Subgroups — #15832117

Order 3328.

616 conjugacy classes of subgroups.

The subgroup lattice has 458 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	#13123467	C₂	1	1	yes	maximal, characteristic
3	#13123466	C₂	1	1	yes	maximal, characteristic
4	#13113626	C₂	1	2	yes	maximal, complemented
5	#13113623	C₂	1	2	yes	maximal, complemented
6	#13113615	C₂	1	2	yes	maximal, complemented
7	#13113613	C₂	1	2	yes	maximal, complemented
8	#13113604	C₂	1	1	yes	maximal, characteristic, complemented
9	#13113603	C₂	1	1	yes	maximal, characteristic, complemented
10	#13113601	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1569	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×#423	C₂²	1	1	yes	characteristic
15	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
16	#11718787	—	2	1	no	—
17	#11718787	C₄	1	2	yes	—
18	#11718779	C₄	1	2	yes	—
19	M₁₆×Dic₁₃	—	2	1	no	—
20	#11718587	C₂²	1	1	yes	characteristic
21	#11718585	C₂²	1	1	yes	characteristic
22	C₄×#6099	C₂²	1	1	yes	characteristic
23	#11718498	C₂²	1	1	yes	characteristic
24	#11718498	C₂²	1	1	yes	characteristic
25	#11718496	—	2	1	no	—
26	#11718496	C₂²	1	2	yes	—
27	#11718494	—	2	1	no	—
28	#11718494	C₂²	1	1	yes	characteristic
29	#11718494	C₂²	1	1	yes	characteristic
30	#11718494	C₂²	1	2	yes	—
31	#11718387	—	2	1	no	—
32	#11718379	—	2	1	no	—
33	#11718368	—	2	1	no	—
34	#11718366	—	2	1	no	—
35	#11718366	C₄	1	2	yes	—
36	#11718366	C₄	1	2	yes	—
37	#11718346	C₂²	1	2	yes	—
38	#11718346	C₂²	1	2	yes	—
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×C₁₃×M₁₆	—	2	1	no	—
51	C₂×C₁₃×M₁₆	C₂×C₄	1	2	yes	—
52	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
53	C₂×C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
54	C₂×C₄×Dic₁₃	D₄	1	1	yes	characteristic
55	C₂×C₄×Dic₁₃	Q₈	1	1	yes	characteristic
56	C₂×#6099	—	2	1	no	—
57	C₂×#6099	C₂×C₄	1	2	yes	—
58	C₂×#6094	—	2	1	no	—
59	C₂×#6094	—	2	1	no	—
60	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
61	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
62	C₄²×D₁₃	D₄	1	1	yes	characteristic
63	C₄²×D₁₃	D₄	1	1	yes	characteristic
64	C₄²×D₁₃	Q₈	1	1	yes	characteristic
65	C₄²×D₁₃	Q₈	1	1	yes	characteristic
66	C₄²×D₁₃	C₂³	1	1	yes	characteristic
67	C₄²×D₁₃	C₂³	1	1	yes	characteristic
68	C₁₃×C₄⋊C₈	—	2	1	no	—
69	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
70	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
71	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
72	C₁₃×C₂²⋊C₈	—	2	1	no	—
73	C₁₃×#97	—	2	1	no	—
74	C₁₃×#97	C₂×C₄	1	2	yes	—
75	C₄×C₈×C₁₃	C₂³	1	2	yes	—
76	C₂²⋊#1055	—	2	1	no	—
77	#88060	—	2	2	no	—
78	#88060	—	2	2	no	—
79	#88060	—	2	1	no	—
80	#88060	—	2	1	no	—
81	#88060	C₂×C₄	1	4	yes	—
