Subgroups — #16016118

Order 3328.

692 conjugacy classes of subgroups.

The subgroup lattice has 420 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, complemented
2	#13123528	C₂	1	1	yes	maximal, characteristic
3	#13116666	C₂	1	2	yes	maximal, complemented
4	#13116661	C₂	1	2	yes	maximal, complemented
5	#13116659	C₂	1	2	yes	maximal, complemented
6	C₁₆×C₂²⋊D₁₃	C₂	1	2	yes	maximal, complemented
7	#13116594	C₂	1	1	yes	maximal, characteristic, complemented
8	#13116450	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#11718099	C₂	1	1	yes	maximal, characteristic, complemented
10	#13116435	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₁₃×#504	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₃×#131	C₂²	1	1	yes	characteristic
13	#11719533	C₄	1	1	yes	characteristic
14	C₂²×C₈×D₁₃	C₂²	1	1	yes	characteristic
15	C₁₃×#504	—	2	4	no	—
16	C₂×C₁₃×M₃₂	C₂²	1	1	yes	characteristic
17	C₂×C₁₃×M₃₂	C₂²	1	2	yes	complemented
18	C₂²×C₁₃×C₁₆	C₂²	1	1	yes	characteristic
19	C₂²×C₁₃×C₁₆	C₂²	1	2	yes	complemented
20	#11718895	C₄	1	1	yes	characteristic
21	#11718788	C₄	1	2	yes	—
22	#11718788	C₄	1	2	yes	—
23	#11718787	C₄	1	1	yes	characteristic
24	#11718780	C₄	1	1	yes	characteristic
25	C₈×C₂²⋊D₁₃	C₂²	1	2	yes	—
26	C₈×C₂²⋊D₁₃	C₂²	1	2	yes	—
27	#11718762	C₂²	1	1	yes	characteristic
28	C₂×#88052	C₂²	1	1	yes	characteristic
29	C₂²×#6090	C₂²	1	1	yes	characteristic
30	D₁₃×M₃₂	—	2	4	no	—
31	C₂×#88038	C₂²	1	2	yes	—
32	C₂×C₁₆×D₁₃	C₂²	1	2	yes	—
33	C₂²⋊#6090	C₂²	1	2	yes	complemented
34	C₂²⋊#6090	C₂²	1	2	yes	complemented
35	#11718099	C₂²	1	1	yes	characteristic
36	#11718099	C₂²	1	1	yes	characteristic
37	#11718099	C₂²	1	1	yes	characteristic
38	#11718099	C₂²	1	1	yes	characteristic
39	#11718094	C₂²	1	2	yes	complemented
40	#11718093	C₂²	1	2	yes	complemented
41	#11718093	C₂²	1	2	yes	complemented
42	C₁₆×Dic₁₃	C₂²	1	2	yes	complemented
43	C₂×C₁₃×#41	C₂×C₄	1	1	yes	characteristic
44	C₂²×C₄×D₁₃	C₂×C₄	1	1	yes	characteristic
45	C₁₃×#131	—	2	2	no	—
46	C₁₃×#131	—	2	2	no	—
47	C₂×C₁₃×M₁₆	C₂×C₄	1	1	yes	characteristic
48	C₂×C₁₃×M₁₆	C₂×C₄	1	2	yes	—
49	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
50	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
51	#88200	C₈	1	1	yes	characteristic
52	#88200	C₈	1	1	yes	characteristic
