Subgroups — #15880792

Order 3328.

700 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	#13117234	C₂	1	1	yes	maximal, characteristic
2	#13115554	C₂	1	1	yes	maximal, characteristic, complemented
3	#13115554	C₂	1	1	yes	maximal, characteristic, complemented
4	#13115446	C₂	1	2	yes	maximal
5	#13115439	C₂	1	2	yes	maximal
6	#13114954	C₂	1	2	yes	maximal, complemented
7	#13114816	C₂	1	1	yes	maximal, characteristic
8	#13114703	C₂	1	1	yes	maximal, characteristic, complemented
9	C₈×C₄⋊Dic₁₃	C₂	1	1	yes	maximal, characteristic, complemented
10	#13114586	C₂	1	2	yes	maximal, complemented
11	C₄×C₁₃×C₂²⋊C₈	C₂	1	1	yes	maximal, characteristic
12	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
13	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
14	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
15	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
16	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
17	#11718873	C₄	1	1	yes	characteristic
18	#11718873	C₄	1	1	yes	characteristic
19	#11718872	C₄	1	2	yes	—
20	C₄×C₂²⋊Dic₁₃	C₂²	1	2	yes	—
21	C₂×C₂²⋊#1055	C₂²	1	2	yes	—
22	C₂×#88055	C₂²	1	2	yes	—
23	C₂×#88054	C₂²	1	2	yes	—
24	C₂×#88054	C₂²	1	2	yes	—
25	C₂×C₈×Dic₁₃	C₂²	1	2	yes	—
26	#11718598	C₄	1	2	yes	—
27	#11718597	C₄	1	1	yes	characteristic
28	#11718597	C₄	1	1	yes	characteristic
29	C₄×C₄⋊Dic₁₃	C₂²	1	1	yes	characteristic
30	C₄×C₄⋊Dic₁₃	C₂²	1	1	yes	characteristic
31	#11718593	C₂²	1	2	yes	—
32	C₂×C₄⋊#1055	C₂²	1	1	yes	characteristic
33	C₂×C₄⋊#1055	C₂²	1	1	yes	characteristic
34	C₁₃×#336	C₂²	1	1	yes	characteristic
35	C₁₃×#336	C₂²	1	1	yes	characteristic
36	#11718142	C₂²	1	2	yes	—
37	#11718142	C₂²	1	2	yes	—
38	#11718142	C₂²	1	2	yes	—
39	#11718142	C₂²	1	2	yes	—
40	#11718116	C₂²	1	2	yes	—
41	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
42	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
43	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
44	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
45	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
46	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
47	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
48	C₂×C₄²×C₁₃	—	2	2	no	—
49	C₂×C₄²×C₁₃	—	2	2	no	—
50	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
51	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
52	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
53	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
