Subgroups — #13128598

Order 1664.

1660 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#88256	C₂	1	2	yes	maximal, complemented
2	C₁₃×#532	C₂	1	1	yes	maximal, characteristic, complemented
3	#11719538	C₂	1	2	yes	maximal, complemented
4	#11719431	C₂	1	2	yes	maximal, complemented
5	#11719422	C₂	1	2	yes	maximal, complemented
6	#11719381	C₂	1	4	yes	maximal, complemented
7	#11719310	C₂	1	4	yes	maximal, complemented
8	D₁₃×#121	C₂	1	4	yes	maximal, complemented
9	#11719256	C₂	1	2	yes	maximal, complemented
10	#11719255	C₂	1	4	yes	maximal, complemented
11	D₄×D₅₂	C₂	1	2	yes	maximal, complemented
12	#11719182	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₄×D₅₂	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₁₃×#41	C₂²	1	2	yes	complemented
15	#88256	—	2	16	no	—
16	C₂×#6131	C₂²	1	4	yes	complemented
17	C₂×D₄×D₁₃	C₂²	1	8	yes	complemented
18	C₂×D₄×D₁₃	C₂²	1	4	yes	complemented
19	C₂×D₄×D₁₃	C₂²	1	4	yes	complemented
20	C₂×#6127	C₂²	1	2	yes	complemented
21	C₂×#6127	C₂²	1	4	yes	complemented
22	C₂²×D₅₂	C₂²	1	1	yes	characteristic
23	C₂²×D₅₂	C₂²	1	4	yes	complemented
24	C₂²×C₄×D₁₃	C₂²	1	2	yes	complemented
25	C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
26	C₁₃×#127	C₂²	1	1	yes	characteristic, complemented
27	C₁₃×#124	C₂²	1	2	yes	complemented
28	C₁₃×#121	C₂²	1	2	yes	complemented
29	C₁₃×#121	C₂²	1	2	yes	complemented
30	C₄×D₄×C₁₃	C₂²	1	2	yes	complemented
31	C₄×D₄×C₁₃	C₂²	1	2	yes	complemented
32	C₂×C₄²×C₁₃	C₂²	1	1	yes	characteristic, complemented
33	#88200	C₂²	1	4	yes	complemented
34	#88193	C₂²	1	8	yes	complemented
35	#88192	C₂²	1	4	yes	complemented
36	#88192	C₂²	1	4	yes	complemented
37	#88191	C₂²	1	8	yes	complemented
38	#88184	C₂²	1	2	yes	complemented
39	#88184	C₂²	1	2	yes	complemented
40	#88184	C₂²	1	4	yes	complemented
41	C₂×#6103	C₂²	1	2	yes	complemented
42	C₂×C₄⋊Dic₁₃	C₂²	1	1	yes	characteristic, complemented
43	#88178	C₂²	1	4	yes	complemented
44	#88149	C₂²	1	4	yes	complemented
45	#88148	C₂²	1	8	yes	complemented
46	C₄⋊C₄×D₁₃	C₂²	1	4	yes	complemented
47	#88138	C₂²	1	8	yes	complemented
48	#88137	C₂²	1	8	yes	complemented
49	#88136	C₂²	1	8	yes	complemented
50	C₂²⋊C₄×D₁₃	C₂²	1	8	yes	complemented
51	#88129	C₂²	1	2	yes	complemented
52	#88128	C₂²	1	1	yes	characteristic, complemented
53	C₄×D₅₂	C₂²	1	2	yes	complemented
54	C₄×D₅₂	C₂²	1	2	yes	complemented
55	C₄×D₅₂	C₂²	1	2	yes	complemented
