Subgroups — #15834341

Order 3328.

794 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×D₈×D₁₃	C₂	1	1	yes	maximal, characteristic
2	#13123572	C₂	1	2	yes	maximal, complemented
3	#13113721	C₂	1	1	yes	maximal, characteristic, complemented
4	#13113668	C₂	1	2	yes	maximal, complemented
5	#13113663	C₂	1	2	yes	maximal, complemented
6	C₈×D₁₀₄	C₂	1	1	yes	maximal, characteristic, complemented
7	#13113630	C₂	1	1	yes	maximal, characteristic, complemented
8	#13113593	C₂	1	1	yes	maximal, characteristic, complemented
9	#13113259	C₂	1	2	yes	maximal, complemented
10	C₈×#6094	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1589	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×D₈×D₁₃	C₄	1	1	yes	characteristic
13	C₂×M₁₆×D₁₃	—	2	2	no	—
14	C₄×D₄×D₁₃	C₂²	1	2	yes	—
15	C₄×C₁₃×D₈	C₂²	1	1	yes	characteristic
16	C₁₃×#436	C₂²	1	2	yes	complemented
17	D₈×Dic₁₃	C₄	1	1	yes	characteristic
18	#11718788	—	2	2	no	—
19	C₄×#6104	C₂²	1	2	yes	—
20	#11718673	C₂²	1	2	yes	complemented
21	D₁₃×#107	C₄	1	1	yes	characteristic
22	#11718533	C₄	1	1	yes	characteristic
23	#11718498	C₂²	1	2	yes	—
24	#11718495	C₂²	1	2	yes	complemented
25	D₁₃×#102	C₄	1	2	yes	—
26	#11718417	C₄	1	2	yes	—
27	#11718389	—	2	2	no	—
28	#11718387	—	2	2	no	—
29	C₄×D₁₀₄	C₂²	1	1	yes	characteristic
30	C₄×#6094	C₂²	1	1	yes	characteristic
31	C₈×D₅₂	C₂²	1	2	yes	complemented
32	#11718346	C₂²	1	1	yes	characteristic
33	C₄×C₈×D₁₃	C₂²	1	1	yes	characteristic
34	C₁₃×#335	C₂²	1	1	yes	characteristic, complemented
35	C₁₃×D₄⋊C₈	C₂²	1	2	yes	complemented
36	C₈²×C₁₃	C₂²	1	1	yes	characteristic, complemented
37	D₄⋊#1055	C₂²	1	2	yes	complemented
38	#11718075	C₂²	1	2	yes	complemented
39	#11718071	C₂²	1	2	yes	complemented
40	#11718051	C₂²	1	2	yes	complemented
41	#11718050	C₂²	1	1	yes	characteristic, complemented
42	#11718047	C₂²	1	1	yes	characteristic, complemented
43	#11718046	C₂²	1	1	yes	characteristic, complemented
44	C₈×#1055	C₂²	1	1	yes	characteristic, complemented
45	C₂×D₄×D₁₃	C₂×C₄	1	2	yes	—
46	C₂²×C₄×D₁₃	—	2	2	no	—
47	C₂×C₁₃×D₈	C₂×C₄	1	1	yes	characteristic
48	C₂×C₁₃×M₁₆	—	2	2	no	—
49	C₄×D₄×C₁₃	C₂³	1	2	yes	—
50	D₄×Dic₁₃	C₂×C₄	1	2	yes	—
51	C₂×#6104	C₂×C₄	1	2	yes	—
52	C₄×C₂²⋊D₁₃	—	2	2	no	—
53	C₂×#6099	—	2	2	no	—
54	D₈×D₁₃	—	2	4	no	—
55	M₁₆×D₁₃	—	4	8	no	—
56	C₂×D₁₀₄	C₂×C₄	1	1	yes	characteristic
57	C₂×#6094	—	2	2	no	—
58	C₂×#6094	D₄	1	1	yes	characteristic
59	C₂×#6094	D₄	1	1	yes	characteristic
60	C₂×C₈×D₁₃	—	2	2	no	—
