Subgroups — #16795044

Order 3328.

684 conjugacy classes of subgroups.

The subgroup lattice has 446 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13131514	C₂	1	1	yes	maximal, characteristic
2	D₁₃⋊#423	C₂	1	1	yes	maximal, characteristic
3	#13130414	C₂	1	2	yes	maximal, complemented
4	#13130413	C₂	1	2	yes	maximal, complemented
5	#13130410	C₂	1	4	yes	maximal, complemented
6	#13130393	C₂	1	2	yes	maximal, complemented
7	#13130390	C₂	1	2	yes	maximal, complemented
8	C₂×#11718494	C₂	1	1	yes	maximal, characteristic
9	C₂×D₁₃⋊M₁₆	—	2	1	no	—
10	C₂×C₄²×D₁₃	C₂²	1	1	yes	characteristic
11	#11719129	—	2	1	no	—
12	#11719129	C₂²	1	1	yes	characteristic
13	#11719129	C₂²	1	2	yes	—
14	#11719129	C₂²	1	1	yes	characteristic
15	#11719126	—	2	1	no	—
16	C₄×#6122	—	2	1	no	—
17	#11719055	—	2	1	no	—
18	#11719054	C₂²	1	2	yes	—
19	#11719053	—	2	1	no	—
20	#11719052	C₂²	1	2	yes	—
21	#11719051	C₂²	1	2	yes	—
22	D₁₃⋊(C₄⋊C₈)	—	2	1	no	—
23	D₁₃⋊(C₄⋊C₈)	C₂²	1	2	yes	—
24	#11719049	—	2	1	no	—
25	C₂×C₁₃×C₄⋊C₈	C₄	1	1	yes	characteristic
26	C₂×#88060	C₄	1	2	yes	—
27	C₂×C₈×Dic₁₃	C₂²	1	2	yes	—
28	C₂×C₄⋊#1055	C₄	1	1	yes	characteristic
29	#11718494	C₄	1	2	yes	—
30	#11718494	C₄	1	1	yes	characteristic
31	#11718494	C₄	1	1	yes	characteristic
32	#11718494	C₂²	1	2	yes	—
33	#11718494	C₂²	1	1	yes	characteristic
34	#11718494	C₂²	1	1	yes	characteristic
35	#11718256	C₂²	1	4	yes	complemented
36	#11718255	C₂²	1	4	yes	complemented
37	#11718254	C₂²	1	4	yes	complemented
38	#11718253	C₂²	1	4	yes	complemented
39	C₂²×C₄×D₁₃	C₂×C₄	1	1	yes	characteristic
40	C₂²×C₄×D₁₃	D₄	1	1	yes	characteristic
41	C₂²×C₄×D₁₃	Q₈	1	1	yes	characteristic
42	C₂×#6122	—	2	2	no	—
43	C₂×#6122	—	2	1	no	—
44	C₂×#6122	—	2	1	no	—
45	D₁₃⋊M₁₆	—	4	4	no	—
46	C₂×#6118	—	2	2	no	—
47	C₂×D₁₃⋊C₈	—	2	2	no	—
48	C₂²×C₈×C₁₃	C₂×C₄	1	2	yes	—
49	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
50	C₂×C₄×Dic₁₃	D₄	1	1	yes	characteristic
51	C₂×C₄×Dic₁₃	Q₈	1	1	yes	characteristic
52	C₂×C₄×Dic₁₃	C₂³	1	1	yes	characteristic
53	C₂²×#1055	C₂×C₄	1	2	yes	—
54	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
55	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
56	C₄²×D₁₃	D₄	1	1	yes	characteristic
57	C₄²×D₁₃	D₄	1	1	yes	characteristic
58	C₄²×D₁₃	Q₈	1	1	yes	characteristic
59	C₄²×D₁₃	Q₈	1	1	yes	characteristic
60	C₄²×D₁₃	C₂³	1	1	yes	characteristic
61	C₄²×D₁₃	C₂³	1	1	yes	characteristic
