Subgroups — D₁₃×#2155 #16015928

Order 3328.

658 conjugacy classes of subgroups.

The subgroup lattice has 478 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₁₃×M₃₂	C₂	1	1	yes	maximal, characteristic
2	C₂×D₁₃×#108	C₂	1	1	yes	maximal, characteristic
3	D₁₃×#427	C₂	1	1	yes	maximal, characteristic
4	#13116610	C₂	1	1	yes	maximal, characteristic, complemented
5	#13116609	C₂	1	1	yes	maximal, characteristic, complemented
6	#13116608	C₂	1	1	yes	maximal, characteristic, complemented
7	#13116607	C₂	1	4	yes	maximal, complemented
8	D₁₃×#365	C₂	1	4	yes	maximal, complemented
9	C₁₃×#2155	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×M₁₆×D₁₃	—	2	1	no	—
11	C₂²×C₈×D₁₃	C₂²	1	1	yes	characteristic
12	D₁₃×#117	—	2	1	no	—
13	C₂×C₁₃×M₃₂	C₂²	1	1	yes	characteristic
14	C₂×C₁₃×#108	C₂²	1	1	yes	characteristic
15	C₁₃×#427	C₂²	1	1	yes	characteristic
16	C₂×#88062	—	2	1	no	—
17	C₂×#88059	C₂²	1	1	yes	characteristic
18	#11718767	C₂²	1	1	yes	characteristic
19	C₂×#88052	C₂²	1	1	yes	characteristic
20	#11718659	—	2	1	no	—
21	D₁₃×M₃₂	C₄	1	2	yes	complemented
22	D₁₃×M₃₂	C₄	1	2	yes	complemented
23	D₁₃×M₃₂	C₂²	1	2	yes	—
24	D₁₃×M₃₂	C₂²	1	2	yes	—
25	C₂×#88038	C₄	1	2	yes	complemented
26	C₂×C₁₆×D₁₃	C₄	1	2	yes	complemented
27	D₁₃×#108	—	2	1	no	—
28	D₁₃×#108	—	2	1	no	—
29	D₁₃×#108	C₂²	1	2	yes	—
30	D₁₃×#108	C₂²	1	2	yes	—
31	#11718541	—	2	1	no	—
32	D₁₃×#107	—	2	1	no	—
33	#11718521	C₂²	1	2	yes	—
34	D₁₃×#106	C₂²	1	2	yes	—
35	C₁₃×#365	C₂²	1	4	yes	complemented
36	#11718105	C₂²	1	4	yes	complemented
37	#11718086	C₂²	1	4	yes	complemented
38	#11718079	C₂²	1	4	yes	complemented
39	C₂²×C₄×D₁₃	D₄	1	1	yes	characteristic
40	C₂×C₁₃×M₁₆	—	2	1	no	—
41	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
42	C₁₃×#117	—	2	1	no	—
43	#88180	—	2	1	no	—
44	C₂×#6099	—	2	1	no	—
45	C₂²×#1055	D₄	1	1	yes	characteristic
46	M₁₆×D₁₃	—	2	2	no	—
47	M₁₆×D₁₃	—	2	2	no	—
48	M₁₆×D₁₃	—	4	1	no	—
49	M₁₆×D₁₃	—	4	1	no	—
50	C₂×#6094	—	4	1	no	—
51	C₂×C₈×D₁₃	—	4	1	no	—
52	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
53	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
54	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
55	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
56	C₂×C₈×D₁₃	D₄	1	1	yes	characteristic
57	C₂×C₈×D₁₃	D₄	1	1	yes	characteristic
58	C₂×C₈×D₁₃	Q₈	1	1	yes	characteristic
59	C₂×C₈×D₁₃	Q₈	1	1	yes	characteristic