56	C₄×D₅₂	C₂²	1	2	yes	complemented
57	C₄×D₅₂	C₂²	1	2	yes	complemented
58	C₄×D₅₂	C₂²	1	2	yes	complemented
59	#88123	C₂²	1	1	yes	characteristic, complemented
60	C₂³×D₁₃	C₂³	1	8	yes	—
61	C₂³×D₁₃	C₂³	1	2	yes	—
62	C₁₃×#41	—	2	8	no	—
63	C₂×Q₈×C₁₃	C₂³	1	2	yes	—
64	C₂×D₄×C₁₃	C₂³	1	2	yes	—
65	C₂×D₄×C₁₃	C₂³	1	2	yes	—
66	C₂×D₄×C₁₃	C₂³	1	4	yes	—
67	C₂×D₄×C₁₃	C₂³	1	2	yes	—
68	C₂²×C₄×C₁₃	C₂³	1	4	yes	—
69	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
70	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
71	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
72	C₂×C₂²⋊D₁₃	C₂³	1	8	yes	—
73	C₂×C₂²⋊D₁₃	C₂³	1	4	yes	—
74	C₂×C₂²⋊D₁₃	C₂³	1	8	yes	—
75	C₂²×Dic₁₃	C₂³	1	2	yes	—
76	#6131	—	2	16	no	—
77	D₄×D₁₃	—	2	32	no	—
78	D₄×D₁₃	—	2	16	no	—
79	D₄×D₁₃	—	4	8	no	—
80	#6127	—	2	8	no	—
81	#6127	—	2	16	no	—
82	C₂×D₅₂	—	2	16	no	—
83	C₂×D₅₂	D₄	1	8	yes	complemented
84	C₂×D₅₂	C₂³	1	2	yes	—
85	C₂×D₅₂	C₂³	1	2	yes	—
86	C₂×D₅₂	C₂³	1	8	yes	—
87	C₂×D₅₂	C₂³	1	2	yes	—
88	C₂×D₅₂	C₂³	1	2	yes	—
89	C₂×D₅₂	C₂³	1	2	yes	—
90	C₂×C₄×D₁₃	—	4	4	no	—
91	C₂×C₄×D₁₃	C₂³	1	4	yes	—
92	C₂×C₄×D₁₃	C₂³	1	4	yes	—
93	C₂×C₄×D₁₃	C₂³	1	8	yes	—
94	C₂×C₄×D₁₃	C₂³	1	4	yes	—
95	C₂×Dic₂₆	C₂³	1	2	yes	—
96	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
97	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
98	C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
99	C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
100	C₄²×C₁₃	C₂³	1	1	yes	characteristic
101	C₄²×C₁₃	C₂³	1	1	yes	characteristic
102	C₄²×C₁₃	C₂³	1	1	yes	characteristic
103	C₄²×C₁₃	C₂³	1	1	yes	characteristic
104	C₂²⋊Dic₁₃	C₂³	1	8	yes	—
105	#6103	C₂³	1	4	yes	—
106	#6103	C₂³	1	4	yes	—
107	#6103	C₂³	1	4	yes	—
108	#6103	C₂³	1	4	yes	—
109	#6103	C₂³	1	8	yes	—
110	C₄⋊Dic₁₃	C₂³	1	2	yes	—
111	C₄⋊Dic₁₃	C₂³	1	2	yes	—
112	C₄⋊Dic₁₃	C₂³	1	2	yes	—
113	C₄⋊Dic₁₃	C₂³	1	2	yes	—
114	#6101	C₂³	1	8	yes	—
115	#3496	—	13	1	no	maximal, Sylow
116	C₂³×C₁₃	C₂⁴	1	4	yes	—
117	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
118	C₂²×D₁₃	—	2	16	no	—
119	C₂²×D₁₃	—	4	2	no	—
120	C₂²×D₁₃	—	4	2	no	—
121	C₂²×D₁₃	—	4	8	no	—
122	C₂²×D₁₃	—	4	8	no	—
123	C₂²×D₁₃	C₂×D₄	1	8	yes	complemented
124	C₂²×D₁₃	C₂⁴	1	4	yes	—
125	C₂²×D₁₃	C₂⁴	1	4	yes	—
126	Q₈×C₁₃	—	2	4	no	—
127	D₄×C₁₃	—	2	8	no	—
128	D₄×C₁₃	—	2	4	no	—
129	D₄×C₁₃	—	2	4	no	—
130	D₄×C₁₃	—	4	2	no	—
131	C₂×C₄×C₁₃	—	2	8	no	—
132	C₂×C₄×C₁₃	—	2	2	no	—
