Subgroups — C₂×C₁₃×#3156 #15746981

Order 3328.

3150 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₃×#137	C₂	1	2	yes	maximal, complemented
2	C₂²×C₁₃×#135	C₂	1	1	yes	maximal, characteristic
3	C₂³×C₁₃×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₁₃×#536	C₂	1	2	yes	maximal, complemented
5	C₁₃×#3156	C₂	1	16	yes	maximal, direct product factor
6	C₂×C₁₃×#497	C₂	1	4	yes	maximal, complemented
7	C₂×C₁₃×#495	C₂	1	2	yes	maximal, complemented
8	C₂×C₁₃×#494	C₂	1	2	yes	maximal, complemented
9	C₂×C₁₃×#405	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×C₁₃×#41	C₂²	1	2	yes	—
11	C₂³×Q₈×C₁₃	C₂²	1	2	yes	—
12	C₂×C₁₃×#137	—	2	16	no	—
13	C₂×C₁₃×#137	C₂²	1	16	yes	complemented
14	C₂×C₁₃×#135	—	2	8	no	—
15	C₂×C₁₃×#135	C₂²	1	8	yes	—
16	C₂²×C₁₃×Q₁₆	—	2	8	no	—
17	C₂²×C₁₃×Q₁₆	C₂²	1	2	yes	—
18	C₂²×C₁₃×Q₁₆	C₂²	1	2	yes	—
19	C₂²×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
20	C₂²×C₁₃×Q₁₆	C₂²	1	4	yes	—
21	C₂²×C₁₃×Q₁₆	C₂²	1	8	yes	complemented
22	C₂²×C₁₃×SD₁₆	C₂²	1	2	yes	—
23	C₂²×C₁₃×SD₁₆	C₂²	1	4	yes	—
24	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic
25	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
26	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
27	C₁₃×#536	—	2	8	no	—
28	C₁₃×#536	C₂²	1	16	yes	complemented
29	C₂×C₁₃×C₄⋊Q₈	C₂²	1	4	yes	—
30	C₂×C₁₃×#124	C₂²	1	4	yes	—
31	C₂×C₁₃×#123	—	2	4	no	—
32	C₂×C₁₃×C₂²⋊Q₈	—	2	4	no	—
33	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
34	C₁₃×#497	C₂²	1	32	yes	complemented
35	C₁₃×#495	C₂²	1	16	yes	complemented
36	C₁₃×#494	C₂²	1	16	yes	complemented
37	C₁₃×#405	C₂²	1	8	yes	complemented
38	C₂×C₁₃×#97	C₂²	1	2	yes	—
39	C₂×C₄×C₈×C₁₃	C₂²	1	2	yes	—
40	C₂×C₁₃×#41	—	2	4	no	—
41	C₂×C₁₃×#41	—	2	8	no	—
42	C₂×C₁₃×#41	—	2	8	no	—
43	C₂×C₁₃×#41	C₂³	1	8	yes	—
44	C₂²×Q₈×C₁₃	—	2	2	no	—
45	C₂²×Q₈×C₁₃	—	2	4	no	—
46	C₂²×Q₈×C₁₃	—	2	8	no	—
47	C₂²×Q₈×C₁₃	—	2	8	no	—
48	C₂²×Q₈×C₁₃	C₂³	1	4	yes	—
49	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
50	C₂²×Q₈×C₁₃	C₂³	1	8	yes	—
51	C₂²×D₄×C₁₃	—	2	2	no	—
52	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
53	C₂³×C₄×C₁₃	—	2	2	no	—
54	C₂³×C₄×C₁₃	—	2	2	no	—
55	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
56	C₁₃×#137	—	2	64	no	—
57	C₁₃×#135	—	2	32	no	—
58	C₂×C₁₃×Q₁₆	—	2	8	no	—
59	C₂×C₁₃×Q₁₆	—	2	8	no	—
60	C₂×C₁₃×Q₁₆	—	2	32	no	—
61	C₂×C₁₃×Q₁₆	—	2	4	no	—
62	C₂×C₁₃×Q₁₆	—	2	16	no	—
63	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	—
64	C₂×C₁₃×Q₁₆	C₂³	1	8	yes	—
65	C₂×C₁₃×Q₁₆	C₂³	1	16	yes	—
66	C₂×C₁₃×Q₁₆	C₂³	1	8	yes	—
67	C₂×C₁₃×SD₁₆	—	2	8	no	—
68	C₂×C₁₃×SD₁₆	—	2	16	no	—
69	C₂×C₁₃×SD₁₆	C₂³	1	16	yes	—
70	C₂×C₁₃×SD₁₆	C₂³	1	8	yes	—
