Subgroups — C₁₇×#22160 #16879904

Order 4352.

880 conjugacy classes of subgroups.

The subgroup lattice has 682 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₇×#460	C₂	1	1	yes	maximal, characteristic
2	C₁₇×#2328	C₂	1	1	yes	maximal, characteristic
3	C₁₇×#2320	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₇×#1982	C₂	1	1	yes	maximal, characteristic
5	C₁₇×#1973	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₇×#1968	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₇×#1949	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₇×#1936	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₇×#1934	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₇×#1877	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₇×#1877	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₇×#1864	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₇×#1862	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₇×#1805	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₇×#1768	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×SD₁₆×C₁₇	C₂²	1	1	yes	characteristic
17	C₂²×SD₁₆×C₁₇	C₂²	1	1	yes	characteristic
18	C₂×C₁₇×#127	C₂²	1	1	yes	characteristic
19	C₂×C₄×Q₈×C₁₇	C₂²	1	1	yes	characteristic
20	C₂×C₄×D₄×C₁₇	C₂²	1	1	yes	characteristic
21	C₂×C₄×D₄×C₁₇	C₂²	1	1	yes	characteristic
22	C₁₇×#460	C₄	1	8	yes	complemented
23	C₂×C₁₇×#107	C₂²	1	1	yes	characteristic
24	C₂×C₁₇×#106	C₂²	1	1	yes	characteristic
25	C₂×C₁₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
26	C₂×C₁₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
27	C₂×C₁₇×#103	C₂²	1	1	yes	characteristic
28	C₂×C₁₇×#103	C₂²	1	1	yes	characteristic
29	C₂×C₁₇×#102	C₂²	1	1	yes	characteristic
30	C₂×C₁₇×#102	C₂²	1	1	yes	characteristic
31	C₂×C₁₇×#102	C₂²	1	1	yes	characteristic
32	C₂×C₁₇×#102	C₂²	1	1	yes	characteristic
33	C₂×C₁₇×#102	C₂²	1	1	yes	characteristic
34	C₂×C₁₇×#102	C₂²	1	1	yes	characteristic
35	C₂×C₁₇×#97	C₂²	1	1	yes	characteristic
36	C₂×C₄×C₈×C₁₇	C₂²	1	1	yes	characteristic
37	C₁₇×#391	C₂²	1	1	yes	characteristic
38	C₁₇×#391	C₂²	1	1	yes	characteristic
39	C₁₇×#390	C₂²	1	1	yes	characteristic
40	C₁₇×#390	C₂²	1	1	yes	characteristic
41	C₁₇×#389	C₂²	1	1	yes	characteristic
42	C₁₇×#389	C₂²	1	1	yes	characteristic
43	C₁₇×#387	—	2	1	no	—
44	C₁₇×#387	—	2	1	no	—
45	C₁₇×#386	—	2	1	no	—
46	C₁₇×#386	—	2	1	no	—
47	C₁₇×#386	—	2	1	no	—
48	C₁₇×#386	—	2	1	no	—
49	C₁₇×#383	—	2	1	no	—
50	C₁₇×#382	—	2	1	no	—
51	C₁₇×#382	C₂²	1	1	yes	characteristic
52	C₄×C₄⋊C₄×C₁₇	C₂²	1	1	yes	characteristic
53	C₁₇×#376	C₂²	1	1	yes	characteristic
54	C₁₇×#340	C₂²	1	1	yes	characteristic
55	C₁₇×#340	C₂²	1	1	yes	characteristic
56	C₁₇×#340	C₂²	1	1	yes	characteristic
57	C₁₇×#340	C₂²	1	1	yes	characteristic
58	C₁₇×#336	C₂²	1	1	yes	characteristic
59	C₁₇×#336	C₂²	1	1	yes	characteristic
60	C₂²×Q₈×C₁₇	C₂³	1	1	yes	characteristic
61	C₂²×D₄×C₁₇	—	2	1	no	—
