Subgroups — C₂²×#19099127 #35195024

Order 20224.

14414 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴×D₃₁₆	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#19099127	C₂	1	48	yes	maximal, direct product factor
3	C₂²×#14579157	C₂	1	2	yes	maximal, complemented
4	C₂²×#14579150	C₂	1	2	yes	maximal, complemented
5	C₂²×#14579135	C₂	1	4	yes	maximal, complemented
6	C₂²×#14579129	C₂	1	4	yes	maximal, complemented
7	C₂²×#14579120	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂³×#41×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂⁵×D₇₉	C₂²	1	2	yes	—
10	C₂³×D₃₁₆	—	2	16	no	—
11	C₂³×D₃₁₆	C₂²	1	2	yes	—
12	C₂³×D₃₁₆	C₂²	1	2	yes	—
13	C₂³×D₃₁₆	C₂²	1	24	yes	complemented
14	C₂³×C₂²⋊D₇₉	C₂²	1	8	yes	complemented
15	#19099127	C₂²	1	256	yes	direct product factor
16	C₂×#14579157	C₂²	1	48	yes	complemented
17	C₂×#14579150	C₂²	1	48	yes	complemented
18	C₂×#14579135	C₂²	1	96	yes	complemented
19	C₂×#14579129	C₂²	1	96	yes	complemented
20	C₂×#14579120	C₂²	1	24	yes	complemented
21	C₂²×C₄⋊Dic₇₉	C₂²	1	2	yes	complemented
22	C₂²×C₂²⋊Dic₇₉	C₂²	1	2	yes	—
23	C₂²×(C₂×D₇₉)⋊C₄	C₂²	1	8	yes	complemented
24	C₂²×C₄×Dic₇₉	C₂²	1	2	yes	complemented
25	C₂²×#41×C₇₉	—	2	16	no	—
26	C₂²×#41×C₇₉	C₂²	1	24	yes	complemented
27	C₂³×Q₈×C₇₉	C₂²	1	1	yes	characteristic, complemented
28	C₂³×D₄×C₇₉	C₂²	1	2	yes	—
29	C₂³×D₄×C₇₉	C₂²	1	1	yes	characteristic, complemented
30	C₂⁴×C₄×C₇₉	C₂²	1	1	yes	characteristic
31	C₂⁴×C₄×C₇₉	C₂²	1	2	yes	complemented
32	C₂⁴×D₇₉	—	2	16	no	—
33	C₂⁴×D₇₉	—	4	16	no	—
34	C₂⁴×D₇₉	C₂³	1	4	yes	—
35	C₂⁴×D₇₉	C₂³	1	24	yes	—
36	C₂²×D₃₁₆	—	2	16	no	—
37	C₂²×D₃₁₆	—	2	16	no	—
38	C₂²×D₃₁₆	—	2	192	no	—
39	C₂²×D₃₁₆	C₂³	1	24	yes	—
40	C₂²×D₃₁₆	C₂³	1	24	yes	—
41	C₂²×D₃₁₆	C₂³	1	64	yes	complemented
42	C₂²×C₂²⋊D₇₉	—	4	32	no	—
43	C₂²×C₂²⋊D₇₉	C₂³	1	96	yes	complemented
44	C₂³×Dic₇₉	C₂³	1	4	yes	—
45	#14579157	C₂³	1	128	yes	complemented