60	C₂×C₈×D₁₃	Q₈	1	1	yes	characteristic
61	C₂×C₈×D₁₃	Q₈	1	1	yes	characteristic
62	C₂×C₈×D₁₃	C₂³	1	1	yes	characteristic
63	C₂×C₈×D₁₃	C₂³	1	1	yes	characteristic
64	#88146	—	2	2	no	—
65	C₄⋊C₄×D₁₃	—	2	2	no	—
66	C₂²⋊C₄×D₁₃	—	4	1	no	—
67	#88131	—	4	1	no	—
68	#88126	—	4	1	no	—
69	C₄²×D₁₃	—	4	1	no	—
70	C₁₃×M₃₂	C₂×C₄	1	2	yes	complemented
71	C₁₃×M₃₂	C₂³	1	2	yes	—
72	C₂×C₁₃×C₁₆	C₂×C₄	1	2	yes	complemented
73	C₁₃×#108	—	2	1	no	—
74	C₁₃×#108	C₂³	1	2	yes	—
75	C₁₃×#107	—	2	1	no	—
76	C₁₃×#106	C₂³	1	2	yes	—
77	#88062	—	2	2	no	—
78	#88062	—	2	2	no	—
79	#88059	—	2	1	no	—
80	#88059	C₂³	1	2	yes	—
81	#88058	—	2	1	no	—
82	#88057	C₂³	1	2	yes	—
83	#88052	C₂×C₄	1	2	yes	complemented
84	#88052	C₂³	1	2	yes	—
85	C₂×#6090	C₂×C₄	1	2	yes	complemented
86	#88048	—	2	2	no	—
87	#88047	—	2	2	no	—
88	#88038	C₂×C₄	1	4	yes	—
89	#88038	C₂×C₄	1	4	yes	complemented
90	C₁₆×D₁₃	C₂×C₄	1	4	yes	—
91	C₁₆×D₁₃	C₂×C₄	1	4	yes	complemented
92	C₂×#2155	—	13	1	no	maximal, Sylow
93	C₂³×D₁₃	SD₁₆	1	1	yes	characteristic
94	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
95	C₂²×Dic₁₃	SD₁₆	1	1	yes	characteristic
96	C₂×C₄×D₁₃	—	4	2	no	—
97	C₂×C₄×D₁₃	C₄⋊C₄	1	1	yes	characteristic
98	C₂×C₄×D₁₃	C₄⋊C₄	1	1	yes	characteristic
99	C₂×C₄×D₁₃	C₄⋊C₄	1	1	yes	characteristic
100	C₂×C₄×D₁₃	C₄⋊C₄	1	1	yes	characteristic
101	C₂×C₄×D₁₃	SD₁₆	1	1	yes	characteristic
102	C₂×C₄×D₁₃	SD₁₆	1	1	yes	characteristic
103	C₂×C₄×D₁₃	SD₁₆	1	1	yes	characteristic
104	C₂×C₄×D₁₃	SD₁₆	1	1	yes	characteristic
105	C₂×C₄×D₁₃	SD₁₆	1	1	yes	characteristic
106	C₂×C₄×D₁₃	SD₁₆	1	1	yes	characteristic
107	C₂×C₄×D₁₃	C₂×D₄	1	1	yes	characteristic
108	C₂×C₄×D₁₃	C₂×D₄	1	1	yes	characteristic
109	C₁₃×M₁₆	—	2	2	no	—
110	C₁₃×M₁₆	—	4	1	no	—
111	C₂×C₈×C₁₃	—	4	1	no	—
112	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
113	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
114	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
115	C₂×C₈×C₁₃	C₂×Q₈	1	1	yes	characteristic
116	C₂×C₈×C₁₃	C₂×Q₈	1	1	yes	characteristic
117	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
118	C₁₃×C₄⋊C₄	—	2	2	no	—
119	C₁₃×C₂²⋊C₄	—	4	1	no	—
120	C₄²×C₁₃	—	4	1	no	—
121	C₂²⋊Dic₁₃	—	4	1	no	—
122	#6103	—	4	2	no	—
123	C₄⋊Dic₁₃	—	2	2	no	—
124	#6101	—	4	2	no	—
125	C₄×Dic₁₃	—	4	1	no	—
126	C₄×Dic₁₃	—	4	2	no	—
127	#6099	—	2	2	no	—
128	#6099	—	4	1	no	—
129	C₂×#1055	—	4	1	no	—
