Subgroups — C₁₇×#24456 #16882200

Order 4352.

1410 conjugacy classes of subgroups.

The subgroup lattice has 944 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₇×#576	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₇×#472	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₇×#3045	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₁₇×#453	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₇×#3008	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₇×#2897	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₇×#2051	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₇×#2045	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₇×#2011	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₇×#2002	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₇×#1907	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₇×#1883	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₇×#1876	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₇×#1866	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₇×#1792	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₁₇×H(5,𝔽₂)	C₂²	1	1	yes	characteristic
17	C₂×C₁₇×H(5,𝔽₂)	C₂²	1	1	yes	characteristic
18	C₁₇×#576	—	2	4	no	—
19	C₁₇×#576	—	2	4	no	—
20	C₂×C₁₇×AGL(1,ℤ/8)	—	2	1	no	—
21	C₂×C₁₇×AGL(1,ℤ/8)	—	2	1	no	—
22	C₂×C₁₇×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
23	C₂×C₁₇×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
24	C₂×C₁₇×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
25	C₂×C₁₇×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic, complemented
26	C₂×C₁₇×#135	—	2	1	no	—
27	C₂×C₁₇×#135	C₂²	1	1	yes	characteristic
28	C₂²×D₈×C₁₇	—	2	1	no	—
29	C₂²×D₈×C₁₇	C₂²	1	1	yes	characteristic
30	C₂²×D₈×C₁₇	C₂²	1	1	yes	characteristic, complemented
31	C₂×C₁₇×#131	C₂²	1	1	yes	characteristic
32	C₂×C₁₇×#131	C₂²	1	1	yes	characteristic, complemented
33	C₁₇×#535	C₂²	1	1	yes	characteristic, complemented
34	C₂×C₁₇×#127	C₂²	1	1	yes	characteristic, complemented
35	C₁₇×#520	C₂²	1	1	yes	characteristic, complemented
36	C₁₇×#472	—	2	4	no	—
37	C₁₇×#464	—	2	1	no	—
38	C₁₇×#463	—	2	1	no	—
39	C₁₇×#460	—	2	1	no	—
40	C₁₇×#459	—	2	1	no	—
41	C₁₇×#453	—	2	4	no	—
42	C₁₇×#449	—	2	1	no	—
43	C₁₇×#449	—	2	1	no	—
44	C₁₇×#447	—	2	1	no	—
45	C₁₇×#447	—	2	1	no	—
46	C₂×C₁₇×#108	C₂²	1	1	yes	characteristic, complemented
47	C₁₇×#424	C₂²	1	1	yes	characteristic, complemented
48	C₂×C₁₇×#104	C₂²	1	1	yes	characteristic
49	C₂×C₁₇×#104	C₂²	1	1	yes	characteristic, complemented
50	C₂×C₁₇×#104	C₂²	1	1	yes	characteristic, complemented
51	C₁₇×#418	—	2	1	no	—
52	C₁₇×#418	C₂²	1	1	yes	characteristic, complemented
53	C₁₇×#418	C₂²	1	1	yes	characteristic, complemented
54	C₁₇×#417	—	2	1	no	—
55	C₁₇×#417	C₂²	1	1	yes	characteristic
56	C₁₇×#417	C₂²	1	1	yes	characteristic, complemented
57	C₁₇×#416	—	2	1	no	—
58	C₁₇×#416	C₂²	1	1	yes	characteristic
59	C₂×C₁₇×#102	—	2	1	no	—
60	C₂×C₁₇×#102	C₂²	1	1	yes	characteristic, complemented
61	C₂×C₁₇×#102	C₂²	1	1	yes	characteristic, complemented
62	C₂×C₁₇×#100	C₂²	1	1	yes	characteristic, complemented
63	C₂×C₁₇×#100	C₂²	1	1	yes	characteristic, complemented
64	C₂×C₁₇×#100	C₂²	1	1	yes	characteristic, complemented
65	C₁₇×#408	C₂²	1	1	yes	characteristic, complemented
66	C₁₇×#390	C₂²	1	1	yes	characteristic, complemented
67	C₁₇×#343	C₂²	1	1	yes	characteristic, complemented
68	C₁₇×#341	C₂²	1	1	yes	characteristic, complemented
69	C₁₇×#339	C₂²	1	1	yes	characteristic, complemented
70	C₁₇×#336	C₂²	1	1	yes	characteristic, complemented
71	C₁₇×H(5,𝔽₂)	—	2	2	no	—
72	C₁₇×H(5,𝔽₂)	—	2	2	no	—
73	C₁₇×H(5,𝔽₂)	—	2	2	no	—
74	C₁₇×H(5,𝔽₂)	—	2	2	no	—
75	C₁₇×H(5,𝔽₂)	—	2	2	no	—
76	C₁₇×H(5,𝔽₂)	—	4	1	no	—
77	C₁₇×H(5,𝔽₂)	—	4	1	no	—
78	C₁₇×H(5,𝔽₂)	D₄	1	4	yes	complemented
79	C₂×#41×C₁₇	—	2	1	no	—
80	C₂×#41×C₁₇	—	2	1	no	—
81	C₂×#41×C₁₇	—	2	1	no	—
82	C₂×#41×C₁₇	—	2	1	no	—
83	C₂×#41×C₁₇	C₂³	1	1	yes	characteristic
84	C₂×#41×C₁₇	C₂³	1	1	yes	characteristic
