	2	2	no	—
215	C₂×C₄×C₁₃	—	4	2	no	—
216	C₂×C₄×C₁₃	—	4	4	no	—
217	C₂×C₄×C₁₃	—	8	8	no	—
218	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
219	C₂×C₄×C₁₃	C₂²×D₄	1	8	yes	—
220	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
221	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
222	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
223	C₈×C₁₃	—	2	4	no	—
224	C₈×C₁₃	—	2	4	no	—
225	#564	—	2	2	no	—
226	#559	C₂²×C₁₃	1	4	yes	—
227	#557	—	2	2	no	—
228	#557	C₂²×C₁₃	1	4	yes	complemented
229	#557	C₂²×C₁₃	1	4	yes	complemented
230	#550	C₂²×C₁₃	1	4	yes	—
231	#546	—	2	4	no	—
232	#541	—	2	4	no	—
233	#541	C₂²×C₁₃	1	4	yes	—
234	#540	—	2	2	no	—
235	#535	C₂²×C₁₃	1	2	yes	—
236	#533	C₂²×C₁₃	1	2	yes	—
237	#533	C₂²×C₁₃	1	1	yes	characteristic
238	#532	—	2	2	no	—
239	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
240	#518	C₂²×C₁₃	1	2	yes	—
241	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
242	#497	C₂²×C₁₃	1	4	yes	complemented
243	#492	C₂²×C₁₃	1	4	yes	—
244	#492	C₂²×C₁₃	1	4	yes	complemented
245	#490	C₂²×C₁₃	1	4	yes	complemented
246	#488	C₂²×C₁₃	1	4	yes	complemented
247	#486	C₂²×C₁₃	1	4	yes	—
248	#485	C₂²×C₁₃	1	4	yes	—
249	#478	C₂²×C₁₃	1	8	yes	complemented
250	#475	C₂²×C₁₃	1	2	yes	complemented
251	#474	C₂²×C₁₃	1	2	yes	complemented
252	#464	C₂²×C₁₃	1	8	yes	complemented
253	#462	C₂²×C₁₃	1	2	yes	complemented
254	#461	C₂²×C₁₃	1	2	yes	complemented
255	#461	C₂²×C₁₃	1	8	yes	complemented
256	#460	C₂²×C₁₃	1	4	yes	—
257	#460	C₂²×C₁₃	1	4	yes	—
258	#460	C₂²×C₁₃	1	8	yes	complemented
259	#452	C₂²×C₁₃	1	4	yes	—
260	#450	C₂²×C₁₃	1	8	yes	—
261	#446	C₂²×C₁₃	1	4	yes	complemented
262	C₈×Q₈	C₂²×C₁₃	1	4	yes	complemented
263	#440	C₂²×C₁₃	1	8	yes	complemented
264	C₄×Q₁₆	C₂²×C₁₃	1	4	yes	complemented
265	C₄×SD₁₆	C₂²×C₁₃	1	4	yes	complemented
266	C₄×SD₁₆	C₂²×C₁₃	1	8	yes	complemented
267	#433	C₂²×C₁₃	1	4	yes	—
268	#431	C₂²×C₁₃	1	2	yes	—
269	C₂²×C₁₃	—	2	1	no	—
270	C₂²×C₁₃	—	2	2	no	—
271	C₂²×C₁₃	—	4	1	no	—
272	C₂²×C₁₃	—	4	4	no	—
273	C₂²×C₁₃	—	4	2	no	—
274	C₂²×C₁₃	—	4	8	no	—
275	C₂²×C₁₃	—	16	4	no	—
276	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
277	C₄×C₁₃	—	2	1	no	—
278	C₄×C₁₃	—	2	2	no	—
279	C₄×C₁₃	—	2	8	no	—
280	C₄×C₁₃	—	4	1	no	—
281	C₄×C₁₃	—	4	4	no	—
282	C₄×C₁₃	—	4	2	no	—
283	C₄×C₁₃	—	4	4	no	—
284	C₄×C₁₃	#577	1	4	yes	—
285	C₄×C₁₃	#585	1	2	yes	—
286	C₂×#41	—	2	4	no	—
287	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
288	C₂²×D₄	—	2	2	no	—
289	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
290	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	—