54	C₂×C₂²⋊Dic₁₃	C₂×C₄	1	2	yes	—
55	C₂×C₂²⋊Dic₁₃	C₂×C₄	1	2	yes	—
56	C₂×C₄⋊Dic₁₃	C₂×C₄	1	1	yes	characteristic
57	C₂×C₄⋊Dic₁₃	C₂×C₄	1	1	yes	characteristic
58	C₂×C₄⋊Dic₁₃	C₂×C₄	1	1	yes	characteristic
59	C₂×C₄⋊Dic₁₃	C₂×C₄	1	1	yes	characteristic
60	C₂×C₄×Dic₁₃	C₂³	1	2	yes	—
61	C₂×C₄×Dic₁₃	C₂³	1	2	yes	—
62	C₂²×#1055	C₂³	1	2	yes	—
63	C₂²×#1055	C₂³	1	2	yes	—
64	C₁₃×C₂²⋊C₈	—	2	2	no	—
65	C₁₃×C₂²⋊C₈	—	2	2	no	—
66	C₄×C₈×C₁₃	—	2	2	no	—
67	C₄×C₈×C₁₃	—	2	2	no	—
68	#88071	C₂×C₄	1	2	yes	—
69	#88071	C₂×C₄	1	2	yes	—
70	#88071	C₂×C₄	1	2	yes	—
71	#88071	C₂×C₄	1	2	yes	—
72	#88071	C₂×C₄	1	2	yes	—
73	#88071	C₂×C₄	1	2	yes	—
74	#88071	C₂×C₄	1	2	yes	—
75	#88071	C₂×C₄	1	2	yes	—
76	C₂²⋊#1055	—	4	2	no	—
77	#88055	—	2	4	no	—
78	#88054	—	4	2	no	—
79	#88054	—	4	2	no	—
80	C₈×Dic₁₃	—	2	4	no	—
81	C₄⋊#1055	—	2	2	no	—
82	C₄⋊#1055	—	2	2	no	—
83	#22633	—	13	1	no	maximal, Sylow
84	C₂⁴×C₁₃	C₂²×C₄	1	1	yes	characteristic
85	C₂²×C₄×C₁₃	—	2	2	no	—
86	C₂²×C₄×C₁₃	—	2	2	no	—
87	C₂²×C₄×C₁₃	—	2	2	no	—
88	C₂²×C₄×C₁₃	—	2	2	no	—
89	C₂²×C₄×C₁₃	—	2	2	no	—
90	C₂²×C₄×C₁₃	—	2	1	no	—
91	C₂²×C₄×C₁₃	—	2	1	no	—
92	C₂²×C₄×C₁₃	—	2	1	no	—
93	C₂²×C₄×C₁₃	—	2	1	no	—
94	C₂²×C₄×C₁₃	—	2	1	no	—
95	C₂²×C₄×C₁₃	—	2	1	no	—
96	C₂²×C₄×C₁₃	—	4	1	no	—
97	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
98	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
99	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
100	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
101	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
102	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
103	C₂²×Dic₁₃	C₂²×C₄	1	2	yes	—
104	C₂²×Dic₁₃	C₂²×C₄	1	2	yes	—
105	C₂²×Dic₁₃	C₂²×C₄	1	2	yes	—
106	C₂²×Dic₁₃	C₂²×C₄	1	2	yes	—
107	C₂×C₈×C₁₃	—	2	1	no	—
108	C₂×C₈×C₁₃	—	2	1	no	—
109	C₂×C₈×C₁₃	—	2	1	no	—
110	C₂×C₈×C₁₃	—	2	1	no	—
111	C₂×C₈×C₁₃	—	2	1	no	—
112	C₂×C₈×C₁₃	—	2	1	no	—
113	C₂×C₈×C₁₃	—	2	1	no	—
114	C₂×C₈×C₁₃	—	2	1	no	—
115	C₂×C₈×C₁₃	—	2	1	no	—
116	C₂×C₈×C₁₃	—	2	1	no	—
117	C₂×C₈×C₁₃	#41	1	2	yes	—
118	C₂×C₈×C₁₃	#41	1	2	yes	—
119	C₄²×C₁₃	—	2	2	no	—
120	C₄²×C₁₃	—	2	2	no	—
121	C₄²×C₁₃	—	2	1	no	—
122	C₄²×C₁₃	—	2	1	no	—
123	C₄²×C₁₃	#41	1	2	yes	—
124	C₄²×C₁₃	#41	1	2	yes	—
125	C₂²⋊Dic₁₃	—	2	4	no	—
126	C₂²⋊Dic₁₃	—	4	2	no	—
127	C₄⋊Dic₁₃	—	2	2	no	—
128	C₄⋊Dic₁₃	—	2	2	no	—
129	C₄⋊Dic₁₃	—	2	2	no	—
130	C₄⋊Dic₁₃	—	2	2	no	—
131	C₄×Dic₁₃	—	2	2	no	—
132	C₄×Dic₁₃	—	2	2	no	—
133	C₄×Dic₁₃	—	2	2	no	—
134	C₄×Dic₁₃	—	2	2	no	—
135	C₂×#1055	—	2	2	no	—
136	C₂×#1055	—	2	2	no	—
137	C₂×#1055	—	2	2	no	—
