Subgroups — C₁₃×#61293 #15747632

Order 3328.

1874 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3506	C₂	1	2	yes	maximal, complemented
2	C₁₃×#3347	C₂	1	8	yes	maximal, complemented
3	C₁₃×#3345	C₂	1	8	yes	maximal, complemented
4	C₁₃×#3162	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#3096	C₂	1	4	yes	maximal, complemented
6	C₁₃×#3077	C₂	1	2	yes	maximal, complemented
7	C₁₃×#3058	C₂	1	2	yes	maximal, complemented
8	C₂×C₁₃×#442	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#2932	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#2912	C₂	1	2	yes	maximal, complemented
11	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic
12	C₂×C₁₃×#131	C₂²	1	2	yes	—
13	C₁₃×#559	—	2	4	no	—
14	C₁₃×#556	—	2	2	no	—
15	C₁₃×#555	C₂²	1	4	yes	complemented
16	C₁₃×#553	C₂²	1	8	yes	complemented
17	C₁₃×#550	—	2	2	no	—
18	C₁₃×#547	C₂²	1	4	yes	complemented
19	C₁₃×#538	—	2	4	no	—
20	C₁₃×#535	C₂²	1	4	yes	—
21	C₁₃×#533	C₂²	1	2	yes	—
22	C₁₃×#532	C₂²	1	1	yes	characteristic
23	C₁₃×#525	—	2	4	no	—
24	C₁₃×#520	C₂²	1	4	yes	—
25	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
26	C₁₃×#501	C₂²	1	4	yes	complemented
27	C₁₃×#501	C₂²	1	4	yes	complemented
28	C₁₃×#482	C₂²	1	8	yes	complemented
29	C₁₃×#482	C₂²	1	8	yes	complemented
30	C₁₃×#481	C₂²	1	8	yes	complemented
31	C₁₃×#480	C₂²	1	8	yes	complemented
32	C₁₃×#478	C₂²	1	8	yes	complemented
33	C₁₃×#476	C₂²	1	4	yes	complemented
34	C₁₃×#474	C₂²	1	4	yes	complemented
35	C₁₃×#469	C₂²	1	4	yes	—
36	C₁₃×#469	C₂²	1	4	yes	—
37	C₁₃×#466	C₂²	1	8	yes	—
38	C₁₃×#442	C₂²	1	8	yes	—
39	C₁₃×#435	C₂²	1	8	yes	complemented
40	C₁₃×#428	C₂²	1	4	yes	—
41	C₁₃×#428	C₂²	1	8	yes	complemented
42	C₁₃×#427	C₂²	1	2	yes	—
43	C₁₃×#427	C₂²	1	2	yes	—
44	C₁₃×#427	C₂²	1	4	yes	complemented
45	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
46	C₂×C₁₃×#106	C₂²	1	4	yes	complemented
47	C₁₃×#423	C₂²	1	1	yes	characteristic
48	C₁₃×#418	C₂²	1	4	yes	—
49	C₂×C₁₃×#102	C₂²	1	2	yes	—
50	C₁₃×#408	C₂²	1	2	yes	—
51	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
52	C₂×C₁₃×#41	—	2	4	no	—
53	C₂×C₁₃×#41	C₂³	1	2	yes	—
54	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
55	C₂³×C₄×C₁₃	—	2	2	no	—
56	C₂×C₁₃×D₈	—	2	4	no	—
57	C₂×C₁₃×D₈	C₂³	1	4	yes	—
58	C₁₃×#131	—	2	8	no	—
59	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
60	C₂×C₁₃×M₁₆	C₂³	1	4	yes	—
61	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
62	C₂²×C₈×C₁₃	C₂³	1	4	yes	—
63	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
