Subgroups — C₂²×D₁₃×#117 #16769475

Order 3328.

14334 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴×C₄×D₁₃	C₂	1	1	yes	maximal, characteristic
2	C₂²×#88180	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×#88146	C₂	1	2	yes	maximal, complemented
4	C₂²×#88126	C₂	1	2	yes	maximal, complemented
5	C₂²×#88131	C₂	1	2	yes	maximal, complemented
6	C₂×D₁₃×#117	C₂	1	48	yes	maximal, direct product factor
7	C₂²×C₄⋊C₄×D₁₃	C₂	1	2	yes	maximal, complemented
8	C₂²×C₂²⋊C₄×D₁₃	C₂	1	2	yes	maximal
9	C₂²×C₄²×D₁₃	C₂	1	2	yes	maximal, complemented
10	C₂²×C₁₃×#117	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂⁵×D₁₃	C₂²	1	1	yes	characteristic
12	C₂⁴×C₄×C₁₃	C₂²	1	1	yes	characteristic
13	C₂⁴×Dic₁₃	C₂²	1	1	yes	characteristic
14	C₂³×C₄×D₁₃	C₄	1	32	yes	complemented
15	C₂³×C₄×D₁₃	C₂²	1	4	yes	—
16	C₂³×C₄×D₁₃	C₂²	1	1	yes	characteristic
17	C₂³×C₄×D₁₃	C₂²	1	1	yes	characteristic
18	C₂³×C₄×D₁₃	C₂²	1	24	yes	—
19	C₂³×C₄×D₁₃	C₂²	1	1	yes	characteristic
20	C₂³×C₄×D₁₃	C₂²	1	1	yes	characteristic
21	C₂×C₁₃×#117	C₂²	1	24	yes	complemented
22	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	complemented
23	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
24	C₂²×C₄²×C₁₃	C₂²	1	2	yes	complemented
25	C₂²×C₂²⋊Dic₁₃	C₂²	1	2	yes	—
26	C₂²×#6103	C₂²	1	4	yes	—
27	C₂×#88180	C₂²	1	24	yes	complemented
28	C₂²×C₄⋊Dic₁₃	C₂²	1	2	yes	complemented
29	C₂²×#6101	C₂²	1	4	yes	complemented
30	C₂²×C₄×Dic₁₃	C₂²	1	4	yes	complemented
31	C₂²×C₄×Dic₁₃	C₂²	1	2	yes	complemented
32	D₁₃×#117	C₂²	1	256	yes	direct product factor
33	C₂×#88146	C₂²	1	48	yes	complemented
34	C₂×C₄⋊C₄×D₁₃	C₂²	1	48	yes	complemented
35	C₂×C₂²⋊C₄×D₁₃	C₂²	1	48	yes	—
36	C₂×#88131	C₂²	1	48	yes	complemented
37	C₂×#88126	C₂²	1	48	yes	complemented
38	C₂×C₄²×D₁₃	C₂²	1	48	yes	complemented
39	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
40	C₂⁴×D₁₃	—	2	16	no	—
41	C₂⁴×D₁₃	C₂×C₄	1	16	yes	—
42	C₂⁴×D₁₃	C₂³	1	12	yes	—
43	C₂⁴×D₁₃	C₂³	1	1	yes	characteristic
