Subgroups — C₁₇×#25458 #16883202

Order 4352.

754 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₇×#499	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₇×#478	C₂	1	1	yes	maximal, characteristic
3	C₁₇×#2566	C₂	1	1	yes	maximal, characteristic
4	C₁₇×#2370	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₇×#2085	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₇×#2083	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₇×#2065	C₂	1	1	yes	maximal, characteristic
8	C₁₇×#2065	C₂	1	1	yes	maximal, characteristic
9	C₁₇×#1989	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₇×#1949	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₇×#1948	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₇×#1939	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₇×#1925	C₂	1	1	yes	maximal, characteristic
14	C₁₇×#1925	C₂	1	1	yes	maximal, characteristic
15	C₄×C₁₇×#102	C₂	1	1	yes	maximal, characteristic
16	C₂×C₁₇×#125	C₂²	1	1	yes	characteristic
17	C₂×C₁₇×#125	C₂²	1	1	yes	characteristic
18	C₂×C₄×D₄×C₁₇	C₂²	1	1	yes	characteristic
19	C₁₇×#499	—	2	4	no	—
20	C₁₇×#478	—	2	4	no	—
21	C₂×C₁₇×#107	C₂²	1	1	yes	characteristic
22	C₂×C₁₇×#107	C₂²	1	1	yes	characteristic
23	C₂×C₁₇×#107	C₂²	1	1	yes	characteristic
24	C₂×C₁₇×#106	C₂²	1	1	yes	characteristic
25	C₂×C₁₇×#106	C₂²	1	1	yes	characteristic
26	C₂×C₁₇×#106	C₂²	1	1	yes	characteristic
27	C₂×C₁₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
28	C₂×C₁₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
29	C₂×C₁₇×C₄⋊C₈	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×C₄×C₈×C₁₇	C₂²	1	1	yes	characteristic
35	C₁₇×#396	—	2	1	no	—
36	C₁₇×#396	—	2	1	no	—
37	C₁₇×#390	C₂²	1	1	yes	characteristic
38	C₁₇×#390	C₂²	1	1	yes	characteristic
39	C₁₇×#389	—	2	1	no	—
40	C₁₇×#389	C₂²	1	1	yes	characteristic
41	C₁₇×#389	C₂²	1	1	yes	characteristic
42	C₁₇×#387	—	2	1	no	—
43	C₁₇×#387	—	2	1	no	—
44	C₁₇×#385	—	2	1	no	—
45	C₁₇×#385	—	2	1	no	—
46	C₁₇×#384	C₂²	1	1	yes	characteristic
47	C₁₇×#382	C₂²	1	1	yes	characteristic
48	C₄×C₄⋊C₄×C₁₇	—	2	1	no	—
49	C₄×C₄⋊C₄×C₁₇	C₂²	1	1	yes	characteristic
50	C₄×C₄⋊C₄×C₁₇	C₂²	1	1	yes	characteristic
51	C₄×C₄⋊C₄×C₁₇	C₂²	1	1	yes	characteristic
52	C₄×C₄⋊C₄×C₁₇	C₂²	1	1	yes	characteristic
53	C₁₇×#340	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×#340	C₂²	1	1	yes	characteristic
59	C₁₇×#336	C₂²	1	1	yes	characteristic
60	C₁₇×#336	C₂²	1	1	yes	characteristic