62	C₂²×D₄×C₁₇	—	2	1	no	—
63	C₂²×D₄×C₁₇	C₂³	1	1	yes	characteristic
64	C₂²×D₄×C₁₇	C₂³	1	1	yes	characteristic
65	C₂³×C₄×C₁₇	—	2	1	no	—
66	C₂³×C₄×C₁₇	—	2	1	no	—
67	C₂×SD₁₆×C₁₇	—	4	1	no	—
68	C₂×SD₁₆×C₁₇	—	4	1	no	—
69	C₂×SD₁₆×C₁₇	—	4	1	no	—
70	C₂×SD₁₆×C₁₇	—	4	1	no	—
71	C₂×SD₁₆×C₁₇	C₂×C₄	1	4	yes	complemented
72	C₂×SD₁₆×C₁₇	C₂×C₄	1	4	yes	complemented
73	C₂²×C₈×C₁₇	C₂³	1	1	yes	characteristic
74	C₂²×C₈×C₁₇	C₂³	1	1	yes	characteristic
75	C₂²×C₈×C₁₇	C₂³	1	1	yes	characteristic
76	C₂²×C₈×C₁₇	C₂³	1	1	yes	characteristic
77	C₁₇×#127	—	2	2	no	—
78	C₁₇×#127	C₂×C₄	1	4	yes	—
79	C₄×Q₈×C₁₇	—	2	2	no	—
80	C₄×Q₈×C₁₇	C₂×C₄	1	4	yes	complemented
81	C₄×D₄×C₁₇	—	4	1	no	—
82	C₄×D₄×C₁₇	—	4	1	no	—
83	C₄×D₄×C₁₇	—	4	1	no	—
84	C₄×D₄×C₁₇	—	4	1	no	—
85	C₂×C₄⋊C₄×C₁₇	—	2	1	no	—
86	C₂×C₄⋊C₄×C₁₇	—	2	1	no	—
87	C₂×C₄⋊C₄×C₁₇	—	2	1	no	—
88	C₂×C₄⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
89	C₂×C₄⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
90	C₂×C₄⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
91	C₂×C₄⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
92	C₂×C₄⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
93	C₂×C₂²⋊C₄×C₁₇	—	2	1	no	—
94	C₂×C₂²⋊C₄×C₁₇	—	2	1	no	—
95	C₂×C₂²⋊C₄×C₁₇	—	2	1	no	—
96	C₂×C₂²⋊C₄×C₁₇	—	2	1	no	—
97	C₂×C₂²⋊C₄×C₁₇	—	2	1	no	—
98	C₂×C₂²⋊C₄×C₁₇	—	2	1	no	—
99	C₂×C₄²×C₁₇	—	2	1	no	—
100	C₂×C₄²×C₁₇	—	2	1	no	—
101	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
102	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
103	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
104	C₁₇×#107	—	4	1	no	—
105	C₁₇×#106	—	4	1	no	—
106	C₁₇×C₄⋊C₈	—	2	2	no	—
107	C₁₇×C₄⋊C₈	C₂×C₄	1	4	yes	complemented
108	C₁₇×#103	—	4	1	no	—
109	C₁₇×#103	—	4	1	no	—
110	C₁₇×#102	—	4	1	no	—
111	C₁₇×#102	—	4	1	no	—
112	C₁₇×#102	—	4	1	no	—
113	C₁₇×#102	—	4	1	no	—
114	C₁₇×#102	C₂×C₄	1	4	yes	complemented
115	C₁₇×#102	C₂×C₄	1	4	yes	complemented
116	C₁₇×#97	—	4	1	no	—
117	C₄×C₈×C₁₇	—	4	1	no	—
118	C₁₇×#95	—	2	1	no	—
119	C₁₇×#95	—	2	1	no	—
120	C₁₇×#95	—	2	1	no	—
121	C₁₇×#95	—	2	1	no	—
122	C₁₇×#95	—	2	1	no	—
123	C₁₇×#95	—	2	1	no	—
124	C₁₇×#95	—	2	1	no	—
125	C₁₇×#95	—	2	1	no	—
126	C₁₇×#95	—	2	1	no	—
127	C₁₇×#95	D₄	1	1	yes	characteristic
128	C₁₇×#95	D₄	1	1	yes	characteristic
129	C₁₇×#95	D₄	1	1	yes	characteristic
130	C₁₇×#95	D₄	1	1	yes	characteristic
131	C₂⁴×C₁₇	—	2	1	no	—
132	C₂⁴×C₁₇	—	2	1	no	—
133	C₂×Q₈×C₁₇	—	2	1	no	—
134	C₂×Q₈×C₁₇	—	2	1	no	—
135	C₂×Q₈×C₁₇	—	2	1	no	—
136	C₂×Q₈×C₁₇	—	2	1	no	—
137	C₂×Q₈×C₁₇	—	2	1	no	—
138	C₂×Q₈×C₁₇	C₂²×C₄	1	2	yes	—
139	C₂×D₄×C₁₇	—	2	4	no	—
140	C₂×D₄×C₁₇	—	2	4	no	—
141	C₂×D₄×C₁₇	—	2	1	no	—
142	C₂×D₄×C₁₇	—	2	1	no	—
143	C₂×D₄×C₁₇	—	2	1	no	—
144	C₂×D₄×C₁₇	—	2	1	no	—
145	C₂×D₄×C₁₇	—	2	1	no	—
146	C₂×D₄×C₁₇	—	2	1	no	—
147	C₂×D₄×C₁₇	—	2	1	no	—
148	C₂×D₄×C₁₇	—	2	1	no	—
149	C₂×D₄×C₁₇	—	2	1	no	—
150	C₂×D₄×C₁₇	—	2	1	no	—
151	C₂×D₄×C₁₇	—	8	1	no	—
