Subgroups — #12065017

Order 1280.

806 conjugacy classes of subgroups.

The subgroup lattice has 386 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#2920	C₂	1	1	yes	maximal, characteristic
2	#10613780	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×#681	C₂	1	1	yes	maximal, characteristic
4	#10601536	C₂	1	4	yes	maximal, complemented
5	#10601535	C₂	1	2	yes	maximal, complemented
6	#10601533	C₂	1	2	yes	maximal, complemented
7	#10600642	C₂	1	4	yes	maximal, complemented
8	C₂²×C₄²×C₅	C₂²	1	1	yes	characteristic
9	C₂²×#681	C₄	1	2	yes	—
10	C₅×#432	C₄	1	2	yes	—
11	C₅×#432	C₄	1	2	yes	—
12	C₅×#431	C₂²	1	2	yes	—
13	C₅×#431	C₂²	1	2	yes	—
14	C₅×#423	C₄	1	2	yes	—
15	C₅×#407	C₄	1	2	yes	—
16	C₄×C₅×M₁₆	C₂²	1	2	yes	—
17	#65496	C₄	1	2	yes	—
18	#65215	C₄	1	2	yes	—
19	#65215	C₄	1	2	yes	—
20	#65214	C₂²	1	2	yes	—
21	#65214	C₂²	1	2	yes	—
22	#65213	C₄	1	2	yes	—
23	C₄×#681	C₄	1	2	yes	—
24	C₄×#681	C₄	1	2	yes	—
25	C₄×#681	C₂²	1	2	yes	—
26	C₄×#681	C₂²	1	2	yes	—
27	C₄×#681	C₂²	1	2	yes	—
28	C₂×#3935	C₄	1	2	yes	—
29	C₂×C₄×#168	C₂²	1	1	yes	characteristic
30	C₂×C₄×#168	C₂²	1	1	yes	characteristic
31	#64675	C₂²	1	4	yes	complemented
32	#64674	C₂²	1	4	yes	complemented
33	#64674	C₂²	1	4	yes	complemented
34	C₈×#168	C₂²	1	4	yes	complemented
35	#17334	—	5	1	no	maximal, Sylow
36	C₂³×C₄×C₅	C₂×C₄	1	1	yes	characteristic
37	C₂³×C₄×C₅	C₂×C₄	1	1	yes	characteristic
38	C₂³×C₄×C₅	C₂×C₄	1	1	yes	characteristic
39	C₂×C₅×M₁₆	C₂×C₄	1	4	yes	—
40	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
41	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
42	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
43	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
44	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
45	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
46	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
47	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
48	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
49	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
50	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
51	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
52	C₂×#681	—	2	8	no	—
53	C₂×#681	C₂×C₄	1	4	yes	—
54	C₂×#681	C₂×C₄	1	4	yes	—
