Subgroups — #15832013

Order 3328.

702 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13123468	C₂	1	1	yes	maximal, characteristic
2	#13123464	C₂	1	1	yes	maximal, characteristic
3	C₂×D₁₃×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic
4	#13113618	C₂	1	4	yes	maximal, complemented
5	#13113611	C₂	1	1	yes	maximal, characteristic, complemented
6	#13113610	C₂	1	1	yes	maximal, characteristic, complemented
7	#13113608	C₂	1	1	yes	maximal, characteristic, complemented
8	#13113585	C₂	1	4	yes	maximal, complemented
9	C₁₃×#1570	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×C₈×D₁₃	—	2	1	no	—
11	C₂×C₄²×D₁₃	C₂²	1	1	yes	characteristic
12	C₁₃×#431	C₂²	1	1	yes	characteristic
13	C₁₃×#423	C₂²	1	1	yes	characteristic
14	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
15	#11718787	—	2	1	no	—
16	M₁₆×Dic₁₃	—	2	1	no	—
17	C₂×#88054	—	2	1	no	—
18	#11718586	C₂²	1	1	yes	characteristic
19	#11718585	C₂²	1	1	yes	characteristic
20	C₂×C₄⋊#1055	C₂²	1	1	yes	characteristic
21	#11718498	C₄	1	2	yes	—
22	#11718496	—	2	1	no	—
23	#11718496	C₄	1	2	yes	—
24	#11718496	C₂²	1	2	yes	—
25	#11718494	—	2	1	no	—
26	#11718494	C₂²	1	2	yes	—
27	D₁₃×C₄⋊C₈	—	2	1	no	—
28	D₁₃×C₄⋊C₈	—	2	1	no	—
29	D₁₃×C₄⋊C₈	C₂²	1	2	yes	—
30	D₁₃×C₄⋊C₈	C₂²	1	2	yes	—
31	#11718387	C₄	1	2	yes	—
32	#11718380	C₄	1	2	yes	—
33	C₄×#6094	C₂²	1	2	yes	—
34	#11718346	C₂²	1	2	yes	—
35	C₁₃×#334	C₂²	1	4	yes	complemented
36	#11718072	C₂²	1	4	yes	complemented
37	#11718071	C₂²	1	4	yes	complemented
38	#11718050	C₂²	1	4	yes	complemented
39	C₂²×C₄×D₁₃	C₂×C₄	1	1	yes	characteristic
40	C₂²×C₄×D₁₃	D₄	1	1	yes	characteristic
41	C₂²×C₄×D₁₃	Q₈	1	1	yes	characteristic
42	C₂×C₁₃×M₁₆	—	2	1	no	—
43	C₂²×C₈×C₁₃	—	2	1	no	—
44	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
45	C₂×C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
46	C₂×C₄×Dic₁₃	D₄	1	1	yes	characteristic
47	C₂×C₄×Dic₁₃	Q₈	1	1	yes	characteristic
48	C₂×#6099	—	2	1	no	—
49	C₂²×#1055	—	2	1	no	—
50	C₂×#6094	C₂×C₄	1	4	yes	—
51	C₂×C₈×D₁₃	—	2	2	no	—
52	C₂×C₈×D₁₃	—	2	2	no	—
53	C₂×C₈×D₁₃	—	4	4	no	—
54	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
55	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
56	C₄²×D₁₃	D₄	1	1	yes	characteristic
57	C₄²×D₁₃	D₄	1	1	yes	characteristic
58	C₄²×D₁₃	Q₈	1	1	yes	characteristic
59	C₄²×D₁₃	Q₈	1	1	yes	characteristic
60	C₄²×D₁₃	C₂³	1	1	yes	characteristic
61	C₄²×D₁₃	C₂³	1	1	yes	characteristic
62	C₁₃×C₄⋊C₈	—	2	1	no	—
63	C₁₃×C₄⋊C₈	—	2	1	no	—
64	C₁₃×C₄⋊C₈	C₂×C₄	1	2	yes	—
65	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
66	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
67	C₁₃×C₂²⋊C₈	C₂×C₄	1	2	yes	—
68	C₄×C₈×C₁₃	C₂³	1	2	yes	—
69	C₂²⋊#1055	C₂×C₄	1	2	yes	—
70	#88060	—	2	2	no	—
71	#88060	—	2	2	no	—
72	#88060	C₂×C₄	1	4	yes	—
73	#88055	—	2	2	no	—