138	C₂×#1055	—	2	2	no	—
139	C₂×#1055	—	2	2	no	—
140	C₂×#1055	—	2	2	no	—
141	#2283	—	13	1	no	—
142	#1939	—	13	1	no	—
143	#1939	—	13	1	no	—
144	#1924	—	13	2	no	—
145	#1923	—	13	2	no	—
146	#1832	—	13	2	no	—
147	#1797	—	13	1	no	—
148	#1770	—	13	1	no	—
149	C₈×C₄⋊C₄	—	13	1	no	—
150	C₄×C₂²⋊C₈	D₁₃	1	1	yes	characteristic
151	#1746	—	13	2	no	—
152	C₂³×C₁₃	—	2	1	no	—
153	C₂³×C₁₃	—	2	1	no	—
154	C₂³×C₁₃	—	2	1	no	—
155	C₂³×C₁₃	—	2	1	no	—
156	C₂³×C₁₃	—	2	1	no	—
157	C₂³×C₁₃	—	2	1	no	—
158	C₂³×C₁₃	#131	1	2	yes	—
159	C₂³×C₁₃	C₂³×C₄	1	1	yes	characteristic
160	C₂×C₄×C₁₃	—	2	1	no	—
161	C₂×C₄×C₁₃	—	2	1	no	—
162	C₂×C₄×C₁₃	—	2	1	no	—
163	C₂×C₄×C₁₃	—	2	1	no	—
164	C₂×C₄×C₁₃	—	2	1	no	—
165	C₂×C₄×C₁₃	—	2	1	no	—
166	C₂×C₄×C₁₃	—	2	1	no	—
167	C₂×C₄×C₁₃	—	2	1	no	—
168	C₂×C₄×C₁₃	—	2	1	no	—
169	C₂×C₄×C₁₃	—	2	1	no	—
170	C₂×C₄×C₁₃	—	2	1	no	—
171	C₂×C₄×C₁₃	—	4	4	no	—
172	C₂×C₄×C₁₃	—	4	1	no	—
173	C₂×C₄×C₁₃	—	4	1	no	—
174	C₂×C₄×C₁₃	—	4	1	no	—
175	C₂×C₄×C₁₃	—	4	1	no	—
176	C₂×C₄×C₁₃	—	4	4	no	—
177	C₂×C₄×C₁₃	#117	1	2	yes	—
178	C₂×C₄×C₁₃	#117	1	2	yes	—
179	C₂×C₄×C₁₃	#131	1	2	yes	—
180	C₂×C₄×C₁₃	#131	1	2	yes	—
181	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
182	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
183	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
184	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
185	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
186	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
187	C₂×Dic₁₃	—	2	2	no	—
188	C₂×Dic₁₃	—	2	2	no	—
189	C₂×Dic₁₃	—	2	2	no	—
190	C₂×Dic₁₃	—	2	2	no	—
191	C₂×Dic₁₃	—	2	2	no	—
192	C₂×Dic₁₃	—	2	2	no	—
193	C₂×Dic₁₃	—	2	2	no	—
194	C₂×Dic₁₃	—	2	2	no	—
195	C₂×Dic₁₃	—	2	2	no	—
196	C₂×Dic₁₃	—	2	2	no	—
197	C₂×Dic₁₃	—	2	2	no	—
198	C₂×Dic₁₃	—	2	2	no	—
199	C₈×C₁₃	—	2	2	no	—
200	C₈×C₁₃	—	2	2	no	—
201	C₈×C₁₃	—	4	1	no	—
202	C₈×C₁₃	—	4	1	no	—
203	#1055	—	4	2	no	—
204	#1055	—	4	2	no	—
205	C₂²×C₄²	C₂×D₁₃	1	1	yes	characteristic
206	C₂×C₄⋊C₈	—	13	1	no	—
207	C₂×C₄⋊C₈	—	13	1	no	—
208	C₂×C₄⋊C₈	—	13	2	no	—
209	C₂×C₄⋊C₈	—	13	2	no	—
210	C₂×C₂²⋊C₈	—	13	2	no	—
211	C₂×C₂²⋊C₈	C₂×D₁₃	1	1	yes	characteristic
212	C₂×C₂²⋊C₈	C₂×D₁₃	1	1	yes	characteristic
213	C₂×#97	—	13	2	no	—
214	C₂×C₄×C₈	—	13	2	no	—
215	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
216	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
217	#383	—	13	2	no	—
218	#382	—	13	1	no	—
219	#382	—	13	1	no	—
220	#381	—	13	2	no	—
221	#380	—	13	1	no	—
222	#380	—	13	1	no	—
