Subgroups — C₁₇×#25415 #16883159

Order 4352.

970 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₇×#494	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₇×#467	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₇×#467	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄×Q₁₆×C₁₇	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₇×#2429	C₂	1	2	yes	maximal
6	C₁₇×#2043	C₂	1	2	yes	maximal, complemented
7	C₁₇×#2001	C₂	1	2	yes	maximal
8	C₁₇×#1969	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₇×#1942	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₇×#1878	C₂	1	2	yes	maximal, complemented
11	C₈×C₂²⋊C₄×C₁₇	C₂	1	1	yes	maximal, characteristic
12	C₂²×Q₁₆×C₁₇	C₂²	1	1	yes	characteristic
13	C₂²×Q₁₆×C₁₇	C₂²	1	2	yes	—
14	C₂²×Q₁₆×C₁₇	C₂²	1	1	yes	characteristic
15	C₂³×C₈×C₁₇	C₂²	1	1	yes	characteristic
16	C₂×C₁₇×C₄⋊Q₈	C₂²	1	2	yes	—
17	C₂×C₁₇×C₂²⋊Q₈	C₂²	1	2	yes	—
18	C₂×C₁₇×C₂²⋊Q₈	C₂²	1	2	yes	—
19	C₂×C₄×Q₈×C₁₇	C₂²	1	2	yes	—
20	C₁₇×#494	—	2	4	no	—
21	C₁₇×#467	—	2	4	no	—
22	C₁₇×#467	—	2	4	no	—
23	C₄×Q₁₆×C₁₇	—	2	4	no	—
24	C₂×C₁₇×#107	C₂²	1	1	yes	characteristic
25	C₂×C₁₇×#107	C₂²	1	1	yes	characteristic
26	C₂×C₁₇×#103	C₂²	1	2	yes	—
27	C₂×C₁₇×#103	C₂²	1	2	yes	—
28	C₂×C₁₇×#103	C₂²	1	2	yes	—
29	C₂×C₁₇×#103	C₂²	1	2	yes	—
30	C₂×C₁₇×C₂²⋊C₈	C₂²	1	1	yes	characteristic
31	C₂×C₄×C₈×C₁₇	C₂²	1	1	yes	characteristic
32	C₂×C₄×C₈×C₁₇	C₂²	1	1	yes	characteristic
33	C₁₇×#398	—	2	2	no	—
34	C₁₇×#396	—	2	2	no	—
35	C₁₇×#391	C₂²	1	2	yes	—
36	C₁₇×#389	—	2	2	no	—
37	C₁₇×#389	C₂²	1	2	yes	—
38	C₁₇×#388	—	2	2	no	—
39	C₄×C₂²⋊C₄×C₁₇	C₂²	1	1	yes	characteristic
40	C₁₇×#340	C₂²	1	2	yes	—
41	C₁₇×#336	C₂²	1	1	yes	characteristic
42	C₁₇×#336	C₂²	1	1	yes	characteristic
43	C₂²×Q₈×C₁₇	C₂³	1	2	yes	—
44	C₂²×Q₈×C₁₇	C₂³	1	2	yes	—
45	C₂³×C₄×C₁₇	C₂³	1	1	yes	characteristic
46	C₂×Q₁₆×C₁₇	—	2	4	no	—
47	C₂×Q₁₆×C₁₇	—	2	2	no	—
48	C₂×Q₁₆×C₁₇	—	2	2	no	—
49	C₂×Q₁₆×C₁₇	—	2	2	no	—
50	C₂×Q₁₆×C₁₇	—	2	2	no	—
51	C₂×Q₁₆×C₁₇	—	2	4	no	—
52	C₂×Q₁₆×C₁₇	—	2	2	no	—
53	C₂×Q₁₆×C₁₇	—	4	2	no	—