133	C₂×C₄×C₁₃	—	4	1	no	—
134	C₂×C₄×C₁₃	C₂×D₄	1	4	yes	complemented
135	C₂×C₄×C₁₃	C₂⁴	1	4	yes	—
136	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
137	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
138	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
139	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
140	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
141	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
142	C₂²⋊D₁₃	—	2	8	no	—
143	C₂²⋊D₁₃	—	2	16	no	—
144	C₂²⋊D₁₃	—	4	8	no	—
145	C₂×Dic₁₃	—	4	2	no	—
146	C₂×Dic₁₃	C₂⁴	1	4	yes	—
147	C₂×Dic₁₃	C₂⁴	1	4	yes	—
148	D₅₂	—	2	16	no	—
149	D₅₂	—	2	4	no	—
150	D₅₂	—	2	4	no	—
151	D₅₂	—	4	2	no	—
152	D₅₂	C₂×D₄	1	8	yes	complemented
153	D₅₂	C₂×D₄	1	8	yes	complemented
154	C₄×D₁₃	—	2	16	no	—
155	C₄×D₁₃	—	2	8	no	—
156	C₄×D₁₃	—	2	8	no	—
157	C₄×D₁₃	—	4	4	no	—
158	Dic₂₆	—	2	4	no	—
159	C₂×H(5,𝔽₂)	—	13	2	no	—
160	#547	—	13	2	no	—
161	#547	—	13	2	no	—
162	#546	—	13	4	no	—
163	#546	—	13	4	no	—
164	D₄²	—	13	2	no	—
165	D₄²	—	13	2	no	—
166	#537	—	13	2	no	—
167	#534	—	13	4	no	—
168	#532	—	13	1	no	—
169	#532	D₁₃	1	1	yes	characteristic, complemented
170	C₂×#121	—	13	4	no	—
171	C₂×C₄×D₄	—	13	1	no	—
172	C₂²×C₁₃	—	2	1	no	—
173	C₂²×C₁₃	—	2	1	no	—
174	C₂²×C₁₃	—	2	4	no	—
175	C₂²×C₁₃	—	2	4	no	—
176	C₂²×C₁₃	—	2	4	no	—
177	C₂²×C₁₃	C₂²×D₄	1	2	yes	—
178	C₂²×C₁₃	C₂⁵	1	1	yes	characteristic
179	C₂×D₁₃	—	2	4	no	—
180	C₂×D₁₃	—	2	4	no	—
181	C₂×D₁₃	—	2	4	no	—
182	C₂×D₁₃	—	2	4	no	—
183	C₂×D₁₃	—	2	4	no	—
184	C₂×D₁₃	—	4	8	no	—
185	C₂×D₁₃	—	8	16	no	—
186	C₂×D₁₃	C₂²×D₄	1	8	yes	—
187	C₄×C₁₃	—	2	4	no	—
188	C₄×C₁₃	—	2	1	no	—
189	C₄×C₁₃	—	2	1	no	—
190	C₄×C₁₃	—	2	1	no	—
191	C₄×C₁₃	C₂²×D₄	1	2	yes	—
192	C₄×C₁₃	C₂²×D₄	1	2	yes	—
193	C₄×C₁₃	H(5,𝔽₂)	1	2	yes	complemented
194	Dic₁₃	—	2	4	no	—
195	Dic₁₃	—	2	4	no	—
196	H(5,𝔽₂)	—	26	16	no	—
197	C₂×#41	—	13	4	no	—
198	C₂×#41	—	13	2	no	—
199	C₂×#41	—	13	4	no	—
200	C₂×#41	C₂×D₁₃	1	2	yes	complemented
201	C₂²×D₄	—	13	8	no	—
202	C₂²×D₄	—	13	4	no	—
203	C₂²×D₄	—	13	4	no	—
204	C₂²×D₄	—	13	1	no	—
205	C₂²×D₄	—	13	4	no	—
206	C₂³×C₄	—	13	2	no	—
207	C₄⋊Q₈	—	13	1	no	—
208	C₄⋊Q₈	C₂×D₁₃	1	1	yes	characteristic, complemented
209	#127	—	13	1	no	—
210	#127	C₂×D₁₃	1	1	yes	characteristic, complemented
211	#124	—	13	2	no	—
212	#124	C₂×D₁₃	1	2	yes	complemented
213	#123	—	13	8	no	—
214	#123	—	13	8	no	—
215	C₂²⋊Q₈	—	13	4	no	—
