Subgroups — D₁₃×#3415 #16769426

Order 3328.

2126 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₁₃×#576	C₂	1	2	yes	maximal, complemented
2	#13127977	C₂	1	1	yes	maximal, characteristic, complemented
3	#13127976	C₂	1	6	yes	maximal, complemented
4	#13127975	C₂	1	2	yes	maximal, complemented
5	#13127974	C₂	1	3	yes	maximal, complemented
6	#13127973	C₂	1	3	yes	maximal, complemented
7	D₁₃×#509	C₂	1	6	yes	maximal, complemented
8	D₁₃×#508	C₂	1	3	yes	maximal, complemented
9	C₂×D₁₃×D₁₆	C₂	1	3	yes	maximal, complemented
10	D₁₃×#504	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#3415	C₂	1	1	yes	maximal, characteristic, complemented
12	D₁₃×H(5,𝔽₂)	—	2	2	no	—
13	C₁₃×#576	C₂²	1	2	yes	complemented
14	#11719540	—	2	2	no	—
15	#11719479	—	2	6	no	—
16	D₁₃×AGL(1,ℤ/8)	—	2	6	no	—
17	#11719474	C₂²	1	6	yes	complemented
18	D₁₃×#135	C₂²	1	6	yes	complemented
19	#11719462	C₂²	1	6	yes	complemented
20	C₂×D₈×D₁₃	C₂²	1	6	yes	complemented
21	#11719457	C₂²	1	2	yes	complemented
22	D₁₃×#131	C₂²	1	1	yes	characteristic
23	C₁₃×#509	C₂²	1	6	yes	complemented
24	C₁₃×#508	C₂²	1	3	yes	complemented
25	C₂×C₁₃×D₁₆	C₂²	1	3	yes	complemented
26	C₁₃×#504	C₂²	1	1	yes	characteristic, complemented
27	#11718855	C₂²	1	6	yes	complemented
28	#11718854	C₂²	1	6	yes	complemented
29	#11718808	C₂²	1	6	yes	complemented
30	C₂×#88066	C₂²	1	6	yes	complemented
31	#11718801	C₂²	1	1	yes	characteristic, complemented
32	#11718580	C₂²	1	3	yes	complemented
33	D₁₃×Q₃₂	C₂²	1	1	yes	characteristic, complemented
34	#11718577	C₂²	1	6	yes	complemented
35	#11718575	C₂²	1	12	yes	complemented
36	D₁₃×SD₃₂	C₂²	1	6	yes	complemented
37	#11718573	C₂²	1	3	yes	complemented
38	#11718572	C₂²	1	12	yes	complemented
39	D₁₃×D₁₆	C₂²	1	3	yes	complemented
40	D₁₃×D₁₆	C₂²	1	6	yes	complemented
41	D₁₃×D₁₆	C₂²	1	6	yes	complemented
42	D₁₃×D₁₆	C₂²	1	6	yes	complemented
43	#11718569	C₂²	1	6	yes	complemented
44	#11718568	C₂²	1	3	yes	complemented
45	D₁₃×M₃₂	C₂²	1	3	yes	complemented
46	#11718565	C₂²	1	3	yes	complemented
