Subgroups — C₁₃×#60619 #15746958

Order 3328.

2206 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×#3458	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#535	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#3140	C₂	1	4	yes	maximal, complemented
4	C₁₃×#3138	C₂	1	4	yes	maximal, complemented
5	C₁₃×#3136	C₂	1	16	yes	maximal, complemented
6	C₁₃×#2896	C₂	1	2	yes	maximal, complemented
7	C₂×C₁₃×#418	C₂	1	2	yes	maximal, complemented
8	C₁₃×#2873	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic
10	C₂³×D₄×C₁₃	C₂²	1	1	yes	characteristic
11	C₂²×C₁₃×M₁₆	C₂²	1	2	yes	—
12	C₁₃×#544	—	2	2	no	—
13	C₁₃×#544	C₂²	1	8	yes	complemented
14	C₁₃×#543	—	2	2	no	—
15	C₁₃×#535	—	2	4	no	—
16	C₁₃×#535	C₂²	1	8	yes	—
17	C₁₃×#533	—	2	4	no	—
18	C₁₃×#533	C₂²	1	4	yes	complemented
19	C₂×C₁₃×#127	C₂²	1	2	yes	—
20	C₂×C₁₃×#124	C₂²	1	2	yes	—
21	C₂×C₁₃×#121	—	2	2	no	—
22	C₂×C₁₃×#120	—	2	2	no	—
23	C₂×C₁₃×#117	C₂²	1	2	yes	—
24	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
25	C₁₃×#490	C₂²	1	16	yes	complemented
26	C₁₃×#489	C₂²	1	16	yes	complemented
27	C₁₃×#488	C₂²	1	16	yes	complemented
28	C₁₃×#486	C₂²	1	16	yes	complemented
29	C₁₃×#419	C₂²	1	4	yes	complemented
30	C₁₃×#418	C₂²	1	8	yes	—
31	C₁₃×#418	C₂²	1	8	yes	complemented
32	C₁₃×#418	C₂²	1	4	yes	complemented
33	C₁₃×#417	C₂²	1	8	yes	complemented
34	C₁₃×#416	C₂²	1	8	yes	complemented
35	C₂×C₁₃×#102	C₂²	1	8	yes	complemented
36	C₁₃×#405	C₂²	1	8	yes	complemented
37	C₄×C₁₃×M₁₆	C₂²	1	4	yes	complemented
38	C₂⁵×C₁₃	—	2	1	no	—
39	C₂×C₁₃×#41	—	2	2	no	—
40	C₂×C₁₃×#41	—	2	8	no	—
41	C₂×C₁₃×#41	C₂³	1	4	yes	—
42	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
43	C₂²×D₄×C₁₃	—	2	1	no	—
44	C₂²×D₄×C₁₃	—	2	1	no	—
45	C₂²×D₄×C₁₃	—	2	2	no	—
46	C₂²×D₄×C₁₃	—	2	4	no	—
47	C₂²×D₄×C₁₃	—	2	8	no	—
48	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
49	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
50	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
51	C₂³×C₄×C₁₃	—	2	1	no	—
52	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
53	C₂×C₁₃×M₁₆	—	2	8	no	—
54	C₂×C₁₃×M₁₆	C₂³	1	4	yes	—
55	C₂×C₁₃×M₁₆	C₂³	1	4	yes	—
56	C₂²×C₈×C₁₃	C₂³	1	4	yes	—
57	C₁₃×C₄⋊Q₈	—	2	8	no	—
58	C₁₃×C₄⋊Q₈	C₂³	1	8	yes	complemented
59	C₁₃×#127	—	2	4	no	—
60	C₁₃×#127	C₂³	1	8	yes	—
61	C₁₃×#125	—	2	8	no	—
62	C₁₃×#125	C₂³	1	8	yes	complemented
63	C₁₃×#124	—	2	4	no	—
64	C₁₃×#124	C₂³	1	8	yes	—
65	C₁₃×C₂²⋊Q₈	—	2	8	no	—
66	C₁₃×C₂²⋊Q₈	—	2	16	no	—
67	C₁₃×#121	—	2	16	no	—
68	C₁₃×#120	—	2	16	no	—
69	C₄×Q₈×C₁₃	—	2	8	no	—
70	C₁₃×#117	—	2	2	no	—
71	C₁₃×#117	—	2	2	no	—
