Subgroups — #16795045

Order 3328.

684 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	#13131513	C₂	1	1	yes	maximal, characteristic
2	D₁₃⋊#423	C₂	1	1	yes	maximal, characteristic
3	#13130412	C₂	1	4	yes	maximal, complemented
4	#13130410	C₂	1	4	yes	maximal, complemented
5	#13130395	C₂	1	1	yes	maximal, characteristic, complemented
6	#13130394	C₂	1	1	yes	maximal, characteristic, complemented
7	#13130392	C₂	1	1	yes	maximal, characteristic, complemented
8	#13130391	C₂	1	1	yes	maximal, characteristic, complemented
9	D₁₃×#431	C₂	1	1	yes	maximal, characteristic
10	C₂×D₁₃⋊M₁₆	—	2	1	no	—
11	C₂×C₄²×D₁₃	C₂²	1	1	yes	characteristic
12	#11719130	—	2	1	no	—
13	#11719129	—	2	1	no	—
14	#11719129	C₂²	1	2	yes	—
15	#11719127	—	2	1	no	—
16	#11719119	C₂²	1	2	yes	—
17	#11719054	C₂²	1	2	yes	—
18	#11719053	—	2	1	no	—
19	#11719052	C₂²	1	1	yes	characteristic
20	#11719052	C₂²	1	1	yes	characteristic
21	#11719052	C₂²	1	1	yes	characteristic
22	#11719052	C₂²	1	1	yes	characteristic
23	#11719051	—	2	1	no	—
24	D₁₃⋊(C₄⋊C₈)	—	2	1	no	—
25	D₁₃⋊(C₄⋊C₈)	C₂²	1	2	yes	—
26	C₄×#6118	—	2	1	no	—
27	C₁₃×#431	C₄	1	1	yes	characteristic
28	#11718586	C₄	1	1	yes	characteristic
29	#11718494	C₂²	1	2	yes	—
30	D₁₃×C₄⋊C₈	C₄	1	2	yes	—
31	D₁₃×C₂²⋊C₈	C₄	1	2	yes	—
32	#11718379	C₂²	1	2	yes	—
33	#11718346	C₄	1	1	yes	characteristic
34	#11718346	C₄	1	1	yes	characteristic
35	C₄×C₈×D₁₃	C₂²	1	1	yes	characteristic
36	C₄×C₈×D₁₃	C₂²	1	1	yes	characteristic
37	#11718256	C₂²	1	4	yes	complemented
38	#11718255	C₂²	1	4	yes	complemented
39	#11718254	C₂²	1	4	yes	complemented
40	#11718253	C₂²	1	4	yes	complemented
41	C₂²×C₄×D₁₃	C₂×C₄	1	1	yes	characteristic
42	C₂²×C₄×D₁₃	D₄	1	1	yes	characteristic
43	C₂²×C₄×D₁₃	Q₈	1	1	yes	characteristic
44	C₂×#6122	—	2	2	no	—
45	D₁₃⋊M₁₆	—	4	4	no	—
46	C₂×#6118	—	2	1	no	—
47	C₂×#6118	—	2	1	no	—
48	C₂×#6118	—	2	1	no	—
49	C₂×#6118	—	2	1	no	—
50	C₂×D₁₃⋊C₈	—	2	2	no	—
51	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
52	C₂×C₄×Dic₁₃	D₄	1	1	yes	characteristic
53	C₂×C₄×Dic₁₃	Q₈	1	1	yes	characteristic
54	C₂×C₄×Dic₁₃	C₂³	1	1	yes	characteristic
55	C₂×C₈×D₁₃	C₂×C₄	1	2	yes	—
56	C₂×C₈×D₁₃	C₂×C₄	1	2	yes	—
57	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
58	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
59	C₄²×D₁₃	D₄	1	1	yes	characteristic
60	C₄²×D₁₃	D₄	1	1	yes	characteristic
61	C₄²×D₁₃	Q₈	1	1	yes	characteristic
62	C₄²×D₁₃	Q₈	1	1	yes	characteristic