46	#14579150	C₂³	1	128	yes	complemented
47	#14579135	C₂³	1	256	yes	complemented
48	#14579129	C₂³	1	256	yes	complemented
49	#14579120	C₂³	1	64	yes	complemented
50	C₂×C₄⋊Dic₇₉	C₂³	1	24	yes	complemented
51	C₂×C₂²⋊Dic₇₉	C₂³	1	24	yes	—
52	C₂×(C₂×D₇₉)⋊C₄	C₂³	1	96	yes	complemented
53	C₂×C₄×Dic₇₉	C₂³	1	24	yes	complemented
54	C₂⁵×C₇₉	C₂³	1	2	yes	—
55	C₂⁵×C₇₉	C₂³	1	1	yes	characteristic
56	C₂×#41×C₇₉	—	2	192	no	—
57	C₂×#41×C₇₉	C₂³	1	64	yes	complemented
58	C₂²×Q₈×C₇₉	—	2	8	no	—
59	C₂²×Q₈×C₇₉	C₂³	1	12	yes	complemented
60	C₂²×D₄×C₇₉	—	2	16	no	—
61	C₂²×D₄×C₇₉	—	2	8	no	—
62	C₂²×D₄×C₇₉	C₂³	1	24	yes	—
63	C₂²×D₄×C₇₉	C₂³	1	12	yes	complemented
64	C₂³×C₄×C₇₉	—	2	16	no	—
65	C₂³×C₄×C₇₉	D₄	1	16	yes	complemented
66	C₂³×C₄×C₇₉	C₂³	1	2	yes	—
67	C₂³×C₄×C₇₉	C₂³	1	1	yes	characteristic
68	C₂³×C₄×C₇₉	C₂³	1	1	yes	characteristic
69	C₂³×C₄×C₇₉	C₂³	1	12	yes	—
70	C₂³×C₄×C₇₉	C₂³	1	24	yes	complemented
71	C₂³×D₇₉	—	2	96	no	—
72	C₂³×D₇₉	—	2	16	no	—
73	C₂³×D₇₉	—	2	32	no	—
74	C₂³×D₇₉	—	4	96	no	—
75	C₂³×D₇₉	—	4	128	no	—
76	C₂³×D₇₉	C₂⁴	1	24	yes	—
77	C₂³×D₇₉	C₂⁴	1	32	yes	—
78	C₂×D₃₁₆	—	2	96	no	—
79	C₂×D₃₁₆	—	2	96	no	—
80	C₂×D₃₁₆	—	2	256	no	—
81	C₂×D₃₁₆	C₂⁴	1	32	yes	—
82	C₂×D₃₁₆	C₂⁴	1	32	yes	—
83	C₂×C₂²⋊D₇₉	—	4	192	no	—
84	C₂×C₂²⋊D₇₉	C₂⁴	1	128	yes	complemented
85	C₂²×Dic₇₉	—	2	16	no	—
86	C₂²×Dic₇₉	C₂⁴	1	24	yes	—
87	C₄⋊Dic₇₉	C₂⁴	1	32	yes	complemented
88	C₂²⋊Dic₇₉	C₂⁴	1	32	yes	—
89	(C₂×D₇₉)⋊C₄	C₂⁴	1	128	yes	complemented
90	C₄×Dic₇₉	C₂⁴	1	32	yes	complemented
91	C₂⁴×C₇₉	—	2	8	no	—
92	C₂⁴×C₇₉	—	2	8	no	—
93	C₂⁴×C₇₉	—	2	16	no	—
94	C₂⁴×C₇₉	C₂×D₄	1	8	yes	—
95	C₂⁴×C₇₉	C₂⁴	1	12	yes	—
96	C₂⁴×C₇₉	C₂⁴	1	6	yes	—
97	C₂⁴×C₇₉	C₂⁴	1	1	yes	characteristic
98	#41×C₇₉	—	2	256	no	—
99	C₂×Q₈×C₇₉	—	2	48	no	—
100	C₂×Q₈×C₇₉	C₂⁴	1	16	yes	complemented
101	C₂×D₄×C₇₉	—	2	96	no	—
102	C₂×D₄×C₇₉	—	2	48	no	—
103	C₂×D₄×C₇₉	C₂⁴	1	32	yes	—
104	C₂×D₄×C₇₉	C₂⁴	1	16	yes	complemented
105	C₂²×C₄×C₇₉	—	2	8	no	—
