Subgroups — C₄×#11719226 #16021156

Order 3328.

4186 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11719226	C₂	1	2	yes	maximal
2	C₂²×C₄×D₅₂	C₂	1	1	yes	maximal, characteristic
3	#13117198	C₂	1	4	yes	maximal, complemented
4	#13117196	C₂	1	4	yes	maximal, complemented
5	#13117192	C₂	1	2	yes	maximal, complemented
6	#13117188	C₂	1	4	yes	maximal, complemented
7	C₄²×D₅₂	C₂	1	4	yes	maximal, complemented
8	C₄×#88147	C₂	1	4	yes	maximal, complemented
9	C₄×#88180	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄×C₂²⋊C₄×D₁₃	C₂	1	4	yes	maximal, complemented
11	C₄×C₁₃×#117	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂³×D₅₂	C₂²	1	1	yes	characteristic
13	C₂³×C₄×D₁₃	C₂²	1	2	yes	—
14	C₂×C₁₃×#117	C₂²	1	2	yes	—
15	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
16	C₂²×#6103	C₂²	1	2	yes	—
17	C₂×#88180	C₂²	1	2	yes	—
18	C₂²×C₄⋊Dic₁₃	C₂²	1	1	yes	characteristic
19	#11719226	C₄	1	32	yes	direct product factor
20	C₂×#88147	C₂²	1	8	yes	—
21	C₂×C₂²⋊C₄×D₁₃	C₂²	1	8	yes	—
22	C₂×C₄×D₅₂	C₄	1	16	yes	complemented
23	C₂×C₄×D₅₂	C₂²	1	2	yes	—
24	C₂×C₄×D₅₂	C₂²	1	8	yes	—
25	C₂×C₄×D₅₂	C₂²	1	2	yes	—
26	C₂×C₄×D₅₂	C₂²	1	2	yes	—
27	C₂×C₄×D₅₂	C₂²	1	2	yes	—
28	C₂×C₄²×D₁₃	C₂²	1	8	yes	complemented
29	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	complemented
30	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	complemented
31	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
32	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
33	C₁₃×#376	C₂²	1	2	yes	complemented
34	C₄³×C₁₃	C₂²	1	2	yes	complemented
35	C₄×C₂²⋊Dic₁₃	C₂²	1	2	yes	—
36	C₄×C₂²⋊Dic₁₃	C₂²	1	2	yes	—
37	C₄⋊C₄×Dic₁₃	C₂²	1	8	yes	complemented
38	C₂²⋊C₄×Dic₁₃	C₂²	1	8	yes	—
39	C₄×#6103	C₂²	1	16	yes	complemented
40	C₄×#6103	C₂²	1	8	yes	complemented
41	C₄×C₄⋊Dic₁₃	C₂²	1	2	yes	complemented
42	C₄×C₄⋊Dic₁₃	C₂²	1	8	yes	complemented
43	C₄×C₄⋊Dic₁₃	C₂²	1	2	yes	complemented
44	#11718593	C₂²	1	2	yes	complemented
45	C₄²×Dic₁₃	C₂²	1	2	yes	complemented
46	#11718327	C₂²	1	16	yes	complemented
47	#11718327	C₂²	1	8	yes	complemented
48	D₁₃×#95	C₂²	1	8	yes	complemented
49	C₂⁴×D₁₃	C₂³	1	2	yes	—
50	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