61	C₂²×D₄×C₁₇	C₂³	1	1	yes	characteristic
62	C₂³×C₄×C₁₇	—	2	1	no	—
63	C₂²×C₈×C₁₇	C₂³	1	1	yes	characteristic
64	C₂²×C₈×C₁₇	C₂³	1	1	yes	characteristic
65	C₂²×C₈×C₁₇	C₂³	1	1	yes	characteristic
66	C₂²×C₈×C₁₇	C₂³	1	1	yes	characteristic
67	C₁₇×#125	—	2	2	no	—
68	C₁₇×#125	—	2	2	no	—
69	C₁₇×#125	—	2	2	no	—
70	C₁₇×#125	D₄	1	4	yes	—
71	C₄×D₄×C₁₇	—	2	2	no	—
72	C₄×D₄×C₁₇	—	2	2	no	—
73	C₂×C₄⋊C₄×C₁₇	—	2	1	no	—
74	C₂×C₄⋊C₄×C₁₇	—	2	1	no	—
75	C₂×C₄⋊C₄×C₁₇	—	2	1	no	—
76	C₂×C₄⋊C₄×C₁₇	—	2	1	no	—
77	C₂×C₄⋊C₄×C₁₇	—	2	1	no	—
78	C₂×C₄⋊C₄×C₁₇	—	2	1	no	—
79	C₂×C₄⋊C₄×C₁₇	—	2	1	no	—
80	C₂×C₄⋊C₄×C₁₇	—	2	1	no	—
81	C₂×C₄⋊C₄×C₁₇	D₄	1	1	yes	characteristic
82	C₂×C₄⋊C₄×C₁₇	D₄	1	1	yes	characteristic
83	C₂×C₄⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
84	C₂×C₄⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
85	C₂×C₄⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
86	C₂×C₄⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
87	C₂×C₄⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
88	C₂×C₄⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
89	C₂×C₄⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
90	C₂×C₂²⋊C₄×C₁₇	—	2	1	no	—
91	C₂×C₂²⋊C₄×C₁₇	—	2	1	no	—
92	C₂×C₂²⋊C₄×C₁₇	—	2	1	no	—
93	C₂×C₂²⋊C₄×C₁₇	—	2	1	no	—
94	C₂×C₂²⋊C₄×C₁₇	—	2	1	no	—
95	C₂×C₄²×C₁₇	—	2	1	no	—
96	C₂×C₄²×C₁₇	—	2	1	no	—
97	C₂×C₄²×C₁₇	—	2	1	no	—
98	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
99	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
100	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
101	C₁₇×#107	—	2	2	no	—
102	C₁₇×#107	—	2	2	no	—
103	C₁₇×#107	—	2	2	no	—
104	C₁₇×#106	—	2	2	no	—
105	C₁₇×#106	—	2	2	no	—
106	C₁₇×#106	—	2	2	no	—
107	C₁₇×C₄⋊C₈	—	2	2	no	—
108	C₁₇×C₄⋊C₈	—	2	2	no	—
109	C₁₇×C₄⋊C₈	—	2	2	no	—
110	C₁₇×#102	—	2	2	no	—
111	C₁₇×#102	—	2	2	no	—
112	C₁₇×#102	—	2	2	no	—
113	C₁₇×#102	Q₈	1	4	yes	—
114	C₄×C₈×C₁₇	—	2	2	no	—
115	C₁₇×#95	—	2	1	no	—
116	C₁₇×#95	—	2	1	no	—
117	C₁₇×#95	—	2	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	D₄	1	1	yes	characteristic
123	C₁₇×#95	D₄	1	1	yes	characteristic
124	C₂⁴×C₁₇	—	2	1	no	—
125	C₂×D₄×C₁₇	—	2	1	no	—
126	C₂×D₄×C₁₇	—	2	1	no	—
127	C₂×D₄×C₁₇	—	2	1	no	—
128	C₂×D₄×C₁₇	—	2	1	no	—
129	C₂×D₄×C₁₇	—	2	1	no	—
130	C₂×D₄×C₁₇	C₂×Q₈	1	2	yes	—
131	C₂²×C₄×C₁₇	—	2	1	no	—
132	C₂²×C₄×C₁₇	—	2	1	no	—
133	C₂²×C₄×C₁₇	—	2	1	no	—
134	C₂²×C₄×C₁₇	—	2	1	no	—
135	C₂²×C₄×C₁₇	—	2	1	no	—
136	C₂²×C₄×C₁₇	—	2	1	no	—
137	C₂²×C₄×C₁₇	—	2	1	no	—