216	C₂²⋊Q₈	—	13	4	no	—
217	#121	—	13	8	no	—
218	#121	—	13	4	no	—
219	#121	—	13	4	no	—
220	#121	—	13	2	no	—
221	#121	—	13	2	no	—
222	#121	—	13	4	no	—
223	#121	—	13	4	no	—
224	#121	—	13	8	no	—
225	#121	C₂×D₁₃	1	2	yes	complemented
226	#121	C₂×D₁₃	1	2	yes	complemented
227	#120	—	13	8	no	—
228	#120	—	13	8	no	—
229	C₄×D₄	—	13	2	no	—
230	C₄×D₄	—	13	2	no	—
231	C₄×D₄	—	13	2	no	—
232	C₄×D₄	—	13	2	no	—
233	C₄×D₄	—	13	2	no	—
234	C₄×D₄	—	13	2	no	—
235	C₄×D₄	C₂×D₁₃	1	2	yes	complemented
236	C₄×D₄	C₂×D₁₃	1	2	yes	complemented
237	C₂×C₄⋊C₄	—	13	1	no	—
238	C₂×C₄⋊C₄	—	13	4	no	—
239	C₂×C₂²⋊C₄	—	13	2	no	—
240	C₂×C₂²⋊C₄	—	13	8	no	—
241	C₂×C₄²	C₂×D₁₃	1	1	yes	characteristic, complemented
242	C₂×C₁₃	—	2	2	no	—
243	C₂×C₁₃	—	4	4	no	—
244	C₂×C₁₃	C₂³×D₄	1	1	yes	characteristic
245	C₂×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
246	C₂×C₁₃	#585	1	1	yes	characteristic
247	D₁₃	—	2	8	no	—
248	D₁₃	—	4	4	no	—
249	C₂⁴	—	13	2	no	—
250	C₂⁴	—	13	8	no	—
251	#41	—	2	8	no	—
252	#41	—	26	16	no	—
253	#41	—	26	16	no	—
254	#41	—	26	8	no	—
255	C₂×Q₈	—	13	2	no	—
256	C₂×Q₈	C₂²×D₁₃	1	2	yes	—
257	C₂×D₄	—	13	8	no	—
258	C₂×D₄	—	13	4	no	—
259	C₂×D₄	—	13	8	no	—
260	C₂×D₄	—	13	8	no	—
261	C₂×D₄	—	13	2	no	—
262	C₂×D₄	—	13	2	no	—
263	C₂×D₄	—	13	2	no	—
264	C₂×D₄	—	13	8	no	—
265	C₂×D₄	—	13	2	no	—
266	C₂×D₄	—	13	2	no	—
267	C₂×D₄	—	26	16	no	—
268	C₂×D₄	—	26	16	no	—
269	C₂×D₄	—	26	32	no	—
270	C₂×D₄	—	52	8	no	—
271	C₂×D₄	C₂²×D₁₃	1	2	yes	—
272	C₂×D₄	C₂²×D₁₃	1	4	yes	—
273	C₂×D₄	C₂²×D₁₃	1	2	yes	—
274	C₂×D₄	C₂²×D₁₃	1	2	yes	—
275	C₂²×C₄	—	13	2	no	—
276	C₂²×C₄	—	13	8	no	—
277	C₂²×C₄	—	13	4	no	—
278	C₂²×C₄	—	13	4	no	—
279	C₂²×C₄	—	13	4	no	—
280	C₂²×C₄	—	52	4	no	—
281	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
282	C₂²×C₄	C₂²×D₁₃	1	4	yes	—
283	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
284	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
285	C₄⋊C₄	—	13	2	no	—
286	C₄⋊C₄	—	13	2	no	—
287	C₄⋊C₄	—	13	2	no	—
288	C₄⋊C₄	—	13	8	no	—
289	C₄⋊C₄	—	13	2	no	—
290	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
291	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
292	C₂²⋊C₄	—	13	8	no	—
293	C₂²⋊C₄	—	13	4	no	—
294	C₂²⋊C₄	—	13	4	no	—
295	C₂²⋊C₄	—	13	4	no	—
296	C₂²⋊C₄	—	13	8	no	—
297	C₂²⋊C₄	—	13	4	no	—
298	C₂²⋊C₄	C₂²×D₁₃	1	4	yes	—
299	C₂²⋊C₄	C₂²×D₁₃	1	4	yes	—
300	C₄²	C₂²×D₁₃	1	1	yes	characteristic
301	C₄²	C₂²×D₁₃	1	1	yes	characteristic
