Subgroups — #16016007

Order 3328.

598 conjugacy classes of subgroups.

The subgroup lattice has 448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#88155	C₂	1	1	yes	maximal, characteristic
2	#13116642	C₂	1	2	yes	maximal, complemented
3	#13116640	C₂	1	2	yes	maximal, complemented
4	#13116635	C₂	1	1	yes	maximal, characteristic, complemented
5	#13116633	C₂	1	1	yes	maximal, characteristic, complemented
6	#13116633	C₂	1	1	yes	maximal, characteristic, complemented
7	#13116593	C₂	1	2	yes	maximal, complemented
8	#13116448	C₂	1	2	yes	maximal
9	C₄×#88038	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄×C₁₆×D₁₃	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#2162	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#88155	C₄	1	1	yes	characteristic
13	C₂×#88155	C₂²	1	1	yes	characteristic
14	C₄×#6127	C₄	1	1	yes	characteristic
15	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
16	#11718762	C₄	1	1	yes	characteristic
17	#11718762	C₂²	1	1	yes	characteristic
18	C₄×#6099	C₄	1	1	yes	characteristic
19	C₂×#88038	C₂²	1	2	yes	—
20	C₂×C₁₆×D₁₃	C₂²	1	2	yes	—
21	#11718350	C₄	1	1	yes	characteristic
22	#11718350	C₄	1	1	yes	characteristic
23	#11718350	C₂²	1	1	yes	characteristic
24	#11718350	C₂²	1	1	yes	characteristic
25	C₄×#6094	C₄	1	1	yes	characteristic
26	C₄×#6094	C₄	1	1	yes	characteristic
27	C₄×C₈×D₁₃	C₂²	1	1	yes	characteristic
28	C₄×C₈×D₁₃	C₂²	1	1	yes	characteristic
29	C₁₃×C₄⋊C₁₆	C₂²	1	2	yes	—
30	C₁₃×C₂²⋊C₁₆	C₂²	1	2	yes	—
31	C₄×C₁₃×C₁₆	C₂²	1	1	yes	characteristic
32	C₄×C₁₃×C₁₆	C₂²	1	1	yes	characteristic
33	C₂²⋊#6090	C₂²	1	2	yes	—
34	#11718099	C₂²	1	2	yes	—
35	#11718099	C₂²	1	2	yes	—
36	#11718094	C₂²	1	2	yes	—
37	#11718093	C₂²	1	2	yes	—
38	#11718093	C₂²	1	2	yes	—
39	C₁₆×Dic₁₃	C₂²	1	2	yes	—
40	C₄⋊#6090	C₂²	1	2	yes	—
41	C₄×#6090	C₂²	1	1	yes	characteristic
42	C₄×#6090	C₂²	1	1	yes	characteristic
43	C₂×#6127	C₂×C₄	1	1	yes	characteristic
44	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
45	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
46	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
47	C₄×C₂²⋊D₁₃	C₈	1	1	yes	characteristic
48	C₄×C₂²⋊D₁₃	C₈	1	1	yes	characteristic
49	C₄×C₂²⋊D₁₃	C₈	1	1	yes	characteristic
50	C₄×C₂²⋊D₁₃	C₈	1	1	yes	characteristic
51	#88180	C₂×C₄	1	1	yes	characteristic
52	C₂×#6099	C₂×C₄	1	1	yes	characteristic
53	C₂×#6099	C₂×C₄	1	1	yes	characteristic
54	#88155	—	2	4	no	—
55	#88155	—	2	4	no	—
56	C₂×#6094	C₂×C₄	1	1	yes	characteristic
57	C₂×#6094	C₂×C₄	1	1	yes	characteristic
58	C₂×#6094	C₂×C₄	1	1	yes	characteristic