130	C₂×#1055	C₄⋊C₄	1	1	yes	characteristic
131	C₂×#1055	C₄⋊C₄	1	1	yes	characteristic
132	C₂×#1055	C₄⋊C₄	1	1	yes	characteristic
133	C₂×#1055	C₄⋊C₄	1	1	yes	characteristic
134	C₂×#1055	C₂×D₄	1	1	yes	characteristic
135	C₂×#1055	C₂×D₄	1	1	yes	characteristic
136	#6094	—	4	2	no	—
137	#6094	—	4	2	no	—
138	C₈×D₁₃	—	4	2	no	—
139	C₈×D₁₃	—	4	2	no	—
140	C₈×D₁₃	C₄⋊C₄	1	1	yes	characteristic
141	C₈×D₁₃	C₄⋊C₄	1	1	yes	characteristic
142	C₈×D₁₃	C₄⋊C₄	1	1	yes	characteristic
143	C₈×D₁₃	C₄⋊C₄	1	1	yes	characteristic
144	C₈×D₁₃	C₄⋊C₄	1	1	yes	characteristic
145	C₈×D₁₃	C₄⋊C₄	1	1	yes	characteristic
146	C₈×D₁₃	C₄⋊C₄	1	1	yes	characteristic
147	C₈×D₁₃	C₄⋊C₄	1	1	yes	characteristic
148	C₈×D₁₃	C₂²×C₄	1	1	yes	characteristic
149	C₈×D₁₃	C₂²×C₄	1	1	yes	characteristic
150	C₈×D₁₃	C₂²×C₄	1	1	yes	characteristic
151	C₈×D₁₃	C₂²×C₄	1	1	yes	characteristic
152	C₈×D₁₃	C₂×Q₈	1	1	yes	characteristic
153	C₈×D₁₃	C₂×Q₈	1	1	yes	characteristic
154	C₈×D₁₃	C₂×Q₈	1	1	yes	characteristic
155	C₈×D₁₃	C₂×Q₈	1	1	yes	characteristic
156	C₁₃×C₁₆	C₂²×C₄	1	4	yes	—
157	#6090	C₂²×C₄	1	4	yes	—
158	C₂²×M₃₂	—	13	1	no	—
159	C₂²×#108	—	13	1	no	—
160	C₂×#427	—	13	1	no	—
161	#2155	—	13	1	no	—
162	#2155	—	13	1	no	—
163	#2155	—	13	1	no	—
164	#2155	—	13	4	no	—
165	#2155	D₁₃	1	1	yes	characteristic, direct product factor
166	C₂×#365	—	13	4	no	—
167	C₂³×C₁₃	C₂×SD₁₆	1	1	yes	characteristic
168	C₂²×D₁₃	—	4	2	no	—
169	C₂²×D₁₃	#106	1	1	yes	characteristic
170	C₂²×D₁₃	#106	1	1	yes	characteristic
171	C₂²×D₁₃	#106	1	1	yes	characteristic
172	C₂²×D₁₃	#106	1	1	yes	characteristic
173	C₂²×D₁₃	C₂×SD₁₆	1	1	yes	characteristic
174	C₂²×D₁₃	C₂×SD₁₆	1	1	yes	characteristic
175	C₂×C₄×C₁₃	—	4	2	no	—
176	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
177	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
178	C₂×C₄×C₁₃	C₂×SD₁₆	1	1	yes	characteristic
179	C₂×C₄×C₁₃	C₂×SD₁₆	1	1	yes	characteristic
180	C₂×C₄×C₁₃	C₂×SD₁₆	1	1	yes	characteristic
181	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
182	C₂×Dic₁₃	—	4	2	no	—
183	C₂×Dic₁₃	#106	1	1	yes	characteristic
184	C₂×Dic₁₃	#106	1	1	yes	characteristic
185	C₂×Dic₁₃	#106	1	1	yes	characteristic
186	C₂×Dic₁₃	#106	1	1	yes	characteristic
187	C₂×Dic₁₃	C₂×SD₁₆	1	1	yes	characteristic
188	C₂×Dic₁₃	C₂×SD₁₆	1	1	yes	characteristic
189	C₄×D₁₃	—	8	4	no	—
190	C₄×D₁₃	#106	1	1	yes	characteristic
191	C₄×D₁₃	#106	1	1	yes	characteristic
