Subgroups — #79423

Order 384.

502 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#901	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×ΓL(1,𝔽₂₅)	C₂	1	1	yes	maximal, characteristic, complemented
3	#5547	C₂	1	1	yes	maximal, characteristic
4	C₃×C₈×D₄	C₂	1	1	yes	maximal, characteristic, complemented
5	#5111	C₂	1	1	yes	maximal, characteristic, complemented
6	#5111	C₂	1	1	yes	maximal, characteristic, complemented
7	#5011	C₂	1	1	yes	maximal, characteristic, complemented
8	#4839	C₂	1	1	yes	maximal, characteristic, complemented
9	#4836	C₂	1	1	yes	maximal, characteristic, complemented
10	#4729	C₂	1	1	yes	maximal, characteristic, complemented
11	#4727	C₂	1	1	yes	maximal, characteristic, complemented
12	#67⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
13	D₃×C₂²⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
14	#4689	C₂	1	1	yes	maximal, characteristic, complemented
15	#4688	C₂	1	1	yes	maximal, characteristic, complemented
16	#2933	—	3	1	no	maximal, Sylow
17	C₂×#235	C₂²	1	1	yes	characteristic
18	C₂²×C₄×D₃	C₂²	1	1	yes	characteristic
19	C₂²×C₃×C₈	C₂²	1	1	yes	characteristic
20	C₂²×C₃×C₈	C₂²	1	1	yes	characteristic, complemented
21	C₃×C₄×D₄	C₂²	1	1	yes	characteristic
22	#939	C₄	1	1	yes	characteristic
23	#937	C₄	1	1	yes	characteristic
24	C₄×#67	C₂²	1	1	yes	characteristic
25	C₄×#67	C₂²	1	1	yes	characteristic
26	C₂×#208	C₂²	1	1	yes	characteristic, complemented
27	C₂²×C₃⋊C₈	C₂²	1	1	yes	characteristic
28	#901	—	2	4	no	—
29	C₂×ΓL(1,𝔽₂₅)	—	2	4	no	—
30	C₂×ΓL(1,𝔽₂₅)	C₂²	1	1	yes	characteristic
31	C₂×ΓL(1,𝔽₂₅)	C₂²	1	1	yes	characteristic
32	C₂×ΓL(1,𝔽₂₅)	C₂²	1	1	yes	characteristic
33	C₂×ΓL(1,𝔽₂₅)	C₂²	1	1	yes	characteristic
34	C₂×ΓL(1,𝔽₂₅)	C₂²	1	1	yes	characteristic, complemented
35	C₂×D₃×C₈	C₂²	1	1	yes	characteristic
36	C₂×D₃×C₈	C₂²	1	1	yes	characteristic
37	C₂×D₃×C₈	C₂²	1	1	yes	characteristic, complemented
38	#896	C₄	1	1	yes	characteristic
39	#894	C₄	1	1	yes	characteristic
40	#884	C₄	1	1	yes	characteristic
41	#883	C₄	1	1	yes	characteristic
42	#882	C₄	1	1	yes	characteristic
43	#878	C₄	1	1	yes	characteristic
44	C₄×D₁₂	C₂²	1	1	yes	characteristic
45	#872	C₂²	1	1	yes	characteristic
46	C₃×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
47	C₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
48	C₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic, complemented