53	#88192	C₈	1	1	yes	characteristic
54	#88192	C₈	1	1	yes	characteristic
55	#88191	C₈	1	2	yes	—
56	#88189	C₈	1	2	yes	—
57	C₄×C₂²⋊D₁₃	C₂×C₄	1	2	yes	—
58	C₄×C₂²⋊D₁₃	C₂×C₄	1	2	yes	—
59	#88180	C₂×C₄	1	1	yes	characteristic
60	C₂×#6099	C₂×C₄	1	1	yes	characteristic
61	C₂²×#1055	C₂×C₄	1	1	yes	characteristic
62	C₂×C₈×D₁₃	—	2	2	no	—
63	C₂×C₈×D₁₃	—	2	2	no	—
64	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
65	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
66	C₂×C₈×D₁₃	C₂³	1	1	yes	characteristic
67	C₂×C₈×D₁₃	C₂³	1	1	yes	characteristic
68	C₁₃×M₃₂	—	2	4	no	—
69	C₁₃×M₃₂	D₄	1	4	yes	complemented
70	C₂×C₁₃×C₁₆	—	2	2	no	—
71	C₂×C₁₃×C₁₆	—	2	4	no	—
72	C₂×C₁₃×C₁₆	C₂³	1	1	yes	characteristic
73	C₂×C₁₃×C₁₆	C₂³	1	1	yes	characteristic
74	C₂×C₁₃×C₁₆	C₂³	1	2	yes	—
75	C₂²⋊#1055	C₂×C₄	1	2	yes	—
76	C₂²⋊#1055	C₂×C₄	1	2	yes	—
77	#88060	C₂×C₄	1	2	yes	—
78	#88060	C₂×C₄	1	2	yes	—
79	#88055	C₂×C₄	1	2	yes	—
80	#88054	C₂×C₄	1	2	yes	—
81	#88054	C₂×C₄	1	2	yes	—
82	C₈×Dic₁₃	C₂³	1	2	yes	—
83	#88052	—	2	2	no	—
84	C₂×#6090	—	2	2	no	—
85	C₂×#6090	C₂³	1	1	yes	characteristic
86	C₂×#6090	C₂³	1	1	yes	characteristic
87	C₂×#6090	C₂³	1	2	yes	—
88	#88038	—	2	4	no	—
89	C₁₆×D₁₃	—	2	4	no	—
90	#33436	—	13	1	no	maximal, Sylow
91	C₂³×D₁₃	C₂×C₈	1	1	yes	characteristic
92	C₁₃×#41	—	2	2	no	—
93	C₁₃×#41	—	2	2	no	—
94	C₂×Q₈×C₁₃	C₂×C₈	1	1	yes	characteristic
95	C₂×D₄×C₁₃	C₂×C₈	1	2	yes	—
96	C₂×D₄×C₁₃	C₂×C₈	1	1	yes	characteristic
97	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
98	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
99	C₂×C₂²⋊D₁₃	C₂×C₈	1	2	yes	—
100	C₂×C₂²⋊D₁₃	C₂×C₈	1	2	yes	—
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	C₁₃×M₁₆	—	2	2	no	—
109	C₁₃×M₁₆	—	2	4	no	—
110	C₂×C₈×C₁₃	—	2	2	no	—
111	C₂×C₈×C₁₃	—	2	2	no	—
112	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
113	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
114	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
115	C₂×C₈×C₁₃	#41	1	2	yes	—
116	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
117	C₂²⋊Dic₁₃	C₂×C₈	1	2	yes	—
118	C₂²⋊Dic₁₃	C₂×C₈	1	2	yes	—
119	C₂²⋊Dic₁₃	C₂×C₈	1	2	yes	—
120	#6103	C₂×C₈	1	2	yes	—
121	#6103	C₂×C₈	1	2	yes	—
122	C₄⋊Dic₁₃	C₂×C₈	1	1	yes	characteristic
123	C₄⋊Dic₁₃	C₂×C₈	1	1	yes	characteristic
124	#6101	C₂×C₈	1	2	yes	—
