Subgroups — #15752644

Order 3328.

1090 conjugacy classes of subgroups.

The subgroup lattice has 522 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13117219	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×C₂²⋊Dic₁₃	C₂	1	1	yes	maximal, characteristic
3	#13112690	C₂	1	4	yes	maximal, complemented
4	C₂×C₁₃×#407	C₂	1	1	yes	maximal, characteristic
5	C₂⁴×C₄×C₁₃	C₂²	1	1	yes	characteristic
6	C₂²×C₁₃×M₁₆	—	2	1	no	—
7	C₂²×C₂²⋊Dic₁₃	—	2	1	no	—
8	C₂×#88180	—	2	1	no	—
9	C₂²×C₄×Dic₁₃	C₄	1	2	yes	complemented
10	C₁₃×#407	—	2	1	no	—
11	C₁₃×#407	—	2	1	no	—
12	C₁₃×#407	C₄	1	2	yes	complemented
13	C₁₃×#407	C₂²	1	2	yes	—
14	C₂×C₁₃×C₂²⋊C₈	—	2	1	no	—
15	C₂×C₁₃×C₂²⋊C₈	C₄	1	2	yes	complemented
16	#11718908	—	2	1	no	—
17	#11718873	—	2	1	no	—
18	#11718873	C₄	1	2	yes	complemented
19	#11718872	C₂²	1	2	yes	—
20	C₄×C₂²⋊Dic₁₃	—	2	1	no	—
21	C₄×C₂²⋊Dic₁₃	—	2	1	no	—
22	C₄×C₂²⋊Dic₁₃	—	2	1	no	—
23	C₄×C₂²⋊Dic₁₃	C₄	1	2	yes	complemented
24	C₄×C₂²⋊Dic₁₃	C₄	1	2	yes	complemented
25	C₄×C₂²⋊Dic₁₃	C₂²	1	2	yes	—
26	C₂×#88071	—	2	1	no	—
27	C₂⁵×C₁₃	D₄	1	1	yes	characteristic
28	C₂³×C₄×C₁₃	—	4	4	no	—
29	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
30	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
31	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
32	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
33	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
34	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
35	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
36	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
37	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
38	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
39	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
40	C₂³×C₄×C₁₃	Q₈	1	1	yes	characteristic
41	C₂³×C₄×C₁₃	Q₈	1	1	yes	characteristic
42	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
43	C₂³×Dic₁₃	—	2	2	no	—
44	C₂×C₁₃×M₁₆	—	2	2	no	—
45	C₂×C₁₃×M₁₆	—	2	2	no	—
46	C₂×C₁₃×M₁₆	—	4	4	no	—
47	C₂²×C₈×C₁₃	—	2	2	no	—
48	C₂×C₂²⋊Dic₁₃	—	2	8	no	—
49	C₂×C₂²⋊Dic₁₃	—	2	2	no	—
50	C₂×C₂²⋊Dic₁₃	—	2	2	no	—