192	C₄×D₁₃	#106	1	1	yes	characteristic
193	C₄×D₁₃	#106	1	1	yes	characteristic
194	C₄×D₁₃	#106	1	1	yes	characteristic
195	C₄×D₁₃	#106	1	1	yes	characteristic
196	C₄×D₁₃	#106	1	1	yes	characteristic
197	C₄×D₁₃	#106	1	1	yes	characteristic
198	C₄×D₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
199	C₄×D₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
200	C₄×D₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
201	C₄×D₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
202	C₄×D₁₃	C₂×SD₁₆	1	1	yes	characteristic
203	C₄×D₁₃	C₂×SD₁₆	1	1	yes	characteristic
204	C₄×D₁₃	C₂×SD₁₆	1	1	yes	characteristic
205	C₄×D₁₃	C₂×SD₁₆	1	1	yes	characteristic
206	C₈×C₁₃	—	4	2	no	—
207	C₈×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
208	C₈×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
209	C₈×C₁₃	C₂³×C₄	1	1	yes	characteristic
210	C₈×C₁₃	C₂²×Q₈	1	1	yes	characteristic
211	#1055	—	4	2	no	—
212	#1055	C₂×C₄⋊C₄	1	1	yes	characteristic
213	#1055	C₂×C₄⋊C₄	1	1	yes	characteristic
214	#1055	C₂×C₄⋊C₄	1	1	yes	characteristic
215	#1055	C₂×C₄⋊C₄	1	1	yes	characteristic
216	C₂²×M₁₆	—	26	1	no	—
217	C₂³×C₈	—	13	1	no	—
218	C₂×#117	—	26	1	no	—
219	C₂×M₃₂	—	13	1	no	—
220	C₂×M₃₂	—	13	2	no	—
221	C₂×M₃₂	—	13	2	no	—
222	C₂×M₃₂	—	13	2	no	—
223	C₂×M₃₂	—	13	2	no	—
224	C₂×M₃₂	—	13	2	no	—
225	C₂×M₃₂	C₂×D₁₃	1	1	yes	characteristic
226	C₂²×C₁₆	—	13	2	no	—
227	C₂×#108	—	13	1	no	—
228	C₂×#108	—	13	2	no	—
229	C₂×#108	—	13	2	no	—
230	C₂×#108	—	26	1	no	—
231	C₂×#108	—	26	1	no	—
232	C₂×#108	—	26	1	no	—
233	C₂×#108	C₂×D₁₃	1	1	yes	characteristic
234	#427	—	13	1	no	—
235	#427	—	13	2	no	—
236	#427	—	26	1	no	—
237	#427	—	26	1	no	—
238	#427	C₂×D₁₃	1	1	yes	characteristic
239	C₂×#107	—	26	1	no	—
240	C₂×#106	—	13	2	no	—
241	#365	—	13	4	no	—
242	#365	—	13	4	no	—
243	#365	—	13	4	no	—
244	#365	C₂×D₁₃	1	4	yes	complemented
245	C₂²×C₁₃	—	4	1	no	—
246	C₂²×C₁₃	C₂×#106	1	1	yes	characteristic
247	C₂²×C₁₃	C₂×#106	1	1	yes	characteristic
248	C₂²×C₁₃	C₂²×SD₁₆	1	1	yes	characteristic
249	C₂×D₁₃	—	2	2	no	—
250	C₂×D₁₃	—	2	2	no	—
251	C₂×D₁₃	—	2	2	no	—
252	C₂×D₁₃	—	4	1	no	—
253	C₂×D₁₃	—	4	1	no	—
254	C₂×D₁₃	—	4	1	no	—
255	C₂×D₁₃	C₂×#106	1	1	yes	characteristic
256	C₂×D₁₃	C₂×#106	1	1	yes	characteristic
257	C₂×D₁₃	C₂×#106	1	1	yes	characteristic
258	C₂×D₁₃	C₂×#106	1	1	yes	characteristic
259	C₄×C₁₃	—	8	2	no	—
260	C₄×C₁₃	C₂×#106	1	1	yes	characteristic
