Subgroups — C₂²×D₄×D₃₁₆ #35195180

Order 20224.

20038 conjugacy classes of subgroups.

The subgroup lattice has 420 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	2	yes	maximal, complemented
2	C₂³×D₄×D₇₉	C₂	1	2	yes	maximal, complemented
3	C₂×D₄×D₃₁₆	C₂	1	48	yes	maximal, direct product factor
4	C₂²×#14579158	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×#14579136	C₂	1	2	yes	maximal, complemented
6	C₂²×#14579135	C₂	1	2	yes	maximal, complemented
7	C₂²×#14579131	C₂	1	4	yes	maximal, complemented
8	C₂²×C₄×D₃₁₆	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×C₄×D₄×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂⁵×D₇₉	C₂²	1	4	yes	complemented
11	C₂³×D₃₁₆	—	2	32	no	—
12	C₂³×D₃₁₆	C₂²	1	1	yes	characteristic
13	C₂³×D₃₁₆	C₂²	1	4	yes	complemented
14	C₂³×D₃₁₆	C₂²	1	2	yes	complemented
15	C₂³×D₃₁₆	C₂²	1	2	yes	complemented
16	C₂³×D₃₁₆	C₂²	1	2	yes	complemented
17	C₂³×D₃₁₆	C₂²	1	48	yes	complemented
18	C₂³×C₂²⋊D₇₉	C₂²	1	4	yes	complemented
19	C₂²×D₄×D₇₉	—	2	32	no	—
20	C₂²×D₄×D₇₉	C₂²	1	48	yes	complemented
21	C₂³×C₄×D₇₉	C₂²	1	2	yes	complemented
22	D₄×D₃₁₆	C₂²	1	256	yes	direct product factor
23	C₂×#14579158	C₂²	1	24	yes	complemented
24	C₂×#14579136	C₂²	1	48	yes	complemented
25	C₂×#14579135	C₂²	1	48	yes	complemented
26	C₂×#14579131	C₂²	1	96	yes	complemented
27	C₂×C₄×D₃₁₆	C₂²	1	24	yes	complemented
28	C₂²×C₄⋊Dic₇₉	C₂²	1	1	yes	characteristic, complemented
29	C₂²×(C₂×D₇₉)⋊C₄	C₂²	1	2	yes	complemented
30	C₂²×(C₂×D₇₉)⋊C₄	C₂²	1	4	yes	complemented
31	C₂³×D₄×C₇₉	C₂²	1	1	yes	characteristic
32	C₂⁴×C₄×C₇₉	C₂²	1	2	yes	complemented
33	C₂×C₄×D₄×C₇₉	C₂²	1	24	yes	complemented
34	C₂²×C₄⋊C₄×C₇₉	C₂²	1	1	yes	characteristic, complemented
35	C₂²×C₂²⋊C₄×C₇₉	C₂²	1	2	yes	complemented
36	C₂²×C₄²×C₇₉	C₂²	1	1	yes	characteristic, complemented
37	C₂⁴×D₇₉	—	2	32	no	—
38	C₂⁴×D₇₉	—	2	32	no	—
39	C₂⁴×D₇₉	—	4	16	no	—
40	C₂⁴×D₇₉	C₂³	1	4	yes	—
41	C₂⁴×D₇₉	C₂³	1	2	yes	—
42	C₂⁴×D₇₉	C₂³	1	48	yes	complemented
43	C₂²×D₃₁₆	—	2	16	no	—
44	C₂²×D₃₁₆	—	2	16	no	—
45	C₂²×D₃₁₆	—	2	32	no	—
46	C₂²×D₃₁₆	—	2	384	no	—
47	C₂²×D₃₁₆	—	4	8	no	—
48	C₂²×D₃₁₆	D₄	1	16	yes	direct product factor
49	C₂²×D₃₁₆	C₂³	1	12	yes	—
50	C₂²×D₃₁₆	C₂³	1	128	yes	complemented
