Subgroups — #16016379

Order 3328.

646 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13123753	C₂	1	1	yes	maximal, characteristic, complemented
2	#13123720	C₂	1	1	yes	maximal, characteristic, complemented
3	#13116735	C₂	1	4	yes	maximal, complemented
4	#13116728	C₂	1	4	yes	maximal, complemented
5	C₂×#11718105	C₂	1	1	yes	maximal, characteristic, complemented
6	#13116585	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#11718158	C₂	1	1	yes	maximal, characteristic, complemented
8	#13116440	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#3414	C₂	1	1	yes	maximal, characteristic
10	C₂×C₁₃×#135	C₂²	1	1	yes	characteristic
11	C₂×C₁₃×#135	C₂²	1	1	yes	characteristic
12	#11719532	—	2	1	no	—
13	#11719524	—	2	1	no	—
14	C₁₃×#510	C₄	1	2	yes	complemented
15	C₁₃×#510	C₂²	1	2	yes	—
16	C₁₃×#509	C₄	1	2	yes	complemented
17	C₁₃×#509	C₂²	1	2	yes	—
18	C₁₃×#508	C₄	1	4	yes	complemented
19	C₂×C₁₃×M₃₂	C₂²	1	1	yes	characteristic
20	#11718897	—	2	1	no	—
21	#11718893	—	2	1	no	—
22	#11718858	C₂²	1	4	yes	—
23	#11718857	—	2	2	no	—
24	#11718845	C₂²	1	2	yes	complemented
25	SD₁₆×Dic₁₃	—	2	2	no	—
26	#11718813	C₂²	1	2	yes	complemented
27	C₂×#88059	C₂²	1	1	yes	characteristic
28	C₂×#88057	C₂²	1	1	yes	characteristic
29	#11718762	C₂²	1	1	yes	characteristic
30	C₂×#88052	C₂²	1	1	yes	characteristic
31	#11718158	C₂²	1	4	yes	—
32	#11718157	C₂²	1	2	yes	complemented
33	#11718155	C₂²	1	2	yes	complemented
34	#11718105	C₂²	1	4	yes	complemented
35	#11718104	C₂²	1	4	yes	complemented
36	C₂×C₁₃×#41	—	2	1	no	—
37	C₂×C₁₃×#41	—	2	1	no	—
38	C₁₃×#135	—	2	1	no	—
39	C₁₃×#135	—	2	1	no	—
40	C₁₃×#135	—	2	1	no	—
41	C₁₃×#135	—	2	1	no	—
42	C₁₃×#135	C₂×C₄	1	2	yes	—
43	C₁₃×#135	C₂×C₄	1	2	yes	—
44	C₁₃×#135	C₂×C₄	1	2	yes	complemented
45	C₁₃×#135	C₂³	1	2	yes	—
46	C₂×C₁₃×Q₁₆	C₂×C₄	1	1	yes	characteristic, complemented
47	C₂×C₁₃×Q₁₆	C₂³	1	1	yes	characteristic
48	C₂×C₁₃×SD₁₆	—	2	1	no	—
49	C₂×C₁₃×SD₁₆	—	2	1	no	—
50	C₂×C₁₃×D₈	C₂×C₄	1	1	yes	characteristic, complemented
51	C₂×C₁₃×D₈	C₂³	1	1	yes	characteristic
52	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
53	#88202	—	2	4	no	—
54	#88202	—	4	2	no	—
55	Q₈×Dic₁₃	—	2	2	no	—
56	D₄×Dic₁₃	—	2	2	no	—
57	D₄×Dic₁₃	—	4	2	no	—
58	#88180	—	4	1	no	—
59	#88180	D₄	1	1	yes	characteristic