59	C₂×#6094	C₂×C₄	1	1	yes	characteristic
60	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
61	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
62	C₂×C₈×D₁₃	C₂³	1	1	yes	characteristic
63	C₂×C₈×D₁₃	C₂³	1	1	yes	characteristic
64	C₄×D₅₂	C₈	1	1	yes	characteristic
65	C₄×D₅₂	C₈	1	1	yes	characteristic
66	#88126	C₂×C₄	1	1	yes	characteristic
67	#88126	C₂×C₄	1	1	yes	characteristic
68	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
69	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
70	C₄×Dic₂₆	C₈	1	1	yes	characteristic
71	C₄×Dic₂₆	C₈	1	1	yes	characteristic
72	C₂×C₁₃×C₁₆	C₂³	1	2	yes	—
73	C₂×C₁₃×C₁₆	C₂³	1	2	yes	—
74	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
75	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
76	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
77	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
78	#88055	C₂×C₄	1	1	yes	characteristic
79	#88055	C₂×C₄	1	1	yes	characteristic
80	#88055	C₂×C₄	1	1	yes	characteristic
81	#88055	C₂×C₄	1	1	yes	characteristic
82	C₈×Dic₁₃	C₂×C₄	1	1	yes	characteristic
83	C₈×Dic₁₃	C₂×C₄	1	1	yes	characteristic
84	C₈×Dic₁₃	C₂³	1	1	yes	characteristic
85	C₈×Dic₁₃	C₂³	1	1	yes	characteristic
86	C₂×#6090	C₂³	1	2	yes	—
87	C₂×#6090	C₂³	1	2	yes	—
88	#88043	C₂×C₄	1	1	yes	characteristic
89	#88043	C₂×C₄	1	1	yes	characteristic
90	C₄×#1055	C₂×C₄	1	1	yes	characteristic
91	C₄×#1055	C₂×C₄	1	1	yes	characteristic
92	#88038	—	2	4	no	—
93	C₁₆×D₁₃	—	2	4	no	—
94	#33420	—	13	1	no	maximal, Sylow
95	C₂²×C₄×C₁₃	C₂×C₈	1	1	yes	characteristic
96	C₂²×C₄×C₁₃	C₂×C₈	1	1	yes	characteristic
97	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
98	C₂×C₂²⋊D₁₃	C₂×C₈	1	1	yes	characteristic
99	C₂×C₂²⋊D₁₃	C₂×C₈	1	1	yes	characteristic
100	#6127	—	2	2	no	—
101	#6127	—	2	2	no	—
102	C₂×D₅₂	C₂×C₈	1	1	yes	characteristic
103	C₂×C₄×D₁₃	C₂×C₈	1	1	yes	characteristic
104	C₂×C₄×D₁₃	C₂×C₈	1	1	yes	characteristic
105	C₂×C₄×D₁₃	C₂×C₈	1	1	yes	characteristic
106	C₂×C₄×D₁₃	C₂×C₈	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×Dic₂₆	C₂×C₈	1	1	yes	characteristic
110	C₂×C₈×C₁₃	—	2	2	no	—
111	C₂×C₈×C₁₃	—	2	2	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	C₂²×C₄	1	1	yes	characteristic
115	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
116	C₄²×C₁₃	C₂×C₈	1	1	yes	characteristic
117	C₄²×C₁₃	C₂×C₈	1	1	yes	characteristic
118	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
119	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
120	C₂²⋊Dic₁₃	C₂×C₈	1	1	yes	characteristic
121	C₂²⋊Dic₁₃	C₂×C₈	1	1	yes	characteristic