62	#88112	—	2	1	no	—
63	#88112	—	2	1	no	—
64	#88112	—	2	2	no	—
65	#88112	—	2	2	no	—
66	#88111	—	2	2	no	—
67	#88111	—	2	2	no	—
68	#88110	—	2	2	no	—
69	C₄⋊#1057	—	2	2	no	—
70	C₄⋊#1057	C₂³	1	2	yes	—
71	C₄⋊#1057	C₂³	1	4	yes	—
72	C₄⋊#1057	C₂³	1	2	yes	—
73	C₄×#1057	—	2	2	no	—
74	C₁₃×C₄⋊C₈	C₂×C₄	1	2	yes	—
75	C₁₃×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
76	C₁₃×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
77	#88060	C₂×C₄	1	2	yes	—
78	#88060	C₂×C₄	1	2	yes	—
79	#88060	C₂×C₄	1	2	yes	—
80	#88060	C₂×C₄	1	2	yes	—
81	C₈×Dic₁₃	C₂×C₄	1	2	yes	—
82	C₈×Dic₁₃	C₂×C₄	1	2	yes	—
83	C₈×Dic₁₃	C₂³	1	2	yes	—
84	C₈×Dic₁₃	C₂³	1	2	yes	—
85	C₄⋊#1055	C₂×C₄	1	2	yes	—
86	C₄⋊#1055	C₂×C₄	1	1	yes	characteristic
87	C₄⋊#1055	C₂×C₄	1	1	yes	characteristic
88	#17817	—	13	1	no	maximal, Sylow
89	C₂³×D₁₃	C₄⋊C₄	1	1	yes	characteristic
90	C₂²×C₄×C₁₃	C₄⋊C₄	1	1	yes	characteristic
91	C₂²×C₄×C₁₃	C₄⋊C₄	1	1	yes	characteristic
92	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
93	C₂²×Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
94	C₂²×Dic₁₃	C₂×D₄	1	1	yes	characteristic
95	C₂²×Dic₁₃	C₂×Q₈	1	1	yes	characteristic
96	C₂×C₄×D₁₃	—	2	2	no	—
97	C₂×C₄×D₁₃	—	2	2	no	—
98	C₂×C₄×D₁₃	—	2	4	no	—
99	C₂×C₄×D₁₃	—	4	1	no	—
100	C₂×C₄×D₁₃	—	4	1	no	—
101	C₂×C₄×D₁₃	C₄⋊C₄	1	1	yes	characteristic
102	C₂×C₄×D₁₃	C₄⋊C₄	1	1	yes	characteristic
103	C₂×C₄×D₁₃	C₄⋊C₄	1	1	yes	characteristic
104	C₂×C₄×D₁₃	C₄⋊C₄	1	1	yes	characteristic
105	C₂×C₄×D₁₃	C₄⋊C₄	1	1	yes	characteristic
106	C₂×C₄×D₁₃	C₄⋊C₄	1	1	yes	characteristic
107	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
108	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
109	C₂×C₄×D₁₃	C₂×D₄	1	1	yes	characteristic
110	C₂×C₄×D₁₃	C₂×D₄	1	1	yes	characteristic
111	C₂×C₄×D₁₃	C₂×Q₈	1	1	yes	characteristic
112	C₂×C₄×D₁₃	C₂×Q₈	1	1	yes	characteristic
113	#6122	—	4	4	no	—
114	#6122	—	4	2	no	—
115	#6122	—	4	2	no	—
116	C₂×#1057	—	2	2	no	—
117	C₂×#1057	—	2	2	no	—
118	C₂×#1057	—	2	4	no	—
119	#6118	—	4	4	no	—
120	D₁₃⋊C₈	—	4	4	no	—
121	C₂×C₈×C₁₃	—	4	2	no	—
122	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
123	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
124	C₄²×C₁₃	C₄⋊C₄	1	1	yes	characteristic
125	C₄²×C₁₃	C₄⋊C₄	1	1	yes	characteristic
126	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
127	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
