Subgroups — C₂×C₁₃×#2186 #15719853

Order 3328.

1198 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×#135	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₁₃×SD₃₂	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₁₃×D₁₆	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₁₃×#466	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2186	C₂	1	8	yes	maximal, direct product factor
6	C₂×C₁₃×#358	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₁₃×#357	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₁₃×C₂²⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×C₁₃×#41	—	2	1	no	—
10	C₂×C₁₃×#135	—	2	4	no	—
11	C₂×C₁₃×#135	—	2	4	no	—
12	C₂×C₁₃×#135	—	2	2	no	—
13	C₂×C₁₃×#135	C₂²	1	4	yes	complemented
14	C₂²×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
15	C₂²×C₁₃×SD₁₆	—	2	1	no	—
16	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic
17	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic
18	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
19	C₂×C₁₃×#121	—	2	1	no	—
20	C₂×C₁₃×SD₃₂	—	2	4	no	—
21	C₂×C₁₃×SD₃₂	C₂²	1	4	yes	complemented
22	C₂×C₁₃×D₁₆	—	2	4	no	—
23	C₂×C₁₃×D₁₆	C₂²	1	4	yes	complemented
24	C₂²×C₁₃×C₁₆	C₂²	1	1	yes	characteristic
25	C₂²×C₁₃×C₁₆	C₂²	1	1	yes	characteristic
26	C₁₃×#466	—	2	2	no	—
27	C₁₃×#466	C₂²	1	4	yes	complemented
28	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
29	C₂×C₁₃×#102	—	2	1	no	—
30	C₁₃×#358	C₂²	1	4	yes	complemented
31	C₁₃×#357	C₂²	1	4	yes	complemented
32	C₁₃×C₂²⋊C₁₆	C₂²	1	4	yes	complemented
33	C₂×C₁₃×#41	—	2	8	no	—
34	C₂×C₁₃×#41	—	2	4	no	—
35	C₂×C₁₃×#41	—	4	4	no	—
36	C₂×C₁₃×#41	—	4	2	no	—
37	C₂²×Q₈×C₁₃	—	2	1	no	—
38	C₂²×D₄×C₁₃	—	2	1	no	—
39	C₂²×D₄×C₁₃	—	2	1	no	—
40	C₂²×D₄×C₁₃	—	4	1	no	—
41	C₂²×D₄×C₁₃	—	4	1	no	—
42	C₂³×C₄×C₁₃	—	4	1	no	—
43	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
44	C₁₃×#135	—	2	16	no	—
45	C₁₃×#135	—	2	8	no	—
46	C₁₃×#135	—	2	8	no	—
47	C₂×C₁₃×Q₁₆	—	2	1	no	—
48	C₂×C₁₃×Q₁₆	—	2	2	no	—
49	C₂×C₁₃×Q₁₆	D₄	1	4	yes	complemented
50	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
51	C₂×C₁₃×SD₁₆	—	2	8	no	—
52	C₂×C₁₃×SD₁₆	—	2	4	no	—
53	C₂×C₁₃×D₈	—	2	1	no	—
54	C₂×C₁₃×D₈	—	2	2	no	—
55	C₂×C₁₃×D₈	—	2	2	no	—
56	C₂×C₁₃×D₈	—	2	2	no	—
57	C₂×C₁₃×D₈	—	2	1	no	—
58	C₂×C₁₃×D₈	D₄	1	4	yes	complemented
59	C₂×C₁₃×D₈	C₂³	1	2	yes	—
60	C₂×C₁₃×D₈	C₂³	1	2	yes	—
61	C₂²×C₈×C₁₃	—	2	2	no	—
62	C₂²×C₈×C₁₃	—	2	2	no	—
63	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
