Subgroups — #15832020

Order 3328.

646 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13123466	C₂	1	1	yes	maximal, characteristic
2	#13123464	C₂	1	1	yes	maximal, characteristic
3	D₁₃×#431	C₂	1	1	yes	maximal, characteristic
4	#13113626	C₂	1	2	yes	maximal, complemented
5	#13113623	C₂	1	2	yes	maximal, complemented
6	#13113617	C₂	1	1	yes	maximal, characteristic, complemented
7	#13113616	C₂	1	1	yes	maximal, characteristic, complemented
8	#13113614	C₂	1	1	yes	maximal, characteristic, complemented
9	#13113587	C₂	1	2	yes	maximal, complemented
10	#13113585	C₂	1	2	yes	maximal, complemented
11	C₁₃×#1572	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₄²×D₁₃	C₂²	1	1	yes	characteristic
13	C₁₃×#432	C₂²	1	1	yes	characteristic
14	C₁₃×#431	C₂²	1	1	yes	characteristic
15	C₁₃×#431	C₂²	1	1	yes	characteristic
16	#11718587	C₂²	1	1	yes	characteristic
17	#11718586	C₂²	1	1	yes	characteristic
18	#11718586	C₂²	1	1	yes	characteristic
19	#11718498	C₄	1	2	yes	—
20	#11718498	C₂²	1	2	yes	—
21	#11718496	C₄	1	2	yes	—
22	#11718494	C₂²	1	2	yes	—
23	#11718494	C₂²	1	2	yes	—
24	D₁₃×C₄⋊C₈	C₂²	1	2	yes	—
25	#11718387	—	2	1	no	—
26	#11718387	C₄	1	2	yes	—
27	D₁₃×C₂²⋊C₈	—	2	1	no	—
28	#11718380	C₄	1	2	yes	—
29	#11718379	—	2	1	no	—
30	#11718379	—	2	1	no	—
31	#11718368	—	2	1	no	—
32	#11718366	—	2	1	no	—
33	C₄×#6094	C₂²	1	1	yes	characteristic
34	C₄×#6094	C₂²	1	1	yes	characteristic
35	#11718346	—	2	1	no	—
36	#11718346	C₂²	1	1	yes	characteristic
37	#11718346	C₂²	1	1	yes	characteristic
38	C₄×C₈×D₁₃	—	2	1	no	—
39	C₁₃×#335	C₂²	1	2	yes	complemented
40	C₁₃×#334	C₂²	1	2	yes	complemented
41	#11718072	C₂²	1	2	yes	complemented
42	#11718072	C₂²	1	2	yes	complemented
43	#11718071	C₂²	1	2	yes	complemented
44	#11718071	C₂²	1	2	yes	complemented
45	#11718050	C₂²	1	2	yes	complemented
46	#11718049	C₂²	1	2	yes	complemented
47	C₂²×C₄×D₁₃	C₂×C₄	1	1	yes	characteristic
48	C₂²×C₄×D₁₃	D₄	1	1	yes	characteristic
49	C₂²×C₄×D₁₃	Q₈	1	1	yes	characteristic
50	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
51	C₂×C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
52	C₂×C₄×Dic₁₃	D₄	1	1	yes	characteristic
53	C₂×C₄×Dic₁₃	Q₈	1	1	yes	characteristic
54	C₂×#6094	—	2	2	no	—
55	C₂×#6094	C₂×C₄	1	2	yes	—
56	C₂×#6094	C₂×C₄	1	2	yes	—
57	C₂×C₈×D₁₃	—	2	2	no	—
58	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
59	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
60	C₄²×D₁₃	D₄	1	1	yes	characteristic
61	C₄²×D₁₃	D₄	1	1	yes	characteristic
