Subgroups — #34307974

Order 20224.

710 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23772066	C₂	1	2	yes	maximal, complemented
2	#23764294	C₂	1	2	yes	maximal
3	#23764050	C₂	1	4	yes	maximal, complemented
4	#23763572	C₂	1	1	yes	maximal, characteristic, complemented
5	#23763420	C₂	1	2	yes	maximal, complemented
6	#23763286	C₂	1	2	yes	maximal, complemented
7	#23763267	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄×#135×C₇₉	C₂	1	1	yes	maximal, characteristic
9	#19098624	—	2	4	no	—
10	#19098620	—	2	2	no	—
11	#19098616	—	2	2	no	—
12	C₂×#14579097	C₂²	1	2	yes	—
13	C₂×#14579097	C₂²	1	2	yes	—
14	#19098587	C₂²	1	2	yes	—
15	C₂×C₄⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
16	C₂×#14579088	C₂²	1	4	yes	—
17	#19098530	C₂²	1	4	yes	—
18	#19098519	C₂²	1	4	yes	—
19	C₂×#14579071	C₂²	1	2	yes	—
20	C₄×C₄⋊Dic₇₉	C₂²	1	1	yes	characteristic
21	#19098322	C₂²	1	4	yes	—
22	#19098317	C₂²	1	2	yes	—
23	C₂×#135×C₇₉	C₂²	1	1	yes	characteristic
24	C₄×#41×C₇₉	C₂²	1	2	yes	—
25	C₄×Q₁₆×C₇₉	C₄	1	1	yes	characteristic, complemented
26	C₄×Q₁₆×C₇₉	C₄	1	1	yes	characteristic, complemented
27	C₄×SD₁₆×C₇₉	C₄	1	2	yes	complemented
28	C₄×SD₁₆×C₇₉	C₄	1	2	yes	complemented
29	C₄×D₈×C₇₉	C₄	1	1	yes	characteristic, complemented
30	C₄×D₈×C₇₉	C₄	1	1	yes	characteristic, complemented
31	#427×C₇₉	C₂²	1	1	yes	characteristic
32	#416×C₇₉	C₂²	1	2	yes	—
33	C₂×C₄×C₈×C₇₉	C₂²	1	1	yes	characteristic
34	C₂×#11929608	C₂³	1	4	yes	—
35	C₂²×C₇₉⋊C₈	C₂³	1	2	yes	—
36	C₂×C₄⋊Dic₇₉	—	2	1	no	—
37	C₂×C₄×Dic₇₉	C₂³	1	2	yes	—
38	#14579097	—	2	4	no	—
39	#14579097	—	4	2	no	—
40	C₄⋊(C₇₉⋊C₈)	—	2	2	no	—
41	C₄⋊(C₇₉⋊C₈)	—	2	2	no	—
42	C₄⋊(C₇₉⋊C₈)	D₄	1	2	yes	—
43	C₄⋊(C₇₉⋊C₈)	D₄	1	2	yes	—
44	#14579088	—	4	4	no	—
45	C₂²⋊(C₇₉⋊C₈)	—	2	4	no	—
46	C₂²⋊(C₇₉⋊C₈)	—	2	4	no	—
47	#14579072	—	2	4	no	—
48	#14579071	—	2	4	no	—
49	C₄×C₇₉⋊C₈	—	2	4	no	—
50	C₇₉⋊#95	—	2	1	no	—
51	C₂×#41×C₇₉	C₂³	1	2	yes	—
52	#135×C₇₉	—	2	2	no	—
53	#135×C₇₉	—	2	2	no	—
54	C₂×Q₁₆×C₇₉	C₂×C₄	1	1	yes	characteristic
55	C₂×SD₁₆×C₇₉	C₂×C₄	1	2	yes	—
56	C₂×D₈×C₇₉	C₂×C₄	1	1	yes	characteristic
57	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
58	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
