Subgroups — C₂×C₁₃×#2816 #15722987

Order 3328.

2998 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₃×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₁₃×#121	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#2816	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₁₃×#399	C₂	1	2	yes	maximal, complemented
5	C₂×C₁₃×#398	C₂	1	2	yes	maximal, complemented
6	C₂×C₁₃×#394	C₂	1	4	yes	maximal, complemented
7	C₂×C₁₃×#394	C₂	1	2	yes	maximal, complemented
8	C₂×C₁₃×#393	C₂	1	2	yes	maximal, complemented
9	C₂×C₁₃×#381	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂³×Q₈×C₁₃	C₂²	1	1	yes	characteristic
11	C₂³×D₄×C₁₃	C₂²	1	2	yes	—
12	C₂³×D₄×C₁₃	C₂²	1	1	yes	characteristic
13	C₂⁴×C₄×C₁₃	C₂²	1	1	yes	characteristic
14	C₂×C₁₃×C₂²⋊Q₈	—	2	8	no	—
15	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	8	yes	complemented
16	C₂×C₁₃×#121	—	2	8	no	—
17	C₂×C₁₃×#121	C₂²	1	8	yes	—
18	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
19	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
20	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
21	C₂²×C₁₃×C₄⋊C₄	C₂²	1	4	yes	—
22	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
23	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
24	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
25	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	—
26	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	—
27	C₁₃×#399	C₂²	1	16	yes	complemented
28	C₁₃×#398	C₂²	1	16	yes	complemented
29	C₁₃×#394	C₂²	1	16	yes	complemented
30	C₁₃×#394	C₂²	1	32	yes	complemented
31	C₁₃×#393	C₂²	1	16	yes	complemented
32	C₁₃×#381	C₂²	1	8	yes	complemented
33	C₂×C₁₃×#95	C₂²	1	2	yes	—
34	C₂×C₁₃×#95	C₂²	1	2	yes	—
35	C₂×C₁₃×#95	C₂²	1	4	yes	—
36	C₂⁵×C₁₃	C₂³	1	2	yes	—
37	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
38	C₂²×Q₈×C₁₃	—	2	4	no	—
39	C₂²×Q₈×C₁₃	—	4	4	no	—
40	C₂²×Q₈×C₁₃	C₂³	1	4	yes	—
41	C₂²×D₄×C₁₃	—	2	8	no	—
42	C₂²×D₄×C₁₃	—	2	4	no	—
43	C₂²×D₄×C₁₃	—	4	4	no	—
44	C₂²×D₄×C₁₃	—	4	8	no	—
45	C₂²×D₄×C₁₃	C₂³	1	8	yes	—
46	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
47	C₂³×C₄×C₁₃	—	4	4	no	—
48	C₂³×C₄×C₁₃	D₄	1	8	yes	—
49	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
50	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
51	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
52	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
53	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
54	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
55	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
56	C₁₃×C₂²⋊Q₈	—	2	32	no	—
57	C₁₃×#121	—	2	32	no	—