138	C₂²×C₄×C₁₇	—	4	2	no	—
139	C₂²×C₄×C₁₇	—	8	1	no	—
140	C₂²×C₄×C₁₇	—	8	1	no	—
141	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
142	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
143	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
144	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
145	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
146	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
147	C₂²×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
148	C₂×C₈×C₁₇	—	2	1	no	—
149	C₂×C₈×C₁₇	—	2	1	no	—
150	C₂×C₈×C₁₇	—	2	1	no	—
151	C₂×C₈×C₁₇	—	2	1	no	—
152	C₂×C₈×C₁₇	—	2	1	no	—
153	C₂×C₈×C₁₇	—	2	1	no	—
154	C₂×C₈×C₁₇	—	2	1	no	—
155	C₂×C₈×C₁₇	—	2	1	no	—
156	C₂×C₈×C₁₇	—	2	1	no	—
157	C₂×C₈×C₁₇	—	2	1	no	—
158	C₂×C₈×C₁₇	C₂×Q₈	1	2	yes	—
159	C₂×C₈×C₁₇	#41	1	2	yes	—
160	C₄⋊C₄×C₁₇	—	2	4	no	—
161	C₄⋊C₄×C₁₇	—	2	4	no	—
162	C₄⋊C₄×C₁₇	—	2	2	no	—
163	C₄⋊C₄×C₁₇	—	2	1	no	—
164	C₄⋊C₄×C₁₇	—	2	1	no	—
165	C₄⋊C₄×C₁₇	—	2	1	no	—
166	C₄⋊C₄×C₁₇	—	2	1	no	—
167	C₄⋊C₄×C₁₇	—	2	1	no	—
168	C₄⋊C₄×C₁₇	—	2	1	no	—
169	C₄⋊C₄×C₁₇	—	2	1	no	—
170	C₄⋊C₄×C₁₇	—	2	1	no	—
171	C₄⋊C₄×C₁₇	—	2	1	no	—
172	C₄⋊C₄×C₁₇	—	2	1	no	—
173	C₄⋊C₄×C₁₇	—	2	1	no	—
174	C₄⋊C₄×C₁₇	—	4	1	no	—
175	C₄⋊C₄×C₁₇	—	4	2	no	—
176	C₄⋊C₄×C₁₇	—	4	2	no	—
177	C₄⋊C₄×C₁₇	—	4	2	no	—
178	C₄⋊C₄×C₁₇	—	8	1	no	—
179	C₄⋊C₄×C₁₇	—	8	1	no	—
180	C₄⋊C₄×C₁₇	—	8	1	no	—
181	C₄⋊C₄×C₁₇	C₂×D₄	1	2	yes	—
182	C₄⋊C₄×C₁₇	C₂×D₄	1	2	yes	—
183	C₄⋊C₄×C₁₇	C₂×Q₈	1	2	yes	—
184	C₂²⋊C₄×C₁₇	—	4	2	no	—
185	C₂²⋊C₄×C₁₇	—	4	2	no	—
186	C₂²⋊C₄×C₁₇	—	4	2	no	—
187	C₂²⋊C₄×C₁₇	—	8	1	no	—
188	C₂²⋊C₄×C₁₇	—	8	1	no	—
189	C₄²×C₁₇	—	2	1	no	—
190	C₄²×C₁₇	—	2	1	no	—
191	C₄²×C₁₇	—	2	1	no	—
192	C₄²×C₁₇	—	2	1	no	—
193	C₄²×C₁₇	—	4	2	no	—
194	C₄²×C₁₇	—	8	1	no	—
195	C₄²×C₁₇	—	8	1	no	—
196	C₄²×C₁₇	C₂×D₄	1	2	yes	—
197	C₄²×C₁₇	#41	1	2	yes	—
198	#25458	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
199	C₂³×C₁₇	—	2	2	no	—
200	C₂³×C₁₇	—	4	1	no	—
201	C₂³×C₁₇	—	4	1	no	—
202	C₂³×C₁₇	—	4	1	no	—
203	C₂³×C₁₇	—	4	1	no	—
204	C₂³×C₁₇	—	4	1	no	—
205	C₂³×C₁₇	—	4	1	no	—
206	C₂³×C₁₇	C₂²×D₄	1	1	yes	characteristic
207	D₄×C₁₇	—	2	2	no	—
208	D₄×C₁₇	—	2	2	no	—
209	D₄×C₁₇	—	4	1	no	—
210	D₄×C₁₇	—	4	1	no	—
211	C₂×C₄×C₁₇	—	2	1	no	—
212	C₂×C₄×C₁₇	—	2	1	no	—
213	C₂×C₄×C₁₇	—	2	1	no	—
214	C₂×C₄×C₁₇	—	2	1	no	—
215	C₂×C₄×C₁₇	—	2	1	no	—
216	C₂×C₄×C₁₇	—	2	1	no	—
217	C₂×C₄×C₁₇	—	2	2	no	—
218	C₂×C₄×C₁₇	—	2	2	no	—
219	C₂×C₄×C₁₇	—	2	1	no	—
220	C₂×C₄×C₁₇	—	2	1	no	—