51	C₂×C₂²⋊Dic₁₃	—	2	2	no	—
52	C₂×C₂²⋊Dic₁₃	—	2	2	no	—
53	C₂×C₂²⋊Dic₁₃	—	2	2	no	—
54	#88180	—	4	4	no	—
55	C₂×C₄⋊Dic₁₃	—	2	2	no	—
56	C₂×C₄×Dic₁₃	—	2	2	no	—
57	C₂×C₄×Dic₁₃	—	2	2	no	—
58	C₂×C₄×Dic₁₃	—	4	4	no	—
59	C₂×C₄×Dic₁₃	C₂×C₄	1	4	yes	—
60	C₁₃×C₂²⋊C₈	—	2	2	no	—
61	C₁₃×C₂²⋊C₈	—	2	2	no	—
62	C₁₃×C₂²⋊C₈	—	2	2	no	—
63	C₁₃×C₂²⋊C₈	C₂×C₄	1	4	yes	complemented
64	#88071	—	2	2	no	—
65	#88071	—	2	2	no	—
66	#88071	—	2	2	no	—
67	#88071	C₂×C₄	1	4	yes	complemented
68	#7942	—	13	1	no	maximal, Sylow
69	C₂⁴×C₁₃	—	2	4	no	—
70	C₂⁴×C₁₃	—	4	2	no	—
71	C₂⁴×C₁₃	—	4	2	no	—
72	C₂⁴×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
73	C₂⁴×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
74	C₂⁴×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
75	C₂⁴×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
76	C₂⁴×C₁₃	C₄⋊C₄	1	1	yes	characteristic
77	C₂⁴×C₁₃	C₄⋊C₄	1	1	yes	characteristic
78	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
79	C₂²×C₄×C₁₃	—	2	4	no	—
80	C₂²×C₄×C₁₃	—	2	4	no	—
81	C₂²×C₄×C₁₃	—	2	4	no	—
82	C₂²×C₄×C₁₃	—	4	2	no	—
83	C₂²×C₄×C₁₃	—	4	2	no	—
84	C₂²×C₄×C₁₃	—	4	2	no	—
85	C₂²×C₄×C₁₃	—	4	2	no	—
86	C₂²×C₄×C₁₃	—	4	2	no	—
87	C₂²×C₄×C₁₃	—	4	2	no	—
88	C₂²×C₄×C₁₃	—	4	2	no	—
89	C₂²×C₄×C₁₃	—	4	2	no	—
90	C₂²×C₄×C₁₃	—	4	2	no	—
91	C₂²×C₄×C₁₃	—	4	2	no	—
92	C₂²×C₄×C₁₃	—	4	2	no	—
93	C₂²×C₄×C₁₃	C₄²	1	1	yes	characteristic
94	C₂²×C₄×C₁₃	C₄²	1	1	yes	characteristic
95	C₂²×C₄×C₁₃	C₄²	1	1	yes	characteristic
96	C₂²×C₄×C₁₃	C₄²	1	1	yes	characteristic
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	C₂²⋊C₄	1	1	yes	characteristic
103	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
104	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
105	C₂²×C₄×C₁₃	C₄⋊C₄	1	1	yes	characteristic
106	C₂²×C₄×C₁₃	C₄⋊C₄	1	1	yes	characteristic
107	C₂²×C₄×C₁₃	C₄⋊C₄	1	1	yes	characteristic
108	C₂²×C₄×C₁₃	C₄⋊C₄	1	1	yes	characteristic
109	C₂²×C₄×C₁₃	C₄⋊C₄	1	1	yes	characteristic
110	C₂²×C₄×C₁₃	C₄⋊C₄	1	1	yes	characteristic
111	C₂²×C₄×C₁₃	C₄⋊C₄	1	1	yes	characteristic
112	C₂²×C₄×C₁₃	C₄⋊C₄	1	1	yes	characteristic
113	C₂²×C₄×C₁₃	C₄⋊C₄	1	1	yes	characteristic