58	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
59	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
60	C₂×C₁₃×C₄⋊C₄	—	2	8	no	—
61	C₂×C₁₃×C₄⋊C₄	—	4	8	no	—
62	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
63	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
64	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
65	C₂×C₁₃×C₄⋊C₄	C₂³	1	16	yes	—
66	C₂×C₁₃×C₂²⋊C₄	—	2	8	no	—
67	C₂×C₁₃×C₂²⋊C₄	—	2	8	no	—
68	C₂×C₁₃×C₂²⋊C₄	—	4	4	no	—
69	C₂×C₁₃×C₂²⋊C₄	—	4	8	no	—
70	C₂×C₁₃×C₂²⋊C₄	—	4	8	no	—
71	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
72	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
73	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
74	C₂×C₁₃×C₂²⋊C₄	C₂³	1	16	yes	—
75	C₂×C₁₃×C₂²⋊C₄	C₂³	1	16	yes	—
76	C₁₃×#95	C₂³	1	8	yes	—
77	C₁₃×#95	C₂³	1	8	yes	—
78	C₁₃×#95	C₂³	1	16	yes	—
79	C₂×#2816	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
80	C₂⁴×C₁₃	—	2	4	no	—
81	C₂⁴×C₁₃	—	2	4	no	—
82	C₂⁴×C₁₃	—	2	4	no	—
83	C₂⁴×C₁₃	—	2	4	no	—
84	C₂⁴×C₁₃	—	2	8	no	—
85	C₂⁴×C₁₃	—	2	8	no	—
86	C₂⁴×C₁₃	—	2	8	no	—
87	C₂⁴×C₁₃	C₂×D₄	1	4	yes	—
88	C₂⁴×C₁₃	C₂⁴	1	4	yes	—
89	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
90	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
91	C₂×Q₈×C₁₃	—	2	8	no	—
92	C₂×Q₈×C₁₃	—	4	8	no	—
93	C₂×Q₈×C₁₃	—	4	16	no	—
94	C₂×D₄×C₁₃	—	2	16	no	—
95	C₂×D₄×C₁₃	—	2	8	no	—
96	C₂×D₄×C₁₃	—	4	8	no	—
97	C₂×D₄×C₁₃	—	4	16	no	—
98	C₂×D₄×C₁₃	—	4	16	no	—
99	C₂×D₄×C₁₃	—	4	32	no	—
100	C₂²×C₄×C₁₃	—	2	4	no	—
101	C₂²×C₄×C₁₃	—	2	4	no	—
102	C₂²×C₄×C₁₃	—	2	4	no	—
103	C₂²×C₄×C₁₃	—	2	4	no	—
104	C₂²×C₄×C₁₃	—	2	4	no	—
105	C₂²×C₄×C₁₃	—	2	4	no	—
106	C₂²×C₄×C₁₃	—	2	8	no	—
107	C₂²×C₄×C₁₃	—	2	8	no	—
108	C₂²×C₄×C₁₃	—	2	8	no	—
109	C₂²×C₄×C₁₃	—	2	4	no	—
110	C₂²×C₄×C₁₃	—	2	8	no	—
111	C₂²×C₄×C₁₃	—	2	8	no	—
112	C₂²×C₄×C₁₃	—	4	16	no	—
113	C₂²×C₄×C₁₃	—	4	8	no	—
114	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
115	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
116	C₂²×C₄×C₁₃	C₂×D₄	1	16	yes	—
117	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
118	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
119	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
120	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
121	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
122	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
123	C₁₃×C₄⋊C₄	—	2	8	no	—
124	C₁₃×C₄⋊C₄	—	2	8	no	—
125	C₁₃×C₄⋊C₄	—	2	16	no	—
126	C₁₃×C₄⋊C₄	—	4	16	no	—
127	C₁₃×C₂²⋊C₄	—	2	16	no	—
128	C₁₃×C₂²⋊C₄	—	2	16	no	—
129	C₁₃×C₂²⋊C₄	—	4	8	no	—
130	C₁₃×C₂²⋊C₄	—	4	16	no	—
131	C₁₃×C₂²⋊C₄	—	4	16	no	—
132	C₂²×C₂²⋊Q₈	C₂×C₁₃	1	1	yes	characteristic, complemented
