Subgroups — C₂×C₁₃×#3206 #15747116

Order 3328.

2414 conjugacy classes of subgroups.

The subgroup lattice has 448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#532	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₁₃×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3206	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₁₃×#492	C₂	1	2	yes	maximal, complemented
5	C₂×C₁₃×#487	C₂	1	2	yes	maximal, complemented
6	C₂×C₁₃×#461	C₂	1	4	yes	maximal, complemented
7	C₂×C₁₃×#448	C₂	1	4	yes	maximal, complemented
8	C₂×C₁₃×#431	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×C₁₃×#41	—	2	1	no	—
10	C₂³×Q₈×C₁₃	C₂²	1	2	yes	—
11	C₂²×C₁₃×SD₁₆	C₂²	1	8	yes	—
12	C₁₃×#532	—	2	4	no	—
13	C₁₃×#532	C₂²	1	8	yes	—
14	C₂×C₁₃×C₄⋊Q₈	—	2	1	no	—
15	C₂×C₁₃×C₄⋊Q₈	—	2	1	no	—
16	C₂×C₁₃×C₄⋊Q₈	—	2	4	no	—
17	C₂×C₁₃×C₄⋊Q₈	C₂²	1	2	yes	—
18	C₂×C₁₃×C₄⋊Q₈	C₂²	1	2	yes	—
19	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
20	C₂×C₁₃×C₄⋊Q₈	C₂²	1	8	yes	complemented
21	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
22	C₂×C₁₃×#124	—	2	1	no	—
23	C₂×C₁₃×#121	—	2	1	no	—
24	C₂×C₁₃×#121	C₂²	1	2	yes	—
25	C₂×C₄×D₄×C₁₃	—	2	1	no	—
26	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
27	C₂²×C₁₃×C₄⋊C₄	—	2	1	no	—
28	C₂²×C₁₃×C₄⋊C₄	—	2	1	no	—
29	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
30	C₁₃×#492	C₂²	1	16	yes	complemented
31	C₁₃×#487	C₂²	1	16	yes	complemented
32	C₁₃×#461	C₂²	1	32	yes	complemented
33	C₁₃×#448	C₂²	1	32	yes	complemented
34	C₁₃×#431	C₂²	1	8	yes	complemented
35	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
36	C₂×C₁₃×#103	C₂²	1	8	yes	—
37	C₂×C₁₃×C₂²⋊C₈	C₂²	1	2	yes	—
38	C₂×C₄×C₈×C₁₃	C₂²	1	2	yes	—
39	C₂×C₁₃×#41	—	2	8	no	—
40	C₂×C₁₃×#41	—	4	8	no	—
41	C₂²×Q₈×C₁₃	—	2	1	no	—
42	C₂²×Q₈×C₁₃	—	2	4	no	—
43	C₂²×Q₈×C₁₃	—	2	2	no	—
44	C₂²×Q₈×C₁₃	—	4	8	no	—
45	C₂²×Q₈×C₁₃	C₂³	1	4	yes	—
46	C₂²×Q₈×C₁₃	C₂³	1	8	yes	—
47	C₂²×D₄×C₁₃	—	2	2	no	—
48	C₂²×D₄×C₁₃	—	2	1	no	—
49	C₂²×D₄×C₁₃	—	2	1	no	—
50	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
51	C₂³×C₄×C₁₃	—	2	2	no	—
52	C₂³×C₄×C₁₃	—	2	2	no	—
53	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
54	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
55	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
56	C₂×C₁₃×SD₁₆	—	4	16	no	—
57	C₂×C₁₃×SD₁₆	C₂³	1	32	yes	—
58	C₂²×C₈×C₁₃	C₂³	1	4	yes	—
59	C₁₃×C₄⋊Q₈	—	2	4	no	—
60	C₁₃×C₄⋊Q₈	—	2	4	no	—
61	C₁₃×C₄⋊Q₈	—	2	8	no	—
62	C₁₃×C₄⋊Q₈	—	2	8	no	—
63	C₁₃×C₄⋊Q₈	—	2	2	no	—
64	C₁₃×C₄⋊Q₈	C₂³	1	8	yes	—
65	C₁₃×C₄⋊Q₈	C₂³	1	8	yes	—
66	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
67	C₁₃×#127	—	2	2	no	—
68	C₁₃×#127	C₂³	1	4	yes	—
69	C₁₃×#124	—	2	8	no	—
70	C₁₃×#121	—	2	8	no	—
71	C₁₃×#121	—	2	4	no	—
72	C₁₃×#121	C₂³	1	8	yes	—
73	C₄×D₄×C₁₃	—	2	8	no	—
74	C₄×D₄×C₁₃	—	2	4	no	—
75	C₄×D₄×C₁₃	C₂³	1	8	yes	—