125	#6101	C₂×C₈	1	2	yes	—
126	C₄×Dic₁₃	C₂²×C₄	1	2	yes	—
127	#6099	—	2	2	no	—
128	C₂×#1055	—	2	2	no	—
129	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
130	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
131	C₂×#1055	C₂²×C₄	1	2	yes	—
132	C₈×D₁₃	—	2	2	no	—
133	C₈×D₁₃	—	2	2	no	—
134	C₈×D₁₃	—	2	1	no	—
135	C₈×D₁₃	—	2	1	no	—
136	C₈×D₁₃	—	2	1	no	—
137	C₈×D₁₃	—	2	1	no	—
138	C₁₃×C₁₆	—	2	1	no	—
139	C₁₃×C₁₆	—	2	1	no	—
140	C₁₃×C₁₆	C₂×D₄	1	4	yes	—
141	#6090	—	2	2	no	—
142	#6090	—	2	1	no	—
143	#6090	—	2	1	no	—
144	C₂×#504	D₁₃	1	1	yes	characteristic, complemented
145	C₂²×M₃₂	—	13	1	no	—
146	#2929	—	13	1	no	—
147	#2169	—	13	2	no	—
148	#2168	—	13	2	no	—
149	#2168	—	13	2	no	—
150	D₄×C₁₆	—	13	2	no	—
151	#2151	—	13	1	no	—
152	#2113	—	13	1	no	—
153	C₂×C₂²⋊C₁₆	—	13	1	no	—
154	#2108	—	13	1	no	—
155	C₂³×C₁₃	C₂²×C₈	1	2	yes	—
156	C₂³×C₁₃	C₂²×C₈	1	1	yes	characteristic
157	C₂²×D₁₃	—	2	2	no	—
158	C₂²×D₁₃	—	2	2	no	—
159	C₂²×D₁₃	—	4	1	no	—
160	C₂²×D₁₃	C₂²×C₈	1	1	yes	characteristic
161	C₂²×D₁₃	C₂²×C₈	1	1	yes	characteristic
162	Q₈×C₁₃	—	2	2	no	—
163	D₄×C₁₃	—	2	4	no	—
164	D₄×C₁₃	—	2	2	no	—
165	C₂×C₄×C₁₃	—	2	2	no	—
166	C₂×C₄×C₁₃	—	2	2	no	—
167	C₂×C₄×C₁₃	C₄×D₄	1	2	yes	—
168	C₂×C₄×C₁₃	C₂²×C₈	1	2	yes	—
169	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
170	C₂×C₄×C₁₃	#131	1	2	yes	—
171	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
172	C₂²⋊D₁₃	—	2	4	no	—
173	C₂²⋊D₁₃	—	4	2	no	—
174	C₂×Dic₁₃	—	2	2	no	—
175	C₂×Dic₁₃	C₂²×C₈	1	2	yes	—
176	C₂×Dic₁₃	C₂²×C₈	1	2	yes	—
177	C₂×Dic₁₃	C₂²×C₈	1	1	yes	characteristic
178	C₂×Dic₁₃	C₂²×C₈	1	1	yes	characteristic
179	C₄×D₁₃	—	2	1	no	—
180	C₄×D₁₃	—	2	1	no	—
181	C₄×D₁₃	—	2	1	no	—
182	C₄×D₁₃	—	2	1	no	—
183	C₄×D₁₃	—	2	2	no	—
184	C₄×D₁₃	—	2	2	no	—
185	C₈×C₁₃	—	2	2	no	—
186	C₈×C₁₃	C₄×D₄	1	2	yes	—
187	C₈×C₁₃	C₂²×D₄	1	1	yes	characteristic
188	C₈×C₁₃	C₂×#41	1	1	yes	characteristic
189	#1055	—	2	1	no	—
190	#1055	—	2	1	no	—
191	#1055	—	2	2	no	—
192	C₂×#131	C₂×D₁₃	1	1	yes	characteristic
193	C₂³×C₈	—	13	1	no	—
194	#525	—	13	1	no	—
195	#504	—	2	4	no	—
196	C₂×M₃₂	—	13	1	no	—
197	C₂×M₃₂	—	13	2	no	—
198	C₂×M₃₂	—	26	4	no	—
199	C₂×M₃₂	C₂×D₁₃	1	1	yes	characteristic
200	C₂×M₃₂	C₂×D₁₃	1	2	yes	complemented
201	C₂²×C₁₆	—	13	1	no	—
202	C₂²×C₁₆	—	13	2	no	—
203	C₂²×C₁₆	C₂×D₁₃	1	1	yes	characteristic
