Subgroups — #16016021

Order 3328.

600 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11718350	C₂	1	1	yes	maximal, characteristic
2	#13116642	C₂	1	2	yes	maximal, complemented
3	#13116641	C₂	1	2	yes	maximal, complemented
4	#13116639	C₂	1	1	yes	maximal, characteristic, complemented
5	#13116636	C₂	1	1	yes	maximal, characteristic, complemented
6	#13116632	C₂	1	1	yes	maximal, characteristic, complemented
7	#13116593	C₂	1	2	yes	maximal, complemented
8	#13116445	C₂	1	1	yes	maximal, characteristic
9	D₁₃×C₂²⋊C₁₆	C₂	1	1	yes	maximal, characteristic
10	#13116431	C₂	1	2	yes	maximal, complemented
11	C₁₃×#2162	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×#6094	C₄	1	1	yes	characteristic
13	C₂²×C₈×D₁₃	C₂²	1	1	yes	characteristic
14	C₂×#88126	C₄	1	1	yes	characteristic
15	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
16	C₂×#88055	C₄	1	1	yes	characteristic
17	C₂×C₈×Dic₁₃	C₂²	1	1	yes	characteristic
18	C₂×#88043	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	C₄	1	1	yes	characteristic
24	#11718350	C₄	1	1	yes	characteristic
25	#11718350	C₂²	1	1	yes	characteristic
26	#11718350	C₂²	1	1	yes	characteristic
27	#11718350	C₂²	1	1	yes	characteristic
28	#11718350	C₂²	1	1	yes	characteristic
29	C₁₃×C₄⋊C₁₆	C₂²	1	2	yes	complemented
30	C₁₃×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic
31	C₁₃×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic
32	C₄×C₁₃×C₁₆	C₂²	1	2	yes	complemented
33	C₂²⋊#6090	C₂²	1	1	yes	characteristic
34	C₂²⋊#6090	C₂²	1	1	yes	characteristic
35	#11718099	C₂²	1	2	yes	—
36	#11718099	C₂²	1	2	yes	—
37	#11718094	C₂²	1	2	yes	complemented
38	#11718093	C₂²	1	2	yes	complemented
39	#11718093	C₂²	1	2	yes	complemented
40	C₁₆×Dic₁₃	C₂²	1	2	yes	complemented
41	C₄⋊#6090	C₂²	1	2	yes	complemented
42	#11718053	C₂²	1	2	yes	complemented
43	C₂²×C₄×D₁₃	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	C₂×#6103	C₈	1	1	yes	characteristic
48	C₂×#6103	C₈	1	1	yes	characteristic
49	C₂×#6101	C₈	1	1	yes	characteristic
50	C₂×#6101	C₈	1	1	yes	characteristic
51	C₂×C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
52	C₂²×#1055	C₂×C₄	1	1	yes	characteristic
53	C₂²×#1055	C₂×C₄	1	1	yes	characteristic
54	C₂×#6094	—	2	4	no	—
55	C₂×#6094	C₂×C₄	1	1	yes	characteristic
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×C₈×D₁₃	—	2	4	no	—
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	#88126	C₈	1	1	yes	characteristic
65	#88126	C₈	1	1	yes	characteristic
66	#88126	C₈	1	1	yes	characteristic
67	#88126	C₈	1	1	yes	characteristic
68	#88126	C₂×C₄	1	1	yes	characteristic
69	#88126	C₂×C₄	1	1	yes	characteristic
70	#88126	C₂×C₄	1	1	yes	characteristic
71	#88126	C₂×C₄	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	#88043	C₂×C₄	1	1	yes	characteristic
91	#88043	C₂×C₄	1	1	yes	characteristic
92	#88038	—	2	4	no	—
93	C₁₆×D₁₃	—	2	4	no	—
94	#33422	—	13	1	no	maximal, Sylow
95	C₂³×D₁₃	C₂×C₈	1	1	yes	characteristic
96	C₂²×C₄×C₁₃	C₂×C₈	1	1	yes	characteristic
97	C₂²×C₄×C₁₃	C₂×C₈	1	1	yes	characteristic
98	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
99	C₂²×Dic₁₃	C₂×C₈	1	1	yes	characteristic