51	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
52	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
53	C₂³×Dic₁₃	C₂³	1	2	yes	—
54	C₂²×D₅₂	C₂×C₄	1	8	yes	—
55	C₂²×D₅₂	C₂×C₄	1	16	yes	—
56	C₂²×D₅₂	C₂³	1	2	yes	—
57	C₂²×D₅₂	C₂³	1	2	yes	—
58	C₂²×C₄×D₁₃	—	4	8	no	—
59	C₂²×C₄×D₁₃	C₂×C₄	1	16	yes	complemented
60	C₂²×C₄×D₁₃	C₂³	1	4	yes	—
61	C₂²×C₄×D₁₃	C₂³	1	4	yes	—
62	C₂²×C₄×D₁₃	C₂³	1	16	yes	—
63	C₁₃×#117	C₂×C₄	1	16	yes	complemented
64	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
65	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
66	C₂×C₄²×C₁₃	C₂×C₄	1	8	yes	complemented
67	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
68	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
69	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
70	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
71	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
72	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
73	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
74	C₂×C₂²⋊Dic₁₃	C₂³	1	4	yes	—
75	C₂×#6103	C₂×C₄	1	16	yes	complemented
76	C₂×#6103	C₂³	1	4	yes	—
77	C₂×#6103	C₂³	1	4	yes	—
78	C₂×#6103	C₂³	1	16	yes	—
79	#88180	C₂×C₄	1	16	yes	complemented
80	C₂×C₄⋊Dic₁₃	C₂×C₄	1	8	yes	complemented
81	C₂×C₄⋊Dic₁₃	C₂³	1	2	yes	—
82	C₂×C₄⋊Dic₁₃	C₂³	1	2	yes	—
83	C₂×C₄⋊Dic₁₃	C₂³	1	4	yes	—
84	C₂×C₄×Dic₁₃	C₂³	1	4	yes	—
85	C₂×C₄×Dic₁₃	C₂³	1	16	yes	—
86	C₂×C₄×Dic₁₃	C₂³	1	4	yes	—
87	C₂×C₄×Dic₁₃	C₂³	1	4	yes	—
88	#88147	C₂×C₄	1	64	yes	complemented
89	C₂²⋊C₄×D₁₃	C₂×C₄	1	64	yes	complemented
90	C₄×D₅₂	C₂×C₄	1	16	yes	complemented
91	C₄×D₅₂	C₂×C₄	1	16	yes	complemented
92	C₄×D₅₂	C₂×C₄	1	16	yes	complemented
93	C₄×D₅₂	C₂×C₄	1	16	yes	complemented
94	C₄×D₅₂	C₂×C₄	1	64	yes	complemented
95	C₄²×D₁₃	—	4	16	no	—
96	C₁₃×#95	C₂³	1	4	yes	—
97	C₁₃×#95	C₂³	1	4	yes	—
98	#88071	C₂³	1	4	yes	—
99	#88071	C₂³	1	16	yes	—
100	#88071	C₂³	1	4	yes	—
101	C₄×#518	—	13	1	no	maximal, Sylow
102	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
103	C₂³×D₁₃	—	4	4	no	—
104	C₂³×D₁₃	—	4	4	no	—
105	C₂³×D₁₃	C₂²×C₄	1	16	yes	—
106	C₂³×D₁₃	C₂²×C₄	1	8	yes	—
107	C₂³×D₁₃	C₂⁴	1	4	yes	—
108	C₂²×C₄×C₁₃	—	2	4	no	—
109	C₂²×C₄×C₁₃	—	4	2	no	—