122	#6103	C₂×C₈	1	1	yes	characteristic
123	#6103	C₂×C₈	1	1	yes	characteristic
124	#6103	C₂×C₈	1	1	yes	characteristic
125	#6103	C₂×C₈	1	1	yes	characteristic
126	C₄⋊Dic₁₃	C₂×C₈	1	1	yes	characteristic
127	C₄⋊Dic₁₃	C₂×C₈	1	1	yes	characteristic
128	#6101	C₂×C₈	1	1	yes	characteristic
129	#6101	C₂×C₈	1	1	yes	characteristic
130	#6101	C₂×C₈	1	1	yes	characteristic
131	#6101	C₂×C₈	1	1	yes	characteristic
132	C₄×Dic₁₃	C₂×C₈	1	1	yes	characteristic
133	C₄×Dic₁₃	C₂×C₈	1	1	yes	characteristic
134	C₄×Dic₁₃	C₂×C₈	1	1	yes	characteristic
135	C₄×Dic₁₃	C₂×C₈	1	1	yes	characteristic
136	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
137	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
138	#6099	—	2	2	no	—
139	#6099	—	2	2	no	—
140	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
141	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
142	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
143	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
144	#6094	—	2	2	no	—
145	#6094	—	2	2	no	—
146	#6094	—	2	2	no	—
147	#6094	—	2	2	no	—
148	C₈×D₁₃	—	2	2	no	—
149	C₈×D₁₃	—	2	2	no	—
150	C₈×D₁₃	M₁₆	1	4	yes	—
151	C₈×D₁₃	#41	1	4	yes	—
152	C₁₃×C₁₆	—	2	2	no	—
153	C₁₃×C₁₆	—	2	2	no	—
154	#6090	—	2	2	no	—
155	#6090	—	2	2	no	—
156	C₄×#131	—	13	1	no	—
157	#2164	—	13	2	no	—
158	#2164	—	13	2	no	—
159	#2162	—	13	1	no	—
160	#2162	—	13	1	no	—
161	#2162	—	13	1	no	—
162	#2162	D₁₃	1	1	yes	characteristic, complemented
163	#2151	—	13	2	no	—
164	#2113	—	13	2	no	—
165	C₄×M₃₂	—	13	1	no	—
166	C₂×C₄×C₁₆	—	13	1	no	—
167	C₂³×C₁₃	C₂²×C₈	1	1	yes	characteristic
168	C₂²×D₁₃	C₂²×C₈	1	1	yes	characteristic
169	C₂²×D₁₃	C₂²×C₈	1	1	yes	characteristic
170	C₂×C₄×C₁₃	—	2	1	no	—
171	C₂×C₄×C₁₃	—	2	1	no	—
172	C₂×C₄×C₁₃	—	2	2	no	—
173	C₂×C₄×C₁₃	—	2	2	no	—
174	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
175	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
176	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
177	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
178	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
179	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
180	C₂²⋊D₁₃	—	2	2	no	—
181	C₂²⋊D₁₃	—	2	2	no	—
182	C₂×Dic₁₃	C₂²×C₈	1	1	yes	characteristic
183	C₂×Dic₁₃	C₂²×C₈	1	1	yes	characteristic
184	C₂×Dic₁₃	C₂²×C₈	1	1	yes	characteristic
185	C₂×Dic₁₃	C₂²×C₈	1	1	yes	characteristic
186	C₂×Dic₁₃	C₂²×C₈	1	1	yes	characteristic
187	C₂×Dic₁₃	C₂²×C₈	1	1	yes	characteristic
188	D₅₂	—	2	2	no	—
189	C₄×D₁₃	—	2	1	no	—
190	C₄×D₁₃	—	2	1	no	—
191	C₄×D₁₃	—	2	2	no	—