85	C₂×#41×C₁₇	C₂³	1	1	yes	characteristic
86	C₂²×D₄×C₁₇	—	2	1	no	—
87	C₂²×D₄×C₁₇	—	2	1	no	—
88	C₂²×D₄×C₁₇	—	2	1	no	—
89	C₂²×D₄×C₁₇	—	2	1	no	—
90	C₂²×D₄×C₁₇	—	4	1	no	—
91	C₂²×D₄×C₁₇	—	4	1	no	—
92	C₂²×D₄×C₁₇	—	4	1	no	—
93	C₂²×D₄×C₁₇	C₂³	1	1	yes	characteristic
94	C₂²×D₄×C₁₇	C₂³	1	1	yes	characteristic
95	C₂²×D₄×C₁₇	C₂³	1	1	yes	characteristic
96	C₁₇×AGL(1,ℤ/8)	—	2	8	no	—
97	C₁₇×AGL(1,ℤ/8)	—	2	8	no	—
98	C₁₇×AGL(1,ℤ/8)	—	2	2	no	—
99	C₁₇×AGL(1,ℤ/8)	—	2	2	no	—
100	C₁₇×AGL(1,ℤ/8)	—	2	2	no	—
101	C₁₇×AGL(1,ℤ/8)	—	2	2	no	—
102	C₁₇×AGL(1,ℤ/8)	—	2	2	no	—
103	C₁₇×AGL(1,ℤ/8)	—	2	2	no	—
104	C₁₇×AGL(1,ℤ/8)	—	2	2	no	—
105	C₁₇×AGL(1,ℤ/8)	D₄	1	4	yes	complemented
106	C₁₇×#135	—	2	8	no	—
107	C₁₇×#135	—	2	2	no	—
108	C₁₇×#135	—	2	2	no	—
109	C₂×Q₁₆×C₁₇	D₄	1	1	yes	characteristic, complemented
110	C₂×SD₁₆×C₁₇	—	2	1	no	—
111	C₂×SD₁₆×C₁₇	—	2	1	no	—
112	C₂×SD₁₆×C₁₇	—	2	1	no	—
113	C₂×SD₁₆×C₁₇	—	2	1	no	—
114	C₂×SD₁₆×C₁₇	D₄	1	1	yes	characteristic, complemented
115	C₂×SD₁₆×C₁₇	D₄	1	1	yes	characteristic, complemented
116	C₂×D₈×C₁₇	—	2	8	no	—
117	C₂×D₈×C₁₇	—	2	1	no	—
118	C₂×D₈×C₁₇	—	2	1	no	—
119	C₂×D₈×C₁₇	—	2	2	no	—
120	C₂×D₈×C₁₇	—	2	2	no	—
121	C₂×D₈×C₁₇	—	2	2	no	—
122	C₂×D₈×C₁₇	—	2	1	no	—
123	C₂×D₈×C₁₇	—	2	1	no	—
124	C₂×D₈×C₁₇	—	2	1	no	—
125	C₂×D₈×C₁₇	—	2	1	no	—
126	C₂×D₈×C₁₇	—	2	1	no	—
127	C₂×D₈×C₁₇	—	2	1	no	—
128	C₂×D₈×C₁₇	—	4	1	no	—
129	C₂×D₈×C₁₇	D₄	1	1	yes	characteristic, complemented
130	C₁₇×#131	—	2	2	no	—
131	C₁₇×#131	—	2	2	no	—
132	C₁₇×#131	—	2	2	no	—
133	C₁₇×#131	—	4	1	no	—
134	C₂×M₁₆×C₁₇	—	2	1	no	—
135	C₂×M₁₆×C₁₇	—	2	1	no	—
136	C₂×M₁₆×C₁₇	C₂³	1	1	yes	characteristic
137	C₂×M₁₆×C₁₇	C₂³	1	1	yes	characteristic
138	C₂×M₁₆×C₁₇	C₂³	1	1	yes	characteristic
139	C₂×M₁₆×C₁₇	C₂³	1	1	yes	characteristic
140	C₂²×C₈×C₁₇	—	2	1	no	—
141	C₂²×C₈×C₁₇	—	2	1	no	—
142	C₂²×C₈×C₁₇	C₂³	1	1	yes	characteristic
143	C₂²×C₈×C₁₇	C₂³	1	1	yes	characteristic
144	C₁₇×#127	—	2	2	no	—
145	C₁₇×#127	—	2	1	no	—
146	C₁₇×#127	—	4	1	no	—
147	C₁₇×#124	—	2	1	no	—
148	C₁₇×#121	—	2	1	no	—
149	C₁₇×#121	—	2	1	no	—
150	C₁₇×#120	—	4	1	no	—
151	C₄×Q₈×C₁₇	—	2	1	no	—
152	C₄×D₄×C₁₇	—	2	1	no	—
153	C₄×D₄×C₁₇	—	4	1	no	—
154	C₁₇×#117	—	2	1	no	—
155	C₁₇×#117	C₂³	1	1	yes	characteristic
156	C₂×C₄⋊C₄×C₁₇	—	2	1	no	—
157	C₂×C₄⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
158	C₂×C₂²⋊C₄×C₁₇	—	4	1	no	—
159	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
160	C₁₇×#108	—	2	2	no	—
161	C₁₇×C₄⋊C₈	—	2	1	no	—
162	C₁₇×C₄⋊C₈	—	2	1	no	—
163	C₁₇×#104	—	2	2	no	—
164	C₁₇×#104	—	2	2	no	—
165	C₁₇×#104	—	4	1	no	—
166	C₁₇×#103	—	2	1	no	—
167	C₁₇×#103	—	2	1	no	—
168	C₁₇×#103	D₄	1	1	yes	characteristic, complemented
169	C₁₇×#103	D₄	1	1	yes	characteristic, complemented
170	C₁₇×#102	—	2	1	no	—
171	C₁₇×#102	—	2	1	no	—
172	C₁₇×#102	—	2	1	no	—
173	C₁₇×#102	—	2	1	no	—
174	C₁₇×#102	—	2	1	no	—
175	C₁₇×#102	—	2	1	no	—
176	C₁₇×#102	—	2	1	no	—
177	C₁₇×#102	—	2	1	no	—
178	C₁₇×#102	—	2	1	no	—
179	C₁₇×#102	—	2	1	no	—
180	C₁₇×#102	D₄	1	1	yes	characteristic, complemented
181	C₁₇×#102	D₄	1	1	yes	characteristic, complemented
182	C₁₇×#100	—	2	2	no	—
183	C₁₇×#100	—	2	2	no	—
184	C₁₇×#100	—	2	2	no	—
185	C₁₇×C₂²⋊C₈	—	2	1	no	—
186	C₁₇×C₂²⋊C₈	—	2	1	no	—
187	C₂⁴×C₁₇	—	2	1	no	—
188	C₂⁴×C₁₇	—	2	1	no	—
189	C₂⁴×C₁₇	—	2	1	no	—
190	C₂⁴×C₁₇	—	4	1	no	—
191	C₂⁴×C₁₇	—	4	1	no	—
192	#41×C₁₇	—	2	1	no	—
193	#41×C₁₇	—	2	1	no	—
194	#41×C₁₇	—	2	1	no	—
195	#41×C₁₇	—	2	1	no	—
196	#41×C₁₇	—	2	4	no	—
197	#41×C₁₇	—	2	4	no	—
198	#41×C₁₇	—	2	4	no	—
199	#41×C₁₇	—	2	1	no	—
200	#41×C₁₇	—	2	1	no	—
201	#41×C₁₇	—	2	1	no	—
202	#41×C₁₇	—	2	1	no	—
203	#41×C₁₇	—	4	2	no	—
204	#41×C₁₇	—	4	2	no	—
205	#41×C₁₇	—	4	2	no	—
206	#41×C₁₇	—	4	2	no	—
207	#41×C₁₇	—	4	2	no	—
208	#41×C₁₇	C₂×D₄	1	2	yes	—
209	#41×C₁₇	C₂×D₄	1	2	yes	—
210	#41×C₁₇	C₂×D₄	1	2	yes	—
211	#41×C₁₇	#41	1	2	yes	—
212	C₂×Q₈×C₁₇	C₂×D₄	1	1	yes	characteristic
213	C₂×Q₈×C₁₇	C₂×D₄	1	1	yes	characteristic
214	C₂×Q₈×C₁₇	C₂×D₄	1	1	yes	characteristic