204	C₂²×C₁₆	C₂×D₁₃	1	2	yes	complemented
205	#435	—	13	2	no	—
206	#435	—	13	2	no	—
207	C₈×D₄	—	13	2	no	—
208	C₈×D₄	—	13	2	no	—
209	#424	—	13	1	no	—
210	#408	—	13	1	no	—
211	#407	—	13	1	no	—
212	#405	—	13	1	no	—
213	C₄⋊C₁₆	—	13	2	no	—
214	C₄⋊C₁₆	—	13	2	no	—
215	C₂²⋊C₁₆	—	13	2	no	—
216	C₂²⋊C₁₆	—	13	2	no	—
217	C₂²⋊C₁₆	—	13	1	no	—
218	C₂²⋊C₁₆	—	13	1	no	—
219	C₂²⋊C₁₆	—	13	1	no	—
220	C₂²⋊C₁₆	—	13	1	no	—
221	#346	—	13	2	no	—
222	C₄×C₁₆	—	13	2	no	—
223	C₂²×C₁₃	—	2	1	no	—
224	C₂²×C₁₃	—	2	1	no	—
225	C₂²×C₁₃	—	2	2	no	—
226	C₂²×C₁₃	—	2	2	no	—
227	C₂²×C₁₃	—	2	2	no	—
228	C₂²×C₁₃	C₈×D₄	1	2	yes	—
229	C₂²×C₁₃	C₂³×C₈	1	1	yes	characteristic
230	C₂×D₁₃	—	2	1	no	—
231	C₂×D₁₃	—	2	1	no	—
232	C₂×D₁₃	—	2	1	no	—
233	C₂×D₁₃	—	2	1	no	—
234	C₂×D₁₃	—	2	1	no	—
235	C₂×D₁₃	—	4	4	no	—
236	C₂×D₁₃	#504	1	2	yes	complemented
237	C₄×C₁₃	—	2	2	no	—
238	C₄×C₁₃	C₈×D₄	1	2	yes	—
239	C₄×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
240	C₄×C₁₃	C₂×#131	1	1	yes	characteristic
241	Dic₁₃	—	2	2	no	—
242	Dic₁₃	—	2	2	no	—
243	Dic₁₃	—	2	1	no	—
244	Dic₁₃	—	2	1	no	—
245	C₂×#41	C₄×D₁₃	1	1	yes	characteristic
246	C₂³×C₄	—	13	1	no	—
247	#131	—	2	2	no	—
248	#131	—	2	2	no	—
249	C₂×M₁₆	—	13	1	no	—
250	C₂×M₁₆	C₄×D₁₃	1	1	yes	characteristic
251	C₂×M₁₆	C₄×D₁₃	1	2	yes	—
252	C₂²×C₈	—	13	1	no	—
253	C₂²×C₈	—	13	1	no	—
254	C₂²×C₈	—	13	1	no	—
255	C₂²×C₈	—	13	1	no	—
256	C₂²×C₈	—	13	1	no	—
257	C₂²×C₈	—	26	2	no	—
258	C₂²×C₈	—	26	2	no	—
259	C₂²×C₈	C₂²×D₁₃	1	2	yes	—
260	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
261	#123	—	13	2	no	—
262	C₂²⋊Q₈	—	13	1	no	—
263	C₂²⋊Q₈	—	13	1	no	—
264	#121	—	13	1	no	—
265	#121	—	13	1	no	—
266	#120	—	13	2	no	—
267	C₄×D₄	—	13	2	no	—
268	C₄×D₄	—	13	2	no	—
269	#117	—	13	1	no	—
270	M₃₂	—	2	4	no	—
271	M₃₂	—	26	2	no	—
272	M₃₂	—	26	4	no	—
273	M₃₂	C₂²⋊D₁₃	1	4	yes	complemented
274	C₂×C₁₆	—	2	2	no	—
275	C₂×C₁₆	—	2	4	no	—
276	C₂×C₁₆	—	13	1	no	—
277	C₂×C₁₆	—	13	1	no	—
278	C₂×C₁₆	—	13	2	no	—
279	C₂×C₁₆	—	26	2	no	—
280	C₂×C₁₆	—	26	4	no	—
281	C₂×C₁₆	C₂²×D₁₃	1	1	yes	characteristic
282	C₂×C₁₆	C₂²×D₁₃	1	1	yes	characteristic
283	C₂×C₁₆	C₂²×D₁₃	1	2	yes	—
284	C₄⋊C₈	—	13	2	no	—
285	C₄⋊C₈	—	13	2	no	—
286	C₂²⋊C₈	—	13	2	no	—
287	C₂²⋊C₈	—	13	2	no	—
288	C₂²⋊C₈	—	13	2	no	—
289	C₂²⋊C₈	—	13	2	no	—
290	#97	—	13	2	no	—