44	C₂⁴×D₁₃	C₂³	1	1	yes	characteristic
45	C₂³×C₄×C₁₃	C₂×C₄	1	16	yes	complemented
46	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
47	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
48	C₂³×C₄×C₁₃	C₂³	1	12	yes	—
49	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
50	C₂³×Dic₁₃	C₂×C₄	1	16	yes	complemented
51	C₂³×Dic₁₃	C₂³	1	4	yes	—
52	C₂³×Dic₁₃	C₂³	1	1	yes	characteristic
53	C₂³×Dic₁₃	C₂³	1	1	yes	characteristic
54	C₂³×Dic₁₃	C₂³	1	12	yes	—
55	C₂²×C₄×D₁₃	—	2	32	no	—
56	C₂²×C₄×D₁₃	C₂×C₄	1	16	yes	—
57	C₂²×C₄×D₁₃	C₂×C₄	1	16	yes	—
58	C₂²×C₄×D₁₃	C₂×C₄	1	384	yes	complemented
59	C₂²×C₄×D₁₃	C₂×C₄	1	16	yes	complemented
60	C₂²×C₄×D₁₃	C₂×C₄	1	16	yes	complemented
61	C₂²×C₄×D₁₃	C₂³	1	48	yes	—
62	C₂²×C₄×D₁₃	C₂³	1	12	yes	—
63	C₂²×C₄×D₁₃	C₂³	1	12	yes	—
64	C₂²×C₄×D₁₃	C₂³	1	12	yes	—
65	C₂²×C₄×D₁₃	C₂³	1	12	yes	—
66	C₂²×C₄×D₁₃	C₂³	1	64	yes	—
67	C₁₃×#117	C₂³	1	64	yes	complemented
68	C₂×C₁₃×C₄⋊C₄	C₂³	1	24	yes	complemented
69	C₂×C₁₃×C₂²⋊C₄	C₂³	1	24	yes	—
70	C₂×C₄²×C₁₃	C₂³	1	24	yes	complemented
71	C₂×C₂²⋊Dic₁₃	C₂³	1	24	yes	—
72	C₂×#6103	C₂³	1	48	yes	—
73	#88180	C₂³	1	64	yes	complemented
74	C₂×C₄⋊Dic₁₃	C₂³	1	24	yes	complemented
75	C₂×#6101	C₂³	1	48	yes	complemented
76	C₂×C₄×Dic₁₃	C₂³	1	24	yes	complemented
77	C₂×C₄×Dic₁₃	C₂³	1	48	yes	complemented
78	#88146	C₂³	1	128	yes	complemented
79	C₄⋊C₄×D₁₃	C₂³	1	128	yes	complemented
80	C₂²⋊C₄×D₁₃	C₂³	1	128	yes	—
81	#88131	C₂³	1	128	yes	complemented
82	#88126	C₂³	1	128	yes	complemented
83	C₄²×D₁₃	C₂³	1	128	yes	complemented
84	C₂³×#117	—	13	1	no	maximal, Sylow
85	C₂⁴×C₁₃	—	2	8	no	—
86	C₂⁴×C₁₃	C₂²×C₄	1	8	yes	—
87	C₂⁴×C₁₃	C₂⁴	1	6	yes	—
88	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
89	C₂³×D₁₃	—	2	8	no	—
90	C₂³×D₁₃	—	2	128	no	—
91	C₂³×D₁₃	—	2	96	no	—
92	C₂³×D₁₃	C₂²×C₄	1	8	yes	—
93	C₂³×D₁₃	C₂²×C₄	1	96	yes	—
94	C₂³×D₁₃	C₂²×C₄	1	8	yes	—
95	C₂³×D₁₃	#41	1	16	yes	—
96	C₂³×D₁₃	C₂⁴	1	16	yes	—
97	C₂³×D₁₃	C₂⁴	1	6	yes	—