54	C₂×Q₁₆×C₁₇	D₄	1	4	yes	—
55	C₂²×C₈×C₁₇	—	2	2	no	—
56	C₂²×C₈×C₁₇	—	2	2	no	—
57	C₂²×C₈×C₁₇	—	2	2	no	—
58	C₂²×C₈×C₁₇	C₂³	1	1	yes	characteristic
59	C₂²×C₈×C₁₇	C₂³	1	1	yes	characteristic
60	C₂²×C₈×C₁₇	C₂³	1	1	yes	characteristic
61	C₂²×C₈×C₁₇	C₂³	1	1	yes	characteristic
62	C₁₇×C₄⋊Q₈	—	2	4	no	—
63	C₁₇×C₄⋊Q₈	—	4	2	no	—
64	C₁₇×C₂²⋊Q₈	—	2	4	no	—
65	C₁₇×C₂²⋊Q₈	—	2	4	no	—
66	C₁₇×C₂²⋊Q₈	—	4	2	no	—
67	C₁₇×C₂²⋊Q₈	—	4	2	no	—
68	C₄×Q₈×C₁₇	—	2	4	no	—
69	C₄×Q₈×C₁₇	—	4	2	no	—
70	C₂×C₄⋊C₄×C₁₇	—	2	2	no	—
71	C₂×C₄⋊C₄×C₁₇	—	2	2	no	—
72	C₂×C₄⋊C₄×C₁₇	—	2	2	no	—
73	C₂×C₄⋊C₄×C₁₇	—	2	2	no	—
74	C₂×C₄⋊C₄×C₁₇	—	2	2	no	—
75	C₂×C₄⋊C₄×C₁₇	—	2	2	no	—
76	C₂×C₄⋊C₄×C₁₇	C₂³	1	2	yes	—
77	C₂×C₄⋊C₄×C₁₇	C₂³	1	2	yes	—
78	C₂×C₂²⋊C₄×C₁₇	—	2	2	no	—
79	C₂×C₂²⋊C₄×C₁₇	—	2	2	no	—
80	C₂×C₂²⋊C₄×C₁₇	D₄	1	1	yes	characteristic
81	C₂×C₂²⋊C₄×C₁₇	D₄	1	1	yes	characteristic
82	C₂×C₄²×C₁₇	—	2	2	no	—
83	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
84	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
85	C₁₇×#107	—	2	2	no	—
86	C₁₇×#107	D₄	1	4	yes	—
87	C₁₇×#103	—	2	4	no	—
88	C₁₇×#103	—	2	4	no	—
89	C₁₇×#103	—	2	4	no	—
90	C₁₇×#103	—	4	2	no	—
91	C₁₇×C₂²⋊C₈	—	2	2	no	—
92	C₄×C₈×C₁₇	—	2	2	no	—
93	C₄×C₈×C₁₇	—	2	2	no	—
94	C₁₇×#95	—	2	2	no	—
95	C₁₇×#95	—	2	2	no	—
96	C₁₇×#95	—	2	2	no	—
97	C₁₇×#95	D₄	1	1	yes	characteristic
98	C₁₇×#95	D₄	1	1	yes	characteristic
99	C₂⁴×C₁₇	C₂×D₄	1	1	yes	characteristic
100	C₂×Q₈×C₁₇	—	2	2	no	—
101	C₂×Q₈×C₁₇	—	2	2	no	—
102	C₂×Q₈×C₁₇	—	2	2	no	—
103	C₂×Q₈×C₁₇	—	2	2	no	—
104	C₂×Q₈×C₁₇	—	2	2	no	—
105	C₂×Q₈×C₁₇	—	2	2	no	—
106	C₂×Q₈×C₁₇	—	2	2	no	—
107	C₂×Q₈×C₁₇	—	2	2	no	—
108	C₂×Q₈×C₁₇	—	2	2	no	—
109	C₂×Q₈×C₁₇	—	2	2	no	—
110	C₂×Q₈×C₁₇	—	2	2	no	—
111	C₂×Q₈×C₁₇	C₂×D₄	1	4	yes	—
112	C₂²×C₄×C₁₇	—	2	2	no	—
113	C₂²×C₄×C₁₇	—	2	2	no	—
114	C₂²×C₄×C₁₇	—	2	1	no	—
115	C₂²×C₄×C₁₇	—	2	1	no	—
116	C₂²×C₄×C₁₇	—	2	1	no	—
117	C₂²×C₄×C₁₇	—	2	1	no	—
118	C₂²×C₄×C₁₇	—	2	1	no	—
119	C₂²×C₄×C₁₇	—	2	1	no	—
120	C₂²×C₄×C₁₇	—	2	2	no	—
121	C₂²×C₄×C₁₇	—	2	2	no	—
122	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
