Subgroups — C₂²×#19099131 #35195026

Order 20224.

14414 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×#11929625	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂³×D₄×D₇₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#19099131	C₂	1	48	yes	maximal, direct product factor
4	C₂²×#14579158	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×#14579157	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×#14579150	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂²×#14579134	C₂	1	4	yes	maximal, complemented
8	C₂²×#14579131	C₂	1	4	yes	maximal, complemented
9	C₂²×#14579118	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×#124×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂⁵×D₇₉	C₂²	1	2	yes	—
12	C₂²×#11929625	—	2	16	no	—
13	C₂²×#11929625	C₂²	1	24	yes	complemented
14	C₂³×D₃₁₆	C₂²	1	2	yes	—
15	C₂³×D₃₁₆	C₂²	1	1	yes	characteristic
16	C₂³×D₃₁₆	C₂²	1	1	yes	characteristic, complemented
17	C₂³×D₃₁₆	C₂²	1	4	yes	complemented
18	C₂³×C₂²⋊D₇₉	C₂²	1	2	yes	—
19	C₂³×C₂²⋊D₇₉	C₂²	1	4	yes	complemented
20	C₂²×D₄×D₇₉	—	2	16	no	—
21	C₂²×D₄×D₇₉	C₂²	1	24	yes	complemented
22	C₂³×C₄×D₇₉	C₂²	1	1	yes	characteristic
23	C₂³×C₄×D₇₉	C₂²	1	2	yes	complemented
24	#19099131	C₂²	1	256	yes	direct product factor
25	C₂×#14579158	C₂²	1	24	yes	complemented
26	C₂×#14579157	C₂²	1	24	yes	complemented
27	C₂×#14579150	C₂²	1	24	yes	complemented
28	C₂×#14579134	C₂²	1	96	yes	complemented
29	C₂×#14579131	C₂²	1	96	yes	complemented
30	C₂×#14579118	C₂²	1	24	yes	complemented
31	C₂²×Dic₇₉⋊C₄	C₂²	1	2	yes	complemented
32	C₂²×(C₂×D₇₉)⋊C₄	C₂²	1	2	yes	—
33	C₂²×(C₂×D₇₉)⋊C₄	C₂²	1	4	yes	complemented
34	C₂²×C₄×Dic₇₉	C₂²	1	1	yes	characteristic, complemented
35	C₂³×Q₈×C₇₉	C₂²	1	1	yes	characteristic, complemented
36	C₂³×D₄×C₇₉	C₂²	1	1	yes	characteristic
37	C₂×#124×C₇₉	C₂²	1	24	yes	complemented
38	C₂²×C₂²⋊C₄×C₇₉	C₂²	1	4	yes	complemented
39	C₂²×C₄²×C₇₉	C₂²	1	1	yes	characteristic, complemented
40	C₂⁴×D₇₉	—	2	16	no	—
41	C₂⁴×D₇₉	—	4	16	no	—