49	C₃×C₄×C₈	C₂²	1	1	yes	characteristic, complemented
50	#830	C₂²	1	1	yes	characteristic
51	#830	C₂²	1	1	yes	characteristic, complemented
52	(C₂×D₃)⋊C₈	C₂²	1	1	yes	characteristic
53	(C₂×D₃)⋊C₈	C₂²	1	1	yes	characteristic
54	(C₂×D₃)⋊C₈	C₂²	1	1	yes	characteristic, complemented
55	(C₂×D₃)⋊C₈	C₂²	1	1	yes	characteristic, complemented
56	#815	C₂²	1	1	yes	characteristic, complemented
57	Dic₃⋊C₈	C₂²	1	1	yes	characteristic, complemented
58	Dic₃⋊C₈	C₂²	1	1	yes	characteristic, complemented
59	C₈×Dic₃	C₂²	1	1	yes	characteristic, complemented
60	C₄⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic, complemented
61	#803	C₂²	1	1	yes	characteristic, complemented
62	C₂×#131	—	3	1	no	—
63	C₂²×M₁₆	—	3	1	no	—
64	#525	—	3	1	no	—
65	#436	—	3	1	no	—
66	#436	—	3	1	no	—
67	#435	—	3	1	no	—
68	#435	—	3	1	no	—
69	#435	—	3	1	no	—
70	#435	—	3	1	no	—
71	C₈×D₄	—	3	1	no	—
72	C₈×D₄	D₃	1	1	yes	characteristic, complemented
73	#424	—	3	1	no	—
74	#408	—	3	1	no	—
75	C₂×C₂²⋊C₈	—	3	1	no	—
76	#405	—	3	1	no	—
77	C₂³×D₃	C₂×C₄	1	1	yes	characteristic
78	C₂×C₃×D₄	C₂×C₄	1	1	yes	characteristic
79	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
80	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
81	C₂×#67	C₂×C₄	1	1	yes	characteristic
82	C₂×#67	C₂×C₄	1	1	yes	characteristic
83	C₂×#67	C₂×C₄	1	1	yes	characteristic
84	C₂×#67	C₂×C₄	1	1	yes	characteristic
85	C₂²×Dic₃	C₂×C₄	1	1	yes	characteristic
86	#235	—	2	2	no	—
87	#235	—	2	2	no	—
88	C₂×D₁₂	C₂×C₄	1	1	yes	characteristic
89	C₂×D₁₂	C₂×C₄	1	1	yes	characteristic
90	C₂×C₄×D₃	—	2	2	no	—
91	C₂×C₄×D₃	—	2	2	no	—
92	C₂×C₄×D₃	C₂×C₄	1	1	yes	characteristic
93	C₂×C₄×D₃	C₂×C₄	1	1	yes	characteristic
94	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
95	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
96	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
97	C₂×Dic₆	C₂×C₄	1	1	yes	characteristic
98	C₂×C₃×C₈	—	2	2	no	—
99	C₂×C₃×C₈	—	2	2	no	—
100	C₂×C₃×C₈	C₂³	1	1	yes	characteristic
101	C₂×C₃×C₈	C₂³	1	1	yes	characteristic
102	C₂×C₃×C₈	C₂³	1	1	yes	characteristic
103	C₂×C₃×C₈	C₂³	1	1	yes	characteristic
104	C₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
105	C₃×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
106	C₃×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
107	C₃×C₄²	C₂³	1	1	yes	characteristic
108	#217	C₂×C₄	1	1	yes	characteristic
109	#217	C₂×C₄	1	1	yes	characteristic