62	C₄²×D₁₃	Q₈	1	1	yes	characteristic
63	C₄²×D₁₃	Q₈	1	1	yes	characteristic
64	C₄²×D₁₃	C₂³	1	1	yes	characteristic
65	C₄²×D₁₃	C₂³	1	1	yes	characteristic
66	C₁₃×C₄⋊C₈	C₂×C₄	1	2	yes	—
67	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
68	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
69	C₁₃×C₂²⋊C₈	—	2	1	no	—
70	C₁₃×C₂²⋊C₈	—	2	1	no	—
71	C₁₃×C₂²⋊C₈	C₂×C₄	1	2	yes	—
72	C₁₃×#97	—	2	1	no	—
73	C₄×C₈×C₁₃	—	2	1	no	—
74	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
75	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
76	C₂²⋊#1055	—	2	1	no	—
77	C₂²⋊#1055	—	2	1	no	—
78	C₂²⋊#1055	C₂×C₄	1	2	yes	—
79	#88060	—	2	2	no	—
80	#88060	—	2	2	no	—
81	#88060	C₂×C₄	1	2	yes	—
82	#88060	C₂×C₄	1	2	yes	—
83	#88055	C₂×C₄	1	2	yes	—
84	#88055	C₂×C₄	1	2	yes	—
85	#88054	—	2	2	no	—
86	#88054	—	2	2	no	—
87	#88054	C₂×C₄	1	2	yes	—
88	#88054	C₂×C₄	1	2	yes	—
89	C₈×Dic₁₃	—	2	2	no	—
90	C₈×Dic₁₃	—	2	2	no	—
91	C₄⋊#1055	C₂×C₄	1	2	yes	—
92	C₄⋊#1055	C₂³	1	2	yes	—
93	C₄⋊#1055	C₂³	1	2	yes	—
94	#88043	—	2	1	no	—
95	C₄×#1055	—	2	1	no	—
96	C₄×#1055	C₂³	1	1	yes	characteristic
97	C₄×#1055	C₂³	1	1	yes	characteristic
98	#17808	—	13	1	no	maximal, Sylow
99	C₂³×D₁₃	C₄⋊C₄	1	1	yes	characteristic
100	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
101	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
102	C₂²×C₄×C₁₃	C₂×Q₈	1	1	yes	characteristic
103	C₂²×Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
104	C₂²×Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
105	C₂²×Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
106	C₂×C₄×D₁₃	—	2	4	no	—
107	C₂×C₄×D₁₃	—	4	2	no	—
108	C₂×C₄×D₁₃	—	4	2	no	—
109	C₂×C₄×D₁₃	C₄⋊C₄	1	1	yes	characteristic
110	C₂×C₄×D₁₃	C₄⋊C₄	1	1	yes	characteristic
111	C₂×C₄×D₁₃	C₄⋊C₄	1	1	yes	characteristic
112	C₂×C₄×D₁₃	C₄⋊C₄	1	1	yes	characteristic
113	C₂×C₄×D₁₃	C₄⋊C₄	1	1	yes	characteristic
114	C₂×C₄×D₁₃	C₄⋊C₄	1	1	yes	characteristic
115	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
116	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
117	C₂×C₄×D₁₃	C₂×D₄	1	1	yes	characteristic
118	C₂×C₄×D₁₃	C₂×D₄	1	1	yes	characteristic
119	C₂×C₄×D₁₃	C₂×Q₈	1	1	yes	characteristic
120	C₂×C₄×D₁₃	C₂×Q₈	1	1	yes	characteristic
121	C₂×C₈×C₁₃	—	2	2	no	—
122	C₂×C₈×C₁₃	—	2	2	no	—
123	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
124	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
125	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
126	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