42	C₂⁴×D₇₉	C₂³	1	2	yes	—
43	C₂⁴×D₇₉	C₂³	1	2	yes	—
44	C₂⁴×D₇₉	C₂³	1	1	yes	characteristic
45	C₂⁴×D₇₉	C₂³	1	24	yes	—
46	C₂×#11929625	—	2	192	no	—
47	C₂×#11929625	C₂³	1	64	yes	complemented
48	C₂²×D₃₁₆	—	2	8	no	—
49	C₂²×D₃₁₆	—	2	8	no	—
50	C₂²×D₃₁₆	—	2	16	no	—
51	C₂²×D₃₁₆	—	4	16	no	—
52	C₂²×D₃₁₆	C₂³	1	24	yes	—
53	C₂²×D₃₁₆	C₂³	1	12	yes	—
54	C₂²×D₃₁₆	C₂³	1	12	yes	complemented
55	C₂²×D₃₁₆	C₂³	1	48	yes	complemented
56	C₂²×C₂²⋊D₇₉	—	2	16	no	—
57	C₂²×C₂²⋊D₇₉	—	4	16	no	—
58	C₂²×C₂²⋊D₇₉	C₂³	1	24	yes	—
59	C₂²×C₂²⋊D₇₉	C₂³	1	48	yes	complemented
60	C₂×D₄×D₇₉	—	2	192	no	—
61	C₂×D₄×D₇₉	C₂³	1	64	yes	complemented
62	C₂³×Dic₇₉	C₂³	1	2	yes	—
63	C₂³×Dic₇₉	C₂³	1	1	yes	characteristic
64	C₂²×C₄×D₇₉	—	2	16	no	—
65	C₂²×C₄×D₇₉	D₄	1	16	yes	complemented
66	C₂²×C₄×D₇₉	C₂³	1	12	yes	—
67	C₂²×C₄×D₇₉	C₂³	1	24	yes	complemented
68	#14579158	C₂³	1	64	yes	complemented
69	#14579157	C₂³	1	64	yes	complemented
70	#14579150	C₂³	1	64	yes	complemented
71	#14579134	C₂³	1	256	yes	complemented
72	#14579131	C₂³	1	256	yes	complemented
73	#14579118	C₂³	1	64	yes	complemented
74	C₂×Dic₇₉⋊C₄	C₂³	1	24	yes	complemented
75	C₂×(C₂×D₇₉)⋊C₄	C₂³	1	24	yes	—
76	C₂×(C₂×D₇₉)⋊C₄	C₂³	1	48	yes	complemented
77	C₂×C₄×Dic₇₉	C₂³	1	12	yes	complemented
78	C₂⁵×C₇₉	C₂³	1	2	yes	—
79	C₂²×Q₈×C₇₉	—	2	8	no	—
80	C₂²×Q₈×C₇₉	C₂³	1	12	yes	complemented
81	C₂²×D₄×C₇₉	—	2	8	no	—
82	C₂²×D₄×C₇₉	C₂³	1	12	yes	—
83	C₂³×C₄×C₇₉	C₂³	1	2	yes	—
84	C₂³×C₄×C₇₉	C₂³	1	2	yes	—
85	C₂³×C₄×C₇₉	C₂³	1	1	yes	characteristic
86	#124×C₇₉	C₂³	1	64	yes	complemented
87	C₂×C₂²⋊C₄×C₇₉	C₂³	1	48	yes	complemented
88	C₂×C₄²×C₇₉	C₂³	1	12	yes	complemented
89	C₂³×D₇₉	—	2	8	no	—
90	C₂³×D₇₉	—	2	8	no	—
91	C₂³×D₇₉	—	2	8	no	—
92	C₂³×D₇₉	—	2	16	no	—
93	C₂³×D₇₉	—	2	16	no	—
94	C₂³×D₇₉	—	2	96	no	—
95	C₂³×D₇₉	—	4	96	no	—
96	C₂³×D₇₉	—	4	128	no	—
97	C₂³×D₇₉	C₂×D₄	1	8	yes	—
98	C₂³×D₇₉	C₂⁴	1	12	yes	—
99	C₂³×D₇₉	C₂⁴	1	12	yes	—
100	C₂³×D₇₉	C₂⁴	1	6	yes	—
101	C₂³×D₇₉	C₂⁴	1	32	yes	—
102	#11929625	—	2	256	no	—
103	C₂×D₃₁₆	—	2	96	no	—
104	C₂×D₃₁₆	—	2	48	no	—
