Subgroups — #15779771

Order 3328.

578 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₆×D₁₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₈×C₂²⋊D₁₃	C₂	1	1	yes	maximal, characteristic
3	C₂×C₂²⋊#6090	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#11718099	C₂	1	1	yes	maximal, characteristic, complemented
5	#13112913	C₂	1	1	yes	maximal, characteristic, complemented
6	#13112913	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₁₃×C₂²⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
9	C₂×C₄×C₂²⋊D₁₃	C₄	1	1	yes	characteristic
10	C₂²×C₈×D₁₃	C₂²	1	1	yes	characteristic
11	C₂²×C₁₃×C₁₆	C₂²	1	1	yes	characteristic
12	C₂²×C₁₃×C₁₆	C₂²	1	1	yes	characteristic
13	C₂×C₂²⋊#1055	C₄	1	1	yes	characteristic
14	C₈×C₂²⋊D₁₃	—	2	2	no	—
15	C₈×C₂²⋊D₁₃	—	2	2	no	—
16	C₂×#88060	C₄	1	1	yes	characteristic
17	C₂×#88054	C₄	1	1	yes	characteristic
18	C₂×C₈×Dic₁₃	C₂²	1	1	yes	characteristic
19	C₂²×#6090	C₂²	1	1	yes	characteristic
20	C₂²×#6090	C₂²	1	1	yes	characteristic
21	C₂×C₁₆×D₁₃	—	2	2	no	—
22	C₂×C₁₆×D₁₃	—	2	2	no	—
23	C₂×C₁₆×D₁₃	—	2	2	no	—
24	C₁₃×C₂²⋊C₁₆	—	2	2	no	—
25	C₂²⋊#6090	—	2	2	no	—
26	#11718099	—	2	2	no	—
27	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
28	C₂²×C₂²⋊D₁₃	C₈	1	1	yes	characteristic
29	C₂²×C₄×D₁₃	C₂×C₄	1	1	yes	characteristic
30	C₂²×C₈×C₁₃	—	2	1	no	—
31	C₂²×C₈×C₁₃	—	2	1	no	—
32	C₂²×C₈×C₁₃	—	2	1	no	—
33	C₂²×C₈×C₁₃	—	2	1	no	—
34	C₂²×C₈×C₁₃	—	2	1	no	—
35	C₂²×C₈×C₁₃	—	2	1	no	—
36	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
37	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
38	C₂×C₂²⋊Dic₁₃	C₈	1	1	yes	characteristic
39	C₄×C₂²⋊D₁₃	—	2	2	no	—
40	C₄×C₂²⋊D₁₃	—	2	2	no	—
41	C₂×#6103	C₈	1	1	yes	characteristic
42	C₂×#6101	C₈	1	1	yes	characteristic
43	C₂×C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
44	C₂²×#1055	C₂×C₄	1	1	yes	characteristic
45	C₂²×#1055	C₂×C₄	1	1	yes	characteristic
46	C₂×C₈×D₁₃	—	2	1	no	—
47	C₂×C₈×D₁₃	—	2	1	no	—
48	C₂×C₈×D₁₃	—	2	1	no	—
49	C₂×C₈×D₁₃	—	2	1	no	—
50	C₂×C₈×D₁₃	D₄	1	2	yes	—
51	C₂×C₈×D₁₃	D₄	1	2	yes	—
52	C₂×C₁₃×C₁₆	—	2	1	no	—
53	C₂×C₁₃×C₁₆	—	2	1	no	—
54	C₂×C₁₃×C₁₆	—	2	1	no	—
55	C₂×C₁₃×C₁₆	—	2	1	no	—
56	C₂×C₁₃×C₁₆	—	2	1	no	—
57	C₂×C₁₃×C₁₆	D₄	1	2	yes	complemented
58	C₂²⋊#1055	—	2	2	no	—
59	#88060	—	2	2	no	—
60	#88054	—	2	2	no	—