106	C₂²×C₄×C₇₉	—	2	96	no	—
107	C₂²×C₄×C₇₉	C₂×D₄	1	8	yes	—
108	C₂²×C₄×C₇₉	C₂×D₄	1	8	yes	—
109	C₂²×C₄×C₇₉	C₂×D₄	1	96	yes	complemented
110	C₂²×C₄×C₇₉	C₂⁴	1	12	yes	—
111	C₂²×C₄×C₇₉	C₂⁴	1	6	yes	—
112	C₂²×C₄×C₇₉	C₂⁴	1	6	yes	—
113	C₂²×C₄×C₇₉	C₂⁴	1	16	yes	—
114	C₂²×C₄×C₇₉	C₂⁴	1	32	yes	complemented
115	C₂³×C₇₉	—	2	32	no	—
116	C₂³×C₇₉	—	2	24	no	—
117	C₂³×C₇₉	—	2	24	no	—
118	C₂³×C₇₉	—	2	48	no	—
119	C₂³×C₇₉	—	4	32	no	—
120	C₂³×C₇₉	C₂²×D₄	1	24	yes	—
121	C₂³×C₇₉	C₂²×D₄	1	4	yes	—
122	C₂³×C₇₉	H(5,𝔽₂)	1	8	yes	—
123	C₂³×C₇₉	C₂⁵	1	8	yes	—
124	C₂³×C₇₉	C₂⁵	1	4	yes	—
125	C₂³×C₇₉	C₂⁵	1	3	yes	—
126	C₂²×D₇₉	—	2	64	no	—
127	C₂²×D₇₉	—	2	48	no	—
128	C₂²×D₇₉	—	2	96	no	—
129	C₂²×D₇₉	—	4	64	no	—
130	C₂²×D₇₉	—	4	384	no	—
131	C₂²×D₇₉	—	4	64	no	—
132	C₂²×D₇₉	C₂⁵	1	16	yes	—
133	Q₈×C₇₉	—	2	32	no	—
134	D₄×C₇₉	—	2	64	no	—
135	D₄×C₇₉	—	2	32	no	—
136	C₂×C₄×C₇₉	—	2	24	no	—
137	C₂×C₄×C₇₉	—	2	64	no	—
138	C₂×C₄×C₇₉	C₂²×D₄	1	24	yes	—
139	C₂×C₄×C₇₉	C₂²×D₄	1	24	yes	—
140	C₂×C₄×C₇₉	C₂²×D₄	1	64	yes	complemented
141	C₂×C₄×C₇₉	C₂⁵	1	8	yes	—
142	C₂×C₄×C₇₉	C₂⁵	1	4	yes	—
143	C₂×C₄×C₇₉	C₂⁵	1	4	yes	—
144	C₂²⋊D₇₉	—	4	128	no	—
145	C₂×Dic₇₉	—	2	48	no	—
146	C₂×Dic₇₉	C₂⁵	1	16	yes	—
147	D₃₁₆	—	2	64	no	—
148	D₃₁₆	—	2	64	no	—
149	C₂²×C₇₉	—	2	8	no	—
150	C₂²×C₇₉	—	2	48	no	—
151	C₂²×C₇₉	—	2	8	no	—
152	C₂²×C₇₉	—	2	16	no	—
153	C₂²×C₇₉	—	4	48	no	—
154	C₂²×C₇₉	#535	1	16	yes	complemented
155	C₂²×C₇₉	C₂³×D₄	1	8	yes	—
156	C₂²×C₇₉	C₂³×D₄	1	6	yes	—
157	C₂²×C₇₉	C₂×H(5,𝔽₂)	1	12	yes	—
158	C₂²×C₇₉	C₂⁶	1	1	yes	characteristic
159	C₂×D₇₉	—	2	16	no	—
160	C₂×D₇₉	—	2	32	no	—
161	C₂×D₇₉	—	4	128	no	—
162	C₂×D₇₉	—	4	96	no	—
163	C₄×C₇₉	—	2	8	no	—
164	C₄×C₇₉	C₂³×D₄	1	8	yes	—
165	C₄×C₇₉	C₂³×D₄	1	8	yes	—
166	Dic₇₉	—	2	16	no	—
167	C₂²×#535	—	79	1	no	maximal, Sylow
168	C₂×C₇₉	—	2	8	no	—
169	C₂×C₇₉	—	4	8	no	—
170	C₂×C₇₉	C₂×#535	1	12	yes	complemented
171	C₂×C₇₉	C₂⁴×D₄	1	1	yes	characteristic
172	C₂×C₇₉	C₂²×H(5,𝔽₂)	1	2	yes	—