64	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
65	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
66	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
67	C₁₃×#127	—	2	4	no	—
68	C₁₃×#127	D₄	1	1	yes	characteristic
69	C₁₃×#126	—	2	8	no	—
70	C₁₃×#125	C₂³	1	4	yes	—
71	C₁₃×#124	—	2	4	no	—
72	C₁₃×#124	—	2	8	no	—
73	C₁₃×#124	D₄	1	2	yes	—
74	C₁₃×#123	—	2	8	no	—
75	C₁₃×#123	—	2	8	no	—
76	C₁₃×C₂²⋊Q₈	—	2	2	no	—
77	C₁₃×C₂²⋊Q₈	—	2	2	no	—
78	C₁₃×C₂²⋊Q₈	—	2	4	no	—
79	C₁₃×#121	—	2	4	no	—
80	C₁₃×#121	—	2	8	no	—
81	C₁₃×#121	D₄	1	4	yes	—
82	C₁₃×#121	C₂³	1	8	yes	—
83	C₁₃×#121	C₂³	1	8	yes	—
84	C₁₃×#120	—	2	8	no	—
85	C₄×Q₈×C₁₃	—	2	4	no	—
86	C₄×Q₈×C₁₃	—	2	2	no	—
87	C₄×Q₈×C₁₃	—	2	2	no	—
88	C₄×D₄×C₁₃	—	2	8	no	—
89	C₄×D₄×C₁₃	—	2	4	no	—
90	C₄×D₄×C₁₃	—	2	8	no	—
91	C₄×D₄×C₁₃	—	2	2	no	—
92	C₄×D₄×C₁₃	—	2	2	no	—
93	C₄×D₄×C₁₃	C₂³	1	4	yes	—
94	C₄×D₄×C₁₃	C₂³	1	4	yes	—
95	C₄×D₄×C₁₃	C₂³	1	4	yes	—
96	C₁₃×#117	—	2	4	no	—
97	C₁₃×#117	C₂³	1	4	yes	—
98	C₁₃×#117	C₂³	1	8	yes	—
99	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
100	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
101	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
102	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
103	C₁₃×#107	C₂³	1	4	yes	—
104	C₁₃×#107	C₂³	1	4	yes	—
105	C₁₃×#107	C₂³	1	8	yes	—
106	C₁₃×#106	C₂³	1	4	yes	—
107	C₁₃×#106	C₂³	1	2	yes	—
108	C₁₃×#106	C₂³	1	8	yes	—
109	C₁₃×#106	C₂³	1	2	yes	—
110	C₁₃×#106	C₂³	1	2	yes	—
111	C₁₃×#106	C₂³	1	2	yes	—
112	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
113	C₁₃×#102	C₂³	1	8	yes	—
114	C₁₃×#102	C₂³	1	8	yes	—
115	C₁₃×#102	C₂³	1	8	yes	—
116	C₁₃×C₂²⋊C₈	C₂³	1	8	yes	—
117	C₁₃×#97	C₂³	1	4	yes	—
118	#61293	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
119	C₂⁴×C₁₃	—	2	2	no	—
120	C₁₃×#41	—	2	4	no	—
121	C₁₃×#41	—	2	4	no	—
122	C₁₃×#41	—	8	8	no	—
123	C₂×Q₈×C₁₃	—	2	2	no	—
124	C₂×Q₈×C₁₃	—	2	2	no	—
125	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
126	C₂×D₄×C₁₃	—	2	8	no	—
127	C₂×D₄×C₁₃	—	2	8	no	—
128	C₂×D₄×C₁₃	—	2	2	no	—
129	C₂×D₄×C₁₃	—	2	4	no	—
130	C₂×D₄×C₁₃	—	2	4	no	—
131	C₂×D₄×C₁₃	C₂×D₄	1	4	yes	—
132	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
133	C₂×D₄×C₁₃	C₂×D₄	1	4	yes	—
134	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
135	C₂²×C₄×C₁₃	—	2	2	no	—
136	C₂²×C₄×C₁₃	—	2	8	no	—
137	C₂²×C₄×C₁₃	—	2	4	no	—
138	C₂²×C₄×C₁₃	—	2	4	no	—
139	C₂²×C₄×C₁₃	—	8	4	no	—
140	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
141	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