114	C₂²×C₄×C₁₃	C₄⋊C₄	1	1	yes	characteristic
115	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
116	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
117	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
118	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
119	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
120	C₂²×C₄×C₁₃	C₂×Q₈	1	1	yes	characteristic
121	C₂²×Dic₁₃	—	2	8	no	—
122	C₂²×Dic₁₃	—	2	4	no	—
123	C₂²×Dic₁₃	—	2	4	no	—
124	C₂²×Dic₁₃	—	4	4	no	—
125	C₂²×Dic₁₃	—	4	4	no	—
126	C₁₃×M₁₆	—	4	4	no	—
127	C₁₃×M₁₆	—	4	4	no	—
128	C₂×C₈×C₁₃	—	2	4	no	—
129	C₂×C₈×C₁₃	—	4	4	no	—
130	C₂²⋊Dic₁₃	—	2	8	no	—
131	C₂²⋊Dic₁₃	—	2	8	no	—
132	C₂²⋊Dic₁₃	—	4	4	no	—
133	C₂²⋊Dic₁₃	—	4	4	no	—
134	C₂²⋊Dic₁₃	—	4	4	no	—
135	C₄⋊Dic₁₃	—	4	4	no	—
136	C₄×Dic₁₃	—	4	4	no	—
137	C₄×Dic₁₃	—	4	4	no	—
138	C₄×Dic₁₃	—	4	4	no	—
139	C₂×#407	D₁₃	1	1	yes	characteristic
140	#2280	—	13	1	no	—
141	C₂×C₄×C₂²⋊C₄	—	13	1	no	—
142	#1284	—	13	4	no	—
143	C₂³×C₁₃	—	2	2	no	—
144	C₂³×C₁₃	—	2	2	no	—
145	C₂³×C₁₃	—	2	2	no	—
146	C₂³×C₁₃	—	2	2	no	—
147	C₂³×C₁₃	—	2	2	no	—
148	C₂³×C₁₃	—	2	2	no	—
149	C₂³×C₁₃	—	2	2	no	—
150	C₂³×C₁₃	—	2	2	no	—
151	C₂³×C₁₃	—	2	2	no	—
152	C₂³×C₁₃	—	2	2	no	—
153	C₂³×C₁₃	—	2	2	no	—
154	C₂³×C₁₃	—	2	2	no	—
155	C₂³×C₁₃	—	4	1	no	—
156	C₂³×C₁₃	—	4	1	no	—
157	C₂³×C₁₃	—	4	1	no	—
158	C₂³×C₁₃	—	4	1	no	—
159	C₂³×C₁₃	—	4	1	no	—
160	C₂³×C₁₃	—	4	1	no	—
161	C₂³×C₁₃	—	4	1	no	—
162	C₂³×C₁₃	—	4	1	no	—
163	C₂³×C₁₃	—	4	16	no	—
164	C₂³×C₁₃	#95	1	1	yes	characteristic
165	C₂³×C₁₃	#95	1	1	yes	characteristic
166	C₂³×C₁₃	#95	1	1	yes	characteristic
167	C₂³×C₁₃	#95	1	1	yes	characteristic
168	C₂³×C₁₃	#104	1	4	yes	—
169	C₂³×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
170	C₂³×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
171	C₂³×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
172	C₂×C₄×C₁₃	—	2	2	no	—
173	C₂×C₄×C₁₃	—	2	2	no	—
174	C₂×C₄×C₁₃	—	2	2	no	—
175	C₂×C₄×C₁₃	—	2	2	no	—
176	C₂×C₄×C₁₃	—	2	2	no	—
177	C₂×C₄×C₁₃	—	2	2	no	—
178	C₂×C₄×C₁₃	—	2	2	no	—
179	C₂×C₄×C₁₃	—	2	2	no	—
180	C₂×C₄×C₁₃	—	2	2	no	—