173	D₇₉	—	4	16	no	—
174	C₂³×#41	D₇₉	1	1	yes	characteristic, complemented
175	C₂⁴×D₄	—	79	1	no	—
176	C₂×#535	—	79	48	no	—
177	C₂²×#127	—	79	2	no	—
178	C₂²×#124	—	79	2	no	—
179	C₂²×#121	—	79	4	no	—
180	C₂²×#120	—	79	4	no	—
181	C₂²×#117	—	79	1	no	—
182	C₇₉	C₂²×#535	1	1	yes	characteristic, complemented, Sylow
183	C₂⁶	—	79	2	no	—
184	C₂²×#41	—	2	16	no	—
185	C₂²×#41	C₂×D₇₉	1	24	yes	complemented
186	C₂³×Q₈	C₂×D₇₉	1	1	yes	characteristic, complemented
187	C₂³×D₄	—	79	8	no	—
188	C₂³×D₄	—	79	2	no	—
189	C₂³×D₄	—	79	2	no	—
190	C₂³×D₄	—	79	24	no	—
191	C₂³×D₄	—	158	16	no	—
192	C₂³×D₄	C₂×D₇₉	1	2	yes	—
193	C₂³×D₄	C₂×D₇₉	1	1	yes	characteristic, complemented
194	C₂⁴×C₄	C₂×D₇₉	1	1	yes	characteristic
195	C₂⁴×C₄	C₂×D₇₉	1	2	yes	complemented
196	#535	—	79	256	no	—
197	C₂×#127	—	79	48	no	—
198	C₂×#124	—	79	48	no	—
199	C₂×#121	—	79	96	no	—
200	C₂×#120	—	79	96	no	—
201	C₂×#117	—	79	24	no	—
202	C₂²×C₄⋊C₄	—	79	2	no	—
203	C₂²×C₂²⋊C₄	—	79	2	no	—
204	C₂²×C₂²⋊C₄	—	79	8	no	—
205	C₂²×C₄²	—	79	2	no	—
206	C₂⁵	—	316	16	no	—
207	C₂⁵	—	79	24	no	—
208	C₂⁵	—	79	4	no	—
209	C₂⁵	—	158	16	no	—
210	C₂⁵	C₂²×D₇₉	1	2	yes	—
211	C₂⁵	C₂²×D₇₉	1	1	yes	characteristic
212	C₂×#41	—	2	192	no	—
213	C₂×#41	C₂²×D₇₉	1	64	yes	complemented
214	C₂²×Q₈	—	2	8	no	—
215	C₂²×Q₈	C₂²×D₇₉	1	12	yes	complemented
216	C₂²×D₄	—	2	16	no	—
217	C₂²×D₄	—	2	8	no	—
218	C₂²×D₄	—	316	32	no	—
219	C₂²×D₄	—	79	96	no	—
220	C₂²×D₄	—	79	24	no	—
221	C₂²×D₄	—	79	24	no	—
222	C₂²×D₄	—	79	64	no	—
223	C₂²×D₄	—	158	16	no	—
224	C₂²×D₄	—	158	16	no	—
225	C₂²×D₄	—	158	192	no	—
226	C₂²×D₄	C₂²×D₇₉	1	24	yes	—
227	C₂²×D₄	C₂²×D₇₉	1	12	yes	complemented
228	C₂³×C₄	—	2	16	no	—
229	C₂³×C₄	—	79	4	no	—
230	C₂³×C₄	C₂²⋊D₇₉	1	16	yes	complemented
231	C₂³×C₄	C₂²×D₇₉	1	2	yes	—
232	C₂³×C₄	C₂²×D₇₉	1	1	yes	characteristic
233	C₂³×C₄	C₂²×D₇₉	1	1	yes	characteristic
234	C₂³×C₄	C₂²×D₇₉	1	12	yes	—
235	C₂³×C₄	C₂²×D₇₉	1	24	yes	complemented
