Subgroups — #15860951

Order 3328.

1010 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	C₂×D₁₃×#108	C₂	1	1	yes	maximal, characteristic
2	D₁₃×#427	C₂	1	1	yes	maximal, characteristic
3	#13123252	C₂	1	2	yes	maximal
4	C₂×#11718369	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	#13114720	C₂	1	1	yes	maximal, characteristic, complemented
8	#13114716	C₂	1	2	yes	maximal, complemented
9	#13114714	C₂	1	2	yes	maximal, complemented
10	#13114544	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×#6094	C₂²	1	1	yes	characteristic
14	C₂²×C₈×D₁₃	C₂²	1	1	yes	characteristic
15	D₁₃×#117	C₂²	1	2	yes	—
16	C₂×#88126	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×C₈×Dic₁₃	C₂²	1	1	yes	characteristic
28	#11718659	C₂²	1	2	yes	—
29	#11718658	C₂²	1	2	yes	—
30	C₂×C₄×#1055	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	#11718369	C₄	1	8	yes	complemented
38	#11718368	—	2	2	no	—
39	#11718350	—	2	2	no	—
40	C₄×#6094	—	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	C₂³	1	1	yes	characteristic
46	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
47	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
48	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
49	C₁₃×#117	C₂³	1	2	yes	—
50	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
51	C₂×#6103	—	2	1	no	—
52	#88180	C₂³	1	2	yes	—
53	C₂×#6101	—	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×#6094	C₂×C₄	1	4	yes	—
62	C₂×#6094	D₄	1	2	yes	—
63	C₂×#6094	D₄	1	2	yes	—
64	C₂×#6094	Q₈	1	4	yes	—
65	C₂×C₈×D₁₃	—	2	2	no	—
66	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
67	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
68	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
69	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
70	C₂×C₈×D₁₃	C₂×C₄	1	4	yes	—
71	C₂×C₈×D₁₃	C₂×C₄	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	#88126	—	2	2	no	—
78	#88126	C₂×C₄	1	4	yes	—
79	C₄²×D₁₃	—	2	2	no	—
80	C₁₃×#108	C₂×C₄	1	4	yes	complemented
81	C₁₃×#107	C₂×C₄	1	2	yes	—
82	C₁₃×#106	C₂×C₄	1	2	yes	—
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	—
89	#88057	C₂×C₄	1	2	yes	—
90	#88055	—	2	2	no	—
91	#88055	—	2	2	no	—
92	#88055	C₂×C₄	1	4	yes	complemented
93	C₈×Dic₁₃	—	2	2	no	—
94	C₈×Dic₁₃	—	2	2	no	—
95	C₈×Dic₁₃	C₂×C₄	1	4	yes	complemented
96	#88048	C₂×C₄	1	4	yes	—
97	#88047	C₂×C₄	1	4	yes	—
98	#88043	—	2	2	no	—
99	C₄×#1055	—	2	2	no	—
100	C₄×#1055	C₂×C₄	1	4	yes	complemented
101	#20446	—	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	C₂²×C₄	1	2	yes	—
109	C₂×C₄×D₁₃	C₂²×C₄	1	2	yes	—