55	C₂×#681	C₂×C₄	1	4	yes	—
56	C₂²×#168	C₂×C₄	1	2	yes	—
57	C₂²×#168	C₂×C₄	1	2	yes	—
58	C₅×C₄⋊C₈	C₂×C₄	1	4	yes	—
59	C₅×C₄⋊C₈	C₂×C₄	1	4	yes	—
60	C₅×C₂²⋊C₈	C₂×C₄	1	4	yes	—
61	C₅×C₂²⋊C₈	C₂×C₄	1	4	yes	—
62	C₅×#97	C₂×C₄	1	4	yes	—
63	C₄×C₅×C₈	C₂³	1	4	yes	—
64	C₂²⋊#168	C₂×C₄	1	4	yes	—
65	C₂²⋊#168	C₂×C₄	1	4	yes	—
66	C₄⋊#168	C₂×C₄	1	4	yes	—
67	C₄⋊#168	C₂×C₄	1	4	yes	—
68	#3935	C₂×C₄	1	4	yes	—
69	#3935	C₂×C₄	1	4	yes	—
70	#3935	C₂×C₄	1	4	yes	—
71	C₄×#168	C₂×C₄	1	2	yes	—
72	C₄×#168	C₂×C₄	1	2	yes	—
73	C₄×#168	C₂³	1	2	yes	—
74	C₄×#168	C₂³	1	4	yes	—
75	C₄×#168	C₂³	1	2	yes	—
76	#2920	—	5	1	no	—
77	#2920	D₅	1	1	yes	characteristic
78	C₂×C₄×M₁₆	—	5	1	no	—
79	#1455	—	5	4	no	—
80	#1453	—	5	4	no	—
81	#1452	—	5	2	no	—
82	#1450	—	5	2	no	—
83	C₂⁴×C₅	C₄²	1	1	yes	characteristic
84	C₂²×C₄×C₅	—	2	4	no	—
85	C₂²×C₄×C₅	—	4	2	no	—
86	C₂²×C₄×C₅	—	4	2	no	—
87	C₂²×C₄×C₅	C₄²	1	1	yes	characteristic
88	C₂²×C₄×C₅	C₄²	1	1	yes	characteristic
89	C₂²×C₄×C₅	C₄²	1	1	yes	characteristic
90	C₂²×C₄×C₅	C₄²	1	1	yes	characteristic
91	C₂²×C₄×C₅	C₄²	1	1	yes	characteristic
92	C₂²×C₄×C₅	C₄²	1	1	yes	characteristic
93	C₂²×C₄×C₅	C₄²	1	1	yes	characteristic
94	C₂²×C₄×C₅	C₄²	1	1	yes	characteristic
95	C₂²×C₄×C₅	C₄²	1	1	yes	characteristic
96	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
97	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
98	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
99	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
100	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
101	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
102	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
103	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
104	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
105	C₅×M₁₆	—	4	4	no	—
106	C₂×C₅×C₈	C₂²×C₄	1	8	yes	—
107	C₄²×C₅	C₄²	1	1	yes	characteristic
108	C₄²×C₅	C₄²	1	1	yes	characteristic
109	C₄²×C₅	C₄²	1	1	yes	characteristic
110	C₄²×C₅	C₄²	1	1	yes	characteristic
111	C₄²×C₅	C₄²	1	1	yes	characteristic
112	C₄²×C₅	C₄²	1	1	yes	characteristic
113	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
114	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
115	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
116	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
