Subgroups — C₂×C₁₃×#2180 #15719805

Order 3328.

646 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#510	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×#444	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₃×#441	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2180	C₂	1	8	yes	maximal, direct product factor
5	C₂×C₁₃×#365	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₁₃×#362	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₁₃×#360	C₂	1	1	yes	maximal, characteristic
8	C₂×C₁₃×#347	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₁₃×#135	C₂²	1	1	yes	characteristic
10	C₂²×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
11	C₂×C₁₃×#131	—	2	1	no	—
12	C₂×C₄×Q₈×C₁₃	—	2	1	no	—
13	C₁₃×#510	C₄	1	4	yes	complemented
14	C₁₃×#510	C₂²	1	4	yes	—
15	C₂×C₁₃×Q₃₂	C₄	1	2	yes	complemented
16	C₂×C₁₃×SD₃₂	C₄	1	2	yes	complemented
17	C₂×C₁₃×M₃₂	C₂²	1	1	yes	characteristic
18	C₂×C₁₃×M₃₂	C₂²	1	1	yes	characteristic
19	C₁₃×#444	—	2	2	no	—
20	C₁₃×#444	C₂²	1	4	yes	—
21	C₁₃×#441	—	2	2	no	—
22	C₁₃×#441	C₂²	1	4	yes	complemented
23	C₂×C₁₃×#108	C₂²	1	1	yes	characteristic
24	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
25	C₂×C₁₃×#104	—	2	1	no	—
26	C₂×C₁₃×#103	—	2	1	no	—
27	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
28	C₁₃×#365	C₂²	1	4	yes	complemented
29	C₁₃×#362	C₂²	1	4	yes	complemented
30	C₁₃×#360	C₂²	1	4	yes	—
31	C₁₃×#347	C₂²	1	4	yes	complemented
32	C₂×C₁₃×#41	—	2	1	no	—
33	C₂²×Q₈×C₁₃	—	2	1	no	—
34	C₁₃×#135	—	2	1	no	—
35	C₁₃×#135	—	2	1	no	—
36	C₁₃×#135	C₂×C₄	1	2	yes	—
37	C₁₃×#135	C₂³	1	2	yes	—
38	C₂×C₁₃×Q₁₆	—	2	1	no	—
39	C₂×C₁₃×Q₁₆	—	2	1	no	—
40	C₂×C₁₃×Q₁₆	—	2	1	no	—
41	C₂×C₁₃×Q₁₆	C₂×C₄	1	2	yes	—
42	C₂×C₁₃×Q₁₆	C₂×C₄	1	1	yes	characteristic
43	C₂×C₁₃×Q₁₆	C₂×C₄	1	2	yes	—
44	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
45	C₂×C₁₃×SD₁₆	—	2	1	no	—
46	C₂×C₁₃×D₈	C₂×C₄	1	1	yes	characteristic
47	C₁₃×#131	—	2	4	no	—
48	C₁₃×#131	—	4	2	no	—
49	C₂×C₁₃×M₁₆	—	2	1	no	—
50	C₂×C₁₃×M₁₆	—	4	1	no	—
51	C₂²×C₈×C₁₃	—	4	1	no	—
52	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
53	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
54	C₄×Q₈×C₁₃	—	2	4	no	—
55	C₄×Q₈×C₁₃	—	4	2	no	—
56	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
57	C₂×C₁₃×C₄⋊C₄	—	4	1	no	—
58	C₂×C₄²×C₁₃	—	4	1	no	—
59	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
60	C₁₃×Q₃₂	C₂×C₄	1	8	yes	complemented
61	C₁₃×SD₃₂	C₂×C₄	1	8	yes	complemented
62	C₁₃×M₃₂	—	2	1	no	—
63	C₁₃×M₃₂	C₂×C₄	1	2	yes	—
64	C₁₃×M₃₂	C₂³	1	2	yes	—
65	C₁₃×M₃₂	C₂³	1	2	yes	—
66	C₂×C₁₃×C₁₆	—	2	1	no	—
67	C₂×C₁₃×C₁₆	C₂×C₄	1	2	yes	—
68	C₁₃×#108	—	2	1	no	—
69	C₁₃×#108	C₂³	1	2	yes	—
70	C₁₃×#106	—	2	1	no	—