192	C₄×D₁₃	—	2	2	no	—
193	C₄×D₁₃	—	2	2	no	—
194	C₄×D₁₃	—	2	2	no	—
195	C₄×D₁₃	#117	1	2	yes	—
196	C₄×D₁₃	C₂×M₁₆	1	2	yes	—
197	Dic₂₆	—	2	2	no	—
198	C₈×C₁₃	—	2	1	no	—
199	C₈×C₁₃	—	2	1	no	—
200	C₈×C₁₃	C₂×M₁₆	1	2	yes	—
201	C₈×C₁₃	C₂×#41	1	2	yes	—
202	#1055	—	2	1	no	—
203	#1055	—	2	1	no	—
204	#1055	#117	1	2	yes	—
205	#1055	C₂×M₁₆	1	2	yes	—
206	C₂×#131	—	13	1	no	—
207	C₂×#131	—	13	1	no	—
208	C₄×#41	—	13	1	no	—
209	C₂×M₃₂	—	13	2	no	—
210	C₂²×C₁₆	—	13	2	no	—
211	#405	—	13	1	no	—
212	#405	—	13	1	no	—
213	#405	—	13	1	no	—
214	#405	—	13	1	no	—
215	#405	—	13	1	no	—
216	#405	—	13	1	no	—
217	C₄×M₁₆	—	13	1	no	—
218	C₄×M₁₆	—	13	1	no	—
219	C₄×M₁₆	—	13	1	no	—
220	C₂×C₄×C₈	—	13	1	no	—
221	C₂×C₄×C₈	—	13	1	no	—
222	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
223	C₄⋊C₁₆	—	13	2	no	—
224	C₄⋊C₁₆	—	13	2	no	—
225	C₄⋊C₁₆	—	13	2	no	—
226	C₄⋊C₁₆	C₂×D₁₃	1	2	yes	—
227	C₂²⋊C₁₆	—	13	2	no	—
228	C₂²⋊C₁₆	—	13	2	no	—
229	C₂²⋊C₁₆	—	13	2	no	—
230	C₂²⋊C₁₆	C₂×D₁₃	1	2	yes	—
231	#346	—	13	2	no	—
232	C₄×C₁₆	—	13	2	no	—
233	C₄×C₁₆	—	13	1	no	—
234	C₄×C₁₆	—	13	1	no	—
235	C₄×C₁₆	C₂×D₁₃	1	1	yes	characteristic
236	C₄×C₁₆	C₂×D₁₃	1	1	yes	characteristic
237	C₂²×C₁₃	—	2	1	no	—
238	C₂²×C₁₃	—	2	1	no	—
239	C₂²×C₁₃	—	2	1	no	—
240	C₂²×C₁₃	C₂³×C₈	1	1	yes	characteristic
241	C₂×D₁₃	—	2	1	no	—
242	C₂×D₁₃	—	2	1	no	—
243	C₂×D₁₃	—	2	1	no	—
244	C₂×D₁₃	—	2	1	no	—
245	C₂×D₁₃	—	2	1	no	—
246	C₂×D₁₃	#431	1	2	yes	—
247	C₄×C₁₃	—	2	1	no	—
248	C₄×C₁₃	—	2	1	no	—
249	C₄×C₁₃	—	2	1	no	—
250	C₄×C₁₃	#504	1	2	yes	—
251	C₄×C₁₃	#504	1	2	yes	—
252	C₄×C₁₃	C₂×#117	1	1	yes	characteristic
253	C₄×C₁₃	C₂²×M₁₆	1	1	yes	characteristic
254	Dic₁₃	—	2	1	no	—
255	Dic₁₃	—	2	1	no	—
256	Dic₁₃	—	2	1	no	—
257	Dic₁₃	—	2	1	no	—
258	Dic₁₃	—	2	1	no	—
259	Dic₁₃	#431	1	2	yes	—
260	C₂×#41	—	13	1	no	—
261	#131	—	26	4	no	—
262	#131	—	26	4	no	—
263	C₂×M₁₆	—	13	1	no	—
264	C₂×M₁₆	—	13	1	no	—
265	C₂×M₁₆	—	13	1	no	—
266	C₂×M₁₆	—	13	1	no	—
267	C₂×M₁₆	—	13	1	no	—
268	C₂×M₁₆	—	13	1	no	—
269	C₂²×C₈	—	13	1	no	—
270	C₂²×C₈	—	13	1	no	—
271	C₂²×C₈	—	13	1	no	—
272	C₂²×C₈	—	13	1	no	—
273	C₂²×C₈	C₄×D₁₃	1	1	yes	characteristic
274	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
275	C₄×Q₈	—	13	1	no	—
276	C₄×Q₈	—	13	1	no	—
277	C₄×D₄	—	13	1	no	—
278	C₄×D₄	—	13	1	no	—
279	C₄×D₄	—	13	1	no	—
280	C₄×D₄	—	13	1	no	—
281	C₄×D₄	—	13	1	no	—
282	C₄×D₄	—	13	1	no	—
283	#117	—	13	1	no	—
284	#117	—	13	1	no	—
285	#117	—	13	1	no	—
286	C₂×C₄²	—	13	1	no	—
287	C₂×C₄²	—	13	1	no	—
288	C₂×C₄²	C₄×D₁₃	1	1	yes	characteristic
289	M₃₂	—	26	4	no	—
290	C₂×C₁₆	—	13	2	no	—