82	#88060	C₂×C₄	1	4	yes	—
83	#88055	—	2	2	no	—
84	#88054	—	2	1	no	—
85	#88054	—	2	1	no	—
86	#88054	C₂×C₄	1	4	yes	—
87	#88054	C₂×C₄	1	4	yes	—
88	C₈×Dic₁₃	—	2	2	no	—
89	C₈×Dic₁₃	—	2	1	no	—
90	C₈×Dic₁₃	—	2	1	no	—
91	C₄⋊#1055	—	2	1	no	—
92	C₄⋊#1055	C₂³	1	2	yes	—
93	C₄⋊#1055	C₂³	1	1	yes	characteristic
94	C₄⋊#1055	C₂³	1	1	yes	characteristic
95	#88043	—	2	1	no	—
96	#88043	C₂×C₄	1	2	yes	—
97	C₄×#1055	C₂³	1	2	yes	—
98	#17823	—	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	—	4	2	no	—
107	C₂×C₄×D₁₃	—	4	2	no	—
108	C₂×C₄×D₁₃	—	4	1	no	—
109	C₂×C₄×D₁₃	—	4	1	no	—
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	C₄⋊C₄	1	1	yes	characteristic
116	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
117	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
118	C₂×C₄×D₁₃	C₂×D₄	1	1	yes	characteristic
119	C₂×C₄×D₁₃	C₂×D₄	1	1	yes	characteristic
120	C₂×C₄×D₁₃	C₂×Q₈	1	1	yes	characteristic
121	C₂×C₄×D₁₃	C₂×Q₈	1	1	yes	characteristic
122	C₁₃×M₁₆	—	4	2	no	—
123	C₁₃×M₁₆	—	4	2	no	—
124	C₂×C₈×C₁₃	—	2	1	no	—
125	C₂×C₈×C₁₃	—	2	1	no	—
126	C₂×C₈×C₁₃	—	2	2	no	—
127	C₂×C₈×C₁₃	C₂²×C₄	1	4	yes	—
128	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
129	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
130	C₄²×C₁₃	C₂×Q₈	1	1	yes	characteristic
131	C₄²×C₁₃	C₂⁴	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	C₄⋊C₄	1	1	yes	characteristic
136	C₄×Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
137	C₄×Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
138	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
139	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
140	C₄×Dic₁₃	C₂×D₄	1	1	yes	characteristic
141	C₄×Dic₁₃	C₂×D₄	1	1	yes	characteristic
142	C₄×Dic₁₃	C₂×Q₈	1	1	yes	characteristic
143	C₄×Dic₁₃	C₂×Q₈	1	1	yes	characteristic
144	#6099	—	4	2	no	—
145	#6099	—	4	2	no	—
146	C₂×#1055	—	2	1	no	—
147	C₂×#1055	—	2	1	no	—
148	C₂×#1055	—	2	2	no	—
149	C₂×#1055	C₂²×C₄	1	4	yes	—
150	#6094	—	4	2	no	—
151	#6094	—	4	2	no	—
152	#2920	—	13	1	no	—
153	#2920	—	13	1	no	—
154	#2920	—	13	1	no	—
155	#1574	—	13	2	no	—
156	#1574	—	13	2	no	—
157	#1572	—	13	2	no	—
158	#1572	—	13	2	no	—
159	#1569	—	13	1	no	—
160	#1569	—	13	1	no	—
161	#1569	—	13	1	no	—
162	#1569	D₁₃	1	1	yes	characteristic, complemented
163	C₂³×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
164	C₂²×D₁₃	—	4	1	no	—
165	C₂²×D₁₃	—	4	1	no	—
166	C₂²×D₁₃	—	4	1	no	—
167	C₂²×D₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
168	C₂²×D₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
169	C₂×C₄×C₁₃	—	2	2	no	—
170	C₂×C₄×C₁₃	—	2	1	no	—
171	C₂×C₄×C₁₃	—	2	1	no	—
172	C₂×C₄×C₁₃	—	4	1	no	—
173	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