61	C₂×C₈×D₁₃	—	2	2	no	—
62	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
63	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
64	#88147	C₂×C₄	1	2	yes	—
65	C₄⋊C₄×D₁₃	C₂×C₄	1	2	yes	—
66	#88135	—	2	2	no	—
67	C₂²⋊C₄×D₁₃	—	2	2	no	—
68	C₄×D₅₂	C₂³	1	2	yes	—
69	C₄²×D₁₃	C₂³	1	1	yes	characteristic
70	C₁₃×#107	C₂×C₄	1	1	yes	characteristic
71	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
72	C₁₃×#102	C₂×C₄	1	2	yes	—
73	C₁₃×C₂²⋊C₈	—	2	2	no	—
74	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
75	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
76	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
77	#88072	C₂×C₄	1	2	yes	—
78	C₂²⋊#1055	—	2	2	no	—
79	#88061	C₂×C₄	1	2	yes	—
80	#88060	—	2	1	no	—
81	#88060	—	2	2	no	—
82	#88060	—	2	2	no	—
83	#88058	C₂×C₄	1	1	yes	characteristic
84	#88055	D₄	1	1	yes	characteristic
85	#88055	D₄	1	1	yes	characteristic
86	#88054	—	2	2	no	—
87	#88054	—	2	1	no	—
88	C₈×Dic₁₃	C₂×C₄	1	1	yes	characteristic
89	C₈×Dic₁₃	C₂×C₄	1	1	yes	characteristic
90	#88049	C₂×C₄	1	2	yes	—
91	#88047	C₂×C₄	1	2	yes	—
92	C₄⋊#1055	C₂³	1	2	yes	—
93	C₄×#1055	C₂³	1	1	yes	characteristic
94	C₄×#1055	C₂³	1	1	yes	characteristic
95	C₄×#1055	C₂³	1	1	yes	characteristic
96	M₁₆×D₈	—	13	1	no	maximal, Sylow
97	C₂³×D₁₃	—	2	2	no	—
98	C₂×D₄×C₁₃	C₂²×C₄	1	2	yes	—
99	C₂²×C₄×C₁₃	—	2	2	no	—
100	C₂×C₂²⋊D₁₃	—	2	2	no	—
101	C₂²×Dic₁₃	—	2	2	no	—
102	D₄×D₁₃	—	2	4	no	—
103	D₄×D₁₃	—	4	2	no	—
104	C₂×D₅₂	C₂²×C₄	1	2	yes	—
105	C₂×C₄×D₁₃	—	2	2	no	—
106	C₂×C₄×D₁₃	—	2	2	no	—
107	C₂×C₄×D₁₃	—	2	2	no	—
108	C₂×C₄×D₁₃	—	4	4	no	—
109	C₂×C₄×D₁₃	—	4	4	no	—
110	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
111	C₂×C₄×D₁₃	C₂×D₄	1	1	yes	characteristic
112	C₂×C₄×D₁₃	#41	1	1	yes	characteristic
113	C₁₃×D₈	—	2	2	no	—
114	C₁₃×M₁₆	—	4	4	no	—
115	C₂×C₈×C₁₃	—	2	2	no	—
116	C₂×C₈×C₁₃	—	2	1	no	—
117	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
118	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
119	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
120	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
121	C₁₃×C₄⋊C₄	C₂²×C₄	1	2	yes	—
122	C₁₃×C₂²⋊C₄	—	2	2	no	—
123	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
124	C₂²⋊Dic₁₃	—	2	2	no	—
125	#6104	—	2	4	no	—
126	#6103	—	2	2	no	—
127	#6103	—	2	2	no	—
128	C₄⋊Dic₁₃	C₂²×C₄	1	2	yes	—
129	#6101	—	2	2	no	—
130	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
131	C₄×Dic₁₃	C₂×D₄	1	1	yes	characteristic