221	C₂×C₄×C₁₇	—	2	1	no	—
222	C₂×C₄×C₁₇	—	2	2	no	—
223	C₂×C₄×C₁₇	—	2	1	no	—
224	C₂×C₄×C₁₇	—	2	1	no	—
225	C₂×C₄×C₁₇	—	2	1	no	—
226	C₂×C₄×C₁₇	—	2	1	no	—
227	C₂×C₄×C₁₇	—	2	1	no	—
228	C₂×C₄×C₁₇	—	2	1	no	—
229	C₂×C₄×C₁₇	—	4	1	no	—
230	C₂×C₄×C₁₇	—	4	1	no	—
231	C₂×C₄×C₁₇	—	4	1	no	—
232	C₂×C₄×C₁₇	—	4	1	no	—
233	C₂×C₄×C₁₇	—	4	1	no	—
234	C₂×C₄×C₁₇	—	4	1	no	—
235	C₂×C₄×C₁₇	—	4	1	no	—
236	C₂×C₄×C₁₇	—	4	1	no	—
237	C₂×C₄×C₁₇	—	4	1	no	—
238	C₂×C₄×C₁₇	—	4	1	no	—
239	C₂×C₄×C₁₇	—	4	1	no	—
240	C₂×C₄×C₁₇	—	4	1	no	—
241	C₂×C₄×C₁₇	—	4	1	no	—
242	C₂×C₄×C₁₇	—	4	1	no	—
243	C₂×C₄×C₁₇	—	4	1	no	—
244	C₂×C₄×C₁₇	—	4	1	no	—
245	C₂×C₄×C₁₇	—	4	1	no	—
246	C₂×C₄×C₁₇	—	4	1	no	—
247	C₂×C₄×C₁₇	—	8	4	no	—
248	C₂×C₄×C₁₇	#121	1	2	yes	—
249	C₂×C₄×C₁₇	#121	1	2	yes	—
250	C₂×C₄×C₁₇	#135	1	2	yes	—
251	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
252	C₂×C₄×C₁₇	C₂²×Q₈	1	1	yes	characteristic
253	C₂×C₄×C₁₇	C₂×#41	1	1	yes	characteristic
254	C₂×C₄×C₁₇	C₂×#41	1	1	yes	characteristic
255	C₂×C₄×C₁₇	2₋¹⁺⁴	1	1	yes	characteristic
256	C₂×C₄×C₁₇	2₋¹⁺⁴	1	1	yes	characteristic
257	C₈×C₁₇	—	2	2	no	—
258	C₈×C₁₇	—	2	2	no	—
259	C₈×C₁₇	—	4	1	no	—
260	C₈×C₁₇	—	4	1	no	—
261	C₂×#499	C₂×C₁₇	1	1	yes	characteristic, complemented
262	C₂×#478	C₂×C₁₇	1	1	yes	characteristic
263	#2566	C₂×C₁₇	1	1	yes	characteristic
264	#2370	C₂×C₁₇	1	1	yes	characteristic, complemented
265	#2085	C₂×C₁₇	1	1	yes	characteristic, complemented
266	#2083	C₂×C₁₇	1	1	yes	characteristic, complemented
267	#2065	C₂×C₁₇	1	1	yes	characteristic
268	#2065	C₂×C₁₇	1	1	yes	characteristic
269	#1989	C₂×C₁₇	1	1	yes	characteristic, complemented
270	#1949	C₂×C₁₇	1	1	yes	characteristic, complemented
271	#1948	C₂×C₁₇	1	1	yes	characteristic, complemented
272	#1939	C₂×C₁₇	1	1	yes	characteristic, complemented
273	#1925	C₂×C₁₇	1	1	yes	characteristic
274	#1925	C₂×C₁₇	1	1	yes	characteristic
275	C₄×#102	C₂×C₁₇	1	1	yes	characteristic
276	C₂²×C₁₇	—	4	2	no	—
277	C₂²×C₁₇	—	4	2	no	—
278	C₂²×C₁₇	—	4	2	no	—
279	C₂²×C₁₇	—	8	1	no	—
280	C₂²×C₁₇	—	8	1	no	—
281	C₂²×C₁₇	—	8	1	no	—
282	C₂²×C₁₇	—	8	1	no	—
283	C₂²×C₁₇	C₂×#121	1	1	yes	characteristic
284	C₂²×C₁₇	#547	1	1	yes	characteristic
285	C₂²×C₁₇	D₄×Q₈	1	1	yes	characteristic
286	C₂²×C₁₇	C₂×#135	1	1	yes	characteristic
287	C₂²×C₁₇	#575	1	1	yes	characteristic
288	C₂²×C₁₇	#576	1	1	yes	characteristic
289	C₂²×C₁₇	#577	1	1	yes	characteristic
290	C₄×C₁₇	—	2	2	no	—
291	C₄×C₁₇	—	2	2	no	—
292	C₄×C₁₇	—	2	2	no	—