128	C₄×Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
129	C₄×Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
130	C₄×Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
131	C₄×Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
132	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
133	C₄×Dic₁₃	C₂×D₄	1	1	yes	characteristic
134	C₄×Dic₁₃	C₂×D₄	1	1	yes	characteristic
135	C₄×Dic₁₃	C₂×D₄	1	1	yes	characteristic
136	C₄×Dic₁₃	C₂×Q₈	1	1	yes	characteristic
137	C₄×Dic₁₃	C₂×Q₈	1	1	yes	characteristic
138	C₄×Dic₁₃	C₂×Q₈	1	1	yes	characteristic
139	C₄×Dic₁₃	C₂⁴	1	1	yes	characteristic
140	C₂×#1055	—	4	2	no	—
141	C₂×#1055	C₂²×C₄	1	2	yes	—
142	C₂×#1055	C₂²×C₄	1	2	yes	—
143	#2920	—	13	1	no	—
144	C₂×#431	—	13	1	no	—
145	C₂×#423	—	13	1	no	—
146	#1574	—	13	2	no	—
147	#1574	—	13	2	no	—
148	#1573	—	13	4	no	—
149	#1567	—	13	2	no	—
150	#1566	—	13	2	no	—
151	C₂³×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
152	C₂²×D₁₃	—	2	2	no	—
153	C₂²×D₁₃	—	2	2	no	—
154	C₂²×D₁₃	—	4	1	no	—
155	C₂²×D₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
156	C₂²×D₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
157	C₂×C₄×C₁₃	—	2	2	no	—
158	C₂×C₄×C₁₃	—	2	1	no	—
159	C₂×C₄×C₁₃	—	2	1	no	—
160	C₂×C₄×C₁₃	—	2	2	no	—
161	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
162	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
163	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
164	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
165	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
166	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
167	C₂×Dic₁₃	—	2	2	no	—
168	C₂×Dic₁₃	—	4	1	no	—
169	C₂×Dic₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
170	C₂×Dic₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
171	C₂×Dic₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
172	C₂×Dic₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
173	C₂×Dic₁₃	AGL(1,ℤ/8)	1	2	yes	—
174	C₂×Dic₁₃	#137	1	2	yes	—
175	C₂×Dic₁₃	C₂²×D₄	1	1	yes	characteristic
176	C₂×Dic₁₃	C₂²×Q₈	1	1	yes	characteristic
177	C₄×D₁₃	—	2	2	no	—
178	C₄×D₁₃	—	2	1	no	—
179	C₄×D₁₃	—	2	1	no	—
180	C₄×D₁₃	—	2	1	no	—
181	C₄×D₁₃	—	2	1	no	—
182	C₄×D₁₃	—	2	2	no	—
183	C₄×D₁₃	—	2	1	no	—
184	C₄×D₁₃	—	2	1	no	—
185	C₄×D₁₃	—	2	1	no	—
186	C₄×D₁₃	—	2	1	no	—
187	C₄×D₁₃	—	2	2	no	—
188	C₄×D₁₃	—	2	2	no	—
