Subgroups — #15755601

Order 3328.

708 conjugacy classes of subgroups.

The subgroup lattice has 490 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#88147	C₂	1	1	yes	maximal, characteristic
2	#13114987	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×#88054	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#11718051	C₂	1	1	yes	maximal, characteristic
5	C₂×#11718075	C₂	1	1	yes	maximal, characteristic
6	#13112677	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#1279	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#88147	C₄	1	1	yes	characteristic
9	C₂×#88147	C₄	1	1	yes	characteristic
10	C₂×C₄×D₅₂	C₂²	1	1	yes	characteristic
11	C₂×C₄²×D₁₃	—	2	1	no	—
12	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
13	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
14	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
15	C₂×#88054	—	2	1	no	—
16	C₂×#88054	—	2	1	no	—
17	C₂×#88054	—	2	1	no	—
18	C₄⋊C₄×Dic₁₃	C₄	1	1	yes	characteristic
19	C₄⋊C₄×Dic₁₃	C₄	1	1	yes	characteristic
20	C₄×#6103	—	2	1	no	—
21	C₄²×Dic₁₃	C₂²	1	1	yes	characteristic
22	C₂×C₄⋊#1055	C₂²	1	1	yes	characteristic
23	C₂×C₄×#1055	C₂²	1	1	yes	characteristic
24	#11718327	—	2	1	no	—
25	#11718327	—	2	1	no	—
26	#11718142	—	2	1	no	—
27	#11718075	—	2	2	no	—
28	#11718051	—	2	2	no	—
29	C₂²×D₅₂	C₂×C₄	1	1	yes	characteristic
30	C₂²×C₄×D₁₃	—	2	1	no	—
31	C₂²×C₄×D₁₃	—	2	1	no	—
32	C₂²×C₄×D₁₃	—	2	1	no	—
33	C₂²×C₈×C₁₃	—	2	1	no	—
34	C₂²×C₈×C₁₃	—	2	1	no	—
35	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
36	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
37	C₂×C₄²×C₁₃	—	2	1	no	—
38	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
39	C₂×#6103	—	2	1	no	—
40	C₂×#6103	—	2	1	no	—
41	C₂×#6103	—	2	1	no	—
42	C₂×C₄⋊Dic₁₃	C₂×C₄	1	1	yes	characteristic
43	C₂×C₄×Dic₁₃	—	2	1	no	—
44	C₂×C₄×Dic₁₃	—	2	1	no	—
45	C₂×C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
46	C₂×C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
47	C₂×C₄×Dic₁₃	D₄	1	1	yes	characteristic
48	C₂×C₄×Dic₁₃	D₄	1	1	yes	characteristic
49	C₂×C₄×Dic₁₃	D₄	1	1	yes	characteristic
50	C₂×C₄×Dic₁₃	D₄	1	1	yes	characteristic
51	C₂²×#1055	—	2	1	no	—
52	C₂²×#1055	—	2	1	no	—