72	C₁₃×#117	D₄	1	4	yes	—
73	C₁₃×#117	C₂³	1	4	yes	—
74	C₁₃×#117	C₂³	1	4	yes	—
75	C₁₃×#117	C₂³	1	4	yes	—
76	C₂×C₁₃×C₄⋊C₄	D₄	1	2	yes	—
77	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
78	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
79	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
80	C₂×C₁₃×C₂²⋊C₄	D₄	1	2	yes	—
81	C₂×C₄²×C₁₃	—	2	2	no	—
82	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
83	C₁₃×#103	C₂³	1	16	yes	complemented
84	C₁₃×#102	C₂³	1	32	yes	—
85	C₁₃×#102	C₂³	1	16	yes	complemented
86	C₁₃×#97	C₂³	1	8	yes	complemented
87	C₄×C₈×C₁₃	C₂³	1	8	yes	complemented
88	#60619	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
89	C₂⁴×C₁₃	—	2	2	no	—
90	C₂⁴×C₁₃	—	2	1	no	—
91	C₂⁴×C₁₃	—	2	4	no	—
92	C₂⁴×C₁₃	—	4	4	no	—
93	C₂⁴×C₁₃	—	8	4	no	—
94	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
95	C₁₃×#41	—	2	8	no	—
96	C₁₃×#41	—	2	8	no	—
97	C₁₃×#41	—	4	8	no	—
98	C₂×Q₈×C₁₃	—	2	1	no	—
99	C₂×Q₈×C₁₃	—	2	8	no	—
100	C₂×Q₈×C₁₃	—	2	4	no	—
101	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
102	C₂×D₄×C₁₃	—	2	4	no	—
103	C₂×D₄×C₁₃	—	2	4	no	—
104	C₂×D₄×C₁₃	—	2	2	no	—
105	C₂×D₄×C₁₃	—	2	1	no	—
106	C₂×D₄×C₁₃	—	2	16	no	—
107	C₂×D₄×C₁₃	—	2	8	no	—
108	C₂×D₄×C₁₃	—	2	8	no	—
109	C₂×D₄×C₁₃	—	2	8	no	—
110	C₂×D₄×C₁₃	—	2	4	no	—
111	C₂×D₄×C₁₃	—	4	4	no	—
112	C₂×D₄×C₁₃	—	4	4	no	—
113	C₂×D₄×C₁₃	—	4	8	no	—
114	C₂×D₄×C₁₃	—	8	8	no	—
115	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
116	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
117	C₂²×C₄×C₁₃	—	2	1	no	—
118	C₂²×C₄×C₁₃	—	2	4	no	—
119	C₂²×C₄×C₁₃	—	2	4	no	—
120	C₂²×C₄×C₁₃	—	4	4	no	—
121	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
122	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
123	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
124	C₂²×C₄×C₁₃	#41	1	8	yes	—
125	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
126	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
127	C₁₃×M₁₆	—	2	8	no	—
128	C₁₃×M₁₆	—	2	8	no	—
129	C₂×C₈×C₁₃	—	2	8	no	—
130	C₂×C₈×C₁₃	C₂⁴	1	8	yes	—
131	C₁₃×C₄⋊C₄	—	2	4	no	—
132	C₁₃×C₄⋊C₄	—	2	8	no	—
133	C₁₃×C₄⋊C₄	—	2	16	no	—
134	C₁₃×C₄⋊C₄	C₂×D₄	1	8	yes	—
135	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
136	C₁₃×C₂²⋊C₄	—	2	4	no	—
137	C₁₃×C₂²⋊C₄	—	2	4	no	—
138	C₁₃×C₂²⋊C₄	—	2	16	no	—
139	C₁₃×C₂²⋊C₄	C₂×D₄	1	8	yes	—
140	C₄²×C₁₃	—	2	4	no	—
141	C₄²×C₁₃	—	2	4	no	—
142	C₄²×C₁₃	C₂×D₄	1	4	yes	—
143	C₄²×C₁₃	C₂⁴	1	4	yes	—
144	#3458	C₂×C₁₃	1	1	yes	characteristic, complemented
145	C₂×#535	C₂×C₁₃	1	1	yes	characteristic
