Subgroups — C₁₇×#25530 #16883274

Order 4352.

1056 conjugacy classes of subgroups.

The subgroup lattice has 870 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₇×#3495	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₇×#3094	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₇×#3055	C₂	1	1	yes	maximal, characteristic
4	C₁₇×#2620	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₇×#2060	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₇×#2038	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₇×#2027	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₇×#2003	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₇×#1901	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₇×#1897	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₇×#1888	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₇×#1883	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₇×#1859	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₇×#1857	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₇×#1733	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₁₇×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
17	C₂²×M₁₆×C₁₇	C₂²	1	1	yes	characteristic
18	C₁₇×#556	—	2	1	no	—
19	C₁₇×#554	—	2	1	no	—
20	C₁₇×#552	—	2	1	no	—
21	C₁₇×#552	—	2	2	no	—
22	C₁₇×#552	—	2	1	no	—
23	C₁₇×#551	—	2	2	no	—
24	C₁₇×#544	C₂²	1	1	yes	characteristic
25	C₁₇×#542	—	2	1	no	—
26	C₁₇×#541	—	2	1	no	—
27	C₁₇×#536	C₂²	1	1	yes	characteristic
28	C₁₇×#533	—	2	1	no	—
29	C₁₇×#529	—	2	1	no	—
30	C₂×C₁₇×#124	C₂²	1	1	yes	characteristic
31	C₁₇×#525	C₂²	1	1	yes	characteristic
32	C₂×C₁₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
33	C₂×C₁₇×#121	C₂²	1	1	yes	characteristic
34	C₁₇×#520	C₂²	1	1	yes	characteristic
35	C₁₇×#519	C₂²	1	1	yes	characteristic
36	C₂×C₁₇×#117	C₂²	1	1	yes	characteristic
37	C₂×C₁₇×#117	C₂²	1	1	yes	characteristic
38	C₁₇×#482	—	2	1	no	—
39	C₁₇×#482	—	2	1	no	—
40	C₁₇×#481	—	2	1	no	—
41	C₁₇×#480	—	2	1	no	—
42	C₁₇×#469	—	2	1	no	—
43	C₁₇×#468	—	2	1	no	—
44	C₁₇×#466	—	2	1	no	—
45	C₁₇×#465	—	2	1	no	—
46	C₁₇×#428	C₂²	1	1	yes	characteristic
47	C₁₇×#428	C₂²	1	1	yes	characteristic
48	C₁₇×#428	C₂²	1	1	yes	characteristic
49	C₂×C₁₇×#104	C₂²	1	1	yes	characteristic
50	C₂×C₁₇×#104	C₂²	1	1	yes	characteristic
51	C₁₇×#418	C₂²	1	1	yes	characteristic
52	C₁₇×#418	C₂²	1	1	yes	characteristic
53	C₁₇×#418	C₂²	1	1	yes	characteristic
54	C₁₇×#417	C₂²	1	1	yes	characteristic
55	C₂×C₁₇×#101	C₂²	1	1	yes	characteristic
56	C₂×C₁₇×#101	C₂²	1	1	yes	characteristic
57	C₁₇×#407	C₂²	1	1	yes	characteristic
58	C₁₇×#396	—	2	2	no	—
59	C₁₇×#394	—	2	2	no	—
60	C₁₇×#391	C₂²	1	1	yes	characteristic
61	C₁₇×#390	C₂²	1	1	yes	characteristic
62	C₁₇×#384	C₂²	1	1	yes	characteristic
63	C₁₇×#343	C₂²	1	1	yes	characteristic
64	C₁₇×#343	C₂²	1	1	yes	characteristic
65	C₁₇×#339	C₂²	1	1	yes	characteristic
66	C₁₇×#339	C₂²	1	1	yes	characteristic
67	C₁₇×#339	C₂²	1	1	yes	characteristic
68	C₁₇×#339	C₂²	1	1	yes	characteristic
69	C₁₇×#339	C₂²	1	1	yes	characteristic
70	C₁₇×#339	C₂²	1	1	yes	characteristic
71	C₂×#41×C₁₇	C₂³	1	1	yes	characteristic
72	C₂²×Q₈×C₁₇	C₂³	1	1	yes	characteristic
73	C₂²×D₄×C₁₇	—	2	1	no	—
74	C₂²×D₄×C₁₇	C₂³	1	1	yes	characteristic
75	C₂³×C₄×C₁₇	C₂³	1	1	yes	characteristic
76	C₁₇×AGL(1,ℤ/8)	—	2	2	no	—
77	C₁₇×AGL(1,ℤ/8)	—	4	1	no	—
78	C₂×SD₁₆×C₁₇	—	2	1	no	—
79	C₂×D₈×C₁₇	—	2	1	no	—
