Subgroups — D₁₃×#1773 #15860929

Order 3328.

1062 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₁₃×#108	C₂	1	1	yes	maximal, characteristic
2	D₁₃×#427	C₂	1	1	yes	maximal, characteristic
3	D₁₃×#405	C₂	1	2	yes	maximal
4	C₂×D₁₃×#97	C₂	1	1	yes	maximal, characteristic
5	#13114723	C₂	1	1	yes	maximal, characteristic, complemented
6	#13114722	C₂	1	1	yes	maximal, characteristic, complemented
7	#13114721	C₂	1	2	yes	maximal, complemented
8	#13114720	C₂	1	1	yes	maximal, characteristic, complemented
9	#13114719	C₂	1	2	yes	maximal, complemented
10	D₁₃×#339	C₂	1	2	yes	maximal
11	C₁₃×#1773	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×M₁₆×D₁₃	C₂²	1	2	yes	—
13	C₂²×C₈×D₁₃	C₂²	1	1	yes	characteristic
14	C₂²×C₈×D₁₃	C₂²	1	1	yes	characteristic
15	D₁₃×#117	C₂²	1	2	yes	—
16	C₂×C₄²×D₁₃	C₂²	1	1	yes	characteristic
17	C₂×C₁₃×#108	C₂²	1	1	yes	characteristic
18	C₁₃×#427	C₂²	1	1	yes	characteristic
19	C₁₃×#405	C₂²	1	2	yes	—
20	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
21	C₂×#88062	C₂²	1	2	yes	—
22	#11718783	C₂²	1	2	yes	—
23	C₂×#88059	C₂²	1	1	yes	characteristic
24	#11718767	C₂²	1	1	yes	characteristic
25	#11718762	C₂²	1	2	yes	—
26	C₂×#88055	C₂²	1	1	yes	characteristic
27	C₂×#88055	C₂²	1	1	yes	characteristic
28	#11718659	C₂²	1	2	yes	—
29	#11718658	C₂²	1	2	yes	—
30	C₂×#88043	C₂²	1	1	yes	characteristic
31	D₁₃×#108	C₄	1	8	yes	complemented
32	#11718541	C₄	1	2	yes	complemented
33	D₁₃×#107	C₄	1	2	yes	complemented
34	#11718521	C₄	1	2	yes	complemented
35	D₁₃×#106	C₄	1	2	yes	complemented
36	#11718369	—	2	2	no	—
37	D₁₃×#97	—	2	2	no	—
38	D₁₃×#97	C₄	1	8	yes	complemented
39	#11718350	—	2	2	no	—
40	C₄×C₈×D₁₃	—	2	2	no	—
41	C₁₃×#339	C₂²	1	2	yes	—
42	#11718147	C₂²	1	2	yes	—
43	#11718124	C₂²	1	2	yes	—
44	#11718115	C₂²	1	2	yes	—
45	C₂²×C₄×D₁₃	—	2	1	no	—
46	C₂²×C₄×D₁₃	C₂³	1	1	yes	characteristic
47	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
48	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
49	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
50	C₁₃×#117	C₂³	1	2	yes	—
51	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
52	#88180	C₂³	1	2	yes	—
53	C₂×C₄×Dic₁₃	—	2	1	no	—
54	C₂×C₄×Dic₁₃	C₂³	1	1	yes	characteristic