98	C₂³×D₁₃	C₂⁴	1	6	yes	—
99	C₂²×C₄×C₁₃	—	2	16	no	—
100	C₂²×C₄×C₁₃	C₂²×C₄	1	8	yes	—
101	C₂²×C₄×C₁₃	C₂²×C₄	1	8	yes	—
102	C₂²×C₄×C₁₃	C₂²×C₄	1	96	yes	complemented
103	C₂²×C₄×C₁₃	C₂⁴	1	24	yes	—
104	C₂²×C₄×C₁₃	C₂⁴	1	6	yes	—
105	C₂²×C₄×C₁₃	C₂⁴	1	6	yes	—
106	C₂²×C₄×C₁₃	C₂⁴	1	16	yes	—
107	C₂²×Dic₁₃	—	2	16	no	—
108	C₂²×Dic₁₃	C₂²×C₄	1	8	yes	—
109	C₂²×Dic₁₃	C₂²×C₄	1	8	yes	—
110	C₂²×Dic₁₃	C₂²×C₄	1	96	yes	complemented
111	C₂²×Dic₁₃	C₂⁴	1	24	yes	—
112	C₂²×Dic₁₃	C₂⁴	1	6	yes	—
113	C₂²×Dic₁₃	C₂⁴	1	6	yes	—
114	C₂²×Dic₁₃	C₂⁴	1	16	yes	—
115	C₂×C₄×D₁₃	—	2	192	no	—
116	C₂×C₄×D₁₃	C₂²×C₄	1	96	yes	—
117	C₂×C₄×D₁₃	C₂²×C₄	1	96	yes	—
118	C₂×C₄×D₁₃	C₂²×C₄	1	512	yes	complemented
119	C₂×C₄×D₁₃	C₂²×C₄	1	96	yes	complemented
120	C₂×C₄×D₁₃	C₂²×C₄	1	96	yes	complemented
121	C₂×C₄×D₁₃	C₂⁴	1	64	yes	—
122	C₂×C₄×D₁₃	C₂⁴	1	16	yes	—
123	C₂×C₄×D₁₃	C₂⁴	1	16	yes	—
124	C₂×C₄×D₁₃	C₂⁴	1	16	yes	—
125	C₂×C₄×D₁₃	C₂⁴	1	16	yes	—
126	C₁₃×C₄⋊C₄	C₂⁴	1	32	yes	complemented
127	C₁₃×C₂²⋊C₄	C₂⁴	1	32	yes	—
128	C₄²×C₁₃	C₂⁴	1	32	yes	complemented
129	C₂²⋊Dic₁₃	C₂⁴	1	32	yes	—
130	#6103	C₂⁴	1	64	yes	—
131	C₄⋊Dic₁₃	C₂⁴	1	32	yes	complemented
132	#6101	C₂⁴	1	64	yes	complemented
133	C₄×Dic₁₃	C₂⁴	1	32	yes	complemented
134	C₄×Dic₁₃	C₂⁴	1	64	yes	complemented
135	C₂⁵×C₄	—	13	1	no	—
136	C₂²×#117	—	13	2	no	—
137	C₂²×#117	—	13	1	no	—
138	C₂²×#117	—	13	48	no	—
139	C₂²×#117	—	13	2	no	—
140	C₂²×#117	—	13	2	no	—
141	C₂²×#117	D₁₃	1	1	yes	characteristic, direct product factor
142	C₂³×C₄⋊C₄	—	13	2	no	—
143	C₂³×C₂²⋊C₄	—	13	2	no	—
144	C₂³×C₄²	—	13	2	no	—
145	C₂³×C₁₃	—	2	32	no	—
146	C₂³×C₁₃	—	2	24	no	—
147	C₂³×C₁₃	C₂³×C₄	1	24	yes	—
148	C₂³×C₁₃	C₂³×C₄	1	4	yes	—
149	C₂³×C₁₃	C₂×#41	1	8	yes	—
150	C₂³×C₁₃	C₂⁵	1	4	yes	—
151	C₂³×C₁₃	C₂⁵	1	3	yes	—
152	C₂²×D₁₃	—	2	32	no	—
153	C₂²×D₁₃	—	2	24	no	—
154	C₂²×D₁₃	—	2	384	no	—
155	C₂²×D₁₃	—	2	64	no	—
156	C₂²×D₁₃	#117	1	64	yes	direct product factor
157	C₂²×D₁₃	C₂³×C₄	1	24	yes	—
158	C₂²×D₁₃	C₂³×C₄	1	64	yes	—