152	C₂×D₄×C₁₇	—	8	1	no	—
153	C₂×D₄×C₁₇	—	8	1	no	—
154	C₂×D₄×C₁₇	—	8	1	no	—
155	C₂×D₄×C₁₇	C₂²×C₄	1	2	yes	—
156	C₂×D₄×C₁₇	C₂²×C₄	1	2	yes	—
157	C₂²×C₄×C₁₇	—	2	1	no	—
158	C₂²×C₄×C₁₇	—	2	1	no	—
159	C₂²×C₄×C₁₇	—	2	1	no	—
160	C₂²×C₄×C₁₇	—	2	1	no	—
161	C₂²×C₄×C₁₇	—	2	1	no	—
162	C₂²×C₄×C₁₇	—	2	1	no	—
163	C₂²×C₄×C₁₇	—	4	2	no	—
164	C₂²×C₄×C₁₇	—	4	2	no	—
165	C₂²×C₄×C₁₇	—	8	1	no	—
166	C₂²×C₄×C₁₇	—	8	1	no	—
167	C₂²×C₄×C₁₇	—	8	1	no	—
168	C₂²×C₄×C₁₇	—	8	1	no	—
169	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
170	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
171	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
172	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
173	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
174	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
175	C₂²×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
176	SD₁₆×C₁₇	—	4	4	no	—
177	SD₁₆×C₁₇	—	4	4	no	—
178	C₂×C₈×C₁₇	—	2	1	no	—
179	C₂×C₈×C₁₇	—	2	1	no	—
180	C₂×C₈×C₁₇	—	2	1	no	—
181	C₂×C₈×C₁₇	—	2	1	no	—
182	C₂×C₈×C₁₇	—	2	1	no	—
183	C₂×C₈×C₁₇	—	2	1	no	—
184	C₂×C₈×C₁₇	—	2	1	no	—
185	C₂×C₈×C₁₇	—	2	1	no	—
186	C₂×C₈×C₁₇	—	2	1	no	—
187	C₂×C₈×C₁₇	—	2	1	no	—
188	C₂×C₈×C₁₇	C₂²×C₄	1	2	yes	—
189	C₂×C₈×C₁₇	C₂²×C₄	1	2	yes	—
190	C₄⋊C₄×C₁₇	—	2	4	no	—
191	C₄⋊C₄×C₁₇	—	2	1	no	—
192	C₄⋊C₄×C₁₇	—	2	1	no	—
193	C₄⋊C₄×C₁₇	—	2	1	no	—
194	C₄⋊C₄×C₁₇	—	2	1	no	—
195	C₄⋊C₄×C₁₇	—	2	1	no	—
196	C₄⋊C₄×C₁₇	—	2	1	no	—
197	C₄⋊C₄×C₁₇	—	2	1	no	—
198	C₄⋊C₄×C₁₇	—	2	1	no	—
199	C₄⋊C₄×C₁₇	—	2	1	no	—
200	C₄⋊C₄×C₁₇	—	8	1	no	—
201	C₄⋊C₄×C₁₇	—	8	1	no	—
202	C₄⋊C₄×C₁₇	C₂²×C₄	1	2	yes	—
203	C₂²⋊C₄×C₁₇	—	4	2	no	—
204	C₂²⋊C₄×C₁₇	—	4	2	no	—
205	C₂²⋊C₄×C₁₇	—	8	1	no	—
206	C₂²⋊C₄×C₁₇	—	8	1	no	—
207	C₂²⋊C₄×C₁₇	—	8	1	no	—
208	C₂²⋊C₄×C₁₇	—	8	1	no	—
209	C₄²×C₁₇	—	2	4	no	—
210	C₄²×C₁₇	—	2	1	no	—
211	C₄²×C₁₇	—	2	1	no	—
212	C₄²×C₁₇	—	2	1	no	—
213	C₄²×C₁₇	—	2	1	no	—
214	C₄²×C₁₇	—	8	1	no	—
215	C₄²×C₁₇	C₂²×C₄	1	2	yes	—
216	C₄²×C₁₇	#41	1	2	yes	—
217	#22160	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
218	C₂³×C₁₇	—	2	2	no	—
219	C₂³×C₁₇	—	2	2	no	—
220	C₂³×C₁₇	—	4	1	no	—
221	C₂³×C₁₇	—	4	1	no	—
222	C₂³×C₁₇	—	4	1	no	—
223	C₂³×C₁₇	—	4	1	no	—
224	C₂³×C₁₇	—	4	1	no	—
225	C₂³×C₁₇	—	4	1	no	—
226	C₂³×C₁₇	—	4	1	no	—
227	C₂³×C₁₇	—	4	1	no	—
228	C₂³×C₁₇	—	4	1	no	—
229	C₂³×C₁₇	—	4	1	no	—
230	C₂³×C₁₇	—	4	1	no	—
231	C₂³×C₁₇	—	4	1	no	—
232	C₂³×C₁₇	C₂²×D₄	1	1	yes	characteristic
233	Q₈×C₁₇	—	2	2	no	—
234	Q₈×C₁₇	—	2	2	no	—
235	Q₈×C₁₇	—	4	1	no	—
236	Q₈×C₁₇	—	4	1	no	—
237	D₄×C₁₇	—	2	2	no	—
238	D₄×C₁₇	—	2	2	no	—
239	D₄×C₁₇	—	2	2	no	—
240	D₄×C₁₇	—	2	2	no	—
241	D₄×C₁₇	—	4	1	no	—
242	D₄×C₁₇	—	4	1	no	—
243	D₄×C₁₇	—	4	1	no	—
244	D₄×C₁₇	—	4	1	no	—
245	D₄×C₁₇	—	8	4	no	—
246	D₄×C₁₇	—	8	4	no	—
247	C₂×C₄×C₁₇	—	2	1	no	—
248	C₂×C₄×C₁₇	—	2	1	no	—
249	C₂×C₄×C₁₇	—	2	1	no	—
250	C₂×C₄×C₁₇	—	2	1	no	—
251	C₂×C₄×C₁₇	—	2	2	no	—
252	C₂×C₄×C₁₇	—	2	2	no	—