64	C₂²×C₈×C₁₃	D₄	1	2	yes	—
65	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
66	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
67	C₁₃×#121	—	2	4	no	—
68	C₁₃×#121	—	4	2	no	—
69	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
70	C₂×C₁₃×C₂²⋊C₄	—	4	1	no	—
71	C₁₃×SD₃₂	—	2	8	no	—
72	C₁₃×D₁₆	—	2	8	no	—
73	C₂×C₁₃×C₁₆	—	2	2	no	—
74	C₂×C₁₃×C₁₆	—	2	2	no	—
75	C₂×C₁₃×C₁₆	C₂³	1	2	yes	—
76	C₂×C₁₃×C₁₆	C₂³	1	2	yes	—
77	C₁₃×#107	—	2	1	no	—
78	C₁₃×#107	C₂³	1	2	yes	—
79	C₁₃×#102	—	2	4	no	—
80	C₂×#2186	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
81	C₂⁴×C₁₃	—	4	1	no	—
82	C₂⁴×C₁₃	—	4	1	no	—
83	C₂⁴×C₁₃	D₈	1	1	yes	characteristic
84	C₁₃×#41	—	2	16	no	—
85	C₁₃×#41	—	4	8	no	—
86	C₁₃×#41	—	4	16	no	—
87	C₂×Q₈×C₁₃	—	2	4	no	—
88	C₂×Q₈×C₁₃	—	2	2	no	—
89	C₂×Q₈×C₁₃	—	4	1	no	—
90	C₂×Q₈×C₁₃	—	4	2	no	—
91	C₂×D₄×C₁₃	—	2	4	no	—
92	C₂×D₄×C₁₃	—	2	2	no	—
93	C₂×D₄×C₁₃	—	2	2	no	—
94	C₂×D₄×C₁₃	—	4	8	no	—
95	C₂×D₄×C₁₃	—	4	4	no	—
96	C₂×D₄×C₁₃	—	4	4	no	—
97	C₂×D₄×C₁₃	—	4	2	no	—
98	C₂×D₄×C₁₃	—	4	1	no	—
99	C₂×D₄×C₁₃	—	4	1	no	—
100	C₂×D₄×C₁₃	—	4	2	no	—
101	C₂×D₄×C₁₃	—	4	2	no	—
102	C₂×D₄×C₁₃	—	8	4	no	—
103	C₂²×C₄×C₁₃	—	2	2	no	—
104	C₂²×C₄×C₁₃	—	2	2	no	—
105	C₂²×C₄×C₁₃	—	4	8	no	—
106	C₂²×C₄×C₁₃	—	4	1	no	—
107	C₂²×C₄×C₁₃	—	4	4	no	—
108	C₂²×C₄×C₁₃	—	4	1	no	—
109	C₂²×C₄×C₁₃	D₈	1	2	yes	—
110	C₂²×C₄×C₁₃	D₈	1	1	yes	characteristic
111	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
112	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
113	C₁₃×Q₁₆	—	2	4	no	—
114	C₁₃×Q₁₆	—	2	2	no	—
115	C₁₃×Q₁₆	C₂×D₄	1	4	yes	complemented
116	C₁₃×SD₁₆	—	2	16	no	—
117	C₁₃×D₈	—	2	4	no	—
118	C₁₃×D₈	—	2	2	no	—
119	C₁₃×D₈	—	2	2	no	—
120	C₁₃×D₈	—	2	2	no	—
121	C₁₃×D₈	—	4	2	no	—
122	C₁₃×D₈	C₂×D₄	1	4	yes	complemented
123	C₂×C₈×C₁₃	—	2	2	no	—
124	C₂×C₈×C₁₃	—	2	4	no	—
125	C₂×C₈×C₁₃	—	2	2	no	—
126	C₂×C₈×C₁₃	—	2	2	no	—
127	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
128	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
129	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
130	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
131	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
132	C₁₃×C₄⋊C₄	—	2	2	no	—
133	C₁₃×C₄⋊C₄	—	4	1	no	—
134	C₁₃×C₂²⋊C₄	—	4	4	no	—
135	C₁₃×C₁₆	—	2	2	no	—
136	C₁₃×C₁₆	—	2	2	no	—
137	C₂²×#135	C₂×C₁₃	1	1	yes	characteristic, complemented
138	C₂²×SD₃₂	C₂×C₁₃	1	1	yes	characteristic, complemented
139	C₂²×D₁₆	C₂×C₁₃	1	1	yes	characteristic, complemented