61	C₈×Dic₁₃	—	2	1	no	—
62	C₈×Dic₁₃	—	2	1	no	—
63	C₂×#6090	—	2	1	no	—
64	C₂×#6090	—	2	1	no	—
65	C₂×#6090	—	2	1	no	—
66	C₂×#6090	—	2	1	no	—
67	C₂×#6090	—	2	1	no	—
68	C₂×#6090	D₄	1	2	yes	complemented
69	C₁₆×D₁₃	—	2	8	no	—
70	#12976	—	13	1	no	maximal, Sylow
71	C₂⁴×C₁₃	C₂×C₈	1	1	yes	characteristic
72	C₂³×D₁₃	C₂×C₈	1	1	yes	characteristic
73	C₂²×C₄×C₁₃	—	2	1	no	—
74	C₂²×C₄×C₁₃	—	2	1	no	—
75	C₂²×C₄×C₁₃	—	2	1	no	—
76	C₂²×C₄×C₁₃	—	2	1	no	—
77	C₂²×C₄×C₁₃	—	2	1	no	—
78	C₂²×C₄×C₁₃	—	2	1	no	—
79	C₂²×C₄×C₁₃	C₂×C₈	1	1	yes	characteristic
80	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
81	C₂×C₂²⋊D₁₃	—	2	2	no	—
82	C₂×C₂²⋊D₁₃	—	2	2	no	—
83	C₂×C₂²⋊D₁₃	C₁₆	1	4	yes	complemented
84	C₂²×Dic₁₃	C₂×C₈	1	1	yes	characteristic
85	C₂²×Dic₁₃	C₂×C₈	1	1	yes	characteristic
86	C₂²×Dic₁₃	C₂×C₈	1	1	yes	characteristic
87	C₂×C₄×D₁₃	—	2	1	no	—
88	C₂×C₄×D₁₃	—	2	1	no	—
89	C₂×C₄×D₁₃	—	2	1	no	—
90	C₂×C₄×D₁₃	—	2	1	no	—
91	C₂×C₄×D₁₃	C₂²⋊C₄	1	2	yes	—
92	C₂×C₄×D₁₃	M₁₆	1	2	yes	—
93	C₂×C₈×C₁₃	—	2	1	no	—
94	C₂×C₈×C₁₃	—	2	1	no	—
95	C₂×C₈×C₁₃	—	2	1	no	—
96	C₂×C₈×C₁₃	—	4	1	no	—
97	C₂×C₈×C₁₃	—	4	1	no	—
98	C₂×C₈×C₁₃	—	4	1	no	—
99	C₂×C₈×C₁₃	—	4	1	no	—
100	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
101	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
102	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
103	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
104	C₂×C₈×C₁₃	#41	1	1	yes	characteristic
105	C₂×C₈×C₁₃	#41	1	1	yes	characteristic
106	C₂²⋊Dic₁₃	—	2	2	no	—
107	#6103	—	2	2	no	—
108	#6101	—	2	2	no	—
109	C₄×Dic₁₃	—	2	1	no	—
110	C₄×Dic₁₃	—	2	1	no	—
111	C₂×#1055	—	2	1	no	—
112	C₂×#1055	—	2	1	no	—
113	C₂×#1055	—	2	1	no	—
114	C₂×#1055	—	2	1	no	—
115	C₂×#1055	—	2	1	no	—
116	C₂×#1055	C₂²⋊C₄	1	2	yes	—
117	C₈×D₁₃	—	2	2	no	—
118	C₈×D₁₃	—	2	2	no	—
119	C₈×D₁₃	—	2	2	no	—
120	C₈×D₁₃	—	2	2	no	—
121	C₁₃×C₁₆	—	2	2	no	—
122	C₁₃×C₁₆	—	4	1	no	—
123	#6090	—	2	2	no	—
124	#6090	—	4	1	no	—
125	C₂³×C₁₆	—	13	1	no	—
126	C₂×C₈×D₄	—	13	1	no	—
127	C₂×C₂²⋊C₁₆	—	13	1	no	—
128	C₂×C₂²⋊C₁₆	—	13	1	no	—
129	C₂×C₂²⋊C₁₆	D₁₃	1	1	yes	characteristic, complemented
130	#1374	—	13	1	no	—
131	#1374	—	13	1	no	—
132	C₂³×C₁₃	—	2	1	no	—
133	C₂³×C₁₃	—	2	1	no	—
134	C₂³×C₁₃	—	2	1	no	—
135	C₂³×C₁₃	—	2	1	no	—
136	C₂³×C₁₃	—	2	1	no	—
137	C₂³×C₁₃	—	2	1	no	—