291	C₂×C₁₆	—	13	2	no	—
292	C₂×C₁₆	—	26	4	no	—
293	C₂×C₁₆	C₂²×D₁₃	1	2	yes	—
294	C₂×C₁₆	C₂²×D₁₃	1	2	yes	—
295	#97	—	13	1	no	—
296	#97	—	13	1	no	—
297	#97	—	13	1	no	—
298	#97	—	13	1	no	—
299	#97	—	13	1	no	—
300	#97	—	13	1	no	—
301	C₄×C₈	—	13	1	no	—
302	C₄×C₈	—	13	1	no	—
303	C₄×C₈	—	13	1	no	—
304	C₄×C₈	—	13	1	no	—
305	C₄×C₈	—	13	1	no	—
306	C₄×C₈	—	13	1	no	—
307	C₄×C₈	C₄×D₁₃	1	1	yes	characteristic
308	C₄×C₈	C₄×D₁₃	1	1	yes	characteristic
309	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
310	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
311	C₂×C₁₃	—	4	1	no	—
312	C₂×C₁₃	C₂×#431	1	1	yes	characteristic
313	C₂×C₁₃	C₂×#504	1	1	yes	characteristic
314	C₂×C₁₃	C₂×#504	1	1	yes	characteristic
315	D₁₃	—	2	2	no	—
316	D₁₃	—	4	1	no	—
317	#41	—	26	2	no	—
318	#41	—	26	2	no	—
319	C₂×Q₈	—	13	1	no	—
320	C₂×D₄	—	13	1	no	—
321	C₂×D₄	—	13	1	no	—
322	C₂×D₄	—	13	1	no	—
323	C₂²×C₄	—	13	1	no	—
324	C₂²×C₄	—	13	1	no	—
325	C₂²×C₄	—	13	1	no	—
326	C₂²×C₄	—	13	1	no	—
327	C₂²×C₄	—	13	1	no	—
328	C₂²×C₄	—	13	1	no	—
329	C₂²×C₄	C₈×D₁₃	1	1	yes	characteristic
330	C₂²×C₄	C₈×D₁₃	1	1	yes	characteristic
331	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
332	M₁₆	—	26	2	no	—
333	M₁₆	—	26	2	no	—
334	M₁₆	—	26	2	no	—
335	M₁₆	—	26	2	no	—
336	M₁₆	—	26	2	no	—
337	M₁₆	—	26	2	no	—
338	C₂×C₈	—	2	2	no	—
339	C₂×C₈	—	2	2	no	—
340	C₂×C₈	—	13	1	no	—
341	C₂×C₈	—	13	1	no	—
342	C₂×C₈	—	13	4	no	—
343	C₂×C₈	—	13	4	no	—
344	C₂×C₈	—	13	1	no	—
345	C₂×C₈	—	13	1	no	—
346	C₂×C₈	—	26	2	no	—
347	C₂×C₈	—	26	2	no	—
348	C₂×C₈	C₂×C₄×D₁₃	1	1	yes	characteristic
349	C₂×C₈	C₂×C₄×D₁₃	1	1	yes	characteristic
350	C₂×C₈	C₂×C₄×D₁₃	1	1	yes	characteristic
351	C₂×C₈	C₂³×D₁₃	1	1	yes	characteristic
352	C₄⋊C₄	—	13	1	no	—
353	C₄⋊C₄	—	13	1	no	—
354	C₄⋊C₄	—	13	1	no	—
355	C₄⋊C₄	—	13	1	no	—
356	C₄⋊C₄	—	13	1	no	—
357	C₄⋊C₄	—	13	1	no	—
358	C₂²⋊C₄	—	13	1	no	—
359	C₂²⋊C₄	—	13	1	no	—
360	C₂²⋊C₄	—	13	1	no	—
361	C₂²⋊C₄	—	13	1	no	—
362	C₂²⋊C₄	—	13	1	no	—
363	C₂²⋊C₄	—	13	1	no	—
364	C₄²	—	13	1	no	—
365	C₄²	—	13	1	no	—
366	C₄²	—	13	1	no	—
367	C₄²	—	13	1	no	—
368	C₄²	—	13	1	no	—
369	C₄²	—	13	1	no	—
370	C₄²	C₈×D₁₃	1	1	yes	characteristic
371	C₄²	C₈×D₁₃	1	1	yes	characteristic
372	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
373	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
374	C₁₆	—	2	2	no	—
375	C₁₆	—	2	2	no	—
376	C₁₆	—	26	2	no	—
377	C₁₆	—	26	2	no	—
378	C₁₃	#33420	1	1	yes	characteristic, complemented, Sylow
379	C₂³	—	13	1	no	—
380	C₂³	—	13	1	no	—
381	C₂³	C₂×C₈×D₁₃	1	1	yes	characteristic
382	Q₈	—	26	2	no	—