189	C₄×D₁₃	—	2	2	no	—
190	C₄×D₁₃	—	4	1	no	—
191	C₄×D₁₃	—	4	1	no	—
192	C₄×D₁₃	#108	1	4	yes	—
193	#1057	—	4	4	no	—
194	#1057	—	4	2	no	—
195	#1057	—	4	2	no	—
196	C₈×C₁₃	—	2	2	no	—
197	C₈×C₁₃	—	2	2	no	—
198	#1055	—	2	2	no	—
199	#1055	—	2	2	no	—
200	C₂²×M₁₆	—	26	1	no	—
201	C₂²×C₄²	—	13	1	no	—
202	#432	—	13	2	no	—
203	#432	—	26	1	no	—
204	#431	—	13	2	no	—
205	#431	—	13	1	no	—
206	#431	—	13	1	no	—
207	#431	—	13	1	no	—
208	#431	—	13	1	no	—
209	#431	—	13	2	no	—
210	#431	—	13	2	no	—
211	#431	—	26	1	no	—
212	#423	—	13	1	no	—
213	#423	—	13	2	no	—
214	#423	—	13	1	no	—
215	#423	—	13	2	no	—
216	#423	—	26	1	no	—
217	#423	—	26	1	no	—
218	C₂×C₄⋊C₈	—	13	1	no	—
219	C₂×C₄⋊C₈	—	13	2	no	—
220	C₂×C₄⋊C₈	—	26	1	no	—
221	C₂×C₄⋊C₈	#261	1	1	yes	characteristic
222	#407	—	26	1	no	—
223	C₂×C₂²⋊C₈	—	13	2	no	—
224	C₄×M₁₆	—	26	1	no	—
225	C₂×C₄×C₈	—	13	2	no	—
226	#335	—	13	4	no	—
227	#335	—	13	4	no	—
228	#334	—	13	4	no	—
229	#334	—	13	4	no	—
230	C₂²×C₁₃	—	2	1	no	—
231	C₂²×C₁₃	—	2	1	no	—
232	C₂²×C₁₃	#428	1	2	yes	—
233	C₂²×C₁₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
234	C₂×D₁₃	—	2	1	no	—
235	C₂×D₁₃	—	2	1	no	—
236	C₂×D₁₃	—	2	1	no	—
237	C₂×D₁₃	—	2	1	no	—
238	C₂×D₁₃	—	2	1	no	—
239	C₂×D₁₃	—	4	4	no	—
240	C₂×D₁₃	C₂×#108	1	2	yes	—
241	C₄×C₁₃	—	2	1	no	—
242	C₄×C₁₃	—	2	1	no	—
243	C₄×C₁₃	—	2	1	no	—
244	C₄×C₁₃	—	2	1	no	—
245	C₄×C₁₃	C₂×#108	1	2	yes	—
246	C₄×C₁₃	#568	1	1	yes	characteristic
247	C₄×C₁₃	#568	1	1	yes	characteristic
248	Dic₁₃	—	2	1	no	—
249	Dic₁₃	—	2	1	no	—
250	Dic₁₃	—	2	1	no	—
251	Dic₁₃	#428	1	2	yes	—
252	Dic₁₃	C₂×#108	1	2	yes	—
253	Dic₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
254	Dic₁₃	C₂×#137	1	1	yes	characteristic
255	C₂³×C₄	—	13	1	no	—
256	C₂³×C₄	—	13	1	no	—
257	C₂³×C₄	—	13	1	no	—
258	C₂×M₁₆	—	26	2	no	—
259	C₂×M₁₆	—	26	2	no	—
260	C₂×M₁₆	—	26	1	no	—
261	C₂×M₁₆	—	26	1	no	—
262	C₂×M₁₆	—	52	4	no	—
263	C₂²×C₈	—	13	2	no	—
264	C₂²×C₈	—	26	2	no	—
265	C₂²×C₈	C₂×#261	1	2	yes	—
266	C₂×C₄²	—	13	1	no	—
267	C₂×C₄²	—	13	1	no	—
268	C₂×C₄²	—	13	1	no	—
269	C₂×C₄²	—	13	1	no	—
270	C₂×C₄²	—	13	1	no	—
271	C₂×C₄²	—	13	1	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	C₂×#261	1	1	yes	characteristic
278	C₄⋊C₈	—	13	2	no	—
279	C₄⋊C₈	—	13	4	no	—
280	C₄⋊C₈	—	13	2	no	—
281	C₄⋊C₈	—	13	2	no	—
282	C₄⋊C₈	—	13	1	no	—
283	C₄⋊C₈	—	13	1	no	—
284	C₄⋊C₈	—	26	2	no	—
285	C₄⋊C₈	—	26	2	no	—