138	C₂³×C₁₃	C₂×C₁₆	1	2	yes	complemented
139	C₂³×C₁₃	C₂²×C₈	1	1	yes	characteristic
140	C₂²×D₁₃	—	2	1	no	—
141	C₂²×D₁₃	—	2	1	no	—
142	C₂²×D₁₃	—	2	1	no	—
143	C₂²×D₁₃	—	2	1	no	—
144	C₂²×D₁₃	C₂²⋊C₈	1	2	yes	—
145	C₂²×D₁₃	C₂×C₁₆	1	2	yes	—
146	C₂²×D₁₃	M₃₂	1	2	yes	—
147	C₂×C₄×C₁₃	—	2	1	no	—
148	C₂×C₄×C₁₃	—	2	1	no	—
149	C₂×C₄×C₁₃	—	2	1	no	—
150	C₂×C₄×C₁₃	—	4	1	no	—
151	C₂×C₄×C₁₃	—	4	1	no	—
152	C₂×C₄×C₁₃	—	4	1	no	—
153	C₂×C₄×C₁₃	—	4	1	no	—
154	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
155	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
156	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
157	C₂×C₄×C₁₃	C₂×M₁₆	1	1	yes	characteristic
158	C₂×C₄×C₁₃	#131	1	1	yes	characteristic
159	C₂×C₄×C₁₃	#131	1	1	yes	characteristic
160	C₂²⋊D₁₃	—	2	8	no	—
161	C₂×Dic₁₃	—	2	1	no	—
162	C₂×Dic₁₃	—	2	1	no	—
163	C₂×Dic₁₃	—	2	1	no	—
164	C₂×Dic₁₃	—	2	1	no	—
165	C₂×Dic₁₃	—	2	1	no	—
166	C₂×Dic₁₃	—	2	1	no	—
167	C₂×Dic₁₃	—	2	1	no	—
168	C₂×Dic₁₃	C₂²⋊C₈	1	2	yes	—
169	C₂×Dic₁₃	C₂×C₁₆	1	2	yes	complemented
170	C₄×D₁₃	—	2	2	no	—
171	C₄×D₁₃	—	2	2	no	—
172	C₄×D₁₃	—	2	2	no	—
173	C₄×D₁₃	—	2	2	no	—
174	C₈×C₁₃	—	4	1	no	—
175	C₈×C₁₃	#120	1	1	yes	characteristic
176	C₈×C₁₃	#121	1	1	yes	characteristic
177	C₈×C₁₃	#121	1	1	yes	characteristic
178	C₈×C₁₃	#123	1	1	yes	characteristic
179	#1055	—	2	2	no	—
180	#1055	—	4	1	no	—
181	C₂³×C₈	—	13	1	no	—
182	C₂³×C₈	C₂×D₁₃	1	1	yes	characteristic
183	C₂×C₄×D₄	—	13	1	no	—
184	C₂²×C₁₆	—	13	1	no	—
185	C₂²×C₁₆	—	13	1	no	—
186	C₂²×C₁₆	—	26	2	no	—
187	C₂²×C₁₆	—	26	2	no	—
188	C₂²×C₁₆	—	26	2	no	—
189	C₂²×C₁₆	C₂×D₁₃	1	1	yes	characteristic
190	C₂²×C₁₆	C₂×D₁₃	1	1	yes	characteristic
191	C₈×D₄	—	26	2	no	—
192	C₈×D₄	—	26	2	no	—
193	C₂×C₄⋊C₈	—	13	1	no	—
194	C₂×C₂²⋊C₈	—	13	1	no	—
195	C₂×C₂²⋊C₈	—	13	1	no	—
196	C₂×C₄×C₈	—	13	1	no	—
197	C₂²⋊C₁₆	—	2	2	no	—
198	C₂²⋊C₁₆	—	26	2	no	—
199	C₂²⋊C₁₆	—	26	2	no	—
200	C₂²×C₁₃	—	2	2	no	—
201	C₂²×C₁₃	—	2	2	no	—
202	C₂²×C₁₃	—	2	2	no	—
203	C₂²×C₁₃	—	4	1	no	—
204	C₂²×C₁₃	—	4	1	no	—
205	C₂²×C₁₃	—	4	1	no	—
206	C₂²×C₁₃	—	4	1	no	—
207	C₂²×C₁₃	C₂×C₂²⋊C₈	1	1	yes	characteristic
208	C₂²×C₁₃	C₈×D₄	1	1	yes	characteristic
209	C₂²×C₁₃	C₈×D₄	1	1	yes	characteristic
210	C₂²×C₁₃	C₂²×C₁₆	1	1	yes	characteristic
211	C₂²×C₁₃	C₂×M₃₂	1	1	yes	characteristic
212	C₂²×C₁₃	#504	1	1	yes	characteristic
