Subgroups — #34178264

Order 20224.

850 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#19098616	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×C₄⋊Dic₇₉	C₂	1	1	yes	maximal, characteristic
3	#23761278	C₂	1	4	yes	maximal
4	C₇₉×#2285	C₂	1	1	yes	maximal, characteristic
5	C₂²×C₄⋊Dic₇₉	—	2	1	no	—
6	C₂²×C₄×Dic₇₉	—	2	1	no	—
7	#19098616	—	2	2	no	—
8	#19098616	C₄	1	4	yes	complemented
9	C₂×C₄⋊(C₇₉⋊C₈)	—	2	1	no	—
10	C₂×C₂²⋊(C₇₉⋊C₈)	C₂²	1	2	yes	—
11	C₂×C₄×C₇₉⋊C₈	—	2	1	no	—
12	C₄×C₄⋊Dic₇₉	—	2	2	no	—
13	C₄×C₄⋊Dic₇₉	C₄	1	4	yes	complemented
14	C₂×C₇₉⋊#95	C₂²	1	2	yes	—
15	C₂×#117×C₇₉	—	2	1	no	—
16	C₂²×C₄²×C₇₉	C₂²	1	1	yes	characteristic
17	#384×C₇₉	C₄	1	2	yes	complemented
18	#382×C₇₉	—	2	1	no	—
19	#380×C₇₉	—	2	1	no	—
20	#380×C₇₉	C₂²	1	2	yes	—
21	C₄×C₄⋊C₄×C₇₉	—	2	1	no	—
22	C₄×C₄⋊C₄×C₇₉	C₄	1	2	yes	complemented
23	C₂³×Dic₇₉	—	2	2	no	—
24	C₂²×C₇₉⋊C₈	—	2	2	no	—
25	C₂×C₄⋊Dic₇₉	—	2	8	no	—
26	C₂×C₄⋊Dic₇₉	—	2	4	no	—
27	C₂×C₄×Dic₇₉	—	2	4	no	—
28	C₂×C₄×Dic₇₉	—	4	2	no	—
29	C₂×C₄×Dic₇₉	—	4	2	no	—
30	C₄⋊(C₇₉⋊C₈)	—	2	4	no	—
31	C₂²⋊(C₇₉⋊C₈)	—	2	2	no	—
32	C₂²⋊(C₇₉⋊C₈)	C₂×C₄	1	4	yes	—
33	C₄×C₇₉⋊C₈	—	2	4	no	—
34	C₇₉⋊#95	—	2	2	no	—
35	C₇₉⋊#95	C₂×C₄	1	4	yes	—
36	C₂³×C₄×C₇₉	D₄	1	1	yes	characteristic
37	C₂³×C₄×C₇₉	D₄	1	1	yes	characteristic
38	C₂³×C₄×C₇₉	C₂³	1	1	yes	characteristic
39	#117×C₇₉	—	4	2	no	—
40	#117×C₇₉	—	4	2	no	—
41	C₂×C₄⋊C₄×C₇₉	—	2	2	no	—
42	C₂×C₄⋊C₄×C₇₉	—	2	2	no	—
43	C₂×C₄⋊C₄×C₇₉	C₂×C₄	1	4	yes	—
44	C₂×C₂²⋊C₄×C₇₉	—	2	2	no	—
45	C₂×C₄²×C₇₉	—	2	2	no	—
46	C₂×C₄²×C₇₉	C₂×C₄	1	2	yes	—
47	C₂×C₄²×C₇₉	C₂×C₄	1	2	yes	—
48	C₂×C₄²×C₇₉	C₂×C₄	1	1	yes	characteristic
49	C₂×C₄²×C₇₉	C₂×C₄	1	1	yes	characteristic
50	C₂×C₄²×C₇₉	D₄	1	1	yes	characteristic
51	C₂×C₄²×C₇₉	D₄	1	1	yes	characteristic
52	C₂×C₄²×C₇₉	D₄	1	2	yes	—
53	C₂×C₄²×C₇₉	Q₈	1	2	yes	—
54	#95×C₇₉	—	2	2	no	—
55	#95×C₇₉	—	2	2	no	—
56	C₂²×Dic₇₉	—	2	8	no	—
57	C₂²×Dic₇₉	—	2	4	no	—
58	C₂²×Dic₇₉	—	4	4	no	—
59	C₂²×Dic₇₉	—	4	2	no	—
60	C₂²×Dic₇₉	—	4	2	no	—
61	C₂×C₇₉⋊C₈	—	2	4	no	—
62	C₂×C₇₉⋊C₈	—	4	4	no	—