383	D₄	—	26	2	no	—
384	D₄	—	26	2	no	—
385	D₄	—	26	2	no	—
386	C₂×C₄	—	2	1	no	—
387	C₂×C₄	—	2	1	no	—
388	C₂×C₄	—	2	2	no	—
389	C₂×C₄	—	2	2	no	—
390	C₂×C₄	—	13	1	no	—
391	C₂×C₄	—	13	2	no	—
392	C₂×C₄	—	13	2	no	—
393	C₂×C₄	—	13	1	no	—
394	C₂×C₄	—	13	1	no	—
395	C₂×C₄	—	13	1	no	—
396	C₂×C₄	—	13	1	no	—
397	C₂×C₄	—	13	1	no	—
398	C₂×C₄	—	26	1	no	—
399	C₂×C₄	—	26	1	no	—
400	C₂×C₄	—	26	2	no	—
401	C₂×C₄	—	26	2	no	—
402	C₂×C₄	—	26	2	no	—
403	C₂×C₄	—	26	2	no	—
404	C₂×C₄	C₂×C₈×D₁₃	1	1	yes	characteristic
405	C₂×C₄	C₂×C₈×D₁₃	1	1	yes	characteristic
406	C₂×C₄	C₂×C₈×D₁₃	1	1	yes	characteristic
407	C₂×C₄	C₂×C₈×D₁₃	1	1	yes	characteristic
408	C₂×C₄	C₂×C₈×D₁₃	1	1	yes	characteristic
409	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
410	C₈	—	2	1	no	—
411	C₈	—	2	1	no	—
412	C₈	—	13	2	no	—
413	C₈	—	13	2	no	—
414	C₈	—	26	1	no	—
415	C₈	—	26	1	no	—
416	C₈	M₁₆×D₁₃	1	2	yes	—
417	C₈	#41×D₁₃	1	2	yes	—
418	C₂²	—	2	1	no	—
419	C₂²	—	2	1	no	—
420	C₂²	—	2	1	no	—
421	C₂²	—	13	2	no	—
422	C₂²	—	26	1	no	—
423	C₂²	—	26	1	no	—
424	C₂²	—	26	1	no	—
425	C₂²	—	26	1	no	—
426	C₂²	—	26	1	no	—
427	C₂²	C₂²×C₈×D₁₃	1	1	yes	characteristic
428	C₄	—	2	1	no	—
429	C₄	—	2	1	no	—
430	C₄	—	2	1	no	—
431	C₄	—	13	2	no	—
432	C₄	—	26	1	no	—
433	C₄	—	26	1	no	—
434	C₄	—	26	1	no	—
435	C₄	—	26	1	no	—
436	C₄	—	26	1	no	—
437	C₄	#11718562	1	2	yes	—
438	C₄	#11718568	1	2	yes	—
439	C₄	D₁₃×#117	1	1	yes	characteristic
440	C₄	C₂×M₁₆×D₁₃	1	1	yes	characteristic
441	C₂	—	4	1	no	—
442	C₂	—	26	2	no	—
443	C₂	—	52	1	no	—
444	C₂	D₁₃×#431	1	1	yes	characteristic
445	C₂	C₂×#11718562	1	1	yes	characteristic
446	C₂	C₂×#11718568	1	1	yes	characteristic

	subgroup	G/H
center	C₄×C₈	C₂²×D₁₃
commutator, socle	C₂²×C₁₃	C₂³×C₈
Frattini	C₂×C₈	C₂³×D₁₃
Fitting	C₁₃×#2162	C₂
prime radical	C₂×#6127	C₂×C₄
cosocle	C₂×C₈×C₁₃	C₂⁴
hypercenter	#2162	D₁₃
hypocenter	C₁₃	#33420
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₄×C₈ ◁ #2162

Complements

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

N	H ≅ G/N	type
2. #13116642	C₂	semidirect
3. #13116640	C₂	semidirect
4. #13116635	C₂	semidirect
5. #13116633	C₂	semidirect
6. #13116633	C₂	semidirect
7. #13116593	C₂	semidirect
9. C₄×#88038	C₂	semidirect
10. C₄×C₁₆×D₁₃	C₂	semidirect
11. C₁₃×#2162	C₂	semidirect
162. #2162	D₁₃	semidirect
378. C₁₃	#33420	semidirect

Maximal subgroups

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

subgroup	index
C₄×#88155	2
#13116642	2
#13116640	2
#13116635	2
#13116633	2
#13116593	2
#13116448	2
C₄×#88038	2
C₄×C₁₆×D₁₃	2
C₁₃×#2162	2
#33420	13