74	#88055	C₂×C₄	1	4	yes	—
75	#88054	—	2	2	no	—
76	#88054	—	2	2	no	—
77	#88054	C₂×C₄	1	4	yes	—
78	C₈×Dic₁₃	—	2	2	no	—
79	C₄⋊#1055	—	2	1	no	—
80	C₄⋊#1055	—	2	1	no	—
81	C₄⋊#1055	C₂×C₄	1	2	yes	—
82	C₄⋊#1055	C₂³	1	2	yes	—
83	C₄⋊#1055	C₂³	1	2	yes	—
84	C₄×#1055	C₂³	1	2	yes	—
85	#17807	—	13	1	no	maximal, Sylow
86	C₂³×D₁₃	C₄⋊C₄	1	1	yes	characteristic
87	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
88	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
89	C₂²×C₄×C₁₃	C₂×Q₈	1	1	yes	characteristic
90	C₂²×Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
91	C₂²×Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
92	C₂²×Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
93	C₂×C₄×D₁₃	—	2	2	no	—
94	C₂×C₄×D₁₃	—	2	2	no	—
95	C₂×C₄×D₁₃	—	2	4	no	—
96	C₂×C₄×D₁₃	—	4	2	no	—
97	C₂×C₄×D₁₃	C₄⋊C₄	1	1	yes	characteristic
98	C₂×C₄×D₁₃	C₄⋊C₄	1	1	yes	characteristic
99	C₂×C₄×D₁₃	C₄⋊C₄	1	1	yes	characteristic
100	C₂×C₄×D₁₃	C₄⋊C₄	1	1	yes	characteristic
101	C₂×C₄×D₁₃	C₄⋊C₄	1	1	yes	characteristic
102	C₂×C₄×D₁₃	C₄⋊C₄	1	1	yes	characteristic
103	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
104	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
105	C₂×C₄×D₁₃	C₂×D₄	1	1	yes	characteristic
106	C₂×C₄×D₁₃	C₂×D₄	1	1	yes	characteristic
107	C₂×C₄×D₁₃	C₂×Q₈	1	1	yes	characteristic
108	C₂×C₄×D₁₃	C₂×Q₈	1	1	yes	characteristic
109	C₁₃×M₁₆	—	4	2	no	—
110	C₂×C₈×C₁₃	—	2	2	no	—
111	C₂×C₈×C₁₃	—	2	2	no	—
112	C₂×C₈×C₁₃	—	4	2	no	—
113	C₂×C₈×C₁₃	C₂²×C₄	1	4	yes	—
114	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
115	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
116	C₄²×C₁₃	C₂×Q₈	1	1	yes	characteristic
117	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
118	C₄×Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
119	C₄×Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
120	C₄×Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
121	C₄×Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
122	C₄×Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
123	C₄×Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
124	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
125	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
126	C₄×Dic₁₃	C₂×D₄	1	1	yes	characteristic
127	C₄×Dic₁₃	C₂×D₄	1	1	yes	characteristic
128	C₄×Dic₁₃	C₂×Q₈	1	1	yes	characteristic
129	C₄×Dic₁₃	C₂×Q₈	1	1	yes	characteristic
130	#6099	—	4	2	no	—
131	C₂×#1055	—	2	2	no	—
132	C₂×#1055	—	2	2	no	—
133	C₂×#1055	—	4	2	no	—
134	C₂×#1055	C₂²×C₄	1	4	yes	—
135	#6094	—	2	8	no	—
136	C₈×D₁₃	—	4	4	no	—
137	C₈×D₁₃	—	4	4	no	—
138	#2920	—	13	1	no	—
139	#2920	—	13	1	no	—
140	C₂²×C₄⋊C₈	—	13	1	no	—
141	#1573	—	13	4	no	—
142	#1571	—	13	1	no	—
143	#1571	—	13	1	no	—
144	#1570	—	13	1	no	—
145	#1570	D₁₃	1	1	yes	characteristic, complemented