127	C₄²×C₁₃	C₂×Q₈	1	1	yes	characteristic
128	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
129	C₄×Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
130	C₄×Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
131	C₄×Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
132	C₄×Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
133	C₄×Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
134	C₄×Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
135	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
136	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
137	C₄×Dic₁₃	C₂×D₄	1	1	yes	characteristic
138	C₄×Dic₁₃	C₂×D₄	1	1	yes	characteristic
139	C₄×Dic₁₃	C₂×Q₈	1	1	yes	characteristic
140	C₄×Dic₁₃	C₂×Q₈	1	1	yes	characteristic
141	C₂×#1055	—	2	2	no	—
142	C₂×#1055	—	2	2	no	—
143	C₂×#1055	C₂²×C₄	1	2	yes	—
144	C₂×#1055	C₂²×C₄	1	2	yes	—
145	#6094	—	2	4	no	—
146	#6094	—	2	4	no	—
147	#6094	—	4	4	no	—
148	C₈×D₁₃	—	4	4	no	—
149	#2920	—	13	1	no	—
150	#2920	—	13	1	no	—
151	C₂×#431	—	13	1	no	—
152	#1574	—	13	2	no	—
153	#1574	—	13	2	no	—
154	#1572	—	13	1	no	—
155	#1572	—	13	1	no	—
156	#1572	—	13	1	no	—
157	#1572	D₁₃	1	1	yes	characteristic, complemented
158	#1565	—	13	2	no	—
159	#1565	—	13	2	no	—
160	C₂³×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
161	C₂²×D₁₃	—	2	2	no	—
162	C₂²×D₁₃	—	4	1	no	—
163	C₂²×D₁₃	—	4	1	no	—
164	C₂²×D₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
165	C₂²×D₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
166	C₂×C₄×C₁₃	—	2	2	no	—
167	C₂×C₄×C₁₃	—	2	2	no	—
168	C₂×C₄×C₁₃	—	4	1	no	—
169	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
170	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
171	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
172	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
173	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
174	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
175	C₂×Dic₁₃	—	2	2	no	—
176	C₂×Dic₁₃	—	2	2	no	—
177	C₂×Dic₁₃	—	4	1	no	—
178	C₂×Dic₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
179	C₂×Dic₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
180	C₂×Dic₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
181	C₂×Dic₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
182	C₂×Dic₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
183	C₂×Dic₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
184	C₄×D₁₃	—	2	2	no	—
185	C₄×D₁₃	—	2	2	no	—
186	C₄×D₁₃	—	2	2	no	—
187	C₄×D₁₃	—	2	2	no	—