236	#127	—	79	128	no	—
237	#124	—	79	128	no	—
238	#121	—	79	256	no	—
239	#120	—	79	256	no	—
240	#117	—	79	64	no	—
241	C₂×C₄⋊C₄	—	79	24	no	—
242	C₂×C₂²⋊C₄	—	79	24	no	—
243	C₂×C₂²⋊C₄	—	79	96	no	—
244	C₂×C₄²	—	79	24	no	—
245	C₂⁴	—	2	8	no	—
246	C₂⁴	—	2	16	no	—
247	C₂⁴	—	2	8	no	—
248	C₂⁴	—	316	128	no	—
249	C₂⁴	—	316	96	no	—
250	C₂⁴	—	79	32	no	—
251	C₂⁴	—	79	24	no	—
252	C₂⁴	—	158	32	no	—
253	C₂⁴	—	158	96	no	—
254	C₂⁴	—	158	16	no	—
255	C₂⁴	C₂×C₂²⋊D₇₉	1	8	yes	—
256	C₂⁴	C₂³×D₇₉	1	12	yes	—
257	C₂⁴	C₂³×D₇₉	1	6	yes	—
258	C₂⁴	C₂³×D₇₉	1	1	yes	characteristic
259	#41	—	2	256	no	—
260	C₂×Q₈	—	2	48	no	—
261	C₂×Q₈	C₂³×D₇₉	1	16	yes	complemented
262	C₂×D₄	—	2	96	no	—
263	C₂×D₄	—	2	48	no	—
264	C₂×D₄	—	316	192	no	—
265	C₂×D₄	—	79	128	no	—
266	C₂×D₄	—	79	32	no	—
267	C₂×D₄	—	79	32	no	—
268	C₂×D₄	—	158	96	no	—
269	C₂×D₄	—	158	96	no	—
270	C₂×D₄	—	158	256	no	—
271	C₂×D₄	C₂³×D₇₉	1	32	yes	—
272	C₂×D₄	C₂³×D₇₉	1	16	yes	complemented
273	C₂²×C₄	—	2	8	no	—
274	C₂²×C₄	—	2	96	no	—
275	C₂²×C₄	—	79	24	no	—
276	C₂²×C₄	—	158	16	no	—
277	C₂²×C₄	C₂×C₂²⋊D₇₉	1	8	yes	—
278	C₂²×C₄	C₂×C₂²⋊D₇₉	1	8	yes	—
279	C₂²×C₄	C₂×C₂²⋊D₇₉	1	96	yes	complemented
280	C₂²×C₄	C₂³×D₇₉	1	12	yes	—
281	C₂²×C₄	C₂³×D₇₉	1	6	yes	—
282	C₂²×C₄	C₂³×D₇₉	1	6	yes	—
283	C₂²×C₄	C₂³×D₇₉	1	16	yes	—
284	C₂²×C₄	C₂³×D₇₉	1	32	yes	complemented
285	C₄⋊C₄	—	79	32	no	—
286	C₂²⋊C₄	—	79	32	no	—
287	C₂²⋊C₄	—	79	128	no	—
288	C₄²	—	79	32	no	—
289	C₂³	—	2	24	no	—
290	C₂³	—	2	32	no	—
291	C₂³	—	2	48	no	—
292	C₂³	—	2	24	no	—
293	C₂³	—	4	32	no	—
294	C₂³	—	316	384	no	—
295	C₂³	—	316	64	no	—
296	C₂³	—	316	64	no	—
297	C₂³	—	79	16	no	—
298	C₂³	—	158	96	no	—
299	C₂³	—	158	64	no	—
300	C₂³	—	158	48	no	—
301	C₂³	C₂²×C₂²⋊D₇₉	1	24	yes	—
302	C₂³	C₂²×C₂²⋊D₇₉	1	4	yes	—
303	C₂³	#14579207	1	8	yes	—
304	C₂³	C₂⁴×D₇₉	1	8	yes	—
305	C₂³	C₂⁴×D₇₉	1	4	yes	—
306	C₂³	C₂⁴×D₇₉	1	3	yes	—
307	Q₈	—	2	32	no	—
308	D₄	—	2	64	no	—