110	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
111	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
112	C₂×C₄×D₁₃	C₂×D₄	1	1	yes	characteristic
113	C₂×C₄×D₁₃	C₂×D₄	1	1	yes	characteristic
114	C₂×C₄×D₁₃	C₂×Q₈	1	2	yes	—
115	C₂×C₄×D₁₃	#41	1	2	yes	—
116	C₁₃×M₁₆	—	2	2	no	—
117	C₁₃×M₁₆	C₂²×C₄	1	4	yes	—
118	C₂×C₈×C₁₃	—	2	2	no	—
119	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
120	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
121	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
122	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
123	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
124	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
125	C₂×C₈×C₁₃	C₂×Q₈	1	2	yes	—
126	C₁₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
127	C₁₃×C₂²⋊C₄	—	2	2	no	—
128	C₄²×C₁₃	—	2	2	no	—
129	C₄²×C₁₃	—	2	1	no	—
130	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
131	C₂²⋊Dic₁₃	—	2	2	no	—
132	#6103	—	2	4	no	—
133	#6103	—	2	4	no	—
134	C₄⋊Dic₁₃	C₂²×C₄	1	4	yes	—
135	#6101	—	2	4	no	—
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	C₂²×C₄	1	2	yes	—
141	#6099	—	2	2	no	—
142	#6099	C₂²×C₄	1	4	yes	—
143	C₂×#1055	—	2	2	no	—
144	C₂×#1055	C₂²×C₄	1	2	yes	—
145	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
146	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
147	C₂×#1055	C₂²×C₄	1	2	yes	—
148	C₂×#1055	C₂²×C₄	1	2	yes	—
149	C₂×#1055	C₂×D₄	1	2	yes	—
150	C₂×#1055	C₂×Q₈	1	2	yes	—
151	#6094	—	2	8	no	—
152	#6094	C₄⋊C₄	1	8	yes	—
153	#6094	C₄⋊C₄	1	8	yes	—
154	C₈×D₁₃	—	2	8	no	—
155	C₈×D₁₃	C₄²	1	4	yes	—
156	C₈×D₁₃	C₄²	1	4	yes	—
157	C₈×D₁₃	C₄²	1	4	yes	—
158	C₈×D₁₃	C₄²	1	4	yes	—
159	C₂²×#108	—	13	1	no	—
160	C₂×#427	—	13	1	no	—
161	#2873	—	13	2	no	—
162	C₂×#405	—	13	1	no	—
163	#1773	—	13	1	no	—
164	#1773	—	13	1	no	—
165	#1773	—	13	1	no	—
166	#1773	D₁₃	1	1	yes	characteristic, complemented
167	#1772	—	13	2	no	—
168	#1772	—	13	2	no	—
169	#1733	—	13	2	no	—
170	C₂³×C₁₃	C₂×#41	1	1	yes	characteristic
171	C₂²×D₁₃	—	4	2	no	—
172	C₂²×D₁₃	#117	1	2	yes	—
173	C₂²×D₁₃	C₄×D₄	1	1	yes	characteristic
174	C₂²×D₁₃	C₄×D₄	1	1	yes	characteristic
175	C₂²×D₁₃	C₄×Q₈	1	2	yes	—
176	C₂×C₄×C₁₃	—	2	2	no	—
177	C₂×C₄×C₁₃	—	2	4	no	—
178	C₂×C₄×C₁₃	—	4	2	no	—
179	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
180	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
181	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
182	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
183	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