55	C₂×#6099	C₂³	1	2	yes	—
56	C₂²×#1055	C₂³	1	1	yes	characteristic
57	C₂²×#1055	C₂³	1	1	yes	characteristic
58	M₁₆×D₁₃	—	2	4	no	—
59	M₁₆×D₁₃	C₂×C₄	1	8	yes	—
60	C₂×#6094	—	2	2	no	—
61	C₂×C₈×D₁₃	—	2	2	no	—
62	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
63	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
64	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
65	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
66	C₂×C₈×D₁₃	C₂×C₄	1	4	yes	—
67	C₂×C₈×D₁₃	C₂×C₄	1	4	yes	—
68	C₂×C₈×D₁₃	C₂×C₄	1	4	yes	—
69	C₂×C₈×D₁₃	D₄	1	2	yes	—
70	C₂×C₈×D₁₃	D₄	1	2	yes	—
71	C₂×C₈×D₁₃	Q₈	1	4	yes	—
72	#88146	C₂×C₄	1	4	yes	—
73	C₄⋊C₄×D₁₃	C₂×C₄	1	4	yes	—
74	C₂²⋊C₄×D₁₃	—	2	2	no	—
75	#88131	—	2	2	no	—
76	#88126	—	2	2	no	—
77	C₄²×D₁₃	—	2	2	no	—
78	C₄²×D₁₃	—	2	2	no	—
79	C₄²×D₁₃	C₂×C₄	1	4	yes	—
80	C₁₃×#108	C₂×C₄	1	4	yes	complemented
81	C₁₃×#107	C₂×C₄	1	2	yes	complemented
82	C₁₃×#106	C₂×C₄	1	2	yes	complemented
83	C₁₃×#97	—	2	2	no	—
84	C₁₃×#97	C₂×C₄	1	4	yes	complemented
85	C₄×C₈×C₁₃	—	2	2	no	—
86	#88062	C₂×C₄	1	8	yes	complemented
87	#88059	C₂×C₄	1	4	yes	complemented
88	#88058	C₂×C₄	1	2	yes	complemented
89	#88057	C₂×C₄	1	2	yes	complemented
90	#88055	—	2	2	no	—
91	#88055	—	2	2	no	—
92	#88055	C₂×C₄	1	4	yes	complemented
93	#88055	C₂×C₄	1	4	yes	complemented
94	C₈×Dic₁₃	—	2	2	no	—
95	C₈×Dic₁₃	—	2	2	no	—
96	#88048	C₂×C₄	1	4	yes	complemented
97	#88047	C₂×C₄	1	4	yes	complemented
98	#88043	—	2	2	no	—
99	#88043	C₂×C₄	1	4	yes	complemented
100	C₄×#1055	—	2	2	no	—
101	C₂×#1773	—	13	1	no	maximal, Sylow
102	C₂³×D₁₃	#41	1	1	yes	characteristic
103	C₂²×C₄×C₁₃	—	2	1	no	—
104	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
105	C₂²×Dic₁₃	—	2	1	no	—
106	C₂²×Dic₁₃	#41	1	1	yes	characteristic
107	C₂×C₄×D₁₃	—	2	4	no	—
108	C₂×C₄×D₁₃	—	2	4	no	—
109	C₂×C₄×D₁₃	—	4	4	no	—
110	C₂×C₄×D₁₃	C₂²×C₄	1	2	yes	—
111	C₂×C₄×D₁₃	C₂²×C₄	1	2	yes	—
112	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
113	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
114	C₂×C₄×D₁₃	C₂×D₄	1	1	yes	characteristic
115	C₂×C₄×D₁₃	C₂×D₄	1	1	yes	characteristic
116	C₂×C₄×D₁₃	C₂×Q₈	1	2	yes	—
117	C₂×C₄×D₁₃	#41	1	2	yes	—
118	C₁₃×M₁₆	—	2	2	no	—
119	C₁₃×M₁₆	C₂²×C₄	1	4	yes	—
120	C₂×C₈×C₁₃	—	2	2	no	—