105	C₂×D₃₁₆	—	2	48	no	—
106	C₂×D₃₁₆	—	4	96	no	—
107	C₂×D₃₁₆	C₂⁴	1	32	yes	—
108	C₂×D₃₁₆	C₂⁴	1	16	yes	—
109	C₂×D₃₁₆	C₂⁴	1	16	yes	complemented
110	C₂×D₃₁₆	C₂⁴	1	64	yes	complemented
111	C₂×C₂²⋊D₇₉	—	2	96	no	—
112	C₂×C₂²⋊D₇₉	—	4	96	no	—
113	C₂×C₂²⋊D₇₉	C₂⁴	1	32	yes	—
114	C₂×C₂²⋊D₇₉	C₂⁴	1	64	yes	complemented
115	D₄×D₇₉	—	2	256	no	—
116	C₂²×Dic₇₉	—	2	8	no	—
117	C₂²×Dic₇₉	C₂×D₄	1	8	yes	—
118	C₂²×Dic₇₉	C₂⁴	1	12	yes	—
119	C₂²×Dic₇₉	C₂⁴	1	6	yes	—
120	C₂×C₄×D₇₉	—	2	96	no	—
121	C₂×C₄×D₇₉	C₂×D₄	1	96	yes	complemented
122	C₂×C₄×D₇₉	C₂⁴	1	16	yes	—
123	C₂×C₄×D₇₉	C₂⁴	1	32	yes	complemented
124	Dic₇₉⋊C₄	C₂⁴	1	32	yes	complemented
125	(C₂×D₇₉)⋊C₄	C₂⁴	1	32	yes	—
126	(C₂×D₇₉)⋊C₄	C₂⁴	1	64	yes	complemented
127	C₄×Dic₇₉	C₂⁴	1	16	yes	complemented
128	C₂⁴×C₇₉	—	2	8	no	—
129	C₂⁴×C₇₉	—	2	16	no	—
130	C₂⁴×C₇₉	C₂⁴	1	12	yes	—
131	C₂⁴×C₇₉	C₂⁴	1	1	yes	characteristic
132	C₂×Q₈×C₇₉	—	2	48	no	—
133	C₂×Q₈×C₇₉	C₂⁴	1	16	yes	complemented
134	C₂×D₄×C₇₉	—	2	48	no	—
135	C₂×D₄×C₇₉	C₂⁴	1	16	yes	—
136	C₂²×C₄×C₇₉	—	2	8	no	—
137	C₂²×C₄×C₇₉	—	2	8	no	—
138	C₂²×C₄×C₇₉	C₂×D₄	1	8	yes	—
139	C₂²×C₄×C₇₉	C₂⁴	1	12	yes	—
140	C₂²×C₄×C₇₉	C₂⁴	1	12	yes	—
141	C₂²×C₄×C₇₉	C₂⁴	1	6	yes	—
142	C₂²⋊C₄×C₇₉	C₂⁴	1	64	yes	complemented
143	C₄²×C₇₉	C₂⁴	1	16	yes	complemented
144	C₂³×C₇₉	—	2	24	no	—
145	C₂³×C₇₉	—	2	48	no	—
146	C₂³×C₇₉	—	4	32	no	—
147	C₂³×C₇₉	C₂²×D₄	1	4	yes	—
148	C₂³×C₇₉	H(5,𝔽₂)	1	8	yes	—
149	C₂³×C₇₉	C₂⁵	1	8	yes	—
150	C₂³×C₇₉	C₂⁵	1	3	yes	—
151	C₂²×D₇₉	—	2	32	no	—
152	C₂²×D₇₉	—	2	24	no	—
153	C₂²×D₇₉	—	2	24	no	—
154	C₂²×D₇₉	—	2	24	no	—
155	C₂²×D₇₉	—	2	48	no	—
156	C₂²×D₇₉	—	2	48	no	—
157	C₂²×D₇₉	—	2	64	no	—
158	C₂²×D₇₉	—	4	64	no	—
159	C₂²×D₇₉	—	4	384	no	—
160	C₂²×D₇₉	—	4	32	no	—
161	C₂²×D₇₉	—	4	32	no	—
162	C₂²×D₇₉	C₂²×D₄	1	24	yes	—
163	C₂²×D₇₉	C₂⁵	1	8	yes	—
164	C₂²×D₇₉	C₂⁵	1	8	yes	—
165	C₂²×D₇₉	C₂⁵	1	4	yes	—
166	Q₈×C₇₉	—	2	32	no	—
167	D₄×C₇₉	—	2	32	no	—
168	C₂×C₄×C₇₉	—	2	24	no	—
169	C₂×C₄×C₇₉	—	2	24	no	—
170	C₂×C₄×C₇₉	C₂²×D₄	1	24	yes	—
171	C₂×C₄×C₇₉	C₂⁵	1	8	yes	—