80	C₂×M₁₆×C₁₇	—	2	1	no	—
81	C₂×M₁₆×C₁₇	—	2	2	no	—
82	C₂×M₁₆×C₁₇	—	4	1	no	—
83	C₂×M₁₆×C₁₇	C₂³	1	1	yes	characteristic
84	C₂×M₁₆×C₁₇	C₂³	1	1	yes	characteristic
85	C₂×M₁₆×C₁₇	C₂³	1	1	yes	characteristic
86	C₂×M₁₆×C₁₇	C₂³	1	1	yes	characteristic
87	C₂²×C₈×C₁₇	—	2	1	no	—
88	C₁₇×C₄⋊Q₈	—	2	1	no	—
89	C₁₇×C₄⋊Q₈	—	2	1	no	—
90	C₁₇×C₄⋊Q₈	—	2	1	no	—
91	C₁₇×#126	—	2	2	no	—
92	C₁₇×#126	—	2	2	no	—
93	C₁₇×#126	—	2	2	no	—
94	C₁₇×#126	—	2	2	no	—
95	C₁₇×#125	—	2	2	no	—
96	C₁₇×#125	—	2	2	no	—
97	C₁₇×#125	—	2	2	no	—
98	C₁₇×#125	—	2	1	no	—
99	C₁₇×#125	—	2	1	no	—
100	C₁₇×#124	—	2	2	no	—
101	C₁₇×#124	—	2	1	no	—
102	C₁₇×#124	—	2	2	no	—
103	C₁₇×#124	—	4	1	no	—
104	C₁₇×#123	—	2	2	no	—
105	C₁₇×#123	—	2	2	no	—
106	C₁₇×#123	—	2	1	no	—
107	C₁₇×#123	—	2	2	no	—
108	C₁₇×C₂²⋊Q₈	—	2	2	no	—
109	C₁₇×C₂²⋊Q₈	—	2	2	no	—
110	C₁₇×C₂²⋊Q₈	—	2	1	no	—
111	C₁₇×C₂²⋊Q₈	—	2	1	no	—
112	C₁₇×C₂²⋊Q₈	—	2	1	no	—
113	C₁₇×C₂²⋊Q₈	—	2	1	no	—
114	C₁₇×C₂²⋊Q₈	—	2	2	no	—
115	C₁₇×C₂²⋊Q₈	—	2	1	no	—
116	C₁₇×C₂²⋊Q₈	—	2	1	no	—
117	C₁₇×C₂²⋊Q₈	D₄	1	1	yes	characteristic
118	C₁₇×C₂²⋊Q₈	D₄	1	1	yes	characteristic
119	C₁₇×#121	—	2	1	no	—
120	C₁₇×#121	—	2	1	no	—
121	C₁₇×#121	—	2	1	no	—
122	C₁₇×#121	—	2	1	no	—
123	C₁₇×#121	D₄	1	1	yes	characteristic
124	C₁₇×#121	D₄	1	1	yes	characteristic
125	C₁₇×#120	—	2	1	no	—
126	C₄×Q₈×C₁₇	—	2	2	no	—
127	C₄×Q₈×C₁₇	—	2	1	no	—
128	C₄×Q₈×C₁₇	—	2	1	no	—
129	C₄×Q₈×C₁₇	—	2	1	no	—
130	C₄×Q₈×C₁₇	—	2	1	no	—
131	C₄×Q₈×C₁₇	—	2	1	no	—
132	C₄×D₄×C₁₇	—	2	2	no	—
133	C₄×D₄×C₁₇	—	2	1	no	—
134	C₄×D₄×C₁₇	—	2	2	no	—
135	C₄×D₄×C₁₇	—	2	1	no	—
136	C₄×D₄×C₁₇	—	2	1	no	—
137	C₁₇×#117	—	2	2	no	—
138	C₁₇×#117	—	2	2	no	—
139	C₁₇×#117	—	2	1	no	—
140	C₁₇×#117	—	2	1	no	—
141	C₁₇×#117	—	2	2	no	—
142	C₁₇×#117	—	2	1	no	—
143	C₁₇×#117	—	2	2	no	—
144	C₁₇×#117	—	4	1	no	—
145	C₁₇×#117	D₄	1	1	yes	characteristic
146	C₁₇×#117	D₄	1	1	yes	characteristic
147	C₁₇×#117	C₂³	1	1	yes	characteristic
148	C₁₇×#117	C₂³	1	1	yes	characteristic
149	C₁₇×#117	C₂³	1	1	yes	characteristic
150	C₂×C₄⋊C₄×C₁₇	—	2	1	no	—
151	C₂×C₄⋊C₄×C₁₇	—	2	1	no	—
152	C₂×C₄⋊C₄×C₁₇	—	2	2	no	—
153	C₂×C₄⋊C₄×C₁₇	D₄	1	2	yes	—
154	C₂×C₄⋊C₄×C₁₇	D₄	1	1	yes	characteristic
155	C₂×C₄⋊C₄×C₁₇	D₄	1	1	yes	characteristic
156	C₂×C₄⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
157	C₂×C₄⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
158	C₂×C₂²⋊C₄×C₁₇	—	2	1	no	—
159	C₂×C₂²⋊C₄×C₁₇	—	2	1	no	—
160	C₂×C₂²⋊C₄×C₁₇	—	2	1	no	—
161	C₂×C₂²⋊C₄×C₁₇	—	2	2	no	—
162	C₂×C₂²⋊C₄×C₁₇	—	2	2	no	—
163	C₂×C₂²⋊C₄×C₁₇	D₄	1	2	yes	—
164	C₂×C₄²×C₁₇	—	2	1	no	—
165	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
166	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
167	C₁₇×#107	—	2	1	no	—
168	C₁₇×#107	—	2	1	no	—
169	C₁₇×#107	—	2	1	no	—
170	C₁₇×#106	—	2	1	no	—
171	C₁₇×#106	—	2	1	no	—
172	C₁₇×#106	—	2	1	no	—
173	C₁₇×#104	—	2	2	no	—
174	C₁₇×#104	—	4	1	no	—
175	C₁₇×#103	—	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	—	2	1	no	—
181	C₁₇×#102	—	2	1	no	—
182	C₁₇×#102	—	2	1	no	—
183	C₁₇×#101	—	2	2	no	—
184	C₁₇×#101	—	4	1	no	—
185	C₁₇×C₂²⋊C₈	—	2	1	no	—
186	C₁₇×C₂²⋊C₈	—	2	1	no	—
187	C₁₇×#95	—	2	2	no	—
188	C₂⁴×C₁₇	—	2	1	no	—
189	C₂⁴×C₁₇	C₂×D₄	1	1	yes	characteristic
190	#41×C₁₇	—	2	1	no	—
191	#41×C₁₇	—	2	1	no	—
192	#41×C₁₇	—	2	1	no	—
193	#41×C₁₇	—	2	1	no	—
194	C₂×Q₈×C₁₇	—	2	2	no	—
195	C₂×Q₈×C₁₇	—	2	1	no	—
196	C₂×Q₈×C₁₇	—	2	1	no	—
197	C₂×Q₈×C₁₇	—	2	1	no	—
198	C₂×Q₈×C₁₇	—	2	1	no	—