121	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
122	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
123	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
124	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
125	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
126	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
127	C₂×C₈×C₁₃	C₂×Q₈	1	2	yes	—
128	C₁₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
129	C₁₃×C₂²⋊C₄	—	2	2	no	—
130	C₄²×C₁₃	—	2	2	no	—
131	C₄²×C₁₃	—	2	1	no	—
132	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
133	C₂²⋊Dic₁₃	—	2	2	no	—
134	#6103	—	2	4	no	—
135	C₄⋊Dic₁₃	C₂²×C₄	1	4	yes	—
136	#6101	—	2	4	no	—
137	C₄×Dic₁₃	—	2	2	no	—
138	C₄×Dic₁₃	—	2	1	no	—
139	C₄×Dic₁₃	—	2	4	no	—
140	C₄×Dic₁₃	—	2	4	no	—
141	C₄×Dic₁₃	C₂²×C₄	1	2	yes	—
142	#6099	—	2	2	no	—
143	#6099	C₂²×C₄	1	4	yes	—
144	C₂×#1055	—	2	2	no	—
145	C₂×#1055	C₂²×C₄	1	2	yes	—
146	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
147	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
148	C₂×#1055	C₂²×C₄	1	2	yes	—
149	C₂×#1055	C₂²×C₄	1	2	yes	—
150	C₂×#1055	C₂×D₄	1	2	yes	—
151	C₂×#1055	C₂×Q₈	1	2	yes	—
152	#6094	—	2	8	no	—
153	C₈×D₁₃	—	2	8	no	—
154	C₈×D₁₃	C₄²	1	4	yes	—
155	C₈×D₁₃	C₄²	1	4	yes	—
156	C₈×D₁₃	C₄²	1	4	yes	—
157	C₈×D₁₃	C₄²	1	4	yes	—
158	C₈×D₁₃	C₄⋊C₄	1	8	yes	—
159	C₈×D₁₃	C₄⋊C₄	1	8	yes	—
160	C₂²×#108	—	13	1	no	—
161	C₂×#427	—	13	1	no	—
162	C₂×#405	—	13	2	no	—
163	C₂²×#97	—	13	1	no	—
164	#1773	—	13	1	no	—
165	#1773	—	13	1	no	—
166	#1773	—	13	2	no	—
167	#1773	—	13	1	no	—
168	#1773	—	13	2	no	—
169	#1773	D₁₃	1	1	yes	characteristic, direct product factor
170	C₂×#339	—	13	2	no	—
171	C₂³×C₁₃	C₂×#41	1	1	yes	characteristic
172	C₂²×D₁₃	—	2	4	no	—
173	C₂²×D₁₃	#117	1	2	yes	—
174	C₂²×D₁₃	C₄×D₄	1	1	yes	characteristic
175	C₂²×D₁₃	C₄×D₄	1	1	yes	characteristic
176	C₂²×D₁₃	C₄×Q₈	1	2	yes	—
177	C₂×C₄×C₁₃	—	2	2	no	—
178	C₂×C₄×C₁₃	—	2	4	no	—
179	C₂×C₄×C₁₃	—	4	2	no	—
180	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
181	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
182	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
183	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
184	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