110	(C₂×D₃)⋊C₄	C₂×C₄	1	1	yes	characteristic
111	(C₂×D₃)⋊C₄	C₂×C₄	1	1	yes	characteristic
112	(C₂×D₃)⋊C₄	C₂×C₄	1	1	yes	characteristic
113	(C₂×D₃)⋊C₄	C₂×C₄	1	1	yes	characteristic
114	(C₂×D₃)⋊C₄	C₂×C₄	1	1	yes	characteristic
115	(C₂×D₃)⋊C₄	C₂×C₄	1	1	yes	characteristic
116	C₄⋊Dic₃	C₂×C₄	1	1	yes	characteristic
117	Dic₃⋊C₄	C₂×C₄	1	1	yes	characteristic
118	Dic₃⋊C₄	C₂×C₄	1	1	yes	characteristic
119	Dic₃⋊C₄	C₂×C₄	1	1	yes	characteristic
120	Dic₃⋊C₄	C₂×C₄	1	1	yes	characteristic
121	C₄×Dic₃	C₂³	1	1	yes	characteristic
122	#208	—	2	2	no	—
123	C₂×C₃⋊C₈	—	2	2	no	—
124	C₂×C₃⋊C₈	C₂³	1	1	yes	characteristic
125	C₂×C₃⋊C₈	C₂³	1	1	yes	characteristic
126	C₂×C₃⋊C₈	C₂³	1	1	yes	characteristic
127	C₂×C₃⋊C₈	C₂³	1	1	yes	characteristic
128	ΓL(1,𝔽₂₅)	—	2	2	no	—
129	ΓL(1,𝔽₂₅)	—	2	2	no	—
130	ΓL(1,𝔽₂₅)	—	2	2	no	—
131	ΓL(1,𝔽₂₅)	—	2	2	no	—
132	ΓL(1,𝔽₂₅)	D₄	1	4	yes	complemented
133	D₃×C₈	—	2	2	no	—
134	D₃×C₈	—	2	2	no	—
135	D₃×C₈	—	2	2	no	—
136	C₂×#41	—	3	1	no	—
137	C₂³×C₄	—	3	1	no	—
138	#131	—	6	4	no	—
139	C₂×M₁₆	—	3	1	no	—
140	C₂×M₁₆	—	3	1	no	—
141	C₂×M₁₆	—	3	1	no	—
142	C₂×M₁₆	—	3	1	no	—
143	C₂×M₁₆	—	3	1	no	—
144	C₂×M₁₆	—	3	1	no	—
145	C₂×M₁₆	—	6	4	no	—
146	C₂²×C₈	—	3	1	no	—
147	C₂²×C₈	—	3	1	no	—
148	C₂²×C₈	—	3	1	no	—
149	C₂²×C₈	—	3	1	no	—
150	C₂²×C₈	C₂×D₃	1	1	yes	characteristic
151	C₂²×C₈	C₂×D₃	1	1	yes	characteristic, complemented
152	#123	—	3	1	no	—
153	#123	—	3	1	no	—
154	C₂²⋊Q₈	—	3	1	no	—
155	C₂²⋊Q₈	—	3	1	no	—
156	#121	—	3	1	no	—
157	#121	—	3	1	no	—
158	#120	—	3	1	no	—
159	#120	—	3	1	no	—
160	C₄×D₄	—	3	1	no	—
161	C₄×D₄	—	3	1	no	—
162	C₄×D₄	—	3	1	no	—
163	C₄×D₄	C₂×D₃	1	1	yes	characteristic
164	#117	—	3	1	no	—
165	C₄⋊C₈	—	3	1	no	—
166	C₄⋊C₈	—	3	1	no	—
167	C₄⋊C₈	—	3	1	no	—
168	C₄⋊C₈	C₂×D₃	1	1	yes	characteristic, complemented
169	C₂²⋊C₈	—	3	1	no	—
170	C₂²⋊C₈	—	3	1	no	—
171	C₂²⋊C₈	—	3	1	no	—
172	C₂²⋊C₈	—	3	1	no	—
173	C₂²⋊C₈	—	3	1	no	—
174	C₂²⋊C₈	—	3	1	no	—
175	C₂²⋊C₈	C₂×D₃	1	1	yes	characteristic
176	C₂²⋊C₈	C₂×D₃	1	1	yes	characteristic, complemented
177	#97	—	3	1	no	—
178	#97	—	3	1	no	—
179	C₄×C₈	—	3	1	no	—
180	C₄×C₈	C₂×D₃	1	1	yes	characteristic, complemented
181	C₂³×C₃	C₂²×C₄	1	1	yes	characteristic
182	C₂³×C₃	C₂²×C₄	1	1	yes	characteristic
183	C₂²×D₃	—	2	2	no	—
184	C₂²×D₃	—	2	2	no	—
185	C₂²×D₃	—	4	1	no	—
186	C₂²×D₃	C₂²×C₄	1	1	yes	characteristic
187	C₂²×D₃	C₂²×C₄	1	1	yes	characteristic
188	C₂²×D₃	C₂²×C₄	1	1	yes	characteristic