110	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
111	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
112	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
113	C₂²×C₄×C₁₃	C₂²×C₄	1	8	yes	—
114	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
115	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
116	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
117	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
118	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
119	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
120	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
121	C₂²×Dic₁₃	—	4	4	no	—
122	C₂²×Dic₁₃	C₂²×C₄	1	8	yes	—
123	C₂²×Dic₁₃	C₂⁴	1	8	yes	—
124	C₂²×Dic₁₃	C₂⁴	1	4	yes	—
125	C₂×D₅₂	C₄²	1	64	yes	complemented
126	C₂×D₅₂	C₂²×C₄	1	8	yes	—
127	C₂×D₅₂	C₂²×C₄	1	8	yes	—
128	C₂×D₅₂	C₂²×C₄	1	16	yes	—
129	C₂×D₅₂	C₂²×C₄	1	16	yes	—
130	C₂×C₄×D₁₃	—	2	16	no	—
131	C₂×C₄×D₁₃	—	4	32	no	—
132	C₂×C₄×D₁₃	—	4	16	no	—
133	C₂×C₄×D₁₃	—	4	8	no	—
134	C₂×C₄×D₁₃	—	4	16	no	—
135	C₂×C₄×D₁₃	C₂²×C₄	1	16	yes	—
136	C₂×C₄×D₁₃	C₂²×C₄	1	16	yes	—
137	C₂×C₄×D₁₃	C₂²×C₄	1	64	yes	complemented
138	C₁₃×C₄⋊C₄	C₂²×C₄	1	16	yes	complemented
139	C₁₃×C₂²⋊C₄	C₂²×C₄	1	16	yes	—
140	C₄²×C₁₃	—	2	8	no	—
141	C₄²×C₁₃	—	4	4	no	—
142	C₄²×C₁₃	C₂²×C₄	1	4	yes	—
143	C₄²×C₁₃	C₂²×C₄	1	4	yes	—
144	C₄²×C₁₃	C₂²×C₄	1	4	yes	—
145	C₄²×C₁₃	C₂²×C₄	1	4	yes	—
146	C₄²×C₁₃	C₂²×C₄	1	16	yes	complemented
147	C₂²⋊Dic₁₃	C₂²×C₄	1	16	yes	—
148	#6103	C₂²×C₄	1	16	yes	—
149	#6103	C₂²×C₄	1	16	yes	—
150	#6103	C₂²×C₄	1	64	yes	complemented
151	C₄⋊Dic₁₃	C₂²×C₄	1	8	yes	—
152	C₄⋊Dic₁₃	C₂²×C₄	1	8	yes	—
153	C₄⋊Dic₁₃	C₂²×C₄	1	16	yes	complemented
154	C₄×Dic₁₃	—	2	8	no	—
155	C₄×Dic₁₃	—	4	16	no	—
156	C₄×Dic₁₃	—	4	4	no	—
157	C₄×Dic₁₃	C₂²×C₄	1	16	yes	complemented
158	C₂×#518	—	13	2	no	—
159	C₂²×C₄×D₄	—	13	1	no	—
160	#2275	—	13	4	no	—
161	#2275	—	13	4	no	—
162	#2274	—	13	2	no	—
163	#2273	—	13	4	no	—
164	C₄²×D₄	—	13	4	no	—
165	C₄²×D₄	—	13	4	no	—
166	C₄×#117	—	13	1	no	—
167	C₄×#117	D₁₃	1	1	yes	characteristic, complemented
168	C₂×C₄×C₂²⋊C₄	—	13	4	no	—
169	C₂³×C₁₃	—	2	2	no	—
170	C₂³×C₁₃	—	2	2	no	—
171	C₂³×C₁₃	C₂³×C₄	1	4	yes	—
172	C₂³×C₁₃	C₂³×C₄	1	2	yes	—