215	C₂×D₄×C₁₇	—	2	1	no	—
216	C₂×D₄×C₁₇	—	2	1	no	—
217	C₂×D₄×C₁₇	—	2	4	no	—
218	C₂×D₄×C₁₇	—	2	4	no	—
219	C₂×D₄×C₁₇	—	2	4	no	—
220	C₂×D₄×C₁₇	—	2	1	no	—
221	C₂×D₄×C₁₇	—	2	1	no	—
222	C₂×D₄×C₁₇	—	2	1	no	—
223	C₂×D₄×C₁₇	—	2	1	no	—
224	C₂×D₄×C₁₇	—	2	1	no	—
225	C₂×D₄×C₁₇	—	2	1	no	—
226	C₂×D₄×C₁₇	—	2	1	no	—
227	C₂×D₄×C₁₇	—	2	1	no	—
228	C₂×D₄×C₁₇	—	2	1	no	—
229	C₂×D₄×C₁₇	—	2	1	no	—
230	C₂×D₄×C₁₇	—	2	1	no	—
231	C₂×D₄×C₁₇	—	2	1	no	—
232	C₂×D₄×C₁₇	—	2	1	no	—
233	C₂×D₄×C₁₇	—	2	1	no	—
234	C₂×D₄×C₁₇	—	2	1	no	—
235	C₂×D₄×C₁₇	—	2	1	no	—
236	C₂×D₄×C₁₇	—	2	1	no	—
237	C₂×D₄×C₁₇	—	4	2	no	—
238	C₂×D₄×C₁₇	—	4	2	no	—
239	C₂×D₄×C₁₇	—	4	2	no	—
240	C₂×D₄×C₁₇	—	4	1	no	—
241	C₂×D₄×C₁₇	—	4	1	no	—
242	C₂×D₄×C₁₇	—	4	1	no	—
243	C₂×D₄×C₁₇	—	4	1	no	—
244	C₂×D₄×C₁₇	—	4	1	no	—
245	C₂×D₄×C₁₇	—	4	1	no	—
246	C₂×D₄×C₁₇	—	4	4	no	—
247	C₂×D₄×C₁₇	—	4	2	no	—
248	C₂×D₄×C₁₇	—	4	4	no	—
249	C₂×D₄×C₁₇	—	4	4	no	—
250	C₂×D₄×C₁₇	—	4	4	no	—
251	C₂×D₄×C₁₇	—	4	2	no	—
252	C₂×D₄×C₁₇	—	4	4	no	—
253	C₂×D₄×C₁₇	—	8	2	no	—
254	C₂×D₄×C₁₇	—	8	2	no	—
255	C₂×D₄×C₁₇	C₂×D₄	1	1	yes	characteristic
256	C₂×D₄×C₁₇	C₂×D₄	1	2	yes	—
257	C₂×D₄×C₁₇	C₂×D₄	1	2	yes	—
258	C₂×D₄×C₁₇	C₂×D₄	1	1	yes	characteristic
259	C₂×D₄×C₁₇	C₂×D₄	1	1	yes	characteristic
260	C₂²×C₄×C₁₇	—	2	1	no	—
261	C₂²×C₄×C₁₇	—	2	1	no	—
262	C₂²×C₄×C₁₇	—	2	1	no	—
263	C₂²×C₄×C₁₇	—	2	1	no	—
264	C₂²×C₄×C₁₇	—	2	1	no	—
265	C₂²×C₄×C₁₇	—	4	1	no	—
266	C₂²×C₄×C₁₇	—	4	1	no	—
267	C₂²×C₄×C₁₇	—	4	1	no	—
268	C₂²×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
269	Q₁₆×C₁₇	—	2	2	no	—
270	SD₁₆×C₁₇	—	2	4	no	—
271	SD₁₆×C₁₇	—	2	4	no	—
272	SD₁₆×C₁₇	—	2	2	no	—
273	SD₁₆×C₁₇	—	2	2	no	—
274	SD₁₆×C₁₇	—	4	2	no	—
275	SD₁₆×C₁₇	—	4	2	no	—
276	D₈×C₁₇	—	2	4	no	—
277	D₈×C₁₇	—	2	4	no	—
278	D₈×C₁₇	—	2	4	no	—
279	D₈×C₁₇	—	2	2	no	—
280	D₈×C₁₇	—	2	4	no	—
281	D₈×C₁₇	—	4	2	no	—
282	D₈×C₁₇	—	4	2	no	—
283	D₈×C₁₇	—	4	2	no	—
284	D₈×C₁₇	—	4	2	no	—
285	M₁₆×C₁₇	—	2	4	no	—
286	M₁₆×C₁₇	—	2	1	no	—
287	M₁₆×C₁₇	—	2	1	no	—
288	M₁₆×C₁₇	—	2	1	no	—
289	M₁₆×C₁₇	—	2	1	no	—
290	M₁₆×C₁₇	—	2	1	no	—
291	M₁₆×C₁₇	—	2	1	no	—
292	M₁₆×C₁₇	—	2	1	no	—
293	M₁₆×C₁₇	—	4	2	no	—
294	M₁₆×C₁₇	C₂×D₄	1	2	yes	—
295	C₂×C₈×C₁₇	—	2	4	no	—
296	C₂×C₈×C₁₇	—	2	1	no	—
297	C₂×C₈×C₁₇	—	2	1	no	—
298	C₂×C₈×C₁₇	—	2	1	no	—
299	C₂×C₈×C₁₇	—	2	1	no	—
300	C₂×C₈×C₁₇	—	2	1	no	—
301	C₂×C₈×C₁₇	—	2	1	no	—
302	C₂×C₈×C₁₇	—	2	1	no	—
303	C₂×C₈×C₁₇	—	2	1	no	—
304	C₂×C₈×C₁₇	—	4	2	no	—
305	C₂×C₈×C₁₇	C₂×D₄	1	1	yes	characteristic
306	C₂×C₈×C₁₇	C₂×D₄	1	1	yes	characteristic
307	C₂×C₈×C₁₇	C₂×D₄	1	1	yes	characteristic
308	C₂×C₈×C₁₇	C₂×D₄	1	1	yes	characteristic
309	C₄⋊C₄×C₁₇	—	2	1	no	—
310	C₄⋊C₄×C₁₇	—	2	1	no	—
311	C₄⋊C₄×C₁₇	—	4	1	no	—
312	C₄⋊C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
313	C₄⋊C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
314	C₂²⋊C₄×C₁₇	—	2	1	no	—
315	C₂²⋊C₄×C₁₇	—	4	1	no	—
316	C₂²⋊C₄×C₁₇	—	4	1	no	—
317	C₂²⋊C₄×C₁₇	—	4	1	no	—
318	C₂²⋊C₄×C₁₇	—	8	2	no	—
319	C₄²×C₁₇	—	2	1	no	—
320	C₄²×C₁₇	—	2	1	no	—
321	C₄²×C₁₇	—	2	1	no	—
322	C₄²×C₁₇	—	4	1	no	—
323	#24456	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
324	C₂³×C₁₇	—	2	1	no	—
325	C₂³×C₁₇	—	2	1	no	—
326	C₂³×C₁₇	—	2	1	no	—
327	C₂³×C₁₇	—	2	2	no	—
328	C₂³×C₁₇	—	2	2	no	—
329	C₂³×C₁₇	—	4	4	no	—
330	C₂³×C₁₇	—	4	4	no	—
331	C₂³×C₁₇	—	4	1	no	—
332	C₂³×C₁₇	—	4	1	no	—
333	C₂³×C₁₇	—	4	1	no	—
334	C₂³×C₁₇	—	4	1	no	—
335	C₂³×C₁₇	—	4	1	no	—
336	C₂³×C₁₇	—	4	1	no	—
337	C₂³×C₁₇	—	4	1	no	—
338	C₂³×C₁₇	—	8	1	no	—
339	C₂³×C₁₇	—	8	1	no	—
340	C₂³×C₁₇	—	8	1	no	—
341	C₂³×C₁₇	—	8	1	no	—
342	C₂³×C₁₇	—	8	1	no	—
343	C₂³×C₁₇	—	8	1	no	—
344	C₂³×C₁₇	—	16	1	no	—
345	C₂³×C₁₇	—	16	1	no	—
346	C₂³×C₁₇	—	16	1	no	—
347	C₂³×C₁₇	—	16	1	no	—
348	C₂³×C₁₇	H(5,𝔽₂)	1	1	yes	characteristic
349	Q₈×C₁₇	—	2	1	no	—
350	Q₈×C₁₇	—	2	1	no	—
351	Q₈×C₁₇	—	2	1	no	—
352	Q₈×C₁₇	—	2	1	no	—
353	Q₈×C₁₇	#120	1	2	yes	—
354	Q₈×C₁₇	#121	1	2	yes	—
355	D₄×C₁₇	—	2	2	no	—
356	D₄×C₁₇	—	2	2	no	—
357	D₄×C₁₇	—	2	2	no	—
358	D₄×C₁₇	—	2	2	no	—
359	D₄×C₁₇	—	2	2	no	—