123	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
124	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
125	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
126	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
127	C₂²×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
128	Q₁₆×C₁₇	—	2	8	no	—
129	Q₁₆×C₁₇	—	4	8	no	—
130	Q₁₆×C₁₇	—	4	4	no	—
131	C₂×C₈×C₁₇	—	2	1	no	—
132	C₂×C₈×C₁₇	—	2	1	no	—
133	C₂×C₈×C₁₇	—	2	1	no	—
134	C₂×C₈×C₁₇	—	2	1	no	—
135	C₂×C₈×C₁₇	—	2	1	no	—
136	C₂×C₈×C₁₇	—	2	1	no	—
137	C₂×C₈×C₁₇	—	2	1	no	—
138	C₂×C₈×C₁₇	—	2	1	no	—
139	C₂×C₈×C₁₇	—	4	4	no	—
140	C₂×C₈×C₁₇	C₂×D₄	1	2	yes	—
141	C₂×C₈×C₁₇	C₂×D₄	1	2	yes	—
142	C₂×C₈×C₁₇	#41	1	2	yes	—
143	C₂×C₈×C₁₇	#41	1	2	yes	—
144	C₄⋊C₄×C₁₇	—	2	2	no	—
145	C₄⋊C₄×C₁₇	—	2	2	no	—
146	C₄⋊C₄×C₁₇	—	2	2	no	—
147	C₄⋊C₄×C₁₇	—	4	4	no	—
148	C₄⋊C₄×C₁₇	—	4	4	no	—
149	C₄⋊C₄×C₁₇	—	4	4	no	—
150	C₄⋊C₄×C₁₇	—	4	4	no	—
151	C₄⋊C₄×C₁₇	—	4	4	no	—
152	C₄⋊C₄×C₁₇	—	4	4	no	—
153	C₄⋊C₄×C₁₇	C₂×D₄	1	4	yes	—
154	C₂²⋊C₄×C₁₇	—	2	2	no	—
155	C₂²⋊C₄×C₁₇	—	4	4	no	—
156	C₂²⋊C₄×C₁₇	—	4	4	no	—
157	C₂²⋊C₄×C₁₇	Q₁₆	1	4	yes	complemented
158	C₄²×C₁₇	—	2	1	no	—
159	C₄²×C₁₇	—	2	1	no	—
160	C₄²×C₁₇	—	2	1	no	—
161	C₄²×C₁₇	—	2	1	no	—
162	C₄²×C₁₇	—	4	4	no	—
163	#25415	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
164	C₂³×C₁₇	—	2	1	no	—
165	C₂³×C₁₇	—	2	1	no	—
166	C₂³×C₁₇	—	2	1	no	—
167	C₂³×C₁₇	—	2	1	no	—
168	C₂³×C₁₇	—	2	1	no	—
169	C₂³×C₁₇	—	2	1	no	—
170	C₂³×C₁₇	C₂×Q₁₆	1	2	yes	—
171	C₂³×C₁₇	C₂²×D₄	1	1	yes	characteristic
172	Q₈×C₁₇	—	2	4	no	—
173	Q₈×C₁₇	—	2	4	no	—
174	Q₈×C₁₇	—	4	2	no	—
175	Q₈×C₁₇	—	4	2	no	—
176	Q₈×C₁₇	—	4	2	no	—
177	Q₈×C₁₇	—	4	2	no	—
178	Q₈×C₁₇	—	4	2	no	—
179	Q₈×C₁₇	—	4	2	no	—
180	C₂×C₄×C₁₇	—	2	1	no	—
181	C₂×C₄×C₁₇	—	2	1	no	—
182	C₂×C₄×C₁₇	—	2	1	no	—
183	C₂×C₄×C₁₇	—	2	1	no	—
184	C₂×C₄×C₁₇	—	2	1	no	—
185	C₂×C₄×C₁₇	—	2	1	no	—
186	C₂×C₄×C₁₇	—	2	1	no	—
187	C₂×C₄×C₁₇	—	2	1	no	—
188	C₂×C₄×C₁₇	—	2	4	no	—
189	C₂×C₄×C₁₇	—	2	4	no	—
190	C₂×C₄×C₁₇	—	2	1	no	—
191	C₂×C₄×C₁₇	—	2	1	no	—