47	C₂×D₂₀₈	C₂²	1	3	yes	complemented
48	#11718562	C₂²	1	3	yes	complemented
49	C₂×C₁₆×D₁₃	C₂²	1	3	yes	complemented
50	C₁₃×H(5,𝔽₂)	—	2	2	no	—
51	#88256	—	2	2	no	—
52	#88256	—	2	6	no	—
53	#88256	—	4	2	no	—
54	#41×D₁₃	—	2	6	no	—
55	#41×D₁₃	—	4	2	no	—
56	#41×D₁₃	D₄	1	1	yes	characteristic
57	#88251	—	2	6	no	—
58	#88251	—	4	6	no	—
59	C₂×D₄×D₁₃	—	2	6	no	—
60	C₂×D₄×D₁₃	—	4	6	no	—
61	C₁₃×AGL(1,ℤ/8)	—	2	6	no	—
62	C₁₃×#135	C₂³	1	6	yes	complemented
63	C₂×C₁₃×D₈	C₂³	1	6	yes	complemented
64	C₁₃×#131	C₂³	1	1	yes	characteristic
65	#88204	—	2	6	no	—
66	#88203	—	2	6	no	—
67	#88202	D₄	1	1	yes	characteristic
68	#88186	—	2	6	no	—
69	C₂×#6104	—	2	6	no	—
70	#88173	C₂³	1	6	yes	complemented
71	Q₁₆×D₁₃	C₂³	1	2	yes	—
72	#88170	—	2	6	no	—
73	#88168	—	2	12	no	—
74	SD₁₆×D₁₃	—	2	6	no	—
75	#88166	C₂³	1	6	yes	complemented
76	#88165	—	2	12	no	—
77	D₈×D₁₃	—	2	6	no	—
78	D₈×D₁₃	—	2	6	no	—
79	D₈×D₁₃	C₂³	1	6	yes	—
80	D₈×D₁₃	C₂³	1	12	yes	complemented
81	#88162	—	2	6	no	—
82	#88161	D₄	1	3	yes	—
83	M₁₆×D₁₃	D₄	1	3	yes	—
84	#88158	C₂³	1	6	yes	complemented
85	C₂×D₁₀₄	C₂³	1	6	yes	complemented
86	#88155	C₂³	1	3	yes	—
87	C₂×C₈×D₁₃	C₂³	1	3	yes	—
88	C₁₃×Q₃₂	C₂³	1	1	yes	characteristic, complemented
89	C₁₃×SD₃₂	C₂³	1	6	yes	complemented
90	C₁₃×D₁₆	C₂³	1	3	yes	complemented
91	C₁₃×D₁₆	C₂³	1	6	yes	complemented
92	C₁₃×M₃₂	C₂³	1	3	yes	complemented
93	C₂×C₁₃×C₁₆	C₂³	1	3	yes	complemented
94	#88069	C₂³	1	2	yes	complemented
95	#88068	C₂³	1	6	yes	complemented
96	#88067	C₂³	1	6	yes	complemented
97	#88066	C₂³	1	6	yes	complemented
98	#88066	C₂³	1	12	yes	complemented
99	#88052	C₂³	1	3	yes	complemented
100	C₂×#6090	C₂³	1	3	yes	complemented
101	Dic₁₀₄	C₂³	1	1	yes	characteristic, complemented
102	#88040	C₂³	1	6	yes	complemented
103	D₂₀₈	C₂³	1	3	yes	complemented
104	D₂₀₈	C₂³	1	6	yes	complemented
105	#88038	C₂³	1	6	yes	complemented
106	C₁₆×D₁₃	C₂³	1	1	yes	characteristic
107	C₁₆×D₁₃	C₂³	1	3	yes	—
108	C₁₆×D₁₃	C₂³	1	3	yes	complemented
109	C₁₆×D₁₃	C₂³	1	3	yes	complemented