360	D₄×C₁₇	—	2	2	no	—
361	D₄×C₁₇	—	2	1	no	—
362	D₄×C₁₇	—	2	2	no	—
363	D₄×C₁₇	—	2	1	no	—
364	D₄×C₁₇	—	2	2	no	—
365	D₄×C₁₇	—	2	1	no	—
366	D₄×C₁₇	—	2	1	no	—
367	D₄×C₁₇	—	4	4	no	—
368	D₄×C₁₇	—	4	4	no	—
369	D₄×C₁₇	—	4	4	no	—
370	D₄×C₁₇	—	4	4	no	—
371	D₄×C₁₇	—	4	1	no	—
372	D₄×C₁₇	—	4	1	no	—
373	D₄×C₁₇	—	4	1	no	—
374	D₄×C₁₇	—	4	1	no	—
375	D₄×C₁₇	—	4	1	no	—
376	D₄×C₁₇	—	4	1	no	—
377	D₄×C₁₇	—	4	1	no	—
378	D₄×C₁₇	—	4	1	no	—
379	D₄×C₁₇	—	4	1	no	—
380	D₄×C₁₇	—	4	1	no	—
381	D₄×C₁₇	—	8	8	no	—
382	D₄×C₁₇	—	16	1	no	—
383	D₄×C₁₇	—	16	1	no	—
384	D₄×C₁₇	#120	1	2	yes	—
385	D₄×C₁₇	#121	1	2	yes	—
386	C₂×C₄×C₁₇	—	2	1	no	—
387	C₂×C₄×C₁₇	—	2	1	no	—
388	C₂×C₄×C₁₇	—	2	2	no	—
389	C₂×C₄×C₁₇	—	2	2	no	—
390	C₂×C₄×C₁₇	—	2	2	no	—
391	C₂×C₄×C₁₇	—	2	2	no	—
392	C₂×C₄×C₁₇	—	2	2	no	—
393	C₂×C₄×C₁₇	—	2	1	no	—
394	C₂×C₄×C₁₇	—	2	1	no	—
395	C₂×C₄×C₁₇	—	2	1	no	—
396	C₂×C₄×C₁₇	—	4	4	no	—
397	C₂×C₄×C₁₇	—	4	4	no	—
398	C₂×C₄×C₁₇	—	4	1	no	—
399	C₂×C₄×C₁₇	—	4	1	no	—
400	C₂×C₄×C₁₇	—	4	1	no	—
401	C₂×C₄×C₁₇	—	4	1	no	—
402	C₂×C₄×C₁₇	—	4	1	no	—
403	C₂×C₄×C₁₇	—	8	1	no	—
404	C₂×C₄×C₁₇	—	16	1	no	—
405	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
406	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
407	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
408	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
409	C₂×C₄×C₁₇	C₂×#41	1	1	yes	characteristic
410	C₂×C₄×C₁₇	H(5,𝔽₂)	1	1	yes	characteristic
411	C₈×C₁₇	—	2	1	no	—
412	C₈×C₁₇	—	2	2	no	—
413	C₈×C₁₇	—	2	1	no	—
414	C₈×C₁₇	—	2	1	no	—
415	C₈×C₁₇	—	2	1	no	—
416	C₈×C₁₇	—	4	1	no	—
417	C₈×C₁₇	—	4	1	no	—
418	C₈×C₁₇	—	4	1	no	—
419	C₂×#576	C₂×C₁₇	1	1	yes	characteristic, complemented
420	C₂×#472	C₂×C₁₇	1	1	yes	characteristic, complemented
421	#3045	C₂×C₁₇	1	1	yes	characteristic, complemented
422	C₂×#453	C₂×C₁₇	1	1	yes	characteristic, complemented
423	#3008	C₂×C₁₇	1	1	yes	characteristic, complemented
424	#2897	C₂×C₁₇	1	1	yes	characteristic, complemented
425	#2051	C₂×C₁₇	1	1	yes	characteristic, complemented
426	#2045	C₂×C₁₇	1	1	yes	characteristic, complemented
427	#2011	C₂×C₁₇	1	1	yes	characteristic, complemented
428	#2002	C₂×C₁₇	1	1	yes	characteristic, complemented
429	#1907	C₂×C₁₇	1	1	yes	characteristic, complemented
430	#1883	C₂×C₁₇	1	1	yes	characteristic, complemented
431	#1876	C₂×C₁₇	1	1	yes	characteristic, complemented
432	#1866	C₂×C₁₇	1	1	yes	characteristic, complemented
433	#1792	C₂×C₁₇	1	1	yes	characteristic, complemented
434	C₂²×C₁₇	—	2	1	no	—
435	C₂²×C₁₇	—	2	1	no	—
436	C₂²×C₁₇	—	2	2	no	—
437	C₂²×C₁₇	—	2	2	no	—
438	C₂²×C₁₇	—	4	1	no	—
439	C₂²×C₁₇	—	4	1	no	—
440	C₂²×C₁₇	—	4	1	no	—
441	C₂²×C₁₇	—	4	1	no	—
442	C₂²×C₁₇	—	4	1	no	—
443	C₂²×C₁₇	—	4	2	no	—
444	C₂²×C₁₇	—	4	2	no	—
445	C₂²×C₁₇	—	4	1	no	—
446	C₂²×C₁₇	—	4	1	no	—
447	C₂²×C₁₇	—	8	2	no	—
448	C₂²×C₁₇	—	8	2	no	—
449	C₂²×C₁₇	—	8	2	no	—
450	C₂²×C₁₇	—	8	1	no	—
451	C₂²×C₁₇	—	8	1	no	—
452	C₂²×C₁₇	—	8	1	no	—
453	C₂²×C₁₇	—	8	1	no	—
454	C₂²×C₁₇	—	8	1	no	—
455	C₂²×C₁₇	—	8	1	no	—
456	C₂²×C₁₇	—	8	1	no	—
457	C₂²×C₁₇	—	16	1	no	—
458	C₂²×C₁₇	—	16	1	no	—
459	C₂²×C₁₇	—	16	1	no	—
460	C₂²×C₁₇	—	16	4	no	—
461	C₂²×C₁₇	—	16	4	no	—
462	C₂²×C₁₇	#534	1	1	yes	characteristic
463	C₂²×C₁₇	D₄²	1	1	yes	characteristic
464	C₂²×C₁₇	#546	1	1	yes	characteristic
465	C₄×C₁₇	—	2	2	no	—
466	C₄×C₁₇	—	2	2	no	—
467	C₄×C₁₇	—	4	2	no	—
468	C₄×C₁₇	—	4	1	no	—
469	C₄×C₁₇	—	4	1	no	—
470	C₄×C₁₇	—	4	1	no	—
471	C₄×C₁₇	—	8	1	no	—
472	C₄×C₁₇	C₂×#120	1	1	yes	characteristic
473	C₄×C₁₇	C₂×#121	1	1	yes	characteristic
474	C₄×C₁₇	D₄²	1	1	yes	characteristic
475	C₄×C₁₇	#546	1	1	yes	characteristic
476	C₂×H(5,𝔽₂)	C₂²×C₁₇	1	1	yes	characteristic
477	C₂×H(5,𝔽₂)	C₂²×C₁₇	1	1	yes	characteristic
478	#576	—	2	4	no	—
479	#576	—	2	4	no	—
480	C₂×AGL(1,ℤ/8)	—	2	1	no	—
481	C₂×AGL(1,ℤ/8)	—	2	1	no	—
482	C₂×AGL(1,ℤ/8)	C₂²×C₁₇	1	1	yes	characteristic
483	C₂×AGL(1,ℤ/8)	C₂²×C₁₇	1	1	yes	characteristic
484	C₂×AGL(1,ℤ/8)	C₂²×C₁₇	1	1	yes	characteristic
