Subgroups — D₁₃×#556 #13128378

Order 1664.

1112 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×#556	C₂	1	1	yes	maximal, characteristic, complemented
2	#11719437	C₂	1	1	yes	maximal, characteristic, complemented
3	D₁₃×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
4	D₁₃×#126	C₂	1	4	yes	maximal, complemented
5	#11719407	C₂	1	4	yes	maximal, complemented
6	D₁₃×#124	C₂	1	2	yes	maximal
7	#11719376	C₂	1	2	yes	maximal, complemented
8	#11719346	C₂	1	2	yes	maximal, complemented
9	D₁₃×C₂²⋊Q₈	C₂	1	2	yes	maximal, complemented
10	#11719289	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×Q₈×D₁₃	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄×Q₈×D₁₃	C₂	1	2	yes	maximal, complemented
13	#11719273	C₂	1	2	yes	maximal, complemented
14	C₄×D₄×D₁₃	C₂	1	1	yes	maximal, characteristic
15	#11719247	C₂	1	1	yes	maximal, characteristic, complemented
16	#11719238	C₂	1	2	yes	maximal, complemented
17	D₁₃×#117	C₂	1	2	yes	maximal, complemented
18	C₂×Q₈×D₁₃	C₂²	1	2	yes	—
19	C₂×Q₈×D₁₃	C₂²	1	1	yes	characteristic
20	C₂×D₄×D₁₃	C₂²	1	1	yes	characteristic
21	C₂²×C₄×D₁₃	C₂²	1	2	yes	—
22	C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
23	C₁₃×#126	C₂²	1	4	yes	complemented
24	C₁₃×#124	C₂²	1	2	yes	—
25	C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
26	C₄×Q₈×C₁₃	C₂²	1	2	yes	complemented
27	C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
28	C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
29	C₁₃×#117	C₂²	1	2	yes	complemented
30	#88201	C₂²	1	2	yes	—
31	#88200	C₂²	1	2	yes	complemented
32	Q₈×Dic₁₃	C₂²	1	2	yes	complemented
33	Q₈×Dic₁₃	C₂²	1	1	yes	characteristic, complemented
34	#88198	C₂²	1	2	yes	complemented
35	#88190	C₂²	1	2	yes	—
36	D₄×Dic₁₃	C₂²	1	1	yes	characteristic
37	C₄×C₂²⋊D₁₃	C₂²	1	2	yes	—
38	#88180	C₂²	1	2	yes	complemented
39	#88178	C₂²	1	2	yes	complemented
40	#88152	C₂²	1	4	yes	complemented
41	#88152	C₂²	1	4	yes	complemented
42	#88152	C₂²	1	4	yes	complemented
43	#88151	C₂²	1	2	yes	complemented
44	#88150	C₂²	1	4	yes	complemented
45	#88147	C₂²	1	1	yes	characteristic
46	#88146	C₂²	1	2	yes	complemented
47	#88146	C₂²	1	2	yes	complemented
48	C₄⋊C₄×D₁₃	C₂²	1	2	yes	—
49	C₄⋊C₄×D₁₃	C₂²	1	2	yes	—
50	C₄⋊C₄×D₁₃	C₂²	1	1	yes	characteristic
51	C₄⋊C₄×D₁₃	C₂²	1	1	yes	characteristic
52	C₄⋊C₄×D₁₃	C₂²	1	4	yes	—