188	C₄×D₁₃	—	2	2	no	—
189	C₄×D₁₃	—	2	2	no	—
190	C₄×D₁₃	—	2	2	no	—
191	C₄×D₁₃	—	4	1	no	—
192	C₄×D₁₃	—	4	1	no	—
193	C₄×D₁₃	—	4	1	no	—
194	C₄×D₁₃	—	4	1	no	—
195	C₄×D₁₃	#131	1	4	yes	—
196	C₈×C₁₃	—	2	2	no	—
197	C₈×C₁₃	—	2	2	no	—
198	C₈×C₁₃	—	4	2	no	—
199	C₈×C₁₃	—	4	2	no	—
200	#1055	—	2	2	no	—
201	#1055	—	2	2	no	—
202	#1055	—	4	2	no	—
203	#1055	—	4	2	no	—
204	C₂²×C₄²	—	13	1	no	—
205	#432	—	13	2	no	—
206	#432	—	13	2	no	—
207	#432	—	13	1	no	—
208	#432	—	26	1	no	—
209	#432	C₂×D₁₃	1	1	yes	characteristic
210	#431	—	13	1	no	—
211	#431	—	13	1	no	—
212	#431	—	13	1	no	—
213	#431	—	13	1	no	—
214	#431	—	13	2	no	—
215	#431	—	13	2	no	—
216	#431	—	26	1	no	—
217	#431	—	26	1	no	—
218	#431	—	26	1	no	—
219	#431	C₂×D₁₃	1	1	yes	characteristic
220	#431	C₂×D₁₃	1	1	yes	characteristic
221	#423	—	13	2	no	—
222	#423	—	13	2	no	—
223	C₂×C₄⋊C₈	—	13	2	no	—
224	#407	—	13	2	no	—
225	#407	—	26	1	no	—
226	C₂×C₂²⋊C₈	—	26	1	no	—
227	C₄×M₁₆	—	13	1	no	—
228	C₄×M₁₆	—	13	1	no	—
229	C₄×M₁₆	—	26	1	no	—
230	C₂×C₄×C₈	—	26	1	no	—
231	#335	—	13	2	no	—
232	#335	—	13	2	no	—
233	#335	—	13	2	no	—
234	#335	C₂×D₁₃	1	2	yes	complemented
235	#334	—	13	2	no	—
236	#334	—	13	2	no	—
237	#334	—	13	2	no	—
238	#334	C₂×D₁₃	1	2	yes	complemented
239	C₂²×C₁₃	—	2	1	no	—
240	C₂²×C₁₃	—	2	1	no	—
241	C₂²×C₁₃	—	2	1	no	—
242	C₂²×C₁₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
243	C₂×D₁₃	—	2	1	no	—
244	C₂×D₁₃	—	2	1	no	—
245	C₂×D₁₃	—	2	1	no	—
246	C₂×D₁₃	—	2	1	no	—
247	C₂×D₁₃	—	2	1	no	—
248	C₂×D₁₃	—	4	4	no	—
249	C₂×D₁₃	#424	1	2	yes	—
250	C₄×C₁₃	—	2	1	no	—
251	C₄×C₁₃	—	2	1	no	—
252	C₄×C₁₃	—	2	1	no	—
253	C₄×C₁₃	—	2	1	no	—
254	C₄×C₁₃	C₂×#131	1	2	yes	—
255	C₄×C₁₃	#575	1	2	yes	—
256	Dic₁₃	—	2	1	no	—
257	Dic₁₃	—	2	1	no	—
258	Dic₁₃	—	2	1	no	—
259	Dic₁₃	—	2	1	no	—
260	Dic₁₃	#424	1	2	yes	—
261	Dic₁₃	#430	1	2	yes	—
262	C₂³×C₄	—	13	1	no	—
263	C₂³×C₄	—	13	1	no	—
264	C₂³×C₄	—	13	1	no	—
265	C₂×M₁₆	—	13	2	no	—
266	C₂×M₁₆	—	13	2	no	—
267	C₂×M₁₆	—	26	2	no	—
268	C₂²×C₈	—	26	2	no	—
269	C₂×C₄²	—	13	1	no	—
270	C₂×C₄²	—	13	1	no	—
271	C₂×C₄²	—	13	1	no	—
272	C₂×C₄²	—	13	1	no	—
273	C₂×C₄²	—	13	1	no	—
274	C₂×C₄²	—	13	1	no	—
275	C₂×C₄²	—	13	1	no	—
276	C₂×C₄²	—	13	1	no	—
277	C₂×C₄²	—	13	1	no	—
278	C₂×C₄²	—	13	1	no	—
279	C₂×C₄²	—	13	1	no	—
280	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
281	C₄⋊C₈	—	13	2	no	—
282	C₄⋊C₈	—	13	2	no	—
283	C₄⋊C₈	—	13	2	no	—
284	C₄⋊C₈	—	13	2	no	—
285	C₄⋊C₈	—	13	2	no	—
286	C₄⋊C₈	—	26	2	no	—
287	C₄⋊C₈	—	26	2	no	—
288	C₄⋊C₈	C₄×D₁₃	1	2	yes	—