192	C₂×C₄×C₁₇	—	2	1	no	—
193	C₂×C₄×C₁₇	—	2	1	no	—
194	C₂×C₄×C₁₇	—	4	2	no	—
195	C₂×C₄×C₁₇	—	4	2	no	—
196	C₂×C₄×C₁₇	—	4	2	no	—
197	C₂×C₄×C₁₇	—	4	2	no	—
198	C₂×C₄×C₁₇	—	4	1	no	—
199	C₂×C₄×C₁₇	—	4	1	no	—
200	C₂×C₄×C₁₇	—	4	1	no	—
201	C₂×C₄×C₁₇	—	4	1	no	—
202	C₂×C₄×C₁₇	—	4	2	no	—
203	C₂×C₄×C₁₇	—	4	2	no	—
204	C₂×C₄×C₁₇	—	4	2	no	—
205	C₂×C₄×C₁₇	—	4	2	no	—
206	C₂×C₄×C₁₇	—	4	2	no	—
207	C₂×C₄×C₁₇	—	4	2	no	—
208	C₂×C₄×C₁₇	C₂×Q₁₆	1	2	yes	—
209	C₂×C₄×C₁₇	C₂×Q₁₆	1	2	yes	—
210	C₂×C₄×C₁₇	#135	1	2	yes	—
211	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
212	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
213	C₂×C₄×C₁₇	C₂×#41	1	1	yes	characteristic
214	C₂×C₄×C₁₇	C₂×#41	1	1	yes	characteristic
215	C₂×C₄×C₁₇	H(5,𝔽₂)	1	1	yes	characteristic
216	C₂×C₄×C₁₇	H(5,𝔽₂)	1	1	yes	characteristic
217	C₈×C₁₇	—	2	2	no	—
218	C₈×C₁₇	—	4	1	no	—
219	C₈×C₁₇	—	4	1	no	—
220	C₈×C₁₇	#121	1	4	yes	—
221	C₂×#494	C₂×C₁₇	1	1	yes	characteristic, complemented
222	C₂×#467	C₂×C₁₇	1	1	yes	characteristic
223	C₂×#467	C₂×C₁₇	1	1	yes	characteristic
224	C₂×C₄×Q₁₆	C₂×C₁₇	1	1	yes	characteristic, complemented
225	#2429	C₂×C₁₇	1	2	yes	—
226	#2043	C₂×C₁₇	1	2	yes	complemented
227	#2001	C₂×C₁₇	1	2	yes	—
228	#1969	C₂×C₁₇	1	1	yes	characteristic, complemented
229	#1942	C₂×C₁₇	1	1	yes	characteristic, complemented
230	#1878	C₂×C₁₇	1	2	yes	complemented
231	C₈×C₂²⋊C₄	C₂×C₁₇	1	1	yes	characteristic
232	C₂²×C₁₇	—	2	2	no	—
233	C₂²×C₁₇	—	2	2	no	—
234	C₂²×C₁₇	—	2	2	no	—
235	C₂²×C₁₇	—	4	1	no	—
236	C₂²×C₁₇	—	4	1	no	—
237	C₂²×C₁₇	—	4	1	no	—
238	C₂²×C₁₇	—	4	1	no	—
239	C₂²×C₁₇	#532	1	1	yes	characteristic
240	C₂²×C₁₇	D₄²	1	1	yes	characteristic
241	C₂²×C₁₇	D₄²	1	1	yes	characteristic
242	C₂²×C₁₇	C₂²×Q₁₆	1	1	yes	characteristic
243	C₂²×C₁₇	C₂×#135	1	1	yes	characteristic
244	C₂²×C₁₇	#578	1	1	yes	characteristic
245	C₂²×C₁₇	#578	1	1	yes	characteristic
246	C₄×C₁₇	—	2	2	no	—
247	C₄×C₁₇	—	2	2	no	—
248	C₄×C₁₇	—	2	2	no	—
249	C₄×C₁₇	—	4	1	no	—
250	C₄×C₁₇	—	4	4	no	—
251	C₄×C₁₇	—	4	1	no	—
252	C₄×C₁₇	—	4	4	no	—