199	C₂×Q₈×C₁₇	—	2	1	no	—
200	C₂×Q₈×C₁₇	—	2	1	no	—
201	C₂×Q₈×C₁₇	C₂×D₄	1	1	yes	characteristic
202	C₂×D₄×C₁₇	—	2	1	no	—
203	C₂×D₄×C₁₇	—	2	1	no	—
204	C₂×D₄×C₁₇	—	2	1	no	—
205	C₂×D₄×C₁₇	—	2	1	no	—
206	C₂×D₄×C₁₇	—	2	1	no	—
207	C₂×D₄×C₁₇	—	2	1	no	—
208	C₂×D₄×C₁₇	—	2	1	no	—
209	C₂×D₄×C₁₇	—	2	1	no	—
210	C₂×D₄×C₁₇	—	2	1	no	—
211	C₂×D₄×C₁₇	—	4	1	no	—
212	C₂×D₄×C₁₇	—	4	1	no	—
213	C₂×D₄×C₁₇	—	8	2	no	—
214	C₂×D₄×C₁₇	C₂×D₄	1	1	yes	characteristic
215	C₂²×C₄×C₁₇	—	2	1	no	—
216	C₂²×C₄×C₁₇	—	2	1	no	—
217	C₂²×C₄×C₁₇	—	2	1	no	—
218	C₂²×C₄×C₁₇	—	2	1	no	—
219	C₂²×C₄×C₁₇	—	2	1	no	—
220	C₂²×C₄×C₁₇	—	2	1	no	—
221	C₂²×C₄×C₁₇	—	2	2	no	—
222	C₂²×C₄×C₁₇	—	2	1	no	—
223	C₂²×C₄×C₁₇	—	2	1	no	—
224	C₂²×C₄×C₁₇	—	2	1	no	—
225	C₂²×C₄×C₁₇	—	2	1	no	—
226	C₂²×C₄×C₁₇	C₂×D₄	1	2	yes	—
227	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
228	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
229	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
230	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
231	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
232	C₂²×C₄×C₁₇	C₂×D₄	1	2	yes	—
233	C₂²×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
234	SD₁₆×C₁₇	—	4	2	no	—
235	D₈×C₁₇	—	4	2	no	—
236	M₁₆×C₁₇	—	2	1	no	—
237	M₁₆×C₁₇	—	2	1	no	—
238	M₁₆×C₁₇	—	2	1	no	—
239	M₁₆×C₁₇	—	2	1	no	—
240	M₁₆×C₁₇	—	2	1	no	—
241	M₁₆×C₁₇	—	2	1	no	—
242	M₁₆×C₁₇	—	2	1	no	—
243	M₁₆×C₁₇	—	4	2	no	—
244	M₁₆×C₁₇	#41	1	2	yes	—
245	C₂×C₈×C₁₇	—	2	1	no	—
246	C₂×C₈×C₁₇	—	2	1	no	—
247	C₂×C₈×C₁₇	—	2	1	no	—
248	C₂×C₈×C₁₇	—	2	1	no	—
249	C₂×C₈×C₁₇	—	4	2	no	—
250	C₄⋊C₄×C₁₇	—	2	2	no	—
251	C₄⋊C₄×C₁₇	—	2	2	no	—
252	C₄⋊C₄×C₁₇	—	2	2	no	—
253	C₄⋊C₄×C₁₇	—	2	2	no	—
254	C₄⋊C₄×C₁₇	—	2	2	no	—
255	C₄⋊C₄×C₁₇	—	2	2	no	—
256	C₄⋊C₄×C₁₇	—	2	2	no	—
257	C₄⋊C₄×C₁₇	—	2	2	no	—
258	C₄⋊C₄×C₁₇	—	2	2	no	—
259	C₄⋊C₄×C₁₇	—	2	1	no	—
260	C₄⋊C₄×C₁₇	—	2	2	no	—
261	C₄⋊C₄×C₁₇	—	2	1	no	—
262	C₄⋊C₄×C₁₇	—	2	1	no	—
263	C₄⋊C₄×C₁₇	—	2	1	no	—
264	C₄⋊C₄×C₁₇	—	2	1	no	—
265	C₄⋊C₄×C₁₇	—	2	1	no	—
266	C₄⋊C₄×C₁₇	—	2	1	no	—
267	C₄⋊C₄×C₁₇	—	2	1	no	—
268	C₄⋊C₄×C₁₇	—	4	2	no	—
269	C₄⋊C₄×C₁₇	—	8	2	no	—
270	C₄⋊C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
271	C₄⋊C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
272	C₄⋊C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
273	C₄⋊C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
274	C₄⋊C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
275	C₄⋊C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
276	C₂²⋊C₄×C₁₇	—	2	2	no	—
277	C₂²⋊C₄×C₁₇	—	2	2	no	—
278	C₂²⋊C₄×C₁₇	—	2	2	no	—
279	C₂²⋊C₄×C₁₇	—	2	2	no	—
280	C₂²⋊C₄×C₁₇	—	2	1	no	—
281	C₂²⋊C₄×C₁₇	—	2	2	no	—
282	C₂²⋊C₄×C₁₇	—	2	1	no	—
283	C₂²⋊C₄×C₁₇	—	2	1	no	—
284	C₂²⋊C₄×C₁₇	—	2	1	no	—
285	C₂²⋊C₄×C₁₇	—	2	1	no	—
286	C₂²⋊C₄×C₁₇	—	2	1	no	—
287	C₂²⋊C₄×C₁₇	—	2	1	no	—
288	C₂²⋊C₄×C₁₇	—	2	1	no	—
289	C₂²⋊C₄×C₁₇	—	2	1	no	—
290	C₂²⋊C₄×C₁₇	—	4	4	no	—
291	C₂²⋊C₄×C₁₇	—	4	2	no	—
292	C₂²⋊C₄×C₁₇	—	4	1	no	—
293	C₂²⋊C₄×C₁₇	—	4	1	no	—
294	C₂²⋊C₄×C₁₇	—	8	2	no	—
295	C₄²×C₁₇	—	2	2	no	—
296	C₄²×C₁₇	—	2	2	no	—
297	C₄²×C₁₇	—	2	2	no	—
298	C₄²×C₁₇	—	2	1	no	—
299	C₄²×C₁₇	—	2	1	no	—
300	C₄²×C₁₇	—	2	1	no	—
301	C₄²×C₁₇	—	2	1	no	—
302	C₄²×C₁₇	—	2	1	no	—
303	C₄²×C₁₇	—	2	1	no	—
304	C₄²×C₁₇	—	2	1	no	—
305	C₄²×C₁₇	—	2	1	no	—
306	C₄²×C₁₇	#41	1	2	yes	—
307	#25530	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
308	C₂³×C₁₇	—	2	1	no	—