159	C₂²×D₁₃	C₂³×C₄	1	24	yes	—
160	C₂²×D₁₃	C₂×#41	1	48	yes	—
161	C₂²×D₁₃	C₂⁵	1	4	yes	—
162	C₂²×D₁₃	C₂⁵	1	4	yes	—
163	C₂×C₄×C₁₃	—	2	48	no	—
164	C₂×C₄×C₁₃	C₂³×C₄	1	24	yes	—
165	C₂×C₄×C₁₃	C₂³×C₄	1	24	yes	—
166	C₂×C₄×C₁₃	C₂³×C₄	1	64	yes	complemented
167	C₂×C₄×C₁₃	C₂⁵	1	16	yes	—
168	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
169	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
170	C₂×Dic₁₃	—	2	48	no	—
171	C₂×Dic₁₃	C₂³×C₄	1	24	yes	—
172	C₂×Dic₁₃	C₂³×C₄	1	24	yes	—
173	C₂×Dic₁₃	C₂³×C₄	1	64	yes	complemented
174	C₂×Dic₁₃	C₂⁵	1	16	yes	—
175	C₂×Dic₁₃	C₂⁵	1	4	yes	—
176	C₂×Dic₁₃	C₂⁵	1	4	yes	—
177	C₄×D₁₃	—	2	128	no	—
178	C₄×D₁₃	C₂³×C₄	1	64	yes	—
179	C₄×D₁₃	C₂³×C₄	1	64	yes	—
180	C₄×D₁₃	C₂³×C₄	1	64	yes	complemented
181	C₄×D₁₃	C₂³×C₄	1	64	yes	complemented
182	C₂⁶	—	13	1	no	—
183	C₂⁴×C₄	—	13	1	no	—
184	C₂⁴×C₄	—	13	32	no	—
185	C₂⁴×C₄	—	13	1	no	—
186	C₂⁴×C₄	—	13	24	no	—
187	C₂⁴×C₄	—	13	1	no	—
188	C₂⁴×C₄	—	13	1	no	—
189	C₂⁴×C₄	—	13	1	no	—
190	C₂⁴×C₄	—	13	4	no	—
191	C₂⁴×C₄	C₂×D₁₃	1	1	yes	characteristic
192	C₂×#117	—	13	24	no	—
193	C₂×#117	—	13	256	no	—
194	C₂×#117	—	13	48	no	—
195	C₂×#117	—	13	48	no	—
196	C₂×#117	—	13	48	no	—
197	C₂×#117	C₂×D₁₃	1	24	yes	direct product factor
198	C₂²×C₄⋊C₄	—	13	4	no	—
199	C₂²×C₄⋊C₄	—	13	2	no	—
200	C₂²×C₄⋊C₄	—	13	48	no	—
201	C₂²×C₄⋊C₄	C₂×D₁₃	1	2	yes	complemented
202	C₂²×C₂²⋊C₄	—	13	2	no	—
203	C₂²×C₂²⋊C₄	—	13	4	no	—
204	C₂²×C₂²⋊C₄	—	13	48	no	—
205	C₂²×C₂²⋊C₄	C₂×D₁₃	1	2	yes	—
206	C₂²×C₄²	—	13	4	no	—
207	C₂²×C₄²	—	13	2	no	—
208	C₂²×C₄²	—	13	48	no	—
209	C₂²×C₄²	C₂×D₁₃	1	2	yes	complemented
210	C₂²×C₁₃	—	2	8	no	—
211	C₂²×C₁₃	—	2	48	no	—
212	C₂²×C₁₃	C₂×#117	1	16	yes	complemented
213	C₂²×C₁₃	C₂⁴×C₄	1	8	yes	—
214	C₂²×C₁₃	C₂⁴×C₄	1	6	yes	—
215	C₂²×C₁₃	C₂²×#41	1	12	yes	—
216	C₂²×C₁₃	C₂⁶	1	1	yes	characteristic
217	C₂×D₁₃	—	2	8	no	—
218	C₂×D₁₃	—	2	48	no	—
219	C₂×D₁₃	—	2	128	no	—
220	C₂×D₁₃	C₂×#117	1	96	yes	direct product factor
221	C₂×D₁₃	C₂⁴×C₄	1	8	yes	—