253	C₂×C₄×C₁₇	—	2	1	no	—
254	C₂×C₄×C₁₇	—	2	1	no	—
255	C₂×C₄×C₁₇	—	2	1	no	—
256	C₂×C₄×C₁₇	—	2	1	no	—
257	C₂×C₄×C₁₇	—	2	1	no	—
258	C₂×C₄×C₁₇	—	2	1	no	—
259	C₂×C₄×C₁₇	—	2	1	no	—
260	C₂×C₄×C₁₇	—	2	1	no	—
261	C₂×C₄×C₁₇	—	2	1	no	—
262	C₂×C₄×C₁₇	—	2	1	no	—
263	C₂×C₄×C₁₇	—	2	1	no	—
264	C₂×C₄×C₁₇	—	2	1	no	—
265	C₂×C₄×C₁₇	—	4	1	no	—
266	C₂×C₄×C₁₇	—	4	1	no	—
267	C₂×C₄×C₁₇	—	4	1	no	—
268	C₂×C₄×C₁₇	—	4	1	no	—
269	C₂×C₄×C₁₇	—	4	1	no	—
270	C₂×C₄×C₁₇	—	4	1	no	—
271	C₂×C₄×C₁₇	—	4	1	no	—
272	C₂×C₄×C₁₇	—	4	1	no	—
273	C₂×C₄×C₁₇	—	4	1	no	—
274	C₂×C₄×C₁₇	—	4	1	no	—
275	C₂×C₄×C₁₇	—	4	1	no	—
276	C₂×C₄×C₁₇	—	4	1	no	—
277	C₂×C₄×C₁₇	—	4	1	no	—
278	C₂×C₄×C₁₇	—	4	1	no	—
279	C₂×C₄×C₁₇	—	4	1	no	—
280	C₂×C₄×C₁₇	—	4	1	no	—
281	C₂×C₄×C₁₇	—	8	4	no	—
282	C₂×C₄×C₁₇	—	8	4	no	—
283	C₂×C₄×C₁₇	C₄×D₄	1	2	yes	—
284	C₂×C₄×C₁₇	C₄×D₄	1	2	yes	—
285	C₂×C₄×C₁₇	C₂³×C₄	1	1	yes	characteristic
286	C₂×C₄×C₁₇	C₂×#41	1	1	yes	characteristic
287	C₂×C₄×C₁₇	H(5,𝔽₂)	1	1	yes	characteristic
288	C₂×C₄×C₁₇	H(5,𝔽₂)	1	1	yes	characteristic
289	C₂×C₄×C₁₇	H(5,𝔽₂)	1	1	yes	characteristic
290	C₂×C₄×C₁₇	2₋¹⁺⁴	1	1	yes	characteristic
291	C₈×C₁₇	—	2	2	no	—
292	C₈×C₁₇	—	2	2	no	—
293	C₈×C₁₇	—	4	1	no	—
294	C₈×C₁₇	—	4	1	no	—
295	C₂×#460	C₂×C₁₇	1	1	yes	characteristic
296	#2328	C₂×C₁₇	1	1	yes	characteristic
297	#2320	C₂×C₁₇	1	1	yes	characteristic, complemented
298	#1982	C₂×C₁₇	1	1	yes	characteristic
299	#1973	C₂×C₁₇	1	1	yes	characteristic, complemented
300	#1968	C₂×C₁₇	1	1	yes	characteristic, complemented
301	#1949	C₂×C₁₇	1	1	yes	characteristic, complemented
302	#1936	C₂×C₁₇	1	1	yes	characteristic, complemented
303	#1934	C₂×C₁₇	1	1	yes	characteristic, complemented
304	#1877	C₂×C₁₇	1	1	yes	characteristic, complemented
305	#1877	C₂×C₁₇	1	1	yes	characteristic, complemented
306	#1864	C₂×C₁₇	1	1	yes	characteristic, complemented
307	#1862	C₂×C₁₇	1	1	yes	characteristic, complemented
308	#1805	C₂×C₁₇	1	1	yes	characteristic, complemented
309	#1768	C₂×C₁₇	1	1	yes	characteristic, complemented
310	C₂²×C₁₇	—	4	2	no	—
311	C₂²×C₁₇	—	4	2	no	—
312	C₂²×C₁₇	—	4	2	no	—
313	C₂²×C₁₇	—	4	2	no	—
314	C₂²×C₁₇	—	4	2	no	—
315	C₂²×C₁₇	—	4	2	no	—
316	C₂²×C₁₇	—	8	1	no	—
317	C₂²×C₁₇	—	8	1	no	—
318	C₂²×C₁₇	—	8	1	no	—
319	C₂²×C₁₇	—	8	1	no	—
320	C₂²×C₁₇	—	8	1	no	—
321	C₂²×C₁₇	—	8	1	no	—
322	C₂²×C₁₇	—	8	1	no	—
323	C₂²×C₁₇	—	8	1	no	—
324	C₂²×C₁₇	C₂×C₄×D₄	1	1	yes	characteristic
325	C₂²×C₁₇	#535	1	1	yes	characteristic
326	C₂²×C₁₇	#537	1	1	yes	characteristic
327	C₂²×C₁₇	#576	1	1	yes	characteristic
328	C₂²×C₁₇	#577	1	1	yes	characteristic
329	C₂²×C₁₇	#577	1	1	yes	characteristic
330	C₂²×C₁₇	#577	1	1	yes	characteristic
331	C₄×C₁₇	—	2	2	no	—
332	C₄×C₁₇	—	2	2	no	—
333	C₄×C₁₇	—	4	2	no	—
334	C₄×C₁₇	—	4	2	no	—
335	C₄×C₁₇	—	4	1	no	—
336	C₄×C₁₇	—	4	1	no	—
337	C₄×C₁₇	—	4	1	no	—
338	C₄×C₁₇	—	4	1	no	—
339	C₄×C₁₇	—	8	1	no	—
340	C₄×C₁₇	—	8	1	no	—
341	C₄×C₁₇	—	8	1	no	—
342	C₄×C₁₇	—	8	1	no	—