485	C₂×AGL(1,ℤ/8)	C₂²×C₁₇	1	1	yes	characteristic, complemented
486	C₂×#135	—	2	1	no	—
487	C₂×#135	C₂²×C₁₇	1	1	yes	characteristic
488	C₂²×D₈	—	2	1	no	—
489	C₂²×D₈	C₂²×C₁₇	1	1	yes	characteristic
490	C₂²×D₈	C₂²×C₁₇	1	1	yes	characteristic, complemented
491	C₂×#131	C₂²×C₁₇	1	1	yes	characteristic
492	C₂×#131	C₂²×C₁₇	1	1	yes	characteristic, complemented
493	#535	C₂²×C₁₇	1	1	yes	characteristic, complemented
494	C₂×#127	C₂²×C₁₇	1	1	yes	characteristic, complemented
495	#520	C₂²×C₁₇	1	1	yes	characteristic, complemented
496	#472	—	2	4	no	—
497	#464	—	2	1	no	—
498	#463	—	2	1	no	—
499	#460	—	2	1	no	—
500	#459	—	2	1	no	—
501	#453	—	2	4	no	—
502	#449	—	2	1	no	—
503	#449	—	2	1	no	—
504	#447	—	2	1	no	—
505	#447	—	2	1	no	—
506	C₂×#108	C₂²×C₁₇	1	1	yes	characteristic, complemented
507	#424	C₂²×C₁₇	1	1	yes	characteristic, complemented
508	C₂×#104	C₂²×C₁₇	1	1	yes	characteristic
509	C₂×#104	C₂²×C₁₇	1	1	yes	characteristic, complemented
510	C₂×#104	C₂²×C₁₇	1	1	yes	characteristic, complemented
511	#418	—	2	1	no	—
512	#418	C₂²×C₁₇	1	1	yes	characteristic, complemented
513	#418	C₂²×C₁₇	1	1	yes	characteristic, complemented
514	#417	—	2	1	no	—
515	#417	C₂²×C₁₇	1	1	yes	characteristic
516	#417	C₂²×C₁₇	1	1	yes	characteristic, complemented
517	#416	—	2	1	no	—
518	#416	C₂²×C₁₇	1	1	yes	characteristic
519	C₂×#102	—	2	1	no	—
520	C₂×#102	C₂²×C₁₇	1	1	yes	characteristic, complemented
521	C₂×#102	C₂²×C₁₇	1	1	yes	characteristic, complemented
522	C₂×#100	C₂²×C₁₇	1	1	yes	characteristic, complemented
523	C₂×#100	C₂²×C₁₇	1	1	yes	characteristic, complemented
524	C₂×#100	C₂²×C₁₇	1	1	yes	characteristic, complemented
525	#408	C₂²×C₁₇	1	1	yes	characteristic, complemented
526	#390	C₂²×C₁₇	1	1	yes	characteristic, complemented
527	#343	C₂²×C₁₇	1	1	yes	characteristic, complemented
528	#341	C₂²×C₁₇	1	1	yes	characteristic, complemented
529	#339	C₂²×C₁₇	1	1	yes	characteristic, complemented
530	#336	C₂²×C₁₇	1	1	yes	characteristic, complemented
531	C₂×C₁₇	—	2	1	no	—
532	C₂×C₁₇	—	2	1	no	—
533	C₂×C₁₇	—	4	2	no	—
534	C₂×C₁₇	—	4	2	no	—
535	C₂×C₁₇	—	8	1	no	—
536	C₂×C₁₇	—	8	2	no	—
537	C₂×C₁₇	—	8	2	no	—
538	C₂×C₁₇	—	16	1	no	—
539	C₂×C₁₇	#2410	1	1	yes	characteristic
540	C₂×C₁₇	#3288	1	1	yes	characteristic
541	C₂×C₁₇	#3292	1	1	yes	characteristic
542	H(5,𝔽₂)	—	2	2	no	—
543	H(5,𝔽₂)	—	2	2	no	—
544	H(5,𝔽₂)	—	2	2	no	—
545	H(5,𝔽₂)	—	2	2	no	—
546	H(5,𝔽₂)	—	2	2	no	—
547	H(5,𝔽₂)	—	4	1	no	—
548	H(5,𝔽₂)	—	4	1	no	—
549	H(5,𝔽₂)	D₄×C₁₇	1	4	yes	complemented
550	C₂×#41	—	2	1	no	—
551	C₂×#41	—	2	1	no	—
552	C₂×#41	—	2	1	no	—
553	C₂×#41	—	2	1	no	—
554	C₂×#41	C₂³×C₁₇	1	1	yes	characteristic
555	C₂×#41	C₂³×C₁₇	1	1	yes	characteristic
556	C₂×#41	C₂³×C₁₇	1	1	yes	characteristic
557	C₂²×D₄	—	2	1	no	—
558	C₂²×D₄	—	2	1	no	—
559	C₂²×D₄	—	2	1	no	—
560	C₂²×D₄	—	2	1	no	—
561	C₂²×D₄	—	4	1	no	—
562	C₂²×D₄	—	4	1	no	—
563	C₂²×D₄	—	4	1	no	—
564	C₂²×D₄	C₂³×C₁₇	1	1	yes	characteristic
565	C₂²×D₄	C₂³×C₁₇	1	1	yes	characteristic
566	C₂²×D₄	C₂³×C₁₇	1	1	yes	characteristic
567	AGL(1,ℤ/8)	—	2	8	no	—
568	AGL(1,ℤ/8)	—	2	8	no	—
569	AGL(1,ℤ/8)	—	2	2	no	—
570	AGL(1,ℤ/8)	—	2	2	no	—
571	AGL(1,ℤ/8)	—	2	2	no	—
572	AGL(1,ℤ/8)	—	2	2	no	—
573	AGL(1,ℤ/8)	—	2	2	no	—
574	AGL(1,ℤ/8)	—	2	2	no	—
575	AGL(1,ℤ/8)	—	2	2	no	—
576	AGL(1,ℤ/8)	D₄×C₁₇	1	4	yes	complemented
577	#135	—	2	8	no	—
578	#135	—	2	2	no	—
579	#135	—	2	2	no	—
580	C₂×Q₁₆	D₄×C₁₇	1	1	yes	characteristic, complemented
581	C₂×SD₁₆	—	2	1	no	—
582	C₂×SD₁₆	—	2	1	no	—
583	C₂×SD₁₆	—	2	1	no	—
584	C₂×SD₁₆	—	2	1	no	—
585	C₂×SD₁₆	D₄×C₁₇	1	1	yes	characteristic, complemented
586	C₂×SD₁₆	D₄×C₁₇	1	1	yes	characteristic, complemented
587	C₂×D₈	—	2	8	no	—
588	C₂×D₈	—	2	1	no	—
589	C₂×D₈	—	2	1	no	—
590	C₂×D₈	—	2	2	no	—
591	C₂×D₈	—	2	2	no	—
592	C₂×D₈	—	2	2	no	—
593	C₂×D₈	—	2	1	no	—
594	C₂×D₈	—	2	1	no	—
595	C₂×D₈	—	2	1	no	—
596	C₂×D₈	—	2	1	no	—
597	C₂×D₈	—	2	1	no	—
598	C₂×D₈	—	2	1	no	—
599	C₂×D₈	—	4	1	no	—
600	C₂×D₈	D₄×C₁₇	1	1	yes	characteristic, complemented