51	C₂²×D₃₁₆	C₂³	1	48	yes	complemented
52	C₂²×D₃₁₆	C₂³	1	24	yes	complemented
53	C₂²×D₃₁₆	C₂³	1	24	yes	complemented
54	C₂²×D₃₁₆	C₂³	1	24	yes	complemented
55	C₂²×C₂²⋊D₇₉	—	2	32	no	—
56	C₂²×C₂²⋊D₇₉	C₂³	1	48	yes	complemented
57	C₂×D₄×D₇₉	—	2	384	no	—
58	C₂×D₄×D₇₉	C₂³	1	128	yes	complemented
59	C₂³×Dic₇₉	C₂³	1	2	yes	—
60	C₂²×C₄×D₇₉	—	2	16	no	—
61	C₂²×C₄×D₇₉	C₂³	1	24	yes	complemented
62	#14579158	C₂³	1	64	yes	complemented
63	#14579136	C₂³	1	128	yes	complemented
64	#14579135	C₂³	1	128	yes	complemented
65	#14579131	C₂³	1	256	yes	complemented
66	C₄×D₃₁₆	C₂³	1	64	yes	complemented
67	C₂×C₄⋊Dic₇₉	C₂³	1	12	yes	complemented
68	C₂×(C₂×D₇₉)⋊C₄	C₂³	1	24	yes	complemented
69	C₂×(C₂×D₇₉)⋊C₄	C₂³	1	48	yes	complemented
70	C₂⁵×C₇₉	C₂³	1	2	yes	—
71	C₂²×D₄×C₇₉	D₄	1	16	yes	complemented
72	C₂²×D₄×C₇₉	C₂³	1	12	yes	—
73	C₂³×C₄×C₇₉	—	2	16	no	—
74	C₂³×C₄×C₇₉	C₂³	1	1	yes	characteristic
75	C₂³×C₄×C₇₉	C₂³	1	2	yes	—
76	C₂³×C₄×C₇₉	C₂³	1	1	yes	characteristic
77	C₂³×C₄×C₇₉	C₂³	1	1	yes	characteristic
78	C₂³×C₄×C₇₉	C₂³	1	24	yes	complemented
79	C₄×D₄×C₇₉	C₂³	1	64	yes	complemented
80	C₂×C₄⋊C₄×C₇₉	C₂³	1	12	yes	complemented
81	C₂×C₂²⋊C₄×C₇₉	C₂³	1	24	yes	complemented
82	C₂×C₄²×C₇₉	C₂³	1	12	yes	complemented
83	C₂³×D₇₉	—	2	8	no	—
84	C₂³×D₇₉	—	2	8	no	—
85	C₂³×D₇₉	—	2	16	no	—
86	C₂³×D₇₉	—	2	16	no	—
87	C₂³×D₇₉	—	2	192	no	—
88	C₂³×D₇₉	—	2	16	no	—
89	C₂³×D₇₉	—	2	192	no	—
90	C₂³×D₇₉	—	4	96	no	—
91	C₂³×D₇₉	—	4	256	no	—
92	C₂³×D₇₉	C₂×D₄	1	16	yes	complemented
93	C₂³×D₇₉	C₂⁴	1	24	yes	—
94	C₂³×D₇₉	C₂⁴	1	12	yes	—
95	C₂³×D₇₉	C₂⁴	1	64	yes	complemented
96	C₂×D₃₁₆	—	2	512	no	—
97	C₂×D₃₁₆	—	2	192	no	—
98	C₂×D₃₁₆	—	2	96	no	—
99	C₂×D₃₁₆	—	2	96	no	—
100	C₂×D₃₁₆	—	4	48	no	—
101	C₂×D₃₁₆	C₂×D₄	1	96	yes	direct product factor
102	C₂×D₃₁₆	C₂⁴	1	16	yes	—
103	C₂×D₃₁₆	C₂⁴	1	64	yes	complemented
104	C₂×D₃₁₆	C₂⁴	1	32	yes	complemented
105	C₂×D₃₁₆	C₂⁴	1	32	yes	complemented
106	C₂×D₃₁₆	C₂⁴	1	32	yes	complemented
107	C₂×C₂²⋊D₇₉	—	2	192	no	—
108	C₂×C₂²⋊D₇₉	C₂⁴	1	64	yes	complemented
109	D₄×D₇₉	—	2	512	no	—
110	C₂²×Dic₇₉	—	2	8	no	—
111	C₂²×Dic₇₉	C₂⁴	1	12	yes	—
112	C₂×C₄×D₇₉	—	2	96	no	—
113	C₂×C₄×D₇₉	C₂⁴	1	32	yes	complemented
114	C₄⋊Dic₇₉	C₂⁴	1	16	yes	complemented