110	C₂×#3415	—	13	1	no	maximal, Sylow
111	C₂³×D₁₃	—	4	6	no	—
112	C₁₃×#41	—	2	6	no	—
113	C₁₃×#41	—	4	2	no	—
114	C₁₃×#41	C₂×D₄	1	1	yes	characteristic
115	C₂×D₄×C₁₃	—	2	6	no	—
116	C₂×D₄×C₁₃	—	4	6	no	—
117	C₂×C₂²⋊D₁₃	—	4	12	no	—
118	C₂×C₂²⋊D₁₃	—	4	6	no	—
119	#6131	—	2	6	no	—
120	#6131	—	4	2	no	—
121	#6131	D₈	1	1	yes	characteristic
122	Q₈×D₁₃	—	2	2	no	—
123	Q₈×D₁₃	D₈	1	1	yes	characteristic
124	#6129	—	2	6	no	—
125	#6129	—	4	6	no	—
126	#6129	—	4	6	no	—
127	#6129	D₈	1	3	yes	—
128	D₄×D₁₃	—	2	6	no	—
129	D₄×D₁₃	—	2	12	no	—
130	D₄×D₁₃	—	4	6	no	—
131	D₄×D₁₃	—	4	6	no	—
132	D₄×D₁₃	—	4	12	no	—
133	D₄×D₁₃	—	4	6	no	—
134	D₄×D₁₃	—	4	6	no	—
135	D₄×D₁₃	—	4	6	no	—
136	D₄×D₁₃	D₈	1	3	yes	—
137	#6127	—	2	6	no	—
138	#6127	—	4	6	no	—
139	#6127	—	4	6	no	—
140	#6127	C₂×D₄	1	3	yes	—
141	C₂×D₅₂	—	2	6	no	—
142	C₂×D₅₂	—	4	6	no	—
143	C₂×C₄×D₁₃	—	4	6	no	—
144	C₂×C₄×D₁₃	C₂×D₄	1	3	yes	—
145	C₁₃×Q₁₆	C₂⁴	1	2	yes	—
146	C₁₃×SD₁₆	—	2	6	no	—
147	C₁₃×D₈	—	2	6	no	—
148	C₁₃×D₈	C₂⁴	1	6	yes	—
149	C₁₃×M₁₆	C₂×D₄	1	3	yes	—
150	C₂×C₈×C₁₃	C₂⁴	1	3	yes	—
151	#6107	—	2	2	no	—
152	#6106	—	2	6	no	—
153	#6105	—	2	6	no	—
154	#6104	—	2	6	no	—
155	#6104	—	2	12	no	—
156	#6099	C₂×D₄	1	3	yes	—
157	C₂×#1055	C₂×D₄	1	3	yes	—
158	Dic₅₂	C₂⁴	1	2	yes	—
159	D₁₀₄	—	2	6	no	—
160	D₁₀₄	C₂⁴	1	6	yes	—
161	#6095	—	2	6	no	—
162	#6094	C₂×D₄	1	6	yes	—
163	C₈×D₁₃	C₂×D₄	1	3	yes	—
164	C₈×D₁₃	C₂×D₄	1	3	yes	—
165	C₈×D₁₃	C₂⁴	1	1	yes	characteristic
166	C₈×D₁₃	C₂⁴	1	3	yes	—
167	C₁₃×C₁₆	C₂⁴	1	1	yes	characteristic
168	C₁₃×C₁₆	C₂⁴	1	3	yes	—
169	#6090	C₂⁴	1	1	yes	characteristic
170	#6090	C₂⁴	1	3	yes	—
171	C₂×#576	—	13	2	no	—
172	#3415	—	13	6	no	—
173	#3415	—	13	3	no	—
174	#3415	—	13	3	no	—
175	#3415	—	13	1	no	—
176	#3415	—	13	2	no	—
177	#3415	D₁₃	1	1	yes	characteristic, direct product factor
178	C₂×#509	—	13	6	no	—
179	C₂×#508	—	13	3	no	—
180	C₂²×D₁₆	—	13	3	no	—
181	C₂×#504	—	13	1	no	—
182	C₂³×C₁₃	—	4	6	no	—
183	C₂²×D₁₃	—	4	6	no	—
184	C₂²×D₁₃	—	4	6	no	—
185	C₂²×D₁₃	—	4	12	no	—
186	C₂²×D₁₃	—	16	12	no	—
187	C₂²×D₁₃	C₂×D₈	1	3	yes	—