222	C₂×D₁₃	C₂⁴×C₄	1	8	yes	—
223	C₂×D₁₃	C₂²×#41	1	16	yes	—
224	C₄×C₁₃	—	2	16	no	—
225	C₄×C₁₃	C₂⁴×C₄	1	8	yes	—
226	C₄×C₁₃	C₂⁴×C₄	1	8	yes	—
227	Dic₁₃	—	2	16	no	—
228	Dic₁₃	C₂⁴×C₄	1	8	yes	—
229	Dic₁₃	C₂⁴×C₄	1	8	yes	—
230	C₂⁵	—	13	1	no	—
231	C₂⁵	—	13	16	no	—
232	C₂⁵	—	13	12	no	—
233	C₂⁵	—	13	1	no	—
234	C₂⁵	—	26	16	no	—
235	C₂⁵	C₂²×D₁₃	1	1	yes	characteristic
236	C₂³×C₄	—	13	16	no	—
237	C₂³×C₄	—	13	1	no	—
238	C₂³×C₄	—	13	12	no	—
239	C₂³×C₄	—	13	1	no	—
240	C₂³×C₄	—	13	16	no	—
241	C₂³×C₄	—	13	16	no	—
242	C₂³×C₄	—	13	16	no	—
243	C₂³×C₄	—	13	16	no	—
244	C₂³×C₄	—	13	384	no	—
245	C₂³×C₄	—	13	12	no	—
246	C₂³×C₄	—	13	12	no	—
247	C₂³×C₄	—	13	12	no	—
248	C₂³×C₄	—	13	64	no	—
249	C₂³×C₄	—	13	12	no	—
250	C₂³×C₄	—	13	4	no	—
251	C₂³×C₄	—	13	48	no	—
252	C₂³×C₄	—	26	32	no	—
253	C₂³×C₄	C₄×D₁₃	1	16	yes	complemented
254	C₂³×C₄	C₂²×D₁₃	1	4	yes	—
255	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
256	C₂³×C₄	C₂²×D₁₃	1	12	yes	—
257	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
258	#117	—	13	64	no	—
259	#117	—	13	128	no	—
260	#117	—	13	128	no	—
261	#117	—	13	128	no	—
262	#117	C₂²×D₁₃	1	64	yes	direct product factor
263	C₂×C₄⋊C₄	—	13	48	no	—
264	C₂×C₄⋊C₄	—	13	24	no	—
265	C₂×C₄⋊C₄	—	13	128	no	—
266	C₂×C₄⋊C₄	C₂²×D₁₃	1	24	yes	complemented
267	C₂×C₂²⋊C₄	—	13	24	no	—
268	C₂×C₂²⋊C₄	—	13	48	no	—
269	C₂×C₂²⋊C₄	—	13	128	no	—
270	C₂×C₂²⋊C₄	C₂²×D₁₃	1	24	yes	—
271	C₂×C₄²	—	13	48	no	—
272	C₂×C₄²	—	13	24	no	—
273	C₂×C₄²	—	13	128	no	—
274	C₂×C₄²	C₂²×D₁₃	1	24	yes	complemented
275	C₂×C₁₃	—	2	8	no	—
276	C₂×C₁₃	C₂²×#117	1	12	yes	complemented
277	C₂×C₁₃	C₂⁵×C₄	1	1	yes	characteristic
278	C₂×C₁₃	C₂³×#41	1	2	yes	—
279	D₁₃	—	2	8	no	—
280	D₁₃	C₂²×#117	1	16	yes	direct product factor
281	C₂⁴	—	2	8	no	—
282	C₂⁴	—	13	8	no	—
283	C₂⁴	—	13	16	no	—
284	C₂⁴	—	13	6	no	—
285	C₂⁴	—	13	96	no	—
286	C₂⁴	—	13	8	no	—
287	C₂⁴	—	13	16	no	—
288	C₂⁴	—	13	6	no	—
289	C₂⁴	—	26	128	no	—
290	C₂⁴	—	26	96	no	—
291	C₂⁴	—	26	8	no	—