172	C₂×C₄×C₇₉	C₂⁵	1	8	yes	—
173	C₂×C₄×C₇₉	C₂⁵	1	4	yes	—
174	C₂²⋊D₇₉	—	2	64	no	—
175	C₂²⋊D₇₉	—	4	64	no	—
176	C₂×Dic₇₉	—	2	24	no	—
177	C₂×Dic₇₉	C₂²×D₄	1	24	yes	—
178	C₂×Dic₇₉	C₂⁵	1	8	yes	—
179	C₂×Dic₇₉	C₂⁵	1	4	yes	—
180	D₃₁₆	—	2	64	no	—
181	D₃₁₆	—	2	32	no	—
182	D₃₁₆	—	2	32	no	—
183	D₃₁₆	—	4	64	no	—
184	C₄×D₇₉	—	2	64	no	—
185	C₄×D₇₉	C₂²×D₄	1	64	yes	complemented
186	C₂²×C₇₉	—	2	8	no	—
187	C₂²×C₇₉	—	2	16	no	—
188	C₂²×C₇₉	—	4	48	no	—
189	C₂²×C₇₉	#535	1	16	yes	complemented
190	C₂²×C₇₉	C₂³×D₄	1	6	yes	—
191	C₂²×C₇₉	C₂×H(5,𝔽₂)	1	12	yes	—
192	C₂²×C₇₉	C₂⁶	1	1	yes	characteristic
193	C₂×D₇₉	—	2	8	no	—
194	C₂×D₇₉	—	2	48	no	—
195	C₂×D₇₉	—	2	8	no	—
196	C₂×D₇₉	—	2	8	no	—
197	C₂×D₇₉	—	2	16	no	—
198	C₂×D₇₉	—	2	16	no	—
199	C₂×D₇₉	—	4	128	no	—
200	C₂×D₇₉	—	4	48	no	—
201	C₂×D₇₉	—	4	48	no	—
202	C₂×D₇₉	C₂³×D₄	1	8	yes	—
203	C₄×C₇₉	—	2	8	no	—
204	C₄×C₇₉	—	2	8	no	—
205	C₄×C₇₉	C₂³×D₄	1	8	yes	—
206	Dic₇₉	—	2	8	no	—
207	Dic₇₉	C₂³×D₄	1	8	yes	—
208	C₂²×#535	—	79	1	no	maximal, Sylow
209	C₂×C₇₉	—	4	8	no	—
210	C₂×C₇₉	C₂×#535	1	12	yes	complemented
211	C₂×C₇₉	C₂⁴×D₄	1	1	yes	characteristic
212	C₂×C₇₉	C₂²×H(5,𝔽₂)	1	2	yes	—
213	D₇₉	—	2	8	no	—
214	D₇₉	—	4	8	no	—
215	D₇₉	—	4	8	no	—
216	C₂³×#41	—	79	1	no	—
217	C₂⁴×D₄	—	79	1	no	—
218	C₂×#535	—	79	48	no	—
219	C₂²×#127	—	79	1	no	—
220	C₂²×#127	—	79	1	no	—
221	C₂²×#124	—	79	1	no	—
222	C₂²×#124	D₇₉	1	1	yes	characteristic, complemented
223	C₂²×#121	—	79	4	no	—
224	C₂²×#120	—	79	4	no	—
225	C₂²×#117	—	79	1	no	—
226	C₇₉	C₂²×#535	1	1	yes	characteristic, complemented, Sylow
227	C₂⁶	—	79	2	no	—
228	C₂²×#41	—	79	24	no	—
229	C₂²×#41	—	158	16	no	—
230	C₂³×Q₈	C₂×D₇₉	1	1	yes	characteristic, complemented
231	C₂³×D₄	—	79	4	no	—
232	C₂³×D₄	—	79	2	no	—
233	C₂³×D₄	—	79	24	no	—
234	C₂³×D₄	—	79	4	no	—
235	C₂³×D₄	—	79	1	no	—
236	C₂³×D₄	—	79	2	no	—
237	C₂³×D₄	—	79	1	no	—
238	C₂³×D₄	—	158	16	no	—
239	C₂³×D₄	C₂×D₇₉	1	1	yes	characteristic
240	C₂⁴×C₄	—	79	1	no	—
241	C₂⁴×C₄	—	79	2	no	—
242	#535	—	79	256	no	—
243	C₂×#127	—	79	24	no	—
