Subgroups — C₁₇×#25523 #16883267

Order 4352.

1132 conjugacy classes of subgroups.

The subgroup lattice has 884 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₇×#3494	C₂	1	1	yes	maximal, characteristic
2	C₁₇×#3095	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₇×#3056	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₇×#2850	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₇×#2061	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₇×#2037	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₇×#2028	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₇×#2004	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₇×#1900	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₇×#1896	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₇×#1885	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₇×#1882	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₇×#1860	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₇×#1856	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₁₇×#339	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₁₇×#137	C₂²	1	1	yes	characteristic
17	C₂²×M₁₆×C₁₇	C₂²	1	1	yes	characteristic
18	C₁₇×#555	—	2	1	no	—
19	C₁₇×#553	—	2	1	no	—
20	C₁₇×#553	—	2	1	no	—
21	C₁₇×#551	—	2	2	no	—
22	C₁₇×#547	—	2	1	no	—
23	C₁₇×#546	—	2	2	no	—
24	C₁₇×#544	C₂²	1	1	yes	characteristic
25	C₁₇×#542	—	2	1	no	—
26	C₁₇×#540	—	2	1	no	—
27	C₁₇×#535	C₂²	1	1	yes	characteristic
28	C₁₇×#532	—	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×#518	C₂²	1	1	yes	characteristic
36	C₂×C₁₇×#117	C₂²	1	1	yes	characteristic
37	C₂²×C₄²×C₁₇	C₂²	1	1	yes	characteristic
38	C₁₇×#485	—	2	1	no	—
39	C₁₇×#485	—	2	1	no	—
40	C₁₇×#484	—	2	1	no	—
41	C₁₇×#483	—	2	1	no	—
42	C₁₇×#470	—	2	1	no	—
43	C₁₇×#468	—	2	1	no	—
44	C₁₇×#467	—	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×#419	C₂²	1	1	yes	characteristic
52	C₁₇×#419	C₂²	1	1	yes	characteristic
53	C₁₇×#419	C₂²	1	1	yes	characteristic
54	C₁₇×#417	C₂²	1	1	yes	characteristic
55	C₂×C₁₇×#100	C₂²	1	1	yes	characteristic
56	C₂×C₁₇×#100	C₂²	1	1	yes	characteristic
57	C₁₇×#407	C₂²	1	1	yes	characteristic
58	C₁₇×#391	C₂²	1	1	yes	characteristic
59	C₁₇×#390	C₂²	1	1	yes	characteristic
60	C₁₇×#388	—	2	2	no	—
61	C₁₇×#386	—	2	2	no	—
62	C₁₇×#382	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	—	2	2	no	—
72	C₂×#41×C₁₇	C₂³	1	1	yes	characteristic
73	C₂²×Q₈×C₁₇	C₂³	1	1	yes	characteristic
74	C₂²×D₄×C₁₇	D₄	1	2	yes	—
75	C₂²×D₄×C₁₇	C₂³	1	1	yes	characteristic
76	C₂³×C₄×C₁₇	—	2	1	no	—
77	C₂³×C₄×C₁₇	C₂³	1	1	yes	characteristic
78	C₁₇×#137	—	2	2	no	—
79	C₁₇×#137	—	4	1	no	—
80	C₂×Q₁₆×C₁₇	—	2	1	no	—
81	C₂×SD₁₆×C₁₇	—	2	1	no	—
82	C₂×M₁₆×C₁₇	—	2	1	no	—
83	C₂×M₁₆×C₁₇	—	2	2	no	—
84	C₂×M₁₆×C₁₇	—	4	1	no	—
85	C₂×M₁₆×C₁₇	C₂³	1	1	yes	characteristic
86	C₂×M₁₆×C₁₇	C₂³	1	1	yes	characteristic
87	C₂×M₁₆×C₁₇	C₂³	1	1	yes	characteristic
88	C₂×M₁₆×C₁₇	C₂³	1	1	yes	characteristic
89	C₂²×C₈×C₁₇	—	2	1	no	—
90	C₁₇×C₄⋊Q₈	—	2	1	no	—
91	C₁₇×C₄⋊Q₈	—	2	1	no	—
92	C₁₇×#127	—	2	1	no	—
93	C₁₇×#126	—	2	2	no	—
94	C₁₇×#126	—	2	2	no	—
95	C₁₇×#125	—	2	1	no	—
96	C₁₇×#125	—	2	1	no	—
97	C₁₇×#124	—	2	2	no	—
98	C₁₇×#124	—	2	2	no	—
99	C₁₇×#124	—	2	1	no	—
