Subgroups — C₁₃×#26273 #15712612

Order 3328.

748 conjugacy classes of subgroups.

The subgroup lattice has 448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3156	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#3097	C₂	1	2	yes	maximal, complemented
3	C₁₃×#2952	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#2052	C₂	1	2	yes	maximal, complemented
5	C₁₃×#2038	C₂	1	2	yes	maximal, complemented
6	C₁₃×#1979	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#1975	C₂	1	1	yes	maximal, characteristic
8	C₁₃×#1971	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1951	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1882	C₂	1	2	yes	maximal, complemented
11	C₁₃×#1773	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₃×#137	C₂²	1	2	yes	—
13	C₂×C₁₃×#135	C₂²	1	1	yes	characteristic
14	C₂²×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
15	C₁₃×#536	C₂²	1	2	yes	—
16	C₁₃×#520	C₂²	1	2	yes	—
17	C₁₃×#497	—	2	2	no	—
18	C₁₃×#495	—	2	1	no	—
19	C₁₃×#494	—	2	1	no	—
20	C₁₃×#485	—	2	2	no	—
21	C₁₃×#485	—	2	2	no	—
22	C₁₃×#484	—	2	2	no	—
23	C₁₃×#483	—	2	2	no	—
24	C₁₃×#442	—	2	1	no	—
25	C₁₃×#441	—	2	1	no	—
26	C₄×C₁₃×SD₁₆	—	2	2	no	—
27	C₂×C₁₃×#108	C₂²	1	1	yes	characteristic
28	C₂×C₁₃×#108	C₂²	1	1	yes	characteristic
29	C₁₃×#428	C₂²	1	2	yes	—
30	C₁₃×#427	C₂²	1	1	yes	characteristic
31	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
32	C₂×C₁₃×#104	C₂²	1	2	yes	—
33	C₁₃×#419	C₂²	1	2	yes	—
34	C₁₃×#417	C₂²	1	2	yes	—
35	C₂×C₁₃×#103	C₂²	1	2	yes	—
36	C₂×C₁₃×#101	C₂²	1	2	yes	—
37	C₁₃×#408	C₂²	1	2	yes	—
38	C₁₃×#405	C₂²	1	1	yes	characteristic
39	C₁₃×#405	C₂²	1	1	yes	characteristic
40	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
41	C₁₃×#391	C₂²	1	2	yes	—
42	C₁₃×#343	C₂²	1	2	yes	—
43	C₁₃×#339	C₂²	1	1	yes	characteristic
44	C₁₃×#339	C₂²	1	1	yes	characteristic
45	C₂×C₁₃×#41	C₂³	1	2	yes	—
46	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
47	C₁₃×#137	—	2	4	no	—
48	C₁₃×#137	—	4	2	no	—
49	C₁₃×#135	—	2	2	no	—
50	C₁₃×#135	—	2	2	no	—
51	C₂×C₁₃×Q₁₆	—	2	2	no	—
52	C₂×C₁₃×Q₁₆	—	2	1	no	—
53	C₂×C₁₃×Q₁₆	—	2	1	no	—
54	C₂×C₁₃×Q₁₆	—	2	2	no	—
55	C₂×C₁₃×Q₁₆	—	2	2	no	—
56	C₂×C₁₃×Q₁₆	D₄	1	1	yes	characteristic
57	C₂×C₁₃×SD₁₆	—	2	2	no	—
58	C₂×C₁₃×SD₁₆	D₄	1	2	yes	—
59	C₂×C₁₃×D₈	D₄	1	1	yes	characteristic
60	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
61	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
62	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
63	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