53	C₄⋊C₄×D₁₃	C₂²	1	2	yes	—
54	#88142	C₂²	1	2	yes	complemented
55	#88142	C₂²	1	2	yes	complemented
56	#88141	C₂²	1	1	yes	characteristic, complemented
57	#88141	C₂²	1	2	yes	complemented
58	#88141	C₂²	1	4	yes	complemented
59	#88141	C₂²	1	2	yes	complemented
60	#88139	C₂²	1	4	yes	—
61	#88139	C₂²	1	4	yes	—
62	#88135	C₂²	1	2	yes	—
63	C₂²⋊C₄×D₁₃	C₂²	1	4	yes	—
64	C₂²⋊C₄×D₁₃	C₂²	1	2	yes	—
65	C₂²⋊C₄×D₁₃	C₂²	1	4	yes	—
66	#88133	C₂²	1	4	yes	complemented
67	#88133	C₂²	1	4	yes	complemented
68	#88133	C₂²	1	4	yes	complemented
69	#88132	C₂²	1	4	yes	complemented
70	#88131	C₂²	1	4	yes	complemented
71	#88130	C₂²	1	4	yes	complemented
72	#88129	C₂²	1	2	yes	—
73	C₄×D₅₂	C₂²	1	1	yes	characteristic
74	#88126	C₂²	1	4	yes	complemented
75	C₄²×D₁₃	C₂²	1	1	yes	characteristic
76	C₄²×D₁₃	C₂²	1	4	yes	—
77	C₄²×D₁₃	C₂²	1	2	yes	—
78	#88123	C₂²	1	1	yes	characteristic, complemented
79	C₄×Dic₂₆	C₂²	1	1	yes	characteristic, complemented
80	C₄×Dic₂₆	C₂²	1	4	yes	complemented
81	C₄×Dic₂₆	C₂²	1	2	yes	complemented
82	C₄×Dic₂₆	C₂²	1	2	yes	complemented
83	C₂³×D₁₃	C₂³	1	2	yes	—
84	C₂×Q₈×C₁₃	C₂³	1	2	yes	—
85	C₂×Q₈×C₁₃	C₂³	1	1	yes	characteristic
86	C₂×D₄×C₁₃	C₂³	1	1	yes	characteristic
87	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
88	C₂×C₂²⋊D₁₃	C₂³	1	2	yes	—
89	C₂²×Dic₁₃	C₂³	1	2	yes	—
90	Q₈×D₁₃	—	2	4	no	—
91	Q₈×D₁₃	—	2	8	no	—
92	D₄×D₁₃	—	2	4	no	—
93	C₂×D₅₂	C₂³	1	1	yes	characteristic
94	C₂×C₄×D₁₃	—	2	8	no	—
95	C₂×C₄×D₁₃	C₂³	1	2	yes	—
96	C₂×C₄×D₁₃	C₂³	1	2	yes	—
97	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
98	C₂×C₄×D₁₃	C₂³	1	4	yes	—
99	C₂×C₄×D₁₃	C₂³	1	2	yes	—
100	C₂×C₄×D₁₃	C₂³	1	2	yes	—
101	C₂×C₄×D₁₃	C₂³	1	2	yes	—
102	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
103	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
104	C₂×Dic₂₆	C₂³	1	2	yes	—
105	C₂×Dic₂₆	C₂³	1	2	yes	—
106	C₂×Dic₂₆	C₂³	1	4	yes	—
107	C₂×Dic₂₆	C₂³	1	1	yes	characteristic
108	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
109	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
110	C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
111	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
112	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
113	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
114	C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