100	C₁₇×#124	—	2	2	no	—
101	C₁₇×#124	—	4	1	no	—
102	C₁₇×#123	—	2	2	no	—
103	C₁₇×#123	—	2	2	no	—
104	C₁₇×#123	—	2	2	no	—
105	C₁₇×#123	—	2	2	no	—
106	C₁₇×#123	—	2	1	no	—
107	C₁₇×C₂²⋊Q₈	—	2	2	no	—
108	C₁₇×C₂²⋊Q₈	—	2	2	no	—
109	C₁₇×C₂²⋊Q₈	—	2	1	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	D₄	1	1	yes	characteristic
114	C₁₇×C₂²⋊Q₈	D₄	1	1	yes	characteristic
115	C₁₇×#121	—	2	2	no	—
116	C₁₇×#121	—	2	2	no	—
117	C₁₇×#121	—	2	2	no	—
118	C₁₇×#121	—	2	1	no	—
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	—	2	1	no	—
124	C₁₇×#121	D₄	1	1	yes	characteristic
125	C₁₇×#121	D₄	1	1	yes	characteristic
126	C₁₇×#120	—	2	1	no	—
127	C₁₇×#120	—	2	2	no	—
128	C₄×Q₈×C₁₇	—	2	1	no	—
129	C₄×D₄×C₁₇	—	2	2	no	—
130	C₄×D₄×C₁₇	—	2	2	no	—
131	C₄×D₄×C₁₇	—	2	1	no	—
132	C₄×D₄×C₁₇	—	2	2	no	—
133	C₄×D₄×C₁₇	—	2	1	no	—
134	C₄×D₄×C₁₇	—	2	1	no	—
135	C₄×D₄×C₁₇	—	2	1	no	—
136	C₄×D₄×C₁₇	—	2	1	no	—
137	C₄×D₄×C₁₇	—	2	1	no	—
138	C₄×D₄×C₁₇	—	2	1	no	—
139	C₁₇×#117	—	2	2	no	—
140	C₁₇×#117	—	2	1	no	—
141	C₁₇×#117	—	2	1	no	—
142	C₁₇×#117	—	2	1	no	—
143	C₁₇×#117	D₄	1	1	yes	characteristic
144	C₁₇×#117	D₄	1	1	yes	characteristic
145	C₁₇×#117	C₂³	1	1	yes	characteristic
146	C₁₇×#117	C₂³	1	1	yes	characteristic
147	C₁₇×#117	C₂³	1	1	yes	characteristic
148	C₂×C₄⋊C₄×C₁₇	—	2	1	no	—
149	C₂×C₄⋊C₄×C₁₇	—	2	1	no	—
150	C₂×C₄⋊C₄×C₁₇	D₄	1	1	yes	characteristic
151	C₂×C₄⋊C₄×C₁₇	D₄	1	1	yes	characteristic
152	C₂×C₄⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
153	C₂×C₄⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
154	C₂×C₂²⋊C₄×C₁₇	—	2	1	no	—
155	C₂×C₂²⋊C₄×C₁₇	—	2	2	no	—
156	C₂×C₂²⋊C₄×C₁₇	—	2	1	no	—
157	C₂×C₂²⋊C₄×C₁₇	—	2	2	no	—
158	C₂×C₂²⋊C₄×C₁₇	—	2	2	no	—
159	C₂×C₂²⋊C₄×C₁₇	D₄	1	2	yes	—
160	C₂×C₄²×C₁₇	—	2	1	no	—
161	C₂×C₄²×C₁₇	—	2	2	no	—
162	C₂×C₄²×C₁₇	—	2	1	no	—
163	C₂×C₄²×C₁₇	—	4	1	no	—
164	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
165	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
166	C₁₇×#107	—	2	1	no	—
167	C₁₇×#107	—	2	1	no	—
168	C₁₇×#107	—	2	1	no	—
169	C₁₇×#106	—	2	1	no	—
170	C₁₇×#106	—	2	1	no	—
171	C₁₇×#106	—	2	1	no	—
172	C₁₇×#104	—	2	2	no	—
173	C₁₇×#104	—	4	1	no	—
174	C₁₇×#103	—	2	1	no	—
175	C₁₇×#103	—	2	1	no	—
176	C₁₇×#103	—	2	1	no	—
177	C₁₇×#103	—	2	1	no	—
178	C₁₇×#103	—	2	1	no	—
179	C₁₇×#103	—	2	1	no	—
180	C₁₇×#103	—	2	1	no	—
181	C₁₇×#102	—	2	1	no	—
182	C₁₇×#100	—	2	2	no	—
183	C₁₇×#100	—	4	1	no	—
184	C₁₇×C₂²⋊C₈	—	2	1	no	—
185	C₁₇×C₂²⋊C₈	—	2	1	no	—
186	C₁₇×#95	—	2	2	no	—
187	C₁₇×#95	—	2	2	no	—
188	C₂⁴×C₁₇	C₂×D₄	1	1	yes	characteristic
189	C₂⁴×C₁₇	C₂×D₄	1	2	yes	—
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	#41×C₁₇	—	8	4	no	—
195	C₂×Q₈×C₁₇	—	2	2	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	—	2	1	no	—
202	C₂×Q₈×C₁₇	C₂×D₄	1	1	yes	characteristic
203	C₂×D₄×C₁₇	—	2	2	no	—
204	C₂×D₄×C₁₇	—	2	1	no	—
205	C₂×D₄×C₁₇	—	2	1	no	—
206	C₂×D₄×C₁₇	—	2	2	no	—
207	C₂×D₄×C₁₇	—	2	2	no	—
208	C₂×D₄×C₁₇	—	2	2	no	—
209	C₂×D₄×C₁₇	—	2	1	no	—
210	C₂×D₄×C₁₇	—	2	1	no	—
211	C₂×D₄×C₁₇	—	2	1	no	—
212	C₂×D₄×C₁₇	—	2	1	no	—
213	C₂×D₄×C₁₇	—	2	1	no	—
214	C₂×D₄×C₁₇	—	2	1	no	—
215	C₂×D₄×C₁₇	—	2	1	no	—
216	C₂×D₄×C₁₇	—	4	4	no	—
217	C₂×D₄×C₁₇	C₂×D₄	1	1	yes	characteristic