181	C₂×C₄×C₁₃	—	2	2	no	—
182	C₂×C₄×C₁₃	—	2	2	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	2	no	—
187	C₂×C₄×C₁₃	—	4	1	no	—
188	C₂×C₄×C₁₃	—	4	1	no	—
189	C₂×C₄×C₁₃	—	4	1	no	—
190	C₂×C₄×C₁₃	—	4	1	no	—
191	C₂×C₄×C₁₃	—	4	1	no	—
192	C₂×C₄×C₁₃	—	4	1	no	—
193	C₂×C₄×C₁₃	—	4	1	no	—
194	C₂×C₄×C₁₃	—	4	1	no	—
195	C₂×C₄×C₁₃	—	4	1	no	—
196	C₂×C₄×C₁₃	—	4	1	no	—
197	C₂×C₄×C₁₃	—	4	1	no	—
198	C₂×C₄×C₁₃	—	4	1	no	—
199	C₂×C₄×C₁₃	#95	1	1	yes	characteristic
200	C₂×C₄×C₁₃	#95	1	1	yes	characteristic
201	C₂×C₄×C₁₃	#95	1	1	yes	characteristic
202	C₂×C₄×C₁₃	#95	1	1	yes	characteristic
203	C₂×C₄×C₁₃	#99	1	4	yes	—
204	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
205	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
206	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
207	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
208	C₂×Dic₁₃	—	2	8	no	—
209	C₂×Dic₁₃	—	4	16	no	—
210	C₂×Dic₁₃	—	4	4	no	—
211	C₂×Dic₁₃	—	4	4	no	—
212	C₂×Dic₁₃	—	4	4	no	—
213	C₂×Dic₁₃	—	4	4	no	—
214	C₂×Dic₁₃	—	4	4	no	—
215	C₈×C₁₃	—	4	4	no	—
216	C₂⁴×C₄	C₂×D₁₃	1	1	yes	characteristic
217	C₂²×M₁₆	—	2	1	no	—
218	C₂×#117	—	26	1	no	—
219	C₂²×C₂²⋊C₄	—	26	1	no	—
220	C₂²×C₄²	—	13	2	no	—
221	#407	—	2	1	no	—
222	#407	—	2	1	no	—
223	#407	Dic₁₃	1	2	yes	complemented
224	#407	C₂×D₁₃	1	2	yes	—
225	C₂×C₂²⋊C₈	—	2	1	no	—
226	C₂×C₂²⋊C₈	Dic₁₃	1	2	yes	complemented
227	#381	—	13	2	no	—
228	#380	—	13	2	no	—
229	#380	—	26	1	no	—
230	#379	—	26	1	no	—
231	C₄×C₂²⋊C₄	—	13	2	no	—
232	C₄×C₂²⋊C₄	—	13	2	no	—
233	C₄×C₂²⋊C₄	—	13	2	no	—
234	C₄×C₂²⋊C₄	—	26	1	no	—
235	C₄×C₂²⋊C₄	—	26	1	no	—
236	C₄×C₂²⋊C₄	—	26	1	no	—
237	C₂×#95	—	26	1	no	—
238	C₂²×C₁₃	—	2	8	no	—
239	C₂²×C₁₃	—	2	1	no	—
240	C₂²×C₁₃	—	2	1	no	—
241	C₂²×C₁₃	—	2	1	no	—
242	C₂²×C₁₃	—	2	1	no	—
243	C₂²×C₁₃	—	2	1	no	—
244	C₂²×C₁₃	—	2	1	no	—
245	C₂²×C₁₃	—	2	1	no	—
246	C₂²×C₁₃	—	2	1	no	—
247	C₂²×C₁₃	—	2	1	no	—
248	C₂²×C₁₃	—	2	1	no	—
249	C₂²×C₁₃	—	2	1	no	—
250	C₂²×C₁₃	—	2	1	no	—
251	C₂²×C₁₃	—	2	1	no	—
252	C₂²×C₁₃	—	2	1	no	—
253	C₂²×C₁₃	—	2	1	no	—
254	C₂²×C₁₃	—	2	1	no	—
255	C₂²×C₁₃	—	4	4	no	—
256	C₂²×C₁₃	—	4	4	no	—