64	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
65	C₁₃×C₄⋊Q₈	—	2	2	no	—
66	C₁₃×#124	—	2	2	no	—
67	C₁₃×#123	—	4	2	no	—
68	C₁₃×C₂²⋊Q₈	—	2	2	no	—
69	C₁₃×C₂²⋊Q₈	—	2	2	no	—
70	C₄×Q₈×C₁₃	—	2	2	no	—
71	C₄×D₄×C₁₃	—	2	2	no	—
72	C₄×D₄×C₁₃	—	4	2	no	—
73	C₁₃×#117	—	2	2	no	—
74	C₁₃×#117	C₂³	1	1	yes	characteristic
75	C₁₃×#117	C₂³	1	1	yes	characteristic
76	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
77	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
78	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
79	C₁₃×#108	—	2	2	no	—
80	C₁₃×#108	—	2	2	no	—
81	C₁₃×#107	—	2	2	no	—
82	C₁₃×#107	D₄	1	2	yes	—
83	C₁₃×#106	—	2	1	no	—
84	C₁₃×#106	—	2	1	no	—
85	C₁₃×#106	—	2	2	no	—
86	C₁₃×#106	D₄	1	2	yes	—
87	C₁₃×#104	—	4	2	no	—
88	C₁₃×#103	—	2	2	no	—
89	C₁₃×#103	—	2	2	no	—
90	C₁₃×#103	—	2	2	no	—
91	C₁₃×#103	—	2	2	no	—
92	C₁₃×#103	—	2	2	no	—
93	C₁₃×#102	—	2	2	no	—
94	C₁₃×#101	—	4	2	no	—
95	C₁₃×C₂²⋊C₈	—	2	2	no	—
96	C₁₃×C₂²⋊C₈	—	2	2	no	—
97	C₁₃×#97	—	2	1	no	—
98	C₁₃×#97	—	2	1	no	—
99	C₁₃×#97	—	2	2	no	—
100	C₄×C₈×C₁₃	—	2	1	no	—
101	C₄×C₈×C₁₃	—	2	1	no	—
102	C₁₃×#95	—	4	2	no	—
103	#26273	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
104	C₁₃×#41	—	2	2	no	—
105	C₁₃×#41	—	2	2	no	—
106	C₁₃×#41	—	2	2	no	—
107	C₁₃×#41	—	2	2	no	—
108	C₂×Q₈×C₁₃	—	2	2	no	—
109	C₂×Q₈×C₁₃	—	2	2	no	—
110	C₂×Q₈×C₁₃	—	2	2	no	—
111	C₂×Q₈×C₁₃	—	2	2	no	—
112	C₂×Q₈×C₁₃	—	2	2	no	—
113	C₂×Q₈×C₁₃	—	2	2	no	—
114	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
115	C₂×D₄×C₁₃	—	2	2	no	—
116	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
117	C₂²×C₄×C₁₃	—	2	2	no	—
118	C₂²×C₄×C₁₃	—	2	1	no	—
119	C₂²×C₄×C₁₃	—	2	2	no	—
120	C₂²×C₄×C₁₃	—	2	2	no	—
121	C₂²×C₄×C₁₃	—	4	2	no	—
122	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
123	C₁₃×Q₁₆	—	2	2	no	—
124	C₁₃×Q₁₆	—	4	4	no	—
125	C₁₃×Q₁₆	—	4	2	no	—
126	C₁₃×Q₁₆	—	4	2	no	—
127	C₁₃×SD₁₆	—	2	4	no	—
128	C₁₃×SD₁₆	—	4	4	no	—
129	C₁₃×D₈	—	2	2	no	—
130	C₁₃×M₁₆	—	2	1	no	—
131	C₁₃×M₁₆	—	2	1	no	—
132	C₁₃×M₁₆	—	2	2	no	—
133	C₁₃×M₁₆	—	2	1	no	—
134	C₁₃×M₁₆	—	2	2	no	—
135	C₁₃×M₁₆	#41	1	2	yes	—
136	C₂×C₈×C₁₃	—	2	1	no	—
137	C₂×C₈×C₁₃	—	2	1	no	—
138	C₂×C₈×C₁₃	—	2	1	no	—
139	C₂×C₈×C₁₃	—	2	1	no	—
140	C₂×C₈×C₁₃	—	2	2	no	—
141	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
142	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
143	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
144	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
145	C₂×C₈×C₁₃	#41	1	2	yes	—