309	C₂³×C₁₇	—	2	1	no	—
310	C₂³×C₁₇	—	2	1	no	—
311	C₂³×C₁₇	—	4	1	no	—
312	C₂³×C₁₇	—	4	1	no	—
313	C₂³×C₁₇	—	4	2	no	—
314	C₂³×C₁₇	—	4	2	no	—
315	C₂³×C₁₇	—	4	1	no	—
316	C₂³×C₁₇	—	4	1	no	—
317	C₂³×C₁₇	—	4	1	no	—
318	C₂³×C₁₇	#120	1	1	yes	characteristic
319	C₂³×C₁₇	#120	1	1	yes	characteristic
320	C₂³×C₁₇	C₂²×D₄	1	1	yes	characteristic
321	Q₈×C₁₇	—	2	1	no	—
322	Q₈×C₁₇	—	2	1	no	—
323	Q₈×C₁₇	—	4	1	no	—
324	Q₈×C₁₇	—	4	1	no	—
325	Q₈×C₁₇	—	4	1	no	—
326	Q₈×C₁₇	—	4	1	no	—
327	Q₈×C₁₇	—	8	2	no	—
328	D₄×C₁₇	—	2	1	no	—
329	D₄×C₁₇	—	2	1	no	—
330	D₄×C₁₇	—	4	2	no	—
331	D₄×C₁₇	—	4	1	no	—
332	D₄×C₁₇	—	4	1	no	—
333	D₄×C₁₇	—	4	1	no	—
334	D₄×C₁₇	—	4	1	no	—
335	D₄×C₁₇	—	4	1	no	—
336	D₄×C₁₇	—	4	1	no	—
337	D₄×C₁₇	—	8	1	no	—
338	D₄×C₁₇	—	8	2	no	—
339	D₄×C₁₇	—	8	2	no	—
340	C₂×C₄×C₁₇	—	2	1	no	—
341	C₂×C₄×C₁₇	—	2	1	no	—
342	C₂×C₄×C₁₇	—	2	1	no	—
343	C₂×C₄×C₁₇	—	2	1	no	—
344	C₂×C₄×C₁₇	—	2	1	no	—
345	C₂×C₄×C₁₇	—	2	1	no	—
346	C₂×C₄×C₁₇	—	2	1	no	—
347	C₂×C₄×C₁₇	—	2	1	no	—
348	C₂×C₄×C₁₇	—	2	1	no	—
349	C₂×C₄×C₁₇	—	2	1	no	—
350	C₂×C₄×C₁₇	—	2	1	no	—
351	C₂×C₄×C₁₇	—	2	1	no	—
352	C₂×C₄×C₁₇	—	2	1	no	—
353	C₂×C₄×C₁₇	—	2	1	no	—
354	C₂×C₄×C₁₇	—	2	1	no	—
355	C₂×C₄×C₁₇	—	2	2	no	—
356	C₂×C₄×C₁₇	—	2	1	no	—
357	C₂×C₄×C₁₇	—	2	1	no	—
358	C₂×C₄×C₁₇	—	2	2	no	—
359	C₂×C₄×C₁₇	—	2	2	no	—
360	C₂×C₄×C₁₇	—	2	2	no	—
361	C₂×C₄×C₁₇	—	2	2	no	—
362	C₂×C₄×C₁₇	—	4	1	no	—
363	C₂×C₄×C₁₇	—	4	1	no	—
364	C₂×C₄×C₁₇	—	4	2	no	—
365	C₂×C₄×C₁₇	—	4	1	no	—
366	C₂×C₄×C₁₇	—	4	1	no	—
367	C₂×C₄×C₁₇	—	4	2	no	—
368	C₂×C₄×C₁₇	—	4	1	no	—
369	C₂×C₄×C₁₇	—	4	2	no	—
370	C₂×C₄×C₁₇	—	4	1	no	—
371	C₂×C₄×C₁₇	—	4	1	no	—
372	C₂×C₄×C₁₇	—	4	1	no	—
373	C₂×C₄×C₁₇	—	8	1	no	—
374	C₂×C₄×C₁₇	—	8	2	no	—
375	C₂×C₄×C₁₇	#120	1	1	yes	characteristic
376	C₂×C₄×C₁₇	#120	1	1	yes	characteristic
377	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
378	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
379	C₂×C₄×C₁₇	C₂×#41	1	1	yes	characteristic
380	C₂×C₄×C₁₇	C₂×#41	1	1	yes	characteristic
381	C₂×C₄×C₁₇	H(5,𝔽₂)	1	1	yes	characteristic
382	C₂×C₄×C₁₇	2₋¹⁺⁴	1	1	yes	characteristic
383	C₈×C₁₇	—	2	2	no	—
384	C₈×C₁₇	—	4	1	no	—
385	C₈×C₁₇	—	4	1	no	—
386	C₈×C₁₇	—	4	1	no	—
387	#3495	C₂×C₁₇	1	1	yes	characteristic, complemented
388	#3094	C₂×C₁₇	1	1	yes	characteristic, complemented
389	#3055	C₂×C₁₇	1	1	yes	characteristic
390	#2620	C₂×C₁₇	1	1	yes	characteristic, complemented
391	#2060	C₂×C₁₇	1	1	yes	characteristic, complemented
392	#2038	C₂×C₁₇	1	1	yes	characteristic, complemented
393	#2027	C₂×C₁₇	1	1	yes	characteristic, complemented
394	#2003	C₂×C₁₇	1	1	yes	characteristic, complemented
395	#1901	C₂×C₁₇	1	1	yes	characteristic, complemented
396	#1897	C₂×C₁₇	1	1	yes	characteristic, complemented
397	#1888	C₂×C₁₇	1	1	yes	characteristic, complemented
398	#1883	C₂×C₁₇	1	1	yes	characteristic, complemented
399	#1859	C₂×C₁₇	1	1	yes	characteristic, complemented
400	#1857	C₂×C₁₇	1	1	yes	characteristic, complemented
401	#1733	C₂×C₁₇	1	1	yes	characteristic, complemented
402	C₂²×C₁₇	—	2	1	no	—
403	C₂²×C₁₇	—	2	1	no	—
404	C₂²×C₁₇	—	2	1	no	—
405	C₂²×C₁₇	—	2	1	no	—
406	C₂²×C₁₇	—	2	1	no	—
407	C₂²×C₁₇	—	2	1	no	—
408	C₂²×C₁₇	—	2	1	no	—
409	C₂²×C₁₇	—	2	1	no	—
410	C₂²×C₁₇	—	4	1	no	—
411	C₂²×C₁₇	—	4	1	no	—
412	C₂²×C₁₇	—	4	1	no	—
413	C₂²×C₁₇	—	8	1	no	—
414	C₂²×C₁₇	—	8	1	no	—
415	C₂²×C₁₇	—	8	2	no	—
416	C₂²×C₁₇	—	8	2	no	—
417	C₂²×C₁₇	—	8	1	no	—
418	C₂²×C₁₇	—	8	1	no	—