343	C₄×C₁₇	#518	1	1	yes	characteristic
344	C₄×C₁₇	#520	1	1	yes	characteristic
345	C₄×C₁₇	#540	1	1	yes	characteristic
346	C₄×C₁₇	#542	1	1	yes	characteristic
347	C₂²×SD₁₆	C₂²×C₁₇	1	1	yes	characteristic
348	C₂²×SD₁₆	C₂²×C₁₇	1	1	yes	characteristic
349	C₂×#127	C₂²×C₁₇	1	1	yes	characteristic
350	C₂×C₄×Q₈	C₂²×C₁₇	1	1	yes	characteristic
351	C₂×C₄×D₄	C₂²×C₁₇	1	1	yes	characteristic
352	C₂×C₄×D₄	C₂²×C₁₇	1	1	yes	characteristic
353	#460	C₄×C₁₇	1	8	yes	complemented
354	C₂×#107	C₂²×C₁₇	1	1	yes	characteristic
355	C₂×#106	C₂²×C₁₇	1	1	yes	characteristic
356	C₂×C₄⋊C₈	C₂²×C₁₇	1	1	yes	characteristic
357	C₂×C₄⋊C₈	C₂²×C₁₇	1	1	yes	characteristic
358	C₂×#103	C₂²×C₁₇	1	1	yes	characteristic
359	C₂×#103	C₂²×C₁₇	1	1	yes	characteristic
360	C₂×#102	C₂²×C₁₇	1	1	yes	characteristic
361	C₂×#102	C₂²×C₁₇	1	1	yes	characteristic
362	C₂×#102	C₂²×C₁₇	1	1	yes	characteristic
363	C₂×#102	C₂²×C₁₇	1	1	yes	characteristic
364	C₂×#102	C₂²×C₁₇	1	1	yes	characteristic
365	C₂×#102	C₂²×C₁₇	1	1	yes	characteristic
366	C₂×#97	C₂²×C₁₇	1	1	yes	characteristic
367	C₂×C₄×C₈	C₂²×C₁₇	1	1	yes	characteristic
368	#391	C₂²×C₁₇	1	1	yes	characteristic
369	#391	C₂²×C₁₇	1	1	yes	characteristic
370	#390	C₂²×C₁₇	1	1	yes	characteristic
371	#390	C₂²×C₁₇	1	1	yes	characteristic
372	#389	C₂²×C₁₇	1	1	yes	characteristic
373	#389	C₂²×C₁₇	1	1	yes	characteristic
374	#387	—	2	1	no	—
375	#387	—	2	1	no	—
376	#386	—	2	1	no	—
377	#386	—	2	1	no	—
378	#386	—	2	1	no	—
379	#386	—	2	1	no	—
380	#383	—	2	1	no	—
381	#382	—	2	1	no	—
382	#382	C₂²×C₁₇	1	1	yes	characteristic
383	C₄×C₄⋊C₄	C₂²×C₁₇	1	1	yes	characteristic
384	#376	C₂²×C₁₇	1	1	yes	characteristic
385	#340	C₂²×C₁₇	1	1	yes	characteristic
386	#340	C₂²×C₁₇	1	1	yes	characteristic
387	#340	C₂²×C₁₇	1	1	yes	characteristic
388	#340	C₂²×C₁₇	1	1	yes	characteristic
389	#336	C₂²×C₁₇	1	1	yes	characteristic
390	#336	C₂²×C₁₇	1	1	yes	characteristic
391	C₂×C₁₇	—	8	2	no	—
392	C₂×C₁₇	—	8	2	no	—
393	C₂×C₁₇	#2324	1	1	yes	characteristic
394	C₂×C₁₇	#2946	1	1	yes	characteristic
395	C₂×C₁₇	#2949	1	1	yes	characteristic
396	C₂×C₁₇	#3222	1	1	yes	characteristic
397	C₂×C₁₇	#3224	1	1	yes	characteristic
398	C₂×C₁₇	#3257	1	1	yes	characteristic
399	C₂×C₁₇	#3260	1	1	yes	characteristic
400	C₂²×Q₈	C₂³×C₁₇	1	1	yes	characteristic
401	C₂²×D₄	—	2	1	no	—
402	C₂²×D₄	—	2	1	no	—
403	C₂²×D₄	C₂³×C₁₇	1	1	yes	characteristic
404	C₂²×D₄	C₂³×C₁₇	1	1	yes	characteristic
405	C₂³×C₄	—	2	1	no	—
406	C₂³×C₄	—	2	1	no	—
407	C₂×SD₁₆	—	4	1	no	—
408	C₂×SD₁₆	—	4	1	no	—
409	C₂×SD₁₆	—	4	1	no	—
410	C₂×SD₁₆	—	4	1	no	—
411	C₂×SD₁₆	C₂×C₄×C₁₇	1	4	yes	complemented
412	C₂×SD₁₆	C₂×C₄×C₁₇	1	4	yes	complemented
413	C₂²×C₈	C₂³×C₁₇	1	1	yes	characteristic
414	C₂²×C₈	C₂³×C₁₇	1	1	yes	characteristic
415	C₂²×C₈	C₂³×C₁₇	1	1	yes	characteristic
416	C₂²×C₈	C₂³×C₁₇	1	1	yes	characteristic
417	#127	—	2	2	no	—
418	#127	C₂×C₄×C₁₇	1	4	yes	—
419	C₄×Q₈	—	2	2	no	—