76	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
77	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
78	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
79	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
80	C₂×C₁₃×C₄⋊C₄	—	2	8	no	—
81	C₂×C₁₃×C₄⋊C₄	—	2	8	no	—
82	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
83	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
84	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
85	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
86	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
87	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
88	C₂×C₄²×C₁₃	D₄	1	4	yes	—
89	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
90	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
91	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
92	C₁₃×C₄⋊C₈	C₂³	1	8	yes	—
93	C₁₃×#103	C₂³	1	32	yes	—
94	C₁₃×C₂²⋊C₈	C₂³	1	8	yes	—
95	C₄×C₈×C₁₃	C₂³	1	8	yes	—
96	C₂×#3206	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
97	C₂⁴×C₁₃	—	2	2	no	—
98	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
99	C₁₃×#41	—	4	32	no	—
100	C₂×Q₈×C₁₃	—	2	4	no	—
101	C₂×Q₈×C₁₃	—	2	8	no	—
102	C₂×Q₈×C₁₃	—	2	4	no	—
103	C₂×Q₈×C₁₃	—	2	16	no	—
104	C₂×Q₈×C₁₃	—	4	16	no	—
105	C₂×Q₈×C₁₃	—	4	8	no	—
106	C₂×Q₈×C₁₃	—	4	16	no	—
107	C₂×Q₈×C₁₃	—	4	4	no	—
108	C₂×Q₈×C₁₃	C₂⁴	1	8	yes	—
109	C₂×D₄×C₁₃	—	2	8	no	—
110	C₂×D₄×C₁₃	—	2	2	no	—
111	C₂×D₄×C₁₃	—	2	4	no	—
112	C₂×D₄×C₁₃	—	2	4	no	—
113	C₂×D₄×C₁₃	—	2	8	no	—
114	C₂×D₄×C₁₃	—	4	8	no	—
115	C₂×D₄×C₁₃	—	4	4	no	—
116	C₂×D₄×C₁₃	—	4	4	no	—
117	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
118	C₂²×C₄×C₁₃	—	2	4	no	—
119	C₂²×C₄×C₁₃	—	2	4	no	—
120	C₂²×C₄×C₁₃	—	2	8	no	—
121	C₂²×C₄×C₁₃	—	2	2	no	—
122	C₂²×C₄×C₁₃	—	2	4	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	SD₁₆	1	8	yes	complemented
127	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
128	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
129	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
130	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
131	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
132	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
133	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
134	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
135	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
136	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
137	C₁₃×SD₁₆	—	4	32	no	—
138	C₂×C₈×C₁₃	—	2	8	no	—
139	C₂×C₈×C₁₃	C₂⁴	1	8	yes	—
140	C₁₃×C₄⋊C₄	—	2	8	no	—
141	C₁₃×C₄⋊C₄	—	2	8	no	—
142	C₁₃×C₄⋊C₄	—	2	8	no	—
143	C₁₃×C₄⋊C₄	—	2	8	no	—
144	C₁₃×C₄⋊C₄	—	2	4	no	—
145	C₁₃×C₄⋊C₄	—	2	2	no	—
146	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
147	C₁₃×C₂²⋊C₄	—	2	8	no	—
148	C₁₃×C₂²⋊C₄	—	2	8	no	—