419	C₂²×C₁₇	—	8	1	no	—
420	C₂²×C₁₇	C₂×#120	1	1	yes	characteristic
421	C₂²×C₁₇	#546	1	1	yes	characteristic
422	C₂²×C₁₇	#547	1	1	yes	characteristic
423	C₄×C₁₇	—	2	1	no	—
424	C₄×C₁₇	—	2	1	no	—
425	C₄×C₁₇	—	4	2	no	—
426	C₄×C₁₇	—	4	2	no	—
427	C₄×C₁₇	—	4	1	no	—
428	C₄×C₁₇	—	4	1	no	—
429	C₄×C₁₇	—	4	1	no	—
430	C₄×C₁₇	—	4	1	no	—
431	C₄×C₁₇	—	4	2	no	—
432	C₄×C₁₇	—	4	1	no	—
433	C₄×C₁₇	—	4	1	no	—
434	C₄×C₁₇	—	4	1	no	—
435	C₄×C₁₇	—	8	1	no	—
436	C₄×C₁₇	—	8	1	no	—
437	C₄×C₁₇	#532	1	1	yes	characteristic
438	C₄×C₁₇	#537	1	1	yes	characteristic
439	C₄×C₁₇	#546	1	1	yes	characteristic
440	C₄×C₁₇	#547	1	1	yes	characteristic
441	C₂×AGL(1,ℤ/8)	C₂²×C₁₇	1	1	yes	characteristic
442	C₂²×M₁₆	C₂²×C₁₇	1	1	yes	characteristic
443	#556	—	2	1	no	—
444	#554	—	2	1	no	—
445	#552	—	2	1	no	—
446	#552	—	2	2	no	—
447	#552	—	2	1	no	—
448	#551	—	2	2	no	—
449	#544	C₂²×C₁₇	1	1	yes	characteristic
450	#542	—	2	1	no	—
451	#541	—	2	1	no	—
452	#536	C₂²×C₁₇	1	1	yes	characteristic
453	#533	—	2	1	no	—
454	#529	—	2	1	no	—
455	C₂×#124	C₂²×C₁₇	1	1	yes	characteristic
456	#525	C₂²×C₁₇	1	1	yes	characteristic
457	C₂×C₂²⋊Q₈	C₂²×C₁₇	1	1	yes	characteristic
458	C₂×#121	C₂²×C₁₇	1	1	yes	characteristic
459	#520	C₂²×C₁₇	1	1	yes	characteristic
460	#519	C₂²×C₁₇	1	1	yes	characteristic
461	C₂×#117	C₂²×C₁₇	1	1	yes	characteristic
462	C₂×#117	C₂²×C₁₇	1	1	yes	characteristic
463	#482	—	2	1	no	—
464	#482	—	2	1	no	—
465	#481	—	2	1	no	—
466	#480	—	2	1	no	—
467	#469	—	2	1	no	—
468	#468	—	2	1	no	—
469	#466	—	2	1	no	—
470	#465	—	2	1	no	—
471	#428	C₂²×C₁₇	1	1	yes	characteristic
472	#428	C₂²×C₁₇	1	1	yes	characteristic
473	#428	C₂²×C₁₇	1	1	yes	characteristic
474	C₂×#104	C₂²×C₁₇	1	1	yes	characteristic
475	C₂×#104	C₂²×C₁₇	1	1	yes	characteristic
476	#418	C₂²×C₁₇	1	1	yes	characteristic
477	#418	C₂²×C₁₇	1	1	yes	characteristic
478	#418	C₂²×C₁₇	1	1	yes	characteristic
479	#417	C₂²×C₁₇	1	1	yes	characteristic
480	C₂×#101	C₂²×C₁₇	1	1	yes	characteristic
481	C₂×#101	C₂²×C₁₇	1	1	yes	characteristic
482	#407	C₂²×C₁₇	1	1	yes	characteristic
483	#396	—	2	2	no	—
484	#394	—	2	2	no	—
485	#391	C₂²×C₁₇	1	1	yes	characteristic
486	#390	C₂²×C₁₇	1	1	yes	characteristic
487	#384	C₂²×C₁₇	1	1	yes	characteristic
488	#343	C₂²×C₁₇	1	1	yes	characteristic
489	#343	C₂²×C₁₇	1	1	yes	characteristic
490	#339	C₂²×C₁₇	1	1	yes	characteristic
491	#339	C₂²×C₁₇	1	1	yes	characteristic
492	#339	C₂²×C₁₇	1	1	yes	characteristic
493	#339	C₂²×C₁₇	1	1	yes	characteristic
494	#339	C₂²×C₁₇	1	1	yes	characteristic
495	#339	C₂²×C₁₇	1	1	yes	characteristic
496	C₂×C₁₇	—	2	1	no	—
497	C₂×C₁₇	—	2	1	no	—
498	C₂×C₁₇	—	4	1	no	—
499	C₂×C₁₇	—	4	1	no	—
500	C₂×C₁₇	—	8	1	no	—
501	C₂×C₁₇	—	16	1	no	—
502	C₂×C₁₇	#2430	1	1	yes	characteristic
503	C₂×C₁₇	#3020	1	1	yes	characteristic
504	C₂×C₁₇	#3021	1	1	yes	characteristic
505	C₂×#41	C₂³×C₁₇	1	1	yes	characteristic
506	C₂²×Q₈	C₂³×C₁₇	1	1	yes	characteristic
507	C₂²×D₄	—	2	1	no	—
508	C₂²×D₄	C₂³×C₁₇	1	1	yes	characteristic
509	C₂³×C₄	C₂³×C₁₇	1	1	yes	characteristic
510	AGL(1,ℤ/8)	—	2	2	no	—
511	AGL(1,ℤ/8)	—	4	1	no	—
512	C₂×SD₁₆	—	2	1	no	—
513	C₂×D₈	—	2	1	no	—
514	C₂×M₁₆	—	2	1	no	—
515	C₂×M₁₆	—	2	2	no	—
516	C₂×M₁₆	—	4	1	no	—
517	C₂×M₁₆	C₂³×C₁₇	1	1	yes	characteristic
518	C₂×M₁₆	C₂³×C₁₇	1	1	yes	characteristic
519	C₂×M₁₆	C₂³×C₁₇	1	1	yes	characteristic
520	C₂×M₁₆	C₂³×C₁₇	1	1	yes	characteristic
521	C₂²×C₈	—	2	1	no	—
522	C₄⋊Q₈	—	2	1	no	—