142	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
143	C₁₃×D₈	—	2	8	no	—
144	C₁₃×M₁₆	—	2	4	no	—
145	C₁₃×M₁₆	—	2	8	no	—
146	C₂×C₈×C₁₃	—	2	2	no	—
147	C₂×C₈×C₁₃	—	2	8	no	—
148	C₂×C₈×C₁₃	#41	1	4	yes	complemented
149	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
150	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
151	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
152	C₁₃×C₄⋊C₄	—	2	2	no	—
153	C₁₃×C₄⋊C₄	—	2	8	no	—
154	C₁₃×C₄⋊C₄	—	2	2	no	—
155	C₁₃×C₄⋊C₄	—	2	4	no	—
156	C₁₃×C₄⋊C₄	—	2	4	no	—
157	C₁₃×C₄⋊C₄	—	2	2	no	—
158	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
159	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
160	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
161	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
162	C₁₃×C₂²⋊C₄	—	2	4	no	—
163	C₁₃×C₂²⋊C₄	—	2	8	no	—
164	C₁₃×C₂²⋊C₄	—	2	4	no	—
165	C₁₃×C₂²⋊C₄	—	2	4	no	—
166	C₁₃×C₂²⋊C₄	—	2	8	no	—
167	C₁₃×C₂²⋊C₄	—	2	8	no	—
168	C₁₃×C₂²⋊C₄	C₂×D₄	1	8	yes	—
169	C₄²×C₁₃	—	2	8	no	—
170	C₄²×C₁₃	—	2	4	no	—
171	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
172	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
173	C₄²×C₁₃	C₂⁴	1	2	yes	—
174	#3506	C₂×C₁₃	1	2	yes	complemented
175	#3347	C₂×C₁₃	1	8	yes	complemented
176	#3345	C₂×C₁₃	1	8	yes	complemented
177	#3162	C₂×C₁₃	1	1	yes	characteristic, complemented
178	#3096	C₂×C₁₃	1	4	yes	complemented
179	#3077	C₂×C₁₃	1	2	yes	complemented
180	#3058	C₂×C₁₃	1	2	yes	complemented
181	C₂×#442	C₂×C₁₃	1	1	yes	characteristic, complemented
182	#2932	C₂×C₁₃	1	1	yes	characteristic, complemented
183	#2912	C₂×C₁₃	1	2	yes	complemented
184	C₂³×C₁₃	—	2	4	no	—
185	C₂³×C₁₃	—	4	4	no	—
186	C₂³×C₁₃	—	8	2	no	—
187	C₂³×C₁₃	—	8	2	no	—
188	C₂³×C₁₃	C₂²×D₄	1	4	yes	—
189	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
190	Q₈×C₁₃	—	2	4	no	—
191	Q₈×C₁₃	—	4	4	no	—
192	Q₈×C₁₃	—	8	2	no	—
193	D₄×C₁₃	—	2	8	no	—
194	D₄×C₁₃	—	2	4	no	—
195	D₄×C₁₃	—	2	4	no	—
196	D₄×C₁₃	—	2	4	no	—
197	D₄×C₁₃	—	4	4	no	—
198	D₄×C₁₃	—	4	4	no	—
199	D₄×C₁₃	—	8	8	no	—
200	D₄×C₁₃	—	8	8	no	—
201	C₂×C₄×C₁₃	—	2	4	no	—
202	C₂×C₄×C₁₃	—	2	4	no	—
203	C₂×C₄×C₁₃	—	2	4	no	—
204	C₂×C₄×C₁₃	—	2	4	no	—
205	C₂×C₄×C₁₃	—	2	4	no	—
206	C₂×C₄×C₁₃	—	4	2	no	—
207	C₂×C₄×C₁₃	—	4	8	no	—
208	C₂×C₄×C₁₃	—	8	4	no	—
209	C₂×C₄×C₁₃	—	8	2	no	—
210	C₂×C₄×C₁₃	—	8	8	no	—
211	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
212	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
213	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