63	C₄⋊Dic₇₉	—	2	16	no	—
64	C₄×Dic₇₉	—	4	8	no	—
65	C₂⁴×C₇₉	C₂×D₄	1	1	yes	characteristic
66	C₂²×C₄×C₇₉	—	2	4	no	—
67	C₂²×C₄×C₇₉	—	2	4	no	—
68	C₂²×C₄×C₇₉	—	4	2	no	—
69	C₂²×C₄×C₇₉	C₂²⋊C₄	1	2	yes	—
70	C₂²×C₄×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
71	C₂²×C₄×C₇₉	C₂²⋊C₄	1	2	yes	—
72	C₂²×C₄×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
73	C₂²×C₄×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
74	C₂²×C₄×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
75	C₂²×C₄×C₇₉	C₄⋊C₄	1	2	yes	—
76	C₂²×C₄×C₇₉	C₄⋊C₄	1	2	yes	—
77	C₂²×C₄×C₇₉	D₈	1	2	yes	—
78	C₂²×C₄×C₇₉	SD₁₆	1	2	yes	—
79	C₂²×C₄×C₇₉	SD₁₆	1	2	yes	—
80	C₂²×C₄×C₇₉	Q₁₆	1	2	yes	—
81	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
82	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
83	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
84	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
85	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
86	C₂²×C₄×C₇₉	C₂×Q₈	1	1	yes	characteristic
87	C₄⋊C₄×C₇₉	—	4	4	no	—
88	C₄⋊C₄×C₇₉	—	4	4	no	—
89	C₄⋊C₄×C₇₉	—	4	4	no	—
90	C₂²⋊C₄×C₇₉	—	4	2	no	—
91	C₂²⋊C₄×C₇₉	—	4	2	no	—
92	C₄²×C₇₉	—	4	4	no	—
93	C₄²×C₇₉	C₄²	1	2	yes	—
94	C₄²×C₇₉	C₄²	1	2	yes	—
95	C₄²×C₇₉	C₂²⋊C₄	1	2	yes	—
96	C₄²×C₇₉	C₂²⋊C₄	1	2	yes	—
97	C₄²×C₇₉	C₄⋊C₄	1	2	yes	—
98	C₄²×C₇₉	C₄⋊C₄	1	2	yes	—
99	C₄²×C₇₉	C₄⋊C₄	1	2	yes	—
100	C₄²×C₇₉	C₄⋊C₄	1	2	yes	—
101	C₂³×C₇₉	—	2	2	no	—
102	C₂³×C₇₉	—	2	2	no	—
103	C₂³×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
104	C₂³×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
105	C₂³×C₇₉	C₂×C₄⋊C₄	1	1	yes	characteristic
106	C₂³×C₇₉	C₂×D₈	1	1	yes	characteristic
107	C₂³×C₇₉	C₂×SD₁₆	1	1	yes	characteristic
108	C₂³×C₇₉	C₂×SD₁₆	1	1	yes	characteristic
109	C₂³×C₇₉	C₂×Q₁₆	1	1	yes	characteristic
110	C₂×C₄×C₇₉	—	2	2	no	—
111	C₂×C₄×C₇₉	—	2	2	no	—
112	C₂×C₄×C₇₉	—	2	2	no	—
113	C₂×C₄×C₇₉	—	2	4	no	—
114	C₂×C₄×C₇₉	—	2	4	no	—
115	C₂×C₄×C₇₉	—	4	1	no	—
116	C₂×C₄×C₇₉	—	4	1	no	—
117	C₂×C₄×C₇₉	—	4	1	no	—
118	C₂×C₄×C₇₉	—	4	1	no	—