292	C₂⁴	C₂×C₄×D₁₃	1	8	yes	—
293	C₂⁴	C₂³×D₁₃	1	6	yes	—
294	C₂⁴	C₂³×D₁₃	1	1	yes	characteristic
295	C₂²×C₄	—	2	16	no	—
296	C₂²×C₄	—	13	8	no	—
297	C₂²×C₄	—	13	8	no	—
298	C₂²×C₄	—	13	96	no	—
299	C₂²×C₄	—	13	6	no	—
300	C₂²×C₄	—	13	6	no	—
301	C₂²×C₄	—	13	16	no	—
302	C₂²×C₄	—	13	96	no	—
303	C₂²×C₄	—	13	96	no	—
304	C₂²×C₄	—	13	96	no	—
305	C₂²×C₄	—	13	96	no	—
306	C₂²×C₄	—	13	512	no	—
307	C₂²×C₄	—	13	16	no	—
308	C₂²×C₄	—	13	16	no	—
309	C₂²×C₄	—	13	16	no	—
310	C₂²×C₄	—	13	16	no	—
311	C₂²×C₄	—	13	24	no	—
312	C₂²×C₄	—	13	64	no	—
313	C₂²×C₄	—	26	192	no	—
314	C₂²×C₄	—	26	16	no	—
315	C₂²×C₄	C₂×C₄×D₁₃	1	8	yes	—
316	C₂²×C₄	C₂×C₄×D₁₃	1	8	yes	—
317	C₂²×C₄	C₂×C₄×D₁₃	1	96	yes	complemented
318	C₂²×C₄	C₂³×D₁₃	1	24	yes	—
319	C₂²×C₄	C₂³×D₁₃	1	6	yes	—
320	C₂²×C₄	C₂³×D₁₃	1	6	yes	—
321	C₂²×C₄	C₂³×D₁₃	1	16	yes	—
322	C₄⋊C₄	—	13	64	no	—
323	C₄⋊C₄	—	13	32	no	—
324	C₄⋊C₄	C₂³×D₁₃	1	32	yes	complemented
325	C₂²⋊C₄	—	13	32	no	—
326	C₂²⋊C₄	—	13	64	no	—
327	C₂²⋊C₄	C₂³×D₁₃	1	32	yes	—
328	C₄²	—	13	64	no	—
329	C₄²	—	13	32	no	—
330	C₄²	C₂³×D₁₃	1	32	yes	complemented
331	C₁₃	C₂³×#117	1	1	yes	characteristic, complemented, Sylow
332	C₂³	—	2	32	no	—
333	C₂³	—	2	24	no	—
334	C₂³	—	13	64	no	—
335	C₂³	—	13	24	no	—
336	C₂³	—	13	48	no	—
337	C₂³	—	13	4	no	—
338	C₂³	—	13	64	no	—
339	C₂³	—	13	24	no	—
340	C₂³	—	13	4	no	—
341	C₂³	—	26	384	no	—
342	C₂³	—	26	64	no	—
343	C₂³	—	26	32	no	—
344	C₂³	—	26	24	no	—
345	C₂³	C₂²×C₄×D₁₃	1	24	yes	—
346	C₂³	C₂²×C₄×D₁₃	1	4	yes	—
347	C₂³	#41×D₁₃	1	8	yes	—
348	C₂³	C₂⁴×D₁₃	1	4	yes	—
349	C₂³	C₂⁴×D₁₃	1	3	yes	—
350	C₂×C₄	—	2	48	no	—
351	C₂×C₄	—	13	24	no	—
352	C₂×C₄	—	13	24	no	—
353	C₂×C₄	—	13	64	no	—
354	C₂×C₄	—	13	4	no	—
355	C₂×C₄	—	13	4	no	—
356	C₂×C₄	—	13	64	no	—
357	C₂×C₄	—	13	64	no	—
358	C₂×C₄	—	13	64	no	—
359	C₂×C₄	—	13	64	no	—
360	C₂×C₄	—	13	16	no	—
361	C₂×C₄	—	26	128	no	—
362	C₂×C₄	—	26	48	no	—
363	C₂×C₄	C₂²×C₄×D₁₃	1	24	yes	—
364	C₂×C₄	C₂²×C₄×D₁₃	1	24	yes	—
365	C₂×C₄	C₂²×C₄×D₁₃	1	64	yes	complemented