189	C₃×D₄	—	2	2	no	—
190	C₂×C₃×C₄	—	2	1	no	—
191	C₂×C₃×C₄	—	2	1	no	—
192	C₂×C₃×C₄	—	2	1	no	—
193	C₂×C₃×C₄	—	2	1	no	—
194	C₂×C₃×C₄	C₂²×C₄	1	1	yes	characteristic
195	C₂×C₃×C₄	C₂²×C₄	1	1	yes	characteristic
196	C₂×C₃×C₄	C₂²×C₄	1	1	yes	characteristic
197	C₂×C₃×C₄	C₂²×C₄	1	1	yes	characteristic
198	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
199	#67	—	2	2	no	—
200	#67	—	2	2	no	—
201	#67	—	2	2	no	—
202	#67	—	4	1	no	—
203	C₂×Dic₃	—	2	2	no	—
204	C₂×Dic₃	C₂²×C₄	1	1	yes	characteristic
205	C₂×Dic₃	C₂²×C₄	1	1	yes	characteristic
206	C₂×Dic₃	C₂²×C₄	1	1	yes	characteristic
207	C₂×Dic₃	C₂²×C₄	1	1	yes	characteristic
208	C₂×Dic₃	C₂²×C₄	1	1	yes	characteristic
209	D₁₂	—	2	2	no	—
210	D₁₂	—	4	1	no	—
211	C₄×D₃	—	2	2	no	—
212	C₄×D₃	—	2	1	no	—
213	C₄×D₃	—	2	1	no	—
214	C₄×D₃	—	2	1	no	—
215	C₄×D₃	—	2	1	no	—
216	C₄×D₃	—	2	2	no	—
217	C₄×D₃	C₂×D₄	1	2	yes	—
218	C₄×D₃	#41	1	2	yes	—
219	Dic₆	—	2	2	no	—
220	C₃×C₈	—	2	1	no	—
221	C₃×C₈	—	2	1	no	—
222	C₃×C₈	—	2	1	no	—
223	C₃×C₈	C₂×D₄	1	2	yes	—
224	C₃⋊C₈	—	2	1	no	—
225	C₃⋊C₈	—	2	1	no	—
226	C₃⋊C₈	—	2	1	no	—
227	C₃⋊C₈	C₂×D₄	1	2	yes	—
228	C₂⁴	—	3	1	no	—
229	#41	—	6	2	no	—
230	#41	—	6	2	no	—
231	C₂×Q₈	—	3	1	no	—
232	C₂×D₄	—	3	1	no	—
233	C₂×D₄	—	3	1	no	—
234	C₂×D₄	—	3	1	no	—
235	C₂×D₄	—	3	1	no	—
236	C₂×D₄	—	3	1	no	—
237	C₂×D₄	—	3	1	no	—
238	C₂×D₄	C₄×D₃	1	1	yes	characteristic
239	C₂²×C₄	—	3	1	no	—
240	C₂²×C₄	—	3	1	no	—
241	C₂²×C₄	—	3	1	no	—
242	C₂²×C₄	—	3	1	no	—
243	C₂²×C₄	—	3	1	no	—
244	C₂²×C₄	—	3	1	no	—
245	C₂²×C₄	—	6	2	no	—
246	C₂²×C₄	—	6	2	no	—
247	C₂²×C₄	C₂²×D₃	1	1	yes	characteristic
248	C₂²×C₄	C₂²×D₃	1	1	yes	characteristic
249	M₁₆	—	3	4	no	—
250	M₁₆	—	6	2	no	—
251	M₁₆	—	6	2	no	—
252	M₁₆	—	6	2	no	—
253	M₁₆	—	6	2	no	—
254	M₁₆	—	6	2	no	—
255	C₂×C₈	—	2	2	no	—
256	C₂×C₈	—	2	2	no	—
257	C₂×C₈	—	3	1	no	—
258	C₂×C₈	—	3	1	no	—
259	C₂×C₈	—	3	1	no	—
260	C₂×C₈	—	3	1	no	—
261	C₂×C₈	—	6	2	no	—
262	C₂×C₈	—	6	2	no	—
263	C₂×C₈	—	6	2	no	—
264	C₂×C₈	—	6	2	no	—
265	C₂×C₈	C₂²×D₃	1	1	yes	characteristic
266	C₂×C₈	C₂²×D₃	1	1	yes	characteristic
267	C₂×C₈	C₂²×D₃	1	1	yes	characteristic
268	C₂×C₈	C₂²×D₃	1	1	yes	characteristic
269	C₄⋊C₄	—	3	1	no	—
270	C₄⋊C₄	—	3	1	no	—
271	C₄⋊C₄	—	3	1	no	—
272	C₄⋊C₄	—	3	1	no	—
273	C₄⋊C₄	—	3	1	no	—
274	C₄⋊C₄	C₄×D₃	1	1	yes	characteristic
275	C₂²⋊C₄	—	3	1	no	—
276	C₂²⋊C₄	—	3	1	no	—
277	C₂²⋊C₄	—	3	1	no	—
278	C₂²⋊C₄	—	3	1	no	—
279	C₂²⋊C₄	—	3	1	no	—