253	C₄×C₁₇	—	8	2	no	—
254	C₄×C₁₇	—	8	2	no	—
255	C₄×C₁₇	C₂×#121	1	1	yes	characteristic
256	C₄×C₁₇	#540	1	1	yes	characteristic
257	C₄×C₁₇	#546	1	1	yes	characteristic
258	C₄×C₁₇	#550	1	1	yes	characteristic
259	C₂²×Q₁₆	C₂²×C₁₇	1	1	yes	characteristic
260	C₂²×Q₁₆	C₂²×C₁₇	1	2	yes	—
261	C₂²×Q₁₆	C₂²×C₁₇	1	1	yes	characteristic
262	C₂³×C₈	C₂²×C₁₇	1	1	yes	characteristic
263	C₂×C₄⋊Q₈	C₂²×C₁₇	1	2	yes	—
264	C₂×C₂²⋊Q₈	C₂²×C₁₇	1	2	yes	—
265	C₂×C₂²⋊Q₈	C₂²×C₁₇	1	2	yes	—
266	C₂×C₄×Q₈	C₂²×C₁₇	1	2	yes	—
267	#494	—	2	4	no	—
268	#467	—	2	4	no	—
269	#467	—	2	4	no	—
270	C₄×Q₁₆	—	2	4	no	—
271	C₂×#107	C₂²×C₁₇	1	1	yes	characteristic
272	C₂×#107	C₂²×C₁₇	1	1	yes	characteristic
273	C₂×#103	C₂²×C₁₇	1	2	yes	—
274	C₂×#103	C₂²×C₁₇	1	2	yes	—
275	C₂×#103	C₂²×C₁₇	1	2	yes	—
276	C₂×#103	C₂²×C₁₇	1	2	yes	—
277	C₂×C₂²⋊C₈	C₂²×C₁₇	1	1	yes	characteristic
278	C₂×C₄×C₈	C₂²×C₁₇	1	1	yes	characteristic
279	C₂×C₄×C₈	C₂²×C₁₇	1	1	yes	characteristic
280	#398	—	2	2	no	—
281	#396	—	2	2	no	—
282	#391	C₂²×C₁₇	1	2	yes	—
283	#389	—	2	2	no	—
284	#389	C₂²×C₁₇	1	2	yes	—
285	#388	—	2	2	no	—
286	C₄×C₂²⋊C₄	C₂²×C₁₇	1	1	yes	characteristic
287	#340	C₂²×C₁₇	1	2	yes	—
288	#336	C₂²×C₁₇	1	1	yes	characteristic
289	#336	C₂²×C₁₇	1	1	yes	characteristic
290	C₂×C₁₇	—	4	2	no	—
291	C₂×C₁₇	#2428	1	1	yes	characteristic
292	C₂×C₁₇	#3170	1	1	yes	characteristic
293	C₂×C₁₇	#3177	1	1	yes	characteristic
294	C₂×C₁₇	#3283	1	1	yes	characteristic
295	C₂×C₁₇	#3285	1	1	yes	characteristic
296	C₂×C₁₇	D₄×Q₁₆	1	1	yes	characteristic
297	C₂×C₁₇	D₄×Q₁₆	1	1	yes	characteristic
298	C₂²×Q₈	C₂³×C₁₇	1	2	yes	—
299	C₂²×Q₈	C₂³×C₁₇	1	2	yes	—
300	C₂³×C₄	C₂³×C₁₇	1	1	yes	characteristic
301	C₂×Q₁₆	—	2	4	no	—
302	C₂×Q₁₆	—	2	2	no	—
303	C₂×Q₁₆	—	2	2	no	—
304	C₂×Q₁₆	—	2	2	no	—
305	C₂×Q₁₆	—	2	2	no	—
306	C₂×Q₁₆	—	2	4	no	—
307	C₂×Q₁₆	—	2	2	no	—
308	C₂×Q₁₆	—	4	2	no	—
309	C₂×Q₁₆	D₄×C₁₇	1	4	yes	—
310	C₂²×C₈	—	2	2	no	—
311	C₂²×C₈	—	2	2	no	—
312	C₂²×C₈	—	2	2	no	—
313	C₂²×C₈	C₂³×C₁₇	1	1	yes	characteristic
314	C₂²×C₈	C₂³×C₁₇	1	1	yes	characteristic