293	C₄×C₁₇	—	4	1	no	—
294	C₄×C₁₇	—	4	1	no	—
295	C₄×C₁₇	—	4	1	no	—
296	C₄×C₁₇	—	4	2	no	—
297	C₄×C₁₇	—	4	2	no	—
298	C₄×C₁₇	—	4	2	no	—
299	C₄×C₁₇	—	8	1	no	—
300	C₄×C₁₇	—	8	1	no	—
301	C₄×C₁₇	—	8	1	no	—
302	C₄×C₁₇	—	8	1	no	—
303	C₄×C₁₇	#533	1	1	yes	characteristic
304	C₄×C₁₇	#541	1	1	yes	characteristic
305	C₄×C₁₇	#548	1	1	yes	characteristic
306	C₄×C₁₇	D₄×Q₈	1	1	yes	characteristic
307	C₂×#125	C₂²×C₁₇	1	1	yes	characteristic
308	C₂×#125	C₂²×C₁₇	1	1	yes	characteristic
309	C₂×C₄×D₄	C₂²×C₁₇	1	1	yes	characteristic
310	#499	—	2	4	no	—
311	#478	—	2	4	no	—
312	C₂×#107	C₂²×C₁₇	1	1	yes	characteristic
313	C₂×#107	C₂²×C₁₇	1	1	yes	characteristic
314	C₂×#107	C₂²×C₁₇	1	1	yes	characteristic
315	C₂×#106	C₂²×C₁₇	1	1	yes	characteristic
316	C₂×#106	C₂²×C₁₇	1	1	yes	characteristic
317	C₂×#106	C₂²×C₁₇	1	1	yes	characteristic
318	C₂×C₄⋊C₈	C₂²×C₁₇	1	1	yes	characteristic
319	C₂×C₄⋊C₈	C₂²×C₁₇	1	1	yes	characteristic
320	C₂×C₄⋊C₈	C₂²×C₁₇	1	1	yes	characteristic
321	C₂×#102	C₂²×C₁₇	1	1	yes	characteristic
322	C₂×#102	C₂²×C₁₇	1	1	yes	characteristic
323	C₂×#102	C₂²×C₁₇	1	1	yes	characteristic
324	C₂×#102	C₂²×C₁₇	1	1	yes	characteristic
325	C₂×C₄×C₈	C₂²×C₁₇	1	1	yes	characteristic
326	#396	—	2	1	no	—
327	#396	—	2	1	no	—
328	#390	C₂²×C₁₇	1	1	yes	characteristic
329	#390	C₂²×C₁₇	1	1	yes	characteristic
330	#389	—	2	1	no	—
331	#389	C₂²×C₁₇	1	1	yes	characteristic
332	#389	C₂²×C₁₇	1	1	yes	characteristic
333	#387	—	2	1	no	—
334	#387	—	2	1	no	—
335	#385	—	2	1	no	—
336	#385	—	2	1	no	—
337	#384	C₂²×C₁₇	1	1	yes	characteristic
338	#382	C₂²×C₁₇	1	1	yes	characteristic
339	C₄×C₄⋊C₄	—	2	1	no	—
340	C₄×C₄⋊C₄	C₂²×C₁₇	1	1	yes	characteristic
341	C₄×C₄⋊C₄	C₂²×C₁₇	1	1	yes	characteristic
342	C₄×C₄⋊C₄	C₂²×C₁₇	1	1	yes	characteristic
343	C₄×C₄⋊C₄	C₂²×C₁₇	1	1	yes	characteristic
344	#340	C₂²×C₁₇	1	1	yes	characteristic
345	#340	C₂²×C₁₇	1	1	yes	characteristic
346	#340	C₂²×C₁₇	1	1	yes	characteristic
347	#340	C₂²×C₁₇	1	1	yes	characteristic
348	#340	C₂²×C₁₇	1	1	yes	characteristic
349	#340	C₂²×C₁₇	1	1	yes	characteristic
350	#336	C₂²×C₁₇	1	1	yes	characteristic
351	#336	C₂²×C₁₇	1	1	yes	characteristic
352	C₂×C₁₇	—	8	2	no	—
353	C₂×C₁₇	#2429	1	1	yes	characteristic
354	C₂×C₁₇	#3035	1	1	yes	characteristic
355	C₂×C₁₇	#3045	1	1	yes	characteristic
356	C₂×C₁₇	#3337	1	1	yes	characteristic
357	C₂×C₁₇	#3355	1	1	yes	characteristic
358	C₂×C₁₇	#3380	1	1	yes	characteristic
359	C₂×C₁₇	#3388	1	1	yes	characteristic