280	C₂²⋊C₄	—	3	1	no	—
281	C₂²⋊C₄	—	3	1	no	—
282	C₂²⋊C₄	—	3	1	no	—
283	C₂²⋊C₄	C₄×D₃	1	1	yes	characteristic
284	C₂²⋊C₄	C₄×D₃	1	1	yes	characteristic
285	C₄²	—	3	1	no	—
286	C₄²	C₂²×D₃	1	1	yes	characteristic
287	C₂²×C₃	—	2	1	no	—
288	C₂²×C₃	—	2	1	no	—
289	C₂²×C₃	—	2	1	no	—
290	C₂²×C₃	—	2	1	no	—
291	C₂²×C₃	—	2	1	no	—
292	C₂²×C₃	#131	1	2	yes	complemented
293	C₂²×C₃	C₂³×C₄	1	1	yes	characteristic
294	C₂×D₃	—	2	1	no	—
295	C₂×D₃	—	2	1	no	—
296	C₂×D₃	—	2	1	no	—
297	C₂×D₃	—	2	1	no	—
298	C₂×D₃	—	2	1	no	—
299	C₂×D₃	—	2	1	no	—
300	C₂×D₃	—	2	1	no	—
301	C₂×D₃	—	2	1	no	—
302	C₂×D₃	—	4	4	no	—
303	C₂×D₃	C₄×D₄	1	2	yes	—
304	C₃×C₄	—	2	1	no	—
305	C₃×C₄	—	2	1	no	—
306	C₃×C₄	—	2	1	no	—
307	C₃×C₄	—	2	1	no	—
308	C₃×C₄	C₂²×D₄	1	1	yes	characteristic
309	C₃×C₄	C₂×#41	1	1	yes	characteristic
310	Dic₃	—	2	1	no	—
311	Dic₃	—	2	1	no	—
312	Dic₃	—	2	1	no	—
313	Dic₃	—	2	1	no	—
314	Dic₃	C₄×D₄	1	2	yes	—
315	C₂³	—	3	1	no	—
316	C₂³	—	3	1	no	—
317	C₂³	—	3	1	no	—
318	C₂³	—	6	2	no	—
319	C₂³	—	6	2	no	—
320	C₂³	—	12	1	no	—
321	C₂³	C₂×C₄×D₃	1	1	yes	characteristic
322	C₂³	C₂×C₄×D₃	1	1	yes	characteristic
323	Q₈	—	6	2	no	—
324	D₄	—	2	2	no	—
325	D₄	—	6	2	no	—
326	D₄	—	6	2	no	—
327	D₄	—	6	2	no	—
328	D₄	—	6	2	no	—
329	D₄	—	12	1	no	—
330	D₄	—	12	1	no	—
331	C₂×C₄	—	2	1	no	—
332	C₂×C₄	—	2	1	no	—
333	C₂×C₄	—	2	1	no	—
334	C₂×C₄	—	2	1	no	—
335	C₂×C₄	—	3	1	no	—
336	C₂×C₄	—	3	2	no	—
337	C₂×C₄	—	3	2	no	—
338	C₂×C₄	—	3	1	no	—
339	C₂×C₄	—	3	1	no	—
340	C₂×C₄	—	3	1	no	—
341	C₂×C₄	—	3	1	no	—
342	C₂×C₄	—	6	2	no	—
343	C₂×C₄	—	6	2	no	—
344	C₂×C₄	—	6	2	no	—
345	C₂×C₄	—	6	1	no	—
346	C₂×C₄	—	6	1	no	—
347	C₂×C₄	—	6	1	no	—
348	C₂×C₄	—	6	1	no	—
349	C₂×C₄	C₂×C₄×D₃	1	1	yes	characteristic
350	C₂×C₄	C₂×C₄×D₃	1	1	yes	characteristic
351	C₂×C₄	C₂×C₄×D₃	1	1	yes	characteristic
352	C₂×C₄	C₂×C₄×D₃	1	1	yes	characteristic
353	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
354	C₈	—	2	1	no	—
355	C₈	—	2	1	no	—
356	C₈	—	2	1	no	—
357	C₈	—	3	2	no	—
358	C₈	—	6	1	no	—
359	C₈	—	6	1	no	—
360	C₈	—	6	1	no	—
361	C₈	D₃×D₄	1	2	yes	—
362	C₂×C₃	—	2	2	no	—
363	C₂×C₃	—	4	1	no	—
364	C₂×C₃	C₂×C₄×D₄	1	1	yes	characteristic
365	C₂×C₃	C₂×#131	1	1	yes	characteristic
366	C₂×C₃	#568	1	1	yes	characteristic
367	D₃	—	2	2	no	—
368	D₃	—	4	1	no	—
369	D₃	—	4	1	no	—
370	C₂²	—	2	1	no	—
371	C₂²	—	2	1	no	—
372	C₂²	—	2	1	no	—
373	C₂²	—	2	1	no	—
374	C₂²	—	2	1	no	—
375	C₂²	—	3	2	no	—
376	C₂²	—	6	1	no	—