115	(C₂×D₇₉)⋊C₄	C₂⁴	1	32	yes	complemented
116	(C₂×D₇₉)⋊C₄	C₂⁴	1	64	yes	complemented
117	C₂⁴×C₇₉	—	2	8	no	—
118	C₂⁴×C₇₉	—	2	8	no	—
119	C₂⁴×C₇₉	C₂×D₄	1	16	yes	complemented
120	C₂⁴×C₇₉	C₂⁴	1	12	yes	—
121	C₂⁴×C₇₉	C₂⁴	1	1	yes	characteristic
122	C₂×D₄×C₇₉	C₂×D₄	1	96	yes	complemented
123	C₂×D₄×C₇₉	C₂⁴	1	16	yes	—
124	C₂²×C₄×C₇₉	—	2	8	no	—
125	C₂²×C₄×C₇₉	—	2	4	no	—
126	C₂²×C₄×C₇₉	—	2	96	no	—
127	C₂²×C₄×C₇₉	C₂×D₄	1	8	yes	complemented
128	C₂²×C₄×C₇₉	C₂×D₄	1	8	yes	complemented
129	C₂²×C₄×C₇₉	C₂⁴	1	6	yes	—
130	C₂²×C₄×C₇₉	C₂⁴	1	12	yes	—
131	C₂²×C₄×C₇₉	C₂⁴	1	6	yes	—
132	C₂²×C₄×C₇₉	C₂⁴	1	6	yes	—
133	C₂²×C₄×C₇₉	C₂⁴	1	32	yes	complemented
134	C₄⋊C₄×C₇₉	C₂⁴	1	16	yes	complemented
135	C₂²⋊C₄×C₇₉	C₂⁴	1	32	yes	complemented
136	C₄²×C₇₉	C₂⁴	1	16	yes	complemented
137	C₂³×C₇₉	—	2	64	no	—
138	C₂³×C₇₉	—	2	24	no	—
139	C₂³×C₇₉	—	2	24	no	—
140	C₂³×C₇₉	C₂²×D₄	1	4	yes	—
141	C₂³×C₇₉	C₂²×D₄	1	4	yes	—
142	C₂³×C₇₉	C₂²×D₄	1	48	yes	complemented
143	C₂³×C₇₉	H(5,𝔽₂)	1	4	yes	—
144	C₂³×C₇₉	C₂⁵	1	8	yes	—
145	C₂³×C₇₉	C₂⁵	1	3	yes	—
146	C₂²×D₇₉	—	2	64	no	—
147	C₂²×D₇₉	—	2	24	no	—
148	C₂²×D₇₉	—	2	24	no	—
149	C₂²×D₇₉	—	2	48	no	—
150	C₂²×D₇₉	—	2	48	no	—
151	C₂²×D₇₉	—	2	128	no	—
152	C₂²×D₇₉	—	2	48	no	—
153	C₂²×D₇₉	—	2	128	no	—
154	C₂²×D₇₉	—	4	64	no	—
155	C₂²×D₇₉	—	4	768	no	—
156	C₂²×D₇₉	—	4	64	no	—
157	C₂²×D₇₉	C₂²×D₄	1	48	yes	complemented
158	C₂²×D₇₉	C₂⁵	1	16	yes	—
159	C₂²×D₇₉	C₂⁵	1	8	yes	—
160	D₄×C₇₉	C₂²×D₄	1	64	yes	complemented
161	C₂×C₄×C₇₉	—	2	24	no	—
162	C₂×C₄×C₇₉	—	2	12	no	—
163	C₂×C₄×C₇₉	—	2	64	no	—
164	C₂×C₄×C₇₉	C₂²×D₄	1	24	yes	complemented
165	C₂×C₄×C₇₉	C₂²×D₄	1	24	yes	complemented
166	C₂×C₄×C₇₉	C₂⁵	1	4	yes	—
167	C₂×C₄×C₇₉	C₂⁵	1	8	yes	—
168	C₂×C₄×C₇₉	C₂⁵	1	4	yes	—
169	C₂×C₄×C₇₉	C₂⁵	1	4	yes	—
170	C₂²⋊D₇₉	—	2	128	no	—
171	C₂×Dic₇₉	—	2	24	no	—
172	C₂×Dic₇₉	C₂⁵	1	8	yes	—
173	D₃₁₆	—	2	128	no	—
174	D₃₁₆	—	2	64	no	—
175	D₃₁₆	—	2	64	no	—
176	D₃₁₆	—	4	32	no	—
177	D₃₁₆	C₂²×D₄	1	64	yes	direct product factor
178	C₄×D₇₉	—	2	64	no	—
179	C₂²×C₇₉	—	2	8	no	—
180	C₂²×C₇₉	—	2	8	no	—
181	C₂²×C₇₉	—	2	96	no	—
182	C₂²×C₇₉	D₄²	1	16	yes	complemented
183	C₂²×C₇₉	C₂³×D₄	1	6	yes	—
184	C₂²×C₇₉	C₂³×D₄	1	6	yes	—
185	C₂²×C₇₉	C₂³×D₄	1	16	yes	complemented