140	C₂×#466	C₂×C₁₃	1	1	yes	characteristic, complemented
141	#2186	C₂×C₁₃	1	8	yes	direct product factor
142	C₂×#358	C₂×C₁₃	1	1	yes	characteristic, complemented
143	C₂×#357	C₂×C₁₃	1	1	yes	characteristic, complemented
144	C₂×C₂²⋊C₁₆	C₂×C₁₃	1	1	yes	characteristic, complemented
145	C₂³×C₁₃	—	2	2	no	—
146	C₂³×C₁₃	—	2	2	no	—
147	C₂³×C₁₃	—	2	2	no	—
148	C₂³×C₁₃	—	4	2	no	—
149	C₂³×C₁₃	—	4	4	no	—
150	C₂³×C₁₃	—	4	2	no	—
151	C₂³×C₁₃	—	8	2	no	—
152	C₂³×C₁₃	—	8	2	no	—
153	C₂³×C₁₃	—	8	2	no	—
154	C₂³×C₁₃	—	8	2	no	—
155	C₂³×C₁₃	—	8	2	no	—
156	C₂³×C₁₃	C₂×D₈	1	2	yes	—
157	C₂³×C₁₃	C₂×D₈	1	1	yes	characteristic
158	Q₈×C₁₃	—	2	4	no	—
159	Q₈×C₁₃	—	4	2	no	—
160	Q₈×C₁₃	—	4	4	no	—
161	D₄×C₁₃	—	2	4	no	—
162	D₄×C₁₃	—	4	16	no	—
163	D₄×C₁₃	—	4	2	no	—
164	D₄×C₁₃	—	4	2	no	—
165	D₄×C₁₃	—	4	2	no	—
166	D₄×C₁₃	—	4	4	no	—
167	D₄×C₁₃	—	8	8	no	—
168	D₄×C₁₃	—	8	2	no	—
169	C₂×C₄×C₁₃	—	2	2	no	—
170	C₂×C₄×C₁₃	—	2	2	no	—
171	C₂×C₄×C₁₃	—	2	2	no	—
172	C₂×C₄×C₁₃	—	2	4	no	—
173	C₂×C₄×C₁₃	—	4	16	no	—
174	C₂×C₄×C₁₃	—	4	2	no	—
175	C₂×C₄×C₁₃	—	4	4	no	—
176	C₂×C₄×C₁₃	—	4	2	no	—
177	C₂×C₄×C₁₃	—	8	2	no	—
178	C₂×C₄×C₁₃	#120	1	2	yes	—
179	C₂×C₄×C₁₃	C₂×D₈	1	2	yes	—
180	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
181	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
182	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
183	C₈×C₁₃	—	2	2	no	—
184	C₈×C₁₃	#120	1	2	yes	—
185	C₈×C₁₃	C₂²×D₄	1	1	yes	characteristic
186	C₈×C₁₃	C₂²×D₄	1	1	yes	characteristic
187	C₂²×#41	—	2	1	no	—
188	C₂×#135	—	2	4	no	—
189	C₂×#135	—	2	4	no	—
190	C₂×#135	—	2	2	no	—
191	C₂×#135	C₂²×C₁₃	1	4	yes	complemented
192	C₂²×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
193	C₂²×SD₁₆	—	2	1	no	—
194	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic
195	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic
196	C₂³×C₈	C₂²×C₁₃	1	1	yes	characteristic
197	C₂×#121	—	2	1	no	—
198	C₂×SD₃₂	—	2	4	no	—
199	C₂×SD₃₂	C₂²×C₁₃	1	4	yes	complemented
200	C₂×D₁₆	—	2	4	no	—
201	C₂×D₁₆	C₂²×C₁₃	1	4	yes	complemented
202	C₂²×C₁₆	C₂²×C₁₃	1	1	yes	characteristic
203	C₂²×C₁₆	C₂²×C₁₃	1	1	yes	characteristic
204	#466	—	2	2	no	—
205	#466	C₂²×C₁₃	1	4	yes	complemented
206	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
207	C₂×#102	—	2	1	no	—
208	#358	C₂²×C₁₃	1	4	yes	complemented
209	#357	C₂²×C₁₃	1	4	yes	complemented
210	C₂²⋊C₁₆	C₂²×C₁₃	1	4	yes	complemented
211	C₂²×C₁₃	—	2	2	no	—
212	C₂²×C₁₃	—	2	2	no	—