100	C₂²×Dic₁₃	C₂×C₈	1	1	yes	characteristic
101	C₂²×Dic₁₃	C₂×C₈	1	1	yes	characteristic
102	C₂×C₄×D₁₃	—	2	2	no	—
103	C₂×C₄×D₁₃	—	2	2	no	—
104	C₂×C₄×D₁₃	C₂×C₈	1	1	yes	characteristic
105	C₂×C₄×D₁₃	C₂×C₈	1	1	yes	characteristic
106	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
107	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
108	C₂×C₈×C₁₃	—	2	2	no	—
109	C₂×C₈×C₁₃	—	2	2	no	—
110	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
111	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
112	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
113	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
114	C₄²×C₁₃	C₂×C₈	1	1	yes	characteristic
115	C₄²×C₁₃	C₂×C₈	1	1	yes	characteristic
116	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
117	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
118	#6103	C₂×C₈	1	1	yes	characteristic
119	#6103	C₂×C₈	1	1	yes	characteristic
120	#6103	C₂×C₈	1	1	yes	characteristic
121	#6103	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	#6101	C₂×C₈	1	1	yes	characteristic
127	#6101	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	#6101	C₂×C₈	1	1	yes	characteristic
133	#6101	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	C₂×#1055	—	2	2	no	—
139	C₂×#1055	—	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	M₁₆	1	4	yes	—
148	C₈×D₁₃	—	2	2	no	—
149	C₈×D₁₃	—	2	2	no	—
150	C₈×D₁₃	—	2	2	no	—
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	C₂×#405	—	13	1	no	—
157	#2164	—	13	2	no	—
158	#2164	—	13	2	no	—
159	#2163	—	13	1	no	—
160	#2163	—	13	1	no	—
161	#2162	—	13	1	no	—
162	#2162	D₁₃	1	1	yes	characteristic, complemented
163	#2151	—	13	2	no	—
164	#2112	—	13	1	no	—
165	C₂×C₂²⋊C₁₆	—	13	1	no	—
166	#2108	—	13	2	no	—
167	C₂³×C₁₃	C₂²×C₈	1	1	yes	characteristic
168	C₂²×D₁₃	—	2	2	no	—
169	C₂²×D₁₃	—	2	2	no	—
170	C₂²×D₁₃	—	4	1	no	—
171	C₂²×D₁₃	C₂²×C₈	1	1	yes	characteristic
172	C₂²×D₁₃	C₂²×C₈	1	1	yes	characteristic
173	C₂×C₄×C₁₃	—	2	2	no	—
174	C₂×C₄×C₁₃	—	2	1	no	—
175	C₂×C₄×C₁₃	—	2	1	no	—
176	C₂×C₄×C₁₃	—	4	1	no	—
177	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
178	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
179	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
180	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
181	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
182	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
183	C₂×Dic₁₃	—	2	2	no	—
184	C₂×Dic₁₃	—	2	2	no	—
185	C₂×Dic₁₃	—	4	1	no	—
186	C₂×Dic₁₃	C₂²×C₈	1	1	yes	characteristic
187	C₂×Dic₁₃	C₂²×C₈	1	1	yes	characteristic
188	C₂×Dic₁₃	C₂²×C₈	1	1	yes	characteristic
189	C₂×Dic₁₃	C₂²×C₈	1	1	yes	characteristic
190	C₂×Dic₁₃	C₂²×C₈	1	1	yes	characteristic
191	C₂×Dic₁₃	C₂²×C₈	1	1	yes	characteristic
192	C₄×D₁₃	—	2	2	no	—
193	C₄×D₁₃	—	2	1	no	—
194	C₄×D₁₃	—	2	1	no	—
195	C₄×D₁₃	—	2	2	no	—
196	C₄×D₁₃	#117	1	2	yes	—
197	C₄×D₁₃	C₂×M₁₆	1	2	yes	—
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	C₂²×M₁₆	—	13	1	no	—
207	C₂³×C₈	—	13	1	no	—
208	C₂×#117	—	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	#405	—	13	1	no	—
218	#405	—	13	1	no	—
219	C₂×#97	—	13	1	no	—