63	C₄²×D₁₃	C₂³	1	1	yes	characteristic
64	C₄²×D₁₃	C₂³	1	1	yes	characteristic
65	C₂²⋊#1057	—	2	2	no	—
66	#88112	—	2	2	no	—
67	#88112	—	2	2	no	—
68	#88111	—	2	2	no	—
69	#88110	—	2	2	no	—
70	C₄⋊#1057	—	2	1	no	—
71	C₄⋊#1057	—	2	1	no	—
72	C₄⋊#1057	—	2	1	no	—
73	C₄⋊#1057	—	2	1	no	—
74	C₄⋊#1057	C₂³	1	2	yes	—
75	C₄⋊#1057	C₂³	1	2	yes	—
76	C₄⋊#1057	C₂³	1	2	yes	—
77	C₄⋊#1057	C₂³	1	2	yes	—
78	C₄×#1057	—	2	2	no	—
79	C₁₃×C₄⋊C₈	C₂×C₄	1	2	yes	—
80	C₁₃×C₂²⋊C₈	C₂×C₄	1	2	yes	—
81	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
82	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
83	C₂²⋊#1055	C₂×C₄	1	2	yes	—
84	#88060	C₂×C₄	1	2	yes	—
85	#88060	C₂×C₄	1	2	yes	—
86	#88054	C₂×C₄	1	2	yes	—
87	#88054	C₂×C₄	1	2	yes	—
88	C₈×Dic₁₃	C₂³	1	2	yes	—
89	C₈×Dic₁₃	C₂³	1	2	yes	—
90	C₄⋊#1055	C₂×C₄	1	2	yes	—
91	C₄×#1055	C₂×C₄	1	1	yes	characteristic
92	C₄×#1055	C₂×C₄	1	1	yes	characteristic
93	#17817	—	13	1	no	maximal, Sylow
94	C₂³×D₁₃	C₄⋊C₄	1	1	yes	characteristic
95	C₂²×C₄×C₁₃	C₄⋊C₄	1	1	yes	characteristic
96	C₂²×C₄×C₁₃	C₄⋊C₄	1	1	yes	characteristic
97	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
98	C₂²×Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
99	C₂²×Dic₁₃	C₂×D₄	1	1	yes	characteristic
100	C₂²×Dic₁₃	C₂×Q₈	1	1	yes	characteristic
101	C₂×C₄×D₁₃	—	2	4	no	—
102	C₂×C₄×D₁₃	—	2	2	no	—
103	C₂×C₄×D₁₃	—	2	2	no	—
104	C₂×C₄×D₁₃	—	4	2	no	—
105	C₂×C₄×D₁₃	C₄⋊C₄	1	1	yes	characteristic
106	C₂×C₄×D₁₃	C₄⋊C₄	1	1	yes	characteristic
107	C₂×C₄×D₁₃	C₄⋊C₄	1	1	yes	characteristic
108	C₂×C₄×D₁₃	C₄⋊C₄	1	1	yes	characteristic
109	C₂×C₄×D₁₃	C₄⋊C₄	1	1	yes	characteristic
110	C₂×C₄×D₁₃	C₄⋊C₄	1	1	yes	characteristic
111	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
112	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
113	C₂×C₄×D₁₃	C₂×D₄	1	1	yes	characteristic
114	C₂×C₄×D₁₃	C₂×D₄	1	1	yes	characteristic
115	C₂×C₄×D₁₃	C₂×Q₈	1	1	yes	characteristic
116	C₂×C₄×D₁₃	C₂×Q₈	1	1	yes	characteristic
117	#6122	—	4	4	no	—
118	C₂×#1057	—	2	2	no	—
119	C₂×#1057	—	2	2	no	—
120	C₂×#1057	—	2	2	no	—
121	C₂×#1057	—	2	2	no	—
122	#6118	—	4	2	no	—
123	#6118	—	4	2	no	—
124	#6118	—	4	2	no	—
125	#6118	—	4	2	no	—
126	D₁₃⋊C₈	—	4	4	no	—
127	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
128	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
129	C₄²×C₁₃	C₄⋊C₄	1	1	yes	characteristic
130	C₄²×C₁₃	C₄⋊C₄	1	1	yes	characteristic
131	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