601	#131	—	2	2	no	—
602	#131	—	2	2	no	—
603	#131	—	2	2	no	—
604	#131	—	4	1	no	—
605	C₂×M₁₆	—	2	1	no	—
606	C₂×M₁₆	—	2	1	no	—
607	C₂×M₁₆	C₂³×C₁₇	1	1	yes	characteristic
608	C₂×M₁₆	C₂³×C₁₇	1	1	yes	characteristic
609	C₂×M₁₆	C₂³×C₁₇	1	1	yes	characteristic
610	C₂×M₁₆	C₂³×C₁₇	1	1	yes	characteristic
611	C₂²×C₈	—	2	1	no	—
612	C₂²×C₈	—	2	1	no	—
613	C₂²×C₈	C₂³×C₁₇	1	1	yes	characteristic
614	C₂²×C₈	C₂³×C₁₇	1	1	yes	characteristic
615	#127	—	2	2	no	—
616	#127	—	2	1	no	—
617	#127	—	4	1	no	—
618	#124	—	2	1	no	—
619	#121	—	2	1	no	—
620	#121	—	2	1	no	—
621	#120	—	4	1	no	—
622	C₄×Q₈	—	2	1	no	—
623	C₄×D₄	—	2	1	no	—
624	C₄×D₄	—	4	1	no	—
625	#117	—	2	1	no	—
626	#117	C₂³×C₁₇	1	1	yes	characteristic
627	C₂×C₄⋊C₄	—	2	1	no	—
628	C₂×C₄⋊C₄	C₂³×C₁₇	1	1	yes	characteristic
629	C₂×C₂²⋊C₄	—	4	1	no	—
630	C₂×C₄²	C₂³×C₁₇	1	1	yes	characteristic
631	#108	—	2	2	no	—
632	C₄⋊C₈	—	2	1	no	—
633	C₄⋊C₈	—	2	1	no	—
634	#104	—	2	2	no	—
635	#104	—	2	2	no	—
636	#104	—	4	1	no	—
637	#103	—	2	1	no	—
638	#103	—	2	1	no	—
639	#103	D₄×C₁₇	1	1	yes	characteristic, complemented
640	#103	D₄×C₁₇	1	1	yes	characteristic, complemented
641	#102	—	2	1	no	—
642	#102	—	2	1	no	—
643	#102	—	2	1	no	—
644	#102	—	2	1	no	—
645	#102	—	2	1	no	—
646	#102	—	2	1	no	—
647	#102	—	2	1	no	—
648	#102	—	2	1	no	—
649	#102	—	2	1	no	—
650	#102	—	2	1	no	—
651	#102	D₄×C₁₇	1	1	yes	characteristic, complemented
652	#102	D₄×C₁₇	1	1	yes	characteristic, complemented
653	#100	—	2	2	no	—
654	#100	—	2	2	no	—
655	#100	—	2	2	no	—
656	C₂²⋊C₈	—	2	1	no	—
657	C₂²⋊C₈	—	2	1	no	—
658	C₁₇	#24456	1	1	yes	characteristic, direct product factor, Sylow
659	C₂⁴	—	2	1	no	—
660	C₂⁴	—	2	1	no	—
661	C₂⁴	—	2	1	no	—
662	C₂⁴	—	4	1	no	—
663	C₂⁴	—	4	1	no	—
664	#41	—	2	1	no	—
665	#41	—	2	1	no	—
666	#41	—	2	1	no	—
667	#41	—	2	1	no	—
668	#41	—	2	4	no	—
669	#41	—	2	4	no	—
670	#41	—	2	4	no	—
671	#41	—	2	1	no	—
672	#41	—	2	1	no	—
673	#41	—	2	1	no	—
674	#41	—	2	1	no	—
675	#41	—	4	2	no	—
676	#41	—	4	2	no	—
677	#41	—	4	2	no	—
678	#41	—	4	2	no	—
679	#41	—	4	2	no	—
680	#41	C₂×D₄×C₁₇	1	2	yes	—
681	#41	C₂×D₄×C₁₇	1	2	yes	—
682	#41	C₂×D₄×C₁₇	1	2	yes	—
683	#41	#41×C₁₇	1	2	yes	—
684	C₂×Q₈	C₂×D₄×C₁₇	1	1	yes	characteristic
685	C₂×Q₈	C₂×D₄×C₁₇	1	1	yes	characteristic
686	C₂×Q₈	C₂×D₄×C₁₇	1	1	yes	characteristic
687	C₂×D₄	—	2	1	no	—
688	C₂×D₄	—	2	1	no	—
689	C₂×D₄	—	2	4	no	—
690	C₂×D₄	—	2	4	no	—
691	C₂×D₄	—	2	4	no	—
692	C₂×D₄	—	2	1	no	—
693	C₂×D₄	—	2	1	no	—
694	C₂×D₄	—	2	1	no	—
695	C₂×D₄	—	2	1	no	—
696	C₂×D₄	—	2	1	no	—
697	C₂×D₄	—	2	1	no	—
698	C₂×D₄	—	2	1	no	—
699	C₂×D₄	—	2	1	no	—
700	C₂×D₄	—	2	1	no	—
701	C₂×D₄	—	2	1	no	—
702	C₂×D₄	—	2	1	no	—
703	C₂×D₄	—	2	1	no	—
704	C₂×D₄	—	2	1	no	—
705	C₂×D₄	—	2	1	no	—
706	C₂×D₄	—	2	1	no	—
707	C₂×D₄	—	2	1	no	—
708	C₂×D₄	—	2	1	no	—
709	C₂×D₄	—	4	2	no	—
710	C₂×D₄	—	4	2	no	—
711	C₂×D₄	—	4	2	no	—
712	C₂×D₄	—	4	1	no	—
713	C₂×D₄	—	4	1	no	—
714	C₂×D₄	—	4	1	no	—
715	C₂×D₄	—	4	1	no	—
716	C₂×D₄	—	4	1	no	—
717	C₂×D₄	—	4	1	no	—
718	C₂×D₄	—	4	4	no	—
719	C₂×D₄	—	4	2	no	—
720	C₂×D₄	—	4	4	no	—
721	C₂×D₄	—	4	4	no	—
722	C₂×D₄	—	4	4	no	—
723	C₂×D₄	—	4	2	no	—
724	C₂×D₄	—	4	4	no	—
725	C₂×D₄	—	8	2	no	—
726	C₂×D₄	—	8	2	no	—
727	C₂×D₄	C₂×D₄×C₁₇	1	2	yes	—
728	C₂×D₄	C₂×D₄×C₁₇	1	2	yes	—
729	C₂×D₄	C₂×D₄×C₁₇	1	1	yes	characteristic
730	C₂×D₄	C₂×D₄×C₁₇	1	1	yes	characteristic
731	C₂×D₄	C₂×D₄×C₁₇	1	1	yes	characteristic
732	C₂²×C₄	—	2	1	no	—
733	C₂²×C₄	—	2	1	no	—
734	C₂²×C₄	—	2	1	no	—
735	C₂²×C₄	—	2	1	no	—
736	C₂²×C₄	—	2	1	no	—
737	C₂²×C₄	—	4	1	no	—
738	C₂²×C₄	—	4	1	no	—
739	C₂²×C₄	—	4	1	no	—
740	C₂²×C₄	C₂⁴×C₁₇	1	1	yes	characteristic
741	Q₁₆	—	2	2	no	—
742	SD₁₆	—	2	4	no	—
743	SD₁₆	—	2	4	no	—
744	SD₁₆	—	2	2	no	—
745	SD₁₆	—	2	2	no	—
746	SD₁₆	—	4	2	no	—
747	SD₁₆	—	4	2	no	—
748	D₈	—	2	4	no	—
749	D₈	—	2	4	no	—
750	D₈	—	2	4	no	—
751	D₈	—	2	2	no	—
752	D₈	—	2	4	no	—
753	D₈	—	4	2	no	—
754	D₈	—	4	2	no	—
755	D₈	—	4	2	no	—
756	D₈	—	4	2	no	—
757	M₁₆	—	2	4	no	—
758	M₁₆	—	2	1	no	—
759	M₁₆	—	2	1	no	—