420	C₄×Q₈	C₂×C₄×C₁₇	1	4	yes	complemented
421	C₄×D₄	—	4	1	no	—
422	C₄×D₄	—	4	1	no	—
423	C₄×D₄	—	4	1	no	—
424	C₄×D₄	—	4	1	no	—
425	C₂×C₄⋊C₄	—	2	1	no	—
426	C₂×C₄⋊C₄	—	2	1	no	—
427	C₂×C₄⋊C₄	—	2	1	no	—
428	C₂×C₄⋊C₄	C₂³×C₁₇	1	1	yes	characteristic
429	C₂×C₄⋊C₄	C₂³×C₁₇	1	1	yes	characteristic
430	C₂×C₄⋊C₄	C₂³×C₁₇	1	1	yes	characteristic
431	C₂×C₄⋊C₄	C₂³×C₁₇	1	1	yes	characteristic
432	C₂×C₄⋊C₄	C₂³×C₁₇	1	1	yes	characteristic
433	C₂×C₂²⋊C₄	—	2	1	no	—
434	C₂×C₂²⋊C₄	—	2	1	no	—
435	C₂×C₂²⋊C₄	—	2	1	no	—
436	C₂×C₂²⋊C₄	—	2	1	no	—
437	C₂×C₂²⋊C₄	—	2	1	no	—
438	C₂×C₂²⋊C₄	—	2	1	no	—
439	C₂×C₄²	—	2	1	no	—
440	C₂×C₄²	—	2	1	no	—
441	C₂×C₄²	C₂³×C₁₇	1	1	yes	characteristic
442	C₂×C₄²	C₂³×C₁₇	1	1	yes	characteristic
443	C₂×C₄²	C₂³×C₁₇	1	1	yes	characteristic
444	#107	—	4	1	no	—
445	#106	—	4	1	no	—
446	C₄⋊C₈	—	2	2	no	—
447	C₄⋊C₈	C₂×C₄×C₁₇	1	4	yes	complemented
448	#103	—	4	1	no	—
449	#103	—	4	1	no	—
450	#102	—	4	1	no	—
451	#102	—	4	1	no	—
452	#102	—	4	1	no	—
453	#102	—	4	1	no	—
454	#102	C₂×C₄×C₁₇	1	4	yes	complemented
455	#102	C₂×C₄×C₁₇	1	4	yes	complemented
456	#97	—	4	1	no	—
457	C₄×C₈	—	4	1	no	—
458	#95	—	2	1	no	—
459	#95	—	2	1	no	—
460	#95	—	2	1	no	—
461	#95	—	2	1	no	—
462	#95	—	2	1	no	—
463	#95	—	2	1	no	—
464	#95	—	2	1	no	—
465	#95	—	2	1	no	—
466	#95	—	2	1	no	—
467	#95	D₄×C₁₇	1	1	yes	characteristic
468	#95	D₄×C₁₇	1	1	yes	characteristic
469	#95	D₄×C₁₇	1	1	yes	characteristic
470	#95	D₄×C₁₇	1	1	yes	characteristic
471	C₁₇	#22160	1	1	yes	characteristic, direct product factor, Sylow
472	C₂⁴	—	2	1	no	—
473	C₂⁴	—	2	1	no	—
474	C₂×Q₈	—	2	1	no	—
475	C₂×Q₈	—	2	1	no	—
476	C₂×Q₈	—	2	1	no	—
477	C₂×Q₈	—	2	1	no	—
478	C₂×Q₈	—	2	1	no	—
479	C₂×Q₈	C₂²×C₄×C₁₇	1	2	yes	—
480	C₂×D₄	—	2	1	no	—
481	C₂×D₄	—	2	1	no	—
482	C₂×D₄	—	2	1	no	—
483	C₂×D₄	—	2	1	no	—
484	C₂×D₄	—	2	1	no	—
485	C₂×D₄	—	2	1	no	—
486	C₂×D₄	—	2	1	no	—
487	C₂×D₄	—	2	1	no	—
488	C₂×D₄	—	2	1	no	—
489	C₂×D₄	—	2	1	no	—
490	C₂×D₄	—	2	4	no	—
491	C₂×D₄	—	2	4	no	—
492	C₂×D₄	—	8	1	no	—
493	C₂×D₄	—	8	1	no	—
494	C₂×D₄	—	8	1	no	—
495	C₂×D₄	—	8	1	no	—
496	C₂×D₄	C₂²×C₄×C₁₇	1	2	yes	—
497	C₂×D₄	C₂²×C₄×C₁₇	1	2	yes	—
498	C₂²×C₄	—	2	1	no	—
499	C₂²×C₄	—	2	1	no	—
500	C₂²×C₄	—	2	1	no	—
501	C₂²×C₄	—	2	1	no	—
502	C₂²×C₄	—	2	1	no	—
503	C₂²×C₄	—	2	1	no	—
504	C₂²×C₄	—	4	2	no	—
505	C₂²×C₄	—	4	2	no	—
506	C₂²×C₄	—	8	1	no	—
507	C₂²×C₄	—	8	1	no	—
508	C₂²×C₄	—	8	1	no	—
509	C₂²×C₄	—	8	1	no	—
510	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
511	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
512	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
513	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
514	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
515	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
516	C₂²×C₄	C₂⁴×C₁₇	1	1	yes	characteristic
517	SD₁₆	—	4	4	no	—
518	SD₁₆	—	4	4	no	—
519	C₂×C₈	—	2	1	no	—
520	C₂×C₈	—	2	1	no	—
521	C₂×C₈	—	2	1	no	—