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	1	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	2	no	—
226	C₂²×C₄×C₁₇	—	2	2	no	—
227	C₂²×C₄×C₁₇	—	2	2	no	—
228	C₂²×C₄×C₁₇	—	2	1	no	—
229	C₂²×C₄×C₁₇	—	2	1	no	—
230	C₂²×C₄×C₁₇	—	2	1	no	—
231	C₂²×C₄×C₁₇	—	2	1	no	—
232	C₂²×C₄×C₁₇	—	4	2	no	—
233	C₂²×C₄×C₁₇	—	4	2	no	—
234	C₂²×C₄×C₁₇	—	4	2	no	—
235	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
236	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
237	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
238	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
239	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
240	C₂²×C₄×C₁₇	C₂×D₄	1	2	yes	—
241	C₂²×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
242	Q₁₆×C₁₇	—	4	2	no	—
243	SD₁₆×C₁₇	—	4	2	no	—
244	M₁₆×C₁₇	—	2	1	no	—
245	M₁₆×C₁₇	—	2	1	no	—
246	M₁₆×C₁₇	—	2	1	no	—
247	M₁₆×C₁₇	—	2	1	no	—
248	M₁₆×C₁₇	—	2	1	no	—
249	M₁₆×C₁₇	—	2	1	no	—
250	M₁₆×C₁₇	—	2	1	no	—
251	M₁₆×C₁₇	—	4	2	no	—
252	M₁₆×C₁₇	#41	1	2	yes	complemented
253	C₂×C₈×C₁₇	—	2	1	no	—
254	C₂×C₈×C₁₇	—	2	1	no	—
255	C₂×C₈×C₁₇	—	2	1	no	—
256	C₂×C₈×C₁₇	—	2	1	no	—
257	C₂×C₈×C₁₇	—	4	2	no	—
258	C₄⋊C₄×C₁₇	—	2	2	no	—
259	C₄⋊C₄×C₁₇	—	2	2	no	—
260	C₄⋊C₄×C₁₇	—	2	2	no	—
261	C₄⋊C₄×C₁₇	—	2	2	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	—	2	1	no	—
269	C₄⋊C₄×C₁₇	—	2	1	no	—
270	C₄⋊C₄×C₁₇	—	4	1	no	—
271	C₄⋊C₄×C₁₇	—	4	1	no	—
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	C₄⋊C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
277	C₄⋊C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
278	C₂²⋊C₄×C₁₇	—	2	2	no	—
279	C₂²⋊C₄×C₁₇	—	2	2	no	—
280	C₂²⋊C₄×C₁₇	—	2	2	no	—
281	C₂²⋊C₄×C₁₇	—	2	2	no	—
282	C₂²⋊C₄×C₁₇	—	2	2	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	—	2	2	no	—
291	C₂²⋊C₄×C₁₇	—	2	1	no	—
292	C₂²⋊C₄×C₁₇	—	2	1	no	—
293	C₂²⋊C₄×C₁₇	—	2	2	no	—
294	C₂²⋊C₄×C₁₇	—	4	4	no	—
295	C₂²⋊C₄×C₁₇	—	4	4	no	—
296	C₂²⋊C₄×C₁₇	—	4	1	no	—
297	C₂²⋊C₄×C₁₇	—	4	1	no	—
298	C₄²×C₁₇	—	2	2	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	—	2	1	no	—
307	C₄²×C₁₇	—	4	2	no	—
308	C₄²×C₁₇	#41	1	2	yes	complemented
309	#25523	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
310	C₂³×C₁₇	—	2	1	no	—
311	C₂³×C₁₇	—	2	1	no	—
312	C₂³×C₁₇	—	2	2	no	—
313	C₂³×C₁₇	—	2	2	no	—
314	C₂³×C₁₇	—	2	1	no	—
315	C₂³×C₁₇	—	2	2	no	—
316	C₂³×C₁₇	—	2	2	no	—
317	C₂³×C₁₇	—	4	1	no	—
318	C₂³×C₁₇	—	4	2	no	—
319	C₂³×C₁₇	—	4	2	no	—
320	C₂³×C₁₇	#120	1	1	yes	characteristic
321	C₂³×C₁₇	#120	1	1	yes	characteristic
322	C₂³×C₁₇	C₂²×D₄	1	1	yes	characteristic
323	Q₈×C₁₇	—	2	1	no	—
324	Q₈×C₁₇	—	2	1	no	—
325	Q₈×C₁₇	—	4	1	no	—
326	Q₈×C₁₇	—	4	1	no	—
327	Q₈×C₁₇	—	4	1	no	—
328	Q₈×C₁₇	—	4	1	no	—
329	Q₈×C₁₇	—	8	2	no	—
330	D₄×C₁₇	—	2	1	no	—
331	D₄×C₁₇	—	2	1	no	—
332	D₄×C₁₇	—	4	1	no	—
333	D₄×C₁₇	—	4	1	no	—
334	D₄×C₁₇	—	4	4	no	—
335	D₄×C₁₇	—	4	2	no	—
336	D₄×C₁₇	—	4	1	no	—
337	D₄×C₁₇	—	4	1	no	—
338	D₄×C₁₇	—	4	1	no	—
339	D₄×C₁₇	—	4	1	no	—
340	D₄×C₁₇	—	8	1	no	—
341	D₄×C₁₇	—	8	2	no	—
342	D₄×C₁₇	—	8	2	no	—
343	D₄×C₁₇	—	8	2	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	2	no	—
355	C₂×C₄×C₁₇	—	2	1	no	—
356	C₂×C₄×C₁₇	—	2	1	no	—
357	C₂×C₄×C₁₇	—	2	1	no	—
358	C₂×C₄×C₁₇	—	2	1	no	—
359	C₂×C₄×C₁₇	—	2	1	no	—