53	#88147	—	2	2	no	—
54	#88147	—	2	2	no	—
55	#88147	—	2	2	no	—
56	#88147	C₈	1	4	yes	complemented
57	C₄×D₅₂	—	2	1	no	—
58	C₄×D₅₂	—	2	1	no	—
59	C₄×D₅₂	D₄	1	2	yes	—
60	C₄×D₅₂	Q₈	1	2	yes	—
61	C₄²×D₁₃	—	4	2	no	—
62	C₄²×D₁₃	—	4	2	no	—
63	C₁₃×C₄⋊C₈	—	2	1	no	—
64	C₁₃×C₄⋊C₈	—	2	1	no	—
65	C₄×C₈×C₁₃	—	2	1	no	—
66	C₄×C₈×C₁₃	—	2	1	no	—
67	C₁₃×#95	—	2	1	no	—
68	#88071	—	2	1	no	—
69	#88071	—	2	1	no	—
70	#88054	—	2	4	no	—
71	#88054	—	4	2	no	—
72	#88054	—	4	2	no	—
73	C₄⋊#1055	—	2	1	no	—
74	C₄⋊#1055	—	2	1	no	—
75	C₄×#1055	—	2	1	no	—
76	C₄×#1055	—	2	1	no	—
77	#8563	—	13	1	no	maximal, Sylow
78	C₂³×D₁₃	—	2	1	no	—
79	C₂²×C₄×C₁₃	—	2	1	no	—
80	C₂²×C₄×C₁₃	—	2	1	no	—
81	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
82	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
83	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
84	C₂²×Dic₁₃	—	2	1	no	—
85	C₂²×Dic₁₃	C₂²⋊C₄	1	1	yes	characteristic
86	C₂²×Dic₁₃	C₂²⋊C₄	1	1	yes	characteristic
87	C₂²×Dic₁₃	C₂²⋊C₄	1	1	yes	characteristic
88	C₂²×Dic₁₃	C₂²⋊C₄	1	1	yes	characteristic
89	C₂×D₅₂	—	2	1	no	—
90	C₂×D₅₂	—	2	1	no	—
91	C₂×D₅₂	—	2	1	no	—
92	C₂×D₅₂	C₄⋊C₄	1	2	yes	—
93	C₂×D₅₂	C₂×C₈	1	2	yes	—
94	C₂×D₅₂	M₁₆	1	2	yes	—
95	C₂×C₄×D₁₃	—	2	4	no	—
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	2	no	—
100	C₂×C₄×D₁₃	—	4	1	no	—
101	C₂×C₄×D₁₃	—	4	1	no	—
102	C₂×C₄×D₁₃	—	4	1	no	—
103	C₂×C₄×D₁₃	—	4	1	no	—
104	C₂×C₄×D₁₃	—	4	2	no	—
105	C₂×C₄×D₁₃	—	4	2	no	—
106	C₂×C₄×D₁₃	—	4	2	no	—
107	C₂×C₈×C₁₃	—	2	2	no	—
108	C₂×C₈×C₁₃	—	4	1	no	—
109	C₂×C₈×C₁₃	—	4	1	no	—
110	C₂×C₈×C₁₃	—	4	1	no	—
111	C₂×C₈×C₁₃	—	4	1	no	—
112	C₂×C₈×C₁₃	—	4	1	no	—
113	C₁₃×C₄⋊C₄	—	2	1	no	—
114	C₁₃×C₄⋊C₄	—	2	1	no	—
115	C₁₃×C₄⋊C₄	C₂×C₈	1	2	yes	—
116	C₁₃×C₄⋊C₄	M₁₆	1	2	yes	—
117	C₄²×C₁₃	—	4	1	no	—
118	C₄²×C₁₃	—	4	1	no	—
119	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
120	C₄²×C₁₃	C₂×Q₈	1	1	yes	characteristic
121	C₄²×C₁₃	#41	1	1	yes	characteristic
122	C₄²×C₁₃	#41	1	1	yes	characteristic
123	#6103	—	2	4	no	—
124	#6103	—	2	2	no	—
125	#6103	—	2	2	no	—
126	#6103	—	2	4	no	—
127	C₄⋊Dic₁₃	—	2	1	no	—
128	C₄⋊Dic₁₃	C₄⋊C₄	1	2	yes	—
129	C₄×Dic₁₃	—	2	1	no	—
130	C₄×Dic₁₃	—	2	1	no	—
131	C₄×Dic₁₃	—	2	1	no	—