257	C₂²×C₁₃	—	4	4	no	—
258	C₂²×C₁₃	—	4	4	no	—
259	C₂²×C₁₃	—	4	4	no	—
260	C₂²×C₁₃	—	4	4	no	—
261	C₂²×C₁₃	H(3,ℤ/4)	1	2	yes	—
262	C₂²×C₁₃	#339	1	2	yes	—
263	C₂²×C₁₃	#339	1	2	yes	—
264	C₂²×C₁₃	C₂×#95	1	1	yes	characteristic
265	C₂²×C₁₃	C₂×#99	1	2	yes	—
266	C₂²×C₁₃	C₂×#104	1	2	yes	—
267	C₄×C₁₃	—	2	1	no	—
268	C₄×C₁₃	—	2	1	no	—
269	C₄×C₁₃	—	2	1	no	—
270	C₄×C₁₃	—	2	1	no	—
271	C₄×C₁₃	—	2	1	no	—
272	C₄×C₁₃	—	2	1	no	—
273	C₄×C₁₃	#342	1	2	yes	—
274	C₄×C₁₃	#342	1	2	yes	—
275	Dic₁₃	—	4	8	no	—
276	Dic₁₃	—	8	4	no	—
277	C₂⁵	D₅₂	1	1	yes	characteristic
278	C₂³×C₄	—	4	4	no	—
279	C₂³×C₄	—	26	2	no	—
280	C₂³×C₄	Dic₂₆	1	1	yes	characteristic
281	C₂³×C₄	Dic₂₆	1	1	yes	characteristic
282	C₂³×C₄	C₄×D₁₃	1	1	yes	characteristic
283	C₂³×C₄	C₄×D₁₃	1	1	yes	characteristic
284	C₂³×C₄	C₄×D₁₃	1	1	yes	characteristic
285	C₂³×C₄	C₄×D₁₃	1	1	yes	characteristic
286	C₂³×C₄	D₅₂	1	1	yes	characteristic
287	C₂³×C₄	C₂×Dic₁₃	1	1	yes	characteristic
288	C₂³×C₄	C₂×Dic₁₃	1	1	yes	characteristic
289	C₂³×C₄	C₂²⋊D₁₃	1	1	yes	characteristic
290	C₂³×C₄	C₂²⋊D₁₃	1	1	yes	characteristic
291	C₂³×C₄	C₂²⋊D₁₃	1	1	yes	characteristic
292	C₂³×C₄	C₂²⋊D₁₃	1	1	yes	characteristic
293	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
294	C₂×M₁₆	—	2	2	no	—
295	C₂×M₁₆	—	2	2	no	—
296	C₂×M₁₆	—	4	4	no	—
297	C₂²×C₈	—	2	2	no	—
298	#117	—	52	4	no	—
299	C₂×C₄⋊C₄	—	26	2	no	—
300	C₂×C₂²⋊C₄	—	26	8	no	—
301	C₂×C₂²⋊C₄	—	26	2	no	—
302	C₂×C₂²⋊C₄	—	26	2	no	—
303	C₂×C₂²⋊C₄	—	26	2	no	—
304	C₂×C₂²⋊C₄	—	26	2	no	—
305	C₂×C₂²⋊C₄	—	26	2	no	—
306	C₂×C₄²	—	13	4	no	—
307	C₂×C₄²	—	26	2	no	—
308	C₂×C₄²	—	26	2	no	—
309	C₂×C₄²	—	52	4	no	—
310	C₂²⋊C₈	—	2	2	no	—
311	C₂²⋊C₈	—	2	2	no	—
312	C₂²⋊C₈	—	2	2	no	—
313	C₂²⋊C₈	C₂×Dic₁₃	1	4	yes	complemented
314	#95	—	13	4	no	—
315	#95	—	26	2	no	—
316	#95	—	26	2	no	—
317	#95	—	26	2	no	—
318	C₂×C₁₃	—	2	2	no	—
319	C₂×C₁₃	—	2	2	no	—
320	C₂×C₁₃	—	2	2	no	—
321	C₂×C₁₃	—	2	2	no	—
322	C₂×C₁₃	—	2	2	no	—
323	C₂×C₁₃	—	4	1	no	—
324	C₂×C₁₃	—	4	1	no	—
325	C₂×C₁₃	C₂×H(3,ℤ/4)	1	1	yes	characteristic
326	C₂×C₁₃	C₂×#339	1	1	yes	characteristic
327	C₂×C₁₃	C₂×#342	1	1	yes	characteristic
328	C₂⁴	—	2	4	no	—