223	C₄×C₄⋊C₄	—	13	1	no	—
224	C₄×C₄⋊C₄	—	13	1	no	—
225	C₄×C₂²⋊C₄	—	13	2	no	—
226	#376	—	13	2	no	—
227	#336	—	13	2	no	—
228	#336	—	13	2	no	—
229	#336	—	13	2	no	—
230	#336	—	13	2	no	—
231	#336	—	13	2	no	—
232	#336	C₂×D₁₃	1	1	yes	characteristic
233	#336	C₂×D₁₃	1	1	yes	characteristic
234	C₂²×C₁₃	—	2	2	no	—
235	C₂²×C₁₃	—	2	2	no	—
236	C₂²×C₁₃	—	2	2	no	—
237	C₂²×C₁₃	—	4	1	no	—
238	C₂²×C₁₃	—	4	1	no	—
239	C₂²×C₁₃	—	4	1	no	—
240	C₂²×C₁₃	—	4	1	no	—
241	C₂²×C₁₃	C₂×#117	1	1	yes	characteristic
242	C₂²×C₁₃	C₄×#41	1	1	yes	characteristic
243	C₂²×C₁₃	#520	1	1	yes	characteristic
244	C₂²×C₁₃	C₂×#131	1	1	yes	characteristic
245	C₂²×C₁₃	C₂×#131	1	1	yes	characteristic
246	C₂²×C₁₃	C₂×#131	1	1	yes	characteristic
247	C₂²×C₁₃	#568	1	1	yes	characteristic
248	C₄×C₁₃	—	2	2	no	—
249	C₄×C₁₃	—	4	1	no	—
250	C₄×C₁₃	—	4	1	no	—
251	C₄×C₁₃	—	4	1	no	—
252	C₄×C₁₃	#433	1	4	yes	—
253	C₄×C₁₃	#552	1	1	yes	characteristic
254	C₄×C₁₃	#552	1	1	yes	characteristic
255	C₄×C₁₃	#555	1	1	yes	characteristic
256	C₄×C₁₃	#555	1	1	yes	characteristic
257	Dic₁₃	—	4	2	no	—
258	Dic₁₃	—	4	2	no	—
259	Dic₁₃	—	4	2	no	—
260	Dic₁₃	—	4	2	no	—
261	C₂³×C₄	C₄×D₁₃	1	1	yes	characteristic
262	C₂³×C₄	C₄×D₁₃	1	1	yes	characteristic
263	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
264	C₂²×C₈	—	13	2	no	—
265	C₂²×C₈	—	13	2	no	—
266	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
267	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
268	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
269	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
270	C₂×C₄⋊C₄	—	13	1	no	—
271	C₂×C₄⋊C₄	—	13	1	no	—
272	C₂×C₄⋊C₄	—	13	1	no	—
273	C₂×C₄⋊C₄	—	13	1	no	—
274	C₂×C₂²⋊C₄	—	13	2	no	—
275	C₂×C₂²⋊C₄	—	13	2	no	—
276	C₂×C₄²	—	2	2	no	—
277	C₂×C₄²	—	2	2	no	—
278	C₂×C₄²	—	13	2	no	—
279	C₂×C₄²	—	13	2	no	—
280	C₂×C₄²	C₄×D₁₃	1	1	yes	characteristic
281	C₂×C₄²	C₄×D₁₃	1	1	yes	characteristic
282	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
283	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
284	C₄⋊C₈	—	26	2	no	—
285	C₄⋊C₈	—	26	2	no	—
286	C₄⋊C₈	—	52	2	no	—
287	C₄⋊C₈	—	52	2	no	—
288	C₂²⋊C₈	—	2	2	no	—
289	C₂²⋊C₈	—	2	2	no	—
290	C₂²⋊C₈	—	52	2	no	—
291	#97	—	26	4	no	—
292	C₄×C₈	—	2	2	no	—
293	C₄×C₈	—	2	2	no	—
294	C₄×C₈	—	26	4	no	—
295	#95	—	13	2	no	—
296	#95	—	13	2	no	—
297	#95	—	13	2	no	—
298	#95	—	13	2	no	—
299	#95	—	13	2	no	—
300	#95	—	13	2	no	—
301	#95	—	13	2	no	—
302	#95	—	13	2	no	—
303	C₂×C₁₃	—	4	2	no	—
304	C₂×C₁₃	#2346	1	1	yes	characteristic