59	C₄×Q₈×C₇₉	C₂×C₄	1	2	yes	—
60	C₄×Q₈×C₇₉	C₂×C₄	1	2	yes	—
61	C₄×D₄×C₇₉	—	2	2	no	—
62	C₄×D₄×C₇₉	—	2	2	no	—
63	C₄×D₄×C₇₉	C₂×C₄	1	2	yes	—
64	C₄×D₄×C₇₉	C₂×C₄	1	2	yes	—
65	#117×C₇₉	—	2	2	no	—
66	#117×C₇₉	C₂³	1	2	yes	—
67	C₂×C₄²×C₇₉	—	2	2	no	—
68	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
69	#107×C₇₉	C₂×C₄	1	1	yes	characteristic
70	#107×C₇₉	C₂×C₄	1	1	yes	characteristic
71	#106×C₇₉	C₂×C₄	1	2	yes	—
72	#103×C₇₉	C₂×C₄	1	2	yes	—
73	#103×C₇₉	C₂×C₄	1	2	yes	—
74	#102×C₇₉	C₂×C₄	1	2	yes	—
75	#102×C₇₉	C₂×C₄	1	2	yes	—
76	C₄×C₈×C₇₉	C₂×C₄	1	1	yes	characteristic
77	C₄×C₈×C₇₉	C₂×C₄	1	1	yes	characteristic
78	C₄×C₈×C₇₉	C₂×C₄	1	1	yes	characteristic
79	C₄×C₈×C₇₉	C₂×C₄	1	1	yes	characteristic
80	C₂²×Dic₇₉	—	2	2	no	—
81	#11929608	—	2	4	no	—
82	#11929608	—	2	4	no	—
83	C₂×C₇₉⋊C₈	—	2	4	no	—
84	C₂×C₇₉⋊C₈	—	2	2	no	—
85	C₂×C₇₉⋊C₈	—	2	2	no	—
86	C₂×C₇₉⋊C₈	C₂×D₄	1	4	yes	—
87	C₄⋊Dic₇₉	—	4	2	no	—
88	C₄×Dic₇₉	—	2	2	no	—
89	C₄×Dic₇₉	—	2	2	no	—
90	#41×C₇₉	—	2	2	no	—
91	#41×C₇₉	—	2	2	no	—
92	#41×C₇₉	—	2	2	no	—
93	#41×C₇₉	—	2	2	no	—
94	C₂×Q₈×C₇₉	C₂²×C₄	1	2	yes	—
95	C₂×D₄×C₇₉	—	2	2	no	—
96	C₂×D₄×C₇₉	C₂²×C₄	1	2	yes	—
97	C₂²×C₄×C₇₉	—	2	2	no	—
98	C₂²×C₄×C₇₉	—	2	2	no	—
99	C₂²×C₄×C₇₉	—	2	2	no	—
100	C₂²×C₄×C₇₉	#41	1	1	yes	characteristic
101	C₂²×C₄×C₇₉	#41	1	1	yes	characteristic
102	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
103	Q₁₆×C₇₉	—	2	2	no	—
104	SD₁₆×C₇₉	—	2	4	no	—
105	D₈×C₇₉	—	2	2	no	—
106	C₂×C₈×C₇₉	—	2	1	no	—
107	C₂×C₈×C₇₉	—	2	1	no	—
108	C₂×C₈×C₇₉	C₂²×C₄	1	1	yes	characteristic
109	C₂×C₈×C₇₉	C₂²×C₄	1	1	yes	characteristic
110	C₂×C₈×C₇₉	C₂²×C₄	1	1	yes	characteristic
111	C₂×C₈×C₇₉	C₂²×C₄	1	1	yes	characteristic
112	C₂×C₈×C₇₉	#41	1	2	yes	—
113	C₂×C₈×C₇₉	#41	1	2	yes	—
114	C₄⋊C₄×C₇₉	—	2	2	no	—
115	C₄⋊C₄×C₇₉	—	2	2	no	—
116	C₄⋊C₄×C₇₉	C₂²×C₄	1	2	yes	—
117	C₄⋊C₄×C₇₉	C₂²×C₄	1	2	yes	—
118	C₂²⋊C₄×C₇₉	—	2	2	no	—
119	C₂²⋊C₄×C₇₉	—	2	2	no	—
120	C₂²⋊C₄×C₇₉	—	2	2	no	—
121	C₄²×C₇₉	—	2	2	no	—
122	C₄²×C₇₉	—	2	2	no	—
123	C₄²×C₇₉	—	2	2	no	—
124	C₄²×C₇₉	C₂²×C₄	1	1	yes	characteristic
125	C₄²×C₇₉	C₂²×C₄	1	1	yes	characteristic
126	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