523	C₄⋊Q₈	—	2	1	no	—
524	C₄⋊Q₈	—	2	1	no	—
525	#126	—	2	2	no	—
526	#126	—	2	2	no	—
527	#126	—	2	2	no	—
528	#126	—	2	2	no	—
529	#125	—	2	2	no	—
530	#125	—	2	2	no	—
531	#125	—	2	2	no	—
532	#125	—	2	1	no	—
533	#125	—	2	1	no	—
534	#124	—	2	2	no	—
535	#124	—	2	1	no	—
536	#124	—	2	2	no	—
537	#124	—	4	1	no	—
538	#123	—	2	2	no	—
539	#123	—	2	2	no	—
540	#123	—	2	1	no	—
541	#123	—	2	2	no	—
542	C₂²⋊Q₈	—	2	2	no	—
543	C₂²⋊Q₈	—	2	2	no	—
544	C₂²⋊Q₈	—	2	1	no	—
545	C₂²⋊Q₈	—	2	1	no	—
546	C₂²⋊Q₈	—	2	1	no	—
547	C₂²⋊Q₈	—	2	1	no	—
548	C₂²⋊Q₈	—	2	2	no	—
549	C₂²⋊Q₈	—	2	1	no	—
550	C₂²⋊Q₈	—	2	1	no	—
551	C₂²⋊Q₈	D₄×C₁₇	1	1	yes	characteristic
552	C₂²⋊Q₈	D₄×C₁₇	1	1	yes	characteristic
553	#121	—	2	1	no	—
554	#121	—	2	1	no	—
555	#121	—	2	1	no	—
556	#121	—	2	1	no	—
557	#121	D₄×C₁₇	1	1	yes	characteristic
558	#121	D₄×C₁₇	1	1	yes	characteristic
559	#120	—	2	1	no	—
560	C₄×Q₈	—	2	2	no	—
561	C₄×Q₈	—	2	1	no	—
562	C₄×Q₈	—	2	1	no	—
563	C₄×Q₈	—	2	1	no	—
564	C₄×Q₈	—	2	1	no	—
565	C₄×Q₈	—	2	1	no	—
566	C₄×D₄	—	2	2	no	—
567	C₄×D₄	—	2	1	no	—
568	C₄×D₄	—	2	2	no	—
569	C₄×D₄	—	2	1	no	—
570	C₄×D₄	—	2	1	no	—
571	#117	—	2	2	no	—
572	#117	—	2	2	no	—
573	#117	—	2	1	no	—
574	#117	—	2	1	no	—
575	#117	—	2	2	no	—
576	#117	—	2	1	no	—
577	#117	—	2	2	no	—
578	#117	—	4	1	no	—
579	#117	D₄×C₁₇	1	1	yes	characteristic
580	#117	D₄×C₁₇	1	1	yes	characteristic
581	#117	C₂³×C₁₇	1	1	yes	characteristic
582	#117	C₂³×C₁₇	1	1	yes	characteristic
583	#117	C₂³×C₁₇	1	1	yes	characteristic
584	C₂×C₄⋊C₄	—	2	1	no	—
585	C₂×C₄⋊C₄	—	2	1	no	—
586	C₂×C₄⋊C₄	—	2	2	no	—
587	C₂×C₄⋊C₄	D₄×C₁₇	1	2	yes	—
588	C₂×C₄⋊C₄	D₄×C₁₇	1	1	yes	characteristic
589	C₂×C₄⋊C₄	D₄×C₁₇	1	1	yes	characteristic
590	C₂×C₄⋊C₄	C₂³×C₁₇	1	1	yes	characteristic
591	C₂×C₄⋊C₄	C₂³×C₁₇	1	1	yes	characteristic
592	C₂×C₂²⋊C₄	—	2	1	no	—
593	C₂×C₂²⋊C₄	—	2	1	no	—
594	C₂×C₂²⋊C₄	—	2	1	no	—
595	C₂×C₂²⋊C₄	—	2	2	no	—
596	C₂×C₂²⋊C₄	—	2	2	no	—
597	C₂×C₂²⋊C₄	D₄×C₁₇	1	2	yes	—
598	C₂×C₄²	—	2	1	no	—
599	C₂×C₄²	C₂³×C₁₇	1	1	yes	characteristic
600	C₂×C₄²	C₂³×C₁₇	1	1	yes	characteristic
601	#107	—	2	1	no	—
602	#107	—	2	1	no	—
603	#107	—	2	1	no	—
604	#106	—	2	1	no	—
605	#106	—	2	1	no	—
606	#106	—	2	1	no	—
607	#104	—	2	2	no	—
608	#104	—	4	1	no	—
609	#103	—	2	1	no	—
610	#102	—	2	1	no	—
611	#102	—	2	1	no	—
612	#102	—	2	1	no	—
613	#102	—	2	1	no	—
614	#102	—	2	1	no	—
615	#102	—	2	1	no	—
616	#102	—	2	1	no	—
617	#101	—	2	2	no	—
618	#101	—	4	1	no	—
619	C₂²⋊C₈	—	2	1	no	—
620	C₂²⋊C₈	—	2	1	no	—
621	#95	—	2	2	no	—
622	C₁₇	#25530	1	1	yes	characteristic, direct product factor, Sylow
623	C₂⁴	—	2	1	no	—
624	C₂⁴	C₂×D₄×C₁₇	1	1	yes	characteristic
625	#41	—	2	1	no	—
626	#41	—	2	1	no	—
627	#41	—	2	1	no	—
628	#41	—	2	1	no	—
629	C₂×Q₈	—	2	2	no	—
630	C₂×Q₈	—	2	1	no	—
631	C₂×Q₈	—	2	1	no	—
632	C₂×Q₈	—	2	1	no	—
633	C₂×Q₈	—	2	1	no	—
634	C₂×Q₈	—	2	1	no	—
635	C₂×Q₈	—	2	1	no	—
636	C₂×Q₈	C₂×D₄×C₁₇	1	1	yes	characteristic
637	C₂×D₄	—	2	1	no	—
638	C₂×D₄	—	2	1	no	—
639	C₂×D₄	—	2	1	no	—
640	C₂×D₄	—	2	1	no	—
641	C₂×D₄	—	2	1	no	—
642	C₂×D₄	—	2	1	no	—
643	C₂×D₄	—	2	1	no	—
644	C₂×D₄	—	2	1	no	—
645	C₂×D₄	—	2	1	no	—
646	C₂×D₄	—	4	1	no	—
647	C₂×D₄	—	4	1	no	—
648	C₂×D₄	—	8	2	no	—
649	C₂×D₄	C₂×D₄×C₁₇	1	1	yes	characteristic
650	C₂²×C₄	—	2	1	no	—
651	C₂²×C₄	—	2	1	no	—
652	C₂²×C₄	—	2	1	no	—
653	C₂²×C₄	—	2	1	no	—
654	C₂²×C₄	—	2	1	no	—
655	C₂²×C₄	—	2	1	no	—
656	C₂²×C₄	—	2	2	no	—
657	C₂²×C₄	—	2	1	no	—
658	C₂²×C₄	—	2	1	no	—