188	Q₈×C₁₃	—	2	2	no	—
189	Q₈×C₁₃	C₂×D₈	1	1	yes	characteristic
190	D₄×C₁₃	—	2	6	no	—
191	D₄×C₁₃	—	4	6	no	—
192	D₄×C₁₃	—	4	6	no	—
193	D₄×C₁₃	C₂×D₈	1	3	yes	—
194	C₂×C₄×C₁₃	—	4	6	no	—
195	C₂×C₄×C₁₃	C₂²×D₄	1	3	yes	—
196	C₂²⋊D₁₃	—	4	6	no	—
197	C₂²⋊D₁₃	—	4	6	no	—
198	C₂²⋊D₁₃	—	4	6	no	—
199	C₂²⋊D₁₃	—	4	12	no	—
200	C₂²⋊D₁₃	C₂×D₈	1	6	yes	—
201	C₂×Dic₁₃	—	4	6	no	—
202	C₂×Dic₁₃	C₂×D₈	1	3	yes	—
203	D₅₂	—	2	6	no	—
204	D₅₂	—	4	6	no	—
205	D₅₂	—	4	6	no	—
206	D₅₂	C₂×D₈	1	3	yes	—
207	C₄×D₁₃	—	4	2	no	—
208	C₄×D₁₃	—	4	6	no	—
209	C₄×D₁₃	—	4	6	no	—
210	C₄×D₁₃	C₂×D₈	1	3	yes	—
211	C₄×D₁₃	C₂×D₈	1	3	yes	—
212	C₄×D₁₃	C₂²×D₄	1	1	yes	characteristic
213	C₄×D₁₃	C₂²×D₄	1	3	yes	—
214	Dic₂₆	—	2	2	no	—
215	Dic₂₆	—	4	2	no	—
216	Dic₂₆	C₂×D₈	1	3	yes	—
217	C₈×C₁₃	C₂²×D₄	1	3	yes	—
218	C₈×C₁₃	C₂⁵	1	1	yes	characteristic
219	#1055	C₂²×D₄	1	1	yes	characteristic
220	#1055	C₂²×D₄	1	3	yes	—
221	C₂×H(5,𝔽₂)	—	26	2	no	—
222	#576	—	13	6	no	—
223	#576	—	13	6	no	—
224	#576	—	13	2	no	—
225	#576	—	26	6	no	—
226	#576	—	26	2	no	—
227	#576	C₂×D₁₃	1	2	yes	complemented
228	C₂×AGL(1,ℤ/8)	—	26	6	no	—
229	C₂×#135	—	13	6	no	—
230	C₂²×D₈	—	13	6	no	—
231	C₂×#131	—	13	1	no	—
232	#509	—	13	6	no	—
233	#509	—	13	6	no	—
234	#509	—	13	12	no	—
235	#509	—	13	12	no	—
236	#509	—	13	6	no	—
237	#509	C₂×D₁₃	1	6	yes	complemented
238	#508	—	13	6	no	—
239	#508	—	13	3	no	—
240	#508	—	13	6	no	—
241	#508	—	13	3	no	—
242	#508	—	13	3	no	—
243	#508	C₂×D₁₃	1	3	yes	complemented
244	C₂×Q₃₂	—	13	1	no	—
245	C₂×SD₃₂	—	13	6	no	—
246	C₂×D₁₆	—	13	6	no	—
247	C₂×D₁₆	—	13	3	no	—
248	C₂×D₁₆	—	13	6	no	—
249	C₂×D₁₆	—	13	6	no	—
250	C₂×D₁₆	—	13	6	no	—
251	C₂×D₁₆	—	13	3	no	—
252	C₂×D₁₆	C₂×D₁₃	1	3	yes	complemented
253	#504	—	13	1	no	—
254	#504	—	13	3	no	—
255	#504	—	13	3	no	—
256	#504	C₂×D₁₃	1	1	yes	characteristic, complemented
257	C₂×M₃₂	—	13	3	no	—
258	C₂²×C₁₆	—	13	3	no	—
259	C₂²×C₁₃	—	4	6	no	—
260	C₂²×C₁₃	—	16	6	no	—
261	C₂²×C₁₃	C₂²×D₈	1	3	yes	—
262	C₂×D₁₃	—	2	6	no	—
263	C₂×D₁₃	—	4	6	no	—
264	C₂×D₁₃	—	8	12	no	—
