Subgroups — #16797260

Order 3328.

1002 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₁₃⋊#431	C₂	1	1	yes	maximal, characteristic
2	C₂×#11719057	C₂	1	1	yes	maximal, characteristic
3	#13130625	C₂	1	4	yes	maximal, complemented
4	#13130564	C₂	1	2	yes	maximal
5	C₂²⋊C₈×#261	C₂	1	2	yes	maximal
6	#13130556	C₂	1	2	yes	maximal, complemented
7	#13130494	C₂	1	2	yes	maximal, complemented
8	D₁₃×#432	C₂	1	1	yes	maximal, characteristic
9	C₂²×C₄×#261	C₂²	1	2	yes	—
10	C₂×C₄²×D₁₃	C₂²	1	1	yes	characteristic
11	C₂×(C₂×#261)⋊C₄	C₄	1	2	yes	—
12	C₂×(C₂×#261)⋊C₄	C₄	1	2	yes	—
13	#11719125	C₄	1	2	yes	complemented
14	D₁₃⋊(C₂²⋊C₈)	C₂²	1	1	yes	characteristic
15	D₁₃⋊(C₂²⋊C₈)	C₂²	1	1	yes	characteristic
16	#11719119	C₄	1	2	yes	complemented
17	C₂×#88100	C₂²	1	4	yes	—
18	C₂×C₈×#261	C₂²	1	4	yes	—
19	#11719057	C₄	1	2	yes	—
20	#11719057	C₄	1	2	yes	—
21	#11719057	C₂²	1	1	yes	characteristic
22	#11719057	C₂²	1	2	yes	—
23	#11719057	C₂²	1	1	yes	characteristic
24	#11719051	C₄	1	2	yes	complemented
25	D₁₃⋊(C₄⋊C₈)	C₂²	1	2	yes	—
26	#11719049	C₄	1	2	yes	complemented
27	C₄×D₁₃⋊C₈	C₂²	1	2	yes	—
28	C₁₃×#432	C₄	1	1	yes	characteristic, complemented
29	#11718587	C₄	1	1	yes	characteristic, complemented
30	#11718496	C₄	1	2	yes	complemented
31	D₁₃×C₄⋊C₈	C₂²	1	2	yes	—
32	D₁₃×C₂²⋊C₈	C₂²	1	2	yes	—
33	#11718380	C₄	1	2	yes	complemented
34	#11718366	C₄	1	2	yes	complemented
35	D₁₃×#97	C₂²	1	2	yes	—
36	(C₂×#261)⋊C₈	C₂²	1	4	yes	—
37	(C₂×#261)⋊C₈	C₂²	1	4	yes	—
38	C₂³×#261	C₂×C₄	1	4	yes	—
39	C₂²×C₄×D₁₃	C₂×C₄	1	1	yes	characteristic
40	C₂²×C₄×D₁₃	C₂×C₄	1	1	yes	characteristic
41	C₂²×C₄×D₁₃	C₂³	1	1	yes	characteristic
42	C₂×C₄×#261	—	2	8	no	—
43	C₂×C₄×#261	C₂×C₄	1	4	yes	—
44	C₂×C₄×#261	C₂³	1	2	yes	—
45	C₂×C₄×#261	C₂³	1	2	yes	—
46	C₂×D₁₃⋊C₈	C₂³	1	2	yes	—
47	C₂×D₁₃⋊C₈	C₂³	1	2	yes	—
48	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
49	C₂×C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
50	C₂×C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
51	C₂×C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
52	C₂×C₈×D₁₃	C₂³	1	4	yes	—
53	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
54	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
55	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
56	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