146	#3140	C₂×C₁₃	1	4	yes	complemented
147	#3138	C₂×C₁₃	1	4	yes	complemented
148	#3136	C₂×C₁₃	1	16	yes	complemented
149	#2896	C₂×C₁₃	1	2	yes	complemented
150	C₂×#418	C₂×C₁₃	1	2	yes	complemented
151	#2873	C₂×C₁₃	1	1	yes	characteristic, complemented
152	C₂³×C₁₃	—	2	4	no	—
153	C₂³×C₁₃	—	2	2	no	—
154	C₂³×C₁₃	—	4	2	no	—
155	C₂³×C₁₃	—	4	4	no	—
156	C₂³×C₁₃	—	4	8	no	—
157	C₂³×C₁₃	—	4	2	no	—
158	C₂³×C₁₃	—	4	4	no	—
159	C₂³×C₁₃	—	4	8	no	—
160	C₂³×C₁₃	—	8	8	no	—
161	C₂³×C₁₃	—	8	16	no	—
162	C₂³×C₁₃	#124	1	4	yes	—
163	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
164	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
165	Q₈×C₁₃	—	2	4	no	—
166	Q₈×C₁₃	—	4	2	no	—
167	Q₈×C₁₃	—	8	8	no	—
168	D₄×C₁₃	—	2	8	no	—
169	D₄×C₁₃	—	2	4	no	—
170	D₄×C₁₃	—	4	8	no	—
171	D₄×C₁₃	—	4	8	no	—
172	D₄×C₁₃	—	4	4	no	—
173	D₄×C₁₃	—	4	2	no	—
174	D₄×C₁₃	—	8	16	no	—
175	C₂×C₄×C₁₃	—	2	8	no	—
176	C₂×C₄×C₁₃	—	2	2	no	—
177	C₂×C₄×C₁₃	—	4	4	no	—
178	C₂×C₄×C₁₃	—	4	2	no	—
179	C₂×C₄×C₁₃	—	4	8	no	—
180	C₂×C₄×C₁₃	—	8	4	no	—
181	C₂×C₄×C₁₃	#124	1	4	yes	—
182	C₂×C₄×C₁₃	#124	1	8	yes	—
183	C₂×C₄×C₁₃	C₂²×D₄	1	8	yes	—
184	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
185	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
186	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
187	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
188	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
189	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
190	C₈×C₁₃	—	2	8	no	—
191	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic
192	C₂³×D₄	C₂²×C₁₃	1	1	yes	characteristic
193	C₂²×M₁₆	C₂²×C₁₃	1	2	yes	—
194	#544	—	2	2	no	—
195	#544	C₂²×C₁₃	1	8	yes	complemented
196	#543	—	2	2	no	—
197	#535	—	2	4	no	—
198	#535	C₂²×C₁₃	1	8	yes	—
199	#533	—	2	4	no	—
200	#533	C₂²×C₁₃	1	4	yes	complemented
201	C₂×#127	C₂²×C₁₃	1	2	yes	—
202	C₂×#124	C₂²×C₁₃	1	2	yes	—
203	C₂×#121	—	2	2	no	—
204	C₂×#120	—	2	2	no	—
205	C₂×#117	C₂²×C₁₃	1	2	yes	—
206	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
207	#490	C₂²×C₁₃	1	16	yes	complemented
208	#489	C₂²×C₁₃	1	16	yes	complemented
209	#488	C₂²×C₁₃	1	16	yes	complemented
210	#486	C₂²×C₁₃	1	16	yes	complemented
211	#419	C₂²×C₁₃	1	4	yes	complemented
212	#418	C₂²×C₁₃	1	8	yes	—
213	#418	C₂²×C₁₃	1	8	yes	complemented
214	#418	C₂²×C₁₃	1	4	yes	complemented
215	#417	C₂²×C₁₃	1	8	yes	complemented
216	#416	C₂²×C₁₃	1	8	yes	complemented
217	C₂×#102	C₂²×C₁₃	1	8	yes	complemented
218	#405	C₂²×C₁₃	1	8	yes	complemented
219	C₄×M₁₆	C₂²×C₁₃	1	4	yes	complemented
220	C₂²×C₁₃	—	2	2	no	—
221	C₂²×C₁₃	—	2	4	no	—