184	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
185	C₂×Dic₁₃	—	2	2	no	—
186	C₂×Dic₁₃	—	2	4	no	—
187	C₂×Dic₁₃	—	4	2	no	—
188	C₂×Dic₁₃	#117	1	2	yes	—
189	C₂×Dic₁₃	C₄×D₄	1	1	yes	characteristic
190	C₂×Dic₁₃	C₄×D₄	1	1	yes	characteristic
191	C₂×Dic₁₃	C₄×Q₈	1	2	yes	—
192	C₄×D₁₃	—	8	4	no	—
193	C₄×D₁₃	C₂×C₄²	1	2	yes	—
194	C₄×D₁₃	C₂×C₄²	1	2	yes	—
195	C₄×D₁₃	C₂×C₄⋊C₄	1	2	yes	—
196	C₄×D₁₃	C₂×C₄⋊C₄	1	2	yes	—
197	C₄×D₁₃	C₄×D₄	1	2	yes	—
198	C₄×D₁₃	C₄×D₄	1	2	yes	—
199	C₄×D₁₃	C₄×Q₈	1	2	yes	—
200	C₄×D₁₃	C₄×Q₈	1	2	yes	—
201	C₈×C₁₃	—	2	4	no	—
202	C₈×C₁₃	C₂×C₄²	1	2	yes	—
203	C₈×C₁₃	C₂×C₄²	1	2	yes	—
204	C₈×C₁₃	C₂×C₄⋊C₄	1	4	yes	—
205	#1055	—	2	4	no	—
206	#1055	C₂×C₄²	1	2	yes	—
207	#1055	C₂×C₄²	1	2	yes	—
208	#1055	C₂×C₄⋊C₄	1	4	yes	—
209	C₂²×M₁₆	—	13	1	no	—
210	C₂²×M₁₆	—	13	2	no	—
211	C₂³×C₈	—	13	1	no	—
212	C₂×#117	—	13	1	no	—
213	C₂×#117	—	13	2	no	—
214	C₂×#108	—	13	2	no	—
215	C₂×#108	—	13	1	no	—
216	C₂×#108	—	13	8	no	—
217	C₂×#108	C₂×D₁₃	1	1	yes	characteristic
218	#427	—	13	1	no	—
219	#427	—	13	2	no	—
220	#427	—	13	2	no	—
221	#427	—	13	2	no	—
222	#427	C₂×D₁₃	1	1	yes	characteristic
223	C₂×#107	—	13	2	no	—
224	C₂×#106	—	13	2	no	—
225	#405	—	13	8	no	—
226	#405	—	13	2	no	—
227	#405	—	13	2	no	—
228	#405	—	13	2	no	—
229	#405	—	26	2	no	—
230	#405	—	26	2	no	—
231	#405	C₂×D₁₃	1	2	yes	—
232	C₄×M₁₆	—	26	2	no	—
233	C₄×M₁₆	—	26	2	no	—
234	C₂×#97	—	13	1	no	—
235	C₂×#97	C₂×D₁₃	1	1	yes	characteristic
236	C₂×C₄×C₈	—	13	1	no	—
237	C₂×C₄×C₈	—	13	1	no	—
238	#339	—	13	2	no	—
239	#339	—	13	2	no	—
240	#339	—	13	2	no	—
241	#339	C₂×D₁₃	1	2	yes	—
242	C₂²×C₁₃	—	2	2	no	—
243	C₂²×C₁₃	C₂×#117	1	1	yes	characteristic
244	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
245	C₂²×C₁₃	C₂×C₄×Q₈	1	1	yes	characteristic
246	C₂×D₁₃	—	2	2	no	—
247	C₂×D₁₃	—	2	2	no	—
248	C₂×D₁₃	—	4	2	no	—
249	C₂×D₁₃	—	4	2	no	—
250	C₂×D₁₃	C₄×C₄⋊C₄	1	2	yes	—
251	C₂×D₁₃	C₄×C₄⋊C₄	1	2	yes	—
252	C₄×C₁₃	—	4	2	no	—
253	C₄×C₁₃	—	4	4	no	—
254	C₄×C₁₃	C₂²×C₄²	1	1	yes	characteristic
255	C₄×C₁₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
256	C₄×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
257	C₄×C₁₃	C₂×C₄×Q₈	1	1	yes	characteristic
258	Dic₁₃	—	4	2	no	—
259	Dic₁₃	—	4	4	no	—
260	Dic₁₃	C₄×C₄⋊C₄	1	2	yes	—
261	Dic₁₃	C₄×C₄⋊C₄	1	2	yes	—
262	C₂³×C₄	—	13	1	no	—
263	C₂×M₁₆	—	13	4	no	—
264	C₂×M₁₆	—	13	2	no	—
265	C₂×M₁₆	—	13	2	no	—
266	C₂×M₁₆	—	13	4	no	—
267	C₂×M₁₆	—	13	2	no	—
268	C₂×M₁₆	—	13	8	no	—
269	C₂×M₁₆	—	26	2	no	—
270	C₂×M₁₆	—	26	4	no	—
271	C₂×M₁₆	C₂²×D₁₃	1	2	yes	—
272	C₂²×C₈	—	13	1	no	—