149	C₄²×C₁₃	C₂×D₄	1	4	yes	—
150	C₄²×C₁₃	C₂×D₄	1	2	yes	—
151	C₄²×C₁₃	C₂×D₄	1	4	yes	—
152	C₄²×C₁₃	C₂×D₄	1	2	yes	—
153	C₄²×C₁₃	C₂⁴	1	2	yes	—
154	C₄²×C₁₃	C₂⁴	1	2	yes	—
155	C₂×#532	C₂×C₁₃	1	1	yes	characteristic
156	C₂²×C₄⋊Q₈	C₂×C₁₃	1	1	yes	characteristic, complemented
157	#3206	C₂×C₁₃	1	16	yes	direct product factor
158	C₂×#492	C₂×C₁₃	1	2	yes	complemented
159	C₂×#487	C₂×C₁₃	1	2	yes	complemented
160	C₂×#461	C₂×C₁₃	1	4	yes	complemented
161	C₂×#448	C₂×C₁₃	1	4	yes	complemented
162	C₂×#431	C₂×C₁₃	1	1	yes	characteristic, complemented
163	C₂³×C₁₃	—	2	2	no	—
164	C₂³×C₁₃	—	2	2	no	—
165	C₂³×C₁₃	—	2	4	no	—
166	C₂³×C₁₃	—	4	4	no	—
167	C₂³×C₁₃	—	4	4	no	—
168	C₂³×C₁₃	—	4	4	no	—
169	C₂³×C₁₃	C₂×SD₁₆	1	4	yes	—
170	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
171	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
172	Q₈×C₁₃	—	2	16	no	—
173	Q₈×C₁₃	—	4	16	no	—
174	Q₈×C₁₃	—	4	8	no	—
175	Q₈×C₁₃	—	4	8	no	—
176	D₄×C₁₃	—	2	8	no	—
177	D₄×C₁₃	—	4	16	no	—
178	D₄×C₁₃	—	4	4	no	—
179	D₄×C₁₃	—	4	8	no	—
180	D₄×C₁₃	—	4	8	no	—
181	C₂×C₄×C₁₃	—	2	2	no	—
182	C₂×C₄×C₁₃	—	2	2	no	—
183	C₂×C₄×C₁₃	—	2	4	no	—
184	C₂×C₄×C₁₃	—	2	8	no	—
185	C₂×C₄×C₁₃	—	2	4	no	—
186	C₂×C₄×C₁₃	—	2	4	no	—
187	C₂×C₄×C₁₃	—	2	8	no	—
188	C₂×C₄×C₁₃	—	4	16	no	—
189	C₂×C₄×C₁₃	—	4	8	no	—
190	C₂×C₄×C₁₃	—	4	4	no	—
191	C₂×C₄×C₁₃	—	4	16	no	—
192	C₂×C₄×C₁₃	C₂×SD₁₆	1	4	yes	—
193	C₂×C₄×C₁₃	C₂×SD₁₆	1	4	yes	—
194	C₂×C₄×C₁₃	C₂×SD₁₆	1	16	yes	complemented
195	C₂×C₄×C₁₃	#137	1	4	yes	—
196	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
197	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
198	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
199	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
200	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
201	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
202	C₂×C₄×C₁₃	H(5,𝔽₂)	1	4	yes	—
203	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
204	C₈×C₁₃	—	2	8	no	—
205	C₂²×#41	—	2	1	no	—
206	C₂³×Q₈	C₂²×C₁₃	1	2	yes	—
207	C₂²×SD₁₆	C₂²×C₁₃	1	8	yes	—
208	#532	—	2	4	no	—
209	#532	C₂²×C₁₃	1	8	yes	—
210	C₂×C₄⋊Q₈	—	2	1	no	—
211	C₂×C₄⋊Q₈	—	2	1	no	—
212	C₂×C₄⋊Q₈	—	2	4	no	—
213	C₂×C₄⋊Q₈	C₂²×C₁₃	1	2	yes	—
214	C₂×C₄⋊Q₈	C₂²×C₁₃	1	2	yes	—
215	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
216	C₂×C₄⋊Q₈	C₂²×C₁₃	1	8	yes	complemented
217	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
218	C₂×#124	—	2	1	no	—
219	C₂×#121	—	2	1	no	—
220	C₂×#121	C₂²×C₁₃	1	2	yes	—
221	C₂×C₄×D₄	—	2	1	no	—
222	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
223	C₂²×C₄⋊C₄	—	2	1	no	—
224	C₂²×C₄⋊C₄	—	2	1	no	—
225	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
226	#492	C₂²×C₁₃	1	16	yes	complemented
227	#487	C₂²×C₁₃	1	16	yes	complemented
228	#461	C₂²×C₁₃	1	32	yes	complemented