57	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
58	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
59	C₄²×D₁₃	C₂³	1	1	yes	characteristic
60	C₄²×D₁₃	C₂³	1	1	yes	characteristic
61	C₂²⋊#1057	C₂×C₄	1	2	yes	—
62	C₂²⋊#1057	C₂×C₄	1	2	yes	—
63	(C₂×#261)⋊C₄	C₂×C₄	1	2	yes	—
64	(C₂×#261)⋊C₄	C₂×C₄	1	2	yes	—
65	(C₂×#261)⋊C₄	C₂×C₄	1	4	yes	—
66	(C₂×#261)⋊C₄	C₂×C₄	1	4	yes	—
67	(C₂×#261)⋊C₄	C₂×C₄	1	2	yes	—
68	(C₂×#261)⋊C₄	C₂×C₄	1	2	yes	—
69	#88112	C₂×C₄	1	4	yes	complemented
70	#88111	C₂×C₄	1	2	yes	—
71	#88111	C₂×C₄	1	2	yes	—
72	C₄⋊#1057	C₂×C₄	1	4	yes	complemented
73	C₄×#1057	C₂×C₄	1	4	yes	complemented
74	C₄×#1057	C₂×C₄	1	4	yes	complemented
75	#88100	—	2	8	no	—
76	C₈×#261	—	2	8	no	—
77	C₁₃×C₄⋊C₈	C₂×C₄	1	2	yes	complemented
78	C₁₃×C₂²⋊C₈	C₂×C₄	1	2	yes	—
79	C₁₃×#97	C₂×C₄	1	2	yes	complemented
80	C₂²⋊#1055	C₂×C₄	1	2	yes	—
81	#88060	C₂×C₄	1	4	yes	—
82	#88055	C₂×C₄	1	4	yes	complemented
83	#88054	C₂×C₄	1	4	yes	complemented
84	C₄⋊#1055	C₂×C₄	1	2	yes	complemented
85	#88043	C₂×C₄	1	2	yes	complemented
86	#20469	—	13	1	no	maximal, Sylow
87	C₂³×D₁₃	C₂²×C₄	1	1	yes	characteristic
88	C₂²×#261	—	2	8	no	—
89	C₂²×#261	—	2	8	no	—
90	C₂²×#261	—	4	4	no	—
91	C₂²×#261	C₂²×C₄	1	4	yes	—
92	C₂²×#261	C₂²×C₄	1	4	yes	—
93	C₂²×C₄×C₁₃	C₄²	1	1	yes	characteristic
94	C₂²×C₄×C₁₃	C₄²	1	1	yes	characteristic
95	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
96	C₂²×Dic₁₃	C₄²	1	1	yes	characteristic
97	C₂²×Dic₁₃	C₄²	1	1	yes	characteristic
98	C₂²×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
99	C₂×C₄×D₁₃	—	2	4	no	—
100	C₂×C₄×D₁₃	—	2	4	no	—
101	C₂×C₄×D₁₃	—	4	2	no	—
102	C₂×C₄×D₁₃	C₄²	1	1	yes	characteristic
103	C₂×C₄×D₁₃	C₄²	1	1	yes	characteristic
104	C₂×C₄×D₁₃	C₄²	1	1	yes	characteristic
105	C₂×C₄×D₁₃	C₄²	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	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
109	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
110	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
111	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
112	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
113	C₂×C₄×D₁₃	C₂⁴	1	1	yes	characteristic
114	C₂×#1057	C₂²×C₄	1	4	yes	—
115	C₂×#1057	C₂²×C₄	1	4	yes	—
116	C₄×#261	—	2	8	no	—
117	C₄×#261	—	2	4	no	—
118	C₄×#261	#41	1	8	yes	—
119	D₁₃⋊C₈	—	2	4	no	—
120	D₁₃⋊C₈	—	2	4	no	—
121	C₂×C₈×C₁₃	C₂²×C₄	1	4	yes	—