186	C₂²×C₇₉	C₂×H(5,𝔽₂)	1	6	yes	—
187	C₂²×C₇₉	C₂⁶	1	1	yes	characteristic
188	C₂×D₇₉	—	2	8	no	—
189	C₂×D₇₉	—	2	8	no	—
190	C₂×D₇₉	—	2	96	no	—
191	C₂×D₇₉	—	2	16	no	—
192	C₂×D₇₉	—	2	16	no	—
193	C₂×D₇₉	—	2	16	no	—
194	C₂×D₇₉	—	4	256	no	—
195	C₂×D₇₉	—	4	96	no	—
196	C₂×D₇₉	C₂³×D₄	1	16	yes	complemented
197	C₄×C₇₉	—	2	8	no	—
198	C₄×C₇₉	—	2	4	no	—
199	C₄×C₇₉	C₂³×D₄	1	8	yes	complemented
200	C₄×C₇₉	C₂³×D₄	1	8	yes	complemented
201	Dic₇₉	—	2	8	no	—
202	C₂²×D₄²	—	79	1	no	maximal, Sylow
203	C₂×C₇₉	—	2	16	no	—
204	C₂×C₇₉	C₂×D₄²	1	12	yes	complemented
205	C₂×C₇₉	C₂⁴×D₄	1	1	yes	characteristic
206	C₂×C₇₉	C₂⁴×D₄	1	1	yes	characteristic
207	C₂×C₇₉	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
208	D₇₉	—	2	16	no	—
209	D₇₉	—	4	16	no	—
210	C₂⁴×D₄	—	79	2	no	—
211	C₂⁴×D₄	—	79	2	no	—
212	C₂×D₄²	—	79	48	no	—
213	C₂²×#127	—	79	1	no	—
214	C₂²×#121	—	79	2	no	—
215	C₂²×#121	—	79	2	no	—
216	C₂²×#120	—	79	4	no	—
217	C₂²×C₄×D₄	—	79	1	no	—
218	C₂²×C₄×D₄	D₇₉	1	1	yes	characteristic, complemented
219	C₇₉	C₂²×D₄²	1	1	yes	characteristic, complemented, Sylow
220	C₂⁶	—	79	4	no	—
221	C₂³×D₄	—	79	4	no	—
222	C₂³×D₄	—	79	48	no	—
223	C₂³×D₄	—	79	2	no	—
224	C₂³×D₄	—	79	1	no	—
225	C₂³×D₄	—	79	4	no	—
226	C₂³×D₄	—	79	2	no	—
227	C₂³×D₄	—	79	2	no	—
228	C₂³×D₄	—	79	48	no	—
229	C₂³×D₄	—	158	32	no	—
230	C₂³×D₄	—	158	32	no	—
231	C₂³×D₄	C₂×D₇₉	1	1	yes	characteristic
232	C₂⁴×C₄	—	79	2	no	—
233	C₂⁴×C₄	C₂×D₇₉	1	2	yes	complemented
234	D₄²	—	79	256	no	—
235	C₂×#127	—	79	24	no	—
236	C₂×#121	—	79	48	no	—
237	C₂×#121	—	79	48	no	—
238	C₂×#120	—	79	96	no	—
239	C₂×C₄×D₄	—	79	24	no	—
240	C₂×C₄×D₄	C₂×D₇₉	1	24	yes	complemented
241	C₂²×C₄⋊C₄	—	79	1	no	—
242	C₂²×C₄⋊C₄	C₂×D₇₉	1	1	yes	characteristic, complemented
243	C₂²×C₂²⋊C₄	—	79	2	no	—
244	C₂²×C₂²⋊C₄	—	79	4	no	—
245	C₂²×C₂²⋊C₄	C₂×D₇₉	1	2	yes	complemented
246	C₂²×C₄²	C₂×D₇₉	1	1	yes	characteristic, complemented
247	C₂⁵	—	316	16	no	—
248	C₂⁵	—	79	48	no	—
249	C₂⁵	—	79	2	no	—
250	C₂⁵	—	79	4	no	—
251	C₂⁵	—	158	32	no	—
252	C₂⁵	—	158	32	no	—
253	C₂⁵	C₂²×D₇₉	1	2	yes	—
254	C₂²×D₄	—	316	8	no	—
255	C₂²×D₄	—	79	48	no	—
256	C₂²×D₄	—	79	128	no	—
257	C₂²×D₄	—	79	16	no	—
258	C₂²×D₄	—	79	24	no	—
259	C₂²×D₄	—	79	12	no	—