291	C₄×C₈	—	13	2	no	—
292	C₂×C₁₃	—	2	2	no	—
293	C₂×C₁₃	—	4	2	no	—
294	C₂×C₁₃	C₂×C₈×D₄	1	1	yes	characteristic
295	C₂×C₁₃	C₂×#504	1	1	yes	characteristic
296	C₂×C₁₃	#3407	1	1	yes	characteristic
297	D₁₃	—	2	2	no	—
298	D₁₃	—	4	1	no	—
299	C₂⁴	—	13	1	no	—
300	#41	—	2	2	no	—
301	#41	—	2	2	no	—
302	C₂×Q₈	C₈×D₁₃	1	1	yes	characteristic
303	C₂×D₄	—	13	2	no	—
304	C₂×D₄	—	13	2	no	—
305	C₂×D₄	C₈×D₁₃	1	2	yes	—
306	C₂×D₄	C₈×D₁₃	1	1	yes	characteristic
307	C₂²×C₄	—	13	1	no	—
308	C₂²×C₄	—	13	1	no	—
309	C₂²×C₄	—	13	1	no	—
310	C₂²×C₄	—	13	1	no	—
311	C₂²×C₄	—	13	1	no	—
312	C₂²×C₄	—	26	2	no	—
313	C₂²×C₄	—	26	2	no	—
314	C₂²×C₄	C₂×C₄×D₁₃	1	2	yes	—
315	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
316	M₁₆	—	2	2	no	—
317	M₁₆	—	2	4	no	—
318	M₁₆	—	26	2	no	—
319	C₂×C₈	—	2	2	no	—
320	C₂×C₈	—	2	2	no	—
321	C₂×C₈	—	13	2	no	—
322	C₂×C₈	—	13	1	no	—
323	C₂×C₈	—	13	1	no	—
324	C₂×C₈	—	26	2	no	—
325	C₂×C₈	—	26	2	no	—
326	C₂×C₈	—	26	2	no	—
327	C₂×C₈	—	26	1	no	—
328	C₂×C₈	—	26	1	no	—
329	C₂×C₈	—	26	1	no	—
330	C₂×C₈	—	26	1	no	—
331	C₂×C₈	C₂×C₄×D₁₃	1	2	yes	—
332	C₂×C₈	C₂×C₄×D₁₃	1	1	yes	characteristic
333	C₂×C₈	#6127	1	2	yes	—
334	C₂×C₈	C₂×C₂²⋊D₁₃	1	2	yes	—
335	C₂×C₈	C₂³×D₁₃	1	1	yes	characteristic
336	C₄⋊C₄	—	13	1	no	—
337	C₄⋊C₄	—	13	1	no	—
338	C₄⋊C₄	—	13	2	no	—
339	C₄⋊C₄	—	13	2	no	—
340	C₂²⋊C₄	—	13	2	no	—
341	C₂²⋊C₄	—	13	2	no	—
342	C₂²⋊C₄	—	13	2	no	—
343	C₂²⋊C₄	—	13	2	no	—
344	C₂²⋊C₄	—	13	2	no	—
345	C₄²	—	13	2	no	—
346	C₁₆	—	2	1	no	—
347	C₁₆	—	2	1	no	—
348	C₁₆	—	26	1	no	—
349	C₁₆	—	26	1	no	—
350	C₁₆	—	26	2	no	—
351	C₁₆	C₂×C₂²⋊D₁₃	1	4	yes	—
352	C₁₃	#33436	1	1	yes	characteristic, complemented, Sylow
353	C₂³	—	13	1	no	—
354	C₂³	—	13	1	no	—
355	C₂³	—	26	2	no	—
356	C₂³	—	26	2	no	—
357	C₂³	—	52	1	no	—
358	C₂³	C₂×C₈×D₁₃	1	2	yes	—
359	C₂³	C₂×C₈×D₁₃	1	1	yes	characteristic
360	Q₈	—	2	2	no	—
361	D₄	—	2	4	no	—
362	D₄	—	2	2	no	—
363	D₄	—	26	4	no	—
364	D₄	—	52	2	no	—
365	C₂×C₄	—	2	2	no	—
366	C₂×C₄	—	2	2	no	—
367	C₂×C₄	—	13	2	no	—
368	C₂×C₄	—	13	2	no	—
369	C₂×C₄	—	13	1	no	—
370	C₂×C₄	—	13	1	no	—
371	C₂×C₄	—	26	2	no	—
372	C₂×C₄	—	26	1	no	—
373	C₂×C₄	—	26	1	no	—
374	C₂×C₄	—	26	1	no	—
375	C₂×C₄	—	26	1	no	—
376	C₂×C₄	—	26	2	no	—
377	C₂×C₄	—	26	2	no	—
378	C₂×C₄	C₂×C₈×D₁₃	1	2	yes	—
379	C₂×C₄	C₂×C₈×D₁₃	1	1	yes	characteristic
380	C₂×C₄	#88155	1	2	yes	—