117	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
118	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
119	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
120	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
121	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
122	C₄²×C₅	C₂⁴	1	1	yes	characteristic
123	#681	—	2	8	no	—
124	#681	—	2	8	no	—
125	#681	—	4	4	no	—
126	C₂×#168	—	2	4	no	—
127	C₂×#168	M₁₆	1	8	yes	complemented
128	C₂×#168	C₂²×C₄	1	4	yes	—
129	C₂×#168	C₂²×C₄	1	8	yes	—
130	C₂×#168	C₂²×C₄	1	4	yes	—
131	C₂²×M₁₆	—	5	2	no	—
132	C₂²×C₄²	C₂×D₅	1	1	yes	characteristic
133	#432	—	5	2	no	—
134	#432	—	5	2	no	—
135	#432	Dic₅	1	2	yes	—
136	#432	Dic₅	1	2	yes	—
137	#431	—	5	2	no	—
138	#431	—	5	2	no	—
139	#431	C₂×D₅	1	2	yes	—
140	#431	C₂×D₅	1	2	yes	—
141	#423	—	5	2	no	—
142	#423	Dic₅	1	2	yes	—
143	#407	—	5	2	no	—
144	#407	Dic₅	1	2	yes	—
145	C₄×M₁₆	—	5	2	no	—
146	C₄×M₁₆	—	5	2	no	—
147	C₄×M₁₆	—	5	2	no	—
148	C₄×M₁₆	—	5	2	no	—
149	C₄×M₁₆	—	5	2	no	—
150	C₄×M₁₆	C₂×D₅	1	2	yes	—
151	C₂×#97	—	5	2	no	—
152	C₂×C₄×C₈	—	5	1	no	—
153	C₂×C₄×C₈	—	5	1	no	—
154	#322	—	5	4	no	—
155	#322	—	5	4	no	—
156	#322	—	5	4	no	—
157	C₈²	—	5	4	no	—
158	C₂³×C₅	—	2	2	no	—
159	C₂³×C₅	—	4	1	no	—
160	C₂³×C₅	—	4	1	no	—
161	C₂³×C₅	C₂×C₄²	1	1	yes	characteristic
162	C₂³×C₅	C₂×C₄²	1	1	yes	characteristic
163	C₂³×C₅	C₂×C₄²	1	1	yes	characteristic
164	C₂×C₄×C₅	—	2	2	no	—
165	C₂×C₄×C₅	—	2	2	no	—
166	C₂×C₄×C₅	—	2	2	no	—
167	C₂×C₄×C₅	—	2	2	no	—
168	C₂×C₄×C₅	—	2	2	no	—
169	C₂×C₄×C₅	—	2	2	no	—
170	C₂×C₄×C₅	—	2	2	no	—
171	C₂×C₄×C₅	—	2	2	no	—
172	C₂×C₄×C₅	—	2	2	no	—
173	C₂×C₄×C₅	—	2	2	no	—
174	C₂×C₄×C₅	—	2	2	no	—
175	C₂×C₄×C₅	—	4	1	no	—
176	C₂×C₄×C₅	—	4	1	no	—
177	C₂×C₄×C₅	—	4	1	no	—
178	C₂×C₄×C₅	—	4	1	no	—
179	C₂×C₄×C₅	—	4	1	no	—
180	C₂×C₄×C₅	—	4	1	no	—
181	C₂×C₄×C₅	C₂×C₄²	1	1	yes	characteristic
182	C₂×C₄×C₅	C₂×C₄²	1	1	yes	characteristic
183	C₂×C₄×C₅	C₂×C₄²	1	1	yes	characteristic
184	C₂×C₄×C₅	C₂×C₄²	1	1	yes	characteristic
185	C₂×C₄×C₅	C₂×C₄²	1	1	yes	characteristic
186	C₂×C₄×C₅	C₂×C₄²	1	1	yes	characteristic
187	C₂×C₄×C₅	C₂×C₄²	1	1	yes	characteristic
188	C₂×C₄×C₅	C₂×C₄²	1	1	yes	characteristic
189	C₂×C₄×C₅	C₂×C₄²	1	1	yes	characteristic
190	C₂×C₄×C₅	C₂×M₁₆	1	4	yes	—