146	#1565	—	13	4	no	—
147	C₂³×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
148	C₂²×D₁₃	—	2	2	no	—
149	C₂²×D₁₃	—	2	2	no	—
150	C₂²×D₁₃	—	2	2	no	—
151	C₂²×D₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
152	C₂²×D₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
153	C₂×C₄×C₁₃	—	2	2	no	—
154	C₂×C₄×C₁₃	—	4	1	no	—
155	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
156	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
157	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
158	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
159	C₂×C₄×C₁₃	#137	1	2	yes	—
160	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
161	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
162	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
163	C₂×Dic₁₃	—	2	2	no	—
164	C₂×Dic₁₃	—	2	2	no	—
165	C₂×Dic₁₃	—	4	1	no	—
166	C₂×Dic₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
167	C₂×Dic₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
168	C₂×Dic₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
169	C₂×Dic₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
170	C₂×Dic₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
171	C₂×Dic₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
172	C₄×D₁₃	—	2	2	no	—
173	C₄×D₁₃	—	2	2	no	—
174	C₄×D₁₃	—	2	2	no	—
175	C₄×D₁₃	—	2	2	no	—
176	C₄×D₁₃	—	2	1	no	—
177	C₄×D₁₃	—	2	1	no	—
178	C₄×D₁₃	—	2	1	no	—
179	C₄×D₁₃	—	2	1	no	—
180	C₄×D₁₃	—	2	2	no	—
181	C₄×D₁₃	—	2	2	no	—
182	C₄×D₁₃	—	2	2	no	—
183	C₄×D₁₃	—	4	1	no	—
184	C₄×D₁₃	—	4	1	no	—
185	C₄×D₁₃	#131	1	4	yes	—
186	C₈×C₁₃	—	2	4	no	—
187	C₈×C₁₃	—	4	2	no	—
188	C₈×C₁₃	—	4	2	no	—
189	#1055	—	2	4	no	—
190	#1055	—	4	2	no	—
191	#1055	—	4	2	no	—
192	C₂³×C₈	—	26	1	no	—
193	C₂²×C₄²	—	13	1	no	—
194	#432	—	13	2	no	—
195	#432	—	13	2	no	—
196	#432	—	13	2	no	—
197	#432	—	26	1	no	—
198	#431	—	13	1	no	—
199	#431	—	13	2	no	—
200	#431	—	13	2	no	—
201	#431	—	26	1	no	—
202	#431	C₂×D₁₃	1	1	yes	characteristic
203	#423	—	13	2	no	—
204	#423	—	13	1	no	—
205	#423	C₂×D₁₃	1	1	yes	characteristic
206	C₂×C₄⋊C₈	—	13	1	no	—
207	C₂×C₄⋊C₈	—	13	2	no	—
208	C₂×C₄⋊C₈	—	13	2	no	—
209	C₂×C₄⋊C₈	—	26	1	no	—
210	C₂×C₄⋊C₈	—	26	1	no	—
211	C₂×C₄⋊C₈	—	26	1	no	—
212	C₂×C₄⋊C₈	C₂×D₁₃	1	1	yes	characteristic
213	#407	—	13	2	no	—
214	#407	—	26	1	no	—
215	C₄×M₁₆	—	13	2	no	—
216	C₄×M₁₆	—	26	1	no	—
217	#335	—	13	4	no	—
218	#335	—	13	4	no	—
219	#334	—	13	4	no	—
220	#334	C₂×D₁₃	1	4	yes	complemented
221	C₂²×C₁₃	—	2	1	no	—
222	C₂²×C₁₃	—	2	1	no	—
223	C₂²×C₁₃	#428	1	2	yes	—
224	C₂²×C₁₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
225	C₂×D₁₃	—	2	8	no	—
226	C₂×D₁₃	—	2	1	no	—
227	C₂×D₁₃	—	2	1	no	—
228	C₂×D₁₃	—	2	1	no	—
229	C₂×D₁₃	—	2	1	no	—
230	C₂×D₁₃	#424	1	2	yes	—
231	C₂×D₁₃	#430	1	2	yes	—
232	C₄×C₁₃	—	2	1	no	—
233	C₄×C₁₃	—	2	1	no	—