132	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
133	C₄×Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
134	C₄×Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
135	C₄×Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
136	C₄×Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
137	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
138	C₄×Dic₁₃	C₂×D₄	1	1	yes	characteristic
139	C₄×Dic₁₃	C₂×D₄	1	1	yes	characteristic
140	C₄×Dic₁₃	C₂×D₄	1	1	yes	characteristic
141	C₄×Dic₁₃	C₂×Q₈	1	1	yes	characteristic
142	C₄×Dic₁₃	C₂×Q₈	1	1	yes	characteristic
143	C₄×Dic₁₃	C₂×Q₈	1	1	yes	characteristic
144	C₄×Dic₁₃	C₂⁴	1	1	yes	characteristic
145	C₂×#1055	C₂²×C₄	1	2	yes	—
146	C₂×#1055	C₂²×C₄	1	2	yes	—
147	C₈×D₁₃	—	4	2	no	—
148	C₈×D₁₃	—	4	2	no	—
149	#2920	—	13	1	no	—
150	C₂×#431	—	13	1	no	—
151	C₂×#423	—	13	1	no	—
152	#1574	—	13	4	no	—
153	#1573	—	13	4	no	—
154	#1567	—	13	1	no	—
155	#1567	—	13	1	no	—
156	#1566	—	13	1	no	—
157	#1566	—	13	1	no	—
158	C₂³×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
159	C₂²×D₁₃	—	2	2	no	—
160	C₂²×D₁₃	—	2	2	no	—
161	C₂²×D₁₃	—	4	1	no	—
162	C₂²×D₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
163	C₂²×D₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
164	C₂×C₄×C₁₃	—	2	2	no	—
165	C₂×C₄×C₁₃	—	2	2	no	—
166	C₂×C₄×C₁₃	—	2	2	no	—
167	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
168	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
169	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
170	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
171	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
172	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
173	C₂×Dic₁₃	—	2	1	no	—
174	C₂×Dic₁₃	—	2	1	no	—
175	C₂×Dic₁₃	—	2	2	no	—
176	C₂×Dic₁₃	—	4	1	no	—
177	C₂×Dic₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
178	C₂×Dic₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
179	C₂×Dic₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
180	C₂×Dic₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
181	C₂×Dic₁₃	C₂²×D₄	1	1	yes	characteristic
182	C₂×Dic₁₃	C₂²×Q₈	1	1	yes	characteristic
183	C₄×D₁₃	—	2	2	no	—
184	C₄×D₁₃	—	2	2	no	—
185	C₄×D₁₃	—	2	2	no	—
186	C₄×D₁₃	—	2	2	no	—
187	C₄×D₁₃	—	2	2	no	—
188	C₄×D₁₃	—	2	2	no	—
189	C₄×D₁₃	—	2	1	no	—
190	C₄×D₁₃	—	2	1	no	—
191	C₄×D₁₃	—	2	2	no	—
192	C₄×D₁₃	—	4	1	no	—
193	C₄×D₁₃	—	4	1	no	—
194	C₄×D₁₃	#108	1	4	yes	—
195	C₄×D₁₃	AGL(1,ℤ/8)	1	2	yes	—