133	C₂²×#121	C₂×C₁₃	1	1	yes	characteristic
134	#2816	C₂×C₁₃	1	16	yes	direct product factor
135	C₂×#399	C₂×C₁₃	1	2	yes	complemented
136	C₂×#398	C₂×C₁₃	1	2	yes	complemented
137	C₂×#394	C₂×C₁₃	1	4	yes	complemented
138	C₂×#394	C₂×C₁₃	1	2	yes	complemented
139	C₂×#393	C₂×C₁₃	1	2	yes	complemented
140	C₂×#381	C₂×C₁₃	1	1	yes	characteristic, complemented
141	C₂³×C₁₃	—	2	8	no	—
142	C₂³×C₁₃	—	2	8	no	—
143	C₂³×C₁₃	—	2	8	no	—
144	C₂³×C₁₃	—	2	4	no	—
145	C₂³×C₁₃	—	2	4	no	—
146	C₂³×C₁₃	—	2	4	no	—
147	C₂³×C₁₃	—	2	4	no	—
148	C₂³×C₁₃	—	2	8	no	—
149	C₂³×C₁₃	—	2	8	no	—
150	C₂³×C₁₃	—	2	8	no	—
151	C₂³×C₁₃	—	4	16	no	—
152	C₂³×C₁₃	—	4	8	no	—
153	C₂³×C₁₃	—	4	8	no	—
154	C₂³×C₁₃	—	4	8	no	—
155	C₂³×C₁₃	—	4	32	no	—
156	C₂³×C₁₃	C₂²×D₄	1	4	yes	—
157	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
158	C₂³×C₁₃	H(5,𝔽₂)	1	4	yes	—
159	C₂³×C₁₃	H(5,𝔽₂)	1	4	yes	—
160	C₂³×C₁₃	2₋¹⁺⁴	1	4	yes	—
161	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
162	Q₈×C₁₃	—	4	16	no	—
163	D₄×C₁₃	—	4	16	no	—
164	D₄×C₁₃	—	4	32	no	—
165	C₂×C₄×C₁₃	—	2	8	no	—
166	C₂×C₄×C₁₃	—	2	8	no	—
167	C₂×C₄×C₁₃	—	2	4	no	—
168	C₂×C₄×C₁₃	—	2	4	no	—
169	C₂×C₄×C₁₃	—	2	4	no	—
170	C₂×C₄×C₁₃	—	2	4	no	—
171	C₂×C₄×C₁₃	—	2	4	no	—
172	C₂×C₄×C₁₃	—	2	4	no	—
173	C₂×C₄×C₁₃	—	2	8	no	—
174	C₂×C₄×C₁₃	—	2	8	no	—
175	C₂×C₄×C₁₃	—	2	8	no	—
176	C₂×C₄×C₁₃	—	2	4	no	—
177	C₂×C₄×C₁₃	—	2	8	no	—
178	C₂×C₄×C₁₃	—	2	8	no	—
179	C₂×C₄×C₁₃	—	4	16	no	—
180	C₂×C₄×C₁₃	—	4	8	no	—
181	C₂×C₄×C₁₃	—	4	8	no	—
182	C₂×C₄×C₁₃	—	4	8	no	—
183	C₂×C₄×C₁₃	—	4	16	no	—
184	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
185	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
186	C₂³×Q₈	C₂²×C₁₃	1	1	yes	characteristic
187	C₂³×D₄	C₂²×C₁₃	1	2	yes	—
188	C₂³×D₄	C₂²×C₁₃	1	1	yes	characteristic
189	C₂⁴×C₄	C₂²×C₁₃	1	1	yes	characteristic
190	C₂×C₂²⋊Q₈	—	2	8	no	—
191	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	8	yes	complemented
192	C₂×#121	—	2	8	no	—
193	C₂×#121	C₂²×C₁₃	1	8	yes	—
194	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
195	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
196	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
197	C₂²×C₄⋊C₄	C₂²×C₁₃	1	4	yes	—
198	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
199	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
200	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	—
201	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	—
202	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
203	#399	C₂²×C₁₃	1	16	yes	complemented
204	#398	C₂²×C₁₃	1	16	yes	complemented
205	#394	C₂²×C₁₃	1	16	yes	complemented
206	#394	C₂²×C₁₃	1	32	yes	complemented