381	C₂×C₄	C₄×C₂²⋊D₁₃	1	2	yes	—
382	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
383	C₈	—	2	2	no	—
384	C₈	—	26	2	no	—
385	C₈	—	26	1	no	—
386	C₈	—	26	1	no	—
387	C₈	C₄×C₂²⋊D₁₃	1	2	yes	—
388	C₈	C₂×#6127	1	1	yes	characteristic
389	C₈	C₂²×C₂²⋊D₁₃	1	1	yes	characteristic
390	C₂²	—	2	1	no	—
391	C₂²	—	2	1	no	—
392	C₂²	—	2	2	no	—
393	C₂²	—	2	2	no	—
394	C₂²	—	2	2	no	—
395	C₂²	—	13	2	no	—
396	C₂²	—	26	1	no	—
397	C₂²	—	26	1	no	—
398	C₂²	—	26	1	no	—
399	C₂²	—	26	1	no	—
400	C₂²	—	26	1	no	—
401	C₂²	—	52	4	no	—
402	C₂²	C₈×C₂²⋊D₁₃	1	2	yes	—
403	C₂²	C₂²×C₈×D₁₃	1	1	yes	characteristic
404	C₄	—	2	2	no	—
405	C₄	—	26	2	no	—
406	C₄	—	26	1	no	—
407	C₄	—	26	1	no	—
408	C₄	—	26	2	no	—
409	C₄	C₈×C₂²⋊D₁₃	1	2	yes	—
410	C₄	C₂×#88155	1	1	yes	characteristic
411	C₄	C₂×C₄×C₂²⋊D₁₃	1	1	yes	characteristic
412	C₂	—	2	2	no	—
413	C₂	—	4	2	no	—
414	C₂	—	26	2	no	—
415	C₂	—	52	1	no	—
416	C₂	C₂×C₈×C₂²⋊D₁₃	1	1	yes	characteristic
417	C₂	D₁₃×#504	1	1	yes	characteristic
418	C₂	#13127937	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₈	C₂³×D₁₃
commutator, socle	C₂²×C₁₃	C₂³×C₈
Fitting	C₂×C₁₃×#504	C₂
prime radical	#11719533	C₄
cosocle	C₂×C₈×C₁₃	C₂⁴
hypercenter	C₂×#504	D₁₃
hypocenter	C₁₃	#33436
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₈ ◁ C₂×#504

Complements

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

N	H ≅ G/N	type
1. C₂×D₁₃×M₃₂	C₂	semidirect
3. #13116666	C₂	semidirect
4. #13116661	C₂	semidirect
5. #13116659	C₂	semidirect
6. C₁₆×C₂²⋊D₁₃	C₂	semidirect
7. #13116594	C₂	semidirect
8. #13116450	C₂	semidirect
9. C₂×#11718099	C₂	semidirect
10. #13116435	C₂	semidirect
11. C₂×C₁₃×#504	C₂	semidirect
17. C₂×C₁₃×M₃₂	C₂²	semidirect
19. C₂²×C₁₃×C₁₆	C₂²	semidirect
33. C₂²⋊#6090	C₂²	semidirect
34. C₂²⋊#6090	C₂²	semidirect
39. #11718094	C₂²	semidirect
40. #11718093	C₂²	semidirect
41. #11718093	C₂²	semidirect
42. C₁₆×Dic₁₃	C₂²	semidirect
69. C₁₃×M₃₂	D₄	semidirect
144. C₂×#504	D₁₃	semidirect
200. C₂×M₃₂	C₂×D₁₃	semidirect
204. C₂²×C₁₆	C₂×D₁₃	semidirect
236. C₂×D₁₃	#504	semidirect
273. M₃₂	C₂²⋊D₁₃	semidirect
352. C₁₃	#33436	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
#13123528	2
#13116666	2
#13116661	2
#13116659	2
C₁₆×C₂²⋊D₁₃	2
#13116594	2
#13116450	2
C₂×#11718099	2
#13116435	2
C₂×C₁₃×#504	2
#33436	13