291	C₂×SD₁₆	C₂³×C₁₃	1	8	yes	—
292	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
293	C₂×SD₁₆	C₂³×C₁₃	1	8	yes	—
294	C₄⋊Q₈	—	2	4	no	—
295	C₄⋊Q₈	D₄×C₁₃	1	2	yes	—
296	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
297	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
298	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
299	#127	—	2	1	no	—
300	#127	—	2	1	no	—
301	#127	C₂³×C₁₃	1	4	yes	—
302	#127	C₂³×C₁₃	1	4	yes	—
303	#126	—	2	8	no	—
304	#125	—	2	4	no	—
305	#125	—	2	8	no	—
306	#125	—	2	8	no	—
307	#125	—	2	8	no	—
308	#125	—	2	2	no	—
309	#125	D₄×C₁₃	1	2	yes	—
310	#125	C₂³×C₁₃	1	4	yes	—
311	#124	—	2	4	no	—
312	#124	C₂³×C₁₃	1	4	yes	—
313	#123	—	2	8	no	—
314	C₂²⋊Q₈	—	2	2	no	—
315	C₂²⋊Q₈	D₄×C₁₃	1	4	yes	—
316	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
317	#121	—	2	4	no	—
318	#121	—	2	4	no	—
319	#121	—	2	8	no	—
320	#120	—	2	4	no	—
321	C₄×Q₈	—	2	4	no	—
322	C₄×Q₈	—	2	4	no	—
323	C₄×Q₈	—	2	2	no	—
324	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
325	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
326	C₄×Q₈	C₂³×C₁₃	1	8	yes	—
327	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
328	C₄×D₄	—	2	2	no	—
329	C₄×D₄	—	2	4	no	—
330	C₄×D₄	—	2	4	no	—
331	C₄×D₄	C₂³×C₁₃	1	2	yes	—
332	C₄×D₄	C₂³×C₁₃	1	8	yes	—
333	#117	—	2	2	no	—
334	#117	—	2	1	no	—
335	#117	C₂³×C₁₃	1	1	yes	characteristic
336	#117	C₂³×C₁₃	1	2	yes	—
337	C₂×C₂²⋊C₄	—	2	4	no	—
338	C₂×C₄²	—	2	1	no	—
339	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
340	#107	C₂³×C₁₃	1	4	yes	—
341	#106	C₂³×C₁₃	1	4	yes	—
342	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
343	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
344	C₄⋊C₈	C₂³×C₁₃	1	8	yes	—
345	#103	C₂³×C₁₃	1	4	yes	—
346	#103	C₂³×C₁₃	1	4	yes	—
347	#103	C₂³×C₁₃	1	4	yes	—
348	#102	C₂³×C₁₃	1	8	yes	—
349	#102	C₂³×C₁₃	1	4	yes	—
350	#102	C₂³×C₁₃	1	8	yes	—
351	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
352	#97	C₂³×C₁₃	1	4	yes	—
353	C₄×C₈	C₂³×C₁₃	1	4	yes	—
354	C₄×C₈	C₂³×C₁₃	1	4	yes	—
355	C₂×C₁₃	—	4	1	no	—
356	C₂×C₁₃	—	8	1	no	—
357	C₂×C₁₃	—	8	4	no	—
358	C₂×C₁₃	#3487	1	1	yes	characteristic
359	C₂×C₁₃	C₂×#577	1	2	yes	—
360	C₂⁴	—	2	2	no	—
361	#41	—	4	2	no	—
362	#41	—	8	8	no	—
363	C₂×Q₈	—	2	2	no	—
364	C₂×Q₈	C₂×D₄×C₁₃	1	4	yes	—
365	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
366	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
367	C₂×D₄	—	2	1	no	—
368	C₂×D₄	—	2	2	no	—
369	C₂×D₄	—	2	4	no	—
370	C₂×D₄	—	2	8	no	—
371	C₂×D₄	—	2	4	no	—
372	C₂×D₄	—	4	4	no	—
373	C₂×D₄	—	8	4	no	—