213	C₂²×C₁₃	—	2	2	no	—
214	C₂²×C₁₃	—	4	4	no	—
215	C₂²×C₁₃	—	4	4	no	—
216	C₂²×C₁₃	—	8	2	no	—
217	C₂²×C₁₃	—	8	2	no	—
218	C₂²×C₁₃	—	8	8	no	—
219	C₂²×C₁₃	—	8	2	no	—
220	C₂²×C₁₃	—	8	2	no	—
221	C₂²×C₁₃	—	8	2	no	—
222	C₂²×C₁₃	—	16	4	no	—
223	C₂²×C₁₃	#447	1	2	yes	—
224	C₂²×C₁₃	#508	1	2	yes	—
225	C₂²×C₁₃	#509	1	2	yes	—
226	C₂²×C₁₃	C₂²×D₈	1	1	yes	characteristic
227	C₄×C₁₃	—	2	2	no	—
228	C₄×C₁₃	—	4	4	no	—
229	C₄×C₁₃	—	8	2	no	—
230	C₄×C₁₃	#447	1	2	yes	—
231	C₄×C₁₃	C₂×#120	1	1	yes	characteristic
232	C₄×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
233	C₂×#41	—	2	8	no	—
234	C₂×#41	—	2	4	no	—
235	C₂×#41	—	4	4	no	—
236	C₂×#41	—	4	2	no	—
237	C₂²×Q₈	—	2	1	no	—
238	C₂²×D₄	—	2	1	no	—
239	C₂²×D₄	—	2	1	no	—
240	C₂²×D₄	—	4	1	no	—
241	C₂²×D₄	—	4	1	no	—
242	C₂³×C₄	—	4	1	no	—
243	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
244	#135	—	2	16	no	—
245	#135	—	2	8	no	—
246	#135	—	2	8	no	—
247	C₂×Q₁₆	—	2	1	no	—
248	C₂×Q₁₆	—	2	2	no	—
249	C₂×Q₁₆	D₄×C₁₃	1	4	yes	complemented
250	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
251	C₂×SD₁₆	—	2	8	no	—
252	C₂×SD₁₆	—	2	4	no	—
253	C₂×D₈	—	2	1	no	—
254	C₂×D₈	—	2	2	no	—
255	C₂×D₈	—	2	2	no	—
256	C₂×D₈	—	2	2	no	—
257	C₂×D₈	—	2	1	no	—
258	C₂×D₈	D₄×C₁₃	1	4	yes	complemented
259	C₂×D₈	C₂³×C₁₃	1	2	yes	—
260	C₂×D₈	C₂³×C₁₃	1	2	yes	—
261	C₂²×C₈	—	2	2	no	—
262	C₂²×C₈	—	2	2	no	—
263	C₂²×C₈	D₄×C₁₃	1	1	yes	characteristic
264	C₂²×C₈	D₄×C₁₃	1	2	yes	—
265	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
266	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
267	#121	—	2	4	no	—
268	#121	—	4	2	no	—
269	C₂×C₄⋊C₄	—	2	1	no	—
270	C₂×C₂²⋊C₄	—	4	1	no	—
271	SD₃₂	—	2	8	no	—
272	D₁₆	—	2	8	no	—
273	C₂×C₁₆	—	2	2	no	—
274	C₂×C₁₆	—	2	2	no	—
275	C₂×C₁₆	C₂³×C₁₃	1	2	yes	—
276	C₂×C₁₆	C₂³×C₁₃	1	2	yes	—
277	#107	—	2	1	no	—
278	#107	C₂³×C₁₃	1	2	yes	—
279	#102	—	2	4	no	—
280	C₂×C₁₃	—	4	2	no	—
281	C₂×C₁₃	—	8	4	no	—
282	C₂×C₁₃	—	16	2	no	—
283	C₂×C₁₃	#2186	1	4	yes	direct product factor
284	C₂×C₁₃	C₂×#447	1	1	yes	characteristic
285	C₂×C₁₃	C₂×#508	1	1	yes	characteristic
286	C₂×C₁₃	C₂×#509	1	1	yes	characteristic
287	C₂⁴	—	4	1	no	—
288	C₂⁴	—	4	1	no	—
289	C₂⁴	C₁₃×D₈	1	1	yes	characteristic
290	#41	—	2	16	no	—
291	#41	—	4	16	no	—
292	#41	—	4	8	no	—
293	C₂×Q₈	—	2	4	no	—
294	C₂×Q₈	—	2	2	no	—
295	C₂×Q₈	—	4	1	no	—
296	C₂×Q₈	—	4	2	no	—
297	C₂×D₄	—	2	4	no	—
298	C₂×D₄	—	2	2	no	—
299	C₂×D₄	—	2	2	no	—
300	C₂×D₄	—	4	8	no	—
301	C₂×D₄	—	4	4	no	—