244	C₂×#127	—	79	24	no	—
245	C₂×#124	—	79	24	no	—
246	C₂×#124	C₂×D₇₉	1	24	yes	complemented
247	C₂×#121	—	79	96	no	—
248	C₂×#120	—	79	96	no	—
249	C₂×#117	—	79	24	no	—
250	C₂²×C₄⋊C₄	—	79	2	no	—
251	C₂²×C₂²⋊C₄	—	79	2	no	—
252	C₂²×C₂²⋊C₄	—	79	4	no	—
253	C₂²×C₂²⋊C₄	C₂×D₇₉	1	4	yes	complemented
254	C₂²×C₄²	—	79	1	no	—
255	C₂²×C₄²	C₂×D₇₉	1	1	yes	characteristic, complemented
256	C₂⁵	—	316	16	no	—
257	C₂⁵	—	79	24	no	—
258	C₂⁵	—	79	1	no	—
259	C₂⁵	—	79	2	no	—
260	C₂⁵	—	79	2	no	—
261	C₂⁵	—	158	16	no	—
262	C₂⁵	C₂²×D₇₉	1	2	yes	—
263	C₂×#41	—	79	64	no	—
264	C₂×#41	—	158	192	no	—
265	C₂²×Q₈	—	2	8	no	—
266	C₂²×Q₈	C₂²×D₇₉	1	12	yes	complemented
267	C₂²×D₄	—	2	8	no	—
268	C₂²×D₄	—	316	16	no	—
269	C₂²×D₄	—	316	16	no	—
270	C₂²×D₄	—	79	48	no	—
271	C₂²×D₄	—	79	24	no	—
272	C₂²×D₄	—	79	64	no	—
273	C₂²×D₄	—	79	48	no	—
274	C₂²×D₄	—	79	24	no	—
275	C₂²×D₄	—	79	12	no	—
276	C₂²×D₄	—	79	12	no	—
277	C₂²×D₄	—	158	16	no	—
278	C₂²×D₄	—	158	192	no	—
279	C₂²×D₄	—	158	16	no	—
280	C₂²×D₄	—	158	8	no	—
281	C₂²×D₄	—	158	8	no	—
282	C₂²×D₄	C₂²×D₇₉	1	12	yes	—
283	C₂³×C₄	—	79	1	no	—
284	C₂³×C₄	—	79	16	no	—
285	C₂³×C₄	—	79	12	no	—
286	C₂³×C₄	—	79	2	no	—
287	C₂³×C₄	—	79	24	no	—
288	C₂³×C₄	—	158	16	no	—
289	C₂³×C₄	C₂²×D₇₉	1	2	yes	—
290	C₂³×C₄	C₂²×D₇₉	1	2	yes	—
291	C₂³×C₄	C₂²×D₇₉	1	1	yes	characteristic
292	#127	—	79	64	no	—
293	#127	—	79	64	no	—
294	#124	—	79	64	no	—
295	#124	C₂²×D₇₉	1	64	yes	complemented
296	#121	—	79	256	no	—
297	#120	—	79	256	no	—
298	#117	—	79	64	no	—
299	C₂×C₄⋊C₄	—	79	24	no	—
300	C₂×C₂²⋊C₄	—	79	24	no	—
301	C₂×C₂²⋊C₄	—	79	48	no	—
302	C₂×C₂²⋊C₄	C₂²×D₇₉	1	48	yes	complemented
303	C₂×C₄²	—	79	12	no	—
304	C₂×C₄²	C₂²×D₇₉	1	12	yes	complemented
305	C₂⁴	—	2	16	no	—
306	C₂⁴	—	2	8	no	—
307	C₂⁴	—	316	96	no	—
308	C₂⁴	—	316	128	no	—
309	C₂⁴	—	79	32	no	—
310	C₂⁴	—	79	6	no	—
311	C₂⁴	—	79	8	no	—
312	C₂⁴	—	79	12	no	—
313	C₂⁴	—	79	12	no	—
314	C₂⁴	—	158	96	no	—
315	C₂⁴	—	158	16	no	—
316	C₂⁴	—	158	16	no	—
317	C₂⁴	—	158	8	no	—
318	C₂⁴	—	158	8	no	—