260	C₂²×D₄	—	79	48	no	—
261	C₂²×D₄	—	79	24	no	—
262	C₂²×D₄	—	79	24	no	—
263	C₂²×D₄	—	79	128	no	—
264	C₂²×D₄	—	158	384	no	—
265	C₂²×D₄	—	158	32	no	—
266	C₂²×D₄	—	158	32	no	—
267	C₂²×D₄	—	158	384	no	—
268	C₂²×D₄	—	158	16	no	—
269	C₂²×D₄	—	158	16	no	—
270	C₂²×D₄	D₃₁₆	1	16	yes	direct product factor
271	C₂²×D₄	C₂²×D₇₉	1	12	yes	—
272	C₂³×C₄	—	2	16	no	—
273	C₂³×C₄	—	79	2	no	—
274	C₂³×C₄	—	79	24	no	—
275	C₂³×C₄	—	158	16	no	—
276	C₂³×C₄	C₂²×D₇₉	1	1	yes	characteristic
277	C₂³×C₄	C₂²×D₇₉	1	2	yes	—
278	C₂³×C₄	C₂²×D₇₉	1	1	yes	characteristic
279	C₂³×C₄	C₂²×D₇₉	1	1	yes	characteristic
280	C₂³×C₄	C₂²×D₇₉	1	24	yes	complemented
281	#127	—	79	64	no	—
282	#121	—	79	128	no	—
283	#121	—	79	128	no	—
284	#120	—	79	256	no	—
285	C₄×D₄	—	79	64	no	—
286	C₄×D₄	C₂²×D₇₉	1	64	yes	complemented
287	C₂×C₄⋊C₄	—	79	12	no	—
288	C₂×C₄⋊C₄	C₂²×D₇₉	1	12	yes	complemented
289	C₂×C₂²⋊C₄	—	79	24	no	—
290	C₂×C₂²⋊C₄	—	79	48	no	—
291	C₂×C₂²⋊C₄	C₂²×D₇₉	1	24	yes	complemented
292	C₂×C₄²	C₂²×D₇₉	1	12	yes	complemented
293	C₂⁴	—	2	8	no	—
294	C₂⁴	—	2	8	no	—
295	C₂⁴	—	316	256	no	—
296	C₂⁴	—	316	96	no	—
297	C₂⁴	—	79	64	no	—
298	C₂⁴	—	79	12	no	—
299	C₂⁴	—	79	16	no	—
300	C₂⁴	—	79	24	no	—
301	C₂⁴	—	158	192	no	—
302	C₂⁴	—	158	16	no	—
303	C₂⁴	—	158	16	no	—
304	C₂⁴	—	158	16	no	—
305	C₂⁴	—	158	192	no	—
306	C₂⁴	—	158	8	no	—
307	C₂⁴	—	158	8	no	—
308	C₂⁴	C₂×D₃₁₆	1	16	yes	complemented
309	C₂⁴	C₂³×D₇₉	1	12	yes	—
310	C₂⁴	C₂³×D₇₉	1	1	yes	characteristic
311	C₂×D₄	—	316	48	no	—
312	C₂×D₄	—	79	64	no	—
313	C₂×D₄	—	79	32	no	—
314	C₂×D₄	—	79	16	no	—
315	C₂×D₄	—	79	64	no	—
316	C₂×D₄	—	79	32	no	—
317	C₂×D₄	—	79	32	no	—
318	C₂×D₄	—	79	96	no	—
319	C₂×D₄	—	158	512	no	—
320	C₂×D₄	—	158	192	no	—
321	C₂×D₄	—	158	192	no	—
322	C₂×D₄	—	158	512	no	—
323	C₂×D₄	—	158	96	no	—
324	C₂×D₄	—	158	96	no	—
325	C₂×D₄	C₂×D₃₁₆	1	96	yes	direct product factor
326	C₂×D₄	C₂³×D₇₉	1	16	yes	—
327	C₂²×C₄	—	2	4	no	—
328	C₂²×C₄	—	2	8	no	—
329	C₂²×C₄	—	2	96	no	—
330	C₂²×C₄	—	79	12	no	—
331	C₂²×C₄	—	79	32	no	—
332	C₂²×C₄	—	158	8	no	—
333	C₂²×C₄	—	158	96	no	—
334	C₂²×C₄	D₄×D₇₉	1	8	yes	complemented
335	C₂²×C₄	C₂×D₃₁₆	1	8	yes	complemented
336	C₂²×C₄	C₂³×D₇₉	1	6	yes	—
337	C₂²×C₄	C₂³×D₇₉	1	12	yes	—