127	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
128	C₂³×C₇₉	—	2	2	no	—
129	C₂³×C₇₉	C₂×#41	1	1	yes	characteristic
130	Q₈×C₇₉	—	2	2	no	—
131	Q₈×C₇₉	—	2	2	no	—
132	D₄×C₇₉	—	2	2	no	—
133	D₄×C₇₉	—	2	2	no	—
134	D₄×C₇₉	—	4	2	no	—
135	D₄×C₇₉	—	4	2	no	—
136	C₂×C₄×C₇₉	—	2	2	no	—
137	C₂×C₄×C₇₉	—	2	2	no	—
138	C₂×C₄×C₇₉	—	2	2	no	—
139	C₂×C₄×C₇₉	—	2	2	no	—
140	C₂×C₄×C₇₉	—	4	1	no	—
141	C₂×C₄×C₇₉	—	4	2	no	—
142	C₂×C₄×C₇₉	—	4	2	no	—
143	C₂×C₄×C₇₉	—	4	4	no	—
144	C₂×C₄×C₇₉	—	8	2	no	—
145	C₂×C₄×C₇₉	C₄×D₄	1	1	yes	characteristic
146	C₂×C₄×C₇₉	C₄×D₄	1	1	yes	characteristic
147	C₂×C₄×C₇₉	C₄×D₄	1	1	yes	characteristic
148	C₂×C₄×C₇₉	C₄×D₄	1	1	yes	characteristic
149	C₂×C₄×C₇₉	C₂³×C₄	1	1	yes	characteristic
150	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
151	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
152	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
153	C₂×C₄×C₇₉	H(5,𝔽₂)	1	1	yes	characteristic
154	C₂×C₄×C₇₉	2₋¹⁺⁴	1	1	yes	characteristic
155	C₂×Dic₇₉	—	4	2	no	—
156	C₂×Dic₇₉	—	4	2	no	—
157	C₂×Dic₇₉	—	4	2	no	—
158	C₈×C₇₉	—	2	1	no	—
159	C₈×C₇₉	—	2	1	no	—
160	C₈×C₇₉	#117	1	2	yes	—
161	C₈×C₇₉	#117	1	2	yes	—
162	C₇₉⋊C₈	—	2	4	no	—
163	C₇₉⋊C₈	—	4	4	no	—
164	C₂²×C₇₉	—	2	1	no	—
165	C₂²×C₇₉	—	2	1	no	—
166	C₂²×C₇₉	—	4	2	no	—
167	C₂²×C₇₉	—	4	2	no	—
168	C₂²×C₇₉	—	4	2	no	—
169	C₂²×C₇₉	C₂×C₄×D₄	1	1	yes	characteristic
170	C₂²×C₇₉	#555	1	1	yes	characteristic
171	C₂²×C₇₉	#556	1	1	yes	characteristic
172	C₄×C₇₉	—	2	1	no	—
173	C₄×C₇₉	—	2	1	no	—
174	C₄×C₇₉	—	2	1	no	—
175	C₄×C₇₉	—	4	2	no	—
176	C₄×C₇₉	—	4	2	no	—
177	C₄×C₇₉	—	4	2	no	—
178	C₄×C₇₉	#444	1	2	yes	—
179	C₄×C₇₉	C₂×#117	1	1	yes	characteristic
180	C₄×C₇₉	#520	1	1	yes	characteristic
181	C₄×C₇₉	#547	1	1	yes	characteristic
182	C₄×C₇₉	#550	1	1	yes	characteristic
183	Dic₇₉	—	8	2	no	—
184	#22803	—	79	1	no	maximal, Sylow
185	C₂×C₇₉	—	2	1	no	—
186	C₂×C₇₉	—	2	1	no	—
187	C₂×C₇₉	—	8	2	no	—
188	C₂×C₇₉	#2354	1	1	yes	characteristic
189	C₂×C₇₉	C₂×#444	1	1	yes	characteristic
190	C₂×C₇₉	#2957	1	1	yes	characteristic
191	C₄×#135	D₇₉	1	1	yes	characteristic
192	#2925	—	79	2	no	—
193	#1975	—	79	2	no	—
194	#1929	—	79	4	no	—
195	#1848	—	79	1	no	—
196	#1806	—	79	2	no	—