760	M₁₆	—	2	1	no	—
761	M₁₆	—	2	1	no	—
762	M₁₆	—	2	1	no	—
763	M₁₆	—	2	1	no	—
764	M₁₆	—	2	1	no	—
765	M₁₆	—	4	2	no	—
766	M₁₆	C₂×D₄×C₁₇	1	2	yes	—
767	C₂×C₈	—	2	4	no	—
768	C₂×C₈	—	2	1	no	—
769	C₂×C₈	—	2	1	no	—
770	C₂×C₈	—	2	1	no	—
771	C₂×C₈	—	2	1	no	—
772	C₂×C₈	—	2	1	no	—
773	C₂×C₈	—	2	1	no	—
774	C₂×C₈	—	2	1	no	—
775	C₂×C₈	—	2	1	no	—
776	C₂×C₈	—	4	2	no	—
777	C₂×C₈	C₂×D₄×C₁₇	1	1	yes	characteristic
778	C₂×C₈	C₂×D₄×C₁₇	1	1	yes	characteristic
779	C₂×C₈	C₂×D₄×C₁₇	1	1	yes	characteristic
780	C₂×C₈	C₂×D₄×C₁₇	1	1	yes	characteristic
781	C₄⋊C₄	—	2	1	no	—
782	C₄⋊C₄	—	2	1	no	—
783	C₄⋊C₄	—	4	1	no	—
784	C₄⋊C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
785	C₄⋊C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
786	C₂²⋊C₄	—	2	1	no	—
787	C₂²⋊C₄	—	4	1	no	—
788	C₂²⋊C₄	—	4	1	no	—
789	C₂²⋊C₄	—	4	1	no	—
790	C₂²⋊C₄	—	8	2	no	—
791	C₄²	—	2	1	no	—
792	C₄²	—	2	1	no	—
793	C₄²	—	2	1	no	—
794	C₄²	—	4	1	no	—
795	C₂³	—	2	1	no	—
796	C₂³	—	2	1	no	—
797	C₂³	—	2	1	no	—
798	C₂³	—	2	2	no	—
799	C₂³	—	2	2	no	—
800	C₂³	—	4	4	no	—
801	C₂³	—	4	4	no	—
802	C₂³	—	4	1	no	—
803	C₂³	—	4	1	no	—
804	C₂³	—	4	1	no	—
805	C₂³	—	4	1	no	—
806	C₂³	—	4	1	no	—
807	C₂³	—	4	1	no	—
808	C₂³	—	4	1	no	—
809	C₂³	—	8	1	no	—
810	C₂³	—	8	1	no	—
811	C₂³	—	8	1	no	—
812	C₂³	—	8	1	no	—
813	C₂³	—	8	1	no	—
814	C₂³	—	8	1	no	—
815	C₂³	—	16	1	no	—
816	C₂³	—	16	1	no	—
817	C₂³	—	16	1	no	—
818	C₂³	—	16	1	no	—
819	C₂³	C₁₇×H(5,𝔽₂)	1	1	yes	characteristic
820	Q₈	—	2	1	no	—
821	Q₈	—	2	1	no	—
822	Q₈	—	2	1	no	—
823	Q₈	—	2	1	no	—
824	Q₈	C₁₇×#120	1	2	yes	—
825	Q₈	C₁₇×#121	1	2	yes	—
826	D₄	—	2	2	no	—
827	D₄	—	2	2	no	—
828	D₄	—	2	2	no	—
829	D₄	—	2	2	no	—
830	D₄	—	2	2	no	—
831	D₄	—	2	2	no	—
832	D₄	—	2	1	no	—
833	D₄	—	2	2	no	—
834	D₄	—	2	1	no	—
835	D₄	—	2	2	no	—
836	D₄	—	2	1	no	—
837	D₄	—	2	1	no	—
838	D₄	—	4	4	no	—
839	D₄	—	4	4	no	—
840	D₄	—	4	4	no	—
841	D₄	—	4	4	no	—
842	D₄	—	4	1	no	—
843	D₄	—	4	1	no	—
844	D₄	—	4	1	no	—
845	D₄	—	4	1	no	—
846	D₄	—	4	1	no	—
847	D₄	—	4	1	no	—
848	D₄	—	4	1	no	—
849	D₄	—	4	1	no	—
850	D₄	—	4	1	no	—
851	D₄	—	4	1	no	—
852	D₄	—	8	8	no	—
853	D₄	—	16	1	no	—
854	D₄	—	16	1	no	—
855	D₄	C₁₇×#120	1	2	yes	—
856	D₄	C₁₇×#121	1	2	yes	—
857	C₂×C₄	—	2	1	no	—
858	C₂×C₄	—	2	1	no	—
859	C₂×C₄	—	2	2	no	—
860	C₂×C₄	—	2	2	no	—
861	C₂×C₄	—	2	2	no	—
862	C₂×C₄	—	2	2	no	—
863	C₂×C₄	—	2	2	no	—
864	C₂×C₄	—	2	1	no	—
865	C₂×C₄	—	2	1	no	—
866	C₂×C₄	—	2	1	no	—
867	C₂×C₄	—	4	4	no	—
868	C₂×C₄	—	4	4	no	—
869	C₂×C₄	—	4	1	no	—
870	C₂×C₄	—	4	1	no	—
871	C₂×C₄	—	4	1	no	—
872	C₂×C₄	—	4	1	no	—
873	C₂×C₄	—	4	1	no	—
874	C₂×C₄	—	8	1	no	—
875	C₂×C₄	—	16	1	no	—
876	C₂×C₄	C₂²×D₄×C₁₇	1	1	yes	characteristic
877	C₂×C₄	C₂²×D₄×C₁₇	1	1	yes	characteristic
878	C₂×C₄	C₂²×D₄×C₁₇	1	1	yes	characteristic
879	C₂×C₄	C₂²×D₄×C₁₇	1	1	yes	characteristic
880	C₂×C₄	C₂×#41×C₁₇	1	1	yes	characteristic
881	C₂×C₄	C₁₇×H(5,𝔽₂)	1	1	yes	characteristic
882	C₈	—	2	1	no	—
883	C₈	—	2	2	no	—
884	C₈	—	2	1	no	—
885	C₈	—	2	1	no	—
886	C₈	—	2	1	no	—
887	C₈	—	4	1	no	—
888	C₈	—	4	1	no	—
889	C₈	—	4	1	no	—
890	C₂²	—	2	1	no	—
891	C₂²	—	2	1	no	—
892	C₂²	—	2	2	no	—
893	C₂²	—	2	2	no	—
894	C₂²	—	4	1	no	—
895	C₂²	—	4	1	no	—
896	C₂²	—	4	1	no	—
897	C₂²	—	4	1	no	—
898	C₂²	—	4	1	no	—
899	C₂²	—	4	1	no	—
900	C₂²	—	4	1	no	—
901	C₂²	—	4	2	no	—
902	C₂²	—	4	2	no	—
903	C₂²	—	8	2	no	—
904	C₂²	—	8	2	no	—
905	C₂²	—	8	2	no	—
906	C₂²	—	8	1	no	—
907	C₂²	—	8	1	no	—
908	C₂²	—	8	1	no	—
909	C₂²	—	8	1	no	—
910	C₂²	—	8	1	no	—
911	C₂²	—	8	1	no	—
912	C₂²	—	8	1	no	—
913	C₂²	—	16	1	no	—
914	C₂²	—	16	1	no	—
915	C₂²	—	16	1	no	—
916	C₂²	—	16	4	no	—
917	C₂²	—	16	4	no	—
918	C₂²	C₁₇×#534	1	1	yes	characteristic
919	C₂²	D₄²×C₁₇	1	1	yes	characteristic
920	C₂²	C₁₇×#546	1	1	yes	characteristic
921	C₄	—	2	2	no	—
922	C₄	—	2	2	no	—
923	C₄	—	4	2	no	—
924	C₄	—	4	1	no	—
925	C₄	—	4	1	no	—
926	C₄	—	4	1	no	—
927	C₄	—	8	1	no	—
928	C₄	C₂×C₁₇×#120	1	1	yes	characteristic
929	C₄	C₂×C₁₇×#121	1	1	yes	characteristic
930	C₄	D₄²×C₁₇	1	1	yes	characteristic