214	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
215	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
216	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
217	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
218	C₈×C₁₃	—	2	4	no	—
219	C₈×C₁₃	—	2	2	no	—
220	C₈×C₁₃	C₂×#41	1	4	yes	—
221	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic
222	C₂×#131	C₂²×C₁₃	1	2	yes	—
223	#559	—	2	4	no	—
224	#556	—	2	2	no	—
225	#555	C₂²×C₁₃	1	4	yes	complemented
226	#553	C₂²×C₁₃	1	8	yes	complemented
227	#550	—	2	2	no	—
228	#547	C₂²×C₁₃	1	4	yes	complemented
229	#538	—	2	4	no	—
230	#535	C₂²×C₁₃	1	4	yes	—
231	#533	C₂²×C₁₃	1	2	yes	—
232	#532	C₂²×C₁₃	1	1	yes	characteristic
233	#525	—	2	4	no	—
234	#520	C₂²×C₁₃	1	4	yes	—
235	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
236	#501	C₂²×C₁₃	1	4	yes	complemented
237	#501	C₂²×C₁₃	1	4	yes	complemented
238	#482	C₂²×C₁₃	1	8	yes	complemented
239	#482	C₂²×C₁₃	1	8	yes	complemented
240	#481	C₂²×C₁₃	1	8	yes	complemented
241	#480	C₂²×C₁₃	1	8	yes	complemented
242	#478	C₂²×C₁₃	1	8	yes	complemented
243	#476	C₂²×C₁₃	1	4	yes	complemented
244	#474	C₂²×C₁₃	1	4	yes	complemented
245	#469	C₂²×C₁₃	1	4	yes	—
246	#469	C₂²×C₁₃	1	4	yes	—
247	#466	C₂²×C₁₃	1	8	yes	—
248	#442	C₂²×C₁₃	1	8	yes	—
249	#435	C₂²×C₁₃	1	8	yes	complemented
250	#428	C₂²×C₁₃	1	4	yes	—
251	#428	C₂²×C₁₃	1	8	yes	complemented
252	#427	C₂²×C₁₃	1	2	yes	—
253	#427	C₂²×C₁₃	1	2	yes	—
254	#427	C₂²×C₁₃	1	4	yes	complemented
255	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
256	C₂×#106	C₂²×C₁₃	1	4	yes	complemented
257	#423	C₂²×C₁₃	1	1	yes	characteristic
258	#418	C₂²×C₁₃	1	4	yes	—
259	C₂×#102	C₂²×C₁₃	1	2	yes	—
260	#408	C₂²×C₁₃	1	2	yes	—
261	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
262	C₂²×C₁₃	—	2	2	no	—
263	C₂²×C₁₃	—	2	8	no	—
264	C₂²×C₁₃	—	2	4	no	—
265	C₂²×C₁₃	—	4	4	no	—
266	C₂²×C₁₃	—	4	4	no	—
267	C₂²×C₁₃	—	4	4	no	—
268	C₂²×C₁₃	—	8	8	no	—
269	C₂²×C₁₃	#547	1	2	yes	—
270	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
271	C₄×C₁₃	—	2	2	no	—
272	C₄×C₁₃	—	2	2	no	—
273	C₄×C₁₃	—	2	4	no	—
274	C₄×C₁₃	—	4	4	no	—
275	C₄×C₁₃	—	4	4	no	—
276	C₄×C₁₃	—	4	4	no	—
277	C₄×C₁₃	#547	1	2	yes	—
278	C₄×C₁₃	C₂²×#41	1	1	yes	characteristic
279	C₄×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
280	C₂×#41	—	2	4	no	—
281	C₂×#41	C₂³×C₁₃	1	2	yes	—
282	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
283	C₂³×C₄	—	2	2	no	—
284	C₂×D₈	—	2	4	no	—
285	C₂×D₈	C₂³×C₁₃	1	4	yes	—
286	#131	—	2	8	no	—
287	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