329	C₂⁴	—	4	2	no	—
330	C₂⁴	—	4	2	no	—
331	C₂⁴	C₄⋊Dic₁₃	1	1	yes	characteristic
332	C₂⁴	C₄⋊Dic₁₃	1	1	yes	characteristic
333	C₂⁴	#6103	1	1	yes	characteristic
334	C₂⁴	#6103	1	1	yes	characteristic
335	C₂⁴	#6103	1	1	yes	characteristic
336	C₂⁴	#6103	1	1	yes	characteristic
337	C₂⁴	C₂×D₅₂	1	1	yes	characteristic
338	C₂²×C₄	—	2	4	no	—
339	C₂²×C₄	—	2	4	no	—
340	C₂²×C₄	—	2	4	no	—
341	C₂²×C₄	—	4	2	no	—
342	C₂²×C₄	—	4	2	no	—
343	C₂²×C₄	—	4	2	no	—
344	C₂²×C₄	—	4	2	no	—
345	C₂²×C₄	—	4	2	no	—
346	C₂²×C₄	—	4	2	no	—
347	C₂²×C₄	—	4	2	no	—
348	C₂²×C₄	—	4	2	no	—
349	C₂²×C₄	—	4	2	no	—
350	C₂²×C₄	—	4	2	no	—
351	C₂²×C₄	—	4	2	no	—
352	C₂²×C₄	—	26	8	no	—
353	C₂²×C₄	—	26	4	no	—
354	C₂²×C₄	—	26	4	no	—
355	C₂²×C₄	—	52	4	no	—
356	C₂²×C₄	—	52	4	no	—
357	C₂²×C₄	C₄×Dic₁₃	1	1	yes	characteristic
358	C₂²×C₄	C₄×Dic₁₃	1	1	yes	characteristic
359	C₂²×C₄	C₄×Dic₁₃	1	1	yes	characteristic
360	C₂²×C₄	C₄×Dic₁₃	1	1	yes	characteristic
361	C₂²×C₄	#6101	1	1	yes	characteristic
362	C₂²×C₄	#6101	1	1	yes	characteristic
363	C₂²×C₄	#6101	1	1	yes	characteristic
364	C₂²×C₄	#6101	1	1	yes	characteristic
365	C₂²×C₄	#6101	1	1	yes	characteristic
366	C₂²×C₄	#6101	1	1	yes	characteristic
367	C₂²×C₄	#6101	1	1	yes	characteristic
368	C₂²×C₄	#6101	1	1	yes	characteristic
369	C₂²×C₄	C₄⋊Dic₁₃	1	1	yes	characteristic
370	C₂²×C₄	C₄⋊Dic₁₃	1	1	yes	characteristic
371	C₂²×C₄	#6103	1	1	yes	characteristic
372	C₂²×C₄	#6103	1	1	yes	characteristic
373	C₂²×C₄	#6103	1	1	yes	characteristic
374	C₂²×C₄	#6103	1	1	yes	characteristic
375	C₂²×C₄	C₂²⋊Dic₁₃	1	1	yes	characteristic
376	C₂²×C₄	C₂²⋊Dic₁₃	1	1	yes	characteristic
377	C₂²×C₄	C₂²⋊Dic₁₃	1	1	yes	characteristic
378	C₂²×C₄	C₂²⋊Dic₁₃	1	1	yes	characteristic
379	C₂²×C₄	C₂×Dic₂₆	1	1	yes	characteristic
380	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
381	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
382	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
383	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
384	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
385	M₁₆	—	4	4	no	—
386	M₁₆	—	4	4	no	—
387	C₂×C₈	—	2	4	no	—