122	C₄²×C₁₃	C₄²	1	1	yes	characteristic
123	C₄²×C₁₃	C₄²	1	1	yes	characteristic
124	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
125	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
126	C₄×Dic₁₃	C₄²	1	1	yes	characteristic
127	C₄×Dic₁₃	C₄²	1	1	yes	characteristic
128	C₄×Dic₁₃	C₄²	1	1	yes	characteristic
129	C₄×Dic₁₃	C₄²	1	1	yes	characteristic
130	C₄×Dic₁₃	C₄²	1	1	yes	characteristic
131	C₄×Dic₁₃	C₄²	1	1	yes	characteristic
132	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
133	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
134	C₄×Dic₁₃	C₂²×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	C₂²×C₄	1	1	yes	characteristic
138	C₂×#1055	C₂²×C₄	1	4	yes	—
139	C₈×D₁₃	—	2	4	no	—
140	C₈×D₁₃	—	2	4	no	—
141	C₂×#432	—	13	1	no	—
142	C₂×#431	—	13	1	no	—
143	C₂×#376	—	13	1	no	—
144	#1768	—	13	4	no	—
145	#1749	—	13	2	no	—
146	C₄×C₂²⋊C₈	—	13	2	no	—
147	#1746	—	13	2	no	—
148	#1726	—	13	2	no	—
149	C₂³×C₁₃	C₂×C₄²	1	1	yes	characteristic
150	C₂²×D₁₃	—	2	2	no	—
151	C₂²×D₁₃	—	2	2	no	—
152	C₂²×D₁₃	C₂×C₄²	1	1	yes	characteristic
153	C₂²×D₁₃	#131	1	4	yes	—
154	C₂²×D₁₃	C₂³×C₄	1	1	yes	characteristic
155	C₂×#261	—	2	4	no	—
156	C₂×#261	—	2	4	no	—
157	C₂×#261	—	2	4	no	—
158	C₂×#261	—	2	4	no	—
159	C₂×#261	—	2	4	no	—
160	C₂×#261	—	4	16	no	—
161	C₂×#261	#117	1	8	yes	—
162	C₂×C₄×C₁₃	—	2	2	no	—
163	C₂×C₄×C₁₃	—	2	2	no	—
164	C₂×C₄×C₁₃	—	4	1	no	—
165	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
166	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
167	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
168	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
169	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
170	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
171	C₂×Dic₁₃	—	2	2	no	—
172	C₂×Dic₁₃	—	2	2	no	—
173	C₂×Dic₁₃	—	4	1	no	—
174	C₂×Dic₁₃	C₂×C₄²	1	1	yes	characteristic
175	C₂×Dic₁₃	C₂×C₄²	1	1	yes	characteristic
176	C₂×Dic₁₃	C₂×C₄²	1	1	yes	characteristic
177	C₂×Dic₁₃	C₂×C₄²	1	1	yes	characteristic
178	C₂×Dic₁₃	C₂×C₄²	1	1	yes	characteristic
179	C₂×Dic₁₃	C₂³×C₄	1	1	yes	characteristic
180	C₄×D₁₃	—	2	2	no	—
181	C₄×D₁₃	—	2	2	no	—
182	C₄×D₁₃	—	2	2	no	—
183	C₄×D₁₃	—	2	2	no	—
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	—	4	1	no	—
190	C₄×D₁₃	—	4	1	no	—
191	C₄×D₁₃	C₂×#41	1	4	yes	—
192	#1057	—	2	4	no	—
193	#1057	—	2	4	no	—