360	C₂²×D₄	C₂³×C₁₇	1	1	yes	characteristic
361	C₂³×C₄	—	2	1	no	—
362	C₂²×C₈	C₂³×C₁₇	1	1	yes	characteristic
363	C₂²×C₈	C₂³×C₁₇	1	1	yes	characteristic
364	C₂²×C₈	C₂³×C₁₇	1	1	yes	characteristic
365	C₂²×C₈	C₂³×C₁₇	1	1	yes	characteristic
366	#125	—	2	2	no	—
367	#125	—	2	2	no	—
368	#125	—	2	2	no	—
369	#125	D₄×C₁₇	1	4	yes	—
370	C₄×D₄	—	2	2	no	—
371	C₄×D₄	—	2	2	no	—
372	C₂×C₄⋊C₄	—	2	1	no	—
373	C₂×C₄⋊C₄	—	2	1	no	—
374	C₂×C₄⋊C₄	—	2	1	no	—
375	C₂×C₄⋊C₄	—	2	1	no	—
376	C₂×C₄⋊C₄	—	2	1	no	—
377	C₂×C₄⋊C₄	—	2	1	no	—
378	C₂×C₄⋊C₄	—	2	1	no	—
379	C₂×C₄⋊C₄	—	2	1	no	—
380	C₂×C₄⋊C₄	D₄×C₁₇	1	1	yes	characteristic
381	C₂×C₄⋊C₄	D₄×C₁₇	1	1	yes	characteristic
382	C₂×C₄⋊C₄	C₂³×C₁₇	1	1	yes	characteristic
383	C₂×C₄⋊C₄	C₂³×C₁₇	1	1	yes	characteristic
384	C₂×C₄⋊C₄	C₂³×C₁₇	1	1	yes	characteristic
385	C₂×C₄⋊C₄	C₂³×C₁₇	1	1	yes	characteristic
386	C₂×C₄⋊C₄	C₂³×C₁₇	1	1	yes	characteristic
387	C₂×C₄⋊C₄	C₂³×C₁₇	1	1	yes	characteristic
388	C₂×C₄⋊C₄	C₂³×C₁₇	1	1	yes	characteristic
389	C₂×C₂²⋊C₄	—	2	1	no	—
390	C₂×C₂²⋊C₄	—	2	1	no	—
391	C₂×C₂²⋊C₄	—	2	1	no	—
392	C₂×C₂²⋊C₄	—	2	1	no	—
393	C₂×C₂²⋊C₄	—	2	1	no	—
394	C₂×C₄²	—	2	1	no	—
395	C₂×C₄²	—	2	1	no	—
396	C₂×C₄²	—	2	1	no	—
397	C₂×C₄²	C₂³×C₁₇	1	1	yes	characteristic
398	C₂×C₄²	C₂³×C₁₇	1	1	yes	characteristic
399	C₂×C₄²	C₂³×C₁₇	1	1	yes	characteristic
400	#107	—	2	2	no	—
401	#107	—	2	2	no	—
402	#107	—	2	2	no	—
403	#106	—	2	2	no	—
404	#106	—	2	2	no	—
405	#106	—	2	2	no	—
406	C₄⋊C₈	—	2	2	no	—
407	C₄⋊C₈	—	2	2	no	—
408	C₄⋊C₈	—	2	2	no	—
409	#102	—	2	2	no	—
410	#102	—	2	2	no	—
411	#102	—	2	2	no	—
412	#102	Q₈×C₁₇	1	4	yes	—
413	C₄×C₈	—	2	2	no	—
414	#95	—	2	1	no	—
415	#95	—	2	1	no	—
416	#95	—	2	1	no	—
417	#95	—	2	1	no	—
418	#95	—	2	1	no	—
419	#95	—	2	1	no	—
420	#95	—	2	1	no	—
421	#95	D₄×C₁₇	1	1	yes	characteristic
422	#95	D₄×C₁₇	1	1	yes	characteristic
423	C₁₇	#25458	1	1	yes	characteristic, direct product factor, Sylow
424	C₂⁴	—	2	1	no	—
425	C₂×D₄	—	2	1	no	—
426	C₂×D₄	—	2	1	no	—
427	C₂×D₄	—	2	1	no	—
428	C₂×D₄	—	2	1	no	—
429	C₂×D₄	—	2	1	no	—
430	C₂×D₄	C₂×Q₈×C₁₇	1	2	yes	—
431	C₂²×C₄	—	2	1	no	—
432	C₂²×C₄	—	2	1	no	—
433	C₂²×C₄	—	2	1	no	—
434	C₂²×C₄	—	2	1	no	—
435	C₂²×C₄	—	2	1	no	—
436	C₂²×C₄	—	2	1	no	—
437	C₂²×C₄	—	2	1	no	—
438	C₂²×C₄	—	4	2	no	—
439	C₂²×C₄	—	8	1	no	—
440	C₂²×C₄	—	8	1	no	—
441	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
442	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
443	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