115	C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
116	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
117	C₄²×C₁₃	C₂³	1	2	yes	—
118	C₄²×C₁₃	C₂³	1	1	yes	characteristic
119	C₄²×C₁₃	C₂³	1	4	yes	—
120	C₂²⋊Dic₁₃	C₂³	1	4	yes	—
121	C₂²⋊Dic₁₃	C₂³	1	4	yes	—
122	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
123	#6103	C₂³	1	4	yes	—
124	#6103	C₂³	1	4	yes	—
125	#6103	C₂³	1	2	yes	—
126	#6103	C₂³	1	4	yes	—
127	#6103	C₂³	1	2	yes	—
128	#6103	C₂³	1	4	yes	—
129	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
130	C₄⋊Dic₁₃	C₂³	1	4	yes	—
131	C₄⋊Dic₁₃	C₂³	1	2	yes	—
132	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
133	C₄⋊Dic₁₃	C₂³	1	2	yes	—
134	C₄⋊Dic₁₃	C₂³	1	2	yes	—
135	#6101	C₂³	1	2	yes	—
136	#6101	C₂³	1	2	yes	—
137	#6101	C₂³	1	2	yes	—
138	#6101	C₂³	1	4	yes	—
139	#6101	C₂³	1	4	yes	—
140	#6101	C₂³	1	2	yes	—
141	#6101	C₂³	1	4	yes	—
142	#6101	C₂³	1	4	yes	—
143	C₄×Dic₁₃	C₂³	1	4	yes	—
144	C₄×Dic₁₃	C₂³	1	2	yes	—
145	C₄×Dic₁₃	C₂³	1	2	yes	—
146	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
147	C₄×Dic₁₃	C₂³	1	4	yes	—
148	C₄×Dic₁₃	C₂³	1	4	yes	—
149	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
150	C₄×Dic₁₃	C₂³	1	2	yes	—
151	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
152	C₂×#556	—	13	1	no	maximal, Sylow
153	C₂³×C₁₃	C₂⁴	1	2	yes	—
154	C₂²×D₁₃	—	2	4	no	—
155	C₂²×D₁₃	—	2	4	no	—
156	C₂²×D₁₃	—	2	4	no	—
157	C₂²×D₁₃	C₂⁴	1	2	yes	—
158	C₂²×D₁₃	C₂⁴	1	1	yes	characteristic
159	Q₈×C₁₃	—	2	4	no	—
160	Q₈×C₁₃	—	2	2	no	—
161	D₄×C₁₃	—	2	2	no	—
162	C₂×C₄×C₁₃	—	2	4	no	—
163	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
164	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
165	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
166	C₂×C₄×C₁₃	C₂⁴	1	4	yes	—
167	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
168	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
169	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
170	C₂²⋊D₁₃	—	2	4	no	—
171	C₂×Dic₁₃	—	2	4	no	—
172	C₂×Dic₁₃	C₂⁴	1	2	yes	—
173	C₂×Dic₁₃	C₂⁴	1	2	yes	—
174	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
175	C₂×Dic₁₃	C₂⁴	1	4	yes	—
176	C₂×Dic₁₃	C₂⁴	1	2	yes	—
177	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
178	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
179	D₅₂	—	2	2	no	—
180	C₄×D₁₃	—	2	4	no	—