305	C₂×C₁₃	C₂×#433	1	1	yes	characteristic
306	C₂×C₁₃	#2924	1	1	yes	characteristic
307	C₂×C₁₃	#2966	1	1	yes	characteristic
308	C₂×C₁₃	#2969	1	1	yes	characteristic
309	C₂×C₁₃	#2993	1	1	yes	characteristic
310	C₂×C₁₃	#2994	1	1	yes	characteristic
311	C₂⁴	C₂×C₄×D₁₃	1	1	yes	characteristic
312	C₂²×C₄	—	2	2	no	—
313	C₂²×C₄	—	2	2	no	—
314	C₂²×C₄	—	2	2	no	—
315	C₂²×C₄	—	2	2	no	—
316	C₂²×C₄	—	2	2	no	—
317	C₂²×C₄	—	2	1	no	—
318	C₂²×C₄	—	2	1	no	—
319	C₂²×C₄	—	2	1	no	—
320	C₂²×C₄	—	2	1	no	—
321	C₂²×C₄	—	2	1	no	—
322	C₂²×C₄	—	2	1	no	—
323	C₂²×C₄	—	4	1	no	—
324	C₂²×C₄	—	13	2	no	—
325	C₂²×C₄	—	13	2	no	—
326	C₂²×C₄	—	13	2	no	—
327	C₂²×C₄	—	13	2	no	—
328	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
329	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
330	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
331	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
332	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
333	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
334	C₂×C₈	—	2	1	no	—
335	C₂×C₈	—	2	1	no	—
336	C₂×C₈	—	2	1	no	—
337	C₂×C₈	—	2	1	no	—
338	C₂×C₈	—	2	1	no	—
339	C₂×C₈	—	2	1	no	—
340	C₂×C₈	—	2	1	no	—
341	C₂×C₈	—	2	1	no	—
342	C₂×C₈	—	2	1	no	—
343	C₂×C₈	—	2	1	no	—
344	C₂×C₈	—	26	2	no	—
345	C₂×C₈	—	26	2	no	—
346	C₂×C₈	—	26	2	no	—
347	C₂×C₈	—	26	2	no	—
348	C₂×C₈	—	26	2	no	—
349	C₂×C₈	—	26	2	no	—
350	C₂×C₈	#6127	1	2	yes	—
351	C₂×C₈	#6127	1	2	yes	—
352	C₄⋊C₄	—	26	2	no	—
353	C₄⋊C₄	—	26	2	no	—
354	C₄⋊C₄	—	26	2	no	—
355	C₄⋊C₄	—	26	2	no	—
356	C₂²⋊C₄	—	26	4	no	—
357	C₂²⋊C₄	—	52	2	no	—
358	C₄²	—	2	2	no	—
359	C₄²	—	2	2	no	—
360	C₄²	—	2	1	no	—
361	C₄²	—	2	1	no	—
362	C₄²	—	26	2	no	—
363	C₄²	—	26	2	no	—
364	C₄²	—	26	2	no	—
365	C₄²	—	26	2	no	—
366	C₄²	#6129	1	2	yes	—
367	C₄²	#6129	1	2	yes	—
368	C₁₃	#22633	1	1	yes	characteristic, complemented, Sylow
369	C₂³	—	2	1	no	—
370	C₂³	—	2	1	no	—
371	C₂³	—	2	1	no	—
372	C₂³	—	2	1	no	—
373	C₂³	—	2	1	no	—
374	C₂³	—	2	1	no	—
375	C₂³	#88155	1	2	yes	—
376	C₂³	C₂²×C₄×D₁₃	1	1	yes	characteristic
377	C₂×C₄	—	2	1	no	—
378	C₂×C₄	—	2	1	no	—
379	C₂×C₄	—	2	1	no	—
380	C₂×C₄	—	2	1	no	—
381	C₂×C₄	—	2	1	no	—
382	C₂×C₄	—	2	1	no	—
383	C₂×C₄	—	2	1	no	—
384	C₂×C₄	—	2	1	no	—
385	C₂×C₄	—	2	1	no	—
386	C₂×C₄	—	2	1	no	—
387	C₂×C₄	—	2	1	no	—
388	C₂×C₄	—	4	4	no	—
389	C₂×C₄	—	4	1	no	—
390	C₂×C₄	—	4	1	no	—
391	C₂×C₄	—	4	1	no	—
392	C₂×C₄	—	4	1	no	—
393	C₂×C₄	—	4	4	no	—
394	C₂×C₄	—	26	2	no	—
395	C₂×C₄	—	26	2	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	2	no	—