173	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
174	C₂²×D₁₃	—	2	8	no	—
175	C₂²×D₁₃	—	2	8	no	—
176	C₂²×D₁₃	—	4	8	no	—
177	C₂²×D₁₃	—	4	8	no	—
178	C₂²×D₁₃	—	4	32	no	—
179	C₂²×D₁₃	C₂×C₄²	1	32	yes	complemented
180	C₂²×D₁₃	C₂³×C₄	1	8	yes	—
181	C₂²×D₁₃	C₂³×C₄	1	16	yes	—
182	C₂×C₄×C₁₃	—	2	8	no	—
183	C₂×C₄×C₁₃	—	2	2	no	—
184	C₂×C₄×C₁₃	—	2	2	no	—
185	C₂×C₄×C₁₃	—	2	2	no	—
186	C₂×C₄×C₁₃	—	2	8	no	—
187	C₂×C₄×C₁₃	—	2	8	no	—
188	C₂×C₄×C₁₃	—	4	4	no	—
189	C₂×C₄×C₁₃	C₂×C₄²	1	16	yes	complemented
190	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
191	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
192	C₂×C₄×C₁₃	C₂³×C₄	1	16	yes	—
193	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
194	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
195	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
196	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
197	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
198	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
199	C₂×C₄×C₁₃	H(5,𝔽₂)	1	4	yes	—
200	C₂×Dic₁₃	—	2	8	no	—
201	C₂×Dic₁₃	—	2	8	no	—
202	C₂×Dic₁₃	—	2	8	no	—
203	C₂×Dic₁₃	—	4	8	no	—
204	C₂×Dic₁₃	C₂³×C₄	1	16	yes	—
205	C₂×Dic₁₃	C₂³×C₄	1	8	yes	—
206	D₅₂	C₂×C₄²	1	32	yes	complemented
207	D₅₂	C₂×C₄²	1	32	yes	complemented
208	C₄×D₁₃	—	2	32	no	—
209	C₄×D₁₃	—	4	16	no	—
210	C₄×D₁₃	—	4	64	no	—
211	C₂³×D₄	—	13	1	no	—
212	C₂⁴×C₄	—	13	2	no	—
213	#518	—	13	32	no	—
214	C₂×C₄×D₄	—	13	8	no	—
215	C₂×C₄×D₄	—	13	16	no	—
216	C₂×C₄×D₄	—	13	2	no	—
217	C₂×C₄×D₄	—	13	2	no	—
218	C₂×C₄×D₄	—	13	2	no	—
219	C₂×C₄×D₄	—	13	2	no	—
220	C₂×C₄×D₄	—	13	8	no	—
221	C₂×#117	—	13	2	no	—
222	C₂×#117	C₂×D₁₃	1	2	yes	—
223	C₂²×C₄⋊C₄	—	13	1	no	—
224	C₂²×C₂²⋊C₄	—	13	2	no	—
225	C₂²×C₂²⋊C₄	—	13	8	no	—
226	C₂²×C₄²	—	13	8	no	—
227	C₂²×C₄²	C₂×D₁₃	1	1	yes	characteristic
228	C₄×C₄⋊C₄	—	13	8	no	—
229	C₄×C₄⋊C₄	—	13	2	no	—
230	C₄×C₄⋊C₄	—	13	2	no	—
231	C₄×C₄⋊C₄	—	13	8	no	—
232	C₄×C₄⋊C₄	C₂×D₁₃	1	2	yes	complemented
233	C₄×C₄⋊C₄	C₂×D₁₃	1	2	yes	complemented
234	C₄×C₂²⋊C₄	—	13	2	no	—
235	C₄×C₂²⋊C₄	—	13	2	no	—
236	C₄×C₂²⋊C₄	—	13	8	no	—
237	C₄×C₂²⋊C₄	—	13	8	no	—
238	C₄×C₂²⋊C₄	—	13	16	no	—
239	C₄×C₂²⋊C₄	—	13	8	no	—
240	C₄×C₂²⋊C₄	—	13	16	no	—