132	C₄×Dic₁₃	—	2	1	no	—
133	C₄×Dic₁₃	—	2	2	no	—
134	C₄×Dic₁₃	—	4	1	no	—
135	C₄×Dic₁₃	—	4	2	no	—
136	C₄×Dic₁₃	—	4	2	no	—
137	C₄×Dic₁₃	C₂×C₈	1	2	yes	—
138	C₄×Dic₁₃	M₁₆	1	2	yes	—
139	C₄×Dic₁₃	D₈	1	2	yes	—
140	C₄×Dic₁₃	SD₁₆	1	2	yes	—
141	C₂×#1055	—	2	2	no	—
142	C₂×#1055	—	4	1	no	—
143	C₂×#1055	—	4	1	no	—
144	C₂×#1055	—	4	1	no	—
145	C₂×#1055	—	4	1	no	—
146	C₂×#1055	—	4	1	no	—
147	C₄²×D₄	—	13	1	no	—
148	#1842	—	13	1	no	—
149	C₄×C₄⋊C₈	—	13	1	no	—
150	C₂×D₄⋊C₈	—	13	1	no	—
151	C₂×D₄⋊C₈	—	13	1	no	—
152	#1279	—	13	1	no	—
153	#1279	D₁₃	1	1	yes	characteristic, complemented
154	C₂³×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
155	C₂²×D₁₃	—	2	2	no	—
156	C₂²×D₁₃	—	2	2	no	—
157	C₂²×D₁₃	—	2	2	no	—
158	C₂²×D₁₃	—	4	1	no	—
159	C₂²×D₁₃	—	4	1	no	—
160	C₂²×D₁₃	—	4	1	no	—
161	C₂²×D₁₃	—	4	1	no	—
162	C₂×C₄×C₁₃	—	2	1	no	—
163	C₂×C₄×C₁₃	—	2	1	no	—
164	C₂×C₄×C₁₃	—	2	2	no	—
165	C₂×C₄×C₁₃	—	2	2	no	—
166	C₂×C₄×C₁₃	—	4	1	no	—
167	C₂×C₄×C₁₃	—	4	1	no	—
168	C₂×C₄×C₁₃	—	4	1	no	—
169	C₂×C₄×C₁₃	—	4	1	no	—
170	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
171	C₂×C₄×C₁₃	#117	1	1	yes	characteristic
172	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
173	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
174	C₂×C₄×C₁₃	C₂²⋊Q₈	1	1	yes	characteristic
175	C₂×C₄×C₁₃	C₂²⋊Q₈	1	1	yes	characteristic
176	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
177	C₂×C₄×C₁₃	C₂×M₁₆	1	1	yes	characteristic
178	C₂×C₄×C₁₃	C₂×M₁₆	1	1	yes	characteristic
179	C₂×C₄×C₁₃	C₂×M₁₆	1	1	yes	characteristic
180	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
181	C₂×C₄×C₁₃	C₂×SD₁₆	1	1	yes	characteristic
182	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	1	yes	characteristic
183	C₂×C₄×C₁₃	#137	1	1	yes	characteristic
184	C₂×Dic₁₃	—	2	1	no	—
185	C₂×Dic₁₃	—	2	1	no	—
186	C₂×Dic₁₃	—	2	1	no	—
187	C₂×Dic₁₃	—	2	1	no	—
188	C₂×Dic₁₃	—	2	2	no	—
189	C₂×Dic₁₃	—	2	1	no	—
190	C₂×Dic₁₃	—	2	1	no	—
191	C₂×Dic₁₃	—	2	1	no	—
192	C₂×Dic₁₃	—	4	1	no	—
193	C₂×Dic₁₃	—	4	1	no	—
194	C₂×Dic₁₃	C₂²⋊C₈	1	2	yes	—
195	C₂×Dic₁₃	C₂²⋊C₈	1	2	yes	—
196	C₂×Dic₁₃	#102	1	2	yes	—
197	C₂×Dic₁₃	#102	1	2	yes	—
198	C₂×Dic₁₃	#104	1	2	yes	—
199	D₅₂	—	2	2	no	—
200	D₅₂	—	2	2	no	—