522	C₂×C₈	—	2	1	no	—
523	C₂×C₈	—	2	1	no	—
524	C₂×C₈	—	2	1	no	—
525	C₂×C₈	—	2	1	no	—
526	C₂×C₈	—	2	1	no	—
527	C₂×C₈	—	2	1	no	—
528	C₂×C₈	—	2	1	no	—
529	C₂×C₈	C₂²×C₄×C₁₇	1	2	yes	—
530	C₂×C₈	C₂²×C₄×C₁₇	1	2	yes	—
531	C₄⋊C₄	—	2	1	no	—
532	C₄⋊C₄	—	2	4	no	—
533	C₄⋊C₄	—	2	1	no	—
534	C₄⋊C₄	—	2	1	no	—
535	C₄⋊C₄	—	2	1	no	—
536	C₄⋊C₄	—	2	1	no	—
537	C₄⋊C₄	—	2	1	no	—
538	C₄⋊C₄	—	2	1	no	—
539	C₄⋊C₄	—	2	1	no	—
540	C₄⋊C₄	—	2	1	no	—
541	C₄⋊C₄	—	8	1	no	—
542	C₄⋊C₄	—	8	1	no	—
543	C₄⋊C₄	C₂²×C₄×C₁₇	1	2	yes	—
544	C₂²⋊C₄	—	4	2	no	—
545	C₂²⋊C₄	—	4	2	no	—
546	C₂²⋊C₄	—	8	1	no	—
547	C₂²⋊C₄	—	8	1	no	—
548	C₂²⋊C₄	—	8	1	no	—
549	C₂²⋊C₄	—	8	1	no	—
550	C₄²	—	2	1	no	—
551	C₄²	—	2	1	no	—
552	C₄²	—	2	1	no	—
553	C₄²	—	2	1	no	—
554	C₄²	—	2	4	no	—
555	C₄²	—	8	1	no	—
556	C₄²	C₂²×C₄×C₁₇	1	2	yes	—
557	C₄²	#41×C₁₇	1	2	yes	—
558	C₂³	—	2	2	no	—
559	C₂³	—	2	2	no	—
560	C₂³	—	4	1	no	—
561	C₂³	—	4	1	no	—
562	C₂³	—	4	1	no	—
563	C₂³	—	4	1	no	—
564	C₂³	—	4	1	no	—
565	C₂³	—	4	1	no	—
566	C₂³	—	4	1	no	—
567	C₂³	—	4	1	no	—
568	C₂³	—	4	1	no	—
569	C₂³	—	4	1	no	—
570	C₂³	—	4	1	no	—
571	C₂³	—	4	1	no	—
572	C₂³	C₂²×D₄×C₁₇	1	1	yes	characteristic
573	Q₈	—	2	2	no	—
574	Q₈	—	2	2	no	—
575	Q₈	—	4	1	no	—
576	Q₈	—	4	1	no	—
577	D₄	—	2	2	no	—
578	D₄	—	2	2	no	—
579	D₄	—	2	2	no	—
580	D₄	—	2	2	no	—
581	D₄	—	4	1	no	—
582	D₄	—	4	1	no	—
583	D₄	—	4	1	no	—
584	D₄	—	4	1	no	—
585	D₄	—	8	4	no	—
586	D₄	—	8	4	no	—
587	C₂×C₄	—	2	1	no	—
588	C₂×C₄	—	2	1	no	—
589	C₂×C₄	—	2	1	no	—
590	C₂×C₄	—	2	1	no	—
591	C₂×C₄	—	2	2	no	—
592	C₂×C₄	—	2	2	no	—
593	C₂×C₄	—	2	1	no	—
594	C₂×C₄	—	2	1	no	—
595	C₂×C₄	—	2	1	no	—
596	C₂×C₄	—	2	1	no	—
597	C₂×C₄	—	2	1	no	—
598	C₂×C₄	—	2	1	no	—
599	C₂×C₄	—	2	1	no	—
600	C₂×C₄	—	2	1	no	—
601	C₂×C₄	—	2	1	no	—
602	C₂×C₄	—	2	1	no	—
603	C₂×C₄	—	2	1	no	—
604	C₂×C₄	—	2	1	no	—
605	C₂×C₄	—	4	1	no	—
606	C₂×C₄	—	4	1	no	—
607	C₂×C₄	—	4	1	no	—
608	C₂×C₄	—	4	1	no	—
609	C₂×C₄	—	4	1	no	—
610	C₂×C₄	—	4	1	no	—
611	C₂×C₄	—	4	1	no	—
612	C₂×C₄	—	4	1	no	—
613	C₂×C₄	—	4	1	no	—
614	C₂×C₄	—	4	1	no	—
615	C₂×C₄	—	4	1	no	—
616	C₂×C₄	—	4	1	no	—
617	C₂×C₄	—	4	1	no	—
618	C₂×C₄	—	4	1	no	—
619	C₂×C₄	—	4	1	no	—
620	C₂×C₄	—	4	1	no	—
621	C₂×C₄	—	8	4	no	—
622	C₂×C₄	—	8	4	no	—
623	C₂×C₄	C₄×D₄×C₁₇	1	2	yes	—
624	C₂×C₄	C₄×D₄×C₁₇	1	2	yes	—
625	C₂×C₄	C₂³×C₄×C₁₇	1	1	yes	characteristic
626	C₂×C₄	C₂×#41×C₁₇	1	1	yes	characteristic
627	C₂×C₄	C₁₇×H(5,𝔽₂)	1	1	yes	characteristic
628	C₂×C₄	C₁₇×H(5,𝔽₂)	1	1	yes	characteristic
629	C₂×C₄	C₁₇×H(5,𝔽₂)	1	1	yes	characteristic
630	C₂×C₄	C₁₇×2₋¹⁺⁴	1	1	yes	characteristic
631	C₈	—	2	2	no	—
632	C₈	—	2	2	no	—
633	C₈	—	4	1	no	—
634	C₈	—	4	1	no	—
635	C₂²	—	4	2	no	—
636	C₂²	—	4	2	no	—
637	C₂²	—	4	2	no	—
638	C₂²	—	4	2	no	—
639	C₂²	—	4	2	no	—
640	C₂²	—	4	2	no	—
641	C₂²	—	8	1	no	—
642	C₂²	—	8	1	no	—
643	C₂²	—	8	1	no	—
644	C₂²	—	8	1	no	—
645	C₂²	—	8	1	no	—
646	C₂²	—	8	1	no	—
647	C₂²	—	8	1	no	—
648	C₂²	—	8	1	no	—