146	C₂×C₈×C₁₃	#41	1	2	yes	—
147	C₁₃×C₄⋊C₄	—	2	2	no	—
148	C₁₃×C₄⋊C₄	—	2	2	no	—
149	C₁₃×C₄⋊C₄	—	4	2	no	—
150	C₁₃×C₄⋊C₄	—	4	2	no	—
151	C₁₃×C₄⋊C₄	—	4	2	no	—
152	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
153	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
154	C₁₃×C₂²⋊C₄	—	2	1	no	—
155	C₁₃×C₂²⋊C₄	—	2	1	no	—
156	C₁₃×C₂²⋊C₄	—	4	2	no	—
157	C₁₃×C₂²⋊C₄	—	4	2	no	—
158	C₁₃×C₂²⋊C₄	—	4	2	no	—
159	C₄²×C₁₃	—	2	1	no	—
160	C₄²×C₁₃	—	2	1	no	—
161	C₄²×C₁₃	—	2	1	no	—
162	C₄²×C₁₃	—	2	1	no	—
163	C₄²×C₁₃	—	4	2	no	—
164	#3156	C₂×C₁₃	1	1	yes	characteristic
165	#3097	C₂×C₁₃	1	2	yes	complemented
166	#2952	C₂×C₁₃	1	1	yes	characteristic
167	#2052	C₂×C₁₃	1	2	yes	complemented
168	#2038	C₂×C₁₃	1	2	yes	complemented
169	#1979	C₂×C₁₃	1	1	yes	characteristic, complemented
170	#1975	C₂×C₁₃	1	1	yes	characteristic
171	#1971	C₂×C₁₃	1	1	yes	characteristic, complemented
172	#1951	C₂×C₁₃	1	1	yes	characteristic, complemented
173	#1882	C₂×C₁₃	1	2	yes	complemented
174	#1773	C₂×C₁₃	1	1	yes	characteristic, complemented
175	C₂³×C₁₃	—	2	2	no	—
176	C₂³×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
177	Q₈×C₁₃	—	2	2	no	—
178	Q₈×C₁₃	—	2	2	no	—
179	Q₈×C₁₃	—	4	2	no	—
180	Q₈×C₁₃	—	4	2	no	—
181	Q₈×C₁₃	—	4	2	no	—
182	Q₈×C₁₃	—	4	2	no	—
183	D₄×C₁₃	—	2	2	no	—
184	D₄×C₁₃	—	2	2	no	—
185	D₄×C₁₃	—	4	2	no	—
186	D₄×C₁₃	—	4	2	no	—
187	C₂×C₄×C₁₃	—	2	2	no	—
188	C₂×C₄×C₁₃	—	2	2	no	—
189	C₂×C₄×C₁₃	—	2	2	no	—
190	C₂×C₄×C₁₃	—	4	2	no	—
191	C₂×C₄×C₁₃	—	4	2	no	—
192	C₂×C₄×C₁₃	—	4	2	no	—
193	C₂×C₄×C₁₃	—	4	1	no	—
194	C₂×C₄×C₁₃	—	4	2	no	—
195	C₂×C₄×C₁₃	—	4	2	no	—
196	C₂×C₄×C₁₃	—	4	2	no	—
197	C₂×C₄×C₁₃	—	4	2	no	—
198	C₂×C₄×C₁₃	—	8	2	no	—
199	C₂×C₄×C₁₃	—	16	2	no	—
200	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
201	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
202	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
203	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
204	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
205	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
206	C₈×C₁₃	—	2	1	no	—
207	C₈×C₁₃	—	2	1	no	—
208	C₈×C₁₃	—	2	2	no	—
209	C₈×C₁₃	—	4	1	no	—
210	C₈×C₁₃	—	4	2	no	—
211	C₈×C₁₃	#123	1	2	yes	—
212	C₈×C₁₃	#123	1	2	yes	—
213	C₂×#137	C₂²×C₁₃	1	2	yes	—
214	C₂×#135	C₂²×C₁₃	1	1	yes	characteristic
215	C₂²×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
216	#536	C₂²×C₁₃	1	2	yes	—
217	#520	C₂²×C₁₃	1	2	yes	—
218	#497	—	2	2	no	—
219	#495	—	2	1	no	—
220	#494	—	2	1	no	—
221	#485	—	2	2	no	—