119	C₂×C₄×C₇₉	—	4	4	no	—
120	C₂×C₄×C₇₉	—	4	4	no	—
121	C₂×C₄×C₇₉	—	4	4	no	—
122	C₂×C₄×C₇₉	#95	1	2	yes	—
123	C₂×C₄×C₇₉	#95	1	2	yes	—
124	C₂×C₄×C₇₉	#95	1	2	yes	—
125	C₂×C₄×C₇₉	#95	1	2	yes	—
126	C₂×C₄×C₇₉	#102	1	4	yes	—
127	C₂×C₄×C₇₉	#102	1	2	yes	—
128	C₂×C₄×C₇₉	#102	1	2	yes	—
129	C₂×C₄×C₇₉	#103	1	4	yes	—
130	C₂×C₄×C₇₉	#103	1	2	yes	—
131	C₂×C₄×C₇₉	#103	1	2	yes	—
132	C₂×C₄×C₇₉	#104	1	4	yes	—
133	C₂×C₄×C₇₉	#106	1	4	yes	—
134	C₂×C₄×C₇₉	#107	1	4	yes	—
135	C₂×C₄×C₇₉	C₂×C₄²	1	1	yes	characteristic
136	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
137	C₂×C₄×C₇₉	C₂×C₄⋊C₄	1	1	yes	characteristic
138	C₂×C₄×C₇₉	C₂×C₄⋊C₄	1	1	yes	characteristic
139	C₂×Dic₇₉	—	2	8	no	—
140	C₂×Dic₇₉	—	4	4	no	—
141	C₂×Dic₇₉	—	4	8	no	—
142	C₂×Dic₇₉	—	4	8	no	—
143	C₂×Dic₇₉	—	4	4	no	—
144	C₇₉⋊C₈	—	4	4	no	—
145	C₂²×C₇₉	—	2	1	no	—
146	C₂²×C₇₉	—	2	1	no	—
147	C₂²×C₇₉	—	2	1	no	—
148	C₂²×C₇₉	—	2	1	no	—
149	C₂²×C₇₉	—	2	2	no	—
150	C₂²×C₇₉	—	2	2	no	—
151	C₂²×C₇₉	—	2	2	no	—
152	C₂²×C₇₉	—	2	2	no	—
153	C₂²×C₇₉	C₂×#95	1	1	yes	characteristic
154	C₂²×C₇₉	#410	1	2	yes	—
155	C₂²×C₇₉	C₂×#102	1	1	yes	characteristic
156	C₂²×C₇₉	C₂×#102	1	1	yes	characteristic
157	C₂²×C₇₉	C₂×#103	1	1	yes	characteristic
158	C₂²×C₇₉	C₂×#103	1	1	yes	characteristic
159	C₂²×C₇₉	C₂×#104	1	2	yes	—
160	C₂²×C₇₉	C₂×#106	1	1	yes	characteristic
161	C₂²×C₇₉	C₂×#107	1	1	yes	characteristic
162	C₄×C₇₉	—	2	2	no	—
163	C₄×C₇₉	—	2	1	no	—
164	C₄×C₇₉	—	2	1	no	—
165	C₄×C₇₉	—	2	1	no	—
166	C₄×C₇₉	—	2	1	no	—
167	C₄×C₇₉	—	8	4	no	—
168	C₄×C₇₉	#339	1	4	yes	—
169	C₄×C₇₉	#340	1	4	yes	—
170	C₄×C₇₉	#340	1	4	yes	—
171	Dic₇₉	—	4	8	no	—
172	#8014	—	79	1	no	maximal, Sylow
173	C₂×C₇₉	—	2	1	no	—
174	C₂×C₇₉	—	2	1	no	—
175	C₂×C₇₉	—	2	1	no	—
176	C₂×C₇₉	—	2	1	no	—
177	C₂×C₇₉	#1502	1	2	yes	—
178	C₂×C₇₉	#1503	1	2	yes	—
179	C₂×C₇₉	C₂×#339	1	1	yes	characteristic
180	C₂×C₇₉	C₂×#340	1	1	yes	characteristic
181	C₂×C₇₉	#1740	1	1	yes	characteristic
182	C₂×#431	—	79	1	no	—
183	#2285	D₇₉	1	1	yes	characteristic
184	C₂×C₄×C₄⋊C₄	—	79	1	no	—