181	C₄×D₁₃	—	2	4	no	—
182	C₄×D₁₃	—	2	8	no	—
183	C₄×D₁₃	—	2	4	no	—
184	C₄×D₁₃	—	2	2	no	—
185	C₄×D₁₃	—	2	4	no	—
186	C₄×D₁₃	—	2	4	no	—
187	C₄×D₁₃	#41	1	4	yes	—
188	C₄×D₁₃	#41	1	4	yes	—
189	Dic₂₆	—	2	4	no	—
190	Dic₂₆	—	2	2	no	—
191	Dic₂₆	—	2	8	no	—
192	Dic₂₆	—	2	4	no	—
193	#556	—	13	1	no	—
194	#556	—	13	4	no	—
195	#556	—	13	2	no	—
196	#556	—	13	2	no	—
197	#556	—	13	2	no	—
198	#556	—	13	1	no	—
199	#556	—	13	1	no	—
200	#556	—	13	2	no	—
201	#556	D₁₃	1	1	yes	characteristic, direct product factor
202	C₂×C₄⋊Q₈	—	13	1	no	—
203	C₂×#126	—	13	4	no	—
204	C₂×#124	—	13	2	no	—
205	C₂×C₂²⋊Q₈	—	13	2	no	—
206	C₂×C₄×Q₈	—	13	2	no	—
207	C₂×C₄×Q₈	—	13	1	no	—
208	C₂×C₄×D₄	—	13	1	no	—
209	C₂×#117	—	13	2	no	—
210	C₂²×C₁₃	—	2	2	no	—
211	C₂²×C₁₃	—	2	2	no	—
212	C₂²×C₁₃	—	2	2	no	—
213	C₂²×C₁₃	C₂⁵	1	1	yes	characteristic
214	C₂×D₁₃	—	2	2	no	—
215	C₂×D₁₃	—	2	2	no	—
216	C₂×D₁₃	—	2	2	no	—
217	C₂×D₁₃	—	4	8	no	—
218	C₂×D₁₃	C₂×#41	1	2	yes	—
219	C₂×D₁₃	C₂×#41	1	2	yes	—
220	C₂×D₁₃	2₋¹⁺⁴	1	2	yes	—
221	C₄×C₁₃	—	2	4	no	—
222	C₄×C₁₃	—	2	2	no	—
223	C₄×C₁₃	—	2	2	no	—
224	C₄×C₁₃	—	2	2	no	—
225	C₄×C₁₃	—	2	1	no	—
226	C₄×C₁₃	C₂×#41	1	2	yes	—
227	C₄×C₁₃	C₂×#41	1	2	yes	—
228	Dic₁₃	—	2	4	no	—
229	Dic₁₃	—	2	2	no	—
230	Dic₁₃	—	2	2	no	—
231	Dic₁₃	—	2	2	no	—
232	Dic₁₃	—	2	1	no	—
233	Dic₁₃	C₂×#41	1	2	yes	—
234	Dic₁₃	C₂×#41	1	2	yes	—
235	C₂²×Q₈	—	13	1	no	—
236	C₂²×Q₈	—	13	2	no	—
237	C₂²×D₄	—	13	1	no	—
238	C₂³×C₄	—	13	2	no	—
239	C₄⋊Q₈	—	13	2	no	—
240	C₄⋊Q₈	—	13	2	no	—
241	C₄⋊Q₈	—	13	2	no	—
242	C₄⋊Q₈	—	13	1	no	—
243	C₄⋊Q₈	C₂×D₁₃	1	1	yes	characteristic, complemented
244	#126	—	13	4	no	—
245	#126	—	13	4	no	—
246	#126	—	13	4	no	—
247	#126	—	13	4	no	—
248	#126	—	13	4	no	—
249	#126	—	13	4	no	—
250	#126	—	13	4	no	—
251	#126	C₂×D₁₃	1	4	yes	complemented
252	#124	—	13	2	no	—
253	#124	—	13	2	no	—
254	#124	—	13	4	no	—
255	#124	—	13	4	no	—
256	#124	—	13	2	no	—
257	#124	C₂×D₁₃	1	2	yes	—
258	C₂²⋊Q₈	—	13	2	no	—
259	C₂²⋊Q₈	—	13	2	no	—
260	C₂²⋊Q₈	—	13	4	no	—
261	C₂²⋊Q₈	—	13	2	no	—
262	C₂²⋊Q₈	—	13	4	no	—
263	C₂²⋊Q₈	C₂×D₁₃	1	2	yes	complemented
264	C₄×Q₈	—	13	2	no	—
265	C₄×Q₈	—	13	1	no	—
266	C₄×Q₈	—	13	4	no	—
267	C₄×Q₈	—	13	2	no	—
268	C₄×Q₈	—	13	2	no	—
269	C₄×Q₈	—	13	1	no	—
270	C₄×Q₈	—	13	2	no	—
271	C₄×Q₈	—	13	4	no	—
272	C₄×Q₈	—	13	2	no	—
273	C₄×Q₈	—	13	1	no	—
274	C₄×Q₈	C₂×D₁₃	1	2	yes	complemented