241	C₄×C₂²⋊C₄	C₂×D₁₃	1	2	yes	—
242	C₄×C₂²⋊C₄	C₂×D₁₃	1	2	yes	—
243	#376	—	13	2	no	—
244	#376	C₂×D₁₃	1	2	yes	complemented
245	C₂×#95	—	13	8	no	—
246	C₄³	—	13	2	no	—
247	C₄³	C₂×D₁₃	1	2	yes	complemented
248	C₂²×C₁₃	—	2	2	no	—
249	C₂²×C₁₃	—	2	2	no	—
250	C₂²×C₁₃	—	2	8	no	—
251	C₂²×C₁₃	C₂²×C₄²	1	4	yes	—
252	C₂²×C₁₃	C₂⁴×C₄	1	1	yes	characteristic
253	C₂²×C₁₃	C₂⁴×C₄	1	2	yes	—
254	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
255	C₂²×C₁₃	#585	1	2	yes	—
256	C₂×D₁₃	—	2	8	no	—
257	C₂×D₁₃	—	2	8	no	—
258	C₂×D₁₃	—	2	32	no	—
259	C₂×D₁₃	—	4	32	no	—
260	C₂×D₁₃	C₂²×C₄²	1	16	yes	—
261	C₄×C₁₃	—	2	2	no	—
262	C₄×C₁₃	—	2	2	no	—
263	C₄×C₁₃	—	2	2	no	—
264	C₄×C₁₃	—	2	16	no	—
265	C₄×C₁₃	C₂²×C₄²	1	4	yes	—
266	C₄×C₁₃	C₂²×C₄²	1	4	yes	—
267	C₄×C₁₃	#518	1	4	yes	complemented
268	Dic₁₃	—	2	8	no	—
269	Dic₁₃	—	2	16	no	—
270	C₂⁵	—	13	2	no	—
271	C₂²×D₄	—	13	8	no	—
272	C₂²×D₄	—	13	16	no	—
273	C₂²×D₄	—	13	2	no	—
274	C₂²×D₄	—	13	2	no	—
275	C₂³×C₄	—	13	2	no	—
276	C₂³×C₄	—	13	4	no	—
277	C₂³×C₄	—	13	16	no	—
278	C₂³×C₄	—	13	16	no	—
279	C₂³×C₄	—	13	4	no	—
280	C₂³×C₄	—	52	8	no	—
281	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
282	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
283	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
284	C₄×D₄	—	13	64	no	—
285	C₄×D₄	—	13	16	no	—
286	C₄×D₄	—	13	16	no	—
287	C₄×D₄	—	13	16	no	—
288	C₄×D₄	—	13	16	no	—
289	C₄×D₄	—	13	64	no	—
290	#117	—	13	16	no	—
291	#117	C₄×D₁₃	1	16	yes	complemented
292	C₂×C₄⋊C₄	—	13	8	no	—
293	C₂×C₄⋊C₄	—	13	2	no	—
294	C₂×C₄⋊C₄	—	13	2	no	—
295	C₂×C₄⋊C₄	—	13	4	no	—
296	C₂×C₄⋊C₄	C₂²×D₁₃	1	4	yes	—
297	C₂×C₂²⋊C₄	—	13	4	no	—
298	C₂×C₂²⋊C₄	—	13	16	no	—
299	C₂×C₂²⋊C₄	—	13	4	no	—
300	C₂×C₂²⋊C₄	—	13	4	no	—
301	C₂×C₂²⋊C₄	—	13	16	no	—
302	C₂×C₂²⋊C₄	—	13	64	no	—
303	C₂×C₂²⋊C₄	C₂²×D₁₃	1	4	yes	—
304	C₂×C₄²	—	13	4	no	—
305	C₂×C₄²	—	13	4	no	—
306	C₂×C₄²	—	13	4	no	—
307	C₂×C₄²	—	13	16	no	—
308	C₂×C₄²	—	52	16	no	—
309	C₂×C₄²	C₄×D₁₃	1	8	yes	complemented
310	C₂×C₄²	C₂²×D₁₃	1	4	yes	—
311	C₂×C₄²	C₂²×D₁₃	1	4	yes	—
312	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
313	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
314	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