132	C₄×Dic₁₃	#41	1	1	yes	characteristic
133	#6099	—	4	4	no	—
134	C₂×#1055	—	2	2	no	—
135	C₂×#1055	—	2	1	no	—
136	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
137	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
138	C₂×#1055	C₂×D₄	1	1	yes	characteristic
139	C₂×#1055	C₂×D₄	1	1	yes	characteristic
140	D₁₀₄	M₁₆	1	4	yes	complemented
141	#6094	—	2	2	no	—
142	#6094	—	4	4	no	—
143	#6094	D₈	1	4	yes	complemented
144	C₈×D₁₃	—	2	2	no	—
145	C₈×D₁₃	—	4	1	no	—
146	C₈×D₁₃	—	4	4	no	—
147	C₈×D₁₃	—	4	4	no	—
148	C₂×C₄×D₈	—	13	1	no	—
149	D₄×M₁₆	—	13	2	no	—
150	#1589	—	13	1	no	—
151	#1589	D₁₃	1	1	yes	characteristic, complemented
152	#1581	—	13	2	no	—
153	#1581	—	13	2	no	—
154	C₈×D₈	—	13	1	no	—
155	C₈×D₈	—	13	1	no	—
156	#1567	—	13	1	no	—
157	#1486	—	13	2	no	—
158	C₈×M₁₆	—	13	1	no	—
159	C₂³×C₁₃	—	2	2	no	—
160	C₂²×D₁₃	—	2	2	no	—
161	C₂²×D₁₃	—	4	4	no	—
162	C₂²×D₁₃	—	4	4	no	—
163	C₂²×D₁₃	—	8	2	no	—
164	C₂²×D₁₃	C₄×D₄	1	1	yes	characteristic
165	D₄×C₁₃	—	2	2	no	—
166	D₄×C₁₃	—	2	2	no	—
167	C₂×C₄×C₁₃	—	2	2	no	—
168	C₂×C₄×C₁₃	—	4	2	no	—
169	C₂×C₄×C₁₃	—	4	2	no	—
170	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
171	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
172	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
173	C₂²⋊D₁₃	—	4	4	no	—
174	C₂×Dic₁₃	—	2	2	no	—
175	C₂×Dic₁₃	—	4	4	no	—
176	C₂×Dic₁₃	C₄×D₄	1	1	yes	characteristic
177	C₂×Dic₁₃	C₄×D₄	1	1	yes	characteristic
178	C₂×Dic₁₃	C₄×D₄	1	1	yes	characteristic
179	D₅₂	—	2	2	no	—
180	D₅₂	C₂×M₁₆	1	4	yes	complemented
181	C₄×D₁₃	—	2	1	no	—
182	C₄×D₁₃	—	2	1	no	—
183	C₄×D₁₃	—	4	1	no	—
184	C₄×D₁₃	—	4	4	no	—
185	C₄×D₁₃	—	4	2	no	—
186	C₄×D₁₃	—	4	2	no	—
187	C₄×D₁₃	—	4	4	no	—
188	C₄×D₁₃	C₂×D₈	1	2	yes	—
189	C₄×D₁₃	#135	1	2	yes	—
190	C₈×C₁₃	—	2	1	no	—
191	C₈×C₁₃	—	2	1	no	—
192	C₈×C₁₃	—	4	1	no	—
193	C₈×C₁₃	—	4	2	no	—
194	C₈×C₁₃	C₂×M₁₆	1	2	yes	complemented
195	C₈×C₁₃	C₂×D₈	1	2	yes	complemented
196	#1055	—	2	1	no	—
197	#1055	—	2	1	no	—
198	#1055	—	2	1	no	—
199	#1055	—	4	1	no	—
200	#1055	—	4	2	no	—
201	#1055	C₂×D₈	1	2	yes	complemented
202	C₂²×D₈	—	13	1	no	—
203	C₂²×M₁₆	—	26	2	no	—
204	C₂×C₄×D₄	—	13	2	no	—
205	C₄×D₈	—	13	1	no	—
206	C₄×D₈	—	13	2	no	—
207	C₄×D₈	—	13	1	no	—
208	C₄×D₈	—	13	2	no	—
209	C₄×D₈	—	13	1	no	—
210	C₄×D₈	C₂×D₁₃	1	1	yes	characteristic
211	#436	—	13	2	no	—
212	#436	C₂×D₁₃	1	2	yes	complemented
213	#435	—	26	2	no	—
214	#435	—	26	2	no	—
215	C₈×D₄	—	13	2	no	—
216	C₈×D₄	—	13	2	no	—