194	C₈×C₁₃	—	2	4	no	—
195	#1055	—	2	4	no	—
196	C₂²×C₄²	—	13	1	no	—
197	C₂²×C₄²	—	13	2	no	—
198	#432	—	13	1	no	—
199	#432	—	13	2	no	—
200	#432	—	13	2	no	—
201	#432	—	13	2	no	—
202	#432	#261	1	1	yes	characteristic, complemented
203	#431	—	13	2	no	—
204	#431	—	13	2	no	—
205	#431	—	13	2	no	—
206	#431	—	13	2	no	—
207	C₂×C₄⋊C₈	—	13	2	no	—
208	C₂×C₄⋊C₈	—	13	2	no	—
209	C₂×C₂²⋊C₈	—	13	1	no	—
210	C₂×C₂²⋊C₈	—	13	1	no	—
211	C₂×C₂²⋊C₈	—	13	2	no	—
212	C₂×#97	—	13	2	no	—
213	C₂×#97	—	13	4	no	—
214	C₂×C₄×C₈	—	13	2	no	—
215	C₂×C₄×C₈	—	13	4	no	—
216	#376	—	13	2	no	—
217	#376	—	13	2	no	—
218	#376	—	13	1	no	—
219	#376	—	13	1	no	—
220	#376	—	13	2	no	—
221	C₂×#95	—	13	2	no	—
222	C₂×#95	—	13	2	no	—
223	#336	—	13	4	no	—
224	#336	—	13	4	no	—
225	C₂²×C₁₃	—	2	1	no	—
226	C₂²×C₁₃	—	2	1	no	—
227	C₂²×C₁₃	#405	1	2	yes	—
228	C₂²×C₁₃	C₂²×C₄²	1	1	yes	characteristic
229	C₂×D₁₃	—	2	1	no	—
230	C₂×D₁₃	—	2	1	no	—
231	C₂×D₁₃	—	2	8	no	—
232	C₂×D₁₃	#405	1	2	yes	—
233	C₂×D₁₃	C₂×#117	1	2	yes	—
234	C₂×D₁₃	C₂×#131	1	2	yes	—
235	C₂×D₁₃	#568	1	2	yes	—
236	#261	—	2	8	no	—
237	#261	—	4	4	no	—
238	C₄×C₁₃	—	2	1	no	—
239	C₄×C₁₃	—	2	1	no	—
240	C₄×C₁₃	—	2	1	no	—
241	C₄×C₁₃	—	2	1	no	—
242	C₄×C₁₃	—	2	1	no	—
243	C₄×C₁₃	C₄×#41	1	2	yes	—
244	Dic₁₃	—	2	1	no	—
245	Dic₁₃	—	2	1	no	—
246	Dic₁₃	—	2	1	no	—
247	Dic₁₃	—	2	1	no	—
248	Dic₁₃	—	2	1	no	—
249	Dic₁₃	C₄×#41	1	2	yes	—
250	C₂³×C₄	—	13	1	no	—
251	C₂³×C₄	—	13	1	no	—
252	C₂³×C₄	—	13	1	no	—
253	C₂³×C₄	—	13	4	no	—
254	C₂²×C₈	—	13	2	no	—
255	C₂²×C₈	—	13	2	no	—
256	C₂²×C₈	—	13	4	no	—
257	C₂×C₄²	—	13	2	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	—	13	1	no	—
268	C₂×C₄²	—	13	1	no	—
269	C₂×C₄²	—	13	2	no	—
270	C₂×C₄²	—	13	4	no	—
271	C₂×C₄²	—	26	8	no	—
272	C₂×C₄²	C₂×#261	1	1	yes	characteristic
273	C₄⋊C₈	—	13	4	no	—
274	C₄⋊C₈	—	13	4	no	—
275	C₄⋊C₈	—	13	4	no	—
276	C₄⋊C₈	—	13	2	no	—
277	C₄⋊C₈	C₂×#261	1	2	yes	complemented
278	C₂²⋊C₈	—	13	2	no	—
279	C₂²⋊C₈	—	13	2	no	—
280	C₂²⋊C₈	—	13	2	no	—
281	C₂²⋊C₈	—	13	2	no	—
282	C₂²⋊C₈	—	13	2	no	—
283	C₂²⋊C₈	—	13	4	no	—
284	C₂²⋊C₈	C₂×#261	1	2	yes	—
285	#97	—	13	4	no	—
286	#97	—	13	2	no	—
287	#97	—	26	8	no	—
288	#97	C₂×#261	1	2	yes	complemented
289	C₄×C₈	—	13	4	no	—
290	C₄×C₈	—	13	4	no	—
291	C₄×C₈	—	26	8	no	—
292	#95	—	13	2	no	—
293	#95	—	13	2	no	—
294	#95	—	13	4	no	—
295	#95	—	13	4	no	—
296	#95	—	13	2	no	—