315	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
316	C₂×C₄²	C₂²×D₁₃	1	4	yes	—
317	#95	—	13	4	no	—
318	#95	—	13	16	no	—
319	#95	—	13	4	no	—
320	#95	C₂²×D₁₃	1	4	yes	—
321	#95	C₂²×D₁₃	1	4	yes	—
322	C₂×C₁₃	—	2	4	no	—
323	C₂×C₁₃	C₂³×C₄²	1	1	yes	characteristic
324	C₂×C₁₃	C₂×#518	1	1	yes	characteristic
325	C₂×C₁₃	#3428	1	1	yes	characteristic
326	C₂×C₁₃	C₄×H(5,𝔽₂)	1	4	yes	—
327	D₁₃	—	2	16	no	—
328	C₂⁴	—	13	4	no	—
329	C₂⁴	—	13	16	no	—
330	C₂⁴	—	13	8	no	—
331	C₂⁴	—	52	4	no	—
332	C₂⁴	—	52	4	no	—
333	C₂⁴	C₂³×D₁₃	1	1	yes	characteristic
334	C₂×D₄	—	13	64	no	—
335	C₂×D₄	—	13	16	no	—
336	C₂×D₄	—	13	8	no	—
337	C₂×D₄	—	13	8	no	—
338	C₂×D₄	—	13	16	no	—
339	C₂²×C₄	—	2	4	no	—
340	C₂²×C₄	—	4	2	no	—
341	C₂²×C₄	—	13	8	no	—
342	C₂²×C₄	—	13	4	no	—
343	C₂²×C₄	—	13	8	no	—
344	C₂²×C₄	—	13	16	no	—
345	C₂²×C₄	—	13	64	no	—
346	C₂²×C₄	—	13	16	no	—
347	C₂²×C₄	—	26	16	no	—
348	C₂²×C₄	—	52	32	no	—
349	C₂²×C₄	—	52	16	no	—
350	C₂²×C₄	—	52	8	no	—
351	C₂²×C₄	—	52	16	no	—
352	C₂²×C₄	—	52	4	no	—
353	C₂²×C₄	C₂×C₄×D₁₃	1	4	yes	—
354	C₂²×C₄	C₂×C₄×D₁₃	1	4	yes	—
355	C₂²×C₄	C₂×C₄×D₁₃	1	4	yes	—
356	C₂²×C₄	C₂×C₄×D₁₃	1	8	yes	—
357	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
358	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
359	C₂²×C₄	C₂³×D₁₃	1	8	yes	—
360	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
361	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
362	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
363	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
364	C₄⋊C₄	—	13	8	no	—
365	C₄⋊C₄	—	13	8	no	—
366	C₄⋊C₄	—	13	16	no	—
367	C₄⋊C₄	C₂×C₄×D₁₃	1	16	yes	complemented
368	C₂²⋊C₄	—	13	16	no	—
369	C₂²⋊C₄	—	13	16	no	—
370	C₂²⋊C₄	—	13	16	no	—
371	C₂²⋊C₄	—	13	64	no	—
372	C₂²⋊C₄	C₂×C₄×D₁₃	1	16	yes	—
373	C₄²	—	2	8	no	—
374	C₄²	—	4	4	no	—
375	C₄²	—	13	16	no	—
376	C₄²	—	26	8	no	—
377	C₄²	—	52	16	no	—
378	C₄²	—	52	4	no	—
379	C₄²	C₂×C₄×D₁₃	1	4	yes	—
380	C₄²	C₂×C₄×D₁₃	1	4	yes	—
381	C₄²	C₂×C₄×D₁₃	1	4	yes	—
382	C₄²	C₂×C₄×D₁₃	1	4	yes	—
383	C₄²	C₂×C₄×D₁₃	1	16	yes	complemented
384	C₁₃	C₄×#518	1	1	yes	characteristic, complemented, Sylow
385	C₂³	—	2	2	no	—
386	C₂³	—	2	2	no	—
387	C₂³	—	13	8	no	—