319	C₂⁴	—	158	8	no	—
320	C₂⁴	C₂³×D₇₉	1	12	yes	—
321	C₂⁴	C₂³×D₇₉	1	1	yes	characteristic
322	#41	—	158	256	no	—
323	C₂×Q₈	—	2	48	no	—
324	C₂×Q₈	C₂³×D₇₉	1	16	yes	complemented
325	C₂×D₄	—	2	48	no	—
326	C₂×D₄	—	316	96	no	—
327	C₂×D₄	—	316	96	no	—
328	C₂×D₄	—	79	64	no	—
329	C₂×D₄	—	79	32	no	—
330	C₂×D₄	—	79	64	no	—
331	C₂×D₄	—	79	32	no	—
332	C₂×D₄	—	79	16	no	—
333	C₂×D₄	—	79	16	no	—
334	C₂×D₄	—	158	96	no	—
335	C₂×D₄	—	158	256	no	—
336	C₂×D₄	—	158	96	no	—
337	C₂×D₄	—	158	48	no	—
338	C₂×D₄	—	158	48	no	—
339	C₂×D₄	C₂³×D₇₉	1	16	yes	—
340	C₂²×C₄	—	2	8	no	—
341	C₂²×C₄	—	2	8	no	—
342	C₂²×C₄	—	79	6	no	—
343	C₂²×C₄	—	79	8	no	—
344	C₂²×C₄	—	79	16	no	—
345	C₂²×C₄	—	79	96	no	—
346	C₂²×C₄	—	79	12	no	—
347	C₂²×C₄	—	79	32	no	—
348	C₂²×C₄	—	158	96	no	—
349	C₂²×C₄	—	158	8	no	—
350	C₂²×C₄	D₄×D₇₉	1	8	yes	—
351	C₂²×C₄	C₂³×D₇₉	1	12	yes	—
352	C₂²×C₄	C₂³×D₇₉	1	12	yes	—
353	C₂²×C₄	C₂³×D₇₉	1	6	yes	—
354	C₄⋊C₄	—	79	32	no	—
355	C₂²⋊C₄	—	79	32	no	—
356	C₂²⋊C₄	—	79	64	no	—
357	C₂²⋊C₄	C₂³×D₇₉	1	64	yes	complemented
358	C₄²	—	79	16	no	—
359	C₄²	C₂³×D₇₉	1	16	yes	complemented
360	C₂³	—	2	48	no	—
361	C₂³	—	2	24	no	—
362	C₂³	—	4	32	no	—
363	C₂³	—	316	64	no	—
364	C₂³	—	316	384	no	—
365	C₂³	—	316	32	no	—
366	C₂³	—	316	32	no	—
367	C₂³	—	79	4	no	—
368	C₂³	—	79	24	no	—
369	C₂³	—	79	8	no	—
370	C₂³	—	79	8	no	—
371	C₂³	—	158	64	no	—
372	C₂³	—	158	48	no	—
373	C₂³	—	158	48	no	—
374	C₂³	—	158	24	no	—
375	C₂³	—	158	24	no	—
376	C₂³	—	158	24	no	—
377	C₂³	—	158	32	no	—
378	C₂³	C₂×D₄×D₇₉	1	4	yes	—
379	C₂³	#14579207	1	8	yes	—
380	C₂³	C₂⁴×D₇₉	1	8	yes	—
381	C₂³	C₂⁴×D₇₉	1	3	yes	—
382	Q₈	—	2	32	no	—
383	D₄	—	2	32	no	—
384	D₄	—	316	64	no	—
385	D₄	—	316	64	no	—
386	D₄	—	158	64	no	—
387	D₄	—	158	64	no	—
388	D₄	—	158	32	no	—
389	D₄	—	158	32	no	—
390	C₂×C₄	—	2	24	no	—
391	C₂×C₄	—	2	24	no	—
392	C₂×C₄	—	79	4	no	—
393	C₂×C₄	—	79	24	no	—
394	C₂×C₄	—	79	64	no	—
395	C₂×C₄	—	79	8	no	—
396	C₂×C₄	—	158	64	no	—
397	C₂×C₄	—	158	24	no	—
398	C₂×C₄	C₂×D₄×D₇₉	1	24	yes	—
399	C₂×C₄	C₂⁴×D₇₉	1	8	yes	—