261	C₄×C₁₃	C₂×#106	1	1	yes	characteristic
262	C₄×C₁₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
263	C₄×C₁₃	C₂²×SD₁₆	1	1	yes	characteristic
264	Dic₁₃	—	8	2	no	—
265	Dic₁₃	C₂×#106	1	1	yes	characteristic
266	Dic₁₃	C₂×#106	1	1	yes	characteristic
267	Dic₁₃	C₂×#106	1	1	yes	characteristic
268	Dic₁₃	C₂×#106	1	1	yes	characteristic
269	C₂³×C₄	—	13	1	no	—
270	C₂×M₁₆	—	2	1	no	—
271	C₂×M₁₆	—	26	2	no	—
272	C₂×M₁₆	—	26	2	no	—
273	C₂×M₁₆	—	26	1	no	—
274	C₂×M₁₆	—	52	1	no	—
275	C₂×M₁₆	—	52	1	no	—
276	C₂×M₁₆	—	52	1	no	—
277	C₂²×C₈	—	13	1	no	—
278	C₂²×C₈	—	13	1	no	—
279	C₂²×C₈	—	13	1	no	—
280	C₂²×C₈	—	13	1	no	—
281	C₂²×C₈	—	13	1	no	—
282	C₂²×C₈	—	13	1	no	—
283	C₂²×C₈	—	13	1	no	—
284	C₂²×C₈	—	13	1	no	—
285	C₂²×C₈	—	13	1	no	—
286	C₂²×C₈	—	13	1	no	—
287	C₂²×C₈	—	13	1	no	—
288	C₂²×C₈	—	13	1	no	—
289	C₂²×C₈	—	13	1	no	—
290	C₂²×C₈	—	52	1	no	—
291	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
292	#117	—	2	1	no	—
293	#117	—	26	2	no	—
294	#117	—	26	1	no	—
295	#117	—	52	1	no	—
296	#117	—	52	1	no	—
297	C₂×C₄⋊C₄	—	26	2	no	—
298	C₂×C₂²⋊C₄	—	52	1	no	—
299	C₂×C₄²	—	52	1	no	—
300	M₃₂	—	13	2	no	—
301	M₃₂	—	13	2	no	—
302	M₃₂	—	13	4	no	—
303	M₃₂	—	13	4	no	—
304	M₃₂	C₄×D₁₃	1	2	yes	complemented
305	M₃₂	C₂²×D₁₃	1	2	yes	—
306	C₂×C₁₆	—	13	2	no	—
307	C₂×C₁₆	—	13	4	no	—
308	C₂×C₁₆	—	13	4	no	—
309	C₂×C₁₆	C₄×D₁₃	1	2	yes	complemented
310	#108	—	2	1	no	—
311	#108	—	13	2	no	—
312	#108	—	26	2	no	—
313	#108	—	26	2	no	—
314	#108	—	26	1	no	—
315	#108	C₂²×D₁₃	1	2	yes	—
316	#107	—	2	1	no	—
317	#107	—	26	2	no	—
318	#107	—	26	1	no	—
319	#106	—	13	2	no	—
320	#106	—	26	2	no	—
321	#106	C₂²×D₁₃	1	2	yes	—
322	C₂×C₁₃	—	2	1	no	—
323	C₂×C₁₃	—	2	1	no	—
324	C₂×C₁₃	—	2	1	no	—
325	C₂×C₁₃	C₂²×#106	1	1	yes	characteristic
326	D₁₃	—	2	1	no	—
327	D₁₃	—	2	1	no	—
328	D₁₃	—	2	1	no	—
329	D₁₃	#2155	1	2	yes	direct product factor
330	C₂⁴	—	13	1	no	—
331	C₂²×C₄	—	13	1	no	—
332	C₂²×C₄	—	13	1	no	—
333	C₂²×C₄	—	13	1	no	—
334	C₂²×C₄	—	13	1	no	—
335	C₂²×C₄	—	13	1	no	—
336	C₂²×C₄	—	13	1	no	—
337	C₂²×C₄	—	13	1	no	—
338	C₂²×C₄	—	13	1	no	—
339	C₂²×C₄	—	13	1	no	—
340	C₂²×C₄	—	13	1	no	—
341	C₂²×C₄	—	13	1	no	—
342	C₂²×C₄	—	13	1	no	—
343	C₂²×C₄	—	13	1	no	—
344	C₂²×C₄	—	52	2	no	—
345	C₂²×C₄	D₄×D₁₃	1	1	yes	characteristic
346	M₁₆	—	2	2	no	—
347	M₁₆	—	4	1	no	—
348	M₁₆	—	26	2	no	—
349	M₁₆	—	52	2	no	—
350	M₁₆	—	52	2	no	—