265	C₂×D₁₃	—	16	12	no	—
266	C₂×D₁₃	—	16	6	no	—
267	C₂×D₁₃	C₂²×D₈	1	3	yes	—
268	C₂×D₁₃	C₂²×D₈	1	1	yes	characteristic
269	C₄×C₁₃	—	4	2	no	—
270	C₄×C₁₃	C₂²×D₈	1	3	yes	—
271	C₄×C₁₃	C₂³×D₄	1	1	yes	characteristic
272	Dic₁₃	—	4	2	no	—
273	Dic₁₃	C₂²×D₈	1	1	yes	characteristic
274	Dic₁₃	C₂²×D₈	1	3	yes	—
275	H(5,𝔽₂)	—	2	2	no	—
276	H(5,𝔽₂)	—	26	6	no	—
277	H(5,𝔽₂)	—	26	6	no	—
278	H(5,𝔽₂)	—	26	2	no	—
279	H(5,𝔽₂)	—	52	6	no	—
280	H(5,𝔽₂)	—	52	2	no	—
281	C₂×#41	—	13	1	no	—
282	C₂×#41	—	26	6	no	—
283	C₂×#41	—	52	2	no	—
284	C₂²×D₄	—	26	6	no	—
285	C₂²×D₄	—	52	6	no	—
286	AGL(1,ℤ/8)	—	2	6	no	—
287	AGL(1,ℤ/8)	—	26	12	no	—
288	AGL(1,ℤ/8)	—	26	12	no	—
289	AGL(1,ℤ/8)	—	26	6	no	—
290	AGL(1,ℤ/8)	—	26	6	no	—
291	AGL(1,ℤ/8)	—	26	6	no	—
292	#135	—	13	6	no	—
293	#135	—	13	6	no	—
294	#135	—	13	6	no	—
295	#135	—	26	6	no	—
296	#135	—	26	6	no	—
297	#135	C₂²×D₁₃	1	6	yes	complemented
298	C₂×Q₁₆	—	13	2	no	—
299	C₂×SD₁₆	—	26	6	no	—
300	C₂×D₈	—	13	6	no	—
301	C₂×D₈	—	13	12	no	—
302	C₂×D₈	—	13	6	no	—
303	C₂×D₈	—	26	6	no	—
304	C₂×D₈	—	26	6	no	—
305	C₂×D₈	—	26	6	no	—
306	C₂×D₈	C₂²×D₁₃	1	6	yes	complemented
307	#131	—	13	1	no	—
308	#131	—	13	3	no	—
309	#131	—	13	3	no	—
310	#131	C₂²×D₁₃	1	1	yes	characteristic
311	C₂×M₁₆	—	13	3	no	—
312	C₂²×C₈	—	13	3	no	—
313	Q₃₂	—	13	2	no	—
314	Q₃₂	—	13	1	no	—
315	Q₃₂	C₂²×D₁₃	1	1	yes	characteristic, complemented
316	SD₃₂	—	13	6	no	—
317	SD₃₂	—	13	6	no	—
318	SD₃₂	—	13	6	no	—
319	SD₃₂	C₂²×D₁₃	1	6	yes	complemented
320	D₁₆	—	13	6	no	—
321	D₁₆	—	13	12	no	—
322	D₁₆	—	13	3	no	—
323	D₁₆	—	13	6	no	—
324	D₁₆	C₂²×D₁₃	1	3	yes	complemented
325	D₁₆	C₂²×D₁₃	1	6	yes	complemented
326	M₃₂	—	13	3	no	—
327	M₃₂	—	13	6	no	—
328	M₃₂	C₂²×D₁₃	1	3	yes	complemented
329	C₂×C₁₆	—	13	3	no	—
330	C₂×C₁₆	—	13	1	no	—
331	C₂×C₁₆	—	13	3	no	—
332	C₂×C₁₆	—	13	3	no	—
333	C₂×C₁₆	—	13	3	no	—
334	C₂×C₁₆	C₂²×D₁₃	1	3	yes	complemented
335	C₂×C₁₃	—	2	3	no	—
336	C₂×C₁₃	—	8	6	no	—
337	C₂×C₁₃	C₂³×D₈	1	1	yes	characteristic
338	D₁₃	—	2	3	no	—
339	D₁₃	—	8	6	no	—