174	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
175	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
176	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
177	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
178	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
179	C₂×Dic₁₃	—	2	2	no	—
180	C₂×Dic₁₃	—	4	1	no	—
181	C₂×Dic₁₃	—	4	1	no	—
182	C₂×Dic₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
183	C₂×Dic₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
184	C₂×Dic₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
185	C₂×Dic₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
186	C₂×Dic₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
187	C₂×Dic₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
188	C₄×D₁₃	—	2	2	no	—
189	C₄×D₁₃	—	2	2	no	—
190	C₄×D₁₃	—	2	1	no	—
191	C₄×D₁₃	—	2	1	no	—
192	C₄×D₁₃	—	2	1	no	—
193	C₄×D₁₃	—	2	1	no	—
194	C₄×D₁₃	—	2	2	no	—
195	C₄×D₁₃	—	2	2	no	—
196	C₄×D₁₃	—	4	1	no	—
197	C₄×D₁₃	—	4	1	no	—
198	C₄×D₁₃	—	4	1	no	—
199	C₄×D₁₃	—	4	1	no	—
200	C₄×D₁₃	—	4	1	no	—
201	C₄×D₁₃	—	4	1	no	—
202	C₈×C₁₃	—	2	4	no	—
203	C₈×C₁₃	—	4	1	no	—
204	C₈×C₁₃	—	4	1	no	—
205	C₈×C₁₃	—	4	2	no	—
206	#1055	—	2	4	no	—
207	#1055	—	4	1	no	—
208	#1055	—	4	1	no	—
209	#1055	—	4	2	no	—
210	C₂²×C₄²	—	13	1	no	—
211	#432	—	13	2	no	—
212	#432	—	13	2	no	—
213	#432	—	13	1	no	—
214	#432	—	13	2	no	—
215	#432	—	26	1	no	—
216	#432	—	26	1	no	—
217	#432	C₂×D₁₃	1	1	yes	characteristic
218	#431	—	13	2	no	—
219	#431	—	13	2	no	—
220	#431	—	13	1	no	—
221	#431	—	13	1	no	—
222	#431	—	13	2	no	—
223	#431	—	26	1	no	—
224	#431	—	26	1	no	—
225	#423	—	13	2	no	—
226	#423	—	13	1	no	—
227	#423	—	13	1	no	—
228	#423	—	13	1	no	—
229	#423	C₂×D₁₃	1	1	yes	characteristic
230	#407	—	13	2	no	—
231	#407	—	26	1	no	—
232	#407	—	26	1	no	—
233	C₄×M₁₆	—	13	1	no	—
234	C₄×M₁₆	—	26	1	no	—
235	C₄×M₁₆	—	26	1	no	—
236	C₄×M₁₆	C₂×D₁₃	1	1	yes	characteristic
237	#335	—	13	2	no	—
238	#335	—	13	2	no	—
239	#335	—	13	2	no	—
240	#335	C₂×D₁₃	1	2	yes	complemented
241	#334	—	13	2	no	—
242	#334	—	13	2	no	—
243	#334	—	13	2	no	—
244	#334	C₂×D₁₃	1	2	yes	complemented
245	C₂²×C₁₃	—	2	1	no	—
246	C₂²×C₁₃	—	2	1	no	—
247	C₂²×C₁₃	—	2	1	no	—
248	C₂²×C₁₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
249	C₂×D₁₃	—	2	1	no	—
250	C₂×D₁₃	—	2	1	no	—
251	C₂×D₁₃	—	2	1	no	—
252	C₂×D₁₃	—	2	1	no	—
253	C₂×D₁₃	—	2	1	no	—
254	C₂×D₁₃	—	2	1	no	—
255	C₂×D₁₃	—	4	4	no	—
256	C₄×C₁₃	—	2	1	no	—
257	C₄×C₁₃	—	2	1	no	—
258	C₄×C₁₃	—	2	1	no	—
259	C₄×C₁₃	—	2	1	no	—
260	C₄×C₁₃	#568	1	2	yes	—
261	C₄×C₁₃	#575	1	1	yes	characteristic
262	C₄×C₁₃	#575	1	1	yes	characteristic
263	Dic₁₃	—	2	1	no	—
264	Dic₁₃	—	2	1	no	—
265	Dic₁₃	—	2	1	no	—