302	C₄²	C₂²×D₁₃	1	1	yes	characteristic
303	C₄²	C₂²×D₁₃	1	1	yes	characteristic
304	C₁₃	#3496	1	1	yes	characteristic, complemented, Sylow
305	C₂³	—	13	4	no	—
306	C₂³	—	13	8	no	—
307	C₂³	—	13	4	no	—
308	C₂³	—	26	16	no	—
309	C₂³	—	52	2	no	—
310	C₂³	—	52	2	no	—
311	C₂³	—	52	8	no	—
312	C₂³	—	52	8	no	—
313	C₂³	C₂³×D₁₃	1	4	yes	—
314	C₂³	C₂³×D₁₃	1	1	yes	characteristic
315	Q₈	—	2	4	no	—
316	Q₈	—	26	4	no	—
317	D₄	—	2	8	no	—
318	D₄	—	2	4	no	—
319	D₄	—	2	4	no	—
320	D₄	—	4	2	no	—
321	D₄	—	13	8	no	—
322	D₄	—	13	8	no	—
323	D₄	—	26	16	no	—
324	D₄	—	26	16	no	—
325	D₄	—	26	8	no	—
326	D₄	—	26	4	no	—
327	D₄	—	26	4	no	—
328	D₄	—	52	2	no	—
329	D₄	—	52	8	no	—
330	C₂×C₄	—	2	8	no	—
331	C₂×C₄	—	2	2	no	—
332	C₂×C₄	—	4	1	no	—
333	C₂×C₄	—	13	4	no	—
334	C₂×C₄	—	13	4	no	—
335	C₂×C₄	—	26	16	no	—
336	C₂×C₄	—	26	8	no	—
337	C₂×C₄	—	26	8	no	—
338	C₂×C₄	—	52	4	no	—
339	C₂×C₄	—	52	2	no	—
340	C₂×C₄	D₄×D₁₃	1	4	yes	complemented
341	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
342	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
343	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
344	C₂×C₄	C₂³×D₁₃	1	4	yes	—
345	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
346	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
347	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
348	C₂²	—	2	1	no	—
349	C₂²	—	2	1	no	—
350	C₂²	—	2	4	no	—
351	C₂²	—	2	4	no	—
352	C₂²	—	2	4	no	—
353	C₂²	—	13	8	no	—
354	C₂²	—	26	4	no	—
355	C₂²	—	26	4	no	—
356	C₂²	—	26	4	no	—
357	C₂²	—	26	4	no	—
358	C₂²	—	26	4	no	—
359	C₂²	—	52	8	no	—
360	C₂²	—	104	16	no	—
361	C₂²	C₂×D₄×D₁₃	1	2	yes	—
362	C₂²	C₂⁴×D₁₃	1	1	yes	characteristic
363	C₄	—	2	4	no	—
364	C₄	—	2	1	no	—
365	C₄	—	2	1	no	—
366	C₄	—	2	1	no	—
367	C₄	—	26	4	no	—
368	C₄	—	26	4	no	—
369	C₄	C₂×D₄×D₁₃	1	2	yes	—
370	C₄	C₂×D₄×D₁₃	1	2	yes	—
371	C₄	#88256	1	2	yes	complemented
372	C₂	—	2	2	no	—
373	C₂	—	4	4	no	—
374	C₂	—	26	8	no	—
375	C₂	—	52	4	no	—
376	C₂	C₂²×D₄×D₁₃	1	1	yes	characteristic
377	C₂	C₂×#88256	1	1	yes	characteristic
378	C₂	#11719648	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₃
commutator, socle, cosocle	C₂²×C₁₃	C₂⁵
Fitting	C₁₃×#532	C₂
hypercenter	#532	D₁₃
hypocenter	C₁₃	#3496
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ #532

Complements

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

N	H ≅ G/N	type
1. C₂×#88256	C₂	semidirect