340	D₁₃	#3415	1	2	yes	direct product factor
341	C₂⁴	—	52	6	no	—
342	#41	—	2	6	no	—
343	#41	—	4	2	no	—
344	#41	—	13	1	no	—
345	#41	—	13	3	no	—
346	#41	—	13	3	no	—
347	#41	—	26	6	no	—
348	#41	—	26	6	no	—
349	#41	—	26	6	no	—
350	#41	—	52	6	no	—
351	#41	—	52	6	no	—
352	#41	—	52	6	no	—
353	#41	—	52	6	no	—
354	#41	—	52	2	no	—
355	#41	D₄×D₁₃	1	1	yes	characteristic
356	C₂×Q₈	—	13	1	no	—
357	C₂×Q₈	—	26	2	no	—
358	C₂×D₄	—	2	6	no	—
359	C₂×D₄	—	4	6	no	—
360	C₂×D₄	—	13	3	no	—
361	C₂×D₄	—	26	6	no	—
362	C₂×D₄	—	26	12	no	—
363	C₂×D₄	—	26	6	no	—
364	C₂×D₄	—	52	6	no	—
365	C₂×D₄	—	52	6	no	—
366	C₂×D₄	—	52	6	no	—
367	C₂×D₄	—	52	6	no	—
368	C₂×D₄	—	52	12	no	—
369	C₂×D₄	—	52	6	no	—
370	C₂×D₄	—	52	6	no	—
371	C₂×D₄	—	52	12	no	—
372	C₂×D₄	—	52	6	no	—
373	C₂²×C₄	—	13	3	no	—
374	C₂²×C₄	—	52	6	no	—
375	Q₁₆	—	13	2	no	—
376	Q₁₆	—	26	2	no	—
377	Q₁₆	C₂³×D₁₃	1	2	yes	—
378	SD₁₆	—	2	6	no	—
379	SD₁₆	—	26	6	no	—
380	SD₁₆	—	26	6	no	—
381	SD₁₆	—	26	6	no	—
382	D₈	—	2	6	no	—
383	D₈	—	13	6	no	—
384	D₈	—	26	6	no	—
385	D₈	—	26	12	no	—
386	D₈	—	26	6	no	—
387	D₈	C₂³×D₁₃	1	6	yes	—
388	M₁₆	—	13	3	no	—
389	M₁₆	—	13	6	no	—
390	M₁₆	D₄×D₁₃	1	3	yes	—
391	C₂×C₈	—	13	3	no	—
392	C₂×C₈	—	13	3	no	—
393	C₂×C₈	—	13	3	no	—
394	C₂×C₈	—	13	1	no	—
395	C₂×C₈	—	13	3	no	—
396	C₂×C₈	C₂³×D₁₃	1	3	yes	—
397	C₁₆	—	13	1	no	—
398	C₁₆	—	13	3	no	—
399	C₁₆	C₂³×D₁₃	1	1	yes	characteristic
400	C₁₆	C₂³×D₁₃	1	3	yes	—
401	C₁₃	C₂×#3415	1	1	yes	characteristic, complemented, Sylow
402	C₂³	—	4	6	no	—
403	C₂³	—	13	3	no	—
404	C₂³	—	52	6	no	—
405	C₂³	—	52	12	no	—
406	C₂³	—	52	6	no	—
407	C₂³	—	208	12	no	—
408	Q₈	—	2	2	no	—
409	Q₈	—	13	3	no	—
410	Q₈	—	26	2	no	—
411	Q₈	—	52	2	no	—
412	Q₈	D₈×D₁₃	1	1	yes	characteristic
413	D₄	—	2	6	no	—
414	D₄	—	4	6	no	—
415	D₄	—	4	6	no	—
416	D₄	—	13	6	no	—
417	D₄	—	13	3	no	—
418	D₄	—	26	6	no	—
419	D₄	—	52	6	no	—
420	D₄	—	52	6	no	—
421	D₄	—	52	12	no	—
422	D₄	—	52	6	no	—
423	D₄	—	52	6	no	—
424	D₄	—	52	6	no	—
425	D₄	D₈×D₁₃	1	3	yes	—
426	C₂×C₄	—	4	6	no	—
427	C₂×C₄	—	13	3	no	—
428	C₂×C₄	—	13	3	no	—