191	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
192	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
193	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
194	C₅×C₈	—	2	8	no	—
195	#168	—	2	4	no	—
196	#168	—	2	8	no	—
197	#168	C₂×M₁₆	1	8	yes	—
198	C₂³×C₄	C₄×D₅	1	1	yes	characteristic
199	C₂³×C₄	C₄×D₅	1	1	yes	characteristic
200	C₂³×C₄	C₂×Dic₅	1	1	yes	characteristic
201	C₂×M₁₆	—	5	4	no	—
202	C₂×M₁₆	—	5	4	no	—
203	C₂×M₁₆	—	5	4	no	—
204	C₂×M₁₆	—	10	8	no	—
205	C₂×M₁₆	C₂×Dic₅	1	4	yes	—
206	C₂²×C₈	—	5	2	no	—
207	C₂²×C₈	—	5	2	no	—
208	C₂×C₄²	C₄×D₅	1	1	yes	characteristic
209	C₂×C₄²	C₄×D₅	1	1	yes	characteristic
210	C₂×C₄²	C₄×D₅	1	1	yes	characteristic
211	C₂×C₄²	C₄×D₅	1	1	yes	characteristic
212	C₂×C₄²	C₄×D₅	1	1	yes	characteristic
213	C₂×C₄²	C₄×D₅	1	1	yes	characteristic
214	C₂×C₄²	C₂×Dic₅	1	1	yes	characteristic
215	C₂×C₄²	C₂×Dic₅	1	1	yes	characteristic
216	C₂×C₄²	C₂×Dic₅	1	1	yes	characteristic
217	C₂×C₄²	C₂²×D₅	1	1	yes	characteristic
218	C₂×C₄²	C₂²×D₅	1	1	yes	characteristic
219	C₂×C₄²	C₂²×D₅	1	1	yes	characteristic
220	C₄⋊C₈	—	5	4	no	—
221	C₄⋊C₈	—	5	4	no	—
222	C₄⋊C₈	C₂×Dic₅	1	4	yes	—
223	C₄⋊C₈	C₂×Dic₅	1	4	yes	—
224	C₂²⋊C₈	—	5	4	no	—
225	C₂²⋊C₈	—	5	4	no	—
226	C₂²⋊C₈	C₂×Dic₅	1	4	yes	—
227	C₂²⋊C₈	C₂×Dic₅	1	4	yes	—
228	#97	—	5	4	no	—
229	#97	—	5	4	no	—
230	#97	—	5	4	no	—
231	#97	C₂×Dic₅	1	4	yes	—
232	C₄×C₈	—	5	2	no	—
233	C₄×C₈	—	5	2	no	—
234	C₄×C₈	—	5	2	no	—
235	C₄×C₈	—	5	4	no	—
236	C₄×C₈	—	5	2	no	—
237	C₄×C₈	C₂²×D₅	1	4	yes	—
238	C₂²×C₅	—	2	1	no	—
239	C₂²×C₅	—	2	1	no	—
240	C₂²×C₅	—	2	1	no	—
241	C₂²×C₅	—	2	1	no	—
242	C₂²×C₅	—	2	1	no	—
243	C₂²×C₅	—	2	1	no	—
244	C₂²×C₅	—	2	1	no	—
245	C₂²×C₅	—	2	1	no	—
246	C₂²×C₅	—	4	4	no	—
247	C₂²×C₅	C₄×M₁₆	1	2	yes	—
248	C₂²×C₅	C₂²×C₄²	1	1	yes	characteristic
249	C₄×C₅	—	2	1	no	—
250	C₄×C₅	—	2	1	no	—
251	C₄×C₅	—	2	1	no	—
252	C₄×C₅	—	2	1	no	—
253	C₄×C₅	—	2	1	no	—
254	C₄×C₅	—	2	1	no	—
255	C₄×C₅	—	2	1	no	—
256	C₄×C₅	—	2	1	no	—
257	C₄×C₅	C₄×M₁₆	1	2	yes	—
258	C₄×C₅	C₂²×M₁₆	1	2	yes	—
259	C₄×C₅	#568	1	2	yes	—
260	C₄×C₅	#568	1	2	yes	—
261	C₂⁴	C₄×Dic₅	1	1	yes	characteristic
262	C₂²×C₄	—	2	4	no	—
263	C₂²×C₄	—	4	2	no	—
264	C₂²×C₄	—	4	2	no	—
265	C₂²×C₄	C₄×Dic₅	1	1	yes	characteristic
266	C₂²×C₄	C₄×Dic₅	1	1	yes	characteristic
267	C₂²×C₄	C₄×Dic₅	1	1	yes	characteristic