217	#431	—	13	1	no	—
218	C₂×#107	—	13	1	no	—
219	#423	—	13	2	no	—
220	C₂×#102	—	13	2	no	—
221	#407	—	26	2	no	—
222	C₄×M₁₆	—	13	1	no	—
223	C₂×C₄×C₈	—	13	1	no	—
224	#335	—	13	2	no	—
225	#335	—	13	1	no	—
226	#335	C₂×D₁₃	1	1	yes	characteristic, complemented
227	D₄⋊C₈	—	13	2	no	—
228	D₄⋊C₈	—	13	2	no	—
229	D₄⋊C₈	—	13	2	no	—
230	D₄⋊C₈	C₂×D₁₃	1	2	yes	complemented
231	#322	—	13	1	no	—
232	#322	—	13	1	no	—
233	C₈²	—	13	1	no	—
234	C₈²	C₂×D₁₃	1	1	yes	characteristic, complemented
235	C₂²×C₁₃	—	4	2	no	—
236	C₂²×C₁₃	—	4	2	no	—
237	C₂²×C₁₃	—	4	2	no	—
238	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
239	C₂×D₁₃	—	2	1	no	—
240	C₂×D₁₃	—	2	1	no	—
241	C₂×D₁₃	—	2	4	no	—
242	C₂×D₁₃	—	4	2	no	—
243	C₂×D₁₃	—	4	2	no	—
244	C₂×D₁₃	—	8	8	no	—
245	C₂×D₁₃	C₄×D₈	1	2	yes	—
246	C₄×C₁₃	—	2	1	no	—
247	C₄×C₁₃	—	4	2	no	—
248	C₄×C₁₃	C₂²×M₁₆	1	1	yes	characteristic
249	C₄×C₁₃	#568	1	1	yes	characteristic
250	C₄×C₁₃	C₂²×D₈	1	1	yes	characteristic
251	C₄×C₁₃	C₂×#135	1	1	yes	characteristic
252	Dic₁₃	—	2	1	no	—
253	Dic₁₃	—	2	1	no	—
254	Dic₁₃	—	4	2	no	—
255	Dic₁₃	C₄×D₈	1	2	yes	—
256	C₂²×D₄	—	13	2	no	—
257	C₂³×C₄	—	26	2	no	—
258	C₂×D₈	—	13	2	no	—
259	C₂×D₈	—	13	1	no	—
260	C₂×D₈	—	26	4	no	—
261	C₂×D₈	C₄×D₁₃	1	1	yes	characteristic
262	C₂×M₁₆	—	2	2	no	—
263	C₂×M₁₆	—	13	1	no	—
264	C₂×M₁₆	—	13	1	no	—
265	C₂×M₁₆	—	26	2	no	—
266	C₂×M₁₆	—	26	2	no	—
267	C₂×M₁₆	—	52	8	no	—
268	C₂²×C₈	—	13	1	no	—
269	C₂²×C₈	—	13	1	no	—
270	C₂²×C₈	—	26	2	no	—
271	C₂²×C₈	—	26	2	no	—
272	C₄×D₄	—	13	2	no	—
273	C₄×D₄	—	13	2	no	—
274	C₄×D₄	—	13	2	no	—
275	C₄×D₄	—	26	2	no	—
276	C₄×D₄	—	26	2	no	—
277	C₄×D₄	C₂²×D₁₃	1	2	yes	—
278	C₂×C₄⋊C₄	—	13	2	no	—
279	C₂×C₂²⋊C₄	—	26	2	no	—
280	C₂×C₄²	—	13	1	no	—
281	#107	—	13	1	no	—
282	#107	—	13	2	no	—
283	#107	C₄×D₁₃	1	1	yes	characteristic
284	C₄⋊C₈	—	13	2	no	—
285	C₄⋊C₈	—	26	2	no	—
286	C₄⋊C₈	—	26	1	no	—
287	C₄⋊C₈	C₂²×D₁₃	1	2	yes	—
288	#102	—	13	2	no	—
289	#102	—	13	2	no	—
290	#102	—	13	2	no	—
291	#102	C₄×D₁₃	1	2	yes	—
292	C₂²⋊C₈	—	2	2	no	—
293	C₂²⋊C₈	—	26	2	no	—
294	C₂²⋊C₈	—	26	1	no	—
295	C₂²⋊C₈	—	26	2	no	—
296	C₂²⋊C₈	—	26	2	no	—
297	#97	—	13	1	no	—
298	#97	—	13	1	no	—
299	C₄×C₈	—	13	1	no	—
300	C₄×C₈	—	13	1	no	—
301	C₄×C₈	—	13	1	no	—
302	C₄×C₈	—	13	1	no	—
303	C₄×C₈	—	13	1	no	—
304	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
305	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
306	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
307	C₂×C₁₃	—	8	2	no	—