286	C₄⋊C₈	—	26	2	no	—
287	C₄⋊C₈	—	26	1	no	—
288	C₄⋊C₈	—	26	1	no	—
289	C₄⋊C₈	C₂×#261	1	2	yes	—
290	C₄⋊C₈	C₂×#261	1	1	yes	characteristic
291	C₄⋊C₈	C₂×#261	1	1	yes	characteristic
292	C₂²⋊C₈	—	13	2	no	—
293	C₂²⋊C₈	—	13	2	no	—
294	C₂²⋊C₈	—	13	2	no	—
295	C₂²⋊C₈	—	13	2	no	—
296	C₂²⋊C₈	—	26	2	no	—
297	C₂²⋊C₈	—	26	2	no	—
298	#97	—	26	2	no	—
299	C₄×C₈	—	13	2	no	—
300	C₄×C₈	—	13	2	no	—
301	C₄×C₈	—	13	2	no	—
302	C₄×C₈	—	13	2	no	—
303	C₄×C₈	—	26	2	no	—
304	C₂×C₁₃	—	2	2	no	—
305	C₂×C₁₃	#2905	1	1	yes	characteristic
306	C₂×C₁₃	C₂×#428	1	1	yes	characteristic
307	C₂×C₁₃	C₂²×#108	1	1	yes	characteristic
308	D₁₃	—	2	2	no	—
309	D₁₃	—	4	1	no	—
310	C₂⁴	—	13	1	no	—
311	C₂²×C₄	—	13	1	no	—
312	C₂²×C₄	—	13	1	no	—
313	C₂²×C₄	—	13	1	no	—
314	C₂²×C₄	—	13	1	no	—
315	C₂²×C₄	—	13	1	no	—
316	C₂²×C₄	—	13	1	no	—
317	C₂²×C₄	—	13	1	no	—
318	C₂²×C₄	—	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	—	26	2	no	—
327	C₂²×C₄	—	26	2	no	—
328	C₂²×C₄	—	26	4	no	—
329	C₂²×C₄	—	52	1	no	—
330	C₂²×C₄	—	52	1	no	—
331	C₂²×C₄	C₄⋊#261	1	1	yes	characteristic
332	C₂²×C₄	C₄⋊#261	1	1	yes	characteristic
333	C₂²×C₄	C₂²×#261	1	1	yes	characteristic
334	M₁₆	—	52	4	no	—
335	M₁₆	—	52	2	no	—
336	M₁₆	—	52	2	no	—
337	M₁₆	—	52	4	no	—
338	C₂×C₈	—	4	2	no	—
339	C₂×C₈	—	13	2	no	—
340	C₂×C₈	—	13	2	no	—
341	C₂×C₈	—	26	2	no	—
342	C₂×C₈	—	26	2	no	—
343	C₂×C₈	—	26	4	no	—
344	C₂×C₈	—	52	2	no	—
345	C₂×C₈	—	52	4	no	—
346	C₂×C₈	C₂²×#261	1	2	yes	—
347	C₂×C₈	C₂²×#261	1	2	yes	—
348	C₄²	—	13	1	no	—
349	C₄²	—	13	1	no	—
350	C₄²	—	13	1	no	—
351	C₄²	—	13	1	no	—
352	C₄²	—	13	1	no	—
353	C₄²	—	13	1	no	—
354	C₄²	—	13	1	no	—
355	C₄²	—	13	1	no	—
356	C₄²	—	13	1	no	—
357	C₄²	—	13	1	no	—
358	C₄²	—	13	1	no	—
359	C₄²	—	13	1	no	—
360	C₄²	C₄⋊#261	1	1	yes	characteristic
361	C₄²	C₄⋊#261	1	1	yes	characteristic
362	C₄²	C₂²×#261	1	1	yes	characteristic
363	C₄²	C₂²×#261	1	1	yes	characteristic
364	C₁₃	#17817	1	1	yes	characteristic, complemented, Sylow
365	C₂³	—	13	1	no	—
366	C₂³	—	13	1	no	—
367	C₂³	—	26	2	no	—
368	C₂³	—	26	2	no	—
369	C₂³	—	52	1	no	—
370	C₂³	C₂×C₄⋊#261	1	1	yes	characteristic
371	C₂×C₄	—	2	2	no	—
372	C₂×C₄	—	2	2	no	—
373	C₂×C₄	—	2	1	no	—
374	C₂×C₄	—	2	1	no	—
375	C₂×C₄	—	13	2	no	—
376	C₂×C₄	—	13	2	no	—
377	C₂×C₄	—	13	1	no	—
378	C₂×C₄	—	13	1	no	—
379	C₂×C₄	—	13	1	no	—
380	C₂×C₄	—	13	4	no	—
381	C₂×C₄	—	13	1	no	—
382	C₂×C₄	—	13	1	no	—