360	C₂×C₄×C₁₇	—	2	1	no	—
361	C₂×C₄×C₁₇	—	2	1	no	—
362	C₂×C₄×C₁₇	—	2	2	no	—
363	C₂×C₄×C₁₇	—	2	2	no	—
364	C₂×C₄×C₁₇	—	4	1	no	—
365	C₂×C₄×C₁₇	—	4	1	no	—
366	C₂×C₄×C₁₇	—	4	1	no	—
367	C₂×C₄×C₁₇	—	4	8	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	2	no	—
373	C₂×C₄×C₁₇	—	4	2	no	—
374	C₂×C₄×C₁₇	—	4	1	no	—
375	C₂×C₄×C₁₇	—	4	1	no	—
376	C₂×C₄×C₁₇	—	4	1	no	—
377	C₂×C₄×C₁₇	—	4	1	no	—
378	C₂×C₄×C₁₇	—	8	1	no	—
379	C₂×C₄×C₁₇	—	8	2	no	—
380	C₂×C₄×C₁₇	—	8	2	no	—
381	C₂×C₄×C₁₇	—	8	2	no	—
382	C₂×C₄×C₁₇	#120	1	1	yes	characteristic
383	C₂×C₄×C₁₇	#120	1	1	yes	characteristic
384	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
385	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
386	C₂×C₄×C₁₇	C₂×#41	1	1	yes	characteristic
387	C₂×C₄×C₁₇	C₂×#41	1	1	yes	characteristic
388	C₂×C₄×C₁₇	H(5,𝔽₂)	1	1	yes	characteristic
389	C₂×C₄×C₁₇	2₋¹⁺⁴	1	1	yes	characteristic
390	C₈×C₁₇	—	2	2	no	—
391	C₈×C₁₇	—	4	1	no	—
392	C₈×C₁₇	—	4	1	no	—
393	C₈×C₁₇	—	4	1	no	—
394	#3494	C₂×C₁₇	1	1	yes	characteristic
395	#3095	C₂×C₁₇	1	1	yes	characteristic, complemented
396	#3056	C₂×C₁₇	1	1	yes	characteristic, complemented
397	#2850	C₂×C₁₇	1	1	yes	characteristic, complemented
398	#2061	C₂×C₁₇	1	1	yes	characteristic, complemented
399	#2037	C₂×C₁₇	1	1	yes	characteristic, complemented
400	#2028	C₂×C₁₇	1	1	yes	characteristic, complemented
401	#2004	C₂×C₁₇	1	1	yes	characteristic, complemented
402	#1900	C₂×C₁₇	1	1	yes	characteristic, complemented
403	#1896	C₂×C₁₇	1	1	yes	characteristic, complemented
404	#1885	C₂×C₁₇	1	1	yes	characteristic, complemented
405	#1882	C₂×C₁₇	1	1	yes	characteristic, complemented
406	#1860	C₂×C₁₇	1	1	yes	characteristic, complemented
407	#1856	C₂×C₁₇	1	1	yes	characteristic, complemented
408	C₂×#339	C₂×C₁₇	1	1	yes	characteristic, complemented
409	C₂²×C₁₇	—	2	1	no	—
410	C₂²×C₁₇	—	2	1	no	—
411	C₂²×C₁₇	—	2	1	no	—
412	C₂²×C₁₇	—	2	1	no	—
413	C₂²×C₁₇	—	2	1	no	—
414	C₂²×C₁₇	—	2	1	no	—
415	C₂²×C₁₇	—	2	1	no	—
416	C₂²×C₁₇	—	4	2	no	—
417	C₂²×C₁₇	—	4	2	no	—
418	C₂²×C₁₇	—	4	1	no	—
419	C₂²×C₁₇	—	4	2	no	—
420	C₂²×C₁₇	—	4	1	no	—
421	C₂²×C₁₇	—	4	2	no	—
422	C₂²×C₁₇	—	4	2	no	—
423	C₂²×C₁₇	—	4	1	no	—
424	C₂²×C₁₇	—	8	2	no	—
425	C₂²×C₁₇	—	8	2	no	—
426	C₂²×C₁₇	#455	1	2	yes	—
427	C₂²×C₁₇	C₂×#120	1	1	yes	characteristic
428	C₂²×C₁₇	#546	1	1	yes	characteristic
429	C₂²×C₁₇	#547	1	1	yes	characteristic
430	C₄×C₁₇	—	2	1	no	—
431	C₄×C₁₇	—	2	1	no	—
432	C₄×C₁₇	—	4	2	no	—
433	C₄×C₁₇	—	4	2	no	—
434	C₄×C₁₇	—	4	1	no	—
435	C₄×C₁₇	—	4	1	no	—
436	C₄×C₁₇	—	4	1	no	—
437	C₄×C₁₇	—	4	2	no	—
438	C₄×C₁₇	—	4	1	no	—
439	C₄×C₁₇	—	4	1	no	—
440	C₄×C₁₇	—	4	1	no	—
441	C₄×C₁₇	—	4	1	no	—
442	C₄×C₁₇	—	8	1	no	—
443	C₄×C₁₇	—	8	1	no	—
444	C₄×C₁₇	#532	1	1	yes	characteristic
445	C₄×C₁₇	#537	1	1	yes	characteristic
446	C₄×C₁₇	#546	1	1	yes	characteristic
447	C₄×C₁₇	#547	1	1	yes	characteristic
448	C₂×#137	C₂²×C₁₇	1	1	yes	characteristic
449	C₂²×M₁₆	C₂²×C₁₇	1	1	yes	characteristic
450	#555	—	2	1	no	—
451	#553	—	2	1	no	—
452	#553	—	2	1	no	—
453	#551	—	2	2	no	—
454	#547	—	2	1	no	—
455	#546	—	2	2	no	—
456	#544	C₂²×C₁₇	1	1	yes	characteristic
457	#542	—	2	1	no	—
458	#540	—	2	1	no	—
459	#535	C₂²×C₁₇	1	1	yes	characteristic