659	C₂²×C₄	—	2	1	no	—
660	C₂²×C₄	—	2	1	no	—
661	C₂²×C₄	C₂×D₄×C₁₇	1	2	yes	—
662	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
663	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
664	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
665	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
666	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
667	C₂²×C₄	C₂×D₄×C₁₇	1	2	yes	—
668	C₂²×C₄	C₂⁴×C₁₇	1	1	yes	characteristic
669	SD₁₆	—	4	2	no	—
670	D₈	—	4	2	no	—
671	M₁₆	—	2	1	no	—
672	M₁₆	—	2	1	no	—
673	M₁₆	—	2	1	no	—
674	M₁₆	—	2	1	no	—
675	M₁₆	—	2	1	no	—
676	M₁₆	—	2	1	no	—
677	M₁₆	—	2	1	no	—
678	M₁₆	—	4	2	no	—
679	M₁₆	#41×C₁₇	1	2	yes	—
680	C₂×C₈	—	2	1	no	—
681	C₂×C₈	—	2	1	no	—
682	C₂×C₈	—	2	1	no	—
683	C₂×C₈	—	2	1	no	—
684	C₂×C₈	—	4	2	no	—
685	C₄⋊C₄	—	2	2	no	—
686	C₄⋊C₄	—	2	2	no	—
687	C₄⋊C₄	—	2	2	no	—
688	C₄⋊C₄	—	2	2	no	—
689	C₄⋊C₄	—	2	2	no	—
690	C₄⋊C₄	—	2	2	no	—
691	C₄⋊C₄	—	2	2	no	—
692	C₄⋊C₄	—	2	2	no	—
693	C₄⋊C₄	—	2	1	no	—
694	C₄⋊C₄	—	2	1	no	—
695	C₄⋊C₄	—	2	1	no	—
696	C₄⋊C₄	—	2	1	no	—
697	C₄⋊C₄	—	2	2	no	—
698	C₄⋊C₄	—	2	2	no	—
699	C₄⋊C₄	—	2	1	no	—
700	C₄⋊C₄	—	2	1	no	—
701	C₄⋊C₄	—	2	1	no	—
702	C₄⋊C₄	—	2	1	no	—
703	C₄⋊C₄	—	4	2	no	—
704	C₄⋊C₄	—	8	2	no	—
705	C₄⋊C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
706	C₄⋊C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
707	C₄⋊C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
708	C₄⋊C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
709	C₄⋊C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
710	C₄⋊C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
711	C₂²⋊C₄	—	2	2	no	—
712	C₂²⋊C₄	—	2	2	no	—
713	C₂²⋊C₄	—	2	2	no	—
714	C₂²⋊C₄	—	2	1	no	—
715	C₂²⋊C₄	—	2	1	no	—
716	C₂²⋊C₄	—	2	1	no	—
717	C₂²⋊C₄	—	2	1	no	—
718	C₂²⋊C₄	—	2	1	no	—
719	C₂²⋊C₄	—	2	2	no	—
720	C₂²⋊C₄	—	2	2	no	—
721	C₂²⋊C₄	—	2	1	no	—
722	C₂²⋊C₄	—	2	1	no	—
723	C₂²⋊C₄	—	2	1	no	—
724	C₂²⋊C₄	—	2	1	no	—
725	C₂²⋊C₄	—	4	4	no	—
726	C₂²⋊C₄	—	4	2	no	—
727	C₂²⋊C₄	—	4	1	no	—
728	C₂²⋊C₄	—	4	1	no	—
729	C₂²⋊C₄	—	8	2	no	—
730	C₄²	—	2	2	no	—
731	C₄²	—	2	2	no	—
732	C₄²	—	2	2	no	—
733	C₄²	—	2	1	no	—
734	C₄²	—	2	1	no	—
735	C₄²	—	2	1	no	—
736	C₄²	—	2	1	no	—
737	C₄²	—	2	1	no	—
738	C₄²	—	2	1	no	—
739	C₄²	—	2	1	no	—
740	C₄²	—	2	1	no	—
741	C₄²	#41×C₁₇	1	2	yes	—
742	C₂³	—	2	1	no	—
743	C₂³	—	2	1	no	—
744	C₂³	—	2	1	no	—
745	C₂³	—	4	1	no	—
746	C₂³	—	4	1	no	—
747	C₂³	—	4	2	no	—
748	C₂³	—	4	2	no	—
749	C₂³	—	4	1	no	—
750	C₂³	—	4	1	no	—
751	C₂³	—	4	1	no	—
752	C₂³	C₁₇×#120	1	1	yes	characteristic
753	C₂³	C₁₇×#120	1	1	yes	characteristic
754	C₂³	C₂²×D₄×C₁₇	1	1	yes	characteristic
755	Q₈	—	2	1	no	—
756	Q₈	—	2	1	no	—
757	Q₈	—	4	1	no	—
758	Q₈	—	4	1	no	—
759	Q₈	—	4	1	no	—
760	Q₈	—	4	1	no	—
761	Q₈	—	8	2	no	—
762	D₄	—	2	1	no	—
763	D₄	—	2	1	no	—
764	D₄	—	4	2	no	—
765	D₄	—	4	1	no	—
766	D₄	—	4	1	no	—
767	D₄	—	4	1	no	—
768	D₄	—	4	1	no	—
769	D₄	—	4	1	no	—
770	D₄	—	4	1	no	—
771	D₄	—	8	1	no	—
772	D₄	—	8	2	no	—
773	D₄	—	8	2	no	—
774	C₂×C₄	—	2	1	no	—
775	C₂×C₄	—	2	1	no	—
776	C₂×C₄	—	2	1	no	—
777	C₂×C₄	—	2	1	no	—
778	C₂×C₄	—	2	1	no	—
779	C₂×C₄	—	2	1	no	—
780	C₂×C₄	—	2	1	no	—
781	C₂×C₄	—	2	1	no	—
782	C₂×C₄	—	2	1	no	—
783	C₂×C₄	—	2	1	no	—
784	C₂×C₄	—	2	1	no	—
785	C₂×C₄	—	2	1	no	—
786	C₂×C₄	—	2	1	no	—
787	C₂×C₄	—	2	1	no	—
788	C₂×C₄	—	2	1	no	—
789	C₂×C₄	—	2	2	no	—
790	C₂×C₄	—	2	1	no	—
791	C₂×C₄	—	2	1	no	—
792	C₂×C₄	—	2	2	no	—