351	M₁₆	—	52	1	no	—
352	C₂×C₈	—	4	1	no	—
353	C₂×C₈	—	13	1	no	—
354	C₂×C₈	—	13	1	no	—
355	C₂×C₈	—	13	1	no	—
356	C₂×C₈	—	13	1	no	—
357	C₂×C₈	—	13	1	no	—
358	C₂×C₈	—	13	1	no	—
359	C₂×C₈	—	13	1	no	—
360	C₂×C₈	—	13	1	no	—
361	C₂×C₈	—	13	1	no	—
362	C₂×C₈	—	13	1	no	—
363	C₂×C₈	—	13	1	no	—
364	C₂×C₈	—	13	1	no	—
365	C₂×C₈	—	13	1	no	—
366	C₂×C₈	—	13	1	no	—
367	C₂×C₈	—	13	1	no	—
368	C₂×C₈	—	13	1	no	—
369	C₂×C₈	—	13	1	no	—
370	C₂×C₈	—	13	1	no	—
371	C₂×C₈	—	13	1	no	—
372	C₂×C₈	—	13	1	no	—
373	C₂×C₈	—	13	1	no	—
374	C₂×C₈	—	13	1	no	—
375	C₂×C₈	—	52	2	no	—
376	C₂×C₈	—	52	2	no	—
377	C₂×C₈	—	52	1	no	—
378	C₂×C₈	C₂×C₄×D₁₃	1	1	yes	characteristic
379	C₂×C₈	C₂×C₄×D₁₃	1	1	yes	characteristic
380	C₂×C₈	D₄×D₁₃	1	1	yes	characteristic
381	C₂×C₈	Q₈×D₁₃	1	1	yes	characteristic
382	C₂×C₈	Q₈×D₁₃	1	1	yes	characteristic
383	C₂×C₈	C₂³×D₁₃	1	1	yes	characteristic
384	C₄⋊C₄	—	2	2	no	—
385	C₄⋊C₄	—	26	2	no	—
386	C₄⋊C₄	—	52	2	no	—
387	C₂²⋊C₄	—	4	1	no	—
388	C₂²⋊C₄	—	52	2	no	—
389	C₂²⋊C₄	—	52	1	no	—
390	C₄²	—	4	1	no	—
391	C₄²	—	52	2	no	—
392	C₄²	—	52	1	no	—
393	C₁₆	—	13	4	no	—
394	C₁₆	C₂×C₄×D₁₃	1	4	yes	—
395	C₁₃	C₂×#2155	1	1	yes	characteristic, complemented, Sylow
396	C₂³	—	13	1	no	—
397	C₂³	—	13	1	no	—
398	C₂³	—	13	1	no	—
399	C₂³	—	13	1	no	—
400	C₂³	—	13	1	no	—
401	C₂³	—	13	1	no	—
402	C₂³	—	52	2	no	—
403	C₂³	SD₁₆×D₁₃	1	1	yes	characteristic
404	C₂×C₄	—	4	2	no	—
405	C₂×C₄	—	13	1	no	—
406	C₂×C₄	—	13	1	no	—
407	C₂×C₄	—	13	1	no	—
408	C₂×C₄	—	13	1	no	—
409	C₂×C₄	—	13	1	no	—
410	C₂×C₄	—	13	1	no	—
411	C₂×C₄	—	13	1	no	—
412	C₂×C₄	—	13	1	no	—
413	C₂×C₄	—	13	1	no	—
414	C₂×C₄	—	13	1	no	—
415	C₂×C₄	—	13	1	no	—
416	C₂×C₄	—	13	1	no	—
417	C₂×C₄	—	13	1	no	—
418	C₂×C₄	—	13	1	no	—
419	C₂×C₄	—	13	1	no	—
420	C₂×C₄	—	13	1	no	—
421	C₂×C₄	—	13	1	no	—
422	C₂×C₄	—	13	1	no	—
423	C₂×C₄	—	13	1	no	—
424	C₂×C₄	—	13	1	no	—
425	C₂×C₄	—	13	1	no	—
426	C₂×C₄	—	13	1	no	—
427	C₂×C₄	—	52	2	no	—
428	C₂×C₄	—	104	4	no	—
429	C₂×C₄	C₄⋊C₄×D₁₃	1	1	yes	characteristic
430	C₂×C₄	C₄⋊C₄×D₁₃	1	1	yes	characteristic
431	C₂×C₄	SD₁₆×D₁₃	1	1	yes	characteristic
432	C₂×C₄	SD₁₆×D₁₃	1	1	yes	characteristic
433	C₂×C₄	SD₁₆×D₁₃	1	1	yes	characteristic
434	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
435	C₈	—	4	2	no	—
436	C₈	—	13	1	no	—
437	C₈	—	13	1	no	—
438	C₈	—	13	1	no	—
439	C₈	—	13	1	no	—
440	C₈	—	52	2	no	—
441	C₈	C₄⋊C₄×D₁₃	1	1	yes	characteristic