60	C₂×C₄⋊Dic₁₃	—	2	1	no	—
61	C₂×C₄⋊Dic₁₃	—	4	1	no	—
62	C₂×#6099	—	2	1	no	—
63	C₂×#6099	—	4	2	no	—
64	C₂×#6099	D₄	1	1	yes	characteristic
65	C₁₃×Q₃₂	C₂×C₄	1	4	yes	complemented
66	C₁₃×SD₃₂	C₂×C₄	1	4	yes	complemented
67	C₁₃×SD₃₂	C₂×C₄	1	4	yes	complemented
68	C₁₃×D₁₆	C₂×C₄	1	4	yes	complemented
69	C₁₃×M₃₂	C₂×C₄	1	2	yes	complemented
70	C₁₃×M₃₂	C₂³	1	2	yes	—
71	C₂×C₁₃×C₁₆	C₂×C₄	1	2	yes	complemented
72	#88077	—	2	4	no	—
73	#88075	—	2	2	no	—
74	#88072	—	2	2	no	—
75	#88059	—	2	1	no	—
76	#88059	C₂³	1	2	yes	—
77	#88057	—	2	1	no	—
78	#88057	C₂³	1	2	yes	—
79	#88055	C₂³	1	2	yes	—
80	C₈×Dic₁₃	D₄	1	2	yes	—
81	#88052	—	2	1	no	—
82	#88052	C₂³	1	2	yes	—
83	C₂×#6090	—	2	1	no	—
84	#33469	—	13	1	no	maximal, Sylow
85	C₁₃×#41	—	2	2	no	—
86	C₁₃×#41	—	2	2	no	—
87	C₁₃×#41	—	2	2	no	—
88	C₁₃×#41	—	2	2	no	—
89	C₁₃×#41	—	4	1	no	—
90	C₁₃×#41	—	4	1	no	—
91	C₁₃×#41	—	4	1	no	—
92	C₁₃×#41	—	4	1	no	—
93	C₂×Q₈×C₁₃	—	2	1	no	—
94	C₂×Q₈×C₁₃	—	2	1	no	—
95	C₂×D₄×C₁₃	—	2	1	no	—
96	C₂×D₄×C₁₃	—	2	1	no	—
97	C₂×D₄×C₁₃	—	4	1	no	—
98	C₂×D₄×C₁₃	—	4	1	no	—
99	C₂²×C₄×C₁₃	—	4	1	no	—
100	C₂²×C₄×C₁₃	—	4	1	no	—
101	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
102	C₂²×Dic₁₃	—	4	2	no	—
103	C₂²×Dic₁₃	—	4	1	no	—
104	C₁₃×Q₁₆	—	2	1	no	—
105	C₁₃×Q₁₆	—	2	1	no	—
106	C₁₃×Q₁₆	C₂²×C₄	1	2	yes	—
107	C₁₃×Q₁₆	C₂²×C₄	1	2	yes	—
108	C₁₃×SD₁₆	—	2	2	no	—
109	C₁₃×SD₁₆	—	2	2	no	—
110	C₁₃×SD₁₆	—	2	2	no	—
111	C₁₃×SD₁₆	—	2	2	no	—
112	C₁₃×D₈	—	2	1	no	—
113	C₁₃×D₈	—	2	1	no	—
114	C₁₃×D₈	C₂²×C₄	1	2	yes	—
115	C₁₃×D₈	C₂²×C₄	1	2	yes	—
116	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
117	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
118	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
119	C₂×C₈×C₁₃	#41	1	1	yes	characteristic
120	C₂×C₈×C₁₃	#41	1	1	yes	characteristic
121	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
122	C₂²⋊Dic₁₃	—	2	1	no	—
123	C₂²⋊Dic₁₃	—	4	2	no	—
124	C₄⋊Dic₁₃	—	2	1	no	—
125	C₄⋊Dic₁₃	—	2	2	no	—
126	C₄⋊Dic₁₃	—	4	2	no	—
127	C₄⋊Dic₁₃	—	4	1	no	—
128	C₄×Dic₁₃	—	4	2	no	—
129	C₄×Dic₁₃	C₂×D₄	1	2	yes	—
130	#6099	—	2	1	no	—
131	#6099	—	2	1	no	—
132	#6099	—	2	2	no	—
133	#6099	—	4	4	no	—
134	#6099	—	4	1	no	—
135	C₂×#1055	—	4	4	no	—
136	C₂×#1055	—	4	1	no	—
137	C₂×#1055	C₂×D₄	1	2	yes	—
138	C₁₃×C₁₆	C₂²×C₄	1	4	yes	—