338	C₂²×C₄	C₂³×D₇₉	1	6	yes	—
339	C₂²×C₄	C₂³×D₇₉	1	6	yes	—
340	C₂²×C₄	C₂³×D₇₉	1	32	yes	complemented
341	C₄⋊C₄	—	79	16	no	—
342	C₄⋊C₄	C₂³×D₇₉	1	16	yes	complemented
343	C₂²⋊C₄	—	79	32	no	—
344	C₂²⋊C₄	—	79	64	no	—
345	C₂²⋊C₄	C₂³×D₇₉	1	32	yes	complemented
346	C₄²	C₂³×D₇₉	1	16	yes	complemented
347	C₂³	—	2	24	no	—
348	C₂³	—	2	64	no	—
349	C₂³	—	2	24	no	—
350	C₂³	—	316	768	no	—
351	C₂³	—	316	64	no	—
352	C₂³	—	316	64	no	—
353	C₂³	—	79	8	no	—
354	C₂³	—	79	48	no	—
355	C₂³	—	79	16	no	—
356	C₂³	—	158	128	no	—
357	C₂³	—	158	48	no	—
358	C₂³	—	158	48	no	—
359	C₂³	—	158	48	no	—
360	C₂³	—	158	128	no	—
361	C₂³	—	158	24	no	—
362	C₂³	—	158	64	no	—
363	C₂³	—	158	24	no	—
364	C₂³	C₂×D₄×D₇₉	1	4	yes	—
365	C₂³	C₂²×D₃₁₆	1	4	yes	—
366	C₂³	C₂²×D₃₁₆	1	48	yes	complemented
367	C₂³	#14579207	1	4	yes	—
368	C₂³	C₂⁴×D₇₉	1	8	yes	—
369	C₂³	C₂⁴×D₇₉	1	3	yes	—
370	D₄	—	316	32	no	—
371	D₄	—	79	64	no	—
372	D₄	—	158	128	no	—
373	D₄	—	158	128	no	—
374	D₄	—	158	64	no	—
375	D₄	—	158	64	no	—
376	D₄	C₂²×D₃₁₆	1	64	yes	direct product factor
377	C₂×C₄	—	2	12	no	—
378	C₂×C₄	—	2	24	no	—
379	C₂×C₄	—	2	64	no	—
380	C₂×C₄	—	79	8	no	—
381	C₂×C₄	—	158	24	no	—
382	C₂×C₄	—	158	64	no	—
383	C₂×C₄	C₂×D₄×D₇₉	1	24	yes	complemented
384	C₂×C₄	C₂²×D₃₁₆	1	24	yes	complemented
385	C₂×C₄	C₂⁴×D₇₉	1	4	yes	—
386	C₂×C₄	C₂⁴×D₇₉	1	8	yes	—
387	C₂×C₄	C₂⁴×D₇₉	1	4	yes	—
388	C₂×C₄	C₂⁴×D₇₉	1	4	yes	—
389	C₂²	—	2	96	no	—
390	C₂²	—	2	8	no	—
391	C₂²	—	2	8	no	—
392	C₂²	—	316	256	no	—
393	C₂²	—	316	96	no	—
394	C₂²	—	79	16	no	—
395	C₂²	—	158	16	no	—
396	C₂²	—	158	16	no	—
397	C₂²	—	158	16	no	—
398	C₂²	—	158	96	no	—
399	C₂²	—	158	8	no	—
400	C₂²	—	158	8	no	—
401	C₂²	D₄×D₃₁₆	1	16	yes	direct product factor
402	C₂²	C₂²×D₄×D₇₉	1	6	yes	—
403	C₂²	C₂³×D₃₁₆	1	6	yes	—
404	C₂²	C₂³×D₃₁₆	1	16	yes	complemented
405	C₂²	C₂×#14579207	1	6	yes	—
406	C₂²	C₂⁵×D₇₉	1	1	yes	characteristic
407	C₄	—	2	8	no	—
408	C₄	—	2	4	no	—
409	C₄	—	158	8	no	—
410	C₄	C₂²×D₄×D₇₉	1	8	yes	complemented
411	C₄	C₂³×D₃₁₆	1	8	yes	complemented
412	C₂	—	2	16	no	—
413	C₂	—	316	16	no	—
414	C₂	—	158	16	no	—
415	C₂	C₂×D₄×D₃₁₆	1	12	yes	direct product factor
416	C₂	C₂³×D₄×D₇₉	1	1	yes	characteristic
417	C₂	C₂⁴×D₃₁₆	1	1	yes	characteristic