297	#95	—	13	2	no	—
298	C₂×C₁₃	—	2	2	no	—
299	C₂×C₁₃	C₄×#117	1	1	yes	characteristic
300	C₂×C₁₃	C₂×#405	1	1	yes	characteristic
301	C₂×C₁₃	#2873	1	1	yes	characteristic
302	D₁₃	—	2	2	no	—
303	D₁₃	#2924	1	4	yes	—
304	C₂⁴	—	13	1	no	—
305	C₂²×C₄	—	13	1	no	—
306	C₂²×C₄	—	13	4	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	—	13	1	no	—
314	C₂²×C₄	—	13	1	no	—
315	C₂²×C₄	—	13	1	no	—
316	C₂²×C₄	—	13	1	no	—
317	C₂²×C₄	—	13	1	no	—
318	C₂²×C₄	—	13	1	no	—
319	C₂²×C₄	—	13	1	no	—
320	C₂²×C₄	—	13	1	no	—
321	C₂²×C₄	—	13	4	no	—
322	C₂²×C₄	—	26	4	no	—
323	C₂²×C₄	—	26	4	no	—
324	C₂²×C₄	—	26	8	no	—
325	C₂²×C₄	—	26	8	no	—
326	C₂²×C₄	—	52	2	no	—
327	C₂²×C₄	—	52	4	no	—
328	C₂²×C₄	C₄×#261	1	1	yes	characteristic
329	C₂²×C₄	C₄×#261	1	1	yes	characteristic
330	C₂²×C₄	C₂²×#261	1	1	yes	characteristic
331	C₂×C₈	—	13	4	no	—
332	C₂×C₈	—	13	4	no	—
333	C₂×C₈	—	13	4	no	—
334	C₂×C₈	—	26	4	no	—
335	C₂×C₈	—	26	4	no	—
336	C₂×C₈	—	26	4	no	—
337	C₂×C₈	—	26	4	no	—
338	C₂×C₈	C₂²×#261	1	4	yes	—
339	C₄²	—	13	8	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	—	13	1	no	—
346	C₄²	—	13	1	no	—
347	C₄²	—	13	1	no	—
348	C₄²	—	13	1	no	—
349	C₄²	—	13	1	no	—
350	C₄²	—	13	1	no	—
351	C₄²	—	13	1	no	—
352	C₄²	—	26	4	no	—
353	C₄²	—	26	8	no	—
354	C₄²	C₄×#261	1	1	yes	characteristic
355	C₄²	C₄×#261	1	1	yes	characteristic
356	C₄²	C₂²×#261	1	1	yes	characteristic
357	C₄²	C₂²×#261	1	1	yes	characteristic
358	C₁₃	#20469	1	1	yes	characteristic, complemented, Sylow
359	C₂³	—	13	1	no	—
360	C₂³	—	13	4	no	—
361	C₂³	—	13	1	no	—
362	C₂³	—	26	2	no	—
363	C₂³	—	26	2	no	—
364	C₂³	C₂×C₄×#261	1	1	yes	characteristic
365	C₂×C₄	—	2	2	no	—
366	C₂×C₄	—	2	2	no	—
367	C₂×C₄	—	4	1	no	—
368	C₂×C₄	—	13	1	no	—
369	C₂×C₄	—	13	4	no	—
370	C₂×C₄	—	13	8	no	—
371	C₂×C₄	—	13	1	no	—
372	C₂×C₄	—	13	1	no	—
373	C₂×C₄	—	13	1	no	—
374	C₂×C₄	—	13	1	no	—
375	C₂×C₄	—	13	1	no	—
376	C₂×C₄	—	26	2	no	—
377	C₂×C₄	—	26	2	no	—
378	C₂×C₄	—	26	2	no	—
379	C₂×C₄	—	26	2	no	—
380	C₂×C₄	—	26	2	no	—
381	C₂×C₄	—	26	2	no	—
382	C₂×C₄	—	26	2	no	—
383	C₂×C₄	—	26	2	no	—
384	C₂×C₄	—	26	2	no	—
385	C₂×C₄	—	26	4	no	—
386	C₂×C₄	—	26	4	no	—
387	C₂×C₄	—	26	2	no	—
388	C₂×C₄	—	26	2	no	—
389	C₂×C₄	—	26	4	no	—
390	C₂×C₄	—	26	4	no	—
391	C₂×C₄	—	26	4	no	—
392	C₂×C₄	—	52	1	no	—
393	C₂×C₄	—	52	1	no	—
394	C₂×C₄	—	52	1	no	—
395	C₂×C₄	—	52	16	no	—
396	C₂×C₄	C₂×C₄×#261	1	1	yes	characteristic