139	#6090	—	2	2	no	—
140	#3414	D₁₃	1	1	yes	characteristic
141	#2957	—	13	1	no	—
142	#2952	—	13	1	no	—
143	AGL(1,ℤ/16)	—	13	4	no	—
144	#2180	—	13	4	no	—
145	C₂×#365	—	13	1	no	—
146	#2148	—	13	1	no	—
147	C₂×#360	—	13	1	no	—
148	#2110	—	13	1	no	—
149	C₂³×C₁₃	—	4	1	no	—
150	C₂³×C₁₃	—	4	1	no	—
151	C₂³×C₁₃	AGL(1,ℤ/8)	1	1	yes	characteristic
152	Q₈×C₁₃	—	2	2	no	—
153	Q₈×C₁₃	—	2	2	no	—
154	Q₈×C₁₃	—	4	1	no	—
155	Q₈×C₁₃	—	4	1	no	—
156	D₄×C₁₃	—	2	2	no	—
157	D₄×C₁₃	—	2	2	no	—
158	D₄×C₁₃	—	4	2	no	—
159	D₄×C₁₃	—	4	2	no	—
160	D₄×C₁₃	—	4	2	no	—
161	D₄×C₁₃	—	4	2	no	—
162	D₄×C₁₃	—	4	1	no	—
163	D₄×C₁₃	—	4	1	no	—
164	C₂×C₄×C₁₃	—	4	1	no	—
165	C₂×C₄×C₁₃	—	4	1	no	—
166	C₂×C₄×C₁₃	—	4	2	no	—
167	C₂×C₄×C₁₃	—	4	2	no	—
168	C₂×C₄×C₁₃	—	4	2	no	—
169	C₂×C₄×C₁₃	—	4	2	no	—
170	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
171	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
172	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	1	yes	characteristic
173	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	1	yes	characteristic
174	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	1	yes	characteristic
175	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
176	C₂×Dic₁₃	—	2	2	no	—
177	C₂×Dic₁₃	—	4	2	no	—
178	C₂×Dic₁₃	—	16	2	no	—
179	C₂×Dic₁₃	—	16	1	no	—
180	C₈×C₁₃	C₄×D₄	1	1	yes	characteristic
181	C₈×C₁₃	C₄×D₄	1	1	yes	characteristic
182	C₈×C₁₃	C₂³×C₄	1	1	yes	characteristic
183	C₈×C₁₃	C₂×#41	1	1	yes	characteristic
184	#1055	—	2	2	no	—
185	#1055	—	4	2	no	—
186	C₂×#135	C₂×D₁₃	1	1	yes	characteristic
187	C₂×#135	C₂×D₁₃	1	1	yes	characteristic
188	#568	—	26	1	no	—
189	#520	—	26	1	no	—
190	#510	Dic₁₃	1	2	yes	complemented
191	#510	C₂×D₁₃	1	2	yes	—
192	#509	Dic₁₃	1	2	yes	complemented
193	#509	C₂×D₁₃	1	2	yes	—
194	#508	Dic₁₃	1	4	yes	complemented
195	C₂×M₃₂	—	13	1	no	—
196	C₂×M₃₂	C₂×D₁₃	1	1	yes	characteristic
197	#444	—	13	4	no	—
198	#443	—	26	2	no	—
199	#442	—	13	2	no	—
200	#441	—	13	2	no	—
201	C₄×SD₁₆	—	26	2	no	—
202	C₂×#108	—	13	1	no	—
203	C₂×#106	—	13	1	no	—
204	#421	—	26	1	no	—
205	#417	—	26	1	no	—
206	#405	—	13	1	no	—
207	#365	—	13	4	no	—
208	#362	—	13	2	no	—
209	#361	—	13	2	no	—
210	#360	—	13	4	no	—
211	#347	—	13	4	no	—
212	C₂²×C₁₃	—	4	1	no	—
213	C₂²×C₁₃	—	4	2	no	—
214	C₂²×C₁₃	—	4	2	no	—