71	C₂×C₁₃×D₈	—	2	4	no	—
72	C₂×C₁₃×D₈	C₂³	1	4	yes	—
73	C₂×C₁₃×M₁₆	D₄	1	8	yes	—
74	C₂×C₁₃×M₁₆	C₂³	1	4	yes	—
75	C₂²×C₈×C₁₃	D₄	1	8	yes	—
76	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
77	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
78	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
79	C₂²×C₈×C₁₃	C₂³	1	4	yes	—
80	C₁₃×C₄⋊Q₈	—	2	8	no	—
81	C₁₃×C₄⋊Q₈	C₂³	1	16	yes	—
82	C₁₃×#124	—	2	8	no	—
83	C₁₃×#124	C₂³	1	16	yes	—
84	C₁₃×#123	—	2	32	no	—
85	C₁₃×C₂²⋊Q₈	—	2	32	no	—
86	C₁₃×#117	D₄	1	4	yes	—
87	C₁₃×#117	C₂³	1	4	yes	—
88	C₂×C₁₃×C₄⋊C₄	—	2	8	no	—
89	C₂×C₁₃×C₄⋊C₄	D₄	1	2	yes	—
90	C₂×C₁₃×C₂²⋊C₄	—	2	8	no	—
91	C₂×C₁₃×C₂²⋊C₄	D₄	1	2	yes	—
92	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
93	C₁₃×#97	C₂³	1	8	yes	—
94	C₄×C₈×C₁₃	C₂³	1	8	yes	—
95	C₂×#3156	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
96	C₂⁴×C₁₃	—	2	2	no	—
97	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
98	C₁₃×#41	—	2	16	no	—
99	C₁₃×#41	—	2	16	no	—
100	C₁₃×#41	—	4	16	no	—
101	C₂×Q₈×C₁₃	—	2	8	no	—
102	C₂×Q₈×C₁₃	—	2	4	no	—
103	C₂×Q₈×C₁₃	—	2	2	no	—
104	C₂×Q₈×C₁₃	—	2	8	no	—
105	C₂×Q₈×C₁₃	—	2	4	no	—
106	C₂×Q₈×C₁₃	—	2	8	no	—
107	C₂×Q₈×C₁₃	—	2	16	no	—
108	C₂×Q₈×C₁₃	—	2	4	no	—
109	C₂×Q₈×C₁₃	—	2	16	no	—
110	C₂×Q₈×C₁₃	—	4	8	no	—
111	C₂×Q₈×C₁₃	—	4	16	no	—
112	C₂×Q₈×C₁₃	C₂⁴	1	8	yes	—
113	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
114	C₂×D₄×C₁₃	—	2	8	no	—
115	C₂×D₄×C₁₃	—	2	4	no	—
116	C₂×D₄×C₁₃	—	2	4	no	—
117	C₂×D₄×C₁₃	—	2	2	no	—
118	C₂×D₄×C₁₃	—	4	8	no	—
119	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
120	C₂²×C₄×C₁₃	—	2	8	no	—
121	C₂²×C₄×C₁₃	—	2	4	no	—
122	C₂²×C₄×C₁₃	—	2	2	no	—
123	C₂²×C₄×C₁₃	—	2	8	no	—
124	C₂²×C₄×C₁₃	—	4	8	no	—
125	C₂²×C₄×C₁₃	—	4	8	no	—
126	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
127	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
128	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
129	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
130	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
131	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
132	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
133	C₁₃×Q₁₆	—	2	16	no	—
134	C₁₃×Q₁₆	—	2	16	no	—
135	C₁₃×Q₁₆	—	2	8	no	—
136	C₁₃×Q₁₆	—	2	32	no	—
137	C₁₃×SD₁₆	—	2	16	no	—
138	C₁₃×SD₁₆	—	2	32	no	—
139	C₁₃×D₈	—	2	8	no	—
140	C₁₃×M₁₆	C₂×D₄	1	16	yes	—
141	C₂×C₈×C₁₃	C₂×D₄	1	4	yes	—
142	C₂×C₈×C₁₃	C₂×D₄	1	4	yes	—
143	C₂×C₈×C₁₃	C₂×D₄	1	16	yes	—
144	C₂×C₈×C₁₃	C₂×D₄	1	8	yes	—
145	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
146	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
147	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