400	C₂×C₄	C₂⁴×D₇₉	1	8	yes	—
401	C₂×C₄	C₂⁴×D₇₉	1	4	yes	—
402	C₂²	—	2	8	no	—
403	C₂²	—	2	16	no	—
404	C₂²	—	4	48	no	—
405	C₂²	—	316	128	no	—
406	C₂²	—	316	48	no	—
407	C₂²	—	316	48	no	—
408	C₂²	—	79	8	no	—
409	C₂²	—	158	8	no	—
410	C₂²	—	158	8	no	—
411	C₂²	—	158	16	no	—
412	C₂²	—	158	16	no	—
413	C₂²	—	158	8	no	—
414	C₂²	—	158	48	no	—
415	C₂²	#19099131	1	16	yes	direct product factor
416	C₂²	C₂²×D₄×D₇₉	1	6	yes	—
417	C₂²	C₂×#14579207	1	12	yes	—
418	C₂²	C₂⁵×D₇₉	1	1	yes	characteristic
419	C₄	—	2	8	no	—
420	C₄	—	2	8	no	—
421	C₄	—	79	8	no	—
422	C₄	—	158	8	no	—
423	C₄	C₂²×D₄×D₇₉	1	8	yes	—
424	C₂	—	4	8	no	—
425	C₂	—	316	8	no	—
426	C₂	—	316	8	no	—
427	C₂	—	158	8	no	—
428	C₂	C₂×#19099131	1	12	yes	direct product factor
429	C₂	C₂³×D₄×D₇₉	1	1	yes	characteristic
430	C₂	C₂²×#14579207	1	2	yes	—

	subgroup	G/H
center	C₂⁴	C₂³×D₇₉
commutator, cosocle	C₂²×C₇₉	C₂⁶
Frattini	C₂²	C₂⁵×D₇₉
Fitting	C₂²×#124×C₇₉	C₂
socle	C₂⁴×C₇₉	C₂⁴
hypercenter	C₂²×#124	D₇₉
hypocenter	C₇₉	C₂²×#535
LCS	G ▷ C₂²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂⁴ ◁ C₂²×#124

Complements

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

N	H ≅ G/N	type
1. C₂³×#11929625	C₂	semidirect
2. C₂³×D₄×D₇₉	C₂	semidirect
3. C₂×#19099131	C₂	direct (N × H)
4. C₂²×#14579158	C₂	semidirect
5. C₂²×#14579157	C₂	semidirect
6. C₂²×#14579150	C₂	semidirect
7. C₂²×#14579134	C₂	semidirect
8. C₂²×#14579131	C₂	semidirect
9. C₂²×#14579118	C₂	semidirect
10. C₂²×#124×C₇₉	C₂	semidirect
13. C₂²×#11929625	C₂²	semidirect
16. C₂³×D₃₁₆	C₂²	semidirect
17. C₂³×D₃₁₆	C₂²	semidirect
19. C₂³×C₂²⋊D₇₉	C₂²	semidirect
21. C₂²×D₄×D₇₉	C₂²	semidirect
23. C₂³×C₄×D₇₉	C₂²	semidirect
24. #19099131	C₂²	direct (N × H)
25. C₂×#14579158	C₂²	semidirect
26. C₂×#14579157	C₂²	semidirect
27. C₂×#14579150	C₂²	semidirect
28. C₂×#14579134	C₂²	semidirect
29. C₂×#14579131	C₂²	semidirect
30. C₂×#14579118	C₂²	semidirect
31. C₂²×Dic₇₉⋊C₄	C₂²	semidirect
33. C₂²×(C₂×D₇₉)⋊C₄	C₂²	semidirect
34. C₂²×C₄×Dic₇₉	C₂²	semidirect