402	C₂×C₄	—	26	2	no	—
403	C₂×C₄	—	26	2	no	—
404	C₂×C₄	—	26	2	no	—
405	C₂×C₄	—	26	2	no	—
406	C₂×C₄	#88131	1	2	yes	—
407	C₂×C₄	#88131	1	2	yes	—
408	C₂×C₄	#88155	1	2	yes	—
409	C₂×C₄	#88161	1	2	yes	—
410	C₂×C₄	C₂×#6127	1	1	yes	characteristic
411	C₂×C₄	C₂×#6127	1	1	yes	characteristic
412	C₂×C₄	C₂×#6129	1	1	yes	characteristic
413	C₂×C₄	C₂×#6129	1	1	yes	characteristic
414	C₂×C₄	#88256	1	1	yes	characteristic
415	C₂×C₄	#88257	1	1	yes	characteristic
416	C₈	—	2	2	no	—
417	C₈	—	2	2	no	—
418	C₈	—	4	1	no	—
419	C₈	—	4	1	no	—
420	C₈	—	52	2	no	—
421	C₈	—	52	2	no	—
422	C₂²	—	2	2	no	—
423	C₂²	—	2	2	no	—
424	C₂²	—	2	2	no	—
425	C₂²	—	4	1	no	—
426	C₂²	—	4	1	no	—
427	C₂²	—	4	1	no	—
428	C₂²	—	4	1	no	—
429	C₂²	C₄×#6127	1	1	yes	characteristic
430	C₂²	C₂×#88131	1	1	yes	characteristic
431	C₂²	#11719228	1	1	yes	characteristic
432	C₂²	C₂×#88155	1	1	yes	characteristic
433	C₂²	C₂×#88155	1	1	yes	characteristic
434	C₂²	C₂×#88161	1	1	yes	characteristic
435	C₂²	#11719450	1	1	yes	characteristic
436	C₄	—	2	2	no	—
437	C₄	—	4	1	no	—
438	C₄	—	4	1	no	—
439	C₄	—	4	1	no	—
440	C₄	—	52	2	no	—
441	C₄	—	52	2	no	—
442	C₄	—	52	2	no	—
443	C₄	—	52	2	no	—
444	C₄	#11718381	1	4	yes	—
445	C₄	#11719246	1	1	yes	characteristic
446	C₄	#11719246	1	1	yes	characteristic
447	C₄	#11719268	1	1	yes	characteristic
448	C₄	#11719268	1	1	yes	characteristic
449	C₂	—	4	2	no	—
450	C₂	#13117719	1	1	yes	characteristic
451	C₂	C₂×#11718381	1	1	yes	characteristic
452	C₂	#13123490	1	1	yes	characteristic
453	C₂	#13123811	1	1	yes	characteristic
454	C₂	#13123840	1	1	yes	characteristic
455	C₂	#13123987	1	1	yes	characteristic
456	C₂	#13123998	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₁₃
commutator, socle	C₂³×C₁₃	C₂³×C₄
Fitting	C₄×C₁₃×C₂²⋊C₈	C₂
prime radical	C₂⁴×C₁₃	C₂²×C₄
cosocle	C₂²×C₄×C₁₃	C₂⁴
hypercenter	C₄×C₂²⋊C₈	D₁₃
hypocenter	C₁₃	#22633
LCS	G ▷ C₂³×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₄×C₂²⋊C₈

Complements

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

N	H ≅ G/N	type
2. #13115554	C₂	semidirect
3. #13115554	C₂	semidirect
6. #13114954	C₂	semidirect
8. #13114703	C₂	semidirect
9. C₈×C₄⋊Dic₁₃	C₂	semidirect
10. #13114586	C₂	semidirect
368. C₁₃	#22633	semidirect

Maximal subgroups

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

subgroup	index
#13117234	2
#13115554	2
#13115446	2
#13115439	2
#13114954	2
#13114816	2
#13114703	2
C₈×C₄⋊Dic₁₃	2
#13114586	2
C₄×C₁₃×C₂²⋊C₈	2
#22633	13