374	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
375	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
376	C₂²×C₄	—	2	1	no	—
377	C₂²×C₄	—	2	2	no	—
378	C₂²×C₄	—	2	8	no	—
379	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
380	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
381	Q₁₆	—	4	4	no	—
382	SD₁₆	—	4	8	no	—
383	SD₁₆	—	4	4	no	—
384	SD₁₆	—	4	8	no	—
385	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
386	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
387	C₄⋊C₄	—	2	2	no	—
388	C₄⋊C₄	—	2	2	no	—
389	C₄⋊C₄	—	2	2	no	—
390	C₄⋊C₄	—	2	2	no	—
391	C₄⋊C₄	—	2	4	no	—
392	C₄⋊C₄	—	2	8	no	—
393	C₄⋊C₄	—	2	8	no	—
394	C₄⋊C₄	—	2	4	no	—
395	C₄⋊C₄	—	2	8	no	—
396	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
397	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
398	C₄⋊C₄	C₂×D₄×C₁₃	1	8	yes	—
399	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
400	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
401	C₂²⋊C₄	—	2	1	no	—
402	C₂²⋊C₄	—	2	4	no	—
403	C₂²⋊C₄	—	2	8	no	—
404	C₂²⋊C₄	—	2	2	no	—
405	C₂²⋊C₄	—	2	8	no	—
406	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
407	C₄²	—	2	1	no	—
408	C₄²	—	2	2	no	—
409	C₄²	—	2	4	no	—
410	C₄²	—	2	8	no	—
411	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
412	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
413	C₄²	C₂⁴×C₁₃	1	2	yes	—
414	C₄²	C₂⁴×C₁₃	1	4	yes	—
415	C₁₃	#61933	1	1	yes	characteristic, direct product factor, Sylow
416	C₂³	—	2	4	no	—
417	C₂³	—	2	1	no	—
418	C₂³	—	4	4	no	—
419	C₂³	—	8	4	no	—
420	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
421	Q₈	—	2	8	no	—
422	Q₈	—	2	4	no	—
423	Q₈	—	2	4	no	—
424	Q₈	—	2	2	no	—
425	Q₈	—	4	4	no	—
426	D₄	—	2	8	no	—
427	D₄	—	2	2	no	—
428	D₄	—	4	4	no	—
429	D₄	—	4	2	no	—
430	D₄	—	4	8	no	—
431	D₄	—	8	4	no	—
432	D₄	—	8	8	no	—
433	C₂×C₄	—	2	4	no	—
434	C₂×C₄	—	2	2	no	—
435	C₂×C₄	—	2	4	no	—
436	C₂×C₄	—	2	4	no	—
437	C₂×C₄	—	2	1	no	—
438	C₂×C₄	—	2	2	no	—
439	C₂×C₄	—	4	2	no	—
440	C₂×C₄	—	4	4	no	—
441	C₂×C₄	—	8	8	no	—
442	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
443	C₂×C₄	C₂²×D₄×C₁₃	1	8	yes	—
444	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
445	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
446	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
447	C₈	—	2	4	no	—
448	C₈	—	2	4	no	—
449	C₂²	—	2	2	no	—
450	C₂²	—	2	1	no	—
451	C₂²	—	4	2	no	—
452	C₂²	—	4	8	no	—
453	C₂²	—	4	1	no	—
454	C₂²	—	4	4	no	—
455	C₂²	—	16	4	no	—
456	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
457	C₄	—	2	2	no	—