148	C₁₃×C₄⋊C₄	—	2	32	no	—
149	C₁₃×C₄⋊C₄	C₂×D₄	1	8	yes	—
150	C₁₃×C₂²⋊C₄	—	2	32	no	—
151	C₁₃×C₂²⋊C₄	C₂×D₄	1	8	yes	—
152	C₄²×C₁₃	C₂×D₄	1	4	yes	—
153	C₄²×C₁₃	C₂⁴	1	4	yes	—
154	C₂²×#137	C₂×C₁₃	1	2	yes	complemented
155	C₂²×#135	C₂×C₁₃	1	1	yes	characteristic
156	C₂³×Q₁₆	C₂×C₁₃	1	1	yes	characteristic, complemented
157	C₂×#536	C₂×C₁₃	1	2	yes	complemented
158	#3156	C₂×C₁₃	1	16	yes	direct product factor
159	C₂×#497	C₂×C₁₃	1	4	yes	complemented
160	C₂×#495	C₂×C₁₃	1	2	yes	complemented
161	C₂×#494	C₂×C₁₃	1	2	yes	complemented
162	C₂×#405	C₂×C₁₃	1	1	yes	characteristic, complemented
163	C₂³×C₁₃	—	2	4	no	—
164	C₂³×C₁₃	—	2	4	no	—
165	C₂³×C₁₃	—	4	4	no	—
166	C₂³×C₁₃	—	4	8	no	—
167	C₂³×C₁₃	#127	1	4	yes	—
168	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
169	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
170	Q₈×C₁₃	—	2	8	no	—
171	Q₈×C₁₃	—	2	4	no	—
172	Q₈×C₁₃	—	2	8	no	—
173	Q₈×C₁₃	—	2	4	no	—
174	Q₈×C₁₃	—	4	16	no	—
175	Q₈×C₁₃	—	4	8	no	—
176	Q₈×C₁₃	—	4	4	no	—
177	D₄×C₁₃	—	2	4	no	—
178	D₄×C₁₃	—	2	4	no	—
179	D₄×C₁₃	—	4	16	no	—
180	D₄×C₁₃	—	4	4	no	—
181	C₂×C₄×C₁₃	—	2	8	no	—
182	C₂×C₄×C₁₃	—	2	8	no	—
183	C₂×C₄×C₁₃	—	2	4	no	—
184	C₂×C₄×C₁₃	—	4	4	no	—
185	C₂×C₄×C₁₃	—	4	16	no	—
186	C₂×C₄×C₁₃	—	4	8	no	—
187	C₂×C₄×C₁₃	—	4	16	no	—
188	C₂×C₄×C₁₃	#127	1	4	yes	—
189	C₂×C₄×C₁₃	#127	1	8	yes	—
190	C₂×C₄×C₁₃	C₂²×D₄	1	8	yes	—
191	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
192	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
193	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
194	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
195	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
196	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
197	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
198	C₈×C₁₃	C₂²×D₄	1	4	yes	—
199	C₈×C₁₃	C₂²×D₄	1	4	yes	—
200	C₈×C₁₃	C₂²×D₄	1	8	yes	—
201	C₂²×#41	C₂²×C₁₃	1	2	yes	—
202	C₂³×Q₈	C₂²×C₁₃	1	2	yes	—
203	C₂×#137	—	2	16	no	—
204	C₂×#137	C₂²×C₁₃	1	16	yes	complemented
205	C₂×#135	—	2	8	no	—
206	C₂×#135	C₂²×C₁₃	1	8	yes	—
207	C₂²×Q₁₆	—	2	8	no	—
208	C₂²×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
209	C₂²×Q₁₆	C₂²×C₁₃	1	2	yes	—
210	C₂²×Q₁₆	C₂²×C₁₃	1	4	yes	—
211	C₂²×Q₁₆	C₂²×C₁₃	1	2	yes	—
212	C₂²×Q₁₆	C₂²×C₁₃	1	8	yes	complemented
213	C₂²×SD₁₆	C₂²×C₁₃	1	4	yes	—
214	C₂²×SD₁₆	C₂²×C₁₃	1	2	yes	—
215	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic
216	C₂²×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
217	C₂³×C₈	C₂²×C₁₃	1	1	yes	characteristic
218	#536	—	2	8	no	—
219	#536	C₂²×C₁₃	1	16	yes	complemented
220	C₂×C₄⋊Q₈	C₂²×C₁₃	1	4	yes	—
221	C₂×#124	C₂²×C₁₃	1	4	yes	—