229	#448	C₂²×C₁₃	1	32	yes	complemented
230	#431	C₂²×C₁₃	1	8	yes	complemented
231	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
232	C₂×#103	C₂²×C₁₃	1	8	yes	—
233	C₂×C₂²⋊C₈	C₂²×C₁₃	1	2	yes	—
234	C₂×C₄×C₈	C₂²×C₁₃	1	2	yes	—
235	C₂²×C₁₃	—	2	2	no	—
236	C₂²×C₁₃	—	2	8	no	—
237	C₂²×C₁₃	—	2	2	no	—
238	C₂²×C₁₃	—	4	4	no	—
239	C₂²×C₁₃	—	4	4	no	—
240	C₂²×C₁₃	—	4	4	no	—
241	C₂²×C₁₃	—	8	8	no	—
242	C₂²×C₁₃	#535	1	2	yes	—
243	C₂²×C₁₃	C₂²×SD₁₆	1	4	yes	—
244	C₂²×C₁₃	C₂²×SD₁₆	1	2	yes	—
245	C₂²×C₁₃	C₂×#137	1	2	yes	—
246	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
247	C₄×C₁₃	—	2	2	no	—
248	C₄×C₁₃	—	2	2	no	—
249	C₄×C₁₃	—	4	8	no	—
250	C₄×C₁₃	—	4	4	no	—
251	C₄×C₁₃	#535	1	2	yes	—
252	C₄×C₁₃	C₂²×SD₁₆	1	4	yes	—
253	C₄×C₁₃	C₂²×SD₁₆	1	4	yes	—
254	C₄×C₁₃	C₂×#137	1	4	yes	—
255	C₄×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
256	C₂×#41	—	2	8	no	—
257	C₂×#41	—	4	8	no	—
258	C₂²×Q₈	—	2	1	no	—
259	C₂²×Q₈	—	2	2	no	—
260	C₂²×Q₈	—	2	4	no	—
261	C₂²×Q₈	—	4	8	no	—
262	C₂²×Q₈	C₂³×C₁₃	1	4	yes	—
263	C₂²×Q₈	C₂³×C₁₃	1	8	yes	—
264	C₂²×D₄	—	2	2	no	—
265	C₂²×D₄	—	2	1	no	—
266	C₂²×D₄	—	2	1	no	—
267	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
268	C₂³×C₄	—	2	2	no	—
269	C₂³×C₄	—	2	2	no	—
270	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
271	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
272	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
273	C₂×SD₁₆	—	4	16	no	—
274	C₂×SD₁₆	C₂³×C₁₃	1	32	yes	—
275	C₂²×C₈	C₂³×C₁₃	1	4	yes	—
276	C₄⋊Q₈	—	2	4	no	—
277	C₄⋊Q₈	—	2	4	no	—
278	C₄⋊Q₈	—	2	8	no	—
279	C₄⋊Q₈	—	2	8	no	—
280	C₄⋊Q₈	—	2	2	no	—
281	C₄⋊Q₈	C₂³×C₁₃	1	8	yes	—
282	C₄⋊Q₈	C₂³×C₁₃	1	8	yes	—
283	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
284	#127	—	2	2	no	—
285	#127	C₂³×C₁₃	1	4	yes	—
286	#124	—	2	8	no	—
287	#121	—	2	8	no	—
288	#121	—	2	4	no	—
289	#121	C₂³×C₁₃	1	8	yes	—
290	C₄×D₄	—	2	8	no	—
291	C₄×D₄	—	2	4	no	—
292	C₄×D₄	C₂³×C₁₃	1	8	yes	—
293	C₂×C₄⋊C₄	—	2	2	no	—
294	C₂×C₄⋊C₄	—	2	2	no	—
295	C₂×C₄⋊C₄	—	2	2	no	—
296	C₂×C₄⋊C₄	—	2	2	no	—
297	C₂×C₄⋊C₄	—	2	8	no	—
298	C₂×C₄⋊C₄	—	2	8	no	—
299	C₂×C₄⋊C₄	—	2	1	no	—
300	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
301	C₂×C₂²⋊C₄	—	2	2	no	—
302	C₂×C₂²⋊C₄	—	2	2	no	—
303	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
304	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
305	C₂×C₄²	D₄×C₁₃	1	4	yes	—
306	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
307	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
308	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
309	C₄⋊C₈	C₂³×C₁₃	1	8	yes	—
310	#103	C₂³×C₁₃	1	32	yes	—
311	C₂²⋊C₈	C₂³×C₁₃	1	8	yes	—
312	C₄×C₈	C₂³×C₁₃	1	8	yes	—
313	C₂×C₁₃	—	2	4	no	—
314	C₂×C₁₃	—	8	4	no	—
315	C₂×C₁₃	#3206	1	4	yes	direct product factor
316	C₂×C₁₃	C₂×#535	1	1	yes	characteristic