458	C₄	—	2	8	no	—
459	C₄	—	2	1	no	—
460	C₄	—	4	2	no	—
461	C₄	—	4	4	no	—
462	C₄	—	4	1	no	—
463	C₄	—	4	4	no	—
464	C₄	C₁₃×#577	1	4	yes	—
465	C₄	C₁₃×#585	1	2	yes	—
466	C₂	—	4	1	no	—
467	C₂	—	8	4	no	—
468	C₂	—	8	1	no	—
469	C₂	C₁₃×#3487	1	1	yes	characteristic
470	C₂	C₂×C₁₃×#577	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
prime radical	C₁₃×#3508	C₂
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×#3556	C₂	semidirect
3. C₁₃×#3400	C₂	semidirect
4. C₁₃×#3392	C₂	semidirect
5. C₁₃×#3368	C₂	semidirect
6. C₁₃×#3365	C₂	semidirect
7. C₁₃×#3222	C₂	semidirect
8. C₁₃×#3208	C₂	semidirect
9. C₁₃×#3123	C₂	semidirect
10. C₁₃×#3107	C₂	semidirect
11. C₁₃×#2986	C₂	semidirect
15. C₁₃×#557	C₂²	semidirect
16. C₁₃×#557	C₂²	semidirect
29. C₁₃×#497	C₂²	semidirect
31. C₁₃×#492	C₂²	semidirect
32. C₁₃×#490	C₂²	semidirect
33. C₁₃×#488	C₂²	semidirect
36. C₁₃×#478	C₂²	semidirect
37. C₁₃×#475	C₂²	semidirect
38. C₁₃×#474	C₂²	semidirect
39. C₁₃×#464	C₂²	semidirect
40. C₁₃×#462	C₂²	semidirect
41. C₁₃×#461	C₂²	semidirect
42. C₁₃×#461	C₂²	semidirect
45. C₁₃×#460	C₂²	semidirect
48. C₁₃×#446	C₂²	semidirect
49. C₈×Q₈×C₁₃	C₂²	semidirect
50. C₁₃×#440	C₂²	semidirect
51. C₄×C₁₃×Q₁₆	C₂²	semidirect
52. C₄×C₁₃×SD₁₆	C₂²	semidirect
53. C₄×C₁₃×SD₁₆	C₂²	semidirect
125. #61933	C₁₃	direct (N × H)
181. #3556	C₂×C₁₃	semidirect
183. #3400	C₂×C₁₃	semidirect
184. #3392	C₂×C₁₃	semidirect
185. #3368	C₂×C₁₃	semidirect
186. #3365	C₂×C₁₃	semidirect
187. #3222	C₂×C₁₃	semidirect
188. #3208	C₂×C₁₃	semidirect
189. #3123	C₂×C₁₃	semidirect
190. #3107	C₂×C₁₃	semidirect
191. #2986	C₂×C₁₃	semidirect
228. #557	C₂²×C₁₃	semidirect
229. #557	C₂²×C₁₃	semidirect
242. #497	C₂²×C₁₃	semidirect
244. #492	C₂²×C₁₃	semidirect
245. #490	C₂²×C₁₃	semidirect
246. #488	C₂²×C₁₃	semidirect
249. #478	C₂²×C₁₃	semidirect
250. #475	C₂²×C₁₃	semidirect
251. #474	C₂²×C₁₃	semidirect
252. #464	C₂²×C₁₃	semidirect
253. #462	C₂²×C₁₃	semidirect
254. #461	C₂²×C₁₃	semidirect
255. #461	C₂²×C₁₃	semidirect
258. #460	C₂²×C₁₃	semidirect
261. #446	C₂²×C₁₃	semidirect
262. C₈×Q₈	C₂²×C₁₃	semidirect
263. #440	C₂²×C₁₃	semidirect
264. C₄×Q₁₆	C₂²×C₁₃	semidirect
265. C₄×SD₁₆	C₂²×C₁₃	semidirect
266. C₄×SD₁₆	C₂²×C₁₃	semidirect
415. C₁₃	#61933	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×#3556	2
C₁₃×#3508	2
C₁₃×#3400	2
C₁₃×#3392	2
C₁₃×#3368	2
C₁₃×#3365	2
C₁₃×#3222	2
C₁₃×#3208	2
C₁₃×#3123	2
C₁₃×#3107	2
C₁₃×#2986	2
#61933	13

Subgroups — C13×#61933 #15748272

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61933 #15748272