383	C₂×C₄	—	13	1	no	—
384	C₂×C₄	—	26	1	no	—
385	C₂×C₄	—	26	1	no	—
386	C₂×C₄	—	26	1	no	—
387	C₂×C₄	—	26	1	no	—
388	C₂×C₄	—	26	2	no	—
389	C₂×C₄	—	26	2	no	—
390	C₂×C₄	—	26	2	no	—
391	C₂×C₄	—	26	2	no	—
392	C₂×C₄	—	26	2	no	—
393	C₂×C₄	—	26	2	no	—
394	C₂×C₄	—	26	1	no	—
395	C₂×C₄	—	26	1	no	—
396	C₂×C₄	—	26	1	no	—
397	C₂×C₄	—	26	1	no	—
398	C₂×C₄	—	52	1	no	—
399	C₂×C₄	—	52	1	no	—
400	C₂×C₄	—	52	1	no	—
401	C₂×C₄	C₂×C₄⋊#261	1	1	yes	characteristic
402	C₂×C₄	C₂×C₄⋊#261	1	1	yes	characteristic
403	C₂×C₄	C₂×C₄⋊#261	1	1	yes	characteristic
404	C₂×C₄	C₂×C₄⋊#261	1	1	yes	characteristic
405	C₂×C₄	C₂×C₄⋊#261	1	1	yes	characteristic
406	C₂×C₄	C₂³×#261	1	1	yes	characteristic
407	C₈	—	2	2	no	—
408	C₈	—	2	2	no	—
409	C₈	—	26	2	no	—
410	C₈	—	26	2	no	—
411	C₈	—	52	4	no	—
412	C₈	—	52	2	no	—
413	C₈	—	52	2	no	—
414	C₂²	—	2	1	no	—
415	C₂²	—	2	1	no	—
416	C₂²	—	13	2	no	—
417	C₂²	—	26	1	no	—
418	C₂²	—	26	1	no	—
419	C₂²	—	26	1	no	—
420	C₂²	—	26	1	no	—
421	C₂²	—	26	1	no	—
422	C₂²	—	52	4	no	—
423	C₂²	#11719098	1	2	yes	—
424	C₂²	C₂²×C₄⋊#261	1	1	yes	characteristic
425	C₄	—	2	1	no	—
426	C₄	—	2	1	no	—
427	C₄	—	2	1	no	—
428	C₄	—	2	1	no	—
429	C₄	—	13	1	no	—
430	C₄	—	13	1	no	—
431	C₄	—	13	2	no	—
432	C₄	—	13	2	no	—
433	C₄	—	26	1	no	—
434	C₄	—	26	1	no	—
435	C₄	—	26	1	no	—
436	C₄	D₁₃⋊#108	1	2	yes	—
437	C₄	#11719621	1	1	yes	characteristic
438	C₄	#11719625	1	1	yes	characteristic
439	C₂	—	2	2	no	—
440	C₂	—	26	2	no	—
441	C₂	—	52	1	no	—
442	C₂	#13131480	1	1	yes	characteristic
443	C₂	C₂×#11719098	1	1	yes	characteristic
444	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	C₂×C₁₃×C₄⋊C₈	C₄
socle	C₂²×C₁₃	C₂²×C₄⋊C₄
prime radical	C₂³×D₁₃	C₄⋊C₄
cosocle	C₄×Dic₁₃	C₂⁴
hypercenter	C₂×C₄⋊C₈	#261
hypocenter	C₁₃	#17817
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₂×C₄⋊C₈

Complements

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

N	H ≅ G/N	type
3. #13130414	C₂	semidirect
4. #13130413	C₂	semidirect
5. #13130410	C₂	semidirect
6. #13130393	C₂	semidirect
7. #13130390	C₂	semidirect
35. #11718256	C₂²	semidirect
36. #11718255	C₂²	semidirect
37. #11718254	C₂²	semidirect
38. #11718253	C₂²	semidirect
364. C₁₃	#17817	semidirect

Maximal subgroups

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

subgroup	index
#13131514	2
D₁₃⋊#423	2
#13130414	2
#13130413	2
#13130410	2
#13130393	2
#13130390	2
C₂×#11718494	2
#17817	13