444	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
445	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
446	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
447	C₂²×C₄	C₂⁴×C₁₇	1	1	yes	characteristic
448	C₂×C₈	—	2	1	no	—
449	C₂×C₈	—	2	1	no	—
450	C₂×C₈	—	2	1	no	—
451	C₂×C₈	—	2	1	no	—
452	C₂×C₈	—	2	1	no	—
453	C₂×C₈	—	2	1	no	—
454	C₂×C₈	—	2	1	no	—
455	C₂×C₈	—	2	1	no	—
456	C₂×C₈	—	2	1	no	—
457	C₂×C₈	—	2	1	no	—
458	C₂×C₈	C₂×Q₈×C₁₇	1	2	yes	—
459	C₂×C₈	#41×C₁₇	1	2	yes	—
460	C₄⋊C₄	—	2	2	no	—
461	C₄⋊C₄	—	2	1	no	—
462	C₄⋊C₄	—	2	1	no	—
463	C₄⋊C₄	—	2	1	no	—
464	C₄⋊C₄	—	2	4	no	—
465	C₄⋊C₄	—	2	4	no	—
466	C₄⋊C₄	—	2	1	no	—
467	C₄⋊C₄	—	2	1	no	—
468	C₄⋊C₄	—	2	1	no	—
469	C₄⋊C₄	—	2	1	no	—
470	C₄⋊C₄	—	2	1	no	—
471	C₄⋊C₄	—	2	1	no	—
472	C₄⋊C₄	—	2	1	no	—
473	C₄⋊C₄	—	2	1	no	—
474	C₄⋊C₄	—	4	1	no	—
475	C₄⋊C₄	—	4	2	no	—
476	C₄⋊C₄	—	4	2	no	—
477	C₄⋊C₄	—	4	2	no	—
478	C₄⋊C₄	—	8	1	no	—
479	C₄⋊C₄	—	8	1	no	—
480	C₄⋊C₄	—	8	1	no	—
481	C₄⋊C₄	C₂×D₄×C₁₇	1	2	yes	—
482	C₄⋊C₄	C₂×D₄×C₁₇	1	2	yes	—
483	C₄⋊C₄	C₂×Q₈×C₁₇	1	2	yes	—
484	C₂²⋊C₄	—	4	2	no	—
485	C₂²⋊C₄	—	4	2	no	—
486	C₂²⋊C₄	—	4	2	no	—
487	C₂²⋊C₄	—	8	1	no	—
488	C₂²⋊C₄	—	8	1	no	—
489	C₄²	—	2	1	no	—
490	C₄²	—	2	1	no	—
491	C₄²	—	2	1	no	—
492	C₄²	—	2	1	no	—
493	C₄²	—	4	2	no	—
494	C₄²	—	8	1	no	—
495	C₄²	—	8	1	no	—
496	C₄²	C₂×D₄×C₁₇	1	2	yes	—
497	C₄²	#41×C₁₇	1	2	yes	—
498	C₂³	—	2	2	no	—
499	C₂³	—	4	1	no	—
500	C₂³	—	4	1	no	—
501	C₂³	—	4	1	no	—
502	C₂³	—	4	1	no	—
503	C₂³	—	4	1	no	—
504	C₂³	—	4	1	no	—
505	C₂³	C₂²×D₄×C₁₇	1	1	yes	characteristic
506	D₄	—	2	2	no	—
507	D₄	—	2	2	no	—
508	D₄	—	4	1	no	—
509	D₄	—	4	1	no	—
510	C₂×C₄	—	2	1	no	—
511	C₂×C₄	—	2	1	no	—
512	C₂×C₄	—	2	1	no	—
513	C₂×C₄	—	2	1	no	—
514	C₂×C₄	—	2	1	no	—
515	C₂×C₄	—	2	1	no	—
516	C₂×C₄	—	2	2	no	—
517	C₂×C₄	—	2	2	no	—
518	C₂×C₄	—	2	1	no	—
519	C₂×C₄	—	2	1	no	—
520	C₂×C₄	—	2	1	no	—
521	C₂×C₄	—	2	2	no	—
522	C₂×C₄	—	2	1	no	—
523	C₂×C₄	—	2	1	no	—
524	C₂×C₄	—	2	1	no	—
525	C₂×C₄	—	2	1	no	—
526	C₂×C₄	—	2	1	no	—
527	C₂×C₄	—	2	1	no	—
528	C₂×C₄	—	4	1	no	—
529	C₂×C₄	—	4	1	no	—
530	C₂×C₄	—	4	1	no	—
531	C₂×C₄	—	4	1	no	—
532	C₂×C₄	—	4	1	no	—
533	C₂×C₄	—	4	1	no	—
534	C₂×C₄	—	4	1	no	—
535	C₂×C₄	—	4	1	no	—
536	C₂×C₄	—	4	1	no	—
537	C₂×C₄	—	4	1	no	—
538	C₂×C₄	—	4	1	no	—
539	C₂×C₄	—	4	1	no	—
540	C₂×C₄	—	4	1	no	—
541	C₂×C₄	—	4	1	no	—
542	C₂×C₄	—	4	1	no	—
543	C₂×C₄	—	4	1	no	—
544	C₂×C₄	—	4	1	no	—
545	C₂×C₄	—	4	1	no	—
546	C₂×C₄	—	8	4	no	—
547	C₂×C₄	C₁₇×#121	1	2	yes	—