222	C₂×#123	—	2	4	no	—
223	C₂×C₂²⋊Q₈	—	2	4	no	—
224	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
225	#497	C₂²×C₁₃	1	32	yes	complemented
226	#495	C₂²×C₁₃	1	16	yes	complemented
227	#494	C₂²×C₁₃	1	16	yes	complemented
228	#405	C₂²×C₁₃	1	8	yes	complemented
229	C₂×#97	C₂²×C₁₃	1	2	yes	—
230	C₂×C₄×C₈	C₂²×C₁₃	1	2	yes	—
231	C₂²×C₁₃	—	2	8	no	—
232	C₂²×C₁₃	—	2	4	no	—
233	C₂²×C₁₃	—	4	4	no	—
234	C₂²×C₁₃	—	4	8	no	—
235	C₂²×C₁₃	—	8	8	no	—
236	C₂²×C₁₃	C₂×#127	1	4	yes	—
237	C₂²×C₁₃	C₂×#127	1	2	yes	—
238	C₂²×C₁₃	#578	1	4	yes	—
239	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
240	C₄×C₁₃	—	2	8	no	—
241	C₄×C₁₃	—	4	4	no	—
242	C₄×C₁₃	—	4	8	no	—
243	C₄×C₁₃	C₂×#127	1	4	yes	—
244	C₄×C₁₃	C₂×#127	1	2	yes	—
245	C₄×C₁₃	C₂³×D₄	1	1	yes	characteristic
246	C₄×C₁₃	C₂³×D₄	1	1	yes	characteristic
247	C₂×#41	—	2	4	no	—
248	C₂×#41	—	2	8	no	—
249	C₂×#41	—	2	8	no	—
250	C₂×#41	C₂³×C₁₃	1	8	yes	—
251	C₂²×Q₈	—	2	2	no	—
252	C₂²×Q₈	—	2	4	no	—
253	C₂²×Q₈	—	2	8	no	—
254	C₂²×Q₈	—	2	8	no	—
255	C₂²×Q₈	C₂³×C₁₃	1	4	yes	—
256	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
257	C₂²×Q₈	C₂³×C₁₃	1	8	yes	—
258	C₂²×D₄	—	2	2	no	—
259	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
260	C₂³×C₄	—	2	2	no	—
261	C₂³×C₄	—	2	2	no	—
262	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
263	#137	—	2	64	no	—
264	#135	—	2	32	no	—
265	C₂×Q₁₆	—	2	8	no	—
266	C₂×Q₁₆	—	2	8	no	—
267	C₂×Q₁₆	—	2	32	no	—
268	C₂×Q₁₆	—	2	4	no	—
269	C₂×Q₁₆	—	2	16	no	—
270	C₂×Q₁₆	C₂³×C₁₃	1	8	yes	—
271	C₂×Q₁₆	C₂³×C₁₃	1	8	yes	—
272	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	—
273	C₂×Q₁₆	C₂³×C₁₃	1	16	yes	—
274	C₂×SD₁₆	—	2	8	no	—
275	C₂×SD₁₆	—	2	16	no	—
276	C₂×SD₁₆	C₂³×C₁₃	1	8	yes	—
277	C₂×SD₁₆	C₂³×C₁₃	1	16	yes	—
278	C₂×D₈	—	2	4	no	—
279	C₂×D₈	C₂³×C₁₃	1	4	yes	—
280	C₂×M₁₆	D₄×C₁₃	1	8	yes	—
281	C₂×M₁₆	C₂³×C₁₃	1	4	yes	—
282	C₂²×C₈	D₄×C₁₃	1	8	yes	—
283	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
284	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
285	C₂²×C₈	C₂³×C₁₃	1	4	yes	—
286	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
287	C₄⋊Q₈	—	2	8	no	—
288	C₄⋊Q₈	C₂³×C₁₃	1	16	yes	—
289	#124	—	2	8	no	—
290	#124	C₂³×C₁₃	1	16	yes	—
291	#123	—	2	32	no	—
292	C₂²⋊Q₈	—	2	32	no	—
293	#117	D₄×C₁₃	1	4	yes	—
294	#117	C₂³×C₁₃	1	4	yes	—
295	C₂×C₄⋊C₄	—	2	8	no	—
296	C₂×C₄⋊C₄	D₄×C₁₃	1	2	yes	—
297	C₂×C₂²⋊C₄	—	2	8	no	—
298	C₂×C₂²⋊C₄	D₄×C₁₃	1	2	yes	—
299	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
300	#97	C₂³×C₁₃	1	8	yes	—
301	C₄×C₈	C₂³×C₁₃	1	8	yes	—
302	C₂×C₁₃	—	2	4	no	—
303	C₂×C₁₃	—	8	4	no	—
304	C₂×C₁₃	#3156	1	4	yes	direct product factor
305	C₂×C₁₃	C₂²×#127	1	1	yes	characteristic