71	C₁₃×#106	C₂³	1	2	yes	—
72	C₁₃×#104	—	2	4	no	—
73	C₁₃×#103	—	2	4	no	—
74	C₁₃×#97	D₄	1	2	yes	—
75	C₁₃×#97	C₂³	1	2	yes	—
76	C₂×#2180	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
77	C₁₃×#41	—	2	2	no	—
78	C₁₃×#41	—	2	2	no	—
79	C₁₃×#41	—	4	1	no	—
80	C₁₃×#41	—	4	1	no	—
81	C₂×Q₈×C₁₃	—	2	1	no	—
82	C₂×Q₈×C₁₃	—	2	2	no	—
83	C₂×Q₈×C₁₃	—	2	2	no	—
84	C₂×Q₈×C₁₃	—	2	2	no	—
85	C₂×Q₈×C₁₃	—	4	1	no	—
86	C₂×Q₈×C₁₃	—	4	1	no	—
87	C₂×Q₈×C₁₃	—	4	1	no	—
88	C₂×D₄×C₁₃	—	2	1	no	—
89	C₂×D₄×C₁₃	—	4	1	no	—
90	C₂²×C₄×C₁₃	—	2	1	no	—
91	C₂²×C₄×C₁₃	—	4	1	no	—
92	C₂²×C₄×C₁₃	—	4	1	no	—
93	C₂²×C₄×C₁₃	—	4	1	no	—
94	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
95	C₁₃×Q₁₆	—	2	2	no	—
96	C₁₃×Q₁₆	—	2	2	no	—
97	C₁₃×Q₁₆	—	2	1	no	—
98	C₁₃×Q₁₆	—	2	2	no	—
99	C₁₃×Q₁₆	C₂²×C₄	1	4	yes	—
100	C₁₃×Q₁₆	C₂²×C₄	1	2	yes	—
101	C₁₃×SD₁₆	—	2	2	no	—
102	C₁₃×SD₁₆	—	2	2	no	—
103	C₁₃×D₈	—	2	1	no	—
104	C₁₃×D₈	C₂²×C₄	1	2	yes	—
105	C₁₃×M₁₆	—	2	2	no	—
106	C₁₃×M₁₆	—	4	4	no	—
107	C₁₃×M₁₆	—	4	1	no	—
108	C₂×C₈×C₁₃	—	2	1	no	—
109	C₂×C₈×C₁₃	—	2	1	no	—
110	C₂×C₈×C₁₃	—	4	4	no	—
111	C₂×C₈×C₁₃	—	4	1	no	—
112	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
113	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
114	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
115	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
116	C₂×C₈×C₁₃	#41	1	1	yes	characteristic
117	C₂×C₈×C₁₃	#41	1	1	yes	characteristic
118	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
119	C₁₃×C₄⋊C₄	—	2	2	no	—
120	C₁₃×C₄⋊C₄	—	4	4	no	—
121	C₁₃×C₄⋊C₄	—	4	1	no	—
122	C₄²×C₁₃	—	2	1	no	—
123	C₄²×C₁₃	—	4	4	no	—
124	C₄²×C₁₃	C₂×D₄	1	2	yes	—
125	C₁₃×C₁₆	—	2	2	no	—
126	C₁₃×C₁₆	C₂²×C₄	1	4	yes	—
127	C₂×#510	C₂×C₁₃	1	1	yes	characteristic
128	C₂×#444	C₂×C₁₃	1	1	yes	characteristic
129	C₂×#441	C₂×C₁₃	1	1	yes	characteristic, complemented
130	#2180	C₂×C₁₃	1	8	yes	direct product factor
131	C₂×#365	C₂×C₁₃	1	1	yes	characteristic, complemented
132	C₂×#362	C₂×C₁₃	1	1	yes	characteristic, complemented
133	C₂×#360	C₂×C₁₃	1	1	yes	characteristic
134	C₂×#347	C₂×C₁₃	1	1	yes	characteristic, complemented
135	C₂³×C₁₃	—	4	1	no	—
136	C₂³×C₁₃	AGL(1,ℤ/8)	1	1	yes	characteristic
137	Q₈×C₁₃	—	2	2	no	—
138	Q₈×C₁₃	—	2	4	no	—
139	Q₈×C₁₃	—	4	2	no	—
140	Q₈×C₁₃	—	4	2	no	—
141	Q₈×C₁₃	—	4	2	no	—
142	Q₈×C₁₃	—	4	1	no	—
143	D₄×C₁₃	—	2	2	no	—
144	D₄×C₁₃	—	4	2	no	—
145	D₄×C₁₃	—	4	2	no	—
146	D₄×C₁₃	—	4	1	no	—
147	C₂×C₄×C₁₃	—	2	2	no	—
148	C₂×C₄×C₁₃	—	4	2	no	—
149	C₂×C₄×C₁₃	—	4	2	no	—
150	C₂×C₄×C₁₃	—	4	2	no	—
151	C₂×C₄×C₁₃	—	4	1	no	—
152	C₂×C₄×C₁₃	—	4	2	no	—
153	C₂×C₄×C₁₃	—	4	2	no	—
154	C₂×C₄×C₁₃	—	4	2	no	—
155	C₂×C₄×C₁₃	—	4	2	no	—
156	C₂×C₄×C₁₃	—	8	2	no	—