222	C₂²×C₁₃	—	4	4	no	—
223	C₂²×C₁₃	—	4	4	no	—
224	C₂²×C₁₃	—	4	8	no	—
225	C₂²×C₁₃	—	4	2	no	—
226	C₂²×C₁₃	—	4	4	no	—
227	C₂²×C₁₃	—	8	4	no	—
228	C₂²×C₁₃	—	8	8	no	—
229	C₂²×C₁₃	—	8	16	no	—
230	C₂²×C₁₃	C₂×#124	1	2	yes	—
231	C₂²×C₁₃	C₂×#124	1	4	yes	—
232	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
233	C₄×C₁₃	—	2	8	no	—
234	C₄×C₁₃	—	4	8	no	—
235	C₄×C₁₃	—	4	2	no	—
236	C₄×C₁₃	C₂×#124	1	4	yes	—
237	C₄×C₁₃	C₂×#124	1	2	yes	—
238	C₄×C₁₃	C₂²×#41	1	2	yes	—
239	C₂⁵	—	2	1	no	—
240	C₂×#41	—	2	2	no	—
241	C₂×#41	—	2	8	no	—
242	C₂×#41	C₂³×C₁₃	1	4	yes	—
243	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
244	C₂²×D₄	—	2	1	no	—
245	C₂²×D₄	—	2	1	no	—
246	C₂²×D₄	—	2	2	no	—
247	C₂²×D₄	—	2	4	no	—
248	C₂²×D₄	—	2	8	no	—
249	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
250	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
251	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
252	C₂³×C₄	—	2	1	no	—
253	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
254	C₂×M₁₆	—	2	8	no	—
255	C₂×M₁₆	C₂³×C₁₃	1	4	yes	—
256	C₂×M₁₆	C₂³×C₁₃	1	4	yes	—
257	C₂²×C₈	C₂³×C₁₃	1	4	yes	—
258	C₄⋊Q₈	—	2	8	no	—
259	C₄⋊Q₈	C₂³×C₁₃	1	8	yes	complemented
260	#127	—	2	4	no	—
261	#127	C₂³×C₁₃	1	8	yes	—
262	#125	—	2	8	no	—
263	#125	C₂³×C₁₃	1	8	yes	complemented
264	#124	—	2	4	no	—
265	#124	C₂³×C₁₃	1	8	yes	—
266	C₂²⋊Q₈	—	2	8	no	—
267	C₂²⋊Q₈	—	2	16	no	—
268	#121	—	2	16	no	—
269	#120	—	2	16	no	—
270	C₄×Q₈	—	2	8	no	—
271	#117	—	2	2	no	—
272	#117	—	2	2	no	—
273	#117	D₄×C₁₃	1	4	yes	—
274	#117	C₂³×C₁₃	1	4	yes	—
275	#117	C₂³×C₁₃	1	4	yes	—
276	#117	C₂³×C₁₃	1	4	yes	—
277	C₂×C₄⋊C₄	D₄×C₁₃	1	2	yes	—
278	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
279	C₂×C₂²⋊C₄	—	2	2	no	—
280	C₂×C₂²⋊C₄	—	2	4	no	—
281	C₂×C₂²⋊C₄	D₄×C₁₃	1	2	yes	—
282	C₂×C₄²	—	2	2	no	—
283	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
284	#103	C₂³×C₁₃	1	16	yes	complemented
285	#102	C₂³×C₁₃	1	32	yes	—
286	#102	C₂³×C₁₃	1	16	yes	complemented
287	#97	C₂³×C₁₃	1	8	yes	complemented
288	C₄×C₈	C₂³×C₁₃	1	8	yes	complemented
289	C₂×C₁₃	—	2	2	no	—
290	C₂×C₁₃	—	2	4	no	—
291	C₂×C₁₃	—	8	2	no	—
292	C₂×C₁₃	—	8	4	no	—
293	C₂×C₁₃	C₂²×#124	1	1	yes	characteristic
294	C₂×C₁₃	#3585	1	2	yes	—
295	C₂⁴	—	2	2	no	—
296	C₂⁴	—	2	1	no	—
297	C₂⁴	—	2	4	no	—
298	C₂⁴	—	4	4	no	—
299	C₂⁴	—	8	4	no	—
300	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
301	#41	—	2	8	no	—
302	#41	—	2	8	no	—
303	#41	—	4	8	no	—
304	C₂×Q₈	—	2	1	no	—
305	C₂×Q₈	—	2	8	no	—
306	C₂×Q₈	—	2	4	no	—
307	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