185	#1294	—	79	4	no	—
186	C₇₉	#8014	1	1	yes	characteristic, complemented, Sylow
187	C₂×#117	—	2	1	no	—
188	C₂²×C₄⋊C₄	—	158	1	no	—
189	C₂²×C₄²	—	158	1	no	—
190	C₂²×C₄²	C₂×D₇₉	1	1	yes	characteristic
191	#431	—	79	4	no	—
192	#431	—	158	2	no	—
193	C₂×C₄⋊C₈	—	158	1	no	—
194	C₂×C₂²⋊C₈	—	79	2	no	—
195	C₂×C₄×C₈	—	158	1	no	—
196	#384	Dic₇₉	1	2	yes	complemented
197	#382	—	2	1	no	—
198	#380	—	2	1	no	—
199	#380	C₂×D₇₉	1	2	yes	—
200	C₄×C₄⋊C₄	—	2	1	no	—
201	C₄×C₄⋊C₄	—	79	4	no	—
202	C₄×C₄⋊C₄	—	158	2	no	—
203	C₄×C₄⋊C₄	Dic₇₉	1	2	yes	complemented
204	C₂×#95	—	79	2	no	—
205	C₂³×C₄	—	158	2	no	—
206	C₂³×C₄	C₂²⋊D₇₉	1	1	yes	characteristic
207	C₂³×C₄	C₂²⋊D₇₉	1	1	yes	characteristic
208	C₂³×C₄	C₂²×D₇₉	1	1	yes	characteristic
209	C₂²×C₈	—	158	2	no	—
210	#117	—	4	2	no	—
211	#117	—	4	2	no	—
212	C₂×C₄⋊C₄	—	2	2	no	—
213	C₂×C₄⋊C₄	—	2	2	no	—
214	C₂×C₄⋊C₄	—	158	8	no	—
215	C₂×C₄⋊C₄	—	158	4	no	—
216	C₂×C₄⋊C₄	C₂×Dic₇₉	1	4	yes	—
217	C₂×C₂²⋊C₄	—	2	2	no	—
218	C₂×C₄²	—	2	2	no	—
219	C₂×C₄²	—	316	2	no	—
220	C₂×C₄²	—	316	2	no	—
221	C₂×C₄²	—	158	4	no	—
222	C₂×C₄²	Dic₁₅₈	1	2	yes	—
223	C₂×C₄²	C₄×D₇₉	1	2	yes	—
224	C₂×C₄²	C₄×D₇₉	1	2	yes	—
225	C₂×C₄²	D₃₁₆	1	2	yes	—
226	C₂×C₄²	C₂×Dic₇₉	1	1	yes	characteristic
227	C₂×C₄²	C₂×Dic₇₉	1	1	yes	characteristic
228	C₂×C₄²	C₂²⋊D₇₉	1	1	yes	characteristic
229	C₂×C₄²	C₂²⋊D₇₉	1	1	yes	characteristic
230	C₄⋊C₈	—	158	4	no	—
231	C₂²⋊C₈	—	79	4	no	—
232	C₂²⋊C₈	—	158	2	no	—
233	C₄×C₈	—	158	4	no	—
234	#95	—	2	2	no	—
235	#95	—	2	2	no	—
236	#95	—	79	4	no	—
237	#95	—	158	2	no	—
238	C₂⁴	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
239	C₂²×C₄	—	2	4	no	—
240	C₂²×C₄	—	2	4	no	—
241	C₂²×C₄	—	4	2	no	—
242	C₂²×C₄	—	316	4	no	—
243	C₂²×C₄	—	316	2	no	—
244	C₂²×C₄	—	316	2	no	—
245	C₂²×C₄	—	158	8	no	—
246	C₂²×C₄	—	158	4	no	—
247	C₂²×C₄	(C₂×D₇₉)⋊C₄	1	2	yes	—
248	C₂²×C₄	(C₂×D₇₉)⋊C₄	1	2	yes	—
249	C₂²×C₄	C₂²⋊Dic₇₉	1	1	yes	characteristic
250	C₂²×C₄	C₂²⋊Dic₇₉	1	1	yes	characteristic
251	C₂²×C₄	C₂²⋊Dic₇₉	1	1	yes	characteristic
252	C₂²×C₄	C₂²⋊Dic₇₉	1	1	yes	characteristic