157	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
158	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
159	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	1	yes	characteristic
160	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	1	yes	characteristic
161	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	1	yes	characteristic
162	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
163	C₈×C₁₃	—	2	2	no	—
164	C₈×C₁₃	—	4	2	no	—
165	C₈×C₁₃	C₄×D₄	1	1	yes	characteristic
166	C₈×C₁₃	C₄×D₄	1	1	yes	characteristic
167	C₈×C₁₃	C₂³×C₄	1	1	yes	characteristic
168	C₈×C₁₃	C₂×#41	1	1	yes	characteristic
169	C₂×#135	C₂²×C₁₃	1	1	yes	characteristic
170	C₂²×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
171	C₂×#131	—	2	1	no	—
172	C₂×C₄×Q₈	—	2	1	no	—
173	#510	C₄×C₁₃	1	4	yes	complemented
174	#510	C₂²×C₁₃	1	4	yes	—
175	C₂×Q₃₂	C₄×C₁₃	1	2	yes	complemented
176	C₂×SD₃₂	C₄×C₁₃	1	2	yes	complemented
177	C₂×M₃₂	C₂²×C₁₃	1	1	yes	characteristic
178	C₂×M₃₂	C₂²×C₁₃	1	1	yes	characteristic
179	#444	—	2	2	no	—
180	#444	C₂²×C₁₃	1	4	yes	—
181	#441	—	2	2	no	—
182	#441	C₂²×C₁₃	1	4	yes	complemented
183	C₂×#108	C₂²×C₁₃	1	1	yes	characteristic
184	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
185	C₂×#104	—	2	1	no	—
186	C₂×#103	—	2	1	no	—
187	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
188	#365	C₂²×C₁₃	1	4	yes	complemented
189	#362	C₂²×C₁₃	1	4	yes	complemented
190	#360	C₂²×C₁₃	1	4	yes	—
191	#347	C₂²×C₁₃	1	4	yes	complemented
192	C₂²×C₁₃	—	2	2	no	—
193	C₂²×C₁₃	—	4	2	no	—
194	C₂²×C₁₃	—	8	2	no	—
195	C₂²×C₁₃	#442	1	1	yes	characteristic
196	C₂²×C₁₃	#442	1	1	yes	characteristic
197	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
198	C₄×C₁₃	—	4	2	no	—
199	C₄×C₁₃	—	4	2	no	—
200	C₄×C₁₃	—	4	4	no	—
201	C₄×C₁₃	—	8	2	no	—
202	C₄×C₁₃	#442	1	1	yes	characteristic
203	C₄×C₁₃	#442	1	1	yes	characteristic
204	C₄×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
205	C₄×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
206	C₂×#41	—	2	1	no	—
207	C₂²×Q₈	—	2	1	no	—
208	#135	—	2	1	no	—
209	#135	—	2	1	no	—
210	#135	C₂×C₄×C₁₃	1	2	yes	—
211	#135	C₂³×C₁₃	1	2	yes	—
212	C₂×Q₁₆	—	2	1	no	—
213	C₂×Q₁₆	—	2	1	no	—
214	C₂×Q₁₆	—	2	1	no	—
215	C₂×Q₁₆	C₂×C₄×C₁₃	1	2	yes	—
216	C₂×Q₁₆	C₂×C₄×C₁₃	1	2	yes	—
217	C₂×Q₁₆	C₂×C₄×C₁₃	1	1	yes	characteristic
218	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
219	C₂×SD₁₆	—	2	1	no	—
220	C₂×D₈	C₂×C₄×C₁₃	1	1	yes	characteristic
221	#131	—	2	4	no	—
222	#131	—	4	2	no	—
223	C₂×M₁₆	—	2	1	no	—
224	C₂×M₁₆	—	4	1	no	—
225	C₂²×C₈	—	4	1	no	—
226	C₂²×C₈	D₄×C₁₃	1	1	yes	characteristic
227	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
228	C₄×Q₈	—	2	4	no	—