931	C₄	C₁₇×#546	1	1	yes	characteristic
932	C₂	—	2	1	no	—
933	C₂	—	2	1	no	—
934	C₂	—	4	2	no	—
935	C₂	—	4	2	no	—
936	C₂	—	8	1	no	—
937	C₂	—	8	2	no	—
938	C₂	—	8	2	no	—
939	C₂	—	16	1	no	—
940	C₂	C₁₇×#2410	1	1	yes	characteristic
941	C₂	C₁₇×#3288	1	1	yes	characteristic
942	C₂	C₁₇×#3292	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₇	D₄²
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₇
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₂²×C₄×C₁₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₇×#576	C₂	semidirect
2. C₂×C₁₇×#472	C₂	semidirect
3. C₁₇×#3045	C₂	semidirect
4. C₂×C₁₇×#453	C₂	semidirect
5. C₁₇×#3008	C₂	semidirect
6. C₁₇×#2897	C₂	semidirect
7. C₁₇×#2051	C₂	semidirect
8. C₁₇×#2045	C₂	semidirect
9. C₁₇×#2011	C₂	semidirect
10. C₁₇×#2002	C₂	semidirect
11. C₁₇×#1907	C₂	semidirect
12. C₁₇×#1883	C₂	semidirect
13. C₁₇×#1876	C₂	semidirect
14. C₁₇×#1866	C₂	semidirect
15. C₁₇×#1792	C₂	semidirect
25. C₂×C₁₇×AGL(1,ℤ/8)	C₂²	semidirect
30. C₂²×D₈×C₁₇	C₂²	semidirect
32. C₂×C₁₇×#131	C₂²	semidirect
33. C₁₇×#535	C₂²	semidirect
34. C₂×C₁₇×#127	C₂²	semidirect
35. C₁₇×#520	C₂²	semidirect
46. C₂×C₁₇×#108	C₂²	semidirect
47. C₁₇×#424	C₂²	semidirect
49. C₂×C₁₇×#104	C₂²	semidirect
50. C₂×C₁₇×#104	C₂²	semidirect
52. C₁₇×#418	C₂²	semidirect
53. C₁₇×#418	C₂²	semidirect
56. C₁₇×#417	C₂²	semidirect
60. C₂×C₁₇×#102	C₂²	semidirect
61. C₂×C₁₇×#102	C₂²	semidirect
62. C₂×C₁₇×#100	C₂²	semidirect
63. C₂×C₁₇×#100	C₂²	semidirect
64. C₂×C₁₇×#100	C₂²	semidirect
65. C₁₇×#408	C₂²	semidirect
66. C₁₇×#390	C₂²	semidirect
67. C₁₇×#343	C₂²	semidirect
68. C₁₇×#341	C₂²	semidirect
69. C₁₇×#339	C₂²	semidirect
70. C₁₇×#336	C₂²	semidirect
78. C₁₇×H(5,𝔽₂)	D₄	semidirect
105. C₁₇×AGL(1,ℤ/8)	D₄	semidirect
109. C₂×Q₁₆×C₁₇	D₄	semidirect
114. C₂×SD₁₆×C₁₇	D₄	semidirect
115. C₂×SD₁₆×C₁₇	D₄	semidirect
129. C₂×D₈×C₁₇	D₄	semidirect
168. C₁₇×#103	D₄	semidirect
169. C₁₇×#103	D₄	semidirect
180. C₁₇×#102	D₄	semidirect
181. C₁₇×#102	D₄	semidirect
323. #24456	C₁₇	direct (N × H)
419. C₂×#576	C₂×C₁₇	semidirect
420. C₂×#472	C₂×C₁₇	semidirect
421. #3045	C₂×C₁₇	semidirect
422. C₂×#453	C₂×C₁₇	semidirect
423. #3008	C₂×C₁₇	semidirect
424. #2897	C₂×C₁₇	semidirect
425. #2051	C₂×C₁₇	semidirect
426. #2045	C₂×C₁₇	semidirect
427. #2011	C₂×C₁₇	semidirect
428. #2002	C₂×C₁₇	semidirect
429. #1907	C₂×C₁₇	semidirect
430. #1883	C₂×C₁₇	semidirect
431. #1876	C₂×C₁₇	semidirect
432. #1866	C₂×C₁₇	semidirect
433. #1792	C₂×C₁₇	semidirect
485. C₂×AGL(1,ℤ/8)	C₂²×C₁₇	semidirect
490. C₂²×D₈	C₂²×C₁₇	semidirect
492. C₂×#131	C₂²×C₁₇	semidirect
493. #535	C₂²×C₁₇	semidirect
494. C₂×#127	C₂²×C₁₇	semidirect
495. #520	C₂²×C₁₇	semidirect
506. C₂×#108	C₂²×C₁₇	semidirect
507. #424	C₂²×C₁₇	semidirect
509. C₂×#104	C₂²×C₁₇	semidirect
510. C₂×#104	C₂²×C₁₇	semidirect
512. #418	C₂²×C₁₇	semidirect
513. #418	C₂²×C₁₇	semidirect
516. #417	C₂²×C₁₇	semidirect
520. C₂×#102	C₂²×C₁₇	semidirect
521. C₂×#102	C₂²×C₁₇	semidirect
522. C₂×#100	C₂²×C₁₇	semidirect
523. C₂×#100	C₂²×C₁₇	semidirect
524. C₂×#100	C₂²×C₁₇	semidirect
525. #408	C₂²×C₁₇	semidirect
526. #390	C₂²×C₁₇	semidirect
527. #343	C₂²×C₁₇	semidirect
528. #341	C₂²×C₁₇	semidirect
529. #339	C₂²×C₁₇	semidirect
530. #336	C₂²×C₁₇	semidirect
549. H(5,𝔽₂)	D₄×C₁₇	semidirect
576. AGL(1,ℤ/8)	D₄×C₁₇	semidirect
580. C₂×Q₁₆	D₄×C₁₇	semidirect
585. C₂×SD₁₆	D₄×C₁₇	semidirect
586. C₂×SD₁₆	D₄×C₁₇	semidirect
600. C₂×D₈	D₄×C₁₇	semidirect
639. #103	D₄×C₁₇	semidirect
640. #103	D₄×C₁₇	semidirect
651. #102	D₄×C₁₇	semidirect
652. #102	D₄×C₁₇	semidirect
658. C₁₇	#24456	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×#576	2
C₂×C₁₇×#472	2
C₁₇×#3045	2
C₂×C₁₇×#453	2
C₁₇×#3008	2
C₁₇×#2897	2
C₁₇×#2051	2
C₁₇×#2045	2
C₁₇×#2011	2
C₁₇×#2002	2
C₁₇×#1907	2
C₁₇×#1883	2
C₁₇×#1876	2
C₁₇×#1866	2
C₁₇×#1792	2
#24456	17

Subgroups — C17×#24456 #16882200

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₇×#24456 #16882200