366	C₂×C₄	C₂⁴×D₁₃	1	16	yes	—
367	C₂×C₄	C₂⁴×D₁₃	1	4	yes	—
368	C₂×C₄	C₂⁴×D₁₃	1	4	yes	—
369	C₂²	—	2	48	no	—
370	C₂²	—	2	8	no	—
371	C₂²	—	13	96	no	—
372	C₂²	—	13	8	no	—
373	C₂²	—	13	16	no	—
374	C₂²	—	13	8	no	—
375	C₂²	—	26	128	no	—
376	C₂²	—	26	48	no	—
377	C₂²	—	26	8	no	—
378	C₂²	D₁₃×#117	1	16	yes	direct product factor
379	C₂²	C₂³×C₄×D₁₃	1	8	yes	—
380	C₂²	C₂³×C₄×D₁₃	1	6	yes	—
381	C₂²	C₂×#41×D₁₃	1	12	yes	—
382	C₂²	C₂⁵×D₁₃	1	1	yes	characteristic
383	C₄	—	2	16	no	—
384	C₄	—	13	8	no	—
385	C₄	—	13	8	no	—
386	C₄	—	26	16	no	—
387	C₄	C₂³×C₄×D₁₃	1	8	yes	—
388	C₄	C₂³×C₄×D₁₃	1	8	yes	—
389	C₂	—	2	8	no	—
390	C₂	—	13	16	no	—
391	C₂	—	26	8	no	—
392	C₂	C₂×D₁₃×#117	1	12	yes	direct product factor
393	C₂	C₂⁴×C₄×D₁₃	1	1	yes	characteristic
394	C₂	C₂²×#41×D₁₃	1	2	yes	—

	subgroup	G/H
center	C₂³×C₄	C₂²×D₁₃
commutator	C₂×C₁₃	C₂⁵×C₄
Frattini	C₂²	C₂⁵×D₁₃
Fitting	C₂²×C₁₃×#117	C₂
socle	C₂⁴×C₁₃	C₂⁴
prime radical	C₂⁵×D₁₃	C₂²
cosocle	C₂²×C₁₃	C₂⁶
hypercenter	C₂²×#117	D₁₃
hypocenter	C₁₃	C₂³×#117
LCS	G ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂³×C₄ ◁ C₂²×#117

Complements

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

N	H ≅ G/N	type
2. C₂²×#88180	C₂	semidirect
3. C₂²×#88146	C₂	semidirect
4. C₂²×#88126	C₂	semidirect
5. C₂²×#88131	C₂	semidirect
6. C₂×D₁₃×#117	C₂	direct (N × H)
7. C₂²×C₄⋊C₄×D₁₃	C₂	semidirect
9. C₂²×C₄²×D₁₃	C₂	semidirect
10. C₂²×C₁₃×#117	C₂	semidirect
14. C₂³×C₄×D₁₃	C₄	semidirect
21. C₂×C₁₃×#117	C₂²	semidirect
22. C₂²×C₁₃×C₄⋊C₄	C₂²	semidirect
24. C₂²×C₄²×C₁₃	C₂²	semidirect
27. C₂×#88180	C₂²	semidirect
28. C₂²×C₄⋊Dic₁₃	C₂²	semidirect
29. C₂²×#6101	C₂²	semidirect
30. C₂²×C₄×Dic₁₃	C₂²	semidirect
31. C₂²×C₄×Dic₁₃	C₂²	semidirect
32. D₁₃×#117	C₂²	direct (N × H)
33. C₂×#88146	C₂²	semidirect
34. C₂×C₄⋊C₄×D₁₃	C₂²	semidirect
36. C₂×#88131	C₂²	semidirect
37. C₂×#88126	C₂²	semidirect
38. C₂×C₄²×D₁₃	C₂²	semidirect
45. C₂³×C₄×C₁₃	C₂×C₄	semidirect