215	C₂²×C₁₃	—	8	1	no	—
216	C₂²×C₁₃	—	8	1	no	—
217	C₂²×C₁₃	—	16	1	no	—
218	C₂²×C₁₃	#442	1	1	yes	characteristic
219	C₂²×C₁₃	#442	1	1	yes	characteristic
220	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
221	C₄×C₁₃	—	4	2	no	—
222	C₄×C₁₃	—	4	2	no	—
223	C₄×C₁₃	#442	1	1	yes	characteristic
224	C₄×C₁₃	#442	1	1	yes	characteristic
225	C₄×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
226	C₄×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
227	Dic₁₃	—	4	2	no	—
228	Dic₁₃	—	8	2	no	—
229	C₂×#41	—	2	1	no	—
230	C₂×#41	—	2	1	no	—
231	#135	—	2	1	no	—
232	#135	—	2	1	no	—
233	#135	—	2	1	no	—
234	#135	—	2	1	no	—
235	#135	C₂×Dic₁₃	1	2	yes	—
236	#135	C₂×Dic₁₃	1	2	yes	—
237	#135	C₂×Dic₁₃	1	2	yes	complemented
238	#135	C₂²×D₁₃	1	2	yes	—
239	C₂×Q₁₆	C₂×Dic₁₃	1	1	yes	characteristic, complemented
240	C₂×Q₁₆	C₂²×D₁₃	1	1	yes	characteristic
241	C₂×SD₁₆	—	2	1	no	—
242	C₂×SD₁₆	—	2	1	no	—
243	C₂×D₈	C₂×Dic₁₃	1	1	yes	characteristic, complemented
244	C₂×D₈	C₂²×D₁₃	1	1	yes	characteristic
245	#131	—	26	4	no	—
246	#131	—	52	2	no	—
247	C₂×M₁₆	—	13	1	no	—
248	C₂×M₁₆	—	26	1	no	—
249	C₂×M₁₆	—	52	2	no	—
250	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
251	C₄×Q₈	—	26	2	no	—
252	C₄×D₄	—	26	2	no	—
253	C₄×D₄	—	52	2	no	—
254	#117	—	13	1	no	—
255	#117	—	52	1	no	—
256	C₂×C₄⋊C₄	—	26	1	no	—
257	C₂×C₄⋊C₄	—	52	1	no	—
258	Q₃₂	C₂×Dic₁₃	1	4	yes	complemented
259	SD₃₂	C₂×Dic₁₃	1	4	yes	complemented
260	SD₃₂	C₂×Dic₁₃	1	4	yes	complemented
261	D₁₆	C₂×Dic₁₃	1	4	yes	complemented
262	M₃₂	—	13	2	no	—
263	M₃₂	—	26	1	no	—
264	M₃₂	C₂×Dic₁₃	1	2	yes	complemented
265	M₃₂	C₂²×D₁₃	1	2	yes	—
266	C₂×C₁₆	—	26	1	no	—
267	C₂×C₁₆	C₂×Dic₁₃	1	2	yes	complemented
268	#108	—	13	2	no	—
269	#108	—	26	1	no	—
270	#106	—	13	2	no	—
271	#106	—	26	1	no	—
272	#104	—	26	4	no	—
273	#103	—	26	2	no	—
274	#102	—	26	2	no	—
275	#97	—	13	2	no	—
276	C₄×C₈	—	13	2	no	—
277	C₂×C₁₃	—	2	1	no	—
278	C₂×C₁₃	—	2	1	no	—
279	C₂×C₁₃	—	2	1	no	—
280	C₂×C₁₃	—	8	2	no	—
281	C₂×C₁₃	—	8	2	no	—
282	C₂×C₁₃	C₂×#442	1	1	yes	characteristic
283	#41	—	2	2	no	—
284	#41	—	2	2	no	—
285	#41	—	2	2	no	—
286	#41	—	2	2	no	—
287	#41	—	4	1	no	—
288	#41	—	4	1	no	—
289	#41	—	4	1	no	—
290	#41	—	4	1	no	—
291	C₂×Q₈	—	2	1	no	—
292	C₂×Q₈	—	2	1	no	—
293	C₂×D₄	—	2	1	no	—
294	C₂×D₄	—	2	1	no	—