266	Dic₁₃	—	2	1	no	—
267	Dic₁₃	—	2	1	no	—
268	Dic₁₃	#430	1	2	yes	—
269	C₂³×C₄	—	13	1	no	—
270	C₂³×C₄	—	13	1	no	—
271	C₂³×C₄	—	13	1	no	—
272	C₂×M₁₆	—	2	1	no	—
273	C₂×M₁₆	—	13	2	no	—
274	C₂×M₁₆	—	26	1	no	—
275	C₂×M₁₆	—	26	1	no	—
276	C₂×M₁₆	—	26	1	no	—
277	C₂×M₁₆	C₄×D₁₃	1	2	yes	—
278	C₂×C₄²	—	13	1	no	—
279	C₂×C₄²	—	13	1	no	—
280	C₂×C₄²	—	13	1	no	—
281	C₂×C₄²	—	13	1	no	—
282	C₂×C₄²	—	13	1	no	—
283	C₂×C₄²	—	13	1	no	—
284	C₂×C₄²	—	13	1	no	—
285	C₂×C₄²	—	13	1	no	—
286	C₂×C₄²	—	13	1	no	—
287	C₂×C₄²	—	13	1	no	—
288	C₂×C₄²	—	13	1	no	—
289	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
290	C₄⋊C₈	—	2	1	no	—
291	C₄⋊C₈	—	13	4	no	—
292	C₄⋊C₈	—	13	4	no	—
293	C₄⋊C₈	—	13	1	no	—
294	C₄⋊C₈	—	13	2	no	—
295	C₄⋊C₈	—	13	1	no	—
296	C₄⋊C₈	—	26	1	no	—
297	C₄⋊C₈	—	26	1	no	—
298	C₄⋊C₈	—	26	1	no	—
299	C₄⋊C₈	C₂²×D₁₃	1	1	yes	characteristic
300	C₄⋊C₈	C₂²×D₁₃	1	2	yes	—
301	C₄⋊C₈	C₂²×D₁₃	1	1	yes	characteristic
302	C₂²⋊C₈	—	2	1	no	—
303	C₂²⋊C₈	—	13	4	no	—
304	C₂²⋊C₈	—	13	4	no	—
305	C₂²⋊C₈	—	26	1	no	—
306	C₂²⋊C₈	—	26	1	no	—
307	C₂²⋊C₈	—	26	2	no	—
308	C₂²⋊C₈	—	26	2	no	—
309	C₂²⋊C₈	—	26	1	no	—
310	#97	—	2	1	no	—
311	#97	—	13	2	no	—
312	#97	—	26	2	no	—
313	#97	—	26	1	no	—
314	#97	C₄×D₁₃	1	2	yes	—
315	C₄×C₈	—	13	2	no	—
316	C₄×C₈	—	26	1	no	—
317	C₄×C₈	—	26	1	no	—
318	C₄×C₈	—	26	2	no	—
319	C₄×C₈	C₂²×D₁₃	1	2	yes	—
320	C₂×C₁₃	—	4	1	no	—
321	C₂×C₁₃	#2905	1	1	yes	characteristic
322	C₂×C₁₃	#2911	1	1	yes	characteristic
323	C₂×C₁₃	C₂×#430	1	1	yes	characteristic
324	D₁₃	—	4	1	no	—
325	D₁₃	—	4	1	no	—
326	C₂⁴	—	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	—	13	1	no	—
336	C₂²×C₄	—	13	1	no	—
337	C₂²×C₄	—	13	1	no	—
338	C₂²×C₄	—	13	1	no	—
339	C₂²×C₄	—	13	1	no	—
340	C₂²×C₄	—	13	1	no	—
341	C₂²×C₄	—	13	1	no	—
342	C₂²×C₄	—	52	2	no	—
343	C₂²×C₄	—	52	1	no	—
344	C₂²×C₄	—	52	1	no	—
345	C₂²×C₄	—	52	2	no	—
346	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
347	C₂²×C₄	D₄×D₁₃	1	1	yes	characteristic
348	C₂²×C₄	Q₈×D₁₃	1	1	yes	characteristic
349	M₁₆	—	4	2	no	—
350	M₁₆	—	4	2	no	—
351	M₁₆	—	52	2	no	—
352	M₁₆	—	52	2	no	—
353	M₁₆	—	52	2	no	—
354	M₁₆	—	52	2	no	—
355	C₂×C₈	—	2	1	no	—
356	C₂×C₈	—	2	1	no	—
357	C₂×C₈	—	2	2	no	—
358	C₂×C₈	—	13	4	no	—
359	C₂×C₈	—	26	1	no	—
360	C₂×C₈	—	26	2	no	—
361	C₂×C₈	—	26	1	no	—
362	C₂×C₈	C₂×C₄×D₁₃	1	4	yes	—
363	C₄²	—	13	1	no	—
364	C₄²	—	13	1	no	—
365	C₄²	—	13	1	no	—
366	C₄²	—	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	—	13	1	no	—
372	C₄²	—	13	1	no	—
373	C₄²	—	13	1	no	—
374	C₄²	—	13	1	no	—
375	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
376	C₄²	D₄×D₁₃	1	1	yes	characteristic
377	C₄²	Q₈×D₁₃	1	1	yes	characteristic
378	C₄²	C₂³×D₁₃	1	1	yes	characteristic