273	C₂²×C₈	—	13	1	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	—	26	2	no	—
281	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
282	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
283	#117	—	13	4	no	—
284	#117	—	13	2	no	—
285	#117	—	13	4	no	—
286	#117	—	26	2	no	—
287	#117	—	26	2	no	—
288	#117	—	26	2	no	—
289	#117	C₂²×D₁₃	1	2	yes	—
290	C₂×C₄⋊C₄	—	13	4	no	—
291	C₂×C₄⋊C₄	—	26	1	no	—
292	C₂×C₂²⋊C₄	—	26	2	no	—
293	C₂×C₂²⋊C₄	—	26	1	no	—
294	C₂×C₄²	—	13	1	no	—
295	C₂×C₄²	—	26	2	no	—
296	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
297	#108	—	13	8	no	—
298	#108	—	13	4	no	—
299	#108	C₄×D₁₃	1	4	yes	complemented
300	#107	—	13	2	no	—
301	#107	—	13	4	no	—
302	#107	C₄×D₁₃	1	2	yes	—
303	#106	—	13	2	no	—
304	#106	—	13	4	no	—
305	#106	C₄×D₁₃	1	2	yes	—
306	#97	—	2	2	no	—
307	#97	—	13	4	no	—
308	#97	—	26	2	no	—
309	#97	—	26	2	no	—
310	#97	—	26	2	no	—
311	#97	C₄×D₁₃	1	4	yes	complemented
312	C₄×C₈	—	2	2	no	—
313	C₄×C₈	—	13	4	no	—
314	C₄×C₈	—	13	4	no	—
315	C₄×C₈	—	26	2	no	—
316	C₄×C₈	—	26	2	no	—
317	C₄×C₈	—	26	2	no	—
318	C₂×C₁₃	—	2	1	no	—
319	C₂×C₁₃	—	2	1	no	—
320	C₂×C₁₃	C₂×C₄×C₄⋊C₄	1	1	yes	characteristic
321	C₂×C₁₃	#2957	1	2	yes	—
322	D₁₃	—	2	2	no	—
323	D₁₃	—	2	2	no	—
324	C₂⁴	—	13	1	no	—
325	C₂²×C₄	—	2	1	no	—
326	C₂²×C₄	—	13	1	no	—
327	C₂²×C₄	—	13	1	no	—
328	C₂²×C₄	—	13	1	no	—
329	C₂²×C₄	—	13	2	no	—
330	C₂²×C₄	—	13	2	no	—
331	C₂²×C₄	—	13	1	no	—
332	C₂²×C₄	—	13	1	no	—
333	C₂²×C₄	—	13	2	no	—
334	C₂²×C₄	—	13	2	no	—
335	C₂²×C₄	—	26	4	no	—
336	C₂²×C₄	—	26	1	no	—
337	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
338	M₁₆	—	2	2	no	—
339	M₁₆	—	13	8	no	—
340	M₁₆	—	13	8	no	—
341	M₁₆	—	13	4	no	—
342	M₁₆	—	26	8	no	—
343	M₁₆	—	26	2	no	—
344	M₁₆	C₂×C₄×D₁₃	1	4	yes	—
345	C₂×C₈	—	2	2	no	—
346	C₂×C₈	—	13	2	no	—
347	C₂×C₈	—	13	2	no	—
348	C₂×C₈	—	13	1	no	—
349	C₂×C₈	—	13	1	no	—
350	C₂×C₈	—	13	2	no	—
351	C₂×C₈	—	13	2	no	—
352	C₂×C₈	—	13	2	no	—
353	C₂×C₈	—	13	4	no	—
354	C₂×C₈	—	13	4	no	—
355	C₂×C₈	—	13	4	no	—
356	C₂×C₈	—	13	4	no	—
357	C₂×C₈	—	26	8	no	—
358	C₂×C₈	—	26	2	no	—
359	C₂×C₈	C₂×C₄×D₁₃	1	2	yes	—
360	C₂×C₈	C₂×C₄×D₁₃	1	1	yes	characteristic
361	C₂×C₈	C₂×C₄×D₁₃	1	1	yes	characteristic
362	C₂×C₈	C₂×C₄×D₁₃	1	2	yes	—
363	C₂×C₈	C₂×C₄×D₁₃	1	2	yes	—
364	C₂×C₈	D₄×D₁₃	1	2	yes	—
365	C₂×C₈	Q₈×D₁₃	1	2	yes	—
366	C₄⋊C₄	—	13	4	no	—
367	C₄⋊C₄	—	26	4	no	—
368	C₄⋊C₄	—	26	4	no	—
369	C₄⋊C₄	C₂×C₄×D₁₃	1	4	yes	—
370	C₂²⋊C₄	—	2	2	no	—
371	C₂²⋊C₄	—	26	4	no	—
372	C₂²⋊C₄	—	26	4	no	—
373	C₂²⋊C₄	—	26	2	no	—
374	C₄²	—	2	2	no	—
375	C₄²	—	2	1	no	—
376	C₄²	—	13	2	no	—
377	C₄²	—	26	4	no	—