268	C₂²×C₄	C₄×Dic₅	1	1	yes	characteristic
269	C₂²×C₄	C₄×Dic₅	1	1	yes	characteristic
270	C₂²×C₄	C₄×Dic₅	1	1	yes	characteristic
271	C₂²×C₄	C₄×Dic₅	1	1	yes	characteristic
272	C₂²×C₄	C₄×Dic₅	1	1	yes	characteristic
273	C₂²×C₄	C₄×Dic₅	1	1	yes	characteristic
274	C₂²×C₄	C₂×C₄×D₅	1	1	yes	characteristic
275	C₂²×C₄	C₂×C₄×D₅	1	1	yes	characteristic
276	C₂²×C₄	C₂×C₄×D₅	1	1	yes	characteristic
277	C₂²×C₄	C₂×C₄×D₅	1	1	yes	characteristic
278	C₂²×C₄	C₂×C₄×D₅	1	1	yes	characteristic
279	C₂²×C₄	C₂×C₄×D₅	1	1	yes	characteristic
280	C₂²×C₄	C₂²×Dic₅	1	1	yes	characteristic
281	C₂²×C₄	C₂²×Dic₅	1	1	yes	characteristic
282	C₂²×C₄	C₂²×Dic₅	1	1	yes	characteristic
283	M₁₆	—	4	4	no	—
284	M₁₆	—	10	8	no	—
285	M₁₆	—	10	8	no	—
286	M₁₆	—	20	4	no	—
287	C₂×C₈	—	5	4	no	—
288	C₂×C₈	—	5	8	no	—
289	C₂×C₈	—	5	4	no	—
290	C₂×C₈	—	5	8	no	—
291	C₂×C₈	—	10	4	no	—
292	C₂×C₈	C₂²×Dic₅	1	8	yes	—
293	C₄²	C₄×Dic₅	1	1	yes	characteristic
294	C₄²	C₄×Dic₅	1	1	yes	characteristic
295	C₄²	C₄×Dic₅	1	1	yes	characteristic
296	C₄²	C₄×Dic₅	1	1	yes	characteristic
297	C₄²	C₄×Dic₅	1	1	yes	characteristic
298	C₄²	C₄×Dic₅	1	1	yes	characteristic
299	C₄²	C₂×C₄×D₅	1	1	yes	characteristic
300	C₄²	C₂×C₄×D₅	1	1	yes	characteristic
301	C₄²	C₂×C₄×D₅	1	1	yes	characteristic
302	C₄²	C₂×C₄×D₅	1	1	yes	characteristic
303	C₄²	C₂×C₄×D₅	1	1	yes	characteristic
304	C₄²	C₂×C₄×D₅	1	1	yes	characteristic
305	C₄²	C₂²×Dic₅	1	1	yes	characteristic
306	C₄²	C₂²×Dic₅	1	1	yes	characteristic
307	C₄²	C₂²×Dic₅	1	1	yes	characteristic
308	C₄²	C₂³×D₅	1	1	yes	characteristic
309	C₂×C₅	—	2	2	no	—
310	C₂×C₅	—	4	1	no	—
311	C₂×C₅	—	4	1	no	—
312	C₂×C₅	C₂×C₄×M₁₆	1	1	yes	characteristic
313	C₂×C₅	#2873	1	1	yes	characteristic
314	C₂×C₅	#2873	1	1	yes	characteristic
315	C₂³	—	2	2	no	—
316	C₂³	—	4	1	no	—
317	C₂³	—	4	1	no	—
318	C₂³	C₂×C₄×Dic₅	1	1	yes	characteristic
319	C₂³	C₂×C₄×Dic₅	1	1	yes	characteristic
320	C₂³	C₂×C₄×Dic₅	1	1	yes	characteristic
321	C₂×C₄	—	2	2	no	—
322	C₂×C₄	—	2	2	no	—
323	C₂×C₄	—	2	2	no	—
324	C₂×C₄	—	2	2	no	—
325	C₂×C₄	—	2	2	no	—
326	C₂×C₄	—	2	2	no	—
327	C₂×C₄	—	2	2	no	—
328	C₂×C₄	—	2	2	no	—
329	C₂×C₄	—	2	2	no	—
330	C₂×C₄	—	2	2	no	—
331	C₂×C₄	—	2	2	no	—
332	C₂×C₄	—	4	1	no	—
333	C₂×C₄	—	4	1	no	—
334	C₂×C₄	—	4	1	no	—
335	C₂×C₄	—	4	1	no	—