253	C₂²×C₄	Dic₇₉⋊C₄	1	2	yes	—
254	C₂²×C₄	Dic₇₉⋊C₄	1	2	yes	—
255	C₂²×C₄	#11929609	1	2	yes	—
256	C₂²×C₄	#11929611	1	2	yes	—
257	C₂²×C₄	#11929612	1	2	yes	—
258	C₂²×C₄	#11929614	1	2	yes	—
259	C₂²×C₄	C₂×C₄×D₇₉	1	1	yes	characteristic
260	C₂²×C₄	C₂×C₄×D₇₉	1	1	yes	characteristic
261	C₂²×C₄	C₂²×Dic₇₉	1	1	yes	characteristic
262	C₂²×C₄	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
263	C₂²×C₄	C₂×D₃₁₆	1	1	yes	characteristic
264	C₂²×C₄	C₂×Dic₁₅₈	1	1	yes	characteristic
265	C₂×C₈	—	316	4	no	—
266	C₂×C₈	—	158	4	no	—
267	C₄⋊C₄	—	4	4	no	—
268	C₄⋊C₄	—	4	4	no	—
269	C₄⋊C₄	—	4	4	no	—
270	C₄⋊C₄	—	158	16	no	—
271	C₂²⋊C₄	—	4	2	no	—
272	C₂²⋊C₄	—	4	2	no	—
273	C₄²	—	4	4	no	—
274	C₄²	—	316	8	no	—
275	C₄²	C₄×Dic₇₉	1	2	yes	—
276	C₄²	C₄×Dic₇₉	1	2	yes	—
277	C₄²	(C₂×D₇₉)⋊C₄	1	2	yes	—
278	C₄²	(C₂×D₇₉)⋊C₄	1	2	yes	—
279	C₄²	Dic₇₉⋊C₄	1	2	yes	—
280	C₄²	Dic₇₉⋊C₄	1	2	yes	—
281	C₄²	C₄⋊Dic₇₉	1	2	yes	—
282	C₄²	C₄⋊Dic₇₉	1	2	yes	—
283	C₂³	—	2	2	no	—
284	C₂³	—	2	2	no	—
285	C₂³	C₂×(C₂×D₇₉)⋊C₄	1	1	yes	characteristic
286	C₂³	C₂×C₂²⋊Dic₇₉	1	1	yes	characteristic
287	C₂³	C₂×Dic₇₉⋊C₄	1	1	yes	characteristic
288	C₂³	C₂×#11929609	1	1	yes	characteristic
289	C₂³	C₂×#11929611	1	1	yes	characteristic
290	C₂³	C₂×#11929612	1	1	yes	characteristic
291	C₂³	C₂×#11929614	1	1	yes	characteristic
292	C₂×C₄	—	2	2	no	—
293	C₂×C₄	—	2	2	no	—
294	C₂×C₄	—	2	2	no	—
295	C₂×C₄	—	2	4	no	—
296	C₂×C₄	—	2	4	no	—
297	C₂×C₄	—	4	1	no	—
298	C₂×C₄	—	4	1	no	—
299	C₂×C₄	—	4	1	no	—
300	C₂×C₄	—	4	1	no	—
301	C₂×C₄	—	4	4	no	—
302	C₂×C₄	—	4	4	no	—
303	C₂×C₄	—	4	4	no	—
304	C₂×C₄	—	316	4	no	—
305	C₂×C₄	—	316	8	no	—
306	C₂×C₄	—	316	8	no	—
307	C₂×C₄	—	316	4	no	—
308	C₂×C₄	—	158	8	no	—
309	C₂×C₄	C₇₉⋊#95	1	2	yes	—
310	C₂×C₄	C₇₉⋊#95	1	2	yes	—
311	C₂×C₄	C₇₉⋊#95	1	2	yes	—
312	C₂×C₄	C₇₉⋊#95	1	2	yes	—
313	C₂×C₄	#14579081	1	4	yes	—
314	C₂×C₄	#14579082	1	2	yes	—
315	C₂×C₄	#14579082	1	2	yes	—
316	C₂×C₄	#14579084	1	4	yes	—
317	C₂×C₄	#14579085	1	2	yes	—
318	C₂×C₄	#14579085	1	2	yes	—
319	C₂×C₄	#14579088	1	4	yes	—