649	C₂²	C₂×C₄×D₄×C₁₇	1	1	yes	characteristic
650	C₂²	C₁₇×#535	1	1	yes	characteristic
651	C₂²	C₁₇×#537	1	1	yes	characteristic
652	C₂²	C₁₇×#576	1	1	yes	characteristic
653	C₂²	C₁₇×#577	1	1	yes	characteristic
654	C₂²	C₁₇×#577	1	1	yes	characteristic
655	C₂²	C₁₇×#577	1	1	yes	characteristic
656	C₄	—	2	2	no	—
657	C₄	—	2	2	no	—
658	C₄	—	4	2	no	—
659	C₄	—	4	1	no	—
660	C₄	—	4	1	no	—
661	C₄	—	4	1	no	—
662	C₄	—	4	1	no	—
663	C₄	—	4	2	no	—
664	C₄	—	8	1	no	—
665	C₄	—	8	1	no	—
666	C₄	—	8	1	no	—
667	C₄	—	8	1	no	—
668	C₄	C₁₇×#518	1	1	yes	characteristic
669	C₄	C₁₇×#520	1	1	yes	characteristic
670	C₄	C₁₇×#540	1	1	yes	characteristic
671	C₄	C₁₇×#542	1	1	yes	characteristic
672	C₂	—	8	2	no	—
673	C₂	—	8	2	no	—
674	C₂	C₁₇×#2324	1	1	yes	characteristic
675	C₂	C₁₇×#2946	1	1	yes	characteristic
676	C₂	C₁₇×#2949	1	1	yes	characteristic
677	C₂	C₁₇×#3222	1	1	yes	characteristic
678	C₂	C₁₇×#3224	1	1	yes	characteristic
679	C₂	C₁₇×#3257	1	1	yes	characteristic
680	C₂	C₁₇×#3260	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₇	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₇
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₇
prime radical	C₂×C₁₇×#127	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₇ ◁ C₁₇×#376 ◁ G

Complements

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

N	H ≅ G/N	type
3. C₁₇×#2320	C₂	semidirect
5. C₁₇×#1973	C₂	semidirect
6. C₁₇×#1968	C₂	semidirect
7. C₁₇×#1949	C₂	semidirect
8. C₁₇×#1936	C₂	semidirect
9. C₁₇×#1934	C₂	semidirect
10. C₁₇×#1877	C₂	semidirect
11. C₁₇×#1877	C₂	semidirect
12. C₁₇×#1864	C₂	semidirect
13. C₁₇×#1862	C₂	semidirect
14. C₁₇×#1805	C₂	semidirect
15. C₁₇×#1768	C₂	semidirect
22. C₁₇×#460	C₄	semidirect
71. C₂×SD₁₆×C₁₇	C₂×C₄	semidirect
72. C₂×SD₁₆×C₁₇	C₂×C₄	semidirect
80. C₄×Q₈×C₁₇	C₂×C₄	semidirect
107. C₁₇×C₄⋊C₈	C₂×C₄	semidirect
114. C₁₇×#102	C₂×C₄	semidirect
115. C₁₇×#102	C₂×C₄	semidirect
217. #22160	C₁₇	direct (N × H)
297. #2320	C₂×C₁₇	semidirect
299. #1973	C₂×C₁₇	semidirect
300. #1968	C₂×C₁₇	semidirect
301. #1949	C₂×C₁₇	semidirect
302. #1936	C₂×C₁₇	semidirect
303. #1934	C₂×C₁₇	semidirect
304. #1877	C₂×C₁₇	semidirect
305. #1877	C₂×C₁₇	semidirect
306. #1864	C₂×C₁₇	semidirect
307. #1862	C₂×C₁₇	semidirect
308. #1805	C₂×C₁₇	semidirect
309. #1768	C₂×C₁₇	semidirect
353. #460	C₄×C₁₇	semidirect
411. C₂×SD₁₆	C₂×C₄×C₁₇	semidirect
412. C₂×SD₁₆	C₂×C₄×C₁₇	semidirect
420. C₄×Q₈	C₂×C₄×C₁₇	semidirect
447. C₄⋊C₈	C₂×C₄×C₁₇	semidirect
454. #102	C₂×C₄×C₁₇	semidirect
455. #102	C₂×C₄×C₁₇	semidirect
471. C₁₇	#22160	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₁₇×#460	2
C₁₇×#2328	2
C₁₇×#2320	2
C₁₇×#1982	2
C₁₇×#1973	2
C₁₇×#1968	2
C₁₇×#1949	2
C₁₇×#1936	2
C₁₇×#1934	2
C₁₇×#1877	2
C₁₇×#1864	2
C₁₇×#1862	2
C₁₇×#1805	2
C₁₇×#1768	2
#22160	17

Subgroups — C17×#22160 #16879904

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₇×#22160 #16879904