397	C₂×C₄	C₂×C₄×#261	1	1	yes	characteristic
398	C₂×C₄	C₂×C₄×#261	1	1	yes	characteristic
399	C₂×C₄	C₂×C₄×#261	1	1	yes	characteristic
400	C₂×C₄	C₂×C₄×#261	1	1	yes	characteristic
401	C₂×C₄	C₂³×#261	1	1	yes	characteristic
402	C₈	—	2	4	no	—
403	C₈	—	26	4	no	—
404	C₈	—	26	4	no	—
405	C₈	—	26	4	no	—
406	C₂²	—	2	1	no	—
407	C₂²	—	2	1	no	—
408	C₂²	—	13	2	no	—
409	C₂²	—	13	2	no	—
410	C₂²	—	13	2	no	—
411	C₂²	—	13	2	no	—
412	C₂²	—	26	8	no	—
413	C₂²	—	26	1	no	—
414	C₂²	—	26	1	no	—
415	C₂²	#11719099	1	2	yes	—
416	C₂²	C₂²×C₄×#261	1	1	yes	characteristic
417	C₄	—	2	1	no	—
418	C₄	—	2	1	no	—
419	C₄	—	2	1	no	—
420	C₄	—	2	1	no	—
421	C₄	—	2	1	no	—
422	C₄	—	13	2	no	—
423	C₄	—	26	8	no	—
424	C₄	—	26	1	no	—
425	C₄	—	26	1	no	—
426	C₄	—	26	1	no	—
427	C₄	—	26	1	no	—
428	C₄	—	26	1	no	—
429	C₄	—	52	4	no	—
430	C₄	#41×#261	1	2	yes	—
431	C₂	—	2	2	no	—
432	C₂	—	13	4	no	—
433	C₂	—	26	2	no	—
434	C₂	#117×#261	1	1	yes	characteristic
435	C₂	C₂×#11719099	1	1	yes	characteristic
436	C₂	#13131399	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂³×#261
commutator, socle	C₂²×C₁₃	C₂²×C₄²
Fitting	C₁₃×#432	C₄
prime radical	C₂³×D₁₃	C₂²×C₄
cosocle	C₂×C₄×D₁₃	C₂⁴
hypercenter	#432	#261
hypocenter	C₁₃	#20469
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ #432

Complements

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

N	H ≅ G/N	type
3. #13130625	C₂	semidirect
6. #13130556	C₂	semidirect
7. #13130494	C₂	semidirect
13. #11719125	C₄	semidirect
16. #11719119	C₄	semidirect
24. #11719051	C₄	semidirect
26. #11719049	C₄	semidirect
28. C₁₃×#432	C₄	semidirect
29. #11718587	C₄	semidirect
30. #11718496	C₄	semidirect
33. #11718380	C₄	semidirect
34. #11718366	C₄	semidirect
69. #88112	C₂×C₄	semidirect
72. C₄⋊#1057	C₂×C₄	semidirect
73. C₄×#1057	C₂×C₄	semidirect
74. C₄×#1057	C₂×C₄	semidirect
77. C₁₃×C₄⋊C₈	C₂×C₄	semidirect
79. C₁₃×#97	C₂×C₄	semidirect
82. #88055	C₂×C₄	semidirect
83. #88054	C₂×C₄	semidirect
84. C₄⋊#1055	C₂×C₄	semidirect
85. #88043	C₂×C₄	semidirect
202. #432	#261	semidirect
277. C₄⋊C₈	C₂×#261	semidirect
288. #97	C₂×#261	semidirect
358. C₁₃	#20469	semidirect

Maximal subgroups

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

subgroup	index
D₁₃⋊#431	2
C₂×#11719057	2
#13130625	2
#13130564	2
C₂²⋊C₈×#261	2
#13130556	2
#13130494	2
D₁₃×#432	2
#20469	13