378	C₄²	—	26	2	no	—
379	C₄²	—	26	1	no	—
380	C₄²	C₂×C₄×D₁₃	1	2	yes	—
381	C₁₃	#20446	1	1	yes	characteristic, complemented, Sylow
382	C₂³	—	13	1	no	—
383	C₂³	—	13	1	no	—
384	C₂³	—	13	2	no	—
385	C₂³	—	13	2	no	—
386	C₂³	—	52	2	no	—
387	C₂³	#41×D₁₃	1	1	yes	characteristic
388	C₂×C₄	—	2	2	no	—
389	C₂×C₄	—	2	4	no	—
390	C₂×C₄	—	4	2	no	—
391	C₂×C₄	—	13	2	no	—
392	C₂×C₄	—	13	1	no	—
393	C₂×C₄	—	13	1	no	—
394	C₂×C₄	—	13	2	no	—
395	C₂×C₄	—	13	2	no	—
396	C₂×C₄	—	13	2	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	—	26	2	no	—
404	C₂×C₄	—	26	4	no	—
405	C₂×C₄	—	52	2	no	—
406	C₂×C₄	—	104	4	no	—
407	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
408	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
409	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
410	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
411	C₂×C₄	C₂×Q₈×D₁₃	1	1	yes	characteristic
412	C₂×C₄	#41×D₁₃	1	1	yes	characteristic
413	C₈	—	2	4	no	—
414	C₈	—	13	2	no	—
415	C₈	—	13	2	no	—
416	C₈	—	13	4	no	—
417	C₈	—	26	4	no	—
418	C₈	C₄²×D₁₃	1	2	yes	—
419	C₈	C₄²×D₁₃	1	2	yes	—
420	C₈	C₄⋊C₄×D₁₃	1	4	yes	—
421	C₂²	—	2	2	no	—
422	C₂²	—	13	2	no	—
423	C₂²	—	13	2	no	—
424	C₂²	—	26	2	no	—
425	C₂²	—	26	2	no	—
426	C₂²	—	52	2	no	—
427	C₂²	—	52	2	no	—
428	C₂²	D₁₃×#117	1	1	yes	characteristic
429	C₂²	C₄×D₄×D₁₃	1	1	yes	characteristic
430	C₂²	C₄×Q₈×D₁₃	1	1	yes	characteristic
431	C₄	—	4	2	no	—
432	C₄	—	4	4	no	—
433	C₄	—	13	2	no	—
434	C₄	—	13	2	no	—
435	C₄	—	52	2	no	—
436	C₄	—	52	4	no	—
437	C₄	C₂×C₄²×D₁₃	1	1	yes	characteristic
438	C₄	C₂×C₄⋊C₄×D₁₃	1	1	yes	characteristic
439	C₄	C₄×D₄×D₁₃	1	1	yes	characteristic
440	C₄	C₄×Q₈×D₁₃	1	1	yes	characteristic
441	C₂	—	2	1	no	—
442	C₂	—	2	1	no	—
443	C₂	—	26	2	no	—
444	C₂	—	26	2	no	—
445	C₂	C₄×C₄⋊C₄×D₁₃	1	1	yes	characteristic
446	C₂	#13123750	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	#20446
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. #13114720	C₂	semidirect
8. #13114716	C₂	semidirect
9. #13114714	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
37. #11718369	C₄	semidirect
80. C₁₃×#108	C₂×C₄	semidirect
84. C₁₃×#97	C₂×C₄	semidirect
86. #88062	C₂×C₄	semidirect
87. #88059	C₂×C₄	semidirect
92. #88055	C₂×C₄	semidirect
95. C₈×Dic₁₃	C₂×C₄	semidirect
100. C₄×#1055	C₂×C₄	semidirect
166. #1773	D₁₃	semidirect
299. #108	C₄×D₁₃	semidirect
311. #97	C₄×D₁₃	semidirect
381. C₁₃	#20446	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
#13123252	2
C₂×#11718369	2
#13114723	2
#13114722	2
#13114720	2
#13114716	2
#13114714	2
#13114544	2
C₁₃×#1773	2
#20446	13