222	#485	—	2	2	no	—
223	#484	—	2	2	no	—
224	#483	—	2	2	no	—
225	#442	—	2	1	no	—
226	#441	—	2	1	no	—
227	C₄×SD₁₆	—	2	2	no	—
228	C₂×#108	C₂²×C₁₃	1	1	yes	characteristic
229	C₂×#108	C₂²×C₁₃	1	1	yes	characteristic
230	#428	C₂²×C₁₃	1	2	yes	—
231	#427	C₂²×C₁₃	1	1	yes	characteristic
232	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
233	C₂×#104	C₂²×C₁₃	1	2	yes	—
234	#419	C₂²×C₁₃	1	2	yes	—
235	#417	C₂²×C₁₃	1	2	yes	—
236	C₂×#103	C₂²×C₁₃	1	2	yes	—
237	C₂×#101	C₂²×C₁₃	1	2	yes	—
238	#408	C₂²×C₁₃	1	2	yes	—
239	#405	C₂²×C₁₃	1	1	yes	characteristic
240	#405	C₂²×C₁₃	1	1	yes	characteristic
241	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
242	#391	C₂²×C₁₃	1	2	yes	—
243	#343	C₂²×C₁₃	1	2	yes	—
244	#339	C₂²×C₁₃	1	1	yes	characteristic
245	#339	C₂²×C₁₃	1	1	yes	characteristic
246	C₂²×C₁₃	—	2	2	no	—
247	C₂²×C₁₃	—	4	2	no	—
248	C₂²×C₁₃	—	4	2	no	—
249	C₂²×C₁₃	—	4	2	no	—
250	C₂²×C₁₃	#540	1	1	yes	characteristic
251	C₂²×C₁₃	D₄²	1	1	yes	characteristic
252	C₂²×C₁₃	#559	1	1	yes	characteristic
253	C₄×C₁₃	—	4	2	no	—
254	C₄×C₁₃	—	4	2	no	—
255	C₄×C₁₃	—	4	2	no	—
256	C₄×C₁₃	—	8	1	no	—
257	C₄×C₁₃	—	8	2	no	—
258	C₄×C₁₃	—	8	2	no	—
259	C₄×C₁₃	C₂×#123	1	1	yes	characteristic
260	C₄×C₁₃	#532	1	1	yes	characteristic
261	C₄×C₁₃	#546	1	1	yes	characteristic
262	C₄×C₁₃	#550	1	1	yes	characteristic
263	C₂×#41	C₂³×C₁₃	1	2	yes	—
264	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
265	#137	—	2	4	no	—
266	#137	—	4	2	no	—
267	#135	—	2	2	no	—
268	#135	—	2	2	no	—
269	C₂×Q₁₆	—	2	2	no	—
270	C₂×Q₁₆	—	2	1	no	—
271	C₂×Q₁₆	—	2	1	no	—
272	C₂×Q₁₆	—	2	2	no	—
273	C₂×Q₁₆	—	2	2	no	—
274	C₂×Q₁₆	D₄×C₁₃	1	1	yes	characteristic
275	C₂×SD₁₆	—	2	2	no	—
276	C₂×SD₁₆	D₄×C₁₃	1	2	yes	—
277	C₂×D₈	D₄×C₁₃	1	1	yes	characteristic
278	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
279	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
280	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
281	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
282	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
283	C₄⋊Q₈	—	2	2	no	—
284	#124	—	2	2	no	—
285	#123	—	4	2	no	—
286	C₂²⋊Q₈	—	2	2	no	—
287	C₂²⋊Q₈	—	2	2	no	—
288	C₄×Q₈	—	2	2	no	—
289	C₄×D₄	—	2	2	no	—
290	C₄×D₄	—	4	2	no	—
291	#117	—	2	2	no	—
292	#117	C₂³×C₁₃	1	1	yes	characteristic
293	#117	C₂³×C₁₃	1	1	yes	characteristic
294	C₂×C₄⋊C₄	—	2	2	no	—
295	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
296	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
297	#108	—	2	2	no	—
298	#108	—	2	2	no	—