288	C₂×M₁₆	C₂³×C₁₃	1	4	yes	—
289	C₂²×C₈	C₂³×C₁₃	1	4	yes	—
290	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
291	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
292	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
293	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
294	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
295	#127	—	2	4	no	—
296	#127	D₄×C₁₃	1	1	yes	characteristic
297	#126	—	2	8	no	—
298	#125	C₂³×C₁₃	1	4	yes	—
299	#124	—	2	4	no	—
300	#124	—	2	8	no	—
301	#124	D₄×C₁₃	1	2	yes	—
302	#123	—	2	8	no	—
303	#123	—	2	8	no	—
304	C₂²⋊Q₈	—	2	2	no	—
305	C₂²⋊Q₈	—	2	2	no	—
306	C₂²⋊Q₈	—	2	4	no	—
307	#121	—	2	4	no	—
308	#121	—	2	8	no	—
309	#121	D₄×C₁₃	1	4	yes	—
310	#121	C₂³×C₁₃	1	8	yes	—
311	#121	C₂³×C₁₃	1	8	yes	—
312	#120	—	2	8	no	—
313	C₄×Q₈	—	2	4	no	—
314	C₄×Q₈	—	2	2	no	—
315	C₄×Q₈	—	2	2	no	—
316	C₄×D₄	—	2	8	no	—
317	C₄×D₄	—	2	4	no	—
318	C₄×D₄	—	2	8	no	—
319	C₄×D₄	—	2	2	no	—
320	C₄×D₄	—	2	2	no	—
321	C₄×D₄	C₂³×C₁₃	1	4	yes	—
322	C₄×D₄	C₂³×C₁₃	1	4	yes	—
323	C₄×D₄	C₂³×C₁₃	1	4	yes	—
324	#117	—	2	4	no	—
325	#117	C₂³×C₁₃	1	4	yes	—
326	#117	C₂³×C₁₃	1	8	yes	—
327	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
328	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
329	C₂×C₂²⋊C₄	—	2	2	no	—
330	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
331	#107	C₂³×C₁₃	1	4	yes	—
332	#107	C₂³×C₁₃	1	4	yes	—
333	#107	C₂³×C₁₃	1	8	yes	—
334	#106	C₂³×C₁₃	1	4	yes	—
335	#106	C₂³×C₁₃	1	2	yes	—
336	#106	C₂³×C₁₃	1	8	yes	—
337	#106	C₂³×C₁₃	1	2	yes	—
338	#106	C₂³×C₁₃	1	2	yes	—
339	#106	C₂³×C₁₃	1	2	yes	—
340	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
341	#102	C₂³×C₁₃	1	8	yes	—
342	#102	C₂³×C₁₃	1	8	yes	—
343	#102	C₂³×C₁₃	1	8	yes	—
344	C₂²⋊C₈	C₂³×C₁₃	1	8	yes	—
345	#97	C₂³×C₁₃	1	4	yes	—
346	C₂×C₁₃	—	2	2	no	—
347	C₂×C₁₃	—	4	4	no	—
348	C₂×C₁₃	—	8	4	no	—
349	C₂×C₁₃	C₂×#547	1	1	yes	characteristic
350	C₂×C₁₃	#3585	1	2	yes	—
351	C₂⁴	—	2	2	no	—
352	#41	—	2	4	no	—
353	#41	—	2	4	no	—
354	#41	—	8	8	no	—
355	C₂×Q₈	—	2	2	no	—
356	C₂×Q₈	—	2	2	no	—
357	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
358	C₂×D₄	—	2	8	no	—
359	C₂×D₄	—	2	8	no	—
360	C₂×D₄	—	2	2	no	—
361	C₂×D₄	—	2	4	no	—
362	C₂×D₄	—	2	4	no	—
363	C₂×D₄	C₂×D₄×C₁₃	1	4	yes	—
364	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
365	C₂×D₄	C₂×D₄×C₁₃	1	4	yes	—
366	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
367	C₂²×C₄	—	2	2	no	—
368	C₂²×C₄	—	2	8	no	—
369	C₂²×C₄	—	2	4	no	—
370	C₂²×C₄	—	2	4	no	—