234	C₄×C₁₃	—	2	1	no	—
235	C₄×C₁₃	#428	1	2	yes	—
236	C₄×C₁₃	C₂×#131	1	2	yes	—
237	C₄×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
238	C₄×C₁₃	C₂×#137	1	1	yes	characteristic
239	Dic₁₃	—	2	1	no	—
240	Dic₁₃	—	2	1	no	—
241	Dic₁₃	—	2	1	no	—
242	Dic₁₃	—	2	1	no	—
243	Dic₁₃	—	2	1	no	—
244	Dic₁₃	#424	1	2	yes	—
245	C₂³×C₄	—	13	1	no	—
246	C₂³×C₄	—	13	1	no	—
247	C₂³×C₄	—	13	1	no	—
248	C₂×M₁₆	—	2	1	no	—
249	C₂×M₁₆	—	13	4	no	—
250	C₂×M₁₆	—	26	1	no	—
251	C₂²×C₈	—	2	1	no	—
252	C₂²×C₈	—	26	2	no	—
253	C₂²×C₈	—	26	2	no	—
254	C₂²×C₈	—	26	1	no	—
255	C₂²×C₈	—	52	4	no	—
256	C₂×C₄²	—	13	1	no	—
257	C₂×C₄²	—	13	1	no	—
258	C₂×C₄²	—	13	1	no	—
259	C₂×C₄²	—	13	1	no	—
260	C₂×C₄²	—	13	1	no	—
261	C₂×C₄²	—	13	1	no	—
262	C₂×C₄²	—	13	1	no	—
263	C₂×C₄²	—	13	1	no	—
264	C₂×C₄²	—	13	1	no	—
265	C₂×C₄²	—	13	1	no	—
266	C₂×C₄²	—	13	1	no	—
267	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
268	C₄⋊C₈	—	2	1	no	—
269	C₄⋊C₈	—	2	1	no	—
270	C₄⋊C₈	—	13	4	no	—
271	C₄⋊C₈	—	13	2	no	—
272	C₄⋊C₈	—	13	2	no	—
273	C₄⋊C₈	—	13	2	no	—
274	C₄⋊C₈	—	26	2	no	—
275	C₄⋊C₈	—	26	2	no	—
276	C₄⋊C₈	—	26	1	no	—
277	C₄⋊C₈	—	26	1	no	—
278	C₄⋊C₈	C₄×D₁₃	1	2	yes	—
279	C₄⋊C₈	C₂²×D₁₃	1	2	yes	—
280	C₄⋊C₈	C₂²×D₁₃	1	2	yes	—
281	C₂²⋊C₈	—	13	2	no	—
282	C₂²⋊C₈	—	13	4	no	—
283	C₂²⋊C₈	—	26	2	no	—
284	C₂²⋊C₈	—	26	2	no	—
285	C₂²⋊C₈	C₄×D₁₃	1	2	yes	—
286	#97	—	13	4	no	—
287	#97	—	26	2	no	—
288	C₄×C₈	—	13	2	no	—
289	C₄×C₈	—	26	2	no	—
290	C₄×C₈	C₂²×D₁₃	1	2	yes	—
291	C₂×C₁₃	—	2	2	no	—
292	C₂×C₁₃	C₂×#424	1	1	yes	characteristic
293	C₂×C₁₃	C₂×#428	1	1	yes	characteristic
294	C₂×C₁₃	C₂×#430	1	1	yes	characteristic
295	D₁₃	—	2	2	no	—
296	D₁₃	—	2	2	no	—
297	C₂⁴	—	13	1	no	—
298	C₂²×C₄	—	13	1	no	—
299	C₂²×C₄	—	13	1	no	—
300	C₂²×C₄	—	13	1	no	—
301	C₂²×C₄	—	13	1	no	—
302	C₂²×C₄	—	13	1	no	—
303	C₂²×C₄	—	13	1	no	—
304	C₂²×C₄	—	13	1	no	—
305	C₂²×C₄	—	13	1	no	—
306	C₂²×C₄	—	13	1	no	—
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	—	13	1	no	—
313	C₂²×C₄	—	26	4	no	—
314	C₂²×C₄	—	26	2	no	—
315	C₂²×C₄	—	26	2	no	—
316	C₂²×C₄	—	52	2	no	—
317	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
318	C₂²×C₄	D₄×D₁₃	1	1	yes	characteristic
319	C₂²×C₄	Q₈×D₁₃	1	1	yes	characteristic
320	M₁₆	—	4	2	no	—
321	M₁₆	—	26	8	no	—
322	M₁₆	—	52	2	no	—
323	C₂×C₈	—	2	2	no	—
324	C₂×C₈	—	2	2	no	—
325	C₂×C₈	—	4	2	no	—
326	C₂×C₈	—	13	4	no	—
327	C₂×C₈	—	26	2	no	—
328	C₂×C₈	—	26	2	no	—
329	C₂×C₈	—	52	4	no	—
330	C₂×C₈	—	52	4	no	—
331	C₂×C₈	—	52	2	no	—
332	C₂×C₈	C₂×C₄×D₁₃	1	4	yes	—
333	C₄²	—	13	1	no	—
334	C₄²	—	13	1	no	—
335	C₄²	—	13	1	no	—
336	C₄²	—	13	1	no	—
337	C₄²	—	13	1	no	—
338	C₄²	—	13	1	no	—
339	C₄²	—	13	1	no	—
340	C₄²	—	13	1	no	—
341	C₄²	—	13	1	no	—
342	C₄²	—	13	1	no	—
343	C₄²	—	13	1	no	—
344	C₄²	—	13	1	no	—
345	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
346	C₄²	D₄×D₁₃	1	1	yes	characteristic