308	C₂×D₄	—	2	4	no	—
309	C₂×D₄	—	2	4	no	—
310	C₂×D₄	—	2	2	no	—
311	C₂×D₄	—	2	1	no	—
312	C₂×D₄	—	2	16	no	—
313	C₂×D₄	—	2	8	no	—
314	C₂×D₄	—	2	8	no	—
315	C₂×D₄	—	2	8	no	—
316	C₂×D₄	—	2	4	no	—
317	C₂×D₄	—	4	4	no	—
318	C₂×D₄	—	4	4	no	—
319	C₂×D₄	—	4	8	no	—
320	C₂×D₄	—	8	8	no	—
321	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
322	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
323	C₂²×C₄	—	2	1	no	—
324	C₂²×C₄	—	2	4	no	—
325	C₂²×C₄	—	2	4	no	—
326	C₂²×C₄	—	4	4	no	—
327	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
328	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
329	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
330	C₂²×C₄	C₁₃×#41	1	8	yes	—
331	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
332	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
333	M₁₆	—	2	8	no	—
334	M₁₆	—	2	8	no	—
335	C₂×C₈	—	2	8	no	—
336	C₂×C₈	C₂⁴×C₁₃	1	8	yes	—
337	C₄⋊C₄	—	2	4	no	—
338	C₄⋊C₄	—	2	8	no	—
339	C₄⋊C₄	—	2	16	no	—
340	C₄⋊C₄	C₂×D₄×C₁₃	1	8	yes	—
341	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
342	C₂²⋊C₄	—	2	4	no	—
343	C₂²⋊C₄	—	2	4	no	—
344	C₂²⋊C₄	—	2	16	no	—
345	C₂²⋊C₄	C₂×D₄×C₁₃	1	8	yes	—
346	C₄²	—	2	4	no	—
347	C₄²	—	2	4	no	—
348	C₄²	C₂×D₄×C₁₃	1	4	yes	—
349	C₄²	C₂⁴×C₁₃	1	4	yes	—
350	C₁₃	#60619	1	1	yes	characteristic, direct product factor, Sylow
351	C₂³	—	2	4	no	—
352	C₂³	—	2	2	no	—
353	C₂³	—	4	2	no	—
354	C₂³	—	4	4	no	—
355	C₂³	—	4	8	no	—
356	C₂³	—	4	2	no	—
357	C₂³	—	4	4	no	—
358	C₂³	—	4	8	no	—
359	C₂³	—	8	8	no	—
360	C₂³	—	8	16	no	—
361	C₂³	C₁₃×#124	1	4	yes	—
362	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
363	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
364	Q₈	—	2	4	no	—
365	Q₈	—	4	2	no	—
366	Q₈	—	8	8	no	—
367	D₄	—	2	8	no	—
368	D₄	—	2	4	no	—
369	D₄	—	4	8	no	—
370	D₄	—	4	8	no	—
371	D₄	—	4	4	no	—
372	D₄	—	4	2	no	—
373	D₄	—	8	16	no	—
374	C₂×C₄	—	2	8	no	—
375	C₂×C₄	—	2	2	no	—
376	C₂×C₄	—	4	4	no	—
377	C₂×C₄	—	4	2	no	—
378	C₂×C₄	—	4	8	no	—
379	C₂×C₄	—	8	4	no	—
380	C₂×C₄	C₁₃×#124	1	4	yes	—
381	C₂×C₄	C₁₃×#124	1	8	yes	—
382	C₂×C₄	C₂²×D₄×C₁₃	1	8	yes	—
383	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
384	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
385	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
386	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
387	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
388	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
389	C₈	—	2	8	no	—
390	C₂²	—	2	2	no	—
391	C₂²	—	2	4	no	—
392	C₂²	—	4	4	no	—
393	C₂²	—	4	4	no	—
394	C₂²	—	4	8	no	—