2. C₁₃×#532	C₂	semidirect
3. #11719538	C₂	semidirect
4. #11719431	C₂	semidirect
5. #11719422	C₂	semidirect
6. #11719381	C₂	semidirect
7. #11719310	C₂	semidirect
8. D₁₃×#121	C₂	semidirect
9. #11719256	C₂	semidirect
10. #11719255	C₂	semidirect
11. D₄×D₅₂	C₂	semidirect
12. #11719182	C₂	semidirect
13. C₂×C₄×D₅₂	C₂	semidirect
14. C₂×C₁₃×#41	C₂²	semidirect
16. C₂×#6131	C₂²	semidirect
17. C₂×D₄×D₁₃	C₂²	semidirect
18. C₂×D₄×D₁₃	C₂²	semidirect
19. C₂×D₄×D₁₃	C₂²	semidirect
20. C₂×#6127	C₂²	semidirect
21. C₂×#6127	C₂²	semidirect
23. C₂²×D₅₂	C₂²	semidirect
24. C₂²×C₄×D₁₃	C₂²	semidirect
25. C₁₃×C₄⋊Q₈	C₂²	semidirect
26. C₁₃×#127	C₂²	semidirect
27. C₁₃×#124	C₂²	semidirect
28. C₁₃×#121	C₂²	semidirect
29. C₁₃×#121	C₂²	semidirect
30. C₄×D₄×C₁₃	C₂²	semidirect
31. C₄×D₄×C₁₃	C₂²	semidirect
32. C₂×C₄²×C₁₃	C₂²	semidirect
33. #88200	C₂²	semidirect
34. #88193	C₂²	semidirect
35. #88192	C₂²	semidirect
36. #88192	C₂²	semidirect
37. #88191	C₂²	semidirect
38. #88184	C₂²	semidirect
39. #88184	C₂²	semidirect
40. #88184	C₂²	semidirect
41. C₂×#6103	C₂²	semidirect
42. C₂×C₄⋊Dic₁₃	C₂²	semidirect
43. #88178	C₂²	semidirect
44. #88149	C₂²	semidirect
45. #88148	C₂²	semidirect
46. C₄⋊C₄×D₁₃	C₂²	semidirect
47. #88138	C₂²	semidirect
48. #88137	C₂²	semidirect
49. #88136	C₂²	semidirect
50. C₂²⋊C₄×D₁₃	C₂²	semidirect
51. #88129	C₂²	semidirect
52. #88128	C₂²	semidirect
53. C₄×D₅₂	C₂²	semidirect
54. C₄×D₅₂	C₂²	semidirect
55. C₄×D₅₂	C₂²	semidirect
56. C₄×D₅₂	C₂²	semidirect
57. C₄×D₅₂	C₂²	semidirect
58. C₄×D₅₂	C₂²	semidirect
59. #88123	C₂²	semidirect
83. C₂×D₅₂	D₄	semidirect
123. C₂²×D₁₃	C₂×D₄	semidirect
134. C₂×C₄×C₁₃	C₂×D₄	semidirect
152. D₅₂	C₂×D₄	semidirect
153. D₅₂	C₂×D₄	semidirect
169. #532	D₁₃	semidirect
193. C₄×C₁₃	H(5,𝔽₂)	semidirect
200. C₂×#41	C₂×D₁₃	semidirect
208. C₄⋊Q₈	C₂×D₁₃	semidirect
210. #127	C₂×D₁₃	semidirect
212. #124	C₂×D₁₃	semidirect
225. #121	C₂×D₁₃	semidirect
226. #121	C₂×D₁₃	semidirect
235. C₄×D₄	C₂×D₁₃	semidirect
236. C₄×D₄	C₂×D₁₃	semidirect
241. C₂×C₄²	C₂×D₁₃	semidirect
304. C₁₃	#3496	semidirect
340. C₂×C₄	D₄×D₁₃	semidirect
371. C₄	#88256	semidirect

Maximal subgroups

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

subgroup	index
C₂×#88256	2
C₁₃×#532	2
#11719538	2
#11719431	2
#11719422	2
#11719381	2
#11719310	2
D₁₃×#121	2
#11719256	2
#11719255	2
D₄×D₅₂	2
#11719182	2
C₂×C₄×D₅₂	2
#3496	13