299	#107	—	2	2	no	—
300	#107	D₄×C₁₃	1	2	yes	—
301	#106	—	2	1	no	—
302	#106	—	2	1	no	—
303	#106	—	2	2	no	—
304	#106	D₄×C₁₃	1	2	yes	—
305	#104	—	4	2	no	—
306	#103	—	2	2	no	—
307	#103	—	2	2	no	—
308	#103	—	2	2	no	—
309	#103	—	2	2	no	—
310	#103	—	2	2	no	—
311	#102	—	2	2	no	—
312	#101	—	4	2	no	—
313	C₂²⋊C₈	—	2	2	no	—
314	C₂²⋊C₈	—	2	2	no	—
315	#97	—	2	1	no	—
316	#97	—	2	1	no	—
317	#97	—	2	2	no	—
318	C₄×C₈	—	2	1	no	—
319	C₄×C₈	—	2	1	no	—
320	#95	—	4	2	no	—
321	C₂×C₁₃	—	2	1	no	—
322	C₂×C₁₃	—	2	1	no	—
323	C₂×C₁₃	—	8	2	no	—
324	C₂×C₁₃	#2445	1	1	yes	characteristic
325	C₂×C₁₃	#3289	1	2	yes	—
326	#41	—	2	2	no	—
327	#41	—	2	2	no	—
328	#41	—	2	2	no	—
329	#41	—	2	2	no	—
330	C₂×Q₈	—	2	2	no	—
331	C₂×Q₈	—	2	2	no	—
332	C₂×Q₈	—	2	2	no	—
333	C₂×Q₈	—	2	2	no	—
334	C₂×Q₈	—	2	2	no	—
335	C₂×Q₈	—	2	2	no	—
336	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
337	C₂×D₄	—	2	2	no	—
338	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
339	C₂²×C₄	—	2	2	no	—
340	C₂²×C₄	—	2	1	no	—
341	C₂²×C₄	—	2	2	no	—
342	C₂²×C₄	—	2	2	no	—
343	C₂²×C₄	—	4	2	no	—
344	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
345	Q₁₆	—	2	2	no	—
346	Q₁₆	—	4	4	no	—
347	Q₁₆	—	4	2	no	—
348	Q₁₆	—	4	2	no	—
349	SD₁₆	—	2	4	no	—
350	SD₁₆	—	4	4	no	—
351	D₈	—	2	2	no	—
352	M₁₆	—	2	1	no	—
353	M₁₆	—	2	1	no	—
354	M₁₆	—	2	2	no	—
355	M₁₆	—	2	1	no	—
356	M₁₆	—	2	2	no	—
357	M₁₆	C₁₃×#41	1	2	yes	—
358	C₂×C₈	—	2	1	no	—
359	C₂×C₈	—	2	1	no	—
360	C₂×C₈	—	2	1	no	—
361	C₂×C₈	—	2	1	no	—
362	C₂×C₈	—	2	2	no	—
363	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
364	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
365	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
366	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
367	C₂×C₈	C₁₃×#41	1	2	yes	—
368	C₂×C₈	C₁₃×#41	1	2	yes	—
369	C₄⋊C₄	—	2	2	no	—
370	C₄⋊C₄	—	2	2	no	—
371	C₄⋊C₄	—	4	2	no	—
372	C₄⋊C₄	—	4	2	no	—
373	C₄⋊C₄	—	4	2	no	—
374	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
375	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
376	C₂²⋊C₄	—	2	1	no	—
377	C₂²⋊C₄	—	2	1	no	—
378	C₂²⋊C₄	—	4	2	no	—
379	C₂²⋊C₄	—	4	2	no	—
380	C₂²⋊C₄	—	4	2	no	—
381	C₄²	—	2	1	no	—
382	C₄²	—	2	1	no	—
383	C₄²	—	2	1	no	—
384	C₄²	—	2	1	no	—
385	C₄²	—	4	2	no	—
386	C₁₃	#26273	1	1	yes	characteristic, direct product factor, Sylow
387	C₂³	—	2	2	no	—
388	C₂³	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
389	Q₈	—	2	2	no	—
390	Q₈	—	2	2	no	—
391	Q₈	—	4	2	no	—
392	Q₈	—	4	2	no	—
393	Q₈	—	4	2	no	—
394	Q₈	—	4	2	no	—