460	#532	—	2	1	no	—
461	#529	—	2	1	no	—
462	C₂×#124	C₂²×C₁₇	1	1	yes	characteristic
463	#525	C₂²×C₁₇	1	1	yes	characteristic
464	C₂×C₂²⋊Q₈	C₂²×C₁₇	1	1	yes	characteristic
465	C₂×#121	C₂²×C₁₇	1	1	yes	characteristic
466	#520	C₂²×C₁₇	1	1	yes	characteristic
467	#518	C₂²×C₁₇	1	1	yes	characteristic
468	C₂×#117	C₂²×C₁₇	1	1	yes	characteristic
469	C₂²×C₄²	C₂²×C₁₇	1	1	yes	characteristic
470	#485	—	2	1	no	—
471	#485	—	2	1	no	—
472	#484	—	2	1	no	—
473	#483	—	2	1	no	—
474	#470	—	2	1	no	—
475	#468	—	2	1	no	—
476	#467	—	2	1	no	—
477	#465	—	2	1	no	—
478	#428	C₂²×C₁₇	1	1	yes	characteristic
479	#428	C₂²×C₁₇	1	1	yes	characteristic
480	#428	C₂²×C₁₇	1	1	yes	characteristic
481	C₂×#104	C₂²×C₁₇	1	1	yes	characteristic
482	C₂×#104	C₂²×C₁₇	1	1	yes	characteristic
483	#419	C₂²×C₁₇	1	1	yes	characteristic
484	#419	C₂²×C₁₇	1	1	yes	characteristic
485	#419	C₂²×C₁₇	1	1	yes	characteristic
486	#417	C₂²×C₁₇	1	1	yes	characteristic
487	C₂×#100	C₂²×C₁₇	1	1	yes	characteristic
488	C₂×#100	C₂²×C₁₇	1	1	yes	characteristic
489	#407	C₂²×C₁₇	1	1	yes	characteristic
490	#391	C₂²×C₁₇	1	1	yes	characteristic
491	#390	C₂²×C₁₇	1	1	yes	characteristic
492	#388	—	2	2	no	—
493	#386	—	2	2	no	—
494	#382	C₂²×C₁₇	1	1	yes	characteristic
495	#343	C₂²×C₁₇	1	1	yes	characteristic
496	#343	C₂²×C₁₇	1	1	yes	characteristic
497	#339	C₂²×C₁₇	1	1	yes	characteristic
498	#339	C₂²×C₁₇	1	1	yes	characteristic
499	#339	C₂²×C₁₇	1	1	yes	characteristic
500	#339	C₂²×C₁₇	1	1	yes	characteristic
501	#339	C₂²×C₁₇	1	1	yes	characteristic
502	#339	C₂²×C₁₇	1	1	yes	characteristic
503	C₂×C₁₇	—	2	1	no	—
504	C₂×C₁₇	—	2	1	no	—
505	C₂×C₁₇	—	2	2	no	—
506	C₂×C₁₇	—	4	1	no	—
507	C₂×C₁₇	—	8	1	no	—
508	C₂×C₁₇	—	8	2	no	—
509	C₂×C₁₇	#2430	1	1	yes	characteristic
510	C₂×C₁₇	C₂×#455	1	1	yes	characteristic
511	C₂×C₁₇	#3018	1	1	yes	characteristic
512	C₂×#41	—	2	2	no	—
513	C₂×#41	C₂³×C₁₇	1	1	yes	characteristic
514	C₂²×Q₈	C₂³×C₁₇	1	1	yes	characteristic
515	C₂²×D₄	D₄×C₁₇	1	2	yes	—
516	C₂²×D₄	C₂³×C₁₇	1	1	yes	characteristic
517	C₂³×C₄	—	2	1	no	—
518	C₂³×C₄	C₂³×C₁₇	1	1	yes	characteristic
519	#137	—	2	2	no	—
520	#137	—	4	1	no	—
521	C₂×Q₁₆	—	2	1	no	—
522	C₂×SD₁₆	—	2	1	no	—
523	C₂×M₁₆	—	2	1	no	—
524	C₂×M₁₆	—	2	2	no	—
525	C₂×M₁₆	—	4	1	no	—
526	C₂×M₁₆	C₂³×C₁₇	1	1	yes	characteristic
527	C₂×M₁₆	C₂³×C₁₇	1	1	yes	characteristic
528	C₂×M₁₆	C₂³×C₁₇	1	1	yes	characteristic
529	C₂×M₁₆	C₂³×C₁₇	1	1	yes	characteristic
530	C₂²×C₈	—	2	1	no	—
531	C₄⋊Q₈	—	2	1	no	—
532	C₄⋊Q₈	—	2	1	no	—
533	#127	—	2	1	no	—
534	#126	—	2	2	no	—
535	#126	—	2	2	no	—
536	#125	—	2	1	no	—
537	#125	—	2	1	no	—
538	#124	—	2	2	no	—
539	#124	—	2	2	no	—
540	#124	—	2	1	no	—
541	#124	—	2	2	no	—
542	#124	—	4	1	no	—
543	#123	—	2	2	no	—
544	#123	—	2	2	no	—
545	#123	—	2	2	no	—
546	#123	—	2	2	no	—
547	#123	—	2	1	no	—
548	C₂²⋊Q₈	—	2	2	no	—
549	C₂²⋊Q₈	—	2	2	no	—
550	C₂²⋊Q₈	—	2	1	no	—
551	C₂²⋊Q₈	—	2	1	no	—
552	C₂²⋊Q₈	—	2	1	no	—
553	C₂²⋊Q₈	—	2	1	no	—
554	C₂²⋊Q₈	D₄×C₁₇	1	1	yes	characteristic
555	C₂²⋊Q₈	D₄×C₁₇	1	1	yes	characteristic
556	#121	—	2	2	no	—
557	#121	—	2	2	no	—
558	#121	—	2	2	no	—
559	#121	—	2	1	no	—
560	#121	—	2	1	no	—
561	#121	—	2	1	no	—
562	#121	—	2	1	no	—
563	#121	—	2	1	no	—
564	#121	—	2	1	no	—