315	C₂²×C₈	C₂³×C₁₇	1	1	yes	characteristic
316	C₂²×C₈	C₂³×C₁₇	1	1	yes	characteristic
317	C₄⋊Q₈	—	2	4	no	—
318	C₄⋊Q₈	—	4	2	no	—
319	C₂²⋊Q₈	—	2	4	no	—
320	C₂²⋊Q₈	—	2	4	no	—
321	C₂²⋊Q₈	—	4	2	no	—
322	C₂²⋊Q₈	—	4	2	no	—
323	C₄×Q₈	—	2	4	no	—
324	C₄×Q₈	—	4	2	no	—
325	C₂×C₄⋊C₄	—	2	2	no	—
326	C₂×C₄⋊C₄	—	2	2	no	—
327	C₂×C₄⋊C₄	—	2	2	no	—
328	C₂×C₄⋊C₄	—	2	2	no	—
329	C₂×C₄⋊C₄	—	2	2	no	—
330	C₂×C₄⋊C₄	—	2	2	no	—
331	C₂×C₄⋊C₄	C₂³×C₁₇	1	2	yes	—
332	C₂×C₄⋊C₄	C₂³×C₁₇	1	2	yes	—
333	C₂×C₂²⋊C₄	—	2	2	no	—
334	C₂×C₂²⋊C₄	—	2	2	no	—
335	C₂×C₂²⋊C₄	D₄×C₁₇	1	1	yes	characteristic
336	C₂×C₂²⋊C₄	D₄×C₁₇	1	1	yes	characteristic
337	C₂×C₄²	—	2	2	no	—
338	C₂×C₄²	C₂³×C₁₇	1	1	yes	characteristic
339	C₂×C₄²	C₂³×C₁₇	1	1	yes	characteristic
340	#107	—	2	2	no	—
341	#107	D₄×C₁₇	1	4	yes	—
342	#103	—	2	4	no	—
343	#103	—	2	4	no	—
344	#103	—	2	4	no	—
345	#103	—	4	2	no	—
346	C₂²⋊C₈	—	2	2	no	—
347	C₄×C₈	—	2	2	no	—
348	C₄×C₈	—	2	2	no	—
349	#95	—	2	2	no	—
350	#95	—	2	2	no	—
351	#95	—	2	2	no	—
352	#95	D₄×C₁₇	1	1	yes	characteristic
353	#95	D₄×C₁₇	1	1	yes	characteristic
354	C₁₇	#25415	1	1	yes	characteristic, direct product factor, Sylow
355	C₂⁴	C₂×D₄×C₁₇	1	1	yes	characteristic
356	C₂×Q₈	—	2	2	no	—
357	C₂×Q₈	—	2	2	no	—
358	C₂×Q₈	—	2	2	no	—
359	C₂×Q₈	—	2	2	no	—
360	C₂×Q₈	—	2	2	no	—
361	C₂×Q₈	—	2	2	no	—
362	C₂×Q₈	—	2	2	no	—
363	C₂×Q₈	—	2	2	no	—
364	C₂×Q₈	—	2	2	no	—
365	C₂×Q₈	—	2	2	no	—
366	C₂×Q₈	—	2	2	no	—
367	C₂×Q₈	C₂×D₄×C₁₇	1	4	yes	—
368	C₂²×C₄	—	2	2	no	—
369	C₂²×C₄	—	2	2	no	—
370	C₂²×C₄	—	2	1	no	—
371	C₂²×C₄	—	2	1	no	—
372	C₂²×C₄	—	2	1	no	—
373	C₂²×C₄	—	2	1	no	—
374	C₂²×C₄	—	2	1	no	—
375	C₂²×C₄	—	2	1	no	—
376	C₂²×C₄	—	2	2	no	—
377	C₂²×C₄	—	2	2	no	—
378	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
379	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
380	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
381	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
382	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
383	C₂²×C₄	C₂⁴×C₁₇	1	1	yes	characteristic
384	Q₁₆	—	2	8	no	—
385	Q₁₆	—	4	8	no	—