229	C₄×Q₈	—	4	2	no	—
230	C₂×C₄⋊C₄	—	2	1	no	—
231	C₂×C₄⋊C₄	—	4	1	no	—
232	C₂×C₄²	—	4	1	no	—
233	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
234	Q₃₂	C₂×C₄×C₁₃	1	8	yes	complemented
235	SD₃₂	C₂×C₄×C₁₃	1	8	yes	complemented
236	M₃₂	—	2	1	no	—
237	M₃₂	C₂×C₄×C₁₃	1	2	yes	—
238	M₃₂	C₂³×C₁₃	1	2	yes	—
239	M₃₂	C₂³×C₁₃	1	2	yes	—
240	C₂×C₁₆	—	2	1	no	—
241	C₂×C₁₆	C₂×C₄×C₁₃	1	2	yes	—
242	#108	—	2	1	no	—
243	#108	C₂³×C₁₃	1	2	yes	—
244	#106	—	2	1	no	—
245	#106	C₂³×C₁₃	1	2	yes	—
246	#104	—	2	4	no	—
247	#103	—	2	4	no	—
248	#97	D₄×C₁₃	1	2	yes	—
249	#97	C₂³×C₁₃	1	2	yes	—
250	C₂×C₁₃	—	2	1	no	—
251	C₂×C₁₃	—	2	1	no	—
252	C₂×C₁₃	—	8	2	no	—
253	C₂×C₁₃	#2180	1	2	yes	direct product factor
254	C₂×C₁₃	C₂×#442	1	1	yes	characteristic
255	#41	—	2	2	no	—
256	#41	—	2	2	no	—
257	#41	—	4	1	no	—
258	#41	—	4	1	no	—
259	C₂×Q₈	—	2	1	no	—
260	C₂×Q₈	—	2	2	no	—
261	C₂×Q₈	—	2	2	no	—
262	C₂×Q₈	—	2	2	no	—
263	C₂×Q₈	—	4	1	no	—
264	C₂×Q₈	—	4	1	no	—
265	C₂×Q₈	—	4	1	no	—
266	C₂×D₄	—	2	1	no	—
267	C₂×D₄	—	4	1	no	—
268	C₂²×C₄	—	2	1	no	—
269	C₂²×C₄	—	4	1	no	—
270	C₂²×C₄	—	4	1	no	—
271	C₂²×C₄	—	4	1	no	—
272	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
273	Q₁₆	—	2	2	no	—
274	Q₁₆	—	2	2	no	—
275	Q₁₆	—	2	1	no	—
276	Q₁₆	—	2	2	no	—
277	Q₁₆	C₂²×C₄×C₁₃	1	4	yes	—
278	Q₁₆	C₂²×C₄×C₁₃	1	2	yes	—
279	SD₁₆	—	2	2	no	—
280	SD₁₆	—	2	2	no	—
281	D₈	—	2	1	no	—
282	D₈	C₂²×C₄×C₁₃	1	2	yes	—
283	M₁₆	—	2	2	no	—
284	M₁₆	—	4	4	no	—
285	M₁₆	—	4	1	no	—
286	C₂×C₈	—	2	1	no	—
287	C₂×C₈	—	2	1	no	—
288	C₂×C₈	—	4	4	no	—
289	C₂×C₈	—	4	1	no	—
290	C₂×C₈	C₂²×C₄×C₁₃	1	1	yes	characteristic
291	C₂×C₈	C₂²×C₄×C₁₃	1	1	yes	characteristic
292	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
293	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
294	C₂×C₈	C₁₃×#41	1	1	yes	characteristic
295	C₂×C₈	C₁₃×#41	1	1	yes	characteristic
296	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
297	C₄⋊C₄	—	2	2	no	—
298	C₄⋊C₄	—	4	4	no	—
299	C₄⋊C₄	—	4	1	no	—
300	C₄²	—	2	1	no	—
301	C₄²	—	4	4	no	—
302	C₄²	C₂×D₄×C₁₃	1	2	yes	—
303	C₁₆	—	2	2	no	—
304	C₁₆	C₂²×C₄×C₁₃	1	4	yes	—
305	C₁₃	C₂×#2180	1	1	yes	characteristic, direct product factor, Sylow
306	C₂³	—	4	1	no	—
307	C₂³	C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
308	Q₈	—	2	2	no	—
309	Q₈	—	2	4	no	—
310	Q₈	—	4	2	no	—
311	Q₈	—	4	2	no	—
312	Q₈	—	4	1	no	—
313	Q₈	—	4	2	no	—
314	D₄	—	2	2	no	—
315	D₄	—	4	2	no	—
316	D₄	—	4	2	no	—
317	D₄	—	4	1	no	—
318	C₂×C₄	—	2	2	no	—
319	C₂×C₄	—	4	2	no	—
320	C₂×C₄	—	4	1	no	—
321	C₂×C₄	—	4	2	no	—
322	C₂×C₄	—	4	2	no	—
323	C₂×C₄	—	4	2	no	—
324	C₂×C₄	—	4	2	no	—
325	C₂×C₄	—	4	2	no	—
326	C₂×C₄	—	4	2	no	—
327	C₂×C₄	—	8	2	no	—
328	C₂×C₄	C₄×D₄×C₁₃	1	1	yes	characteristic