306	C₂×C₁₃	C₂×#578	1	2	yes	—
307	C₂⁴	—	2	2	no	—
308	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
309	#41	—	2	16	no	—
310	#41	—	2	16	no	—
311	#41	—	4	16	no	—
312	C₂×Q₈	—	2	8	no	—
313	C₂×Q₈	—	2	4	no	—
314	C₂×Q₈	—	2	2	no	—
315	C₂×Q₈	—	2	8	no	—
316	C₂×Q₈	—	2	4	no	—
317	C₂×Q₈	—	2	8	no	—
318	C₂×Q₈	—	2	16	no	—
319	C₂×Q₈	—	2	4	no	—
320	C₂×Q₈	—	2	16	no	—
321	C₂×Q₈	—	4	8	no	—
322	C₂×Q₈	—	4	16	no	—
323	C₂×Q₈	C₂⁴×C₁₃	1	8	yes	—
324	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
325	C₂×D₄	—	2	8	no	—
326	C₂×D₄	—	2	4	no	—
327	C₂×D₄	—	2	4	no	—
328	C₂×D₄	—	2	2	no	—
329	C₂×D₄	—	4	8	no	—
330	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
331	C₂²×C₄	—	2	4	no	—
332	C₂²×C₄	—	2	2	no	—
333	C₂²×C₄	—	2	8	no	—
334	C₂²×C₄	—	2	8	no	—
335	C₂²×C₄	—	4	8	no	—
336	C₂²×C₄	—	4	8	no	—
337	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
338	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
339	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
340	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
341	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
342	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
343	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
344	Q₁₆	—	2	16	no	—
345	Q₁₆	—	2	16	no	—
346	Q₁₆	—	2	8	no	—
347	Q₁₆	—	2	32	no	—
348	SD₁₆	—	2	16	no	—
349	SD₁₆	—	2	32	no	—
350	D₈	—	2	8	no	—
351	M₁₆	C₂×D₄×C₁₃	1	16	yes	—
352	C₂×C₈	C₂×D₄×C₁₃	1	4	yes	—
353	C₂×C₈	C₂×D₄×C₁₃	1	4	yes	—
354	C₂×C₈	C₂×D₄×C₁₃	1	16	yes	—
355	C₂×C₈	C₂×D₄×C₁₃	1	8	yes	—
356	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
357	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
358	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
359	C₄⋊C₄	—	2	32	no	—
360	C₄⋊C₄	C₂×D₄×C₁₃	1	8	yes	—
361	C₂²⋊C₄	—	2	32	no	—
362	C₂²⋊C₄	C₂×D₄×C₁₃	1	8	yes	—
363	C₄²	C₂×D₄×C₁₃	1	4	yes	—
364	C₄²	C₂⁴×C₁₃	1	4	yes	—
365	C₁₃	C₂×#3156	1	1	yes	characteristic, direct product factor, Sylow
366	C₂³	—	2	4	no	—
367	C₂³	—	2	4	no	—
368	C₂³	—	4	4	no	—
369	C₂³	—	4	8	no	—
370	C₂³	C₁₃×#127	1	4	yes	—
371	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
372	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
373	Q₈	—	2	8	no	—
374	Q₈	—	2	4	no	—
375	Q₈	—	2	8	no	—
376	Q₈	—	2	4	no	—
377	Q₈	—	4	16	no	—
378	Q₈	—	4	8	no	—
379	Q₈	—	4	4	no	—
380	D₄	—	2	4	no	—
381	D₄	—	2	4	no	—
382	D₄	—	4	16	no	—
383	D₄	—	4	4	no	—
384	C₂×C₄	—	2	8	no	—
385	C₂×C₄	—	2	8	no	—
386	C₂×C₄	—	2	4	no	—
387	C₂×C₄	—	4	4	no	—
388	C₂×C₄	—	4	16	no	—
389	C₂×C₄	—	4	8	no	—
390	C₂×C₄	—	4	16	no	—
391	C₂×C₄	C₁₃×#127	1	4	yes	—
392	C₂×C₄	C₁₃×#127	1	8	yes	—
393	C₂×C₄	C₂²×D₄×C₁₃	1	8	yes	—