317	C₂×C₁₃	C₂³×SD₁₆	1	1	yes	characteristic
318	C₂×C₁₃	C₂²×#137	1	1	yes	characteristic
319	C₂⁴	—	2	2	no	—
320	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
321	#41	—	4	32	no	—
322	C₂×Q₈	—	2	4	no	—
323	C₂×Q₈	—	2	8	no	—
324	C₂×Q₈	—	2	4	no	—
325	C₂×Q₈	—	2	16	no	—
326	C₂×Q₈	—	4	16	no	—
327	C₂×Q₈	—	4	8	no	—
328	C₂×Q₈	—	4	16	no	—
329	C₂×Q₈	—	4	4	no	—
330	C₂×Q₈	C₂⁴×C₁₃	1	8	yes	—
331	C₂×D₄	—	2	8	no	—
332	C₂×D₄	—	2	2	no	—
333	C₂×D₄	—	2	4	no	—
334	C₂×D₄	—	2	4	no	—
335	C₂×D₄	—	2	8	no	—
336	C₂×D₄	—	4	8	no	—
337	C₂×D₄	—	4	4	no	—
338	C₂×D₄	—	4	4	no	—
339	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
340	C₂²×C₄	—	2	4	no	—
341	C₂²×C₄	—	2	4	no	—
342	C₂²×C₄	—	2	2	no	—
343	C₂²×C₄	—	2	8	no	—
344	C₂²×C₄	—	2	4	no	—
345	C₂²×C₄	—	2	8	no	—
346	C₂²×C₄	—	4	8	no	—
347	C₂²×C₄	—	4	8	no	—
348	C₂²×C₄	C₁₃×SD₁₆	1	8	yes	complemented
349	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
350	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
351	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
352	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
353	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
354	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
355	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
356	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
357	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
358	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
359	SD₁₆	—	4	32	no	—
360	C₂×C₈	—	2	8	no	—
361	C₂×C₈	C₂⁴×C₁₃	1	8	yes	—
362	C₄⋊C₄	—	2	8	no	—
363	C₄⋊C₄	—	2	8	no	—
364	C₄⋊C₄	—	2	8	no	—
365	C₄⋊C₄	—	2	8	no	—
366	C₄⋊C₄	—	2	4	no	—
367	C₄⋊C₄	—	2	2	no	—
368	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
369	C₂²⋊C₄	—	2	8	no	—
370	C₂²⋊C₄	—	2	8	no	—
371	C₄²	C₂×D₄×C₁₃	1	4	yes	—
372	C₄²	C₂×D₄×C₁₃	1	2	yes	—
373	C₄²	C₂×D₄×C₁₃	1	4	yes	—
374	C₄²	C₂×D₄×C₁₃	1	2	yes	—
375	C₄²	C₂⁴×C₁₃	1	2	yes	—
376	C₄²	C₂⁴×C₁₃	1	2	yes	—
377	C₁₃	C₂×#3206	1	1	yes	characteristic, direct product factor, Sylow
378	C₂³	—	2	2	no	—
379	C₂³	—	2	2	no	—
380	C₂³	—	2	4	no	—
381	C₂³	—	4	4	no	—
382	C₂³	—	4	4	no	—
383	C₂³	—	4	4	no	—
384	C₂³	C₂×C₁₃×SD₁₆	1	4	yes	—
385	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
386	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
387	Q₈	—	2	16	no	—
388	Q₈	—	4	16	no	—
389	Q₈	—	4	8	no	—
390	Q₈	—	4	8	no	—
391	D₄	—	2	8	no	—
392	D₄	—	4	16	no	—
393	D₄	—	4	4	no	—
394	D₄	—	4	8	no	—
395	D₄	—	4	8	no	—
396	C₂×C₄	—	2	2	no	—
397	C₂×C₄	—	2	2	no	—
398	C₂×C₄	—	2	4	no	—
399	C₂×C₄	—	2	8	no	—
400	C₂×C₄	—	2	4	no	—
401	C₂×C₄	—	2	4	no	—
402	C₂×C₄	—	2	8	no	—
403	C₂×C₄	—	4	16	no	—
404	C₂×C₄	—	4	8	no	—
405	C₂×C₄	—	4	4	no	—
406	C₂×C₄	—	4	16	no	—
407	C₂×C₄	C₂×C₁₃×SD₁₆	1	4	yes	—
408	C₂×C₄	C₂×C₁₃×SD₁₆	1	4	yes	—
409	C₂×C₄	C₂×C₁₃×SD₁₆	1	16	yes	complemented
410	C₂×C₄	C₁₃×#137	1	4	yes	—