201	D₅₂	—	2	2	no	—
202	D₅₂	C₄⋊C₈	1	4	yes	complemented
203	C₄×D₁₃	—	4	8	no	—
204	C₄×D₁₃	—	4	2	no	—
205	C₄×D₁₃	—	4	2	no	—
206	C₄×D₁₃	—	4	2	no	—
207	C₄×D₁₃	—	4	2	no	—
208	C₄×D₁₃	—	4	8	no	—
209	C₈×C₁₃	—	4	2	no	—
210	C₈×C₁₃	—	8	1	no	—
211	#1055	—	4	2	no	—
212	#1055	—	8	1	no	—
213	C₂×C₄×D₄	—	13	1	no	—
214	C₂×C₄×D₄	—	13	1	no	—
215	C₂×C₄×D₄	—	13	1	no	—
216	C₂²×C₄²	—	26	1	no	—
217	C₂×C₄⋊C₈	—	13	1	no	—
218	C₂×C₄⋊C₈	—	26	1	no	—
219	C₂×C₄⋊C₈	—	26	1	no	—
220	C₂×C₄⋊C₈	—	26	1	no	—
221	C₂×C₄⋊C₈	C₂×D₁₃	1	1	yes	characteristic
222	C₂×C₄×C₈	—	13	1	no	—
223	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
224	C₄×C₄⋊C₄	—	13	1	no	—
225	C₄×C₄⋊C₄	—	13	1	no	—
226	C₄×C₄⋊C₄	C₂×D₁₃	1	1	yes	characteristic
227	C₄×C₂²⋊C₄	—	26	1	no	—
228	C₄×C₂²⋊C₄	—	26	1	no	—
229	C₄×C₂²⋊C₄	—	26	1	no	—
230	C₄³	—	13	1	no	—
231	#336	—	26	1	no	—
232	D₄⋊C₈	—	26	2	no	—
233	D₄⋊C₈	—	26	2	no	—
234	C₂²×C₁₃	#380	1	1	yes	characteristic
235	C₂²×C₁₃	C₂×C₂²⋊C₈	1	1	yes	characteristic
236	C₂²×C₁₃	#407	1	1	yes	characteristic
237	C₂²×C₁₃	C₂×#102	1	1	yes	characteristic
238	C₂²×C₁₃	#417	1	1	yes	characteristic
239	C₂²×C₁₃	C₂×#104	1	1	yes	characteristic
240	C₂²×C₁₃	#421	1	1	yes	characteristic
241	C₂×D₁₃	—	2	4	no	—
242	C₂×D₁₃	—	4	2	no	—
243	C₂×D₁₃	—	4	2	no	—
244	C₂×D₁₃	—	4	2	no	—
245	C₂×D₁₃	—	4	2	no	—
246	C₂×D₁₃	—	4	2	no	—
247	C₂×D₁₃	—	4	2	no	—
248	C₄×C₁₃	—	2	1	no	—
249	C₄×C₁₃	—	2	1	no	—
250	C₄×C₁₃	—	4	2	no	—
251	C₄×C₁₃	—	4	2	no	—
252	C₄×C₁₃	C₂×C₄⋊C₈	1	1	yes	characteristic
253	C₄×C₁₃	#423	1	1	yes	characteristic
254	C₄×C₁₃	#431	1	1	yes	characteristic
255	C₄×C₁₃	#432	1	1	yes	characteristic
256	C₄×C₁₃	#459	1	1	yes	characteristic
257	C₄×C₁₃	#461	1	1	yes	characteristic
258	C₄×C₁₃	#474	1	1	yes	characteristic
259	C₄×C₁₃	#476	1	1	yes	characteristic
260	Dic₁₃	—	2	2	no	—
261	Dic₁₃	—	2	2	no	—
262	Dic₁₃	—	4	2	no	—
263	Dic₁₃	—	4	1	no	—
264	Dic₁₃	D₄⋊C₈	1	4	yes	complemented
265	C₂²×D₄	—	13	1	no	—
266	C₂³×C₄	—	26	1	no	—
267	C₂³×C₄	—	26	1	no	—
268	C₂³×C₄	—	26	1	no	—
269	C₂²×C₈	—	2	1	no	—
270	C₂²×C₈	—	2	1	no	—
271	C₂²×C₈	—	26	1	no	—
272	C₂²×C₈	—	26	1	no	—
273	C₄×D₄	—	13	4	no	—
274	C₄×D₄	—	13	2	no	—
275	C₄×D₄	—	13	2	no	—
276	C₄×D₄	—	26	2	no	—
277	C₄×D₄	—	26	2	no	—