196	C₄×D₁₃	#137	1	2	yes	—
197	#1057	—	4	2	no	—
198	#1057	—	4	2	no	—
199	#1057	—	4	2	no	—
200	#1057	—	4	2	no	—
201	C₈×C₁₃	—	2	2	no	—
202	C₈×C₁₃	—	2	2	no	—
203	#1055	—	2	2	no	—
204	#1055	—	2	2	no	—
205	C₂²×M₁₆	—	26	1	no	—
206	C₂²×C₄²	—	13	1	no	—
207	#432	—	13	2	no	—
208	#432	—	26	1	no	—
209	#431	—	13	1	no	—
210	#431	—	13	2	no	—
211	#431	—	13	2	no	—
212	#431	—	13	1	no	—
213	#431	—	13	1	no	—
214	#431	—	13	2	no	—
215	#431	—	26	1	no	—
216	#431	#261	1	1	yes	characteristic
217	#423	—	13	1	no	—
218	#423	—	13	1	no	—
219	#423	—	13	1	no	—
220	#423	—	13	1	no	—
221	#423	—	13	2	no	—
222	#423	—	26	1	no	—
223	#423	—	26	1	no	—
224	C₂×C₄⋊C₈	—	13	2	no	—
225	C₂×C₄⋊C₈	—	13	2	no	—
226	C₂×C₄⋊C₈	—	26	1	no	—
227	#407	—	26	1	no	—
228	C₂×C₂²⋊C₈	—	13	2	no	—
229	C₄×M₁₆	—	26	1	no	—
230	C₂×C₄×C₈	—	13	1	no	—
231	C₂×C₄×C₈	—	13	1	no	—
232	#335	—	13	4	no	—
233	#335	—	13	4	no	—
234	#334	—	13	4	no	—
235	#334	—	13	4	no	—
236	C₂²×C₁₃	—	2	1	no	—
237	C₂²×C₁₃	—	2	1	no	—
238	C₂²×C₁₃	—	2	1	no	—
239	C₂²×C₁₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
240	C₂×D₁₃	—	2	1	no	—
241	C₂×D₁₃	—	2	1	no	—
242	C₂×D₁₃	—	2	1	no	—
243	C₂×D₁₃	—	2	1	no	—
244	C₂×D₁₃	—	4	4	no	—
245	C₂×D₁₃	#428	1	2	yes	—
246	C₂×D₁₃	C₂×#108	1	2	yes	—
247	C₄×C₁₃	—	2	1	no	—
248	C₄×C₁₃	—	2	1	no	—
249	C₄×C₁₃	—	2	1	no	—
250	C₄×C₁₃	#428	1	2	yes	—
251	C₄×C₁₃	C₂×#108	1	2	yes	—
252	C₄×C₁₃	#568	1	2	yes	—
253	Dic₁₃	—	2	1	no	—
254	Dic₁₃	—	2	1	no	—
255	Dic₁₃	—	2	1	no	—
256	Dic₁₃	—	2	1	no	—
257	Dic₁₃	C₂×#108	1	2	yes	—
258	Dic₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
259	Dic₁₃	C₂×#137	1	1	yes	characteristic
260	C₂³×C₄	—	13	1	no	—
261	C₂³×C₄	—	13	1	no	—
262	C₂³×C₄	—	13	1	no	—
263	C₂×M₁₆	—	26	1	no	—
264	C₂×M₁₆	—	26	1	no	—
265	C₂×M₁₆	—	26	2	no	—
266	C₂×M₁₆	—	26	1	no	—
267	C₂×M₁₆	—	26	1	no	—
268	C₂×M₁₆	—	52	4	no	—
269	C₂²×C₈	—	13	2	no	—
270	C₂²×C₈	—	13	2	no	—
271	C₂²×C₈	—	26	2	no	—
272	C₂×C₄²	—	13	1	no	—
273	C₂×C₄²	—	13	1	no	—
274	C₂×C₄²	—	13	1	no	—
275	C₂×C₄²	—	13	1	no	—
276	C₂×C₄²	—	13	1	no	—
277	C₂×C₄²	—	13	1	no	—
278	C₂×C₄²	—	13	1	no	—
279	C₂×C₄²	—	13	1	no	—
280	C₂×C₄²	—	13	1	no	—
281	C₂×C₄²	—	13	1	no	—
282	C₂×C₄²	—	13	1	no	—
283	C₂×C₄²	C₂×#261	1	1	yes	characteristic
284	C₄⋊C₈	—	13	2	no	—
285	C₄⋊C₈	—	13	2	no	—
286	C₄⋊C₈	—	13	2	no	—
287	C₄⋊C₈	—	13	2	no	—
288	C₄⋊C₈	—	13	2	no	—
289	C₄⋊C₈	—	13	2	no	—
290	C₄⋊C₈	—	13	2	no	—
291	C₄⋊C₈	—	26	1	no	—
292	C₄⋊C₈	—	26	1	no	—
293	C₄⋊C₈	—	26	1	no	—
294	C₄⋊C₈	—	26	1	no	—