388	C₂³	—	13	16	no	—
389	C₂³	—	13	32	no	—
390	C₂³	—	26	8	no	—
391	C₂³	—	26	8	no	—
392	C₂³	—	52	8	no	—
393	C₂³	—	52	8	no	—
394	C₂³	—	52	32	no	—
395	C₂³	C₂²×C₄×D₁₃	1	4	yes	—
396	C₂³	C₂²×C₄×D₁₃	1	2	yes	—
397	C₂³	C₂⁴×D₁₃	1	1	yes	characteristic
398	D₄	—	13	32	no	—
399	D₄	—	13	32	no	—
400	C₂×C₄	—	2	8	no	—
401	C₂×C₄	—	2	2	no	—
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	2	8	no	—
404	C₂×C₄	—	2	2	no	—
405	C₂×C₄	—	2	8	no	—
406	C₂×C₄	—	4	4	no	—
407	C₂×C₄	—	13	16	no	—
408	C₂×C₄	—	13	8	no	—
409	C₂×C₄	—	26	8	no	—
410	C₂×C₄	—	26	8	no	—
411	C₂×C₄	—	26	8	no	—
412	C₂×C₄	—	26	32	no	—
413	C₂×C₄	—	52	64	no	—
414	C₂×C₄	—	52	16	no	—
415	C₂×C₄	—	52	8	no	—
416	C₂×C₄	C₄²×D₁₃	1	16	yes	complemented
417	C₂×C₄	C₂²×C₄×D₁₃	1	2	yes	—
418	C₂×C₄	C₂²×C₄×D₁₃	1	2	yes	—
419	C₂×C₄	C₂²×C₄×D₁₃	1	2	yes	—
420	C₂×C₄	C₂²×C₄×D₁₃	1	16	yes	—
421	C₂×C₄	C₂²×C₄×D₁₃	1	4	yes	—
422	C₂×C₄	C₂²×C₄×D₁₃	1	2	yes	—
423	C₂×C₄	C₂²×C₄×D₁₃	1	2	yes	—
424	C₂×C₄	C₂²×C₄×D₁₃	1	4	yes	—
425	C₂×C₄	C₂²×C₄×D₁₃	1	2	yes	—
426	C₂×C₄	#88256	1	4	yes	—
427	C₂²	—	2	2	no	—
428	C₂²	—	2	2	no	—
429	C₂²	—	2	8	no	—
430	C₂²	—	13	16	no	—
431	C₂²	—	26	8	no	—
432	C₂²	—	26	8	no	—
433	C₂²	—	26	32	no	—
434	C₂²	—	52	32	no	—
435	C₂²	C₂×C₄²×D₁₃	1	4	yes	—
436	C₂²	C₂³×C₄×D₁₃	1	1	yes	characteristic
437	C₂²	C₂³×C₄×D₁₃	1	2	yes	—
438	C₂²	C₂×#88256	1	2	yes	—
439	C₂²	#11719648	1	2	yes	—
440	C₄	—	2	2	no	—
441	C₄	—	2	2	no	—
442	C₄	—	2	2	no	—
443	C₄	—	2	16	no	—
444	C₄	—	26	8	no	—
445	C₄	—	26	16	no	—
446	C₄	C₂×C₄²×D₁₃	1	4	yes	—
447	C₄	C₂×C₄²×D₁₃	1	4	yes	—
448	C₄	#11719226	1	4	yes	direct product factor
449	C₂	—	2	4	no	—
450	C₂	—	26	16	no	—
451	C₂	C₂²×C₄²×D₁₃	1	1	yes	characteristic
452	C₂	C₂×#11719226	1	1	yes	characteristic
453	C₂	#13128037	1	1	yes	characteristic
454	C₂	C₄×#88256	1	4	yes	—

	subgroup	G/H
center	C₂²×C₄	C₂³×D₁₃
commutator	C₂×C₁₃	C₂³×C₄²
Frattini	C₂³	C₂⁴×D₁₃
Fitting	C₄×C₁₃×#117	C₂
socle, cosocle	C₂³×C₁₃	C₂⁵
prime radical	C₂³×D₅₂	C₂²
hypercenter	C₄×#117	D₁₃
hypocenter	C₁₃	C₄×#518
LCS	G ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₄×#117

Complements

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

N	H ≅ G/N	type
3. #13117198	C₂	semidirect
4. #13117196	C₂	semidirect