309	D₄	—	2	32	no	—
310	D₄	—	316	128	no	—
311	D₄	—	158	64	no	—
312	D₄	—	158	64	no	—
313	C₂×C₄	—	2	24	no	—
314	C₂×C₄	—	2	64	no	—
315	C₂×C₄	—	79	16	no	—
316	C₂×C₄	—	158	48	no	—
317	C₂×C₄	C₂²×C₂²⋊D₇₉	1	24	yes	—
318	C₂×C₄	C₂²×C₂²⋊D₇₉	1	24	yes	—
319	C₂×C₄	C₂²×C₂²⋊D₇₉	1	64	yes	complemented
320	C₂×C₄	C₂⁴×D₇₉	1	8	yes	—
321	C₂×C₄	C₂⁴×D₇₉	1	4	yes	—
322	C₂×C₄	C₂⁴×D₇₉	1	4	yes	—
323	C₂²	—	2	8	no	—
324	C₂²	—	2	48	no	—
325	C₂²	—	2	8	no	—
326	C₂²	—	2	16	no	—
327	C₂²	—	4	48	no	—
328	C₂²	—	316	128	no	—
329	C₂²	—	316	96	no	—
330	C₂²	—	158	16	no	—
331	C₂²	—	158	32	no	—
332	C₂²	#19099127	1	16	yes	direct product factor
333	C₂²	C₂³×C₂²⋊D₇₉	1	8	yes	—
334	C₂²	C₂³×C₂²⋊D₇₉	1	6	yes	—
335	C₂²	C₂×#14579207	1	12	yes	—
336	C₂²	C₂⁵×D₇₉	1	1	yes	characteristic
337	C₄	—	2	8	no	—
338	C₄	—	158	16	no	—
339	C₄	C₂³×C₂²⋊D₇₉	1	8	yes	—
340	C₄	C₂³×C₂²⋊D₇₉	1	8	yes	—
341	C₂	—	2	8	no	—
342	C₂	—	4	8	no	—
343	C₂	—	316	16	no	—
344	C₂	C₂×#19099127	1	12	yes	direct product factor
345	C₂	C₂⁴×C₂²⋊D₇₉	1	1	yes	characteristic
346	C₂	C₂²×#14579207	1	2	yes	—

	subgroup	G/H
center	C₂⁴	C₂³×D₇₉
commutator, cosocle	C₂²×C₇₉	C₂⁶
Frattini	C₂²	C₂⁵×D₇₉
Fitting	C₂³×#41×C₇₉	C₂
socle	C₂⁴×C₇₉	C₂⁴
hypercenter	C₂³×#41	D₇₉
hypocenter	C₇₉	C₂²×#535
LCS	G ▷ C₂²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂⁴ ◁ C₂³×#41

Complements

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

N	H ≅ G/N	type
1. C₂⁴×D₃₁₆	C₂	semidirect
2. C₂×#19099127	C₂	direct (N × H)
3. C₂²×#14579157	C₂	semidirect
4. C₂²×#14579150	C₂	semidirect
5. C₂²×#14579135	C₂	semidirect
6. C₂²×#14579129	C₂	semidirect
7. C₂²×#14579120	C₂	semidirect
8. C₂³×#41×C₇₉	C₂	semidirect
13. C₂³×D₃₁₆	C₂²	semidirect
14. C₂³×C₂²⋊D₇₉	C₂²	semidirect
15. #19099127	C₂²	direct (N × H)
16. C₂×#14579157	C₂²	semidirect
17. C₂×#14579150	C₂²	semidirect
18. C₂×#14579135	C₂²	semidirect
19. C₂×#14579129	C₂²	semidirect
20. C₂×#14579120	C₂²	semidirect