429	C₂×C₄	—	13	3	no	—
430	C₂×C₄	—	13	1	no	—
431	C₂×C₄	—	13	3	no	—
432	C₂×C₄	—	52	6	no	—
433	C₂×C₄	—	52	2	no	—
434	C₂×C₄	—	52	6	no	—
435	C₂×C₄	—	52	6	no	—
436	C₂×C₄	C₂×D₄×D₁₃	1	3	yes	—
437	C₈	—	13	1	no	—
438	C₈	—	13	3	no	—
439	C₈	C₂×D₄×D₁₃	1	3	yes	—
440	C₈	C₂⁴×D₁₃	1	1	yes	characteristic
441	C₂²	—	4	6	no	—
442	C₂²	—	13	1	no	—
443	C₂²	—	13	3	no	—
444	C₂²	—	16	6	no	—
445	C₂²	—	26	6	no	—
446	C₂²	—	52	6	no	—
447	C₂²	—	104	12	no	—
448	C₂²	—	208	6	no	—
449	C₂²	—	208	12	no	—
450	C₂²	C₂×D₈×D₁₃	1	3	yes	—
451	C₄	—	4	2	no	—
452	C₄	—	13	1	no	—
453	C₄	—	13	3	no	—
454	C₄	—	52	2	no	—
455	C₄	C₂×D₈×D₁₃	1	3	yes	—
456	C₄	C₂²×D₄×D₁₃	1	1	yes	characteristic
457	C₂	—	2	3	no	—
458	C₂	—	8	6	no	—
459	C₂	—	13	2	no	—
460	C₂	—	26	3	no	—
461	C₂	—	104	6	no	—
462	C₂	C₂²×D₈×D₁₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂	C₂²×D₈×D₁₃
commutator, cosocle	C₈×C₁₃	C₂⁵
Frattini	C₈	C₂⁴×D₁₃
Fitting	C₁₃×#3415	C₂
socle	C₂×C₁₃	C₂³×D₈
hypercenter	#3415	D₁₃
hypocenter	C₁₃	C₂×#3415
LCS	G ▷ C₈×C₁₃ ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂ ◁ #41 ◁ #131 ◁ #3415

Complements

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

N	H ≅ G/N	type
1. D₁₃×#576	C₂	semidirect
2. #13127977	C₂	semidirect
3. #13127976	C₂	semidirect
4. #13127975	C₂	semidirect
5. #13127974	C₂	semidirect
6. #13127973	C₂	semidirect
7. D₁₃×#509	C₂	semidirect
8. D₁₃×#508	C₂	semidirect
9. C₂×D₁₃×D₁₆	C₂	semidirect
10. D₁₃×#504	C₂	semidirect
11. C₁₃×#3415	C₂	semidirect
13. C₁₃×#576	C₂²	semidirect
17. #11719474	C₂²	semidirect
18. D₁₃×#135	C₂²	semidirect
19. #11719462	C₂²	semidirect
20. C₂×D₈×D₁₃	C₂²	semidirect
21. #11719457	C₂²	semidirect
23. C₁₃×#509	C₂²	semidirect
24. C₁₃×#508	C₂²	semidirect
25. C₂×C₁₃×D₁₆	C₂²	semidirect
26. C₁₃×#504	C₂²	semidirect
27. #11718855	C₂²	semidirect
28. #11718854	C₂²	semidirect
29. #11718808	C₂²	semidirect
30. C₂×#88066	C₂²	semidirect
31. #11718801	C₂²	semidirect
32. #11718580	C₂²	semidirect
33. D₁₃×Q₃₂	C₂²	semidirect
34. #11718577	C₂²	semidirect