278	C₄×D₄	—	26	2	no	—
279	C₄×D₄	—	26	1	no	—
280	C₄×D₄	—	26	1	no	—
281	C₂×C₄⋊C₄	—	13	1	no	—
282	C₂×C₄⋊C₄	C₄×D₁₃	1	1	yes	characteristic
283	C₂×C₄⋊C₄	C₄×D₁₃	1	1	yes	characteristic
284	C₂×C₂²⋊C₄	—	26	1	no	—
285	C₂×C₂²⋊C₄	—	26	1	no	—
286	C₂×C₂²⋊C₄	—	26	1	no	—
287	C₂×C₄²	—	2	1	no	—
288	C₂×C₄²	—	13	1	no	—
289	C₂×C₄²	—	13	1	no	—
290	C₂×C₄²	—	13	1	no	—
291	C₂×C₄²	—	13	1	no	—
292	C₂×C₄²	—	13	1	no	—
293	C₂×C₄²	—	13	1	no	—
294	C₂×C₄²	—	26	1	no	—
295	C₂×C₄²	—	26	1	no	—
296	C₂×C₄²	—	52	2	no	—
297	C₂×C₄²	—	52	2	no	—
298	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
299	C₄⋊C₈	—	2	1	no	—
300	C₄⋊C₈	—	2	1	no	—
301	C₄⋊C₈	—	26	4	no	—
302	C₄⋊C₈	—	26	1	no	—
303	C₄⋊C₈	—	26	1	no	—
304	C₄⋊C₈	—	52	2	no	—
305	C₄⋊C₈	—	52	2	no	—
306	C₄×C₈	—	2	1	no	—
307	C₄×C₈	—	2	1	no	—
308	C₄×C₈	—	26	1	no	—
309	C₄×C₈	—	26	1	no	—
310	#95	—	2	1	no	—
311	#95	—	26	1	no	—
312	#95	—	26	1	no	—
313	C₂×C₁₃	C₂×D₄⋊C₈	1	1	yes	characteristic
314	C₂×C₁₃	#1477	1	1	yes	characteristic
315	C₂×C₁₃	#1486	1	1	yes	characteristic
316	C₂×C₁₃	#1489	1	1	yes	characteristic
317	C₂×C₁₃	#1797	1	1	yes	characteristic
318	C₂×C₁₃	#1802	1	1	yes	characteristic
319	C₂×C₁₃	#1806	1	1	yes	characteristic
320	D₁₃	—	4	4	no	—
321	C₂⁴	—	26	1	no	—
322	C₂×D₄	—	13	2	no	—
323	C₂×D₄	—	13	2	no	—
324	C₂×D₄	—	13	2	no	—
325	C₂×D₄	—	26	1	no	—
326	C₂×D₄	—	26	1	no	—
327	C₂×D₄	—	26	1	no	—
328	C₂²×C₄	—	2	1	no	—
329	C₂²×C₄	—	2	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	4	no	—
335	C₂²×C₄	—	26	4	no	—
336	C₂²×C₄	—	26	1	no	—
337	C₂²×C₄	—	26	2	no	—
338	C₂²×C₄	—	26	2	no	—
339	C₂²×C₄	—	52	2	no	—
340	C₂²×C₄	—	52	2	no	—
341	C₂²×C₄	—	52	2	no	—
342	C₂²×C₄	—	52	2	no	—
343	C₂²×C₄	—	52	1	no	—
344	C₂²×C₄	—	52	1	no	—
345	C₂²×C₄	—	52	1	no	—
346	C₂²×C₄	—	52	1	no	—
347	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
348	C₂²×C₄	D₄×D₁₃	1	1	yes	characteristic
349	C₂²×C₄	D₄×D₁₃	1	1	yes	characteristic
350	C₂×C₈	—	2	2	no	—
351	C₂×C₈	—	4	1	no	—
352	C₂×C₈	—	4	1	no	—
353	C₂×C₈	—	4	1	no	—
354	C₂×C₈	—	4	1	no	—
355	C₂×C₈	—	4	1	no	—
356	C₂×C₈	—	26	2	no	—
357	C₂×C₈	—	52	1	no	—
358	C₂×C₈	—	52	1	no	—
359	C₂×C₈	—	52	1	no	—
360	C₂×C₈	—	52	1	no	—
361	C₂×C₈	—	52	1	no	—
362	C₄⋊C₄	—	2	1	no	—