411	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
412	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
413	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
414	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
415	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
416	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
417	C₂×C₄	C₁₃×H(5,𝔽₂)	1	4	yes	—
418	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
419	C₈	—	2	8	no	—
420	C₂²	—	2	2	no	—
421	C₂²	—	2	2	no	—
422	C₂²	—	2	8	no	—
423	C₂²	—	4	4	no	—
424	C₂²	—	4	4	no	—
425	C₂²	—	4	4	no	—
426	C₂²	—	8	8	no	—
427	C₂²	C₁₃×#535	1	2	yes	—
428	C₂²	C₂²×C₁₃×SD₁₆	1	4	yes	—
429	C₂²	C₂²×C₁₃×SD₁₆	1	2	yes	—
430	C₂²	C₂×C₁₃×#137	1	2	yes	—
431	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
432	C₄	—	2	2	no	—
433	C₄	—	2	2	no	—
434	C₄	—	4	4	no	—
435	C₄	—	4	8	no	—
436	C₄	C₁₃×#535	1	2	yes	—
437	C₄	C₂²×C₁₃×SD₁₆	1	4	yes	—
438	C₄	C₂²×C₁₃×SD₁₆	1	4	yes	—
439	C₄	C₂×C₁₃×#137	1	4	yes	—
440	C₄	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
441	C₂	—	2	4	no	—
442	C₂	—	8	4	no	—
443	C₂	C₁₃×#3206	1	4	yes	direct product factor
444	C₂	C₂×C₁₃×#535	1	1	yes	characteristic
445	C₂	C₂³×C₁₃×SD₁₆	1	1	yes	characteristic
446	C₂	C₂²×C₁₃×#137	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
prime radical	C₂×C₁₃×#532	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂²×C₄²×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂²×C₁₃×C₄⋊Q₈	C₂	semidirect
3. C₁₃×#3206	C₂	direct (N × H)
4. C₂×C₁₃×#492	C₂	semidirect
5. C₂×C₁₃×#487	C₂	semidirect
6. C₂×C₁₃×#461	C₂	semidirect
7. C₂×C₁₃×#448	C₂	semidirect
8. C₂×C₁₃×#431	C₂	semidirect
20. C₂×C₁₃×C₄⋊Q₈	C₂²	semidirect
30. C₁₃×#492	C₂²	semidirect
31. C₁₃×#487	C₂²	semidirect
32. C₁₃×#461	C₂²	semidirect
33. C₁₃×#448	C₂²	semidirect
34. C₁₃×#431	C₂²	semidirect
96. C₂×#3206	C₁₃	direct (N × H)
126. C₂²×C₄×C₁₃	SD₁₆	semidirect
156. C₂²×C₄⋊Q₈	C₂×C₁₃	semidirect
157. #3206	C₂×C₁₃	direct (N × H)
158. C₂×#492	C₂×C₁₃	semidirect
159. C₂×#487	C₂×C₁₃	semidirect
160. C₂×#461	C₂×C₁₃	semidirect
161. C₂×#448	C₂×C₁₃	semidirect
162. C₂×#431	C₂×C₁₃	semidirect
194. C₂×C₄×C₁₃	C₂×SD₁₆	semidirect
216. C₂×C₄⋊Q₈	C₂²×C₁₃	semidirect
226. #492	C₂²×C₁₃	semidirect
227. #487	C₂²×C₁₃	semidirect
228. #461	C₂²×C₁₃	semidirect
229. #448	C₂²×C₁₃	semidirect
230. #431	C₂²×C₁₃	semidirect
315. C₂×C₁₃	#3206	direct (N × H)
348. C₂²×C₄	C₁₃×SD₁₆	semidirect
377. C₁₃	C₂×#3206	direct (N × H)
409. C₂×C₄	C₂×C₁₃×SD₁₆	semidirect
443. C₂	C₁₃×#3206	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×C₁₃×#532	2
C₂²×C₁₃×C₄⋊Q₈	2
C₁₃×#3206	2
C₂×C₁₃×#492	2
C₂×C₁₃×#487	2
C₂×C₁₃×#461	2
C₂×C₁₃×#448	2
C₂×C₁₃×#431	2
C₂×#3206	13

Subgroups — C2×C13×#3206 #15747116

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#3206 #15747116