395	C₂²	—	4	2	no	—
396	C₂²	—	4	4	no	—
397	C₂²	—	8	4	no	—
398	C₂²	—	8	8	no	—
399	C₂²	—	8	16	no	—
400	C₂²	C₂×C₁₃×#124	1	2	yes	—
401	C₂²	C₂×C₁₃×#124	1	4	yes	—
402	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
403	C₄	—	2	8	no	—
404	C₄	—	4	8	no	—
405	C₄	—	4	2	no	—
406	C₄	C₂×C₁₃×#124	1	4	yes	—
407	C₄	C₂×C₁₃×#124	1	2	yes	—
408	C₄	C₂²×C₁₃×#41	1	2	yes	—
409	C₂	—	2	2	no	—
410	C₂	—	2	4	no	—
411	C₂	—	8	4	no	—
412	C₂	—	8	2	no	—
413	C₂	C₂²×C₁₃×#124	1	1	yes	characteristic
414	C₂	C₁₃×#3585	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
prime radical	C₂×C₁₃×#535	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
1. C₁₃×#3458	C₂	semidirect
3. C₁₃×#3140	C₂	semidirect
4. C₁₃×#3138	C₂	semidirect
5. C₁₃×#3136	C₂	semidirect
6. C₁₃×#2896	C₂	semidirect
7. C₂×C₁₃×#418	C₂	semidirect
8. C₁₃×#2873	C₂	semidirect
13. C₁₃×#544	C₂²	semidirect
18. C₁₃×#533	C₂²	semidirect
25. C₁₃×#490	C₂²	semidirect
26. C₁₃×#489	C₂²	semidirect
27. C₁₃×#488	C₂²	semidirect
28. C₁₃×#486	C₂²	semidirect
29. C₁₃×#419	C₂²	semidirect
31. C₁₃×#418	C₂²	semidirect
32. C₁₃×#418	C₂²	semidirect
33. C₁₃×#417	C₂²	semidirect
34. C₁₃×#416	C₂²	semidirect
35. C₂×C₁₃×#102	C₂²	semidirect
36. C₁₃×#405	C₂²	semidirect
37. C₄×C₁₃×M₁₆	C₂²	semidirect
58. C₁₃×C₄⋊Q₈	C₂³	semidirect
62. C₁₃×#125	C₂³	semidirect
83. C₁₃×#103	C₂³	semidirect
85. C₁₃×#102	C₂³	semidirect
86. C₁₃×#97	C₂³	semidirect
87. C₄×C₈×C₁₃	C₂³	semidirect
88. #60619	C₁₃	direct (N × H)
144. #3458	C₂×C₁₃	semidirect
146. #3140	C₂×C₁₃	semidirect
147. #3138	C₂×C₁₃	semidirect
148. #3136	C₂×C₁₃	semidirect
149. #2896	C₂×C₁₃	semidirect
150. C₂×#418	C₂×C₁₃	semidirect
151. #2873	C₂×C₁₃	semidirect
195. #544	C₂²×C₁₃	semidirect
200. #533	C₂²×C₁₃	semidirect
207. #490	C₂²×C₁₃	semidirect
208. #489	C₂²×C₁₃	semidirect
209. #488	C₂²×C₁₃	semidirect
210. #486	C₂²×C₁₃	semidirect
211. #419	C₂²×C₁₃	semidirect
213. #418	C₂²×C₁₃	semidirect
214. #418	C₂²×C₁₃	semidirect
215. #417	C₂²×C₁₃	semidirect
216. #416	C₂²×C₁₃	semidirect
217. C₂×#102	C₂²×C₁₃	semidirect
218. #405	C₂²×C₁₃	semidirect
219. C₄×M₁₆	C₂²×C₁₃	semidirect
259. C₄⋊Q₈	C₂³×C₁₃	semidirect
263. #125	C₂³×C₁₃	semidirect
284. #103	C₂³×C₁₃	semidirect
286. #102	C₂³×C₁₃	semidirect
287. #97	C₂³×C₁₃	semidirect
288. C₄×C₈	C₂³×C₁₃	semidirect
350. C₁₃	#60619	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×#3458	2
C₂×C₁₃×#535	2
C₁₃×#3140	2
C₁₃×#3138	2
C₁₃×#3136	2
C₁₃×#2896	2
C₂×C₁₃×#418	2
C₁₃×#2873	2
#60619	13

Subgroups — C13×#60619 #15746958

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#60619 #15746958