207	#393	C₂²×C₁₃	1	16	yes	complemented
208	#381	C₂²×C₁₃	1	8	yes	complemented
209	C₂×#95	C₂²×C₁₃	1	4	yes	—
210	C₂×#95	C₂²×C₁₃	1	2	yes	—
211	C₂×#95	C₂²×C₁₃	1	2	yes	—
212	C₂²×C₁₃	—	2	4	no	—
213	C₂²×C₁₃	—	2	4	no	—
214	C₂²×C₁₃	—	2	4	no	—
215	C₂²×C₁₃	—	4	16	no	—
216	C₂²×C₁₃	—	4	8	no	—
217	C₂²×C₁₃	—	4	4	no	—
218	C₂²×C₁₃	—	4	4	no	—
219	C₂²×C₁₃	—	4	4	no	—
220	C₂²×C₁₃	—	4	16	no	—
221	C₂²×C₁₃	—	8	16	no	—
222	C₂²×C₁₃	#534	1	4	yes	—
223	C₂²×C₁₃	#535	1	4	yes	—
224	C₂²×C₁₃	#536	1	4	yes	—
225	C₂²×C₁₃	#562	1	16	yes	—
226	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
227	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
228	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
229	C₂²×C₁₃	C₂×2₋¹⁺⁴	1	2	yes	—
230	C₄×C₁₃	—	2	4	no	—
231	C₄×C₁₃	—	2	4	no	—
232	C₄×C₁₃	—	4	4	no	—
233	C₄×C₁₃	—	4	4	no	—
234	C₄×C₁₃	—	4	4	no	—
235	C₄×C₁₃	—	4	8	no	—
236	C₂⁵	C₂³×C₁₃	1	2	yes	—
237	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic
238	C₂²×Q₈	—	2	4	no	—
239	C₂²×Q₈	—	4	4	no	—
240	C₂²×Q₈	C₂³×C₁₃	1	4	yes	—
241	C₂²×D₄	—	2	8	no	—
242	C₂²×D₄	—	2	4	no	—
243	C₂²×D₄	—	4	4	no	—
244	C₂²×D₄	—	4	8	no	—
245	C₂²×D₄	C₂³×C₁₃	1	8	yes	—
246	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
247	C₂³×C₄	—	4	4	no	—
248	C₂³×C₄	D₄×C₁₃	1	8	yes	—
249	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
250	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
251	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
252	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
253	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
254	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
255	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
256	C₂²⋊Q₈	—	2	32	no	—
257	#121	—	2	32	no	—
258	C₂×C₄⋊C₄	—	2	4	no	—
259	C₂×C₄⋊C₄	—	2	4	no	—
260	C₂×C₄⋊C₄	—	2	8	no	—
261	C₂×C₄⋊C₄	—	4	8	no	—
262	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
263	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
264	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
265	C₂×C₄⋊C₄	C₂³×C₁₃	1	16	yes	—
266	C₂×C₂²⋊C₄	—	2	8	no	—
267	C₂×C₂²⋊C₄	—	2	8	no	—
268	C₂×C₂²⋊C₄	—	4	4	no	—
269	C₂×C₂²⋊C₄	—	4	8	no	—
270	C₂×C₂²⋊C₄	—	4	8	no	—
271	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
272	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
273	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
274	C₂×C₂²⋊C₄	C₂³×C₁₃	1	16	yes	—
275	C₂×C₂²⋊C₄	C₂³×C₁₃	1	16	yes	—
276	#95	C₂³×C₁₃	1	8	yes	—
277	#95	C₂³×C₁₃	1	8	yes	—
278	#95	C₂³×C₁₃	1	16	yes	—
279	C₂×C₁₃	—	4	4	no	—
280	C₂×C₁₃	—	8	4	no	—
281	C₂×C₁₃	#2816	1	8	yes	direct product factor
282	C₂×C₁₃	C₂×#534	1	1	yes	characteristic