377	C₂²	—	6	1	no	—
378	C₂²	—	6	1	no	—
379	C₂²	—	6	1	no	—
380	C₂²	—	6	1	no	—
381	C₂²	—	6	1	no	—
382	C₂²	—	6	1	no	—
383	C₂²	—	6	1	no	—
384	C₂²	—	12	4	no	—
385	C₂²	#901	1	2	yes	complemented
386	C₂²	C₂²×C₄×D₃	1	1	yes	characteristic
387	C₄	—	2	1	no	—
388	C₄	—	2	1	no	—
389	C₄	—	2	1	no	—
390	C₄	—	2	1	no	—
391	C₄	—	3	2	no	—
392	C₄	—	6	1	no	—
393	C₄	—	6	1	no	—
394	C₄	—	6	1	no	—
395	C₄	—	6	1	no	—
396	C₄	C₂×D₃×D₄	1	1	yes	characteristic
397	C₄	D₃×#41	1	1	yes	characteristic
398	C₃	#2933	1	1	yes	characteristic, complemented, Sylow
399	C₂	—	2	2	no	—
400	C₂	—	4	1	no	—
401	C₂	—	6	2	no	—
402	C₂	—	12	1	no	—
403	C₂	—	12	1	no	—
404	C₂	C₄×D₃×D₄	1	1	yes	characteristic
405	C₂	C₂×#901	1	1	yes	characteristic
406	C₂	#5750	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂³×D₃
commutator, socle	C₂²×C₃	C₂³×C₄
Fitting	C₃×C₈×D₄	C₂
prime radical	#5547	C₂
cosocle	C₂×C₃×C₄	C₂⁴
hypercenter	C₈×D₄	D₃
hypocenter	C₃	#2933
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₄ ◁ C₈×D₄

Complements

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

N	H ≅ G/N	type
1. C₂×#901	C₂	semidirect
2. C₂²×ΓL(1,𝔽₂₅)	C₂	semidirect
4. C₃×C₈×D₄	C₂	semidirect
5. #5111	C₂	semidirect
6. #5111	C₂	semidirect
7. #5011	C₂	semidirect
8. #4839	C₂	semidirect
9. #4836	C₂	semidirect
10. #4729	C₂	semidirect
11. #4727	C₂	semidirect
12. #67⋊C₈	C₂	semidirect
13. D₃×C₂²⋊C₈	C₂	semidirect
14. #4689	C₂	semidirect
15. #4688	C₂	semidirect
20. C₂²×C₃×C₈	C₂²	semidirect
26. C₂×#208	C₂²	semidirect
34. C₂×ΓL(1,𝔽₂₅)	C₂²	semidirect
37. C₂×D₃×C₈	C₂²	semidirect
46. C₃×C₄⋊C₈	C₂²	semidirect
48. C₃×C₂²⋊C₈	C₂²	semidirect
49. C₃×C₄×C₈	C₂²	semidirect
51. #830	C₂²	semidirect
54. (C₂×D₃)⋊C₈	C₂²	semidirect
55. (C₂×D₃)⋊C₈	C₂²	semidirect
56. #815	C₂²	semidirect
57. Dic₃⋊C₈	C₂²	semidirect
58. Dic₃⋊C₈	C₂²	semidirect
59. C₈×Dic₃	C₂²	semidirect
60. C₄⋊(C₃⋊C₈)	C₂²	semidirect
61. #803	C₂²	semidirect
72. C₈×D₄	D₃	semidirect
132. ΓL(1,𝔽₂₅)	D₄	semidirect
151. C₂²×C₈	C₂×D₃	semidirect
168. C₄⋊C₈	C₂×D₃	semidirect
176. C₂²⋊C₈	C₂×D₃	semidirect
180. C₄×C₈	C₂×D₃	semidirect
292. C₂²×C₃	#131	semidirect
385. C₂²	#901	semidirect
398. C₃	#2933	semidirect

Maximal subgroups

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

subgroup	index
C₂×#901	2
C₂²×ΓL(1,𝔽₂₅)	2
#5547	2
C₃×C₈×D₄	2
#5111	2
#5011	2
#4839	2
#4836	2
#4729	2
#4727	2
#67⋊C₈	2
D₃×C₂²⋊C₈	2
#4689	2
#4688	2
#2933	3