329	C₂×C₄	C₄×D₄×C₁₃	1	1	yes	characteristic
330	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
331	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
332	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
333	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
334	C₈	—	2	2	no	—
335	C₈	—	4	2	no	—
336	C₈	C₄×D₄×C₁₃	1	1	yes	characteristic
337	C₈	C₄×D₄×C₁₃	1	1	yes	characteristic
338	C₈	C₂³×C₄×C₁₃	1	1	yes	characteristic
339	C₈	C₂×C₁₃×#41	1	1	yes	characteristic
340	C₂²	—	2	2	no	—
341	C₂²	—	4	2	no	—
342	C₂²	—	8	2	no	—
343	C₂²	C₁₃×#442	1	1	yes	characteristic
344	C₂²	C₁₃×#442	1	1	yes	characteristic
345	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
346	C₄	—	4	2	no	—
347	C₄	—	4	2	no	—
348	C₄	—	4	4	no	—
349	C₄	—	8	2	no	—
350	C₄	C₁₃×#442	1	1	yes	characteristic
351	C₄	C₁₃×#442	1	1	yes	characteristic
352	C₄	C₂×C₄×D₄×C₁₃	1	1	yes	characteristic
353	C₄	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
354	C₂	—	2	1	no	—
355	C₂	—	2	1	no	—
356	C₂	—	8	2	no	—
357	C₂	C₁₃×#2180	1	2	yes	direct product factor
358	C₂	C₂×C₁₃×#442	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	#442
commutator	C₈	C₂³×C₄×C₁₃
Frattini, cosocle	C₂×C₈	C₂⁴×C₁₃
prime radical	C₂×C₁₃×#135	C₂²
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂²×C₄×C₁₃ ◁ C₂×C₁₃×#97 ◁ G

Complements

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

N	H ≅ G/N	type
3. C₂×C₁₃×#441	C₂	semidirect
4. C₁₃×#2180	C₂	direct (N × H)
5. C₂×C₁₃×#365	C₂	semidirect
6. C₂×C₁₃×#362	C₂	semidirect
8. C₂×C₁₃×#347	C₂	semidirect
13. C₁₃×#510	C₄	semidirect
15. C₂×C₁₃×Q₃₂	C₄	semidirect
16. C₂×C₁₃×SD₃₂	C₄	semidirect
22. C₁₃×#441	C₂²	semidirect
28. C₁₃×#365	C₂²	semidirect
29. C₁₃×#362	C₂²	semidirect
31. C₁₃×#347	C₂²	semidirect
60. C₁₃×Q₃₂	C₂×C₄	semidirect
61. C₁₃×SD₃₂	C₂×C₄	semidirect
76. C₂×#2180	C₁₃	direct (N × H)
129. C₂×#441	C₂×C₁₃	semidirect
130. #2180	C₂×C₁₃	direct (N × H)
131. C₂×#365	C₂×C₁₃	semidirect
132. C₂×#362	C₂×C₁₃	semidirect
134. C₂×#347	C₂×C₁₃	semidirect
173. #510	C₄×C₁₃	semidirect
175. C₂×Q₃₂	C₄×C₁₃	semidirect
176. C₂×SD₃₂	C₄×C₁₃	semidirect
182. #441	C₂²×C₁₃	semidirect
188. #365	C₂²×C₁₃	semidirect
189. #362	C₂²×C₁₃	semidirect
191. #347	C₂²×C₁₃	semidirect
234. Q₃₂	C₂×C₄×C₁₃	semidirect
235. SD₃₂	C₂×C₄×C₁₃	semidirect
253. C₂×C₁₃	#2180	direct (N × H)
305. C₁₃	C₂×#2180	direct (N × H)
357. C₂	C₁₃×#2180	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×#510	2
C₂×C₁₃×#444	2
C₂×C₁₃×#441	2
C₁₃×#2180	2
C₂×C₁₃×#365	2
C₂×C₁₃×#362	2
C₂×C₁₃×#360	2
C₂×C₁₃×#347	2
C₂×#2180	13

Subgroups — C2×C13×#2180 #15719805

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#2180 #15719805