793	C₂×C₄	—	2	2	no	—
794	C₂×C₄	—	2	2	no	—
795	C₂×C₄	—	2	2	no	—
796	C₂×C₄	—	4	1	no	—
797	C₂×C₄	—	4	1	no	—
798	C₂×C₄	—	4	2	no	—
799	C₂×C₄	—	4	1	no	—
800	C₂×C₄	—	4	1	no	—
801	C₂×C₄	—	4	2	no	—
802	C₂×C₄	—	4	1	no	—
803	C₂×C₄	—	4	2	no	—
804	C₂×C₄	—	4	1	no	—
805	C₂×C₄	—	4	1	no	—
806	C₂×C₄	—	4	1	no	—
807	C₂×C₄	—	8	1	no	—
808	C₂×C₄	—	8	2	no	—
809	C₂×C₄	C₁₇×#120	1	1	yes	characteristic
810	C₂×C₄	C₁₇×#120	1	1	yes	characteristic
811	C₂×C₄	C₂²×D₄×C₁₇	1	1	yes	characteristic
812	C₂×C₄	C₂²×D₄×C₁₇	1	1	yes	characteristic
813	C₂×C₄	C₂×#41×C₁₇	1	1	yes	characteristic
814	C₂×C₄	C₂×#41×C₁₇	1	1	yes	characteristic
815	C₂×C₄	C₁₇×H(5,𝔽₂)	1	1	yes	characteristic
816	C₂×C₄	C₁₇×2₋¹⁺⁴	1	1	yes	characteristic
817	C₈	—	2	2	no	—
818	C₈	—	4	1	no	—
819	C₈	—	4	1	no	—
820	C₈	—	4	1	no	—
821	C₂²	—	2	1	no	—
822	C₂²	—	2	1	no	—
823	C₂²	—	2	1	no	—
824	C₂²	—	2	1	no	—
825	C₂²	—	2	1	no	—
826	C₂²	—	2	1	no	—
827	C₂²	—	2	1	no	—
828	C₂²	—	2	1	no	—
829	C₂²	—	4	1	no	—
830	C₂²	—	4	1	no	—
831	C₂²	—	4	1	no	—
832	C₂²	—	8	1	no	—
833	C₂²	—	8	1	no	—
834	C₂²	—	8	2	no	—
835	C₂²	—	8	2	no	—
836	C₂²	—	8	1	no	—
837	C₂²	—	8	1	no	—
838	C₂²	—	8	1	no	—
839	C₂²	C₂×C₁₇×#120	1	1	yes	characteristic
840	C₂²	C₁₇×#546	1	1	yes	characteristic
841	C₂²	C₁₇×#547	1	1	yes	characteristic
842	C₄	—	2	1	no	—
843	C₄	—	2	1	no	—
844	C₄	—	4	2	no	—
845	C₄	—	4	1	no	—
846	C₄	—	4	1	no	—
847	C₄	—	4	1	no	—
848	C₄	—	4	2	no	—
849	C₄	—	4	1	no	—
850	C₄	—	4	1	no	—
851	C₄	—	4	1	no	—
852	C₄	—	4	2	no	—
853	C₄	—	4	1	no	—
854	C₄	—	8	1	no	—
855	C₄	—	8	1	no	—
856	C₄	C₁₇×#532	1	1	yes	characteristic
857	C₄	C₁₇×#537	1	1	yes	characteristic
858	C₄	C₁₇×#546	1	1	yes	characteristic
859	C₄	C₁₇×#547	1	1	yes	characteristic
860	C₂	—	2	1	no	—
861	C₂	—	2	1	no	—
862	C₂	—	4	1	no	—
863	C₂	—	4	1	no	—
864	C₂	—	8	1	no	—
865	C₂	—	16	1	no	—
866	C₂	C₁₇×#2430	1	1	yes	characteristic
867	C₂	C₁₇×#3020	1	1	yes	characteristic
868	C₂	C₁₇×#3021	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₇	C₂×#120
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₇
prime radical	C₁₇×#3055	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₂³×C₄×C₁₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₇×#3495	C₂	semidirect
2. C₁₇×#3094	C₂	semidirect
4. C₁₇×#2620	C₂	semidirect
5. C₁₇×#2060	C₂	semidirect
6. C₁₇×#2038	C₂	semidirect
7. C₁₇×#2027	C₂	semidirect
8. C₁₇×#2003	C₂	semidirect
9. C₁₇×#1901	C₂	semidirect
10. C₁₇×#1897	C₂	semidirect
11. C₁₇×#1888	C₂	semidirect
12. C₁₇×#1883	C₂	semidirect
13. C₁₇×#1859	C₂	semidirect
14. C₁₇×#1857	C₂	semidirect
15. C₁₇×#1733	C₂	semidirect
307. #25530	C₁₇	direct (N × H)
387. #3495	C₂×C₁₇	semidirect
388. #3094	C₂×C₁₇	semidirect
390. #2620	C₂×C₁₇	semidirect
391. #2060	C₂×C₁₇	semidirect
392. #2038	C₂×C₁₇	semidirect
393. #2027	C₂×C₁₇	semidirect
394. #2003	C₂×C₁₇	semidirect
395. #1901	C₂×C₁₇	semidirect
396. #1897	C₂×C₁₇	semidirect
397. #1888	C₂×C₁₇	semidirect
398. #1883	C₂×C₁₇	semidirect
399. #1859	C₂×C₁₇	semidirect
400. #1857	C₂×C₁₇	semidirect
401. #1733	C₂×C₁₇	semidirect
622. C₁₇	#25530	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₇×#3495	2
C₁₇×#3094	2
C₁₇×#3055	2
C₁₇×#2620	2
C₁₇×#2060	2
C₁₇×#2038	2
C₁₇×#2027	2
C₁₇×#2003	2
C₁₇×#1901	2
C₁₇×#1897	2
C₁₇×#1888	2
C₁₇×#1883	2
C₁₇×#1859	2
C₁₇×#1857	2
C₁₇×#1733	2
#25530	17

Subgroups — C17×#25530 #16883274

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₇×#25530 #16883274