363	C₄⋊C₄	—	2	1	no	—
364	C₄⋊C₄	—	13	2	no	—
365	C₄⋊C₄	—	26	1	no	—
366	C₄⋊C₄	C₈×D₁₃	1	2	yes	—
367	C₄⋊C₄	#6094	1	2	yes	—
368	C₂²⋊C₄	—	26	4	no	—
369	C₂²⋊C₄	—	26	4	no	—
370	C₂²⋊C₄	—	26	2	no	—
371	C₂²⋊C₄	—	26	2	no	—
372	C₄²	—	4	1	no	—
373	C₄²	—	4	1	no	—
374	C₄²	—	13	2	no	—
375	C₄²	—	13	2	no	—
376	C₄²	—	13	2	no	—
377	C₄²	—	13	2	no	—
378	C₄²	—	26	2	no	—
379	C₄²	—	26	1	no	—
380	C₄²	—	26	1	no	—
381	C₄²	—	26	1	no	—
382	C₄²	—	26	1	no	—
383	C₄²	—	52	1	no	—
384	C₄²	—	52	2	no	—
385	C₄²	—	52	2	no	—
386	C₄²	#6127	1	1	yes	characteristic
387	C₄²	#6127	1	1	yes	characteristic
388	C₄²	D₄×D₁₃	1	1	yes	characteristic
389	C₄²	Q₈×D₁₃	1	1	yes	characteristic
390	C₁₃	#8563	1	1	yes	characteristic, complemented, Sylow
391	C₂³	—	26	2	no	—
392	C₂³	—	26	2	no	—
393	C₂³	—	26	2	no	—
394	C₂³	—	52	1	no	—
395	C₂³	—	52	1	no	—
396	C₂³	—	52	1	no	—
397	C₂³	—	52	1	no	—
398	C₂³	C₂²⋊C₄×D₁₃	1	1	yes	characteristic
399	D₄	—	13	4	no	—
400	D₄	—	26	2	no	—
401	D₄	—	26	2	no	—
402	D₄	—	26	2	no	—
403	C₂×C₄	—	2	1	no	—
404	C₂×C₄	—	2	1	no	—
405	C₂×C₄	—	2	2	no	—
406	C₂×C₄	—	2	2	no	—
407	C₂×C₄	—	4	1	no	—
408	C₂×C₄	—	4	1	no	—
409	C₂×C₄	—	4	1	no	—
410	C₂×C₄	—	4	1	no	—
411	C₂×C₄	—	13	2	no	—
412	C₂×C₄	—	13	2	no	—
413	C₂×C₄	—	13	2	no	—
414	C₂×C₄	—	13	2	no	—
415	C₂×C₄	—	13	2	no	—
416	C₂×C₄	—	26	1	no	—
417	C₂×C₄	—	26	1	no	—
418	C₂×C₄	—	26	1	no	—
419	C₂×C₄	—	26	1	no	—
420	C₂×C₄	—	26	1	no	—
421	C₂×C₄	—	26	1	no	—
422	C₂×C₄	—	26	2	no	—
423	C₂×C₄	—	26	1	no	—
424	C₂×C₄	—	52	8	no	—
425	C₂×C₄	—	52	8	no	—
426	C₂×C₄	—	52	1	no	—
427	C₂×C₄	—	52	1	no	—
428	C₂×C₄	—	52	2	no	—
429	C₂×C₄	—	52	2	no	—
430	C₂×C₄	—	52	2	no	—
431	C₂×C₄	—	52	2	no	—
432	C₂×C₄	#88126	1	1	yes	characteristic
433	C₂×C₄	#88138	1	1	yes	characteristic
434	C₂×C₄	#88138	1	1	yes	characteristic
435	C₂×C₄	C₄⋊C₄×D₁₃	1	1	yes	characteristic
436	C₂×C₄	#88150	1	1	yes	characteristic
437	C₂×C₄	#88150	1	1	yes	characteristic
438	C₂×C₄	C₂×C₈×D₁₃	1	1	yes	characteristic
439	C₂×C₄	C₂×#6094	1	1	yes	characteristic
440	C₂×C₄	M₁₆×D₁₃	1	1	yes	characteristic
441	C₂×C₄	M₁₆×D₁₃	1	1	yes	characteristic
442	C₂×C₄	D₈×D₁₃	1	1	yes	characteristic
443	C₂×C₄	SD₁₆×D₁₃	1	1	yes	characteristic
444	C₂×C₄	#88168	1	1	yes	characteristic