197	#1773	—	79	2	no	—
198	#1770	—	79	1	no	—
199	C₇₉	#22803	1	1	yes	characteristic, complemented, Sylow
200	C₂×#135	C₂×D₇₉	1	1	yes	characteristic
201	C₄×#41	C₂×D₇₉	1	2	yes	—
202	C₄×Q₁₆	Dic₇₉	1	1	yes	characteristic, complemented
203	C₄×Q₁₆	Dic₇₉	1	1	yes	characteristic, complemented
204	C₄×SD₁₆	Dic₇₉	1	2	yes	complemented
205	C₄×SD₁₆	Dic₇₉	1	2	yes	complemented
206	C₄×D₈	Dic₇₉	1	1	yes	characteristic, complemented
207	C₄×D₈	Dic₇₉	1	1	yes	characteristic, complemented
208	#433	—	158	4	no	—
209	#432	—	158	2	no	—
210	#431	—	158	2	no	—
211	C₂×#108	—	79	2	no	—
212	C₂×#108	—	79	2	no	—
213	#427	C₂×D₇₉	1	1	yes	characteristic
214	#423	—	79	2	no	—
215	C₂×C₄⋊C₈	—	79	1	no	—
216	C₂×#104	—	79	4	no	—
217	#416	C₂×D₇₉	1	2	yes	—
218	#408	—	79	4	no	—
219	#405	—	79	4	no	—
220	C₂×#97	—	79	2	no	—
221	C₂×C₄×C₈	C₂×D₇₉	1	1	yes	characteristic
222	C₄×C₄⋊C₄	—	79	1	no	—
223	#339	—	79	4	no	—
224	#336	—	79	2	no	—
225	C₂×#41	C₂²×D₇₉	1	2	yes	—
226	#135	—	2	2	no	—
227	#135	—	2	2	no	—
228	C₂×Q₁₆	C₂×Dic₇₉	1	1	yes	characteristic
229	C₂×SD₁₆	C₂×Dic₇₉	1	2	yes	—
230	C₂×D₈	C₂×Dic₇₉	1	1	yes	characteristic
231	C₂×M₁₆	—	79	4	no	—
232	C₂²×C₈	—	79	2	no	—
233	C₂²×C₈	C₂²×D₇₉	1	1	yes	characteristic
234	C₂²×C₈	C₂²×D₇₉	1	1	yes	characteristic
235	C₄×Q₈	C₂×Dic₇₉	1	2	yes	—
236	C₄×Q₈	C₂×Dic₇₉	1	2	yes	—
237	C₄×D₄	—	2	2	no	—
238	C₄×D₄	—	2	2	no	—
239	C₄×D₄	C₂×Dic₇₉	1	2	yes	—
240	C₄×D₄	C₂×Dic₇₉	1	2	yes	—
241	#117	—	2	2	no	—
242	#117	C₂²×D₇₉	1	2	yes	—
243	C₂×C₄⋊C₄	—	158	1	no	—
244	C₂×C₄²	—	2	2	no	—
245	C₂×C₄²	—	79	2	no	—
246	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
247	#108	—	316	2	no	—
248	#108	—	158	4	no	—
249	#107	C₂×Dic₇₉	1	1	yes	characteristic
250	#107	C₂×Dic₇₉	1	1	yes	characteristic
251	#106	C₂×Dic₇₉	1	2	yes	—
252	C₄⋊C₈	—	79	2	no	—
253	C₄⋊C₈	—	79	2	no	—
254	C₄⋊C₈	—	158	2	no	—
255	C₄⋊C₈	—	158	2	no	—
256	#104	—	316	4	no	—
257	#103	C₂×Dic₇₉	1	2	yes	—
258	#103	C₂×Dic₇₉	1	2	yes	—
259	#102	C₂×Dic₇₉	1	2	yes	—
260	#102	C₂×Dic₇₉	1	2	yes	—
261	C₂²⋊C₈	—	158	4	no	—
262	C₂²⋊C₈	—	158	4	no	—
263	#97	—	158	4	no	—
264	#97	—	158	4	no	—
265	C₄×C₈	—	158	4	no	—
266	C₄×C₈	C₂×Dic₇₉	1	1	yes	characteristic
267	C₄×C₈	C₂×Dic₇₉	1	1	yes	characteristic