283	C₂×C₁₃	C₂×#535	1	1	yes	characteristic
284	C₂×C₁₃	C₂×#536	1	1	yes	characteristic
285	C₂×C₁₃	C₂×#562	1	4	yes	—
286	C₂⁴	—	2	4	no	—
287	C₂⁴	—	2	4	no	—
288	C₂⁴	—	2	4	no	—
289	C₂⁴	—	2	4	no	—
290	C₂⁴	—	2	8	no	—
291	C₂⁴	—	2	8	no	—
292	C₂⁴	—	2	8	no	—
293	C₂⁴	C₂×D₄×C₁₃	1	4	yes	—
294	C₂⁴	C₂⁴×C₁₃	1	4	yes	—
295	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
296	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
297	C₂×Q₈	—	2	8	no	—
298	C₂×Q₈	—	4	8	no	—
299	C₂×Q₈	—	4	16	no	—
300	C₂×D₄	—	2	16	no	—
301	C₂×D₄	—	2	8	no	—
302	C₂×D₄	—	4	8	no	—
303	C₂×D₄	—	4	16	no	—
304	C₂×D₄	—	4	16	no	—
305	C₂×D₄	—	4	32	no	—
306	C₂²×C₄	—	2	4	no	—
307	C₂²×C₄	—	2	4	no	—
308	C₂²×C₄	—	2	4	no	—
309	C₂²×C₄	—	2	4	no	—
310	C₂²×C₄	—	2	4	no	—
311	C₂²×C₄	—	2	4	no	—
312	C₂²×C₄	—	2	8	no	—
313	C₂²×C₄	—	2	8	no	—
314	C₂²×C₄	—	2	8	no	—
315	C₂²×C₄	—	2	4	no	—
316	C₂²×C₄	—	2	8	no	—
317	C₂²×C₄	—	2	8	no	—
318	C₂²×C₄	—	4	16	no	—
319	C₂²×C₄	—	4	8	no	—
320	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
321	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
322	C₂²×C₄	C₂×D₄×C₁₃	1	16	yes	—
323	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
324	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
325	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
326	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
327	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
328	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
329	C₄⋊C₄	—	2	8	no	—
330	C₄⋊C₄	—	2	8	no	—
331	C₄⋊C₄	—	2	16	no	—
332	C₄⋊C₄	—	4	16	no	—
333	C₂²⋊C₄	—	2	16	no	—
334	C₂²⋊C₄	—	2	16	no	—
335	C₂²⋊C₄	—	4	8	no	—
336	C₂²⋊C₄	—	4	16	no	—
337	C₂²⋊C₄	—	4	16	no	—
338	C₁₃	C₂×#2816	1	1	yes	characteristic, direct product factor, Sylow
339	C₂³	—	2	8	no	—
340	C₂³	—	2	8	no	—
341	C₂³	—	2	8	no	—
342	C₂³	—	2	4	no	—
343	C₂³	—	2	4	no	—
344	C₂³	—	2	4	no	—
345	C₂³	—	2	4	no	—
346	C₂³	—	2	8	no	—
347	C₂³	—	2	8	no	—
348	C₂³	—	2	8	no	—
349	C₂³	—	4	16	no	—
350	C₂³	—	4	8	no	—
351	C₂³	—	4	8	no	—
352	C₂³	—	4	8	no	—
353	C₂³	—	4	32	no	—
354	C₂³	C₂²×D₄×C₁₃	1	4	yes	—
355	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
356	C₂³	C₁₃×H(5,𝔽₂)	1	4	yes	—
357	C₂³	C₁₃×H(5,𝔽₂)	1	4	yes	—
358	C₂³	C₁₃×2₋¹⁺⁴	1	4	yes	—
359	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
360	Q₈	—	4	16	no	—
361	D₄	—	4	16	no	—
362	D₄	—	4	32	no	—
363	C₂×C₄	—	2	8	no	—
364	C₂×C₄	—	2	8	no	—
365	C₂×C₄	—	2	4	no	—
366	C₂×C₄	—	2	4	no	—
367	C₂×C₄	—	2	4	no	—
368	C₂×C₄	—	2	4	no	—
369	C₂×C₄	—	2	4	no	—
370	C₂×C₄	—	2	8	no	—
371	C₂×C₄	—	2	4	no	—
372	C₂×C₄	—	2	8	no	—
373	C₂×C₄	—	2	8	no	—
374	C₂×C₄	—	2	4	no	—
375	C₂×C₄	—	2	8	no	—