565	#121	D₄×C₁₇	1	1	yes	characteristic
566	#121	D₄×C₁₇	1	1	yes	characteristic
567	#120	—	2	1	no	—
568	#120	—	2	2	no	—
569	C₄×Q₈	—	2	1	no	—
570	C₄×D₄	—	2	2	no	—
571	C₄×D₄	—	2	2	no	—
572	C₄×D₄	—	2	1	no	—
573	C₄×D₄	—	2	2	no	—
574	C₄×D₄	—	2	1	no	—
575	C₄×D₄	—	2	1	no	—
576	C₄×D₄	—	2	1	no	—
577	C₄×D₄	—	2	1	no	—
578	C₄×D₄	—	2	1	no	—
579	C₄×D₄	—	2	1	no	—
580	#117	—	2	2	no	—
581	#117	—	2	1	no	—
582	#117	—	2	1	no	—
583	#117	—	2	1	no	—
584	#117	D₄×C₁₇	1	1	yes	characteristic
585	#117	D₄×C₁₇	1	1	yes	characteristic
586	#117	C₂³×C₁₇	1	1	yes	characteristic
587	#117	C₂³×C₁₇	1	1	yes	characteristic
588	#117	C₂³×C₁₇	1	1	yes	characteristic
589	C₂×C₄⋊C₄	—	2	1	no	—
590	C₂×C₄⋊C₄	—	2	1	no	—
591	C₂×C₄⋊C₄	D₄×C₁₇	1	1	yes	characteristic
592	C₂×C₄⋊C₄	D₄×C₁₇	1	1	yes	characteristic
593	C₂×C₄⋊C₄	C₂³×C₁₇	1	1	yes	characteristic
594	C₂×C₄⋊C₄	C₂³×C₁₇	1	1	yes	characteristic
595	C₂×C₂²⋊C₄	—	2	1	no	—
596	C₂×C₂²⋊C₄	—	2	2	no	—
597	C₂×C₂²⋊C₄	—	2	1	no	—
598	C₂×C₂²⋊C₄	—	2	2	no	—
599	C₂×C₂²⋊C₄	—	2	2	no	—
600	C₂×C₂²⋊C₄	D₄×C₁₇	1	2	yes	—
601	C₂×C₄²	—	2	1	no	—
602	C₂×C₄²	—	2	2	no	—
603	C₂×C₄²	—	2	1	no	—
604	C₂×C₄²	—	4	1	no	—
605	C₂×C₄²	C₂³×C₁₇	1	1	yes	characteristic
606	C₂×C₄²	C₂³×C₁₇	1	1	yes	characteristic
607	#107	—	2	1	no	—
608	#107	—	2	1	no	—
609	#107	—	2	1	no	—
610	#106	—	2	1	no	—
611	#106	—	2	1	no	—
612	#106	—	2	1	no	—
613	#104	—	2	2	no	—
614	#104	—	4	1	no	—
615	#103	—	2	1	no	—
616	#103	—	2	1	no	—
617	#103	—	2	1	no	—
618	#103	—	2	1	no	—
619	#103	—	2	1	no	—
620	#103	—	2	1	no	—
621	#103	—	2	1	no	—
622	#102	—	2	1	no	—
623	#100	—	2	2	no	—
624	#100	—	4	1	no	—
625	C₂²⋊C₈	—	2	1	no	—
626	C₂²⋊C₈	—	2	1	no	—
627	#95	—	2	2	no	—
628	#95	—	2	2	no	—
629	C₁₇	#25523	1	1	yes	characteristic, direct product factor, Sylow
630	C₂⁴	C₂×D₄×C₁₇	1	1	yes	characteristic
631	C₂⁴	C₂×D₄×C₁₇	1	2	yes	—
632	#41	—	2	1	no	—
633	#41	—	2	1	no	—
634	#41	—	2	1	no	—
635	#41	—	2	1	no	—
636	#41	—	8	4	no	—
637	C₂×Q₈	—	2	2	no	—
638	C₂×Q₈	—	2	1	no	—
639	C₂×Q₈	—	2	1	no	—
640	C₂×Q₈	—	2	1	no	—
641	C₂×Q₈	—	2	1	no	—
642	C₂×Q₈	—	2	1	no	—
643	C₂×Q₈	—	2	1	no	—
644	C₂×Q₈	C₂×D₄×C₁₇	1	1	yes	characteristic
645	C₂×D₄	—	2	1	no	—
646	C₂×D₄	—	2	1	no	—
647	C₂×D₄	—	2	2	no	—
648	C₂×D₄	—	2	2	no	—
649	C₂×D₄	—	2	2	no	—
650	C₂×D₄	—	2	1	no	—
651	C₂×D₄	—	2	2	no	—
652	C₂×D₄	—	2	1	no	—
653	C₂×D₄	—	2	1	no	—
654	C₂×D₄	—	2	1	no	—
655	C₂×D₄	—	2	1	no	—
656	C₂×D₄	—	2	1	no	—
657	C₂×D₄	—	2	1	no	—
658	C₂×D₄	—	4	4	no	—
659	C₂×D₄	C₂×D₄×C₁₇	1	1	yes	characteristic
660	C₂²×C₄	—	2	1	no	—
661	C₂²×C₄	—	2	1	no	—
662	C₂²×C₄	—	2	1	no	—
663	C₂²×C₄	—	2	1	no	—
664	C₂²×C₄	—	2	1	no	—
665	C₂²×C₄	—	2	1	no	—
666	C₂²×C₄	—	2	1	no	—
667	C₂²×C₄	—	2	2	no	—
668	C₂²×C₄	—	2	2	no	—
669	C₂²×C₄	—	2	2	no	—
670	C₂²×C₄	—	2	1	no	—
671	C₂²×C₄	—	2	1	no	—
672	C₂²×C₄	—	2	1	no	—
673	C₂²×C₄	—	2	1	no	—
674	C₂²×C₄	—	4	2	no	—
675	C₂²×C₄	—	4	2	no	—
676	C₂²×C₄	—	4	2	no	—
677	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
678	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
679	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
680	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
681	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
682	C₂²×C₄	C₂×D₄×C₁₇	1	2	yes	—
683	C₂²×C₄	C₂⁴×C₁₇	1	1	yes	characteristic