442	C₈	C₄⋊C₄×D₁₃	1	1	yes	characteristic
443	C₈	C₂²×C₄×D₁₃	1	1	yes	characteristic
444	C₈	C₂×Q₈×D₁₃	1	1	yes	characteristic
445	C₂²	—	4	1	no	—
446	C₂²	—	13	1	no	—
447	C₂²	—	13	1	no	—
448	C₂²	—	13	1	no	—
449	C₂²	—	13	1	no	—
450	C₂²	—	26	2	no	—
451	C₂²	—	26	2	no	—
452	C₂²	—	26	2	no	—
453	C₂²	—	52	1	no	—
454	C₂²	—	52	1	no	—
455	C₂²	—	52	1	no	—
456	C₂²	D₁₃×#106	1	1	yes	characteristic
457	C₂²	D₁₃×#106	1	1	yes	characteristic
458	C₂²	C₂×SD₁₆×D₁₃	1	1	yes	characteristic
459	C₄	—	8	2	no	—
460	C₄	—	13	1	no	—
461	C₄	—	13	1	no	—
462	C₄	—	13	1	no	—
463	C₄	—	13	1	no	—
464	C₄	—	104	2	no	—
465	C₄	D₁₃×#106	1	1	yes	characteristic
466	C₄	D₁₃×#106	1	1	yes	characteristic
467	C₄	C₂×C₄⋊C₄×D₁₃	1	1	yes	characteristic
468	C₄	C₂×SD₁₆×D₁₃	1	1	yes	characteristic
469	C₂	—	2	1	no	—
470	C₂	—	2	1	no	—
471	C₂	—	2	1	no	—
472	C₂	—	13	2	no	—
473	C₂	—	26	1	no	—
474	C₂	—	26	1	no	—
475	C₂	—	26	1	no	—
476	C₂	C₂×D₁₃×#106	1	1	yes	characteristic

	subgroup	G/H
center	C₄	D₁₃×#106
commutator	C₈×C₁₃	C₂³×C₄
Frattini	C₂×C₈	C₂³×D₁₃
Fitting	C₁₃×#2155	C₂
socle	C₂×C₁₃	C₂²×#106
prime radical	C₂³×D₁₃	SD₁₆
cosocle	C₂×C₈×C₁₃	C₂⁴
hypercenter	#2155	D₁₃
hypocenter	C₁₃	C₂×#2155
LCS	G ▷ C₈×C₁₃ ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ #2155

Complements

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

N	H ≅ G/N	type
4. #13116610	C₂	semidirect
5. #13116609	C₂	semidirect
6. #13116608	C₂	semidirect
7. #13116607	C₂	semidirect
8. D₁₃×#365	C₂	semidirect
9. C₁₃×#2155	C₂	semidirect
21. D₁₃×M₃₂	C₄	semidirect
22. D₁₃×M₃₂	C₄	semidirect
25. C₂×#88038	C₄	semidirect
26. C₂×C₁₆×D₁₃	C₄	semidirect
35. C₁₃×#365	C₂²	semidirect
36. #11718105	C₂²	semidirect
37. #11718086	C₂²	semidirect
38. #11718079	C₂²	semidirect
70. C₁₃×M₃₂	C₂×C₄	semidirect
72. C₂×C₁₃×C₁₆	C₂×C₄	semidirect
83. #88052	C₂×C₄	semidirect
85. C₂×#6090	C₂×C₄	semidirect
89. #88038	C₂×C₄	semidirect
91. C₁₆×D₁₃	C₂×C₄	semidirect
165. #2155	D₁₃	direct (N × H)
244. #365	C₂×D₁₃	semidirect
304. M₃₂	C₄×D₁₃	semidirect
309. C₂×C₁₆	C₄×D₁₃	semidirect
329. D₁₃	#2155	direct (N × H)
395. C₁₃	C₂×#2155	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₁₃×M₃₂	2
C₂×D₁₃×#108	2
D₁₃×#427	2
#13116610	2
#13116609	2
#13116608	2
#13116607	2
D₁₃×#365	2
C₁₃×#2155	2
C₂×#2155	13

Subgroups — D13×#2155 #16015928

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₁₃×#2155 #16015928