35. #11718575	C₂²	semidirect
36. D₁₃×SD₃₂	C₂²	semidirect
37. #11718573	C₂²	semidirect
38. #11718572	C₂²	semidirect
39. D₁₃×D₁₆	C₂²	semidirect
40. D₁₃×D₁₆	C₂²	semidirect
41. D₁₃×D₁₆	C₂²	semidirect
42. D₁₃×D₁₆	C₂²	semidirect
43. #11718569	C₂²	semidirect
44. #11718568	C₂²	semidirect
45. D₁₃×M₃₂	C₂²	semidirect
46. #11718565	C₂²	semidirect
47. C₂×D₂₀₈	C₂²	semidirect
48. #11718562	C₂²	semidirect
49. C₂×C₁₆×D₁₃	C₂²	semidirect
62. C₁₃×#135	C₂³	semidirect
63. C₂×C₁₃×D₈	C₂³	semidirect
70. #88173	C₂³	semidirect
75. #88166	C₂³	semidirect
80. D₈×D₁₃	C₂³	semidirect
84. #88158	C₂³	semidirect
85. C₂×D₁₀₄	C₂³	semidirect
88. C₁₃×Q₃₂	C₂³	semidirect
89. C₁₃×SD₃₂	C₂³	semidirect
90. C₁₃×D₁₆	C₂³	semidirect
91. C₁₃×D₁₆	C₂³	semidirect
92. C₁₃×M₃₂	C₂³	semidirect
93. C₂×C₁₃×C₁₆	C₂³	semidirect
94. #88069	C₂³	semidirect
95. #88068	C₂³	semidirect
96. #88067	C₂³	semidirect
97. #88066	C₂³	semidirect
98. #88066	C₂³	semidirect
99. #88052	C₂³	semidirect
100. C₂×#6090	C₂³	semidirect
101. Dic₁₀₄	C₂³	semidirect
102. #88040	C₂³	semidirect
103. D₂₀₈	C₂³	semidirect
104. D₂₀₈	C₂³	semidirect
105. #88038	C₂³	semidirect
108. C₁₆×D₁₃	C₂³	semidirect
109. C₁₆×D₁₃	C₂³	semidirect
177. #3415	D₁₃	direct (N × H)
227. #576	C₂×D₁₃	semidirect
237. #509	C₂×D₁₃	semidirect
243. #508	C₂×D₁₃	semidirect
252. C₂×D₁₆	C₂×D₁₃	semidirect
256. #504	C₂×D₁₃	semidirect
297. #135	C₂²×D₁₃	semidirect
306. C₂×D₈	C₂²×D₁₃	semidirect
315. Q₃₂	C₂²×D₁₃	semidirect
319. SD₃₂	C₂²×D₁₃	semidirect
324. D₁₆	C₂²×D₁₃	semidirect
325. D₁₆	C₂²×D₁₃	semidirect
328. M₃₂	C₂²×D₁₃	semidirect
334. C₂×C₁₆	C₂²×D₁₃	semidirect
340. D₁₃	#3415	direct (N × H)
401. C₁₃	C₂×#3415	semidirect

Maximal subgroups

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

subgroup	index
D₁₃×#576	2
#13127977	2
#13127976	2
#13127975	2
#13127974	2
#13127973	2
D₁₃×#509	2
D₁₃×#508	2
C₂×D₁₃×D₁₆	2
D₁₃×#504	2
C₁₃×#3415	2
C₂×#3415	13

Subgroups — D13×#3415 #16769426

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₁₃×#3415 #16769426