185	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
186	C₂×Dic₁₃	—	2	2	no	—
187	C₂×Dic₁₃	—	2	4	no	—
188	C₂×Dic₁₃	—	4	2	no	—
189	C₂×Dic₁₃	#117	1	2	yes	—
190	C₂×Dic₁₃	C₄×D₄	1	1	yes	characteristic
191	C₂×Dic₁₃	C₄×D₄	1	1	yes	characteristic
192	C₂×Dic₁₃	C₄×Q₈	1	2	yes	—
193	C₄×D₁₃	—	4	8	no	—
194	C₄×D₁₃	—	4	8	no	—
195	C₄×D₁₃	C₂×C₄²	1	2	yes	—
196	C₄×D₁₃	C₂×C₄²	1	2	yes	—
197	C₄×D₁₃	C₂×C₄⋊C₄	1	2	yes	—
198	C₄×D₁₃	C₂×C₄⋊C₄	1	2	yes	—
199	C₄×D₁₃	C₄×D₄	1	2	yes	—
200	C₄×D₁₃	C₄×D₄	1	2	yes	—
201	C₄×D₁₃	C₄×Q₈	1	2	yes	—
202	C₄×D₁₃	C₄×Q₈	1	2	yes	—
203	C₈×C₁₃	—	2	4	no	—
204	C₈×C₁₃	C₂×C₄²	1	2	yes	—
205	C₈×C₁₃	C₂×C₄²	1	2	yes	—
206	C₈×C₁₃	C₂×C₄⋊C₄	1	4	yes	—
207	#1055	—	2	4	no	—
208	#1055	C₂×C₄²	1	2	yes	—
209	#1055	C₂×C₄²	1	2	yes	—
210	#1055	C₂×C₄⋊C₄	1	4	yes	—
211	C₂²×M₁₆	—	13	2	no	—
212	C₂³×C₈	—	13	1	no	—
213	C₂³×C₈	—	13	1	no	—
214	C₂×#117	—	13	2	no	—
215	C₂²×C₄²	—	13	1	no	—
216	C₂×#108	—	13	2	no	—
217	C₂×#108	—	13	1	no	—
218	C₂×#108	—	13	8	no	—
219	C₂×#108	C₂×D₁₃	1	1	yes	characteristic
220	#427	—	13	1	no	—
221	#427	—	13	2	no	—
222	#427	—	13	2	no	—
223	#427	—	13	2	no	—
224	#427	C₂×D₁₃	1	1	yes	characteristic
225	C₂×#107	—	13	2	no	—
226	C₂×#106	—	13	2	no	—
227	#405	—	13	2	no	—
228	#405	—	13	2	no	—
229	#405	—	13	2	no	—
230	#405	—	26	2	no	—
231	#405	—	26	2	no	—
232	#405	C₂×D₁₃	1	2	yes	—
233	C₂×#97	—	13	1	no	—
234	C₂×#97	—	13	1	no	—
235	C₂×#97	—	13	1	no	—
236	C₂×#97	—	13	8	no	—
237	C₂×#97	—	26	2	no	—
238	C₂×#97	C₂×D₁₃	1	1	yes	characteristic
239	C₂×C₄×C₈	—	26	2	no	—
240	#339	—	13	2	no	—
241	#339	—	13	2	no	—
242	#339	—	13	2	no	—
243	#339	C₂×D₁₃	1	2	yes	—
244	C₂²×C₁₃	—	2	2	no	—
245	C₂²×C₁₃	C₂×#117	1	1	yes	characteristic
246	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
247	C₂²×C₁₃	C₂×C₄×Q₈	1	1	yes	characteristic
248	C₂×D₁₃	—	2	2	no	—
249	C₂×D₁₃	—	2	4	no	—
250	C₂×D₁₃	—	2	4	no	—
251	C₂×D₁₃	C₄×C₄⋊C₄	1	2	yes	—
252	C₂×D₁₃	C₄×C₄⋊C₄	1	2	yes	—
253	C₂×D₁₃	#444	1	4	yes	—
254	C₄×C₁₃	—	4	2	no	—
255	C₄×C₁₃	—	4	4	no	—
256	C₄×C₁₃	C₂²×C₄²	1	1	yes	characteristic
257	C₄×C₁₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
258	C₄×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
259	C₄×C₁₃	C₂×C₄×Q₈	1	1	yes	characteristic