275	C₄×Q₈	C₂×D₁₃	1	1	yes	characteristic, complemented
276	C₄×D₄	—	13	1	no	—
277	C₄×D₄	—	13	2	no	—
278	C₄×D₄	—	13	1	no	—
279	C₄×D₄	—	13	2	no	—
280	C₄×D₄	—	13	1	no	—
281	C₄×D₄	C₂×D₁₃	1	1	yes	characteristic
282	#117	—	13	2	no	—
283	#117	—	13	2	no	—
284	#117	—	13	2	no	—
285	#117	—	13	4	no	—
286	#117	—	13	4	no	—
287	#117	C₂×D₁₃	1	2	yes	complemented
288	C₂×C₄⋊C₄	—	13	1	no	—
289	C₂×C₄⋊C₄	—	13	2	no	—
290	C₂×C₄⋊C₄	—	13	1	no	—
291	C₂×C₄⋊C₄	—	13	4	no	—
292	C₂×C₄⋊C₄	—	13	2	no	—
293	C₂×C₄⋊C₄	—	13	2	no	—
294	C₂×C₂²⋊C₄	—	13	4	no	—
295	C₂×C₂²⋊C₄	—	13	2	no	—
296	C₂×C₂²⋊C₄	—	13	4	no	—
297	C₂×C₄²	—	13	4	no	—
298	C₂×C₄²	—	13	1	no	—
299	C₂×C₄²	—	13	2	no	—
300	C₂×C₁₃	—	4	2	no	—
301	C₂×C₁₃	C₂²×#41	1	1	yes	characteristic
302	C₂×C₁₃	C₂²×#41	1	1	yes	characteristic
303	C₂×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
304	D₁₃	—	4	2	no	—
305	D₁₃	#556	1	4	yes	direct product factor
306	C₂⁴	—	13	2	no	—
307	C₂×Q₈	—	13	2	no	—
308	C₂×Q₈	—	13	1	no	—
309	C₂×Q₈	—	13	4	no	—
310	C₂×Q₈	—	13	2	no	—
311	C₂×Q₈	—	26	4	no	—
312	C₂×Q₈	—	26	8	no	—
313	C₂×Q₈	C₂²×D₁₃	1	1	yes	characteristic
314	C₂×Q₈	C₂²×D₁₃	1	2	yes	—
315	C₂×D₄	—	13	2	no	—
316	C₂×D₄	—	13	1	no	—
317	C₂×D₄	—	26	4	no	—
318	C₂×D₄	C₂²×D₁₃	1	1	yes	characteristic
319	C₂²×C₄	—	13	1	no	—
320	C₂²×C₄	—	13	1	no	—
321	C₂²×C₄	—	13	2	no	—
322	C₂²×C₄	—	13	2	no	—
323	C₂²×C₄	—	13	2	no	—
324	C₂²×C₄	—	13	1	no	—
325	C₂²×C₄	—	13	4	no	—
326	C₂²×C₄	—	13	2	no	—
327	C₂²×C₄	—	13	2	no	—
328	C₂²×C₄	—	13	2	no	—
329	C₂²×C₄	—	26	8	no	—
330	C₂²×C₄	C₂²×D₁₃	1	2	yes	—
331	C₄⋊C₄	—	13	2	no	—
332	C₄⋊C₄	—	13	1	no	—
333	C₄⋊C₄	—	13	4	no	—
334	C₄⋊C₄	—	13	2	no	—
335	C₄⋊C₄	—	13	2	no	—
336	C₄⋊C₄	—	13	1	no	—
337	C₄⋊C₄	—	13	4	no	—
338	C₄⋊C₄	—	13	4	no	—
339	C₄⋊C₄	—	13	4	no	—
340	C₄⋊C₄	—	13	2	no	—
341	C₄⋊C₄	—	13	2	no	—
342	C₄⋊C₄	—	13	2	no	—
343	C₄⋊C₄	—	13	4	no	—
344	C₄⋊C₄	—	13	2	no	—
345	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
346	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
347	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
348	C₄⋊C₄	C₂²×D₁₃	1	4	yes	—
349	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
350	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
351	C₂²⋊C₄	—	13	4	no	—
352	C₂²⋊C₄	—	13	2	no	—
353	C₂²⋊C₄	—	13	4	no	—
354	C₂²⋊C₄	—	13	4	no	—
355	C₂²⋊C₄	—	13	4	no	—
356	C₂²⋊C₄	—	13	2	no	—