220	C₂×#97	—	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	complemented
227	C₂²⋊C₁₆	—	13	1	no	—
228	C₂²⋊C₁₆	—	13	1	no	—
229	C₂²⋊C₁₆	—	13	2	no	—
230	C₂²⋊C₁₆	—	13	2	no	—
231	C₂²⋊C₁₆	C₂×D₁₃	1	1	yes	characteristic
232	C₂²⋊C₁₆	C₂×D₁₃	1	1	yes	characteristic
233	#346	—	13	2	no	—
234	#346	—	13	2	no	—
235	C₄×C₁₆	—	13	2	no	—
236	C₄×C₁₆	C₂×D₁₃	1	2	yes	complemented
237	C₂²×C₁₃	—	2	1	no	—
238	C₂²×C₁₃	—	2	1	no	—
239	C₂²×C₁₃	#504	1	2	yes	—
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	—	4	4	no	—
247	C₂×D₁₃	#431	1	2	yes	—
248	C₄×C₁₃	—	2	1	no	—
249	C₄×C₁₃	—	2	1	no	—
250	C₄×C₁₃	—	2	1	no	—
251	C₄×C₁₃	—	2	1	no	—
252	C₄×C₁₃	—	2	1	no	—
253	C₄×C₁₃	C₂×#117	1	1	yes	characteristic
254	C₄×C₁₃	C₂²×M₁₆	1	1	yes	characteristic
255	Dic₁₃	—	2	1	no	—
256	Dic₁₃	—	2	1	no	—
257	Dic₁₃	—	2	1	no	—
258	Dic₁₃	—	2	1	no	—
259	Dic₁₃	—	2	1	no	—
260	Dic₁₃	#431	1	2	yes	—
261	C₂³×C₄	—	13	1	no	—
262	C₂×M₁₆	—	13	1	no	—
263	C₂×M₁₆	—	13	1	no	—
264	C₂×M₁₆	—	13	1	no	—
265	C₂×M₁₆	—	13	1	no	—
266	C₂×M₁₆	—	26	4	no	—
267	C₂²×C₈	—	13	1	no	—
268	C₂²×C₈	—	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	—	26	4	no	—
274	C₂²×C₈	C₄×D₁₃	1	1	yes	characteristic
275	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
276	#117	—	13	1	no	—
277	#117	—	13	1	no	—
278	#117	—	13	1	no	—
279	#117	—	13	1	no	—
280	#117	—	13	1	no	—
281	#117	—	13	1	no	—
282	#117	—	13	1	no	—
283	#117	—	13	1	no	—
284	C₂×C₄⋊C₄	—	13	1	no	—
285	C₂×C₄⋊C₄	—	13	1	no	—
286	C₂×C₂²⋊C₄	—	13	1	no	—
287	C₂×C₂²⋊C₄	—	13	1	no	—
288	C₂×C₄²	—	13	1	no	—
289	C₂×C₄²	C₄×D₁₃	1	1	yes	characteristic
290	M₃₂	—	26	4	no	—
291	C₂×C₁₆	—	13	2	no	—
292	C₂×C₁₆	—	13	2	no	—
293	C₂×C₁₆	—	26	4	no	—
294	C₂×C₁₆	C₂²×D₁₃	1	2	yes	—
295	C₂×C₁₆	C₂²×D₁₃	1	2	yes	—
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	#97	—	13	1	no	—
302	#97	—	13	1	no	—
303	#97	—	13	1	no	—
304	C₄×C₈	—	13	1	no	—
305	C₄×C₈	—	13	1	no	—
306	C₄×C₈	—	13	1	no	—
307	C₄×C₈	—	13	1	no	—
308	C₄×C₈	C₄×D₁₃	1	1	yes	characteristic
309	C₄×C₈	C₄×D₁₃	1	1	yes	characteristic
310	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
311	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
312	C₂×C₁₃	—	2	2	no	—
313	C₂×C₁₃	C₂×#431	1	1	yes	characteristic
314	C₂×C₁₃	C₂×#504	1	1	yes	characteristic
315	C₂×C₁₃	#3407	1	1	yes	characteristic
316	D₁₃	—	2	2	no	—
317	D₁₃	—	4	1	no	—
318	C₂⁴	—	13	1	no	—
319	C₂²×C₄	—	13	1	no	—
320	C₂²×C₄	—	13	1	no	—
321	C₂²×C₄	—	13	1	no	—
322	C₂²×C₄	—	13	1	no	—
323	C₂²×C₄	—	13	1	no	—
324	C₂²×C₄	—	13	1	no	—
325	C₂²×C₄	—	13	1	no	—
326	C₂²×C₄	—	26	2	no	—
327	C₂²×C₄	—	26	2	no	—
328	C₂²×C₄	C₈×D₁₃	1	1	yes	characteristic
329	C₂²×C₄	C₈×D₁₃	1	1	yes	characteristic
330	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
331	M₁₆	—	13	4	no	—
332	M₁₆	—	26	2	no	—
333	M₁₆	—	26	2	no	—
334	M₁₆	—	26	2	no	—
335	C₂×C₈	—	2	2	no	—
336	C₂×C₈	—	2	2	no	—
337	C₂×C₈	—	13	1	no	—
338	C₂×C₈	—	13	1	no	—
339	C₂×C₈	—	13	4	no	—
340	C₂×C₈	—	13	1	no	—
341	C₂×C₈	—	13	1	no	—
342	C₂×C₈	—	26	2	no	—
343	C₂×C₈	—	26	2	no	—
344	C₂×C₈	—	26	2	no	—
345	C₂×C₈	—	26	2	no	—
346	C₂×C₈	—	26	2	no	—
347	C₂×C₈	C₂×C₄×D₁₃	1	1	yes	characteristic
348	C₂×C₈	C₂×C₄×D₁₃	1	1	yes	characteristic
349	C₂×C₈	C₂×C₄×D₁₃	1	1	yes	characteristic