302	C₂×D₄	—	4	4	no	—
303	C₂×D₄	—	4	2	no	—
304	C₂×D₄	—	4	1	no	—
305	C₂×D₄	—	4	1	no	—
306	C₂×D₄	—	4	2	no	—
307	C₂×D₄	—	4	2	no	—
308	C₂×D₄	—	8	4	no	—
309	C₂²×C₄	—	2	2	no	—
310	C₂²×C₄	—	2	2	no	—
311	C₂²×C₄	—	4	8	no	—
312	C₂²×C₄	—	4	1	no	—
313	C₂²×C₄	—	4	4	no	—
314	C₂²×C₄	—	4	1	no	—
315	C₂²×C₄	C₁₃×D₈	1	1	yes	characteristic
316	C₂²×C₄	C₁₃×D₈	1	2	yes	—
317	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
318	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
319	Q₁₆	—	2	4	no	—
320	Q₁₆	—	2	2	no	—
321	Q₁₆	C₂×D₄×C₁₃	1	4	yes	complemented
322	SD₁₆	—	2	16	no	—
323	D₈	—	2	4	no	—
324	D₈	—	2	2	no	—
325	D₈	—	2	2	no	—
326	D₈	—	2	2	no	—
327	D₈	—	4	2	no	—
328	D₈	C₂×D₄×C₁₃	1	4	yes	complemented
329	C₂×C₈	—	2	2	no	—
330	C₂×C₈	—	2	4	no	—
331	C₂×C₈	—	2	2	no	—
332	C₂×C₈	—	2	2	no	—
333	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
334	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
335	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
336	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
337	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
338	C₄⋊C₄	—	2	2	no	—
339	C₄⋊C₄	—	4	1	no	—
340	C₂²⋊C₄	—	4	4	no	—
341	C₁₆	—	2	2	no	—
342	C₁₆	—	2	2	no	—
343	C₁₃	C₂×#2186	1	1	yes	characteristic, direct product factor, Sylow
344	C₂³	—	2	2	no	—
345	C₂³	—	2	2	no	—
346	C₂³	—	2	2	no	—
347	C₂³	—	4	4	no	—
348	C₂³	—	4	2	no	—
349	C₂³	—	4	2	no	—
350	C₂³	—	8	2	no	—
351	C₂³	—	8	2	no	—
352	C₂³	—	8	2	no	—
353	C₂³	—	8	2	no	—
354	C₂³	—	8	2	no	—
355	C₂³	C₂×C₁₃×D₈	1	2	yes	—
356	C₂³	C₂×C₁₃×D₈	1	1	yes	characteristic
357	Q₈	—	2	4	no	—
358	Q₈	—	4	4	no	—
359	Q₈	—	4	2	no	—
360	D₄	—	2	4	no	—
361	D₄	—	4	16	no	—
362	D₄	—	4	4	no	—
363	D₄	—	4	2	no	—
364	D₄	—	4	2	no	—
365	D₄	—	4	2	no	—
366	D₄	—	8	8	no	—
367	D₄	—	8	2	no	—
368	C₂×C₄	—	2	2	no	—
369	C₂×C₄	—	2	4	no	—
370	C₂×C₄	—	2	2	no	—
371	C₂×C₄	—	2	2	no	—
372	C₂×C₄	—	4	16	no	—
373	C₂×C₄	—	4	4	no	—
374	C₂×C₄	—	4	2	no	—
375	C₂×C₄	—	4	2	no	—
376	C₂×C₄	—	8	2	no	—
377	C₂×C₄	C₁₃×#120	1	2	yes	—
378	C₂×C₄	C₂×C₁₃×D₈	1	2	yes	—
379	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
380	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
381	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
382	C₈	—	2	2	no	—
383	C₈	C₁₃×#120	1	2	yes	—
384	C₈	C₂²×D₄×C₁₃	1	1	yes	characteristic
385	C₈	C₂²×D₄×C₁₃	1	1	yes	characteristic
386	C₂²	—	2	2	no	—
387	C₂²	—	2	2	no	—
388	C₂²	—	2	2	no	—
389	C₂²	—	4	4	no	—
390	C₂²	—	4	4	no	—