260	Dic₁₃	—	4	2	no	—
261	Dic₁₃	—	4	4	no	—
262	Dic₁₃	C₄×C₄⋊C₄	1	2	yes	—
263	Dic₁₃	C₄×C₄⋊C₄	1	2	yes	—
264	C₂³×C₄	—	13	1	no	—
265	C₂³×C₄	—	26	1	no	—
266	C₂×M₁₆	—	13	2	no	—
267	C₂×M₁₆	—	13	8	no	—
268	C₂×M₁₆	—	26	2	no	—
269	C₂×M₁₆	—	26	4	no	—
270	C₂×M₁₆	C₂²×D₁₃	1	2	yes	—
271	C₂²×C₈	—	13	1	no	—
272	C₂²×C₈	—	13	1	no	—
273	C₂²×C₈	—	13	4	no	—
274	C₂²×C₈	—	13	4	no	—
275	C₂²×C₈	—	13	1	no	—
276	C₂²×C₈	—	13	1	no	—
277	C₂²×C₈	—	13	1	no	—
278	C₂²×C₈	—	13	1	no	—
279	C₂²×C₈	—	13	4	no	—
280	C₂²×C₈	—	13	2	no	—
281	C₂²×C₈	—	13	2	no	—
282	C₂²×C₈	—	13	4	no	—
283	C₂²×C₈	—	26	2	no	—
284	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
285	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
286	#117	—	13	2	no	—
287	#117	—	13	4	no	—
288	#117	—	26	2	no	—
289	#117	—	26	2	no	—
290	#117	C₂²×D₁₃	1	2	yes	—
291	C₂×C₄⋊C₄	—	13	4	no	—
292	C₂×C₂²⋊C₄	—	26	2	no	—
293	C₂×C₄²	—	13	1	no	—
294	C₂×C₄²	—	13	4	no	—
295	C₂×C₄²	—	26	2	no	—
296	C₂×C₄²	—	26	2	no	—
297	C₂×C₄²	—	26	1	no	—
298	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
299	#108	—	13	8	no	—
300	#108	—	13	4	no	—
301	#108	C₄×D₁₃	1	4	yes	complemented
302	#107	—	13	2	no	—
303	#107	—	13	4	no	—
304	#107	C₄×D₁₃	1	2	yes	complemented
305	#106	—	13	2	no	—
306	#106	—	13	4	no	—
307	#106	C₄×D₁₃	1	2	yes	complemented
308	#97	—	2	2	no	—
309	#97	—	13	4	no	—
310	#97	—	13	4	no	—
311	#97	—	13	4	no	—
312	#97	—	26	2	no	—
313	#97	—	26	2	no	—
314	#97	—	26	2	no	—
315	#97	C₄×D₁₃	1	4	yes	complemented
316	C₄×C₈	—	2	2	no	—
317	C₄×C₈	—	26	2	no	—
318	C₄×C₈	—	26	2	no	—
319	C₄×C₈	—	26	2	no	—
320	C₂×C₁₃	—	2	1	no	—
321	C₂×C₁₃	—	2	1	no	—
322	C₂×C₁₃	C₂×C₄×C₄⋊C₄	1	1	yes	characteristic
323	C₂×C₁₃	C₂×#444	1	2	yes	—
324	D₁₃	—	2	2	no	—
325	D₁₃	#1773	1	4	yes	direct product factor
326	C₂⁴	—	13	1	no	—
327	C₂²×C₄	—	2	1	no	—
328	C₂²×C₄	—	13	1	no	—
329	C₂²×C₄	—	13	2	no	—
330	C₂²×C₄	—	13	1	no	—
331	C₂²×C₄	—	13	1	no	—
332	C₂²×C₄	—	13	2	no	—
333	C₂²×C₄	—	13	1	no	—
334	C₂²×C₄	—	13	1	no	—
335	C₂²×C₄	—	13	2	no	—
336	C₂²×C₄	—	13	2	no	—
337	C₂²×C₄	—	26	4	no	—
338	C₂²×C₄	—	26	4	no	—
339	C₂²×C₄	—	26	1	no	—
340	C₂²×C₄	—	52	4	no	—
341	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
342	M₁₆	—	2	2	no	—
343	M₁₆	—	13	4	no	—
344	M₁₆	—	26	8	no	—