268	C₄×C₈	C₂×Dic₇₉	1	1	yes	characteristic
269	C₄×C₈	C₂×Dic₇₉	1	1	yes	characteristic
270	#95	—	158	1	no	—
271	#41	—	2	2	no	—
272	#41	—	2	2	no	—
273	#41	—	2	2	no	—
274	#41	—	2	2	no	—
275	C₂×Q₈	C₂²×Dic₇₉	1	2	yes	—
276	C₂×D₄	—	2	2	no	—
277	C₂×D₄	C₂²×Dic₇₉	1	2	yes	—
278	C₂²×C₄	—	2	2	no	—
279	C₂²×C₄	—	2	2	no	—
280	C₂²×C₄	—	2	2	no	—
281	C₂²×C₄	—	158	2	no	—
282	C₂²×C₄	#11929623	1	1	yes	characteristic
283	C₂²×C₄	#11929623	1	1	yes	characteristic
284	C₂²×C₄	C₂³×D₇₉	1	1	yes	characteristic
285	Q₁₆	—	2	2	no	—
286	SD₁₆	—	2	4	no	—
287	D₈	—	2	2	no	—
288	M₁₆	—	158	4	no	—
289	M₁₆	—	158	4	no	—
290	C₂×C₈	—	2	1	no	—
291	C₂×C₈	—	2	1	no	—
292	C₂×C₈	—	79	4	no	—
293	C₂×C₈	—	158	4	no	—
294	C₂×C₈	—	158	2	no	—
295	C₂×C₈	—	158	2	no	—
296	C₂×C₈	C₂²×Dic₇₉	1	1	yes	characteristic
297	C₂×C₈	C₂²×Dic₇₉	1	1	yes	characteristic
298	C₂×C₈	C₂²×Dic₇₉	1	1	yes	characteristic
299	C₂×C₈	C₂²×Dic₇₉	1	1	yes	characteristic
300	C₂×C₈	#11929624	1	2	yes	—
301	C₂×C₈	#11929624	1	2	yes	—
302	C₄⋊C₄	—	2	2	no	—
303	C₄⋊C₄	—	2	2	no	—
304	C₄⋊C₄	—	316	2	no	—
305	C₄⋊C₄	C₂²×Dic₇₉	1	2	yes	—
306	C₄⋊C₄	C₂²×Dic₇₉	1	2	yes	—
307	C₂²⋊C₄	—	2	2	no	—
308	C₂²⋊C₄	—	2	2	no	—
309	C₂²⋊C₄	—	2	2	no	—
310	C₄²	—	2	2	no	—
311	C₄²	—	2	2	no	—
312	C₄²	—	2	2	no	—
313	C₄²	—	158	2	no	—
314	C₄²	—	158	2	no	—
315	C₄²	C₂²×Dic₇₉	1	1	yes	characteristic
316	C₄²	C₂²×Dic₇₉	1	1	yes	characteristic
317	C₄²	D₄×D₇₉	1	1	yes	characteristic
318	C₄²	D₄×D₇₉	1	1	yes	characteristic
319	C₂³	—	2	2	no	—
320	C₂³	C₂×#11929623	1	1	yes	characteristic
321	Q₈	—	2	2	no	—
322	Q₈	—	2	2	no	—
323	D₄	—	2	2	no	—
324	D₄	—	2	2	no	—
325	D₄	—	4	2	no	—
326	D₄	—	4	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	—	4	1	no	—
332	C₂×C₄	—	4	4	no	—
333	C₂×C₄	—	4	2	no	—
334	C₂×C₄	—	4	2	no	—
335	C₂×C₄	—	8	2	no	—
336	C₂×C₄	—	316	2	no	—
337	C₂×C₄	—	316	2	no	—
338	C₂×C₄	—	316	2	no	—
339	C₂×C₄	D₄×Dic₇₉	1	1	yes	characteristic
340	C₂×C₄	D₄×Dic₇₉	1	1	yes	characteristic
341	C₂×C₄	D₄×Dic₇₉	1	1	yes	characteristic
342	C₂×C₄	D₄×Dic₇₉	1	1	yes	characteristic
343	C₂×C₄	C₂³×Dic₇₉	1	1	yes	characteristic
344	C₂×C₄	C₂×D₄×D₇₉	1	1	yes	characteristic
345	C₂×C₄	C₂×#11929624	1	1	yes	characteristic