295	C₄⋊C₈	—	26	2	no	—
296	C₄⋊C₈	—	26	2	no	—
297	C₄⋊C₈	C₂×#261	1	2	yes	—
298	C₂²⋊C₈	—	13	2	no	—
299	C₂²⋊C₈	—	13	2	no	—
300	C₂²⋊C₈	—	13	2	no	—
301	C₂²⋊C₈	—	26	2	no	—
302	C₂²⋊C₈	—	26	2	no	—
303	C₂²⋊C₈	C₂×#261	1	2	yes	—
304	#97	—	26	2	no	—
305	C₄×C₈	—	13	2	no	—
306	C₄×C₈	—	13	2	no	—
307	C₄×C₈	—	13	1	no	—
308	C₄×C₈	—	13	1	no	—
309	C₄×C₈	—	26	2	no	—
310	C₄×C₈	C₂×#261	1	1	yes	characteristic
311	C₄×C₈	C₂×#261	1	1	yes	characteristic
312	C₂×C₁₃	—	4	1	no	—
313	C₂×C₁₃	#2905	1	1	yes	characteristic
314	C₂×C₁₃	C₂×#428	1	1	yes	characteristic
315	C₂×C₁₃	C₂²×#108	1	1	yes	characteristic
316	D₁₃	—	2	2	no	—
317	D₁₃	—	2	2	no	—
318	C₂⁴	—	13	1	no	—
319	C₂²×C₄	—	13	1	no	—
320	C₂²×C₄	—	13	1	no	—
321	C₂²×C₄	—	13	1	no	—
322	C₂²×C₄	—	13	1	no	—
323	C₂²×C₄	—	13	1	no	—
324	C₂²×C₄	—	13	1	no	—
325	C₂²×C₄	—	13	1	no	—
326	C₂²×C₄	—	13	1	no	—
327	C₂²×C₄	—	13	1	no	—
328	C₂²×C₄	—	13	1	no	—
329	C₂²×C₄	—	13	1	no	—
330	C₂²×C₄	—	13	1	no	—
331	C₂²×C₄	—	13	1	no	—
332	C₂²×C₄	—	13	1	no	—
333	C₂²×C₄	—	13	1	no	—
334	C₂²×C₄	—	26	2	no	—
335	C₂²×C₄	—	26	4	no	—
336	C₂²×C₄	—	26	2	no	—
337	C₂²×C₄	—	52	2	no	—
338	C₂²×C₄	C₄⋊#261	1	1	yes	characteristic
339	C₂²×C₄	C₄⋊#261	1	1	yes	characteristic
340	C₂²×C₄	C₂²×#261	1	1	yes	characteristic
341	M₁₆	—	52	2	no	—
342	M₁₆	—	52	2	no	—
343	M₁₆	—	52	2	no	—
344	M₁₆	—	52	2	no	—
345	M₁₆	—	52	4	no	—
346	C₂×C₈	—	13	2	no	—
347	C₂×C₈	—	13	2	no	—
348	C₂×C₈	—	26	2	no	—
349	C₂×C₈	—	26	2	no	—
350	C₂×C₈	—	26	2	no	—
351	C₂×C₈	—	26	2	no	—
352	C₂×C₈	—	52	2	no	—
353	C₂×C₈	—	52	2	no	—
354	C₂×C₈	—	52	4	no	—
355	C₂×C₈	C₂²×#261	1	2	yes	—
356	C₂×C₈	C₂²×#261	1	2	yes	—
357	C₄²	—	13	1	no	—
358	C₄²	—	13	1	no	—
359	C₄²	—	13	1	no	—
360	C₄²	—	13	1	no	—
361	C₄²	—	13	1	no	—
362	C₄²	—	13	1	no	—
363	C₄²	—	13	1	no	—
364	C₄²	—	13	1	no	—
365	C₄²	—	13	1	no	—
366	C₄²	—	13	1	no	—
367	C₄²	—	13	1	no	—
368	C₄²	—	13	1	no	—
369	C₄²	C₄⋊#261	1	1	yes	characteristic
370	C₄²	C₄⋊#261	1	1	yes	characteristic
371	C₄²	C₂²×#261	1	1	yes	characteristic
372	C₄²	C₂²×#261	1	1	yes	characteristic
373	C₁₃	#17817	1	1	yes	characteristic, complemented, Sylow
374	C₂³	—	13	1	no	—
375	C₂³	—	13	1	no	—
376	C₂³	—	26	2	no	—
377	C₂³	—	26	2	no	—
378	C₂³	—	52	1	no	—
379	C₂³	C₂×C₄⋊#261	1	1	yes	characteristic
380	C₂×C₄	—	2	2	no	—
381	C₂×C₄	—	2	2	no	—
382	C₂×C₄	—	2	2	no	—
383	C₂×C₄	—	13	1	no	—
384	C₂×C₄	—	13	1	no	—
385	C₂×C₄	—	13	4	no	—
386	C₂×C₄	—	13	2	no	—
387	C₂×C₄	—	13	2	no	—
388	C₂×C₄	—	13	1	no	—
389	C₂×C₄	—	13	1	no	—