21. C₂²×C₄⋊Dic₇₉	C₂²	semidirect
23. C₂²×(C₂×D₇₉)⋊C₄	C₂²	semidirect
24. C₂²×C₄×Dic₇₉	C₂²	semidirect
26. C₂²×#41×C₇₉	C₂²	semidirect
27. C₂³×Q₈×C₇₉	C₂²	semidirect
29. C₂³×D₄×C₇₉	C₂²	semidirect
31. C₂⁴×C₄×C₇₉	C₂²	semidirect
41. C₂²×D₃₁₆	C₂³	semidirect
43. C₂²×C₂²⋊D₇₉	C₂³	semidirect
45. #14579157	C₂³	semidirect
46. #14579150	C₂³	semidirect
47. #14579135	C₂³	semidirect
48. #14579129	C₂³	semidirect
49. #14579120	C₂³	semidirect
50. C₂×C₄⋊Dic₇₉	C₂³	semidirect
52. C₂×(C₂×D₇₉)⋊C₄	C₂³	semidirect
53. C₂×C₄×Dic₇₉	C₂³	semidirect
57. C₂×#41×C₇₉	C₂³	semidirect
59. C₂²×Q₈×C₇₉	C₂³	semidirect
63. C₂²×D₄×C₇₉	C₂³	semidirect
65. C₂³×C₄×C₇₉	D₄	semidirect
70. C₂³×C₄×C₇₉	C₂³	semidirect
84. C₂×C₂²⋊D₇₉	C₂⁴	semidirect
87. C₄⋊Dic₇₉	C₂⁴	semidirect
89. (C₂×D₇₉)⋊C₄	C₂⁴	semidirect
90. C₄×Dic₇₉	C₂⁴	semidirect
100. C₂×Q₈×C₇₉	C₂⁴	semidirect
104. C₂×D₄×C₇₉	C₂⁴	semidirect
109. C₂²×C₄×C₇₉	C₂×D₄	semidirect
114. C₂²×C₄×C₇₉	C₂⁴	semidirect
140. C₂×C₄×C₇₉	C₂²×D₄	semidirect
154. C₂²×C₇₉	#535	semidirect
170. C₂×C₇₉	C₂×#535	semidirect
174. C₂³×#41	D₇₉	semidirect
182. C₇₉	C₂²×#535	semidirect
185. C₂²×#41	C₂×D₇₉	semidirect
186. C₂³×Q₈	C₂×D₇₉	semidirect
193. C₂³×D₄	C₂×D₇₉	semidirect
195. C₂⁴×C₄	C₂×D₇₉	semidirect
213. C₂×#41	C₂²×D₇₉	semidirect
215. C₂²×Q₈	C₂²×D₇₉	semidirect
227. C₂²×D₄	C₂²×D₇₉	semidirect
230. C₂³×C₄	C₂²⋊D₇₉	semidirect
235. C₂³×C₄	C₂²×D₇₉	semidirect
261. C₂×Q₈	C₂³×D₇₉	semidirect
272. C₂×D₄	C₂³×D₇₉	semidirect
279. C₂²×C₄	C₂×C₂²⋊D₇₉	semidirect
284. C₂²×C₄	C₂³×D₇₉	semidirect
319. C₂×C₄	C₂²×C₂²⋊D₇₉	semidirect
332. C₂²	#19099127	direct (N × H)
344. C₂	C₂×#19099127	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂⁴×D₃₁₆	2
C₂×#19099127	2
C₂²×#14579157	2
C₂²×#14579150	2
C₂²×#14579135	2
C₂²×#14579129	2
C₂²×#14579120	2
C₂³×#41×C₇₉	2
C₂²×#535	79

Subgroups — C22×#19099127 #35195024

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×#19099127 #35195024