548	C₂×C₄	C₁₇×#121	1	2	yes	—
549	C₂×C₄	C₁₇×#135	1	2	yes	—
550	C₂×C₄	C₂²×D₄×C₁₇	1	1	yes	characteristic
551	C₂×C₄	C₂²×Q₈×C₁₇	1	1	yes	characteristic
552	C₂×C₄	C₂×#41×C₁₇	1	1	yes	characteristic
553	C₂×C₄	C₂×#41×C₁₇	1	1	yes	characteristic
554	C₂×C₄	C₁₇×2₋¹⁺⁴	1	1	yes	characteristic
555	C₂×C₄	C₁₇×2₋¹⁺⁴	1	1	yes	characteristic
556	C₈	—	2	2	no	—
557	C₈	—	2	2	no	—
558	C₈	—	4	1	no	—
559	C₈	—	4	1	no	—
560	C₂²	—	4	2	no	—
561	C₂²	—	4	2	no	—
562	C₂²	—	4	2	no	—
563	C₂²	—	8	1	no	—
564	C₂²	—	8	1	no	—
565	C₂²	—	8	1	no	—
566	C₂²	—	8	1	no	—
567	C₂²	C₂×C₁₇×#121	1	1	yes	characteristic
568	C₂²	C₁₇×#547	1	1	yes	characteristic
569	C₂²	D₄×Q₈×C₁₇	1	1	yes	characteristic
570	C₂²	C₂×C₁₇×#135	1	1	yes	characteristic
571	C₂²	C₁₇×#575	1	1	yes	characteristic
572	C₂²	C₁₇×#576	1	1	yes	characteristic
573	C₂²	C₁₇×#577	1	1	yes	characteristic
574	C₄	—	2	2	no	—
575	C₄	—	2	2	no	—
576	C₄	—	2	2	no	—
577	C₄	—	4	2	no	—
578	C₄	—	4	2	no	—
579	C₄	—	4	1	no	—
580	C₄	—	4	1	no	—
581	C₄	—	4	1	no	—
582	C₄	—	4	2	no	—
583	C₄	—	8	1	no	—
584	C₄	—	8	1	no	—
585	C₄	—	8	1	no	—
586	C₄	—	8	1	no	—
587	C₄	C₁₇×#533	1	1	yes	characteristic
588	C₄	C₁₇×#541	1	1	yes	characteristic
589	C₄	C₁₇×#548	1	1	yes	characteristic
590	C₄	D₄×Q₈×C₁₇	1	1	yes	characteristic
591	C₂	—	8	2	no	—
592	C₂	C₁₇×#2429	1	1	yes	characteristic
593	C₂	C₁₇×#3035	1	1	yes	characteristic
594	C₂	C₁₇×#3045	1	1	yes	characteristic
595	C₂	C₁₇×#3337	1	1	yes	characteristic
596	C₂	C₁₇×#3355	1	1	yes	characteristic
597	C₂	C₁₇×#3380	1	1	yes	characteristic
598	C₂	C₁₇×#3388	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₇×#499	C₂	semidirect
4. C₁₇×#2370	C₂	semidirect
5. C₁₇×#2085	C₂	semidirect
6. C₁₇×#2083	C₂	semidirect
9. C₁₇×#1989	C₂	semidirect
10. C₁₇×#1949	C₂	semidirect
11. C₁₇×#1948	C₂	semidirect
12. C₁₇×#1939	C₂	semidirect
198. #25458	C₁₇	direct (N × H)
261. C₂×#499	C₂×C₁₇	semidirect
264. #2370	C₂×C₁₇	semidirect
265. #2085	C₂×C₁₇	semidirect
266. #2083	C₂×C₁₇	semidirect
269. #1989	C₂×C₁₇	semidirect
270. #1949	C₂×C₁₇	semidirect
271. #1948	C₂×C₁₇	semidirect
272. #1939	C₂×C₁₇	semidirect
423. C₁₇	#25458	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×#499	2
C₂×C₁₇×#478	2
C₁₇×#2566	2
C₁₇×#2370	2
C₁₇×#2085	2
C₁₇×#2083	2
C₁₇×#2065	2
C₁₇×#1989	2
C₁₇×#1949	2
C₁₇×#1948	2
C₁₇×#1939	2
C₁₇×#1925	2
C₄×C₁₇×#102	2
#25458	17

Subgroups — C17×#25458 #16883202

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₇×#25458 #16883202