684	Q₁₆	—	4	2	no	—
685	SD₁₆	—	4	2	no	—
686	M₁₆	—	2	1	no	—
687	M₁₆	—	2	1	no	—
688	M₁₆	—	2	1	no	—
689	M₁₆	—	2	1	no	—
690	M₁₆	—	2	1	no	—
691	M₁₆	—	2	1	no	—
692	M₁₆	—	2	1	no	—
693	M₁₆	—	4	2	no	—
694	M₁₆	#41×C₁₇	1	2	yes	complemented
695	C₂×C₈	—	2	1	no	—
696	C₂×C₈	—	2	1	no	—
697	C₂×C₈	—	2	1	no	—
698	C₂×C₈	—	2	1	no	—
699	C₂×C₈	—	4	2	no	—
700	C₄⋊C₄	—	2	2	no	—
701	C₄⋊C₄	—	2	2	no	—
702	C₄⋊C₄	—	2	2	no	—
703	C₄⋊C₄	—	2	2	no	—
704	C₄⋊C₄	—	2	1	no	—
705	C₄⋊C₄	—	2	1	no	—
706	C₄⋊C₄	—	2	1	no	—
707	C₄⋊C₄	—	2	1	no	—
708	C₄⋊C₄	—	2	1	no	—
709	C₄⋊C₄	—	2	1	no	—
710	C₄⋊C₄	—	2	1	no	—
711	C₄⋊C₄	—	2	1	no	—
712	C₄⋊C₄	—	4	1	no	—
713	C₄⋊C₄	—	4	1	no	—
714	C₄⋊C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
715	C₄⋊C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
716	C₄⋊C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
717	C₄⋊C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
718	C₄⋊C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
719	C₄⋊C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
720	C₂²⋊C₄	—	2	2	no	—
721	C₂²⋊C₄	—	2	2	no	—
722	C₂²⋊C₄	—	2	2	no	—
723	C₂²⋊C₄	—	2	2	no	—
724	C₂²⋊C₄	—	2	2	no	—
725	C₂²⋊C₄	—	2	1	no	—
726	C₂²⋊C₄	—	2	1	no	—
727	C₂²⋊C₄	—	2	1	no	—
728	C₂²⋊C₄	—	2	1	no	—
729	C₂²⋊C₄	—	2	1	no	—
730	C₂²⋊C₄	—	2	1	no	—
731	C₂²⋊C₄	—	2	1	no	—
732	C₂²⋊C₄	—	2	2	no	—
733	C₂²⋊C₄	—	2	2	no	—
734	C₂²⋊C₄	—	2	1	no	—
735	C₂²⋊C₄	—	2	1	no	—
736	C₂²⋊C₄	—	4	4	no	—
737	C₂²⋊C₄	—	4	4	no	—
738	C₂²⋊C₄	—	4	1	no	—
739	C₂²⋊C₄	—	4	1	no	—
740	C₄²	—	2	2	no	—
741	C₄²	—	2	1	no	—
742	C₄²	—	2	1	no	—
743	C₄²	—	2	1	no	—
744	C₄²	—	2	1	no	—
745	C₄²	—	2	1	no	—
746	C₄²	—	2	1	no	—
747	C₄²	—	2	1	no	—
748	C₄²	—	2	1	no	—
749	C₄²	—	4	2	no	—
750	C₄²	#41×C₁₇	1	2	yes	complemented
751	C₂³	—	2	1	no	—
752	C₂³	—	2	1	no	—
753	C₂³	—	2	2	no	—
754	C₂³	—	2	2	no	—
755	C₂³	—	2	1	no	—
756	C₂³	—	2	2	no	—
757	C₂³	—	2	2	no	—
758	C₂³	—	4	1	no	—
759	C₂³	—	4	2	no	—
760	C₂³	—	4	2	no	—
761	C₂³	C₁₇×#120	1	1	yes	characteristic
762	C₂³	C₁₇×#120	1	1	yes	characteristic
763	C₂³	C₂²×D₄×C₁₇	1	1	yes	characteristic
764	Q₈	—	2	1	no	—
765	Q₈	—	2	1	no	—
766	Q₈	—	4	1	no	—
767	Q₈	—	4	1	no	—
768	Q₈	—	4	1	no	—
769	Q₈	—	4	1	no	—
770	Q₈	—	8	2	no	—
771	D₄	—	2	1	no	—
772	D₄	—	2	1	no	—
773	D₄	—	4	1	no	—
774	D₄	—	4	1	no	—
775	D₄	—	4	4	no	—
776	D₄	—	4	2	no	—
777	D₄	—	4	1	no	—
778	D₄	—	4	1	no	—
779	D₄	—	4	1	no	—
780	D₄	—	4	1	no	—
781	D₄	—	8	2	no	—
782	D₄	—	8	1	no	—
783	D₄	—	8	2	no	—
784	D₄	—	8	2	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	1	no	—
790	C₂×C₄	—	2	1	no	—
791	C₂×C₄	—	2	1	no	—
792	C₂×C₄	—	2	1	no	—
793	C₂×C₄	—	2	1	no	—
794	C₂×C₄	—	2	1	no	—
795	C₂×C₄	—	2	2	no	—
796	C₂×C₄	—	2	1	no	—
797	C₂×C₄	—	2	1	no	—
798	C₂×C₄	—	2	1	no	—
799	C₂×C₄	—	2	1	no	—
800	C₂×C₄	—	2	1	no	—
801	C₂×C₄	—	2	1	no	—
802	C₂×C₄	—	2	1	no	—
803	C₂×C₄	—	2	2	no	—
804	C₂×C₄	—	2	2	no	—
805	C₂×C₄	—	4	1	no	—
806	C₂×C₄	—	4	1	no	—
807	C₂×C₄	—	4	1	no	—
808	C₂×C₄	—	4	8	no	—
809	C₂×C₄	—	4	1	no	—
810	C₂×C₄	—	4	2	no	—
811	C₂×C₄	—	4	1	no	—
812	C₂×C₄	—	4	1	no	—
813	C₂×C₄	—	4	2	no	—
814	C₂×C₄	—	4	2	no	—
815	C₂×C₄	—	4	1	no	—
816	C₂×C₄	—	4	1	no	—
817	C₂×C₄	—	4	1	no	—
818	C₂×C₄	—	4	1	no	—
819	C₂×C₄	—	8	1	no	—
820	C₂×C₄	—	8	2	no	—
821	C₂×C₄	—	8	2	no	—