371	C₂²×C₄	—	8	4	no	—
372	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
373	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
374	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
375	D₈	—	2	8	no	—
376	M₁₆	—	2	4	no	—
377	M₁₆	—	2	8	no	—
378	C₂×C₈	—	2	2	no	—
379	C₂×C₈	—	2	8	no	—
380	C₂×C₈	C₁₃×#41	1	4	yes	complemented
381	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
382	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
383	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
384	C₄⋊C₄	—	2	2	no	—
385	C₄⋊C₄	—	2	8	no	—
386	C₄⋊C₄	—	2	2	no	—
387	C₄⋊C₄	—	2	4	no	—
388	C₄⋊C₄	—	2	4	no	—
389	C₄⋊C₄	—	2	2	no	—
390	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
391	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
392	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
393	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
394	C₂²⋊C₄	—	2	4	no	—
395	C₂²⋊C₄	—	2	8	no	—
396	C₂²⋊C₄	—	2	4	no	—
397	C₂²⋊C₄	—	2	4	no	—
398	C₂²⋊C₄	—	2	8	no	—
399	C₂²⋊C₄	—	2	8	no	—
400	C₂²⋊C₄	C₂×D₄×C₁₃	1	8	yes	—
401	C₄²	—	2	8	no	—
402	C₄²	—	2	4	no	—
403	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
404	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
405	C₄²	C₂⁴×C₁₃	1	2	yes	—
406	C₁₃	#61293	1	1	yes	characteristic, direct product factor, Sylow
407	C₂³	—	2	4	no	—
408	C₂³	—	4	4	no	—
409	C₂³	—	8	2	no	—
410	C₂³	—	8	2	no	—
411	C₂³	C₂²×D₄×C₁₃	1	4	yes	—
412	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
413	Q₈	—	2	4	no	—
414	Q₈	—	4	4	no	—
415	Q₈	—	8	2	no	—
416	D₄	—	2	8	no	—
417	D₄	—	2	4	no	—
418	D₄	—	2	4	no	—
419	D₄	—	2	4	no	—
420	D₄	—	4	4	no	—
421	D₄	—	4	4	no	—
422	D₄	—	8	8	no	—
423	D₄	—	8	8	no	—
424	C₂×C₄	—	2	4	no	—
425	C₂×C₄	—	2	4	no	—
426	C₂×C₄	—	2	4	no	—
427	C₂×C₄	—	2	4	no	—
428	C₂×C₄	—	2	4	no	—
429	C₂×C₄	—	4	2	no	—
430	C₂×C₄	—	4	8	no	—
431	C₂×C₄	—	8	4	no	—
432	C₂×C₄	—	8	2	no	—
433	C₂×C₄	—	8	8	no	—
434	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
435	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
436	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
437	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
438	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
439	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
440	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
441	C₈	—	2	4	no	—
442	C₈	—	2	2	no	—
443	C₈	C₂×C₁₃×#41	1	4	yes	—
444	C₂²	—	2	2	no	—
445	C₂²	—	2	8	no	—
446	C₂²	—	2	4	no	—
447	C₂²	—	4	4	no	—
448	C₂²	—	4	4	no	—
449	C₂²	—	4	4	no	—