320	C₂×C₄	#14579092	1	4	yes	—
321	C₂×C₄	#14579094	1	4	yes	—
322	C₂×C₄	C₂×C₄×Dic₇₉	1	1	yes	characteristic
323	C₂×C₄	C₂×(C₂×D₇₉)⋊C₄	1	1	yes	characteristic
324	C₂×C₄	C₂×Dic₇₉⋊C₄	1	1	yes	characteristic
325	C₂×C₄	C₂×C₄⋊Dic₇₉	1	1	yes	characteristic
326	C₈	—	316	4	no	—
327	C₂²	—	2	1	no	—
328	C₂²	—	2	1	no	—
329	C₂²	—	2	1	no	—
330	C₂²	—	2	1	no	—
331	C₂²	—	2	2	no	—
332	C₂²	—	2	2	no	—
333	C₂²	—	2	2	no	—
334	C₂²	—	2	2	no	—
335	C₂²	C₂×C₇₉⋊#95	1	1	yes	characteristic
336	C₂²	#19098537	1	2	yes	—
337	C₂²	C₂×#14579081	1	1	yes	characteristic
338	C₂²	C₂×#14579082	1	1	yes	characteristic
339	C₂²	C₂×#14579084	1	1	yes	characteristic
340	C₂²	C₂×#14579085	1	1	yes	characteristic
341	C₂²	C₂×#14579088	1	2	yes	—
342	C₂²	C₂×#14579092	1	1	yes	characteristic
343	C₂²	C₂×#14579094	1	1	yes	characteristic
344	C₄	—	2	2	no	—
345	C₄	—	2	1	no	—
346	C₄	—	2	1	no	—
347	C₄	—	2	1	no	—
348	C₄	—	2	1	no	—
349	C₄	—	8	4	no	—
350	C₄	—	316	8	no	—
351	C₄	#19098322	1	4	yes	—
352	C₄	#19098325	1	4	yes	—
353	C₄	#19098325	1	4	yes	—
354	C₂	—	2	1	no	—
355	C₂	—	2	1	no	—
356	C₂	—	2	1	no	—
357	C₂	—	2	1	no	—
358	C₂	#23761895	1	2	yes	—
359	C₂	#23761899	1	2	yes	—
360	C₂	C₂×#19098322	1	1	yes	characteristic
361	C₂	C₂×#19098325	1	1	yes	characteristic
362	C₂	#23763133	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂²⋊Dic₇₉
commutator	C₂×C₄×C₇₉	C₂×C₄²
Frattini	C₂³×C₄	C₂²×D₇₉
Fitting	C₇₉×#2285	C₂
socle	C₂³×C₇₉	C₂×C₂²⋊C₄
prime radical	C₂⁴×C₇₉	C₂×D₄
cosocle	C₂³×C₄×C₇₉	C₂³
hypercenter	#2285	D₇₉
hypocenter	C₇₉	#8014
LCS	G ▷ C₂×C₄×C₇₉ ▷ C₂²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₂²×C₄² ◁ #2285

Complements

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

N	H ≅ G/N	type
8. #19098616	C₄	semidirect
13. C₄×C₄⋊Dic₇₉	C₄	semidirect
17. #384×C₇₉	C₄	semidirect
22. C₄×C₄⋊C₄×C₇₉	C₄	semidirect
186. C₇₉	#8014	semidirect
196. #384	Dic₇₉	semidirect
203. C₄×C₄⋊C₄	Dic₇₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#19098616	2
C₂×C₄×C₄⋊Dic₇₉	2
#23761278	2
C₇₉×#2285	2
#8014	79