336	C₂×C₄	—	4	1	no	—
337	C₂×C₄	—	4	1	no	—
338	C₂×C₄	D₅×M₁₆	1	4	yes	—
339	C₂×C₄	C₂×C₄×Dic₅	1	1	yes	characteristic
340	C₂×C₄	C₂×C₄×Dic₅	1	1	yes	characteristic
341	C₂×C₄	C₂×C₄×Dic₅	1	1	yes	characteristic
342	C₂×C₄	C₂×C₄×Dic₅	1	1	yes	characteristic
343	C₂×C₄	C₂×C₄×Dic₅	1	1	yes	characteristic
344	C₂×C₄	C₂×C₄×Dic₅	1	1	yes	characteristic
345	C₂×C₄	C₂×C₄×Dic₅	1	1	yes	characteristic
346	C₂×C₄	C₂×C₄×Dic₅	1	1	yes	characteristic
347	C₂×C₄	C₂×C₄×Dic₅	1	1	yes	characteristic
348	C₂×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
349	C₂×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
350	C₂×C₄	C₂³×Dic₅	1	1	yes	characteristic
351	C₈	—	2	8	no	—
352	C₈	—	5	8	no	—
353	C₈	—	10	4	no	—
354	C₈	—	10	8	no	—
355	C₅	#17334	1	1	yes	characteristic, complemented, Sylow
356	C₂²	—	2	1	no	—
357	C₂²	—	2	1	no	—
358	C₂²	—	2	1	no	—
359	C₂²	—	2	1	no	—
360	C₂²	—	2	1	no	—
361	C₂²	—	2	1	no	—
362	C₂²	—	2	1	no	—
363	C₂²	—	2	1	no	—
364	C₂²	—	4	4	no	—
365	C₂²	M₁₆×Dic₅	1	2	yes	—
366	C₂²	C₂²×C₄×Dic₅	1	1	yes	characteristic
367	C₄	—	2	1	no	—
368	C₄	—	2	1	no	—
369	C₄	—	2	1	no	—
370	C₄	—	2	1	no	—
371	C₄	—	2	1	no	—
372	C₄	—	2	1	no	—
373	C₄	—	2	1	no	—
374	C₄	—	2	1	no	—
375	C₄	M₁₆×Dic₅	1	2	yes	—
376	C₄	C₂×D₅×M₁₆	1	2	yes	—
377	C₄	#66079	1	2	yes	—
378	C₄	#66153	1	2	yes	—
379	C₂	—	2	2	no	—
380	C₂	—	4	1	no	—
381	C₂	—	4	1	no	—
382	C₂	#10613933	1	1	yes	characteristic
383	C₂	C₂×M₁₆×Dic₅	1	1	yes	characteristic
384	C₂	#10615478	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₄²	C₂³×D₅
commutator, socle	C₂²×C₅	C₂²×C₄²
Fitting	C₅×#2920	C₂
prime radical	C₂⁴×C₅	C₄²
cosocle	C₄²×C₅	C₂⁴
hypercenter	#2920	D₅
hypocenter	C₅	#17334
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₄² ◁ #2920

Complements

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

N	H ≅ G/N	type
4. #10601536	C₂	semidirect
5. #10601535	C₂	semidirect
6. #10601533	C₂	semidirect
7. #10600642	C₂	semidirect
31. #64675	C₂²	semidirect
32. #64674	C₂²	semidirect
33. #64674	C₂²	semidirect
34. C₈×#168	C₂²	semidirect
127. C₂×#168	M₁₆	semidirect
355. C₅	#17334	semidirect

Maximal subgroups

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

subgroup	index
C₅×#2920	2
#10613780	2
C₂×C₄×#681	2
#10601536	2
#10601535	2
#10601533	2
#10600642	2
#17334	5