308	C₂×C₁₃	D₄×M₁₆	1	1	yes	characteristic
309	C₂×C₁₃	C₂×C₄×D₈	1	1	yes	characteristic
310	C₂×C₁₃	#2957	1	1	yes	characteristic
311	D₁₃	—	2	2	no	—
312	D₁₃	—	4	4	no	—
313	C₂⁴	—	26	2	no	—
314	C₂×D₄	—	13	2	no	—
315	C₂×D₄	—	26	2	no	—
316	C₂×D₄	—	26	4	no	—
317	C₂×D₄	—	52	2	no	—
318	C₂×D₄	C₂×C₄×D₁₃	1	2	yes	—
319	C₂²×C₄	—	2	2	no	—
320	C₂²×C₄	—	13	1	no	—
321	C₂²×C₄	—	13	1	no	—
322	C₂²×C₄	—	13	1	no	—
323	C₂²×C₄	—	26	2	no	—
324	C₂²×C₄	—	26	2	no	—
325	C₂²×C₄	—	26	2	no	—
326	C₂²×C₄	—	26	2	no	—
327	C₂²×C₄	—	52	4	no	—
328	C₂²×C₄	—	52	4	no	—
329	D₈	—	2	2	no	—
330	D₈	—	13	4	no	—
331	D₈	—	26	4	no	—
332	M₁₆	—	4	4	no	—
333	M₁₆	—	13	4	no	—
334	M₁₆	—	26	2	no	—
335	M₁₆	—	52	4	no	—
336	M₁₆	—	52	4	no	—
337	C₂×C₈	—	2	2	no	—
338	C₂×C₈	—	2	1	no	—
339	C₂×C₈	—	13	1	no	—
340	C₂×C₈	—	13	1	no	—
341	C₂×C₈	—	13	1	no	—
342	C₂×C₈	—	13	1	no	—
343	C₂×C₈	—	26	2	no	—
344	C₂×C₈	—	26	2	no	—
345	C₂×C₈	—	26	1	no	—
346	C₂×C₈	—	52	1	no	—
347	C₂×C₈	—	52	4	no	—
348	C₂×C₈	—	52	4	no	—
349	C₂×C₈	C₂×C₄×D₁₃	1	1	yes	characteristic
350	C₂×C₈	C₂×C₄×D₁₃	1	1	yes	characteristic
351	C₂×C₈	D₄×D₁₃	1	1	yes	characteristic
352	C₂×C₈	D₄×D₁₃	1	1	yes	characteristic
353	C₄⋊C₄	—	13	2	no	—
354	C₄⋊C₄	—	26	2	no	—
355	C₄⋊C₄	C₂×C₄×D₁₃	1	2	yes	—
356	C₂²⋊C₄	—	2	2	no	—
357	C₂²⋊C₄	—	26	2	no	—
358	C₂²⋊C₄	—	26	2	no	—
359	C₂²⋊C₄	—	26	2	no	—
360	C₄²	—	13	1	no	—
361	C₄²	—	13	1	no	—
362	C₄²	—	13	1	no	—
363	C₄²	C₂³×D₁₃	1	1	yes	characteristic
364	C₁₃	M₁₆×D₈	1	1	yes	characteristic, complemented, Sylow
365	C₂³	—	2	2	no	—
366	C₂³	—	13	1	no	—
367	C₂³	—	26	2	no	—
368	C₂³	—	52	4	no	—
369	C₂³	—	52	4	no	—
370	C₂³	—	104	2	no	—
371	D₄	—	2	2	no	—
372	D₄	—	2	2	no	—
373	D₄	—	13	4	no	—
374	D₄	—	26	2	no	—
375	D₄	—	52	4	no	—
376	C₂×C₄	—	2	2	no	—
377	C₂×C₄	—	4	2	no	—
378	C₂×C₄	—	4	2	no	—
379	C₂×C₄	—	13	1	no	—
380	C₂×C₄	—	13	2	no	—
381	C₂×C₄	—	13	2	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	2	no	—
387	C₂×C₄	—	52	1	no	—
388	C₂×C₄	—	52	4	no	—
389	C₂×C₄	—	52	4	no	—
390	C₂×C₄	—	52	4	no	—
391	C₂×C₄	—	52	2	no	—
392	C₂×C₄	—	52	2	no	—
393	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
394	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
395	C₂×C₄	#41×D₁₃	1	1	yes	characteristic
396	C₈	—	2	1	no	—
397	C₈	—	2	1	no	—
398	C₈	—	4	1	no	—
399	C₈	—	4	2	no	—
400	C₈	—	13	2	no	—
401	C₈	—	26	1	no	—
402	C₈	—	26	1	no	—
403	C₈	—	26	1	no	—
404	C₈	—	52	1	no	—
405	C₈	—	52	2	no	—
406	C₈	M₁₆×D₁₃	1	2	yes	complemented
407	C₈	D₈×D₁₃	1	2	yes	complemented