445	C₂×C₄	#88172	1	1	yes	characteristic
446	C₈	—	4	2	no	—
447	C₈	—	8	1	no	—
448	C₈	—	52	2	no	—
449	C₈	—	104	1	no	—
450	C₂²	—	26	4	no	—
451	C₂²	—	52	2	no	—
452	C₂²	—	52	2	no	—
453	C₂²	—	52	2	no	—
454	C₂²	—	52	2	no	—
455	C₂²	—	52	2	no	—
456	C₂²	—	52	2	no	—
457	C₂²	#11718328	1	1	yes	characteristic
458	C₂²	D₁₃×C₂²⋊C₈	1	1	yes	characteristic
459	C₂²	#11718387	1	1	yes	characteristic
460	C₂²	D₁₃×#102	1	1	yes	characteristic
461	C₂²	#11718464	1	1	yes	characteristic
462	C₂²	D₁₃×#104	1	1	yes	characteristic
463	C₂²	#11718482	1	1	yes	characteristic
464	C₄	—	2	1	no	—
465	C₄	—	2	1	no	—
466	C₄	—	4	2	no	—
467	C₄	—	4	2	no	—
468	C₄	—	13	4	no	—
469	C₄	—	26	2	no	—
470	C₄	—	26	2	no	—
471	C₄	—	52	1	no	—
472	C₄	—	52	2	no	—
473	C₄	#11718346	1	1	yes	characteristic
474	C₄	#11718366	1	1	yes	characteristic
475	C₄	#11718447	1	1	yes	characteristic
476	C₄	#11718479	1	1	yes	characteristic
477	C₄	D₁₃×C₄⋊C₈	1	1	yes	characteristic
478	C₄	#11718498	1	1	yes	characteristic
479	C₄	#11718531	1	1	yes	characteristic
480	C₄	#11718551	1	1	yes	characteristic
481	C₂	—	52	4	no	—
482	C₂	D₁₃×D₄⋊C₈	1	1	yes	characteristic
483	C₂	#13113222	1	1	yes	characteristic
484	C₂	#13113259	1	1	yes	characteristic
485	C₂	#13113274	1	1	yes	characteristic
486	C₂	#13114815	1	1	yes	characteristic
487	C₂	#13114835	1	1	yes	characteristic
488	C₂	#13114855	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	D₄×D₁₃
commutator	C₂×C₄×C₁₃	C₂²×C₈
Frattini	C₂×C₄²	C₂²×D₁₃
Fitting	C₁₃×#1279	C₂
socle	C₂³×C₁₃	C₂×C₂²⋊C₄
prime radical	C₂²×D₅₂	C₂×C₄
cosocle	C₂×C₄²×C₁₃	C₂³
hypercenter	#1279	D₁₃
hypocenter	C₁₃	#8563
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄² ◁ #1279

Complements

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

N	H ≅ G/N	type
2. #13114987	C₂	semidirect
3. C₄×#88054	C₂	semidirect
6. #13112677	C₂	semidirect
7. C₁₃×#1279	C₂	semidirect
56. #88147	C₈	semidirect
153. #1279	D₁₃	semidirect
202. D₅₂	C₄⋊C₈	semidirect
264. Dic₁₃	D₄⋊C₈	semidirect
390. C₁₃	#8563	semidirect

Maximal subgroups

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

subgroup	index
C₄×#88147	2
#13114987	2
C₄×#88054	2
C₂×#11718051	2
C₂×#11718075	2
#13112677	2
C₁₃×#1279	2
#8563	13