418	C₂	C₂²×#14579207	1	1	yes	characteristic

	subgroup	G/H
center	C₂⁴	C₂³×D₇₉
commutator, cosocle	C₂²×C₇₉	C₂⁶
Frattini	C₂²	C₂⁵×D₇₉
Fitting	C₂²×C₄×D₄×C₇₉	C₂
socle	C₂⁴×C₇₉	C₂⁴
hypercenter	C₂²×C₄×D₄	D₇₉
hypocenter	C₇₉	C₂²×D₄²
LCS	G ▷ C₂²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂⁴ ◁ C₂²×C₄×D₄

Complements

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

N	H ≅ G/N	type
1. C₂⁴×D₃₁₆	C₂	semidirect
2. C₂³×D₄×D₇₉	C₂	semidirect
3. C₂×D₄×D₃₁₆	C₂	direct (N × H)
4. C₂²×#14579158	C₂	semidirect
5. C₂²×#14579136	C₂	semidirect
6. C₂²×#14579135	C₂	semidirect
7. C₂²×#14579131	C₂	semidirect
8. C₂²×C₄×D₃₁₆	C₂	semidirect
9. C₂²×C₄×D₄×C₇₉	C₂	semidirect
10. C₂⁵×D₇₉	C₂²	semidirect
13. C₂³×D₃₁₆	C₂²	semidirect
14. C₂³×D₃₁₆	C₂²	semidirect
15. C₂³×D₃₁₆	C₂²	semidirect
16. C₂³×D₃₁₆	C₂²	semidirect
17. C₂³×D₃₁₆	C₂²	semidirect
18. C₂³×C₂²⋊D₇₉	C₂²	semidirect
20. C₂²×D₄×D₇₉	C₂²	semidirect
21. C₂³×C₄×D₇₉	C₂²	semidirect
22. D₄×D₃₁₆	C₂²	direct (N × H)
23. C₂×#14579158	C₂²	semidirect
24. C₂×#14579136	C₂²	semidirect
25. C₂×#14579135	C₂²	semidirect
26. C₂×#14579131	C₂²	semidirect
27. C₂×C₄×D₃₁₆	C₂²	semidirect
28. C₂²×C₄⋊Dic₇₉	C₂²	semidirect
29. C₂²×(C₂×D₇₉)⋊C₄	C₂²	semidirect
30. C₂²×(C₂×D₇₉)⋊C₄	C₂²	semidirect
32. C₂⁴×C₄×C₇₉	C₂²	semidirect
33. C₂×C₄×D₄×C₇₉	C₂²	semidirect
34. C₂²×C₄⋊C₄×C₇₉	C₂²	semidirect
35. C₂²×C₂²⋊C₄×C₇₉	C₂²	semidirect
36. C₂²×C₄²×C₇₉	C₂²	semidirect
42. C₂⁴×D₇₉	C₂³	semidirect
48. C₂²×D₃₁₆	D₄	direct (N × H)
50. C₂²×D₃₁₆	C₂³	semidirect
51. C₂²×D₃₁₆	C₂³	semidirect
52. C₂²×D₃₁₆	C₂³	semidirect
53. C₂²×D₃₁₆	C₂³	semidirect
54. C₂²×D₃₁₆	C₂³	semidirect
56. C₂²×C₂²⋊D₇₉	C₂³	semidirect
58. C₂×D₄×D₇₉	C₂³	semidirect
61. C₂²×C₄×D₇₉	C₂³	semidirect
62. #14579158	C₂³	semidirect
63. #14579136	C₂³	semidirect
64. #14579135	C₂³	semidirect
65. #14579131	C₂³	semidirect
66. C₄×D₃₁₆	C₂³	semidirect
67. C₂×C₄⋊Dic₇₉	C₂³	semidirect
68. C₂×(C₂×D₇₉)⋊C₄	C₂³	semidirect
69. C₂×(C₂×D₇₉)⋊C₄	C₂³	semidirect
71. C₂²×D₄×C₇₉	D₄	semidirect
78. C₂³×C₄×C₇₉	C₂³	semidirect
79. C₄×D₄×C₇₉	C₂³	semidirect
80. C₂×C₄⋊C₄×C₇₉	C₂³	semidirect
81. C₂×C₂²⋊C₄×C₇₉	C₂³	semidirect
82. C₂×C₄²×C₇₉	C₂³	semidirect
92. C₂³×D₇₉	C₂×D₄	semidirect
95. C₂³×D₇₉	C₂⁴	semidirect