391	C₂²	—	8	2	no	—
392	C₂²	—	8	2	no	—
393	C₂²	—	8	8	no	—
394	C₂²	—	8	2	no	—
395	C₂²	—	8	2	no	—
396	C₂²	—	8	2	no	—
397	C₂²	—	16	4	no	—
398	C₂²	C₁₃×#447	1	2	yes	—
399	C₂²	C₁₃×#508	1	2	yes	—
400	C₂²	C₁₃×#509	1	2	yes	—
401	C₂²	C₂²×C₁₃×D₈	1	1	yes	characteristic
402	C₄	—	2	2	no	—
403	C₄	—	4	4	no	—
404	C₄	—	8	2	no	—
405	C₄	C₁₃×#447	1	2	yes	—
406	C₄	C₂×C₁₃×#120	1	1	yes	characteristic
407	C₄	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
408	C₂	—	4	2	no	—
409	C₂	—	8	4	no	—
410	C₂	—	16	2	no	—
411	C₂	C₁₃×#2186	1	4	yes	direct product factor
412	C₂	C₂×C₁₃×#447	1	1	yes	characteristic
413	C₂	C₂×C₁₃×#508	1	1	yes	characteristic
414	C₂	C₂×C₁₃×#509	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₁₃
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂³×C₄×C₁₃ ◁ C₂³×C₈×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×C₁₃×#135	C₂	semidirect
2. C₂²×C₁₃×SD₃₂	C₂	semidirect
3. C₂²×C₁₃×D₁₆	C₂	semidirect
4. C₂×C₁₃×#466	C₂	semidirect
5. C₁₃×#2186	C₂	direct (N × H)
6. C₂×C₁₃×#358	C₂	semidirect
7. C₂×C₁₃×#357	C₂	semidirect
8. C₂×C₁₃×C₂²⋊C₁₆	C₂	semidirect
13. C₂×C₁₃×#135	C₂²	semidirect
21. C₂×C₁₃×SD₃₂	C₂²	semidirect
23. C₂×C₁₃×D₁₆	C₂²	semidirect
27. C₁₃×#466	C₂²	semidirect
30. C₁₃×#358	C₂²	semidirect
31. C₁₃×#357	C₂²	semidirect
32. C₁₃×C₂²⋊C₁₆	C₂²	semidirect
49. C₂×C₁₃×Q₁₆	D₄	semidirect
58. C₂×C₁₃×D₈	D₄	semidirect
80. C₂×#2186	C₁₃	direct (N × H)
115. C₁₃×Q₁₆	C₂×D₄	semidirect
122. C₁₃×D₈	C₂×D₄	semidirect
137. C₂²×#135	C₂×C₁₃	semidirect
138. C₂²×SD₃₂	C₂×C₁₃	semidirect
139. C₂²×D₁₆	C₂×C₁₃	semidirect
140. C₂×#466	C₂×C₁₃	semidirect
141. #2186	C₂×C₁₃	direct (N × H)
142. C₂×#358	C₂×C₁₃	semidirect
143. C₂×#357	C₂×C₁₃	semidirect
144. C₂×C₂²⋊C₁₆	C₂×C₁₃	semidirect
191. C₂×#135	C₂²×C₁₃	semidirect
199. C₂×SD₃₂	C₂²×C₁₃	semidirect
201. C₂×D₁₆	C₂²×C₁₃	semidirect
205. #466	C₂²×C₁₃	semidirect
208. #358	C₂²×C₁₃	semidirect
209. #357	C₂²×C₁₃	semidirect
210. C₂²⋊C₁₆	C₂²×C₁₃	semidirect
249. C₂×Q₁₆	D₄×C₁₃	semidirect
258. C₂×D₈	D₄×C₁₃	semidirect
283. C₂×C₁₃	#2186	direct (N × H)
321. Q₁₆	C₂×D₄×C₁₃	semidirect
328. D₈	C₂×D₄×C₁₃	semidirect
343. C₁₃	C₂×#2186	direct (N × H)
411. C₂	C₁₃×#2186	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×#135	2
C₂²×C₁₃×SD₃₂	2
C₂²×C₁₃×D₁₆	2
C₂×C₁₃×#466	2
C₁₃×#2186	2
C₂×C₁₃×#358	2
C₂×C₁₃×#357	2
C₂×C₁₃×C₂²⋊C₁₆	2
C₂×#2186	13

Subgroups — C2×C13×#2186 #15719853

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#2186 #15719853