379	C₁₃	#17823	1	1	yes	characteristic, complemented, Sylow
380	C₂³	—	13	1	no	—
381	C₂³	—	13	1	no	—
382	C₂³	—	52	1	no	—
383	C₂³	—	52	1	no	—
384	C₂³	—	52	1	no	—
385	C₂³	C₄⋊C₄×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	1	no	—
392	C₂×C₄	—	13	1	no	—
393	C₂×C₄	—	13	1	no	—
394	C₂×C₄	—	13	1	no	—
395	C₂×C₄	—	13	1	no	—
396	C₂×C₄	—	26	2	no	—
397	C₂×C₄	—	26	2	no	—
398	C₂×C₄	—	26	2	no	—
399	C₂×C₄	—	26	2	no	—
400	C₂×C₄	—	26	2	no	—
401	C₂×C₄	—	26	1	no	—
402	C₂×C₄	—	26	1	no	—
403	C₂×C₄	—	26	1	no	—
404	C₂×C₄	—	26	1	no	—
405	C₂×C₄	—	52	1	no	—
406	C₂×C₄	—	52	1	no	—
407	C₂×C₄	—	52	1	no	—
408	C₂×C₄	—	52	1	no	—
409	C₂×C₄	—	52	1	no	—
410	C₂×C₄	—	52	1	no	—
411	C₂×C₄	—	52	1	no	—
412	C₂×C₄	—	52	1	no	—
413	C₂×C₄	C₄⋊C₄×D₁₃	1	1	yes	characteristic
414	C₂×C₄	C₄⋊C₄×D₁₃	1	1	yes	characteristic
415	C₂×C₄	C₄⋊C₄×D₁₃	1	1	yes	characteristic
416	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
417	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
418	C₂×C₄	C₂×Q₈×D₁₃	1	1	yes	characteristic
419	C₈	—	2	4	no	—
420	C₈	—	4	2	no	—
421	C₈	—	4	1	no	—
422	C₈	—	4	1	no	—
423	C₈	—	26	4	no	—
424	C₈	—	52	1	no	—
425	C₈	—	52	1	no	—
426	C₈	—	52	2	no	—
427	C₂²	—	2	1	no	—
428	C₂²	—	2	1	no	—
429	C₂²	—	2	1	no	—
430	C₂²	—	26	1	no	—
431	C₂²	—	26	1	no	—
432	C₂²	—	26	1	no	—
433	C₂²	—	26	1	no	—
434	C₂²	—	26	1	no	—
435	C₂²	—	26	1	no	—
436	C₂²	—	52	4	no	—
437	C₂²	C₂×C₄⋊C₄×D₁₃	1	1	yes	characteristic
438	C₄	—	2	1	no	—
439	C₄	—	2	1	no	—
440	C₄	—	2	1	no	—
441	C₄	—	2	1	no	—
442	C₄	—	13	2	no	—
443	C₄	—	26	1	no	—
444	C₄	—	26	1	no	—
445	C₄	—	26	1	no	—
446	C₄	—	26	1	no	—
447	C₄	—	26	1	no	—
448	C₄	#11719450	1	2	yes	—
449	C₄	#11719478	1	1	yes	characteristic
450	C₄	#11719482	1	1	yes	characteristic
451	C₂	—	4	1	no	—
452	C₂	—	52	1	no	—
453	C₂	—	52	1	no	—
454	C₂	#13123398	1	1	yes	characteristic
455	C₂	#13123423	1	1	yes	characteristic
456	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×#1569	C₂
socle	C₂²×C₁₃	C₂²×C₄⋊C₄
prime radical	C₂³×D₁₃	C₄⋊C₄
cosocle	C₄²×C₁₃	C₂⁴
hypercenter	#1569	D₁₃
hypocenter	C₁₃	#17823
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1569

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. #13113615	C₂	semidirect
7. #13113613	C₂	semidirect
8. #13113604	C₂	semidirect
9. #13113603	C₂	semidirect
10. #13113601	C₂	semidirect
11. C₁₃×#1569	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
162. #1569	D₁₃	semidirect
240. #335	C₂×D₁₃	semidirect
244. #334	C₂×D₁₃	semidirect
379. C₁₃	#17823	semidirect

Maximal subgroups

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

subgroup	index
#13123468	2
#13123467	2
#13123466	2
#13113626	2
#13113623	2
#13113615	2
#13113613	2
#13113604	2
#13113603	2
#13113601	2
C₁₃×#1569	2
#17823	13