450	C₂²	—	8	8	no	—
451	C₂²	C₁₃×#547	1	2	yes	—
452	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
453	C₄	—	2	2	no	—
454	C₄	—	2	2	no	—
455	C₄	—	2	4	no	—
456	C₄	—	4	4	no	—
457	C₄	—	4	4	no	—
458	C₄	—	4	4	no	—
459	C₄	C₁₃×#547	1	2	yes	—
460	C₄	C₂²×C₁₃×#41	1	1	yes	characteristic
461	C₄	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
462	C₂	—	2	2	no	—
463	C₂	—	4	4	no	—
464	C₂	—	8	4	no	—
465	C₂	C₂×C₁₃×#547	1	1	yes	characteristic
466	C₂	C₁₃×#3585	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₁₃×#532 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3506	C₂	semidirect
2. C₁₃×#3347	C₂	semidirect
3. C₁₃×#3345	C₂	semidirect
4. C₁₃×#3162	C₂	semidirect
5. C₁₃×#3096	C₂	semidirect
6. C₁₃×#3077	C₂	semidirect
7. C₁₃×#3058	C₂	semidirect
8. C₂×C₁₃×#442	C₂	semidirect
9. C₁₃×#2932	C₂	semidirect
10. C₁₃×#2912	C₂	semidirect
15. C₁₃×#555	C₂²	semidirect
16. C₁₃×#553	C₂²	semidirect
18. C₁₃×#547	C₂²	semidirect
26. C₁₃×#501	C₂²	semidirect
27. C₁₃×#501	C₂²	semidirect
28. C₁₃×#482	C₂²	semidirect
29. C₁₃×#482	C₂²	semidirect
30. C₁₃×#481	C₂²	semidirect
31. C₁₃×#480	C₂²	semidirect
32. C₁₃×#478	C₂²	semidirect
33. C₁₃×#476	C₂²	semidirect
34. C₁₃×#474	C₂²	semidirect
39. C₁₃×#435	C₂²	semidirect
41. C₁₃×#428	C₂²	semidirect
44. C₁₃×#427	C₂²	semidirect
46. C₂×C₁₃×#106	C₂²	semidirect
118. #61293	C₁₃	direct (N × H)
148. C₂×C₈×C₁₃	#41	semidirect
174. #3506	C₂×C₁₃	semidirect
175. #3347	C₂×C₁₃	semidirect
176. #3345	C₂×C₁₃	semidirect
177. #3162	C₂×C₁₃	semidirect
178. #3096	C₂×C₁₃	semidirect
179. #3077	C₂×C₁₃	semidirect
180. #3058	C₂×C₁₃	semidirect
181. C₂×#442	C₂×C₁₃	semidirect
182. #2932	C₂×C₁₃	semidirect
183. #2912	C₂×C₁₃	semidirect
225. #555	C₂²×C₁₃	semidirect
226. #553	C₂²×C₁₃	semidirect
228. #547	C₂²×C₁₃	semidirect
236. #501	C₂²×C₁₃	semidirect
237. #501	C₂²×C₁₃	semidirect
238. #482	C₂²×C₁₃	semidirect
239. #482	C₂²×C₁₃	semidirect
240. #481	C₂²×C₁₃	semidirect
241. #480	C₂²×C₁₃	semidirect
242. #478	C₂²×C₁₃	semidirect
243. #476	C₂²×C₁₃	semidirect
244. #474	C₂²×C₁₃	semidirect
249. #435	C₂²×C₁₃	semidirect
251. #428	C₂²×C₁₃	semidirect
254. #427	C₂²×C₁₃	semidirect
256. C₂×#106	C₂²×C₁₃	semidirect
380. C₂×C₈	C₁₃×#41	semidirect
406. C₁₃	#61293	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×#3506	2
C₁₃×#3347	2
C₁₃×#3345	2
C₁₃×#3162	2
C₁₃×#3096	2
C₁₃×#3077	2
C₁₃×#3058	2
C₂×C₁₃×#442	2
C₁₃×#2932	2
C₁₃×#2912	2
#61293	13

Subgroups — C13×#61293 #15747632

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61293 #15747632