386	Q₁₆	—	4	4	no	—
387	C₂×C₈	—	2	1	no	—
388	C₂×C₈	—	2	1	no	—
389	C₂×C₈	—	2	1	no	—
390	C₂×C₈	—	2	1	no	—
391	C₂×C₈	—	2	1	no	—
392	C₂×C₈	—	2	1	no	—
393	C₂×C₈	—	2	1	no	—
394	C₂×C₈	—	2	1	no	—
395	C₂×C₈	—	4	4	no	—
396	C₂×C₈	C₂×D₄×C₁₇	1	2	yes	—
397	C₂×C₈	C₂×D₄×C₁₇	1	2	yes	—
398	C₂×C₈	#41×C₁₇	1	2	yes	—
399	C₂×C₈	#41×C₁₇	1	2	yes	—
400	C₄⋊C₄	—	2	2	no	—
401	C₄⋊C₄	—	2	2	no	—
402	C₄⋊C₄	—	2	2	no	—
403	C₄⋊C₄	—	4	4	no	—
404	C₄⋊C₄	—	4	4	no	—
405	C₄⋊C₄	—	4	4	no	—
406	C₄⋊C₄	—	4	4	no	—
407	C₄⋊C₄	—	4	4	no	—
408	C₄⋊C₄	—	4	4	no	—
409	C₄⋊C₄	C₂×D₄×C₁₇	1	4	yes	—
410	C₂²⋊C₄	—	2	2	no	—
411	C₂²⋊C₄	—	4	4	no	—
412	C₂²⋊C₄	—	4	4	no	—
413	C₂²⋊C₄	Q₁₆×C₁₇	1	4	yes	complemented
414	C₄²	—	2	1	no	—
415	C₄²	—	2	1	no	—
416	C₄²	—	2	1	no	—
417	C₄²	—	2	1	no	—
418	C₄²	—	4	4	no	—
419	C₂³	—	2	1	no	—
420	C₂³	—	2	1	no	—
421	C₂³	—	2	1	no	—
422	C₂³	—	2	1	no	—
423	C₂³	—	2	1	no	—
424	C₂³	—	2	1	no	—
425	C₂³	C₂×Q₁₆×C₁₇	1	2	yes	—
426	C₂³	C₂²×D₄×C₁₇	1	1	yes	characteristic
427	Q₈	—	2	4	no	—
428	Q₈	—	2	4	no	—
429	Q₈	—	4	2	no	—
430	Q₈	—	4	2	no	—
431	Q₈	—	4	2	no	—
432	Q₈	—	4	2	no	—
433	Q₈	—	4	2	no	—
434	Q₈	—	4	2	no	—
435	C₂×C₄	—	2	1	no	—
436	C₂×C₄	—	2	1	no	—
437	C₂×C₄	—	2	1	no	—
438	C₂×C₄	—	2	1	no	—
439	C₂×C₄	—	2	1	no	—
440	C₂×C₄	—	2	1	no	—
441	C₂×C₄	—	2	1	no	—
442	C₂×C₄	—	2	1	no	—
443	C₂×C₄	—	2	4	no	—
444	C₂×C₄	—	2	4	no	—
445	C₂×C₄	—	2	1	no	—
446	C₂×C₄	—	2	1	no	—
447	C₂×C₄	—	2	1	no	—
448	C₂×C₄	—	2	1	no	—
449	C₂×C₄	—	4	2	no	—
450	C₂×C₄	—	4	2	no	—
451	C₂×C₄	—	4	2	no	—
452	C₂×C₄	—	4	2	no	—
453	C₂×C₄	—	4	1	no	—
454	C₂×C₄	—	4	1	no	—
455	C₂×C₄	—	4	1	no	—
456	C₂×C₄	—	4	1	no	—
457	C₂×C₄	—	4	2	no	—
458	C₂×C₄	—	4	2	no	—
459	C₂×C₄	—	4	2	no	—
460	C₂×C₄	—	4	2	no	—
461	C₂×C₄	—	4	2	no	—
462	C₂×C₄	—	4	2	no	—
463	C₂×C₄	C₂×Q₁₆×C₁₇	1	2	yes	—
464	C₂×C₄	C₂×Q₁₆×C₁₇	1	2	yes	—
465	C₂×C₄	C₁₇×#135	1	2	yes	—
466	C₂×C₄	C₂²×D₄×C₁₇	1	1	yes	characteristic
467	C₂×C₄	C₂²×D₄×C₁₇	1	1	yes	characteristic
468	C₂×C₄	C₂×#41×C₁₇	1	1	yes	characteristic
469	C₂×C₄	C₂×#41×C₁₇	1	1	yes	characteristic
470	C₂×C₄	C₁₇×H(5,𝔽₂)	1	1	yes	characteristic