5. #13117192	C₂	semidirect
6. #13117188	C₂	semidirect
7. C₄²×D₅₂	C₂	semidirect
8. C₄×#88147	C₂	semidirect
9. C₄×#88180	C₂	semidirect
10. C₄×C₂²⋊C₄×D₁₃	C₂	semidirect
11. C₄×C₁₃×#117	C₂	semidirect
19. #11719226	C₄	direct (N × H)
22. C₂×C₄×D₅₂	C₄	semidirect
28. C₂×C₄²×D₁₃	C₂²	semidirect
29. C₄×C₁₃×C₄⋊C₄	C₂²	semidirect
30. C₄×C₁₃×C₄⋊C₄	C₂²	semidirect
33. C₁₃×#376	C₂²	semidirect
34. C₄³×C₁₃	C₂²	semidirect
37. C₄⋊C₄×Dic₁₃	C₂²	semidirect
39. C₄×#6103	C₂²	semidirect
40. C₄×#6103	C₂²	semidirect
41. C₄×C₄⋊Dic₁₃	C₂²	semidirect
42. C₄×C₄⋊Dic₁₃	C₂²	semidirect
43. C₄×C₄⋊Dic₁₃	C₂²	semidirect
44. #11718593	C₂²	semidirect
45. C₄²×Dic₁₃	C₂²	semidirect
46. #11718327	C₂²	semidirect
47. #11718327	C₂²	semidirect
48. D₁₃×#95	C₂²	semidirect
59. C₂²×C₄×D₁₃	C₂×C₄	semidirect
63. C₁₃×#117	C₂×C₄	semidirect
66. C₂×C₄²×C₁₃	C₂×C₄	semidirect
75. C₂×#6103	C₂×C₄	semidirect
79. #88180	C₂×C₄	semidirect
80. C₂×C₄⋊Dic₁₃	C₂×C₄	semidirect
88. #88147	C₂×C₄	semidirect
89. C₂²⋊C₄×D₁₃	C₂×C₄	semidirect
90. C₄×D₅₂	C₂×C₄	semidirect
91. C₄×D₅₂	C₂×C₄	semidirect
92. C₄×D₅₂	C₂×C₄	semidirect
93. C₄×D₅₂	C₂×C₄	semidirect
94. C₄×D₅₂	C₂×C₄	semidirect
125. C₂×D₅₂	C₄²	semidirect
137. C₂×C₄×D₁₃	C₂²×C₄	semidirect
138. C₁₃×C₄⋊C₄	C₂²×C₄	semidirect
146. C₄²×C₁₃	C₂²×C₄	semidirect
150. #6103	C₂²×C₄	semidirect
153. C₄⋊Dic₁₃	C₂²×C₄	semidirect
157. C₄×Dic₁₃	C₂²×C₄	semidirect
167. C₄×#117	D₁₃	semidirect
179. C₂²×D₁₃	C₂×C₄²	semidirect
189. C₂×C₄×C₁₃	C₂×C₄²	semidirect
206. D₅₂	C₂×C₄²	semidirect
207. D₅₂	C₂×C₄²	semidirect
232. C₄×C₄⋊C₄	C₂×D₁₃	semidirect
233. C₄×C₄⋊C₄	C₂×D₁₃	semidirect
244. #376	C₂×D₁₃	semidirect
247. C₄³	C₂×D₁₃	semidirect
267. C₄×C₁₃	#518	semidirect
291. #117	C₄×D₁₃	semidirect
309. C₂×C₄²	C₄×D₁₃	semidirect
367. C₄⋊C₄	C₂×C₄×D₁₃	semidirect
383. C₄²	C₂×C₄×D₁₃	semidirect
384. C₁₃	C₄×#518	semidirect
416. C₂×C₄	C₄²×D₁₃	semidirect
448. C₄	#11719226	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#11719226	2
C₂²×C₄×D₅₂	2
#13117198	2
#13117196	2
#13117192	2
#13117188	2
C₄²×D₅₂	2
C₄×#88147	2
C₄×#88180	2
C₄×C₂²⋊C₄×D₁₃	2
C₄×C₁₃×#117	2
C₄×#518	13

Subgroups — C4×#11719226 #16021156

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#11719226 #16021156