289	C₄⋊C₈	C₂²×D₁₃	1	2	yes	—
290	C₄⋊C₈	C₂²×D₁₃	1	2	yes	—
291	C₂²⋊C₈	—	2	1	no	—
292	C₂²⋊C₈	—	2	1	no	—
293	C₂²⋊C₈	—	13	2	no	—
294	C₂²⋊C₈	—	13	2	no	—
295	C₂²⋊C₈	—	13	2	no	—
296	C₂²⋊C₈	—	26	2	no	—
297	C₂²⋊C₈	—	26	2	no	—
298	C₂²⋊C₈	—	26	1	no	—
299	C₂²⋊C₈	—	26	1	no	—
300	C₂²⋊C₈	C₄×D₁₃	1	2	yes	—
301	#97	—	2	1	no	—
302	#97	—	13	2	no	—
303	#97	—	13	2	no	—
304	#97	—	26	1	no	—
305	C₄×C₈	—	2	1	no	—
306	C₄×C₈	—	13	1	no	—
307	C₄×C₈	—	13	1	no	—
308	C₄×C₈	—	26	2	no	—
309	C₄×C₈	—	26	2	no	—
310	C₄×C₈	—	26	1	no	—
311	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
312	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
313	C₂×C₁₃	—	4	1	no	—
314	C₂×C₁₃	C₂×#424	1	1	yes	characteristic
315	C₂×C₁₃	#2911	1	1	yes	characteristic
316	C₂×C₁₃	C₂×#430	1	1	yes	characteristic
317	D₁₃	—	2	2	no	—
318	D₁₃	—	4	1	no	—
319	C₂⁴	—	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	—	13	1	no	—
327	C₂²×C₄	—	13	1	no	—
328	C₂²×C₄	—	13	1	no	—
329	C₂²×C₄	—	13	1	no	—
330	C₂²×C₄	—	13	1	no	—
331	C₂²×C₄	—	13	1	no	—
332	C₂²×C₄	—	13	1	no	—
333	C₂²×C₄	—	13	1	no	—
334	C₂²×C₄	—	13	1	no	—
335	C₂²×C₄	—	26	4	no	—
336	C₂²×C₄	—	52	2	no	—
337	C₂²×C₄	—	52	2	no	—
338	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
339	C₂²×C₄	D₄×D₁₃	1	1	yes	characteristic
340	C₂²×C₄	Q₈×D₁₃	1	1	yes	characteristic
341	M₁₆	—	26	4	no	—
342	M₁₆	—	26	4	no	—
343	M₁₆	—	52	4	no	—
344	C₂×C₈	—	2	2	no	—
345	C₂×C₈	—	2	2	no	—
346	C₂×C₈	—	13	2	no	—
347	C₂×C₈	—	13	2	no	—
348	C₂×C₈	—	26	2	no	—
349	C₂×C₈	—	26	2	no	—
350	C₂×C₈	—	52	4	no	—
351	C₂×C₈	C₂×C₄×D₁₃	1	2	yes	—
352	C₂×C₈	C₂×C₄×D₁₃	1	2	yes	—
353	C₄²	—	13	1	no	—
354	C₄²	—	13	1	no	—
355	C₄²	—	13	1	no	—
356	C₄²	—	13	1	no	—
357	C₄²	—	13	1	no	—
358	C₄²	—	13	1	no	—
359	C₄²	—	13	1	no	—
360	C₄²	—	13	1	no	—
361	C₄²	—	13	1	no	—
362	C₄²	—	13	1	no	—
363	C₄²	—	13	1	no	—
364	C₄²	—	13	1	no	—
365	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
366	C₄²	D₄×D₁₃	1	1	yes	characteristic
367	C₄²	Q₈×D₁₃	1	1	yes	characteristic
368	C₄²	C₂³×D₁₃	1	1	yes	characteristic
369	C₁₃	#17808	1	1	yes	characteristic, complemented, Sylow
370	C₂³	—	13	1	no	—
371	C₂³	—	13	1	no	—
372	C₂³	—	26	2	no	—
373	C₂³	—	52	1	no	—
374	C₂³	—	52	1	no	—
375	C₂³	C₄⋊C₄×D₁₃	1	1	yes	characteristic
376	C₂×C₄	—	2	2	no	—
377	C₂×C₄	—	2	2	no	—
378	C₂×C₄	—	4	1	no	—
379	C₂×C₄	—	13	1	no	—
380	C₂×C₄	—	13	1	no	—
381	C₂×C₄	—	13	4	no	—
382	C₂×C₄	—	13	1	no	—
383	C₂×C₄	—	13	1	no	—
384	C₂×C₄	—	13	1	no	—
385	C₂×C₄	—	13	1	no	—
386	C₂×C₄	—	26	2	no	—
387	C₂×C₄	—	26	2	no	—