350	C₂×C₈	C₂³×D₁₃	1	1	yes	characteristic
351	C₄⋊C₄	—	13	1	no	—
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	C₄⋊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	C₂²⋊C₄	—	13	1	no	—
365	C₂²⋊C₄	—	13	1	no	—
366	C₂²⋊C₄	—	13	1	no	—
367	C₄²	—	13	1	no	—
368	C₄²	—	13	1	no	—
369	C₄²	—	13	1	no	—
370	C₄²	—	13	1	no	—
371	C₄²	C₈×D₁₃	1	1	yes	characteristic
372	C₄²	C₈×D₁₃	1	1	yes	characteristic
373	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
374	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
375	C₁₆	—	2	2	no	—
376	C₁₆	—	2	2	no	—
377	C₁₆	—	26	2	no	—
378	C₁₆	—	26	2	no	—
379	C₁₃	#33422	1	1	yes	characteristic, complemented, Sylow
380	C₂³	—	13	1	no	—
381	C₂³	—	13	1	no	—
382	C₂³	—	26	2	no	—
383	C₂³	—	26	2	no	—
384	C₂³	—	52	1	no	—
385	C₂³	C₂×C₈×D₁₃	1	1	yes	characteristic
386	C₂×C₄	—	2	2	no	—
387	C₂×C₄	—	2	1	no	—
388	C₂×C₄	—	2	1	no	—
389	C₂×C₄	—	4	1	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	2	no	—
399	C₂×C₄	—	26	2	no	—
400	C₂×C₄	—	26	2	no	—
401	C₂×C₄	—	26	2	no	—
402	C₂×C₄	—	26	1	no	—
403	C₂×C₄	—	26	1	no	—
404	C₂×C₄	—	52	1	no	—
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	C₂×C₈×D₁₃	1	1	yes	characteristic
410	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
411	C₈	—	2	1	no	—
412	C₈	—	2	1	no	—
413	C₈	—	13	2	no	—
414	C₈	—	13	2	no	—
415	C₈	—	26	1	no	—
416	C₈	—	26	1	no	—
417	C₈	M₁₆×D₁₃	1	2	yes	—
418	C₈	#41×D₁₃	1	2	yes	—
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	—	52	4	no	—
428	C₂²	#11718562	1	2	yes	—
429	C₂²	C₂²×C₈×D₁₃	1	1	yes	characteristic
430	C₄	—	2	1	no	—
431	C₄	—	2	1	no	—
432	C₄	—	2	1	no	—
433	C₄	—	2	1	no	—
434	C₄	—	2	1	no	—
435	C₄	—	13	2	no	—
436	C₄	—	26	1	no	—
437	C₄	—	26	1	no	—
438	C₄	—	26	1	no	—
439	C₄	—	26	1	no	—
440	C₄	—	26	1	no	—
441	C₄	D₁₃×#117	1	1	yes	characteristic
442	C₄	C₂×M₁₆×D₁₃	1	1	yes	characteristic
443	C₂	—	2	2	no	—
444	C₂	—	26	2	no	—
445	C₂	—	52	1	no	—
446	C₂	D₁₃×#431	1	1	yes	characteristic
447	C₂	C₂×#11718562	1	1	yes	characteristic
448	C₂	#13127938	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₈	C₂³×D₁₃
commutator, socle	C₂²×C₁₃	C₂³×C₈
Fitting	C₁₃×#2162	C₂
prime radical	C₂³×D₁₃	C₂×C₈
cosocle	C₂×C₈×C₁₃	C₂⁴
hypercenter	#2162	D₁₃
hypocenter	C₁₃	#33422
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₈ ◁ #2162

Complements

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

N	H ≅ G/N	type
2. #13116642	C₂	semidirect
3. #13116641	C₂	semidirect
4. #13116639	C₂	semidirect
5. #13116636	C₂	semidirect
6. #13116632	C₂	semidirect
7. #13116593	C₂	semidirect
10. #13116431	C₂	semidirect
11. C₁₃×#2162	C₂	semidirect
29. C₁₃×C₄⋊C₁₆	C₂²	semidirect
32. C₄×C₁₃×C₁₆	C₂²	semidirect
37. #11718094	C₂²	semidirect
38. #11718093	C₂²	semidirect
39. #11718093	C₂²	semidirect
40. C₁₆×Dic₁₃	C₂²	semidirect
41. C₄⋊#6090	C₂²	semidirect
42. #11718053	C₂²	semidirect
162. #2162	D₁₃	semidirect
226. C₄⋊C₁₆	C₂×D₁₃	semidirect
236. C₄×C₁₆	C₂×D₁₃	semidirect
379. C₁₃	#33422	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11718350	2
#13116642	2
#13116641	2
#13116639	2
#13116636	2
#13116632	2
#13116593	2
#13116445	2
D₁₃×C₂²⋊C₁₆	2
#13116431	2
C₁₃×#2162	2
#33422	13