390	C₂×C₄	—	13	1	no	—
391	C₂×C₄	—	13	1	no	—
392	C₂×C₄	—	26	1	no	—
393	C₂×C₄	—	26	1	no	—
394	C₂×C₄	—	26	2	no	—
395	C₂×C₄	—	26	2	no	—
396	C₂×C₄	—	26	2	no	—
397	C₂×C₄	—	26	1	no	—
398	C₂×C₄	—	26	1	no	—
399	C₂×C₄	—	26	2	no	—
400	C₂×C₄	—	26	2	no	—
401	C₂×C₄	—	26	2	no	—
402	C₂×C₄	—	26	2	no	—
403	C₂×C₄	—	26	2	no	—
404	C₂×C₄	—	52	1	no	—
405	C₂×C₄	—	52	1	no	—
406	C₂×C₄	—	52	1	no	—
407	C₂×C₄	C₂×C₄⋊#261	1	1	yes	characteristic
408	C₂×C₄	C₂×C₄⋊#261	1	1	yes	characteristic
409	C₂×C₄	C₂×C₄⋊#261	1	1	yes	characteristic
410	C₂×C₄	C₂×C₄⋊#261	1	1	yes	characteristic
411	C₂×C₄	C₂×C₄⋊#261	1	1	yes	characteristic
412	C₂×C₄	C₂³×#261	1	1	yes	characteristic
413	C₈	—	2	2	no	—
414	C₈	—	2	2	no	—
415	C₈	—	26	2	no	—
416	C₈	—	26	2	no	—
417	C₈	—	52	2	no	—
418	C₈	—	52	2	no	—
419	C₈	—	52	2	no	—
420	C₈	—	52	2	no	—
421	C₂²	—	2	1	no	—
422	C₂²	—	2	1	no	—
423	C₂²	—	2	1	no	—
424	C₂²	—	13	2	no	—
425	C₂²	—	13	2	no	—
426	C₂²	—	26	1	no	—
427	C₂²	—	26	1	no	—
428	C₂²	—	26	1	no	—
429	C₂²	—	26	1	no	—
430	C₂²	—	52	4	no	—
431	C₂²	C₂²×C₄⋊#261	1	1	yes	characteristic
432	C₄	—	2	1	no	—
433	C₄	—	2	1	no	—
434	C₄	—	2	1	no	—
435	C₄	—	13	1	no	—
436	C₄	—	13	1	no	—
437	C₄	—	13	2	no	—
438	C₄	—	26	1	no	—
439	C₄	—	26	1	no	—
440	C₄	—	26	1	no	—
441	C₄	—	26	1	no	—
442	C₄	D₁₃⋊#108	1	2	yes	—
443	C₄	#11719098	1	2	yes	—
444	C₄	#11719629	1	2	yes	—
445	C₂	—	4	1	no	—
446	C₂	—	26	2	no	—
447	C₂	—	26	2	no	—
448	C₂	#13131479	1	1	yes	characteristic
449	C₂	C₂×#11719098	1	1	yes	characteristic
450	C₂	C₂×D₁₃⋊#108	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²×C₄⋊#261
commutator	C₂×C₄×C₁₃	C₂³×C₄
Frattini	C₂×C₄	C₂³×#261
Fitting	C₁₃×#431	C₄
socle	C₂²×C₁₃	C₂²×C₄⋊C₄
prime radical	C₂³×D₁₃	C₄⋊C₄
cosocle	C₄×Dic₁₃	C₂⁴
hypercenter	#431	#261
hypocenter	C₁₃	#17817
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #431

Complements

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

N	H ≅ G/N	type
3. #13130412	C₂	semidirect
4. #13130410	C₂	semidirect
5. #13130395	C₂	semidirect
6. #13130394	C₂	semidirect
7. #13130392	C₂	semidirect
8. #13130391	C₂	semidirect
37. #11718256	C₂²	semidirect
38. #11718255	C₂²	semidirect
39. #11718254	C₂²	semidirect
40. #11718253	C₂²	semidirect
373. C₁₃	#17817	semidirect

Maximal subgroups

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

subgroup	index
#13131513	2
D₁₃⋊#423	2
#13130412	2
#13130410	2
#13130395	2
#13130394	2
#13130392	2
#13130391	2
D₁₃×#431	2
#17817	13