346	C₂×C₄	C₂×#11929624	1	1	yes	characteristic
347	C₂×C₄	#14579207	1	1	yes	characteristic
348	C₂×C₄	#14579208	1	1	yes	characteristic
349	C₈	—	2	1	no	—
350	C₈	—	2	1	no	—
351	C₈	—	316	4	no	—
352	C₈	—	158	4	no	—
353	C₈	#14579120	1	2	yes	—
354	C₈	#14579120	1	2	yes	—
355	C₂²	—	2	1	no	—
356	C₂²	—	2	1	no	—
357	C₂²	—	4	2	no	—
358	C₂²	—	4	2	no	—
359	C₂²	—	4	2	no	—
360	C₂²	C₂×D₄×Dic₇₉	1	1	yes	characteristic
361	C₂²	#19099278	1	1	yes	characteristic
362	C₂²	#19099283	1	1	yes	characteristic
363	C₄	—	2	1	no	—
364	C₄	—	2	1	no	—
365	C₄	—	2	1	no	—
366	C₄	—	4	2	no	—
367	C₄	—	4	2	no	—
368	C₄	—	4	2	no	—
369	C₄	—	632	2	no	—
370	C₄	#19098685	1	2	yes	—
371	C₄	C₂×#14579120	1	1	yes	characteristic
372	C₄	#19099046	1	1	yes	characteristic
373	C₄	#19099218	1	1	yes	characteristic
374	C₄	#19099234	1	1	yes	characteristic
375	C₂	—	2	1	no	—
376	C₂	—	2	1	no	—
377	C₂	—	8	2	no	—
378	C₂	#23766349	1	1	yes	characteristic
379	C₂	C₂×#19098685	1	1	yes	characteristic
380	C₂	#23772317	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₇₉
commutator	C₂×C₄×C₇₉	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₇₉
Fitting	C₄×#135×C₇₉	C₂
socle	C₂²×C₇₉	C₂×C₄×D₄
prime radical	C₂×#135×C₇₉	C₂²
cosocle	C₂²×C₄×C₇₉	C₂⁴
hypercenter	C₄×#135	D₇₉
hypocenter	C₇₉	#22803
LCS	G ▷ C₂×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₄×#135

Complements

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

N	H ≅ G/N	type
1. #23772066	C₂	semidirect
3. #23764050	C₂	semidirect
4. #23763572	C₂	semidirect
5. #23763420	C₂	semidirect
6. #23763286	C₂	semidirect
7. #23763267	C₂	semidirect
25. C₄×Q₁₆×C₇₉	C₄	semidirect
26. C₄×Q₁₆×C₇₉	C₄	semidirect
27. C₄×SD₁₆×C₇₉	C₄	semidirect
28. C₄×SD₁₆×C₇₉	C₄	semidirect
29. C₄×D₈×C₇₉	C₄	semidirect
30. C₄×D₈×C₇₉	C₄	semidirect
199. C₇₉	#22803	semidirect
202. C₄×Q₁₆	Dic₇₉	semidirect
203. C₄×Q₁₆	Dic₇₉	semidirect
204. C₄×SD₁₆	Dic₇₉	semidirect
205. C₄×SD₁₆	Dic₇₉	semidirect
206. C₄×D₈	Dic₇₉	semidirect
207. C₄×D₈	Dic₇₉	semidirect

Maximal subgroups

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

subgroup	index
#23772066	2
#23764294	2
#23764050	2
#23763572	2
#23763420	2
#23763286	2
#23763267	2
C₄×#135×C₇₉	2
#22803	79