101. C₂×D₃₁₆	C₂×D₄	direct (N × H)
103. C₂×D₃₁₆	C₂⁴	semidirect
104. C₂×D₃₁₆	C₂⁴	semidirect
105. C₂×D₃₁₆	C₂⁴	semidirect
106. C₂×D₃₁₆	C₂⁴	semidirect
108. C₂×C₂²⋊D₇₉	C₂⁴	semidirect
113. C₂×C₄×D₇₉	C₂⁴	semidirect
114. C₄⋊Dic₇₉	C₂⁴	semidirect
115. (C₂×D₇₉)⋊C₄	C₂⁴	semidirect
116. (C₂×D₇₉)⋊C₄	C₂⁴	semidirect
119. C₂⁴×C₇₉	C₂×D₄	semidirect
122. C₂×D₄×C₇₉	C₂×D₄	semidirect
127. C₂²×C₄×C₇₉	C₂×D₄	semidirect
128. C₂²×C₄×C₇₉	C₂×D₄	semidirect
133. C₂²×C₄×C₇₉	C₂⁴	semidirect
134. C₄⋊C₄×C₇₉	C₂⁴	semidirect
135. C₂²⋊C₄×C₇₉	C₂⁴	semidirect
136. C₄²×C₇₉	C₂⁴	semidirect
142. C₂³×C₇₉	C₂²×D₄	semidirect
157. C₂²×D₇₉	C₂²×D₄	semidirect
160. D₄×C₇₉	C₂²×D₄	semidirect
164. C₂×C₄×C₇₉	C₂²×D₄	semidirect
165. C₂×C₄×C₇₉	C₂²×D₄	semidirect
177. D₃₁₆	C₂²×D₄	direct (N × H)
182. C₂²×C₇₉	D₄²	semidirect
185. C₂²×C₇₉	C₂³×D₄	semidirect
196. C₂×D₇₉	C₂³×D₄	semidirect
199. C₄×C₇₉	C₂³×D₄	semidirect
200. C₄×C₇₉	C₂³×D₄	semidirect
204. C₂×C₇₉	C₂×D₄²	semidirect
218. C₂²×C₄×D₄	D₇₉	semidirect
219. C₇₉	C₂²×D₄²	semidirect
233. C₂⁴×C₄	C₂×D₇₉	semidirect
240. C₂×C₄×D₄	C₂×D₇₉	semidirect
242. C₂²×C₄⋊C₄	C₂×D₇₉	semidirect
245. C₂²×C₂²⋊C₄	C₂×D₇₉	semidirect
246. C₂²×C₄²	C₂×D₇₉	semidirect
270. C₂²×D₄	D₃₁₆	direct (N × H)
280. C₂³×C₄	C₂²×D₇₉	semidirect
286. C₄×D₄	C₂²×D₇₉	semidirect
288. C₂×C₄⋊C₄	C₂²×D₇₉	semidirect
291. C₂×C₂²⋊C₄	C₂²×D₇₉	semidirect
292. C₂×C₄²	C₂²×D₇₉	semidirect
308. C₂⁴	C₂×D₃₁₆	semidirect
325. C₂×D₄	C₂×D₃₁₆	direct (N × H)
334. C₂²×C₄	D₄×D₇₉	semidirect
335. C₂²×C₄	C₂×D₃₁₆	semidirect
340. C₂²×C₄	C₂³×D₇₉	semidirect
342. C₄⋊C₄	C₂³×D₇₉	semidirect
345. C₂²⋊C₄	C₂³×D₇₉	semidirect
346. C₄²	C₂³×D₇₉	semidirect
366. C₂³	C₂²×D₃₁₆	semidirect
376. D₄	C₂²×D₃₁₆	direct (N × H)
383. C₂×C₄	C₂×D₄×D₇₉	semidirect
384. C₂×C₄	C₂²×D₃₁₆	semidirect
401. C₂²	D₄×D₃₁₆	direct (N × H)
404. C₂²	C₂³×D₃₁₆	semidirect
410. C₄	C₂²×D₄×D₇₉	semidirect
411. C₄	C₂³×D₃₁₆	semidirect
415. C₂	C₂×D₄×D₃₁₆	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
C₂³×D₄×D₇₉	2
C₂×D₄×D₃₁₆	2
C₂²×#14579158	2
C₂²×#14579136	2
C₂²×#14579135	2
C₂²×#14579131	2
C₂²×C₄×D₃₁₆	2
C₂²×C₄×D₄×C₇₉	2
C₂²×D₄²	79

Subgroups — C22×D4×D316 #35195180

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×D₄×D₃₁₆ #35195180