357	C₂²⋊C₄	—	13	2	no	—
358	C₂²⋊C₄	—	13	4	no	—
359	C₂²⋊C₄	—	13	4	no	—
360	C₂²⋊C₄	C₂²×D₁₃	1	4	yes	—
361	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
362	C₂²⋊C₄	C₂²×D₁₃	1	4	yes	—
363	C₄²	—	13	4	no	—
364	C₄²	—	13	4	no	—
365	C₄²	—	13	4	no	—
366	C₄²	—	13	1	no	—
367	C₄²	—	13	1	no	—
368	C₄²	—	13	1	no	—
369	C₄²	—	13	2	no	—
370	C₄²	—	13	2	no	—
371	C₄²	—	13	2	no	—
372	C₄²	C₂²×D₁₃	1	4	yes	—
373	C₄²	C₂²×D₁₃	1	1	yes	characteristic
374	C₄²	C₂²×D₁₃	1	2	yes	—
375	C₁₃	C₂×#556	1	1	yes	characteristic, complemented, Sylow
376	C₂³	—	13	1	no	—
377	C₂³	—	13	2	no	—
378	C₂³	—	26	4	no	—
379	C₂³	—	26	4	no	—
380	C₂³	—	26	4	no	—
381	C₂³	C₂³×D₁₃	1	2	yes	—
382	Q₈	—	2	2	no	—
383	Q₈	—	2	4	no	—
384	Q₈	—	26	4	no	—
385	Q₈	—	26	8	no	—
386	Q₈	—	26	2	no	—
387	Q₈	—	26	4	no	—
388	D₄	—	2	2	no	—
389	D₄	—	26	4	no	—
390	D₄	—	26	2	no	—
391	C₂×C₄	—	2	4	no	—
392	C₂×C₄	—	13	1	no	—
393	C₂×C₄	—	13	1	no	—
394	C₂×C₄	—	13	4	no	—
395	C₂×C₄	—	13	4	no	—
396	C₂×C₄	—	13	2	no	—
397	C₂×C₄	—	13	2	no	—
398	C₂×C₄	—	13	1	no	—
399	C₂×C₄	—	13	4	no	—
400	C₂×C₄	—	13	2	no	—
401	C₂×C₄	—	26	4	no	—
402	C₂×C₄	—	26	4	no	—
403	C₂×C₄	—	26	2	no	—
404	C₂×C₄	—	26	4	no	—
405	C₂×C₄	—	26	4	no	—
406	C₂×C₄	—	26	8	no	—
407	C₂×C₄	—	26	4	no	—
408	C₂×C₄	—	26	4	no	—
409	C₂×C₄	C₂³×D₁₃	1	2	yes	—
410	C₂×C₄	C₂³×D₁₃	1	2	yes	—
411	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
412	C₂×C₄	C₂³×D₁₃	1	4	yes	—
413	C₂×C₄	C₂³×D₁₃	1	2	yes	—
414	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
415	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
416	C₂²	—	2	2	no	—
417	C₂²	—	2	2	no	—
418	C₂²	—	2	2	no	—
419	C₂²	—	13	2	no	—
420	C₂²	—	13	2	no	—
421	C₂²	—	13	2	no	—
422	C₂²	—	26	2	no	—
423	C₂²	—	26	2	no	—
424	C₂²	—	26	2	no	—
425	C₂²	—	52	8	no	—
426	C₂²	C₂⁴×D₁₃	1	1	yes	characteristic
427	C₄	—	2	2	no	—
428	C₄	—	2	2	no	—
429	C₄	—	2	4	no	—
430	C₄	—	2	2	no	—
431	C₄	—	2	1	no	—
432	C₄	—	13	2	no	—
433	C₄	—	13	2	no	—
434	C₄	—	26	2	no	—
435	C₄	—	26	2	no	—
436	C₄	—	26	4	no	—
437	C₄	—	26	2	no	—
438	C₄	—	26	1	no	—
439	C₄	#41×D₁₃	1	2	yes	—
440	C₄	#41×D₁₃	1	2	yes	—
441	C₂	—	4	2	no	—
442	C₂	—	13	4	no	—
443	C₂	—	52	2	no	—
444	C₂	C₂×#41×D₁₃	1	1	yes	characteristic
445	C₂	C₂×#41×D₁₃	1	1	yes	characteristic
446	C₂	D₁₃×2₋¹⁺⁴	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₃
commutator, socle, cosocle	C₂²×C₁₃	C₂⁵