50. C₂³×Dic₁₃	C₂×C₄	semidirect
58. C₂²×C₄×D₁₃	C₂×C₄	semidirect
59. C₂²×C₄×D₁₃	C₂×C₄	semidirect
60. C₂²×C₄×D₁₃	C₂×C₄	semidirect
67. C₁₃×#117	C₂³	semidirect
68. C₂×C₁₃×C₄⋊C₄	C₂³	semidirect
70. C₂×C₄²×C₁₃	C₂³	semidirect
73. #88180	C₂³	semidirect
74. C₂×C₄⋊Dic₁₃	C₂³	semidirect
75. C₂×#6101	C₂³	semidirect
76. C₂×C₄×Dic₁₃	C₂³	semidirect
77. C₂×C₄×Dic₁₃	C₂³	semidirect
78. #88146	C₂³	semidirect
79. C₄⋊C₄×D₁₃	C₂³	semidirect
81. #88131	C₂³	semidirect
82. #88126	C₂³	semidirect
83. C₄²×D₁₃	C₂³	semidirect
102. C₂²×C₄×C₁₃	C₂²×C₄	semidirect
110. C₂²×Dic₁₃	C₂²×C₄	semidirect
118. C₂×C₄×D₁₃	C₂²×C₄	semidirect
119. C₂×C₄×D₁₃	C₂²×C₄	semidirect
120. C₂×C₄×D₁₃	C₂²×C₄	semidirect
126. C₁₃×C₄⋊C₄	C₂⁴	semidirect
128. C₄²×C₁₃	C₂⁴	semidirect
131. C₄⋊Dic₁₃	C₂⁴	semidirect
132. #6101	C₂⁴	semidirect
133. C₄×Dic₁₃	C₂⁴	semidirect
134. C₄×Dic₁₃	C₂⁴	semidirect
141. C₂²×#117	D₁₃	direct (N × H)
156. C₂²×D₁₃	#117	direct (N × H)
166. C₂×C₄×C₁₃	C₂³×C₄	semidirect
173. C₂×Dic₁₃	C₂³×C₄	semidirect
180. C₄×D₁₃	C₂³×C₄	semidirect
181. C₄×D₁₃	C₂³×C₄	semidirect
197. C₂×#117	C₂×D₁₃	direct (N × H)
201. C₂²×C₄⋊C₄	C₂×D₁₃	semidirect
209. C₂²×C₄²	C₂×D₁₃	semidirect
212. C₂²×C₁₃	C₂×#117	semidirect
220. C₂×D₁₃	C₂×#117	direct (N × H)
253. C₂³×C₄	C₄×D₁₃	semidirect
262. #117	C₂²×D₁₃	direct (N × H)
266. C₂×C₄⋊C₄	C₂²×D₁₃	semidirect
274. C₂×C₄²	C₂²×D₁₃	semidirect
276. C₂×C₁₃	C₂²×#117	semidirect
280. D₁₃	C₂²×#117	direct (N × H)
317. C₂²×C₄	C₂×C₄×D₁₃	semidirect
324. C₄⋊C₄	C₂³×D₁₃	semidirect
330. C₄²	C₂³×D₁₃	semidirect
331. C₁₃	C₂³×#117	semidirect
365. C₂×C₄	C₂²×C₄×D₁₃	semidirect
378. C₂²	D₁₃×#117	direct (N × H)
392. C₂	C₂×D₁₃×#117	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂⁴×C₄×D₁₃	2
C₂²×#88180	2
C₂²×#88146	2
C₂²×#88126	2
C₂²×#88131	2
C₂×D₁₃×#117	2
C₂²×C₄⋊C₄×D₁₃	2
C₂²×C₂²⋊C₄×D₁₃	2
C₂²×C₄²×D₁₃	2
C₂²×C₁₃×#117	2
C₂³×#117	13

Subgroups — C22×D13×#117 #16769475

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×D₁₃×#117 #16769475