347	C₄²	Q₈×D₁₃	1	1	yes	characteristic
348	C₄²	C₂³×D₁₃	1	1	yes	characteristic
349	C₁₃	#17807	1	1	yes	characteristic, complemented, Sylow
350	C₂³	—	13	1	no	—
351	C₂³	—	13	1	no	—
352	C₂³	—	26	2	no	—
353	C₂³	—	26	2	no	—
354	C₂³	—	26	2	no	—
355	C₂³	C₄⋊C₄×D₁₃	1	1	yes	characteristic
356	C₂×C₄	—	2	2	no	—
357	C₂×C₄	—	4	1	no	—
358	C₂×C₄	—	13	1	no	—
359	C₂×C₄	—	13	4	no	—
360	C₂×C₄	—	13	1	no	—
361	C₂×C₄	—	13	1	no	—
362	C₂×C₄	—	13	1	no	—
363	C₂×C₄	—	13	1	no	—
364	C₂×C₄	—	13	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	2	no	—
370	C₂×C₄	—	26	2	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	—	52	1	no	—
379	C₂×C₄	—	52	1	no	—
380	C₂×C₄	—	52	1	no	—
381	C₂×C₄	C₄⋊C₄×D₁₃	1	1	yes	characteristic
382	C₂×C₄	C₄⋊C₄×D₁₃	1	1	yes	characteristic
383	C₂×C₄	C₄⋊C₄×D₁₃	1	1	yes	characteristic
384	C₂×C₄	#88168	1	2	yes	—
385	C₂×C₄	#88169	1	2	yes	—
386	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
387	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
388	C₂×C₄	C₂×Q₈×D₁₃	1	1	yes	characteristic
389	C₈	—	2	4	no	—
390	C₈	—	4	2	no	—
391	C₈	—	4	2	no	—
392	C₈	—	26	4	no	—
393	C₈	—	52	2	no	—
394	C₈	—	52	2	no	—
395	C₂²	—	2	1	no	—
396	C₂²	—	2	1	no	—
397	C₂²	—	13	2	no	—
398	C₂²	—	13	2	no	—
399	C₂²	—	26	8	no	—
400	C₂²	—	26	1	no	—
401	C₂²	—	26	1	no	—
402	C₂²	—	26	1	no	—
403	C₂²	—	26	1	no	—
404	C₂²	#11718522	1	2	yes	—
405	C₂²	C₂×C₄⋊C₄×D₁₃	1	1	yes	characteristic
406	C₄	—	2	1	no	—
407	C₄	—	2	1	no	—
408	C₄	—	2	1	no	—
409	C₄	—	13	2	no	—
410	C₄	—	26	1	no	—
411	C₄	—	26	1	no	—
412	C₄	—	26	1	no	—
413	C₄	—	26	1	no	—
414	C₄	—	26	1	no	—
415	C₄	#11718522	1	2	yes	—
416	C₄	D₁₃×#131	1	2	yes	—
417	C₄	C₂×#88168	1	1	yes	characteristic
418	C₄	C₂×#88169	1	1	yes	characteristic
419	C₂	—	2	2	no	—
420	C₂	—	26	2	no	—
421	C₂	—	26	2	no	—
422	C₂	D₁₃×#424	1	1	yes	characteristic
423	C₂	C₂×#11718522	1	1	yes	characteristic
424	C₂	D₁₃×#430	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×#1570	C₂
socle	C₂²×C₁₃	C₂²×C₄⋊C₄
prime radical	C₂³×D₁₃	C₄⋊C₄
cosocle	C₄²×C₁₃	C₂⁴
hypercenter	#1570	D₁₃
hypocenter	C₁₃	#17807
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1570

Complements

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

N	H ≅ G/N	type
4. #13113618	C₂	semidirect
5. #13113611	C₂	semidirect
6. #13113610	C₂	semidirect
7. #13113608	C₂	semidirect
8. #13113585	C₂	semidirect
9. C₁₃×#1570	C₂	semidirect
35. C₁₃×#334	C₂²	semidirect
36. #11718072	C₂²	semidirect
37. #11718071	C₂²	semidirect
38. #11718050	C₂²	semidirect
145. #1570	D₁₃	semidirect
220. #334	C₂×D₁₃	semidirect
349. C₁₃	#17807	semidirect

Maximal subgroups

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

subgroup	index
#13123468	2
#13123464	2
C₂×D₁₃×C₄⋊C₈	2
#13113618	2
#13113611	2
#13113610	2
#13113608	2
#13113585	2
C₁₃×#1570	2
#17807	13