213	C₂²×C₁₃	#504	1	1	yes	characteristic
214	C₂×D₁₃	—	2	2	no	—
215	C₂×D₁₃	—	2	2	no	—
216	C₂×D₁₃	—	2	2	no	—
217	C₂×D₁₃	—	2	2	no	—
218	C₂×D₁₃	—	2	2	no	—
219	C₂×D₁₃	—	2	2	no	—
220	C₂×D₁₃	C₂²⋊C₁₆	1	4	yes	complemented
221	C₄×C₁₃	—	4	1	no	—
222	C₄×C₁₃	#386	1	1	yes	characteristic
223	C₄×C₁₃	#408	1	1	yes	characteristic
224	C₄×C₁₃	#435	1	1	yes	characteristic
225	C₄×C₁₃	#435	1	1	yes	characteristic
226	Dic₁₃	—	2	2	no	—
227	Dic₁₃	—	2	2	no	—
228	Dic₁₃	—	4	1	no	—
229	C₂²×D₄	—	13	1	no	—
230	C₂³×C₄	—	13	1	no	—
231	C₂³×C₄	C₄×D₁₃	1	1	yes	characteristic
232	C₂²×C₈	—	2	1	no	—
233	C₂²×C₈	—	2	1	no	—
234	C₂²×C₈	—	2	1	no	—
235	C₂²×C₈	—	2	1	no	—
236	C₂²×C₈	—	2	1	no	—
237	C₂²×C₈	—	2	1	no	—
238	C₂²×C₈	—	13	1	no	—
239	C₂²×C₈	—	13	2	no	—
240	C₂²×C₈	—	13	2	no	—
241	C₂²×C₈	—	13	1	no	—
242	C₂²×C₈	—	26	1	no	—
243	C₂²×C₈	—	26	1	no	—
244	C₂²×C₈	—	26	1	no	—
245	C₂²×C₈	—	26	1	no	—
246	C₂²×C₈	C₄×D₁₃	1	1	yes	characteristic
247	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
248	C₄×D₄	—	26	2	no	—
249	C₄×D₄	—	26	2	no	—
250	C₂×C₄⋊C₄	—	13	1	no	—
251	C₂×C₂²⋊C₄	—	13	1	no	—
252	C₂×C₂²⋊C₄	—	13	1	no	—
253	C₂×C₄²	—	13	1	no	—
254	C₂×C₁₆	—	2	1	no	—
255	C₂×C₁₆	—	2	1	no	—
256	C₂×C₁₆	—	2	1	no	—
257	C₂×C₁₆	—	2	1	no	—
258	C₂×C₁₆	—	2	1	no	—
259	C₂×C₁₆	—	13	2	no	—
260	C₂×C₁₆	—	26	8	no	—
261	C₂×C₁₆	—	26	1	no	—
262	C₂×C₁₆	—	26	1	no	—
263	C₂×C₁₆	—	26	1	no	—
264	C₂×C₁₆	—	26	1	no	—
265	C₂×C₁₆	—	26	1	no	—
266	C₂×C₁₆	C₂²⋊D₁₃	1	2	yes	complemented
267	C₄⋊C₈	—	26	2	no	—
268	C₂²⋊C₈	—	26	2	no	—
269	C₂²⋊C₈	—	26	2	no	—
270	C₄×C₈	—	26	1	no	—
271	C₄×C₈	—	26	1	no	—
272	C₂×C₁₃	—	4	2	no	—
273	C₂×C₁₃	#1869	1	1	yes	characteristic
274	C₂×C₁₃	C₂×C₂²⋊C₁₆	1	1	yes	characteristic
275	C₂×C₁₃	#2113	1	1	yes	characteristic
276	C₂×C₁₃	D₄×C₁₆	1	1	yes	characteristic
277	C₂×C₁₃	D₄×C₁₆	1	1	yes	characteristic
278	C₂×C₁₃	#2168	1	1	yes	characteristic
279	C₂×C₁₃	#2168	1	1	yes	characteristic
280	D₁₃	—	2	4	no	—
281	C₂⁴	—	13	1	no	—
282	C₂⁴	C₈×D₁₃	1	1	yes	characteristic
283	C₂×D₄	—	13	4	no	—
284	C₂×D₄	—	26	2	no	—
285	C₂×D₄	—	26	2	no	—
286	C₂²×C₄	—	2	1	no	—
287	C₂²×C₄	—	2	1	no	—
288	C₂²×C₄	—	2	1	no	—
289	C₂²×C₄	—	2	1	no	—
290	C₂²×C₄	—	2	1	no	—
291	C₂²×C₄	—	2	1	no	—
292	C₂²×C₄	—	13	1	no	—
293	C₂²×C₄	—	13	1	no	—
294	C₂²×C₄	—	13	2	no	—
295	C₂²×C₄	—	13	2	no	—