394	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
395	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
396	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
397	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
398	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
399	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
400	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
401	C₈	C₂²×D₄×C₁₃	1	4	yes	—
402	C₈	C₂²×D₄×C₁₃	1	4	yes	—
403	C₈	C₂²×D₄×C₁₃	1	8	yes	—
404	C₂²	—	2	4	no	—
405	C₂²	—	2	8	no	—
406	C₂²	—	4	8	no	—
407	C₂²	—	4	4	no	—
408	C₂²	—	8	8	no	—
409	C₂²	C₂×C₁₃×#127	1	4	yes	—
410	C₂²	C₂×C₁₃×#127	1	2	yes	—
411	C₂²	C₁₃×#578	1	4	yes	—
412	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
413	C₄	—	2	8	no	—
414	C₄	—	4	4	no	—
415	C₄	—	4	8	no	—
416	C₄	C₂×C₁₃×#127	1	4	yes	—
417	C₄	C₂×C₁₃×#127	1	2	yes	—
418	C₄	C₂³×D₄×C₁₃	1	1	yes	characteristic
419	C₄	C₂³×D₄×C₁₃	1	1	yes	characteristic
420	C₂	—	2	4	no	—
421	C₂	—	8	4	no	—
422	C₂	C₁₃×#3156	1	4	yes	direct product factor
423	C₂	C₂²×C₁₃×#127	1	1	yes	characteristic
424	C₂	C₂×C₁₃×#578	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
prime radical	C₂²×C₁₃×#135	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂×C₁₃×#117 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×C₁₃×#137	C₂	semidirect
3. C₂³×C₁₃×Q₁₆	C₂	semidirect
4. C₂×C₁₃×#536	C₂	semidirect
5. C₁₃×#3156	C₂	direct (N × H)
6. C₂×C₁₃×#497	C₂	semidirect
7. C₂×C₁₃×#495	C₂	semidirect
8. C₂×C₁₃×#494	C₂	semidirect
9. C₂×C₁₃×#405	C₂	semidirect
13. C₂×C₁₃×#137	C₂²	semidirect
21. C₂²×C₁₃×Q₁₆	C₂²	semidirect
28. C₁₃×#536	C₂²	semidirect
34. C₁₃×#497	C₂²	semidirect
35. C₁₃×#495	C₂²	semidirect
36. C₁₃×#494	C₂²	semidirect
37. C₁₃×#405	C₂²	semidirect
95. C₂×#3156	C₁₃	direct (N × H)
154. C₂²×#137	C₂×C₁₃	semidirect
156. C₂³×Q₁₆	C₂×C₁₃	semidirect
157. C₂×#536	C₂×C₁₃	semidirect
158. #3156	C₂×C₁₃	direct (N × H)
159. C₂×#497	C₂×C₁₃	semidirect
160. C₂×#495	C₂×C₁₃	semidirect
161. C₂×#494	C₂×C₁₃	semidirect
162. C₂×#405	C₂×C₁₃	semidirect
204. C₂×#137	C₂²×C₁₃	semidirect
212. C₂²×Q₁₆	C₂²×C₁₃	semidirect
219. #536	C₂²×C₁₃	semidirect
225. #497	C₂²×C₁₃	semidirect
226. #495	C₂²×C₁₃	semidirect
227. #494	C₂²×C₁₃	semidirect
228. #405	C₂²×C₁₃	semidirect
304. C₂×C₁₃	#3156	direct (N × H)
365. C₁₃	C₂×#3156	direct (N × H)
422. C₂	C₁₃×#3156	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₁₃×#137	2
C₂²×C₁₃×#135	2
C₂³×C₁₃×Q₁₆	2
C₂×C₁₃×#536	2
C₁₃×#3156	2
C₂×C₁₃×#497	2
C₂×C₁₃×#495	2
C₂×C₁₃×#494	2
C₂×C₁₃×#405	2
C₂×#3156	13

Subgroups — C2×C13×#3156 #15746981

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#3156 #15746981