822	C₂×C₄	—	8	2	no	—
823	C₂×C₄	C₁₇×#120	1	1	yes	characteristic
824	C₂×C₄	C₁₇×#120	1	1	yes	characteristic
825	C₂×C₄	C₂²×D₄×C₁₇	1	1	yes	characteristic
826	C₂×C₄	C₂²×D₄×C₁₇	1	1	yes	characteristic
827	C₂×C₄	C₂×#41×C₁₇	1	1	yes	characteristic
828	C₂×C₄	C₂×#41×C₁₇	1	1	yes	characteristic
829	C₂×C₄	C₁₇×H(5,𝔽₂)	1	1	yes	characteristic
830	C₂×C₄	C₁₇×2₋¹⁺⁴	1	1	yes	characteristic
831	C₈	—	2	2	no	—
832	C₈	—	4	1	no	—
833	C₈	—	4	1	no	—
834	C₈	—	4	1	no	—
835	C₂²	—	2	1	no	—
836	C₂²	—	2	1	no	—
837	C₂²	—	2	1	no	—
838	C₂²	—	2	1	no	—
839	C₂²	—	2	1	no	—
840	C₂²	—	2	1	no	—
841	C₂²	—	2	1	no	—
842	C₂²	—	4	2	no	—
843	C₂²	—	4	2	no	—
844	C₂²	—	4	1	no	—
845	C₂²	—	4	2	no	—
846	C₂²	—	4	2	no	—
847	C₂²	—	4	1	no	—
848	C₂²	—	4	1	no	—
849	C₂²	—	4	2	no	—
850	C₂²	—	8	2	no	—
851	C₂²	—	8	2	no	—
852	C₂²	C₁₇×#455	1	2	yes	—
853	C₂²	C₂×C₁₇×#120	1	1	yes	characteristic
854	C₂²	C₁₇×#546	1	1	yes	characteristic
855	C₂²	C₁₇×#547	1	1	yes	characteristic
856	C₄	—	2	1	no	—
857	C₄	—	2	1	no	—
858	C₄	—	4	2	no	—
859	C₄	—	4	2	no	—
860	C₄	—	4	1	no	—
861	C₄	—	4	1	no	—
862	C₄	—	4	2	no	—
863	C₄	—	4	1	no	—
864	C₄	—	4	1	no	—
865	C₄	—	4	1	no	—
866	C₄	—	4	1	no	—
867	C₄	—	4	1	no	—
868	C₄	—	8	1	no	—
869	C₄	—	8	1	no	—
870	C₄	C₁₇×#532	1	1	yes	characteristic
871	C₄	C₁₇×#537	1	1	yes	characteristic
872	C₄	C₁₇×#546	1	1	yes	characteristic
873	C₄	C₁₇×#547	1	1	yes	characteristic
874	C₂	—	2	1	no	—
875	C₂	—	2	1	no	—
876	C₂	—	2	2	no	—
877	C₂	—	4	1	no	—
878	C₂	—	8	2	no	—
879	C₂	—	8	1	no	—
880	C₂	C₁₇×#2430	1	1	yes	characteristic
881	C₂	C₂×C₁₇×#455	1	1	yes	characteristic
882	C₂	C₁₇×#3018	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₇	C₂×#120
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₇
prime radical	C₁₇×#3494	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
2. C₁₇×#3095	C₂	semidirect
3. C₁₇×#3056	C₂	semidirect
4. C₁₇×#2850	C₂	semidirect
5. C₁₇×#2061	C₂	semidirect
6. C₁₇×#2037	C₂	semidirect
7. C₁₇×#2028	C₂	semidirect
8. C₁₇×#2004	C₂	semidirect
9. C₁₇×#1900	C₂	semidirect
10. C₁₇×#1896	C₂	semidirect
11. C₁₇×#1885	C₂	semidirect
12. C₁₇×#1882	C₂	semidirect
13. C₁₇×#1860	C₂	semidirect
14. C₁₇×#1856	C₂	semidirect
15. C₂×C₁₇×#339	C₂	semidirect
252. M₁₆×C₁₇	#41	semidirect
308. C₄²×C₁₇	#41	semidirect
309. #25523	C₁₇	direct (N × H)
395. #3095	C₂×C₁₇	semidirect
396. #3056	C₂×C₁₇	semidirect
397. #2850	C₂×C₁₇	semidirect
398. #2061	C₂×C₁₇	semidirect
399. #2037	C₂×C₁₇	semidirect
400. #2028	C₂×C₁₇	semidirect
401. #2004	C₂×C₁₇	semidirect
402. #1900	C₂×C₁₇	semidirect
403. #1896	C₂×C₁₇	semidirect
404. #1885	C₂×C₁₇	semidirect
405. #1882	C₂×C₁₇	semidirect
406. #1860	C₂×C₁₇	semidirect
407. #1856	C₂×C₁₇	semidirect
408. C₂×#339	C₂×C₁₇	semidirect
629. C₁₇	#25523	direct (N × H)
694. M₁₆	#41×C₁₇	semidirect
750. C₄²	#41×C₁₇	semidirect

Maximal subgroups

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

subgroup	index
C₁₇×#3494	2
C₁₇×#3095	2
C₁₇×#3056	2
C₁₇×#2850	2
C₁₇×#2061	2
C₁₇×#2037	2
C₁₇×#2028	2
C₁₇×#2004	2
C₁₇×#1900	2
C₁₇×#1896	2
C₁₇×#1885	2
C₁₇×#1882	2
C₁₇×#1860	2
C₁₇×#1856	2
C₂×C₁₇×#339	2
#25523	17

Subgroups — C17×#25523 #16883267

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₇×#25523 #16883267