345	M₁₆	—	26	2	no	—
346	M₁₆	C₂×C₄×D₁₃	1	4	yes	—
347	C₂×C₈	—	2	2	no	—
348	C₂×C₈	—	13	2	no	—
349	C₂×C₈	—	13	2	no	—
350	C₂×C₈	—	13	1	no	—
351	C₂×C₈	—	13	1	no	—
352	C₂×C₈	—	13	2	no	—
353	C₂×C₈	—	13	2	no	—
354	C₂×C₈	—	13	2	no	—
355	C₂×C₈	—	13	4	no	—
356	C₂×C₈	—	13	4	no	—
357	C₂×C₈	—	13	4	no	—
358	C₂×C₈	—	13	4	no	—
359	C₂×C₈	—	13	8	no	—
360	C₂×C₈	—	13	8	no	—
361	C₂×C₈	—	26	8	no	—
362	C₂×C₈	—	26	2	no	—
363	C₂×C₈	C₂×C₄×D₁₃	1	2	yes	—
364	C₂×C₈	C₂×C₄×D₁₃	1	1	yes	characteristic
365	C₂×C₈	C₂×C₄×D₁₃	1	1	yes	characteristic
366	C₂×C₈	C₂×C₄×D₁₃	1	2	yes	—
367	C₂×C₈	C₂×C₄×D₁₃	1	2	yes	—
368	C₂×C₈	D₄×D₁₃	1	2	yes	—
369	C₂×C₈	Q₈×D₁₃	1	2	yes	—
370	C₄⋊C₄	—	13	4	no	—
371	C₄⋊C₄	—	26	4	no	—
372	C₄⋊C₄	C₂×C₄×D₁₃	1	4	yes	—
373	C₂²⋊C₄	—	2	2	no	—
374	C₂²⋊C₄	—	26	4	no	—
375	C₂²⋊C₄	—	26	2	no	—
376	C₄²	—	2	2	no	—
377	C₄²	—	2	1	no	—
378	C₄²	—	13	2	no	—
379	C₄²	—	26	4	no	—
380	C₄²	—	26	4	no	—
381	C₄²	—	26	2	no	—
382	C₄²	—	26	1	no	—
383	C₄²	C₂×C₄×D₁₃	1	2	yes	—
384	C₁₃	C₂×#1773	1	1	yes	characteristic, complemented, Sylow
385	C₂³	—	13	1	no	—
386	C₂³	—	13	2	no	—
387	C₂³	—	13	1	no	—
388	C₂³	—	13	2	no	—
389	C₂³	—	26	4	no	—
390	C₂³	#41×D₁₃	1	1	yes	characteristic
391	C₂×C₄	—	2	2	no	—
392	C₂×C₄	—	2	4	no	—
393	C₂×C₄	—	4	2	no	—
394	C₂×C₄	—	13	2	no	—
395	C₂×C₄	—	13	1	no	—
396	C₂×C₄	—	13	1	no	—
397	C₂×C₄	—	13	2	no	—
398	C₂×C₄	—	13	2	no	—
399	C₂×C₄	—	13	2	no	—
400	C₂×C₄	—	13	2	no	—
401	C₂×C₄	—	13	2	no	—
402	C₂×C₄	—	13	2	no	—
403	C₂×C₄	—	13	2	no	—
404	C₂×C₄	—	13	2	no	—
405	C₂×C₄	—	13	2	no	—
406	C₂×C₄	—	26	2	no	—
407	C₂×C₄	—	26	4	no	—
408	C₂×C₄	—	52	8	no	—
409	C₂×C₄	—	52	8	no	—
410	C₂×C₄	—	52	2	no	—
411	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
412	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
413	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
414	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
415	C₂×C₄	C₂×Q₈×D₁₃	1	1	yes	characteristic
416	C₂×C₄	#41×D₁₃	1	1	yes	characteristic
417	C₈	—	2	4	no	—
418	C₈	—	13	2	no	—
419	C₈	—	13	2	no	—
420	C₈	—	13	4	no	—
421	C₈	—	26	4	no	—
422	C₈	C₄²×D₁₃	1	2	yes	—
423	C₈	C₄²×D₁₃	1	2	yes	—
424	C₈	C₄⋊C₄×D₁₃	1	4	yes	—
425	C₂²	—	2	2	no	—
426	C₂²	—	13	4	no	—
427	C₂²	—	13	2	no	—
428	C₂²	—	13	2	no	—
429	C₂²	—	26	4	no	—