296	C₂²×C₄	—	13	1	no	—
297	C₂²×C₄	—	26	1	no	—
298	C₂²×C₄	—	26	1	no	—
299	C₂²×C₄	—	26	1	no	—
300	C₂²×C₄	—	26	1	no	—
301	C₂²×C₄	C₈×D₁₃	1	1	yes	characteristic
302	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
303	C₂×C₈	—	2	1	no	—
304	C₂×C₈	—	2	1	no	—
305	C₂×C₈	—	2	1	no	—
306	C₂×C₈	—	4	1	no	—
307	C₂×C₈	—	4	1	no	—
308	C₂×C₈	—	4	1	no	—
309	C₂×C₈	—	4	1	no	—
310	C₂×C₈	—	13	2	no	—
311	C₂×C₈	—	26	1	no	—
312	C₂×C₈	—	26	1	no	—
313	C₂×C₈	—	26	2	no	—
314	C₂×C₈	—	26	2	no	—
315	C₂×C₈	—	26	2	no	—
316	C₂×C₈	—	26	2	no	—
317	C₂×C₈	—	26	1	no	—
318	C₂×C₈	—	26	1	no	—
319	C₂×C₈	—	26	1	no	—
320	C₂×C₈	#6127	1	1	yes	characteristic
321	C₂×C₈	D₄×D₁₃	1	1	yes	characteristic
322	C₂×C₈	D₄×D₁₃	1	1	yes	characteristic
323	C₂×C₈	D₄×D₁₃	1	1	yes	characteristic
324	C₂×C₈	#6129	1	1	yes	characteristic
325	C₂×C₈	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
326	C₄⋊C₄	—	26	2	no	—
327	C₂²⋊C₄	—	26	2	no	—
328	C₂²⋊C₄	—	26	2	no	—
329	C₄²	—	26	1	no	—
330	C₄²	—	26	1	no	—
331	C₁₆	—	2	2	no	—
332	C₁₆	—	4	1	no	—
333	C₁₆	—	26	2	no	—
334	C₁₆	—	52	1	no	—
335	C₁₃	#12976	1	1	yes	characteristic, complemented, Sylow
336	C₂³	—	2	1	no	—
337	C₂³	—	2	1	no	—
338	C₂³	—	2	1	no	—
339	C₂³	—	2	1	no	—
340	C₂³	—	2	1	no	—
341	C₂³	—	2	1	no	—
342	C₂³	—	13	2	no	—
343	C₂³	—	13	2	no	—
344	C₂³	—	13	2	no	—
345	C₂³	—	26	1	no	—
346	C₂³	—	26	1	no	—
347	C₂³	—	26	1	no	—
348	C₂³	—	26	1	no	—
349	C₂³	C₁₆×D₁₃	1	2	yes	complemented
350	C₂³	C₂×C₈×D₁₃	1	1	yes	characteristic
351	D₄	—	26	8	no	—
352	C₂×C₄	—	2	1	no	—
353	C₂×C₄	—	2	1	no	—
354	C₂×C₄	—	2	1	no	—
355	C₂×C₄	—	4	1	no	—
356	C₂×C₄	—	4	1	no	—
357	C₂×C₄	—	4	1	no	—
358	C₂×C₄	—	4	1	no	—
359	C₂×C₄	—	13	2	no	—
360	C₂×C₄	—	13	2	no	—
361	C₂×C₄	—	26	1	no	—
362	C₂×C₄	—	26	1	no	—
363	C₂×C₄	—	26	1	no	—
364	C₂×C₄	—	26	1	no	—
365	C₂×C₄	—	26	2	no	—
366	C₂×C₄	—	26	2	no	—
367	C₂×C₄	—	26	2	no	—
368	C₂×C₄	—	26	2	no	—
369	C₂×C₄	—	26	1	no	—
370	C₂×C₄	—	26	1	no	—
371	C₂×C₄	—	26	1	no	—
372	C₂×C₄	C₂²⋊C₄×D₁₃	1	1	yes	characteristic
373	C₂×C₄	#88135	1	1	yes	characteristic
374	C₂×C₄	#88155	1	1	yes	characteristic
375	C₂×C₄	M₁₆×D₁₃	1	1	yes	characteristic
376	C₂×C₄	#88161	1	1	yes	characteristic
377	C₂×C₄	C₄×C₂²⋊D₁₃	1	1	yes	characteristic
378	C₈	—	4	1	no	—
379	C₈	—	26	2	no	—
380	C₈	—	52	1	no	—
381	C₈	#88137	1	1	yes	characteristic