388	C₂×C₈	—	4	4	no	—
389	C₄⋊C₄	—	52	4	no	—
390	C₂²⋊C₄	—	26	8	no	—
391	C₂²⋊C₄	—	26	8	no	—
392	C₂²⋊C₄	—	52	4	no	—
393	C₂²⋊C₄	—	52	4	no	—
394	C₂²⋊C₄	—	52	4	no	—
395	C₄²	—	52	4	no	—
396	C₄²	—	52	4	no	—
397	C₄²	—	52	4	no	—
398	C₁₃	#7942	1	1	yes	characteristic, complemented, Sylow
399	C₂³	—	2	2	no	—
400	C₂³	—	2	2	no	—
401	C₂³	—	2	2	no	—
402	C₂³	—	2	2	no	—
403	C₂³	—	2	2	no	—
404	C₂³	—	2	2	no	—
405	C₂³	—	2	2	no	—
406	C₂³	—	2	2	no	—
407	C₂³	—	2	2	no	—
408	C₂³	—	2	2	no	—
409	C₂³	—	2	2	no	—
410	C₂³	—	2	2	no	—
411	C₂³	—	4	1	no	—
412	C₂³	—	4	1	no	—
413	C₂³	—	4	1	no	—
414	C₂³	—	4	1	no	—
415	C₂³	—	4	1	no	—
416	C₂³	—	4	1	no	—
417	C₂³	—	4	1	no	—
418	C₂³	—	4	1	no	—
419	C₂³	—	4	16	no	—
420	C₂³	#88065	1	4	yes	—
421	C₂³	#88071	1	1	yes	characteristic
422	C₂³	#88071	1	1	yes	characteristic
423	C₂³	#88071	1	1	yes	characteristic
424	C₂³	#88071	1	1	yes	characteristic
425	C₂³	C₂×C₄⋊Dic₁₃	1	1	yes	characteristic
426	C₂³	C₂×#6103	1	1	yes	characteristic
427	C₂³	C₂×#6103	1	1	yes	characteristic
428	C₂×C₄	—	2	2	no	—
429	C₂×C₄	—	2	2	no	—
430	C₂×C₄	—	2	2	no	—
431	C₂×C₄	—	2	2	no	—
432	C₂×C₄	—	2	2	no	—
433	C₂×C₄	—	2	2	no	—
434	C₂×C₄	—	2	2	no	—
435	C₂×C₄	—	2	2	no	—
436	C₂×C₄	—	2	2	no	—
437	C₂×C₄	—	2	2	no	—
438	C₂×C₄	—	2	2	no	—
439	C₂×C₄	—	2	2	no	—
440	C₂×C₄	—	2	2	no	—
441	C₂×C₄	—	2	2	no	—
442	C₂×C₄	—	2	2	no	—
443	C₂×C₄	—	4	1	no	—
444	C₂×C₄	—	4	1	no	—
445	C₂×C₄	—	4	1	no	—
446	C₂×C₄	—	4	1	no	—
447	C₂×C₄	—	4	1	no	—
448	C₂×C₄	—	4	1	no	—
449	C₂×C₄	—	4	1	no	—
450	C₂×C₄	—	4	1	no	—
451	C₂×C₄	—	4	1	no	—
452	C₂×C₄	—	4	1	no	—
453	C₂×C₄	—	4	1	no	—
454	C₂×C₄	—	4	1	no	—
455	C₂×C₄	—	26	8	no	—
456	C₂×C₄	—	52	16	no	—
457	C₂×C₄	—	52	4	no	—
458	C₂×C₄	—	52	4	no	—
459	C₂×C₄	—	52	4	no	—
460	C₂×C₄	—	52	4	no	—
461	C₂×C₄	—	52	4	no	—
462	C₂×C₄	#88046	1	4	yes	—
463	C₂×C₄	#88071	1	1	yes	characteristic
464	C₂×C₄	#88071	1	1	yes	characteristic
465	C₂×C₄	#88071	1	1	yes	characteristic
466	C₂×C₄	#88071	1	1	yes	characteristic
467	C₂×C₄	C₂×C₄×Dic₁₃	1	1	yes	characteristic
468	C₂×C₄	C₂×#6101	1	1	yes	characteristic
469	C₂×C₄	C₂×#6101	1	1	yes	characteristic