408	C₂²	—	4	2	no	—
409	C₂²	—	4	2	no	—
410	C₂²	—	4	2	no	—
411	C₂²	—	13	2	no	—
412	C₂²	—	26	1	no	—
413	C₂²	—	26	1	no	—
414	C₂²	—	26	4	no	—
415	C₂²	—	52	2	no	—
416	C₂²	—	52	2	no	—
417	C₂²	—	104	8	no	—
418	C₂²	C₄×D₄×D₁₃	1	1	yes	characteristic
419	C₄	—	2	1	no	—
420	C₄	—	4	2	no	—
421	C₄	—	13	2	no	—
422	C₄	—	26	1	no	—
423	C₄	—	26	1	no	—
424	C₄	—	52	2	no	—
425	C₄	C₂×M₁₆×D₁₃	1	1	yes	characteristic
426	C₄	#11719455	1	1	yes	characteristic
427	C₄	C₂×D₈×D₁₃	1	1	yes	characteristic
428	C₄	D₁₃×#135	1	1	yes	characteristic
429	C₂	—	8	2	no	—
430	C₂	—	26	2	no	—
431	C₂	—	52	4	no	—
432	C₂	#13123572	1	1	yes	characteristic
433	C₂	C₄×D₈×D₁₃	1	1	yes	characteristic
434	C₂	#13123748	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₁₃
commutator	C₂×C₄×C₁₃	C₂³×C₄
Frattini	C₄²	C₂³×D₁₃
Fitting	C₁₃×#1589	C₂
socle	C₂²×C₁₃	C₂×C₄×D₄
prime radical	C₂×D₈×D₁₃	C₄
cosocle	C₄²×C₁₃	C₂⁴
hypercenter	#1589	D₁₃
hypocenter	C₁₃	M₁₆×D₈
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #1589

Complements

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

N	H ≅ G/N	type
2. #13123572	C₂	semidirect
3. #13113721	C₂	semidirect
4. #13113668	C₂	semidirect
5. #13113663	C₂	semidirect
6. C₈×D₁₀₄	C₂	semidirect
7. #13113630	C₂	semidirect
8. #13113593	C₂	semidirect
9. #13113259	C₂	semidirect
10. C₈×#6094	C₂	semidirect
11. C₁₃×#1589	C₂	semidirect
16. C₁₃×#436	C₂²	semidirect
20. #11718673	C₂²	semidirect
24. #11718495	C₂²	semidirect
31. C₈×D₅₂	C₂²	semidirect
34. C₁₃×#335	C₂²	semidirect
35. C₁₃×D₄⋊C₈	C₂²	semidirect
36. C₈²×C₁₃	C₂²	semidirect
37. D₄⋊#1055	C₂²	semidirect
38. #11718075	C₂²	semidirect
39. #11718071	C₂²	semidirect
40. #11718051	C₂²	semidirect
41. #11718050	C₂²	semidirect
42. #11718047	C₂²	semidirect
43. #11718046	C₂²	semidirect
44. C₈×#1055	C₂²	semidirect
140. D₁₀₄	M₁₆	semidirect
143. #6094	D₈	semidirect
151. #1589	D₁₃	semidirect
180. D₅₂	C₂×M₁₆	semidirect
194. C₈×C₁₃	C₂×M₁₆	semidirect
195. C₈×C₁₃	C₂×D₈	semidirect
201. #1055	C₂×D₈	semidirect
212. #436	C₂×D₁₃	semidirect
226. #335	C₂×D₁₃	semidirect
230. D₄⋊C₈	C₂×D₁₃	semidirect
234. C₈²	C₂×D₁₃	semidirect
364. C₁₃	M₁₆×D₈	semidirect
406. C₈	M₁₆×D₁₃	semidirect
407. C₈	D₈×D₁₃	semidirect

Maximal subgroups

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

subgroup	index
C₄×D₈×D₁₃	2
#13123572	2
#13113721	2
#13113668	2
#13113663	2
C₈×D₁₀₄	2
#13113630	2
#13113593	2
#13113259	2
C₈×#6094	2
C₁₃×#1589	2
M₁₆×D₈	13