382	C₈	#88138	1	1	yes	characteristic
383	C₈	#88191	1	1	yes	characteristic
384	C₈	#88192	1	1	yes	characteristic
385	C₂²	—	2	2	no	—
386	C₂²	—	2	2	no	—
387	C₂²	—	2	2	no	—
388	C₂²	—	4	1	no	—
389	C₂²	—	4	1	no	—
390	C₂²	—	4	1	no	—
391	C₂²	—	4	1	no	—
392	C₂²	—	13	4	no	—
393	C₂²	—	26	2	no	—
394	C₂²	—	26	2	no	—
395	C₂²	—	26	2	no	—
396	C₂²	—	26	2	no	—
397	C₂²	—	26	2	no	—
398	C₂²	—	26	2	no	—
399	C₂²	D₁₃×C₂²⋊C₈	1	1	yes	characteristic
400	C₂²	#11718386	1	1	yes	characteristic
401	C₂²	C₂×C₁₆×D₁₃	1	1	yes	characteristic
402	C₂²	#11718562	1	1	yes	characteristic
403	C₂²	D₁₃×M₃₂	1	1	yes	characteristic
404	C₂²	#11718568	1	1	yes	characteristic
405	C₂²	C₈×C₂²⋊D₁₃	1	1	yes	characteristic
406	C₄	—	4	1	no	—
407	C₄	—	26	2	no	—
408	C₄	—	26	2	no	—
409	C₄	—	52	1	no	—
410	C₄	#11718388	1	1	yes	characteristic
411	C₄	#11718389	1	1	yes	characteristic
412	C₄	#11718617	1	1	yes	characteristic
413	C₄	#11718788	1	1	yes	characteristic
414	C₂	—	4	2	no	—
415	C₂	—	26	4	no	—
416	C₂	#13115125	1	1	yes	characteristic
417	C₂	D₁₃×C₂²⋊C₁₆	1	1	yes	characteristic
418	C₂	#13116448	1	1	yes	characteristic
419	C₂	#13116653	1	1	yes	characteristic
420	C₂	C₁₆×C₂²⋊D₁₃	1	1	yes	characteristic
421	C₂	#13116659	1	1	yes	characteristic
422	C₂	#13116664	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²×C₈	C₂²×D₁₃
commutator	C₂²×C₁₃	C₂²×C₁₆
Fitting	C₂×C₁₃×C₂²⋊C₁₆	C₂
socle	C₂³×C₁₃	C₂²×C₈
prime radical	C₂²×C₂²⋊D₁₃	C₈
cosocle	C₂²×C₈×C₁₃	C₂³
hypercenter	C₂×C₂²⋊C₁₆	D₁₃
hypocenter	C₁₃	#12976
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂²×C₈ ◁ C₂×C₂²⋊C₁₆

Complements

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

N	H ≅ G/N	type
1. C₂²×C₁₆×D₁₃	C₂	semidirect
3. C₂×C₂²⋊#6090	C₂	semidirect
4. C₂×#11718099	C₂	semidirect
5. #13112913	C₂	semidirect
6. #13112913	C₂	semidirect
7. C₂×C₁₃×C₂²⋊C₁₆	C₂	semidirect
57. C₂×C₁₃×C₁₆	D₄	semidirect
68. C₂×#6090	D₄	semidirect
83. C₂×C₂²⋊D₁₃	C₁₆	semidirect
129. C₂×C₂²⋊C₁₆	D₁₃	semidirect
138. C₂³×C₁₃	C₂×C₁₆	semidirect
169. C₂×Dic₁₃	C₂×C₁₆	semidirect
220. C₂×D₁₃	C₂²⋊C₁₆	semidirect
266. C₂×C₁₆	C₂²⋊D₁₃	semidirect
335. C₁₃	#12976	semidirect
349. C₂³	C₁₆×D₁₃	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₁₆×D₁₃	2
C₂×C₈×C₂²⋊D₁₃	2
C₂×C₂²⋊#6090	2
C₂×#11718099	2
#13112913	2
C₂×C₁₃×C₂²⋊C₁₆	2
#12976	13