Fitting	C₁₃×#556	C₂
prime radical	C₂×D₄×D₁₃	C₂²
hypercenter	#556	D₁₃
hypocenter	C₁₃	C₂×#556
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ #556

Complements

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

N	H ≅ G/N	type
1. C₁₃×#556	C₂	semidirect
2. #11719437	C₂	semidirect
3. D₁₃×C₄⋊Q₈	C₂	semidirect
4. D₁₃×#126	C₂	semidirect
5. #11719407	C₂	semidirect
7. #11719376	C₂	semidirect
8. #11719346	C₂	semidirect
9. D₁₃×C₂²⋊Q₈	C₂	semidirect
10. #11719289	C₂	semidirect
11. C₄×Q₈×D₁₃	C₂	semidirect
12. C₄×Q₈×D₁₃	C₂	semidirect
13. #11719273	C₂	semidirect
15. #11719247	C₂	semidirect
16. #11719238	C₂	semidirect
17. D₁₃×#117	C₂	semidirect
22. C₁₃×C₄⋊Q₈	C₂²	semidirect
23. C₁₃×#126	C₂²	semidirect
25. C₁₃×C₂²⋊Q₈	C₂²	semidirect
26. C₄×Q₈×C₁₃	C₂²	semidirect
27. C₄×Q₈×C₁₃	C₂²	semidirect
29. C₁₃×#117	C₂²	semidirect
31. #88200	C₂²	semidirect
32. Q₈×Dic₁₃	C₂²	semidirect
33. Q₈×Dic₁₃	C₂²	semidirect
34. #88198	C₂²	semidirect
38. #88180	C₂²	semidirect
39. #88178	C₂²	semidirect
40. #88152	C₂²	semidirect
41. #88152	C₂²	semidirect
42. #88152	C₂²	semidirect
43. #88151	C₂²	semidirect
44. #88150	C₂²	semidirect
46. #88146	C₂²	semidirect
47. #88146	C₂²	semidirect
54. #88142	C₂²	semidirect
55. #88142	C₂²	semidirect
56. #88141	C₂²	semidirect
57. #88141	C₂²	semidirect
58. #88141	C₂²	semidirect
59. #88141	C₂²	semidirect
66. #88133	C₂²	semidirect
67. #88133	C₂²	semidirect
68. #88133	C₂²	semidirect
69. #88132	C₂²	semidirect
70. #88131	C₂²	semidirect
71. #88130	C₂²	semidirect
74. #88126	C₂²	semidirect
78. #88123	C₂²	semidirect
79. C₄×Dic₂₆	C₂²	semidirect
80. C₄×Dic₂₆	C₂²	semidirect
81. C₄×Dic₂₆	C₂²	semidirect
82. C₄×Dic₂₆	C₂²	semidirect
201. #556	D₁₃	direct (N × H)
243. C₄⋊Q₈	C₂×D₁₃	semidirect
251. #126	C₂×D₁₃	semidirect
263. C₂²⋊Q₈	C₂×D₁₃	semidirect
274. C₄×Q₈	C₂×D₁₃	semidirect
275. C₄×Q₈	C₂×D₁₃	semidirect
287. #117	C₂×D₁₃	semidirect
305. D₁₃	#556	direct (N × H)
375. C₁₃	C₂×#556	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₁₃×#556	2
#11719437	2
D₁₃×C₄⋊Q₈	2
D₁₃×#126	2
#11719407	2
D₁₃×#124	2
#11719376	2
#11719346	2
D₁₃×C₂²⋊Q₈	2
#11719289	2
C₄×Q₈×D₁₃	2
#11719273	2
C₄×D₄×D₁₃	2
#11719247	2
#11719238	2
D₁₃×#117	2
C₂×#556	13

Subgroups — D13×#556 #13128378

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₁₃×#556 #13128378