376	C₂×C₄	—	2	8	no	—
377	C₂×C₄	—	4	16	no	—
378	C₂×C₄	—	4	8	no	—
379	C₂×C₄	—	4	8	no	—
380	C₂×C₄	—	4	8	no	—
381	C₂×C₄	—	4	16	no	—
382	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
383	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
384	C₂²	—	2	4	no	—
385	C₂²	—	2	4	no	—
386	C₂²	—	2	4	no	—
387	C₂²	—	4	8	no	—
388	C₂²	—	4	16	no	—
389	C₂²	—	4	16	no	—
390	C₂²	—	4	4	no	—
391	C₂²	—	4	4	no	—
392	C₂²	—	4	4	no	—
393	C₂²	—	8	16	no	—
394	C₂²	C₁₃×#534	1	4	yes	—
395	C₂²	C₁₃×#535	1	4	yes	—
396	C₂²	C₁₃×#536	1	4	yes	—
397	C₂²	C₁₃×#562	1	16	yes	—
398	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
399	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
400	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
401	C₂²	C₂×C₁₃×2₋¹⁺⁴	1	2	yes	—
402	C₄	—	2	4	no	—
403	C₄	—	2	4	no	—
404	C₄	—	4	8	no	—
405	C₄	—	4	4	no	—
406	C₄	—	4	4	no	—
407	C₄	—	4	4	no	—
408	C₂	—	4	4	no	—
409	C₂	—	8	4	no	—
410	C₂	C₁₃×#2816	1	8	yes	direct product factor
411	C₂	C₂×C₁₃×#534	1	1	yes	characteristic
412	C₂	C₂×C₁₃×#535	1	1	yes	characteristic
413	C₂	C₂×C₁₃×#536	1	1	yes	characteristic
414	C₂	C₂×C₁₃×#562	1	4	yes	—

	subgroup	G/H
center, socle	C₂⁴×C₁₃	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃
prime radical	C₂²×C₁₃×#121	C₂
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×C₁₃×C₂²⋊Q₈	C₂	semidirect
3. C₁₃×#2816	C₂	direct (N × H)
4. C₂×C₁₃×#399	C₂	semidirect
5. C₂×C₁₃×#398	C₂	semidirect
6. C₂×C₁₃×#394	C₂	semidirect
7. C₂×C₁₃×#394	C₂	semidirect
8. C₂×C₁₃×#393	C₂	semidirect
9. C₂×C₁₃×#381	C₂	semidirect
15. C₂×C₁₃×C₂²⋊Q₈	C₂²	semidirect
27. C₁₃×#399	C₂²	semidirect
28. C₁₃×#398	C₂²	semidirect
29. C₁₃×#394	C₂²	semidirect
30. C₁₃×#394	C₂²	semidirect
31. C₁₃×#393	C₂²	semidirect
32. C₁₃×#381	C₂²	semidirect
79. C₂×#2816	C₁₃	direct (N × H)
132. C₂²×C₂²⋊Q₈	C₂×C₁₃	semidirect
134. #2816	C₂×C₁₃	direct (N × H)
135. C₂×#399	C₂×C₁₃	semidirect
136. C₂×#398	C₂×C₁₃	semidirect
137. C₂×#394	C₂×C₁₃	semidirect
138. C₂×#394	C₂×C₁₃	semidirect
139. C₂×#393	C₂×C₁₃	semidirect
140. C₂×#381	C₂×C₁₃	semidirect
191. C₂×C₂²⋊Q₈	C₂²×C₁₃	semidirect
203. #399	C₂²×C₁₃	semidirect
204. #398	C₂²×C₁₃	semidirect
205. #394	C₂²×C₁₃	semidirect
206. #394	C₂²×C₁₃	semidirect
207. #393	C₂²×C₁₃	semidirect
208. #381	C₂²×C₁₃	semidirect
281. C₂×C₁₃	#2816	direct (N × H)
338. C₁₃	C₂×#2816	direct (N × H)
410. C₂	C₁₃×#2816	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×C₂²⋊Q₈	2
C₂²×C₁₃×#121	2
C₁₃×#2816	2
C₂×C₁₃×#399	2
C₂×C₁₃×#398	2
C₂×C₁₃×#394	2
C₂×C₁₃×#393	2
C₂×C₁₃×#381	2
C₂×#2816	13

Subgroups — C2×C13×#2816 #15722987

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#2816 #15722987