295	C₂×D₄	—	4	1	no	—
296	C₂×D₄	—	4	1	no	—
297	C₂²×C₄	—	4	1	no	—
298	C₂²×C₄	—	4	1	no	—
299	C₂²×C₄	—	52	2	no	—
300	C₂²×C₄	—	52	1	no	—
301	C₂²×C₄	D₄×D₁₃	1	1	yes	characteristic
302	Q₁₆	—	2	1	no	—
303	Q₁₆	—	2	1	no	—
304	Q₁₆	C₂²×Dic₁₃	1	2	yes	—
305	Q₁₆	C₂²×Dic₁₃	1	2	yes	—
306	SD₁₆	—	2	2	no	—
307	SD₁₆	—	2	2	no	—
308	SD₁₆	—	2	2	no	—
309	SD₁₆	—	2	2	no	—
310	D₈	—	2	1	no	—
311	D₈	—	2	1	no	—
312	D₈	C₂²×Dic₁₃	1	2	yes	—
313	D₈	C₂²×Dic₁₃	1	2	yes	—
314	M₁₆	—	26	1	no	—
315	M₁₆	—	26	1	no	—
316	M₁₆	—	26	2	no	—
317	M₁₆	—	52	4	no	—
318	M₁₆	—	52	1	no	—
319	C₂×C₈	—	13	2	no	—
320	C₂×C₈	—	52	4	no	—
321	C₂×C₈	—	52	1	no	—
322	C₂×C₈	D₄×D₁₃	1	1	yes	characteristic
323	C₂×C₈	#6129	1	1	yes	characteristic
324	C₂×C₈	#6129	1	1	yes	characteristic
325	C₂×C₈	C₂²×Dic₁₃	1	1	yes	characteristic
326	C₂×C₈	C₂²×Dic₁₃	1	1	yes	characteristic
327	C₂×C₈	C₂³×D₁₃	1	1	yes	characteristic
328	C₄⋊C₄	—	26	1	no	—
329	C₄⋊C₄	—	26	2	no	—
330	C₄⋊C₄	—	52	2	no	—
331	C₄⋊C₄	—	52	1	no	—
332	C₂²⋊C₄	—	26	1	no	—
333	C₂²⋊C₄	—	52	2	no	—
334	C₄²	—	13	2	no	—
335	C₄²	—	52	2	no	—
336	C₁₆	—	26	2	no	—
337	C₁₆	C₂²×Dic₁₃	1	4	yes	—
338	C₁₃	#33469	1	1	yes	characteristic, complemented, Sylow
339	C₂³	—	4	1	no	—
340	C₂³	—	4	1	no	—
341	C₂³	#88165	1	1	yes	characteristic
342	Q₈	—	2	2	no	—
343	Q₈	—	2	2	no	—
344	Q₈	—	4	1	no	—
345	Q₈	—	4	1	no	—
346	D₄	—	2	2	no	—
347	D₄	—	2	2	no	—
348	D₄	—	4	2	no	—
349	D₄	—	4	2	no	—
350	D₄	—	4	2	no	—
351	D₄	—	4	2	no	—
352	D₄	—	4	1	no	—
353	D₄	—	4	1	no	—
354	C₂×C₄	—	4	1	no	—
355	C₂×C₄	—	4	1	no	—
356	C₂×C₄	—	4	2	no	—
357	C₂×C₄	—	4	2	no	—
358	C₂×C₄	—	4	2	no	—
359	C₂×C₄	—	4	2	no	—
360	C₂×C₄	—	26	2	no	—
361	C₂×C₄	—	52	2	no	—
362	C₂×C₄	—	208	2	no	—
363	C₂×C₄	—	208	1	no	—
364	C₂×C₄	#88165	1	1	yes	characteristic
365	C₂×C₄	#88165	1	1	yes	characteristic
366	C₂×C₄	#88165	1	1	yes	characteristic
367	C₂×C₄	D₄×Dic₁₃	1	1	yes	characteristic
368	C₂×C₄	D₄×Dic₁₃	1	1	yes	characteristic
369	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
370	C₈	—	26	2	no	—
371	C₈	—	52	2	no	—
372	C₈	D₄×Dic₁₃	1	1	yes	characteristic
373	C₈	D₄×Dic₁₃	1	1	yes	characteristic
374	C₈	C₂×#6129	1	1	yes	characteristic
375	C₈	C₂³×Dic₁₃	1	1	yes	characteristic
376	C₂²	—	4	1	no	—
377	C₂²	—	4	2	no	—
378	C₂²	—	4	2	no	—
379	C₂²	—	8	1	no	—
380	C₂²	—	8	1	no	—
381	C₂²	—	16	1	no	—