471	C₂×C₄	C₁₇×H(5,𝔽₂)	1	1	yes	characteristic
472	C₈	—	2	2	no	—
473	C₈	—	4	1	no	—
474	C₈	—	4	1	no	—
475	C₈	C₁₇×#121	1	4	yes	—
476	C₂²	—	2	2	no	—
477	C₂²	—	2	2	no	—
478	C₂²	—	2	2	no	—
479	C₂²	—	4	1	no	—
480	C₂²	—	4	1	no	—
481	C₂²	—	4	1	no	—
482	C₂²	—	4	1	no	—
483	C₂²	C₁₇×#532	1	1	yes	characteristic
484	C₂²	D₄²×C₁₇	1	1	yes	characteristic
485	C₂²	D₄²×C₁₇	1	1	yes	characteristic
486	C₂²	C₂²×Q₁₆×C₁₇	1	1	yes	characteristic
487	C₂²	C₂×C₁₇×#135	1	1	yes	characteristic
488	C₂²	C₁₇×#578	1	1	yes	characteristic
489	C₂²	C₁₇×#578	1	1	yes	characteristic
490	C₄	—	2	2	no	—
491	C₄	—	2	2	no	—
492	C₄	—	2	2	no	—
493	C₄	—	4	1	no	—
494	C₄	—	4	4	no	—
495	C₄	—	4	1	no	—
496	C₄	—	4	4	no	—
497	C₄	—	8	2	no	—
498	C₄	—	8	2	no	—
499	C₄	C₂×C₁₇×#121	1	1	yes	characteristic
500	C₄	C₁₇×#540	1	1	yes	characteristic
501	C₄	C₁₇×#546	1	1	yes	characteristic
502	C₄	C₁₇×#550	1	1	yes	characteristic
503	C₂	—	4	2	no	—
504	C₂	C₁₇×#2428	1	1	yes	characteristic
505	C₂	C₁₇×#3170	1	1	yes	characteristic
506	C₂	C₁₇×#3177	1	1	yes	characteristic
507	C₂	C₁₇×#3283	1	1	yes	characteristic
508	C₂	C₁₇×#3285	1	1	yes	characteristic
509	C₂	D₄×Q₁₆×C₁₇	1	1	yes	characteristic
510	C₂	D₄×Q₁₆×C₁₇	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₇×#494	C₂	semidirect
4. C₂×C₄×Q₁₆×C₁₇	C₂	semidirect
6. C₁₇×#2043	C₂	semidirect
8. C₁₇×#1969	C₂	semidirect
9. C₁₇×#1942	C₂	semidirect
10. C₁₇×#1878	C₂	semidirect
157. C₂²⋊C₄×C₁₇	Q₁₆	semidirect
163. #25415	C₁₇	direct (N × H)
221. C₂×#494	C₂×C₁₇	semidirect
224. C₂×C₄×Q₁₆	C₂×C₁₇	semidirect
226. #2043	C₂×C₁₇	semidirect
228. #1969	C₂×C₁₇	semidirect
229. #1942	C₂×C₁₇	semidirect
230. #1878	C₂×C₁₇	semidirect
354. C₁₇	#25415	direct (N × H)
413. C₂²⋊C₄	Q₁₆×C₁₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₇×#494	2
C₂×C₁₇×#467	2
C₂×C₄×Q₁₆×C₁₇	2
C₁₇×#2429	2
C₁₇×#2043	2
C₁₇×#2001	2
C₁₇×#1969	2
C₁₇×#1942	2
C₁₇×#1878	2
C₈×C₂²⋊C₄×C₁₇	2
#25415	17

Subgroups — C17×#25415 #16883159

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₇×#25415 #16883159