388	C₂×C₄	—	26	2	no	—
389	C₂×C₄	—	26	2	no	—
390	C₂×C₄	—	26	2	no	—
391	C₂×C₄	—	26	2	no	—
392	C₂×C₄	—	26	2	no	—
393	C₂×C₄	—	26	2	no	—
394	C₂×C₄	—	26	2	no	—
395	C₂×C₄	—	52	1	no	—
396	C₂×C₄	—	52	1	no	—
397	C₂×C₄	—	52	1	no	—
398	C₂×C₄	—	52	1	no	—
399	C₂×C₄	—	52	1	no	—
400	C₂×C₄	C₄⋊C₄×D₁₃	1	1	yes	characteristic
401	C₂×C₄	C₄⋊C₄×D₁₃	1	1	yes	characteristic
402	C₂×C₄	C₄⋊C₄×D₁₃	1	1	yes	characteristic
403	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
404	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
405	C₂×C₄	C₂×Q₈×D₁₃	1	1	yes	characteristic
406	C₈	—	2	2	no	—
407	C₈	—	2	2	no	—
408	C₈	—	4	2	no	—
409	C₈	—	4	2	no	—
410	C₈	—	26	2	no	—
411	C₈	—	26	2	no	—
412	C₈	—	52	2	no	—
413	C₈	—	52	2	no	—
414	C₂²	—	2	1	no	—
415	C₂²	—	2	1	no	—
416	C₂²	—	2	1	no	—
417	C₂²	—	13	2	no	—
418	C₂²	—	26	1	no	—
419	C₂²	—	26	1	no	—
420	C₂²	—	26	1	no	—
421	C₂²	—	26	1	no	—
422	C₂²	—	26	1	no	—
423	C₂²	—	52	4	no	—
424	C₂²	C₂×C₄⋊C₄×D₁₃	1	1	yes	characteristic
425	C₄	—	2	1	no	—
426	C₄	—	2	1	no	—
427	C₄	—	2	1	no	—
428	C₄	—	2	1	no	—
429	C₄	—	13	2	no	—
430	C₄	—	13	2	no	—
431	C₄	—	26	1	no	—
432	C₄	—	26	1	no	—
433	C₄	—	26	1	no	—
434	C₄	—	26	1	no	—
435	C₄	D₁₃×#131	1	2	yes	—
436	C₄	#11719473	1	2	yes	—
437	C₂	—	4	1	no	—
438	C₂	—	26	2	no	—
439	C₂	—	52	1	no	—
440	C₂	D₁₃×#424	1	1	yes	characteristic
441	C₂	#13123424	1	1	yes	characteristic
442	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×#1572	C₂
socle	C₂²×C₁₃	C₂²×C₄⋊C₄
prime radical	C₂³×D₁₃	C₄⋊C₄
cosocle	C₄²×C₁₃	C₂⁴
hypercenter	#1572	D₁₃
hypocenter	C₁₃	#17808
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1572

Complements

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

N	H ≅ G/N	type
4. #13113626	C₂	semidirect
5. #13113623	C₂	semidirect
6. #13113617	C₂	semidirect
7. #13113616	C₂	semidirect
8. #13113614	C₂	semidirect
9. #13113587	C₂	semidirect
10. #13113585	C₂	semidirect
11. C₁₃×#1572	C₂	semidirect
39. C₁₃×#335	C₂²	semidirect
40. C₁₃×#334	C₂²	semidirect
41. #11718072	C₂²	semidirect
42. #11718072	C₂²	semidirect
43. #11718071	C₂²	semidirect
44. #11718071	C₂²	semidirect
45. #11718050	C₂²	semidirect
46. #11718049	C₂²	semidirect
157. #1572	D₁₃	semidirect
234. #335	C₂×D₁₃	semidirect
238. #334	C₂×D₁₃	semidirect
369. C₁₃	#17808	semidirect

Maximal subgroups

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

subgroup	index
#13123466	2
#13123464	2
D₁₃×#431	2
#13113626	2
#13113623	2
#13113617	2
#13113616	2
#13113614	2
#13113587	2
#13113585	2
C₁₃×#1572	2
#17808	13