382	C₂²	#11718813	1	1	yes	characteristic
383	C₂²	#11718813	1	1	yes	characteristic
384	C₂²	C₂×#88165	1	1	yes	characteristic
385	C₄	—	4	2	no	—
386	C₄	—	4	2	no	—
387	C₄	—	52	2	no	—
388	C₄	—	104	2	no	—
389	C₄	#11718813	1	1	yes	characteristic
390	C₄	#11718813	1	1	yes	characteristic
391	C₄	C₂×#88165	1	1	yes	characteristic
392	C₄	C₂×D₄×Dic₁₃	1	1	yes	characteristic
393	C₂	—	2	1	no	—
394	C₂	—	2	1	no	—
395	C₂	—	2	1	no	—
396	C₂	—	8	2	no	—
397	C₂	—	8	2	no	—
398	C₂	C₂×#11718813	1	1	yes	characteristic

	subgroup	G/H
center	C₂	C₂×#11718813
commutator	C₈×C₁₃	C₂³×C₄
Frattini	C₂×C₈	C₂³×D₁₃
Fitting, prime radical	C₁₃×#3414	C₂
socle	C₂×C₁₃	C₂×#442
cosocle	C₂×C₈×C₁₃	C₂⁴
hypercenter	#3414	D₁₃
hypocenter	C₁₃	#33469
LCS	G ▷ C₈×C₁₃ ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ #3414

Complements

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

N	H ≅ G/N	type
1. #13123753	C₂	semidirect
2. #13123720	C₂	semidirect
3. #13116735	C₂	semidirect
4. #13116728	C₂	semidirect
5. C₂×#11718105	C₂	semidirect
6. #13116585	C₂	semidirect
7. C₂×#11718158	C₂	semidirect
8. #13116440	C₂	semidirect
14. C₁₃×#510	C₄	semidirect
16. C₁₃×#509	C₄	semidirect
18. C₁₃×#508	C₄	semidirect
24. #11718845	C₂²	semidirect
26. #11718813	C₂²	semidirect
32. #11718157	C₂²	semidirect
33. #11718155	C₂²	semidirect
34. #11718105	C₂²	semidirect
35. #11718104	C₂²	semidirect
44. C₁₃×#135	C₂×C₄	semidirect
46. C₂×C₁₃×Q₁₆	C₂×C₄	semidirect
50. C₂×C₁₃×D₈	C₂×C₄	semidirect
65. C₁₃×Q₃₂	C₂×C₄	semidirect
66. C₁₃×SD₃₂	C₂×C₄	semidirect
67. C₁₃×SD₃₂	C₂×C₄	semidirect
68. C₁₃×D₁₆	C₂×C₄	semidirect
69. C₁₃×M₃₂	C₂×C₄	semidirect
71. C₂×C₁₃×C₁₆	C₂×C₄	semidirect
190. #510	Dic₁₃	semidirect
192. #509	Dic₁₃	semidirect
194. #508	Dic₁₃	semidirect
237. #135	C₂×Dic₁₃	semidirect
239. C₂×Q₁₆	C₂×Dic₁₃	semidirect
243. C₂×D₈	C₂×Dic₁₃	semidirect
258. Q₃₂	C₂×Dic₁₃	semidirect
259. SD₃₂	C₂×Dic₁₃	semidirect
260. SD₃₂	C₂×Dic₁₃	semidirect
261. D₁₆	C₂×Dic₁₃	semidirect
264. M₃₂	C₂×Dic₁₃	semidirect
267. C₂×C₁₆	C₂×Dic₁₃	semidirect
338. C₁₃	#33469	semidirect

Maximal subgroups

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

subgroup	index
#13123753	2
#13123720	2
#13116735	2
#13116728	2
C₂×#11718105	2
#13116585	2
C₂×#11718158	2
#13116440	2
C₁₃×#3414	2
#33469	13