35. C₂³×Q₈×C₇₉	C₂²	semidirect
37. C₂×#124×C₇₉	C₂²	semidirect
38. C₂²×C₂²⋊C₄×C₇₉	C₂²	semidirect
39. C₂²×C₄²×C₇₉	C₂²	semidirect
47. C₂×#11929625	C₂³	semidirect
54. C₂²×D₃₁₆	C₂³	semidirect
55. C₂²×D₃₁₆	C₂³	semidirect
59. C₂²×C₂²⋊D₇₉	C₂³	semidirect
61. C₂×D₄×D₇₉	C₂³	semidirect
65. C₂²×C₄×D₇₉	D₄	semidirect
67. C₂²×C₄×D₇₉	C₂³	semidirect
68. #14579158	C₂³	semidirect
69. #14579157	C₂³	semidirect
70. #14579150	C₂³	semidirect
71. #14579134	C₂³	semidirect
72. #14579131	C₂³	semidirect
73. #14579118	C₂³	semidirect
74. C₂×Dic₇₉⋊C₄	C₂³	semidirect
76. C₂×(C₂×D₇₉)⋊C₄	C₂³	semidirect
77. C₂×C₄×Dic₇₉	C₂³	semidirect
80. C₂²×Q₈×C₇₉	C₂³	semidirect
86. #124×C₇₉	C₂³	semidirect
87. C₂×C₂²⋊C₄×C₇₉	C₂³	semidirect
88. C₂×C₄²×C₇₉	C₂³	semidirect
109. C₂×D₃₁₆	C₂⁴	semidirect
110. C₂×D₃₁₆	C₂⁴	semidirect
114. C₂×C₂²⋊D₇₉	C₂⁴	semidirect
121. C₂×C₄×D₇₉	C₂×D₄	semidirect
123. C₂×C₄×D₇₉	C₂⁴	semidirect
124. Dic₇₉⋊C₄	C₂⁴	semidirect
126. (C₂×D₇₉)⋊C₄	C₂⁴	semidirect
127. C₄×Dic₇₉	C₂⁴	semidirect
133. C₂×Q₈×C₇₉	C₂⁴	semidirect
142. C₂²⋊C₄×C₇₉	C₂⁴	semidirect
143. C₄²×C₇₉	C₂⁴	semidirect
185. C₄×D₇₉	C₂²×D₄	semidirect
189. C₂²×C₇₉	#535	semidirect
210. C₂×C₇₉	C₂×#535	semidirect
222. C₂²×#124	D₇₉	semidirect
226. C₇₉	C₂²×#535	semidirect
230. C₂³×Q₈	C₂×D₇₉	semidirect
246. C₂×#124	C₂×D₇₉	semidirect
253. C₂²×C₂²⋊C₄	C₂×D₇₉	semidirect
255. C₂²×C₄²	C₂×D₇₉	semidirect
266. C₂²×Q₈	C₂²×D₇₉	semidirect
295. #124	C₂²×D₇₉	semidirect
302. C₂×C₂²⋊C₄	C₂²×D₇₉	semidirect
304. C₂×C₄²	C₂²×D₇₉	semidirect
324. C₂×Q₈	C₂³×D₇₉	semidirect
357. C₂²⋊C₄	C₂³×D₇₉	semidirect
359. C₄²	C₂³×D₇₉	semidirect
415. C₂²	#19099131	direct (N × H)
428. C₂	C₂×#19099131	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×#11929625	2
C₂³×D₄×D₇₉	2
C₂×#19099131	2
C₂²×#14579158	2
C₂²×#14579157	2
C₂²×#14579150	2
C₂²×#14579134	2
C₂²×#14579131	2
C₂²×#14579118	2
C₂²×#124×C₇₉	2
C₂²×#535	79

Subgroups — C22×#19099131 #35195026

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×#19099131 #35195026