395	D₄	—	2	2	no	—
396	D₄	—	2	2	no	—
397	D₄	—	4	2	no	—
398	D₄	—	4	2	no	—
399	C₂×C₄	—	2	2	no	—
400	C₂×C₄	—	2	2	no	—
401	C₂×C₄	—	2	2	no	—
402	C₂×C₄	—	4	2	no	—
403	C₂×C₄	—	4	2	no	—
404	C₂×C₄	—	4	2	no	—
405	C₂×C₄	—	4	1	no	—
406	C₂×C₄	—	4	2	no	—
407	C₂×C₄	—	4	2	no	—
408	C₂×C₄	—	4	2	no	—
409	C₂×C₄	—	4	2	no	—
410	C₂×C₄	—	8	2	no	—
411	C₂×C₄	—	16	2	no	—
412	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
413	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
414	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
415	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
416	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
417	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
418	C₈	—	2	1	no	—
419	C₈	—	2	1	no	—
420	C₈	—	2	2	no	—
421	C₈	—	4	1	no	—
422	C₈	—	4	2	no	—
423	C₈	C₁₃×#123	1	2	yes	—
424	C₈	C₁₃×#123	1	2	yes	—
425	C₂²	—	2	2	no	—
426	C₂²	—	4	2	no	—
427	C₂²	—	4	2	no	—
428	C₂²	—	4	2	no	—
429	C₂²	C₁₃×#540	1	1	yes	characteristic
430	C₂²	D₄²×C₁₃	1	1	yes	characteristic
431	C₂²	C₁₃×#559	1	1	yes	characteristic
432	C₄	—	4	2	no	—
433	C₄	—	4	2	no	—
434	C₄	—	4	2	no	—
435	C₄	—	8	1	no	—
436	C₄	—	8	2	no	—
437	C₄	—	8	2	no	—
438	C₄	C₂×C₁₃×#123	1	1	yes	characteristic
439	C₄	C₁₃×#532	1	1	yes	characteristic
440	C₄	C₁₃×#546	1	1	yes	characteristic
441	C₄	C₁₃×#550	1	1	yes	characteristic
442	C₂	—	2	1	no	—
443	C₂	—	2	1	no	—
444	C₂	—	8	2	no	—
445	C₂	C₁₃×#2445	1	1	yes	characteristic
446	C₂	C₁₃×#3289	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₃	D₄²
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂×C₁₃×#135	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂²×C₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₃×#3097	C₂	semidirect
4. C₁₃×#2052	C₂	semidirect
5. C₁₃×#2038	C₂	semidirect
6. C₁₃×#1979	C₂	semidirect
8. C₁₃×#1971	C₂	semidirect
9. C₁₃×#1951	C₂	semidirect
10. C₁₃×#1882	C₂	semidirect
11. C₁₃×#1773	C₂	semidirect
103. #26273	C₁₃	direct (N × H)
165. #3097	C₂×C₁₃	semidirect
167. #2052	C₂×C₁₃	semidirect
168. #2038	C₂×C₁₃	semidirect
169. #1979	C₂×C₁₃	semidirect
171. #1971	C₂×C₁₃	semidirect
172. #1951	C₂×C₁₃	semidirect
173. #1882	C₂×C₁₃	semidirect
174. #1773	C₂×C₁₃	semidirect
386. C₁₃	#26273	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×#3156	2
C₁₃×#3097	2
C₁₃×#2952	2
C₁₃×#2052	2
C₁₃×#2038	2
C₁₃×#1979	2
C₁₃×#1975	2
C₁₃×#1971	2
C₁₃×#1951	2
C₁₃×#1882	2
C₁₃×#1773	2
#26273	13

Subgroups — C13×#26273 #15712612

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#26273 #15712612