470	C₂×C₄	C₂×C₂²⋊Dic₁₃	1	1	yes	characteristic
471	C₈	—	4	4	no	—
472	C₂²	—	2	8	no	—
473	C₂²	—	2	1	no	—
474	C₂²	—	2	1	no	—
475	C₂²	—	2	1	no	—
476	C₂²	—	2	1	no	—
477	C₂²	—	2	1	no	—
478	C₂²	—	2	1	no	—
479	C₂²	—	2	1	no	—
480	C₂²	—	2	1	no	—
481	C₂²	—	2	1	no	—
482	C₂²	—	2	1	no	—
483	C₂²	—	2	1	no	—
484	C₂²	—	2	1	no	—
485	C₂²	—	2	1	no	—
486	C₂²	—	2	1	no	—
487	C₂²	—	2	1	no	—
488	C₂²	—	2	1	no	—
489	C₂²	—	4	4	no	—
490	C₂²	—	4	4	no	—
491	C₂²	—	4	4	no	—
492	C₂²	—	4	4	no	—
493	C₂²	—	4	4	no	—
494	C₂²	—	4	4	no	—
495	C₂²	#11718147	1	2	yes	—
496	C₂²	#11718147	1	2	yes	—
497	C₂²	#11718149	1	2	yes	—
498	C₂²	C₂×#88046	1	2	yes	—
499	C₂²	C₂×#88065	1	2	yes	—
500	C₂²	C₂×#88071	1	1	yes	characteristic
501	C₄	—	2	1	no	—
502	C₄	—	2	1	no	—
503	C₄	—	2	1	no	—
504	C₄	—	2	1	no	—
505	C₄	—	2	1	no	—
506	C₄	—	2	1	no	—
507	C₄	—	52	8	no	—
508	C₄	—	104	4	no	—
509	C₄	#11718119	1	2	yes	—
510	C₄	#11718119	1	2	yes	—
511	C₂	—	2	2	no	—
512	C₂	—	2	2	no	—
513	C₂	—	2	2	no	—
514	C₂	—	2	2	no	—
515	C₂	—	2	2	no	—
516	C₂	—	4	1	no	—
517	C₂	—	4	1	no	—
518	C₂	C₂×#11718149	1	1	yes	characteristic
519	C₂	C₂×#11718147	1	1	yes	characteristic
520	C₂	C₂×#11718119	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#88071
commutator	C₂×C₄×C₁₃	C₂×C₄²
Frattini	C₂³×C₄	C₂²×D₁₃
Fitting	C₂×C₁₃×#407	C₂
socle	C₂²×C₁₃	C₂×#95
prime radical	C₂⁵×C₁₃	D₄
cosocle	C₂³×C₄×C₁₃	C₂³
hypercenter	C₂×#407	D₁₃
hypocenter	C₁₃	#7942
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂⁴×C₄ ◁ C₂×#407

Complements

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

N	H ≅ G/N	type
3. #13112690	C₂	semidirect
9. C₂²×C₄×Dic₁₃	C₄	semidirect
12. C₁₃×#407	C₄	semidirect
15. C₂×C₁₃×C₂²⋊C₈	C₄	semidirect
18. #11718873	C₄	semidirect
23. C₄×C₂²⋊Dic₁₃	C₄	semidirect
24. C₄×C₂²⋊Dic₁₃	C₄	semidirect
63. C₁₃×C₂²⋊C₈	C₂×C₄	semidirect
67. #88071	C₂×C₄	semidirect
223. #407	Dic₁₃	semidirect
226. C₂×C₂²⋊C₈	Dic₁₃	semidirect
313. C₂²⋊C₈	C₂×Dic₁₃	semidirect
398. C₁₃	#7942	semidirect

Maximal subgroups

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

subgroup	index
#13117219	2
C₂×C₄×C₂²⋊Dic₁₃	2
#13112690	2
C₂×C₁₃×#407	2
#7942	13