430	C₂²	—	26	4	no	—
431	C₂²	—	26	2	no	—
432	C₂²	D₁₃×#117	1	1	yes	characteristic
433	C₂²	C₄×D₄×D₁₃	1	1	yes	characteristic
434	C₂²	C₄×Q₈×D₁₃	1	1	yes	characteristic
435	C₄	—	4	2	no	—
436	C₄	—	4	4	no	—
437	C₄	—	13	2	no	—
438	C₄	—	13	2	no	—
439	C₄	—	52	2	no	—
440	C₄	—	52	4	no	—
441	C₄	C₂×C₄²×D₁₃	1	1	yes	characteristic
442	C₄	C₂×C₄⋊C₄×D₁₃	1	1	yes	characteristic
443	C₄	C₄×D₄×D₁₃	1	1	yes	characteristic
444	C₄	C₄×Q₈×D₁₃	1	1	yes	characteristic
445	C₂	—	2	1	no	—
446	C₂	—	2	1	no	—
447	C₂	—	13	4	no	—
448	C₂	—	26	2	no	—
449	C₂	C₄×C₄⋊C₄×D₁₃	1	1	yes	characteristic
450	C₂	D₁₃×#444	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₁₃
commutator	C₄×C₁₃	C₂²×C₄²
Frattini	C₂²×C₄	C₂³×D₁₃
Fitting	C₁₃×#1773	C₂
socle	C₂²×C₁₃	C₂×C₄×D₄
prime radical	C₂³×D₁₃	#41
cosocle	C₂²×C₄×C₁₃	C₂⁴
hypercenter	#1773	D₁₃
hypocenter	C₁₃	C₂×#1773
LCS	G ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₈ ◁ #1773

Complements

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

N	H ≅ G/N	type
5. #13114723	C₂	semidirect
6. #13114722	C₂	semidirect
7. #13114721	C₂	semidirect
8. #13114720	C₂	semidirect
9. #13114719	C₂	semidirect
11. C₁₃×#1773	C₂	semidirect
31. D₁₃×#108	C₄	semidirect
32. #11718541	C₄	semidirect
33. D₁₃×#107	C₄	semidirect
34. #11718521	C₄	semidirect
35. D₁₃×#106	C₄	semidirect
38. D₁₃×#97	C₄	semidirect
80. C₁₃×#108	C₂×C₄	semidirect
81. C₁₃×#107	C₂×C₄	semidirect
82. C₁₃×#106	C₂×C₄	semidirect
84. C₁₃×#97	C₂×C₄	semidirect
86. #88062	C₂×C₄	semidirect
87. #88059	C₂×C₄	semidirect
88. #88058	C₂×C₄	semidirect
89. #88057	C₂×C₄	semidirect
92. #88055	C₂×C₄	semidirect
93. #88055	C₂×C₄	semidirect
96. #88048	C₂×C₄	semidirect
97. #88047	C₂×C₄	semidirect
99. #88043	C₂×C₄	semidirect
169. #1773	D₁₃	direct (N × H)
301. #108	C₄×D₁₃	semidirect
304. #107	C₄×D₁₃	semidirect
307. #106	C₄×D₁₃	semidirect
315. #97	C₄×D₁₃	semidirect
325. D₁₃	#1773	direct (N × H)
384. C₁₃	C₂×#1773	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₁₃×#108	2
D₁₃×#427	2
D₁₃×#405	2
C₂×D₁₃×#97	2
#13114723	2
#13114722	2
#13114721	2
#13114720	2
#13114719	2
D₁₃×#339	2
C₁₃×#1773	2
C₂×#1773	13

Subgroups — D13×#1773 #15860929

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₁₃×#1773 #15860929